/*************************************************************************
ALGLIB 3.19.0 (source code generated 2022-06-07)
Copyright (c) Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifdef _MSC_VER
#define _CRT_SECURE_NO_WARNINGS
#endif
#include "stdafx.h"
#include "statistics.h"

// disable some irrelevant warnings
#if (AE_COMPILER==AE_MSVC) && !defined(AE_ALL_WARNINGS)
#pragma warning(disable:4100)
#pragma warning(disable:4127)
#pragma warning(disable:4611)
#pragma warning(disable:4702)
#pragma warning(disable:4996)
#endif

/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS IMPLEMENTATION OF C++ INTERFACE
//
/////////////////////////////////////////////////////////////////////////
namespace alglib
{

#if defined(AE_COMPILE_BASESTAT) || !defined(AE_PARTIAL_BUILD)

#endif

#if defined(AE_COMPILE_CORRELATIONTESTS) || !defined(AE_PARTIAL_BUILD)

#endif

#if defined(AE_COMPILE_JARQUEBERA) || !defined(AE_PARTIAL_BUILD)

#endif

#if defined(AE_COMPILE_VARIANCETESTS) || !defined(AE_PARTIAL_BUILD)

#endif

#if defined(AE_COMPILE_WSR) || !defined(AE_PARTIAL_BUILD)

#endif

#if defined(AE_COMPILE_MANNWHITNEYU) || !defined(AE_PARTIAL_BUILD)

#endif

#if defined(AE_COMPILE_STEST) || !defined(AE_PARTIAL_BUILD)

#endif

#if defined(AE_COMPILE_STUDENTTTESTS) || !defined(AE_PARTIAL_BUILD)

#endif

#if defined(AE_COMPILE_BASESTAT) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Calculation of the distribution moments: mean, variance, skewness, kurtosis.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

OUTPUT PARAMETERS
    Mean    -   mean.
    Variance-   variance.
    Skewness-   skewness (if variance<>0; zero otherwise).
    Kurtosis-   kurtosis (if variance<>0; zero otherwise).

NOTE: variance is calculated by dividing sum of squares by N-1, not N.

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void samplemoments(const real_1d_array &x, const ae_int_t n, double &mean, double &variance, double &skewness, double &kurtosis, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::samplemoments(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &mean, &variance, &skewness, &kurtosis, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Calculation of the distribution moments: mean, variance, skewness, kurtosis.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

OUTPUT PARAMETERS
    Mean    -   mean.
    Variance-   variance.
    Skewness-   skewness (if variance<>0; zero otherwise).
    Kurtosis-   kurtosis (if variance<>0; zero otherwise).

NOTE: variance is calculated by dividing sum of squares by N-1, not N.

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void samplemoments(const real_1d_array &x, double &mean, double &variance, double &skewness, double &kurtosis, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;

    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::samplemoments(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &mean, &variance, &skewness, &kurtosis, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Calculation of the mean.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:

This function return result  which calculated by 'SampleMoments' function
and stored at 'Mean' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplemean(const real_1d_array &x, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::samplemean(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}

/*************************************************************************
Calculation of the mean.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:

This function return result  which calculated by 'SampleMoments' function
and stored at 'Mean' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double samplemean(const real_1d_array &x, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;

    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::samplemean(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}
#endif

/*************************************************************************
Calculation of the variance.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:

This function return result  which calculated by 'SampleMoments' function
and stored at 'Variance' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplevariance(const real_1d_array &x, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::samplevariance(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}

/*************************************************************************
Calculation of the variance.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:

This function return result  which calculated by 'SampleMoments' function
and stored at 'Variance' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double samplevariance(const real_1d_array &x, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;

    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::samplevariance(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}
#endif

/*************************************************************************
Calculation of the skewness.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:

This function return result  which calculated by 'SampleMoments' function
and stored at 'Skewness' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double sampleskewness(const real_1d_array &x, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::sampleskewness(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}

/*************************************************************************
Calculation of the skewness.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:

This function return result  which calculated by 'SampleMoments' function
and stored at 'Skewness' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double sampleskewness(const real_1d_array &x, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;

    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::sampleskewness(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}
#endif

/*************************************************************************
Calculation of the kurtosis.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:

This function return result  which calculated by 'SampleMoments' function
and stored at 'Kurtosis' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplekurtosis(const real_1d_array &x, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::samplekurtosis(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}

/*************************************************************************
Calculation of the kurtosis.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:

This function return result  which calculated by 'SampleMoments' function
and stored at 'Kurtosis' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double samplekurtosis(const real_1d_array &x, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;

    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::samplekurtosis(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}
#endif

/*************************************************************************
ADev

Input parameters:
    X   -   sample
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X

Output parameters:
    ADev-   ADev

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void sampleadev(const real_1d_array &x, const ae_int_t n, double &adev, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::sampleadev(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &adev, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
ADev

Input parameters:
    X   -   sample
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X

Output parameters:
    ADev-   ADev

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void sampleadev(const real_1d_array &x, double &adev, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;

    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::sampleadev(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &adev, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Median calculation.

Input parameters:
    X   -   sample (array indexes: [0..N-1])
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X

Output parameters:
    Median

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void samplemedian(const real_1d_array &x, const ae_int_t n, double &median, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::samplemedian(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &median, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Median calculation.

Input parameters:
    X   -   sample (array indexes: [0..N-1])
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X

Output parameters:
    Median

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void samplemedian(const real_1d_array &x, double &median, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;

    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::samplemedian(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &median, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Percentile calculation.

Input parameters:
    X   -   sample (array indexes: [0..N-1])
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X
    P   -   percentile (0<=P<=1)

Output parameters:
    V   -   percentile

  -- ALGLIB --
     Copyright 01.03.2008 by Bochkanov Sergey
*************************************************************************/
void samplepercentile(const real_1d_array &x, const ae_int_t n, const double p, double &v, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::samplepercentile(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, p, &v, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Percentile calculation.

Input parameters:
    X   -   sample (array indexes: [0..N-1])
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X
    P   -   percentile (0<=P<=1)

Output parameters:
    V   -   percentile

  -- ALGLIB --
     Copyright 01.03.2008 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void samplepercentile(const real_1d_array &x, const double p, double &v, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;

    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::samplepercentile(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, p, &v, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
2-sample covariance

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    covariance (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
double cov2(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::cov2(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}

/*************************************************************************
2-sample covariance

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    covariance (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double cov2(const real_1d_array &x, const real_1d_array &y, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    if( (x.length()!=y.length()))
        _ALGLIB_CPP_EXCEPTION("Error while calling 'cov2': looks like one of arguments has wrong size");
    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::cov2(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}
#endif

/*************************************************************************
Pearson product-moment correlation coefficient

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    Pearson product-moment correlation coefficient
    (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
double pearsoncorr2(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::pearsoncorr2(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}

/*************************************************************************
Pearson product-moment correlation coefficient

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    Pearson product-moment correlation coefficient
    (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double pearsoncorr2(const real_1d_array &x, const real_1d_array &y, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    if( (x.length()!=y.length()))
        _ALGLIB_CPP_EXCEPTION("Error while calling 'pearsoncorr2': looks like one of arguments has wrong size");
    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::pearsoncorr2(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}
#endif

/*************************************************************************
Spearman's rank correlation coefficient

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    Spearman's rank correlation coefficient
    (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double spearmancorr2(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::spearmancorr2(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}

/*************************************************************************
Spearman's rank correlation coefficient

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    Spearman's rank correlation coefficient
    (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double spearmancorr2(const real_1d_array &x, const real_1d_array &y, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    if( (x.length()!=y.length()))
        _ALGLIB_CPP_EXCEPTION("Error while calling 'spearmancorr2': looks like one of arguments has wrong size");
    n = x.length();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::spearmancorr2(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}
#endif

/*************************************************************************
Covariance matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], covariance matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void covm(const real_2d_array &x, const ae_int_t n, const ae_int_t m, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::covm(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), n, m, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Covariance matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], covariance matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void covm(const real_2d_array &x, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    ae_int_t m;

    n = x.rows();
    m = x.cols();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::covm(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), n, m, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Pearson product-moment correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrm(const real_2d_array &x, const ae_int_t n, const ae_int_t m, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::pearsoncorrm(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), n, m, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Pearson product-moment correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void pearsoncorrm(const real_2d_array &x, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    ae_int_t m;

    n = x.rows();
    m = x.cols();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::pearsoncorrm(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), n, m, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Spearman's rank correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void spearmancorrm(const real_2d_array &x, const ae_int_t n, const ae_int_t m, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::spearmancorrm(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), n, m, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Spearman's rank correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spearmancorrm(const real_2d_array &x, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    ae_int_t m;

    n = x.rows();
    m = x.cols();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::spearmancorrm(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), n, m, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Cross-covariance matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-covariance matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void covm2(const real_2d_array &x, const real_2d_array &y, const ae_int_t n, const ae_int_t m1, const ae_int_t m2, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::covm2(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_matrix*>(y.c_ptr()), n, m1, m2, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Cross-covariance matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-covariance matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void covm2(const real_2d_array &x, const real_2d_array &y, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    ae_int_t m1;
    ae_int_t m2;
    if( (x.rows()!=y.rows()))
        _ALGLIB_CPP_EXCEPTION("Error while calling 'covm2': looks like one of arguments has wrong size");
    n = x.rows();
    m1 = x.cols();
    m2 = y.cols();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::covm2(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_matrix*>(y.c_ptr()), n, m1, m2, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Pearson product-moment cross-correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrm2(const real_2d_array &x, const real_2d_array &y, const ae_int_t n, const ae_int_t m1, const ae_int_t m2, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::pearsoncorrm2(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_matrix*>(y.c_ptr()), n, m1, m2, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Pearson product-moment cross-correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void pearsoncorrm2(const real_2d_array &x, const real_2d_array &y, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    ae_int_t m1;
    ae_int_t m2;
    if( (x.rows()!=y.rows()))
        _ALGLIB_CPP_EXCEPTION("Error while calling 'pearsoncorrm2': looks like one of arguments has wrong size");
    n = x.rows();
    m1 = x.cols();
    m2 = y.cols();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::pearsoncorrm2(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_matrix*>(y.c_ptr()), n, m1, m2, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Spearman's rank cross-correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void spearmancorrm2(const real_2d_array &x, const real_2d_array &y, const ae_int_t n, const ae_int_t m1, const ae_int_t m2, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::spearmancorrm2(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_matrix*>(y.c_ptr()), n, m1, m2, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Spearman's rank cross-correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spearmancorrm2(const real_2d_array &x, const real_2d_array &y, real_2d_array &c, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t n;
    ae_int_t m1;
    ae_int_t m2;
    if( (x.rows()!=y.rows()))
        _ALGLIB_CPP_EXCEPTION("Error while calling 'spearmancorrm2': looks like one of arguments has wrong size");
    n = x.rows();
    m1 = x.cols();
    m2 = y.cols();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::spearmancorrm2(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_matrix*>(y.c_ptr()), n, m1, m2, const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
This function replaces data in XY by their ranks:
* XY is processed row-by-row
* rows are processed separately
* tied data are correctly handled (tied ranks are calculated)
* ranking starts from 0, ends at NFeatures-1
* sum of within-row values is equal to (NFeatures-1)*NFeatures/2

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    XY      -   array[NPoints,NFeatures], dataset
    NPoints -   number of points
    NFeatures-  number of features

OUTPUT PARAMETERS:
    XY      -   data are replaced by their within-row ranks;
                ranking starts from 0, ends at NFeatures-1

  -- ALGLIB --
     Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
void rankdata(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nfeatures, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::rankdata(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nfeatures, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
This function replaces data in XY by their ranks:
* XY is processed row-by-row
* rows are processed separately
* tied data are correctly handled (tied ranks are calculated)
* ranking starts from 0, ends at NFeatures-1
* sum of within-row values is equal to (NFeatures-1)*NFeatures/2

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    XY      -   array[NPoints,NFeatures], dataset
    NPoints -   number of points
    NFeatures-  number of features

OUTPUT PARAMETERS:
    XY      -   data are replaced by their within-row ranks;
                ranking starts from 0, ends at NFeatures-1

  -- ALGLIB --
     Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void rankdata(real_2d_array &xy, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t npoints;
    ae_int_t nfeatures;

    npoints = xy.rows();
    nfeatures = xy.cols();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::rankdata(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nfeatures, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
This function replaces data in XY by their CENTERED ranks:
* XY is processed row-by-row
* rows are processed separately
* tied data are correctly handled (tied ranks are calculated)
* centered ranks are just usual ranks, but centered in such way  that  sum
  of within-row values is equal to 0.0.
* centering is performed by subtracting mean from each row, i.e it changes
  mean value, but does NOT change higher moments

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    XY      -   array[NPoints,NFeatures], dataset
    NPoints -   number of points
    NFeatures-  number of features

OUTPUT PARAMETERS:
    XY      -   data are replaced by their within-row ranks;
                ranking starts from 0, ends at NFeatures-1

  -- ALGLIB --
     Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
void rankdatacentered(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nfeatures, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::rankdatacentered(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nfeatures, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
This function replaces data in XY by their CENTERED ranks:
* XY is processed row-by-row
* rows are processed separately
* tied data are correctly handled (tied ranks are calculated)
* centered ranks are just usual ranks, but centered in such way  that  sum
  of within-row values is equal to 0.0.
* centering is performed by subtracting mean from each row, i.e it changes
  mean value, but does NOT change higher moments

  ! COMMERCIAL EDITION OF ALGLIB:
  !
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  !
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    XY      -   array[NPoints,NFeatures], dataset
    NPoints -   number of points
    NFeatures-  number of features

OUTPUT PARAMETERS:
    XY      -   data are replaced by their within-row ranks;
                ranking starts from 0, ends at NFeatures-1

  -- ALGLIB --
     Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void rankdatacentered(real_2d_array &xy, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;    
    ae_int_t npoints;
    ae_int_t nfeatures;

    npoints = xy.rows();
    nfeatures = xy.cols();
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::rankdatacentered(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nfeatures, &_alglib_env_state);

    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

/*************************************************************************
Obsolete function, we recommend to use PearsonCorr2().

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double pearsoncorrelation(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::pearsoncorrelation(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}

/*************************************************************************
Obsolete function, we recommend to use SpearmanCorr2().

    -- ALGLIB --
    Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double spearmanrankcorrelation(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return 0;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    double result = alglib_impl::spearmanrankcorrelation(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return *(reinterpret_cast<double*>(&result));
}
#endif

#if defined(AE_COMPILE_CORRELATIONTESTS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Pearson's correlation coefficient significance test

This test checks hypotheses about whether X  and  Y  are  samples  of  two
continuous  distributions  having  zero  correlation  or   whether   their
correlation is non-zero.

The following tests are performed:
    * two-tailed test (null hypothesis - X and Y have zero correlation)
    * left-tailed test (null hypothesis - the correlation  coefficient  is
      greater than or equal to 0)
    * right-tailed test (null hypothesis - the correlation coefficient  is
      less than or equal to 0).

Requirements:
    * the number of elements in each sample is not less than 5
    * normality of distributions of X and Y.

Input parameters:
    R   -   Pearson's correlation coefficient for X and Y
    N   -   number of elements in samples, N>=5.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrelationsignificance(const double r, const ae_int_t n, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::pearsoncorrelationsignificance(r, n, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Spearman's rank correlation coefficient significance test

This test checks hypotheses about whether X  and  Y  are  samples  of  two
continuous  distributions  having  zero  correlation  or   whether   their
correlation is non-zero.

The following tests are performed:
    * two-tailed test (null hypothesis - X and Y have zero correlation)
    * left-tailed test (null hypothesis - the correlation  coefficient  is
      greater than or equal to 0)
    * right-tailed test (null hypothesis - the correlation coefficient  is
      less than or equal to 0).

Requirements:
    * the number of elements in each sample is not less than 5.

The test is non-parametric and doesn't require distributions X and Y to be
normal.

Input parameters:
    R   -   Spearman's rank correlation coefficient for X and Y
    N   -   number of elements in samples, N>=5.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void spearmanrankcorrelationsignificance(const double r, const ae_int_t n, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::spearmanrankcorrelationsignificance(r, n, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

#if defined(AE_COMPILE_JARQUEBERA) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Jarque-Bera test

This test checks hypotheses about the fact that a  given  sample  X  is  a
sample of normal random variable.

Requirements:
    * the number of elements in the sample is not less than 5.

Input parameters:
    X   -   sample. Array whose index goes from 0 to N-1.
    N   -   size of the sample. N>=5

Output parameters:
    P           -   p-value for the test

Accuracy of the approximation used (5<=N<=1951):

p-value  	    relative error (5<=N<=1951)
[1, 0.1]            < 1%
[0.1, 0.01]         < 2%
[0.01, 0.001]       < 6%
[0.001, 0]          wasn't measured

For N>1951 accuracy wasn't measured but it shouldn't be sharply  different
from table values.

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void jarqueberatest(const real_1d_array &x, const ae_int_t n, double &p, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::jarqueberatest(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, &p, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

#if defined(AE_COMPILE_VARIANCETESTS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Two-sample F-test

This test checks three hypotheses about dispersions of the given  samples.
The following tests are performed:
    * two-tailed test (null hypothesis - the dispersions are equal)
    * left-tailed test (null hypothesis  -  the  dispersion  of  the first
      sample is greater than or equal to  the  dispersion  of  the  second
      sample).
    * right-tailed test (null hypothesis - the  dispersion  of  the  first
      sample is less than or equal to the dispersion of the second sample)

The test is based on the following assumptions:
    * the given samples have normal distributions
    * the samples are independent.

Input parameters:
    X   -   sample 1. Array whose index goes from 0 to N-1.
    N   -   sample size.
    Y   -   sample 2. Array whose index goes from 0 to M-1.
    M   -   sample size.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

  -- ALGLIB --
     Copyright 19.09.2006 by Bochkanov Sergey
*************************************************************************/
void ftest(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::ftest(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), m, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
One-sample chi-square test

This test checks three hypotheses about the dispersion of the given sample
The following tests are performed:
    * two-tailed test (null hypothesis - the dispersion equals  the  given
      number)
    * left-tailed test (null hypothesis - the dispersion is  greater  than
      or equal to the given number)
    * right-tailed test (null hypothesis  -  dispersion is  less  than  or
      equal to the given number).

Test is based on the following assumptions:
    * the given sample has a normal distribution.

Input parameters:
    X           -   sample 1. Array whose index goes from 0 to N-1.
    N           -   size of the sample.
    Variance    -   dispersion value to compare with.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

  -- ALGLIB --
     Copyright 19.09.2006 by Bochkanov Sergey
*************************************************************************/
void onesamplevariancetest(const real_1d_array &x, const ae_int_t n, const double variance, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::onesamplevariancetest(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, variance, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

#if defined(AE_COMPILE_WSR) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Wilcoxon signed-rank test

This test checks three hypotheses about the median  of  the  given sample.
The following tests are performed:
    * two-tailed test (null hypothesis - the median is equal to the  given
      value)
    * left-tailed test (null hypothesis - the median is  greater  than  or
      equal to the given value)
    * right-tailed test (null hypothesis  -  the  median  is  less than or
      equal to the given value)

Requirements:
    * the scale of measurement should be ordinal, interval or  ratio (i.e.
      the test could not be applied to nominal variables).
    * the distribution should be continuous and symmetric relative to  its
      median.
    * number of distinct values in the X array should be greater than 4

The test is non-parametric and doesn't require distribution X to be normal

Input parameters:
    X       -   sample. Array whose index goes from 0 to N-1.
    N       -   size of the sample.
    Median  -   assumed median value.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

To calculate p-values, special approximation is used. This method lets  us
calculate p-values with two decimal places in interval [0.0001, 1].

"Two decimal places" does not sound very impressive, but in  practice  the
relative error of less than 1% is enough to make a decision.

There is no approximation outside the [0.0001, 1] interval. Therefore,  if
the significance level outlies this interval, the test returns 0.0001.

  -- ALGLIB --
     Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void wilcoxonsignedranktest(const real_1d_array &x, const ae_int_t n, const double e, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::wilcoxonsignedranktest(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, e, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

#if defined(AE_COMPILE_MANNWHITNEYU) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Mann-Whitney U-test

This test checks hypotheses about whether X  and  Y  are  samples  of  two
continuous distributions of the same shape  and  same  median  or  whether
their medians are different.

The following tests are performed:
    * two-tailed test (null hypothesis - the medians are equal)
    * left-tailed test (null hypothesis - the median of the  first  sample
      is greater than or equal to the median of the second sample)
    * right-tailed test (null hypothesis - the median of the first  sample
      is less than or equal to the median of the second sample).

Requirements:
    * the samples are independent
    * X and Y are continuous distributions (or discrete distributions well-
      approximating continuous distributions)
    * distributions of X and Y have the  same  shape.  The  only  possible
      difference is their position (i.e. the value of the median)
    * the number of elements in each sample is not less than 5
    * the scale of measurement should be ordinal, interval or ratio  (i.e.
      the test could not be applied to nominal variables).

The test is non-parametric and doesn't require distributions to be normal.

Input parameters:
    X   -   sample 1. Array whose index goes from 0 to N-1.
    N   -   size of the sample. N>=5
    Y   -   sample 2. Array whose index goes from 0 to M-1.
    M   -   size of the sample. M>=5

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

To calculate p-values, special approximation is used. This method lets  us
calculate p-values with satisfactory  accuracy  in  interval  [0.0001, 1].
There is no approximation outside the [0.0001, 1] interval. Therefore,  if
the significance level outlies this interval, the test returns 0.0001.

Relative precision of approximation of p-value:

N          M          Max.err.   Rms.err.
5..10      N..10      1.4e-02    6.0e-04
5..10      N..100     2.2e-02    5.3e-06
10..15     N..15      1.0e-02    3.2e-04
10..15     N..100     1.0e-02    2.2e-05
15..100    N..100     6.1e-03    2.7e-06

For N,M>100 accuracy checks weren't put into  practice,  but  taking  into
account characteristics of asymptotic approximation used, precision should
not be sharply different from the values for interval [5, 100].

NOTE: P-value approximation was  optimized  for  0.0001<=p<=0.2500.  Thus,
      P's outside of this interval are enforced to these bounds. Say,  you
      may quite often get P equal to exactly 0.25 or 0.0001.

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void mannwhitneyutest(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::mannwhitneyutest(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), m, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

#if defined(AE_COMPILE_STEST) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Sign test

This test checks three hypotheses about the median of  the  given  sample.
The following tests are performed:
    * two-tailed test (null hypothesis - the median is equal to the  given
      value)
    * left-tailed test (null hypothesis - the median is  greater  than  or
      equal to the given value)
    * right-tailed test (null hypothesis - the  median  is  less  than  or
      equal to the given value)

Requirements:
    * the scale of measurement should be ordinal, interval or ratio  (i.e.
      the test could not be applied to nominal variables).

The test is non-parametric and doesn't require distribution X to be normal

Input parameters:
    X       -   sample. Array whose index goes from 0 to N-1.
    N       -   size of the sample.
    Median  -   assumed median value.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

While   calculating   p-values   high-precision   binomial    distribution
approximation is used, so significance levels have about 15 exact digits.

  -- ALGLIB --
     Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void onesamplesigntest(const real_1d_array &x, const ae_int_t n, const double median, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::onesamplesigntest(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, median, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif

#if defined(AE_COMPILE_STUDENTTTESTS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
One-sample t-test

This test checks three hypotheses about the mean of the given sample.  The
following tests are performed:
    * two-tailed test (null hypothesis - the mean is equal  to  the  given
      value)
    * left-tailed test (null hypothesis - the  mean  is  greater  than  or
      equal to the given value)
    * right-tailed test (null hypothesis - the mean is less than or  equal
      to the given value).

The test is based on the assumption that  a  given  sample  has  a  normal
distribution and  an  unknown  dispersion.  If  the  distribution  sharply
differs from normal, the test will work incorrectly.

INPUT PARAMETERS:
    X       -   sample. Array whose index goes from 0 to N-1.
    N       -   size of sample, N>=0
    Mean    -   assumed value of the mean.

OUTPUT PARAMETERS:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

NOTE: this function correctly handles degenerate cases:
      * when N=0, all p-values are set to 1.0
      * when variance of X[] is exactly zero, p-values are set
        to 1.0 or 0.0, depending on difference between sample mean and
        value of mean being tested.


  -- ALGLIB --
     Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void studentttest1(const real_1d_array &x, const ae_int_t n, const double mean, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::studentttest1(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, mean, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Two-sample pooled test

This test checks three hypotheses about the mean of the given samples. The
following tests are performed:
    * two-tailed test (null hypothesis - the means are equal)
    * left-tailed test (null hypothesis - the mean of the first sample  is
      greater than or equal to the mean of the second sample)
    * right-tailed test (null hypothesis - the mean of the first sample is
      less than or equal to the mean of the second sample).

Test is based on the following assumptions:
    * given samples have normal distributions
    * dispersions are equal
    * samples are independent.

Input parameters:
    X       -   sample 1. Array whose index goes from 0 to N-1.
    N       -   size of sample.
    Y       -   sample 2. Array whose index goes from 0 to M-1.
    M       -   size of sample.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

NOTE: this function correctly handles degenerate cases:
      * when N=0 or M=0, all p-values are set to 1.0
      * when both samples has exactly zero variance, p-values are set
        to 1.0 or 0.0, depending on difference between means.

  -- ALGLIB --
     Copyright 18.09.2006 by Bochkanov Sergey
*************************************************************************/
void studentttest2(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::studentttest2(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), m, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}

/*************************************************************************
Two-sample unpooled test

This test checks three hypotheses about the mean of the given samples. The
following tests are performed:
    * two-tailed test (null hypothesis - the means are equal)
    * left-tailed test (null hypothesis - the mean of the first sample  is
      greater than or equal to the mean of the second sample)
    * right-tailed test (null hypothesis - the mean of the first sample is
      less than or equal to the mean of the second sample).

Test is based on the following assumptions:
    * given samples have normal distributions
    * samples are independent.
Equality of variances is NOT required.

Input parameters:
    X - sample 1. Array whose index goes from 0 to N-1.
    N - size of the sample.
    Y - sample 2. Array whose index goes from 0 to M-1.
    M - size of the sample.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

NOTE: this function correctly handles degenerate cases:
      * when N=0 or M=0, all p-values are set to 1.0
      * when both samples has zero variance, p-values are set
        to 1.0 or 0.0, depending on difference between means.
      * when only one sample has zero variance, test reduces to 1-sample
        version.

  -- ALGLIB --
     Copyright 18.09.2006 by Bochkanov Sergey
*************************************************************************/
void unequalvariancettest(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, double &bothtails, double &lefttail, double &righttail, const xparams _xparams)
{
    jmp_buf _break_jump;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    if( setjmp(_break_jump) )
    {
#if !defined(AE_NO_EXCEPTIONS)
        _ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
        _ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
        return;
#endif
    }
    ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
    if( _xparams.flags!=0x0 )
        ae_state_set_flags(&_alglib_env_state, _xparams.flags);
    alglib_impl::unequalvariancettest(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), m, &bothtails, &lefttail, &righttail, &_alglib_env_state);
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return;
}
#endif
}

/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS IMPLEMENTATION OF COMPUTATIONAL CORE
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
#if defined(AE_COMPILE_BASESTAT) || !defined(AE_PARTIAL_BUILD)
static void basestat_rankdatarec(/* Real    */ ae_matrix* xy,
     ae_int_t i0,
     ae_int_t i1,
     ae_int_t nfeatures,
     ae_bool iscentered,
     ae_shared_pool* pool,
     ae_int_t basecasecost,
     ae_state *_state);
ae_bool _trypexec_basestat_rankdatarec(/* Real    */ ae_matrix* xy,
    ae_int_t i0,
    ae_int_t i1,
    ae_int_t nfeatures,
    ae_bool iscentered,
    ae_shared_pool* pool,
    ae_int_t basecasecost, ae_state *_state);
static void basestat_rankdatabasecase(/* Real    */ ae_matrix* xy,
     ae_int_t i0,
     ae_int_t i1,
     ae_int_t nfeatures,
     ae_bool iscentered,
     apbuffers* buf0,
     apbuffers* buf1,
     ae_state *_state);
ae_bool _trypexec_basestat_rankdatabasecase(/* Real    */ ae_matrix* xy,
    ae_int_t i0,
    ae_int_t i1,
    ae_int_t nfeatures,
    ae_bool iscentered,
    apbuffers* buf0,
    apbuffers* buf1, ae_state *_state);


#endif
#if defined(AE_COMPILE_CORRELATIONTESTS) || !defined(AE_PARTIAL_BUILD)
static double correlationtests_spearmantail5(double s, ae_state *_state);
static double correlationtests_spearmantail6(double s, ae_state *_state);
static double correlationtests_spearmantail7(double s, ae_state *_state);
static double correlationtests_spearmantail8(double s, ae_state *_state);
static double correlationtests_spearmantail9(double s, ae_state *_state);
static double correlationtests_spearmantail(double t,
     ae_int_t n,
     ae_state *_state);


#endif
#if defined(AE_COMPILE_JARQUEBERA) || !defined(AE_PARTIAL_BUILD)
static void jarquebera_jarqueberastatistic(/* Real    */ ae_vector* x,
     ae_int_t n,
     double* s,
     ae_state *_state);
static double jarquebera_jarqueberaapprox(ae_int_t n,
     double s,
     ae_state *_state);
static double jarquebera_jbtbl5(double s, ae_state *_state);
static double jarquebera_jbtbl6(double s, ae_state *_state);
static double jarquebera_jbtbl7(double s, ae_state *_state);
static double jarquebera_jbtbl8(double s, ae_state *_state);
static double jarquebera_jbtbl9(double s, ae_state *_state);
static double jarquebera_jbtbl10(double s, ae_state *_state);
static double jarquebera_jbtbl11(double s, ae_state *_state);
static double jarquebera_jbtbl12(double s, ae_state *_state);
static double jarquebera_jbtbl13(double s, ae_state *_state);
static double jarquebera_jbtbl14(double s, ae_state *_state);
static double jarquebera_jbtbl15(double s, ae_state *_state);
static double jarquebera_jbtbl16(double s, ae_state *_state);
static double jarquebera_jbtbl17(double s, ae_state *_state);
static double jarquebera_jbtbl18(double s, ae_state *_state);
static double jarquebera_jbtbl19(double s, ae_state *_state);
static double jarquebera_jbtbl20(double s, ae_state *_state);
static double jarquebera_jbtbl30(double s, ae_state *_state);
static double jarquebera_jbtbl50(double s, ae_state *_state);
static double jarquebera_jbtbl65(double s, ae_state *_state);
static double jarquebera_jbtbl100(double s, ae_state *_state);
static double jarquebera_jbtbl130(double s, ae_state *_state);
static double jarquebera_jbtbl200(double s, ae_state *_state);
static double jarquebera_jbtbl301(double s, ae_state *_state);
static double jarquebera_jbtbl501(double s, ae_state *_state);
static double jarquebera_jbtbl701(double s, ae_state *_state);
static double jarquebera_jbtbl1401(double s, ae_state *_state);
static void jarquebera_jbcheb(double x,
     double c,
     double* tj,
     double* tj1,
     double* r,
     ae_state *_state);


#endif
#if defined(AE_COMPILE_VARIANCETESTS) || !defined(AE_PARTIAL_BUILD)


#endif
#if defined(AE_COMPILE_WSR) || !defined(AE_PARTIAL_BUILD)
static void wsr_wcheb(double x,
     double c,
     double* tj,
     double* tj1,
     double* r,
     ae_state *_state);
static double wsr_w5(double s, ae_state *_state);
static double wsr_w6(double s, ae_state *_state);
static double wsr_w7(double s, ae_state *_state);
static double wsr_w8(double s, ae_state *_state);
static double wsr_w9(double s, ae_state *_state);
static double wsr_w10(double s, ae_state *_state);
static double wsr_w11(double s, ae_state *_state);
static double wsr_w12(double s, ae_state *_state);
static double wsr_w13(double s, ae_state *_state);
static double wsr_w14(double s, ae_state *_state);
static double wsr_w15(double s, ae_state *_state);
static double wsr_w16(double s, ae_state *_state);
static double wsr_w17(double s, ae_state *_state);
static double wsr_w18(double s, ae_state *_state);
static double wsr_w19(double s, ae_state *_state);
static double wsr_w20(double s, ae_state *_state);
static double wsr_w21(double s, ae_state *_state);
static double wsr_w22(double s, ae_state *_state);
static double wsr_w23(double s, ae_state *_state);
static double wsr_w24(double s, ae_state *_state);
static double wsr_w25(double s, ae_state *_state);
static double wsr_w26(double s, ae_state *_state);
static double wsr_w27(double s, ae_state *_state);
static double wsr_w28(double s, ae_state *_state);
static double wsr_w29(double s, ae_state *_state);
static double wsr_w30(double s, ae_state *_state);
static double wsr_w40(double s, ae_state *_state);
static double wsr_w60(double s, ae_state *_state);
static double wsr_w120(double s, ae_state *_state);
static double wsr_w200(double s, ae_state *_state);
static double wsr_wsigma(double s, ae_int_t n, ae_state *_state);


#endif
#if defined(AE_COMPILE_MANNWHITNEYU) || !defined(AE_PARTIAL_BUILD)
static void mannwhitneyu_ucheb(double x,
     double c,
     double* tj,
     double* tj1,
     double* r,
     ae_state *_state);
static double mannwhitneyu_uninterpolate(double p1,
     double p2,
     double p3,
     ae_int_t n,
     ae_state *_state);
static double mannwhitneyu_usigma000(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);
static double mannwhitneyu_usigma075(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);
static double mannwhitneyu_usigma150(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);
static double mannwhitneyu_usigma225(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);
static double mannwhitneyu_usigma300(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);
static double mannwhitneyu_usigma333(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);
static double mannwhitneyu_usigma367(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);
static double mannwhitneyu_usigma400(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);
static double mannwhitneyu_utbln5n5(double s, ae_state *_state);
static double mannwhitneyu_utbln5n6(double s, ae_state *_state);
static double mannwhitneyu_utbln5n7(double s, ae_state *_state);
static double mannwhitneyu_utbln5n8(double s, ae_state *_state);
static double mannwhitneyu_utbln5n9(double s, ae_state *_state);
static double mannwhitneyu_utbln5n10(double s, ae_state *_state);
static double mannwhitneyu_utbln5n11(double s, ae_state *_state);
static double mannwhitneyu_utbln5n12(double s, ae_state *_state);
static double mannwhitneyu_utbln5n13(double s, ae_state *_state);
static double mannwhitneyu_utbln5n14(double s, ae_state *_state);
static double mannwhitneyu_utbln5n15(double s, ae_state *_state);
static double mannwhitneyu_utbln5n16(double s, ae_state *_state);
static double mannwhitneyu_utbln5n17(double s, ae_state *_state);
static double mannwhitneyu_utbln5n18(double s, ae_state *_state);
static double mannwhitneyu_utbln5n19(double s, ae_state *_state);
static double mannwhitneyu_utbln5n20(double s, ae_state *_state);
static double mannwhitneyu_utbln5n21(double s, ae_state *_state);
static double mannwhitneyu_utbln5n22(double s, ae_state *_state);
static double mannwhitneyu_utbln5n23(double s, ae_state *_state);
static double mannwhitneyu_utbln5n24(double s, ae_state *_state);
static double mannwhitneyu_utbln5n25(double s, ae_state *_state);
static double mannwhitneyu_utbln5n26(double s, ae_state *_state);
static double mannwhitneyu_utbln5n27(double s, ae_state *_state);
static double mannwhitneyu_utbln5n28(double s, ae_state *_state);
static double mannwhitneyu_utbln5n29(double s, ae_state *_state);
static double mannwhitneyu_utbln5n30(double s, ae_state *_state);
static double mannwhitneyu_utbln5n100(double s, ae_state *_state);
static double mannwhitneyu_utbln6n6(double s, ae_state *_state);
static double mannwhitneyu_utbln6n7(double s, ae_state *_state);
static double mannwhitneyu_utbln6n8(double s, ae_state *_state);
static double mannwhitneyu_utbln6n9(double s, ae_state *_state);
static double mannwhitneyu_utbln6n10(double s, ae_state *_state);
static double mannwhitneyu_utbln6n11(double s, ae_state *_state);
static double mannwhitneyu_utbln6n12(double s, ae_state *_state);
static double mannwhitneyu_utbln6n13(double s, ae_state *_state);
static double mannwhitneyu_utbln6n14(double s, ae_state *_state);
static double mannwhitneyu_utbln6n15(double s, ae_state *_state);
static double mannwhitneyu_utbln6n30(double s, ae_state *_state);
static double mannwhitneyu_utbln6n100(double s, ae_state *_state);
static double mannwhitneyu_utbln7n7(double s, ae_state *_state);
static double mannwhitneyu_utbln7n8(double s, ae_state *_state);
static double mannwhitneyu_utbln7n9(double s, ae_state *_state);
static double mannwhitneyu_utbln7n10(double s, ae_state *_state);
static double mannwhitneyu_utbln7n11(double s, ae_state *_state);
static double mannwhitneyu_utbln7n12(double s, ae_state *_state);
static double mannwhitneyu_utbln7n13(double s, ae_state *_state);
static double mannwhitneyu_utbln7n14(double s, ae_state *_state);
static double mannwhitneyu_utbln7n15(double s, ae_state *_state);
static double mannwhitneyu_utbln7n30(double s, ae_state *_state);
static double mannwhitneyu_utbln7n100(double s, ae_state *_state);
static double mannwhitneyu_utbln8n8(double s, ae_state *_state);
static double mannwhitneyu_utbln8n9(double s, ae_state *_state);
static double mannwhitneyu_utbln8n10(double s, ae_state *_state);
static double mannwhitneyu_utbln8n11(double s, ae_state *_state);
static double mannwhitneyu_utbln8n12(double s, ae_state *_state);
static double mannwhitneyu_utbln8n13(double s, ae_state *_state);
static double mannwhitneyu_utbln8n14(double s, ae_state *_state);
static double mannwhitneyu_utbln8n15(double s, ae_state *_state);
static double mannwhitneyu_utbln8n30(double s, ae_state *_state);
static double mannwhitneyu_utbln8n100(double s, ae_state *_state);
static double mannwhitneyu_utbln9n9(double s, ae_state *_state);
static double mannwhitneyu_utbln9n10(double s, ae_state *_state);
static double mannwhitneyu_utbln9n11(double s, ae_state *_state);
static double mannwhitneyu_utbln9n12(double s, ae_state *_state);
static double mannwhitneyu_utbln9n13(double s, ae_state *_state);
static double mannwhitneyu_utbln9n14(double s, ae_state *_state);
static double mannwhitneyu_utbln9n15(double s, ae_state *_state);
static double mannwhitneyu_utbln9n30(double s, ae_state *_state);
static double mannwhitneyu_utbln9n100(double s, ae_state *_state);
static double mannwhitneyu_utbln10n10(double s, ae_state *_state);
static double mannwhitneyu_utbln10n11(double s, ae_state *_state);
static double mannwhitneyu_utbln10n12(double s, ae_state *_state);
static double mannwhitneyu_utbln10n13(double s, ae_state *_state);
static double mannwhitneyu_utbln10n14(double s, ae_state *_state);
static double mannwhitneyu_utbln10n15(double s, ae_state *_state);
static double mannwhitneyu_utbln10n30(double s, ae_state *_state);
static double mannwhitneyu_utbln10n100(double s, ae_state *_state);
static double mannwhitneyu_utbln11n11(double s, ae_state *_state);
static double mannwhitneyu_utbln11n12(double s, ae_state *_state);
static double mannwhitneyu_utbln11n13(double s, ae_state *_state);
static double mannwhitneyu_utbln11n14(double s, ae_state *_state);
static double mannwhitneyu_utbln11n15(double s, ae_state *_state);
static double mannwhitneyu_utbln11n30(double s, ae_state *_state);
static double mannwhitneyu_utbln11n100(double s, ae_state *_state);
static double mannwhitneyu_utbln12n12(double s, ae_state *_state);
static double mannwhitneyu_utbln12n13(double s, ae_state *_state);
static double mannwhitneyu_utbln12n14(double s, ae_state *_state);
static double mannwhitneyu_utbln12n15(double s, ae_state *_state);
static double mannwhitneyu_utbln12n30(double s, ae_state *_state);
static double mannwhitneyu_utbln12n100(double s, ae_state *_state);
static double mannwhitneyu_utbln13n13(double s, ae_state *_state);
static double mannwhitneyu_utbln13n14(double s, ae_state *_state);
static double mannwhitneyu_utbln13n15(double s, ae_state *_state);
static double mannwhitneyu_utbln13n30(double s, ae_state *_state);
static double mannwhitneyu_utbln13n100(double s, ae_state *_state);
static double mannwhitneyu_utbln14n14(double s, ae_state *_state);
static double mannwhitneyu_utbln14n15(double s, ae_state *_state);
static double mannwhitneyu_utbln14n30(double s, ae_state *_state);
static double mannwhitneyu_utbln14n100(double s, ae_state *_state);
static double mannwhitneyu_usigma(double s,
     ae_int_t n1,
     ae_int_t n2,
     ae_state *_state);


#endif
#if defined(AE_COMPILE_STEST) || !defined(AE_PARTIAL_BUILD)


#endif
#if defined(AE_COMPILE_STUDENTTTESTS) || !defined(AE_PARTIAL_BUILD)


#endif

#if defined(AE_COMPILE_BASESTAT) || !defined(AE_PARTIAL_BUILD)


/*************************************************************************
Calculation of the distribution moments: mean, variance, skewness, kurtosis.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X
    
OUTPUT PARAMETERS
    Mean    -   mean.
    Variance-   variance.
    Skewness-   skewness (if variance<>0; zero otherwise).
    Kurtosis-   kurtosis (if variance<>0; zero otherwise).

NOTE: variance is calculated by dividing sum of squares by N-1, not N.

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void samplemoments(/* Real    */ ae_vector* x,
     ae_int_t n,
     double* mean,
     double* variance,
     double* skewness,
     double* kurtosis,
     ae_state *_state)
{
    ae_int_t i;
    double v;
    double v1;
    double v2;
    double stddev;

    *mean = 0;
    *variance = 0;
    *skewness = 0;
    *kurtosis = 0;

    ae_assert(n>=0, "SampleMoments: N<0", _state);
    ae_assert(x->cnt>=n, "SampleMoments: Length(X)<N!", _state);
    ae_assert(isfinitevector(x, n, _state), "SampleMoments: X is not finite vector", _state);
    
    /*
     * Init, special case 'N=0'
     */
    *mean = (double)(0);
    *variance = (double)(0);
    *skewness = (double)(0);
    *kurtosis = (double)(0);
    stddev = (double)(0);
    if( n<=0 )
    {
        return;
    }
    
    /*
     * Mean
     */
    for(i=0; i<=n-1; i++)
    {
        *mean = *mean+x->ptr.p_double[i];
    }
    *mean = *mean/n;
    
    /*
     * Variance (using corrected two-pass algorithm)
     */
    if( n!=1 )
    {
        v1 = (double)(0);
        for(i=0; i<=n-1; i++)
        {
            v1 = v1+ae_sqr(x->ptr.p_double[i]-(*mean), _state);
        }
        v2 = (double)(0);
        for(i=0; i<=n-1; i++)
        {
            v2 = v2+(x->ptr.p_double[i]-(*mean));
        }
        v2 = ae_sqr(v2, _state)/n;
        *variance = (v1-v2)/(n-1);
        if( ae_fp_less(*variance,(double)(0)) )
        {
            *variance = (double)(0);
        }
        stddev = ae_sqrt(*variance, _state);
    }
    
    /*
     * Skewness and kurtosis
     */
    if( ae_fp_neq(stddev,(double)(0)) )
    {
        for(i=0; i<=n-1; i++)
        {
            v = (x->ptr.p_double[i]-(*mean))/stddev;
            v2 = ae_sqr(v, _state);
            *skewness = *skewness+v2*v;
            *kurtosis = *kurtosis+ae_sqr(v2, _state);
        }
        *skewness = *skewness/n;
        *kurtosis = *kurtosis/n-3;
    }
}


/*************************************************************************
Calculation of the mean.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:
                
This function return result  which calculated by 'SampleMoments' function
and stored at 'Mean' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplemean(/* Real    */ ae_vector* x,
     ae_int_t n,
     ae_state *_state)
{
    double mean;
    double tmp0;
    double tmp1;
    double tmp2;
    double result;


    samplemoments(x, n, &mean, &tmp0, &tmp1, &tmp2, _state);
    result = mean;
    return result;
}


/*************************************************************************
Calculation of the variance.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:
                
This function return result  which calculated by 'SampleMoments' function
and stored at 'Variance' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplevariance(/* Real    */ ae_vector* x,
     ae_int_t n,
     ae_state *_state)
{
    double variance;
    double tmp0;
    double tmp1;
    double tmp2;
    double result;


    samplemoments(x, n, &tmp0, &variance, &tmp1, &tmp2, _state);
    result = variance;
    return result;
}


/*************************************************************************
Calculation of the skewness.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:
                
This function return result  which calculated by 'SampleMoments' function
and stored at 'Skewness' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double sampleskewness(/* Real    */ ae_vector* x,
     ae_int_t n,
     ae_state *_state)
{
    double skewness;
    double tmp0;
    double tmp1;
    double tmp2;
    double result;


    samplemoments(x, n, &tmp0, &tmp1, &skewness, &tmp2, _state);
    result = skewness;
    return result;
}


/*************************************************************************
Calculation of the kurtosis.

INPUT PARAMETERS:
    X       -   sample
    N       -   N>=0, sample size:
                * if given, only leading N elements of X are processed
                * if not given, automatically determined from size of X

NOTE:
                
This function return result  which calculated by 'SampleMoments' function
and stored at 'Kurtosis' variable.


  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplekurtosis(/* Real    */ ae_vector* x,
     ae_int_t n,
     ae_state *_state)
{
    double kurtosis;
    double tmp0;
    double tmp1;
    double tmp2;
    double result;


    samplemoments(x, n, &tmp0, &tmp1, &tmp2, &kurtosis, _state);
    result = kurtosis;
    return result;
}


/*************************************************************************
ADev

Input parameters:
    X   -   sample
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X
    
Output parameters:
    ADev-   ADev

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void sampleadev(/* Real    */ ae_vector* x,
     ae_int_t n,
     double* adev,
     ae_state *_state)
{
    ae_int_t i;
    double mean;

    *adev = 0;

    ae_assert(n>=0, "SampleADev: N<0", _state);
    ae_assert(x->cnt>=n, "SampleADev: Length(X)<N!", _state);
    ae_assert(isfinitevector(x, n, _state), "SampleADev: X is not finite vector", _state);
    
    /*
     * Init, handle N=0
     */
    mean = (double)(0);
    *adev = (double)(0);
    if( n<=0 )
    {
        return;
    }
    
    /*
     * Mean
     */
    for(i=0; i<=n-1; i++)
    {
        mean = mean+x->ptr.p_double[i];
    }
    mean = mean/n;
    
    /*
     * ADev
     */
    for(i=0; i<=n-1; i++)
    {
        *adev = *adev+ae_fabs(x->ptr.p_double[i]-mean, _state);
    }
    *adev = *adev/n;
}


/*************************************************************************
Median calculation.

Input parameters:
    X   -   sample (array indexes: [0..N-1])
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X

Output parameters:
    Median

  -- ALGLIB --
     Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void samplemedian(/* Real    */ ae_vector* x,
     ae_int_t n,
     double* median,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_vector _x;
    ae_int_t i;
    ae_int_t ir;
    ae_int_t j;
    ae_int_t l;
    ae_int_t midp;
    ae_int_t k;
    double a;
    double tval;

    ae_frame_make(_state, &_frame_block);
    memset(&_x, 0, sizeof(_x));
    ae_vector_init_copy(&_x, x, _state, ae_true);
    x = &_x;
    *median = 0;

    ae_assert(n>=0, "SampleMedian: N<0", _state);
    ae_assert(x->cnt>=n, "SampleMedian: Length(X)<N!", _state);
    ae_assert(isfinitevector(x, n, _state), "SampleMedian: X is not finite vector", _state);
    
    /*
     * Some degenerate cases
     */
    *median = (double)(0);
    if( n<=0 )
    {
        ae_frame_leave(_state);
        return;
    }
    if( n==1 )
    {
        *median = x->ptr.p_double[0];
        ae_frame_leave(_state);
        return;
    }
    if( n==2 )
    {
        *median = 0.5*(x->ptr.p_double[0]+x->ptr.p_double[1]);
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Common case, N>=3.
     * Choose X[(N-1)/2]
     */
    l = 0;
    ir = n-1;
    k = (n-1)/2;
    for(;;)
    {
        if( ir<=l+1 )
        {
            
            /*
             * 1 or 2 elements in partition
             */
            if( ir==l+1&&ae_fp_less(x->ptr.p_double[ir],x->ptr.p_double[l]) )
            {
                tval = x->ptr.p_double[l];
                x->ptr.p_double[l] = x->ptr.p_double[ir];
                x->ptr.p_double[ir] = tval;
            }
            break;
        }
        else
        {
            midp = (l+ir)/2;
            tval = x->ptr.p_double[midp];
            x->ptr.p_double[midp] = x->ptr.p_double[l+1];
            x->ptr.p_double[l+1] = tval;
            if( ae_fp_greater(x->ptr.p_double[l],x->ptr.p_double[ir]) )
            {
                tval = x->ptr.p_double[l];
                x->ptr.p_double[l] = x->ptr.p_double[ir];
                x->ptr.p_double[ir] = tval;
            }
            if( ae_fp_greater(x->ptr.p_double[l+1],x->ptr.p_double[ir]) )
            {
                tval = x->ptr.p_double[l+1];
                x->ptr.p_double[l+1] = x->ptr.p_double[ir];
                x->ptr.p_double[ir] = tval;
            }
            if( ae_fp_greater(x->ptr.p_double[l],x->ptr.p_double[l+1]) )
            {
                tval = x->ptr.p_double[l];
                x->ptr.p_double[l] = x->ptr.p_double[l+1];
                x->ptr.p_double[l+1] = tval;
            }
            i = l+1;
            j = ir;
            a = x->ptr.p_double[l+1];
            for(;;)
            {
                do
                {
                    i = i+1;
                }
                while(ae_fp_less(x->ptr.p_double[i],a));
                do
                {
                    j = j-1;
                }
                while(ae_fp_greater(x->ptr.p_double[j],a));
                if( j<i )
                {
                    break;
                }
                tval = x->ptr.p_double[i];
                x->ptr.p_double[i] = x->ptr.p_double[j];
                x->ptr.p_double[j] = tval;
            }
            x->ptr.p_double[l+1] = x->ptr.p_double[j];
            x->ptr.p_double[j] = a;
            if( j>=k )
            {
                ir = j-1;
            }
            if( j<=k )
            {
                l = i;
            }
        }
    }
    
    /*
     * If N is odd, return result
     */
    if( n%2==1 )
    {
        *median = x->ptr.p_double[k];
        ae_frame_leave(_state);
        return;
    }
    a = x->ptr.p_double[n-1];
    for(i=k+1; i<=n-1; i++)
    {
        if( ae_fp_less(x->ptr.p_double[i],a) )
        {
            a = x->ptr.p_double[i];
        }
    }
    *median = 0.5*(x->ptr.p_double[k]+a);
    ae_frame_leave(_state);
}


/*************************************************************************
Percentile calculation.

Input parameters:
    X   -   sample (array indexes: [0..N-1])
    N   -   N>=0, sample size:
            * if given, only leading N elements of X are processed
            * if not given, automatically determined from size of X
    P   -   percentile (0<=P<=1)

Output parameters:
    V   -   percentile

  -- ALGLIB --
     Copyright 01.03.2008 by Bochkanov Sergey
*************************************************************************/
void samplepercentile(/* Real    */ ae_vector* x,
     ae_int_t n,
     double p,
     double* v,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_vector _x;
    ae_int_t i1;
    double t;
    ae_vector rbuf;

    ae_frame_make(_state, &_frame_block);
    memset(&_x, 0, sizeof(_x));
    memset(&rbuf, 0, sizeof(rbuf));
    ae_vector_init_copy(&_x, x, _state, ae_true);
    x = &_x;
    *v = 0;
    ae_vector_init(&rbuf, 0, DT_REAL, _state, ae_true);

    ae_assert(n>=0, "SamplePercentile: N<0", _state);
    ae_assert(x->cnt>=n, "SamplePercentile: Length(X)<N!", _state);
    ae_assert(isfinitevector(x, n, _state), "SamplePercentile: X is not finite vector", _state);
    ae_assert(ae_isfinite(p, _state), "SamplePercentile: incorrect P!", _state);
    ae_assert(ae_fp_greater_eq(p,(double)(0))&&ae_fp_less_eq(p,(double)(1)), "SamplePercentile: incorrect P!", _state);
    tagsortfast(x, &rbuf, n, _state);
    if( ae_fp_eq(p,(double)(0)) )
    {
        *v = x->ptr.p_double[0];
        ae_frame_leave(_state);
        return;
    }
    if( ae_fp_eq(p,(double)(1)) )
    {
        *v = x->ptr.p_double[n-1];
        ae_frame_leave(_state);
        return;
    }
    t = p*(n-1);
    i1 = ae_ifloor(t, _state);
    t = t-ae_ifloor(t, _state);
    *v = x->ptr.p_double[i1]*(1-t)+x->ptr.p_double[i1+1]*t;
    ae_frame_leave(_state);
}


/*************************************************************************
2-sample covariance

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    covariance (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
double cov2(/* Real    */ ae_vector* x,
     /* Real    */ ae_vector* y,
     ae_int_t n,
     ae_state *_state)
{
    ae_int_t i;
    double xmean;
    double ymean;
    double v;
    double x0;
    double y0;
    double s;
    ae_bool samex;
    ae_bool samey;
    double result;


    ae_assert(n>=0, "Cov2: N<0", _state);
    ae_assert(x->cnt>=n, "Cov2: Length(X)<N!", _state);
    ae_assert(y->cnt>=n, "Cov2: Length(Y)<N!", _state);
    ae_assert(isfinitevector(x, n, _state), "Cov2: X is not finite vector", _state);
    ae_assert(isfinitevector(y, n, _state), "Cov2: Y is not finite vector", _state);
    
    /*
     * Special case
     */
    if( n<=1 )
    {
        result = (double)(0);
        return result;
    }
    
    /*
     * Calculate mean.
     *
     *
     * Additonally we calculate SameX and SameY -
     * flag variables which are set to True when
     * all X[] (or Y[]) contain exactly same value.
     *
     * If at least one of them is True, we return zero
     * (othwerwise we risk to get nonzero covariation
     * because of roundoff).
     */
    xmean = (double)(0);
    ymean = (double)(0);
    samex = ae_true;
    samey = ae_true;
    x0 = x->ptr.p_double[0];
    y0 = y->ptr.p_double[0];
    v = (double)1/(double)n;
    for(i=0; i<=n-1; i++)
    {
        s = x->ptr.p_double[i];
        samex = samex&&ae_fp_eq(s,x0);
        xmean = xmean+s*v;
        s = y->ptr.p_double[i];
        samey = samey&&ae_fp_eq(s,y0);
        ymean = ymean+s*v;
    }
    if( samex||samey )
    {
        result = (double)(0);
        return result;
    }
    
    /*
     * covariance
     */
    v = (double)1/(double)(n-1);
    result = (double)(0);
    for(i=0; i<=n-1; i++)
    {
        result = result+v*(x->ptr.p_double[i]-xmean)*(y->ptr.p_double[i]-ymean);
    }
    return result;
}


/*************************************************************************
Pearson product-moment correlation coefficient

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    Pearson product-moment correlation coefficient
    (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
double pearsoncorr2(/* Real    */ ae_vector* x,
     /* Real    */ ae_vector* y,
     ae_int_t n,
     ae_state *_state)
{
    ae_int_t i;
    double xmean;
    double ymean;
    double v;
    double x0;
    double y0;
    double s;
    ae_bool samex;
    ae_bool samey;
    double xv;
    double yv;
    double t1;
    double t2;
    double result;


    ae_assert(n>=0, "PearsonCorr2: N<0", _state);
    ae_assert(x->cnt>=n, "PearsonCorr2: Length(X)<N!", _state);
    ae_assert(y->cnt>=n, "PearsonCorr2: Length(Y)<N!", _state);
    ae_assert(isfinitevector(x, n, _state), "PearsonCorr2: X is not finite vector", _state);
    ae_assert(isfinitevector(y, n, _state), "PearsonCorr2: Y is not finite vector", _state);
    
    /*
     * Special case
     */
    if( n<=1 )
    {
        result = (double)(0);
        return result;
    }
    
    /*
     * Calculate mean.
     *
     *
     * Additonally we calculate SameX and SameY -
     * flag variables which are set to True when
     * all X[] (or Y[]) contain exactly same value.
     *
     * If at least one of them is True, we return zero
     * (othwerwise we risk to get nonzero correlation
     * because of roundoff).
     */
    xmean = (double)(0);
    ymean = (double)(0);
    samex = ae_true;
    samey = ae_true;
    x0 = x->ptr.p_double[0];
    y0 = y->ptr.p_double[0];
    v = (double)1/(double)n;
    for(i=0; i<=n-1; i++)
    {
        s = x->ptr.p_double[i];
        samex = samex&&ae_fp_eq(s,x0);
        xmean = xmean+s*v;
        s = y->ptr.p_double[i];
        samey = samey&&ae_fp_eq(s,y0);
        ymean = ymean+s*v;
    }
    if( samex||samey )
    {
        result = (double)(0);
        return result;
    }
    
    /*
     * numerator and denominator
     */
    s = (double)(0);
    xv = (double)(0);
    yv = (double)(0);
    for(i=0; i<=n-1; i++)
    {
        t1 = x->ptr.p_double[i]-xmean;
        t2 = y->ptr.p_double[i]-ymean;
        xv = xv+ae_sqr(t1, _state);
        yv = yv+ae_sqr(t2, _state);
        s = s+t1*t2;
    }
    if( ae_fp_eq(xv,(double)(0))||ae_fp_eq(yv,(double)(0)) )
    {
        result = (double)(0);
    }
    else
    {
        result = s/(ae_sqrt(xv, _state)*ae_sqrt(yv, _state));
    }
    return result;
}


/*************************************************************************
Spearman's rank correlation coefficient

Input parameters:
    X       -   sample 1 (array indexes: [0..N-1])
    Y       -   sample 2 (array indexes: [0..N-1])
    N       -   N>=0, sample size:
                * if given, only N leading elements of X/Y are processed
                * if not given, automatically determined from input sizes

Result:
    Spearman's rank correlation coefficient
    (zero for N=0 or N=1)

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double spearmancorr2(/* Real    */ ae_vector* x,
     /* Real    */ ae_vector* y,
     ae_int_t n,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_vector _x;
    ae_vector _y;
    apbuffers buf;
    double result;

    ae_frame_make(_state, &_frame_block);
    memset(&_x, 0, sizeof(_x));
    memset(&_y, 0, sizeof(_y));
    memset(&buf, 0, sizeof(buf));
    ae_vector_init_copy(&_x, x, _state, ae_true);
    x = &_x;
    ae_vector_init_copy(&_y, y, _state, ae_true);
    y = &_y;
    _apbuffers_init(&buf, _state, ae_true);

    ae_assert(n>=0, "SpearmanCorr2: N<0", _state);
    ae_assert(x->cnt>=n, "SpearmanCorr2: Length(X)<N!", _state);
    ae_assert(y->cnt>=n, "SpearmanCorr2: Length(Y)<N!", _state);
    ae_assert(isfinitevector(x, n, _state), "SpearmanCorr2: X is not finite vector", _state);
    ae_assert(isfinitevector(y, n, _state), "SpearmanCorr2: Y is not finite vector", _state);
    
    /*
     * Special case
     */
    if( n<=1 )
    {
        result = (double)(0);
        ae_frame_leave(_state);
        return result;
    }
    rankx(x, n, ae_false, &buf, _state);
    rankx(y, n, ae_false, &buf, _state);
    result = pearsoncorr2(x, y, n, _state);
    ae_frame_leave(_state);
    return result;
}


/*************************************************************************
Covariance matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  ! 
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  ! 
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], covariance matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void covm(/* Real    */ ae_matrix* x,
     ae_int_t n,
     ae_int_t m,
     /* Real    */ ae_matrix* c,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_matrix _x;
    ae_int_t i;
    ae_int_t j;
    double v;
    ae_vector t;
    ae_vector x0;
    ae_vector same;

    ae_frame_make(_state, &_frame_block);
    memset(&_x, 0, sizeof(_x));
    memset(&t, 0, sizeof(t));
    memset(&x0, 0, sizeof(x0));
    memset(&same, 0, sizeof(same));
    ae_matrix_init_copy(&_x, x, _state, ae_true);
    x = &_x;
    ae_matrix_clear(c);
    ae_vector_init(&t, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&x0, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&same, 0, DT_BOOL, _state, ae_true);

    ae_assert(n>=0, "CovM: N<0", _state);
    ae_assert(m>=1, "CovM: M<1", _state);
    ae_assert(x->rows>=n, "CovM: Rows(X)<N!", _state);
    ae_assert(x->cols>=m||n==0, "CovM: Cols(X)<M!", _state);
    ae_assert(apservisfinitematrix(x, n, m, _state), "CovM: X contains infinite/NAN elements", _state);
    
    /*
     * N<=1, return zero
     */
    if( n<=1 )
    {
        ae_matrix_set_length(c, m, m, _state);
        for(i=0; i<=m-1; i++)
        {
            for(j=0; j<=m-1; j++)
            {
                c->ptr.pp_double[i][j] = (double)(0);
            }
        }
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Calculate means,
     * check for constant columns
     */
    ae_vector_set_length(&t, m, _state);
    ae_vector_set_length(&x0, m, _state);
    ae_vector_set_length(&same, m, _state);
    ae_matrix_set_length(c, m, m, _state);
    for(i=0; i<=m-1; i++)
    {
        t.ptr.p_double[i] = (double)(0);
        same.ptr.p_bool[i] = ae_true;
    }
    ae_v_move(&x0.ptr.p_double[0], 1, &x->ptr.pp_double[0][0], 1, ae_v_len(0,m-1));
    v = (double)1/(double)n;
    for(i=0; i<=n-1; i++)
    {
        ae_v_addd(&t.ptr.p_double[0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m-1), v);
        for(j=0; j<=m-1; j++)
        {
            same.ptr.p_bool[j] = same.ptr.p_bool[j]&&ae_fp_eq(x->ptr.pp_double[i][j],x0.ptr.p_double[j]);
        }
    }
    
    /*
     * * center variables;
     * * if we have constant columns, these columns are
     *   artificially zeroed (they must be zero in exact arithmetics,
     *   but unfortunately floating point ops are not exact).
     * * calculate upper half of symmetric covariance matrix
     */
    for(i=0; i<=n-1; i++)
    {
        ae_v_sub(&x->ptr.pp_double[i][0], 1, &t.ptr.p_double[0], 1, ae_v_len(0,m-1));
        for(j=0; j<=m-1; j++)
        {
            if( same.ptr.p_bool[j] )
            {
                x->ptr.pp_double[i][j] = (double)(0);
            }
        }
    }
    rmatrixsyrk(m, n, (double)1/(double)(n-1), x, 0, 0, 1, 0.0, c, 0, 0, ae_true, _state);
    rmatrixenforcesymmetricity(c, m, ae_true, _state);
    ae_frame_leave(_state);
}


/*************************************************************************
Pearson product-moment correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  ! 
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  ! 
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrm(/* Real    */ ae_matrix* x,
     ae_int_t n,
     ae_int_t m,
     /* Real    */ ae_matrix* c,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_vector t;
    ae_int_t i;
    ae_int_t j;
    double v;

    ae_frame_make(_state, &_frame_block);
    memset(&t, 0, sizeof(t));
    ae_matrix_clear(c);
    ae_vector_init(&t, 0, DT_REAL, _state, ae_true);

    ae_assert(n>=0, "PearsonCorrM: N<0", _state);
    ae_assert(m>=1, "PearsonCorrM: M<1", _state);
    ae_assert(x->rows>=n, "PearsonCorrM: Rows(X)<N!", _state);
    ae_assert(x->cols>=m||n==0, "PearsonCorrM: Cols(X)<M!", _state);
    ae_assert(apservisfinitematrix(x, n, m, _state), "PearsonCorrM: X contains infinite/NAN elements", _state);
    ae_vector_set_length(&t, m, _state);
    covm(x, n, m, c, _state);
    for(i=0; i<=m-1; i++)
    {
        if( ae_fp_greater(c->ptr.pp_double[i][i],(double)(0)) )
        {
            t.ptr.p_double[i] = 1/ae_sqrt(c->ptr.pp_double[i][i], _state);
        }
        else
        {
            t.ptr.p_double[i] = 0.0;
        }
    }
    for(i=0; i<=m-1; i++)
    {
        v = t.ptr.p_double[i];
        for(j=0; j<=m-1; j++)
        {
            c->ptr.pp_double[i][j] = c->ptr.pp_double[i][j]*v*t.ptr.p_double[j];
        }
    }
    ae_frame_leave(_state);
}


/*************************************************************************
Spearman's rank correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  ! 
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  ! 
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X are used
            * if not given, automatically determined from input size
    M   -   M>0, number of variables:
            * if given, only leading M columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M,M], correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void spearmancorrm(/* Real    */ ae_matrix* x,
     ae_int_t n,
     ae_int_t m,
     /* Real    */ ae_matrix* c,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_int_t i;
    ae_int_t j;
    apbuffers buf;
    ae_matrix xc;
    ae_vector t;
    double v;
    double vv;
    double x0;
    ae_bool b;

    ae_frame_make(_state, &_frame_block);
    memset(&buf, 0, sizeof(buf));
    memset(&xc, 0, sizeof(xc));
    memset(&t, 0, sizeof(t));
    ae_matrix_clear(c);
    _apbuffers_init(&buf, _state, ae_true);
    ae_matrix_init(&xc, 0, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&t, 0, DT_REAL, _state, ae_true);

    ae_assert(n>=0, "SpearmanCorrM: N<0", _state);
    ae_assert(m>=1, "SpearmanCorrM: M<1", _state);
    ae_assert(x->rows>=n, "SpearmanCorrM: Rows(X)<N!", _state);
    ae_assert(x->cols>=m||n==0, "SpearmanCorrM: Cols(X)<M!", _state);
    ae_assert(apservisfinitematrix(x, n, m, _state), "SpearmanCorrM: X contains infinite/NAN elements", _state);
    
    /*
     * N<=1, return zero
     */
    if( n<=1 )
    {
        ae_matrix_set_length(c, m, m, _state);
        for(i=0; i<=m-1; i++)
        {
            for(j=0; j<=m-1; j++)
            {
                c->ptr.pp_double[i][j] = (double)(0);
            }
        }
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Allocate
     */
    ae_vector_set_length(&t, ae_maxint(n, m, _state), _state);
    ae_matrix_set_length(c, m, m, _state);
    
    /*
     * Replace data with ranks
     */
    ae_matrix_set_length(&xc, m, n, _state);
    rmatrixtranspose(n, m, x, 0, 0, &xc, 0, 0, _state);
    rankdata(&xc, m, n, _state);
    
    /*
     * 1. Calculate means, check for constant columns
     * 2. Center variables, constant  columns are
     *   artificialy zeroed (they must be zero in exact arithmetics,
     *   but unfortunately floating point is not exact).
     */
    for(i=0; i<=m-1; i++)
    {
        
        /*
         * Calculate:
         * * V - mean value of I-th variable
         * * B - True in case all variable values are same
         */
        v = (double)(0);
        b = ae_true;
        x0 = xc.ptr.pp_double[i][0];
        for(j=0; j<=n-1; j++)
        {
            vv = xc.ptr.pp_double[i][j];
            v = v+vv;
            b = b&&ae_fp_eq(vv,x0);
        }
        v = v/n;
        
        /*
         * Center/zero I-th variable
         */
        if( b )
        {
            
            /*
             * Zero
             */
            for(j=0; j<=n-1; j++)
            {
                xc.ptr.pp_double[i][j] = 0.0;
            }
        }
        else
        {
            
            /*
             * Center
             */
            for(j=0; j<=n-1; j++)
            {
                xc.ptr.pp_double[i][j] = xc.ptr.pp_double[i][j]-v;
            }
        }
    }
    
    /*
     * Calculate upper half of symmetric covariance matrix
     */
    rmatrixsyrk(m, n, (double)1/(double)(n-1), &xc, 0, 0, 0, 0.0, c, 0, 0, ae_true, _state);
    
    /*
     * Calculate Pearson coefficients (upper triangle)
     */
    for(i=0; i<=m-1; i++)
    {
        if( ae_fp_greater(c->ptr.pp_double[i][i],(double)(0)) )
        {
            t.ptr.p_double[i] = 1/ae_sqrt(c->ptr.pp_double[i][i], _state);
        }
        else
        {
            t.ptr.p_double[i] = 0.0;
        }
    }
    for(i=0; i<=m-1; i++)
    {
        v = t.ptr.p_double[i];
        for(j=i; j<=m-1; j++)
        {
            c->ptr.pp_double[i][j] = c->ptr.pp_double[i][j]*v*t.ptr.p_double[j];
        }
    }
    
    /*
     * force symmetricity
     */
    rmatrixenforcesymmetricity(c, m, ae_true, _state);
    ae_frame_leave(_state);
}


/*************************************************************************
Cross-covariance matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  ! 
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  ! 
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-covariance matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void covm2(/* Real    */ ae_matrix* x,
     /* Real    */ ae_matrix* y,
     ae_int_t n,
     ae_int_t m1,
     ae_int_t m2,
     /* Real    */ ae_matrix* c,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_matrix _x;
    ae_matrix _y;
    ae_int_t i;
    ae_int_t j;
    double v;
    ae_vector t;
    ae_vector x0;
    ae_vector y0;
    ae_vector samex;
    ae_vector samey;

    ae_frame_make(_state, &_frame_block);
    memset(&_x, 0, sizeof(_x));
    memset(&_y, 0, sizeof(_y));
    memset(&t, 0, sizeof(t));
    memset(&x0, 0, sizeof(x0));
    memset(&y0, 0, sizeof(y0));
    memset(&samex, 0, sizeof(samex));
    memset(&samey, 0, sizeof(samey));
    ae_matrix_init_copy(&_x, x, _state, ae_true);
    x = &_x;
    ae_matrix_init_copy(&_y, y, _state, ae_true);
    y = &_y;
    ae_matrix_clear(c);
    ae_vector_init(&t, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&x0, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&y0, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&samex, 0, DT_BOOL, _state, ae_true);
    ae_vector_init(&samey, 0, DT_BOOL, _state, ae_true);

    ae_assert(n>=0, "CovM2: N<0", _state);
    ae_assert(m1>=1, "CovM2: M1<1", _state);
    ae_assert(m2>=1, "CovM2: M2<1", _state);
    ae_assert(x->rows>=n, "CovM2: Rows(X)<N!", _state);
    ae_assert(x->cols>=m1||n==0, "CovM2: Cols(X)<M1!", _state);
    ae_assert(apservisfinitematrix(x, n, m1, _state), "CovM2: X contains infinite/NAN elements", _state);
    ae_assert(y->rows>=n, "CovM2: Rows(Y)<N!", _state);
    ae_assert(y->cols>=m2||n==0, "CovM2: Cols(Y)<M2!", _state);
    ae_assert(apservisfinitematrix(y, n, m2, _state), "CovM2: X contains infinite/NAN elements", _state);
    
    /*
     * N<=1, return zero
     */
    if( n<=1 )
    {
        ae_matrix_set_length(c, m1, m2, _state);
        for(i=0; i<=m1-1; i++)
        {
            for(j=0; j<=m2-1; j++)
            {
                c->ptr.pp_double[i][j] = (double)(0);
            }
        }
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Allocate
     */
    ae_vector_set_length(&t, ae_maxint(m1, m2, _state), _state);
    ae_vector_set_length(&x0, m1, _state);
    ae_vector_set_length(&y0, m2, _state);
    ae_vector_set_length(&samex, m1, _state);
    ae_vector_set_length(&samey, m2, _state);
    ae_matrix_set_length(c, m1, m2, _state);
    
    /*
     * * calculate means of X
     * * center X
     * * if we have constant columns, these columns are
     *   artificially zeroed (they must be zero in exact arithmetics,
     *   but unfortunately floating point ops are not exact).
     */
    for(i=0; i<=m1-1; i++)
    {
        t.ptr.p_double[i] = (double)(0);
        samex.ptr.p_bool[i] = ae_true;
    }
    ae_v_move(&x0.ptr.p_double[0], 1, &x->ptr.pp_double[0][0], 1, ae_v_len(0,m1-1));
    v = (double)1/(double)n;
    for(i=0; i<=n-1; i++)
    {
        ae_v_addd(&t.ptr.p_double[0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m1-1), v);
        for(j=0; j<=m1-1; j++)
        {
            samex.ptr.p_bool[j] = samex.ptr.p_bool[j]&&ae_fp_eq(x->ptr.pp_double[i][j],x0.ptr.p_double[j]);
        }
    }
    for(i=0; i<=n-1; i++)
    {
        ae_v_sub(&x->ptr.pp_double[i][0], 1, &t.ptr.p_double[0], 1, ae_v_len(0,m1-1));
        for(j=0; j<=m1-1; j++)
        {
            if( samex.ptr.p_bool[j] )
            {
                x->ptr.pp_double[i][j] = (double)(0);
            }
        }
    }
    
    /*
     * Repeat same steps for Y
     */
    for(i=0; i<=m2-1; i++)
    {
        t.ptr.p_double[i] = (double)(0);
        samey.ptr.p_bool[i] = ae_true;
    }
    ae_v_move(&y0.ptr.p_double[0], 1, &y->ptr.pp_double[0][0], 1, ae_v_len(0,m2-1));
    v = (double)1/(double)n;
    for(i=0; i<=n-1; i++)
    {
        ae_v_addd(&t.ptr.p_double[0], 1, &y->ptr.pp_double[i][0], 1, ae_v_len(0,m2-1), v);
        for(j=0; j<=m2-1; j++)
        {
            samey.ptr.p_bool[j] = samey.ptr.p_bool[j]&&ae_fp_eq(y->ptr.pp_double[i][j],y0.ptr.p_double[j]);
        }
    }
    for(i=0; i<=n-1; i++)
    {
        ae_v_sub(&y->ptr.pp_double[i][0], 1, &t.ptr.p_double[0], 1, ae_v_len(0,m2-1));
        for(j=0; j<=m2-1; j++)
        {
            if( samey.ptr.p_bool[j] )
            {
                y->ptr.pp_double[i][j] = (double)(0);
            }
        }
    }
    
    /*
     * calculate cross-covariance matrix
     */
    rmatrixgemm(m1, m2, n, (double)1/(double)(n-1), x, 0, 0, 1, y, 0, 0, 0, 0.0, c, 0, 0, _state);
    ae_frame_leave(_state);
}


/*************************************************************************
Pearson product-moment cross-correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  ! 
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  ! 
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrm2(/* Real    */ ae_matrix* x,
     /* Real    */ ae_matrix* y,
     ae_int_t n,
     ae_int_t m1,
     ae_int_t m2,
     /* Real    */ ae_matrix* c,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_matrix _x;
    ae_matrix _y;
    ae_int_t i;
    ae_int_t j;
    double v;
    ae_vector t;
    ae_vector x0;
    ae_vector y0;
    ae_vector sx;
    ae_vector sy;
    ae_vector samex;
    ae_vector samey;

    ae_frame_make(_state, &_frame_block);
    memset(&_x, 0, sizeof(_x));
    memset(&_y, 0, sizeof(_y));
    memset(&t, 0, sizeof(t));
    memset(&x0, 0, sizeof(x0));
    memset(&y0, 0, sizeof(y0));
    memset(&sx, 0, sizeof(sx));
    memset(&sy, 0, sizeof(sy));
    memset(&samex, 0, sizeof(samex));
    memset(&samey, 0, sizeof(samey));
    ae_matrix_init_copy(&_x, x, _state, ae_true);
    x = &_x;
    ae_matrix_init_copy(&_y, y, _state, ae_true);
    y = &_y;
    ae_matrix_clear(c);
    ae_vector_init(&t, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&x0, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&y0, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&sx, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&sy, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&samex, 0, DT_BOOL, _state, ae_true);
    ae_vector_init(&samey, 0, DT_BOOL, _state, ae_true);

    ae_assert(n>=0, "PearsonCorrM2: N<0", _state);
    ae_assert(m1>=1, "PearsonCorrM2: M1<1", _state);
    ae_assert(m2>=1, "PearsonCorrM2: M2<1", _state);
    ae_assert(x->rows>=n, "PearsonCorrM2: Rows(X)<N!", _state);
    ae_assert(x->cols>=m1||n==0, "PearsonCorrM2: Cols(X)<M1!", _state);
    ae_assert(apservisfinitematrix(x, n, m1, _state), "PearsonCorrM2: X contains infinite/NAN elements", _state);
    ae_assert(y->rows>=n, "PearsonCorrM2: Rows(Y)<N!", _state);
    ae_assert(y->cols>=m2||n==0, "PearsonCorrM2: Cols(Y)<M2!", _state);
    ae_assert(apservisfinitematrix(y, n, m2, _state), "PearsonCorrM2: X contains infinite/NAN elements", _state);
    
    /*
     * N<=1, return zero
     */
    if( n<=1 )
    {
        ae_matrix_set_length(c, m1, m2, _state);
        for(i=0; i<=m1-1; i++)
        {
            for(j=0; j<=m2-1; j++)
            {
                c->ptr.pp_double[i][j] = (double)(0);
            }
        }
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Allocate
     */
    ae_vector_set_length(&t, ae_maxint(m1, m2, _state), _state);
    ae_vector_set_length(&x0, m1, _state);
    ae_vector_set_length(&y0, m2, _state);
    ae_vector_set_length(&sx, m1, _state);
    ae_vector_set_length(&sy, m2, _state);
    ae_vector_set_length(&samex, m1, _state);
    ae_vector_set_length(&samey, m2, _state);
    ae_matrix_set_length(c, m1, m2, _state);
    
    /*
     * * calculate means of X
     * * center X
     * * if we have constant columns, these columns are
     *   artificially zeroed (they must be zero in exact arithmetics,
     *   but unfortunately floating point ops are not exact).
     * * calculate column variances
     */
    for(i=0; i<=m1-1; i++)
    {
        t.ptr.p_double[i] = (double)(0);
        samex.ptr.p_bool[i] = ae_true;
        sx.ptr.p_double[i] = (double)(0);
    }
    ae_v_move(&x0.ptr.p_double[0], 1, &x->ptr.pp_double[0][0], 1, ae_v_len(0,m1-1));
    v = (double)1/(double)n;
    for(i=0; i<=n-1; i++)
    {
        ae_v_addd(&t.ptr.p_double[0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m1-1), v);
        for(j=0; j<=m1-1; j++)
        {
            samex.ptr.p_bool[j] = samex.ptr.p_bool[j]&&ae_fp_eq(x->ptr.pp_double[i][j],x0.ptr.p_double[j]);
        }
    }
    for(i=0; i<=n-1; i++)
    {
        ae_v_sub(&x->ptr.pp_double[i][0], 1, &t.ptr.p_double[0], 1, ae_v_len(0,m1-1));
        for(j=0; j<=m1-1; j++)
        {
            if( samex.ptr.p_bool[j] )
            {
                x->ptr.pp_double[i][j] = (double)(0);
            }
            sx.ptr.p_double[j] = sx.ptr.p_double[j]+x->ptr.pp_double[i][j]*x->ptr.pp_double[i][j];
        }
    }
    for(j=0; j<=m1-1; j++)
    {
        sx.ptr.p_double[j] = ae_sqrt(sx.ptr.p_double[j]/(n-1), _state);
    }
    
    /*
     * Repeat same steps for Y
     */
    for(i=0; i<=m2-1; i++)
    {
        t.ptr.p_double[i] = (double)(0);
        samey.ptr.p_bool[i] = ae_true;
        sy.ptr.p_double[i] = (double)(0);
    }
    ae_v_move(&y0.ptr.p_double[0], 1, &y->ptr.pp_double[0][0], 1, ae_v_len(0,m2-1));
    v = (double)1/(double)n;
    for(i=0; i<=n-1; i++)
    {
        ae_v_addd(&t.ptr.p_double[0], 1, &y->ptr.pp_double[i][0], 1, ae_v_len(0,m2-1), v);
        for(j=0; j<=m2-1; j++)
        {
            samey.ptr.p_bool[j] = samey.ptr.p_bool[j]&&ae_fp_eq(y->ptr.pp_double[i][j],y0.ptr.p_double[j]);
        }
    }
    for(i=0; i<=n-1; i++)
    {
        ae_v_sub(&y->ptr.pp_double[i][0], 1, &t.ptr.p_double[0], 1, ae_v_len(0,m2-1));
        for(j=0; j<=m2-1; j++)
        {
            if( samey.ptr.p_bool[j] )
            {
                y->ptr.pp_double[i][j] = (double)(0);
            }
            sy.ptr.p_double[j] = sy.ptr.p_double[j]+y->ptr.pp_double[i][j]*y->ptr.pp_double[i][j];
        }
    }
    for(j=0; j<=m2-1; j++)
    {
        sy.ptr.p_double[j] = ae_sqrt(sy.ptr.p_double[j]/(n-1), _state);
    }
    
    /*
     * calculate cross-covariance matrix
     */
    rmatrixgemm(m1, m2, n, (double)1/(double)(n-1), x, 0, 0, 1, y, 0, 0, 0, 0.0, c, 0, 0, _state);
    
    /*
     * Divide by standard deviations
     */
    for(i=0; i<=m1-1; i++)
    {
        if( ae_fp_neq(sx.ptr.p_double[i],(double)(0)) )
        {
            sx.ptr.p_double[i] = 1/sx.ptr.p_double[i];
        }
        else
        {
            sx.ptr.p_double[i] = 0.0;
        }
    }
    for(i=0; i<=m2-1; i++)
    {
        if( ae_fp_neq(sy.ptr.p_double[i],(double)(0)) )
        {
            sy.ptr.p_double[i] = 1/sy.ptr.p_double[i];
        }
        else
        {
            sy.ptr.p_double[i] = 0.0;
        }
    }
    for(i=0; i<=m1-1; i++)
    {
        v = sx.ptr.p_double[i];
        for(j=0; j<=m2-1; j++)
        {
            c->ptr.pp_double[i][j] = c->ptr.pp_double[i][j]*v*sy.ptr.p_double[j];
        }
    }
    ae_frame_leave(_state);
}


/*************************************************************************
Spearman's rank cross-correlation matrix

  ! COMMERCIAL EDITION OF ALGLIB:
  ! 
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! * hardware vendor (Intel) implementations of linear algebra primitives
  !   (C++ and C# versions, x86/x64 platform)
  ! 
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    X   -   array[N,M1], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    Y   -   array[N,M2], sample matrix:
            * J-th column corresponds to J-th variable
            * I-th row corresponds to I-th observation
    N   -   N>=0, number of observations:
            * if given, only leading N rows of X/Y are used
            * if not given, automatically determined from input sizes
    M1  -   M1>0, number of variables in X:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size
    M2  -   M2>0, number of variables in Y:
            * if given, only leading M1 columns of X are used
            * if not given, automatically determined from input size

OUTPUT PARAMETERS:
    C   -   array[M1,M2], cross-correlation matrix (zero if N=0 or N=1)

  -- ALGLIB --
     Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void spearmancorrm2(/* Real    */ ae_matrix* x,
     /* Real    */ ae_matrix* y,
     ae_int_t n,
     ae_int_t m1,
     ae_int_t m2,
     /* Real    */ ae_matrix* c,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_int_t i;
    ae_int_t j;
    double v;
    double v2;
    double vv;
    ae_bool b;
    ae_vector t;
    double x0;
    double y0;
    ae_vector sx;
    ae_vector sy;
    ae_matrix xc;
    ae_matrix yc;
    apbuffers buf;

    ae_frame_make(_state, &_frame_block);
    memset(&t, 0, sizeof(t));
    memset(&sx, 0, sizeof(sx));
    memset(&sy, 0, sizeof(sy));
    memset(&xc, 0, sizeof(xc));
    memset(&yc, 0, sizeof(yc));
    memset(&buf, 0, sizeof(buf));
    ae_matrix_clear(c);
    ae_vector_init(&t, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&sx, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&sy, 0, DT_REAL, _state, ae_true);
    ae_matrix_init(&xc, 0, 0, DT_REAL, _state, ae_true);
    ae_matrix_init(&yc, 0, 0, DT_REAL, _state, ae_true);
    _apbuffers_init(&buf, _state, ae_true);

    ae_assert(n>=0, "SpearmanCorrM2: N<0", _state);
    ae_assert(m1>=1, "SpearmanCorrM2: M1<1", _state);
    ae_assert(m2>=1, "SpearmanCorrM2: M2<1", _state);
    ae_assert(x->rows>=n, "SpearmanCorrM2: Rows(X)<N!", _state);
    ae_assert(x->cols>=m1||n==0, "SpearmanCorrM2: Cols(X)<M1!", _state);
    ae_assert(apservisfinitematrix(x, n, m1, _state), "SpearmanCorrM2: X contains infinite/NAN elements", _state);
    ae_assert(y->rows>=n, "SpearmanCorrM2: Rows(Y)<N!", _state);
    ae_assert(y->cols>=m2||n==0, "SpearmanCorrM2: Cols(Y)<M2!", _state);
    ae_assert(apservisfinitematrix(y, n, m2, _state), "SpearmanCorrM2: X contains infinite/NAN elements", _state);
    
    /*
     * N<=1, return zero
     */
    if( n<=1 )
    {
        ae_matrix_set_length(c, m1, m2, _state);
        for(i=0; i<=m1-1; i++)
        {
            for(j=0; j<=m2-1; j++)
            {
                c->ptr.pp_double[i][j] = (double)(0);
            }
        }
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Allocate
     */
    ae_vector_set_length(&t, ae_maxint(ae_maxint(m1, m2, _state), n, _state), _state);
    ae_vector_set_length(&sx, m1, _state);
    ae_vector_set_length(&sy, m2, _state);
    ae_matrix_set_length(c, m1, m2, _state);
    
    /*
     * Replace data with ranks
     */
    ae_matrix_set_length(&xc, m1, n, _state);
    ae_matrix_set_length(&yc, m2, n, _state);
    rmatrixtranspose(n, m1, x, 0, 0, &xc, 0, 0, _state);
    rmatrixtranspose(n, m2, y, 0, 0, &yc, 0, 0, _state);
    rankdata(&xc, m1, n, _state);
    rankdata(&yc, m2, n, _state);
    
    /*
     * 1. Calculate means, variances, check for constant columns
     * 2. Center variables, constant  columns are
     *   artificialy zeroed (they must be zero in exact arithmetics,
     *   but unfortunately floating point is not exact).
     *
     * Description of variables:
     * * V - mean value of I-th variable
     * * V2- variance
     * * VV-temporary
     * * B - True in case all variable values are same
     */
    for(i=0; i<=m1-1; i++)
    {
        v = (double)(0);
        v2 = 0.0;
        b = ae_true;
        x0 = xc.ptr.pp_double[i][0];
        for(j=0; j<=n-1; j++)
        {
            vv = xc.ptr.pp_double[i][j];
            v = v+vv;
            b = b&&ae_fp_eq(vv,x0);
        }
        v = v/n;
        if( b )
        {
            for(j=0; j<=n-1; j++)
            {
                xc.ptr.pp_double[i][j] = 0.0;
            }
        }
        else
        {
            for(j=0; j<=n-1; j++)
            {
                vv = xc.ptr.pp_double[i][j];
                xc.ptr.pp_double[i][j] = vv-v;
                v2 = v2+(vv-v)*(vv-v);
            }
        }
        sx.ptr.p_double[i] = ae_sqrt(v2/(n-1), _state);
    }
    for(i=0; i<=m2-1; i++)
    {
        v = (double)(0);
        v2 = 0.0;
        b = ae_true;
        y0 = yc.ptr.pp_double[i][0];
        for(j=0; j<=n-1; j++)
        {
            vv = yc.ptr.pp_double[i][j];
            v = v+vv;
            b = b&&ae_fp_eq(vv,y0);
        }
        v = v/n;
        if( b )
        {
            for(j=0; j<=n-1; j++)
            {
                yc.ptr.pp_double[i][j] = 0.0;
            }
        }
        else
        {
            for(j=0; j<=n-1; j++)
            {
                vv = yc.ptr.pp_double[i][j];
                yc.ptr.pp_double[i][j] = vv-v;
                v2 = v2+(vv-v)*(vv-v);
            }
        }
        sy.ptr.p_double[i] = ae_sqrt(v2/(n-1), _state);
    }
    
    /*
     * calculate cross-covariance matrix
     */
    rmatrixgemm(m1, m2, n, (double)1/(double)(n-1), &xc, 0, 0, 0, &yc, 0, 0, 1, 0.0, c, 0, 0, _state);
    
    /*
     * Divide by standard deviations
     */
    for(i=0; i<=m1-1; i++)
    {
        if( ae_fp_neq(sx.ptr.p_double[i],(double)(0)) )
        {
            sx.ptr.p_double[i] = 1/sx.ptr.p_double[i];
        }
        else
        {
            sx.ptr.p_double[i] = 0.0;
        }
    }
    for(i=0; i<=m2-1; i++)
    {
        if( ae_fp_neq(sy.ptr.p_double[i],(double)(0)) )
        {
            sy.ptr.p_double[i] = 1/sy.ptr.p_double[i];
        }
        else
        {
            sy.ptr.p_double[i] = 0.0;
        }
    }
    for(i=0; i<=m1-1; i++)
    {
        v = sx.ptr.p_double[i];
        for(j=0; j<=m2-1; j++)
        {
            c->ptr.pp_double[i][j] = c->ptr.pp_double[i][j]*v*sy.ptr.p_double[j];
        }
    }
    ae_frame_leave(_state);
}


/*************************************************************************
This function replaces data in XY by their ranks:
* XY is processed row-by-row
* rows are processed separately
* tied data are correctly handled (tied ranks are calculated)
* ranking starts from 0, ends at NFeatures-1
* sum of within-row values is equal to (NFeatures-1)*NFeatures/2

  ! COMMERCIAL EDITION OF ALGLIB:
  ! 
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! 
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    XY      -   array[NPoints,NFeatures], dataset
    NPoints -   number of points
    NFeatures-  number of features

OUTPUT PARAMETERS:
    XY      -   data are replaced by their within-row ranks;
                ranking starts from 0, ends at NFeatures-1

  -- ALGLIB --
     Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
void rankdata(/* Real    */ ae_matrix* xy,
     ae_int_t npoints,
     ae_int_t nfeatures,
     ae_state *_state)
{
    ae_frame _frame_block;
    apbuffers buf0;
    apbuffers buf1;
    ae_int_t basecasecost;
    ae_shared_pool pool;

    ae_frame_make(_state, &_frame_block);
    memset(&buf0, 0, sizeof(buf0));
    memset(&buf1, 0, sizeof(buf1));
    memset(&pool, 0, sizeof(pool));
    _apbuffers_init(&buf0, _state, ae_true);
    _apbuffers_init(&buf1, _state, ae_true);
    ae_shared_pool_init(&pool, _state, ae_true);

    ae_assert(npoints>=0, "RankData: NPoints<0", _state);
    ae_assert(nfeatures>=1, "RankData: NFeatures<1", _state);
    ae_assert(xy->rows>=npoints, "RankData: Rows(XY)<NPoints", _state);
    ae_assert(xy->cols>=nfeatures||npoints==0, "RankData: Cols(XY)<NFeatures", _state);
    ae_assert(apservisfinitematrix(xy, npoints, nfeatures, _state), "RankData: XY contains infinite/NAN elements", _state);
    
    /*
     * Basecase cost is a maximum cost of basecase problems.
     * Problems harded than that cost will be split.
     *
     * Problem cost is assumed to be NPoints*NFeatures*log2(NFeatures),
     * which is proportional, but NOT equal to number of FLOPs required
     * to solve problem.
     *
     * Try to use serial code for basecase problems, no SMP functionality, no shared pools.
     */
    basecasecost = 10000;
    if( ae_fp_less(rmul3((double)(npoints), (double)(nfeatures), logbase2((double)(nfeatures), _state), _state),(double)(basecasecost)) )
    {
        basestat_rankdatabasecase(xy, 0, npoints, nfeatures, ae_false, &buf0, &buf1, _state);
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Parallel code
     */
    ae_shared_pool_set_seed(&pool, &buf0, sizeof(buf0), _apbuffers_init, _apbuffers_init_copy, _apbuffers_destroy, _state);
    basestat_rankdatarec(xy, 0, npoints, nfeatures, ae_false, &pool, basecasecost, _state);
    ae_frame_leave(_state);
}


/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_rankdata(/* Real    */ ae_matrix* xy,
    ae_int_t npoints,
    ae_int_t nfeatures,
    ae_state *_state)
{
    return ae_false;
}


/*************************************************************************
This function replaces data in XY by their CENTERED ranks:
* XY is processed row-by-row
* rows are processed separately
* tied data are correctly handled (tied ranks are calculated)
* centered ranks are just usual ranks, but centered in such way  that  sum
  of within-row values is equal to 0.0.
* centering is performed by subtracting mean from each row, i.e it changes
  mean value, but does NOT change higher moments

  ! COMMERCIAL EDITION OF ALGLIB:
  ! 
  ! Commercial Edition of ALGLIB includes following important improvements
  ! of this function:
  ! * high-performance native backend with same C# interface (C# version)
  ! * multithreading support (C++ and C# versions)
  ! 
  ! We recommend you to read 'Working with commercial version' section  of
  ! ALGLIB Reference Manual in order to find out how to  use  performance-
  ! related features provided by commercial edition of ALGLIB.

INPUT PARAMETERS:
    XY      -   array[NPoints,NFeatures], dataset
    NPoints -   number of points
    NFeatures-  number of features

OUTPUT PARAMETERS:
    XY      -   data are replaced by their within-row ranks;
                ranking starts from 0, ends at NFeatures-1

  -- ALGLIB --
     Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
void rankdatacentered(/* Real    */ ae_matrix* xy,
     ae_int_t npoints,
     ae_int_t nfeatures,
     ae_state *_state)
{
    ae_frame _frame_block;
    apbuffers buf0;
    apbuffers buf1;
    ae_int_t basecasecost;
    ae_shared_pool pool;

    ae_frame_make(_state, &_frame_block);
    memset(&buf0, 0, sizeof(buf0));
    memset(&buf1, 0, sizeof(buf1));
    memset(&pool, 0, sizeof(pool));
    _apbuffers_init(&buf0, _state, ae_true);
    _apbuffers_init(&buf1, _state, ae_true);
    ae_shared_pool_init(&pool, _state, ae_true);

    ae_assert(npoints>=0, "RankData: NPoints<0", _state);
    ae_assert(nfeatures>=1, "RankData: NFeatures<1", _state);
    ae_assert(xy->rows>=npoints, "RankData: Rows(XY)<NPoints", _state);
    ae_assert(xy->cols>=nfeatures||npoints==0, "RankData: Cols(XY)<NFeatures", _state);
    ae_assert(apservisfinitematrix(xy, npoints, nfeatures, _state), "RankData: XY contains infinite/NAN elements", _state);
    
    /*
     * Basecase cost is a maximum cost of basecase problems.
     * Problems harded than that cost will be split.
     *
     * Problem cost is assumed to be NPoints*NFeatures*log2(NFeatures),
     * which is proportional, but NOT equal to number of FLOPs required
     * to solve problem.
     *
     * Try to use serial code, no SMP functionality, no shared pools.
     */
    basecasecost = 10000;
    if( ae_fp_less(rmul3((double)(npoints), (double)(nfeatures), logbase2((double)(nfeatures), _state), _state),(double)(basecasecost)) )
    {
        basestat_rankdatabasecase(xy, 0, npoints, nfeatures, ae_true, &buf0, &buf1, _state);
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Parallel code
     */
    ae_shared_pool_set_seed(&pool, &buf0, sizeof(buf0), _apbuffers_init, _apbuffers_init_copy, _apbuffers_destroy, _state);
    basestat_rankdatarec(xy, 0, npoints, nfeatures, ae_true, &pool, basecasecost, _state);
    ae_frame_leave(_state);
}


/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_rankdatacentered(/* Real    */ ae_matrix* xy,
    ae_int_t npoints,
    ae_int_t nfeatures,
    ae_state *_state)
{
    return ae_false;
}


/*************************************************************************
Obsolete function, we recommend to use PearsonCorr2().

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double pearsoncorrelation(/* Real    */ ae_vector* x,
     /* Real    */ ae_vector* y,
     ae_int_t n,
     ae_state *_state)
{
    double result;


    result = pearsoncorr2(x, y, n, _state);
    return result;
}


/*************************************************************************
Obsolete function, we recommend to use SpearmanCorr2().

    -- ALGLIB --
    Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double spearmanrankcorrelation(/* Real    */ ae_vector* x,
     /* Real    */ ae_vector* y,
     ae_int_t n,
     ae_state *_state)
{
    double result;


    result = spearmancorr2(x, y, n, _state);
    return result;
}


/*************************************************************************
Recurrent code for RankData(), splits problem into  subproblems  or  calls
basecase code (depending on problem complexity).

INPUT PARAMETERS:
    XY      -   array[NPoints,NFeatures], dataset
    I0      -   index of first row to process
    I1      -   index of past-the-last row to process;
                this function processes half-interval [I0,I1).
    NFeatures-  number of features
    IsCentered- whether ranks are centered or not:
                * True      -   ranks are centered in such way that  their
                                within-row sum is zero
                * False     -   ranks are not centered
    Pool    -   shared pool which holds temporary buffers
                (APBuffers structure)
    BasecaseCost-minimum cost of the problem which will be split

OUTPUT PARAMETERS:
    XY      -   data in [I0,I1) are replaced by their within-row ranks;
                ranking starts from 0, ends at NFeatures-1

  -- ALGLIB --
     Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
static void basestat_rankdatarec(/* Real    */ ae_matrix* xy,
     ae_int_t i0,
     ae_int_t i1,
     ae_int_t nfeatures,
     ae_bool iscentered,
     ae_shared_pool* pool,
     ae_int_t basecasecost,
     ae_state *_state)
{
    ae_frame _frame_block;
    apbuffers *buf0;
    ae_smart_ptr _buf0;
    apbuffers *buf1;
    ae_smart_ptr _buf1;
    double problemcost;
    ae_int_t im;

    ae_frame_make(_state, &_frame_block);
    memset(&_buf0, 0, sizeof(_buf0));
    memset(&_buf1, 0, sizeof(_buf1));
    ae_smart_ptr_init(&_buf0, (void**)&buf0, _state, ae_true);
    ae_smart_ptr_init(&_buf1, (void**)&buf1, _state, ae_true);

    ae_assert(i1>=i0, "RankDataRec: internal error", _state);
    
    /*
     * Try to activate parallelism
     */
    if( i1-i0>=4&&ae_fp_greater_eq(rmul3((double)(i1-i0), (double)(nfeatures), logbase2((double)(nfeatures), _state), _state),smpactivationlevel(_state)) )
    {
        if( _trypexec_basestat_rankdatarec(xy,i0,i1,nfeatures,iscentered,pool,basecasecost, _state) )
        {
            ae_frame_leave(_state);
            return;
        }
    }
    
    /*
     * Recursively split problem, if it is too large
     */
    problemcost = rmul3((double)(i1-i0), (double)(nfeatures), logbase2((double)(nfeatures), _state), _state);
    if( i1-i0>=2&&ae_fp_greater(problemcost,spawnlevel(_state)) )
    {
        im = (i1+i0)/2;
        basestat_rankdatarec(xy, i0, im, nfeatures, iscentered, pool, basecasecost, _state);
        basestat_rankdatarec(xy, im, i1, nfeatures, iscentered, pool, basecasecost, _state);
        ae_frame_leave(_state);
        return;
    }
    
    /*
     * Retrieve buffers from pool, call serial code, return buffers to pool
     */
    ae_shared_pool_retrieve(pool, &_buf0, _state);
    ae_shared_pool_retrieve(pool, &_buf1, _state);
    basestat_rankdatabasecase(xy, i0, i1, nfeatures, iscentered, buf0, buf1, _state);
    ae_shared_pool_recycle(pool, &_buf0, _state);
    ae_shared_pool_recycle(pool, &_buf1, _state);
    ae_frame_leave(_state);
}


/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_basestat_rankdatarec(/* Real    */ ae_matrix* xy,
    ae_int_t i0,
    ae_int_t i1,
    ae_int_t nfeatures,
    ae_bool iscentered,
    ae_shared_pool* pool,
    ae_int_t basecasecost,
    ae_state *_state)
{
    return ae_false;
}


/*************************************************************************
Basecase code for RankData(), performs actual work on subset of data using
temporary buffer passed as parameter.

INPUT PARAMETERS:
    XY      -   array[NPoints,NFeatures], dataset
    I0      -   index of first row to process
    I1      -   index of past-the-last row to process;
                this function processes half-interval [I0,I1).
    NFeatures-  number of features
    IsCentered- whether ranks are centered or not:
                * True      -   ranks are centered in such way that  their
                                within-row sum is zero
                * False     -   ranks are not centered
    Buf0    -   temporary buffers, may be empty (this function automatically
                allocates/reuses buffers).
    Buf1    -   temporary buffers, may be empty (this function automatically
                allocates/reuses buffers).

OUTPUT PARAMETERS:
    XY      -   data in [I0,I1) are replaced by their within-row ranks;
                ranking starts from 0, ends at NFeatures-1

  -- ALGLIB --
     Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
static void basestat_rankdatabasecase(/* Real    */ ae_matrix* xy,
     ae_int_t i0,
     ae_int_t i1,
     ae_int_t nfeatures,
     ae_bool iscentered,
     apbuffers* buf0,
     apbuffers* buf1,
     ae_state *_state)
{
    ae_int_t i;


    ae_assert(i1>=i0, "RankDataBasecase: internal error", _state);
    if( buf1->ra0.cnt<nfeatures )
    {
        ae_vector_set_length(&buf1->ra0, nfeatures, _state);
    }
    for(i=i0; i<=i1-1; i++)
    {
        ae_v_move(&buf1->ra0.ptr.p_double[0], 1, &xy->ptr.pp_double[i][0], 1, ae_v_len(0,nfeatures-1));
        rankx(&buf1->ra0, nfeatures, iscentered, buf0, _state);
        ae_v_move(&xy->ptr.pp_double[i][0], 1, &buf1->ra0.ptr.p_double[0], 1, ae_v_len(0,nfeatures-1));
    }
}


/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_basestat_rankdatabasecase(/* Real    */ ae_matrix* xy,
    ae_int_t i0,
    ae_int_t i1,
    ae_int_t nfeatures,
    ae_bool iscentered,
    apbuffers* buf0,
    apbuffers* buf1,
    ae_state *_state)
{
    return ae_false;
}


#endif
#if defined(AE_COMPILE_CORRELATIONTESTS) || !defined(AE_PARTIAL_BUILD)


/*************************************************************************
Pearson's correlation coefficient significance test

This test checks hypotheses about whether X  and  Y  are  samples  of  two
continuous  distributions  having  zero  correlation  or   whether   their
correlation is non-zero.

The following tests are performed:
    * two-tailed test (null hypothesis - X and Y have zero correlation)
    * left-tailed test (null hypothesis - the correlation  coefficient  is
      greater than or equal to 0)
    * right-tailed test (null hypothesis - the correlation coefficient  is
      less than or equal to 0).

Requirements:
    * the number of elements in each sample is not less than 5
    * normality of distributions of X and Y.

Input parameters:
    R   -   Pearson's correlation coefficient for X and Y
    N   -   number of elements in samples, N>=5.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrelationsignificance(double r,
     ae_int_t n,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    double t;
    double p;

    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;

    
    /*
     * Some special cases
     */
    if( ae_fp_greater_eq(r,(double)(1)) )
    {
        *bothtails = 0.0;
        *lefttail = 1.0;
        *righttail = 0.0;
        return;
    }
    if( ae_fp_less_eq(r,(double)(-1)) )
    {
        *bothtails = 0.0;
        *lefttail = 0.0;
        *righttail = 1.0;
        return;
    }
    if( n<5 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * General case
     */
    t = r*ae_sqrt((n-2)/(1-ae_sqr(r, _state)), _state);
    p = studenttdistribution(n-2, t, _state);
    *bothtails = 2*ae_minreal(p, 1-p, _state);
    *lefttail = p;
    *righttail = 1-p;
}


/*************************************************************************
Spearman's rank correlation coefficient significance test

This test checks hypotheses about whether X  and  Y  are  samples  of  two
continuous  distributions  having  zero  correlation  or   whether   their
correlation is non-zero.

The following tests are performed:
    * two-tailed test (null hypothesis - X and Y have zero correlation)
    * left-tailed test (null hypothesis - the correlation  coefficient  is
      greater than or equal to 0)
    * right-tailed test (null hypothesis - the correlation coefficient  is
      less than or equal to 0).

Requirements:
    * the number of elements in each sample is not less than 5.

The test is non-parametric and doesn't require distributions X and Y to be
normal.

Input parameters:
    R   -   Spearman's rank correlation coefficient for X and Y
    N   -   number of elements in samples, N>=5.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void spearmanrankcorrelationsignificance(double r,
     ae_int_t n,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    double t;
    double p;

    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;

    
    /*
     * Special case
     */
    if( n<5 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * General case
     */
    if( ae_fp_greater_eq(r,(double)(1)) )
    {
        t = 1.0E10;
    }
    else
    {
        if( ae_fp_less_eq(r,(double)(-1)) )
        {
            t = -1.0E10;
        }
        else
        {
            t = r*ae_sqrt((n-2)/(1-ae_sqr(r, _state)), _state);
        }
    }
    if( ae_fp_less(t,(double)(0)) )
    {
        p = correlationtests_spearmantail(t, n, _state);
        *bothtails = 2*p;
        *lefttail = p;
        *righttail = 1-p;
    }
    else
    {
        p = correlationtests_spearmantail(-t, n, _state);
        *bothtails = 2*p;
        *lefttail = 1-p;
        *righttail = p;
    }
}


/*************************************************************************
Tail(S, 5)
*************************************************************************/
static double correlationtests_spearmantail5(double s, ae_state *_state)
{
    double result;


    if( ae_fp_less(s,0.000e+00) )
    {
        result = studenttdistribution(3, -s, _state);
        return result;
    }
    if( ae_fp_greater_eq(s,3.580e+00) )
    {
        result = 8.304e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,2.322e+00) )
    {
        result = 4.163e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.704e+00) )
    {
        result = 6.641e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.303e+00) )
    {
        result = 1.164e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.003e+00) )
    {
        result = 1.748e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,7.584e-01) )
    {
        result = 2.249e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,5.468e-01) )
    {
        result = 2.581e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,3.555e-01) )
    {
        result = 3.413e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.759e-01) )
    {
        result = 3.911e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.741e-03) )
    {
        result = 4.747e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,0.000e+00) )
    {
        result = 5.248e-01;
        return result;
    }
    result = (double)(0);
    return result;
}


/*************************************************************************
Tail(S, 6)
*************************************************************************/
static double correlationtests_spearmantail6(double s, ae_state *_state)
{
    double result;


    if( ae_fp_less(s,1.001e+00) )
    {
        result = studenttdistribution(4, -s, _state);
        return result;
    }
    if( ae_fp_greater_eq(s,5.663e+00) )
    {
        result = 1.366e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.834e+00) )
    {
        result = 8.350e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,2.968e+00) )
    {
        result = 1.668e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.430e+00) )
    {
        result = 2.921e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.045e+00) )
    {
        result = 5.144e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.747e+00) )
    {
        result = 6.797e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.502e+00) )
    {
        result = 8.752e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.295e+00) )
    {
        result = 1.210e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.113e+00) )
    {
        result = 1.487e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.001e+00) )
    {
        result = 1.780e-01;
        return result;
    }
    result = (double)(0);
    return result;
}


/*************************************************************************
Tail(S, 7)
*************************************************************************/
static double correlationtests_spearmantail7(double s, ae_state *_state)
{
    double result;


    if( ae_fp_less(s,1.001e+00) )
    {
        result = studenttdistribution(5, -s, _state);
        return result;
    }
    if( ae_fp_greater_eq(s,8.159e+00) )
    {
        result = 2.081e-04;
        return result;
    }
    if( ae_fp_greater_eq(s,5.620e+00) )
    {
        result = 1.393e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,4.445e+00) )
    {
        result = 3.398e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.728e+00) )
    {
        result = 6.187e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.226e+00) )
    {
        result = 1.200e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.844e+00) )
    {
        result = 1.712e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.539e+00) )
    {
        result = 2.408e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.285e+00) )
    {
        result = 3.320e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.068e+00) )
    {
        result = 4.406e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.879e+00) )
    {
        result = 5.478e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.710e+00) )
    {
        result = 6.946e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.559e+00) )
    {
        result = 8.331e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,1.420e+00) )
    {
        result = 1.001e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.292e+00) )
    {
        result = 1.180e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.173e+00) )
    {
        result = 1.335e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.062e+00) )
    {
        result = 1.513e-01;
        return result;
    }
    if( ae_fp_greater_eq(s,1.001e+00) )
    {
        result = 1.770e-01;
        return result;
    }
    result = (double)(0);
    return result;
}


/*************************************************************************
Tail(S, 8)
*************************************************************************/
static double correlationtests_spearmantail8(double s, ae_state *_state)
{
    double result;


    if( ae_fp_less(s,2.001e+00) )
    {
        result = studenttdistribution(6, -s, _state);
        return result;
    }
    if( ae_fp_greater_eq(s,1.103e+01) )
    {
        result = 2.194e-05;
        return result;
    }
    if( ae_fp_greater_eq(s,7.685e+00) )
    {
        result = 2.008e-04;
        return result;
    }
    if( ae_fp_greater_eq(s,6.143e+00) )
    {
        result = 5.686e-04;
        return result;
    }
    if( ae_fp_greater_eq(s,5.213e+00) )
    {
        result = 1.138e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,4.567e+00) )
    {
        result = 2.310e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,4.081e+00) )
    {
        result = 3.634e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.697e+00) )
    {
        result = 5.369e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.381e+00) )
    {
        result = 7.708e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.114e+00) )
    {
        result = 1.087e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.884e+00) )
    {
        result = 1.397e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.682e+00) )
    {
        result = 1.838e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.502e+00) )
    {
        result = 2.288e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.340e+00) )
    {
        result = 2.883e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.192e+00) )
    {
        result = 3.469e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.057e+00) )
    {
        result = 4.144e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.001e+00) )
    {
        result = 4.804e-02;
        return result;
    }
    result = (double)(0);
    return result;
}


/*************************************************************************
Tail(S, 9)
*************************************************************************/
static double correlationtests_spearmantail9(double s, ae_state *_state)
{
    double result;


    if( ae_fp_less(s,2.001e+00) )
    {
        result = studenttdistribution(7, -s, _state);
        return result;
    }
    if( ae_fp_greater_eq(s,9.989e+00) )
    {
        result = 2.306e-05;
        return result;
    }
    if( ae_fp_greater_eq(s,8.069e+00) )
    {
        result = 8.167e-05;
        return result;
    }
    if( ae_fp_greater_eq(s,6.890e+00) )
    {
        result = 1.744e-04;
        return result;
    }
    if( ae_fp_greater_eq(s,6.077e+00) )
    {
        result = 3.625e-04;
        return result;
    }
    if( ae_fp_greater_eq(s,5.469e+00) )
    {
        result = 6.450e-04;
        return result;
    }
    if( ae_fp_greater_eq(s,4.991e+00) )
    {
        result = 1.001e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,4.600e+00) )
    {
        result = 1.514e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,4.272e+00) )
    {
        result = 2.213e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.991e+00) )
    {
        result = 2.990e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.746e+00) )
    {
        result = 4.101e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.530e+00) )
    {
        result = 5.355e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.336e+00) )
    {
        result = 6.887e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.161e+00) )
    {
        result = 8.598e-03;
        return result;
    }
    if( ae_fp_greater_eq(s,3.002e+00) )
    {
        result = 1.065e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.855e+00) )
    {
        result = 1.268e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.720e+00) )
    {
        result = 1.552e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.595e+00) )
    {
        result = 1.836e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.477e+00) )
    {
        result = 2.158e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.368e+00) )
    {
        result = 2.512e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.264e+00) )
    {
        result = 2.942e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.166e+00) )
    {
        result = 3.325e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.073e+00) )
    {
        result = 3.800e-02;
        return result;
    }
    if( ae_fp_greater_eq(s,2.001e+00) )
    {
        result = 4.285e-02;
        return result;
    }
    result = (double)(0);
    return result;
}


/*************************************************************************
Tail(T,N), accepts T<0
*************************************************************************/
static double correlationtests_spearmantail(double t,
     ae_int_t n,
     ae_state *_state)
{
    double result;


    if( n==5 )
    {
        result = correlationtests_spearmantail5(-t, _state);
        return result;
    }
    if( n==6 )
    {
        result = correlationtests_spearmantail6(-t, _state);
        return result;
    }
    if( n==7 )
    {
        result = correlationtests_spearmantail7(-t, _state);
        return result;
    }
    if( n==8 )
    {
        result = correlationtests_spearmantail8(-t, _state);
        return result;
    }
    if( n==9 )
    {
        result = correlationtests_spearmantail9(-t, _state);
        return result;
    }
    result = studenttdistribution(n-2, t, _state);
    return result;
}


#endif
#if defined(AE_COMPILE_JARQUEBERA) || !defined(AE_PARTIAL_BUILD)


/*************************************************************************
Jarque-Bera test

This test checks hypotheses about the fact that a  given  sample  X  is  a
sample of normal random variable.

Requirements:
    * the number of elements in the sample is not less than 5.

Input parameters:
    X   -   sample. Array whose index goes from 0 to N-1.
    N   -   size of the sample. N>=5

Output parameters:
    P           -   p-value for the test

Accuracy of the approximation used (5<=N<=1951):

p-value  	    relative error (5<=N<=1951)
[1, 0.1]            < 1%
[0.1, 0.01]         < 2%
[0.01, 0.001]       < 6%
[0.001, 0]          wasn't measured

For N>1951 accuracy wasn't measured but it shouldn't be sharply  different
from table values.

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void jarqueberatest(/* Real    */ ae_vector* x,
     ae_int_t n,
     double* p,
     ae_state *_state)
{
    double s;

    *p = 0;

    
    /*
     * N is too small
     */
    if( n<5 )
    {
        *p = 1.0;
        return;
    }
    
    /*
     * N is large enough
     */
    jarquebera_jarqueberastatistic(x, n, &s, _state);
    *p = jarquebera_jarqueberaapprox(n, s, _state);
}


static void jarquebera_jarqueberastatistic(/* Real    */ ae_vector* x,
     ae_int_t n,
     double* s,
     ae_state *_state)
{
    ae_int_t i;
    double v;
    double v1;
    double v2;
    double stddev;
    double mean;
    double variance;
    double skewness;
    double kurtosis;

    *s = 0;

    mean = (double)(0);
    variance = (double)(0);
    skewness = (double)(0);
    kurtosis = (double)(0);
    stddev = (double)(0);
    ae_assert(n>1, "Assertion failed", _state);
    
    /*
     * Mean
     */
    for(i=0; i<=n-1; i++)
    {
        mean = mean+x->ptr.p_double[i];
    }
    mean = mean/n;
    
    /*
     * Variance (using corrected two-pass algorithm)
     */
    if( n!=1 )
    {
        v1 = (double)(0);
        for(i=0; i<=n-1; i++)
        {
            v1 = v1+ae_sqr(x->ptr.p_double[i]-mean, _state);
        }
        v2 = (double)(0);
        for(i=0; i<=n-1; i++)
        {
            v2 = v2+(x->ptr.p_double[i]-mean);
        }
        v2 = ae_sqr(v2, _state)/n;
        variance = (v1-v2)/(n-1);
        if( ae_fp_less(variance,(double)(0)) )
        {
            variance = (double)(0);
        }
        stddev = ae_sqrt(variance, _state);
    }
    
    /*
     * Skewness and kurtosis
     */
    if( ae_fp_neq(stddev,(double)(0)) )
    {
        for(i=0; i<=n-1; i++)
        {
            v = (x->ptr.p_double[i]-mean)/stddev;
            v2 = ae_sqr(v, _state);
            skewness = skewness+v2*v;
            kurtosis = kurtosis+ae_sqr(v2, _state);
        }
        skewness = skewness/n;
        kurtosis = kurtosis/n-3;
    }
    
    /*
     * Statistic
     */
    *s = (double)n/(double)6*(ae_sqr(skewness, _state)+ae_sqr(kurtosis, _state)/4);
}


static double jarquebera_jarqueberaapprox(ae_int_t n,
     double s,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_vector vx;
    ae_vector vy;
    ae_matrix ctbl;
    double t1;
    double t2;
    double t3;
    double t;
    double f1;
    double f2;
    double f3;
    double f12;
    double f23;
    double x;
    double result;

    ae_frame_make(_state, &_frame_block);
    memset(&vx, 0, sizeof(vx));
    memset(&vy, 0, sizeof(vy));
    memset(&ctbl, 0, sizeof(ctbl));
    ae_vector_init(&vx, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&vy, 0, DT_REAL, _state, ae_true);
    ae_matrix_init(&ctbl, 0, 0, DT_REAL, _state, ae_true);

    result = (double)(1);
    x = s;
    if( n<5 )
    {
        ae_frame_leave(_state);
        return result;
    }
    
    /*
     * N = 5..20 are tabulated
     */
    if( n>=5&&n<=20 )
    {
        if( n==5 )
        {
            result = ae_exp(jarquebera_jbtbl5(x, _state), _state);
        }
        if( n==6 )
        {
            result = ae_exp(jarquebera_jbtbl6(x, _state), _state);
        }
        if( n==7 )
        {
            result = ae_exp(jarquebera_jbtbl7(x, _state), _state);
        }
        if( n==8 )
        {
            result = ae_exp(jarquebera_jbtbl8(x, _state), _state);
        }
        if( n==9 )
        {
            result = ae_exp(jarquebera_jbtbl9(x, _state), _state);
        }
        if( n==10 )
        {
            result = ae_exp(jarquebera_jbtbl10(x, _state), _state);
        }
        if( n==11 )
        {
            result = ae_exp(jarquebera_jbtbl11(x, _state), _state);
        }
        if( n==12 )
        {
            result = ae_exp(jarquebera_jbtbl12(x, _state), _state);
        }
        if( n==13 )
        {
            result = ae_exp(jarquebera_jbtbl13(x, _state), _state);
        }
        if( n==14 )
        {
            result = ae_exp(jarquebera_jbtbl14(x, _state), _state);
        }
        if( n==15 )
        {
            result = ae_exp(jarquebera_jbtbl15(x, _state), _state);
        }
        if( n==16 )
        {
            result = ae_exp(jarquebera_jbtbl16(x, _state), _state);
        }
        if( n==17 )
        {
            result = ae_exp(jarquebera_jbtbl17(x, _state), _state);
        }
        if( n==18 )
        {
            result = ae_exp(jarquebera_jbtbl18(x, _state), _state);
        }
        if( n==19 )
        {
            result = ae_exp(jarquebera_jbtbl19(x, _state), _state);
        }
        if( n==20 )
        {
            result = ae_exp(jarquebera_jbtbl20(x, _state), _state);
        }
        ae_frame_leave(_state);
        return result;
    }
    
    /*
     * N = 20, 30, 50 are tabulated.
     * In-between values are interpolated
     * using interpolating polynomial of the second degree.
     */
    if( n>20&&n<=50 )
    {
        t1 = -1.0/20.0;
        t2 = -1.0/30.0;
        t3 = -1.0/50.0;
        t = -1.0/n;
        f1 = jarquebera_jbtbl20(x, _state);
        f2 = jarquebera_jbtbl30(x, _state);
        f3 = jarquebera_jbtbl50(x, _state);
        f12 = ((t-t2)*f1+(t1-t)*f2)/(t1-t2);
        f23 = ((t-t3)*f2+(t2-t)*f3)/(t2-t3);
        result = ((t-t3)*f12+(t1-t)*f23)/(t1-t3);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        result = ae_exp(result, _state);
        ae_frame_leave(_state);
        return result;
    }
    
    /*
     * N = 50, 65, 100 are tabulated.
     * In-between values are interpolated
     * using interpolating polynomial of the second degree.
     */
    if( n>50&&n<=100 )
    {
        t1 = -1.0/50.0;
        t2 = -1.0/65.0;
        t3 = -1.0/100.0;
        t = -1.0/n;
        f1 = jarquebera_jbtbl50(x, _state);
        f2 = jarquebera_jbtbl65(x, _state);
        f3 = jarquebera_jbtbl100(x, _state);
        f12 = ((t-t2)*f1+(t1-t)*f2)/(t1-t2);
        f23 = ((t-t3)*f2+(t2-t)*f3)/(t2-t3);
        result = ((t-t3)*f12+(t1-t)*f23)/(t1-t3);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        result = ae_exp(result, _state);
        ae_frame_leave(_state);
        return result;
    }
    
    /*
     * N = 100, 130, 200 are tabulated.
     * In-between values are interpolated
     * using interpolating polynomial of the second degree.
     */
    if( n>100&&n<=200 )
    {
        t1 = -1.0/100.0;
        t2 = -1.0/130.0;
        t3 = -1.0/200.0;
        t = -1.0/n;
        f1 = jarquebera_jbtbl100(x, _state);
        f2 = jarquebera_jbtbl130(x, _state);
        f3 = jarquebera_jbtbl200(x, _state);
        f12 = ((t-t2)*f1+(t1-t)*f2)/(t1-t2);
        f23 = ((t-t3)*f2+(t2-t)*f3)/(t2-t3);
        result = ((t-t3)*f12+(t1-t)*f23)/(t1-t3);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        result = ae_exp(result, _state);
        ae_frame_leave(_state);
        return result;
    }
    
    /*
     * N = 200, 301, 501 are tabulated.
     * In-between values are interpolated
     * using interpolating polynomial of the second degree.
     */
    if( n>200&&n<=501 )
    {
        t1 = -1.0/200.0;
        t2 = -1.0/301.0;
        t3 = -1.0/501.0;
        t = -1.0/n;
        f1 = jarquebera_jbtbl200(x, _state);
        f2 = jarquebera_jbtbl301(x, _state);
        f3 = jarquebera_jbtbl501(x, _state);
        f12 = ((t-t2)*f1+(t1-t)*f2)/(t1-t2);
        f23 = ((t-t3)*f2+(t2-t)*f3)/(t2-t3);
        result = ((t-t3)*f12+(t1-t)*f23)/(t1-t3);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        result = ae_exp(result, _state);
        ae_frame_leave(_state);
        return result;
    }
    
    /*
     * N = 501, 701, 1401 are tabulated.
     * In-between values are interpolated
     * using interpolating polynomial of the second degree.
     */
    if( n>501&&n<=1401 )
    {
        t1 = -1.0/501.0;
        t2 = -1.0/701.0;
        t3 = -1.0/1401.0;
        t = -1.0/n;
        f1 = jarquebera_jbtbl501(x, _state);
        f2 = jarquebera_jbtbl701(x, _state);
        f3 = jarquebera_jbtbl1401(x, _state);
        f12 = ((t-t2)*f1+(t1-t)*f2)/(t1-t2);
        f23 = ((t-t3)*f2+(t2-t)*f3)/(t2-t3);
        result = ((t-t3)*f12+(t1-t)*f23)/(t1-t3);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        result = ae_exp(result, _state);
        ae_frame_leave(_state);
        return result;
    }
    
    /*
     * Asymptotic expansion
     */
    if( n>1401 )
    {
        result = -0.5*x+(jarquebera_jbtbl1401(x, _state)+0.5*x)*ae_sqrt((double)1401/(double)n, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        result = ae_exp(result, _state);
        ae_frame_leave(_state);
        return result;
    }
    ae_frame_leave(_state);
    return result;
}


static double jarquebera_jbtbl5(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,0.4000) )
    {
        x = 2*(s-0.000000)/0.400000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.097885e-20, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.854501e-20, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.756616e-20, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,1.1000) )
    {
        x = 2*(s-0.400000)/0.700000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.324545e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.075941e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.772272e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.175686e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.576162e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.126861e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.434425e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.790359e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.809178e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.479704e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.717040e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.294170e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.880632e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.023344e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.601531e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.920403e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -5.188419e+02*(s-1.100000e+00)-4.767297e+00;
    return result;
}


static double jarquebera_jbtbl6(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,0.2500) )
    {
        x = 2*(s-0.000000)/0.250000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.274707e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.700471e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.425764e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,1.3000) )
    {
        x = 2*(s-0.250000)/1.050000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.339000e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.011104e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.168177e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.085666e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.738606e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.022876e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.462402e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.908270e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.230772e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.006996e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.410222e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.893768e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.114564e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,1.8500) )
    {
        x = 2*(s-1.300000)/0.550000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.794311e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.578700e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.394664e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.928290e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.813273e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.076063e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.835380e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.013013e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.058903e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.856915e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.710887e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.770029e+02*(s-1.850000e+00)-1.371015e+01;
    return result;
}


static double jarquebera_jbtbl7(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,1.4000) )
    {
        x = 2*(s-0.000000)/1.400000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.093681e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.695911e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.473192e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.203236e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.590379e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.291876e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.132007e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.411147e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.180067e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.487610e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.436561e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,3.0000) )
    {
        x = 2*(s-1.400000)/1.600000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.947854e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.772675e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.707912e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.691171e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.132795e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.481310e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.867536e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.772327e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.033387e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.378277e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.497964e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.636814e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.581640e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,3.2000) )
    {
        x = 2*(s-3.000000)/0.200000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -7.511008e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.140472e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.682053e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.568561e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.933930e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.140472e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.895025e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.140472e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.933930e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.568561e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.682053e+00, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.824116e+03*(s-3.200000e+00)-1.440330e+01;
    return result;
}


static double jarquebera_jbtbl8(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,1.3000) )
    {
        x = 2*(s-0.000000)/1.300000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -7.199015e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.095921e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.736828e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.047438e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.484320e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.937923e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.810470e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.139780e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.708443e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,2.0000) )
    {
        x = 2*(s-1.300000)/0.700000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -3.378966e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.802461e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.547593e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.241042e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.203274e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.201990e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.125597e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.584426e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.546069e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,5.0000) )
    {
        x = 2*(s-2.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.828366e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.137533e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.016671e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.745637e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.189801e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.621610e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.741122e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.516368e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.552085e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.787029e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.359774e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -5.087028e+00*(s-5.000000e+00)-1.071300e+01;
    return result;
}


static double jarquebera_jbtbl9(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,1.3000) )
    {
        x = 2*(s-0.000000)/1.300000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.279320e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.277151e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.669339e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.086149e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.333816e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.871249e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.007048e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.482245e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.355615e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,2.0000) )
    {
        x = 2*(s-1.300000)/0.700000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.981430e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.972248e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.747737e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.808530e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.888305e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.001302e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.378767e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.108510e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.915372e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,7.0000) )
    {
        x = 2*(s-2.000000)/5.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.387463e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.845231e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.809956e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.543461e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.880397e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.160074e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.356527e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.394428e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.619892e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.758763e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.790977e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -2.020952e+00*(s-7.000000e+00)-9.516623e+00;
    return result;
}


static double jarquebera_jbtbl10(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,1.2000) )
    {
        x = 2*(s-0.000000)/1.200000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.590993e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.562730e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.353934e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.069933e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.849151e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.931406e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.636295e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.178340e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.917749e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,2.0000) )
    {
        x = 2*(s-1.200000)/0.800000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.537658e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.962401e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.838715e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.055792e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.580316e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.781701e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.770362e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.838983e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.999052e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,7.0000) )
    {
        x = 2*(s-2.000000)/5.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.337524e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.877029e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.734650e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.249254e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.320250e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.432266e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -8.711035e-01*(s-7.000000e+00)-7.212811e+00;
    return result;
}


static double jarquebera_jbtbl11(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,1.2000) )
    {
        x = 2*(s-0.000000)/1.200000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.339517e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.051558e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.000992e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.022547e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.808401e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.592870e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.575081e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.086173e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.089011e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,2.2500) )
    {
        x = 2*(s-1.200000)/1.050000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.523221e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.068388e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.179661e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.555524e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.238964e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.364320e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.895771e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.762774e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.201340e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,8.0000) )
    {
        x = 2*(s-2.250000)/5.750000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.212179e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.684579e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.299519e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.606261e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.310869e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.320115e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -5.715445e-01*(s-8.000000e+00)-6.845834e+00;
    return result;
}


static double jarquebera_jbtbl12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,1.0000) )
    {
        x = 2*(s-0.000000)/1.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.736742e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.657836e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.047209e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.319599e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.545631e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.280445e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.815679e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.213519e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.256838e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,3.0000) )
    {
        x = 2*(s-1.000000)/2.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.573947e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.515287e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.611880e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.271311e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.495815e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.141186e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.180886e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.388211e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.890761e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.233175e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.946156e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,12.0000) )
    {
        x = 2*(s-3.000000)/9.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.947819e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.034157e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.878986e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.078603e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.990977e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.866215e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.897866e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.512252e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.073743e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.022621e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.501343e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -2.877243e-01*(s-1.200000e+01)-7.936839e+00;
    return result;
}


static double jarquebera_jbtbl13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,1.0000) )
    {
        x = 2*(s-0.000000)/1.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.713276e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.557541e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.459092e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.044145e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.546132e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.002374e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.349456e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.025669e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.590242e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,3.0000) )
    {
        x = 2*(s-1.000000)/2.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.454383e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.467539e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.270774e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.075763e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.611647e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.990785e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.109212e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.135031e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.915919e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.522390e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.144701e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,13.0000) )
    {
        x = 2*(s-3.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.736127e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.920809e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.175858e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.002049e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.158966e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.157781e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.762172e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.780347e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.193310e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.442421e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.547756e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -2.799944e-01*(s-1.300000e+01)-7.566269e+00;
    return result;
}


static double jarquebera_jbtbl14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,1.0000) )
    {
        x = 2*(s-0.000000)/1.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.698527e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.479081e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.640733e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.466899e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.469485e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.150009e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.965975e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.710210e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.327808e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,3.0000) )
    {
        x = 2*(s-1.000000)/2.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -2.350359e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.421365e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.960468e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.149167e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.361109e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.976022e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.082700e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.563328e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.453123e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.917559e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.151067e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-3.000000)/12.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.746892e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.010441e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.566146e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.129690e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.929724e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.524227e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.192933e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.254730e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.620685e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.289618e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.112350e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -2.590621e-01*(s-1.500000e+01)-7.632238e+00;
    return result;
}


static double jarquebera_jbtbl15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,2.0000) )
    {
        x = 2*(s-0.000000)/2.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.043660e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.361653e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.009497e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.951784e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.377903e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.003253e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.271309e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,5.0000) )
    {
        x = 2*(s-2.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -3.582778e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.349578e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.476514e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.717385e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.222591e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.635124e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.815993e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,17.0000) )
    {
        x = 2*(s-5.000000)/12.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.115476e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.655936e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.404310e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.663794e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.868618e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.381447e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.444801e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.581503e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.468696e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.728509e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.206470e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.927937e-01*(s-1.700000e+01)-7.700983e+00;
    return result;
}


static double jarquebera_jbtbl16(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,2.0000) )
    {
        x = 2*(s-0.000000)/2.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.002570e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.298141e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.832803e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.877026e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.539436e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.439658e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.756911e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,5.0000) )
    {
        x = 2*(s-2.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -3.486198e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.242944e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.020002e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.130531e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.512373e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.054876e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.556839e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,20.0000) )
    {
        x = 2*(s-5.000000)/15.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.241608e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.832655e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.340545e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.361143e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.283219e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.484549e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.805968e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.057243e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.454439e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.177513e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.819209e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -2.391580e-01*(s-2.000000e+01)-7.963205e+00;
    return result;
}


static double jarquebera_jbtbl17(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,3.0000) )
    {
        x = 2*(s-0.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.566973e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.810330e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.840039e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.337294e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.383549e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.556515e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.656965e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.404569e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.447867e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,6.0000) )
    {
        x = 2*(s-3.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -3.905684e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.222920e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.146667e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.809176e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.057028e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.211838e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.099683e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.161105e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.225465e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,24.0000) )
    {
        x = 2*(s-6.000000)/18.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.594282e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.917838e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.455980e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.999589e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.604263e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.484445e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.819937e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.930390e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.771761e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.232581e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.029083e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -2.127771e-01*(s-2.400000e+01)-8.400197e+00;
    return result;
}


static double jarquebera_jbtbl18(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,3.0000) )
    {
        x = 2*(s-0.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.526802e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.762373e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.598890e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.189437e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.971721e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.823067e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.064501e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.014932e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.953513e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,6.0000) )
    {
        x = 2*(s-3.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -3.818669e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.070918e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.277196e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.879817e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.887357e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.638451e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.502800e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.165796e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.034960e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,20.0000) )
    {
        x = 2*(s-6.000000)/14.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.010656e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.496296e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.002227e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.338250e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.137036e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.586202e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.736384e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.332251e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.877982e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.160963e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.547247e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.684623e-01*(s-2.000000e+01)-7.428883e+00;
    return result;
}


static double jarquebera_jbtbl19(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,3.0000) )
    {
        x = 2*(s-0.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.490213e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.719633e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.459123e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.034878e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.113868e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.030922e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.054022e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.525623e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.277360e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,6.0000) )
    {
        x = 2*(s-3.000000)/3.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -3.744750e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.977749e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.223716e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.363889e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.711774e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.557257e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.254794e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.034207e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.498107e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,20.0000) )
    {
        x = 2*(s-6.000000)/14.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.872768e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.430689e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.136575e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.726627e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.421110e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.581510e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.559520e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.838208e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.428839e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.170682e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.006647e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.539373e-01*(s-2.000000e+01)-7.206941e+00;
    return result;
}


static double jarquebera_jbtbl20(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.854794e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.948947e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.632184e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.139397e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.006237e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.810031e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.573620e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.951242e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.274092e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.464196e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.882139e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.575144e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.822804e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.061348e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.908404e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.978353e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.030989e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.327151e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.346404e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.840051e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.578551e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.813886e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.905973e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.358489e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.450795e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.941157e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.432418e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.070537e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.375654e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.367378e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.890859e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.679782e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -7.015854e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.487737e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.244254e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.318007e-01*(s-2.500000e+01)-7.742185e+00;
    return result;
}


static double jarquebera_jbtbl30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.630822e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.724298e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.872756e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.658268e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.573597e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.994157e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.994825e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.394303e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.785029e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.990264e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.037838e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.755546e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.774473e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.821395e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.392603e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.353313e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.539322e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.197018e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.396848e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.804293e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.867928e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.768758e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.211792e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.925799e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.046235e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.536469e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.489642e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.263462e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.177316e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.590637e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.028212e-01*(s-2.500000e+01)-6.855288e+00;
    return result;
}


static double jarquebera_jbtbl50(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.436279e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.519711e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.148699e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.001204e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.207620e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.034778e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.220322e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.033260e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.588280e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.851653e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.287733e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.234645e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.189127e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.429738e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.058822e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 9.086776e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.445783e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.311671e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.261298e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.496987e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.605249e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.162282e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.921095e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.888603e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.080113e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -9.313116e-02*(s-2.500000e+01)-6.479154e+00;
    return result;
}


static double jarquebera_jbtbl65(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.360024e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.434631e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.514580e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 7.332038e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.158197e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.121233e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.051056e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.148601e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.214233e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.487977e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.424720e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.116715e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.043152e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.718149e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.313701e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.097305e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.181031e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.256975e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.858951e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.895179e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.933237e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -9.443768e-02*(s-2.500000e+01)-6.419137e+00;
    return result;
}


static double jarquebera_jbtbl100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.257021e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.313418e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.628931e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.264287e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.518487e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.499826e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.836044e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.056508e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.279690e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.665746e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.290012e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.487632e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.704465e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.211669e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.866099e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.399767e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.498208e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.080097e-01*(s-2.500000e+01)-6.481094e+00;
    return result;
}


static double jarquebera_jbtbl130(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.207999e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.253864e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.618032e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.112729e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.210546e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.732602e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.410527e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.026324e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.331990e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.779129e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.674749e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.669077e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.679136e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 8.833221e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -5.893951e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.475304e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.116734e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.045722e-01*(s-2.500000e+01)-6.510314e+00;
    return result;
}


static double jarquebera_jbtbl200(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.146155e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.177398e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.297970e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.869745e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.717288e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.982108e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.427636e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.034235e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.455006e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.942996e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.973795e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.418812e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.156778e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.896705e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.086071e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.152176e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.725393e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.132404e-01*(s-2.500000e+01)-6.764034e+00;
    return result;
}


static double jarquebera_jbtbl301(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.104290e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.125800e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.595847e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.219666e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.502210e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.414543e-05, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.754115e-05, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.065955e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.582060e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.004472e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -4.709092e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.105779e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.197391e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.386780e-04, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.311384e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.918763e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.626584e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.293626e-01*(s-2.500000e+01)-7.066995e+00;
    return result;
}


static double jarquebera_jbtbl501(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.067426e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.079765e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -5.463005e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 6.875659e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.127574e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.740694e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.044502e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.746714e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 3.810594e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.197111e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.628194e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -8.846221e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.386405e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.418332e-01*(s-2.500000e+01)-7.468952e+00;
    return result;
}


static double jarquebera_jbtbl701(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.050999e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.059769e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -3.922680e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 4.847054e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.192182e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.860007e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.963942e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.838711e-02, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.893112e-04, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.159788e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -6.917851e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -9.817020e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.383727e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -1.532706e-01*(s-2.500000e+01)-7.845715e+00;
    return result;
}


static double jarquebera_jbtbl1401(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    if( ae_fp_less_eq(s,4.0000) )
    {
        x = 2*(s-0.000000)/4.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -1.026266e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.030061e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.259222e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 2.536254e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,15.0000) )
    {
        x = 2*(s-4.000000)/11.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -4.329849e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -2.095443e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 1.759363e-01, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -7.751359e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -6.124368e-03, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.793114e-03, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    if( ae_fp_less_eq(s,25.0000) )
    {
        x = 2*(s-15.000000)/10.000000-1;
        tj = (double)(1);
        tj1 = x;
        jarquebera_jbcheb(x, -7.544330e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, -1.225382e+00, &tj, &tj1, &result, _state);
        jarquebera_jbcheb(x, 5.392349e-02, &tj, &tj1, &result, _state);
        if( ae_fp_greater(result,(double)(0)) )
        {
            result = (double)(0);
        }
        return result;
    }
    result = -2.019375e-01*(s-2.500000e+01)-8.715788e+00;
    return result;
}


static void jarquebera_jbcheb(double x,
     double c,
     double* tj,
     double* tj1,
     double* r,
     ae_state *_state)
{
    double t;


    *r = *r+c*(*tj);
    t = 2*x*(*tj1)-(*tj);
    *tj = *tj1;
    *tj1 = t;
}


#endif
#if defined(AE_COMPILE_VARIANCETESTS) || !defined(AE_PARTIAL_BUILD)


/*************************************************************************
Two-sample F-test

This test checks three hypotheses about dispersions of the given  samples.
The following tests are performed:
    * two-tailed test (null hypothesis - the dispersions are equal)
    * left-tailed test (null hypothesis  -  the  dispersion  of  the first
      sample is greater than or equal to  the  dispersion  of  the  second
      sample).
    * right-tailed test (null hypothesis - the  dispersion  of  the  first
      sample is less than or equal to the dispersion of the second sample)

The test is based on the following assumptions:
    * the given samples have normal distributions
    * the samples are independent.

Input parameters:
    X   -   sample 1. Array whose index goes from 0 to N-1.
    N   -   sample size.
    Y   -   sample 2. Array whose index goes from 0 to M-1.
    M   -   sample size.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

  -- ALGLIB --
     Copyright 19.09.2006 by Bochkanov Sergey
*************************************************************************/
void ftest(/* Real    */ ae_vector* x,
     ae_int_t n,
     /* Real    */ ae_vector* y,
     ae_int_t m,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    ae_int_t i;
    double xmean;
    double ymean;
    double xvar;
    double yvar;
    ae_int_t df1;
    ae_int_t df2;
    double stat;

    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;

    if( n<=2||m<=2 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * Mean
     */
    xmean = (double)(0);
    for(i=0; i<=n-1; i++)
    {
        xmean = xmean+x->ptr.p_double[i];
    }
    xmean = xmean/n;
    ymean = (double)(0);
    for(i=0; i<=m-1; i++)
    {
        ymean = ymean+y->ptr.p_double[i];
    }
    ymean = ymean/m;
    
    /*
     * Variance (using corrected two-pass algorithm)
     */
    xvar = (double)(0);
    for(i=0; i<=n-1; i++)
    {
        xvar = xvar+ae_sqr(x->ptr.p_double[i]-xmean, _state);
    }
    xvar = xvar/(n-1);
    yvar = (double)(0);
    for(i=0; i<=m-1; i++)
    {
        yvar = yvar+ae_sqr(y->ptr.p_double[i]-ymean, _state);
    }
    yvar = yvar/(m-1);
    if( ae_fp_eq(xvar,(double)(0))||ae_fp_eq(yvar,(double)(0)) )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * Statistic
     */
    df1 = n-1;
    df2 = m-1;
    stat = ae_minreal(xvar/yvar, yvar/xvar, _state);
    *bothtails = 1-(fdistribution(df1, df2, 1/stat, _state)-fdistribution(df1, df2, stat, _state));
    *lefttail = fdistribution(df1, df2, xvar/yvar, _state);
    *righttail = 1-(*lefttail);
}


/*************************************************************************
One-sample chi-square test

This test checks three hypotheses about the dispersion of the given sample
The following tests are performed:
    * two-tailed test (null hypothesis - the dispersion equals  the  given
      number)
    * left-tailed test (null hypothesis - the dispersion is  greater  than
      or equal to the given number)
    * right-tailed test (null hypothesis  -  dispersion is  less  than  or
      equal to the given number).

Test is based on the following assumptions:
    * the given sample has a normal distribution.

Input parameters:
    X           -   sample 1. Array whose index goes from 0 to N-1.
    N           -   size of the sample.
    Variance    -   dispersion value to compare with.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

  -- ALGLIB --
     Copyright 19.09.2006 by Bochkanov Sergey
*************************************************************************/
void onesamplevariancetest(/* Real    */ ae_vector* x,
     ae_int_t n,
     double variance,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    ae_int_t i;
    double xmean;
    double xvar;
    double s;
    double stat;

    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;

    if( n<=1 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * Mean
     */
    xmean = (double)(0);
    for(i=0; i<=n-1; i++)
    {
        xmean = xmean+x->ptr.p_double[i];
    }
    xmean = xmean/n;
    
    /*
     * Variance
     */
    xvar = (double)(0);
    for(i=0; i<=n-1; i++)
    {
        xvar = xvar+ae_sqr(x->ptr.p_double[i]-xmean, _state);
    }
    xvar = xvar/(n-1);
    if( ae_fp_eq(xvar,(double)(0)) )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * Statistic
     */
    stat = (n-1)*xvar/variance;
    s = chisquaredistribution((double)(n-1), stat, _state);
    *bothtails = 2*ae_minreal(s, 1-s, _state);
    *lefttail = s;
    *righttail = 1-(*lefttail);
}


#endif
#if defined(AE_COMPILE_WSR) || !defined(AE_PARTIAL_BUILD)


/*************************************************************************
Wilcoxon signed-rank test

This test checks three hypotheses about the median  of  the  given sample.
The following tests are performed:
    * two-tailed test (null hypothesis - the median is equal to the  given
      value)
    * left-tailed test (null hypothesis - the median is  greater  than  or
      equal to the given value)
    * right-tailed test (null hypothesis  -  the  median  is  less than or
      equal to the given value)

Requirements:
    * the scale of measurement should be ordinal, interval or  ratio (i.e.
      the test could not be applied to nominal variables).
    * the distribution should be continuous and symmetric relative to  its
      median.
    * number of distinct values in the X array should be greater than 4

The test is non-parametric and doesn't require distribution X to be normal

Input parameters:
    X       -   sample. Array whose index goes from 0 to N-1.
    N       -   size of the sample.
    Median  -   assumed median value.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

To calculate p-values, special approximation is used. This method lets  us
calculate p-values with two decimal places in interval [0.0001, 1].

"Two decimal places" does not sound very impressive, but in  practice  the
relative error of less than 1% is enough to make a decision.

There is no approximation outside the [0.0001, 1] interval. Therefore,  if
the significance level outlies this interval, the test returns 0.0001.

  -- ALGLIB --
     Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void wilcoxonsignedranktest(/* Real    */ ae_vector* x,
     ae_int_t n,
     double e,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_vector _x;
    ae_int_t i;
    ae_int_t j;
    ae_int_t k;
    ae_int_t t;
    double tmp;
    ae_int_t tmpi;
    ae_int_t ns;
    ae_vector r;
    ae_vector c;
    double w;
    double p;
    double mp;
    double s;
    double sigma;
    double mu;

    ae_frame_make(_state, &_frame_block);
    memset(&_x, 0, sizeof(_x));
    memset(&r, 0, sizeof(r));
    memset(&c, 0, sizeof(c));
    ae_vector_init_copy(&_x, x, _state, ae_true);
    x = &_x;
    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;
    ae_vector_init(&r, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&c, 0, DT_INT, _state, ae_true);

    
    /*
     * Prepare
     */
    if( n<5 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        ae_frame_leave(_state);
        return;
    }
    ns = 0;
    for(i=0; i<=n-1; i++)
    {
        if( ae_fp_eq(x->ptr.p_double[i],e) )
        {
            continue;
        }
        x->ptr.p_double[ns] = x->ptr.p_double[i];
        ns = ns+1;
    }
    if( ns<5 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        ae_frame_leave(_state);
        return;
    }
    ae_vector_set_length(&r, ns-1+1, _state);
    ae_vector_set_length(&c, ns-1+1, _state);
    for(i=0; i<=ns-1; i++)
    {
        r.ptr.p_double[i] = ae_fabs(x->ptr.p_double[i]-e, _state);
        c.ptr.p_int[i] = i;
    }
    
    /*
     * sort {R, C}
     */
    if( ns!=1 )
    {
        i = 2;
        do
        {
            t = i;
            while(t!=1)
            {
                k = t/2;
                if( ae_fp_greater_eq(r.ptr.p_double[k-1],r.ptr.p_double[t-1]) )
                {
                    t = 1;
                }
                else
                {
                    tmp = r.ptr.p_double[k-1];
                    r.ptr.p_double[k-1] = r.ptr.p_double[t-1];
                    r.ptr.p_double[t-1] = tmp;
                    tmpi = c.ptr.p_int[k-1];
                    c.ptr.p_int[k-1] = c.ptr.p_int[t-1];
                    c.ptr.p_int[t-1] = tmpi;
                    t = k;
                }
            }
            i = i+1;
        }
        while(i<=ns);
        i = ns-1;
        do
        {
            tmp = r.ptr.p_double[i];
            r.ptr.p_double[i] = r.ptr.p_double[0];
            r.ptr.p_double[0] = tmp;
            tmpi = c.ptr.p_int[i];
            c.ptr.p_int[i] = c.ptr.p_int[0];
            c.ptr.p_int[0] = tmpi;
            t = 1;
            while(t!=0)
            {
                k = 2*t;
                if( k>i )
                {
                    t = 0;
                }
                else
                {
                    if( k<i )
                    {
                        if( ae_fp_greater(r.ptr.p_double[k],r.ptr.p_double[k-1]) )
                        {
                            k = k+1;
                        }
                    }
                    if( ae_fp_greater_eq(r.ptr.p_double[t-1],r.ptr.p_double[k-1]) )
                    {
                        t = 0;
                    }
                    else
                    {
                        tmp = r.ptr.p_double[k-1];
                        r.ptr.p_double[k-1] = r.ptr.p_double[t-1];
                        r.ptr.p_double[t-1] = tmp;
                        tmpi = c.ptr.p_int[k-1];
                        c.ptr.p_int[k-1] = c.ptr.p_int[t-1];
                        c.ptr.p_int[t-1] = tmpi;
                        t = k;
                    }
                }
            }
            i = i-1;
        }
        while(i>=1);
    }
    
    /*
     * compute tied ranks
     */
    i = 0;
    while(i<=ns-1)
    {
        j = i+1;
        while(j<=ns-1)
        {
            if( ae_fp_neq(r.ptr.p_double[j],r.ptr.p_double[i]) )
            {
                break;
            }
            j = j+1;
        }
        for(k=i; k<=j-1; k++)
        {
            r.ptr.p_double[k] = 1+(double)(i+j-1)/(double)2;
        }
        i = j;
    }
    
    /*
     * Compute W+
     */
    w = (double)(0);
    for(i=0; i<=ns-1; i++)
    {
        if( ae_fp_greater(x->ptr.p_double[c.ptr.p_int[i]],e) )
        {
            w = w+r.ptr.p_double[i];
        }
    }
    
    /*
     * Result
     */
    mu = rmul2((double)(ns), (double)(ns+1), _state)/4;
    sigma = ae_sqrt(mu*(2*ns+1)/6, _state);
    s = (w-mu)/sigma;
    if( ae_fp_less_eq(s,(double)(0)) )
    {
        p = ae_exp(wsr_wsigma(-(w-mu)/sigma, ns, _state), _state);
        mp = 1-ae_exp(wsr_wsigma(-(w-1-mu)/sigma, ns, _state), _state);
    }
    else
    {
        mp = ae_exp(wsr_wsigma((w-mu)/sigma, ns, _state), _state);
        p = 1-ae_exp(wsr_wsigma((w+1-mu)/sigma, ns, _state), _state);
    }
    *lefttail = ae_maxreal(p, 1.0E-4, _state);
    *righttail = ae_maxreal(mp, 1.0E-4, _state);
    *bothtails = 2*ae_minreal(*lefttail, *righttail, _state);
    ae_frame_leave(_state);
}


/*************************************************************************
Sequential Chebyshev interpolation.
*************************************************************************/
static void wsr_wcheb(double x,
     double c,
     double* tj,
     double* tj1,
     double* r,
     ae_state *_state)
{
    double t;


    *r = *r+c*(*tj);
    t = 2*x*(*tj1)-(*tj);
    *tj = *tj1;
    *tj1 = t;
}


/*************************************************************************
Tail(S, 5)
*************************************************************************/
static double wsr_w5(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-3.708099e+00*s+7.500000e+00, _state);
    if( w>=7 )
    {
        r = -6.931e-01;
    }
    if( w==6 )
    {
        r = -9.008e-01;
    }
    if( w==5 )
    {
        r = -1.163e+00;
    }
    if( w==4 )
    {
        r = -1.520e+00;
    }
    if( w==3 )
    {
        r = -1.856e+00;
    }
    if( w==2 )
    {
        r = -2.367e+00;
    }
    if( w==1 )
    {
        r = -2.773e+00;
    }
    if( w<=0 )
    {
        r = -3.466e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 6)
*************************************************************************/
static double wsr_w6(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-4.769696e+00*s+1.050000e+01, _state);
    if( w>=10 )
    {
        r = -6.931e-01;
    }
    if( w==9 )
    {
        r = -8.630e-01;
    }
    if( w==8 )
    {
        r = -1.068e+00;
    }
    if( w==7 )
    {
        r = -1.269e+00;
    }
    if( w==6 )
    {
        r = -1.520e+00;
    }
    if( w==5 )
    {
        r = -1.856e+00;
    }
    if( w==4 )
    {
        r = -2.213e+00;
    }
    if( w==3 )
    {
        r = -2.549e+00;
    }
    if( w==2 )
    {
        r = -3.060e+00;
    }
    if( w==1 )
    {
        r = -3.466e+00;
    }
    if( w<=0 )
    {
        r = -4.159e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 7)
*************************************************************************/
static double wsr_w7(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-5.916080e+00*s+1.400000e+01, _state);
    if( w>=14 )
    {
        r = -6.325e-01;
    }
    if( w==13 )
    {
        r = -7.577e-01;
    }
    if( w==12 )
    {
        r = -9.008e-01;
    }
    if( w==11 )
    {
        r = -1.068e+00;
    }
    if( w==10 )
    {
        r = -1.241e+00;
    }
    if( w==9 )
    {
        r = -1.451e+00;
    }
    if( w==8 )
    {
        r = -1.674e+00;
    }
    if( w==7 )
    {
        r = -1.908e+00;
    }
    if( w==6 )
    {
        r = -2.213e+00;
    }
    if( w==5 )
    {
        r = -2.549e+00;
    }
    if( w==4 )
    {
        r = -2.906e+00;
    }
    if( w==3 )
    {
        r = -3.243e+00;
    }
    if( w==2 )
    {
        r = -3.753e+00;
    }
    if( w==1 )
    {
        r = -4.159e+00;
    }
    if( w<=0 )
    {
        r = -4.852e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 8)
*************************************************************************/
static double wsr_w8(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-7.141428e+00*s+1.800000e+01, _state);
    if( w>=18 )
    {
        r = -6.399e-01;
    }
    if( w==17 )
    {
        r = -7.494e-01;
    }
    if( w==16 )
    {
        r = -8.630e-01;
    }
    if( w==15 )
    {
        r = -9.913e-01;
    }
    if( w==14 )
    {
        r = -1.138e+00;
    }
    if( w==13 )
    {
        r = -1.297e+00;
    }
    if( w==12 )
    {
        r = -1.468e+00;
    }
    if( w==11 )
    {
        r = -1.653e+00;
    }
    if( w==10 )
    {
        r = -1.856e+00;
    }
    if( w==9 )
    {
        r = -2.079e+00;
    }
    if( w==8 )
    {
        r = -2.326e+00;
    }
    if( w==7 )
    {
        r = -2.601e+00;
    }
    if( w==6 )
    {
        r = -2.906e+00;
    }
    if( w==5 )
    {
        r = -3.243e+00;
    }
    if( w==4 )
    {
        r = -3.599e+00;
    }
    if( w==3 )
    {
        r = -3.936e+00;
    }
    if( w==2 )
    {
        r = -4.447e+00;
    }
    if( w==1 )
    {
        r = -4.852e+00;
    }
    if( w<=0 )
    {
        r = -5.545e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 9)
*************************************************************************/
static double wsr_w9(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-8.440972e+00*s+2.250000e+01, _state);
    if( w>=22 )
    {
        r = -6.931e-01;
    }
    if( w==21 )
    {
        r = -7.873e-01;
    }
    if( w==20 )
    {
        r = -8.912e-01;
    }
    if( w==19 )
    {
        r = -1.002e+00;
    }
    if( w==18 )
    {
        r = -1.120e+00;
    }
    if( w==17 )
    {
        r = -1.255e+00;
    }
    if( w==16 )
    {
        r = -1.394e+00;
    }
    if( w==15 )
    {
        r = -1.547e+00;
    }
    if( w==14 )
    {
        r = -1.717e+00;
    }
    if( w==13 )
    {
        r = -1.895e+00;
    }
    if( w==12 )
    {
        r = -2.079e+00;
    }
    if( w==11 )
    {
        r = -2.287e+00;
    }
    if( w==10 )
    {
        r = -2.501e+00;
    }
    if( w==9 )
    {
        r = -2.742e+00;
    }
    if( w==8 )
    {
        r = -3.019e+00;
    }
    if( w==7 )
    {
        r = -3.294e+00;
    }
    if( w==6 )
    {
        r = -3.599e+00;
    }
    if( w==5 )
    {
        r = -3.936e+00;
    }
    if( w==4 )
    {
        r = -4.292e+00;
    }
    if( w==3 )
    {
        r = -4.629e+00;
    }
    if( w==2 )
    {
        r = -5.140e+00;
    }
    if( w==1 )
    {
        r = -5.545e+00;
    }
    if( w<=0 )
    {
        r = -6.238e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 10)
*************************************************************************/
static double wsr_w10(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-9.810708e+00*s+2.750000e+01, _state);
    if( w>=27 )
    {
        r = -6.931e-01;
    }
    if( w==26 )
    {
        r = -7.745e-01;
    }
    if( w==25 )
    {
        r = -8.607e-01;
    }
    if( w==24 )
    {
        r = -9.551e-01;
    }
    if( w==23 )
    {
        r = -1.057e+00;
    }
    if( w==22 )
    {
        r = -1.163e+00;
    }
    if( w==21 )
    {
        r = -1.279e+00;
    }
    if( w==20 )
    {
        r = -1.402e+00;
    }
    if( w==19 )
    {
        r = -1.533e+00;
    }
    if( w==18 )
    {
        r = -1.674e+00;
    }
    if( w==17 )
    {
        r = -1.826e+00;
    }
    if( w==16 )
    {
        r = -1.983e+00;
    }
    if( w==15 )
    {
        r = -2.152e+00;
    }
    if( w==14 )
    {
        r = -2.336e+00;
    }
    if( w==13 )
    {
        r = -2.525e+00;
    }
    if( w==12 )
    {
        r = -2.727e+00;
    }
    if( w==11 )
    {
        r = -2.942e+00;
    }
    if( w==10 )
    {
        r = -3.170e+00;
    }
    if( w==9 )
    {
        r = -3.435e+00;
    }
    if( w==8 )
    {
        r = -3.713e+00;
    }
    if( w==7 )
    {
        r = -3.987e+00;
    }
    if( w==6 )
    {
        r = -4.292e+00;
    }
    if( w==5 )
    {
        r = -4.629e+00;
    }
    if( w==4 )
    {
        r = -4.986e+00;
    }
    if( w==3 )
    {
        r = -5.322e+00;
    }
    if( w==2 )
    {
        r = -5.833e+00;
    }
    if( w==1 )
    {
        r = -6.238e+00;
    }
    if( w<=0 )
    {
        r = -6.931e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 11)
*************************************************************************/
static double wsr_w11(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-1.124722e+01*s+3.300000e+01, _state);
    if( w>=33 )
    {
        r = -6.595e-01;
    }
    if( w==32 )
    {
        r = -7.279e-01;
    }
    if( w==31 )
    {
        r = -8.002e-01;
    }
    if( w==30 )
    {
        r = -8.782e-01;
    }
    if( w==29 )
    {
        r = -9.615e-01;
    }
    if( w==28 )
    {
        r = -1.050e+00;
    }
    if( w==27 )
    {
        r = -1.143e+00;
    }
    if( w==26 )
    {
        r = -1.243e+00;
    }
    if( w==25 )
    {
        r = -1.348e+00;
    }
    if( w==24 )
    {
        r = -1.459e+00;
    }
    if( w==23 )
    {
        r = -1.577e+00;
    }
    if( w==22 )
    {
        r = -1.700e+00;
    }
    if( w==21 )
    {
        r = -1.832e+00;
    }
    if( w==20 )
    {
        r = -1.972e+00;
    }
    if( w==19 )
    {
        r = -2.119e+00;
    }
    if( w==18 )
    {
        r = -2.273e+00;
    }
    if( w==17 )
    {
        r = -2.437e+00;
    }
    if( w==16 )
    {
        r = -2.607e+00;
    }
    if( w==15 )
    {
        r = -2.788e+00;
    }
    if( w==14 )
    {
        r = -2.980e+00;
    }
    if( w==13 )
    {
        r = -3.182e+00;
    }
    if( w==12 )
    {
        r = -3.391e+00;
    }
    if( w==11 )
    {
        r = -3.617e+00;
    }
    if( w==10 )
    {
        r = -3.863e+00;
    }
    if( w==9 )
    {
        r = -4.128e+00;
    }
    if( w==8 )
    {
        r = -4.406e+00;
    }
    if( w==7 )
    {
        r = -4.680e+00;
    }
    if( w==6 )
    {
        r = -4.986e+00;
    }
    if( w==5 )
    {
        r = -5.322e+00;
    }
    if( w==4 )
    {
        r = -5.679e+00;
    }
    if( w==3 )
    {
        r = -6.015e+00;
    }
    if( w==2 )
    {
        r = -6.526e+00;
    }
    if( w==1 )
    {
        r = -6.931e+00;
    }
    if( w<=0 )
    {
        r = -7.625e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 12)
*************************************************************************/
static double wsr_w12(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-1.274755e+01*s+3.900000e+01, _state);
    if( w>=39 )
    {
        r = -6.633e-01;
    }
    if( w==38 )
    {
        r = -7.239e-01;
    }
    if( w==37 )
    {
        r = -7.878e-01;
    }
    if( w==36 )
    {
        r = -8.556e-01;
    }
    if( w==35 )
    {
        r = -9.276e-01;
    }
    if( w==34 )
    {
        r = -1.003e+00;
    }
    if( w==33 )
    {
        r = -1.083e+00;
    }
    if( w==32 )
    {
        r = -1.168e+00;
    }
    if( w==31 )
    {
        r = -1.256e+00;
    }
    if( w==30 )
    {
        r = -1.350e+00;
    }
    if( w==29 )
    {
        r = -1.449e+00;
    }
    if( w==28 )
    {
        r = -1.552e+00;
    }
    if( w==27 )
    {
        r = -1.660e+00;
    }
    if( w==26 )
    {
        r = -1.774e+00;
    }
    if( w==25 )
    {
        r = -1.893e+00;
    }
    if( w==24 )
    {
        r = -2.017e+00;
    }
    if( w==23 )
    {
        r = -2.148e+00;
    }
    if( w==22 )
    {
        r = -2.285e+00;
    }
    if( w==21 )
    {
        r = -2.429e+00;
    }
    if( w==20 )
    {
        r = -2.581e+00;
    }
    if( w==19 )
    {
        r = -2.738e+00;
    }
    if( w==18 )
    {
        r = -2.902e+00;
    }
    if( w==17 )
    {
        r = -3.076e+00;
    }
    if( w==16 )
    {
        r = -3.255e+00;
    }
    if( w==15 )
    {
        r = -3.443e+00;
    }
    if( w==14 )
    {
        r = -3.645e+00;
    }
    if( w==13 )
    {
        r = -3.852e+00;
    }
    if( w==12 )
    {
        r = -4.069e+00;
    }
    if( w==11 )
    {
        r = -4.310e+00;
    }
    if( w==10 )
    {
        r = -4.557e+00;
    }
    if( w==9 )
    {
        r = -4.821e+00;
    }
    if( w==8 )
    {
        r = -5.099e+00;
    }
    if( w==7 )
    {
        r = -5.373e+00;
    }
    if( w==6 )
    {
        r = -5.679e+00;
    }
    if( w==5 )
    {
        r = -6.015e+00;
    }
    if( w==4 )
    {
        r = -6.372e+00;
    }
    if( w==3 )
    {
        r = -6.708e+00;
    }
    if( w==2 )
    {
        r = -7.219e+00;
    }
    if( w==1 )
    {
        r = -7.625e+00;
    }
    if( w<=0 )
    {
        r = -8.318e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 13)
*************************************************************************/
static double wsr_w13(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-1.430909e+01*s+4.550000e+01, _state);
    if( w>=45 )
    {
        r = -6.931e-01;
    }
    if( w==44 )
    {
        r = -7.486e-01;
    }
    if( w==43 )
    {
        r = -8.068e-01;
    }
    if( w==42 )
    {
        r = -8.683e-01;
    }
    if( w==41 )
    {
        r = -9.328e-01;
    }
    if( w==40 )
    {
        r = -1.001e+00;
    }
    if( w==39 )
    {
        r = -1.072e+00;
    }
    if( w==38 )
    {
        r = -1.146e+00;
    }
    if( w==37 )
    {
        r = -1.224e+00;
    }
    if( w==36 )
    {
        r = -1.306e+00;
    }
    if( w==35 )
    {
        r = -1.392e+00;
    }
    if( w==34 )
    {
        r = -1.481e+00;
    }
    if( w==33 )
    {
        r = -1.574e+00;
    }
    if( w==32 )
    {
        r = -1.672e+00;
    }
    if( w==31 )
    {
        r = -1.773e+00;
    }
    if( w==30 )
    {
        r = -1.879e+00;
    }
    if( w==29 )
    {
        r = -1.990e+00;
    }
    if( w==28 )
    {
        r = -2.104e+00;
    }
    if( w==27 )
    {
        r = -2.224e+00;
    }
    if( w==26 )
    {
        r = -2.349e+00;
    }
    if( w==25 )
    {
        r = -2.479e+00;
    }
    if( w==24 )
    {
        r = -2.614e+00;
    }
    if( w==23 )
    {
        r = -2.755e+00;
    }
    if( w==22 )
    {
        r = -2.902e+00;
    }
    if( w==21 )
    {
        r = -3.055e+00;
    }
    if( w==20 )
    {
        r = -3.215e+00;
    }
    if( w==19 )
    {
        r = -3.380e+00;
    }
    if( w==18 )
    {
        r = -3.551e+00;
    }
    if( w==17 )
    {
        r = -3.733e+00;
    }
    if( w==16 )
    {
        r = -3.917e+00;
    }
    if( w==15 )
    {
        r = -4.113e+00;
    }
    if( w==14 )
    {
        r = -4.320e+00;
    }
    if( w==13 )
    {
        r = -4.534e+00;
    }
    if( w==12 )
    {
        r = -4.762e+00;
    }
    if( w==11 )
    {
        r = -5.004e+00;
    }
    if( w==10 )
    {
        r = -5.250e+00;
    }
    if( w==9 )
    {
        r = -5.514e+00;
    }
    if( w==8 )
    {
        r = -5.792e+00;
    }
    if( w==7 )
    {
        r = -6.066e+00;
    }
    if( w==6 )
    {
        r = -6.372e+00;
    }
    if( w==5 )
    {
        r = -6.708e+00;
    }
    if( w==4 )
    {
        r = -7.065e+00;
    }
    if( w==3 )
    {
        r = -7.401e+00;
    }
    if( w==2 )
    {
        r = -7.912e+00;
    }
    if( w==1 )
    {
        r = -8.318e+00;
    }
    if( w<=0 )
    {
        r = -9.011e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 14)
*************************************************************************/
static double wsr_w14(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-1.592953e+01*s+5.250000e+01, _state);
    if( w>=52 )
    {
        r = -6.931e-01;
    }
    if( w==51 )
    {
        r = -7.428e-01;
    }
    if( w==50 )
    {
        r = -7.950e-01;
    }
    if( w==49 )
    {
        r = -8.495e-01;
    }
    if( w==48 )
    {
        r = -9.067e-01;
    }
    if( w==47 )
    {
        r = -9.664e-01;
    }
    if( w==46 )
    {
        r = -1.029e+00;
    }
    if( w==45 )
    {
        r = -1.094e+00;
    }
    if( w==44 )
    {
        r = -1.162e+00;
    }
    if( w==43 )
    {
        r = -1.233e+00;
    }
    if( w==42 )
    {
        r = -1.306e+00;
    }
    if( w==41 )
    {
        r = -1.383e+00;
    }
    if( w==40 )
    {
        r = -1.463e+00;
    }
    if( w==39 )
    {
        r = -1.546e+00;
    }
    if( w==38 )
    {
        r = -1.632e+00;
    }
    if( w==37 )
    {
        r = -1.722e+00;
    }
    if( w==36 )
    {
        r = -1.815e+00;
    }
    if( w==35 )
    {
        r = -1.911e+00;
    }
    if( w==34 )
    {
        r = -2.011e+00;
    }
    if( w==33 )
    {
        r = -2.115e+00;
    }
    if( w==32 )
    {
        r = -2.223e+00;
    }
    if( w==31 )
    {
        r = -2.334e+00;
    }
    if( w==30 )
    {
        r = -2.450e+00;
    }
    if( w==29 )
    {
        r = -2.570e+00;
    }
    if( w==28 )
    {
        r = -2.694e+00;
    }
    if( w==27 )
    {
        r = -2.823e+00;
    }
    if( w==26 )
    {
        r = -2.956e+00;
    }
    if( w==25 )
    {
        r = -3.095e+00;
    }
    if( w==24 )
    {
        r = -3.238e+00;
    }
    if( w==23 )
    {
        r = -3.387e+00;
    }
    if( w==22 )
    {
        r = -3.541e+00;
    }
    if( w==21 )
    {
        r = -3.700e+00;
    }
    if( w==20 )
    {
        r = -3.866e+00;
    }
    if( w==19 )
    {
        r = -4.038e+00;
    }
    if( w==18 )
    {
        r = -4.215e+00;
    }
    if( w==17 )
    {
        r = -4.401e+00;
    }
    if( w==16 )
    {
        r = -4.592e+00;
    }
    if( w==15 )
    {
        r = -4.791e+00;
    }
    if( w==14 )
    {
        r = -5.004e+00;
    }
    if( w==13 )
    {
        r = -5.227e+00;
    }
    if( w==12 )
    {
        r = -5.456e+00;
    }
    if( w==11 )
    {
        r = -5.697e+00;
    }
    if( w==10 )
    {
        r = -5.943e+00;
    }
    if( w==9 )
    {
        r = -6.208e+00;
    }
    if( w==8 )
    {
        r = -6.485e+00;
    }
    if( w==7 )
    {
        r = -6.760e+00;
    }
    if( w==6 )
    {
        r = -7.065e+00;
    }
    if( w==5 )
    {
        r = -7.401e+00;
    }
    if( w==4 )
    {
        r = -7.758e+00;
    }
    if( w==3 )
    {
        r = -8.095e+00;
    }
    if( w==2 )
    {
        r = -8.605e+00;
    }
    if( w==1 )
    {
        r = -9.011e+00;
    }
    if( w<=0 )
    {
        r = -9.704e+00;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 15)
*************************************************************************/
static double wsr_w15(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-1.760682e+01*s+6.000000e+01, _state);
    if( w>=60 )
    {
        r = -6.714e-01;
    }
    if( w==59 )
    {
        r = -7.154e-01;
    }
    if( w==58 )
    {
        r = -7.613e-01;
    }
    if( w==57 )
    {
        r = -8.093e-01;
    }
    if( w==56 )
    {
        r = -8.593e-01;
    }
    if( w==55 )
    {
        r = -9.114e-01;
    }
    if( w==54 )
    {
        r = -9.656e-01;
    }
    if( w==53 )
    {
        r = -1.022e+00;
    }
    if( w==52 )
    {
        r = -1.081e+00;
    }
    if( w==51 )
    {
        r = -1.142e+00;
    }
    if( w==50 )
    {
        r = -1.205e+00;
    }
    if( w==49 )
    {
        r = -1.270e+00;
    }
    if( w==48 )
    {
        r = -1.339e+00;
    }
    if( w==47 )
    {
        r = -1.409e+00;
    }
    if( w==46 )
    {
        r = -1.482e+00;
    }
    if( w==45 )
    {
        r = -1.558e+00;
    }
    if( w==44 )
    {
        r = -1.636e+00;
    }
    if( w==43 )
    {
        r = -1.717e+00;
    }
    if( w==42 )
    {
        r = -1.801e+00;
    }
    if( w==41 )
    {
        r = -1.888e+00;
    }
    if( w==40 )
    {
        r = -1.977e+00;
    }
    if( w==39 )
    {
        r = -2.070e+00;
    }
    if( w==38 )
    {
        r = -2.166e+00;
    }
    if( w==37 )
    {
        r = -2.265e+00;
    }
    if( w==36 )
    {
        r = -2.366e+00;
    }
    if( w==35 )
    {
        r = -2.472e+00;
    }
    if( w==34 )
    {
        r = -2.581e+00;
    }
    if( w==33 )
    {
        r = -2.693e+00;
    }
    if( w==32 )
    {
        r = -2.809e+00;
    }
    if( w==31 )
    {
        r = -2.928e+00;
    }
    if( w==30 )
    {
        r = -3.051e+00;
    }
    if( w==29 )
    {
        r = -3.179e+00;
    }
    if( w==28 )
    {
        r = -3.310e+00;
    }
    if( w==27 )
    {
        r = -3.446e+00;
    }
    if( w==26 )
    {
        r = -3.587e+00;
    }
    if( w==25 )
    {
        r = -3.732e+00;
    }
    if( w==24 )
    {
        r = -3.881e+00;
    }
    if( w==23 )
    {
        r = -4.036e+00;
    }
    if( w==22 )
    {
        r = -4.195e+00;
    }
    if( w==21 )
    {
        r = -4.359e+00;
    }
    if( w==20 )
    {
        r = -4.531e+00;
    }
    if( w==19 )
    {
        r = -4.707e+00;
    }
    if( w==18 )
    {
        r = -4.888e+00;
    }
    if( w==17 )
    {
        r = -5.079e+00;
    }
    if( w==16 )
    {
        r = -5.273e+00;
    }
    if( w==15 )
    {
        r = -5.477e+00;
    }
    if( w==14 )
    {
        r = -5.697e+00;
    }
    if( w==13 )
    {
        r = -5.920e+00;
    }
    if( w==12 )
    {
        r = -6.149e+00;
    }
    if( w==11 )
    {
        r = -6.390e+00;
    }
    if( w==10 )
    {
        r = -6.636e+00;
    }
    if( w==9 )
    {
        r = -6.901e+00;
    }
    if( w==8 )
    {
        r = -7.178e+00;
    }
    if( w==7 )
    {
        r = -7.453e+00;
    }
    if( w==6 )
    {
        r = -7.758e+00;
    }
    if( w==5 )
    {
        r = -8.095e+00;
    }
    if( w==4 )
    {
        r = -8.451e+00;
    }
    if( w==3 )
    {
        r = -8.788e+00;
    }
    if( w==2 )
    {
        r = -9.299e+00;
    }
    if( w==1 )
    {
        r = -9.704e+00;
    }
    if( w<=0 )
    {
        r = -1.040e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 16)
*************************************************************************/
static double wsr_w16(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-1.933908e+01*s+6.800000e+01, _state);
    if( w>=68 )
    {
        r = -6.733e-01;
    }
    if( w==67 )
    {
        r = -7.134e-01;
    }
    if( w==66 )
    {
        r = -7.551e-01;
    }
    if( w==65 )
    {
        r = -7.986e-01;
    }
    if( w==64 )
    {
        r = -8.437e-01;
    }
    if( w==63 )
    {
        r = -8.905e-01;
    }
    if( w==62 )
    {
        r = -9.391e-01;
    }
    if( w==61 )
    {
        r = -9.895e-01;
    }
    if( w==60 )
    {
        r = -1.042e+00;
    }
    if( w==59 )
    {
        r = -1.096e+00;
    }
    if( w==58 )
    {
        r = -1.152e+00;
    }
    if( w==57 )
    {
        r = -1.210e+00;
    }
    if( w==56 )
    {
        r = -1.270e+00;
    }
    if( w==55 )
    {
        r = -1.331e+00;
    }
    if( w==54 )
    {
        r = -1.395e+00;
    }
    if( w==53 )
    {
        r = -1.462e+00;
    }
    if( w==52 )
    {
        r = -1.530e+00;
    }
    if( w==51 )
    {
        r = -1.600e+00;
    }
    if( w==50 )
    {
        r = -1.673e+00;
    }
    if( w==49 )
    {
        r = -1.748e+00;
    }
    if( w==48 )
    {
        r = -1.825e+00;
    }
    if( w==47 )
    {
        r = -1.904e+00;
    }
    if( w==46 )
    {
        r = -1.986e+00;
    }
    if( w==45 )
    {
        r = -2.071e+00;
    }
    if( w==44 )
    {
        r = -2.158e+00;
    }
    if( w==43 )
    {
        r = -2.247e+00;
    }
    if( w==42 )
    {
        r = -2.339e+00;
    }
    if( w==41 )
    {
        r = -2.434e+00;
    }
    if( w==40 )
    {
        r = -2.532e+00;
    }
    if( w==39 )
    {
        r = -2.632e+00;
    }
    if( w==38 )
    {
        r = -2.735e+00;
    }
    if( w==37 )
    {
        r = -2.842e+00;
    }
    if( w==36 )
    {
        r = -2.951e+00;
    }
    if( w==35 )
    {
        r = -3.064e+00;
    }
    if( w==34 )
    {
        r = -3.179e+00;
    }
    if( w==33 )
    {
        r = -3.298e+00;
    }
    if( w==32 )
    {
        r = -3.420e+00;
    }
    if( w==31 )
    {
        r = -3.546e+00;
    }
    if( w==30 )
    {
        r = -3.676e+00;
    }
    if( w==29 )
    {
        r = -3.810e+00;
    }
    if( w==28 )
    {
        r = -3.947e+00;
    }
    if( w==27 )
    {
        r = -4.088e+00;
    }
    if( w==26 )
    {
        r = -4.234e+00;
    }
    if( w==25 )
    {
        r = -4.383e+00;
    }
    if( w==24 )
    {
        r = -4.538e+00;
    }
    if( w==23 )
    {
        r = -4.697e+00;
    }
    if( w==22 )
    {
        r = -4.860e+00;
    }
    if( w==21 )
    {
        r = -5.029e+00;
    }
    if( w==20 )
    {
        r = -5.204e+00;
    }
    if( w==19 )
    {
        r = -5.383e+00;
    }
    if( w==18 )
    {
        r = -5.569e+00;
    }
    if( w==17 )
    {
        r = -5.762e+00;
    }
    if( w==16 )
    {
        r = -5.960e+00;
    }
    if( w==15 )
    {
        r = -6.170e+00;
    }
    if( w==14 )
    {
        r = -6.390e+00;
    }
    if( w==13 )
    {
        r = -6.613e+00;
    }
    if( w==12 )
    {
        r = -6.842e+00;
    }
    if( w==11 )
    {
        r = -7.083e+00;
    }
    if( w==10 )
    {
        r = -7.329e+00;
    }
    if( w==9 )
    {
        r = -7.594e+00;
    }
    if( w==8 )
    {
        r = -7.871e+00;
    }
    if( w==7 )
    {
        r = -8.146e+00;
    }
    if( w==6 )
    {
        r = -8.451e+00;
    }
    if( w==5 )
    {
        r = -8.788e+00;
    }
    if( w==4 )
    {
        r = -9.144e+00;
    }
    if( w==3 )
    {
        r = -9.481e+00;
    }
    if( w==2 )
    {
        r = -9.992e+00;
    }
    if( w==1 )
    {
        r = -1.040e+01;
    }
    if( w<=0 )
    {
        r = -1.109e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 17)
*************************************************************************/
static double wsr_w17(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-2.112463e+01*s+7.650000e+01, _state);
    if( w>=76 )
    {
        r = -6.931e-01;
    }
    if( w==75 )
    {
        r = -7.306e-01;
    }
    if( w==74 )
    {
        r = -7.695e-01;
    }
    if( w==73 )
    {
        r = -8.097e-01;
    }
    if( w==72 )
    {
        r = -8.514e-01;
    }
    if( w==71 )
    {
        r = -8.946e-01;
    }
    if( w==70 )
    {
        r = -9.392e-01;
    }
    if( w==69 )
    {
        r = -9.853e-01;
    }
    if( w==68 )
    {
        r = -1.033e+00;
    }
    if( w==67 )
    {
        r = -1.082e+00;
    }
    if( w==66 )
    {
        r = -1.133e+00;
    }
    if( w==65 )
    {
        r = -1.185e+00;
    }
    if( w==64 )
    {
        r = -1.240e+00;
    }
    if( w==63 )
    {
        r = -1.295e+00;
    }
    if( w==62 )
    {
        r = -1.353e+00;
    }
    if( w==61 )
    {
        r = -1.412e+00;
    }
    if( w==60 )
    {
        r = -1.473e+00;
    }
    if( w==59 )
    {
        r = -1.536e+00;
    }
    if( w==58 )
    {
        r = -1.600e+00;
    }
    if( w==57 )
    {
        r = -1.666e+00;
    }
    if( w==56 )
    {
        r = -1.735e+00;
    }
    if( w==55 )
    {
        r = -1.805e+00;
    }
    if( w==54 )
    {
        r = -1.877e+00;
    }
    if( w==53 )
    {
        r = -1.951e+00;
    }
    if( w==52 )
    {
        r = -2.028e+00;
    }
    if( w==51 )
    {
        r = -2.106e+00;
    }
    if( w==50 )
    {
        r = -2.186e+00;
    }
    if( w==49 )
    {
        r = -2.269e+00;
    }
    if( w==48 )
    {
        r = -2.353e+00;
    }
    if( w==47 )
    {
        r = -2.440e+00;
    }
    if( w==46 )
    {
        r = -2.530e+00;
    }
    if( w==45 )
    {
        r = -2.621e+00;
    }
    if( w==44 )
    {
        r = -2.715e+00;
    }
    if( w==43 )
    {
        r = -2.812e+00;
    }
    if( w==42 )
    {
        r = -2.911e+00;
    }
    if( w==41 )
    {
        r = -3.012e+00;
    }
    if( w==40 )
    {
        r = -3.116e+00;
    }
    if( w==39 )
    {
        r = -3.223e+00;
    }
    if( w==38 )
    {
        r = -3.332e+00;
    }
    if( w==37 )
    {
        r = -3.445e+00;
    }
    if( w==36 )
    {
        r = -3.560e+00;
    }
    if( w==35 )
    {
        r = -3.678e+00;
    }
    if( w==34 )
    {
        r = -3.799e+00;
    }
    if( w==33 )
    {
        r = -3.924e+00;
    }
    if( w==32 )
    {
        r = -4.052e+00;
    }
    if( w==31 )
    {
        r = -4.183e+00;
    }
    if( w==30 )
    {
        r = -4.317e+00;
    }
    if( w==29 )
    {
        r = -4.456e+00;
    }
    if( w==28 )
    {
        r = -4.597e+00;
    }
    if( w==27 )
    {
        r = -4.743e+00;
    }
    if( w==26 )
    {
        r = -4.893e+00;
    }
    if( w==25 )
    {
        r = -5.047e+00;
    }
    if( w==24 )
    {
        r = -5.204e+00;
    }
    if( w==23 )
    {
        r = -5.367e+00;
    }
    if( w==22 )
    {
        r = -5.534e+00;
    }
    if( w==21 )
    {
        r = -5.706e+00;
    }
    if( w==20 )
    {
        r = -5.884e+00;
    }
    if( w==19 )
    {
        r = -6.066e+00;
    }
    if( w==18 )
    {
        r = -6.254e+00;
    }
    if( w==17 )
    {
        r = -6.451e+00;
    }
    if( w==16 )
    {
        r = -6.654e+00;
    }
    if( w==15 )
    {
        r = -6.864e+00;
    }
    if( w==14 )
    {
        r = -7.083e+00;
    }
    if( w==13 )
    {
        r = -7.306e+00;
    }
    if( w==12 )
    {
        r = -7.535e+00;
    }
    if( w==11 )
    {
        r = -7.776e+00;
    }
    if( w==10 )
    {
        r = -8.022e+00;
    }
    if( w==9 )
    {
        r = -8.287e+00;
    }
    if( w==8 )
    {
        r = -8.565e+00;
    }
    if( w==7 )
    {
        r = -8.839e+00;
    }
    if( w==6 )
    {
        r = -9.144e+00;
    }
    if( w==5 )
    {
        r = -9.481e+00;
    }
    if( w==4 )
    {
        r = -9.838e+00;
    }
    if( w==3 )
    {
        r = -1.017e+01;
    }
    if( w==2 )
    {
        r = -1.068e+01;
    }
    if( w==1 )
    {
        r = -1.109e+01;
    }
    if( w<=0 )
    {
        r = -1.178e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 18)
*************************************************************************/
static double wsr_w18(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-2.296193e+01*s+8.550000e+01, _state);
    if( w>=85 )
    {
        r = -6.931e-01;
    }
    if( w==84 )
    {
        r = -7.276e-01;
    }
    if( w==83 )
    {
        r = -7.633e-01;
    }
    if( w==82 )
    {
        r = -8.001e-01;
    }
    if( w==81 )
    {
        r = -8.381e-01;
    }
    if( w==80 )
    {
        r = -8.774e-01;
    }
    if( w==79 )
    {
        r = -9.179e-01;
    }
    if( w==78 )
    {
        r = -9.597e-01;
    }
    if( w==77 )
    {
        r = -1.003e+00;
    }
    if( w==76 )
    {
        r = -1.047e+00;
    }
    if( w==75 )
    {
        r = -1.093e+00;
    }
    if( w==74 )
    {
        r = -1.140e+00;
    }
    if( w==73 )
    {
        r = -1.188e+00;
    }
    if( w==72 )
    {
        r = -1.238e+00;
    }
    if( w==71 )
    {
        r = -1.289e+00;
    }
    if( w==70 )
    {
        r = -1.342e+00;
    }
    if( w==69 )
    {
        r = -1.396e+00;
    }
    if( w==68 )
    {
        r = -1.452e+00;
    }
    if( w==67 )
    {
        r = -1.509e+00;
    }
    if( w==66 )
    {
        r = -1.568e+00;
    }
    if( w==65 )
    {
        r = -1.628e+00;
    }
    if( w==64 )
    {
        r = -1.690e+00;
    }
    if( w==63 )
    {
        r = -1.753e+00;
    }
    if( w==62 )
    {
        r = -1.818e+00;
    }
    if( w==61 )
    {
        r = -1.885e+00;
    }
    if( w==60 )
    {
        r = -1.953e+00;
    }
    if( w==59 )
    {
        r = -2.023e+00;
    }
    if( w==58 )
    {
        r = -2.095e+00;
    }
    if( w==57 )
    {
        r = -2.168e+00;
    }
    if( w==56 )
    {
        r = -2.244e+00;
    }
    if( w==55 )
    {
        r = -2.321e+00;
    }
    if( w==54 )
    {
        r = -2.400e+00;
    }
    if( w==53 )
    {
        r = -2.481e+00;
    }
    if( w==52 )
    {
        r = -2.564e+00;
    }
    if( w==51 )
    {
        r = -2.648e+00;
    }
    if( w==50 )
    {
        r = -2.735e+00;
    }
    if( w==49 )
    {
        r = -2.824e+00;
    }
    if( w==48 )
    {
        r = -2.915e+00;
    }
    if( w==47 )
    {
        r = -3.008e+00;
    }
    if( w==46 )
    {
        r = -3.104e+00;
    }
    if( w==45 )
    {
        r = -3.201e+00;
    }
    if( w==44 )
    {
        r = -3.301e+00;
    }
    if( w==43 )
    {
        r = -3.403e+00;
    }
    if( w==42 )
    {
        r = -3.508e+00;
    }
    if( w==41 )
    {
        r = -3.615e+00;
    }
    if( w==40 )
    {
        r = -3.724e+00;
    }
    if( w==39 )
    {
        r = -3.836e+00;
    }
    if( w==38 )
    {
        r = -3.950e+00;
    }
    if( w==37 )
    {
        r = -4.068e+00;
    }
    if( w==36 )
    {
        r = -4.188e+00;
    }
    if( w==35 )
    {
        r = -4.311e+00;
    }
    if( w==34 )
    {
        r = -4.437e+00;
    }
    if( w==33 )
    {
        r = -4.565e+00;
    }
    if( w==32 )
    {
        r = -4.698e+00;
    }
    if( w==31 )
    {
        r = -4.833e+00;
    }
    if( w==30 )
    {
        r = -4.971e+00;
    }
    if( w==29 )
    {
        r = -5.113e+00;
    }
    if( w==28 )
    {
        r = -5.258e+00;
    }
    if( w==27 )
    {
        r = -5.408e+00;
    }
    if( w==26 )
    {
        r = -5.561e+00;
    }
    if( w==25 )
    {
        r = -5.717e+00;
    }
    if( w==24 )
    {
        r = -5.878e+00;
    }
    if( w==23 )
    {
        r = -6.044e+00;
    }
    if( w==22 )
    {
        r = -6.213e+00;
    }
    if( w==21 )
    {
        r = -6.388e+00;
    }
    if( w==20 )
    {
        r = -6.569e+00;
    }
    if( w==19 )
    {
        r = -6.753e+00;
    }
    if( w==18 )
    {
        r = -6.943e+00;
    }
    if( w==17 )
    {
        r = -7.144e+00;
    }
    if( w==16 )
    {
        r = -7.347e+00;
    }
    if( w==15 )
    {
        r = -7.557e+00;
    }
    if( w==14 )
    {
        r = -7.776e+00;
    }
    if( w==13 )
    {
        r = -7.999e+00;
    }
    if( w==12 )
    {
        r = -8.228e+00;
    }
    if( w==11 )
    {
        r = -8.469e+00;
    }
    if( w==10 )
    {
        r = -8.715e+00;
    }
    if( w==9 )
    {
        r = -8.980e+00;
    }
    if( w==8 )
    {
        r = -9.258e+00;
    }
    if( w==7 )
    {
        r = -9.532e+00;
    }
    if( w==6 )
    {
        r = -9.838e+00;
    }
    if( w==5 )
    {
        r = -1.017e+01;
    }
    if( w==4 )
    {
        r = -1.053e+01;
    }
    if( w==3 )
    {
        r = -1.087e+01;
    }
    if( w==2 )
    {
        r = -1.138e+01;
    }
    if( w==1 )
    {
        r = -1.178e+01;
    }
    if( w<=0 )
    {
        r = -1.248e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 19)
*************************************************************************/
static double wsr_w19(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-2.484955e+01*s+9.500000e+01, _state);
    if( w>=95 )
    {
        r = -6.776e-01;
    }
    if( w==94 )
    {
        r = -7.089e-01;
    }
    if( w==93 )
    {
        r = -7.413e-01;
    }
    if( w==92 )
    {
        r = -7.747e-01;
    }
    if( w==91 )
    {
        r = -8.090e-01;
    }
    if( w==90 )
    {
        r = -8.445e-01;
    }
    if( w==89 )
    {
        r = -8.809e-01;
    }
    if( w==88 )
    {
        r = -9.185e-01;
    }
    if( w==87 )
    {
        r = -9.571e-01;
    }
    if( w==86 )
    {
        r = -9.968e-01;
    }
    if( w==85 )
    {
        r = -1.038e+00;
    }
    if( w==84 )
    {
        r = -1.080e+00;
    }
    if( w==83 )
    {
        r = -1.123e+00;
    }
    if( w==82 )
    {
        r = -1.167e+00;
    }
    if( w==81 )
    {
        r = -1.213e+00;
    }
    if( w==80 )
    {
        r = -1.259e+00;
    }
    if( w==79 )
    {
        r = -1.307e+00;
    }
    if( w==78 )
    {
        r = -1.356e+00;
    }
    if( w==77 )
    {
        r = -1.407e+00;
    }
    if( w==76 )
    {
        r = -1.458e+00;
    }
    if( w==75 )
    {
        r = -1.511e+00;
    }
    if( w==74 )
    {
        r = -1.565e+00;
    }
    if( w==73 )
    {
        r = -1.621e+00;
    }
    if( w==72 )
    {
        r = -1.678e+00;
    }
    if( w==71 )
    {
        r = -1.736e+00;
    }
    if( w==70 )
    {
        r = -1.796e+00;
    }
    if( w==69 )
    {
        r = -1.857e+00;
    }
    if( w==68 )
    {
        r = -1.919e+00;
    }
    if( w==67 )
    {
        r = -1.983e+00;
    }
    if( w==66 )
    {
        r = -2.048e+00;
    }
    if( w==65 )
    {
        r = -2.115e+00;
    }
    if( w==64 )
    {
        r = -2.183e+00;
    }
    if( w==63 )
    {
        r = -2.253e+00;
    }
    if( w==62 )
    {
        r = -2.325e+00;
    }
    if( w==61 )
    {
        r = -2.398e+00;
    }
    if( w==60 )
    {
        r = -2.472e+00;
    }
    if( w==59 )
    {
        r = -2.548e+00;
    }
    if( w==58 )
    {
        r = -2.626e+00;
    }
    if( w==57 )
    {
        r = -2.706e+00;
    }
    if( w==56 )
    {
        r = -2.787e+00;
    }
    if( w==55 )
    {
        r = -2.870e+00;
    }
    if( w==54 )
    {
        r = -2.955e+00;
    }
    if( w==53 )
    {
        r = -3.042e+00;
    }
    if( w==52 )
    {
        r = -3.130e+00;
    }
    if( w==51 )
    {
        r = -3.220e+00;
    }
    if( w==50 )
    {
        r = -3.313e+00;
    }
    if( w==49 )
    {
        r = -3.407e+00;
    }
    if( w==48 )
    {
        r = -3.503e+00;
    }
    if( w==47 )
    {
        r = -3.601e+00;
    }
    if( w==46 )
    {
        r = -3.702e+00;
    }
    if( w==45 )
    {
        r = -3.804e+00;
    }
    if( w==44 )
    {
        r = -3.909e+00;
    }
    if( w==43 )
    {
        r = -4.015e+00;
    }
    if( w==42 )
    {
        r = -4.125e+00;
    }
    if( w==41 )
    {
        r = -4.236e+00;
    }
    if( w==40 )
    {
        r = -4.350e+00;
    }
    if( w==39 )
    {
        r = -4.466e+00;
    }
    if( w==38 )
    {
        r = -4.585e+00;
    }
    if( w==37 )
    {
        r = -4.706e+00;
    }
    if( w==36 )
    {
        r = -4.830e+00;
    }
    if( w==35 )
    {
        r = -4.957e+00;
    }
    if( w==34 )
    {
        r = -5.086e+00;
    }
    if( w==33 )
    {
        r = -5.219e+00;
    }
    if( w==32 )
    {
        r = -5.355e+00;
    }
    if( w==31 )
    {
        r = -5.493e+00;
    }
    if( w==30 )
    {
        r = -5.634e+00;
    }
    if( w==29 )
    {
        r = -5.780e+00;
    }
    if( w==28 )
    {
        r = -5.928e+00;
    }
    if( w==27 )
    {
        r = -6.080e+00;
    }
    if( w==26 )
    {
        r = -6.235e+00;
    }
    if( w==25 )
    {
        r = -6.394e+00;
    }
    if( w==24 )
    {
        r = -6.558e+00;
    }
    if( w==23 )
    {
        r = -6.726e+00;
    }
    if( w==22 )
    {
        r = -6.897e+00;
    }
    if( w==21 )
    {
        r = -7.074e+00;
    }
    if( w==20 )
    {
        r = -7.256e+00;
    }
    if( w==19 )
    {
        r = -7.443e+00;
    }
    if( w==18 )
    {
        r = -7.636e+00;
    }
    if( w==17 )
    {
        r = -7.837e+00;
    }
    if( w==16 )
    {
        r = -8.040e+00;
    }
    if( w==15 )
    {
        r = -8.250e+00;
    }
    if( w==14 )
    {
        r = -8.469e+00;
    }
    if( w==13 )
    {
        r = -8.692e+00;
    }
    if( w==12 )
    {
        r = -8.921e+00;
    }
    if( w==11 )
    {
        r = -9.162e+00;
    }
    if( w==10 )
    {
        r = -9.409e+00;
    }
    if( w==9 )
    {
        r = -9.673e+00;
    }
    if( w==8 )
    {
        r = -9.951e+00;
    }
    if( w==7 )
    {
        r = -1.023e+01;
    }
    if( w==6 )
    {
        r = -1.053e+01;
    }
    if( w==5 )
    {
        r = -1.087e+01;
    }
    if( w==4 )
    {
        r = -1.122e+01;
    }
    if( w==3 )
    {
        r = -1.156e+01;
    }
    if( w==2 )
    {
        r = -1.207e+01;
    }
    if( w==1 )
    {
        r = -1.248e+01;
    }
    if( w<=0 )
    {
        r = -1.317e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 20)
*************************************************************************/
static double wsr_w20(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-2.678619e+01*s+1.050000e+02, _state);
    if( w>=105 )
    {
        r = -6.787e-01;
    }
    if( w==104 )
    {
        r = -7.078e-01;
    }
    if( w==103 )
    {
        r = -7.378e-01;
    }
    if( w==102 )
    {
        r = -7.686e-01;
    }
    if( w==101 )
    {
        r = -8.004e-01;
    }
    if( w==100 )
    {
        r = -8.330e-01;
    }
    if( w==99 )
    {
        r = -8.665e-01;
    }
    if( w==98 )
    {
        r = -9.010e-01;
    }
    if( w==97 )
    {
        r = -9.363e-01;
    }
    if( w==96 )
    {
        r = -9.726e-01;
    }
    if( w==95 )
    {
        r = -1.010e+00;
    }
    if( w==94 )
    {
        r = -1.048e+00;
    }
    if( w==93 )
    {
        r = -1.087e+00;
    }
    if( w==92 )
    {
        r = -1.128e+00;
    }
    if( w==91 )
    {
        r = -1.169e+00;
    }
    if( w==90 )
    {
        r = -1.211e+00;
    }
    if( w==89 )
    {
        r = -1.254e+00;
    }
    if( w==88 )
    {
        r = -1.299e+00;
    }
    if( w==87 )
    {
        r = -1.344e+00;
    }
    if( w==86 )
    {
        r = -1.390e+00;
    }
    if( w==85 )
    {
        r = -1.438e+00;
    }
    if( w==84 )
    {
        r = -1.486e+00;
    }
    if( w==83 )
    {
        r = -1.536e+00;
    }
    if( w==82 )
    {
        r = -1.587e+00;
    }
    if( w==81 )
    {
        r = -1.639e+00;
    }
    if( w==80 )
    {
        r = -1.692e+00;
    }
    if( w==79 )
    {
        r = -1.746e+00;
    }
    if( w==78 )
    {
        r = -1.802e+00;
    }
    if( w==77 )
    {
        r = -1.859e+00;
    }
    if( w==76 )
    {
        r = -1.916e+00;
    }
    if( w==75 )
    {
        r = -1.976e+00;
    }
    if( w==74 )
    {
        r = -2.036e+00;
    }
    if( w==73 )
    {
        r = -2.098e+00;
    }
    if( w==72 )
    {
        r = -2.161e+00;
    }
    if( w==71 )
    {
        r = -2.225e+00;
    }
    if( w==70 )
    {
        r = -2.290e+00;
    }
    if( w==69 )
    {
        r = -2.357e+00;
    }
    if( w==68 )
    {
        r = -2.426e+00;
    }
    if( w==67 )
    {
        r = -2.495e+00;
    }
    if( w==66 )
    {
        r = -2.566e+00;
    }
    if( w==65 )
    {
        r = -2.639e+00;
    }
    if( w==64 )
    {
        r = -2.713e+00;
    }
    if( w==63 )
    {
        r = -2.788e+00;
    }
    if( w==62 )
    {
        r = -2.865e+00;
    }
    if( w==61 )
    {
        r = -2.943e+00;
    }
    if( w==60 )
    {
        r = -3.023e+00;
    }
    if( w==59 )
    {
        r = -3.104e+00;
    }
    if( w==58 )
    {
        r = -3.187e+00;
    }
    if( w==57 )
    {
        r = -3.272e+00;
    }
    if( w==56 )
    {
        r = -3.358e+00;
    }
    if( w==55 )
    {
        r = -3.446e+00;
    }
    if( w==54 )
    {
        r = -3.536e+00;
    }
    if( w==53 )
    {
        r = -3.627e+00;
    }
    if( w==52 )
    {
        r = -3.721e+00;
    }
    if( w==51 )
    {
        r = -3.815e+00;
    }
    if( w==50 )
    {
        r = -3.912e+00;
    }
    if( w==49 )
    {
        r = -4.011e+00;
    }
    if( w==48 )
    {
        r = -4.111e+00;
    }
    if( w==47 )
    {
        r = -4.214e+00;
    }
    if( w==46 )
    {
        r = -4.318e+00;
    }
    if( w==45 )
    {
        r = -4.425e+00;
    }
    if( w==44 )
    {
        r = -4.534e+00;
    }
    if( w==43 )
    {
        r = -4.644e+00;
    }
    if( w==42 )
    {
        r = -4.757e+00;
    }
    if( w==41 )
    {
        r = -4.872e+00;
    }
    if( w==40 )
    {
        r = -4.990e+00;
    }
    if( w==39 )
    {
        r = -5.109e+00;
    }
    if( w==38 )
    {
        r = -5.232e+00;
    }
    if( w==37 )
    {
        r = -5.356e+00;
    }
    if( w==36 )
    {
        r = -5.484e+00;
    }
    if( w==35 )
    {
        r = -5.614e+00;
    }
    if( w==34 )
    {
        r = -5.746e+00;
    }
    if( w==33 )
    {
        r = -5.882e+00;
    }
    if( w==32 )
    {
        r = -6.020e+00;
    }
    if( w==31 )
    {
        r = -6.161e+00;
    }
    if( w==30 )
    {
        r = -6.305e+00;
    }
    if( w==29 )
    {
        r = -6.453e+00;
    }
    if( w==28 )
    {
        r = -6.603e+00;
    }
    if( w==27 )
    {
        r = -6.757e+00;
    }
    if( w==26 )
    {
        r = -6.915e+00;
    }
    if( w==25 )
    {
        r = -7.076e+00;
    }
    if( w==24 )
    {
        r = -7.242e+00;
    }
    if( w==23 )
    {
        r = -7.411e+00;
    }
    if( w==22 )
    {
        r = -7.584e+00;
    }
    if( w==21 )
    {
        r = -7.763e+00;
    }
    if( w==20 )
    {
        r = -7.947e+00;
    }
    if( w==19 )
    {
        r = -8.136e+00;
    }
    if( w==18 )
    {
        r = -8.330e+00;
    }
    if( w==17 )
    {
        r = -8.530e+00;
    }
    if( w==16 )
    {
        r = -8.733e+00;
    }
    if( w==15 )
    {
        r = -8.943e+00;
    }
    if( w==14 )
    {
        r = -9.162e+00;
    }
    if( w==13 )
    {
        r = -9.386e+00;
    }
    if( w==12 )
    {
        r = -9.614e+00;
    }
    if( w==11 )
    {
        r = -9.856e+00;
    }
    if( w==10 )
    {
        r = -1.010e+01;
    }
    if( w==9 )
    {
        r = -1.037e+01;
    }
    if( w==8 )
    {
        r = -1.064e+01;
    }
    if( w==7 )
    {
        r = -1.092e+01;
    }
    if( w==6 )
    {
        r = -1.122e+01;
    }
    if( w==5 )
    {
        r = -1.156e+01;
    }
    if( w==4 )
    {
        r = -1.192e+01;
    }
    if( w==3 )
    {
        r = -1.225e+01;
    }
    if( w==2 )
    {
        r = -1.276e+01;
    }
    if( w==1 )
    {
        r = -1.317e+01;
    }
    if( w<=0 )
    {
        r = -1.386e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 21)
*************************************************************************/
static double wsr_w21(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-2.877064e+01*s+1.155000e+02, _state);
    if( w>=115 )
    {
        r = -6.931e-01;
    }
    if( w==114 )
    {
        r = -7.207e-01;
    }
    if( w==113 )
    {
        r = -7.489e-01;
    }
    if( w==112 )
    {
        r = -7.779e-01;
    }
    if( w==111 )
    {
        r = -8.077e-01;
    }
    if( w==110 )
    {
        r = -8.383e-01;
    }
    if( w==109 )
    {
        r = -8.697e-01;
    }
    if( w==108 )
    {
        r = -9.018e-01;
    }
    if( w==107 )
    {
        r = -9.348e-01;
    }
    if( w==106 )
    {
        r = -9.685e-01;
    }
    if( w==105 )
    {
        r = -1.003e+00;
    }
    if( w==104 )
    {
        r = -1.039e+00;
    }
    if( w==103 )
    {
        r = -1.075e+00;
    }
    if( w==102 )
    {
        r = -1.112e+00;
    }
    if( w==101 )
    {
        r = -1.150e+00;
    }
    if( w==100 )
    {
        r = -1.189e+00;
    }
    if( w==99 )
    {
        r = -1.229e+00;
    }
    if( w==98 )
    {
        r = -1.269e+00;
    }
    if( w==97 )
    {
        r = -1.311e+00;
    }
    if( w==96 )
    {
        r = -1.353e+00;
    }
    if( w==95 )
    {
        r = -1.397e+00;
    }
    if( w==94 )
    {
        r = -1.441e+00;
    }
    if( w==93 )
    {
        r = -1.486e+00;
    }
    if( w==92 )
    {
        r = -1.533e+00;
    }
    if( w==91 )
    {
        r = -1.580e+00;
    }
    if( w==90 )
    {
        r = -1.628e+00;
    }
    if( w==89 )
    {
        r = -1.677e+00;
    }
    if( w==88 )
    {
        r = -1.728e+00;
    }
    if( w==87 )
    {
        r = -1.779e+00;
    }
    if( w==86 )
    {
        r = -1.831e+00;
    }
    if( w==85 )
    {
        r = -1.884e+00;
    }
    if( w==84 )
    {
        r = -1.939e+00;
    }
    if( w==83 )
    {
        r = -1.994e+00;
    }
    if( w==82 )
    {
        r = -2.051e+00;
    }
    if( w==81 )
    {
        r = -2.108e+00;
    }
    if( w==80 )
    {
        r = -2.167e+00;
    }
    if( w==79 )
    {
        r = -2.227e+00;
    }
    if( w==78 )
    {
        r = -2.288e+00;
    }
    if( w==77 )
    {
        r = -2.350e+00;
    }
    if( w==76 )
    {
        r = -2.414e+00;
    }
    if( w==75 )
    {
        r = -2.478e+00;
    }
    if( w==74 )
    {
        r = -2.544e+00;
    }
    if( w==73 )
    {
        r = -2.611e+00;
    }
    if( w==72 )
    {
        r = -2.679e+00;
    }
    if( w==71 )
    {
        r = -2.748e+00;
    }
    if( w==70 )
    {
        r = -2.819e+00;
    }
    if( w==69 )
    {
        r = -2.891e+00;
    }
    if( w==68 )
    {
        r = -2.964e+00;
    }
    if( w==67 )
    {
        r = -3.039e+00;
    }
    if( w==66 )
    {
        r = -3.115e+00;
    }
    if( w==65 )
    {
        r = -3.192e+00;
    }
    if( w==64 )
    {
        r = -3.270e+00;
    }
    if( w==63 )
    {
        r = -3.350e+00;
    }
    if( w==62 )
    {
        r = -3.432e+00;
    }
    if( w==61 )
    {
        r = -3.515e+00;
    }
    if( w==60 )
    {
        r = -3.599e+00;
    }
    if( w==59 )
    {
        r = -3.685e+00;
    }
    if( w==58 )
    {
        r = -3.772e+00;
    }
    if( w==57 )
    {
        r = -3.861e+00;
    }
    if( w==56 )
    {
        r = -3.952e+00;
    }
    if( w==55 )
    {
        r = -4.044e+00;
    }
    if( w==54 )
    {
        r = -4.138e+00;
    }
    if( w==53 )
    {
        r = -4.233e+00;
    }
    if( w==52 )
    {
        r = -4.330e+00;
    }
    if( w==51 )
    {
        r = -4.429e+00;
    }
    if( w==50 )
    {
        r = -4.530e+00;
    }
    if( w==49 )
    {
        r = -4.632e+00;
    }
    if( w==48 )
    {
        r = -4.736e+00;
    }
    if( w==47 )
    {
        r = -4.842e+00;
    }
    if( w==46 )
    {
        r = -4.950e+00;
    }
    if( w==45 )
    {
        r = -5.060e+00;
    }
    if( w==44 )
    {
        r = -5.172e+00;
    }
    if( w==43 )
    {
        r = -5.286e+00;
    }
    if( w==42 )
    {
        r = -5.402e+00;
    }
    if( w==41 )
    {
        r = -5.520e+00;
    }
    if( w==40 )
    {
        r = -5.641e+00;
    }
    if( w==39 )
    {
        r = -5.763e+00;
    }
    if( w==38 )
    {
        r = -5.889e+00;
    }
    if( w==37 )
    {
        r = -6.016e+00;
    }
    if( w==36 )
    {
        r = -6.146e+00;
    }
    if( w==35 )
    {
        r = -6.278e+00;
    }
    if( w==34 )
    {
        r = -6.413e+00;
    }
    if( w==33 )
    {
        r = -6.551e+00;
    }
    if( w==32 )
    {
        r = -6.692e+00;
    }
    if( w==31 )
    {
        r = -6.835e+00;
    }
    if( w==30 )
    {
        r = -6.981e+00;
    }
    if( w==29 )
    {
        r = -7.131e+00;
    }
    if( w==28 )
    {
        r = -7.283e+00;
    }
    if( w==27 )
    {
        r = -7.439e+00;
    }
    if( w==26 )
    {
        r = -7.599e+00;
    }
    if( w==25 )
    {
        r = -7.762e+00;
    }
    if( w==24 )
    {
        r = -7.928e+00;
    }
    if( w==23 )
    {
        r = -8.099e+00;
    }
    if( w==22 )
    {
        r = -8.274e+00;
    }
    if( w==21 )
    {
        r = -8.454e+00;
    }
    if( w==20 )
    {
        r = -8.640e+00;
    }
    if( w==19 )
    {
        r = -8.829e+00;
    }
    if( w==18 )
    {
        r = -9.023e+00;
    }
    if( w==17 )
    {
        r = -9.223e+00;
    }
    if( w==16 )
    {
        r = -9.426e+00;
    }
    if( w==15 )
    {
        r = -9.636e+00;
    }
    if( w==14 )
    {
        r = -9.856e+00;
    }
    if( w==13 )
    {
        r = -1.008e+01;
    }
    if( w==12 )
    {
        r = -1.031e+01;
    }
    if( w==11 )
    {
        r = -1.055e+01;
    }
    if( w==10 )
    {
        r = -1.079e+01;
    }
    if( w==9 )
    {
        r = -1.106e+01;
    }
    if( w==8 )
    {
        r = -1.134e+01;
    }
    if( w==7 )
    {
        r = -1.161e+01;
    }
    if( w==6 )
    {
        r = -1.192e+01;
    }
    if( w==5 )
    {
        r = -1.225e+01;
    }
    if( w==4 )
    {
        r = -1.261e+01;
    }
    if( w==3 )
    {
        r = -1.295e+01;
    }
    if( w==2 )
    {
        r = -1.346e+01;
    }
    if( w==1 )
    {
        r = -1.386e+01;
    }
    if( w<=0 )
    {
        r = -1.456e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 22)
*************************************************************************/
static double wsr_w22(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-3.080179e+01*s+1.265000e+02, _state);
    if( w>=126 )
    {
        r = -6.931e-01;
    }
    if( w==125 )
    {
        r = -7.189e-01;
    }
    if( w==124 )
    {
        r = -7.452e-01;
    }
    if( w==123 )
    {
        r = -7.722e-01;
    }
    if( w==122 )
    {
        r = -7.999e-01;
    }
    if( w==121 )
    {
        r = -8.283e-01;
    }
    if( w==120 )
    {
        r = -8.573e-01;
    }
    if( w==119 )
    {
        r = -8.871e-01;
    }
    if( w==118 )
    {
        r = -9.175e-01;
    }
    if( w==117 )
    {
        r = -9.486e-01;
    }
    if( w==116 )
    {
        r = -9.805e-01;
    }
    if( w==115 )
    {
        r = -1.013e+00;
    }
    if( w==114 )
    {
        r = -1.046e+00;
    }
    if( w==113 )
    {
        r = -1.080e+00;
    }
    if( w==112 )
    {
        r = -1.115e+00;
    }
    if( w==111 )
    {
        r = -1.151e+00;
    }
    if( w==110 )
    {
        r = -1.187e+00;
    }
    if( w==109 )
    {
        r = -1.224e+00;
    }
    if( w==108 )
    {
        r = -1.262e+00;
    }
    if( w==107 )
    {
        r = -1.301e+00;
    }
    if( w==106 )
    {
        r = -1.340e+00;
    }
    if( w==105 )
    {
        r = -1.381e+00;
    }
    if( w==104 )
    {
        r = -1.422e+00;
    }
    if( w==103 )
    {
        r = -1.464e+00;
    }
    if( w==102 )
    {
        r = -1.506e+00;
    }
    if( w==101 )
    {
        r = -1.550e+00;
    }
    if( w==100 )
    {
        r = -1.594e+00;
    }
    if( w==99 )
    {
        r = -1.640e+00;
    }
    if( w==98 )
    {
        r = -1.686e+00;
    }
    if( w==97 )
    {
        r = -1.733e+00;
    }
    if( w==96 )
    {
        r = -1.781e+00;
    }
    if( w==95 )
    {
        r = -1.830e+00;
    }
    if( w==94 )
    {
        r = -1.880e+00;
    }
    if( w==93 )
    {
        r = -1.930e+00;
    }
    if( w==92 )
    {
        r = -1.982e+00;
    }
    if( w==91 )
    {
        r = -2.034e+00;
    }
    if( w==90 )
    {
        r = -2.088e+00;
    }
    if( w==89 )
    {
        r = -2.142e+00;
    }
    if( w==88 )
    {
        r = -2.198e+00;
    }
    if( w==87 )
    {
        r = -2.254e+00;
    }
    if( w==86 )
    {
        r = -2.312e+00;
    }
    if( w==85 )
    {
        r = -2.370e+00;
    }
    if( w==84 )
    {
        r = -2.429e+00;
    }
    if( w==83 )
    {
        r = -2.490e+00;
    }
    if( w==82 )
    {
        r = -2.551e+00;
    }
    if( w==81 )
    {
        r = -2.614e+00;
    }
    if( w==80 )
    {
        r = -2.677e+00;
    }
    if( w==79 )
    {
        r = -2.742e+00;
    }
    if( w==78 )
    {
        r = -2.808e+00;
    }
    if( w==77 )
    {
        r = -2.875e+00;
    }
    if( w==76 )
    {
        r = -2.943e+00;
    }
    if( w==75 )
    {
        r = -3.012e+00;
    }
    if( w==74 )
    {
        r = -3.082e+00;
    }
    if( w==73 )
    {
        r = -3.153e+00;
    }
    if( w==72 )
    {
        r = -3.226e+00;
    }
    if( w==71 )
    {
        r = -3.300e+00;
    }
    if( w==70 )
    {
        r = -3.375e+00;
    }
    if( w==69 )
    {
        r = -3.451e+00;
    }
    if( w==68 )
    {
        r = -3.529e+00;
    }
    if( w==67 )
    {
        r = -3.607e+00;
    }
    if( w==66 )
    {
        r = -3.687e+00;
    }
    if( w==65 )
    {
        r = -3.769e+00;
    }
    if( w==64 )
    {
        r = -3.851e+00;
    }
    if( w==63 )
    {
        r = -3.935e+00;
    }
    if( w==62 )
    {
        r = -4.021e+00;
    }
    if( w==61 )
    {
        r = -4.108e+00;
    }
    if( w==60 )
    {
        r = -4.196e+00;
    }
    if( w==59 )
    {
        r = -4.285e+00;
    }
    if( w==58 )
    {
        r = -4.376e+00;
    }
    if( w==57 )
    {
        r = -4.469e+00;
    }
    if( w==56 )
    {
        r = -4.563e+00;
    }
    if( w==55 )
    {
        r = -4.659e+00;
    }
    if( w==54 )
    {
        r = -4.756e+00;
    }
    if( w==53 )
    {
        r = -4.855e+00;
    }
    if( w==52 )
    {
        r = -4.955e+00;
    }
    if( w==51 )
    {
        r = -5.057e+00;
    }
    if( w==50 )
    {
        r = -5.161e+00;
    }
    if( w==49 )
    {
        r = -5.266e+00;
    }
    if( w==48 )
    {
        r = -5.374e+00;
    }
    if( w==47 )
    {
        r = -5.483e+00;
    }
    if( w==46 )
    {
        r = -5.594e+00;
    }
    if( w==45 )
    {
        r = -5.706e+00;
    }
    if( w==44 )
    {
        r = -5.821e+00;
    }
    if( w==43 )
    {
        r = -5.938e+00;
    }
    if( w==42 )
    {
        r = -6.057e+00;
    }
    if( w==41 )
    {
        r = -6.177e+00;
    }
    if( w==40 )
    {
        r = -6.300e+00;
    }
    if( w==39 )
    {
        r = -6.426e+00;
    }
    if( w==38 )
    {
        r = -6.553e+00;
    }
    if( w==37 )
    {
        r = -6.683e+00;
    }
    if( w==36 )
    {
        r = -6.815e+00;
    }
    if( w==35 )
    {
        r = -6.949e+00;
    }
    if( w==34 )
    {
        r = -7.086e+00;
    }
    if( w==33 )
    {
        r = -7.226e+00;
    }
    if( w==32 )
    {
        r = -7.368e+00;
    }
    if( w==31 )
    {
        r = -7.513e+00;
    }
    if( w==30 )
    {
        r = -7.661e+00;
    }
    if( w==29 )
    {
        r = -7.813e+00;
    }
    if( w==28 )
    {
        r = -7.966e+00;
    }
    if( w==27 )
    {
        r = -8.124e+00;
    }
    if( w==26 )
    {
        r = -8.285e+00;
    }
    if( w==25 )
    {
        r = -8.449e+00;
    }
    if( w==24 )
    {
        r = -8.617e+00;
    }
    if( w==23 )
    {
        r = -8.789e+00;
    }
    if( w==22 )
    {
        r = -8.965e+00;
    }
    if( w==21 )
    {
        r = -9.147e+00;
    }
    if( w==20 )
    {
        r = -9.333e+00;
    }
    if( w==19 )
    {
        r = -9.522e+00;
    }
    if( w==18 )
    {
        r = -9.716e+00;
    }
    if( w==17 )
    {
        r = -9.917e+00;
    }
    if( w==16 )
    {
        r = -1.012e+01;
    }
    if( w==15 )
    {
        r = -1.033e+01;
    }
    if( w==14 )
    {
        r = -1.055e+01;
    }
    if( w==13 )
    {
        r = -1.077e+01;
    }
    if( w==12 )
    {
        r = -1.100e+01;
    }
    if( w==11 )
    {
        r = -1.124e+01;
    }
    if( w==10 )
    {
        r = -1.149e+01;
    }
    if( w==9 )
    {
        r = -1.175e+01;
    }
    if( w==8 )
    {
        r = -1.203e+01;
    }
    if( w==7 )
    {
        r = -1.230e+01;
    }
    if( w==6 )
    {
        r = -1.261e+01;
    }
    if( w==5 )
    {
        r = -1.295e+01;
    }
    if( w==4 )
    {
        r = -1.330e+01;
    }
    if( w==3 )
    {
        r = -1.364e+01;
    }
    if( w==2 )
    {
        r = -1.415e+01;
    }
    if( w==1 )
    {
        r = -1.456e+01;
    }
    if( w<=0 )
    {
        r = -1.525e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 23)
*************************************************************************/
static double wsr_w23(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-3.287856e+01*s+1.380000e+02, _state);
    if( w>=138 )
    {
        r = -6.813e-01;
    }
    if( w==137 )
    {
        r = -7.051e-01;
    }
    if( w==136 )
    {
        r = -7.295e-01;
    }
    if( w==135 )
    {
        r = -7.544e-01;
    }
    if( w==134 )
    {
        r = -7.800e-01;
    }
    if( w==133 )
    {
        r = -8.061e-01;
    }
    if( w==132 )
    {
        r = -8.328e-01;
    }
    if( w==131 )
    {
        r = -8.601e-01;
    }
    if( w==130 )
    {
        r = -8.880e-01;
    }
    if( w==129 )
    {
        r = -9.166e-01;
    }
    if( w==128 )
    {
        r = -9.457e-01;
    }
    if( w==127 )
    {
        r = -9.755e-01;
    }
    if( w==126 )
    {
        r = -1.006e+00;
    }
    if( w==125 )
    {
        r = -1.037e+00;
    }
    if( w==124 )
    {
        r = -1.069e+00;
    }
    if( w==123 )
    {
        r = -1.101e+00;
    }
    if( w==122 )
    {
        r = -1.134e+00;
    }
    if( w==121 )
    {
        r = -1.168e+00;
    }
    if( w==120 )
    {
        r = -1.202e+00;
    }
    if( w==119 )
    {
        r = -1.237e+00;
    }
    if( w==118 )
    {
        r = -1.273e+00;
    }
    if( w==117 )
    {
        r = -1.309e+00;
    }
    if( w==116 )
    {
        r = -1.347e+00;
    }
    if( w==115 )
    {
        r = -1.384e+00;
    }
    if( w==114 )
    {
        r = -1.423e+00;
    }
    if( w==113 )
    {
        r = -1.462e+00;
    }
    if( w==112 )
    {
        r = -1.502e+00;
    }
    if( w==111 )
    {
        r = -1.543e+00;
    }
    if( w==110 )
    {
        r = -1.585e+00;
    }
    if( w==109 )
    {
        r = -1.627e+00;
    }
    if( w==108 )
    {
        r = -1.670e+00;
    }
    if( w==107 )
    {
        r = -1.714e+00;
    }
    if( w==106 )
    {
        r = -1.758e+00;
    }
    if( w==105 )
    {
        r = -1.804e+00;
    }
    if( w==104 )
    {
        r = -1.850e+00;
    }
    if( w==103 )
    {
        r = -1.897e+00;
    }
    if( w==102 )
    {
        r = -1.944e+00;
    }
    if( w==101 )
    {
        r = -1.993e+00;
    }
    if( w==100 )
    {
        r = -2.042e+00;
    }
    if( w==99 )
    {
        r = -2.093e+00;
    }
    if( w==98 )
    {
        r = -2.144e+00;
    }
    if( w==97 )
    {
        r = -2.195e+00;
    }
    if( w==96 )
    {
        r = -2.248e+00;
    }
    if( w==95 )
    {
        r = -2.302e+00;
    }
    if( w==94 )
    {
        r = -2.356e+00;
    }
    if( w==93 )
    {
        r = -2.412e+00;
    }
    if( w==92 )
    {
        r = -2.468e+00;
    }
    if( w==91 )
    {
        r = -2.525e+00;
    }
    if( w==90 )
    {
        r = -2.583e+00;
    }
    if( w==89 )
    {
        r = -2.642e+00;
    }
    if( w==88 )
    {
        r = -2.702e+00;
    }
    if( w==87 )
    {
        r = -2.763e+00;
    }
    if( w==86 )
    {
        r = -2.825e+00;
    }
    if( w==85 )
    {
        r = -2.888e+00;
    }
    if( w==84 )
    {
        r = -2.951e+00;
    }
    if( w==83 )
    {
        r = -3.016e+00;
    }
    if( w==82 )
    {
        r = -3.082e+00;
    }
    if( w==81 )
    {
        r = -3.149e+00;
    }
    if( w==80 )
    {
        r = -3.216e+00;
    }
    if( w==79 )
    {
        r = -3.285e+00;
    }
    if( w==78 )
    {
        r = -3.355e+00;
    }
    if( w==77 )
    {
        r = -3.426e+00;
    }
    if( w==76 )
    {
        r = -3.498e+00;
    }
    if( w==75 )
    {
        r = -3.571e+00;
    }
    if( w==74 )
    {
        r = -3.645e+00;
    }
    if( w==73 )
    {
        r = -3.721e+00;
    }
    if( w==72 )
    {
        r = -3.797e+00;
    }
    if( w==71 )
    {
        r = -3.875e+00;
    }
    if( w==70 )
    {
        r = -3.953e+00;
    }
    if( w==69 )
    {
        r = -4.033e+00;
    }
    if( w==68 )
    {
        r = -4.114e+00;
    }
    if( w==67 )
    {
        r = -4.197e+00;
    }
    if( w==66 )
    {
        r = -4.280e+00;
    }
    if( w==65 )
    {
        r = -4.365e+00;
    }
    if( w==64 )
    {
        r = -4.451e+00;
    }
    if( w==63 )
    {
        r = -4.539e+00;
    }
    if( w==62 )
    {
        r = -4.628e+00;
    }
    if( w==61 )
    {
        r = -4.718e+00;
    }
    if( w==60 )
    {
        r = -4.809e+00;
    }
    if( w==59 )
    {
        r = -4.902e+00;
    }
    if( w==58 )
    {
        r = -4.996e+00;
    }
    if( w==57 )
    {
        r = -5.092e+00;
    }
    if( w==56 )
    {
        r = -5.189e+00;
    }
    if( w==55 )
    {
        r = -5.287e+00;
    }
    if( w==54 )
    {
        r = -5.388e+00;
    }
    if( w==53 )
    {
        r = -5.489e+00;
    }
    if( w==52 )
    {
        r = -5.592e+00;
    }
    if( w==51 )
    {
        r = -5.697e+00;
    }
    if( w==50 )
    {
        r = -5.804e+00;
    }
    if( w==49 )
    {
        r = -5.912e+00;
    }
    if( w==48 )
    {
        r = -6.022e+00;
    }
    if( w==47 )
    {
        r = -6.133e+00;
    }
    if( w==46 )
    {
        r = -6.247e+00;
    }
    if( w==45 )
    {
        r = -6.362e+00;
    }
    if( w==44 )
    {
        r = -6.479e+00;
    }
    if( w==43 )
    {
        r = -6.598e+00;
    }
    if( w==42 )
    {
        r = -6.719e+00;
    }
    if( w==41 )
    {
        r = -6.842e+00;
    }
    if( w==40 )
    {
        r = -6.967e+00;
    }
    if( w==39 )
    {
        r = -7.094e+00;
    }
    if( w==38 )
    {
        r = -7.224e+00;
    }
    if( w==37 )
    {
        r = -7.355e+00;
    }
    if( w==36 )
    {
        r = -7.489e+00;
    }
    if( w==35 )
    {
        r = -7.625e+00;
    }
    if( w==34 )
    {
        r = -7.764e+00;
    }
    if( w==33 )
    {
        r = -7.905e+00;
    }
    if( w==32 )
    {
        r = -8.049e+00;
    }
    if( w==31 )
    {
        r = -8.196e+00;
    }
    if( w==30 )
    {
        r = -8.345e+00;
    }
    if( w==29 )
    {
        r = -8.498e+00;
    }
    if( w==28 )
    {
        r = -8.653e+00;
    }
    if( w==27 )
    {
        r = -8.811e+00;
    }
    if( w==26 )
    {
        r = -8.974e+00;
    }
    if( w==25 )
    {
        r = -9.139e+00;
    }
    if( w==24 )
    {
        r = -9.308e+00;
    }
    if( w==23 )
    {
        r = -9.481e+00;
    }
    if( w==22 )
    {
        r = -9.658e+00;
    }
    if( w==21 )
    {
        r = -9.840e+00;
    }
    if( w==20 )
    {
        r = -1.003e+01;
    }
    if( w==19 )
    {
        r = -1.022e+01;
    }
    if( w==18 )
    {
        r = -1.041e+01;
    }
    if( w==17 )
    {
        r = -1.061e+01;
    }
    if( w==16 )
    {
        r = -1.081e+01;
    }
    if( w==15 )
    {
        r = -1.102e+01;
    }
    if( w==14 )
    {
        r = -1.124e+01;
    }
    if( w==13 )
    {
        r = -1.147e+01;
    }
    if( w==12 )
    {
        r = -1.169e+01;
    }
    if( w==11 )
    {
        r = -1.194e+01;
    }
    if( w==10 )
    {
        r = -1.218e+01;
    }
    if( w==9 )
    {
        r = -1.245e+01;
    }
    if( w==8 )
    {
        r = -1.272e+01;
    }
    if( w==7 )
    {
        r = -1.300e+01;
    }
    if( w==6 )
    {
        r = -1.330e+01;
    }
    if( w==5 )
    {
        r = -1.364e+01;
    }
    if( w==4 )
    {
        r = -1.400e+01;
    }
    if( w==3 )
    {
        r = -1.433e+01;
    }
    if( w==2 )
    {
        r = -1.484e+01;
    }
    if( w==1 )
    {
        r = -1.525e+01;
    }
    if( w<=0 )
    {
        r = -1.594e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 24)
*************************************************************************/
static double wsr_w24(double s, ae_state *_state)
{
    ae_int_t w;
    double r;
    double result;


    r = (double)(0);
    w = ae_round(-3.500000e+01*s+1.500000e+02, _state);
    if( w>=150 )
    {
        r = -6.820e-01;
    }
    if( w==149 )
    {
        r = -7.044e-01;
    }
    if( w==148 )
    {
        r = -7.273e-01;
    }
    if( w==147 )
    {
        r = -7.507e-01;
    }
    if( w==146 )
    {
        r = -7.746e-01;
    }
    if( w==145 )
    {
        r = -7.990e-01;
    }
    if( w==144 )
    {
        r = -8.239e-01;
    }
    if( w==143 )
    {
        r = -8.494e-01;
    }
    if( w==142 )
    {
        r = -8.754e-01;
    }
    if( w==141 )
    {
        r = -9.020e-01;
    }
    if( w==140 )
    {
        r = -9.291e-01;
    }
    if( w==139 )
    {
        r = -9.567e-01;
    }
    if( w==138 )
    {
        r = -9.849e-01;
    }
    if( w==137 )
    {
        r = -1.014e+00;
    }
    if( w==136 )
    {
        r = -1.043e+00;
    }
    if( w==135 )
    {
        r = -1.073e+00;
    }
    if( w==134 )
    {
        r = -1.103e+00;
    }
    if( w==133 )
    {
        r = -1.135e+00;
    }
    if( w==132 )
    {
        r = -1.166e+00;
    }
    if( w==131 )
    {
        r = -1.198e+00;
    }
    if( w==130 )
    {
        r = -1.231e+00;
    }
    if( w==129 )
    {
        r = -1.265e+00;
    }
    if( w==128 )
    {
        r = -1.299e+00;
    }
    if( w==127 )
    {
        r = -1.334e+00;
    }
    if( w==126 )
    {
        r = -1.369e+00;
    }
    if( w==125 )
    {
        r = -1.405e+00;
    }
    if( w==124 )
    {
        r = -1.441e+00;
    }
    if( w==123 )
    {
        r = -1.479e+00;
    }
    if( w==122 )
    {
        r = -1.517e+00;
    }
    if( w==121 )
    {
        r = -1.555e+00;
    }
    if( w==120 )
    {
        r = -1.594e+00;
    }
    if( w==119 )
    {
        r = -1.634e+00;
    }
    if( w==118 )
    {
        r = -1.675e+00;
    }
    if( w==117 )
    {
        r = -1.716e+00;
    }
    if( w==116 )
    {
        r = -1.758e+00;
    }
    if( w==115 )
    {
        r = -1.800e+00;
    }
    if( w==114 )
    {
        r = -1.844e+00;
    }
    if( w==113 )
    {
        r = -1.888e+00;
    }
    if( w==112 )
    {
        r = -1.932e+00;
    }
    if( w==111 )
    {
        r = -1.978e+00;
    }
    if( w==110 )
    {
        r = -2.024e+00;
    }
    if( w==109 )
    {
        r = -2.070e+00;
    }
    if( w==108 )
    {
        r = -2.118e+00;
    }
    if( w==107 )
    {
        r = -2.166e+00;
    }
    if( w==106 )
    {
        r = -2.215e+00;
    }
    if( w==105 )
    {
        r = -2.265e+00;
    }
    if( w==104 )
    {
        r = -2.316e+00;
    }
    if( w==103 )
    {
        r = -2.367e+00;
    }
    if( w==102 )
    {
        r = -2.419e+00;
    }
    if( w==101 )
    {
        r = -2.472e+00;
    }
    if( w==100 )
    {
        r = -2.526e+00;
    }
    if( w==99 )
    {
        r = -2.580e+00;
    }
    if( w==98 )
    {
        r = -2.636e+00;
    }
    if( w==97 )
    {
        r = -2.692e+00;
    }
    if( w==96 )
    {
        r = -2.749e+00;
    }
    if( w==95 )
    {
        r = -2.806e+00;
    }
    if( w==94 )
    {
        r = -2.865e+00;
    }
    if( w==93 )
    {
        r = -2.925e+00;
    }
    if( w==92 )
    {
        r = -2.985e+00;
    }
    if( w==91 )
    {
        r = -3.046e+00;
    }
    if( w==90 )
    {
        r = -3.108e+00;
    }
    if( w==89 )
    {
        r = -3.171e+00;
    }
    if( w==88 )
    {
        r = -3.235e+00;
    }
    if( w==87 )
    {
        r = -3.300e+00;
    }
    if( w==86 )
    {
        r = -3.365e+00;
    }
    if( w==85 )
    {
        r = -3.432e+00;
    }
    if( w==84 )
    {
        r = -3.499e+00;
    }
    if( w==83 )
    {
        r = -3.568e+00;
    }
    if( w==82 )
    {
        r = -3.637e+00;
    }
    if( w==81 )
    {
        r = -3.708e+00;
    }
    if( w==80 )
    {
        r = -3.779e+00;
    }
    if( w==79 )
    {
        r = -3.852e+00;
    }
    if( w==78 )
    {
        r = -3.925e+00;
    }
    if( w==77 )
    {
        r = -4.000e+00;
    }
    if( w==76 )
    {
        r = -4.075e+00;
    }
    if( w==75 )
    {
        r = -4.151e+00;
    }
    if( w==74 )
    {
        r = -4.229e+00;
    }
    if( w==73 )
    {
        r = -4.308e+00;
    }
    if( w==72 )
    {
        r = -4.387e+00;
    }
    if( w==71 )
    {
        r = -4.468e+00;
    }
    if( w==70 )
    {
        r = -4.550e+00;
    }
    if( w==69 )
    {
        r = -4.633e+00;
    }
    if( w==68 )
    {
        r = -4.718e+00;
    }
    if( w==67 )
    {
        r = -4.803e+00;
    }
    if( w==66 )
    {
        r = -4.890e+00;
    }
    if( w==65 )
    {
        r = -4.978e+00;
    }
    if( w==64 )
    {
        r = -5.067e+00;
    }
    if( w==63 )
    {
        r = -5.157e+00;
    }
    if( w==62 )
    {
        r = -5.249e+00;
    }
    if( w==61 )
    {
        r = -5.342e+00;
    }
    if( w==60 )
    {
        r = -5.436e+00;
    }
    if( w==59 )
    {
        r = -5.531e+00;
    }
    if( w==58 )
    {
        r = -5.628e+00;
    }
    if( w==57 )
    {
        r = -5.727e+00;
    }
    if( w==56 )
    {
        r = -5.826e+00;
    }
    if( w==55 )
    {
        r = -5.927e+00;
    }
    if( w==54 )
    {
        r = -6.030e+00;
    }
    if( w==53 )
    {
        r = -6.134e+00;
    }
    if( w==52 )
    {
        r = -6.240e+00;
    }
    if( w==51 )
    {
        r = -6.347e+00;
    }
    if( w==50 )
    {
        r = -6.456e+00;
    }
    if( w==49 )
    {
        r = -6.566e+00;
    }
    if( w==48 )
    {
        r = -6.678e+00;
    }
    if( w==47 )
    {
        r = -6.792e+00;
    }
    if( w==46 )
    {
        r = -6.907e+00;
    }
    if( w==45 )
    {
        r = -7.025e+00;
    }
    if( w==44 )
    {
        r = -7.144e+00;
    }
    if( w==43 )
    {
        r = -7.265e+00;
    }
    if( w==42 )
    {
        r = -7.387e+00;
    }
    if( w==41 )
    {
        r = -7.512e+00;
    }
    if( w==40 )
    {
        r = -7.639e+00;
    }
    if( w==39 )
    {
        r = -7.768e+00;
    }
    if( w==38 )
    {
        r = -7.899e+00;
    }
    if( w==37 )
    {
        r = -8.032e+00;
    }
    if( w==36 )
    {
        r = -8.167e+00;
    }
    if( w==35 )
    {
        r = -8.305e+00;
    }
    if( w==34 )
    {
        r = -8.445e+00;
    }
    if( w==33 )
    {
        r = -8.588e+00;
    }
    if( w==32 )
    {
        r = -8.733e+00;
    }
    if( w==31 )
    {
        r = -8.881e+00;
    }
    if( w==30 )
    {
        r = -9.031e+00;
    }
    if( w==29 )
    {
        r = -9.185e+00;
    }
    if( w==28 )
    {
        r = -9.341e+00;
    }
    if( w==27 )
    {
        r = -9.501e+00;
    }
    if( w==26 )
    {
        r = -9.664e+00;
    }
    if( w==25 )
    {
        r = -9.830e+00;
    }
    if( w==24 )
    {
        r = -1.000e+01;
    }
    if( w==23 )
    {
        r = -1.017e+01;
    }
    if( w==22 )
    {
        r = -1.035e+01;
    }
    if( w==21 )
    {
        r = -1.053e+01;
    }
    if( w==20 )
    {
        r = -1.072e+01;
    }
    if( w==19 )
    {
        r = -1.091e+01;
    }
    if( w==18 )
    {
        r = -1.110e+01;
    }
    if( w==17 )
    {
        r = -1.130e+01;
    }
    if( w==16 )
    {
        r = -1.151e+01;
    }
    if( w==15 )
    {
        r = -1.172e+01;
    }
    if( w==14 )
    {
        r = -1.194e+01;
    }
    if( w==13 )
    {
        r = -1.216e+01;
    }
    if( w==12 )
    {
        r = -1.239e+01;
    }
    if( w==11 )
    {
        r = -1.263e+01;
    }
    if( w==10 )
    {
        r = -1.287e+01;
    }
    if( w==9 )
    {
        r = -1.314e+01;
    }
    if( w==8 )
    {
        r = -1.342e+01;
    }
    if( w==7 )
    {
        r = -1.369e+01;
    }
    if( w==6 )
    {
        r = -1.400e+01;
    }
    if( w==5 )
    {
        r = -1.433e+01;
    }
    if( w==4 )
    {
        r = -1.469e+01;
    }
    if( w==3 )
    {
        r = -1.503e+01;
    }
    if( w==2 )
    {
        r = -1.554e+01;
    }
    if( w==1 )
    {
        r = -1.594e+01;
    }
    if( w<=0 )
    {
        r = -1.664e+01;
    }
    result = r;
    return result;
}


/*************************************************************************
Tail(S, 25)
*************************************************************************/
static double wsr_w25(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -5.150509e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.695528e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.437637e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.611906e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -7.625722e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.579892e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.086876e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.906543e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.354881e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 1.007195e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -8.437327e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 26)
*************************************************************************/
static double wsr_w26(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -5.117622e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.635159e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.395167e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.382823e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -6.531987e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.060112e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -8.203697e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.516523e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.431364e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 6.384553e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -3.238369e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 27)
*************************************************************************/
static double wsr_w27(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -5.089731e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.584248e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.359966e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.203696e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.753344e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.761891e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -7.096897e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.419108e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.581214e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 3.033766e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.901441e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 28)
*************************************************************************/
static double wsr_w28(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -5.065046e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.539163e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.328939e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.046376e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.061515e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.469271e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.711578e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -8.389153e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.250575e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 4.047245e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.128555e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 29)
*************************************************************************/
static double wsr_w29(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -5.043413e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.499756e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.302137e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.915129e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.516329e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.260064e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.817269e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.478130e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.111668e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 4.093451e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.135860e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 30)
*************************************************************************/
static double wsr_w30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -5.024071e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.464515e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.278342e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.800030e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.046294e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.076162e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -3.968677e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.911679e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -8.619185e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 5.125362e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -3.984370e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 40)
*************************************************************************/
static double wsr_w40(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -4.904809e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.248327e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.136698e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.170982e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.824427e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -3.888648e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.344929e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 2.790407e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.619858e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 3.359121e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.883026e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 60)
*************************************************************************/
static double wsr_w60(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -4.809656e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.077191e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.029402e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -7.507931e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -6.506226e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.391278e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.263635e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 2.302271e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.384348e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 1.865587e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.622355e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 120)
*************************************************************************/
static double wsr_w120(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -4.729426e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.934426e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -9.433231e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.492504e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 1.673948e-05, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -6.077014e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -7.215768e-05, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 9.086734e-05, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -8.447980e-05, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 6.705028e-05, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.828507e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 200)
*************************************************************************/
static double wsr_w200(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/4.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    wsr_wcheb(x, -4.700240e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.883080e+00, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -9.132168e-01, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -3.512684e-02, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 1.726342e-03, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -5.189796e-04, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -1.628659e-06, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 4.261786e-05, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -4.002498e-05, &tj, &tj1, &result, _state);
    wsr_wcheb(x, 3.146287e-05, &tj, &tj1, &result, _state);
    wsr_wcheb(x, -2.727576e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S,N), S>=0
*************************************************************************/
static double wsr_wsigma(double s, ae_int_t n, ae_state *_state)
{
    double f0;
    double f1;
    double f2;
    double f3;
    double f4;
    double x0;
    double x1;
    double x2;
    double x3;
    double x4;
    double x;
    double result;


    result = (double)(0);
    if( n==5 )
    {
        result = wsr_w5(s, _state);
    }
    if( n==6 )
    {
        result = wsr_w6(s, _state);
    }
    if( n==7 )
    {
        result = wsr_w7(s, _state);
    }
    if( n==8 )
    {
        result = wsr_w8(s, _state);
    }
    if( n==9 )
    {
        result = wsr_w9(s, _state);
    }
    if( n==10 )
    {
        result = wsr_w10(s, _state);
    }
    if( n==11 )
    {
        result = wsr_w11(s, _state);
    }
    if( n==12 )
    {
        result = wsr_w12(s, _state);
    }
    if( n==13 )
    {
        result = wsr_w13(s, _state);
    }
    if( n==14 )
    {
        result = wsr_w14(s, _state);
    }
    if( n==15 )
    {
        result = wsr_w15(s, _state);
    }
    if( n==16 )
    {
        result = wsr_w16(s, _state);
    }
    if( n==17 )
    {
        result = wsr_w17(s, _state);
    }
    if( n==18 )
    {
        result = wsr_w18(s, _state);
    }
    if( n==19 )
    {
        result = wsr_w19(s, _state);
    }
    if( n==20 )
    {
        result = wsr_w20(s, _state);
    }
    if( n==21 )
    {
        result = wsr_w21(s, _state);
    }
    if( n==22 )
    {
        result = wsr_w22(s, _state);
    }
    if( n==23 )
    {
        result = wsr_w23(s, _state);
    }
    if( n==24 )
    {
        result = wsr_w24(s, _state);
    }
    if( n==25 )
    {
        result = wsr_w25(s, _state);
    }
    if( n==26 )
    {
        result = wsr_w26(s, _state);
    }
    if( n==27 )
    {
        result = wsr_w27(s, _state);
    }
    if( n==28 )
    {
        result = wsr_w28(s, _state);
    }
    if( n==29 )
    {
        result = wsr_w29(s, _state);
    }
    if( n==30 )
    {
        result = wsr_w30(s, _state);
    }
    if( n>30 )
    {
        x = 1.0/n;
        x0 = 1.0/30;
        f0 = wsr_w30(s, _state);
        x1 = 1.0/40;
        f1 = wsr_w40(s, _state);
        x2 = 1.0/60;
        f2 = wsr_w60(s, _state);
        x3 = 1.0/120;
        f3 = wsr_w120(s, _state);
        x4 = 1.0/200;
        f4 = wsr_w200(s, _state);
        f1 = ((x-x0)*f1-(x-x1)*f0)/(x1-x0);
        f2 = ((x-x0)*f2-(x-x2)*f0)/(x2-x0);
        f3 = ((x-x0)*f3-(x-x3)*f0)/(x3-x0);
        f4 = ((x-x0)*f4-(x-x4)*f0)/(x4-x0);
        f2 = ((x-x1)*f2-(x-x2)*f1)/(x2-x1);
        f3 = ((x-x1)*f3-(x-x3)*f1)/(x3-x1);
        f4 = ((x-x1)*f4-(x-x4)*f1)/(x4-x1);
        f3 = ((x-x2)*f3-(x-x3)*f2)/(x3-x2);
        f4 = ((x-x2)*f4-(x-x4)*f2)/(x4-x2);
        f4 = ((x-x3)*f4-(x-x4)*f3)/(x4-x3);
        result = f4;
    }
    return result;
}


#endif
#if defined(AE_COMPILE_MANNWHITNEYU) || !defined(AE_PARTIAL_BUILD)


/*************************************************************************
Mann-Whitney U-test

This test checks hypotheses about whether X  and  Y  are  samples  of  two
continuous distributions of the same shape  and  same  median  or  whether
their medians are different.

The following tests are performed:
    * two-tailed test (null hypothesis - the medians are equal)
    * left-tailed test (null hypothesis - the median of the  first  sample
      is greater than or equal to the median of the second sample)
    * right-tailed test (null hypothesis - the median of the first  sample
      is less than or equal to the median of the second sample).

Requirements:
    * the samples are independent
    * X and Y are continuous distributions (or discrete distributions well-
      approximating continuous distributions)
    * distributions of X and Y have the  same  shape.  The  only  possible
      difference is their position (i.e. the value of the median)
    * the number of elements in each sample is not less than 5
    * the scale of measurement should be ordinal, interval or ratio  (i.e.
      the test could not be applied to nominal variables).

The test is non-parametric and doesn't require distributions to be normal.

Input parameters:
    X   -   sample 1. Array whose index goes from 0 to N-1.
    N   -   size of the sample. N>=5
    Y   -   sample 2. Array whose index goes from 0 to M-1.
    M   -   size of the sample. M>=5

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

To calculate p-values, special approximation is used. This method lets  us
calculate p-values with satisfactory  accuracy  in  interval  [0.0001, 1].
There is no approximation outside the [0.0001, 1] interval. Therefore,  if
the significance level outlies this interval, the test returns 0.0001.

Relative precision of approximation of p-value:

N          M          Max.err.   Rms.err.
5..10      N..10      1.4e-02    6.0e-04
5..10      N..100     2.2e-02    5.3e-06
10..15     N..15      1.0e-02    3.2e-04
10..15     N..100     1.0e-02    2.2e-05
15..100    N..100     6.1e-03    2.7e-06

For N,M>100 accuracy checks weren't put into  practice,  but  taking  into
account characteristics of asymptotic approximation used, precision should
not be sharply different from the values for interval [5, 100].

NOTE: P-value approximation was  optimized  for  0.0001<=p<=0.2500.  Thus,
      P's outside of this interval are enforced to these bounds. Say,  you
      may quite often get P equal to exactly 0.25 or 0.0001.

  -- ALGLIB --
     Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void mannwhitneyutest(/* Real    */ ae_vector* x,
     ae_int_t n,
     /* Real    */ ae_vector* y,
     ae_int_t m,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    ae_frame _frame_block;
    ae_int_t i;
    ae_int_t j;
    ae_int_t k;
    ae_int_t t;
    double tmp;
    ae_int_t tmpi;
    ae_int_t ns;
    ae_vector r;
    ae_vector c;
    double u;
    double p;
    double mp;
    double s;
    double sigma;
    double mu;
    ae_int_t tiecount;
    ae_vector tiesize;

    ae_frame_make(_state, &_frame_block);
    memset(&r, 0, sizeof(r));
    memset(&c, 0, sizeof(c));
    memset(&tiesize, 0, sizeof(tiesize));
    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;
    ae_vector_init(&r, 0, DT_REAL, _state, ae_true);
    ae_vector_init(&c, 0, DT_INT, _state, ae_true);
    ae_vector_init(&tiesize, 0, DT_INT, _state, ae_true);

    
    /*
     * Prepare
     */
    if( n<=4||m<=4 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        ae_frame_leave(_state);
        return;
    }
    ns = n+m;
    ae_vector_set_length(&r, ns-1+1, _state);
    ae_vector_set_length(&c, ns-1+1, _state);
    for(i=0; i<=n-1; i++)
    {
        r.ptr.p_double[i] = x->ptr.p_double[i];
        c.ptr.p_int[i] = 0;
    }
    for(i=0; i<=m-1; i++)
    {
        r.ptr.p_double[n+i] = y->ptr.p_double[i];
        c.ptr.p_int[n+i] = 1;
    }
    
    /*
     * sort {R, C}
     */
    if( ns!=1 )
    {
        i = 2;
        do
        {
            t = i;
            while(t!=1)
            {
                k = t/2;
                if( ae_fp_greater_eq(r.ptr.p_double[k-1],r.ptr.p_double[t-1]) )
                {
                    t = 1;
                }
                else
                {
                    tmp = r.ptr.p_double[k-1];
                    r.ptr.p_double[k-1] = r.ptr.p_double[t-1];
                    r.ptr.p_double[t-1] = tmp;
                    tmpi = c.ptr.p_int[k-1];
                    c.ptr.p_int[k-1] = c.ptr.p_int[t-1];
                    c.ptr.p_int[t-1] = tmpi;
                    t = k;
                }
            }
            i = i+1;
        }
        while(i<=ns);
        i = ns-1;
        do
        {
            tmp = r.ptr.p_double[i];
            r.ptr.p_double[i] = r.ptr.p_double[0];
            r.ptr.p_double[0] = tmp;
            tmpi = c.ptr.p_int[i];
            c.ptr.p_int[i] = c.ptr.p_int[0];
            c.ptr.p_int[0] = tmpi;
            t = 1;
            while(t!=0)
            {
                k = 2*t;
                if( k>i )
                {
                    t = 0;
                }
                else
                {
                    if( k<i )
                    {
                        if( ae_fp_greater(r.ptr.p_double[k],r.ptr.p_double[k-1]) )
                        {
                            k = k+1;
                        }
                    }
                    if( ae_fp_greater_eq(r.ptr.p_double[t-1],r.ptr.p_double[k-1]) )
                    {
                        t = 0;
                    }
                    else
                    {
                        tmp = r.ptr.p_double[k-1];
                        r.ptr.p_double[k-1] = r.ptr.p_double[t-1];
                        r.ptr.p_double[t-1] = tmp;
                        tmpi = c.ptr.p_int[k-1];
                        c.ptr.p_int[k-1] = c.ptr.p_int[t-1];
                        c.ptr.p_int[t-1] = tmpi;
                        t = k;
                    }
                }
            }
            i = i-1;
        }
        while(i>=1);
    }
    
    /*
     * compute tied ranks
     */
    i = 0;
    tiecount = 0;
    ae_vector_set_length(&tiesize, ns-1+1, _state);
    while(i<=ns-1)
    {
        j = i+1;
        while(j<=ns-1)
        {
            if( ae_fp_neq(r.ptr.p_double[j],r.ptr.p_double[i]) )
            {
                break;
            }
            j = j+1;
        }
        for(k=i; k<=j-1; k++)
        {
            r.ptr.p_double[k] = 1+(double)(i+j-1)/(double)2;
        }
        tiesize.ptr.p_int[tiecount] = j-i;
        tiecount = tiecount+1;
        i = j;
    }
    
    /*
     * Compute U
     */
    u = (double)(0);
    for(i=0; i<=ns-1; i++)
    {
        if( c.ptr.p_int[i]==0 )
        {
            u = u+r.ptr.p_double[i];
        }
    }
    u = rmul2((double)(n), (double)(m), _state)+rmul2((double)(n), (double)(n+1), _state)*0.5-u;
    
    /*
     * Result
     */
    mu = rmul2((double)(n), (double)(m), _state)/2;
    tmp = ns*(ae_sqr((double)(ns), _state)-1)/12;
    for(i=0; i<=tiecount-1; i++)
    {
        tmp = tmp-tiesize.ptr.p_int[i]*(ae_sqr((double)(tiesize.ptr.p_int[i]), _state)-1)/12;
    }
    sigma = ae_sqrt(rmul2((double)(n), (double)(m), _state)/ns/(ns-1)*tmp, _state);
    s = (u-mu)/sigma;
    if( ae_fp_less_eq(s,(double)(0)) )
    {
        p = ae_exp(mannwhitneyu_usigma(-(u-mu)/sigma, n, m, _state), _state);
        mp = 1-ae_exp(mannwhitneyu_usigma(-(u-1-mu)/sigma, n, m, _state), _state);
    }
    else
    {
        mp = ae_exp(mannwhitneyu_usigma((u-mu)/sigma, n, m, _state), _state);
        p = 1-ae_exp(mannwhitneyu_usigma((u+1-mu)/sigma, n, m, _state), _state);
    }
    *lefttail = boundval(ae_maxreal(mp, 1.0E-4, _state), 0.0001, 0.2500, _state);
    *righttail = boundval(ae_maxreal(p, 1.0E-4, _state), 0.0001, 0.2500, _state);
    *bothtails = 2*ae_minreal(*lefttail, *righttail, _state);
    ae_frame_leave(_state);
}


/*************************************************************************
Sequential Chebyshev interpolation.
*************************************************************************/
static void mannwhitneyu_ucheb(double x,
     double c,
     double* tj,
     double* tj1,
     double* r,
     ae_state *_state)
{
    double t;


    *r = *r+c*(*tj);
    t = 2*x*(*tj1)-(*tj);
    *tj = *tj1;
    *tj1 = t;
}


/*************************************************************************
Three-point polynomial interpolation.
*************************************************************************/
static double mannwhitneyu_uninterpolate(double p1,
     double p2,
     double p3,
     ae_int_t n,
     ae_state *_state)
{
    double t1;
    double t2;
    double t3;
    double t;
    double p12;
    double p23;
    double result;


    t1 = 1.0/15.0;
    t2 = 1.0/30.0;
    t3 = 1.0/100.0;
    t = 1.0/n;
    p12 = ((t-t2)*p1+(t1-t)*p2)/(t1-t2);
    p23 = ((t-t3)*p2+(t2-t)*p3)/(t2-t3);
    result = ((t-t3)*p12+(t1-t)*p23)/(t1-t3);
    return result;
}


/*************************************************************************
Tail(0, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma000(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double p1;
    double p2;
    double p3;
    double result;


    p1 = mannwhitneyu_uninterpolate(-6.76984e-01, -6.83700e-01, -6.89873e-01, n2, _state);
    p2 = mannwhitneyu_uninterpolate(-6.83700e-01, -6.87311e-01, -6.90957e-01, n2, _state);
    p3 = mannwhitneyu_uninterpolate(-6.89873e-01, -6.90957e-01, -6.92175e-01, n2, _state);
    result = mannwhitneyu_uninterpolate(p1, p2, p3, n1, _state);
    return result;
}


/*************************************************************************
Tail(0.75, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma075(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double p1;
    double p2;
    double p3;
    double result;


    p1 = mannwhitneyu_uninterpolate(-1.44500e+00, -1.45906e+00, -1.47063e+00, n2, _state);
    p2 = mannwhitneyu_uninterpolate(-1.45906e+00, -1.46856e+00, -1.47644e+00, n2, _state);
    p3 = mannwhitneyu_uninterpolate(-1.47063e+00, -1.47644e+00, -1.48100e+00, n2, _state);
    result = mannwhitneyu_uninterpolate(p1, p2, p3, n1, _state);
    return result;
}


/*************************************************************************
Tail(1.5, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma150(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double p1;
    double p2;
    double p3;
    double result;


    p1 = mannwhitneyu_uninterpolate(-2.65380e+00, -2.67352e+00, -2.69011e+00, n2, _state);
    p2 = mannwhitneyu_uninterpolate(-2.67352e+00, -2.68591e+00, -2.69659e+00, n2, _state);
    p3 = mannwhitneyu_uninterpolate(-2.69011e+00, -2.69659e+00, -2.70192e+00, n2, _state);
    result = mannwhitneyu_uninterpolate(p1, p2, p3, n1, _state);
    return result;
}


/*************************************************************************
Tail(2.25, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma225(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double p1;
    double p2;
    double p3;
    double result;


    p1 = mannwhitneyu_uninterpolate(-4.41465e+00, -4.42260e+00, -4.43702e+00, n2, _state);
    p2 = mannwhitneyu_uninterpolate(-4.42260e+00, -4.41639e+00, -4.41928e+00, n2, _state);
    p3 = mannwhitneyu_uninterpolate(-4.43702e+00, -4.41928e+00, -4.41030e+00, n2, _state);
    result = mannwhitneyu_uninterpolate(p1, p2, p3, n1, _state);
    return result;
}


/*************************************************************************
Tail(3.0, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma300(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double p1;
    double p2;
    double p3;
    double result;


    p1 = mannwhitneyu_uninterpolate(-6.89839e+00, -6.83477e+00, -6.82340e+00, n2, _state);
    p2 = mannwhitneyu_uninterpolate(-6.83477e+00, -6.74559e+00, -6.71117e+00, n2, _state);
    p3 = mannwhitneyu_uninterpolate(-6.82340e+00, -6.71117e+00, -6.64929e+00, n2, _state);
    result = mannwhitneyu_uninterpolate(p1, p2, p3, n1, _state);
    return result;
}


/*************************************************************************
Tail(3.33, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma333(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double p1;
    double p2;
    double p3;
    double result;


    p1 = mannwhitneyu_uninterpolate(-8.31272e+00, -8.17096e+00, -8.13125e+00, n2, _state);
    p2 = mannwhitneyu_uninterpolate(-8.17096e+00, -8.00156e+00, -7.93245e+00, n2, _state);
    p3 = mannwhitneyu_uninterpolate(-8.13125e+00, -7.93245e+00, -7.82502e+00, n2, _state);
    result = mannwhitneyu_uninterpolate(p1, p2, p3, n1, _state);
    return result;
}


/*************************************************************************
Tail(3.66, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma367(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double p1;
    double p2;
    double p3;
    double result;


    p1 = mannwhitneyu_uninterpolate(-9.98837e+00, -9.70844e+00, -9.62087e+00, n2, _state);
    p2 = mannwhitneyu_uninterpolate(-9.70844e+00, -9.41156e+00, -9.28998e+00, n2, _state);
    p3 = mannwhitneyu_uninterpolate(-9.62087e+00, -9.28998e+00, -9.11686e+00, n2, _state);
    result = mannwhitneyu_uninterpolate(p1, p2, p3, n1, _state);
    return result;
}


/*************************************************************************
Tail(4.0, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma400(ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double p1;
    double p2;
    double p3;
    double result;


    p1 = mannwhitneyu_uninterpolate(-1.20250e+01, -1.14911e+01, -1.13231e+01, n2, _state);
    p2 = mannwhitneyu_uninterpolate(-1.14911e+01, -1.09927e+01, -1.07937e+01, n2, _state);
    p3 = mannwhitneyu_uninterpolate(-1.13231e+01, -1.07937e+01, -1.05285e+01, n2, _state);
    result = mannwhitneyu_uninterpolate(p1, p2, p3, n1, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 5)
*************************************************************************/
static double mannwhitneyu_utbln5n5(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/2.611165e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -2.596264e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.412086e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.858542e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.614282e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.372686e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.524731e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.435331e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.284665e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.184141e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.298360e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 7.447272e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.938769e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.276205e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.138481e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.684625e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.558104e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 6)
*************************************************************************/
static double mannwhitneyu_utbln5n6(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/2.738613e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -2.810459e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.684429e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.712858e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.009324e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.644391e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.034173e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.953498e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.279293e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.563485e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.971952e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.506309e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.541406e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.283205e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.016347e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.221626e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.286752e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 7)
*************************************************************************/
static double mannwhitneyu_utbln5n7(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/2.841993e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -2.994677e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.923264e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.506190e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.054280e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.794587e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.726290e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.534180e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.517845e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.904428e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.882443e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.482988e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.114875e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.515082e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.996056e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.293581e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.349444e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 8)
*************************************************************************/
static double mannwhitneyu_utbln5n8(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/2.927700e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.155727e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.135078e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.247203e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.309697e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.993725e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.567219e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.383704e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.002188e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.487322e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.443899e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.688270e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.600339e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.874948e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.811593e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.072353e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.659457e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 9)
*************************************************************************/
static double mannwhitneyu_utbln5n9(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.298162e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.325016e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.939852e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.563029e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.222652e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.195200e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.445665e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.204792e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.775217e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.527781e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.221948e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.242968e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.607959e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.771285e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.694026e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.481190e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 10)
*************************************************************************/
static double mannwhitneyu_utbln5n10(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.061862e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.425360e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.496710e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.587658e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.812005e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.427637e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.515702e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.406867e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.796295e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.237591e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.654249e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.181165e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.011665e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.417927e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.534880e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.791255e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.871512e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 11)
*************************************************************************/
static double mannwhitneyu_utbln5n11(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.115427e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.539959e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.652998e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.196503e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.054363e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.618848e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.109411e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.786668e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.215648e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.484220e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.935991e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.396191e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.894177e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.206979e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.519055e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.210326e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.189679e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 12)
*************************************************************************/
static double mannwhitneyu_utbln5n12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.162278e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.644007e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.796173e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.771177e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.290043e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.794686e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.702110e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.185959e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.416259e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.592056e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.201530e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.754365e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.978945e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.012032e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.304579e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.100378e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.728269e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 13)
*************************************************************************/
static double mannwhitneyu_utbln5n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.203616e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.739120e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.928117e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.031605e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.519403e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.962648e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.292183e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.809293e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.465156e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.456278e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.446055e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.109490e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.218256e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.941479e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.058603e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.824402e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.830947e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 14)
*************************************************************************/
static double mannwhitneyu_utbln5n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.240370e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.826559e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.050370e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.083408e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.743164e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.012030e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.884686e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.059656e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.327521e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.134026e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.584201e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.440618e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.524133e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.990007e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.887334e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.534977e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.705395e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 15)
*************************************************************************/
static double mannwhitneyu_utbln5n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.851572e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.082033e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.095983e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.814595e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.073148e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.420213e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.517175e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.344180e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.371393e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.711443e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.228569e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.683483e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.267112e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.156044e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.131316e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.301023e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 16)
*************************************************************************/
static double mannwhitneyu_utbln5n16(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.852210e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.077482e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.091186e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.797282e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.084994e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.667054e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.843909e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.456732e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.039830e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.723508e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.940608e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.478285e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.649144e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.237703e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.707410e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.874293e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 17)
*************************************************************************/
static double mannwhitneyu_utbln5n17(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.851752e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.071259e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.084700e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.758898e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.073846e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.684838e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.964936e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.782442e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.956362e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.984727e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.196936e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.558262e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.690746e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.364855e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.401006e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.546748e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 18)
*************************************************************************/
static double mannwhitneyu_utbln5n18(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.850840e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.064799e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.077651e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.712659e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.049217e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.571333e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.929809e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.752044e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.949464e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.896101e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.614460e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.384357e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.489113e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.445725e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.945636e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.424653e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 19)
*************************************************************************/
static double mannwhitneyu_utbln5n19(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.850027e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.059159e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.071106e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.669960e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.022780e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.442555e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.851335e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.433865e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.514465e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.332989e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.606099e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.341945e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.402164e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.039761e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.512831e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.284427e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 20)
*************************************************************************/
static double mannwhitneyu_utbln5n20(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.849651e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.054729e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.065747e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.636243e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.003234e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.372789e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.831551e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.763090e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.830626e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.122384e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.108328e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.557983e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.945666e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.965696e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.493236e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.162591e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 21)
*************************************************************************/
static double mannwhitneyu_utbln5n21(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.849649e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.051155e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.061430e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.608869e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.902788e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.346562e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.874709e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.682887e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.026206e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.534551e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.990575e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.713334e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.737011e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.304571e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.133110e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.123457e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 22)
*************************************************************************/
static double mannwhitneyu_utbln5n22(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.849598e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.047605e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.057264e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.579513e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.749602e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.275137e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.881768e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.177374e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.981056e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.696290e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.886803e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.085378e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.675242e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.426367e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.039613e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.662378e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 23)
*************************************************************************/
static double mannwhitneyu_utbln5n23(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.849269e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.043761e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.052735e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.544683e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.517503e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.112082e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.782070e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.549483e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.747329e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.694263e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.147141e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.526209e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.039173e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.235615e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.656546e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.014423e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 24)
*************************************************************************/
static double mannwhitneyu_utbln5n24(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.848925e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.040178e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.048355e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.510198e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.261134e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.915864e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.627423e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.307345e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.732992e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.869652e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.494176e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.047533e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.178439e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.424171e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.829195e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.840810e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 25)
*************************************************************************/
static double mannwhitneyu_utbln5n25(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.848937e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.037512e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.044866e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.483269e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.063682e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.767778e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.508540e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.332756e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.881511e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.124041e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.368456e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.930499e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.779630e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.029528e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.658678e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.289695e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 26)
*************************************************************************/
static double mannwhitneyu_utbln5n26(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.849416e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.035915e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.042493e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.466021e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.956432e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.698914e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.465689e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.035254e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.674614e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.492734e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.014021e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.944953e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.255750e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.075841e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.989330e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.134862e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 27)
*************************************************************************/
static double mannwhitneyu_utbln5n27(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.850070e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.034815e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.040650e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.453117e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.886426e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.661702e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.452346e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.002476e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.720126e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.001400e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.729826e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.740640e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.206333e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.366093e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.193471e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.804091e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 28)
*************************************************************************/
static double mannwhitneyu_utbln5n28(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.850668e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.033786e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.038853e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.440281e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.806020e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.612883e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.420436e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.787982e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.535230e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.263121e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.849609e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.863967e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.391610e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.720294e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.952273e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.901413e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 29)
*************************************************************************/
static double mannwhitneyu_utbln5n29(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.851217e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.032834e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.037113e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.427762e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.719146e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.557172e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.375498e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.452033e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.187516e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.916936e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.065533e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.067301e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.615824e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.432244e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.417795e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.710038e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 30)
*************************************************************************/
static double mannwhitneyu_utbln5n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.851845e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.032148e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.035679e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.417758e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.655330e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.522132e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.352106e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.326911e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.064969e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.813321e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.683881e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.813346e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.627085e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.832107e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.519336e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.888530e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 5, 100)
*************************************************************************/
static double mannwhitneyu_utbln5n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.250000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.877940e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.039324e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.022243e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.305825e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.960119e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.112000e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.138868e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.418164e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.174520e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.489617e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.878301e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.302233e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.054113e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.458862e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.186591e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.623412e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 6)
*************************************************************************/
static double mannwhitneyu_utbln6n6(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/2.882307e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.054075e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.998804e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.681518e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.067578e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.709435e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.952661e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.641700e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.304572e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.336275e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.770385e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.401891e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.246148e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.442663e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.502866e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.105855e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.739371e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 7)
*************************************************************************/
static double mannwhitneyu_utbln6n7(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.000000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.265287e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.274613e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.582352e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.334293e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.915502e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.108091e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.546701e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.298827e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.891501e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.313717e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.989501e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.914594e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.062372e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.158841e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.596443e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.185662e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 8)
*************************************************************************/
static double mannwhitneyu_utbln6n8(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.098387e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.450954e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.520462e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.420299e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.604853e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.165840e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.008756e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.723402e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.843521e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.883405e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.720980e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.301709e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.948034e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.776243e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.623736e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.742068e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.796927e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 9)
*************************************************************************/
static double mannwhitneyu_utbln6n9(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.181981e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.616113e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.741650e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.204487e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.873068e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.446794e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.632286e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.266481e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.280067e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.780687e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.480242e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.592200e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.581019e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.264231e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.347174e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.167535e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.092185e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 10)
*************************************************************************/
static double mannwhitneyu_utbln6n10(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.253957e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.764382e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.942366e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.939896e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.137812e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.720270e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.281070e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.901060e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.824937e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.802812e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.258132e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.233536e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.085530e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.212151e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.001329e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.226048e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.035298e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 11)
*************************************************************************/
static double mannwhitneyu_utbln6n11(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.316625e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.898597e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.125710e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.063297e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.396852e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.990126e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.927977e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.726500e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.858745e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.654590e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.217736e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.989770e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.768493e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.924364e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.140215e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.647914e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.924802e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 12)
*************************************************************************/
static double mannwhitneyu_utbln6n12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.371709e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.020941e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.294250e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.128842e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.650389e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.248611e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.578510e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.162852e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.746982e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.454209e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.128042e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.936650e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.530794e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.665192e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.994144e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.662249e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.368541e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 13)
*************************************************************************/
static double mannwhitneyu_utbln6n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.420526e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.133167e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.450016e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.191088e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.898220e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.050249e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.226901e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.471113e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.007470e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.049420e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.059074e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.881249e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.452780e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.441805e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.787493e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.483957e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.481590e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 14)
*************************************************************************/
static double mannwhitneyu_utbln6n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.450000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.201268e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.542568e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.226965e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.046029e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.136657e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.786757e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.843748e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.588022e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.253029e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.667188e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.788330e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.474545e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.540494e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.951188e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.863323e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.220904e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 15)
*************************************************************************/
static double mannwhitneyu_utbln6n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.450000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.195689e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.526567e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.213617e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.975035e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.118480e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.859142e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.083312e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.298720e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.766708e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.026356e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.093113e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.135168e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.136376e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.190870e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.435972e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.413129e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 30)
*************************************************************************/
static double mannwhitneyu_utbln6n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.450000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.166269e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.427399e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.118239e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.360847e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.745885e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.025041e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.187179e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.432089e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.408451e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.388774e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.795560e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.304136e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.258516e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.180236e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.388679e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.836027e-06, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 6, 100)
*************************************************************************/
static double mannwhitneyu_utbln6n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.450000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.181350e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.417919e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.094201e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.195883e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.818937e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.514202e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.125047e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.022148e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.284181e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.157766e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.023752e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.127985e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.221690e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.516179e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.501398e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.380220e-06, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 7)
*************************************************************************/
static double mannwhitneyu_utbln7n7(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.130495e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.501264e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.584790e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.577311e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.617002e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.145186e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.023462e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.408251e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.626515e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.072492e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.722926e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.095445e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.842602e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.751427e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.008927e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.892431e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.772386e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 8)
*************************************************************************/
static double mannwhitneyu_utbln7n8(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.240370e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.709965e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.862154e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.504541e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.900195e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.439995e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.678028e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.485540e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.437047e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.440092e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.114227e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.516569e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.829457e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.787550e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.761866e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.991911e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.533481e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 9)
*************************************************************************/
static double mannwhitneyu_utbln7n9(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.334314e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.896550e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.112671e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.037277e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.181695e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.765190e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.360116e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.695960e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.780578e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.963843e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.616148e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.852104e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.390744e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.014041e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.888101e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.467474e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.004611e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 10)
*************************************************************************/
static double mannwhitneyu_utbln7n10(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.415650e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.064844e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.340749e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.118888e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.459730e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.097781e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.057688e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.097406e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.209262e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.065641e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.196677e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.313994e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.827157e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.822284e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.389090e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.340850e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.395172e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 11)
*************************************************************************/
static double mannwhitneyu_utbln7n11(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.486817e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.217795e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.549783e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.195905e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.733093e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.428447e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.760093e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.431676e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.717152e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.032199e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.832423e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.905979e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.302799e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.464371e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.456211e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.736244e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.140712e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 12)
*************************************************************************/
static double mannwhitneyu_utbln7n12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.500000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.235822e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.564100e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.190813e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.686546e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.395083e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.967359e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.747096e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.304144e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.903198e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.134906e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.175035e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.266224e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.892931e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.604706e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.070459e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.427010e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 13)
*************************************************************************/
static double mannwhitneyu_utbln7n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.500000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.222204e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.532300e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.164642e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.523768e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.531984e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.467857e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.483804e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.524136e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.077740e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.745218e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.602085e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.828831e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.994070e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.873879e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.341937e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.706444e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 14)
*************************************************************************/
static double mannwhitneyu_utbln7n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.500000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.211763e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.507542e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.143640e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.395755e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.808020e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.044259e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.182308e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.057325e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.724255e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.303900e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.113148e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.102514e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.559442e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.634986e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.776476e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.054489e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 15)
*************************************************************************/
static double mannwhitneyu_utbln7n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.500000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.204898e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.489960e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.129172e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.316741e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.506107e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.983676e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.258013e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.262515e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.984156e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.912108e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.974023e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.056195e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.090842e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.232620e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.816339e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.020421e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 30)
*************************************************************************/
static double mannwhitneyu_utbln7n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.500000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.176536e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.398705e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.045481e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.821982e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.962304e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.698132e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.062667e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.282353e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.014836e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.035683e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.004137e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.801453e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.920705e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.518735e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.821501e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.801008e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 7, 100)
*************************************************************************/
static double mannwhitneyu_utbln7n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.500000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.188337e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.386949e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.022834e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.686517e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.323516e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.399392e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.644333e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.617044e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.031396e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.792066e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.675457e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.673416e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.258552e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.174214e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.073644e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.349958e-06, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 8)
*************************************************************************/
static double mannwhitneyu_utbln8n8(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.360672e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -3.940217e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.168913e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.051485e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.195325e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.775196e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.385506e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.244902e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.525632e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.771275e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.332874e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.079599e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.882551e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.407944e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.769844e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.062433e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.872535e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 9)
*************************************************************************/
static double mannwhitneyu_utbln8n9(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.464102e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.147004e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.446939e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.146155e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.488561e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.144561e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.116917e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.205667e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.515661e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.618616e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.599011e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.457324e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.482917e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.488267e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.469823e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.957591e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.058326e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 10)
*************************************************************************/
static double mannwhitneyu_utbln8n10(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.554093e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.334282e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.700860e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.235253e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.778489e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.527324e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.862885e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.589781e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.507355e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.717526e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.215726e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.848696e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.918854e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.219614e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.753761e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.573688e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.602177e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 11)
*************************************************************************/
static double mannwhitneyu_utbln8n11(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.600000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.421882e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.812457e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.266153e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.849344e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.971527e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.258944e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.944820e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.894685e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.031836e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.514330e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.351660e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.206748e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.492600e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.005338e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.780099e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.673599e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 12)
*************************************************************************/
static double mannwhitneyu_utbln8n12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.600000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.398211e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.762214e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.226296e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.603837e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.643223e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.502438e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.544574e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.647734e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.442259e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.011484e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.384758e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.998259e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.659985e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.331046e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.638478e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.056785e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 13)
*************************************************************************/
static double mannwhitneyu_utbln8n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.600000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.380670e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.724511e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.195851e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.420511e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.609928e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.893999e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.115919e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.291410e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.339664e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.801548e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.534710e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.793250e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.806718e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.384624e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.120582e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.936453e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 14)
*************************************************************************/
static double mannwhitneyu_utbln8n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.600000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.368494e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.697171e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.174440e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.300621e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.087393e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.685826e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.085254e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.525658e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.966647e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.453388e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.826066e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.501958e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.336297e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.251972e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.118456e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.415959e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 15)
*************************************************************************/
static double mannwhitneyu_utbln8n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.600000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.358397e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.674485e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.155941e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.195780e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.544830e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.426183e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.309902e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.650956e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.068874e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.538544e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.192525e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.073905e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.079673e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.423572e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.579647e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.765904e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 30)
*************************************************************************/
static double mannwhitneyu_utbln8n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.600000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.318823e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.567159e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.064864e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.688413e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.153712e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.309389e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.226861e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.523815e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.780987e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.166866e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.922431e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.466397e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.690036e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.008185e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.271903e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.534751e-06, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 8, 100)
*************************************************************************/
static double mannwhitneyu_utbln8n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.600000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.324531e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.547071e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.038129e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.541549e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.525605e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.044992e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.085713e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.017871e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.459226e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.092064e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.024349e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 7.366347e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.385637e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.321722e-08, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.439286e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.058079e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 9)
*************************************************************************/
static double mannwhitneyu_utbln9n9(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.576237e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.372857e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.750859e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.248233e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.792868e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.559372e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.894941e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.643256e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.091370e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.285034e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.112997e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.806229e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.150741e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.509825e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.891051e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.485013e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.343653e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 10)
*************************************************************************/
static double mannwhitneyu_utbln9n10(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.516726e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.939333e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.305046e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.935326e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.029141e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.420592e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.053140e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.065930e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.523581e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.544888e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.813741e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.510631e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.536057e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.833815e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.189692e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.615050e-03, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 11)
*************************************************************************/
static double mannwhitneyu_utbln9n11(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.481308e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.867483e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.249072e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.591790e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.400128e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.341992e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.463680e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.487211e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.671196e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.343472e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.544146e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.802335e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.117084e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.217443e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.858766e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.193687e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 12)
*************************************************************************/
static double mannwhitneyu_utbln9n12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.456776e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.817037e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.209788e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.362108e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.171356e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.661557e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.026141e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.361908e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.093885e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.298389e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.663603e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.768522e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.579015e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.868677e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.440652e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.523037e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 13)
*************************************************************************/
static double mannwhitneyu_utbln9n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.438840e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.779308e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.180614e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.196489e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.346621e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.234857e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.796211e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.575715e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.525647e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.964651e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.275235e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.299124e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.397416e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.295781e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.237619e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 7.269692e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 14)
*************************************************************************/
static double mannwhitneyu_utbln9n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.425981e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.751545e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.159543e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.086570e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.917446e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.120112e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.175519e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.515473e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.727772e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.070629e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.677569e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.876953e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.233502e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.508182e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.120389e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.847212e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 15)
*************************************************************************/
static double mannwhitneyu_utbln9n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.414952e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.727612e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.140634e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.981231e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.382635e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.853575e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.571051e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.567625e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.214197e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.448700e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.712669e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.015050e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.438610e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.301363e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.309386e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.164772e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 30)
*************************************************************************/
static double mannwhitneyu_utbln9n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.370720e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.615712e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.050023e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.504775e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.318265e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.646826e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.741492e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.735360e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.966911e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.100738e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.348991e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.527687e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.917286e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.397466e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.360175e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.892252e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 9, 100)
*************************************************************************/
static double mannwhitneyu_utbln9n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.372506e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.590966e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.021758e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.359849e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.755519e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.533166e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.936659e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.634913e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.730053e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.791845e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.030682e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.228663e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.631175e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.636749e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.404599e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.789872e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 10, 10)
*************************************************************************/
static double mannwhitneyu_utbln10n10(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.468831e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.844398e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.231728e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.486073e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.781321e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.971425e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.215371e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.828451e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.419872e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.430165e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.740363e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.049211e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.269371e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.211393e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.232314e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.016081e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 10, 11)
*************************************************************************/
static double mannwhitneyu_utbln10n11(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.437998e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.782296e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.184732e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.219585e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.457012e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.296008e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.481501e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.527940e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.953426e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.563840e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.574403e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.535775e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.338037e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.002654e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.852676e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.318132e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 10, 12)
*************************************************************************/
static double mannwhitneyu_utbln10n12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.416082e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.737458e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.150952e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.036884e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.609030e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.908684e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.439666e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.162647e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.451601e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.148757e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.803981e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.731621e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.346903e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.013151e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.956148e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.438381e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 10, 13)
*************************************************************************/
static double mannwhitneyu_utbln10n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.399480e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.702863e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.124829e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.897428e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.979802e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.634368e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.180461e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.484926e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.864376e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.186576e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.886925e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.836828e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.074756e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.209547e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.883266e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.380143e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 10, 14)
*************************************************************************/
static double mannwhitneyu_utbln10n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.386924e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.676124e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.104740e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.793826e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.558886e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.492462e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.052903e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.917782e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.878696e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.576046e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.764551e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.288778e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.757658e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.299101e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.265197e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.384503e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 10, 15)
*************************************************************************/
static double mannwhitneyu_utbln10n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.376846e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.654247e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.088083e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.705945e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.169677e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.317213e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.264836e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.548024e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.633910e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.505621e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.658588e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.320254e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.175277e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.122317e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.675688e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.661363e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 10, 30)
*************************************************************************/
static double mannwhitneyu_utbln10n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.333977e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.548099e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.004444e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.291014e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.523674e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.828211e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.716917e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.894256e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.433371e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.522675e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.764192e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.140235e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.629230e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.541895e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.944946e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.726360e-06, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 10, 100)
*************************************************************************/
static double mannwhitneyu_utbln10n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.650000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.334008e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.522316e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.769627e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.158110e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.053650e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.242235e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.173571e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.033661e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.824732e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.084420e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.610036e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.728155e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.217130e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.340966e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.001235e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.694052e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 11, 11)
*************************************************************************/
static double mannwhitneyu_utbln11n11(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.519760e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.880694e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.200698e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.174092e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.072304e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.054773e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.506613e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.813942e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.223644e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.417416e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.499166e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.194332e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 7.369096e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.968590e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.630532e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.061000e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 11, 12)
*************************************************************************/
static double mannwhitneyu_utbln11n12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.495790e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.832622e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.165420e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.987306e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.265621e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.723537e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.347406e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.353464e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.613369e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.102522e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.237709e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.665652e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.626903e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.167518e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.564455e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.047320e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 11, 13)
*************************************************************************/
static double mannwhitneyu_utbln11n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.477880e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.796242e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.138769e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.851739e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.722104e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.548304e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.176683e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.817895e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.842451e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.935870e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.421777e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.238831e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.867026e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.458255e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.306259e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.961487e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 11, 14)
*************************************************************************/
static double mannwhitneyu_utbln11n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.463683e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.766969e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.117082e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.739574e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.238865e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.350306e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.425871e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.640172e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.660633e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.879883e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.349658e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.271795e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.304544e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.024201e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.816867e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.596787e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 11, 15)
*************************************************************************/
static double mannwhitneyu_utbln11n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.452526e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.743570e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.099705e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.650612e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.858285e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.187036e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.689241e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.294360e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.072623e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.278008e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.322382e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.131558e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.305669e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.825627e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.332689e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.120973e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 11, 30)
*************************************************************************/
static double mannwhitneyu_utbln11n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.402621e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.627440e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.011333e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.224126e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.232856e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.859347e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.377381e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.756709e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.033230e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.875472e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.608399e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.102943e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.740693e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.343139e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.196878e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.658062e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 11, 100)
*************************************************************************/
static double mannwhitneyu_utbln11n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.398795e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.596486e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.814761e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.085187e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.766529e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.379425e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.986351e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.214705e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.360075e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.260869e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.033307e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.727087e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.393883e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.242989e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.111928e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.898823e-09, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 12, 12)
*************************************************************************/
static double mannwhitneyu_utbln12n12(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.472616e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.786627e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.132099e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.817523e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.570179e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.479511e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.799492e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.565350e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.530139e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.380132e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.242761e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.576269e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.018771e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.933911e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.002799e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.022048e-06, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 12, 13)
*************************************************************************/
static double mannwhitneyu_utbln12n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.454800e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.750794e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.105988e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.684754e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.011826e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.262579e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.044492e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.478741e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.322165e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.621104e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.068753e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.468396e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.056235e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.327375e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.914877e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.784191e-04, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 12, 14)
*************************************************************************/
static double mannwhitneyu_utbln12n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.440910e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.722404e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.085254e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.579439e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.563738e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.066730e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.129346e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.014531e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.129679e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.000909e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.996174e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.377924e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.936304e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.051098e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.025820e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 8.730585e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 12, 15)
*************************************************************************/
static double mannwhitneyu_utbln12n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.430123e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.700008e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.068971e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.499725e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.250897e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.473145e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.680008e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.483350e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.766992e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.891081e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.015140e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.977756e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.707414e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.114786e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.238865e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.381445e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 12, 30)
*************************************************************************/
static double mannwhitneyu_utbln12n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.380023e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.585782e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.838583e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.103394e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.834015e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.635212e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.948212e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.574169e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.747980e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.833672e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.722433e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.181038e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.206473e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.716003e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.476434e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.217700e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 12, 100)
*************************************************************************/
static double mannwhitneyu_utbln12n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.700000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.374567e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.553481e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.541334e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.701907e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.414757e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.404103e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.234388e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.453762e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.311060e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.317501e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.713888e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.309583e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.019804e-08, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.224829e-09, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.349019e-08, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.893302e-08, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 13, 13)
*************************************************************************/
static double mannwhitneyu_utbln13n13(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.541046e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.859047e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.130164e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.689719e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.950693e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.231455e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.976550e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.538455e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.245603e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.142647e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.831434e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.032483e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.488405e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.156927e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.949279e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.532700e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 13, 14)
*************************************************************************/
static double mannwhitneyu_utbln13n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.525655e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.828341e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.108110e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.579552e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.488307e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.032328e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.988741e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.766394e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.388950e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.338179e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.133440e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.023518e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.110570e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.202332e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.056132e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.536323e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 13, 15)
*************************************************************************/
static double mannwhitneyu_utbln13n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.513585e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.803952e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.090686e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.495310e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.160314e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.073124e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.480313e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.478239e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.140914e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.311541e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.677105e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.115464e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.578563e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.044604e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.888939e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 2.395644e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 13, 30)
*************************************************************************/
static double mannwhitneyu_utbln13n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.455999e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.678434e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.995491e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.078100e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.705220e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.258739e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.671526e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.185458e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.507764e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.411446e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.044355e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.285765e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.345282e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.066940e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.962037e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.723644e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 13, 100)
*************************************************************************/
static double mannwhitneyu_utbln13n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.446787e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.640804e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.671552e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.364990e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.274444e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.047440e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.161439e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.171729e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.562171e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.359762e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.275494e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.747635e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.700292e-08, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.565559e-09, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 5.005396e-09, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 3.335794e-09, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 14, 14)
*************************************************************************/
static double mannwhitneyu_utbln14n14(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.510624e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.798584e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.087107e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.478532e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.098050e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.855986e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.409083e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.299536e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.176177e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.479417e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.812761e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -5.225872e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 4.516521e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 6.730551e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 9.237563e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.611820e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 14, 15)
*************************************************************************/
static double mannwhitneyu_utbln14n15(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.498681e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.774668e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.070267e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.399348e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.807239e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.845763e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.071773e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.261698e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.011695e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.305946e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.879295e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.999439e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.904438e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.944986e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.373908e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.140794e-05, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 14, 30)
*************************************************************************/
static double mannwhitneyu_utbln14n30(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.440378e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.649587e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.807829e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.989753e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.463646e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.586580e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -6.745917e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.635398e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.923172e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.446699e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.613892e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.214073e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.651683e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.272777e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.464988e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.109803e-07, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, 14, 100)
*************************************************************************/
static double mannwhitneyu_utbln14n100(double s, ae_state *_state)
{
    double x;
    double tj;
    double tj1;
    double result;


    result = (double)(0);
    x = ae_minreal(2*(s-0.000000e+00)/3.750000e+00-1, 1.0, _state);
    tj = (double)(1);
    tj1 = x;
    mannwhitneyu_ucheb(x, -4.429701e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -4.610577e+00, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -9.482675e-01, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.605550e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.062151e-02, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.525154e-03, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.835983e-04, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -8.411440e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.744901e-05, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.318850e-06, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.692100e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -1.536270e-07, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -3.705888e-08, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -7.999599e-09, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, -2.908395e-09, &tj, &tj1, &result, _state);
    mannwhitneyu_ucheb(x, 1.546923e-09, &tj, &tj1, &result, _state);
    return result;
}


/*************************************************************************
Tail(S, N1, N2)
*************************************************************************/
static double mannwhitneyu_usigma(double s,
     ae_int_t n1,
     ae_int_t n2,
     ae_state *_state)
{
    double f0;
    double f1;
    double f2;
    double f3;
    double f4;
    double s0;
    double s1;
    double s2;
    double s3;
    double s4;
    double result;


    result = (double)(0);
    
    /*
     * N1=5, N2 = 5, 6, 7, ...
     */
    if( ae_minint(n1, n2, _state)==5 )
    {
        if( ae_maxint(n1, n2, _state)==5 )
        {
            result = mannwhitneyu_utbln5n5(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==6 )
        {
            result = mannwhitneyu_utbln5n6(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==7 )
        {
            result = mannwhitneyu_utbln5n7(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==8 )
        {
            result = mannwhitneyu_utbln5n8(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==9 )
        {
            result = mannwhitneyu_utbln5n9(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==10 )
        {
            result = mannwhitneyu_utbln5n10(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==11 )
        {
            result = mannwhitneyu_utbln5n11(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==12 )
        {
            result = mannwhitneyu_utbln5n12(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln5n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln5n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln5n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==16 )
        {
            result = mannwhitneyu_utbln5n16(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==17 )
        {
            result = mannwhitneyu_utbln5n17(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==18 )
        {
            result = mannwhitneyu_utbln5n18(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==19 )
        {
            result = mannwhitneyu_utbln5n19(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==20 )
        {
            result = mannwhitneyu_utbln5n20(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==21 )
        {
            result = mannwhitneyu_utbln5n21(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==22 )
        {
            result = mannwhitneyu_utbln5n22(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==23 )
        {
            result = mannwhitneyu_utbln5n23(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==24 )
        {
            result = mannwhitneyu_utbln5n24(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==25 )
        {
            result = mannwhitneyu_utbln5n25(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==26 )
        {
            result = mannwhitneyu_utbln5n26(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==27 )
        {
            result = mannwhitneyu_utbln5n27(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==28 )
        {
            result = mannwhitneyu_utbln5n28(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==29 )
        {
            result = mannwhitneyu_utbln5n29(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>29 )
        {
            f0 = mannwhitneyu_utbln5n15(s, _state);
            f1 = mannwhitneyu_utbln5n30(s, _state);
            f2 = mannwhitneyu_utbln5n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=6, N2 = 6, 7, 8, ...
     */
    if( ae_minint(n1, n2, _state)==6 )
    {
        if( ae_maxint(n1, n2, _state)==6 )
        {
            result = mannwhitneyu_utbln6n6(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==7 )
        {
            result = mannwhitneyu_utbln6n7(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==8 )
        {
            result = mannwhitneyu_utbln6n8(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==9 )
        {
            result = mannwhitneyu_utbln6n9(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==10 )
        {
            result = mannwhitneyu_utbln6n10(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==11 )
        {
            result = mannwhitneyu_utbln6n11(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==12 )
        {
            result = mannwhitneyu_utbln6n12(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln6n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln6n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln6n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln6n15(s, _state);
            f1 = mannwhitneyu_utbln6n30(s, _state);
            f2 = mannwhitneyu_utbln6n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=7, N2 = 7, 8, ...
     */
    if( ae_minint(n1, n2, _state)==7 )
    {
        if( ae_maxint(n1, n2, _state)==7 )
        {
            result = mannwhitneyu_utbln7n7(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==8 )
        {
            result = mannwhitneyu_utbln7n8(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==9 )
        {
            result = mannwhitneyu_utbln7n9(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==10 )
        {
            result = mannwhitneyu_utbln7n10(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==11 )
        {
            result = mannwhitneyu_utbln7n11(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==12 )
        {
            result = mannwhitneyu_utbln7n12(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln7n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln7n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln7n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln7n15(s, _state);
            f1 = mannwhitneyu_utbln7n30(s, _state);
            f2 = mannwhitneyu_utbln7n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=8, N2 = 8, 9, 10, ...
     */
    if( ae_minint(n1, n2, _state)==8 )
    {
        if( ae_maxint(n1, n2, _state)==8 )
        {
            result = mannwhitneyu_utbln8n8(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==9 )
        {
            result = mannwhitneyu_utbln8n9(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==10 )
        {
            result = mannwhitneyu_utbln8n10(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==11 )
        {
            result = mannwhitneyu_utbln8n11(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==12 )
        {
            result = mannwhitneyu_utbln8n12(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln8n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln8n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln8n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln8n15(s, _state);
            f1 = mannwhitneyu_utbln8n30(s, _state);
            f2 = mannwhitneyu_utbln8n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=9, N2 = 9, 10, ...
     */
    if( ae_minint(n1, n2, _state)==9 )
    {
        if( ae_maxint(n1, n2, _state)==9 )
        {
            result = mannwhitneyu_utbln9n9(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==10 )
        {
            result = mannwhitneyu_utbln9n10(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==11 )
        {
            result = mannwhitneyu_utbln9n11(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==12 )
        {
            result = mannwhitneyu_utbln9n12(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln9n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln9n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln9n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln9n15(s, _state);
            f1 = mannwhitneyu_utbln9n30(s, _state);
            f2 = mannwhitneyu_utbln9n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=10, N2 = 10, 11, ...
     */
    if( ae_minint(n1, n2, _state)==10 )
    {
        if( ae_maxint(n1, n2, _state)==10 )
        {
            result = mannwhitneyu_utbln10n10(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==11 )
        {
            result = mannwhitneyu_utbln10n11(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==12 )
        {
            result = mannwhitneyu_utbln10n12(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln10n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln10n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln10n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln10n15(s, _state);
            f1 = mannwhitneyu_utbln10n30(s, _state);
            f2 = mannwhitneyu_utbln10n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=11, N2 = 11, 12, ...
     */
    if( ae_minint(n1, n2, _state)==11 )
    {
        if( ae_maxint(n1, n2, _state)==11 )
        {
            result = mannwhitneyu_utbln11n11(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==12 )
        {
            result = mannwhitneyu_utbln11n12(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln11n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln11n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln11n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln11n15(s, _state);
            f1 = mannwhitneyu_utbln11n30(s, _state);
            f2 = mannwhitneyu_utbln11n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=12, N2 = 12, 13, ...
     */
    if( ae_minint(n1, n2, _state)==12 )
    {
        if( ae_maxint(n1, n2, _state)==12 )
        {
            result = mannwhitneyu_utbln12n12(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln12n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln12n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln12n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln12n15(s, _state);
            f1 = mannwhitneyu_utbln12n30(s, _state);
            f2 = mannwhitneyu_utbln12n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=13, N2 = 13, 14, ...
     */
    if( ae_minint(n1, n2, _state)==13 )
    {
        if( ae_maxint(n1, n2, _state)==13 )
        {
            result = mannwhitneyu_utbln13n13(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln13n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln13n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln13n15(s, _state);
            f1 = mannwhitneyu_utbln13n30(s, _state);
            f2 = mannwhitneyu_utbln13n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1=14, N2 = 14, 15, ...
     */
    if( ae_minint(n1, n2, _state)==14 )
    {
        if( ae_maxint(n1, n2, _state)==14 )
        {
            result = mannwhitneyu_utbln14n14(s, _state);
        }
        if( ae_maxint(n1, n2, _state)==15 )
        {
            result = mannwhitneyu_utbln14n15(s, _state);
        }
        if( ae_maxint(n1, n2, _state)>15 )
        {
            f0 = mannwhitneyu_utbln14n15(s, _state);
            f1 = mannwhitneyu_utbln14n30(s, _state);
            f2 = mannwhitneyu_utbln14n100(s, _state);
            result = mannwhitneyu_uninterpolate(f0, f1, f2, ae_maxint(n1, n2, _state), _state);
        }
        return result;
    }
    
    /*
     * N1 >= 15, N2 >= 15
     */
    if( ae_fp_greater(s,(double)(4)) )
    {
        s = (double)(4);
    }
    if( ae_fp_less(s,(double)(3)) )
    {
        s0 = 0.000000e+00;
        f0 = mannwhitneyu_usigma000(n1, n2, _state);
        s1 = 7.500000e-01;
        f1 = mannwhitneyu_usigma075(n1, n2, _state);
        s2 = 1.500000e+00;
        f2 = mannwhitneyu_usigma150(n1, n2, _state);
        s3 = 2.250000e+00;
        f3 = mannwhitneyu_usigma225(n1, n2, _state);
        s4 = 3.000000e+00;
        f4 = mannwhitneyu_usigma300(n1, n2, _state);
        f1 = ((s-s0)*f1-(s-s1)*f0)/(s1-s0);
        f2 = ((s-s0)*f2-(s-s2)*f0)/(s2-s0);
        f3 = ((s-s0)*f3-(s-s3)*f0)/(s3-s0);
        f4 = ((s-s0)*f4-(s-s4)*f0)/(s4-s0);
        f2 = ((s-s1)*f2-(s-s2)*f1)/(s2-s1);
        f3 = ((s-s1)*f3-(s-s3)*f1)/(s3-s1);
        f4 = ((s-s1)*f4-(s-s4)*f1)/(s4-s1);
        f3 = ((s-s2)*f3-(s-s3)*f2)/(s3-s2);
        f4 = ((s-s2)*f4-(s-s4)*f2)/(s4-s2);
        f4 = ((s-s3)*f4-(s-s4)*f3)/(s4-s3);
        result = f4;
    }
    else
    {
        s0 = 3.000000e+00;
        f0 = mannwhitneyu_usigma300(n1, n2, _state);
        s1 = 3.333333e+00;
        f1 = mannwhitneyu_usigma333(n1, n2, _state);
        s2 = 3.666667e+00;
        f2 = mannwhitneyu_usigma367(n1, n2, _state);
        s3 = 4.000000e+00;
        f3 = mannwhitneyu_usigma400(n1, n2, _state);
        f1 = ((s-s0)*f1-(s-s1)*f0)/(s1-s0);
        f2 = ((s-s0)*f2-(s-s2)*f0)/(s2-s0);
        f3 = ((s-s0)*f3-(s-s3)*f0)/(s3-s0);
        f2 = ((s-s1)*f2-(s-s2)*f1)/(s2-s1);
        f3 = ((s-s1)*f3-(s-s3)*f1)/(s3-s1);
        f3 = ((s-s2)*f3-(s-s3)*f2)/(s3-s2);
        result = f3;
    }
    return result;
}


#endif
#if defined(AE_COMPILE_STEST) || !defined(AE_PARTIAL_BUILD)


/*************************************************************************
Sign test

This test checks three hypotheses about the median of  the  given  sample.
The following tests are performed:
    * two-tailed test (null hypothesis - the median is equal to the  given
      value)
    * left-tailed test (null hypothesis - the median is  greater  than  or
      equal to the given value)
    * right-tailed test (null hypothesis - the  median  is  less  than  or
      equal to the given value)

Requirements:
    * the scale of measurement should be ordinal, interval or ratio  (i.e.
      the test could not be applied to nominal variables).

The test is non-parametric and doesn't require distribution X to be normal

Input parameters:
    X       -   sample. Array whose index goes from 0 to N-1.
    N       -   size of the sample.
    Median  -   assumed median value.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

While   calculating   p-values   high-precision   binomial    distribution
approximation is used, so significance levels have about 15 exact digits.

  -- ALGLIB --
     Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void onesamplesigntest(/* Real    */ ae_vector* x,
     ae_int_t n,
     double median,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    ae_int_t i;
    ae_int_t gtcnt;
    ae_int_t necnt;

    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;

    if( n<=1 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * Calculate:
     * GTCnt - count of x[i]>Median
     * NECnt - count of x[i]<>Median
     */
    gtcnt = 0;
    necnt = 0;
    for(i=0; i<=n-1; i++)
    {
        if( ae_fp_greater(x->ptr.p_double[i],median) )
        {
            gtcnt = gtcnt+1;
        }
        if( ae_fp_neq(x->ptr.p_double[i],median) )
        {
            necnt = necnt+1;
        }
    }
    if( necnt==0 )
    {
        
        /*
         * all x[i] are equal to Median.
         * So we can conclude that Median is a true median :)
         */
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    *bothtails = ae_minreal(2*binomialdistribution(ae_minint(gtcnt, necnt-gtcnt, _state), necnt, 0.5, _state), 1.0, _state);
    *lefttail = binomialdistribution(gtcnt, necnt, 0.5, _state);
    *righttail = binomialcdistribution(gtcnt-1, necnt, 0.5, _state);
}


#endif
#if defined(AE_COMPILE_STUDENTTTESTS) || !defined(AE_PARTIAL_BUILD)


/*************************************************************************
One-sample t-test

This test checks three hypotheses about the mean of the given sample.  The
following tests are performed:
    * two-tailed test (null hypothesis - the mean is equal  to  the  given
      value)
    * left-tailed test (null hypothesis - the  mean  is  greater  than  or
      equal to the given value)
    * right-tailed test (null hypothesis - the mean is less than or  equal
      to the given value).

The test is based on the assumption that  a  given  sample  has  a  normal
distribution and  an  unknown  dispersion.  If  the  distribution  sharply
differs from normal, the test will work incorrectly.

INPUT PARAMETERS:
    X       -   sample. Array whose index goes from 0 to N-1.
    N       -   size of sample, N>=0
    Mean    -   assumed value of the mean.

OUTPUT PARAMETERS:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

NOTE: this function correctly handles degenerate cases:
      * when N=0, all p-values are set to 1.0
      * when variance of X[] is exactly zero, p-values are set
        to 1.0 or 0.0, depending on difference between sample mean and
        value of mean being tested.


  -- ALGLIB --
     Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void studentttest1(/* Real    */ ae_vector* x,
     ae_int_t n,
     double mean,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    ae_int_t i;
    double xmean;
    double x0;
    double v;
    ae_bool samex;
    double xvariance;
    double xstddev;
    double v1;
    double v2;
    double stat;
    double s;

    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;

    if( n<=0 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * Mean
     */
    xmean = (double)(0);
    x0 = x->ptr.p_double[0];
    samex = ae_true;
    for(i=0; i<=n-1; i++)
    {
        v = x->ptr.p_double[i];
        xmean = xmean+v;
        samex = samex&&ae_fp_eq(v,x0);
    }
    if( samex )
    {
        xmean = x0;
    }
    else
    {
        xmean = xmean/n;
    }
    
    /*
     * Variance (using corrected two-pass algorithm)
     */
    xvariance = (double)(0);
    xstddev = (double)(0);
    if( n!=1&&!samex )
    {
        v1 = (double)(0);
        for(i=0; i<=n-1; i++)
        {
            v1 = v1+ae_sqr(x->ptr.p_double[i]-xmean, _state);
        }
        v2 = (double)(0);
        for(i=0; i<=n-1; i++)
        {
            v2 = v2+(x->ptr.p_double[i]-xmean);
        }
        v2 = ae_sqr(v2, _state)/n;
        xvariance = (v1-v2)/(n-1);
        if( ae_fp_less(xvariance,(double)(0)) )
        {
            xvariance = (double)(0);
        }
        xstddev = ae_sqrt(xvariance, _state);
    }
    if( ae_fp_eq(xstddev,(double)(0)) )
    {
        if( ae_fp_eq(xmean,mean) )
        {
            *bothtails = 1.0;
        }
        else
        {
            *bothtails = 0.0;
        }
        if( ae_fp_greater_eq(xmean,mean) )
        {
            *lefttail = 1.0;
        }
        else
        {
            *lefttail = 0.0;
        }
        if( ae_fp_less_eq(xmean,mean) )
        {
            *righttail = 1.0;
        }
        else
        {
            *righttail = 0.0;
        }
        return;
    }
    
    /*
     * Statistic
     */
    stat = (xmean-mean)/(xstddev/ae_sqrt((double)(n), _state));
    s = studenttdistribution(n-1, stat, _state);
    *bothtails = 2*ae_minreal(s, 1-s, _state);
    *lefttail = s;
    *righttail = 1-s;
}


/*************************************************************************
Two-sample pooled test

This test checks three hypotheses about the mean of the given samples. The
following tests are performed:
    * two-tailed test (null hypothesis - the means are equal)
    * left-tailed test (null hypothesis - the mean of the first sample  is
      greater than or equal to the mean of the second sample)
    * right-tailed test (null hypothesis - the mean of the first sample is
      less than or equal to the mean of the second sample).

Test is based on the following assumptions:
    * given samples have normal distributions
    * dispersions are equal
    * samples are independent.

Input parameters:
    X       -   sample 1. Array whose index goes from 0 to N-1.
    N       -   size of sample.
    Y       -   sample 2. Array whose index goes from 0 to M-1.
    M       -   size of sample.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

NOTE: this function correctly handles degenerate cases:
      * when N=0 or M=0, all p-values are set to 1.0
      * when both samples has exactly zero variance, p-values are set
        to 1.0 or 0.0, depending on difference between means.

  -- ALGLIB --
     Copyright 18.09.2006 by Bochkanov Sergey
*************************************************************************/
void studentttest2(/* Real    */ ae_vector* x,
     ae_int_t n,
     /* Real    */ ae_vector* y,
     ae_int_t m,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    ae_int_t i;
    ae_bool samex;
    ae_bool samey;
    double x0;
    double y0;
    double xmean;
    double ymean;
    double v;
    double stat;
    double s;
    double p;

    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;

    if( n<=0||m<=0 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * Mean
     */
    xmean = (double)(0);
    x0 = x->ptr.p_double[0];
    samex = ae_true;
    for(i=0; i<=n-1; i++)
    {
        v = x->ptr.p_double[i];
        xmean = xmean+v;
        samex = samex&&ae_fp_eq(v,x0);
    }
    if( samex )
    {
        xmean = x0;
    }
    else
    {
        xmean = xmean/n;
    }
    ymean = (double)(0);
    y0 = y->ptr.p_double[0];
    samey = ae_true;
    for(i=0; i<=m-1; i++)
    {
        v = y->ptr.p_double[i];
        ymean = ymean+v;
        samey = samey&&ae_fp_eq(v,y0);
    }
    if( samey )
    {
        ymean = y0;
    }
    else
    {
        ymean = ymean/m;
    }
    
    /*
     * S
     */
    s = (double)(0);
    if( n+m>2 )
    {
        for(i=0; i<=n-1; i++)
        {
            s = s+ae_sqr(x->ptr.p_double[i]-xmean, _state);
        }
        for(i=0; i<=m-1; i++)
        {
            s = s+ae_sqr(y->ptr.p_double[i]-ymean, _state);
        }
        s = ae_sqrt(s*((double)1/(double)n+(double)1/(double)m)/(n+m-2), _state);
    }
    if( ae_fp_eq(s,(double)(0)) )
    {
        if( ae_fp_eq(xmean,ymean) )
        {
            *bothtails = 1.0;
        }
        else
        {
            *bothtails = 0.0;
        }
        if( ae_fp_greater_eq(xmean,ymean) )
        {
            *lefttail = 1.0;
        }
        else
        {
            *lefttail = 0.0;
        }
        if( ae_fp_less_eq(xmean,ymean) )
        {
            *righttail = 1.0;
        }
        else
        {
            *righttail = 0.0;
        }
        return;
    }
    
    /*
     * Statistic
     */
    stat = (xmean-ymean)/s;
    p = studenttdistribution(n+m-2, stat, _state);
    *bothtails = 2*ae_minreal(p, 1-p, _state);
    *lefttail = p;
    *righttail = 1-p;
}


/*************************************************************************
Two-sample unpooled test

This test checks three hypotheses about the mean of the given samples. The
following tests are performed:
    * two-tailed test (null hypothesis - the means are equal)
    * left-tailed test (null hypothesis - the mean of the first sample  is
      greater than or equal to the mean of the second sample)
    * right-tailed test (null hypothesis - the mean of the first sample is
      less than or equal to the mean of the second sample).

Test is based on the following assumptions:
    * given samples have normal distributions
    * samples are independent.
Equality of variances is NOT required.

Input parameters:
    X - sample 1. Array whose index goes from 0 to N-1.
    N - size of the sample.
    Y - sample 2. Array whose index goes from 0 to M-1.
    M - size of the sample.

Output parameters:
    BothTails   -   p-value for two-tailed test.
                    If BothTails is less than the given significance level
                    the null hypothesis is rejected.
    LeftTail    -   p-value for left-tailed test.
                    If LeftTail is less than the given significance level,
                    the null hypothesis is rejected.
    RightTail   -   p-value for right-tailed test.
                    If RightTail is less than the given significance level
                    the null hypothesis is rejected.

NOTE: this function correctly handles degenerate cases:
      * when N=0 or M=0, all p-values are set to 1.0
      * when both samples has zero variance, p-values are set
        to 1.0 or 0.0, depending on difference between means.
      * when only one sample has zero variance, test reduces to 1-sample
        version.

  -- ALGLIB --
     Copyright 18.09.2006 by Bochkanov Sergey
*************************************************************************/
void unequalvariancettest(/* Real    */ ae_vector* x,
     ae_int_t n,
     /* Real    */ ae_vector* y,
     ae_int_t m,
     double* bothtails,
     double* lefttail,
     double* righttail,
     ae_state *_state)
{
    ae_int_t i;
    ae_bool samex;
    ae_bool samey;
    double x0;
    double y0;
    double xmean;
    double ymean;
    double xvar;
    double yvar;
    double v;
    double df;
    double p;
    double stat;
    double c;

    *bothtails = 0;
    *lefttail = 0;
    *righttail = 0;

    if( n<=0||m<=0 )
    {
        *bothtails = 1.0;
        *lefttail = 1.0;
        *righttail = 1.0;
        return;
    }
    
    /*
     * Mean
     */
    xmean = (double)(0);
    x0 = x->ptr.p_double[0];
    samex = ae_true;
    for(i=0; i<=n-1; i++)
    {
        v = x->ptr.p_double[i];
        xmean = xmean+v;
        samex = samex&&ae_fp_eq(v,x0);
    }
    if( samex )
    {
        xmean = x0;
    }
    else
    {
        xmean = xmean/n;
    }
    ymean = (double)(0);
    y0 = y->ptr.p_double[0];
    samey = ae_true;
    for(i=0; i<=m-1; i++)
    {
        v = y->ptr.p_double[i];
        ymean = ymean+v;
        samey = samey&&ae_fp_eq(v,y0);
    }
    if( samey )
    {
        ymean = y0;
    }
    else
    {
        ymean = ymean/m;
    }
    
    /*
     * Variance (using corrected two-pass algorithm)
     */
    xvar = (double)(0);
    if( n>=2&&!samex )
    {
        for(i=0; i<=n-1; i++)
        {
            xvar = xvar+ae_sqr(x->ptr.p_double[i]-xmean, _state);
        }
        xvar = xvar/(n-1);
    }
    yvar = (double)(0);
    if( m>=2&&!samey )
    {
        for(i=0; i<=m-1; i++)
        {
            yvar = yvar+ae_sqr(y->ptr.p_double[i]-ymean, _state);
        }
        yvar = yvar/(m-1);
    }
    
    /*
     * Handle different special cases
     * (one or both variances are zero).
     */
    if( ae_fp_eq(xvar,(double)(0))&&ae_fp_eq(yvar,(double)(0)) )
    {
        if( ae_fp_eq(xmean,ymean) )
        {
            *bothtails = 1.0;
        }
        else
        {
            *bothtails = 0.0;
        }
        if( ae_fp_greater_eq(xmean,ymean) )
        {
            *lefttail = 1.0;
        }
        else
        {
            *lefttail = 0.0;
        }
        if( ae_fp_less_eq(xmean,ymean) )
        {
            *righttail = 1.0;
        }
        else
        {
            *righttail = 0.0;
        }
        return;
    }
    if( ae_fp_eq(xvar,(double)(0)) )
    {
        
        /*
         * X is constant, unpooled 2-sample test reduces to 1-sample test.
         *
         * NOTE: right-tail and left-tail must be passed to 1-sample
         *       t-test in reverse order because we reverse order of
         *       of samples.
         */
        studentttest1(y, m, xmean, bothtails, righttail, lefttail, _state);
        return;
    }
    if( ae_fp_eq(yvar,(double)(0)) )
    {
        
        /*
         * Y is constant, unpooled 2-sample test reduces to 1-sample test.
         */
        studentttest1(x, n, ymean, bothtails, lefttail, righttail, _state);
        return;
    }
    
    /*
     * Statistic
     */
    stat = (xmean-ymean)/ae_sqrt(xvar/n+yvar/m, _state);
    c = xvar/n/(xvar/n+yvar/m);
    df = rmul2((double)(n-1), (double)(m-1), _state)/((m-1)*ae_sqr(c, _state)+(n-1)*ae_sqr(1-c, _state));
    if( ae_fp_greater(stat,(double)(0)) )
    {
        p = 1-0.5*incompletebeta(df/2, 0.5, df/(df+ae_sqr(stat, _state)), _state);
    }
    else
    {
        p = 0.5*incompletebeta(df/2, 0.5, df/(df+ae_sqr(stat, _state)), _state);
    }
    *bothtails = 2*ae_minreal(p, 1-p, _state);
    *lefttail = p;
    *righttail = 1-p;
}


#endif

}

