/*
//
//  Copyright 1997-2009 Torsten Rohlfing
//
//  Copyright 2004-2010, 2013 SRI International
//
//  This file is part of the Computational Morphometry Toolkit.
//
//  http://www.nitrc.org/projects/cmtk/
//
//  The Computational Morphometry Toolkit 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, either version 3 of
//  the License, or (at your option) any later version.
//
//  The Computational Morphometry Toolkit 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.
//
//  You should have received a copy of the GNU General Public License along
//  with the Computational Morphometry Toolkit.  If not, see
//  <http://www.gnu.org/licenses/>.
//
//  $Revision: 4812 $
//
//  $LastChangedDate: 2013-09-09 14:26:32 -0700 (Mon, 09 Sep 2013) $
//
//  $LastChangedBy: torstenrohlfing $
//
*/
/*************************************************************************
Cephes Math Library Release 2.8:  June, 2000
Copyright by Stephen L. Moshier

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from C to
      pseudocode.

See subroutines comments for additional copyrights.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:

- Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer listed
  in this license in the documentation and/or other materials
  provided with the distribution.

- Neither the name of the copyright holders nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*************************************************************************/


#include "gammaf.h"

namespace
alglib
{

ap::real_value_type gammastirf(ap::real_value_type x);

/*************************************************************************
Gamma function

Input parameters:
    X   -   argument

Domain:
    0 < X < 171.6
    -170 < X < 0, X is not an integer.

Relative error:
 arithmetic   domain     # trials      peak         rms
    IEEE    -170,-33      20000       2.3e-15     3.3e-16
    IEEE     -33,  33     20000       9.4e-16     2.2e-16
    IEEE      33, 171.6   20000       2.3e-15     3.2e-16

Cephes Math Library Release 2.8:  June, 2000
Original copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
Translated to AlgoPascal by Bochkanov Sergey (2005, 2006, 2007).
*************************************************************************/
ap::real_value_type gamma(ap::real_value_type x)
{
    ap::real_value_type result;
    ap::real_value_type p;
    ap::real_value_type pp;
    ap::real_value_type q;
    ap::real_value_type qq;
    ap::real_value_type z;
    int i;
    ap::real_value_type sgngam;

    sgngam = 1;
    q = fabs(x);
    if( q>33.0 )
    {
        if( x<0.0 )
        {
            p = ap::ifloor(q);
            i = ap::round(p);
            if( i%2==0 )
            {
                sgngam = -1;
            }
            z = q-p;
            if( z>0.5 )
            {
                p = p+1;
                z = q-p;
            }
            z = q*sin(ap::pi()*z);
            z = fabs(z);
            z = ap::pi()/(z*gammastirf(q));
        }
        else
        {
            z = gammastirf(x);
        }
        result = sgngam*z;
        return result;
    }
    z = 1;
    while(x>=3)
    {
        x = x-1;
        z = z*x;
    }
    while(x<0)
    {
        if( x>-0.000000001 )
        {
            result = z/((1+0.5772156649015329*x)*x);
            return result;
        }
        z = z/x;
        x = x+1;
    }
    while(x<2)
    {
        if( x<0.000000001 )
        {
            result = z/((1+0.5772156649015329*x)*x);
            return result;
        }
        z = z/x;
        x = x+1.0;
    }
    if( x==2 )
    {
        result = z;
        return result;
    }
    x = x-2.0;
    pp = 1.60119522476751861407E-4;
    pp = 1.19135147006586384913E-3+x*pp;
    pp = 1.04213797561761569935E-2+x*pp;
    pp = 4.76367800457137231464E-2+x*pp;
    pp = 2.07448227648435975150E-1+x*pp;
    pp = 4.94214826801497100753E-1+x*pp;
    pp = 9.99999999999999996796E-1+x*pp;
    qq = -2.31581873324120129819E-5;
    qq = 5.39605580493303397842E-4+x*qq;
    qq = -4.45641913851797240494E-3+x*qq;
    qq = 1.18139785222060435552E-2+x*qq;
    qq = 3.58236398605498653373E-2+x*qq;
    qq = -2.34591795718243348568E-1+x*qq;
    qq = 7.14304917030273074085E-2+x*qq;
    qq = 1.00000000000000000320+x*qq;
    result = z*pp/qq;
    return result;
}


/*************************************************************************
Natural logarithm of gamma function

Input parameters:
    X       -   argument

Result:
    logarithm of the absolute value of the Gamma(X).

Output parameters:
    SgnGam  -   sign(Gamma(X))

Domain:
    0 < X < 2.55e305
    -2.55e305 < X < 0, X is not an integer.

ACCURACY:
arithmetic      domain        # trials     peak         rms
   IEEE    0, 3                 28000     5.4e-16     1.1e-16
   IEEE    2.718, 2.556e305     40000     3.5e-16     8.3e-17
The error criterion was relative when the function magnitude
was greater than one but absolute when it was less than one.

The following test used the relative error criterion, though
at certain points the relative error could be much higher than
indicated.
   IEEE    -200, -4             10000     4.8e-16     1.3e-16

Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
Translated to AlgoPascal by Bochkanov Sergey (2005, 2006, 2007).
*************************************************************************/
ap::real_value_type lngamma(ap::real_value_type x, ap::real_value_type& sgngam)
{
    ap::real_value_type result;
    ap::real_value_type a;
    ap::real_value_type b;
    ap::real_value_type c;
    ap::real_value_type p;
    ap::real_value_type q;
    ap::real_value_type u;
    ap::real_value_type w;
    ap::real_value_type z;
    int i;
    ap::real_value_type logpi;
    ap::real_value_type ls2pi;
    ap::real_value_type tmp;

    sgngam = 1;
    logpi = 1.14472988584940017414;
    ls2pi = 0.91893853320467274178;
    if( x<-34.0 )
    {
        q = -x;
        w = lngamma(q, tmp);
        p = ap::ifloor(q);
        i = ap::round(p);
        if( i%2==0 )
        {
            sgngam = -1;
        }
        else
        {
            sgngam = 1;
        }
        z = q-p;
        if( z>0.5 )
        {
            p = p+1;
            z = p-q;
        }
        z = q*sin(ap::pi()*z);
        result = logpi-log(z)-w;
        return result;
    }
    if( x<13 )
    {
        z = 1;
        p = 0;
        u = x;
        while(u>=3)
        {
            p = p-1;
            u = x+p;
            z = z*u;
        }
        while(u<2)
        {
            z = z/u;
            p = p+1;
            u = x+p;
        }
        if( z<0 )
        {
            sgngam = -1;
            z = -z;
        }
        else
        {
            sgngam = 1;
        }
        if( u==2 )
        {
            result = log(z);
            return result;
        }
        p = p-2;
        x = x+p;
        b = -1378.25152569120859100;
        b = -38801.6315134637840924+x*b;
        b = -331612.992738871184744+x*b;
        b = -1162370.97492762307383+x*b;
        b = -1721737.00820839662146+x*b;
        b = -853555.664245765465627+x*b;
        c = 1;
        c = -351.815701436523470549+x*c;
        c = -17064.2106651881159223+x*c;
        c = -220528.590553854454839+x*c;
        c = -1139334.44367982507207+x*c;
        c = -2532523.07177582951285+x*c;
        c = -2018891.41433532773231+x*c;
        p = x*b/c;
        result = log(z)+p;
        return result;
    }
    q = (x-0.5)*log(x)-x+ls2pi;
    if( x>100000000 )
    {
        result = q;
        return result;
    }
    p = 1/(x*x);
    if( x>=1000.0 )
    {
        q = q+((7.9365079365079365079365*0.0001*p-2.7777777777777777777778*0.001)*p+0.0833333333333333333333)/x;
    }
    else
    {
        a = 8.11614167470508450300*0.0001;
        a = -5.95061904284301438324*0.0001+p*a;
        a = 7.93650340457716943945*0.0001+p*a;
        a = -2.77777777730099687205*0.001+p*a;
        a = 8.33333333333331927722*0.01+p*a;
        q = q+a/x;
    }
    result = q;
    return result;
}


ap::real_value_type gammastirf(ap::real_value_type x)
{
    ap::real_value_type result;
    ap::real_value_type y;
    ap::real_value_type w;
    ap::real_value_type v;
    ap::real_value_type stir;

    w = 1/x;
    stir = 7.87311395793093628397E-4;
    stir = -2.29549961613378126380E-4+w*stir;
    stir = -2.68132617805781232825E-3+w*stir;
    stir = 3.47222221605458667310E-3+w*stir;
    stir = 8.33333333333482257126E-2+w*stir;
    w = 1+w*stir;
    y = exp(x);
    if( x>143.01608 )
    {
        v = pow((ap::real_value_type)x, (ap::real_value_type)(0.5*x-0.25));
        y = v*(v/y);
    }
    else
    {
        y = pow((ap::real_value_type)x, (ap::real_value_type)(x-0.5))/y;
    }
    result = 2.50662827463100050242*y*w;
    return result;
}

} // namespace alglib
