source: trunk/sources/ALGLIB/dawson.cs @ 2567

/*************************************************************************
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.

>>> 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 >>>
*************************************************************************/

using System;

namespace alglib
{
    public class dawson
    {
        /*************************************************************************
        Dawson's Integral

        Approximates the integral

                                    x
                                    -
                             2     | |        2
         dawsn(x)  =  exp( -x  )   |    exp( t  ) dt
                                 | |
                                  -
                                  0

        Three different rational approximations are employed, for
        the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.

        ACCURACY:

                             Relative error:
        arithmetic   domain     # trials      peak         rms
           IEEE      0,10        10000       6.9e-16     1.0e-16

        Cephes Math Library Release 2.8:  June, 2000
        Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
        *************************************************************************/
        public static double dawsonintegral(double x)
        {
            double result = 0;
            double x2 = 0;
            double y = 0;
            int sg = 0;
            double an = 0;
            double ad = 0;
            double bn = 0;
            double bd = 0;
            double cn = 0;
            double cd = 0;

            sg = 1;
            if( (double)(x)<(double)(0) )
            {
                sg = -1;
                x = -x;
            }
            if( (double)(x)<(double)(3.25) )
            {
                x2 = x*x;
                an = 1.13681498971755972054E-11;
                an = an*x2+8.49262267667473811108E-10;
                an = an*x2+1.94434204175553054283E-8;
                an = an*x2+9.53151741254484363489E-7;
                an = an*x2+3.07828309874913200438E-6;
                an = an*x2+3.52513368520288738649E-4;
                an = an*x2+-8.50149846724410912031E-4;
                an = an*x2+4.22618223005546594270E-2;
                an = an*x2+-9.17480371773452345351E-2;
                an = an*x2+9.99999999999999994612E-1;
                ad = 2.40372073066762605484E-11;
                ad = ad*x2+1.48864681368493396752E-9;
                ad = ad*x2+5.21265281010541664570E-8;
                ad = ad*x2+1.27258478273186970203E-6;
                ad = ad*x2+2.32490249820789513991E-5;
                ad = ad*x2+3.25524741826057911661E-4;
                ad = ad*x2+3.48805814657162590916E-3;
                ad = ad*x2+2.79448531198828973716E-2;
                ad = ad*x2+1.58874241960120565368E-1;
                ad = ad*x2+5.74918629489320327824E-1;
                ad = ad*x2+1.00000000000000000539E0;
                y = x*an/ad;
                result = sg*y;
                return result;
            }
            x2 = 1.0/(x*x);
            if( (double)(x)<(double)(6.25) )
            {
                bn = 5.08955156417900903354E-1;
                bn = bn*x2-2.44754418142697847934E-1;
                bn = bn*x2+9.41512335303534411857E-2;
                bn = bn*x2-2.18711255142039025206E-2;
                bn = bn*x2+3.66207612329569181322E-3;
                bn = bn*x2-4.23209114460388756528E-4;
                bn = bn*x2+3.59641304793896631888E-5;
                bn = bn*x2-2.14640351719968974225E-6;
                bn = bn*x2+9.10010780076391431042E-8;
                bn = bn*x2-2.40274520828250956942E-9;
                bn = bn*x2+3.59233385440928410398E-11;
                bd = 1.00000000000000000000E0;
                bd = bd*x2-6.31839869873368190192E-1;
                bd = bd*x2+2.36706788228248691528E-1;
                bd = bd*x2-5.31806367003223277662E-2;
                bd = bd*x2+8.48041718586295374409E-3;
                bd = bd*x2-9.47996768486665330168E-4;
                bd = bd*x2+7.81025592944552338085E-5;
                bd = bd*x2-4.55875153252442634831E-6;
                bd = bd*x2+1.89100358111421846170E-7;
                bd = bd*x2-4.91324691331920606875E-9;
                bd = bd*x2+7.18466403235734541950E-11;
                y = 1.0/x+x2*bn/(bd*x);
                result = sg*0.5*y;
                return result;
            }
            if( (double)(x)>(double)(1.0E9) )
            {
                result = sg*0.5/x;
                return result;
            }
            cn = -5.90592860534773254987E-1;
            cn = cn*x2+6.29235242724368800674E-1;
            cn = cn*x2-1.72858975380388136411E-1;
            cn = cn*x2+1.64837047825189632310E-2;
            cn = cn*x2-4.86827613020462700845E-4;
            cd = 1.00000000000000000000E0;
            cd = cd*x2-2.69820057197544900361E0;
            cd = cd*x2+1.73270799045947845857E0;
            cd = cd*x2-3.93708582281939493482E-1;
            cd = cd*x2+3.44278924041233391079E-2;
            cd = cd*x2-9.73655226040941223894E-4;
            y = 1.0/x+x2*cn/(cd*x);
            result = sg*0.5*y;
            return result;
        }
    }
}