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/* dawsn.c
*
* Dawson's Integral
*
*
*
* SYNOPSIS:
*
* double x, y, dawsn();
*
* y = dawsn( x );
*
*
*
* DESCRIPTION:
*
* 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
*
*
*/
/* dawsn.c */
/*
* Cephes Math Library Release 2.1: January, 1989
* Copyright 1984, 1987, 1989 by Stephen L. Moshier
* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include "mconf.h"
/* Dawson's integral, interval 0 to 3.25 */
static double AN[10] = {
1.13681498971755972054E-11,
8.49262267667473811108E-10,
1.94434204175553054283E-8,
9.53151741254484363489E-7,
3.07828309874913200438E-6,
3.52513368520288738649E-4,
-8.50149846724410912031E-4,
4.22618223005546594270E-2,
-9.17480371773452345351E-2,
9.99999999999999994612E-1,
};
static double AD[11] = {
2.40372073066762605484E-11,
1.48864681368493396752E-9,
5.21265281010541664570E-8,
1.27258478273186970203E-6,
2.32490249820789513991E-5,
3.25524741826057911661E-4,
3.48805814657162590916E-3,
2.79448531198828973716E-2,
1.58874241960120565368E-1,
5.74918629489320327824E-1,
1.00000000000000000539E0,
};
/* interval 3.25 to 6.25 */
static double BN[11] = {
5.08955156417900903354E-1,
-2.44754418142697847934E-1,
9.41512335303534411857E-2,
-2.18711255142039025206E-2,
3.66207612329569181322E-3,
-4.23209114460388756528E-4,
3.59641304793896631888E-5,
-2.14640351719968974225E-6,
9.10010780076391431042E-8,
-2.40274520828250956942E-9,
3.59233385440928410398E-11,
};
static double BD[10] = {
/* 1.00000000000000000000E0, */
-6.31839869873368190192E-1,
2.36706788228248691528E-1,
-5.31806367003223277662E-2,
8.48041718586295374409E-3,
-9.47996768486665330168E-4,
7.81025592944552338085E-5,
-4.55875153252442634831E-6,
1.89100358111421846170E-7,
-4.91324691331920606875E-9,
7.18466403235734541950E-11,
};
/* 6.25 to infinity */
static double CN[5] = {
-5.90592860534773254987E-1,
6.29235242724368800674E-1,
-1.72858975380388136411E-1,
1.64837047825189632310E-2,
-4.86827613020462700845E-4,
};
static double CD[5] = {
/* 1.00000000000000000000E0, */
-2.69820057197544900361E0,
1.73270799045947845857E0,
-3.93708582281939493482E-1,
3.44278924041233391079E-2,
-9.73655226040941223894E-4,
};
extern double MACHEP;
double dawsn(xx)
double xx;
{
double x, y;
int sign;
sign = 1;
if (xx < 0.0) {
sign = -1;
xx = -xx;
}
if (xx < 3.25) {
x = xx * xx;
y = xx * polevl(x, AN, 9) / polevl(x, AD, 10);
return (sign * y);
}
x = 1.0 / (xx * xx);
if (xx < 6.25) {
y = 1.0 / xx + x * polevl(x, BN, 10) / (p1evl(x, BD, 10) * xx);
return (sign * 0.5 * y);
}
if (xx > 1.0e9)
return ((sign * 0.5) / xx);
/* 6.25 to infinity */
y = 1.0 / xx + x * polevl(x, CN, 4) / (p1evl(x, CD, 5) * xx);
return (sign * 0.5 * y);
}
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