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-rw-r--r--libm/double/dawsn.c392
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diff --git a/libm/double/dawsn.c b/libm/double/dawsn.c
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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
- * DEC 0,10 6000 7.4e-17 1.4e-17
- *
- *
- */
-
-/* dawsn.c */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-/* Dawson's integral, interval 0 to 3.25 */
-#ifdef UNK
-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,
-};
-#endif
-#ifdef DEC
-static unsigned short AN[40] = {
-0027107,0176630,0075752,0107612,
-0030551,0070604,0166707,0127727,
-0031647,0002210,0117120,0056376,
-0033177,0156026,0141275,0140627,
-0033516,0112200,0037035,0165515,
-0035270,0150613,0016423,0105634,
-0135536,0156227,0023515,0044413,
-0037055,0015273,0105147,0064025,
-0137273,0163145,0014460,0166465,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short AD[44] = {
-0027323,0067372,0115566,0131320,
-0030714,0114432,0074206,0006637,
-0032137,0160671,0044203,0026344,
-0033252,0146656,0020247,0100231,
-0034303,0003346,0123260,0022433,
-0035252,0125460,0173041,0155415,
-0036144,0113747,0125203,0124617,
-0036744,0166232,0143671,0133670,
-0037442,0127755,0162625,0000100,
-0040023,0026736,0003604,0106265,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short AN[40] = {
-0x51f1,0x0f7d,0xffb3,0x3da8,
-0xf5fb,0x9db8,0x2e30,0x3e0d,
-0x0ba0,0x13ca,0xe091,0x3e54,
-0xb833,0xd857,0xfb82,0x3eaf,
-0xbd6a,0x07c3,0xd290,0x3ec9,
-0x7174,0x63a2,0x1a31,0x3f37,
-0xa921,0xe4e9,0xdb92,0xbf4b,
-0xed03,0x714c,0xa357,0x3fa5,
-0x1da7,0xa326,0x7ccc,0xbfb7,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short AD[44] = {
-0xd65a,0x536e,0x6ddf,0x3dba,
-0xc1b4,0x4f10,0x9323,0x3e19,
-0x659c,0x2910,0xfc37,0x3e6b,
-0xf013,0xc414,0x59b5,0x3eb5,
-0x04a3,0xd4d6,0x60dc,0x3ef8,
-0x3b62,0x1ec4,0x5566,0x3f35,
-0x7532,0xf550,0x92fc,0x3f6c,
-0x36f7,0x58f7,0x9d93,0x3f9c,
-0xa008,0xbcb2,0x55fd,0x3fc4,
-0x9197,0xc0f0,0x65bb,0x3fe2,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short AN[40] = {
-0x3da8,0xffb3,0x0f7d,0x51f1,
-0x3e0d,0x2e30,0x9db8,0xf5fb,
-0x3e54,0xe091,0x13ca,0x0ba0,
-0x3eaf,0xfb82,0xd857,0xb833,
-0x3ec9,0xd290,0x07c3,0xbd6a,
-0x3f37,0x1a31,0x63a2,0x7174,
-0xbf4b,0xdb92,0xe4e9,0xa921,
-0x3fa5,0xa357,0x714c,0xed03,
-0xbfb7,0x7ccc,0xa326,0x1da7,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short AD[44] = {
-0x3dba,0x6ddf,0x536e,0xd65a,
-0x3e19,0x9323,0x4f10,0xc1b4,
-0x3e6b,0xfc37,0x2910,0x659c,
-0x3eb5,0x59b5,0xc414,0xf013,
-0x3ef8,0x60dc,0xd4d6,0x04a3,
-0x3f35,0x5566,0x1ec4,0x3b62,
-0x3f6c,0x92fc,0xf550,0x7532,
-0x3f9c,0x9d93,0x58f7,0x36f7,
-0x3fc4,0x55fd,0xbcb2,0xa008,
-0x3fe2,0x65bb,0xc0f0,0x9197,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-/* interval 3.25 to 6.25 */
-#ifdef UNK
-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,
-};
-#endif
-#ifdef DEC
-static unsigned short BN[44] = {
-0040002,0045342,0113762,0004360,
-0137572,0120346,0172745,0144046,
-0037300,0151134,0123440,0117047,
-0136663,0025423,0014755,0046026,
-0036157,0177561,0027535,0046744,
-0135335,0161052,0071243,0146535,
-0034426,0154060,0164506,0135625,
-0133420,0005356,0100017,0151334,
-0032303,0066137,0024013,0046212,
-0131045,0016612,0066270,0047574,
-0027435,0177025,0060625,0116363,
-};
-static unsigned short BD[40] = {
-/*0040200,0000000,0000000,0000000,*/
-0140041,0140101,0174552,0037073,
-0037562,0061503,0124271,0160756,
-0137131,0151760,0073210,0110534,
-0036412,0170562,0117017,0155377,
-0135570,0101374,0074056,0037276,
-0034643,0145376,0001516,0060636,
-0133630,0173540,0121344,0155231,
-0032513,0005602,0134516,0007144,
-0131250,0150540,0075747,0105341,
-0027635,0177020,0012465,0125402,
-};
-#endif
-#ifdef IBMPC
-static unsigned short BN[44] = {
-0x411e,0x52fe,0x495c,0x3fe0,
-0xb905,0xdebc,0x541c,0xbfcf,
-0x13c5,0x94e4,0x1a4b,0x3fb8,
-0xa983,0x633d,0x6562,0xbf96,
-0xa9bd,0x25eb,0xffee,0x3f6d,
-0x79ac,0x4e54,0xbc45,0xbf3b,
-0xd773,0x1d28,0xdb06,0x3f02,
-0xfa5b,0xd001,0x015d,0xbec2,
-0x6991,0xe501,0x6d8b,0x3e78,
-0x09f0,0x4d97,0xa3b1,0xbe24,
-0xb39e,0xac32,0xbfc2,0x3dc3,
-};
-static unsigned short BD[40] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x47c7,0x3f2d,0x3808,0xbfe4,
-0x3c3e,0x7517,0x4c68,0x3fce,
-0x122b,0x0ed1,0x3a7e,0xbfab,
-0xfb60,0x53c1,0x5e2e,0x3f81,
-0xc7d8,0x8f05,0x105f,0xbf4f,
-0xcc34,0xc069,0x795f,0x3f14,
-0x9b53,0x145c,0x1eec,0xbed3,
-0xc1cd,0x5729,0x6170,0x3e89,
-0xf15c,0x0f7c,0x1a2c,0xbe35,
-0xb560,0x02a6,0xbfc2,0x3dd3,
-};
-#endif
-#ifdef MIEEE
-static unsigned short BN[44] = {
-0x3fe0,0x495c,0x52fe,0x411e,
-0xbfcf,0x541c,0xdebc,0xb905,
-0x3fb8,0x1a4b,0x94e4,0x13c5,
-0xbf96,0x6562,0x633d,0xa983,
-0x3f6d,0xffee,0x25eb,0xa9bd,
-0xbf3b,0xbc45,0x4e54,0x79ac,
-0x3f02,0xdb06,0x1d28,0xd773,
-0xbec2,0x015d,0xd001,0xfa5b,
-0x3e78,0x6d8b,0xe501,0x6991,
-0xbe24,0xa3b1,0x4d97,0x09f0,
-0x3dc3,0xbfc2,0xac32,0xb39e,
-};
-static unsigned short BD[40] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xbfe4,0x3808,0x3f2d,0x47c7,
-0x3fce,0x4c68,0x7517,0x3c3e,
-0xbfab,0x3a7e,0x0ed1,0x122b,
-0x3f81,0x5e2e,0x53c1,0xfb60,
-0xbf4f,0x105f,0x8f05,0xc7d8,
-0x3f14,0x795f,0xc069,0xcc34,
-0xbed3,0x1eec,0x145c,0x9b53,
-0x3e89,0x6170,0x5729,0xc1cd,
-0xbe35,0x1a2c,0x0f7c,0xf15c,
-0x3dd3,0xbfc2,0x02a6,0xb560,
-};
-#endif
-
-/* 6.25 to infinity */
-#ifdef UNK
-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,
-};
-#endif
-#ifdef DEC
-static unsigned short CN[20] = {
-0140027,0030427,0176477,0074402,
-0040041,0012617,0112375,0162657,
-0137461,0000761,0074120,0135160,
-0036607,0004325,0117246,0115525,
-0135377,0036345,0064750,0047732,
-};
-static unsigned short CD[20] = {
-/*0040200,0000000,0000000,0000000,*/
-0140454,0127521,0071653,0133415,
-0040335,0144540,0016105,0045241,
-0137711,0112053,0155034,0062237,
-0037015,0002102,0177442,0074546,
-0135577,0036345,0064750,0052152,
-};
-#endif
-#ifdef IBMPC
-static unsigned short CN[20] = {
-0xef20,0xffa7,0xe622,0xbfe2,
-0xbcb6,0xf29f,0x22b1,0x3fe4,
-0x174e,0x2f0a,0x203e,0xbfc6,
-0xd36b,0xb3d4,0xe11a,0x3f90,
-0x09fb,0xad3d,0xe79c,0xbf3f,
-};
-static unsigned short CD[20] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x76e2,0x2e75,0x95ea,0xc005,
-0xa954,0x0388,0xb92c,0x3ffb,
-0x8c94,0x7b43,0x3285,0xbfd9,
-0x4f2d,0x5fe4,0xa088,0x3fa1,
-0x0a8d,0xad3d,0xe79c,0xbf4f,
-};
-#endif
-#ifdef MIEEE
-static unsigned short CN[20] = {
-0xbfe2,0xe622,0xffa7,0xef20,
-0x3fe4,0x22b1,0xf29f,0xbcb6,
-0xbfc6,0x203e,0x2f0a,0x174e,
-0x3f90,0xe11a,0xb3d4,0xd36b,
-0xbf3f,0xe79c,0xad3d,0x09fb,
-};
-static unsigned short CD[20] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xc005,0x95ea,0x2e75,0x76e2,
-0x3ffb,0xb92c,0x0388,0xa954,
-0xbfd9,0x3285,0x7b43,0x8c94,
-0x3fa1,0xa088,0x5fe4,0x4f2d,
-0xbf4f,0xe79c,0xad3d,0x0a8d,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double chbevl ( double, void *, int );
-extern double sqrt ( double );
-extern double fabs ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-#else
-double chbevl(), sqrt(), fabs(), polevl(), p1evl();
-#endif
-extern double PI, 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 );
-}