Totally rework the math library, this time based on the MacOs X

math library (which is itself based on the math lib from FreeBSD).
 -Erik

1 files changed, 0 insertions, 515 deletions

diff --git a/libm/double/fresnl.c b/libm/double/fresnl.c
deleted file mode 100644
index 0872d107a..000000000
--- a/libm/double/fresnl.c
+++ /dev/null
@@ -1,515 +0,0 @@
-/*							fresnl.c
- *
- *	Fresnel integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, S, C;
- * void fresnl();
- *
- * fresnl( x, _&S, _&C );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the Fresnel integrals
- *
- *           x
- *           -
- *          | |
- * C(x) =   |   cos(pi/2 t**2) dt,
- *        | |
- *         -
- *          0
- *
- *           x
- *           -
- *          | |
- * S(x) =   |   sin(pi/2 t**2) dt.
- *        | |
- *         -
- *          0
- *
- *
- * The integrals are evaluated by a power series for x < 1.
- * For x >= 1 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
- * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
- *
- *
- *
- * ACCURACY:
- *
- *  Relative error.
- *
- * Arithmetic  function   domain     # trials      peak         rms
- *   IEEE       S(x)      0, 10       10000       2.0e-15     3.2e-16
- *   IEEE       C(x)      0, 10       10000       1.8e-15     3.3e-16
- *   DEC        S(x)      0, 10        6000       2.2e-16     3.9e-17
- *   DEC        C(x)      0, 10        5000       2.3e-16     3.9e-17
- */
-
-/*
-Cephes Math Library Release 2.8:  June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* S(x) for small x */
-#ifdef UNK
-static double sn[6] = {
--2.99181919401019853726E3,
- 7.08840045257738576863E5,
--6.29741486205862506537E7,
- 2.54890880573376359104E9,
--4.42979518059697779103E10,
- 3.18016297876567817986E11,
-};
-static double sd[6] = {
-/* 1.00000000000000000000E0,*/
- 2.81376268889994315696E2,
- 4.55847810806532581675E4,
- 5.17343888770096400730E6,
- 4.19320245898111231129E8,
- 2.24411795645340920940E10,
- 6.07366389490084639049E11,
-};
-#endif
-#ifdef DEC
-static unsigned short sn[24] = {
-0143072,0176433,0065455,0127034,
-0045055,0007200,0134540,0026661,
-0146560,0035061,0023667,0127545,
-0050027,0166503,0002673,0153756,
-0151045,0002721,0121737,0102066,
-0051624,0013177,0033451,0021271,
-};
-static unsigned short sd[24] = {
-/*0040200,0000000,0000000,0000000,*/
-0042214,0130051,0112070,0101617,
-0044062,0010307,0172346,0152510,
-0045635,0160575,0143200,0136642,
-0047307,0171215,0127457,0052361,
-0050647,0031447,0032621,0013510,
-0052015,0064733,0117362,0012653,
-};
-#endif
-#ifdef IBMPC
-static unsigned short sn[24] = {
-0xb5c3,0x6d65,0x5fa3,0xc0a7,
-0x05b6,0x172c,0xa1d0,0x4125,
-0xf5ed,0x24f6,0x0746,0xc18e,
-0x7afe,0x60b7,0xfda8,0x41e2,
-0xf087,0x347b,0xa0ba,0xc224,
-0x2457,0xe6e5,0x82cf,0x4252,
-};
-static unsigned short sd[24] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x1072,0x3287,0x9605,0x4071,
-0xdaa9,0xfe9c,0x4218,0x40e6,
-0x17b4,0xb8d0,0xbc2f,0x4153,
-0xea9e,0xb5e5,0xfe51,0x41b8,
-0x22e9,0xe6b2,0xe664,0x4214,
-0x42b5,0x73de,0xad3b,0x4261,
-};
-#endif
-#ifdef MIEEE
-static unsigned short sn[24] = {
-0xc0a7,0x5fa3,0x6d65,0xb5c3,
-0x4125,0xa1d0,0x172c,0x05b6,
-0xc18e,0x0746,0x24f6,0xf5ed,
-0x41e2,0xfda8,0x60b7,0x7afe,
-0xc224,0xa0ba,0x347b,0xf087,
-0x4252,0x82cf,0xe6e5,0x2457,
-};
-static unsigned short sd[24] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4071,0x9605,0x3287,0x1072,
-0x40e6,0x4218,0xfe9c,0xdaa9,
-0x4153,0xbc2f,0xb8d0,0x17b4,
-0x41b8,0xfe51,0xb5e5,0xea9e,
-0x4214,0xe664,0xe6b2,0x22e9,
-0x4261,0xad3b,0x73de,0x42b5,
-};
-#endif
-
-/* C(x) for small x */
-#ifdef UNK
-static double cn[6] = {
--4.98843114573573548651E-8,
- 9.50428062829859605134E-6,
--6.45191435683965050962E-4,
- 1.88843319396703850064E-2,
--2.05525900955013891793E-1,
- 9.99999999999999998822E-1,
-};
-static double cd[7] = {
- 3.99982968972495980367E-12,
- 9.15439215774657478799E-10,
- 1.25001862479598821474E-7,
- 1.22262789024179030997E-5,
- 8.68029542941784300606E-4,
- 4.12142090722199792936E-2,
- 1.00000000000000000118E0,
-};
-#endif
-#ifdef DEC
-static unsigned short cn[24] = {
-0132126,0040141,0063733,0013231,
-0034037,0072223,0010200,0075637,
-0135451,0021020,0073264,0036057,
-0036632,0131520,0101316,0060233,
-0137522,0072541,0136124,0132202,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short cd[28] = {
-0026614,0135503,0051776,0032631,
-0030573,0121116,0154033,0126712,
-0032406,0034100,0012442,0106212,
-0034115,0017567,0150520,0164623,
-0035543,0106171,0177336,0146351,
-0037050,0150073,0000607,0171635,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short cn[24] = {
-0x62d3,0x2cfb,0xc80c,0xbe6a,
-0x0f74,0x6210,0xee92,0x3ee3,
-0x8786,0x0ed6,0x2442,0xbf45,
-0xcc13,0x1059,0x566a,0x3f93,
-0x9690,0x378a,0x4eac,0xbfca,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short cd[28] = {
-0xc6b3,0x6a7f,0x9768,0x3d91,
-0x75b9,0xdb03,0x7449,0x3e0f,
-0x5191,0x02a4,0xc708,0x3e80,
-0x1d32,0xfa2a,0xa3ee,0x3ee9,
-0xd99d,0x3fdb,0x718f,0x3f4c,
-0xfe74,0x6030,0x1a07,0x3fa5,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short cn[24] = {
-0xbe6a,0xc80c,0x2cfb,0x62d3,
-0x3ee3,0xee92,0x6210,0x0f74,
-0xbf45,0x2442,0x0ed6,0x8786,
-0x3f93,0x566a,0x1059,0xcc13,
-0xbfca,0x4eac,0x378a,0x9690,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short cd[28] = {
-0x3d91,0x9768,0x6a7f,0xc6b3,
-0x3e0f,0x7449,0xdb03,0x75b9,
-0x3e80,0xc708,0x02a4,0x5191,
-0x3ee9,0xa3ee,0xfa2a,0x1d32,
-0x3f4c,0x718f,0x3fdb,0xd99d,
-0x3fa5,0x1a07,0x6030,0xfe74,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-/* Auxiliary function f(x) */
-#ifdef UNK
-static double fn[10] = {
-  4.21543555043677546506E-1,
-  1.43407919780758885261E-1,
-  1.15220955073585758835E-2,
-  3.45017939782574027900E-4,
-  4.63613749287867322088E-6,
-  3.05568983790257605827E-8,
-  1.02304514164907233465E-10,
-  1.72010743268161828879E-13,
-  1.34283276233062758925E-16,
-  3.76329711269987889006E-20,
-};
-static double fd[10] = {
-/*  1.00000000000000000000E0,*/
-  7.51586398353378947175E-1,
-  1.16888925859191382142E-1,
-  6.44051526508858611005E-3,
-  1.55934409164153020873E-4,
-  1.84627567348930545870E-6,
-  1.12699224763999035261E-8,
-  3.60140029589371370404E-11,
-  5.88754533621578410010E-14,
-  4.52001434074129701496E-17,
-  1.25443237090011264384E-20,
-};
-#endif
-#ifdef DEC
-static unsigned short fn[40] = {
-0037727,0152216,0106601,0016214,
-0037422,0154606,0112710,0071355,
-0036474,0143453,0154253,0166545,
-0035264,0161606,0022250,0073743,
-0033633,0110036,0024653,0136246,
-0032003,0036652,0041164,0036413,
-0027740,0174122,0046305,0036726,
-0025501,0125270,0121317,0167667,
-0023032,0150555,0076175,0047443,
-0020061,0133570,0070130,0027657,
-};
-static unsigned short fd[40] = {
-/*0040200,0000000,0000000,0000000,*/
-0040100,0063767,0054413,0151452,
-0037357,0061566,0007243,0065754,
-0036323,0005365,0033552,0133625,
-0035043,0101123,0000275,0165402,
-0033367,0146614,0110623,0023647,
-0031501,0116644,0125222,0144263,
-0027436,0062051,0117235,0001411,
-0025204,0111543,0056370,0036201,
-0022520,0071351,0015227,0122144,
-0017554,0172240,0112713,0005006,
-};
-#endif
-#ifdef IBMPC
-static unsigned short fn[40] = {
-0x2391,0xd1b0,0xfa91,0x3fda,
-0x0e5e,0xd2b9,0x5b30,0x3fc2,
-0x7dad,0x7b15,0x98e5,0x3f87,
-0x0efc,0xc495,0x9c70,0x3f36,
-0x7795,0xc535,0x7203,0x3ed3,
-0x87a1,0x484e,0x67b5,0x3e60,
-0xa7bb,0x4998,0x1f0a,0x3ddc,
-0xfdf7,0x1459,0x3557,0x3d48,
-0xa9e4,0xaf8f,0x5a2d,0x3ca3,
-0x05f6,0x0e0b,0x36ef,0x3be6,
-};
-static unsigned short fd[40] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x7a65,0xeb21,0x0cfe,0x3fe8,
-0x6d7d,0xc1d4,0xec6e,0x3fbd,
-0x56f3,0xa6ed,0x615e,0x3f7a,
-0xbd60,0x6017,0x704a,0x3f24,
-0x64f5,0x9232,0xf9b1,0x3ebe,
-0x5916,0x9552,0x33b4,0x3e48,
-0xa061,0x33d3,0xcc85,0x3dc3,
-0x0790,0x6b9f,0x926c,0x3d30,
-0xf48d,0x2352,0x0e5d,0x3c8a,
-0x6141,0x12b9,0x9e94,0x3bcd,
-};
-#endif
-#ifdef MIEEE
-static unsigned short fn[40] = {
-0x3fda,0xfa91,0xd1b0,0x2391,
-0x3fc2,0x5b30,0xd2b9,0x0e5e,
-0x3f87,0x98e5,0x7b15,0x7dad,
-0x3f36,0x9c70,0xc495,0x0efc,
-0x3ed3,0x7203,0xc535,0x7795,
-0x3e60,0x67b5,0x484e,0x87a1,
-0x3ddc,0x1f0a,0x4998,0xa7bb,
-0x3d48,0x3557,0x1459,0xfdf7,
-0x3ca3,0x5a2d,0xaf8f,0xa9e4,
-0x3be6,0x36ef,0x0e0b,0x05f6,
-};
-static unsigned short fd[40] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x3fe8,0x0cfe,0xeb21,0x7a65,
-0x3fbd,0xec6e,0xc1d4,0x6d7d,
-0x3f7a,0x615e,0xa6ed,0x56f3,
-0x3f24,0x704a,0x6017,0xbd60,
-0x3ebe,0xf9b1,0x9232,0x64f5,
-0x3e48,0x33b4,0x9552,0x5916,
-0x3dc3,0xcc85,0x33d3,0xa061,
-0x3d30,0x926c,0x6b9f,0x0790,
-0x3c8a,0x0e5d,0x2352,0xf48d,
-0x3bcd,0x9e94,0x12b9,0x6141,
-};
-#endif
-
-
-/* Auxiliary function g(x) */
-#ifdef UNK
-static double gn[11] = {
-  5.04442073643383265887E-1,
-  1.97102833525523411709E-1,
-  1.87648584092575249293E-2,
-  6.84079380915393090172E-4,
-  1.15138826111884280931E-5,
-  9.82852443688422223854E-8,
-  4.45344415861750144738E-10,
-  1.08268041139020870318E-12,
-  1.37555460633261799868E-15,
-  8.36354435630677421531E-19,
-  1.86958710162783235106E-22,
-};
-static double gd[11] = {
-/*  1.00000000000000000000E0,*/
-  1.47495759925128324529E0,
-  3.37748989120019970451E-1,
-  2.53603741420338795122E-2,
-  8.14679107184306179049E-4,
-  1.27545075667729118702E-5,
-  1.04314589657571990585E-7,
-  4.60680728146520428211E-10,
-  1.10273215066240270757E-12,
-  1.38796531259578871258E-15,
-  8.39158816283118707363E-19,
-  1.86958710162783236342E-22,
-};
-#endif
-#ifdef DEC
-static unsigned short gn[44] = {
-0040001,0021435,0120406,0053123,
-0037511,0152523,0037703,0122011,
-0036631,0134302,0122721,0110235,
-0035463,0051712,0043215,0114732,
-0034101,0025677,0147725,0057630,
-0032323,0010342,0067523,0002206,
-0030364,0152247,0110007,0054107,
-0026230,0057654,0035464,0047124,
-0023706,0036401,0167705,0045440,
-0021166,0154447,0105632,0142461,
-0016142,0002353,0011175,0170530,
-};
-static unsigned short gd[44] = {
-/*0040200,0000000,0000000,0000000,*/
-0040274,0145551,0016742,0127005,
-0037654,0166557,0076416,0015165,
-0036717,0140217,0030675,0050111,
-0035525,0110060,0076405,0070502,
-0034125,0176061,0060120,0031730,
-0032340,0001615,0054343,0120501,
-0030375,0041414,0070747,0107060,
-0026233,0031034,0160757,0074526,
-0023710,0003341,0137100,0144664,
-0021167,0126414,0023774,0015435,
-0016142,0002353,0011175,0170530,
-};
-#endif
-#ifdef IBMPC
-static unsigned short gn[44] = {
-0xcaca,0xb420,0x2463,0x3fe0,
-0x7481,0x67f8,0x3aaa,0x3fc9,
-0x3214,0x54ba,0x3718,0x3f93,
-0xb33b,0x48d1,0x6a79,0x3f46,
-0xabf3,0xf9fa,0x2577,0x3ee8,
-0x6091,0x4dea,0x621c,0x3e7a,
-0xeb09,0xf200,0x9a94,0x3dfe,
-0x89cb,0x8766,0x0bf5,0x3d73,
-0xa964,0x3df8,0xc7a0,0x3cd8,
-0x58a6,0xf173,0xdb24,0x3c2e,
-0xbe2b,0x624f,0x409d,0x3b6c,
-};
-static unsigned short gd[44] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x55c1,0x23bc,0x996d,0x3ff7,
-0xc34f,0xefa1,0x9dad,0x3fd5,
-0xaa09,0xe637,0xf811,0x3f99,
-0xae28,0x0fa0,0xb206,0x3f4a,
-0x067b,0x2c0a,0xbf86,0x3eea,
-0x7428,0xab1c,0x0071,0x3e7c,
-0xf1c6,0x8e3c,0xa861,0x3dff,
-0xef2b,0x9c3d,0x6643,0x3d73,
-0x1936,0x37c8,0x00dc,0x3cd9,
-0x8364,0x84ff,0xf5a1,0x3c2e,
-0xbe2b,0x624f,0x409d,0x3b6c,
-};
-#endif
-#ifdef MIEEE
-static unsigned short gn[44] = {
-0x3fe0,0x2463,0xb420,0xcaca,
-0x3fc9,0x3aaa,0x67f8,0x7481,
-0x3f93,0x3718,0x54ba,0x3214,
-0x3f46,0x6a79,0x48d1,0xb33b,
-0x3ee8,0x2577,0xf9fa,0xabf3,
-0x3e7a,0x621c,0x4dea,0x6091,
-0x3dfe,0x9a94,0xf200,0xeb09,
-0x3d73,0x0bf5,0x8766,0x89cb,
-0x3cd8,0xc7a0,0x3df8,0xa964,
-0x3c2e,0xdb24,0xf173,0x58a6,
-0x3b6c,0x409d,0x624f,0xbe2b,
-};
-static unsigned short gd[44] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x3ff7,0x996d,0x23bc,0x55c1,
-0x3fd5,0x9dad,0xefa1,0xc34f,
-0x3f99,0xf811,0xe637,0xaa09,
-0x3f4a,0xb206,0x0fa0,0xae28,
-0x3eea,0xbf86,0x2c0a,0x067b,
-0x3e7c,0x0071,0xab1c,0x7428,
-0x3dff,0xa861,0x8e3c,0xf1c6,
-0x3d73,0x6643,0x9c3d,0xef2b,
-0x3cd9,0x00dc,0x37c8,0x1936,
-0x3c2e,0xf5a1,0x84ff,0x8364,
-0x3b6c,0x409d,0x624f,0xbe2b,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double cos ( double );
-extern double sin ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-#else
-double fabs(), cos(), sin(), polevl(), p1evl();
-#endif
-extern double PI, PIO2, MACHEP;
-
-int fresnl( xxa, ssa, cca )
-double xxa, *ssa, *cca;
-{
-double f, g, cc, ss, c, s, t, u;
-double x, x2;
-
-x = fabs(xxa);
-x2 = x * x;
-if( x2 < 2.5625 )
-	{
-	t = x2 * x2;
-	ss = x * x2 * polevl( t, sn, 5)/p1evl( t, sd, 6 );
-	cc = x * polevl( t, cn, 5)/polevl(t, cd, 6 );
-	goto done;
-	}
-
-
-
-
-
-
-if( x > 36974.0 )
-	{
-	cc = 0.5;
-	ss = 0.5;
-	goto done;
-	}
-
-
-/*		Asymptotic power series auxiliary functions
- *		for large argument
- */
-	x2 = x * x;
-	t = PI * x2;
-	u = 1.0/(t * t);
-	t = 1.0/t;
-	f = 1.0 - u * polevl( u, fn, 9)/p1evl(u, fd, 10);
-	g = t * polevl( u, gn, 10)/p1evl(u, gd, 11);
-
-	t = PIO2 * x2;
-	c = cos(t);
-	s = sin(t);
-	t = PI * x;
-	cc = 0.5  +  (f * s  -  g * c)/t;
-	ss = 0.5  -  (f * c  +  g * s)/t;
-
-done:
-if( xxa < 0.0 )
-	{
-	cc = -cc;
-	ss = -ss;
-	}
-
-*cca = cc;
-*ssa = ss;
-return(0);
-}