From 7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 Mon Sep 17 00:00:00 2001 From: Eric Andersen Date: Thu, 22 Nov 2001 14:04:29 +0000 Subject: 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 --- libm/double/fresnl.c | 515 --------------------------------------------------- 1 file changed, 515 deletions(-) delete mode 100644 libm/double/fresnl.c (limited to 'libm/double/fresnl.c') 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 - -/* 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); -} -- cgit v1.2.3