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-rw-r--r--libm/double/fresnl.c515
1 files changed, 515 insertions, 0 deletions
diff --git a/libm/double/fresnl.c b/libm/double/fresnl.c
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+++ b/libm/double/fresnl.c
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+/* 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);
+}
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