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sici.c

/*                                        sici.c
 *
 *    Sine and cosine integrals
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, Ci, Si, sici();
 *
 * sici( x, &Si, &Ci );
 *
 *
 * DESCRIPTION:
 *
 * Evaluates the integrals
 *
 *                          x
 *                          -
 *                         |  cos t - 1
 *   Ci(x) = eul + ln x +  |  --------- dt,
 *                         |      t
 *                        -
 *                         0
 *             x
 *             -
 *            |  sin t
 *   Si(x) =  |  ----- dt
 *            |    t
 *           -
 *            0
 *
 * where eul = 0.57721566490153286061 is Euler's constant.
 * The integrals are approximated by rational functions.
 * For x > 8 auxiliary functions f(x) and g(x) are employed
 * such that
 *
 * Ci(x) = f(x) sin(x) - g(x) cos(x)
 * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
 *
 *
 * ACCURACY:
 *    Test interval = [0,50].
 * Absolute error, except relative when > 1:
 * arithmetic   function   # trials      peak         rms
 *    IEEE        Si        30000       4.4e-16     7.3e-17
 *    IEEE        Ci        30000       6.9e-16     5.1e-17
 *    DEC         Si         5000       4.4e-17     9.0e-18
 *    DEC         Ci         5300       7.9e-17     5.2e-18
 */

/*
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 <math.h>
#include "mconf.h"
#include "cephes.h"

#ifdef UNK
static double SN[] = {
-8.39167827910303881427E-11,
 4.62591714427012837309E-8,
-9.75759303843632795789E-6,
 9.76945438170435310816E-4,
-4.13470316229406538752E-2,
 1.00000000000000000302E0,
};
static double SD[] = {
  2.03269266195951942049E-12,
  1.27997891179943299903E-9,
  4.41827842801218905784E-7,
  9.96412122043875552487E-5,
  1.42085239326149893930E-2,
  9.99999999999999996984E-1,
};
#endif
#ifdef DEC
static unsigned short SN[] = {
0127670,0104362,0167505,0035161,
0032106,0127177,0032131,0056461,
0134043,0132213,0000476,0172351,
0035600,0006331,0064761,0032665,
0137051,0055601,0044667,0017645,
0040200,0000000,0000000,0000000,
};
static unsigned short SD[] = {
0026417,0004674,0052064,0001573,
0030657,0165501,0014666,0131526,
0032755,0032133,0034147,0024124,
0034720,0173167,0166624,0154477,
0036550,0145336,0063534,0063220,
0040200,0000000,0000000,0000000,
};
#endif
#ifdef IBMPC
static unsigned short SN[] = {
0xa74e,0x5de8,0x111e,0xbdd7,
0x2ba6,0xe68b,0xd5cf,0x3e68,
0xde9d,0x6027,0x7691,0xbee4,
0x26b7,0x2d3e,0x019b,0x3f50,
0xe3f5,0x2936,0x2b70,0xbfa5,
0x0000,0x0000,0x0000,0x3ff0,
};
static unsigned short SD[] = {
0x806f,0x8a86,0xe137,0x3d81,
0xd66b,0x2336,0xfd68,0x3e15,
0xe50a,0x670c,0xa68b,0x3e9d,
0x9b28,0xfdb2,0x1ece,0x3f1a,
0x8cd2,0xcceb,0x195b,0x3f8d,
0x0000,0x0000,0x0000,0x3ff0,
};
#endif
#ifdef MIEEE
static unsigned short SN[] = {
0xbdd7,0x111e,0x5de8,0xa74e,
0x3e68,0xd5cf,0xe68b,0x2ba6,
0xbee4,0x7691,0x6027,0xde9d,
0x3f50,0x019b,0x2d3e,0x26b7,
0xbfa5,0x2b70,0x2936,0xe3f5,
0x3ff0,0x0000,0x0000,0x0000,
};
static unsigned short SD[] = {
0x3d81,0xe137,0x8a86,0x806f,
0x3e15,0xfd68,0x2336,0xd66b,
0x3e9d,0xa68b,0x670c,0xe50a,
0x3f1a,0x1ece,0xfdb2,0x9b28,
0x3f8d,0x195b,0xcceb,0x8cd2,
0x3ff0,0x0000,0x0000,0x0000,
};
#endif
#ifdef UNK
static double CN[] = {
 2.02524002389102268789E-11,
-1.35249504915790756375E-8,
 3.59325051419993077021E-6,
-4.74007206873407909465E-4,
 2.89159652607555242092E-2,
-1.00000000000000000080E0,
};
static double CD[] = {
  4.07746040061880559506E-12,
  3.06780997581887812692E-9,
  1.23210355685883423679E-6,
  3.17442024775032769882E-4,
  5.10028056236446052392E-2,
  4.00000000000000000080E0,
};
#endif
#ifdef DEC
static unsigned short CN[] = {
0027262,0022131,0160257,0020166,
0131550,0055534,0077637,0000557,
0033561,0021622,0161463,0026575,
0135370,0102053,0116333,0000466,
0036754,0160454,0122022,0024622,
0140200,0000000,0000000,0000000,
};
static unsigned short CD[] = {
0026617,0073177,0107543,0104425,
0031122,0150573,0156453,0041517,
0033245,0057301,0077706,0110510,
0035246,0067130,0165424,0044543,
0037120,0164121,0061206,0053657,
0040600,0000000,0000000,0000000,
};
#endif
#ifdef IBMPC
static unsigned short CN[] = {
0xe40f,0x3c15,0x448b,0x3db6,
0xe02e,0x8ff3,0x0b6b,0xbe4d,
0x65b0,0x5c66,0x2472,0x3ece,
0x6027,0x739b,0x1085,0xbf3f,
0x4532,0x9482,0x9c25,0x3f9d,
0x0000,0x0000,0x0000,0xbff0,
};
static unsigned short CD[] = {
0x7123,0xf1ec,0xeecf,0x3d91,
0x686a,0x7ba5,0x5a2f,0x3e2a,
0xd229,0x2ff8,0xabd8,0x3eb4,
0x892c,0x1d62,0xcdcb,0x3f34,
0xcaf6,0x2c50,0x1d0a,0x3faa,
0x0000,0x0000,0x0000,0x4010,
};
#endif
#ifdef MIEEE
static unsigned short CN[] = {
0x3db6,0x448b,0x3c15,0xe40f,
0xbe4d,0x0b6b,0x8ff3,0xe02e,
0x3ece,0x2472,0x5c66,0x65b0,
0xbf3f,0x1085,0x739b,0x6027,
0x3f9d,0x9c25,0x9482,0x4532,
0xbff0,0x0000,0x0000,0x0000,
};
static unsigned short CD[] = {
0x3d91,0xeecf,0xf1ec,0x7123,
0x3e2a,0x5a2f,0x7ba5,0x686a,
0x3eb4,0xabd8,0x2ff8,0xd229,
0x3f34,0xcdcb,0x1d62,0x892c,
0x3faa,0x1d0a,0x2c50,0xcaf6,
0x4010,0x0000,0x0000,0x0000,
};
#endif


#ifdef UNK
static double FN4[] = {
  4.23612862892216586994E0,
  5.45937717161812843388E0,
  1.62083287701538329132E0,
  1.67006611831323023771E-1,
  6.81020132472518137426E-3,
  1.08936580650328664411E-4,
  5.48900223421373614008E-7,
};
static double FD4[] = {
/*  1.00000000000000000000E0,*/
  8.16496634205391016773E0,
  7.30828822505564552187E0,
  1.86792257950184183883E0,
  1.78792052963149907262E-1,
  7.01710668322789753610E-3,
  1.10034357153915731354E-4,
  5.48900252756255700982E-7,
};
#endif
#ifdef DEC
static unsigned short FN4[] = {
0040607,0107135,0120133,0153471,
0040656,0131467,0140424,0017567,
0040317,0073563,0121610,0002511,
0037453,0001710,0000040,0006334,
0036337,0024033,0176003,0171425,
0034744,0072341,0121657,0126035,
0033023,0054042,0154652,0000451,
};
static unsigned short FD4[] = {
/*0040200,0000000,0000000,0000000,*/
0041002,0121663,0137500,0177450,
0040751,0156577,0042213,0061552,
0040357,0014026,0045465,0147265,
0037467,0012503,0110413,0131772,
0036345,0167701,0155706,0160551,
0034746,0141076,0162250,0123547,
0033023,0054043,0056706,0151050,
};
#endif
#ifdef IBMPC
static unsigned short FN4[] = {
0x7ae7,0xb40b,0xf1cb,0x4010,
0x83ef,0xf822,0xd666,0x4015,
0x00a9,0x7471,0xeeee,0x3ff9,
0x019c,0x0004,0x6079,0x3fc5,
0x7e63,0x7f80,0xe503,0x3f7b,
0xf584,0x3475,0x8e9c,0x3f1c,
0x4025,0x5b35,0x6b04,0x3ea2,
};
static unsigned short FD4[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x1fe5,0x77e8,0x5476,0x4020,
0x6c6d,0xe891,0x3baf,0x401d,
0xb9d7,0xc966,0xe302,0x3ffd,
0x767f,0x7221,0xe2a8,0x3fc6,
0xdc2d,0x3b78,0xbdf8,0x3f7c,
0x14ed,0xdc95,0xd847,0x3f1c,
0xda45,0x6bb8,0x6b04,0x3ea2,
};
#endif
#ifdef MIEEE
static unsigned short FN4[] = {
0x4010,0xf1cb,0xb40b,0x7ae7,
0x4015,0xd666,0xf822,0x83ef,
0x3ff9,0xeeee,0x7471,0x00a9,
0x3fc5,0x6079,0x0004,0x019c,
0x3f7b,0xe503,0x7f80,0x7e63,
0x3f1c,0x8e9c,0x3475,0xf584,
0x3ea2,0x6b04,0x5b35,0x4025,
};
static unsigned short FD4[] = {
/* 0x3ff0,0x0000,0x0000,0x0000,*/
0x4020,0x5476,0x77e8,0x1fe5,
0x401d,0x3baf,0xe891,0x6c6d,
0x3ffd,0xe302,0xc966,0xb9d7,
0x3fc6,0xe2a8,0x7221,0x767f,
0x3f7c,0xbdf8,0x3b78,0xdc2d,
0x3f1c,0xd847,0xdc95,0x14ed,
0x3ea2,0x6b04,0x6bb8,0xda45,
};
#endif

#ifdef UNK
static double FN8[] = {
  4.55880873470465315206E-1,
  7.13715274100146711374E-1,
  1.60300158222319456320E-1,
  1.16064229408124407915E-2,
  3.49556442447859055605E-4,
  4.86215430826454749482E-6,
  3.20092790091004902806E-8,
  9.41779576128512936592E-11,
  9.70507110881952024631E-14,
};
static double FD8[] = {
/*  1.00000000000000000000E0,*/
  9.17463611873684053703E-1,
  1.78685545332074536321E-1,
  1.22253594771971293032E-2,
  3.58696481881851580297E-4,
  4.92435064317881464393E-6,
  3.21956939101046018377E-8,
  9.43720590350276732376E-11,
  9.70507110881952025725E-14,
};
#endif
#ifdef DEC
static unsigned short FN8[] = {
0037751,0064467,0142332,0164573,
0040066,0133013,0050352,0071102,
0037444,0022671,0102157,0013535,
0036476,0024335,0136423,0146444,
0035267,0042253,0164110,0110460,
0033643,0022626,0062535,0060320,
0032011,0075223,0010110,0153413,
0027717,0014572,0011360,0014034,
0025332,0104755,0004563,0152354,
};
static unsigned short FD8[] = {
/*0040200,0000000,0000000,0000000,*/
0040152,0157345,0030104,0075616,
0037466,0174527,0172740,0071060,
0036510,0046337,0144272,0156552,
0035274,0007555,0042537,0015572,
0033645,0035731,0112465,0026474,
0032012,0043612,0030613,0030123,
0027717,0103277,0004564,0151000,
0025332,0104755,0004563,0152354,
};
#endif
#ifdef IBMPC
static unsigned short FN8[] = {
0x5d2f,0xf89b,0x2d26,0x3fdd,
0x4e48,0x6a1d,0xd6c1,0x3fe6,
0xe2ec,0x308d,0x84b7,0x3fc4,
0x79a4,0xb7a2,0xc51b,0x3f87,
0x1226,0x7d09,0xe895,0x3f36,
0xac1a,0xccab,0x64b2,0x3ed4,
0x1ae1,0x6209,0x2f52,0x3e61,
0x0304,0x425e,0xe32f,0x3dd9,
0x7a9d,0xa12e,0x513d,0x3d3b,
};
static unsigned short FD8[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x8f72,0xa608,0x5bdc,0x3fed,
0x0e46,0xfebc,0xdf2a,0x3fc6,
0x5bad,0xf917,0x099b,0x3f89,
0xe36f,0xa8ab,0x81ed,0x3f37,
0xa5a8,0x32a6,0xa77b,0x3ed4,
0x660a,0x4631,0x48f1,0x3e61,
0x9a40,0xe12e,0xf0d7,0x3dd9,
0x7a9d,0xa12e,0x513d,0x3d3b,
};
#endif
#ifdef MIEEE
static unsigned short FN8[] = {
0x3fdd,0x2d26,0xf89b,0x5d2f,
0x3fe6,0xd6c1,0x6a1d,0x4e48,
0x3fc4,0x84b7,0x308d,0xe2ec,
0x3f87,0xc51b,0xb7a2,0x79a4,
0x3f36,0xe895,0x7d09,0x1226,
0x3ed4,0x64b2,0xccab,0xac1a,
0x3e61,0x2f52,0x6209,0x1ae1,
0x3dd9,0xe32f,0x425e,0x0304,
0x3d3b,0x513d,0xa12e,0x7a9d,
};
static unsigned short FD8[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x3fed,0x5bdc,0xa608,0x8f72,
0x3fc6,0xdf2a,0xfebc,0x0e46,
0x3f89,0x099b,0xf917,0x5bad,
0x3f37,0x81ed,0xa8ab,0xe36f,
0x3ed4,0xa77b,0x32a6,0xa5a8,
0x3e61,0x48f1,0x4631,0x660a,
0x3dd9,0xf0d7,0xe12e,0x9a40,
0x3d3b,0x513d,0xa12e,0x7a9d,
};
#endif

#ifdef UNK
static double GN4[] = {
  8.71001698973114191777E-2,
  6.11379109952219284151E-1,
  3.97180296392337498885E-1,
  7.48527737628469092119E-2,
  5.38868681462177273157E-3,
  1.61999794598934024525E-4,
  1.97963874140963632189E-6,
  7.82579040744090311069E-9,
};
static double GD4[] = {
/*  1.00000000000000000000E0,*/
  1.64402202413355338886E0,
  6.66296701268987968381E-1,
  9.88771761277688796203E-2,
  6.22396345441768420760E-3,
  1.73221081474177119497E-4,
  2.02659182086343991969E-6,
  7.82579218933534490868E-9,
};
#endif
#ifdef DEC
static unsigned short GN4[] = {
0037262,0060622,0164572,0157515,
0040034,0101527,0061263,0147204,
0037713,0055467,0037475,0144512,
0037231,0046151,0035234,0045261,
0036260,0111624,0150617,0053536,
0035051,0157175,0016675,0155456,
0033404,0154757,0041211,0000055,
0031406,0071060,0130322,0033322,
};
static unsigned short GD4[] = {
/* 0040200,0000000,0000000,0000000,*/
0040322,0067520,0046707,0053275,
0040052,0111153,0126542,0005516,
0037312,0100035,0167121,0014552,
0036313,0171143,0137176,0014213,
0035065,0121256,0012033,0150603,
0033410,0000225,0013121,0071643,
0031406,0071062,0131152,0150454,
};
#endif
#ifdef IBMPC
static unsigned short GN4[] = {
0x5bea,0x5d2f,0x4c32,0x3fb6,
0x79d1,0xec56,0x906a,0x3fe3,
0xb929,0xe7e7,0x6b66,0x3fd9,
0x8956,0x2753,0x298d,0x3fb3,
0xeaec,0x9a31,0x1272,0x3f76,
0xbb66,0xa3b7,0x3bcf,0x3f25,
0x2006,0xe851,0x9b3d,0x3ec0,
0x46da,0x161a,0xce46,0x3e40,
};
static unsigned short GD4[] = {
/* 0x0000,0x0000,0x0000,0x3ff0,*/
0xead8,0x09b8,0x4dea,0x3ffa,
0x416a,0x75ac,0x524d,0x3fe5,
0x232d,0xbdca,0x5003,0x3fb9,
0xc311,0x77cf,0x7e4c,0x3f79,
0x7a30,0xc283,0xb455,0x3f26,
0x2e74,0xa2ca,0x0012,0x3ec1,
0x5a26,0x564d,0xce46,0x3e40,
};
#endif
#ifdef MIEEE
static unsigned short GN4[] = {
0x3fb6,0x4c32,0x5d2f,0x5bea,
0x3fe3,0x906a,0xec56,0x79d1,
0x3fd9,0x6b66,0xe7e7,0xb929,
0x3fb3,0x298d,0x2753,0x8956,
0x3f76,0x1272,0x9a31,0xeaec,
0x3f25,0x3bcf,0xa3b7,0xbb66,
0x3ec0,0x9b3d,0xe851,0x2006,
0x3e40,0xce46,0x161a,0x46da,
};
static unsigned short GD4[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x3ffa,0x4dea,0x09b8,0xead8,
0x3fe5,0x524d,0x75ac,0x416a,
0x3fb9,0x5003,0xbdca,0x232d,
0x3f79,0x7e4c,0x77cf,0xc311,
0x3f26,0xb455,0xc283,0x7a30,
0x3ec1,0x0012,0xa2ca,0x2e74,
0x3e40,0xce46,0x564d,0x5a26,
};
#endif

#ifdef UNK
static double GN8[] = {
  6.97359953443276214934E-1,
  3.30410979305632063225E-1,
  3.84878767649974295920E-2,
  1.71718239052347903558E-3,
  3.48941165502279436777E-5,
  3.47131167084116673800E-7,
  1.70404452782044526189E-9,
  3.85945925430276600453E-12,
  3.14040098946363334640E-15,
};
static double GD8[] = {
/*  1.00000000000000000000E0,*/
  1.68548898811011640017E0,
  4.87852258695304967486E-1,
  4.67913194259625806320E-2,
  1.90284426674399523638E-3,
  3.68475504442561108162E-5,
  3.57043223443740838771E-7,
  1.72693748966316146736E-9,
  3.87830166023954706752E-12,
  3.14040098946363335242E-15,
};
#endif
#ifdef DEC
static unsigned short GN8[] = {
0040062,0103056,0110624,0033123,
0037651,0025640,0136266,0145647,
0037035,0122566,0137770,0061777,
0035741,0011424,0065311,0013370,
0034422,0055505,0134324,0016755,
0032672,0056530,0022565,0014747,
0030752,0031674,0114735,0013162,
0026607,0145353,0022020,0123625,
0024142,0045054,0060033,0016505,
};
static unsigned short GD8[] = {
/*0040200,0000000,0000000,0000000,*/
0040327,0137032,0064331,0136425,
0037771,0143705,0070300,0105711,
0037077,0124101,0025275,0035356,
0035771,0064333,0145103,0105357,
0034432,0106301,0105311,0010713,
0032677,0127645,0120034,0157551,
0030755,0054466,0010743,0105566,
0026610,0072242,0142530,0135744,
0024142,0045054,0060033,0016505,
};
#endif
#ifdef IBMPC
static unsigned short GN8[] = {
0x86ca,0xd232,0x50c5,0x3fe6,
0xd975,0x1796,0x2574,0x3fd5,
0x0c80,0xd7ff,0xb4ae,0x3fa3,
0x22df,0x8d59,0x2262,0x3f5c,
0x83be,0xb71a,0x4b68,0x3f02,
0xa33d,0x04ae,0x4bab,0x3e97,
0xa2ce,0x933b,0x4677,0x3e1d,
0x14f3,0x6482,0xf95d,0x3d90,
0x63a9,0x8c03,0x4945,0x3cec,
};
static unsigned short GD8[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x37a3,0x4d1b,0xf7c3,0x3ffa,
0x1179,0xae18,0x38f8,0x3fdf,
0xa75e,0x2557,0xf508,0x3fa7,
0x715e,0x7948,0x2d1b,0x3f5f,
0x2239,0x3159,0x5198,0x3f03,
0x9bed,0xb403,0xf5f4,0x3e97,
0x716f,0xc23c,0xab26,0x3e1d,
0x177c,0x58ab,0x0e94,0x3d91,
0x63a9,0x8c03,0x4945,0x3cec,
};
#endif
#ifdef MIEEE
static unsigned short GN8[] = {
0x3fe6,0x50c5,0xd232,0x86ca,
0x3fd5,0x2574,0x1796,0xd975,
0x3fa3,0xb4ae,0xd7ff,0x0c80,
0x3f5c,0x2262,0x8d59,0x22df,
0x3f02,0x4b68,0xb71a,0x83be,
0x3e97,0x4bab,0x04ae,0xa33d,
0x3e1d,0x4677,0x933b,0xa2ce,
0x3d90,0xf95d,0x6482,0x14f3,
0x3cec,0x4945,0x8c03,0x63a9,
};
static unsigned short GD8[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x3ffa,0xf7c3,0x4d1b,0x37a3,
0x3fdf,0x38f8,0xae18,0x1179,
0x3fa7,0xf508,0x2557,0xa75e,
0x3f5f,0x2d1b,0x7948,0x715e,
0x3f03,0x5198,0x3159,0x2239,
0x3e97,0xf5f4,0xb403,0x9bed,
0x3e1d,0xab26,0xc23c,0x716f,
0x3d91,0x0e94,0x58ab,0x177c,
0x3cec,0x4945,0x8c03,0x63a9,
};
#endif

#define EUL 0.57721566490153286061
extern double MAXNUM, PIO2, MACHEP;


int sici(double x,double* si,double* ci )
{
double z, c, s, f, g;
short sign;

if( x < 0.0 )
      {
      sign = -1;
      x = -x;
      }
else
      sign = 0;


if( x == 0.0 )
      {
      *si = 0.0;
      *ci = -MAXNUM;
      return( 0 );
      }


if( x > 1.0e9 )
      {
      *si = PIO2 - cos(x)/x;
      *ci = sin(x)/x;
      }



if( x > 4.0 )
      goto asympt;

z = x * x;
s = x * polevl( z, SN, 5 ) / polevl( z, SD, 5 );
c = z * polevl( z, CN, 5 ) / polevl( z, CD, 5 );

if( sign )
      s = -s;
*si = s;
*ci = EUL + log(x) + c; /* real part if x < 0 */
return(0);



/* The auxiliary functions are:
 *
 *
 * *si = *si - PIO2;
 * c = cos(x);
 * s = sin(x);
 *
 * t = *ci * s - *si * c;
 * a = *ci * c + *si * s;
 *
 * *si = t;
 * *ci = -a;
 */


asympt:

s = sin(x);
c = cos(x);
z = 1.0/(x*x);
if( x < 8.0 )
      {
      f = polevl( z, FN4, 6 ) / (x * p1evl( z, FD4, 7 ));
      g = z * polevl( z, GN4, 7 ) / p1evl( z, GD4, 7 );
      }
else
      {
      f = polevl( z, FN8, 8 ) / (x * p1evl( z, FD8, 8 ));
      g = z * polevl( z, GN8, 8 ) / p1evl( z, GD8, 9 );
      }
*si = PIO2 - f * c - g * s;
if( sign )
      *si = -( *si );
*ci = f * s - g * c;

return(0);
}

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