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Diffstat (limited to 'libm/double/shichi.c')
| -rw-r--r-- | libm/double/shichi.c | 599 |
1 files changed, 599 insertions, 0 deletions
diff --git a/libm/double/shichi.c b/libm/double/shichi.c new file mode 100644 index 000000000..a1497fc34 --- /dev/null +++ b/libm/double/shichi.c @@ -0,0 +1,599 @@ +/* shichi.c + * + * Hyperbolic sine and cosine integrals + * + * + * + * SYNOPSIS: + * + * double x, Chi, Shi, shichi(); + * + * shichi( x, &Chi, &Shi ); + * + * + * DESCRIPTION: + * + * Approximates the integrals + * + * x + * - + * | | cosh t - 1 + * Chi(x) = eul + ln x + | ----------- dt, + * | | t + * - + * 0 + * + * x + * - + * | | sinh t + * Shi(x) = | ------ dt + * | | t + * - + * 0 + * + * where eul = 0.57721566490153286061 is Euler's constant. + * The integrals are evaluated by power series for x < 8 + * and by Chebyshev expansions for x between 8 and 88. + * For large x, both functions approach exp(x)/2x. + * Arguments greater than 88 in magnitude return MAXNUM. + * + * + * ACCURACY: + * + * Test interval 0 to 88. + * Relative error: + * arithmetic function # trials peak rms + * DEC Shi 3000 9.1e-17 + * IEEE Shi 30000 6.9e-16 1.6e-16 + * Absolute error, except relative when |Chi| > 1: + * DEC Chi 2500 9.3e-17 + * IEEE Chi 30000 8.4e-16 1.4e-16 + */ + +/* +Cephes Math Library Release 2.8: June, 2000 +Copyright 1984, 1987, 2000 by Stephen L. Moshier +*/ + + +#include <math.h> + +#ifdef UNK +/* x exp(-x) shi(x), inverted interval 8 to 18 */ +static double S1[] = { + 1.83889230173399459482E-17, +-9.55485532279655569575E-17, + 2.04326105980879882648E-16, + 1.09896949074905343022E-15, +-1.31313534344092599234E-14, + 5.93976226264314278932E-14, +-3.47197010497749154755E-14, +-1.40059764613117131000E-12, + 9.49044626224223543299E-12, +-1.61596181145435454033E-11, +-1.77899784436430310321E-10, + 1.35455469767246947469E-9, +-1.03257121792819495123E-9, +-3.56699611114982536845E-8, + 1.44818877384267342057E-7, + 7.82018215184051295296E-7, +-5.39919118403805073710E-6, +-3.12458202168959833422E-5, + 8.90136741950727517826E-5, + 2.02558474743846862168E-3, + 2.96064440855633256972E-2, + 1.11847751047257036625E0 +}; + +/* x exp(-x) shi(x), inverted interval 18 to 88 */ +static double S2[] = { +-1.05311574154850938805E-17, + 2.62446095596355225821E-17, + 8.82090135625368160657E-17, +-3.38459811878103047136E-16, +-8.30608026366935789136E-16, + 3.93397875437050071776E-15, + 1.01765565969729044505E-14, +-4.21128170307640802703E-14, +-1.60818204519802480035E-13, + 3.34714954175994481761E-13, + 2.72600352129153073807E-12, + 1.66894954752839083608E-12, +-3.49278141024730899554E-11, +-1.58580661666482709598E-10, +-1.79289437183355633342E-10, + 1.76281629144264523277E-9, + 1.69050228879421288846E-8, + 1.25391771228487041649E-7, + 1.16229947068677338732E-6, + 1.61038260117376323993E-5, + 3.49810375601053973070E-4, + 1.28478065259647610779E-2, + 1.03665722588798326712E0 +}; +#endif + +#ifdef DEC +static unsigned short S1[] = { +0022251,0115635,0165120,0006574, +0122734,0050751,0020305,0101356, +0023153,0111154,0011103,0177462, +0023636,0060321,0060253,0124246, +0124554,0106655,0152525,0166400, +0025205,0140145,0171006,0106556, +0125034,0056427,0004205,0176022, +0126305,0016731,0025011,0134453, +0027046,0172453,0112604,0116235, +0127216,0022071,0116600,0137667, +0130103,0115126,0071104,0052535, +0030672,0025450,0010071,0141414, +0130615,0165136,0132137,0177737, +0132031,0031611,0074436,0175407, +0032433,0077602,0104345,0060076, +0033121,0165741,0167177,0172433, +0133665,0025262,0174621,0022612, +0134403,0006761,0124566,0145405, +0034672,0126332,0034737,0116744, +0036004,0137654,0037332,0131766, +0036762,0104466,0121445,0124326, +0040217,0025105,0062145,0042640 +}; + +static unsigned short S2[] = { +0122102,0041774,0016051,0055137, +0022362,0010125,0007651,0015773, +0022713,0062551,0040227,0071645, +0123303,0015732,0025731,0146570, +0123557,0064016,0002067,0067711, +0024215,0136214,0132374,0124234, +0024467,0051425,0071066,0064210, +0125075,0124305,0135123,0024170, +0125465,0010261,0005560,0034232, +0025674,0066602,0030724,0174557, +0026477,0151520,0051510,0067250, +0026352,0161076,0113154,0116271, +0127431,0116470,0177465,0127274, +0130056,0056174,0170315,0013321, +0130105,0020575,0075327,0036710, +0030762,0043625,0113046,0125035, +0031621,0033211,0154354,0022077, +0032406,0121555,0074270,0041141, +0033234,0000116,0041611,0173743, +0034207,0013263,0174715,0115563, +0035267,0063300,0175753,0117266, +0036522,0077633,0033255,0136200, +0040204,0130457,0014454,0166254 +}; +#endif + +#ifdef IBMPC +static unsigned short S1[] = { +0x01b0,0xbd4a,0x3373,0x3c75, +0xb05e,0x2418,0x8a3d,0xbc9b, +0x7fe6,0x8248,0x724d,0x3cad, +0x7515,0x2c15,0xcc1a,0x3cd3, +0xbda0,0xbaaa,0x91b5,0xbd0d, +0xd1ae,0xbe40,0xb80c,0x3d30, +0xbf82,0xe110,0x8ba2,0xbd23, +0x3725,0x2541,0xa3bb,0xbd78, +0x9394,0x72b0,0xdea5,0x3da4, +0x17f7,0x33b0,0xc487,0xbdb1, +0x8aac,0xce48,0x734a,0xbde8, +0x3862,0x0207,0x4565,0x3e17, +0xfffc,0xd68b,0xbd4b,0xbe11, +0xdf61,0x2f23,0x2671,0xbe63, +0xac08,0x511c,0x6ff0,0x3e83, +0xfea3,0x3dcf,0x3d7c,0x3eaa, +0x24b1,0x5f32,0xa556,0xbed6, +0xd961,0x352e,0x61be,0xbf00, +0xf3bd,0x473b,0x559b,0x3f17, +0x567f,0x87db,0x97f5,0x3f60, +0xb51b,0xd464,0x5126,0x3f9e, +0xa8b4,0xac8c,0xe548,0x3ff1 +}; + +static unsigned short S2[] = { +0x2b4c,0x8385,0x487f,0xbc68, +0x237f,0xa1f5,0x420a,0x3c7e, +0xee75,0x2812,0x6cad,0x3c99, +0x39af,0x457b,0x637b,0xbcb8, +0xedf9,0xc086,0xed01,0xbccd, +0x9513,0x969f,0xb791,0x3cf1, +0xcd11,0xae46,0xea62,0x3d06, +0x650f,0xb74a,0xb518,0xbd27, +0x0713,0x216e,0xa216,0xbd46, +0x9f2e,0x463a,0x8db0,0x3d57, +0x0dd5,0x0a69,0xfa6a,0x3d87, +0x9397,0xd2cd,0x5c47,0x3d7d, +0xb5d8,0x1fe6,0x33a7,0xbdc3, +0xa2da,0x9e19,0xcb8f,0xbde5, +0xe7b9,0xaf5a,0xa42f,0xbde8, +0xd544,0xb2c4,0x48f2,0x3e1e, +0x8488,0x3b1d,0x26d1,0x3e52, +0x084c,0xaf17,0xd46d,0x3e80, +0x3efc,0xc871,0x8009,0x3eb3, +0xb36e,0x7f39,0xe2d6,0x3ef0, +0x73d7,0x1f7d,0xecd8,0x3f36, +0xb790,0x66d5,0x4ff3,0x3f8a, +0x9d96,0xe325,0x9625,0x3ff0 +}; +#endif + +#ifdef MIEEE +static unsigned short S1[] = { +0x3c75,0x3373,0xbd4a,0x01b0, +0xbc9b,0x8a3d,0x2418,0xb05e, +0x3cad,0x724d,0x8248,0x7fe6, +0x3cd3,0xcc1a,0x2c15,0x7515, +0xbd0d,0x91b5,0xbaaa,0xbda0, +0x3d30,0xb80c,0xbe40,0xd1ae, +0xbd23,0x8ba2,0xe110,0xbf82, +0xbd78,0xa3bb,0x2541,0x3725, +0x3da4,0xdea5,0x72b0,0x9394, +0xbdb1,0xc487,0x33b0,0x17f7, +0xbde8,0x734a,0xce48,0x8aac, +0x3e17,0x4565,0x0207,0x3862, +0xbe11,0xbd4b,0xd68b,0xfffc, +0xbe63,0x2671,0x2f23,0xdf61, +0x3e83,0x6ff0,0x511c,0xac08, +0x3eaa,0x3d7c,0x3dcf,0xfea3, +0xbed6,0xa556,0x5f32,0x24b1, +0xbf00,0x61be,0x352e,0xd961, +0x3f17,0x559b,0x473b,0xf3bd, +0x3f60,0x97f5,0x87db,0x567f, +0x3f9e,0x5126,0xd464,0xb51b, +0x3ff1,0xe548,0xac8c,0xa8b4 +}; + +static unsigned short S2[] = { +0xbc68,0x487f,0x8385,0x2b4c, +0x3c7e,0x420a,0xa1f5,0x237f, +0x3c99,0x6cad,0x2812,0xee75, +0xbcb8,0x637b,0x457b,0x39af, +0xbccd,0xed01,0xc086,0xedf9, +0x3cf1,0xb791,0x969f,0x9513, +0x3d06,0xea62,0xae46,0xcd11, +0xbd27,0xb518,0xb74a,0x650f, +0xbd46,0xa216,0x216e,0x0713, +0x3d57,0x8db0,0x463a,0x9f2e, +0x3d87,0xfa6a,0x0a69,0x0dd5, +0x3d7d,0x5c47,0xd2cd,0x9397, +0xbdc3,0x33a7,0x1fe6,0xb5d8, +0xbde5,0xcb8f,0x9e19,0xa2da, +0xbde8,0xa42f,0xaf5a,0xe7b9, +0x3e1e,0x48f2,0xb2c4,0xd544, +0x3e52,0x26d1,0x3b1d,0x8488, +0x3e80,0xd46d,0xaf17,0x084c, +0x3eb3,0x8009,0xc871,0x3efc, +0x3ef0,0xe2d6,0x7f39,0xb36e, +0x3f36,0xecd8,0x1f7d,0x73d7, +0x3f8a,0x4ff3,0x66d5,0xb790, +0x3ff0,0x9625,0xe325,0x9d96 +}; +#endif + + +#ifdef UNK +/* x exp(-x) chin(x), inverted interval 8 to 18 */ +static double C1[] = { +-8.12435385225864036372E-18, + 2.17586413290339214377E-17, + 5.22624394924072204667E-17, +-9.48812110591690559363E-16, + 5.35546311647465209166E-15, +-1.21009970113732918701E-14, +-6.00865178553447437951E-14, + 7.16339649156028587775E-13, +-2.93496072607599856104E-12, +-1.40359438136491256904E-12, + 8.76302288609054966081E-11, +-4.40092476213282340617E-10, +-1.87992075640569295479E-10, + 1.31458150989474594064E-8, +-4.75513930924765465590E-8, +-2.21775018801848880741E-7, + 1.94635531373272490962E-6, + 4.33505889257316408893E-6, +-6.13387001076494349496E-5, +-3.13085477492997465138E-4, + 4.97164789823116062801E-4, + 2.64347496031374526641E-2, + 1.11446150876699213025E0 +}; + +/* x exp(-x) chin(x), inverted interval 18 to 88 */ +static double C2[] = { + 8.06913408255155572081E-18, +-2.08074168180148170312E-17, +-5.98111329658272336816E-17, + 2.68533951085945765591E-16, + 4.52313941698904694774E-16, +-3.10734917335299464535E-15, +-4.42823207332531972288E-15, + 3.49639695410806959872E-14, + 6.63406731718911586609E-14, +-3.71902448093119218395E-13, +-1.27135418132338309016E-12, + 2.74851141935315395333E-12, + 2.33781843985453438400E-11, + 2.71436006377612442764E-11, +-2.56600180000355990529E-10, +-1.61021375163803438552E-9, +-4.72543064876271773512E-9, +-3.00095178028681682282E-9, + 7.79387474390914922337E-8, + 1.06942765566401507066E-6, + 1.59503164802313196374E-5, + 3.49592575153777996871E-4, + 1.28475387530065247392E-2, + 1.03665693917934275131E0 +}; +#endif + +#ifdef DEC +static unsigned short C1[] = { +0122025,0157055,0021702,0021427, +0022310,0130043,0123265,0022340, +0022561,0002231,0017746,0013043, +0123610,0136375,0002352,0024467, +0024300,0171555,0141300,0000446, +0124531,0176777,0126210,0035616, +0125207,0046604,0167760,0077132, +0026111,0120666,0026606,0064143, +0126516,0103615,0054127,0005436, +0126305,0104721,0025415,0004134, +0027700,0131556,0164725,0157553, +0130361,0170602,0077274,0055406, +0130116,0131420,0125472,0017231, +0031541,0153747,0177312,0056304, +0132114,0035517,0041545,0043151, +0132556,0020415,0110044,0172442, +0033402,0117041,0031152,0010364, +0033621,0072737,0050647,0013720, +0134600,0121366,0140010,0063265, +0135244,0022637,0013756,0044742, +0035402,0052052,0006523,0043564, +0036730,0106660,0020277,0162146, +0040216,0123254,0135147,0005724 +}; + +static unsigned short C2[] = { +0022024,0154550,0104311,0144257, +0122277,0165037,0133443,0155601, +0122611,0165102,0157053,0055252, +0023232,0146235,0153511,0113222, +0023402,0057340,0145304,0010471, +0124137,0164171,0113071,0100002, +0124237,0105473,0056130,0022022, +0025035,0073266,0056746,0164433, +0025225,0061313,0055600,0165407, +0125721,0056312,0107613,0051215, +0126262,0166534,0115336,0066653, +0026501,0064307,0127442,0065573, +0027315,0121375,0142020,0045356, +0027356,0140764,0070641,0046570, +0130215,0010503,0146335,0177737, +0130735,0047134,0015215,0163665, +0131242,0056523,0155276,0050053, +0131116,0034515,0050707,0163512, +0032247,0057507,0107545,0032007, +0033217,0104501,0021706,0025047, +0034205,0146413,0033746,0076562, +0035267,0044605,0065355,0002772, +0036522,0077173,0130716,0170304, +0040204,0130454,0130571,0027270 +}; +#endif + +#ifdef IBMPC +static unsigned short C1[] = { +0x4463,0xa478,0xbbc5,0xbc62, +0xa49c,0x74d6,0x1604,0x3c79, +0xc2c4,0x23fc,0x2093,0x3c8e, +0x4527,0xa09d,0x179f,0xbcd1, +0x0025,0xb858,0x1e6d,0x3cf8, +0x0772,0xf591,0x3fbf,0xbd0b, +0x0fcb,0x9dfe,0xe9b0,0xbd30, +0xcd0c,0xc5b0,0x3436,0x3d69, +0xe164,0xab0a,0xd0f1,0xbd89, +0xa10c,0x2561,0xb13a,0xbd78, +0xbbed,0xdd3a,0x166d,0x3dd8, +0x8b61,0x4fd7,0x3e30,0xbdfe, +0x43d3,0x1567,0xd662,0xbde9, +0x4b98,0xffd9,0x3afc,0x3e4c, +0xa8cd,0xe86c,0x8769,0xbe69, +0x9ea4,0xb204,0xc421,0xbe8d, +0x421f,0x264d,0x53c4,0x3ec0, +0xe2fa,0xea34,0x2ebb,0x3ed2, +0x0cd7,0xd801,0x145e,0xbf10, +0xc93c,0xe2fd,0x84b3,0xbf34, +0x68ef,0x41aa,0x4a85,0x3f40, +0xfc8d,0x0417,0x11b6,0x3f9b, +0xe17b,0x974c,0xd4d5,0x3ff1 +}; + +static unsigned short C2[] = { +0x3916,0x1119,0x9b2d,0x3c62, +0x7b70,0xf6e4,0xfd43,0xbc77, +0x6b55,0x5bc5,0x3d48,0xbc91, +0x32d2,0xbae9,0x5993,0x3cb3, +0x8227,0x1958,0x4bdc,0x3cc0, +0x3000,0x32c7,0xfd0f,0xbceb, +0x0482,0x6b8b,0xf167,0xbcf3, +0xdd23,0xcbbc,0xaed6,0x3d23, +0x1d61,0x6b70,0xac59,0x3d32, +0x6a52,0x51f1,0x2b99,0xbd5a, +0xcdb5,0x935b,0x5dab,0xbd76, +0x4d6f,0xf5e4,0x2d18,0x3d88, +0x095e,0xb882,0xb45f,0x3db9, +0x29af,0x8e34,0xd83e,0x3dbd, +0xbffc,0x799b,0xa228,0xbdf1, +0xbcf7,0x8351,0xa9cb,0xbe1b, +0xca05,0x7b57,0x4baa,0xbe34, +0xfce9,0xaa38,0xc729,0xbe29, +0xa681,0xf1ec,0xebe8,0x3e74, +0xc545,0x2478,0xf128,0x3eb1, +0xcfae,0x66fc,0xb9a1,0x3ef0, +0xa0bf,0xad5d,0xe930,0x3f36, +0xde19,0x7639,0x4fcf,0x3f8a, +0x25d7,0x962f,0x9625,0x3ff0 +}; +#endif + +#ifdef MIEEE +static unsigned short C1[] = { +0xbc62,0xbbc5,0xa478,0x4463, +0x3c79,0x1604,0x74d6,0xa49c, +0x3c8e,0x2093,0x23fc,0xc2c4, +0xbcd1,0x179f,0xa09d,0x4527, +0x3cf8,0x1e6d,0xb858,0x0025, +0xbd0b,0x3fbf,0xf591,0x0772, +0xbd30,0xe9b0,0x9dfe,0x0fcb, +0x3d69,0x3436,0xc5b0,0xcd0c, +0xbd89,0xd0f1,0xab0a,0xe164, +0xbd78,0xb13a,0x2561,0xa10c, +0x3dd8,0x166d,0xdd3a,0xbbed, +0xbdfe,0x3e30,0x4fd7,0x8b61, +0xbde9,0xd662,0x1567,0x43d3, +0x3e4c,0x3afc,0xffd9,0x4b98, +0xbe69,0x8769,0xe86c,0xa8cd, +0xbe8d,0xc421,0xb204,0x9ea4, +0x3ec0,0x53c4,0x264d,0x421f, +0x3ed2,0x2ebb,0xea34,0xe2fa, +0xbf10,0x145e,0xd801,0x0cd7, +0xbf34,0x84b3,0xe2fd,0xc93c, +0x3f40,0x4a85,0x41aa,0x68ef, +0x3f9b,0x11b6,0x0417,0xfc8d, +0x3ff1,0xd4d5,0x974c,0xe17b +}; + +static unsigned short C2[] = { +0x3c62,0x9b2d,0x1119,0x3916, +0xbc77,0xfd43,0xf6e4,0x7b70, +0xbc91,0x3d48,0x5bc5,0x6b55, +0x3cb3,0x5993,0xbae9,0x32d2, +0x3cc0,0x4bdc,0x1958,0x8227, +0xbceb,0xfd0f,0x32c7,0x3000, +0xbcf3,0xf167,0x6b8b,0x0482, +0x3d23,0xaed6,0xcbbc,0xdd23, +0x3d32,0xac59,0x6b70,0x1d61, +0xbd5a,0x2b99,0x51f1,0x6a52, +0xbd76,0x5dab,0x935b,0xcdb5, +0x3d88,0x2d18,0xf5e4,0x4d6f, +0x3db9,0xb45f,0xb882,0x095e, +0x3dbd,0xd83e,0x8e34,0x29af, +0xbdf1,0xa228,0x799b,0xbffc, +0xbe1b,0xa9cb,0x8351,0xbcf7, +0xbe34,0x4baa,0x7b57,0xca05, +0xbe29,0xc729,0xaa38,0xfce9, +0x3e74,0xebe8,0xf1ec,0xa681, +0x3eb1,0xf128,0x2478,0xc545, +0x3ef0,0xb9a1,0x66fc,0xcfae, +0x3f36,0xe930,0xad5d,0xa0bf, +0x3f8a,0x4fcf,0x7639,0xde19, +0x3ff0,0x9625,0x962f,0x25d7 +}; +#endif + + + +/* Sine and cosine integrals */ + +#ifdef ANSIPROT +extern double log ( double ); +extern double exp ( double ); +extern double fabs ( double ); +extern double chbevl ( double, void *, int ); +#else +double log(), exp(), fabs(), chbevl(); +#endif +#define EUL 0.57721566490153286061 +extern double MACHEP, MAXNUM, PIO2; + +int shichi( x, si, ci ) +double x; +double *si, *ci; +{ +double k, z, c, s, a; +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 >= 8.0 ) + goto chb; + +z = x * x; + +/* Direct power series expansion */ + +a = 1.0; +s = 1.0; +c = 0.0; +k = 2.0; + +do + { + a *= z/k; + c += a/k; + k += 1.0; + a /= k; + s += a/k; + k += 1.0; + } +while( fabs(a/s) > MACHEP ); + +s *= x; +goto done; + + +chb: + +if( x < 18.0 ) + { + a = (576.0/x - 52.0)/10.0; + k = exp(x) / x; + s = k * chbevl( a, S1, 22 ); + c = k * chbevl( a, C1, 23 ); + goto done; + } + +if( x <= 88.0 ) + { + a = (6336.0/x - 212.0)/70.0; + k = exp(x) / x; + s = k * chbevl( a, S2, 23 ); + c = k * chbevl( a, C2, 24 ); + goto done; + } +else + { + if( sign ) + *si = -MAXNUM; + else + *si = MAXNUM; + *ci = MAXNUM; + return(0); + } +done: +if( sign ) + s = -s; + +*si = s; + +*ci = EUL + log(x) + c; +return(0); +} |