uClibc now has a math library. muahahahaha!

 -Erik

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);
+}