uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 599 insertions, 0 deletions

diff --git a/libm/double/zetac.c b/libm/double/zetac.c
new file mode 100644
index 000000000..cc28590b3
--- /dev/null
+++ b/libm/double/zetac.c
@@ -0,0 +1,599 @@
+ /*							zetac.c
+ *
+ *	Riemann zeta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, zetac();
+ *
+ * y = zetac( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ *                inf.
+ *                 -    -x
+ *   zetac(x)  =   >   k   ,   x > 1,
+ *                 -
+ *                k=2
+ *
+ * is related to the Riemann zeta function by
+ *
+ *	Riemann zeta(x) = zetac(x) + 1.
+ *
+ * Extension of the function definition for x < 1 is implemented.
+ * Zero is returned for x > log2(MAXNUM).
+ *
+ * An overflow error may occur for large negative x, due to the
+ * gamma function in the reflection formula.
+ *
+ * ACCURACY:
+ *
+ * Tabulated values have full machine accuracy.
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      1,50        10000       9.8e-16	    1.3e-16
+ *    DEC       1,50         2000       1.1e-16     1.9e-17
+ *
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern double MAXNUM, PI;
+
+/* Riemann zeta(x) - 1
+ * for integer arguments between 0 and 30.
+ */
+#ifdef UNK
+static double azetac[] = {
+-1.50000000000000000000E0,
+ 1.70141183460469231730E38, /* infinity. */
+ 6.44934066848226436472E-1,
+ 2.02056903159594285400E-1,
+ 8.23232337111381915160E-2,
+ 3.69277551433699263314E-2,
+ 1.73430619844491397145E-2,
+ 8.34927738192282683980E-3,
+ 4.07735619794433937869E-3,
+ 2.00839282608221441785E-3,
+ 9.94575127818085337146E-4,
+ 4.94188604119464558702E-4,
+ 2.46086553308048298638E-4,
+ 1.22713347578489146752E-4,
+ 6.12481350587048292585E-5,
+ 3.05882363070204935517E-5,
+ 1.52822594086518717326E-5,
+ 7.63719763789976227360E-6,
+ 3.81729326499983985646E-6,
+ 1.90821271655393892566E-6,
+ 9.53962033872796113152E-7,
+ 4.76932986787806463117E-7,
+ 2.38450502727732990004E-7,
+ 1.19219925965311073068E-7,
+ 5.96081890512594796124E-8,
+ 2.98035035146522801861E-8,
+ 1.49015548283650412347E-8,
+ 7.45071178983542949198E-9,
+ 3.72533402478845705482E-9,
+ 1.86265972351304900640E-9,
+ 9.31327432419668182872E-10
+};
+#endif
+
+#ifdef DEC
+static unsigned short azetac[] = {
+0140300,0000000,0000000,0000000,
+0077777,0177777,0177777,0177777,
+0040045,0015146,0022460,0076462,
+0037516,0164001,0036001,0104116,
+0037250,0114425,0061754,0022033,
+0037027,0040616,0145174,0146670,
+0036616,0011411,0100444,0104437,
+0036410,0145550,0051474,0161067,
+0036205,0115527,0141434,0133506,
+0036003,0117475,0100553,0053403,
+0035602,0056147,0045567,0027703,
+0035401,0106157,0111054,0145242,
+0035201,0002455,0113151,0101015,
+0035000,0126235,0004273,0157260,
+0034600,0071127,0112647,0005261,
+0034400,0045736,0057610,0157550,
+0034200,0031146,0172621,0074172,
+0034000,0020603,0115503,0032007,
+0033600,0013114,0124672,0023135,
+0033400,0007330,0043715,0151117,
+0033200,0004742,0145043,0033514,
+0033000,0003225,0152624,0004411,
+0032600,0002143,0033166,0035746,
+0032400,0001354,0074234,0026143,
+0032200,0000762,0147776,0170220,
+0032000,0000514,0072452,0130631,
+0031600,0000335,0114266,0063315,
+0031400,0000223,0132710,0041045,
+0031200,0000142,0073202,0153426,
+0031000,0000101,0121400,0152065,
+0030600,0000053,0140525,0072761
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short azetac[] = {
+0x0000,0x0000,0x0000,0xbff8,
+0xffff,0xffff,0xffff,0x7fef,
+0x0fa6,0xc4a6,0xa34c,0x3fe4,
+0x310a,0x2780,0xdd00,0x3fc9,
+0x8483,0xac7d,0x1322,0x3fb5,
+0x99b7,0xd94f,0xe831,0x3fa2,
+0x9124,0x3024,0xc261,0x3f91,
+0x9c47,0x0a67,0x196d,0x3f81,
+0x96e9,0xf863,0xb36a,0x3f70,
+0x6ae0,0xb02d,0x73e7,0x3f60,
+0xe5f8,0xe96e,0x4b8c,0x3f50,
+0x9954,0xf245,0x318d,0x3f40,
+0x3042,0xb2cd,0x20a5,0x3f30,
+0x7bd6,0xa117,0x1593,0x3f20,
+0xe156,0xf2b4,0x0e4a,0x3f10,
+0x1bed,0xcbf1,0x097b,0x3f00,
+0x2f0f,0xdeb2,0x064c,0x3ef0,
+0x6681,0x7368,0x0430,0x3ee0,
+0x44cc,0x9537,0x02c9,0x3ed0,
+0xba4a,0x08f9,0x01db,0x3ec0,
+0x66ea,0x5944,0x013c,0x3eb0,
+0x8121,0xbab2,0x00d2,0x3ea0,
+0xc77d,0x66ce,0x008c,0x3e90,
+0x858c,0x8f13,0x005d,0x3e80,
+0xde12,0x59ff,0x003e,0x3e70,
+0x5633,0x8ea5,0x0029,0x3e60,
+0xccda,0xb316,0x001b,0x3e50,
+0x0845,0x76b9,0x0012,0x3e40,
+0x5ae3,0x4ed0,0x000c,0x3e30,
+0x1a87,0x3460,0x0008,0x3e20,
+0xaebe,0x782a,0x0005,0x3e10
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short azetac[] = {
+0xbff8,0x0000,0x0000,0x0000,
+0x7fef,0xffff,0xffff,0xffff,
+0x3fe4,0xa34c,0xc4a6,0x0fa6,
+0x3fc9,0xdd00,0x2780,0x310a,
+0x3fb5,0x1322,0xac7d,0x8483,
+0x3fa2,0xe831,0xd94f,0x99b7,
+0x3f91,0xc261,0x3024,0x9124,
+0x3f81,0x196d,0x0a67,0x9c47,
+0x3f70,0xb36a,0xf863,0x96e9,
+0x3f60,0x73e7,0xb02d,0x6ae0,
+0x3f50,0x4b8c,0xe96e,0xe5f8,
+0x3f40,0x318d,0xf245,0x9954,
+0x3f30,0x20a5,0xb2cd,0x3042,
+0x3f20,0x1593,0xa117,0x7bd6,
+0x3f10,0x0e4a,0xf2b4,0xe156,
+0x3f00,0x097b,0xcbf1,0x1bed,
+0x3ef0,0x064c,0xdeb2,0x2f0f,
+0x3ee0,0x0430,0x7368,0x6681,
+0x3ed0,0x02c9,0x9537,0x44cc,
+0x3ec0,0x01db,0x08f9,0xba4a,
+0x3eb0,0x013c,0x5944,0x66ea,
+0x3ea0,0x00d2,0xbab2,0x8121,
+0x3e90,0x008c,0x66ce,0xc77d,
+0x3e80,0x005d,0x8f13,0x858c,
+0x3e70,0x003e,0x59ff,0xde12,
+0x3e60,0x0029,0x8ea5,0x5633,
+0x3e50,0x001b,0xb316,0xccda,
+0x3e40,0x0012,0x76b9,0x0845,
+0x3e30,0x000c,0x4ed0,0x5ae3,
+0x3e20,0x0008,0x3460,0x1a87,
+0x3e10,0x0005,0x782a,0xaebe
+};
+#endif
+
+
+/* 2**x (1 - 1/x) (zeta(x) - 1) = P(1/x)/Q(1/x), 1 <= x <= 10 */
+#ifdef UNK
+static double P[9] = {
+  5.85746514569725319540E11,
+  2.57534127756102572888E11,
+  4.87781159567948256438E10,
+  5.15399538023885770696E9,
+  3.41646073514754094281E8,
+  1.60837006880656492731E7,
+  5.92785467342109522998E5,
+  1.51129169964938823117E4,
+  2.01822444485997955865E2,
+};
+static double Q[8] = {
+/*  1.00000000000000000000E0,*/
+  3.90497676373371157516E11,
+  5.22858235368272161797E10,
+  5.64451517271280543351E9,
+  3.39006746015350418834E8,
+  1.79410371500126453702E7,
+  5.66666825131384797029E5,
+  1.60382976810944131506E4,
+  1.96436237223387314144E2,
+};
+#endif
+#ifdef DEC
+static unsigned short P[36] = {
+0052010,0060466,0101211,0134657,
+0051557,0154353,0135060,0064411,
+0051065,0133157,0133514,0133633,
+0050231,0114735,0035036,0111344,
+0047242,0164327,0146036,0033545,
+0046165,0065364,0130045,0011005,
+0045020,0134427,0075073,0134107,
+0043554,0021653,0000440,0177426,
+0042111,0151213,0134312,0021402,
+};
+static unsigned short Q[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0051665,0153363,0054252,0137010,
+0051102,0143645,0121415,0036107,
+0050250,0034073,0131133,0036465,
+0047241,0123250,0150037,0070012,
+0046210,0160426,0111463,0116507,
+0045012,0054255,0031674,0173612,
+0043572,0114460,0151520,0012221,
+0042104,0067655,0037037,0137421,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P[36] = {
+0x3736,0xd051,0x0c26,0x4261,
+0x0d21,0x7746,0xfb1d,0x424d,
+0x96f3,0xf6e9,0xb6cd,0x4226,
+0xd25c,0xa743,0x333b,0x41f3,
+0xc6ed,0xf983,0x5d1a,0x41b4,
+0xa241,0x9604,0xad5e,0x416e,
+0x7709,0xef47,0x1722,0x4122,
+0x1fe3,0x6024,0x8475,0x40cd,
+0x4460,0x7719,0x3a51,0x4069,
+};
+static unsigned short Q[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x57c1,0x6b15,0xbade,0x4256,
+0xa789,0xb461,0x58f4,0x4228,
+0x67a7,0x764b,0x0707,0x41f5,
+0xee01,0x1a03,0x34d5,0x41b4,
+0x73a9,0xd266,0x1c22,0x4171,
+0x9ef1,0xa677,0x4b15,0x4121,
+0x0292,0x1a6a,0x5326,0x40cf,
+0xf7e2,0xa7c3,0x8df5,0x4068,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P[36] = {
+0x4261,0x0c26,0xd051,0x3736,
+0x424d,0xfb1d,0x7746,0x0d21,
+0x4226,0xb6cd,0xf6e9,0x96f3,
+0x41f3,0x333b,0xa743,0xd25c,
+0x41b4,0x5d1a,0xf983,0xc6ed,
+0x416e,0xad5e,0x9604,0xa241,
+0x4122,0x1722,0xef47,0x7709,
+0x40cd,0x8475,0x6024,0x1fe3,
+0x4069,0x3a51,0x7719,0x4460,
+};
+static unsigned short Q[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4256,0xbade,0x6b15,0x57c1,
+0x4228,0x58f4,0xb461,0xa789,
+0x41f5,0x0707,0x764b,0x67a7,
+0x41b4,0x34d5,0x1a03,0xee01,
+0x4171,0x1c22,0xd266,0x73a9,
+0x4121,0x4b15,0xa677,0x9ef1,
+0x40cf,0x5326,0x1a6a,0x0292,
+0x4068,0x8df5,0xa7c3,0xf7e2,
+};
+#endif
+
+/* log(zeta(x) - 1 - 2**-x), 10 <= x <= 50 */
+#ifdef UNK
+static double A[11] = {
+ 8.70728567484590192539E6,
+ 1.76506865670346462757E8,
+ 2.60889506707483264896E10,
+ 5.29806374009894791647E11,
+ 2.26888156119238241487E13,
+ 3.31884402932705083599E14,
+ 5.13778997975868230192E15,
+-1.98123688133907171455E15,
+-9.92763810039983572356E16,
+ 7.82905376180870586444E16,
+ 9.26786275768927717187E16,
+};
+static double B[10] = {
+/* 1.00000000000000000000E0,*/
+-7.92625410563741062861E6,
+-1.60529969932920229676E8,
+-2.37669260975543221788E10,
+-4.80319584350455169857E11,
+-2.07820961754173320170E13,
+-2.96075404507272223680E14,
+-4.86299103694609136686E15,
+ 5.34589509675789930199E15,
+ 5.71464111092297631292E16,
+-1.79915597658676556828E16,
+};
+#endif
+#ifdef DEC
+static unsigned short A[44] = {
+0046004,0156325,0126302,0131567,
+0047050,0052177,0015271,0136466,
+0050702,0060271,0070727,0171112,
+0051766,0132727,0064363,0145042,
+0053245,0012466,0056000,0117230,
+0054226,0166155,0174275,0170213,
+0055222,0003127,0112544,0101322,
+0154741,0036625,0010346,0053767,
+0156260,0054653,0154052,0031113,
+0056213,0011152,0021000,0007111,
+0056244,0120534,0040576,0163262,
+};
+static unsigned short B[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0145761,0161734,0033026,0015520,
+0147031,0013743,0017355,0036703,
+0150661,0011720,0061061,0136402,
+0151737,0125216,0070274,0164414,
+0153227,0032653,0127211,0145250,
+0154206,0121666,0123774,0042035,
+0155212,0033352,0125154,0132533,
+0055227,0170201,0110775,0072132,
+0056113,0003133,0127132,0122303,
+0155577,0126351,0141462,0171037,
+};
+#endif
+#ifdef IBMPC
+static unsigned short A[44] = {
+0x566f,0xb598,0x9b9a,0x4160,
+0x37a7,0xe357,0x0a8f,0x41a5,
+0xfe49,0x2e3a,0x4c17,0x4218,
+0x7944,0xed1e,0xd6ba,0x425e,
+0x13d3,0xcb80,0xa2a6,0x42b4,
+0xbe11,0xbf17,0xdd8d,0x42f2,
+0x905a,0xf2ac,0x40ca,0x4332,
+0xcaff,0xa21c,0x27b2,0xc31c,
+0x4649,0x7b05,0x0b35,0xc376,
+0x01c9,0x4440,0x624d,0x4371,
+0xdcd6,0x882f,0x942b,0x4374,
+};
+static unsigned short B[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xc36a,0x86c2,0x3c7b,0xc15e,
+0xa7b8,0x63dd,0x22fc,0xc1a3,
+0x37a0,0x0c46,0x227a,0xc216,
+0x9d22,0xce17,0xf551,0xc25b,
+0x3955,0x75d1,0xe6b5,0xc2b2,
+0x8884,0xd4ff,0xd476,0xc2f0,
+0x96ab,0x554d,0x46dd,0xc331,
+0xae8b,0x323f,0xfe10,0x4332,
+0x5498,0x75cb,0x60cb,0x4369,
+0x5e44,0x3866,0xf59d,0xc34f,
+};
+#endif
+#ifdef MIEEE
+static unsigned short A[44] = {
+0x4160,0x9b9a,0xb598,0x566f,
+0x41a5,0x0a8f,0xe357,0x37a7,
+0x4218,0x4c17,0x2e3a,0xfe49,
+0x425e,0xd6ba,0xed1e,0x7944,
+0x42b4,0xa2a6,0xcb80,0x13d3,
+0x42f2,0xdd8d,0xbf17,0xbe11,
+0x4332,0x40ca,0xf2ac,0x905a,
+0xc31c,0x27b2,0xa21c,0xcaff,
+0xc376,0x0b35,0x7b05,0x4649,
+0x4371,0x624d,0x4440,0x01c9,
+0x4374,0x942b,0x882f,0xdcd6,
+};
+static unsigned short B[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc15e,0x3c7b,0x86c2,0xc36a,
+0xc1a3,0x22fc,0x63dd,0xa7b8,
+0xc216,0x227a,0x0c46,0x37a0,
+0xc25b,0xf551,0xce17,0x9d22,
+0xc2b2,0xe6b5,0x75d1,0x3955,
+0xc2f0,0xd476,0xd4ff,0x8884,
+0xc331,0x46dd,0x554d,0x96ab,
+0x4332,0xfe10,0x323f,0xae8b,
+0x4369,0x60cb,0x75cb,0x5498,
+0xc34f,0xf59d,0x3866,0x5e44,
+};
+#endif
+
+/* (1-x) (zeta(x) - 1), 0 <= x <= 1 */
+
+#ifdef UNK
+static double R[6] = {
+-3.28717474506562731748E-1,
+ 1.55162528742623950834E1,
+-2.48762831680821954401E2,
+ 1.01050368053237678329E3,
+ 1.26726061410235149405E4,
+-1.11578094770515181334E5,
+};
+static double S[5] = {
+/* 1.00000000000000000000E0,*/
+ 1.95107674914060531512E1,
+ 3.17710311750646984099E2,
+ 3.03835500874445748734E3,
+ 2.03665876435770579345E4,
+ 7.43853965136767874343E4,
+};
+#endif
+#ifdef DEC
+static unsigned short R[24] = {
+0137650,0046650,0022502,0040316,
+0041170,0041222,0057666,0142216,
+0142170,0141510,0167741,0075646,
+0042574,0120074,0046505,0106053,
+0043506,0001154,0130073,0101413,
+0144331,0166414,0020560,0131652,
+};
+static unsigned short S[20] = {
+/*0040200,0000000,0000000,0000000,*/
+0041234,0013015,0042073,0113570,
+0042236,0155353,0077325,0077445,
+0043075,0162656,0016646,0031723,
+0043637,0016454,0157636,0071126,
+0044221,0044262,0140365,0146434,
+};
+#endif
+#ifdef IBMPC
+static unsigned short R[24] = {
+0x481a,0x04a8,0x09b5,0xbfd5,
+0xd892,0x4bf6,0x0852,0x402f,
+0x2f75,0x1dfc,0x1869,0xc06f,
+0xb185,0x89a8,0x9407,0x408f,
+0x7061,0x9607,0xc04d,0x40c8,
+0x1675,0x842e,0x3da1,0xc0fb,
+};
+static unsigned short S[20] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x72ef,0xa887,0x82c1,0x4033,
+0xafe5,0x6fda,0xdb5d,0x4073,
+0xc67a,0xc3b4,0xbcb5,0x40a7,
+0xce4b,0x9bf3,0xe3a5,0x40d3,
+0xb9a3,0x581e,0x2916,0x40f2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short R[24] = {
+0xbfd5,0x09b5,0x04a8,0x481a,
+0x402f,0x0852,0x4bf6,0xd892,
+0xc06f,0x1869,0x1dfc,0x2f75,
+0x408f,0x9407,0x89a8,0xb185,
+0x40c8,0xc04d,0x9607,0x7061,
+0xc0fb,0x3da1,0x842e,0x1675,
+};
+static unsigned short S[20] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4033,0x82c1,0xa887,0x72ef,
+0x4073,0xdb5d,0x6fda,0xafe5,
+0x40a7,0xbcb5,0xc3b4,0xc67a,
+0x40d3,0xe3a5,0x9bf3,0xce4b,
+0x40f2,0x2916,0x581e,0xb9a3,
+};
+#endif
+
+#define MAXL2 127
+
+/*
+ * Riemann zeta function, minus one
+ */
+#ifdef ANSIPROT
+extern double sin ( double );
+extern double floor ( double );
+extern double gamma ( double );
+extern double pow ( double, double );
+extern double exp ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+double zetac ( double );
+#else
+double sin(), floor(), gamma(), pow(), exp();
+double polevl(), p1evl(), zetac();
+#endif
+extern double MACHEP;
+
+double zetac(x)
+double x;
+{
+int i;
+double a, b, s, w;
+
+if( x < 0.0 )
+	{
+#ifdef DEC
+	if( x < -30.8148 )
+#else
+	if( x < -170.6243 )
+#endif
+		{
+		mtherr( "zetac", OVERFLOW );
+		return(0.0);
+		}
+	s = 1.0 - x;
+	w = zetac( s );
+	b = sin(0.5*PI*x) * pow(2.0*PI, x) * gamma(s) * (1.0 + w) / PI;
+	return(b - 1.0);
+	}
+
+if( x >= MAXL2 )
+	return(0.0);	/* because first term is 2**-x */
+
+/* Tabulated values for integer argument */
+w = floor(x);
+if( w == x )
+	{
+	i = x;
+	if( i < 31 )
+		{
+#ifdef UNK
+		return( azetac[i] );
+#else
+		return( *(double *)&azetac[4*i]  );
+#endif
+		}
+	}
+
+
+if( x < 1.0 )
+	{
+	w = 1.0 - x;
+	a = polevl( x, R, 5 ) / ( w * p1evl( x, S, 5 ));
+	return( a );
+	}
+
+if( x == 1.0 )
+	{
+	mtherr( "zetac", SING );
+	return( MAXNUM );
+	}
+
+if( x <= 10.0 )
+	{
+	b = pow( 2.0, x ) * (x - 1.0);
+	w = 1.0/x;
+	s = (x * polevl( w, P, 8 )) / (b * p1evl( w, Q, 8 ));
+	return( s );
+	}
+
+if( x <= 50.0 )
+	{
+	b = pow( 2.0, -x );
+	w = polevl( x, A, 10 ) / p1evl( x, B, 10 );
+	w = exp(w) + b;
+	return(w);
+	}
+
+
+/* Basic sum of inverse powers */
+
+
+s = 0.0;
+a = 1.0;
+do
+	{
+	a += 2.0;
+	b = pow( a, -x );
+	s += b;
+	}
+while( b/s > MACHEP );
+
+b = pow( 2.0, -x );
+s = (s + b)/(1.0-b);
+return(s);
+}