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-rw-r--r--libm/double/zetac.c599
1 files changed, 0 insertions, 599 deletions
diff --git a/libm/double/zetac.c b/libm/double/zetac.c
deleted file mode 100644
index cc28590b3..000000000
--- a/libm/double/zetac.c
+++ /dev/null
@@ -1,599 +0,0 @@
- /* 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);
-}
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