From 7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 Mon Sep 17 00:00:00 2001 From: Eric Andersen Date: Thu, 22 Nov 2001 14:04:29 +0000 Subject: Totally rework the math library, this time based on the MacOs X math library (which is itself based on the math lib from FreeBSD). -Erik --- libm/double/i0.c | 397 ------------------------------------------------------- 1 file changed, 397 deletions(-) delete mode 100644 libm/double/i0.c (limited to 'libm/double/i0.c') diff --git a/libm/double/i0.c b/libm/double/i0.c deleted file mode 100644 index a4844ab7e..000000000 --- a/libm/double/i0.c +++ /dev/null @@ -1,397 +0,0 @@ -/* i0.c - * - * Modified Bessel function of order zero - * - * - * - * SYNOPSIS: - * - * double x, y, i0(); - * - * y = i0( x ); - * - * - * - * DESCRIPTION: - * - * Returns modified Bessel function of order zero of the - * argument. - * - * The function is defined as i0(x) = j0( ix ). - * - * The range is partitioned into the two intervals [0,8] and - * (8, infinity). Chebyshev polynomial expansions are employed - * in each interval. - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * DEC 0,30 6000 8.2e-17 1.9e-17 - * IEEE 0,30 30000 5.8e-16 1.4e-16 - * - */ - /* i0e.c - * - * Modified Bessel function of order zero, - * exponentially scaled - * - * - * - * SYNOPSIS: - * - * double x, y, i0e(); - * - * y = i0e( x ); - * - * - * - * DESCRIPTION: - * - * Returns exponentially scaled modified Bessel function - * of order zero of the argument. - * - * The function is defined as i0e(x) = exp(-|x|) j0( ix ). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0,30 30000 5.4e-16 1.2e-16 - * See i0(). - * - */ - -/* i0.c */ - - -/* -Cephes Math Library Release 2.8: June, 2000 -Copyright 1984, 1987, 2000 by Stephen L. Moshier -*/ - -#include - -/* Chebyshev coefficients for exp(-x) I0(x) - * in the interval [0,8]. - * - * lim(x->0){ exp(-x) I0(x) } = 1. - */ - -#ifdef UNK -static double A[] = -{ --4.41534164647933937950E-18, - 3.33079451882223809783E-17, --2.43127984654795469359E-16, - 1.71539128555513303061E-15, --1.16853328779934516808E-14, - 7.67618549860493561688E-14, --4.85644678311192946090E-13, - 2.95505266312963983461E-12, --1.72682629144155570723E-11, - 9.67580903537323691224E-11, --5.18979560163526290666E-10, - 2.65982372468238665035E-9, --1.30002500998624804212E-8, - 6.04699502254191894932E-8, --2.67079385394061173391E-7, - 1.11738753912010371815E-6, --4.41673835845875056359E-6, - 1.64484480707288970893E-5, --5.75419501008210370398E-5, - 1.88502885095841655729E-4, --5.76375574538582365885E-4, - 1.63947561694133579842E-3, --4.32430999505057594430E-3, - 1.05464603945949983183E-2, --2.37374148058994688156E-2, - 4.93052842396707084878E-2, --9.49010970480476444210E-2, - 1.71620901522208775349E-1, --3.04682672343198398683E-1, - 6.76795274409476084995E-1 -}; -#endif - -#ifdef DEC -static unsigned short A[] = { -0121642,0162671,0004646,0103567, -0022431,0115424,0135755,0026104, -0123214,0023533,0110365,0156635, -0023767,0033304,0117662,0172716, -0124522,0100426,0012277,0157531, -0025254,0155062,0054461,0030465, -0126010,0131143,0013560,0153604, -0026517,0170577,0006336,0114437, -0127227,0162253,0152243,0052734, -0027724,0142766,0061641,0160200, -0130416,0123760,0116564,0125262, -0031066,0144035,0021246,0054641, -0131537,0053664,0060131,0102530, -0032201,0155664,0165153,0020652, -0132617,0061434,0074423,0176145, -0033225,0174444,0136147,0122542, -0133624,0031576,0056453,0020470, -0034211,0175305,0172321,0041314, -0134561,0054462,0147040,0165315, -0035105,0124333,0120203,0162532, -0135427,0013750,0174257,0055221, -0035726,0161654,0050220,0100162, -0136215,0131361,0000325,0041110, -0036454,0145417,0117357,0017352, -0136702,0072367,0104415,0133574, -0037111,0172126,0072505,0014544, -0137302,0055601,0120550,0033523, -0037457,0136543,0136544,0043002, -0137633,0177536,0001276,0066150, -0040055,0041164,0100655,0010521 -}; -#endif - -#ifdef IBMPC -static unsigned short A[] = { -0xd0ef,0x2134,0x5cb7,0xbc54, -0xa589,0x977d,0x3362,0x3c83, -0xbbb4,0x721e,0x84eb,0xbcb1, -0x5eba,0x93f6,0xe6d8,0x3cde, -0xfbeb,0xc297,0x5022,0xbd0a, -0x2627,0x4b26,0x9b46,0x3d35, -0x1af0,0x62ee,0x164c,0xbd61, -0xd324,0xe19b,0xfe2f,0x3d89, -0x6abc,0x7a94,0xfc95,0xbdb2, -0x3c10,0xcc74,0x98be,0x3dda, -0x9556,0x13ae,0xd4fe,0xbe01, -0xcb34,0xa454,0xd903,0x3e26, -0x30ab,0x8c0b,0xeaf6,0xbe4b, -0x6435,0x9d4d,0x3b76,0x3e70, -0x7f8d,0x8f22,0xec63,0xbe91, -0xf4ac,0x978c,0xbf24,0x3eb2, -0x6427,0xcba5,0x866f,0xbed2, -0x2859,0xbe9a,0x3f58,0x3ef1, -0x1d5a,0x59c4,0x2b26,0xbf0e, -0x7cab,0x7410,0xb51b,0x3f28, -0xeb52,0x1f15,0xe2fd,0xbf42, -0x100e,0x8a12,0xdc75,0x3f5a, -0xa849,0x201a,0xb65e,0xbf71, -0xe3dd,0xf3dd,0x9961,0x3f85, -0xb6f0,0xf121,0x4e9e,0xbf98, -0xa32d,0xcea8,0x3e8a,0x3fa9, -0x06ea,0x342d,0x4b70,0xbfb8, -0x88c0,0x77ac,0xf7ac,0x3fc5, -0xcd8d,0xc057,0x7feb,0xbfd3, -0xa22a,0x9035,0xa84e,0x3fe5, -}; -#endif - -#ifdef MIEEE -static unsigned short A[] = { -0xbc54,0x5cb7,0x2134,0xd0ef, -0x3c83,0x3362,0x977d,0xa589, -0xbcb1,0x84eb,0x721e,0xbbb4, -0x3cde,0xe6d8,0x93f6,0x5eba, -0xbd0a,0x5022,0xc297,0xfbeb, -0x3d35,0x9b46,0x4b26,0x2627, -0xbd61,0x164c,0x62ee,0x1af0, -0x3d89,0xfe2f,0xe19b,0xd324, -0xbdb2,0xfc95,0x7a94,0x6abc, -0x3dda,0x98be,0xcc74,0x3c10, -0xbe01,0xd4fe,0x13ae,0x9556, -0x3e26,0xd903,0xa454,0xcb34, -0xbe4b,0xeaf6,0x8c0b,0x30ab, -0x3e70,0x3b76,0x9d4d,0x6435, -0xbe91,0xec63,0x8f22,0x7f8d, -0x3eb2,0xbf24,0x978c,0xf4ac, -0xbed2,0x866f,0xcba5,0x6427, -0x3ef1,0x3f58,0xbe9a,0x2859, -0xbf0e,0x2b26,0x59c4,0x1d5a, -0x3f28,0xb51b,0x7410,0x7cab, -0xbf42,0xe2fd,0x1f15,0xeb52, -0x3f5a,0xdc75,0x8a12,0x100e, -0xbf71,0xb65e,0x201a,0xa849, -0x3f85,0x9961,0xf3dd,0xe3dd, -0xbf98,0x4e9e,0xf121,0xb6f0, -0x3fa9,0x3e8a,0xcea8,0xa32d, -0xbfb8,0x4b70,0x342d,0x06ea, -0x3fc5,0xf7ac,0x77ac,0x88c0, -0xbfd3,0x7feb,0xc057,0xcd8d, -0x3fe5,0xa84e,0x9035,0xa22a -}; -#endif - - -/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x) - * in the inverted interval [8,infinity]. - * - * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi). - */ - -#ifdef UNK -static double B[] = -{ --7.23318048787475395456E-18, --4.83050448594418207126E-18, - 4.46562142029675999901E-17, - 3.46122286769746109310E-17, --2.82762398051658348494E-16, --3.42548561967721913462E-16, - 1.77256013305652638360E-15, - 3.81168066935262242075E-15, --9.55484669882830764870E-15, --4.15056934728722208663E-14, - 1.54008621752140982691E-14, - 3.85277838274214270114E-13, - 7.18012445138366623367E-13, --1.79417853150680611778E-12, --1.32158118404477131188E-11, --3.14991652796324136454E-11, - 1.18891471078464383424E-11, - 4.94060238822496958910E-10, - 3.39623202570838634515E-9, - 2.26666899049817806459E-8, - 2.04891858946906374183E-7, - 2.89137052083475648297E-6, - 6.88975834691682398426E-5, - 3.36911647825569408990E-3, - 8.04490411014108831608E-1 -}; -#endif - -#ifdef DEC -static unsigned short B[] = { -0122005,0066672,0123124,0054311, -0121662,0033323,0030214,0104602, -0022515,0170300,0113314,0020413, -0022437,0117350,0035402,0007146, -0123243,0000135,0057220,0177435, -0123305,0073476,0144106,0170702, -0023777,0071755,0017527,0154373, -0024211,0052214,0102247,0033270, -0124454,0017763,0171453,0012322, -0125072,0166316,0075505,0154616, -0024612,0133770,0065376,0025045, -0025730,0162143,0056036,0001632, -0026112,0015077,0150464,0063542, -0126374,0101030,0014274,0065457, -0127150,0077271,0125763,0157617, -0127412,0104350,0040713,0120445, -0027121,0023765,0057500,0001165, -0030407,0147146,0003643,0075644, -0031151,0061445,0044422,0156065, -0031702,0132224,0003266,0125551, -0032534,0000076,0147153,0005555, -0033502,0004536,0004016,0026055, -0034620,0076433,0142314,0171215, -0036134,0146145,0013454,0101104, -0040115,0171425,0062500,0047133 -}; -#endif - -#ifdef IBMPC -static unsigned short B[] = { -0x8b19,0x54ca,0xadb7,0xbc60, -0x9130,0x6611,0x46da,0xbc56, -0x8421,0x12d9,0xbe18,0x3c89, -0x41cd,0x0760,0xf3dd,0x3c83, -0x1fe4,0xabd2,0x600b,0xbcb4, -0xde38,0xd908,0xaee7,0xbcb8, -0xfb1f,0xa3ea,0xee7d,0x3cdf, -0xe6d7,0x9094,0x2a91,0x3cf1, -0x629a,0x7e65,0x83fe,0xbd05, -0xbb32,0xcf68,0x5d99,0xbd27, -0xc545,0x0d5f,0x56ff,0x3d11, -0xc073,0x6b83,0x1c8c,0x3d5b, -0x8cec,0xfa26,0x4347,0x3d69, -0x8d66,0x0317,0x9043,0xbd7f, -0x7bf2,0x357e,0x0fd7,0xbdad, -0x7425,0x0839,0x511d,0xbdc1, -0x004f,0xabe8,0x24fe,0x3daa, -0x6f75,0xc0f4,0xf9cc,0x3e00, -0x5b87,0xa922,0x2c64,0x3e2d, -0xd56d,0x80d6,0x5692,0x3e58, -0x616e,0xd9cd,0x8007,0x3e8b, -0xc586,0xc101,0x412b,0x3ec8, -0x9e52,0x7899,0x0fa3,0x3f12, -0x9049,0xa2e5,0x998c,0x3f6b, -0x09cb,0xaca8,0xbe62,0x3fe9 -}; -#endif - -#ifdef MIEEE -static unsigned short B[] = { -0xbc60,0xadb7,0x54ca,0x8b19, -0xbc56,0x46da,0x6611,0x9130, -0x3c89,0xbe18,0x12d9,0x8421, -0x3c83,0xf3dd,0x0760,0x41cd, -0xbcb4,0x600b,0xabd2,0x1fe4, -0xbcb8,0xaee7,0xd908,0xde38, -0x3cdf,0xee7d,0xa3ea,0xfb1f, -0x3cf1,0x2a91,0x9094,0xe6d7, -0xbd05,0x83fe,0x7e65,0x629a, -0xbd27,0x5d99,0xcf68,0xbb32, -0x3d11,0x56ff,0x0d5f,0xc545, -0x3d5b,0x1c8c,0x6b83,0xc073, -0x3d69,0x4347,0xfa26,0x8cec, -0xbd7f,0x9043,0x0317,0x8d66, -0xbdad,0x0fd7,0x357e,0x7bf2, -0xbdc1,0x511d,0x0839,0x7425, -0x3daa,0x24fe,0xabe8,0x004f, -0x3e00,0xf9cc,0xc0f4,0x6f75, -0x3e2d,0x2c64,0xa922,0x5b87, -0x3e58,0x5692,0x80d6,0xd56d, -0x3e8b,0x8007,0xd9cd,0x616e, -0x3ec8,0x412b,0xc101,0xc586, -0x3f12,0x0fa3,0x7899,0x9e52, -0x3f6b,0x998c,0xa2e5,0x9049, -0x3fe9,0xbe62,0xaca8,0x09cb -}; -#endif - -#ifdef ANSIPROT -extern double chbevl ( double, void *, int ); -extern double exp ( double ); -extern double sqrt ( double ); -#else -double chbevl(), exp(), sqrt(); -#endif - -double i0(x) -double x; -{ -double y; - -if( x < 0 ) - x = -x; -if( x <= 8.0 ) - { - y = (x/2.0) - 2.0; - return( exp(x) * chbevl( y, A, 30 ) ); - } - -return( exp(x) * chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) ); - -} - - - - -double i0e( x ) -double x; -{ -double y; - -if( x < 0 ) - x = -x; -if( x <= 8.0 ) - { - y = (x/2.0) - 2.0; - return( chbevl( y, A, 30 ) ); - } - -return( chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) ); - -} -- cgit v1.2.3