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/k1.c | 335 ------------------------------------------------------- 1 file changed, 335 deletions(-) delete mode 100644 libm/double/k1.c (limited to 'libm/double/k1.c') diff --git a/libm/double/k1.c b/libm/double/k1.c deleted file mode 100644 index a96305355..000000000 --- a/libm/double/k1.c +++ /dev/null @@ -1,335 +0,0 @@ -/* k1.c - * - * Modified Bessel function, third kind, order one - * - * - * - * SYNOPSIS: - * - * double x, y, k1(); - * - * y = k1( x ); - * - * - * - * DESCRIPTION: - * - * Computes the modified Bessel function of the third kind - * of order one of the argument. - * - * The range is partitioned into the two intervals [0,2] and - * (2, infinity). Chebyshev polynomial expansions are employed - * in each interval. - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * DEC 0, 30 3300 8.9e-17 2.2e-17 - * IEEE 0, 30 30000 1.2e-15 1.6e-16 - * - * ERROR MESSAGES: - * - * message condition value returned - * k1 domain x <= 0 MAXNUM - * - */ - /* k1e.c - * - * Modified Bessel function, third kind, order one, - * exponentially scaled - * - * - * - * SYNOPSIS: - * - * double x, y, k1e(); - * - * y = k1e( x ); - * - * - * - * DESCRIPTION: - * - * Returns exponentially scaled modified Bessel function - * of the third kind of order one of the argument: - * - * k1e(x) = exp(x) * k1(x). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0, 30 30000 7.8e-16 1.2e-16 - * See k1(). - * - */ - -/* -Cephes Math Library Release 2.8: June, 2000 -Copyright 1984, 1987, 2000 by Stephen L. Moshier -*/ - -#include - -/* Chebyshev coefficients for x(K1(x) - log(x/2) I1(x)) - * in the interval [0,2]. - * - * lim(x->0){ x(K1(x) - log(x/2) I1(x)) } = 1. - */ - -#ifdef UNK -static double A[] = -{ --7.02386347938628759343E-18, --2.42744985051936593393E-15, --6.66690169419932900609E-13, --1.41148839263352776110E-10, --2.21338763073472585583E-8, --2.43340614156596823496E-6, --1.73028895751305206302E-4, --6.97572385963986435018E-3, --1.22611180822657148235E-1, --3.53155960776544875667E-1, - 1.52530022733894777053E0 -}; -#endif - -#ifdef DEC -static unsigned short A[] = { -0122001,0110501,0164746,0151255, -0124056,0165213,0150034,0147377, -0126073,0124026,0167207,0001044, -0130033,0030735,0141061,0033116, -0131676,0020350,0121341,0107175, -0133443,0046631,0062031,0070716, -0135065,0067427,0026435,0164022, -0136344,0112234,0165752,0006222, -0137373,0015622,0017016,0155636, -0137664,0150333,0125730,0067240, -0040303,0036411,0130200,0043120 -}; -#endif - -#ifdef IBMPC -static unsigned short A[] = { -0xda56,0x3d3c,0x3228,0xbc60, -0x99e0,0x7a03,0xdd51,0xbce5, -0xe045,0xddd0,0x7502,0xbd67, -0x26ca,0xb846,0x663b,0xbde3, -0x31d0,0x145c,0xc41d,0xbe57, -0x2e3a,0x2c83,0x69b3,0xbec4, -0xbd02,0xe5a3,0xade2,0xbf26, -0x4192,0x9d7d,0x9293,0xbf7c, -0xdb74,0x43c1,0x6372,0xbfbf, -0x0dd4,0x757b,0x9a1b,0xbfd6, -0x08ca,0x3610,0x67a1,0x3ff8 -}; -#endif - -#ifdef MIEEE -static unsigned short A[] = { -0xbc60,0x3228,0x3d3c,0xda56, -0xbce5,0xdd51,0x7a03,0x99e0, -0xbd67,0x7502,0xddd0,0xe045, -0xbde3,0x663b,0xb846,0x26ca, -0xbe57,0xc41d,0x145c,0x31d0, -0xbec4,0x69b3,0x2c83,0x2e3a, -0xbf26,0xade2,0xe5a3,0xbd02, -0xbf7c,0x9293,0x9d7d,0x4192, -0xbfbf,0x6372,0x43c1,0xdb74, -0xbfd6,0x9a1b,0x757b,0x0dd4, -0x3ff8,0x67a1,0x3610,0x08ca -}; -#endif - - - -/* Chebyshev coefficients for exp(x) sqrt(x) K1(x) - * in the interval [2,infinity]. - * - * lim(x->inf){ exp(x) sqrt(x) K1(x) } = sqrt(pi/2). - */ - -#ifdef UNK -static double B[] = -{ --5.75674448366501715755E-18, - 1.79405087314755922667E-17, --5.68946255844285935196E-17, - 1.83809354436663880070E-16, --6.05704724837331885336E-16, - 2.03870316562433424052E-15, --7.01983709041831346144E-15, - 2.47715442448130437068E-14, --8.97670518232499435011E-14, - 3.34841966607842919884E-13, --1.28917396095102890680E-12, - 5.13963967348173025100E-12, --2.12996783842756842877E-11, - 9.21831518760500529508E-11, --4.19035475934189648750E-10, - 2.01504975519703286596E-9, --1.03457624656780970260E-8, - 5.74108412545004946722E-8, --3.50196060308781257119E-7, - 2.40648494783721712015E-6, --1.93619797416608296024E-5, - 1.95215518471351631108E-4, --2.85781685962277938680E-3, - 1.03923736576817238437E-1, - 2.72062619048444266945E0 -}; -#endif - -#ifdef DEC -static unsigned short B[] = { -0121724,0061352,0013041,0150076, -0022245,0074324,0016172,0173232, -0122603,0030250,0135670,0165221, -0023123,0165362,0023561,0060124, -0123456,0112436,0141654,0073623, -0024022,0163557,0077564,0006753, -0124374,0165221,0131014,0026524, -0024737,0017512,0144250,0175451, -0125312,0021456,0123136,0076633, -0025674,0077720,0020125,0102607, -0126265,0067543,0007744,0043701, -0026664,0152702,0033002,0074202, -0127273,0055234,0120016,0071733, -0027712,0133200,0042441,0075515, -0130346,0057000,0015456,0074470, -0031012,0074441,0051636,0111155, -0131461,0136444,0177417,0002101, -0032166,0111743,0032176,0021410, -0132674,0001224,0076555,0027060, -0033441,0077430,0135226,0106663, -0134242,0065610,0167155,0113447, -0035114,0131304,0043664,0102163, -0136073,0045065,0171465,0122123, -0037324,0152767,0147401,0017732, -0040456,0017275,0050061,0062120, -}; -#endif - -#ifdef IBMPC -static unsigned short B[] = { -0x3a08,0x42c4,0x8c5d,0xbc5a, -0x5ed3,0x838f,0xaf1a,0x3c74, -0x1d52,0x1777,0x6615,0xbc90, -0x2c0b,0x44ee,0x7d5e,0x3caa, -0x8ef2,0xd875,0xd2a3,0xbcc5, -0x81bd,0xefee,0x5ced,0x3ce2, -0x85ab,0x3641,0x9d52,0xbcff, -0x1f65,0x5915,0xe3e9,0x3d1b, -0xcfb3,0xd4cb,0x4465,0xbd39, -0xb0b1,0x040a,0x8ffa,0x3d57, -0x88f8,0x61fc,0xadec,0xbd76, -0x4f10,0x46c0,0x9ab8,0x3d96, -0xce7b,0x9401,0x6b53,0xbdb7, -0x2f6a,0x08a4,0x56d0,0x3dd9, -0xcf27,0x0365,0xcbc0,0xbdfc, -0xd24e,0x2a73,0x4f24,0x3e21, -0xe088,0x9fe1,0x37a4,0xbe46, -0xc461,0x668f,0xd27c,0x3e6e, -0xa5c6,0x8fad,0x8052,0xbe97, -0xd1b6,0x1752,0x2fe3,0x3ec4, -0xb2e5,0x1dcd,0x4d71,0xbef4, -0x908e,0x88f6,0x9658,0x3f29, -0xb48a,0xbe66,0x6946,0xbf67, -0x23fb,0xf9e0,0x9abe,0x3fba, -0x2c8a,0xaa06,0xc3d7,0x4005 -}; -#endif - -#ifdef MIEEE -static unsigned short B[] = { -0xbc5a,0x8c5d,0x42c4,0x3a08, -0x3c74,0xaf1a,0x838f,0x5ed3, -0xbc90,0x6615,0x1777,0x1d52, -0x3caa,0x7d5e,0x44ee,0x2c0b, -0xbcc5,0xd2a3,0xd875,0x8ef2, -0x3ce2,0x5ced,0xefee,0x81bd, -0xbcff,0x9d52,0x3641,0x85ab, -0x3d1b,0xe3e9,0x5915,0x1f65, -0xbd39,0x4465,0xd4cb,0xcfb3, -0x3d57,0x8ffa,0x040a,0xb0b1, -0xbd76,0xadec,0x61fc,0x88f8, -0x3d96,0x9ab8,0x46c0,0x4f10, -0xbdb7,0x6b53,0x9401,0xce7b, -0x3dd9,0x56d0,0x08a4,0x2f6a, -0xbdfc,0xcbc0,0x0365,0xcf27, -0x3e21,0x4f24,0x2a73,0xd24e, -0xbe46,0x37a4,0x9fe1,0xe088, -0x3e6e,0xd27c,0x668f,0xc461, -0xbe97,0x8052,0x8fad,0xa5c6, -0x3ec4,0x2fe3,0x1752,0xd1b6, -0xbef4,0x4d71,0x1dcd,0xb2e5, -0x3f29,0x9658,0x88f6,0x908e, -0xbf67,0x6946,0xbe66,0xb48a, -0x3fba,0x9abe,0xf9e0,0x23fb, -0x4005,0xc3d7,0xaa06,0x2c8a -}; -#endif - -#ifdef ANSIPROT -extern double chbevl ( double, void *, int ); -extern double exp ( double ); -extern double i1 ( double ); -extern double log ( double ); -extern double sqrt ( double ); -#else -double chbevl(), exp(), i1(), log(), sqrt(); -#endif -extern double PI; -extern double MINLOG, MAXNUM; - -double k1(x) -double x; -{ -double y, z; - -z = 0.5 * x; -if( z <= 0.0 ) - { - mtherr( "k1", DOMAIN ); - return( MAXNUM ); - } - -if( x <= 2.0 ) - { - y = x * x - 2.0; - y = log(z) * i1(x) + chbevl( y, A, 11 ) / x; - return( y ); - } - -return( exp(-x) * chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) ); -} - - - - -double k1e( x ) -double x; -{ -double y; - -if( x <= 0.0 ) - { - mtherr( "k1e", DOMAIN ); - return( MAXNUM ); - } - -if( x <= 2.0 ) - { - y = x * x - 2.0; - y = log( 0.5 * x ) * i1(x) + chbevl( y, A, 11 ) / x; - return( y * exp(x) ); - } - -return( chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) ); -} -- cgit v1.2.3