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Diffstat (limited to 'libm/double/k0.c')
-rw-r--r-- | libm/double/k0.c | 333 |
1 files changed, 0 insertions, 333 deletions
diff --git a/libm/double/k0.c b/libm/double/k0.c deleted file mode 100644 index 7d09cb4a1..000000000 --- a/libm/double/k0.c +++ /dev/null @@ -1,333 +0,0 @@ -/* k0.c - * - * Modified Bessel function, third kind, order zero - * - * - * - * SYNOPSIS: - * - * double x, y, k0(); - * - * y = k0( x ); - * - * - * - * DESCRIPTION: - * - * Returns modified Bessel function of the third kind - * of order zero of the argument. - * - * The range is partitioned into the two intervals [0,8] and - * (8, infinity). Chebyshev polynomial expansions are employed - * in each interval. - * - * - * - * ACCURACY: - * - * Tested at 2000 random points between 0 and 8. Peak absolute - * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15. - * Relative error: - * arithmetic domain # trials peak rms - * DEC 0, 30 3100 1.3e-16 2.1e-17 - * IEEE 0, 30 30000 1.2e-15 1.6e-16 - * - * ERROR MESSAGES: - * - * message condition value returned - * K0 domain x <= 0 MAXNUM - * - */ -/* k0e() - * - * Modified Bessel function, third kind, order zero, - * exponentially scaled - * - * - * - * SYNOPSIS: - * - * double x, y, k0e(); - * - * y = k0e( x ); - * - * - * - * DESCRIPTION: - * - * Returns exponentially scaled modified Bessel function - * of the third kind of order zero of the argument. - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0, 30 30000 1.4e-15 1.4e-16 - * See k0(). - * - */ - -/* -Cephes Math Library Release 2.8: June, 2000 -Copyright 1984, 1987, 2000 by Stephen L. Moshier -*/ - -#include <math.h> - -/* Chebyshev coefficients for K0(x) + log(x/2) I0(x) - * in the interval [0,2]. The odd order coefficients are all - * zero; only the even order coefficients are listed. - * - * lim(x->0){ K0(x) + log(x/2) I0(x) } = -EUL. - */ - -#ifdef UNK -static double A[] = -{ - 1.37446543561352307156E-16, - 4.25981614279661018399E-14, - 1.03496952576338420167E-11, - 1.90451637722020886025E-9, - 2.53479107902614945675E-7, - 2.28621210311945178607E-5, - 1.26461541144692592338E-3, - 3.59799365153615016266E-2, - 3.44289899924628486886E-1, --5.35327393233902768720E-1 -}; -#endif - -#ifdef DEC -static unsigned short A[] = { -0023036,0073417,0032477,0165673, -0025077,0154126,0016046,0012517, -0027066,0011342,0035211,0005041, -0031002,0160233,0037454,0050224, -0032610,0012747,0037712,0173741, -0034277,0144007,0172147,0162375, -0035645,0140563,0125431,0165626, -0037023,0057662,0125124,0102051, -0037660,0043304,0004411,0166707, -0140011,0005467,0047227,0130370 -}; -#endif - -#ifdef IBMPC -static unsigned short A[] = { -0xfd77,0xe6a7,0xcee1,0x3ca3, -0xc2aa,0xc384,0xfb0a,0x3d27, -0x2144,0x4751,0xc25c,0x3da6, -0x8a13,0x67e5,0x5c13,0x3e20, -0x5efc,0xe7f9,0x02bc,0x3e91, -0xfca0,0xfe8c,0xf900,0x3ef7, -0x3d73,0x7563,0xb82e,0x3f54, -0x9085,0x554a,0x6bf6,0x3fa2, -0x3db9,0x8121,0x08d8,0x3fd6, -0xf61f,0xe9d2,0x2166,0xbfe1 -}; -#endif - -#ifdef MIEEE -static unsigned short A[] = { -0x3ca3,0xcee1,0xe6a7,0xfd77, -0x3d27,0xfb0a,0xc384,0xc2aa, -0x3da6,0xc25c,0x4751,0x2144, -0x3e20,0x5c13,0x67e5,0x8a13, -0x3e91,0x02bc,0xe7f9,0x5efc, -0x3ef7,0xf900,0xfe8c,0xfca0, -0x3f54,0xb82e,0x7563,0x3d73, -0x3fa2,0x6bf6,0x554a,0x9085, -0x3fd6,0x08d8,0x8121,0x3db9, -0xbfe1,0x2166,0xe9d2,0xf61f -}; -#endif - - - -/* Chebyshev coefficients for exp(x) sqrt(x) K0(x) - * in the inverted interval [2,infinity]. - * - * lim(x->inf){ exp(x) sqrt(x) K0(x) } = sqrt(pi/2). - */ - -#ifdef UNK -static double B[] = { - 5.30043377268626276149E-18, --1.64758043015242134646E-17, - 5.21039150503902756861E-17, --1.67823109680541210385E-16, - 5.51205597852431940784E-16, --1.84859337734377901440E-15, - 6.34007647740507060557E-15, --2.22751332699166985548E-14, - 8.03289077536357521100E-14, --2.98009692317273043925E-13, - 1.14034058820847496303E-12, --4.51459788337394416547E-12, - 1.85594911495471785253E-11, --7.95748924447710747776E-11, - 3.57739728140030116597E-10, --1.69753450938905987466E-9, - 8.57403401741422608519E-9, --4.66048989768794782956E-8, - 2.76681363944501510342E-7, --1.83175552271911948767E-6, - 1.39498137188764993662E-5, --1.28495495816278026384E-4, - 1.56988388573005337491E-3, --3.14481013119645005427E-2, - 2.44030308206595545468E0 -}; -#endif - -#ifdef DEC -static unsigned short B[] = { -0021703,0106456,0076144,0173406, -0122227,0173144,0116011,0030033, -0022560,0044562,0006506,0067642, -0123101,0076243,0123273,0131013, -0023436,0157713,0056243,0141331, -0124005,0032207,0063726,0164664, -0024344,0066342,0051756,0162300, -0124710,0121365,0154053,0077022, -0025264,0161166,0066246,0077420, -0125647,0141671,0006443,0103212, -0026240,0076431,0077147,0160445, -0126636,0153741,0174002,0105031, -0027243,0040102,0035375,0163073, -0127656,0176256,0113476,0044653, -0030304,0125544,0006377,0130104, -0130751,0047257,0110537,0127324, -0031423,0046400,0014772,0012164, -0132110,0025240,0155247,0112570, -0032624,0105314,0007437,0021574, -0133365,0155243,0174306,0116506, -0034152,0004776,0061643,0102504, -0135006,0136277,0036104,0175023, -0035715,0142217,0162474,0115022, -0137000,0147671,0065177,0134356, -0040434,0026754,0175163,0044070 -}; -#endif - -#ifdef IBMPC -static unsigned short B[] = { -0x9ee1,0xcf8c,0x71a5,0x3c58, -0x2603,0x9381,0xfecc,0xbc72, -0xcdf4,0x41a8,0x092e,0x3c8e, -0x7641,0x74d7,0x2f94,0xbca8, -0x785b,0x6b94,0xdbf9,0x3cc3, -0xdd36,0xecfa,0xa690,0xbce0, -0xdc98,0x4a7d,0x8d9c,0x3cfc, -0x6fc2,0xbb05,0x145e,0xbd19, -0xcfe2,0xcd94,0x9c4e,0x3d36, -0x70d1,0x21a4,0xf877,0xbd54, -0xfc25,0x2fcc,0x0fa3,0x3d74, -0x5143,0x3f00,0xdafc,0xbd93, -0xbcc7,0x475f,0x6808,0x3db4, -0xc935,0xd2e7,0xdf95,0xbdd5, -0xf608,0x819f,0x956c,0x3df8, -0xf5db,0xf22b,0x29d5,0xbe1d, -0x428e,0x033f,0x69a0,0x3e42, -0xf2af,0x1b54,0x0554,0xbe69, -0xe46f,0x81e3,0x9159,0x3e92, -0xd3a9,0x7f18,0xbb54,0xbebe, -0x70a9,0xcc74,0x413f,0x3eed, -0x9f42,0xe788,0xd797,0xbf20, -0x9342,0xfca7,0xb891,0x3f59, -0xf71e,0x2d4f,0x19f7,0xbfa0, -0x6907,0x9f4e,0x85bd,0x4003 -}; -#endif - -#ifdef MIEEE -static unsigned short B[] = { -0x3c58,0x71a5,0xcf8c,0x9ee1, -0xbc72,0xfecc,0x9381,0x2603, -0x3c8e,0x092e,0x41a8,0xcdf4, -0xbca8,0x2f94,0x74d7,0x7641, -0x3cc3,0xdbf9,0x6b94,0x785b, -0xbce0,0xa690,0xecfa,0xdd36, -0x3cfc,0x8d9c,0x4a7d,0xdc98, -0xbd19,0x145e,0xbb05,0x6fc2, -0x3d36,0x9c4e,0xcd94,0xcfe2, -0xbd54,0xf877,0x21a4,0x70d1, -0x3d74,0x0fa3,0x2fcc,0xfc25, -0xbd93,0xdafc,0x3f00,0x5143, -0x3db4,0x6808,0x475f,0xbcc7, -0xbdd5,0xdf95,0xd2e7,0xc935, -0x3df8,0x956c,0x819f,0xf608, -0xbe1d,0x29d5,0xf22b,0xf5db, -0x3e42,0x69a0,0x033f,0x428e, -0xbe69,0x0554,0x1b54,0xf2af, -0x3e92,0x9159,0x81e3,0xe46f, -0xbebe,0xbb54,0x7f18,0xd3a9, -0x3eed,0x413f,0xcc74,0x70a9, -0xbf20,0xd797,0xe788,0x9f42, -0x3f59,0xb891,0xfca7,0x9342, -0xbfa0,0x19f7,0x2d4f,0xf71e, -0x4003,0x85bd,0x9f4e,0x6907 -}; -#endif - -/* k0.c */ -#ifdef ANSIPROT -extern double chbevl ( double, void *, int ); -extern double exp ( double ); -extern double i0 ( double ); -extern double log ( double ); -extern double sqrt ( double ); -#else -double chbevl(), exp(), i0(), log(), sqrt(); -#endif -extern double PI; -extern double MAXNUM; - -double k0(x) -double x; -{ -double y, z; - -if( x <= 0.0 ) - { - mtherr( "k0", DOMAIN ); - return( MAXNUM ); - } - -if( x <= 2.0 ) - { - y = x * x - 2.0; - y = chbevl( y, A, 10 ) - log( 0.5 * x ) * i0(x); - return( y ); - } -z = 8.0/x - 2.0; -y = exp(-x) * chbevl( z, B, 25 ) / sqrt(x); -return(y); -} - - - - -double k0e( x ) -double x; -{ -double y; - -if( x <= 0.0 ) - { - mtherr( "k0e", DOMAIN ); - return( MAXNUM ); - } - -if( x <= 2.0 ) - { - y = x * x - 2.0; - y = chbevl( y, A, 10 ) - log( 0.5 * x ) * i0(x); - return( y * exp(x) ); - } - -y = chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x); -return(y); -} |