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authorEric Andersen <andersen@codepoet.org>2001-11-22 14:04:29 +0000
committerEric Andersen <andersen@codepoet.org>2001-11-22 14:04:29 +0000
commit7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 (patch)
tree3a7e8476e868ae15f4da1b7ce26b2db6f434468c /libm/double/j1.c
parentc117dd5fb183afb1a4790a6f6110d88704be6bf8 (diff)
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
Diffstat (limited to 'libm/double/j1.c')
-rw-r--r--libm/double/j1.c515
1 files changed, 0 insertions, 515 deletions
diff --git a/libm/double/j1.c b/libm/double/j1.c
deleted file mode 100644
index 95e46ea79..000000000
--- a/libm/double/j1.c
+++ /dev/null
@@ -1,515 +0,0 @@
-/* j1.c
- *
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, j1();
- *
- * y = j1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 8] and
- * (8, infinity). In the first interval a 24 term Chebyshev
- * expansion is used. In the second, the asymptotic
- * trigonometric representation is employed using two
- * rational functions of degree 5/5.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 4.0e-17 1.1e-17
- * IEEE 0, 30 30000 2.6e-16 1.1e-16
- *
- *
- */
- /* y1.c
- *
- * Bessel function of second kind of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1();
- *
- * y = y1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind of order one
- * of the argument.
- *
- * The domain is divided into the intervals [0, 8] and
- * (8, infinity). In the first interval a 25 term Chebyshev
- * expansion is used, and a call to j1() is required.
- * In the second, the asymptotic trigonometric representation
- * is employed using two rational functions of degree 5/5.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 8.6e-17 1.3e-17
- * IEEE 0, 30 30000 1.0e-15 1.3e-16
- *
- * (error criterion relative when |y1| > 1).
- *
- */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-/*
-#define PIO4 .78539816339744830962
-#define THPIO4 2.35619449019234492885
-#define SQ2OPI .79788456080286535588
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double RP[4] = {
--8.99971225705559398224E8,
- 4.52228297998194034323E11,
--7.27494245221818276015E13,
- 3.68295732863852883286E15,
-};
-static double RQ[8] = {
-/* 1.00000000000000000000E0,*/
- 6.20836478118054335476E2,
- 2.56987256757748830383E5,
- 8.35146791431949253037E7,
- 2.21511595479792499675E10,
- 4.74914122079991414898E12,
- 7.84369607876235854894E14,
- 8.95222336184627338078E16,
- 5.32278620332680085395E18,
-};
-#endif
-#ifdef DEC
-static unsigned short RP[16] = {
-0147526,0110742,0063322,0077052,
-0051722,0112720,0065034,0061530,
-0153604,0052227,0033147,0105650,
-0055121,0055025,0032276,0022015,
-};
-static unsigned short RQ[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0042433,0032610,0155604,0033473,
-0044572,0173320,0067270,0006616,
-0046637,0045246,0162225,0006606,
-0050645,0004773,0157577,0053004,
-0052612,0033734,0001667,0176501,
-0054462,0054121,0173147,0121367,
-0056237,0002777,0121451,0176007,
-0057623,0136253,0131601,0044710,
-};
-#endif
-#ifdef IBMPC
-static unsigned short RP[16] = {
-0x4fc5,0x4cda,0xd23c,0xc1ca,
-0x8c6b,0x0d43,0x52ba,0x425a,
-0xf175,0xe6cc,0x8a92,0xc2d0,
-0xc482,0xa697,0x2b42,0x432a,
-};
-static unsigned short RQ[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x86e7,0x1b70,0x66b1,0x4083,
-0x01b2,0x0dd7,0x5eda,0x410f,
-0xa1b1,0xdc92,0xe954,0x4193,
-0xeac1,0x7bef,0xa13f,0x4214,
-0xffa8,0x8076,0x46fb,0x4291,
-0xf45f,0x3ecc,0x4b0a,0x4306,
-0x3f81,0xf465,0xe0bf,0x4373,
-0x2939,0x7670,0x7795,0x43d2,
-};
-#endif
-#ifdef MIEEE
-static unsigned short RP[16] = {
-0xc1ca,0xd23c,0x4cda,0x4fc5,
-0x425a,0x52ba,0x0d43,0x8c6b,
-0xc2d0,0x8a92,0xe6cc,0xf175,
-0x432a,0x2b42,0xa697,0xc482,
-};
-static unsigned short RQ[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4083,0x66b1,0x1b70,0x86e7,
-0x410f,0x5eda,0x0dd7,0x01b2,
-0x4193,0xe954,0xdc92,0xa1b1,
-0x4214,0xa13f,0x7bef,0xeac1,
-0x4291,0x46fb,0x8076,0xffa8,
-0x4306,0x4b0a,0x3ecc,0xf45f,
-0x4373,0xe0bf,0xf465,0x3f81,
-0x43d2,0x7795,0x7670,0x2939,
-};
-#endif
-
-#ifdef UNK
-static double PP[7] = {
- 7.62125616208173112003E-4,
- 7.31397056940917570436E-2,
- 1.12719608129684925192E0,
- 5.11207951146807644818E0,
- 8.42404590141772420927E0,
- 5.21451598682361504063E0,
- 1.00000000000000000254E0,
-};
-static double PQ[7] = {
- 5.71323128072548699714E-4,
- 6.88455908754495404082E-2,
- 1.10514232634061696926E0,
- 5.07386386128601488557E0,
- 8.39985554327604159757E0,
- 5.20982848682361821619E0,
- 9.99999999999999997461E-1,
-};
-#endif
-#ifdef DEC
-static unsigned short PP[28] = {
-0035507,0144542,0061543,0024326,
-0037225,0145105,0017766,0022661,
-0040220,0043766,0010254,0133255,
-0040643,0113047,0142611,0151521,
-0041006,0144344,0055351,0074261,
-0040646,0156520,0120574,0006416,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short PQ[28] = {
-0035425,0142330,0115041,0165514,
-0037214,0177352,0145105,0052026,
-0040215,0072515,0141207,0073255,
-0040642,0056427,0137222,0106405,
-0041006,0062716,0166427,0165450,
-0040646,0133352,0035425,0123304,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short PP[28] = {
-0x651b,0x4c6c,0xf92c,0x3f48,
-0xc4b6,0xa3fe,0xb948,0x3fb2,
-0x96d6,0xc215,0x08fe,0x3ff2,
-0x3a6a,0xf8b1,0x72c4,0x4014,
-0x2f16,0x8b5d,0xd91c,0x4020,
-0x81a2,0x142f,0xdbaa,0x4014,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short PQ[28] = {
-0x3d69,0x1344,0xb89b,0x3f42,
-0xaa83,0x5948,0x9fdd,0x3fb1,
-0xeed6,0xb850,0xaea9,0x3ff1,
-0x51a1,0xf7d2,0x4ba2,0x4014,
-0xfd65,0xdda2,0xccb9,0x4020,
-0xb4d9,0x4762,0xd6dd,0x4014,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short PP[28] = {
-0x3f48,0xf92c,0x4c6c,0x651b,
-0x3fb2,0xb948,0xa3fe,0xc4b6,
-0x3ff2,0x08fe,0xc215,0x96d6,
-0x4014,0x72c4,0xf8b1,0x3a6a,
-0x4020,0xd91c,0x8b5d,0x2f16,
-0x4014,0xdbaa,0x142f,0x81a2,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short PQ[28] = {
-0x3f42,0xb89b,0x1344,0x3d69,
-0x3fb1,0x9fdd,0x5948,0xaa83,
-0x3ff1,0xaea9,0xb850,0xeed6,
-0x4014,0x4ba2,0xf7d2,0x51a1,
-0x4020,0xccb9,0xdda2,0xfd65,
-0x4014,0xd6dd,0x4762,0xb4d9,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-#ifdef UNK
-static double QP[8] = {
- 5.10862594750176621635E-2,
- 4.98213872951233449420E0,
- 7.58238284132545283818E1,
- 3.66779609360150777800E2,
- 7.10856304998926107277E2,
- 5.97489612400613639965E2,
- 2.11688757100572135698E2,
- 2.52070205858023719784E1,
-};
-static double QQ[7] = {
-/* 1.00000000000000000000E0,*/
- 7.42373277035675149943E1,
- 1.05644886038262816351E3,
- 4.98641058337653607651E3,
- 9.56231892404756170795E3,
- 7.99704160447350683650E3,
- 2.82619278517639096600E3,
- 3.36093607810698293419E2,
-};
-#endif
-#ifdef DEC
-static unsigned short QP[32] = {
-0037121,0037723,0055605,0151004,
-0040637,0066656,0031554,0077264,
-0041627,0122714,0153170,0161466,
-0042267,0061712,0036520,0140145,
-0042461,0133315,0131573,0071176,
-0042425,0057525,0147500,0013201,
-0042123,0130122,0061245,0154131,
-0041311,0123772,0064254,0172650,
-};
-static unsigned short QQ[28] = {
-/*0040200,0000000,0000000,0000000,*/
-0041624,0074603,0002112,0101670,
-0042604,0007135,0010162,0175565,
-0043233,0151510,0157757,0172010,
-0043425,0064506,0112006,0104276,
-0043371,0164125,0032271,0164242,
-0043060,0121425,0122750,0136013,
-0042250,0005773,0053472,0146267,
-};
-#endif
-#ifdef IBMPC
-static unsigned short QP[32] = {
-0xba40,0x6b70,0x27fa,0x3faa,
-0x8fd6,0xc66d,0xedb5,0x4013,
-0x1c67,0x9acf,0xf4b9,0x4052,
-0x180d,0x47aa,0xec79,0x4076,
-0x6e50,0xb66f,0x36d9,0x4086,
-0x02d0,0xb9e8,0xabea,0x4082,
-0xbb0b,0x4c54,0x760a,0x406a,
-0x9eb5,0x4d15,0x34ff,0x4039,
-};
-static unsigned short QQ[28] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x5077,0x6089,0x8f30,0x4052,
-0x5f6f,0xa20e,0x81cb,0x4090,
-0xfe81,0x1bfd,0x7a69,0x40b3,
-0xd118,0xd280,0xad28,0x40c2,
-0x3d14,0xa697,0x3d0a,0x40bf,
-0x1781,0xb4bd,0x1462,0x40a6,
-0x5997,0x6ae7,0x017f,0x4075,
-};
-#endif
-#ifdef MIEEE
-static unsigned short QP[32] = {
-0x3faa,0x27fa,0x6b70,0xba40,
-0x4013,0xedb5,0xc66d,0x8fd6,
-0x4052,0xf4b9,0x9acf,0x1c67,
-0x4076,0xec79,0x47aa,0x180d,
-0x4086,0x36d9,0xb66f,0x6e50,
-0x4082,0xabea,0xb9e8,0x02d0,
-0x406a,0x760a,0x4c54,0xbb0b,
-0x4039,0x34ff,0x4d15,0x9eb5,
-};
-static unsigned short QQ[28] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4052,0x8f30,0x6089,0x5077,
-0x4090,0x81cb,0xa20e,0x5f6f,
-0x40b3,0x7a69,0x1bfd,0xfe81,
-0x40c2,0xad28,0xd280,0xd118,
-0x40bf,0x3d0a,0xa697,0x3d14,
-0x40a6,0x1462,0xb4bd,0x1781,
-0x4075,0x017f,0x6ae7,0x5997,
-};
-#endif
-
-#ifdef UNK
-static double YP[6] = {
- 1.26320474790178026440E9,
--6.47355876379160291031E11,
- 1.14509511541823727583E14,
--8.12770255501325109621E15,
- 2.02439475713594898196E17,
--7.78877196265950026825E17,
-};
-static double YQ[8] = {
-/* 1.00000000000000000000E0,*/
- 5.94301592346128195359E2,
- 2.35564092943068577943E5,
- 7.34811944459721705660E7,
- 1.87601316108706159478E10,
- 3.88231277496238566008E12,
- 6.20557727146953693363E14,
- 6.87141087355300489866E16,
- 3.97270608116560655612E18,
-};
-#endif
-#ifdef DEC
-static unsigned short YP[24] = {
-0047626,0112763,0013715,0133045,
-0152026,0134552,0142033,0024411,
-0053720,0045245,0102210,0077565,
-0155347,0000321,0136415,0102031,
-0056463,0146550,0055633,0032605,
-0157054,0171012,0167361,0054265,
-};
-static unsigned short YQ[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0042424,0111515,0044773,0153014,
-0044546,0005405,0171307,0075774,
-0046614,0023575,0047105,0063556,
-0050613,0143034,0101533,0156026,
-0052541,0175367,0166514,0114257,
-0054415,0014466,0134350,0171154,
-0056164,0017436,0025075,0022101,
-0057534,0103614,0103663,0121772,
-};
-#endif
-#ifdef IBMPC
-static unsigned short YP[24] = {
-0xb6c5,0x62f9,0xd2be,0x41d2,
-0x6521,0x5883,0xd72d,0xc262,
-0x0fef,0xb091,0x0954,0x42da,
-0xb083,0x37a1,0xe01a,0xc33c,
-0x66b1,0x0b73,0x79ad,0x4386,
-0x2b17,0x5dde,0x9e41,0xc3a5,
-};
-static unsigned short YQ[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x7ac2,0xa93f,0x9269,0x4082,
-0xef7f,0xbe58,0xc160,0x410c,
-0xacee,0xa9c8,0x84ef,0x4191,
-0x7b83,0x906b,0x78c3,0x4211,
-0x9316,0xfda9,0x3f5e,0x428c,
-0x1e4e,0xd71d,0xa326,0x4301,
-0xa488,0xc547,0x83e3,0x436e,
-0x747f,0x90f6,0x90f1,0x43cb,
-};
-#endif
-#ifdef MIEEE
-static unsigned short YP[24] = {
-0x41d2,0xd2be,0x62f9,0xb6c5,
-0xc262,0xd72d,0x5883,0x6521,
-0x42da,0x0954,0xb091,0x0fef,
-0xc33c,0xe01a,0x37a1,0xb083,
-0x4386,0x79ad,0x0b73,0x66b1,
-0xc3a5,0x9e41,0x5dde,0x2b17,
-};
-static unsigned short YQ[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4082,0x9269,0xa93f,0x7ac2,
-0x410c,0xc160,0xbe58,0xef7f,
-0x4191,0x84ef,0xa9c8,0xacee,
-0x4211,0x78c3,0x906b,0x7b83,
-0x428c,0x3f5e,0xfda9,0x9316,
-0x4301,0xa326,0xd71d,0x1e4e,
-0x436e,0x83e3,0xc547,0xa488,
-0x43cb,0x90f1,0x90f6,0x747f,
-};
-#endif
-
-
-#ifdef UNK
-static double Z1 = 1.46819706421238932572E1;
-static double Z2 = 4.92184563216946036703E1;
-#endif
-
-#ifdef DEC
-static unsigned short DZ1[] = {0041152,0164532,0006114,0010540};
-static unsigned short DZ2[] = {0041504,0157663,0001625,0020621};
-#define Z1 (*(double *)DZ1)
-#define Z2 (*(double *)DZ2)
-#endif
-
-#ifdef IBMPC
-static unsigned short DZ1[] = {0x822c,0x4189,0x5d2b,0x402d};
-static unsigned short DZ2[] = {0xa432,0x6072,0x9bf6,0x4048};
-#define Z1 (*(double *)DZ1)
-#define Z2 (*(double *)DZ2)
-#endif
-
-#ifdef MIEEE
-static unsigned short DZ1[] = {0x402d,0x5d2b,0x4189,0x822c};
-static unsigned short DZ2[] = {0x4048,0x9bf6,0x6072,0xa432};
-#define Z1 (*(double *)DZ1)
-#define Z2 (*(double *)DZ2)
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double log ( double );
-extern double sin ( double );
-extern double cos ( double );
-extern double sqrt ( double );
-double j1 ( double );
-#else
-double polevl(), p1evl(), log(), sin(), cos(), sqrt();
-double j1();
-#endif
-extern double TWOOPI, THPIO4, SQ2OPI;
-
-double j1(x)
-double x;
-{
-double w, z, p, q, xn;
-
-w = x;
-if( x < 0 )
- w = -x;
-
-if( w <= 5.0 )
- {
- z = x * x;
- w = polevl( z, RP, 3 ) / p1evl( z, RQ, 8 );
- w = w * x * (z - Z1) * (z - Z2);
- return( w );
- }
-
-w = 5.0/x;
-z = w * w;
-p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
-q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
-xn = x - THPIO4;
-p = p * cos(xn) - w * q * sin(xn);
-return( p * SQ2OPI / sqrt(x) );
-}
-
-
-extern double MAXNUM;
-
-double y1(x)
-double x;
-{
-double w, z, p, q, xn;
-
-if( x <= 5.0 )
- {
- if( x <= 0.0 )
- {
- mtherr( "y1", DOMAIN );
- return( -MAXNUM );
- }
- z = x * x;
- w = x * (polevl( z, YP, 5 ) / p1evl( z, YQ, 8 ));
- w += TWOOPI * ( j1(x) * log(x) - 1.0/x );
- return( w );
- }
-
-w = 5.0/x;
-z = w * w;
-p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
-q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
-xn = x - THPIO4;
-p = p * sin(xn) + w * q * cos(xn);
-return( p * SQ2OPI / sqrt(x) );
-}