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

1 files changed, 0 insertions, 543 deletions

diff --git a/libm/double/j0.c b/libm/double/j0.c
deleted file mode 100644
index c0f1bd4b8..000000000
--- a/libm/double/j0.c
+++ /dev/null
@@ -1,543 +0,0 @@
-/*							j0.c
- *
- *	Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, j0();
- *
- * y = j0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order zero of the argument.
- *
- * The domain is divided into the intervals [0, 5] and
- * (5, infinity). In the first interval the following rational
- * approximation is used:
- *
- *
- *        2         2
- * (w - r  ) (w - r  ) P (w) / Q (w)
- *       1         2    3       8
- *
- *            2
- * where w = x  and the two r's are zeros of the function.
- *
- * In the second interval, the Hankel asymptotic expansion
- * is employed with two rational functions of degree 6/6
- * and 7/7.
- *
- *
- *
- * ACCURACY:
- *
- *                      Absolute error:
- * arithmetic   domain     # trials      peak         rms
- *    DEC       0, 30       10000       4.4e-17     6.3e-18
- *    IEEE      0, 30       60000       4.2e-16     1.1e-16
- *
- */
-/*							y0.c
- *
- *	Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y0();
- *
- * y = y0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 5] and
- * (5, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- *   y0(x)  = R(x)  +   2 * log(x) * j0(x) / PI.
- * Thus a call to j0() is required.
- *
- * In the second interval, the Hankel asymptotic expansion
- * is employed with two rational functions of degree 6/6
- * and 7/7.
- *
- *
- *
- * ACCURACY:
- *
- *  Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic   domain     # trials      peak         rms
- *    DEC       0, 30        9400       7.0e-17     7.9e-18
- *    IEEE      0, 30       30000       1.3e-15     1.6e-16
- *
- */
-
-/*
-Cephes Math Library Release 2.8:  June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-/* Note: all coefficients satisfy the relative error criterion
- * except YP, YQ which are designed for absolute error. */
-
-#include <math.h>
-
-#ifdef UNK
-static double PP[7] = {
-  7.96936729297347051624E-4,
-  8.28352392107440799803E-2,
-  1.23953371646414299388E0,
-  5.44725003058768775090E0,
-  8.74716500199817011941E0,
-  5.30324038235394892183E0,
-  9.99999999999999997821E-1,
-};
-static double PQ[7] = {
-  9.24408810558863637013E-4,
-  8.56288474354474431428E-2,
-  1.25352743901058953537E0,
-  5.47097740330417105182E0,
-  8.76190883237069594232E0,
-  5.30605288235394617618E0,
-  1.00000000000000000218E0,
-};
-#endif
-#ifdef DEC
-static unsigned short PP[28] = {
-0035520,0164604,0140733,0054470,
-0037251,0122605,0115356,0107170,
-0040236,0124412,0071500,0056303,
-0040656,0047737,0045720,0045263,
-0041013,0172143,0045004,0142103,
-0040651,0132045,0026241,0026406,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short PQ[28] = {
-0035562,0052006,0070034,0134666,
-0037257,0057055,0055242,0123424,
-0040240,0071626,0046630,0032371,
-0040657,0011077,0032013,0012731,
-0041014,0030307,0050331,0006414,
-0040651,0145457,0065021,0150304,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short PP[28] = {
-0x6b27,0x983b,0x1d30,0x3f4a,
-0xd1cf,0xb35d,0x34b0,0x3fb5,
-0x0b98,0x4e68,0xd521,0x3ff3,
-0x0956,0xe97a,0xc9fb,0x4015,
-0x9888,0x6940,0x7e8c,0x4021,
-0x25a1,0xa594,0x3684,0x4015,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short PQ[28] = {
-0x9737,0xce03,0x4a80,0x3f4e,
-0x54e3,0xab54,0xebc5,0x3fb5,
-0x069f,0xc9b3,0x0e72,0x3ff4,
-0x62bb,0xe681,0xe247,0x4015,
-0x21a1,0xea1b,0x8618,0x4021,
-0x3a19,0xed42,0x3965,0x4015,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short PP[28] = {
-0x3f4a,0x1d30,0x983b,0x6b27,
-0x3fb5,0x34b0,0xb35d,0xd1cf,
-0x3ff3,0xd521,0x4e68,0x0b98,
-0x4015,0xc9fb,0xe97a,0x0956,
-0x4021,0x7e8c,0x6940,0x9888,
-0x4015,0x3684,0xa594,0x25a1,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short PQ[28] = {
-0x3f4e,0x4a80,0xce03,0x9737,
-0x3fb5,0xebc5,0xab54,0x54e3,
-0x3ff4,0x0e72,0xc9b3,0x069f,
-0x4015,0xe247,0xe681,0x62bb,
-0x4021,0x8618,0xea1b,0x21a1,
-0x4015,0x3965,0xed42,0x3a19,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-#ifdef UNK
-static double QP[8] = {
--1.13663838898469149931E-2,
--1.28252718670509318512E0,
--1.95539544257735972385E1,
--9.32060152123768231369E1,
--1.77681167980488050595E2,
--1.47077505154951170175E2,
--5.14105326766599330220E1,
--6.05014350600728481186E0,
-};
-static double QQ[7] = {
-/*  1.00000000000000000000E0,*/
-  6.43178256118178023184E1,
-  8.56430025976980587198E2,
-  3.88240183605401609683E3,
-  7.24046774195652478189E3,
-  5.93072701187316984827E3,
-  2.06209331660327847417E3,
-  2.42005740240291393179E2,
-};
-#endif
-#ifdef DEC
-static unsigned short QP[32] = {
-0136472,0035021,0142451,0141115,
-0140244,0024731,0150620,0105642,
-0141234,0067177,0124161,0060141,
-0141672,0064572,0151557,0043036,
-0142061,0127141,0003127,0043517,
-0142023,0011727,0060271,0144544,
-0141515,0122142,0126620,0143150,
-0140701,0115306,0106715,0007344,
-};
-static unsigned short QQ[28] = {
-/*0040200,0000000,0000000,0000000,*/
-0041600,0121272,0004741,0026544,
-0042526,0015605,0105654,0161771,
-0043162,0123155,0165644,0062645,
-0043342,0041675,0167576,0130756,
-0043271,0052720,0165631,0154214,
-0043000,0160576,0034614,0172024,
-0042162,0000570,0030500,0051235,
-};
-#endif
-#ifdef IBMPC
-static unsigned short QP[32] = {
-0x384a,0x38a5,0x4742,0xbf87,
-0x1174,0x3a32,0x853b,0xbff4,
-0x2c0c,0xf50e,0x8dcf,0xc033,
-0xe8c4,0x5a6d,0x4d2f,0xc057,
-0xe8ea,0x20ca,0x35cc,0xc066,
-0x392d,0xec17,0x627a,0xc062,
-0x18cd,0x55b2,0xb48c,0xc049,
-0xa1dd,0xd1b9,0x3358,0xc018,
-};
-static unsigned short QQ[28] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x25ac,0x413c,0x1457,0x4050,
-0x9c7f,0xb175,0xc370,0x408a,
-0x8cb5,0xbd74,0x54cd,0x40ae,
-0xd63e,0xbdef,0x4877,0x40bc,
-0x3b11,0x1d73,0x2aba,0x40b7,
-0x9e82,0xc731,0x1c2f,0x40a0,
-0x0a54,0x0628,0x402f,0x406e,
-};
-#endif
-#ifdef MIEEE
-static unsigned short QP[32] = {
-0xbf87,0x4742,0x38a5,0x384a,
-0xbff4,0x853b,0x3a32,0x1174,
-0xc033,0x8dcf,0xf50e,0x2c0c,
-0xc057,0x4d2f,0x5a6d,0xe8c4,
-0xc066,0x35cc,0x20ca,0xe8ea,
-0xc062,0x627a,0xec17,0x392d,
-0xc049,0xb48c,0x55b2,0x18cd,
-0xc018,0x3358,0xd1b9,0xa1dd,
-};
-static unsigned short QQ[28] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4050,0x1457,0x413c,0x25ac,
-0x408a,0xc370,0xb175,0x9c7f,
-0x40ae,0x54cd,0xbd74,0x8cb5,
-0x40bc,0x4877,0xbdef,0xd63e,
-0x40b7,0x2aba,0x1d73,0x3b11,
-0x40a0,0x1c2f,0xc731,0x9e82,
-0x406e,0x402f,0x0628,0x0a54,
-};
-#endif
-
-
-#ifdef UNK
-static double YP[8] = {
- 1.55924367855235737965E4,
--1.46639295903971606143E7,
- 5.43526477051876500413E9,
--9.82136065717911466409E11,
- 8.75906394395366999549E13,
--3.46628303384729719441E15,
- 4.42733268572569800351E16,
--1.84950800436986690637E16,
-};
-static double YQ[7] = {
-/* 1.00000000000000000000E0,*/
- 1.04128353664259848412E3,
- 6.26107330137134956842E5,
- 2.68919633393814121987E8,
- 8.64002487103935000337E10,
- 2.02979612750105546709E13,
- 3.17157752842975028269E15,
- 2.50596256172653059228E17,
-};
-#endif
-#ifdef DEC
-static unsigned short YP[32] = {
-0043563,0120677,0042264,0046166,
-0146137,0140371,0113444,0042260,
-0050241,0175707,0100502,0063344,
-0152144,0125737,0007265,0164526,
-0053637,0051621,0163035,0060546,
-0155105,0004416,0107306,0060023,
-0056035,0045133,0030132,0000024,
-0155603,0065132,0144061,0131732,
-};
-static unsigned short YQ[28] = {
-/*0040200,0000000,0000000,0000000,*/
-0042602,0024422,0135557,0162663,
-0045030,0155665,0044075,0160135,
-0047200,0035432,0105446,0104005,
-0051240,0167331,0056063,0022743,
-0053223,0127746,0025764,0012160,
-0055064,0044206,0177532,0145545,
-0056536,0111375,0163715,0127201,
-};
-#endif
-#ifdef IBMPC
-static unsigned short YP[32] = {
-0x898f,0xe896,0x7437,0x40ce,
-0x8896,0x32e4,0xf81f,0xc16b,
-0x4cdd,0xf028,0x3f78,0x41f4,
-0xbd2b,0xe1d6,0x957b,0xc26c,
-0xac2d,0x3cc3,0xea72,0x42d3,
-0xcc02,0xd1d8,0xa121,0xc328,
-0x4003,0x660b,0xa94b,0x4363,
-0x367b,0x5906,0x6d4b,0xc350,
-};
-static unsigned short YQ[28] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xfcb6,0x576d,0x4522,0x4090,
-0xbc0c,0xa907,0x1b76,0x4123,
-0xd101,0x5164,0x0763,0x41b0,
-0x64bc,0x2b86,0x1ddb,0x4234,
-0x828e,0xc57e,0x75fc,0x42b2,
-0x596d,0xdfeb,0x8910,0x4326,
-0xb5d0,0xbcf9,0xd25f,0x438b,
-};
-#endif
-#ifdef MIEEE
-static unsigned short YP[32] = {
-0x40ce,0x7437,0xe896,0x898f,
-0xc16b,0xf81f,0x32e4,0x8896,
-0x41f4,0x3f78,0xf028,0x4cdd,
-0xc26c,0x957b,0xe1d6,0xbd2b,
-0x42d3,0xea72,0x3cc3,0xac2d,
-0xc328,0xa121,0xd1d8,0xcc02,
-0x4363,0xa94b,0x660b,0x4003,
-0xc350,0x6d4b,0x5906,0x367b,
-};
-static unsigned short YQ[28] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4090,0x4522,0x576d,0xfcb6,
-0x4123,0x1b76,0xa907,0xbc0c,
-0x41b0,0x0763,0x5164,0xd101,
-0x4234,0x1ddb,0x2b86,0x64bc,
-0x42b2,0x75fc,0xc57e,0x828e,
-0x4326,0x8910,0xdfeb,0x596d,
-0x438b,0xd25f,0xbcf9,0xb5d0,
-};
-#endif
-
-#ifdef UNK
-/*  5.783185962946784521175995758455807035071 */
-static double DR1 = 5.78318596294678452118E0;
-/* 30.47126234366208639907816317502275584842 */
-static double DR2 = 3.04712623436620863991E1;
-#endif
-
-#ifdef DEC
-static unsigned short R1[] = {0040671,0007734,0001061,0056734};
-#define DR1 *(double *)R1
-static unsigned short R2[] = {0041363,0142445,0030416,0165567};
-#define DR2 *(double *)R2
-#endif
-
-#ifdef IBMPC
-static unsigned short R1[] = {0x2bbb,0x8046,0x21fb,0x4017};
-#define DR1 *(double *)R1
-static unsigned short R2[] = {0xdd6f,0xa621,0x78a4,0x403e};
-#define DR2 *(double *)R2
-#endif
-
-#ifdef MIEEE
-static unsigned short R1[] = {0x4017,0x21fb,0x8046,0x2bbb};
-#define DR1 *(double *)R1
-static unsigned short R2[] = {0x403e,0x78a4,0xa621,0xdd6f};
-#define DR2 *(double *)R2
-#endif
-
-#ifdef UNK
-static double RP[4] = {
--4.79443220978201773821E9,
- 1.95617491946556577543E12,
--2.49248344360967716204E14,
- 9.70862251047306323952E15,
-};
-static double RQ[8] = {
-/* 1.00000000000000000000E0,*/
- 4.99563147152651017219E2,
- 1.73785401676374683123E5,
- 4.84409658339962045305E7,
- 1.11855537045356834862E10,
- 2.11277520115489217587E12,
- 3.10518229857422583814E14,
- 3.18121955943204943306E16,
- 1.71086294081043136091E18,
-};
-#endif
-#ifdef DEC
-static unsigned short RP[16] = {
-0150216,0161235,0064344,0014450,
-0052343,0135216,0035624,0144153,
-0154142,0130247,0003310,0003667,
-0055411,0173703,0047772,0176635,
-};
-static unsigned short RQ[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0042371,0144025,0032265,0136137,
-0044451,0133131,0132420,0151466,
-0046470,0144641,0072540,0030636,
-0050446,0126600,0045042,0044243,
-0052365,0172633,0110301,0071063,
-0054215,0032424,0062272,0043513,
-0055742,0005013,0171731,0072335,
-0057275,0170646,0036663,0013134,
-};
-#endif
-#ifdef IBMPC
-static unsigned short RP[16] = {
-0x8325,0xad1c,0xdc53,0xc1f1,
-0x990d,0xc772,0x7751,0x427c,
-0x00f7,0xe0d9,0x5614,0xc2ec,
-0x5fb4,0x69ff,0x3ef8,0x4341,
-};
-static unsigned short RQ[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xb78c,0xa696,0x3902,0x407f,
-0x1a67,0x36a2,0x36cb,0x4105,
-0x0634,0x2eac,0x1934,0x4187,
-0x4914,0x0944,0xd5b0,0x4204,
-0x2e46,0x7218,0xbeb3,0x427e,
-0x48e9,0x8c97,0xa6a2,0x42f1,
-0x2e9c,0x7e7b,0x4141,0x435c,
-0x62cc,0xc7b6,0xbe34,0x43b7,
-};
-#endif
-#ifdef MIEEE
-static unsigned short RP[16] = {
-0xc1f1,0xdc53,0xad1c,0x8325,
-0x427c,0x7751,0xc772,0x990d,
-0xc2ec,0x5614,0xe0d9,0x00f7,
-0x4341,0x3ef8,0x69ff,0x5fb4,
-};
-static unsigned short RQ[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x407f,0x3902,0xa696,0xb78c,
-0x4105,0x36cb,0x36a2,0x1a67,
-0x4187,0x1934,0x2eac,0x0634,
-0x4204,0xd5b0,0x0944,0x4914,
-0x427e,0xbeb3,0x7218,0x2e46,
-0x42f1,0xa6a2,0x8c97,0x48e9,
-0x435c,0x4141,0x7e7b,0x2e9c,
-0x43b7,0xbe34,0xc7b6,0x62cc,
-};
-#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 j0 ( double );
-#else
-double polevl(), p1evl(), log(), sin(), cos(), sqrt();
-double j0();
-#endif
-extern double TWOOPI, SQ2OPI, PIO4;
-
-double j0(x)
-double x;
-{
-double w, z, p, q, xn;
-
-if( x < 0 )
-	x = -x;
-
-if( x <= 5.0 )
-	{
-	z = x * x;
-	if( x < 1.0e-5 )
-		return( 1.0 - z/4.0 );
-
-	p = (z - DR1) * (z - DR2);
-	p = p * polevl( z, RP, 3)/p1evl( z, RQ, 8 );
-	return( p );
-	}
-
-w = 5.0/x;
-q = 25.0/(x*x);
-p = polevl( q, PP, 6)/polevl( q, PQ, 6 );
-q = polevl( q, QP, 7)/p1evl( q, QQ, 7 );
-xn = x - PIO4;
-p = p * cos(xn) - w * q * sin(xn);
-return( p * SQ2OPI / sqrt(x) );
-}
-
-/*							y0() 2	*/
-/* Bessel function of second kind, order zero	*/
-
-/* Rational approximation coefficients YP[], YQ[] are used here.
- * The function computed is  y0(x)  -  2 * log(x) * j0(x) / PI,
- * whose value at x = 0 is  2 * ( log(0.5) + EUL ) / PI
- * = 0.073804295108687225.
- */
-
-/*
-#define PIO4 .78539816339744830962
-#define SQ2OPI .79788456080286535588
-*/
-extern double MAXNUM;
-
-double y0(x)
-double x;
-{
-double w, z, p, q, xn;
-
-if( x <= 5.0 )
-	{
-	if( x <= 0.0 )
-		{
-		mtherr( "y0", DOMAIN );
-		return( -MAXNUM );
-		}
-	z = x * x;
-	w = polevl( z, YP, 7) / p1evl( z, YQ, 7 );
-	w += TWOOPI * log(x) * j0(x);
-	return( w );
-	}
-
-w = 5.0/x;
-z = 25.0 / (x * x);
-p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
-q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
-xn = x - PIO4;
-p = p * sin(xn) + w * q * cos(xn);
-return( p * SQ2OPI / sqrt(x) );
-}