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, 685 deletions

diff --git a/libm/double/gamma.c b/libm/double/gamma.c
deleted file mode 100644
index 341b4e915..000000000
--- a/libm/double/gamma.c
+++ /dev/null
@@ -1,685 +0,0 @@
-/*							gamma.c
- *
- *	Gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, gamma();
- * extern int sgngam;
- *
- * y = gamma( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns gamma function of the argument.  The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngam.
- * This variable is also filled in by the logarithmic gamma
- * function lgam().
- *
- * Arguments |x| <= 34 are reduced by recurrence and the function
- * approximated by a rational function of degree 6/7 in the
- * interval (2,3).  Large arguments are handled by Stirling's
- * formula. Large negative arguments are made positive using
- * a reflection formula.  
- *
- *
- * ACCURACY:
- *
- *                      Relative error:
- * arithmetic   domain     # trials      peak         rms
- *    DEC      -34, 34      10000       1.3e-16     2.5e-17
- *    IEEE    -170,-33      20000       2.3e-15     3.3e-16
- *    IEEE     -33,  33     20000       9.4e-16     2.2e-16
- *    IEEE      33, 171.6   20000       2.3e-15     3.2e-16
- *
- * Error for arguments outside the test range will be larger
- * owing to error amplification by the exponential function.
- *
- */
-/*							lgam()
- *
- *	Natural logarithm of gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, lgam();
- * extern int sgngam;
- *
- * y = lgam( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of the absolute
- * value of the gamma function of the argument.
- * The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngam.
- *
- * For arguments greater than 13, the logarithm of the gamma
- * function is approximated by the logarithmic version of
- * Stirling's formula using a polynomial approximation of
- * degree 4. Arguments between -33 and +33 are reduced by
- * recurrence to the interval [2,3] of a rational approximation.
- * The cosecant reflection formula is employed for arguments
- * less than -33.
- *
- * Arguments greater than MAXLGM return MAXNUM and an error
- * message.  MAXLGM = 2.035093e36 for DEC
- * arithmetic or 2.556348e305 for IEEE arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- *
- * arithmetic      domain        # trials     peak         rms
- *    DEC     0, 3                  7000     5.2e-17     1.3e-17
- *    DEC     2.718, 2.035e36       5000     3.9e-17     9.9e-18
- *    IEEE    0, 3                 28000     5.4e-16     1.1e-16
- *    IEEE    2.718, 2.556e305     40000     3.5e-16     8.3e-17
- * The error criterion was relative when the function magnitude
- * was greater than one but absolute when it was less than one.
- *
- * The following test used the relative error criterion, though
- * at certain points the relative error could be much higher than
- * indicated.
- *    IEEE    -200, -4             10000     4.8e-16     1.3e-16
- *
- */
-
-/*							gamma.c	*/
-/*	gamma function	*/
-
-/*
-Cephes Math Library Release 2.8:  June, 2000
-Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
-  1.60119522476751861407E-4,
-  1.19135147006586384913E-3,
-  1.04213797561761569935E-2,
-  4.76367800457137231464E-2,
-  2.07448227648435975150E-1,
-  4.94214826801497100753E-1,
-  9.99999999999999996796E-1
-};
-static double Q[] = {
--2.31581873324120129819E-5,
- 5.39605580493303397842E-4,
--4.45641913851797240494E-3,
- 1.18139785222060435552E-2,
- 3.58236398605498653373E-2,
--2.34591795718243348568E-1,
- 7.14304917030273074085E-2,
- 1.00000000000000000320E0
-};
-#define MAXGAM 171.624376956302725
-static double LOGPI = 1.14472988584940017414;
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0035047,0162701,0146301,0005234,
-0035634,0023437,0032065,0176530,
-0036452,0137157,0047330,0122574,
-0037103,0017310,0143041,0017232,
-0037524,0066516,0162563,0164605,
-0037775,0004671,0146237,0014222,
-0040200,0000000,0000000,0000000
-};
-static unsigned short Q[] = {
-0134302,0041724,0020006,0116565,
-0035415,0072121,0044251,0025634,
-0136222,0003447,0035205,0121114,
-0036501,0107552,0154335,0104271,
-0037022,0135717,0014776,0171471,
-0137560,0034324,0165024,0037021,
-0037222,0045046,0047151,0161213,
-0040200,0000000,0000000,0000000
-};
-#define MAXGAM 34.84425627277176174
-static unsigned short LPI[4] = {
-0040222,0103202,0043475,0006750,
-};
-#define LOGPI *(double *)LPI
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x2153,0x3998,0xfcb8,0x3f24,
-0xbfab,0xe686,0x84e3,0x3f53,
-0x14b0,0xe9db,0x57cd,0x3f85,
-0x23d3,0x18c4,0x63d9,0x3fa8,
-0x7d31,0xdcae,0x8da9,0x3fca,
-0xe312,0x3993,0xa137,0x3fdf,
-0x0000,0x0000,0x0000,0x3ff0
-};
-static unsigned short Q[] = {
-0xd3af,0x8400,0x487a,0xbef8,
-0x2573,0x2915,0xae8a,0x3f41,
-0xb44a,0xe750,0x40e4,0xbf72,
-0xb117,0x5b1b,0x31ed,0x3f88,
-0xde67,0xe33f,0x5779,0x3fa2,
-0x87c2,0x9d42,0x071a,0xbfce,
-0x3c51,0xc9cd,0x4944,0x3fb2,
-0x0000,0x0000,0x0000,0x3ff0
-};
-#define MAXGAM 171.624376956302725
-static unsigned short LPI[4] = {
-0xa1bd,0x48e7,0x50d0,0x3ff2,
-};
-#define LOGPI *(double *)LPI
-#endif 
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3f24,0xfcb8,0x3998,0x2153,
-0x3f53,0x84e3,0xe686,0xbfab,
-0x3f85,0x57cd,0xe9db,0x14b0,
-0x3fa8,0x63d9,0x18c4,0x23d3,
-0x3fca,0x8da9,0xdcae,0x7d31,
-0x3fdf,0xa137,0x3993,0xe312,
-0x3ff0,0x0000,0x0000,0x0000
-};
-static unsigned short Q[] = {
-0xbef8,0x487a,0x8400,0xd3af,
-0x3f41,0xae8a,0x2915,0x2573,
-0xbf72,0x40e4,0xe750,0xb44a,
-0x3f88,0x31ed,0x5b1b,0xb117,
-0x3fa2,0x5779,0xe33f,0xde67,
-0xbfce,0x071a,0x9d42,0x87c2,
-0x3fb2,0x4944,0xc9cd,0x3c51,
-0x3ff0,0x0000,0x0000,0x0000
-};
-#define MAXGAM 171.624376956302725
-static unsigned short LPI[4] = {
-0x3ff2,0x50d0,0x48e7,0xa1bd,
-};
-#define LOGPI *(double *)LPI
-#endif 
-
-/* Stirling's formula for the gamma function */
-#if UNK
-static double STIR[5] = {
- 7.87311395793093628397E-4,
--2.29549961613378126380E-4,
--2.68132617805781232825E-3,
- 3.47222221605458667310E-3,
- 8.33333333333482257126E-2,
-};
-#define MAXSTIR 143.01608
-static double SQTPI = 2.50662827463100050242E0;
-#endif
-#if DEC
-static unsigned short STIR[20] = {
-0035516,0061622,0144553,0112224,
-0135160,0131531,0037460,0165740,
-0136057,0134460,0037242,0077270,
-0036143,0107070,0156306,0027751,
-0037252,0125252,0125252,0146064,
-};
-#define MAXSTIR 26.77
-static unsigned short SQT[4] = {
-0040440,0066230,0177661,0034055,
-};
-#define SQTPI *(double *)SQT
-#endif
-#if IBMPC
-static unsigned short STIR[20] = {
-0x7293,0x592d,0xcc72,0x3f49,
-0x1d7c,0x27e6,0x166b,0xbf2e,
-0x4fd7,0x07d4,0xf726,0xbf65,
-0xc5fd,0x1b98,0x71c7,0x3f6c,
-0x5986,0x5555,0x5555,0x3fb5,
-};
-#define MAXSTIR 143.01608
-static unsigned short SQT[4] = {
-0x2706,0x1ff6,0x0d93,0x4004,
-};
-#define SQTPI *(double *)SQT
-#endif
-#if MIEEE
-static unsigned short STIR[20] = {
-0x3f49,0xcc72,0x592d,0x7293,
-0xbf2e,0x166b,0x27e6,0x1d7c,
-0xbf65,0xf726,0x07d4,0x4fd7,
-0x3f6c,0x71c7,0x1b98,0xc5fd,
-0x3fb5,0x5555,0x5555,0x5986,
-};
-#define MAXSTIR 143.01608
-static unsigned short SQT[4] = {
-0x4004,0x0d93,0x1ff6,0x2706,
-};
-#define SQTPI *(double *)SQT
-#endif
-
-int sgngam = 0;
-extern int sgngam;
-extern double MAXLOG, MAXNUM, PI;
-#ifdef ANSIPROT
-extern double pow ( double, double );
-extern double log ( double );
-extern double exp ( double );
-extern double sin ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double floor ( double );
-extern double fabs ( double );
-extern int isnan ( double );
-extern int isfinite ( double );
-static double stirf ( double );
-double lgam ( double );
-#else
-double pow(), log(), exp(), sin(), polevl(), p1evl(), floor(), fabs();
-int isnan(), isfinite();
-static double stirf();
-double lgam();
-#endif
-#ifdef INFINITIES
-extern double INFINITY;
-#endif
-#ifdef NANS
-extern double NAN;
-#endif
-
-/* Gamma function computed by Stirling's formula.
- * The polynomial STIR is valid for 33 <= x <= 172.
- */
-static double stirf(x)
-double x;
-{
-double y, w, v;
-
-w = 1.0/x;
-w = 1.0 + w * polevl( w, STIR, 4 );
-y = exp(x);
-if( x > MAXSTIR )
-	{ /* Avoid overflow in pow() */
-	v = pow( x, 0.5 * x - 0.25 );
-	y = v * (v / y);
-	}
-else
-	{
-	y = pow( x, x - 0.5 ) / y;
-	}
-y = SQTPI * y * w;
-return( y );
-}
-
-
-
-double gamma(x)
-double x;
-{
-double p, q, z;
-int i;
-
-sgngam = 1;
-#ifdef NANS
-if( isnan(x) )
-	return(x);
-#endif
-#ifdef INFINITIES
-#ifdef NANS
-if( x == INFINITY )
-	return(x);
-if( x == -INFINITY )
-	return(NAN);
-#else
-if( !isfinite(x) )
-	return(x);
-#endif
-#endif
-q = fabs(x);
-
-if( q > 33.0 )
-	{
-	if( x < 0.0 )
-		{
-		p = floor(q);
-		if( p == q )
-			{
-#ifdef NANS
-gamnan:
-			mtherr( "gamma", DOMAIN );
-			return (NAN);
-#else
-			goto goverf;
-#endif
-			}
-		i = p;
-		if( (i & 1) == 0 )
-			sgngam = -1;
-		z = q - p;
-		if( z > 0.5 )
-			{
-			p += 1.0;
-			z = q - p;
-			}
-		z = q * sin( PI * z );
-		if( z == 0.0 )
-			{
-#ifdef INFINITIES
-			return( sgngam * INFINITY);
-#else
-goverf:
-			mtherr( "gamma", OVERFLOW );
-			return( sgngam * MAXNUM);
-#endif
-			}
-		z = fabs(z);
-		z = PI/(z * stirf(q) );
-		}
-	else
-		{
-		z = stirf(x);
-		}
-	return( sgngam * z );
-	}
-
-z = 1.0;
-while( x >= 3.0 )
-	{
-	x -= 1.0;
-	z *= x;
-	}
-
-while( x < 0.0 )
-	{
-	if( x > -1.E-9 )
-		goto small;
-	z /= x;
-	x += 1.0;
-	}
-
-while( x < 2.0 )
-	{
-	if( x < 1.e-9 )
-		goto small;
-	z /= x;
-	x += 1.0;
-	}
-
-if( x == 2.0 )
-	return(z);
-
-x -= 2.0;
-p = polevl( x, P, 6 );
-q = polevl( x, Q, 7 );
-return( z * p / q );
-
-small:
-if( x == 0.0 )
-	{
-#ifdef INFINITIES
-#ifdef NANS
-	  goto gamnan;
-#else
-	  return( INFINITY );
-#endif
-#else
-	mtherr( "gamma", SING );
-	return( MAXNUM );
-#endif
-	}
-else
-	return( z/((1.0 + 0.5772156649015329 * x) * x) );
-}
-
-
-
-/* A[]: Stirling's formula expansion of log gamma
- * B[], C[]: log gamma function between 2 and 3
- */
-#ifdef UNK
-static double A[] = {
- 8.11614167470508450300E-4,
--5.95061904284301438324E-4,
- 7.93650340457716943945E-4,
--2.77777777730099687205E-3,
- 8.33333333333331927722E-2
-};
-static double B[] = {
--1.37825152569120859100E3,
--3.88016315134637840924E4,
--3.31612992738871184744E5,
--1.16237097492762307383E6,
--1.72173700820839662146E6,
--8.53555664245765465627E5
-};
-static double C[] = {
-/* 1.00000000000000000000E0, */
--3.51815701436523470549E2,
--1.70642106651881159223E4,
--2.20528590553854454839E5,
--1.13933444367982507207E6,
--2.53252307177582951285E6,
--2.01889141433532773231E6
-};
-/* log( sqrt( 2*pi ) ) */
-static double LS2PI  =  0.91893853320467274178;
-#define MAXLGM 2.556348e305
-#endif
-
-#ifdef DEC
-static unsigned short A[] = {
-0035524,0141201,0034633,0031405,
-0135433,0176755,0126007,0045030,
-0035520,0006371,0003342,0172730,
-0136066,0005540,0132605,0026407,
-0037252,0125252,0125252,0125132
-};
-static unsigned short B[] = {
-0142654,0044014,0077633,0035410,
-0144027,0110641,0125335,0144760,
-0144641,0165637,0142204,0047447,
-0145215,0162027,0146246,0155211,
-0145322,0026110,0010317,0110130,
-0145120,0061472,0120300,0025363
-};
-static unsigned short C[] = {
-/*0040200,0000000,0000000,0000000*/
-0142257,0164150,0163630,0112622,
-0143605,0050153,0156116,0135272,
-0144527,0056045,0145642,0062332,
-0145213,0012063,0106250,0001025,
-0145432,0111254,0044577,0115142,
-0145366,0071133,0050217,0005122
-};
-/* log( sqrt( 2*pi ) ) */
-static unsigned short LS2P[] = {040153,037616,041445,0172645,};
-#define LS2PI *(double *)LS2P
-#define MAXLGM 2.035093e36
-#endif
-
-#ifdef IBMPC
-static unsigned short A[] = {
-0x6661,0x2733,0x9850,0x3f4a,
-0xe943,0xb580,0x7fbd,0xbf43,
-0x5ebb,0x20dc,0x019f,0x3f4a,
-0xa5a1,0x16b0,0xc16c,0xbf66,
-0x554b,0x5555,0x5555,0x3fb5
-};
-static unsigned short B[] = {
-0x6761,0x8ff3,0x8901,0xc095,
-0xb93e,0x355b,0xf234,0xc0e2,
-0x89e5,0xf890,0x3d73,0xc114,
-0xdb51,0xf994,0xbc82,0xc131,
-0xf20b,0x0219,0x4589,0xc13a,
-0x055e,0x5418,0x0c67,0xc12a
-};
-static unsigned short C[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x12b2,0x1cf3,0xfd0d,0xc075,
-0xd757,0x7b89,0xaa0d,0xc0d0,
-0x4c9b,0xb974,0xeb84,0xc10a,
-0x0043,0x7195,0x6286,0xc131,
-0xf34c,0x892f,0x5255,0xc143,
-0xe14a,0x6a11,0xce4b,0xc13e
-};
-/* log( sqrt( 2*pi ) ) */
-static unsigned short LS2P[] = {
-0xbeb5,0xc864,0x67f1,0x3fed
-};
-#define LS2PI *(double *)LS2P
-#define MAXLGM 2.556348e305
-#endif
-
-#ifdef MIEEE
-static unsigned short A[] = {
-0x3f4a,0x9850,0x2733,0x6661,
-0xbf43,0x7fbd,0xb580,0xe943,
-0x3f4a,0x019f,0x20dc,0x5ebb,
-0xbf66,0xc16c,0x16b0,0xa5a1,
-0x3fb5,0x5555,0x5555,0x554b
-};
-static unsigned short B[] = {
-0xc095,0x8901,0x8ff3,0x6761,
-0xc0e2,0xf234,0x355b,0xb93e,
-0xc114,0x3d73,0xf890,0x89e5,
-0xc131,0xbc82,0xf994,0xdb51,
-0xc13a,0x4589,0x0219,0xf20b,
-0xc12a,0x0c67,0x5418,0x055e
-};
-static unsigned short C[] = {
-0xc075,0xfd0d,0x1cf3,0x12b2,
-0xc0d0,0xaa0d,0x7b89,0xd757,
-0xc10a,0xeb84,0xb974,0x4c9b,
-0xc131,0x6286,0x7195,0x0043,
-0xc143,0x5255,0x892f,0xf34c,
-0xc13e,0xce4b,0x6a11,0xe14a
-};
-/* log( sqrt( 2*pi ) ) */
-static unsigned short LS2P[] = {
-0x3fed,0x67f1,0xc864,0xbeb5
-};
-#define LS2PI *(double *)LS2P
-#define MAXLGM 2.556348e305
-#endif
-
-
-/* Logarithm of gamma function */
-
-
-double lgam(x)
-double x;
-{
-double p, q, u, w, z;
-int i;
-
-sgngam = 1;
-#ifdef NANS
-if( isnan(x) )
-	return(x);
-#endif
-
-#ifdef INFINITIES
-if( !isfinite(x) )
-	return(INFINITY);
-#endif
-
-if( x < -34.0 )
-	{
-	q = -x;
-	w = lgam(q); /* note this modifies sgngam! */
-	p = floor(q);
-	if( p == q )
-		{
-lgsing:
-#ifdef INFINITIES
-		mtherr( "lgam", SING );
-		return (INFINITY);
-#else
-		goto loverf;
-#endif
-		}
-	i = p;
-	if( (i & 1) == 0 )
-		sgngam = -1;
-	else
-		sgngam = 1;
-	z = q - p;
-	if( z > 0.5 )
-		{
-		p += 1.0;
-		z = p - q;
-		}
-	z = q * sin( PI * z );
-	if( z == 0.0 )
-		goto lgsing;
-/*	z = log(PI) - log( z ) - w;*/
-	z = LOGPI - log( z ) - w;
-	return( z );
-	}
-
-if( x < 13.0 )
-	{
-	z = 1.0;
-	p = 0.0;
-	u = x;
-	while( u >= 3.0 )
-		{
-		p -= 1.0;
-		u = x + p;
-		z *= u;
-		}
-	while( u < 2.0 )
-		{
-		if( u == 0.0 )
-			goto lgsing;
-		z /= u;
-		p += 1.0;
-		u = x + p;
-		}
-	if( z < 0.0 )
-		{
-		sgngam = -1;
-		z = -z;
-		}
-	else
-		sgngam = 1;
-	if( u == 2.0 )
-		return( log(z) );
-	p -= 2.0;
-	x = x + p;
-	p = x * polevl( x, B, 5 ) / p1evl( x, C, 6);
-	return( log(z) + p );
-	}
-
-if( x > MAXLGM )
-	{
-#ifdef INFINITIES
-	return( sgngam * INFINITY );
-#else
-loverf:
-	mtherr( "lgam", OVERFLOW );
-	return( sgngam * MAXNUM );
-#endif
-	}
-
-q = ( x - 0.5 ) * log(x) - x + LS2PI;
-if( x > 1.0e8 )
-	return( q );
-
-p = 1.0/(x*x);
-if( x >= 1000.0 )
-	q += ((   7.9365079365079365079365e-4 * p
-		- 2.7777777777777777777778e-3) *p
-		+ 0.0833333333333333333333) / x;
-else
-	q += polevl( p, A, 4 ) / x;
-return( q );
-}