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, 464 deletions

diff --git a/libm/double/mtst.c b/libm/double/mtst.c
deleted file mode 100644
index 2559d2340..000000000
--- a/libm/double/mtst.c
+++ /dev/null
@@ -1,464 +0,0 @@
-/*   mtst.c
- Consistency tests for math functions.
- To get strict rounding rules on a 386 or 68000 computer,
- define SETPREC to 1.
-
- With NTRIALS=10000, the following are typical results for
- IEEE double precision arithmetic.
-
-Consistency test of math functions.
-Max and rms relative errors for 10000 random arguments.
-x =   cbrt(   cube(x) ):  max = 0.00E+00   rms = 0.00E+00
-x =   atan(    tan(x) ):  max = 2.21E-16   rms = 3.27E-17
-x =    sin(   asin(x) ):  max = 2.13E-16   rms = 2.95E-17
-x =   sqrt( square(x) ):  max = 0.00E+00   rms = 0.00E+00
-x =    log(    exp(x) ):  max = 1.11E-16 A rms = 4.35E-18 A
-x =   tanh(  atanh(x) ):  max = 2.22E-16   rms = 2.43E-17
-x =  asinh(   sinh(x) ):  max = 2.05E-16   rms = 3.49E-18
-x =  acosh(   cosh(x) ):  max = 1.43E-15 A rms = 1.54E-17 A
-x =  log10(  exp10(x) ):  max = 5.55E-17 A rms = 1.27E-18 A
-x = pow( pow(x,a),1/a ):  max = 7.60E-14   rms = 1.05E-15
-x =    cos(   acos(x) ):  max = 2.22E-16 A rms = 6.90E-17 A
-*/
-
-/*
-Cephes Math Library Release 2.8:  June, 2000
-Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
-*/
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <math.h>
-
-#ifndef NTRIALS
-#define NTRIALS 10000
-#endif
-
-#define SETPREC 1
-#define STRTST 0
-
-#define WTRIALS (NTRIALS/5)
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double sqrt ( double );
-extern double cbrt ( double );
-extern double exp ( double );
-extern double log ( double );
-extern double exp10 ( double );
-extern double log10 ( double );
-extern double tan ( double );
-extern double atan ( double );
-extern double sin ( double );
-extern double asin ( double );
-extern double cos ( double );
-extern double acos ( double );
-extern double pow ( double, double );
-extern double tanh ( double );
-extern double atanh ( double );
-extern double sinh ( double );
-extern double asinh ( double x );
-extern double cosh ( double );
-extern double acosh ( double );
-extern double gamma ( double );
-extern double lgam ( double );
-#else
-double fabs(), sqrt(), cbrt(), exp(), log();
-double exp10(), log10(), tan(), atan();
-double sin(), asin(), cos(), acos(), pow();
-double tanh(), atanh(), sinh(), asinh(), cosh(), acosh();
-double gamma(), lgam();
-#endif
-
-/* C9X spells lgam lgamma.  */
-#define GLIBC2 0
-#if GLIBC2
-double lgamma (double);
-#endif
-
-#if SETPREC
-int dprec();
-#endif
-
-int drand();
-/* void exit(); */
-/* int printf(); */
-
-
-/* Provide inverses for square root and cube root: */
-double square(x)
-double x;
-{
-return( x * x );
-}
-
-double cube(x)
-double x;
-{
-return( x * x * x );
-}
-
-/* lookup table for each function */
-struct fundef
-	{
-	char *nam1;		/* the function */
-	double (*name )();
-	char *nam2;		/* its inverse  */
-	double (*inv )();
-	int nargs;		/* number of function arguments */
-	int tstyp;		/* type code of the function */
-	long ctrl;		/* relative error flag */
-	double arg1w;		/* width of domain for 1st arg */
-	double arg1l;		/* lower bound domain 1st arg */
-	long arg1f;		/* flags, e.g. integer arg */
-	double arg2w;		/* same info for args 2, 3, 4 */
-	double arg2l;
-	long arg2f;
-/*
-	double arg3w;
-	double arg3l;
-	long arg3f;
-	double arg4w;
-	double arg4l;
-	long arg4f;
-*/
-	};
-
-
-/* fundef.ctrl bits: */
-#define RELERR 1
-
-/* fundef.tstyp  test types: */
-#define POWER 1 
-#define ELLIP 2 
-#define GAMMA 3
-#define WRONK1 4
-#define WRONK2 5
-#define WRONK3 6
-
-/* fundef.argNf  argument flag bits: */
-#define INT 2
-#define EXPSCAL 4
-
-extern double MINLOG;
-extern double MAXLOG;
-extern double PI;
-extern double PIO2;
-/*
-define MINLOG -170.0
-define MAXLOG +170.0
-define PI 3.14159265358979323846
-define PIO2 1.570796326794896619
-*/
-
-#define NTESTS 12
-struct fundef defs[NTESTS] = {
-{"  cube",   cube,   "  cbrt",   cbrt, 1, 0, 1, 2002.0, -1001.0, 0,
-0.0, 0.0, 0},
-{"   tan",    tan,   "  atan",   atan, 1, 0, 1,    0.0,     0.0,  0,
-0.0, 0.0, 0},
-{"  asin",   asin,   "   sin",    sin, 1, 0, 1,   2.0,      -1.0,  0,
-0.0, 0.0, 0},
-{"square", square,   "  sqrt",   sqrt, 1, 0, 1, 170.0,    -85.0, EXPSCAL,
-0.0, 0.0, 0},
-{"   exp",    exp,   "   log",    log, 1, 0, 0, 340.0,    -170.0,  0,
-0.0, 0.0, 0},
-{" atanh",  atanh,   "  tanh",   tanh, 1, 0, 1,    2.0,    -1.0,  0,
-0.0, 0.0, 0},
-{"  sinh",   sinh,   " asinh",  asinh, 1, 0, 1, 340.0,   0.0,  0,
-0.0, 0.0, 0},
-{"  cosh",   cosh,   " acosh",  acosh, 1, 0, 0, 340.0,      0.0,  0,
-0.0, 0.0, 0},
-{" exp10",  exp10,   " log10",  log10, 1, 0, 0, 340.0,    -170.0,  0,
-0.0, 0.0, 0},
-{"pow",       pow,      "pow",    pow, 2, POWER, 1, 21.0, 0.0,   0,
-42.0, -21.0, 0},
-{"  acos",   acos,   "   cos",    cos, 1, 0, 0,   2.0,      -1.0,  0,
-0.0, 0.0, 0},
-#if GLIBC2
-{ "gamma",  gamma,     "lgamma",   lgamma, 1, GAMMA, 0, 34.0, 0.0,   0,
-0.0, 0.0, 0},
-#else
-{ "gamma",  gamma,     "lgam",   lgam, 1, GAMMA, 0, 34.0, 0.0,   0,
-0.0, 0.0, 0},
-#endif
-};
-
-static char *headrs[] = {
-"x = %s( %s(x) ): ",
-"x = %s( %s(x,a),1/a ): ",	/* power */
-"Legendre %s, %s: ",		/* ellip */
-"%s(x) = log(%s(x)): ",		/* gamma */
-"Wronksian of %s, %s: ",
-"Wronksian of %s, %s: ",
-"Wronksian of %s, %s: "
-};
- 
-static double yy1 = 0.0;
-static double y2 = 0.0;
-static double y3 = 0.0;
-static double y4 = 0.0;
-static double a = 0.0;
-static double x = 0.0;
-static double y = 0.0;
-static double z = 0.0;
-static double e = 0.0;
-static double max = 0.0;
-static double rmsa = 0.0;
-static double rms = 0.0;
-static double ave = 0.0;
-
-
-int main()
-{
-double (*fun )();
-double (*ifun )();
-struct fundef *d;
-int i, k, itst;
-int m, ntr;
-
-#if SETPREC
-dprec();  /* set coprocessor precision */
-#endif
-ntr = NTRIALS;
-printf( "Consistency test of math functions.\n" );
-printf( "Max and rms relative errors for %d random arguments.\n",
-	ntr );
-
-/* Initialize machine dependent parameters: */
-defs[1].arg1w = PI;
-defs[1].arg1l = -PI/2.0;
-/* Microsoft C has trouble with denormal numbers. */
-#if 0
-defs[3].arg1w = MAXLOG;
-defs[3].arg1l = -MAXLOG/2.0;
-defs[4].arg1w = 2*MAXLOG;
-defs[4].arg1l = -MAXLOG;
-#endif
-defs[6].arg1w = 2.0*MAXLOG;
-defs[6].arg1l = -MAXLOG;
-defs[7].arg1w = MAXLOG;
-defs[7].arg1l = 0.0;
-
-
-/* Outer loop, on the test number: */
-
-for( itst=STRTST; itst<NTESTS; itst++ )
-{
-d = &defs[itst];
-k = 0;
-m = 0;
-max = 0.0;
-rmsa = 0.0;
-ave = 0.0;
-fun = d->name;
-ifun = d->inv;
-
-/* Absolute error criterion starts with gamma function
- * (put all such at end of table)
- */
-if( d->tstyp == GAMMA )
-	printf( "Absolute error criterion (but relative if >1):\n" );
-
-/* Smaller number of trials for Wronksians
- * (put them at end of list)
- */
-if( d->tstyp == WRONK1 )
-	{
-	ntr = WTRIALS;
-	printf( "Absolute error and only %d trials:\n", ntr );
-	}
-
-printf( headrs[d->tstyp], d->nam2, d->nam1 );
-
-for( i=0; i<ntr; i++ )
-{
-m++;
-
-/* make random number(s) in desired range(s) */
-switch( d->nargs )
-{
-
-default:
-goto illegn;
-	
-case 2:
-drand( &a );
-a = d->arg2w *  ( a - 1.0 )  +  d->arg2l;
-if( d->arg2f & EXPSCAL )
-	{
-	a = exp(a);
-	drand( &y2 );
-	a -= 1.0e-13 * a * y2;
-	}
-if( d->arg2f & INT )
-	{
-	k = a + 0.25;
-	a = k;
-	}
-
-case 1:
-drand( &x );
-x = d->arg1w *  ( x - 1.0 )  +  d->arg1l;
-if( d->arg1f & EXPSCAL )
-	{
-	x = exp(x);
-	drand( &a );
-	x += 1.0e-13 * x * a;
-	}
-}
-
-
-/* compute function under test */
-switch( d->nargs )
-	{
-	case 1:
-	switch( d->tstyp )
-		{
-		case ELLIP:
-		yy1 = ( *(fun) )(x);
-		y2 = ( *(fun) )(1.0-x);
-		y3 = ( *(ifun) )(x);
-		y4 = ( *(ifun) )(1.0-x);
-		break;
-
-#if 1
-		case GAMMA:
-#if GLIBC2
-		y = lgamma(x);
-#else
-		y = lgam(x);
-#endif
-		x = log( gamma(x) );
-		break;
-#endif
-		default:
-		z = ( *(fun) )(x);
-		y = ( *(ifun) )(z);
-		}
-	break;
-	
-	case 2:
-	if( d->arg2f & INT )
-		{
-		switch( d->tstyp )
-			{
-			case WRONK1:
-			yy1 = (*fun)( k, x ); /* jn */
-			y2 = (*fun)( k+1, x );
-			y3 = (*ifun)( k, x ); /* yn */
-			y4 = (*ifun)( k+1, x );	
-			break;
-
-			case WRONK2:
-			yy1 = (*fun)( a, x ); /* iv */
-			y2 = (*fun)( a+1.0, x );
-			y3 = (*ifun)( k, x ); /* kn */	
-			y4 = (*ifun)( k+1, x );	
-			break;
-
-			default:
-			z = (*fun)( k, x );
-			y = (*ifun)( k, z );
-			}
-		}
-	else
-		{
-		if( d->tstyp == POWER )
-			{
-			z = (*fun)( x, a );
-			y = (*ifun)( z, 1.0/a );
-			}
-		else
-			{
-			z = (*fun)( a, x );
-			y = (*ifun)( a, z );
-			}
-		}
-	break;
-
-
-	default:
-illegn:
-	printf( "Illegal nargs= %d", d->nargs );
-	exit(1);
-	}	
-
-switch( d->tstyp )
-	{
-	case WRONK1:
-	e = (y2*y3 - yy1*y4) - 2.0/(PI*x); /* Jn, Yn */
-	break;
-
-	case WRONK2:
-	e = (y2*y3 + yy1*y4) - 1.0/x; /* In, Kn */
-	break;
-	
-	case ELLIP:
-	e = (yy1-y3)*y4 + y3*y2 - PIO2;
-	break;
-
-	default:
-	e = y - x;
-	break;
-	}
-
-if( d->ctrl & RELERR )
-	e /= x;
-else
-	{
-	if( fabs(x) > 1.0 )
-		e /= x;
-	}
-
-ave += e;
-/* absolute value of error */
-if( e < 0 )
-	e = -e;
-
-/* peak detect the error */
-if( e > max )
-	{
-	max = e;
-
-	if( e > 1.0e-10 )
-		{
-		printf("x %.6E z %.6E y %.6E max %.4E\n",
-		 x, z, y, max);
-		if( d->tstyp == POWER )
-			{
-			printf( "a %.6E\n", a );
-			}
-		if( d->tstyp >= WRONK1 )
-			{
-		printf( "yy1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
-		 yy1, y2, y3, y4, k, x );
-			}
-		}
-
-/*
-	printf("%.8E %.8E %.4E %6ld \n", x, y, max, n);
-	printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, max, n);
-	printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, max, n);
-	printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, max, n);
-	printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
-		a, b, c, x, y, max, n);
-*/
-	}
-
-/* accumulate rms error	*/
-e *= 1.0e16;	/* adjust range */
-rmsa += e * e;	/* accumulate the square of the error */
-}
-
-/* report after NTRIALS trials */
-rms = 1.0e-16 * sqrt( rmsa/m );
-if(d->ctrl & RELERR)
-	printf(" max = %.2E   rms = %.2E\n", max, rms );
-else
-	printf(" max = %.2E A rms = %.2E A\n", max, rms );
-} /* loop on itst */
-
-exit(0);
-}