uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 464 insertions, 0 deletions

diff --git a/libm/double/mtst.c b/libm/double/mtst.c
new file mode 100644
index 000000000..2559d2340
--- /dev/null
+++ b/libm/double/mtst.c
@@ -0,0 +1,464 @@
+/*   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);
+}