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-/* 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);
-}