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/* mtst.c
Consistency tests for math functions.
With NTRIALS=10000, the following are typical results for
an alleged IEEE long double precision arithmetic:
Consistency test of math functions.
Max and rms errors for 10000 random arguments.
A = absolute error criterion (but relative if >1):
Otherwise, estimate is of relative error
x = cbrt( cube(x) ): max = 7.65E-20 rms = 4.39E-21
x = atan( tan(x) ): max = 2.01E-19 rms = 3.96E-20
x = sin( asin(x) ): max = 2.15E-19 rms = 3.00E-20
x = sqrt( square(x) ): max = 0.00E+00 rms = 0.00E+00
x = log( exp(x) ): max = 5.42E-20 A rms = 1.87E-21 A
x = log2( exp2(x) ): max = 1.08E-19 A rms = 3.37E-21 A
x = log10( exp10(x) ): max = 2.71E-20 A rms = 6.76E-22 A
x = acosh( cosh(x) ): max = 3.13E-18 A rms = 3.21E-20 A
x = pow( pow(x,a),1/a ): max = 1.25E-17 rms = 1.70E-19
x = tanh( atanh(x) ): max = 1.08E-19 rms = 1.16E-20
x = asinh( sinh(x) ): max = 1.03E-19 rms = 2.94E-21
x = cos( acos(x) ): max = 1.63E-19 A rms = 4.37E-20 A
lgam(x) = log(gamma(x)): max = 2.31E-19 A rms = 5.93E-20 A
x = ndtri( ndtr(x) ): max = 5.07E-17 rms = 7.03E-19
x = ndtr( ndtri(x) ): max = 1.40E-18 rms = 1.57E-19
Legendre ellpk, ellpe: max = 7.59E-19 A rms = 1.72E-19 A
Absolute error and only 2000 trials:
Wronksian of Yn, Jn: max = 6.40E-18 A rms = 1.49E-19 A
Relative error and only 100 trials:
x = stdtri(stdtr(k,x) ): max = 6.73E-19 rms = 2.46E-19
*/
/*
Cephes Math Library Release 2.3: November, 1995
Copyright 1984, 1987, 1988, 1995 by Stephen L. Moshier
*/
#include "mconf.h"
/* C9X spells lgam lgamma. */
#define GLIBC2 0
#define NTRIALS 10000
#define WTRIALS (NTRIALS/5)
#define STRTST 0
/* Note, fabsl may be an intrinsic function. */
#ifdef ANSIPROT
extern long double fabsl ( long double );
extern long double sqrtl ( long double );
extern long double cbrtl ( long double );
extern long double expl ( long double );
extern long double logl ( long double );
extern long double tanl ( long double );
extern long double atanl ( long double );
extern long double sinl ( long double );
extern long double asinl ( long double );
extern long double cosl ( long double );
extern long double acosl ( long double );
extern long double powl ( long double, long double );
extern long double tanhl ( long double );
extern long double atanhl ( long double );
extern long double sinhl ( long double );
extern long double asinhl ( long double );
extern long double coshl ( long double );
extern long double acoshl ( long double );
extern long double exp2l ( long double );
extern long double log2l ( long double );
extern long double exp10l ( long double );
extern long double log10l ( long double );
extern long double gammal ( long double );
extern long double lgaml ( long double );
extern long double jnl ( int, long double );
extern long double ynl ( int, long double );
extern long double ndtrl ( long double );
extern long double ndtril ( long double );
extern long double stdtrl ( int, long double );
extern long double stdtril ( int, long double );
extern long double ellpel ( long double );
extern long double ellpkl ( long double );
extern void exit (int);
#else
long double fabsl(), sqrtl();
long double cbrtl(), expl(), logl(), tanl(), atanl();
long double sinl(), asinl(), cosl(), acosl(), powl();
long double tanhl(), atanhl(), sinhl(), asinhl(), coshl(), acoshl();
long double exp2l(), log2l(), exp10l(), log10l();
long double gammal(), lgaml(), jnl(), ynl(), ndtrl(), ndtril();
long double stdtrl(), stdtril(), ellpel(), ellpkl();
void exit ();
#endif
extern int merror;
#if GLIBC2
long double lgammal(long double);
#endif
/*
NYI:
double iv(), kn();
*/
/* Provide inverses for square root and cube root: */
long double squarel(x)
long double x;
{
return( x * x );
}
long double cubel(x)
long double x;
{
return( x * x * x );
}
/* lookup table for each function */
struct fundef
{
char *nam1; /* the function */
long double (*name )();
char *nam2; /* its inverse */
long double (*inv )();
int nargs; /* number of function arguments */
int tstyp; /* type code of the function */
long ctrl; /* relative error flag */
long double arg1w; /* width of domain for 1st arg */
long double arg1l; /* lower bound domain 1st arg */
long arg1f; /* flags, e.g. integer arg */
long double arg2w; /* same info for args 2, 3, 4 */
long double arg2l;
long arg2f;
/*
double arg3w;
double arg3l;
long arg3f;
double arg4w;
double arg4l;
long arg4f;
*/
};
/* fundef.ctrl bits: */
#define RELERR 1
#define EXPSCAL 4
/* fundef.tstyp test types: */
#define POWER 1
#define ELLIP 2
#define GAMMA 3
#define WRONK1 4
#define WRONK2 5
#define WRONK3 6
#define STDTR 7
/* fundef.argNf argument flag bits: */
#define INT 2
extern long double MINLOGL;
extern long double MAXLOGL;
extern long double PIL;
extern long double PIO2L;
/*
define MINLOG -170.0
define MAXLOG +170.0
define PI 3.14159265358979323846
define PIO2 1.570796326794896619
*/
#define NTESTS 18
struct fundef defs[NTESTS] = {
{" cube", cubel, " cbrt", cbrtl, 1, 0, 1, 2000.0L, -1000.0L, 0,
0.0, 0.0, 0},
{" tan", tanl, " atan", atanl, 1, 0, 1, 0.0L, 0.0L, 0,
0.0, 0.0, 0},
{" asin", asinl, " sin", sinl, 1, 0, 1, 2.0L, -1.0L, 0,
0.0, 0.0, 0},
{"square", squarel, " sqrt", sqrtl, 1, 0, 1, 170.0L, -85.0L, EXPSCAL,
0.0, 0.0, 0},
{" exp", expl, " log", logl, 1, 0, 0, 340.0L, -170.0L, 0,
0.0, 0.0, 0},
{" exp2", exp2l, " log2", log2l, 1, 0, 0, 340.0L, -170.0L, 0,
0.0, 0.0, 0},
{" exp10", exp10l, " log10", log10l, 1, 0, 0, 340.0L, -170.0L, 0,
0.0, 0.0, 0},
{" cosh", coshl, " acosh", acoshl, 1, 0, 0, 340.0L, 0.0L, 0,
0.0, 0.0, 0},
{"pow", powl, "pow", powl, 2, POWER, 1, 25.0L, 0.0L, 0,
50.0, -25.0, 0},
{" atanh", atanhl, " tanh", tanhl, 1, 0, 1, 2.0L, -1.0L, 0,
0.0, 0.0, 0},
{" sinh", sinhl, " asinh", asinhl, 1, 0, 1, 340.0L, 0.0L, 0,
0.0, 0.0, 0},
{" acos", acosl, " cos", cosl, 1, 0, 0, 2.0L, -1.0L, 0,
0.0, 0.0, 0},
#if GLIBC2
/*
{ "gamma", gammal, "lgammal", lgammal, 1, GAMMA, 0, 34.0, 0.0, 0,
0.0, 0.0, 0},
*/
#else
{ "gamma", gammal, "lgam", lgaml, 1, GAMMA, 0, 34.0, 0.0, 0,
0.0, 0.0, 0},
{ " ndtr", ndtrl, " ndtri", ndtril, 1, 0, 1, 10.0L, -10.0L, 0,
0.0, 0.0, 0},
{ " ndtri", ndtril, " ndtr", ndtrl, 1, 0, 1, 1.0L, 0.0L, 0,
0.0, 0.0, 0},
{" ellpe", ellpel, " ellpk", ellpkl, 1, ELLIP, 0, 1.0L, 0.0L, 0,
0.0, 0.0, 0},
{ "stdtr", stdtrl, "stdtri", stdtril, 2, STDTR, 1, 4.0L, -2.0L, 0,
30.0, 1.0, INT},
{ " Jn", jnl, " Yn", ynl, 2, WRONK1, 0, 30.0, 0.1, 0,
40.0, -20.0, INT},
#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: ", /* wronk1 */
"Wronksian of %s, %s: ", /* wronk2 */
"Wronksian of %s, %s: ", /* wronk3 */
"x = %s(%s(k,x) ): ", /* stdtr */
};
static long double y1 = 0.0;
static long double y2 = 0.0;
static long double y3 = 0.0;
static long double y4 = 0.0;
static long double a = 0.0;
static long double x = 0.0;
static long double y = 0.0;
static long double z = 0.0;
static long double e = 0.0;
static long double max = 0.0;
static long double rmsa = 0.0;
static long double rms = 0.0;
static long double ave = 0.0;
static double da, db, dc, dd;
int ldrand();
int printf();
int
main()
{
long double (*fun )();
long double (*ifun )();
struct fundef *d;
int i, k, itst;
int m, ntr;
ntr = NTRIALS;
printf( "Consistency test of math functions.\n" );
printf( "Max and rms errors for %d random arguments.\n",
ntr );
printf( "A = absolute error criterion (but relative if >1):\n" );
printf( "Otherwise, estimate is of relative error\n" );
/* Initialize machine dependent parameters to test near the
* largest an smallest possible arguments. To compare different
* machines, use the same test intervals for all systems.
*/
defs[1].arg1w = PIL;
defs[1].arg1l = -PIL/2.0;
/*
defs[3].arg1w = MAXLOGL;
defs[3].arg1l = -MAXLOGL/2.0;
defs[4].arg1w = 2.0*MAXLOGL;
defs[4].arg1l = -MAXLOGL;
defs[6].arg1w = 2.0*MAXLOGL;
defs[6].arg1l = -MAXLOGL;
defs[7].arg1w = MAXLOGL;
defs[7].arg1l = 0.0;
*/
/* Outer loop, on the test number: */
for( itst=STRTST; itst<NTESTS; itst++ )
{
d = &defs[itst];
m = 0;
max = 0.0L;
rmsa = 0.0L;
ave = 0.0L;
fun = d->name;
ifun = d->inv;
/* 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 );
}
else if( d->tstyp == STDTR )
{
ntr = NTRIALS/100;
printf( "Relative error and only %d trials:\n", ntr );
}
/*
y1 = d->arg1l;
y2 = d->arg1w;
da = y1;
db = y2;
printf( "arg1l = %.4e, arg1w = %.4e\n", da, db );
*/
printf( headrs[d->tstyp], d->nam2, d->nam1 );
for( i=0; i<ntr; i++ )
{
m++;
k = 0;
/* make random number(s) in desired range(s) */
switch( d->nargs )
{
default:
goto illegn;
case 2:
ldrand( &a );
a = d->arg2w * ( a - 1.0L ) + d->arg2l;
if( d->arg2f & EXPSCAL )
{
a = expl(a);
ldrand( &y2 );
a -= 1.0e-13L * a * (y2 - 1.0L);
}
if( d->arg2f & INT )
{
k = a + 0.25L;
a = k;
}
case 1:
ldrand( &x );
y1 = d->arg1l;
y2 = d->arg1w;
x = y2 * ( x - 1.0L ) + y1;
if( x < y1 )
x = y1;
y1 += y2;
if( x > y1 )
x = y1;
if( d->arg1f & EXPSCAL )
{
x = expl(x);
ldrand( &y2 );
x += 1.0e-13L * x * (y2 - 1.0L);
}
}
/* compute function under test */
switch( d->nargs )
{
case 1:
switch( d->tstyp )
{
case ELLIP:
y1 = ( *(fun) )(x);
y2 = ( *(fun) )(1.0L-x);
y3 = ( *(ifun) )(x);
y4 = ( *(ifun) )(1.0L-x);
break;
#if 1
case GAMMA:
y = lgaml(x);
x = logl( gammal(x) );
break;
#endif
default:
z = ( *(fun) )(x);
y = ( *(ifun) )(z);
}
/*
if( merror )
{
printf( "error: x = %.15e, z = %.15e, y = %.15e\n",
(double )x, (double )z, (double )y );
}
*/
break;
case 2:
if( d->arg2f & INT )
{
switch( d->tstyp )
{
case WRONK1:
y1 = (*fun)( k, x ); /* jn */
y2 = (*fun)( k+1, x );
y3 = (*ifun)( k, x ); /* yn */
y4 = (*ifun)( k+1, x );
break;
case WRONK2:
y1 = (*fun)( a, x ); /* iv */
y2 = (*fun)( a+1.0L, 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, 1.0L/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:
/* Jn, Yn */
/* e = (y2*y3 - y1*y4) - 2.0L/(PIL*x);*/
e = x*(y2*y3 - y1*y4) - 2.0L/PIL;
break;
case WRONK2:
/* In, Kn */
/* e = (y2*y3 + y1*y4) - 1.0L/x; */
e = x*(y2*y3 + y1*y4) - 1.0L;
break;
case ELLIP:
e = (y1-y3)*y4 + y3*y2 - PIO2L;
break;
default:
e = y - x;
break;
}
if( d->ctrl & RELERR )
{
if( x != 0.0L )
e /= x;
else
printf( "warning, x == 0\n" );
}
else
{
if( fabsl(x) > 1.0L )
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-10L )
{
da = x;
db = z;
dc = y;
dd = max;
printf("x %.6E z %.6E y %.6E max %.4E\n",
da, db, dc, dd );
/*
if( d->tstyp >= WRONK1 )
{
printf( "y1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
(double )y1, (double )y2, (double )y3,
(double )y4, k, (double )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 *= 1.0e16L; /* adjust range */
rmsa += e * e; /* accumulate the square of the error */
}
/* report after NTRIALS trials */
rms = 1.0e-16L * sqrtl( rmsa/m );
da = max;
db = rms;
if(d->ctrl & RELERR)
printf(" max = %.2E rms = %.2E\n", da, db );
else
printf(" max = %.2E A rms = %.2E A\n", da, db );
} /* loop on itst */
exit (0);
return 0;
}
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