path: root/tests/tmul.c

/* Test file for mpfr_mul.

Copyright 1999, 2001, 2002 Free Software Foundation, Inc.

This file is part of the MPFR Library.

The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#include <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
#include "mpfr-test.h"

void check _PROTO((double, double, mp_rnd_t, unsigned int,
		   unsigned int, unsigned int, double));
void check53 _PROTO((double, double, mp_rnd_t, double));
void check24 _PROTO((float, float, mp_rnd_t, float));
void check_float _PROTO((void));
void check_sign _PROTO((void));
void check_exact _PROTO((void));
void check_max _PROTO((void));
void check_min _PROTO((void));

/* checks that x*y gives the same results in double
   and with mpfr with 53 bits of precision */
void
check (double x, double y, mp_rnd_t rnd_mode, unsigned int px, 
       unsigned int py, unsigned int pz, double res)
{
  double z1, z2; mpfr_t xx, yy, zz;

  mpfr_init2 (xx, px);
  mpfr_init2 (yy, py);
  mpfr_init2 (zz, pz);
  mpfr_set_d(xx, x, rnd_mode);
  mpfr_set_d(yy, y, rnd_mode);
  mpfr_mul(zz, xx, yy, rnd_mode);
#ifdef TEST
  mpfr_set_machine_rnd_mode(rnd_mode);
#endif
  z1 = (res==0.0) ? x*y : res;
  z2 = mpfr_get_d(zz);
  if (z1!=z2 && (z1>=MINNORM || z1<=-MINNORM)) {
    printf("mpfr_mul ");
    if (res==0.0) printf("differs from libm.a"); else printf("failed");
      printf(" for x=%1.20e y=%1.20e with rnd_mode=%s\n", x, y,
	     mpfr_print_rnd_mode(rnd_mode));
    printf("libm.a gives %1.20e, mpfr_mul gives %1.20e\n", z1, z2);
    if (res!=0.0) exit(1);
  }
  mpfr_clear(xx); mpfr_clear(yy); mpfr_clear(zz);
}

void
check53 (double x, double y, mp_rnd_t rnd_mode, double z1)
{
  double z2; mpfr_t xx, yy, zz;

  mpfr_init2 (xx, 53);
  mpfr_init2 (yy, 53);
  mpfr_init2 (zz, 53);
  mpfr_set_d (xx, x, rnd_mode);
  mpfr_set_d (yy, y, rnd_mode);
  mpfr_mul (zz, xx, yy, rnd_mode);
  z2 = mpfr_get_d (zz);
  if (z1!=z2 && (!isnan(z1) || !isnan(z2))) {
    printf("mpfr_mul failed for x=%1.20e y=%1.20e with rnd_mode=%s\n",
	   x, y, mpfr_print_rnd_mode(rnd_mode));
    printf("libm.a gives %1.20e, mpfr_mul gives %1.20e\n", z1, z2);
    exit(1);
  }
  mpfr_clear(xx); mpfr_clear(yy); mpfr_clear(zz);
}

/* checks that x*y gives the same results in double
   and with mpfr with 24 bits of precision */
void
check24 (float x, float y, mp_rnd_t rnd_mode, float z1)
{
  float z2; mpfr_t xx, yy, zz;

  mpfr_init2 (xx, 24);
  mpfr_init2 (yy, 24);
  mpfr_init2 (zz, 24);
  mpfr_set_d (xx, x, rnd_mode);
  mpfr_set_d (yy, y, rnd_mode);
  mpfr_mul (zz, xx, yy, rnd_mode);
  z2 = (float) mpfr_get_d (zz);
  if (z1!=z2) {
    printf("mpfr_mul failed for x=%1.0f y=%1.0f with prec=24 and rnd_mode=%s\n", x, y, mpfr_print_rnd_mode(rnd_mode));
    printf("libm.a gives %1.0f, mpfr_mul gives %1.0f\n", z1, z2);
    exit(1);
  }
  mpfr_clear(xx); mpfr_clear(yy); mpfr_clear(zz);
}

/* the following examples come from the paper "Number-theoretic Test 
   Generation for Directed Rounding" from Michael Parks, Table 1 */
void
check_float (void)
{
  check24(8388609.0,  8388609.0, GMP_RNDN, 70368760954880.0);
  check24(16777213.0, 8388609.0, GMP_RNDN, 140737479966720.0);
  check24(8388611.0,  8388609.0, GMP_RNDN, 70368777732096.0);
  check24(12582911.0, 8388610.0, GMP_RNDN, 105553133043712.0);
  check24(12582914.0, 8388610.0, GMP_RNDN, 105553158209536.0);
  check24(13981013.0, 8388611.0, GMP_RNDN, 117281279442944.0);
  check24(11184811.0, 8388611.0, GMP_RNDN, 93825028587520.0);
  check24(11184810.0, 8388611.0, GMP_RNDN, 93825020198912.0);
  check24(13981014.0, 8388611.0, GMP_RNDN, 117281287831552.0);

  check24(8388609.0,  8388609.0, GMP_RNDZ, 70368760954880.0);
  check24(16777213.0, 8388609.0, GMP_RNDZ, 140737471578112.0);
  check24(8388611.0,  8388609.0, GMP_RNDZ, 70368777732096.0);
  check24(12582911.0, 8388610.0, GMP_RNDZ, 105553124655104.0);
  check24(12582914.0, 8388610.0, GMP_RNDZ, 105553158209536.0);
  check24(13981013.0, 8388611.0, GMP_RNDZ, 117281271054336.0);
  check24(11184811.0, 8388611.0, GMP_RNDZ, 93825028587520.0);
  check24(11184810.0, 8388611.0, GMP_RNDZ, 93825011810304.0);
  check24(13981014.0, 8388611.0, GMP_RNDZ, 117281287831552.0);

  check24(8388609.0,  8388609.0, GMP_RNDU, 70368769343488.0);
  check24(16777213.0, 8388609.0, GMP_RNDU, 140737479966720.0);
  check24(8388611.0,  8388609.0, GMP_RNDU, 70368786120704.0);
  check24(12582911.0, 8388610.0, GMP_RNDU, 105553133043712.0);
  check24(12582914.0, 8388610.0, GMP_RNDU, 105553166598144.0);
  check24(13981013.0, 8388611.0, GMP_RNDU, 117281279442944.0);
  check24(11184811.0, 8388611.0, GMP_RNDU, 93825036976128.0);
  check24(11184810.0, 8388611.0, GMP_RNDU, 93825020198912.0);
  check24(13981014.0, 8388611.0, GMP_RNDU, 117281296220160.0);

  check24(8388609.0,  8388609.0, GMP_RNDD, 70368760954880.0);
  check24(16777213.0, 8388609.0, GMP_RNDD, 140737471578112.0);
  check24(8388611.0,  8388609.0, GMP_RNDD, 70368777732096.0);
  check24(12582911.0, 8388610.0, GMP_RNDD, 105553124655104.0);
  check24(12582914.0, 8388610.0, GMP_RNDD, 105553158209536.0);
  check24(13981013.0, 8388611.0, GMP_RNDD, 117281271054336.0);
  check24(11184811.0, 8388611.0, GMP_RNDD, 93825028587520.0);
  check24(11184810.0, 8388611.0, GMP_RNDD, 93825011810304.0);
  check24(13981014.0, 8388611.0, GMP_RNDD, 117281287831552.0);
}

/* check sign of result */
void
check_sign (void)
{
  mpfr_t a, b;

  mpfr_init2 (a, 53);
  mpfr_init2 (b, 53);
  mpfr_set_d(a, -1.0, GMP_RNDN);
  mpfr_set_d(b, 2.0, GMP_RNDN);
  mpfr_mul(a, b, b, GMP_RNDN);
  if (mpfr_get_d(a) != 4.0) {
    fprintf(stderr,"2.0*2.0 gives %1.20e\n", mpfr_get_d(a)); exit(1);
  }
  mpfr_clear(a); mpfr_clear(b);
}

/* checks that the inexact return value is correct */
void
check_exact (void)
{
  mpfr_t a, b, c, d;
  mp_prec_t prec;
  int i, inexact;
  mp_rnd_t rnd;

  mpfr_init (a);
  mpfr_init (b);
  mpfr_init (c);
  mpfr_init (d);

  mpfr_set_prec (a, 17);
  mpfr_set_prec (b, 17);
  mpfr_set_prec (c, 32);
  mpfr_set_str_raw (a, "1.1000111011000100e-1");
  mpfr_set_str_raw (b, "1.0010001111100111e-1");
  if (mpfr_mul (c, a, b, GMP_RNDZ))
    {
      fprintf (stderr, "wrong return value (1)\n");
      exit (1);
    }

  for (prec = 2; prec < 100; prec++)
    {
      mpfr_set_prec (a, prec);
      mpfr_set_prec (b, prec);
      mpfr_set_prec (c, 2 * prec - 2);
      mpfr_set_prec (d, 2 * prec);
      for (i = 0; i < 1000; i++)
	{
	  mpfr_random (a);
	  mpfr_random (b);
	  rnd = LONG_RAND() % 4;
	  inexact = mpfr_mul (c, a, b, rnd);
	  if (mpfr_mul (d, a, b, rnd)) /* should be always exact */
	    {
	      fprintf (stderr, "unexpected inexact return value\n");
	      exit (1);
	    }
	  if ((inexact == 0) && mpfr_cmp (c, d))
	    {
	      fprintf (stderr, "inexact=0 but results differ\n");
	      exit (1);
	    }
	  else if (inexact && (mpfr_cmp (c, d) == 0))
	    {
	      fprintf (stderr, "inexact!=0 but results agree\n");
	      fprintf (stderr, "prec=%u rnd=%s a=", (unsigned int) prec,
		       mpfr_print_rnd_mode (rnd));
	      mpfr_out_str (stderr, 2, 0, a, rnd);
	      fprintf (stderr, "\nb=");
	      mpfr_out_str (stderr, 2, 0, b, rnd);
	      fprintf (stderr, "\nc=");
	      mpfr_out_str (stderr, 2, 0, c, rnd);
	      fprintf (stderr, "\nd=");
	      mpfr_out_str (stderr, 2, 0, d, rnd);
	      fprintf (stderr, "\n");
	      exit (1);
	    }
	}
    }

  mpfr_clear (a);
  mpfr_clear (b);
  mpfr_clear (c);
  mpfr_clear (d);
}

void
check_max(void)
{
  mpfr_t xx, yy, zz;

  mpfr_init2(xx, 4);
  mpfr_init2(yy, 4);
  mpfr_init2(zz, 4);
  mpfr_set_d(xx, 11.0/16, GMP_RNDN);
  mpfr_mul_2si(xx, xx, MPFR_EMAX_DEFAULT/2, GMP_RNDN);
  mpfr_set_d(yy, 11.0/16, GMP_RNDN);
  mpfr_mul_2si(yy, yy, MPFR_EMAX_DEFAULT - MPFR_EMAX_DEFAULT/2 + 1, GMP_RNDN);
  mpfr_clear_flags();
  mpfr_mul(zz, xx, yy, GMP_RNDU);
  if (!(mpfr_overflow_p() && MPFR_IS_INF(zz)))
    {
      printf("check_max failed (should be an overflow)\n");
      exit(1);
    }

  mpfr_clear_flags();
  mpfr_mul(zz, xx, yy, GMP_RNDD);
  if (mpfr_overflow_p() || MPFR_IS_INF(zz))
    {
      printf("check_max failed (should NOT be an overflow)\n");
      exit(1);
    }
  mpfr_set_d(xx, 15.0/16, GMP_RNDN);
  mpfr_mul_2si(xx, xx, MPFR_EMAX_DEFAULT, GMP_RNDN);
  if (!(MPFR_IS_FP(xx) && MPFR_IS_FP(zz)))
    {
      printf("check_max failed (internal error)\n");
      exit(1);
    }
  if (mpfr_cmp(xx, zz) != 0)
    {
      printf("check_max failed: got ");
      mpfr_out_str(stdout, 2, 0, zz, GMP_RNDZ);
      printf(" instead of ");
      mpfr_out_str(stdout, 2, 0, xx, GMP_RNDZ);
      printf("\n");
      exit(1);
    }

  mpfr_clear(xx);
  mpfr_clear(yy);
  mpfr_clear(zz);
}

void
check_min(void)
{
  mpfr_t xx, yy, zz;

  mpfr_init2(xx, 4);
  mpfr_init2(yy, 4);
  mpfr_init2(zz, 3);
  mpfr_set_d(xx, 15.0/16, GMP_RNDN);
  mpfr_mul_2si(xx, xx, MPFR_EMIN_DEFAULT/2, GMP_RNDN);
  mpfr_set_d(yy, 15.0/16, GMP_RNDN);
  mpfr_mul_2si(yy, yy, MPFR_EMIN_DEFAULT - MPFR_EMIN_DEFAULT/2 - 1, GMP_RNDN);
  mpfr_mul(zz, xx, yy, GMP_RNDD);
  if (mpfr_sgn(zz) != 0)
    {
      printf("check_min failed: got ");
      mpfr_out_str(stdout, 2, 0, zz, GMP_RNDZ);
      printf(" instead of 0\n");
      exit(1);
    }

  mpfr_mul(zz, xx, yy, GMP_RNDU);
  mpfr_set_d(xx, 0.5, GMP_RNDN);
  mpfr_mul_2si(xx, xx, MPFR_EMIN_DEFAULT, GMP_RNDN);
  if (mpfr_sgn(xx) <= 0)
    {
      printf("check_min failed (internal error)\n");
      exit(1);
    }
  if (mpfr_cmp(xx, zz) != 0)
    {
      printf("check_min failed: got ");
      mpfr_out_str(stdout, 2, 0, zz, GMP_RNDZ);
      printf(" instead of ");
      mpfr_out_str(stdout, 2, 0, xx, GMP_RNDZ);
      printf("\n");
      exit(1);
    }

  mpfr_clear(xx);
  mpfr_clear(yy);
  mpfr_clear(zz);
}

int
main (int argc, char *argv[])
{
#ifdef TEST
  double x, y, z; int i, prec, rnd_mode;
#endif

  check_exact ();
  check_float ();
  check53 (0.0, DBL_POS_INF, GMP_RNDN, DBL_NAN);
  check53(1.0, DBL_POS_INF, GMP_RNDN, DBL_POS_INF);
  check53(-1.0, DBL_POS_INF, GMP_RNDN, DBL_NEG_INF);
  check53(DBL_NAN, 0.0, GMP_RNDN, DBL_NAN); 
  check53(1.0, DBL_NAN, GMP_RNDN, DBL_NAN); 
  check53(6.9314718055994530941514e-1, 0.0, GMP_RNDZ, 0.0);
  check53(0.0, 6.9314718055994530941514e-1, GMP_RNDZ, 0.0);
  check_sign();
  check53(-4.165000000e4, -0.00004801920768307322868063274915, GMP_RNDN, 2.0); 
  check53(2.71331408349172961467e-08, -6.72658901114033715233e-165, GMP_RNDZ,
	  -1.8251348697787782844e-172);
  check53(0.31869277231188065, 0.88642843322303122, GMP_RNDZ,
	  2.8249833483992453642e-1);
  check(8.47622108205396074254e-01, 3.24039313247872939883e-01, GMP_RNDU,
	28, 45, 2, 0.375);
  check(2.63978122803639081440e-01, 6.8378615379333496093e-1, GMP_RNDN,
	34, 23, 31, 0.180504585267044603);
  check(1.0, 0.11835170935876249132, GMP_RNDU, 6, 41, 36, 0.1183517093595583);
  check53(67108865.0, 134217729.0, GMP_RNDN, 9.007199456067584e15);
  check(1.37399642157394197284e-01, 2.28877275604219221350e-01, GMP_RNDN,
	49, 15, 32, 0.0314472340833162888);
  check(4.03160720978664954828e-01, 5.85483042917246621073e-01, GMP_RNDZ,
	51, 22, 32, 0.2360436821472831);
  check(3.90798504668055102229e-14, 9.85394674650308388664e-04, GMP_RNDN,
	46, 22, 12, 0.385027296503914762e-16);
  check(4.58687081072827851358e-01, 2.20543551472118792844e-01, GMP_RNDN,
	49, 3, 2, 0.09375);
  check_max();
  check_min();
#ifdef TEST
  SEED_RAND (time(NULL));
  prec = (argc<2) ? 53 : atoi(argv[1]);
  rnd_mode = (argc<3) ? -1 : atoi(argv[2]);
  for (i=0;i<1000000;) {
    x = drand();
    y = drand();
    z = x*y; if (z<0) z=-z;
    if (z<1e+308 && z>1e-308) /* don't test overflow/underflow for now */
      { i++;
      check(x, y, (rnd_mode==-1) ? LONG_RAND()%4 : rnd_mode, 
	    prec, prec, prec, 0.0);
      }
  } 
#endif

  return 0;
}