tdiv.c

a very popular packet of cryptography tools,it encloses the most common used algorithm and protocols

/* Test file for mpfr_div.

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

#define check53(n, d, rnd, res) check4(n, d, rnd, 53, res)

void check4 _PROTO((double, double, mp_rnd_t, int, double)); 
void check24 _PROTO((float, float, mp_rnd_t, float)); 
void check_float _PROTO((void)); 
void check_convergence _PROTO((void)); 
void check_lowr _PROTO((void));
void check_inexact _PROTO((void));
void check_nan _PROTO((void));

void
check4 (double N, double D, mp_rnd_t rnd_mode, int p, double Q)
{
  mpfr_t q, n, d; double Q2;

  mpfr_init2(q, p); mpfr_init2(n, p); mpfr_init2(d, p);
  mpfr_set_d(n, N, rnd_mode);
  mpfr_set_d(d, D, rnd_mode);
  mpfr_div(q, n, d, rnd_mode);
#ifdef MPFR_HAVE_FESETROUND
  mpfr_set_machine_rnd_mode(rnd_mode);
#endif
  if (Q==0.0) Q = N/D;
  Q2 = mpfr_get_d1 (q);
  if (p==53 && Q!=Q2 && (!isnan(Q) || !isnan(Q2))) {
    printf("mpfr_div failed for n=%1.20e, d=%1.20e, rnd_mode=%s\n",
	   N, D, mpfr_print_rnd_mode(rnd_mode));
    printf("expected quotient is %1.20e, got %1.20e (%d ulp)\n", Q, Q2,
	   ulp(Q2, Q));
    exit(1);
  }
  mpfr_clear(q); mpfr_clear(n); mpfr_clear(d);  
}

void
check24 (float N, float D, mp_rnd_t rnd_mode, float Q)
{
  mpfr_t q, n, d; float Q2;

  mpfr_init2(q, 24); mpfr_init2(n, 24); mpfr_init2(d, 24);
  mpfr_set_d(n, N, rnd_mode);
  mpfr_set_d(d, D, rnd_mode);
  mpfr_div(q, n, d, rnd_mode);
  Q2 = mpfr_get_d1 (q);
  if (Q!=Q2) {
    printf("mpfr_div failed for n=%1.10e, d=%1.10e, prec=24, rnd_mode=%s\n",
	   N, D, mpfr_print_rnd_mode(rnd_mode));
    printf("expected quotient is %1.10e, got %1.10e\n", Q, Q2);
    exit(1);
  }
  mpfr_clear(q); mpfr_clear(n); mpfr_clear(d);  
}

/* the following examples come from the paper "Number-theoretic Test 
   Generation for Directed Rounding" from Michael Parks, Table 2 */
void
check_float(void)
{
  float b=8388608.0; /* 2^23 */

  check24(b*8388610.0, 8388609.0, GMP_RNDN, 8.388609e6);
  check24(b*16777215.0, 16777213.0, GMP_RNDN, 8.388609e6);
  check24(b*8388612.0, 8388611.0, GMP_RNDN, 8.388609e6);
  check24(b*12582914.0, 12582911.0, GMP_RNDN, 8.38861e6);
  check24(12582913.0, 12582910.0, GMP_RNDN, 1.000000238);
  check24(b*16777215.0, 8388609.0, GMP_RNDN, 1.6777213e7);
  check24(b*8388612.0, 8388609.0, GMP_RNDN, 8.388611e6);
  check24(b*12582914.0, 8388610.0, GMP_RNDN, 1.2582911e7);
  check24(b*12582913.0, 8388610.0, GMP_RNDN, 1.258291e7);

  check24(b*8388610.0, 8388609.0, GMP_RNDZ, 8.388608e6);
  check24(b*16777215.0, 16777213.0, GMP_RNDZ, 8.388609e6);
  check24(b*8388612.0, 8388611.0, GMP_RNDZ, 8.388608e6);
  check24(b*12582914.0, 12582911.0, GMP_RNDZ, 8.38861e6);
  check24(12582913.0, 12582910.0, GMP_RNDZ, 1.000000238);
  check24(b*16777215.0, 8388609.0, GMP_RNDZ, 1.6777213e7);
  check24(b*8388612.0, 8388609.0, GMP_RNDZ, 8.38861e6);
  check24(b*12582914.0, 8388610.0, GMP_RNDZ, 1.2582911e7);
  check24(b*12582913.0, 8388610.0, GMP_RNDZ, 1.258291e7);

  check24(b*8388610.0, 8388609.0, GMP_RNDU, 8.388609e6);
  check24(b*16777215.0, 16777213.0, GMP_RNDU, 8.38861e6);
  check24(b*8388612.0, 8388611.0, GMP_RNDU, 8.388609e6);
  check24(b*12582914.0, 12582911.0, GMP_RNDU, 8.388611e6);
  check24(12582913.0, 12582910.0, GMP_RNDU, 1.000000357);
  check24(b*16777215.0, 8388609.0, GMP_RNDU, 1.6777214e7);
  check24(b*8388612.0, 8388609.0, GMP_RNDU, 8.388611e6);
  check24(b*12582914.0, 8388610.0, GMP_RNDU, 1.2582912e7);
  check24(b*12582913.0, 8388610.0, GMP_RNDU, 1.2582911e7);

  check24(b*8388610.0, 8388609.0, GMP_RNDD, 8.388608e6);
  check24(b*16777215.0, 16777213.0, GMP_RNDD, 8.388609e6);
  check24(b*8388612.0, 8388611.0, GMP_RNDD, 8.388608e6);
  check24(b*12582914.0, 12582911.0, GMP_RNDD, 8.38861e6);
  check24(12582913.0, 12582910.0, GMP_RNDD, 1.000000238);
  check24(b*16777215.0, 8388609.0, GMP_RNDD, 1.6777213e7);
  check24(b*8388612.0, 8388609.0, GMP_RNDD, 8.38861e6);
  check24(b*12582914.0, 8388610.0, GMP_RNDD, 1.2582911e7);
  check24(b*12582913.0, 8388610.0, GMP_RNDD, 1.258291e7);
}

void
check_convergence (void)
{
  mpfr_t x, y; int i, j;
  
  mpfr_init2(x, 130); 
  mpfr_set_str_raw(x, "0.1011111101011010101000001010011111101000011100011101010011111011000011001010000000111100100111110011001010110100100001001000111001E6944");
  mpfr_init2(y, 130);
  mpfr_set_ui(y, 5, GMP_RNDN);
  mpfr_div(x, x, y, GMP_RNDD); /* exact division */

  mpfr_set_prec(x, 64);
  mpfr_set_prec(y, 64);
  mpfr_set_str_raw(x, "0.10010010011011010100101001010111100000101110010010101E55");
  mpfr_set_str_raw(y, "0.1E585");
  mpfr_div(x, x, y, GMP_RNDN);
  mpfr_set_str_raw(y, "0.10010010011011010100101001010111100000101110010010101E-529");
  if (mpfr_cmp(x, y)) {
    fprintf(stderr, "Error in mpfr_div for prec=64, rnd=GMP_RNDN\n");
    printf("got        "); mpfr_print_binary(x); putchar('\n');
    printf("instead of "); mpfr_print_binary(y); putchar('\n');
    exit(1);
  }

  for (i=32; i<=64; i+=32) {
      mpfr_set_prec(x, i);
      mpfr_set_prec(y, i);
      mpfr_set_d(x, 1.0, GMP_RNDN);
      for (j=0;j<4;j++) {
	mpfr_set_d(y, 1.0, GMP_RNDN);
	mpfr_div(y, x, y, j);
	if (mpfr_cmp_ui(y, 1)) {
	  fprintf(stderr, "mpfr_div failed for x=1.0, y=1.0, prec=%u rnd=%s\n",
		  i, mpfr_print_rnd_mode(j));
	  printf("got "); mpfr_print_binary(y); putchar('\n');
	  exit(1);
	}
      }
  }

  mpfr_clear(x); mpfr_clear(y);
}

void
check_lowr (void)
{
  mpfr_t x, y, z, z2, z3, tmp; 
  int k, c; 
  

  mpfr_init2 (x, 1000);
  mpfr_init2 (y, 100);
  mpfr_init2 (tmp, 850);
  mpfr_init2 (z, 10);
  mpfr_init2 (z2, 10);
  mpfr_init2 (z3, 50); 

  for (k = 1; k < 10000; k++) 
    {
      mpfr_random (z);
      mpfr_random (tmp);
      mpfr_mul (x, z, tmp, GMP_RNDN);
      c = mpfr_div (z2, x, tmp, GMP_RNDN);

      if (c || mpfr_cmp(z2, z))
	{
	  fprintf(stderr, "Error in mpfr_div rnd=GMP_RNDN\n");
	  printf("Dividing "); 
	  printf("got        "); mpfr_print_binary(z2); putchar('\n');
	  printf("instead of "); mpfr_print_binary(z); putchar('\n');
	  printf("inex flag = %d\n", c); 
	  exit(1);
	}
    }

  mpfr_set_prec(z2, 9); 
  for (k = 1; k < 10000; k++) 
    {
      mpfr_random(z); 
      mpfr_random(tmp); 
      mpfr_mul(x, z, tmp, GMP_RNDN); 
      c = mpfr_div(z2, x, tmp, GMP_RNDN); 

      if ((mpfr_cmp(z2, z) == 0 && c) || c == -1)
	{
	  fprintf(stderr, "Error in mpfr_div rnd=GMP_RNDN\n");
	  printf("Dividing "); 
	  printf("got        "); mpfr_print_binary(z2); putchar('\n');
	  printf("instead of "); mpfr_print_binary(z); putchar('\n');
	  printf("inex flag = %d\n", c); 
	  exit(1);
	}
      else if (c == 2) 
	{
	  mpfr_add_one_ulp(z, GMP_RNDN); 
	  if (mpfr_cmp(z2, z))
	    {
	      fprintf(stderr, "Error in mpfr_div [even rnd?] rnd=GMP_RNDN\n");
	      printf("Dividing "); 
	      printf("got        "); mpfr_print_binary(z2); putchar('\n');
	      printf("instead of "); mpfr_print_binary(z); putchar('\n');
	      printf("inex flag = %d\n", 1); 
	      exit(1); 	      
	    }
	}
      else if (c == -2)
	{ 
	  mpfr_sub_one_ulp(z, GMP_RNDN); 
	  if (mpfr_cmp(z2, z))
	    {
	      fprintf(stderr, "Error in mpfr_div [even rnd?] rnd=GMP_RNDN\n");
	      printf("Dividing "); 
	      printf("got        "); mpfr_print_binary(z2); putchar('\n');
	      printf("instead of "); mpfr_print_binary(z); putchar('\n');
	      printf("inex flag = %d\n", 1); 
	      exit(1); 	      
	    }
	}	  
    }


  mpfr_set_prec(x, 1000);   
  mpfr_set_prec(y, 100); 
  mpfr_set_prec(tmp, 850); 
  mpfr_set_prec(z, 10); 
  mpfr_set_prec(z2, 10);

  /* almost exact divisions */
  for (k = 1; k < 10000; k++) 
    {
      mpfr_random(z); 
      mpfr_random(tmp); 
      mpfr_mul(x, z, tmp, GMP_RNDN); 
      mpfr_set(y, tmp, GMP_RNDD); 
      mpfr_add_one_ulp(x, GMP_RNDN); 

      c = mpfr_div(z2, x, y, GMP_RNDD); 
      mpfr_div(z3, x, y, GMP_RNDD); 
      mpfr_set(z, z3, GMP_RNDD); 

      if (c != -1 || mpfr_cmp(z2, z))
	{
	  fprintf(stderr, "Error in mpfr_div rnd=GMP_RNDD\n");
	  printf("got        "); mpfr_print_binary(z2); putchar('\n');
	  printf("instead of "); mpfr_print_binary(z); putchar('\n');
	  printf("inex flag = %d\n", c); 
	  exit(1);
	}

      mpfr_set(y, tmp, GMP_RNDU); 
      c = mpfr_div(z2, x, y, GMP_RNDU); 
      mpfr_div(z3, x, y, GMP_RNDU); 
      mpfr_set(z, z3, GMP_RNDU); 
      if (c != 1 || mpfr_cmp(z2, z))
	{
	  fprintf(stderr, "Error in mpfr_div rnd=GMP_RNDU\n");
	  printf("got        "); mpfr_print_binary(z2); putchar('\n');
	  printf("instead of "); mpfr_print_binary(z); putchar('\n');
	  printf("inex flag = %d\n", c); 
	  exit(1);
	}      
    }

  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);
  mpfr_clear (z2);
  mpfr_clear (z3);
  mpfr_clear (tmp);
}

#define MAX_PREC 100

void
check_inexact (void)
{
  mpfr_t x, y, z, u;
  mp_prec_t px, py, pu;
  int inexact, cmp;
  mp_rnd_t rnd;
  
  mpfr_init (x);
  mpfr_init (y);
  mpfr_init (z);
  mpfr_init (u);

  mpfr_set_prec (x, 33);
  mpfr_set_str_raw (x, "0.101111100011011101010011101100001E0");
  mpfr_set_prec (u, 2);
  mpfr_set_str_raw (u, "0.1E0");
  mpfr_set_prec (y, 28);
  if ((inexact = mpfr_div (y, x, u, GMP_RNDN) >= 0))
    {
      fprintf (stderr, "Wrong inexact flag (1): expected -1, got %d\n",
	       inexact);
      exit (1);
    }

  mpfr_set_prec (x, 129);
  mpfr_set_str_raw (x, "0.111110101111001100000101011100101100110011011101010001000110110101100101000010000001110110100001101010001010100010001111001101010E-2"); 
  mpfr_set_prec (u, 15);
  mpfr_set_str_raw (u, "0.101101000001100E-1");
  mpfr_set_prec (y, 92);
  if ((inexact = mpfr_div (y, x, u, GMP_RNDN) <= 0))
    {
      fprintf (stderr, "Wrong inexact flag (1): expected 1, got %d\n",
	       inexact);
      mpfr_print_binary(y); putchar('\n'); 
      exit (1);
    }

  for (px=2; px<MAX_PREC; px++)
    {
      mpfr_set_prec (x, px);
      mpfr_random (x);
      for (pu=2; pu<=MAX_PREC; pu++)
	{
	  mpfr_set_prec (u, pu);
	  do { mpfr_random (u); } while (mpfr_cmp_ui (u, 0) == 0);
	  for (py=2; py<=MAX_PREC; py++)
	    {
	      mpfr_set_prec (y, py);
	      mpfr_set_prec (z, py + pu);
	      for (rnd=0; rnd<4; rnd++)
		{
		  inexact = mpfr_div (y, x, u, rnd);
		  if (mpfr_mul (z, y, u, rnd))
		    {
		      fprintf (stderr, "z <- y * u should be exact\n");
		      exit (1);
		    }
		  cmp = mpfr_cmp (z, x);
		  if (((inexact == 0) && (cmp != 0)) ||
		      ((inexact > 0) && (cmp <= 0)) ||
		      ((inexact < 0) && (cmp >= 0)))
		    {
		      fprintf (stderr, "Wrong inexact flag for rnd=%s\n",
			   mpfr_print_rnd_mode(rnd));
		      printf ("expected %d, got %d\n", cmp, inexact);
		      printf ("x="); mpfr_print_binary (x); putchar ('\n');
		      printf ("u="); mpfr_print_binary (u); putchar ('\n');
		      printf ("y="); mpfr_print_binary (y); putchar ('\n');
		      printf ("y*u="); mpfr_print_binary (z); putchar ('\n');
		      exit (1);
		    }
		}
	    }
	}
    }

  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);
  mpfr_clear (u);
}

void
check_nan (void)
{
  mpfr_t  a, d, q;

  mpfr_init2 (a, 100L);
  mpfr_init2 (d, 100L);
  mpfr_init2 (q, 100L);

  /* 1/nan == nan */
  mpfr_set_ui (a, 1L, GMP_RNDN);
  MPFR_SET_NAN (d);
  ASSERT_ALWAYS (mpfr_div (q, a, d, GMP_RNDZ) == 0); /* exact */
  ASSERT_ALWAYS (mpfr_nan_p (q));

  /* nan/1 == nan */
  MPFR_SET_NAN (a);
  mpfr_set_ui (d, 1L, GMP_RNDN);
  ASSERT_ALWAYS (mpfr_div (q, a, d, GMP_RNDZ) == 0); /* exact */
  ASSERT_ALWAYS (mpfr_nan_p (q));

  /* +inf/1 == +inf */
  MPFR_CLEAR_FLAGS (a);
  MPFR_SET_INF (a);
  MPFR_SET_POS (a);
  mpfr_set_ui (d, 1L, GMP_RNDN);
  ASSERT_ALWAYS (mpfr_div (q, a, d, GMP_RNDZ) == 0); /* exact */
  ASSERT_ALWAYS (mpfr_inf_p (q));
  ASSERT_ALWAYS (mpfr_sgn (q) > 0);

  /* 1/+inf == 0 */
  mpfr_set_ui (a, 1L, GMP_RNDN);
  MPFR_CLEAR_FLAGS (d);
  MPFR_SET_INF (d);
  MPFR_SET_POS (d);
  ASSERT_ALWAYS (mpfr_div (q, a, d, GMP_RNDZ) == 0); /* exact */
  ASSERT_ALWAYS (mpfr_number_p (q));
  ASSERT_ALWAYS (mpfr_sgn (q) == 0);

  /* 0/0 == nan */
  mpfr_set_ui (a, 0L, GMP_RNDN);
  mpfr_set_ui (d, 0L, GMP_RNDN);
  ASSERT_ALWAYS (mpfr_div (q, a, d, GMP_RNDZ) == 0); /* exact */
  ASSERT_ALWAYS (mpfr_nan_p (q));

  /* +inf/+inf == nan */
  MPFR_CLEAR_FLAGS (a);
  MPFR_SET_INF (a);
  MPFR_SET_POS (a);
  MPFR_CLEAR_FLAGS (d);
  MPFR_SET_INF (d);
  MPFR_SET_POS (d);
  ASSERT_ALWAYS (mpfr_div (q, a, d, GMP_RNDZ) == 0); /* exact */
  ASSERT_ALWAYS (mpfr_nan_p (q));

  mpfr_clear (a);
  mpfr_clear (d);
  mpfr_clear (q);
}


int
main (int argc, char *argv[])
{
  mpfr_t x, y, z; 

#ifdef MPFR_HAVE_FESETROUND
  int N, i;
  double n, d, e;

  mpfr_test_init ();
#endif

  check_inexact(); 

  mpfr_init2 (x, 64);
  mpfr_init2 (y, 64);
  mpfr_init2 (z, 64);

  mpfr_set_str_raw(x, "1.00100100110110101001010010101111000001011100100101010000000000E54"); 
  mpfr_set_str_raw(y, "1.00000000000000000000000000000000000000000000000000000000000000E584"); 
  mpfr_div(z, x, y, GMP_RNDU); 

  check_nan ();
  check_lowr(); 
  check_float(); /* checks single precision */
  check_convergence();
  check53(0.0, 1.0, GMP_RNDZ, 0.0);
  check53(-7.4988969224688591e63, 4.8816866450288732e306, GMP_RNDD,
	  -1.5361282826510687291e-243);
  check53(-1.33225773037748601769e+199, 3.63449540676937123913e+79, GMP_RNDZ,
	  -3.6655920045905428978e119);
  check4(4.0, 4.503599627370496e15, GMP_RNDZ, 62, 0.0);
  check4(1.0, 2.10263340267725788209e+187, GMP_RNDU, 65, 0.0);
  check4(2.44394909079968374564e-150, 2.10263340267725788209e+187, GMP_RNDU,
	 65, 0.0);
  check53(9.89438396044940256501e-134, 5.93472984109987421717e-67, GMP_RNDU,
	  1.6672003992376663654e-67);
  check53(9.89438396044940256501e-134, -5.93472984109987421717e-67, GMP_RNDU,
	  -1.6672003992376663654e-67);
  check53(-4.53063926135729747564e-308, 7.02293374921793516813e-84, GMP_RNDD,
	  -6.4512060388748850857e-225);
  check53(6.25089225176473806123e-01, -2.35527154824420243364e-230, GMP_RNDD,
	  -2.6540006635008291192e229);
  check53(6.52308934689126e15, -1.62063546601505417497e273, GMP_RNDN,
	  -4.0250194961676020848e-258);
  check53(1.04636807108079349236e-189, 3.72295730823253012954e-292, GMP_RNDZ,
	  2.810583051186143125e102);

#ifdef MPFR_HAVE_FESETROUND
  N = (argc>1) ? atoi(argv[1]) : 10000;
  SEED_RAND (time(NULL));
  for (i=0;i<N;i++)
    {
      do { n = drand(); d = drand(); e = ABS(n)/ABS(d); }
      /* smallest normalized is 2^(-1022), largest is 2^(1023)*(2-2^(-52)) */
      while (e>=MAXNORM || e<MINNORM);
      check4 (n, d, LONG_RAND() % 4, 53, 0.0);
    }
#endif

  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);

  return 0;
}