texp.c

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

/* Test file for mpfr_exp.

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 <math.h>
#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"

int check3 _PROTO((double, mp_rnd_t, double)); 
int check_large _PROTO((double, int, mp_rnd_t)); 
int check_worst_case _PROTO((double, double)); 
int check_worst_cases _PROTO((void)); 
void compare_exp2_exp3 _PROTO((int)); 

int maxu=0;

#define check(d, r) check3(d, r, 0.0)

/* returns the number of ulp of error */
int
check3 (double d, mp_rnd_t rnd, double e)
{
  mpfr_t x, y; double f; int u=0, ck=0;

  mpfr_init2(x, 53); mpfr_init2(y, 53);
#ifdef MPFR_HAVE_FESETROUND
  mpfr_set_machine_rnd_mode(rnd);
#endif
  if (e==0.0) e = exp(d); else ck=1; /* really check */
  mpfr_set_d(x, d, rnd); 
  mpfr_exp(y, x, rnd); 
  f = mpfr_get_d1 (y);
  if (f != e && (!isnan(f) || !isnan(e))) {
    u = ulp(e, f);
    if (u<0) {
      if (u == (mp_limb_t) 1 << (mp_bits_per_limb-1)) u += 1;
      u=-u;
    }
    if (u!=0) {
      if (ck) {
	printf("mpfr_exp failed for x=%1.20e, rnd=%s\n", d,
	       mpfr_print_rnd_mode(rnd));
	printf("expected result is %1.20e, got %1.20e, dif=%d ulp\n",e,f,u);
	exit(1);
      }
      else if (u>maxu) {
	maxu=u;
	printf("mpfr_exp differs from libm.a for x=%1.20e, rnd=%s\n",d,
	       mpfr_print_rnd_mode(rnd));
	printf("libm.a gave %1.20e, mpfr_exp got %1.20e, dif=%d ulp\n",e,f,u);
      }
    }
  }
  mpfr_clear(x); mpfr_clear(y);
  return u;
}

/* computes n bits of exp(d) */
int
check_large (double d, int n, mp_rnd_t rnd)
{
  mpfr_t x; mpfr_t y;
  
  mpfr_init2(x, n); mpfr_init2(y, n);
  if (d==0.0) { /* try exp(Pi*sqrt(163)/3)-640320 */
    mpfr_set_d(x, 163.0, rnd);
    mpfr_sqrt(x, x, rnd);
    mpfr_const_pi(y, rnd);
    mpfr_mul(x, x, y, rnd);
    mpfr_div_ui(x, x, 3, rnd);
  }
  else mpfr_set_d(x, d, rnd);
  mpfr_exp (y, x, rnd);
  if (d==0.0) {
    mpfr_set_d(x, 640320.0, rnd);
    mpfr_sub(y, y, x, rnd);
    printf("exp(Pi*sqrt(163)/3)-640320=");
  }
  else printf("exp(%1.20e)=",d); 
  mpfr_out_str(stdout, 10, 0, y, rnd);
  putchar('\n');
  printf(" ="); mpfr_print_binary(y); putchar('\n');
  if (n==53) printf(" =%1.20e\n", mpfr_get_d1 (y));

  mpfr_clear(x); mpfr_clear(y);
  return 0;
}

/* expx is the value of exp(X) rounded towards -infinity */
int
check_worst_case (double X, double expx)
{
  mpfr_t x, y;

  mpfr_init2(x, 53); mpfr_init2(y, 53);
  mpfr_set_d(x, X, GMP_RNDN);
  mpfr_exp(y, x, GMP_RNDD);
  if (mpfr_get_d1 (y) != expx) {
    fprintf(stderr, "exp(x) rounded towards -infinity is wrong\n"); exit(1);
  }
  mpfr_exp(x, x, GMP_RNDN);
  mpfr_set_d(x, X, GMP_RNDN);
  mpfr_exp(x, x, GMP_RNDU);
  mpfr_add_one_ulp(y, GMP_RNDN);
  if (mpfr_cmp(x,y)) {
    fprintf(stderr, "exp(x) rounded towards +infinity is wrong\n"); exit(1);
  }
  mpfr_clear(x); mpfr_clear(y);
  return 0;
}

/* worst cases communicated by Jean-Michel Muller and Vincent Lefevre */
int
check_worst_cases (void)
{
  mpfr_t x; mpfr_t y;

  mpfr_init(x);
  mpfr_set_prec (x, 53);

  check_worst_case(4.44089209850062517562e-16, 1.00000000000000022204);
  check_worst_case(6.39488462184069720009e-14, 1.00000000000006372680);
  check_worst_case(1.84741111297455401935e-12, 1.00000000000184718907);
  check_worst_case(1.76177628026265550074e-10, 1.00000000017617751702);
  check3(1.76177628026265550074e-10, GMP_RNDN, 1.00000000017617773906);
  check_worst_case(7.54175277499595900852e-10, 1.00000000075417516676);
  check3(7.54175277499595900852e-10, GMP_RNDN, 1.00000000075417538881);
  /* bug found by Vincent Lefe`vre on December 8, 1999 */
  check3(-5.42410311287441459172e+02, GMP_RNDN, 2.7176584868845723e-236);
  /* further cases communicated by Vincent Lefe`vre on January 27, 2000 */
  check3(-1.32920285897904911589e-10, GMP_RNDN, 0.999999999867079769622);
  check3(-1.44037948245738330735e-10, GMP_RNDN, 0.9999999998559621072757);
  check3(-1.66795910430705305937e-10, GMP_RNDZ, 0.9999999998332040895832);
  check3(-1.64310953745426656203e-10, GMP_RNDN, 0.9999999998356891017792);
  check3(-1.38323574826034659172e-10, GMP_RNDZ, 0.9999999998616764251835);
  check3(-1.23621668465115401498e-10, GMP_RNDZ, 0.9999999998763783315425);

  mpfr_set_prec (x, 601);
  mpfr_set_str_raw (x, "0.1000100010110110101110100101000100001110000100000100010100001110110111000010010110000111010010001011110010011101111111011101010001100110111100100001101101000111111011010010011001001100110111110010010010101010100011110110010010101111000111110011111110101101100111101100001000110000000111010100001111000000011101000011111101010011010010110101101010100010000000001001000111111111011011010011010100101101111101000101100011101111000110111010010100011001100000010001111011110110111101011011000100011000010100110101001101001111110110001111101000110010011101100100101000001010011011010010110100001101110100100E0");
  mpfr_init2 (y, 601);
  mpfr_exp_2 (y, x, GMP_RNDD);
  mpfr_exp3 (x, x, GMP_RNDD);
  if (mpfr_cmp (x, y)) {
    fprintf (stderr, "mpfr_exp_2 and mpfr_exp3 for prec=601\n");
    exit (1);
  }

  mpfr_clear (x);
  mpfr_clear (y);
  return 0;
}

void
compare_exp2_exp3 (int n)
{
  mpfr_t x, y, z; int prec; mp_rnd_t rnd;

  mpfr_init (x);
  mpfr_init (y);
  mpfr_init (z);
  for (prec=20; prec<=n; prec++)
    {
      mpfr_set_prec (x, prec);
      mpfr_set_prec (y, prec);
      mpfr_set_prec (z, prec);
      mpfr_random (x);
      rnd = LONG_RAND() % 4;
      mpfr_exp_2 (y, x, rnd);
      mpfr_exp3 (z, x, rnd);
      if (mpfr_cmp (y,z))
        {
          printf ("mpfr_exp_2 and mpfr_exp3 disagree for rnd=%s and\nx=",
                  mpfr_print_rnd_mode (rnd));
          mpfr_print_binary (x);
          putchar ('\n');
          printf ("mpfr_exp_2 gives  ");
          mpfr_print_binary (y);
          putchar ('\n');
          printf ("mpfr_exp3 gives ");
          mpfr_print_binary (z);
          putchar ('\n');
          exit (1);
        }
  }
  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);
}

#define TEST_FUNCTION mpfr_exp
#include "tgeneric.c"

int
main (int argc, char *argv[])
{
#ifdef MPFR_HAVE_FESETROUND
  int i, N, s=0, e, maxe=0;
  double lo, hi;
#endif
  double d;

  test_generic (2, 100, 100);

  if (argc == 4)
    {
      check_large (atof(argv[1]), atoi(argv[2]), atoi(argv[3])); 
      exit(1);
    }

  compare_exp2_exp3(500);
  check_worst_cases();
  check3(0.0, GMP_RNDU, 1.0);
  check3(-8.88024741073346941839e-17, GMP_RNDU, 1.0);
  check3(8.70772839244701057915e-01, GMP_RNDN, 2.38875626491680437269);
  check3(1.0, GMP_RNDN, 2.71828182845904509080);
  check3(-3.42135637628104173534e-07, GMP_RNDZ, 0.999999657864420798958);
  /* worst case for argument reduction, very near from 5*log(2),
     thanks to Jean-Michel Muller
   */
  check3(3.4657359027997265421, GMP_RNDN, 32.0);
  check3(3.4657359027997265421, GMP_RNDU, 32.0);
  check3(3.4657359027997265421, GMP_RNDD, 31.999999999999996447);
  check3(2.26523754332090625496e+01, GMP_RNDD, 6.8833785261699581146e9);
  check3(1.31478962104089092122e+01, GMP_RNDZ, 5.12930793917860137299e+05);
  check3(4.25637507920002378103e-01, GMP_RNDU, 1.53056585656161181497e+00);
  check3(6.26551618962329307459e-16, GMP_RNDU, 1.00000000000000066613e+00);
  check3(-3.35589513871216568383e-03, GMP_RNDD, 9.96649729583626853291e-01);
  check3(1.95151388850007272424e+01, GMP_RNDU, 2.98756340674767792225e+08);
  check3(2.45045953503350730784e+01, GMP_RNDN, 4.38743344916128387451e+10);
  check3(2.58165606081678085104e+01, GMP_RNDD, 1.62925781879432281494e+11);
  check3(-2.36539020084338638128e+01, GMP_RNDZ, 5.33630792749924762447e-11);
  check3(2.39211946135858077866e+01, GMP_RNDU, 2.44817704330214385986e+10);
  check3(-2.78190533055889162029e+01, GMP_RNDZ, 8.2858803483596879512e-13); 
  check3(2.64028186174889789584e+01, GMP_RNDD, 2.9281844652878973388e11);
  check3(2.92086338843268329413e+01, GMP_RNDZ, 4.8433797301907177734e12);
  check3(-2.46355324071459982349e+01, GMP_RNDZ, 1.9995129297760994791e-11);
  check3(-2.23509444608605427618e+01, GMP_RNDZ, 1.9638492867489702307e-10);
  check3(-2.41175390197331687148e+01, GMP_RNDD, 3.3564940885530624592e-11);
  check3(2.46363885231578088053e+01, GMP_RNDU, 5.0055014282693267822e10);
  d = 7819821913254249.0 / 70368744177664.0;
  check3(d, GMP_RNDN, 1.8262572323517295459e48);
  check3(-3.56196340354684821250e+02, GMP_RNDN, 2.0225297096141478156e-155);
  check3(6.59678273772710895173e+02, GMP_RNDU, 3.1234469273830195529e286); 
  check3(5.13772529701934331570e+02, GMP_RNDD, 1.3445427121297197752e223); 
  check3(3.57430211008718345056e+02, GMP_RNDD, 1.6981197246857298443e155); 
  check3(3.82001814471465536371e+02, GMP_RNDU, 7.9667300591087367805e165); 
  check3(5.92396038219384422518e+02, GMP_RNDD, 1.880747529554661989e257); 
  check3(-5.02678550462488090034e+02, GMP_RNDU, 4.8919201895446217839e-219);
  check3(5.30015757134837031117e+02, GMP_RNDD, 1.5237672861171573939e230);
  check3(5.16239362447650933063e+02, GMP_RNDZ, 1.5845518406744492105e224);
  check3(6.00812634798592370977e-01, GMP_RNDN, 1.823600119339019443);
#ifdef MPFR_HAVE_FESETROUND
  SEED_RAND (time(NULL));
  N = (argc==1) ? 0 : atoi(argv[1]);
  lo = (argc>=3) ? atof(argv[2]) : -7.083964185e2;
  hi = (argc>=4) ? atof(argv[3]) : 7.097827129e2;
  for (i=0;i<N;i++) {
    /* select d such that exp(d) can be represented as a normalized
       machine double-precision number, 
       i.e. 2^(-1022) <= exp(d) <= 2^(1023)*(2-2^(-52)) */
    d = lo + (hi-lo)*DBL_RAND();
    e = check(d, LONG_RAND() % 4);
    s += e;
    if (e>maxe) maxe=e;
  }
  if (N) printf("mean error=%1.2e max error=%d\n", (double)s/(double)N,maxe);
#endif

  return 0;
}