/* Test file for mpfr_exp.
Copyright 1999, 2001-2017 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU 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 3 of the License, or (at your
option) any later version.
The GNU 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 GNU MPFR Library; see the file COPYING.LESSER. If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#include "mpfr-test.h"
#ifdef CHECK_EXTERNAL
static int
test_exp (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
{
int res;
int ok = rnd_mode == MPFR_RNDN && mpfr_number_p (b) && mpfr_get_prec (a)>=53;
if (ok)
{
mpfr_print_raw (b);
}
res = mpfr_exp (a, b, rnd_mode);
if (ok)
{
printf (" ");
mpfr_print_raw (a);
printf ("\n");
}
return res;
}
#else
#define test_exp mpfr_exp
#endif
/* returns the number of ulp of error */
static void
check3 (const char *op, mpfr_rnd_t rnd, const char *res)
{
mpfr_t x, y;
mpfr_inits2 (53, x, y, (mpfr_ptr) 0);
/* y negative. If we forget to set the sign in mpfr_exp, we'll see it. */
mpfr_set_si (y, -1, MPFR_RNDN);
mpfr_set_str1 (x, op);
test_exp (y, x, rnd);
if (mpfr_cmp_str1 (y, res) )
{
printf ("mpfr_exp failed for x=%s, rnd=%s\n",
op, mpfr_print_rnd_mode (rnd));
printf ("expected result is %s, got ", res);
mpfr_out_str (stdout, 10, 0, y, MPFR_RNDN);
putchar('\n');
exit (1);
}
mpfr_clears (x, y, (mpfr_ptr) 0);
}
/* expx is the value of exp(X) rounded toward -infinity */
static void
check_worst_case (const char *Xs, const char *expxs)
{
mpfr_t x, y;
mpfr_inits2 (53, x, y, (mpfr_ptr) 0);
mpfr_set_str1(x, Xs);
test_exp(y, x, MPFR_RNDD);
if (mpfr_cmp_str1 (y, expxs))
{
printf ("exp(x) rounded toward -infinity is wrong\n");
exit(1);
}
mpfr_set_str1(x, Xs);
test_exp(x, x, MPFR_RNDU);
mpfr_nexttoinf (y);
if (mpfr_cmp(x,y))
{
printf ("exp(x) rounded toward +infinity is wrong\n");
exit(1);
}
mpfr_clears (x, y, (mpfr_ptr) 0);
}
/* worst cases communicated by Jean-Michel Muller and Vincent Lefevre */
static 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", MPFR_RNDN, "1.00000000017617773906");
check_worst_case("7.54175277499595900852e-10", "1.00000000075417516676");
check3("7.54175277499595900852e-10", MPFR_RNDN, "1.00000000075417538881");
/* bug found by Vincent Lefe`vre on December 8, 1999 */
check3("-5.42410311287441459172e+02", MPFR_RNDN, "2.7176584868845723e-236");
/* further cases communicated by Vincent Lefe`vre on January 27, 2000 */
check3("-1.32920285897904911589e-10", MPFR_RNDN, "0.999999999867079769622");
check3("-1.44037948245738330735e-10", MPFR_RNDN, "0.9999999998559621072757");
check3("-1.66795910430705305937e-10", MPFR_RNDZ, "0.9999999998332040895832");
check3("-1.64310953745426656203e-10", MPFR_RNDN, "0.9999999998356891017792");
check3("-1.38323574826034659172e-10", MPFR_RNDZ, "0.9999999998616764251835");
check3("-1.23621668465115401498e-10", MPFR_RNDZ, "0.9999999998763783315425");
mpfr_set_prec (x, 601);
mpfr_set_str (x, "0.88b6ba510e10450edc258748bc9dfdd466f21b47ed264cdf24aa8f64af1f3fad9ec2301d43c0743f534b5aa20091ff6d352df458ef1ba519811ef6f5b11853534fd8fa32764a0a6d2d0dd20@0", 16, MPFR_RNDZ);
mpfr_init2 (y, 601);
mpfr_exp_2 (y, x, MPFR_RNDD);
mpfr_exp_3 (x, x, MPFR_RNDD);
if (mpfr_cmp (x, y))
{
printf ("mpfr_exp_2 and mpfr_exp_3 differ for prec=601\n");
printf ("mpfr_exp_2 gives ");
mpfr_out_str (stdout, 2, 0, y, MPFR_RNDN);
printf ("\nmpfr_exp_3 gives ");
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_prec (x, 13001);
mpfr_set_prec (y, 13001);
mpfr_urandomb (x, RANDS);
mpfr_exp_3 (y, x, MPFR_RNDN);
mpfr_exp_2 (x, x, MPFR_RNDN);
if (mpfr_cmp (x, y))
{
printf ("mpfr_exp_2 and mpfr_exp_3 differ for prec=13001\n");
exit (1);
}
mpfr_set_prec (x, 118);
mpfr_set_str_binary (x, "0.1110010100011101010000111110011000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86");
mpfr_set_prec (y, 118);
mpfr_exp_2 (y, x, MPFR_RNDU);
mpfr_exp_3 (x, x, MPFR_RNDU);
if (mpfr_cmp (x, y))
{
printf ("mpfr_exp_2 and mpfr_exp_3 differ for prec=118\n");
printf ("mpfr_exp_2 gives ");
mpfr_out_str (stdout, 2, 0, y, MPFR_RNDN);
printf ("\nmpfr_exp_3 gives ");
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
return 0;
}
static void
compare_exp2_exp3 (mpfr_prec_t p0, mpfr_prec_t p1)
{
mpfr_t x, y, z;
mpfr_prec_t prec;
mpfr_rnd_t rnd;
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
for (prec = p0; prec <= p1; prec ++)
{
mpfr_set_prec (x, prec);
mpfr_set_prec (y, prec);
mpfr_set_prec (z, prec);
do
mpfr_urandomb (x, RANDS);
while (MPFR_IS_ZERO (x)); /* 0 is handled by mpfr_exp only */
rnd = RND_RAND ();
mpfr_exp_2 (y, x, rnd);
mpfr_exp_3 (z, x, rnd);
if (mpfr_cmp (y,z))
{
printf ("mpfr_exp_2 and mpfr_exp_3 disagree for rnd=%s and\nx=",
mpfr_print_rnd_mode (rnd));
mpfr_print_binary (x);
puts ("");
printf ("mpfr_exp_2 gives ");
mpfr_print_binary (y);
puts ("");
printf ("mpfr_exp_3 gives ");
mpfr_print_binary (z);
puts ("");
exit (1);
}
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
static void
check_large (void)
{
mpfr_t x, z;
mpfr_prec_t prec;
/* bug found by Patrick Pe'lissier on 7 Jun 2004 */
prec = 203780;
mpfr_init2 (x, prec);
mpfr_init2 (z, prec);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_sqrt (x, x, MPFR_RNDN);
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
mpfr_exp_3 (z, x, MPFR_RNDN);
mpfr_clear (x);
mpfr_clear (z);
}
#define TEST_FUNCTION test_exp
#define TEST_RANDOM_EMIN -36
#define TEST_RANDOM_EMAX 36
#include "tgeneric.c"
static void
check_special (void)
{
mpfr_t x, y, z;
mpfr_exp_t emin, emax;
emin = mpfr_get_emin ();
emax = mpfr_get_emax ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
/* check exp(NaN) = NaN */
mpfr_set_nan (x);
test_exp (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for exp(NaN)\n");
exit (1);
}
/* check exp(+inf) = +inf */
mpfr_set_inf (x, 1);
test_exp (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for exp(+inf)\n");
exit (1);
}
/* check exp(-inf) = +0 */
mpfr_set_inf (x, -1);
test_exp (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) < 0)
{
printf ("Error for exp(-inf)\n");
exit (1);
}
/* Check overflow. Corner case of mpfr_exp_2 */
mpfr_set_prec (x, 64);
mpfr_set_emax (MPFR_EMAX_DEFAULT);
mpfr_set_emin (MPFR_EMIN_DEFAULT);
mpfr_set_str (x,
"0.1011000101110010000101111111010100001100000001110001100111001101E30",
2, MPFR_RNDN);
mpfr_exp (x, x, MPFR_RNDD);
if (mpfr_cmp_str (x,
".1111111111111111111111111111111111111111111111111111111111111111E1073741823",
2, MPFR_RNDN) != 0)
{
printf ("Wrong overflow detection in mpfr_exp\n");
mpfr_dump (x);
exit (1);
}
/* Check underflow. Corner case of mpfr_exp_2 */
mpfr_set_str (x,
"-0.1011000101110010000101111111011111010001110011110111100110101100E30",
2, MPFR_RNDN);
mpfr_exp (x, x, MPFR_RNDN);
if (mpfr_cmp_str (x, "0.1E-1073741823", 2, MPFR_RNDN) != 0)
{
printf ("Wrong underflow (1) detection in mpfr_exp\n");
mpfr_dump (x);
exit (1);
}
mpfr_set_str (x,
"-0.1011001101110010000101111111011111010001110011110111100110111101E30",
2, MPFR_RNDN);
mpfr_exp (x, x, MPFR_RNDN);
if (mpfr_cmp_ui (x, 0) != 0)
{
printf ("Wrong underflow (2) detection in mpfr_exp\n");
mpfr_dump (x);
exit (1);
}
/* Check overflow. Corner case of mpfr_exp_3 */
if (MPFR_PREC_MAX >= MPFR_EXP_THRESHOLD + 10 && MPFR_PREC_MAX >= 64)
{
/* this ensures that for small MPFR_EXP_THRESHOLD, the following
mpfr_set_str conversion is exact */
mpfr_set_prec (x, (MPFR_EXP_THRESHOLD + 10 > 64)
? MPFR_EXP_THRESHOLD + 10 : 64);
mpfr_set_str (x,
"0.1011000101110010000101111111010100001100000001110001100111001101E30",
2, MPFR_RNDN);
mpfr_clear_overflow ();
mpfr_exp (x, x, MPFR_RNDD);
if (!mpfr_overflow_p ())
{
printf ("Wrong overflow detection in mpfr_exp_3\n");
mpfr_dump (x);
exit (1);
}
/* Check underflow. Corner case of mpfr_exp_3 */
mpfr_set_str (x,
"-0.1011000101110010000101111111011111010001110011110111100110101100E30",
2, MPFR_RNDN);
mpfr_clear_underflow ();
mpfr_exp (x, x, MPFR_RNDN);
if (!mpfr_underflow_p ())
{
printf ("Wrong underflow detection in mpfr_exp_3\n");
mpfr_dump (x);
exit (1);
}
mpfr_set_prec (x, 53);
}
/* check overflow */
set_emax (10);
mpfr_set_ui (x, 7, MPFR_RNDN);
test_exp (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for exp(7) for emax=10\n");
exit (1);
}
set_emax (emax);
/* check underflow */
set_emin (-10);
mpfr_set_si (x, -9, MPFR_RNDN);
test_exp (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) < 0)
{
printf ("Error for exp(-9) for emin=-10\n");
printf ("Expected +0\n");
printf ("Got "); mpfr_print_binary (y); puts ("");
exit (1);
}
set_emin (emin);
/* check case EXP(x) < -precy */
mpfr_set_prec (y, 2);
mpfr_set_str_binary (x, "-0.1E-3");
test_exp (y, x, MPFR_RNDD);
if (mpfr_cmp_ui_2exp (y, 3, -2))
{
printf ("Error for exp(-1/16), prec=2, RNDD\n");
printf ("expected 0.11, got ");
mpfr_dump (y);
exit (1);
}
test_exp (y, x, MPFR_RNDZ);
if (mpfr_cmp_ui_2exp (y, 3, -2))
{
printf ("Error for exp(-1/16), prec=2, RNDZ\n");
printf ("expected 0.11, got ");
mpfr_dump (y);
exit (1);
}
mpfr_set_str_binary (x, "0.1E-3");
test_exp (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 1))
{
printf ("Error for exp(1/16), prec=2, RNDN\n");
exit (1);
}
test_exp (y, x, MPFR_RNDU);
if (mpfr_cmp_ui_2exp (y, 3, -1))
{
printf ("Error for exp(1/16), prec=2, RNDU\n");
exit (1);
}
/* bug reported by Franky Backeljauw, 28 Mar 2003 */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str_binary (x, "1.1101011000111101011110000111010010101001101001110111e28");
test_exp (y, x, MPFR_RNDN);
mpfr_set_prec (x, 153);
mpfr_set_prec (z, 153);
mpfr_set_str_binary (x, "1.1101011000111101011110000111010010101001101001110111e28");
test_exp (z, x, MPFR_RNDN);
mpfr_prec_round (z, 53, MPFR_RNDN);
if (mpfr_cmp (y, z))
{
printf ("Error in mpfr_exp for large argument\n");
exit (1);
}
/* corner cases in mpfr_exp_3 */
mpfr_set_prec (x, 2);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_set_prec (y, 2);
mpfr_exp_3 (y, x, MPFR_RNDN);
/* Check some little things about overflow detection */
set_emin (-125);
set_emax (128);
mpfr_set_prec (x, 107);
mpfr_set_prec (y, 107);
mpfr_set_str_binary (x, "0.11110000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000"
"00000000E4");
test_exp (y, x, MPFR_RNDN);
if (mpfr_cmp_str (y, "0.11000111100001100110010101111101011010010101010000"
"1101110111100010111001011111111000110111001011001101010"
"01E22", 2, MPFR_RNDN))
{
printf ("Special overflow error (1)\n");
mpfr_dump (y);
exit (1);
}
set_emin (emin);
set_emax (emax);
/* Check for overflow producing a segfault with HUGE exponent */
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_mul_2ui (x, x, 32, MPFR_RNDN);
test_exp (y, x, MPFR_RNDN); /* Can't test return value: May overflow or not*/
/* Bug due to wrong approximation of (x)/log2 */
mpfr_set_prec (x, 163);
mpfr_set_str (x, "-4.28ac8fceeadcda06bb56359017b1c81b85b392e7", 16,
MPFR_RNDN);
mpfr_exp (x, x, MPFR_RNDN);
if (mpfr_cmp_str (x, "3.fffffffffffffffffffffffffffffffffffffffe8@-2",
16, MPFR_RNDN))
{
printf ("Error for x= -4.28ac8fceeadcda06bb56359017b1c81b85b392e7");
printf ("expected 3.fffffffffffffffffffffffffffffffffffffffe8@-2");
printf ("Got ");
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
}
/* bug found by Guillaume Melquiond, 13 Sep 2005 */
mpfr_set_prec (x, 53);
mpfr_set_str_binary (x, "-1E-400");
mpfr_exp (x, x, MPFR_RNDZ);
if (mpfr_cmp_ui (x, 1) == 0)
{
printf ("Error for exp(-2^(-400))\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
/* check sign of inexact flag */
static void
check_inexact (void)
{
mpfr_t x, y;
int inexact;
mpfr_init2 (x, 53);
mpfr_init2 (y, 53);
mpfr_set_str_binary (x,
"1.0000000000001001000110100100101000001101101011100101e2");
inexact = test_exp (y, x, MPFR_RNDN);
if (inexact <= 0)
{
printf ("Wrong inexact flag (Got %d instead of 1)\n", inexact);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
static void
check_exp10(void)
{
mpfr_t x;
int inexact;
mpfr_init2 (x, 200);
mpfr_set_ui(x, 4, MPFR_RNDN);
inexact = mpfr_exp10 (x, x, MPFR_RNDN);
if (mpfr_cmp_ui(x, 10*10*10*10))
{
printf ("exp10: Wrong returned value\n");
exit (1);
}
if (inexact != 0)
{
printf ("exp10: Wrong inexact flag\n");
exit (1);
}
mpfr_clear (x);
}
static void
overflowed_exp0 (void)
{
mpfr_t x, y;
int emax, i, inex, rnd, err = 0;
mpfr_exp_t old_emax;
old_emax = mpfr_get_emax ();
mpfr_init2 (x, 8);
mpfr_init2 (y, 8);
for (emax = -1; emax <= 0; emax++)
{
mpfr_set_ui_2exp (y, 1, emax, MPFR_RNDN);
mpfr_nextbelow (y);
set_emax (emax); /* 1 is not representable. */
/* and if emax < 0, 1 - eps is not representable either. */
for (i = -1; i <= 1; i++)
RND_LOOP (rnd)
{
mpfr_set_si_2exp (x, i, -512 * ABS (i), MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_exp (x, x, (mpfr_rnd_t) rnd);
if ((i >= 0 || emax < 0 || rnd == MPFR_RNDN || rnd == MPFR_RNDU) &&
! mpfr_overflow_p ())
{
printf ("Error in overflowed_exp0 (i = %d, rnd = %s):\n"
" The overflow flag is not set.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (rnd == MPFR_RNDZ || rnd == MPFR_RNDD)
{
if (inex >= 0)
{
printf ("Error in overflowed_exp0 (i = %d, rnd = %s):\n"
" The inexact value must be negative.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! mpfr_equal_p (x, y))
{
printf ("Error in overflowed_exp0 (i = %d, rnd = %s):\n"
" Got ", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (x);
printf (" instead of 0.11111111E%d.\n", emax);
err = 1;
}
}
else
{
if (inex <= 0)
{
printf ("Error in overflowed_exp0 (i = %d, rnd = %s):\n"
" The inexact value must be positive.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! (mpfr_inf_p (x) && MPFR_SIGN (x) > 0))
{
printf ("Error in overflowed_exp0 (i = %d, rnd = %s):\n"
" Got ", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (x);
printf (" instead of +Inf.\n");
err = 1;
}
}
}
set_emax (old_emax);
}
if (err)
exit (1);
mpfr_clear (x);
mpfr_clear (y);
}
/* This bug occurs in mpfr_exp_2 on a Linux-64 machine, r5475. */
static void
bug20080731 (void)
{
mpfr_exp_t emin;
mpfr_t x, y1, y2;
mpfr_prec_t prec = 64;
emin = mpfr_get_emin ();
set_emin (MPFR_EMIN_MIN);
mpfr_init2 (x, 200);
mpfr_set_str (x, "-2.c5c85fdf473de6af278ece700fcbdabd03cd0cb9ca62d8b62c@7",
16, MPFR_RNDN);
mpfr_init2 (y1, prec);
mpfr_exp (y1, x, MPFR_RNDU);
/* Compute the result with a higher internal precision. */
mpfr_init2 (y2, 300);
mpfr_exp (y2, x, MPFR_RNDU);
mpfr_prec_round (y2, prec, MPFR_RNDU);
if (mpfr_cmp0 (y1, y2) != 0)
{
printf ("Error in bug20080731\nExpected ");
mpfr_out_str (stdout, 16, 0, y2, MPFR_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 16, 0, y1, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_clears (x, y1, y2, (mpfr_ptr) 0);
set_emin (emin);
}
/* Emulate mpfr_exp with mpfr_exp_3 in the general case. */
static int
exp_3 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
int inexact;
inexact = mpfr_exp_3 (y, x, rnd_mode);
return mpfr_check_range (y, inexact, rnd_mode);
}
static void
underflow_up (int extended_emin)
{
mpfr_t minpos, x, y, t, t2;
int precx, precy;
int inex;
int rnd;
int e3;
int i, j;
mpfr_init2 (minpos, 2);
mpfr_set_ui (minpos, 0, MPFR_RNDN);
mpfr_nextabove (minpos);
/* Let's test values near the underflow boundary.
*
* Minimum representable positive number: minpos = 2^(emin - 1).
* Let's choose an MPFR number x = log(minpos) + eps, with |eps| small
* (note: eps cannot be 0, and cannot be a rational number either).
* Then exp(x) = minpos * exp(eps) ~= minpos * (1 + eps + eps^2).
* We will compute y = rnd(exp(x)) in some rounding mode, precision p.
* 1. If eps > 0, then in any rounding mode:
* rnd(exp(x)) >= minpos and no underflow.
* So, let's take x1 = rndu(log(minpos)) in some precision.
* 2. If eps < 0, then exp(x) < minpos and the result will be either 0
* or minpos. An underflow always occurs in MPFR_RNDZ and MPFR_RNDD,
* but not necessarily in MPFR_RNDN and MPFR_RNDU (this is underflow
* after rounding in an unbounded exponent range). If -a < eps < -b,
* minpos * (1 - a) < exp(x) < minpos * (1 - b + b^2).
* - If eps > -2^(-p), no underflow in MPFR_RNDU.
* - If eps > -2^(-p-1), no underflow in MPFR_RNDN.
* - If eps < - (2^(-p-1) + 2^(-2p-1)), underflow in MPFR_RNDN.
* - If eps < - (2^(-p) + 2^(-2p+1)), underflow in MPFR_RNDU.
* - In MPFR_RNDN, result is minpos iff exp(eps) > 1/2, i.e.
* - log(2) < eps < ...
*
* Moreover, since precy < MPFR_EXP_THRESHOLD (to avoid tests that take
* too much time), mpfr_exp() always selects mpfr_exp_2(); so, we need
* to test mpfr_exp_3() too. This will be done via the e3 variable:
* e3 = 0: mpfr_exp(), thus mpfr_exp_2().
* e3 = 1: mpfr_exp_3(), via the exp_3() wrapper.
* i.e.: inex = e3 ? exp_3 (y, x, rnd) : mpfr_exp (y, x, rnd);
*/
/* Case eps > 0. In revision 5461 (trunk) on a 64-bit Linux machine:
* Incorrect flags in underflow_up, eps > 0, MPFR_RNDN and extended emin
* for precx = 96, precy = 16, mpfr_exp_3
* Got 9 instead of 8.
* Note: testing this case in several precisions for x and y introduces
* some useful random. Indeed, the bug is not always triggered.
* Fixed in r5469.
*/
for (precx = 16; precx <= 128; precx += 16)
{
mpfr_init2 (x, precx);
mpfr_log (x, minpos, MPFR_RNDU);
for (precy = 16; precy <= 128; precy += 16)
{
mpfr_init2 (y, precy);
for (e3 = 0; e3 <= 1; e3++)
{
RND_LOOP (rnd)
{
int err = 0;
mpfr_clear_flags ();
inex = e3 ? exp_3 (y, x, (mpfr_rnd_t) rnd)
: mpfr_exp (y, x, (mpfr_rnd_t) rnd);
if (__gmpfr_flags != MPFR_FLAGS_INEXACT)
{
printf ("Incorrect flags in underflow_up, eps > 0, %s",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precx = %d, precy = %d, %s\n",
precx, precy, e3 ? "mpfr_exp_3" : "mpfr_exp");
printf ("Got %u instead of %u.\n", __gmpfr_flags,
(unsigned int) MPFR_FLAGS_INEXACT);
err = 1;
}
if (mpfr_cmp0 (y, minpos) < 0)
{
printf ("Incorrect result in underflow_up, eps > 0, %s",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precx = %d, precy = %d, %s\n",
precx, precy, e3 ? "mpfr_exp_3" : "mpfr_exp");
mpfr_dump (y);
err = 1;
}
MPFR_ASSERTN (inex != 0);
if (rnd == MPFR_RNDD || rnd == MPFR_RNDZ)
MPFR_ASSERTN (inex < 0);
if (rnd == MPFR_RNDU)
MPFR_ASSERTN (inex > 0);
if (err)
exit (1);
}
}
mpfr_clear (y);
}
mpfr_clear (x);
}
/* Case - log(2) < eps < 0 in MPFR_RNDN, starting with small-precision x;
* only check the result and the ternary value.
* Previous to r5453 (trunk), on 32-bit and 64-bit machines, this fails
* for precx = 65 and precy = 16, e.g.:
* exp_2.c:264: assertion failed: ...
* because mpfr_sub (r, x, r, MPFR_RNDU); yields a null value. This is
* fixed in r5453 by going to next Ziv's iteration.
*/
for (precx = sizeof(mpfr_exp_t) * CHAR_BIT + 1; precx <= 81; precx += 8)
{
mpfr_init2 (x, precx);
mpfr_log (x, minpos, MPFR_RNDD); /* |ulp| <= 1/2 */
for (precy = 16; precy <= 128; precy += 16)
{
mpfr_init2 (y, precy);
inex = mpfr_exp (y, x, MPFR_RNDN);
if (inex <= 0 || mpfr_cmp0 (y, minpos) != 0)
{
printf ("Error in underflow_up, - log(2) < eps < 0");
if (extended_emin)
printf (" and extended emin");
printf (" for prec = %d\nExpected ", precy);
mpfr_out_str (stdout, 16, 0, minpos, MPFR_RNDN);
printf (" (minimum positive MPFR number) and inex > 0\nGot ");
mpfr_out_str (stdout, 16, 0, y, MPFR_RNDN);
printf ("\nwith inex = %d\n", inex);
exit (1);
}
mpfr_clear (y);
}
mpfr_clear (x);
}
/* Cases eps ~ -2^(-p) and eps ~ -2^(-p-1). More precisely,
* _ for j = 0, eps > -2^(-(p+i)),
* _ for j = 1, eps < - (2^(-(p+i)) + 2^(1-2(p+i))),
* where i = 0 or 1.
*/
mpfr_inits2 (2, t, t2, (mpfr_ptr) 0);
for (precy = 16; precy <= 128; precy += 16)
{
mpfr_set_ui_2exp (t, 1, - precy, MPFR_RNDN); /* 2^(-p) */
mpfr_set_ui_2exp (t2, 1, 1 - 2 * precy, MPFR_RNDN); /* 2^(-2p+1) */
precx = sizeof(mpfr_exp_t) * CHAR_BIT + 2 * precy + 8;
mpfr_init2 (x, precx);
mpfr_init2 (y, precy);
for (i = 0; i <= 1; i++)
{
for (j = 0; j <= 1; j++)
{
if (j == 0)
{
/* Case eps > -2^(-(p+i)). */
mpfr_log (x, minpos, MPFR_RNDU);
}
else /* j == 1 */
{
/* Case eps < - (2^(-(p+i)) + 2^(1-2(p+i))). */
mpfr_log (x, minpos, MPFR_RNDD);
inex = mpfr_sub (x, x, t2, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
}
inex = mpfr_sub (x, x, t, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
RND_LOOP (rnd)
for (e3 = 0; e3 <= 1; e3++)
{
int err = 0;
unsigned int flags;
flags = MPFR_FLAGS_INEXACT |
(((rnd == MPFR_RNDU || rnd == MPFR_RNDA)
&& (i == 1 || j == 0)) ||
(rnd == MPFR_RNDN && (i == 1 && j == 0)) ?
0 : MPFR_FLAGS_UNDERFLOW);
mpfr_clear_flags ();
inex = e3 ? exp_3 (y, x, (mpfr_rnd_t) rnd)
: mpfr_exp (y, x, (mpfr_rnd_t) rnd);
if (__gmpfr_flags != flags)
{
printf ("Incorrect flags in underflow_up, %s",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precx = %d, precy = %d, ",
precx, precy);
if (j == 0)
printf ("eps >~ -2^(-%d)", precy + i);
else
printf ("eps <~ - (2^(-%d) + 2^(%d))",
precy + i, 1 - 2 * (precy + i));
printf (", %s\n", e3 ? "mpfr_exp_3" : "mpfr_exp");
printf ("Got %u instead of %u.\n",
__gmpfr_flags, flags);
err = 1;
}
if (rnd == MPFR_RNDU || rnd == MPFR_RNDA || rnd == MPFR_RNDN ?
mpfr_cmp0 (y, minpos) != 0 : MPFR_NOTZERO (y))
{
printf ("Incorrect result in underflow_up, %s",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precx = %d, precy = %d, ",
precx, precy);
if (j == 0)
printf ("eps >~ -2^(-%d)", precy + i);
else
printf ("eps <~ - (2^(-%d) + 2^(%d))",
precy + i, 1 - 2 * (precy + i));
printf (", %s\n", e3 ? "mpfr_exp_3" : "mpfr_exp");
mpfr_dump (y);
err = 1;
}
if (err)
exit (1);
} /* for (e3 ...) */
} /* for (j ...) */
mpfr_div_2si (t, t, 1, MPFR_RNDN);
mpfr_div_2si (t2, t2, 2, MPFR_RNDN);
} /* for (i ...) */
mpfr_clears (x, y, (mpfr_ptr) 0);
} /* for (precy ...) */
mpfr_clears (t, t2, (mpfr_ptr) 0);
/* Case exp(eps) ~= 1/2, i.e. eps ~= - log(2).
* We choose x0 and x1 with high enough precision such that:
* x0 = rndd(rndd(log(minpos)) - rndu(log(2)))
* x1 = rndu(rndu(log(minpos)) - rndd(log(2)))
* In revision 5507 (trunk) on a 64-bit Linux machine, this fails:
* Error in underflow_up, eps >~ - log(2) and extended emin
* for precy = 16, mpfr_exp
* Expected 1.0@-1152921504606846976 (minimum positive MPFR number),
* inex > 0 and flags = 9
* Got 0
* with inex = -1 and flags = 9
* due to a double-rounding problem in mpfr_mul_2si when rescaling
* the result.
*/
mpfr_inits2 (sizeof(mpfr_exp_t) * CHAR_BIT + 64, x, t, (mpfr_ptr) 0);
for (i = 0; i <= 1; i++)
{
mpfr_log (x, minpos, i ? MPFR_RNDU : MPFR_RNDD);
mpfr_const_log2 (t, i ? MPFR_RNDD : MPFR_RNDU);
mpfr_sub (x, x, t, i ? MPFR_RNDU : MPFR_RNDD);
for (precy = 16; precy <= 128; precy += 16)
{
mpfr_init2 (y, precy);
for (e3 = 0; e3 <= 1; e3++)
{
unsigned int flags, uflags =
MPFR_FLAGS_INEXACT | MPFR_FLAGS_UNDERFLOW;
mpfr_clear_flags ();
inex = e3 ? exp_3 (y, x, MPFR_RNDN) : mpfr_exp (y, x, MPFR_RNDN);
flags = __gmpfr_flags;
if (flags != uflags ||
(i ? (inex <= 0 || mpfr_cmp0 (y, minpos) != 0)
: (inex >= 0 || MPFR_NOTZERO (y))))
{
printf ("Error in underflow_up, eps %c~ - log(2)",
i ? '>' : '<');
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precy = %d, %s\nExpected ", precy,
e3 ? "mpfr_exp_3" : "mpfr_exp");
if (i)
{
mpfr_out_str (stdout, 16, 0, minpos, MPFR_RNDN);
printf (" (minimum positive MPFR number),\ninex >");
}
else
{
printf ("+0, inex <");
}
printf (" 0 and flags = %u\nGot ", uflags);
mpfr_out_str (stdout, 16, 0, y, MPFR_RNDN);
printf ("\nwith inex = %d and flags = %u\n", inex, flags);
exit (1);
}
}
mpfr_clear (y);
}
}
mpfr_clears (x, t, (mpfr_ptr) 0);
mpfr_clear (minpos);
}
static void
underflow (void)
{
mpfr_exp_t emin;
underflow_up (0);
emin = mpfr_get_emin ();
set_emin (MPFR_EMIN_MIN);
if (mpfr_get_emin () != emin)
{
underflow_up (1);
set_emin (emin);
}
}
int
main (int argc, char *argv[])
{
tests_start_mpfr ();
if (argc > 1)
check_large ();
check_inexact ();
check_special ();
test_generic (2, 100, 100);
compare_exp2_exp3 (20, 1000);
check_worst_cases();
check3("0.0", MPFR_RNDU, "1.0");
check3("-1e-170", MPFR_RNDU, "1.0");
check3("-1e-170", MPFR_RNDN, "1.0");
check3("-8.88024741073346941839e-17", MPFR_RNDU, "1.0");
check3("8.70772839244701057915e-01", MPFR_RNDN, "2.38875626491680437269");
check3("1.0", MPFR_RNDN, "2.71828182845904509080");
check3("-3.42135637628104173534e-07", MPFR_RNDZ, "0.999999657864420798958");
/* worst case for argument reduction, very near from 5*log(2),
thanks to Jean-Michel Muller */
check3("3.4657359027997265421", MPFR_RNDN, "32.0");
check3("3.4657359027997265421", MPFR_RNDU, "32.0");
check3("3.4657359027997265421", MPFR_RNDD, "31.999999999999996447");
check3("2.26523754332090625496e+01", MPFR_RNDD, "6.8833785261699581146e9");
check3("1.31478962104089092122e+01", MPFR_RNDZ, "5.12930793917860137299e+05");
check3("4.25637507920002378103e-01", MPFR_RNDU, "1.53056585656161181497e+00");
check3("6.26551618962329307459e-16", MPFR_RNDU, "1.00000000000000066613e+00");
check3("-3.35589513871216568383e-03",MPFR_RNDD, "9.96649729583626853291e-01");
check3("1.95151388850007272424e+01", MPFR_RNDU, "2.98756340674767792225e+08");
check3("2.45045953503350730784e+01", MPFR_RNDN, "4.38743344916128387451e+10");
check3("2.58165606081678085104e+01", MPFR_RNDD, "1.62925781879432281494e+11");
check3("-2.36539020084338638128e+01",MPFR_RNDZ, "5.33630792749924762447e-11");
check3("2.39211946135858077866e+01", MPFR_RNDU, "2.44817704330214385986e+10");
check3("-2.78190533055889162029e+01",MPFR_RNDZ, "8.2858803483596879512e-13");
check3("2.64028186174889789584e+01", MPFR_RNDD, "2.9281844652878973388e11");
check3("2.92086338843268329413e+01", MPFR_RNDZ, "4.8433797301907177734e12");
check3("-2.46355324071459982349e+01",MPFR_RNDZ, "1.9995129297760994791e-11");
check3("-2.23509444608605427618e+01",MPFR_RNDZ, "1.9638492867489702307e-10");
check3("-2.41175390197331687148e+01",MPFR_RNDD, "3.3564940885530624592e-11");
check3("2.46363885231578088053e+01", MPFR_RNDU, "5.0055014282693267822e10");
check3("111.1263531080090984914932050742208957672119140625", MPFR_RNDN, "1.8262572323517295459e48");
check3("-3.56196340354684821250e+02",MPFR_RNDN, "2.0225297096141478156e-155");
check3("6.59678273772710895173e+02", MPFR_RNDU, "3.1234469273830195529e286");
check3("5.13772529701934331570e+02", MPFR_RNDD, "1.3445427121297197752e223");
check3("3.57430211008718345056e+02", MPFR_RNDD, "1.6981197246857298443e155");
check3("3.82001814471465536371e+02", MPFR_RNDU, "7.9667300591087367805e165");
check3("5.92396038219384422518e+02", MPFR_RNDD, "1.880747529554661989e257");
check3("-5.02678550462488090034e+02",MPFR_RNDU, "4.8919201895446217839e-219");
check3("5.30015757134837031117e+02", MPFR_RNDD, "1.5237672861171573939e230");
check3("5.16239362447650933063e+02", MPFR_RNDZ, "1.5845518406744492105e224");
check3("6.00812634798592370977e-01", MPFR_RNDN, "1.823600119339019443");
check_exp10 ();
bug20080731 ();
overflowed_exp0 ();
underflow ();
data_check ("data/exp", mpfr_exp, "mpfr_exp");
bad_cases (mpfr_exp, mpfr_log, "mpfr_exp", 0, -256, 255, 4, 128, 800, 50);
tests_end_mpfr ();
return 0;
}