/* Test file for mpfr_mul.
Copyright 1999, 2001-2020 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
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#include "mpfr-test.h"
#ifdef CHECK_EXTERNAL
static int
test_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
int res;
int ok = rnd_mode == MPFR_RNDN && mpfr_number_p (b) && mpfr_number_p (c);
if (ok)
{
mpfr_print_raw (b);
printf (" ");
mpfr_print_raw (c);
}
res = mpfr_mul (a, b, c, rnd_mode);
if (ok)
{
printf (" ");
mpfr_print_raw (a);
printf ("\n");
}
return res;
}
#else
#define test_mul mpfr_mul
#endif
/* checks that xs * ys gives the expected result res */
static void
check (const char *xs, const char *ys, mpfr_rnd_t rnd_mode,
unsigned int px, unsigned int py, unsigned int pz, const char *res)
{
mpfr_t xx, yy, zz;
mpfr_init2 (xx, px);
mpfr_init2 (yy, py);
mpfr_init2 (zz, pz);
mpfr_set_str1 (xx, xs);
mpfr_set_str1 (yy, ys);
test_mul(zz, xx, yy, rnd_mode);
if (mpfr_cmp_str1 (zz, res) )
{
printf ("(1) mpfr_mul failed for x=%s y=%s with rnd=%s\n",
xs, ys, mpfr_print_rnd_mode (rnd_mode));
printf ("correct is %s, mpfr_mul gives ", res);
mpfr_out_str (stdout, 10, 0, zz, MPFR_RNDN);
putchar ('\n');
exit (1);
}
mpfr_clear (xx);
mpfr_clear (yy);
mpfr_clear (zz);
}
static void
check53 (const char *xs, const char *ys, mpfr_rnd_t rnd_mode, const char *zs)
{
mpfr_t xx, yy, zz;
mpfr_inits2 (53, xx, yy, zz, (mpfr_ptr) 0);
mpfr_set_str1 (xx, xs);
mpfr_set_str1 (yy, ys);
test_mul (zz, xx, yy, rnd_mode);
if (mpfr_cmp_str1 (zz, zs) )
{
printf ("(2) mpfr_mul failed for x=%s y=%s with rnd=%s\n",
xs, ys, mpfr_print_rnd_mode(rnd_mode));
printf ("correct result is %s,\n mpfr_mul gives ", zs);
mpfr_out_str (stdout, 10, 0, zz, MPFR_RNDN);
putchar ('\n');
exit (1);
}
mpfr_clears (xx, yy, zz, (mpfr_ptr) 0);
}
/* checks that x*y gives the right result with 24 bits of precision */
static void
check24 (const char *xs, const char *ys, mpfr_rnd_t rnd_mode, const char *zs)
{
mpfr_t xx, yy, zz;
mpfr_inits2 (24, xx, yy, zz, (mpfr_ptr) 0);
mpfr_set_str1 (xx, xs);
mpfr_set_str1 (yy, ys);
test_mul (zz, xx, yy, rnd_mode);
if (mpfr_cmp_str1 (zz, zs) )
{
printf ("(3) mpfr_mul failed for x=%s y=%s with "
"rnd=%s\n", xs, ys, mpfr_print_rnd_mode(rnd_mode));
printf ("correct result is gives %s, mpfr_mul gives ", zs);
mpfr_out_str (stdout, 10, 0, zz, MPFR_RNDN);
putchar ('\n');
exit (1);
}
mpfr_clears (xx, yy, zz, (mpfr_ptr) 0);
}
/* the following examples come from the paper "Number-theoretic Test
Generation for Directed Rounding" from Michael Parks, Table 1 */
static void
check_float (void)
{
check24("8388609.0", "8388609.0", MPFR_RNDN, "70368760954880.0");
check24("16777213.0", "8388609.0", MPFR_RNDN, "140737479966720.0");
check24("8388611.0", "8388609.0", MPFR_RNDN, "70368777732096.0");
check24("12582911.0", "8388610.0", MPFR_RNDN, "105553133043712.0");
check24("12582914.0", "8388610.0", MPFR_RNDN, "105553158209536.0");
check24("13981013.0", "8388611.0", MPFR_RNDN, "117281279442944.0");
check24("11184811.0", "8388611.0", MPFR_RNDN, "93825028587520.0");
check24("11184810.0", "8388611.0", MPFR_RNDN, "93825020198912.0");
check24("13981014.0", "8388611.0", MPFR_RNDN, "117281287831552.0");
check24("8388609.0", "8388609.0", MPFR_RNDZ, "70368760954880.0");
check24("16777213.0", "8388609.0", MPFR_RNDZ, "140737471578112.0");
check24("8388611.0", "8388609.0", MPFR_RNDZ, "70368777732096.0");
check24("12582911.0", "8388610.0", MPFR_RNDZ, "105553124655104.0");
check24("12582914.0", "8388610.0", MPFR_RNDZ, "105553158209536.0");
check24("13981013.0", "8388611.0", MPFR_RNDZ, "117281271054336.0");
check24("11184811.0", "8388611.0", MPFR_RNDZ, "93825028587520.0");
check24("11184810.0", "8388611.0", MPFR_RNDZ, "93825011810304.0");
check24("13981014.0", "8388611.0", MPFR_RNDZ, "117281287831552.0");
check24("8388609.0", "8388609.0", MPFR_RNDU, "70368769343488.0");
check24("16777213.0", "8388609.0", MPFR_RNDU, "140737479966720.0");
check24("8388611.0", "8388609.0", MPFR_RNDU, "70368786120704.0");
check24("12582911.0", "8388610.0", MPFR_RNDU, "105553133043712.0");
check24("12582914.0", "8388610.0", MPFR_RNDU, "105553166598144.0");
check24("13981013.0", "8388611.0", MPFR_RNDU, "117281279442944.0");
check24("11184811.0", "8388611.0", MPFR_RNDU, "93825036976128.0");
check24("11184810.0", "8388611.0", MPFR_RNDU, "93825020198912.0");
check24("13981014.0", "8388611.0", MPFR_RNDU, "117281296220160.0");
check24("8388609.0", "8388609.0", MPFR_RNDD, "70368760954880.0");
check24("16777213.0", "8388609.0", MPFR_RNDD, "140737471578112.0");
check24("8388611.0", "8388609.0", MPFR_RNDD, "70368777732096.0");
check24("12582911.0", "8388610.0", MPFR_RNDD, "105553124655104.0");
check24("12582914.0", "8388610.0", MPFR_RNDD, "105553158209536.0");
check24("13981013.0", "8388611.0", MPFR_RNDD, "117281271054336.0");
check24("11184811.0", "8388611.0", MPFR_RNDD, "93825028587520.0");
check24("11184810.0", "8388611.0", MPFR_RNDD, "93825011810304.0");
check24("13981014.0", "8388611.0", MPFR_RNDD, "117281287831552.0");
}
/* check sign of result */
static void
check_sign (void)
{
mpfr_t a, b;
mpfr_init2 (a, 53);
mpfr_init2 (b, 53);
mpfr_set_si (a, -1, MPFR_RNDN);
mpfr_set_ui (b, 2, MPFR_RNDN);
test_mul(a, b, b, MPFR_RNDN);
if (mpfr_cmp_ui (a, 4) )
{
printf ("2.0*2.0 gives \n");
mpfr_out_str (stdout, 10, 0, a, MPFR_RNDN);
putchar ('\n');
exit (1);
}
mpfr_clear(a); mpfr_clear(b);
}
/* checks that the inexact return value is correct */
static void
check_exact (void)
{
mpfr_t a, b, c, d;
mpfr_prec_t prec;
int i, inexact;
mpfr_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_binary (a, "1.1000111011000100e-1");
mpfr_set_str_binary (b, "1.0010001111100111e-1");
if (test_mul (c, a, b, MPFR_RNDZ))
{
printf ("wrong return value (1)\n");
exit (1);
}
for (prec = MPFR_PREC_MIN; prec < 100; prec++)
{
mpfr_set_prec (a, prec);
mpfr_set_prec (b, prec);
/* for prec=1, ensure PREC(c) >= 1 */
mpfr_set_prec (c, 2 * prec - 2 + (prec == 1));
mpfr_set_prec (d, 2 * prec);
for (i = 0; i < 1000; i++)
{
mpfr_urandomb (a, RANDS);
mpfr_urandomb (b, RANDS);
rnd = RND_RAND ();
inexact = test_mul (c, a, b, rnd);
if (test_mul (d, a, b, rnd)) /* should be always exact */
{
printf ("unexpected inexact return value\n");
exit (1);
}
if ((inexact == 0) && mpfr_cmp (c, d) && rnd != MPFR_RNDF)
{
printf ("rnd=%s: inexact=0 but results differ\n",
mpfr_print_rnd_mode (rnd));
printf ("a=");
mpfr_out_str (stdout, 2, 0, a, rnd);
printf ("\nb=");
mpfr_out_str (stdout, 2, 0, b, rnd);
printf ("\nc=");
mpfr_out_str (stdout, 2, 0, c, rnd);
printf ("\nd=");
mpfr_out_str (stdout, 2, 0, d, rnd);
printf ("\n");
exit (1);
}
else if (inexact && (mpfr_cmp (c, d) == 0) && rnd != MPFR_RNDF)
{
printf ("inexact!=0 but results agree\n");
printf ("prec=%u rnd=%s a=", (unsigned int) prec,
mpfr_print_rnd_mode (rnd));
mpfr_out_str (stdout, 2, 0, a, rnd);
printf ("\nb=");
mpfr_out_str (stdout, 2, 0, b, rnd);
printf ("\nc=");
mpfr_out_str (stdout, 2, 0, c, rnd);
printf ("\nd=");
mpfr_out_str (stdout, 2, 0, d, rnd);
printf ("\n");
exit (1);
}
}
}
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
mpfr_clear (d);
}
static void
check_max (void)
{
mpfr_t xx, yy, zz;
mpfr_exp_t emin;
int inex;
mpfr_init2(xx, 4);
mpfr_init2(yy, 4);
mpfr_init2(zz, 4);
mpfr_set_str1 (xx, "0.68750");
mpfr_mul_2si(xx, xx, MPFR_EMAX_DEFAULT/2, MPFR_RNDN);
mpfr_set_str1 (yy, "0.68750");
mpfr_mul_2si(yy, yy, MPFR_EMAX_DEFAULT - MPFR_EMAX_DEFAULT/2 + 1, MPFR_RNDN);
mpfr_clear_flags();
test_mul(zz, xx, yy, MPFR_RNDU);
if (!(mpfr_overflow_p() && MPFR_IS_INF(zz)))
{
printf("check_max failed (should be an overflow)\n");
exit(1);
}
mpfr_clear_flags();
test_mul(zz, xx, yy, MPFR_RNDD);
if (mpfr_overflow_p() || MPFR_IS_INF(zz))
{
printf("check_max failed (should NOT be an overflow)\n");
exit(1);
}
mpfr_set_str1 (xx, "0.93750");
mpfr_mul_2si(xx, xx, MPFR_EMAX_DEFAULT, MPFR_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, MPFR_RNDZ);
printf(" instead of ");
mpfr_out_str(stdout, 2, 0, xx, MPFR_RNDZ);
printf("\n");
exit(1);
}
/* check underflow */
emin = mpfr_get_emin ();
set_emin (0);
mpfr_set_str_binary (xx, "0.1E0");
mpfr_set_str_binary (yy, "0.1E0");
test_mul (zz, xx, yy, MPFR_RNDN);
/* exact result is 0.1E-1, which should round to 0 */
MPFR_ASSERTN(mpfr_cmp_ui (zz, 0) == 0 && MPFR_IS_POS(zz));
set_emin (emin);
/* coverage test for mpfr_powerof2_raw */
emin = mpfr_get_emin ();
set_emin (0);
mpfr_set_prec (xx, mp_bits_per_limb + 1);
mpfr_set_str_binary (xx, "0.1E0");
mpfr_nextabove (xx);
mpfr_set_str_binary (yy, "0.1E0");
test_mul (zz, xx, yy, MPFR_RNDN);
/* exact result is just above 0.1E-1, which should round to minfloat */
MPFR_ASSERTN(mpfr_cmp (zz, yy) == 0);
set_emin (emin);
/* coverage test for mulders.c, case n > MUL_FFT_THRESHOLD */
mpfr_set_prec (xx, (MUL_FFT_THRESHOLD + 1) * GMP_NUMB_BITS);
mpfr_set_prec (yy, (MUL_FFT_THRESHOLD + 1) * GMP_NUMB_BITS);
mpfr_set_prec (zz, (MUL_FFT_THRESHOLD + 1) * GMP_NUMB_BITS);
mpfr_set_ui (xx, 1, MPFR_RNDN);
mpfr_nextbelow (xx);
mpfr_set_ui (yy, 1, MPFR_RNDN);
mpfr_nextabove (yy);
/* xx = 1 - 2^(-p), yy = 1 + 2^(1-p), where p = PREC(x),
thus xx * yy should be rounded to 1 */
inex = mpfr_mul (zz, xx, yy, MPFR_RNDN);
MPFR_ASSERTN(inex < 0);
MPFR_ASSERTN(mpfr_cmp_ui (zz, 1) == 0);
mpfr_clear(xx);
mpfr_clear(yy);
mpfr_clear(zz);
}
static void
check_min(void)
{
mpfr_t xx, yy, zz;
mpfr_init2(xx, 4);
mpfr_init2(yy, 4);
mpfr_init2(zz, 3);
mpfr_set_str1(xx, "0.9375");
mpfr_mul_2si(xx, xx, MPFR_EMIN_DEFAULT/2, MPFR_RNDN);
mpfr_set_str1(yy, "0.9375");
mpfr_mul_2si(yy, yy, MPFR_EMIN_DEFAULT - MPFR_EMIN_DEFAULT/2 - 1, MPFR_RNDN);
test_mul(zz, xx, yy, MPFR_RNDD);
if (MPFR_NOTZERO (zz))
{
printf("check_min failed: got ");
mpfr_out_str(stdout, 2, 0, zz, MPFR_RNDZ);
printf(" instead of 0\n");
exit(1);
}
test_mul(zz, xx, yy, MPFR_RNDU);
mpfr_set_str1 (xx, "0.5");
mpfr_mul_2si(xx, xx, MPFR_EMIN_DEFAULT, MPFR_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, MPFR_RNDZ);
printf(" instead of ");
mpfr_out_str(stdout, 2, 0, xx, MPFR_RNDZ);
printf("\n");
exit(1);
}
mpfr_clear(xx);
mpfr_clear(yy);
mpfr_clear(zz);
}
static void
check_nans (void)
{
mpfr_t p, x, y;
mpfr_init2 (x, 123L);
mpfr_init2 (y, 123L);
mpfr_init2 (p, 123L);
/* nan * 0 == nan */
mpfr_set_nan (x);
mpfr_set_ui (y, 0L, MPFR_RNDN);
test_mul (p, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (p));
/* 1 * nan == nan */
mpfr_set_ui (x, 1L, MPFR_RNDN);
mpfr_set_nan (y);
test_mul (p, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (p));
/* 0 * +inf == nan */
mpfr_set_ui (x, 0L, MPFR_RNDN);
mpfr_set_nan (y);
test_mul (p, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (p));
/* +1 * +inf == +inf */
mpfr_set_ui (x, 1L, MPFR_RNDN);
mpfr_set_inf (y, 1);
test_mul (p, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (p));
MPFR_ASSERTN (mpfr_sgn (p) > 0);
/* -1 * +inf == -inf */
mpfr_set_si (x, -1L, MPFR_RNDN);
mpfr_set_inf (y, 1);
test_mul (p, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (p));
MPFR_ASSERTN (mpfr_sgn (p) < 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (p);
}
#define BUFSIZE 1552
static void
get_string (char *s, FILE *fp)
{
int c, n = BUFSIZE;
while ((c = getc (fp)) != '\n')
{
if (c == EOF)
{
printf ("Error in get_string: end of file\n");
exit (1);
}
*(unsigned char *)s++ = c;
if (--n == 0)
{
printf ("Error in get_string: buffer is too small\n");
exit (1);
}
}
*s = '\0';
}
static void
check_regression (void)
{
mpfr_t x, y, z;
int i;
FILE *fp;
char s[BUFSIZE];
mpfr_inits2 (6177, x, y, z, (mpfr_ptr) 0);
/* we read long strings from a file since ISO C90 does not support strings of
length > 509 */
fp = src_fopen ("tmul.dat", "r");
if (fp == NULL)
{
fprintf (stderr, "Error, cannot open tmul.dat in srcdir\n");
exit (1);
}
get_string (s, fp);
mpfr_set_str (y, s, 16, MPFR_RNDN);
get_string (s, fp);
mpfr_set_str (z, s, 16, MPFR_RNDN);
i = mpfr_mul (x, y, z, MPFR_RNDN);
get_string (s, fp);
if (mpfr_cmp_str (x, s, 16, MPFR_RNDN) != 0 || i != -1)
{
printf ("Regression test 1 failed (i=%d, expected -1)\nx=", i);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
fclose (fp);
mpfr_set_prec (x, 606);
mpfr_set_prec (y, 606);
mpfr_set_prec (z, 606);
mpfr_set_str (y, "-f.ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff92daefc3f8052ca9f58736564d9e93e62d324@-1", 16, MPFR_RNDN);
mpfr_set_str (z, "-f.ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff92daefc3f8052ca9f58736564d9e93e62d324@-1", 16, MPFR_RNDN);
i = mpfr_mul (x, y, z, MPFR_RNDU);
mpfr_set_str (y, "f.ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff25b5df87f00a5953eb0e6cac9b3d27cc5a64c@-1", 16, MPFR_RNDN);
if (mpfr_cmp (x, y) || i <= 0)
{
printf ("Regression test (2) failed! (i=%d - Expected 1)\n", i);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_set_prec (x, 184);
mpfr_set_prec (y, 92);
mpfr_set_prec (z, 1023);
mpfr_set_str (y, "6.9b8c8498882770d8038c3b0@-1", 16, MPFR_RNDN);
mpfr_set_str (z, "7.44e24b986e7fb296f1e936ce749fec3504cbf0d5ba769466b1c9f1578115efd5d29b4c79271191a920a99280c714d3a657ad6e3afbab77ffce9d697e9bb9110e26d676069afcea8b69f1d1541f2365042d80a97c21dcccd8ace4f1bb58b49922003e738e6f37bb82ef653cb2e87f763974e6ae50ae54e7724c38b80653e3289@255", 16, MPFR_RNDN);
i = mpfr_mul (x, y, z, MPFR_RNDU);
mpfr_set_prec (y, 184);
mpfr_set_str (y, "3.0080038f2ac5054e3e71ccbb95f76aaab2221715025a28@255",
16, MPFR_RNDN);
if (mpfr_cmp (x, y) || i <= 0)
{
printf ("Regression test (4) failed! (i=%d - expected 1)\n", i);
printf ("Ref: 3.0080038f2ac5054e3e71ccbb95f76aaab2221715025a28@255\n"
"Got: ");
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_prec (x, 908);
mpfr_set_prec (y, 908);
mpfr_set_prec (z, 908);
mpfr_set_str (y, "-f.fffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"ffffffffffffffffffffffffffffffffffffffffffffffffffffff99be91f83ec6f0ed28a3d42"
"e6e9a327230345ea6@-1", 16, MPFR_RNDN);
mpfr_set_str (z, "-f.fffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"ffffffffffffffffffffffffffffffffffffffffffffffffffffff99be91f83ec6f0ed28a3d42"
"e6e9a327230345ea6@-1", 16, MPFR_RNDN);
i = mpfr_mul (x, y, z, MPFR_RNDU);
mpfr_set_str (y, "f.ffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"fffffffffffffffffffffffffffffffffffffffffffffffffffff337d23f07d8de1da5147a85c"
"dd3464e46068bd4d@-1", 16, MPFR_RNDN);
if (mpfr_cmp (x, y) || i <= 0)
{
printf ("Regression test (5) failed! (i=%d - expected 1)\n", i);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 40);
mpfr_set_prec (z, 53);
mpfr_set_str (y, "4.1ffffffff8", 16, MPFR_RNDN);
mpfr_set_str (z, "4.2000000ffe0000@-4", 16, MPFR_RNDN);
i = mpfr_mul (x, y, z, MPFR_RNDN);
if (mpfr_cmp_str (x, "1.104000041d6c0@-3", 16, MPFR_RNDN) != 0
|| i <= 0)
{
printf ("Regression test (6) failed! (i=%d - expected 1)\nx=", i);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN);
printf ("\nMore prec=");
mpfr_set_prec (x, 93);
mpfr_mul (x, y, z, MPFR_RNDN);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_prec (x, 439);
mpfr_set_prec (y, 393);
mpfr_set_str (y, "-1.921fb54442d18469898cc51701b839a252049c1114cf98e804177d"
"4c76273644a29410f31c6809bbdf2a33679a748636600",
16, MPFR_RNDN);
i = mpfr_mul (x, y, y, MPFR_RNDU);
if (mpfr_cmp_str (x, "2.77a79937c8bbcb495b89b36602306b1c2159a8ff834288a19a08"
"84094f1cda3dc426da61174c4544a173de83c2500f8bfea2e0569e3698",
16, MPFR_RNDN) != 0
|| i <= 0)
{
printf ("Regression test (7) failed! (i=%d - expected 1)\nx=", i);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_prec (x, 1023);
mpfr_set_prec (y, 1023);
mpfr_set_prec (z, 511);
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_ui (y, 42, MPFR_RNDN);
i = mpfr_mul (z, x, y, MPFR_RNDN);
if (mpfr_cmp_ui (z, 17*42) != 0 || i != 0)
{
printf ("Regression test (8) failed! (i=%d - expected 0)\nz=", i);
mpfr_out_str (stdout, 16, 0, z, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
#define TEST_FUNCTION test_mul
#define TWO_ARGS
#define RAND_FUNCTION(x) mpfr_random2(x, MPFR_LIMB_SIZE (x), randlimb () % 100, RANDS)
#include "tgeneric.c"
/* multiplies x by 53-bit approximation of Pi */
static int
mpfr_mulpi (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t r)
{
mpfr_t z;
int inex;
mpfr_init2 (z, 53);
mpfr_set_str_binary (z, "11.001001000011111101101010100010001000010110100011");
inex = mpfr_mul (y, x, z, r);
mpfr_clear (z);
return inex;
}
static void
valgrind20110503 (void)
{
mpfr_t a, b, c;
mpfr_init2 (a, 2);
mpfr_init2 (b, 2005);
mpfr_init2 (c, 2);
mpfr_set_ui (b, 5, MPFR_RNDN);
mpfr_nextabove (b);
mpfr_set_ui (c, 1, MPFR_RNDN);
mpfr_mul (a, b, c, MPFR_RNDZ);
/* After the call to mpfr_mulhigh_n, valgrind complains:
Conditional jump or move depends on uninitialised value(s) */
mpfr_clears (a, b, c, (mpfr_ptr) 0);
}
static void
testall_rndf (mpfr_prec_t pmax)
{
mpfr_t a, b, c, d;
mpfr_prec_t pa, pb, pc;
for (pa = MPFR_PREC_MIN; pa <= pmax; pa++)
{
mpfr_init2 (a, pa);
mpfr_init2 (d, pa);
for (pb = MPFR_PREC_MIN; pb <= pmax; pb++)
{
mpfr_init2 (b, pb);
mpfr_set_ui (b, 1, MPFR_RNDN);
while (mpfr_cmp_ui (b, 2) < 0)
{
for (pc = MPFR_PREC_MIN; pc <= pmax; pc++)
{
mpfr_init2 (c, pc);
mpfr_set_ui (c, 1, MPFR_RNDN);
while (mpfr_cmp_ui (c, 2) < 0)
{
mpfr_mul (a, b, c, MPFR_RNDF);
mpfr_mul (d, b, c, MPFR_RNDD);
if (!mpfr_equal_p (a, d))
{
mpfr_mul (d, b, c, MPFR_RNDU);
if (!mpfr_equal_p (a, d))
{
printf ("Error: mpfr_mul(a,b,c,RNDF) does not "
"match RNDD/RNDU\n");
printf ("b="); mpfr_dump (b);
printf ("c="); mpfr_dump (c);
printf ("a="); mpfr_dump (a);
exit (1);
}
}
mpfr_nextabove (c);
}
mpfr_clear (c);
}
mpfr_nextabove (b);
}
mpfr_clear (b);
}
mpfr_clear (a);
mpfr_clear (d);
}
}
/* Check underflow flag corresponds to *after* rounding.
*
* More precisely, we want to test mpfr_mul on inputs b and c such that
* EXP(b*c) < emin but EXP(round(b*c, p, rnd)) = emin. Thus an underflow
* must not be generated.
*/
static void
test_underflow (mpfr_prec_t pmax)
{
mpfr_exp_t emin;
mpfr_prec_t p;
mpfr_t a0, a, b, c;
int inex;
mpfr_init2 (a0, MPFR_PREC_MIN);
emin = mpfr_get_emin ();
mpfr_setmin (a0, emin); /* 0.5 * 2^emin */
/* for RNDN, we want b*c < 0.5 * 2^emin but RNDN(b*c, p) = 0.5 * 2^emin,
thus b*c >= (0.5 - 1/4 * ulp_p(0.5)) * 2^emin */
for (p = MPFR_PREC_MIN; p <= pmax; p++)
{
mpfr_init2 (a, p + 1);
mpfr_init2 (b, p + 10);
mpfr_init2 (c, p + 10);
do mpfr_urandomb (b, RANDS); while (MPFR_IS_ZERO (b));
inex = mpfr_set_ui_2exp (a, 1, -1, MPFR_RNDZ); /* a = 0.5 */
MPFR_ASSERTN (inex == 0);
mpfr_nextbelow (a); /* 0.5 - 1/2*ulp_{p+1}(0.5) = 0.5 - 1/4*ulp_p(0.5) */
inex = mpfr_div (c, a, b, MPFR_RNDU);
/* 0.5 - 1/4 * ulp_p(0.5) = a <= b*c < 0.5 */
mpfr_mul_2si (b, b, emin / 2, MPFR_RNDZ);
mpfr_mul_2si (c, c, (emin - 1) / 2, MPFR_RNDZ);
/* now (0.5 - 1/4 * ulp_p(0.5)) * 2^emin <= b*c < 0.5 * 2^emin,
thus b*c should be rounded to 0.5 * 2^emin */
mpfr_set_prec (a, p);
mpfr_clear_underflow ();
mpfr_mul (a, b, c, MPFR_RNDN);
if (mpfr_underflow_p () || ! mpfr_equal_p (a, a0))
{
printf ("Error, b*c incorrect or underflow flag incorrectly set"
" for emin=%" MPFR_EXP_FSPEC "d, rnd=%s\n",
(mpfr_eexp_t) emin, mpfr_print_rnd_mode (MPFR_RNDN));
printf ("b="); mpfr_dump (b);
printf ("c="); mpfr_dump (c);
printf ("a="); mpfr_dump (a);
mpfr_set_prec (a, mpfr_get_prec (b) + mpfr_get_prec (c));
mpfr_mul_2ui (b, b, 1, MPFR_RNDN);
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
printf ("Exact 2*a="); mpfr_dump (a);
exit (1);
}
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
/* for RNDU, we want b*c < 0.5*2^emin but RNDU(b*c, p) = 0.5*2^emin thus
b*c > (0.5 - 1/2 * ulp_p(0.5)) * 2^emin */
for (p = MPFR_PREC_MIN; p <= pmax; p++)
{
mpfr_init2 (a, p);
mpfr_init2 (b, p + 10);
mpfr_init2 (c, p + 10);
do mpfr_urandomb (b, RANDS); while (MPFR_IS_ZERO (b));
inex = mpfr_set_ui_2exp (a, 1, -1, MPFR_RNDZ); /* a = 0.5 */
MPFR_ASSERTN (inex == 0);
mpfr_nextbelow (a); /* 0.5 - 1/2 * ulp_p(0.5) */
inex = mpfr_div (c, a, b, MPFR_RNDU);
/* 0.5 - 1/2 * ulp_p(0.5) <= b*c < 0.5 */
mpfr_mul_2si (b, b, emin / 2, MPFR_RNDZ);
mpfr_mul_2si (c, c, (emin - 1) / 2, MPFR_RNDZ);
if (inex == 0)
mpfr_nextabove (c); /* ensures b*c > (0.5 - 1/2 * ulp_p(0.5)) * 2^emin.
Warning: for p=1, 0.5 - 1/2 * ulp_p(0.5)
= 0.25, thus b*c > 2^(emin-2), which should
also be rounded up with p=1 to 0.5 * 2^emin
with an unbounded exponent range. */
mpfr_clear_underflow ();
mpfr_mul (a, b, c, MPFR_RNDU);
if (mpfr_underflow_p () || ! mpfr_equal_p (a, a0))
{
printf ("Error, b*c incorrect or underflow flag incorrectly set"
" for emin=%" MPFR_EXP_FSPEC "d, rnd=%s\n",
(mpfr_eexp_t) emin, mpfr_print_rnd_mode (MPFR_RNDU));
printf ("b="); mpfr_dump (b);
printf ("c="); mpfr_dump (c);
printf ("a="); mpfr_dump (a);
mpfr_set_prec (a, mpfr_get_prec (b) + mpfr_get_prec (c));
mpfr_mul_2ui (b, b, 1, MPFR_RNDN);
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
printf ("Exact 2*a="); mpfr_dump (a);
exit (1);
}
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
mpfr_clear (a0);
}
/* checks special case where no underflow should occur */
static void
bug20161209 (void)
{
mpfr_exp_t emin;
mpfr_t x, y, z;
emin = mpfr_get_emin ();
set_emin (-1);
/* test for mpfr_mul_1 for 64-bit limb, mpfr_mul_2 for 32-bit limb */
mpfr_init2 (x, 53);
mpfr_init2 (y, 53);
mpfr_init2 (z, 53);
mpfr_set_str_binary (x, "0.101000001E-1"); /* x = 321/2^10 */
mpfr_set_str_binary (y, "0.110011000010100101111000011011000111011000001E-1");
/* y = 28059810762433/2^46 */
/* x * y = (2^53+1)/2^56 = 0.001...000[1]000..., and should round to 0.25 */
mpfr_mul (z, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -2) == 0);
/* test for mpfr_mul_2 for 64-bit limb */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_set_prec (z, 65);
mpfr_set_str_binary (x, "0.101101000010010110100001E-1"); /* 11806113/2^25 */
mpfr_set_str_binary (y, "0.101101011110010101011010001111111001100001E-1");
/* y = 3124947910241/2^43 */
/* x * y = (2^65+1)/2^68 = 0.001...000[1]000..., and should round to 0.25 */
mpfr_mul (z, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -2) == 0);
/* test for the generic code */
mpfr_set_prec (x, 54);
mpfr_set_prec (y, 55);
mpfr_set_prec (z, 53);
mpfr_set_str_binary (x, "0.101000001E-1");
mpfr_set_str_binary (y, "0.110011000010100101111000011011000111011000001E-1");
mpfr_mul (z, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -2) == 0);
/* another test for the generic code */
mpfr_set_prec (x, 66);
mpfr_set_prec (y, 67);
mpfr_set_prec (z, 65);
mpfr_set_str_binary (x, "0.101101000010010110100001E-1");
mpfr_set_str_binary (y, "0.101101011110010101011010001111111001100001E-1");
mpfr_mul (z, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -2) == 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
set_emin (emin);
}
/* test for case in mpfr_mul_1() where:
ax = __gmpfr_emin - 1
ap[0] == ~mask
rnd_mode = MPFR_RNDZ.
Whatever the values of rb and sb, we should round to zero (underflow). */
static void
bug20161209a (void)
{
mpfr_exp_t emin;
mpfr_t x, y, z;
emin = mpfr_get_emin ();
set_emin (-1);
mpfr_init2 (x, 53);
mpfr_init2 (y, 53);
mpfr_init2 (z, 53);
/* case rb = sb = 0 */
mpfr_set_str_binary (x, "0.11010010100110000110110011111E-1");
mpfr_set_str_binary (y, "0.1001101110011000110100001");
/* x = 441650591/2^30, y = 20394401/2^25 */
/* x * y = (2^53-1)/2^55 = 0.00111...111[0]000..., and should round to 0 */
mpfr_mul (z, x, y, MPFR_RNDZ);
MPFR_ASSERTN(mpfr_zero_p (z));
/* case rb = 1, sb = 0 */
mpfr_set_str_binary (x, "0.111111111000000000000000000111111111E-1");
mpfr_set_str_binary (y, "0.1000000001000000001");
/* x = 68585259519/2^37, y = 262657/2^19 */
/* x * y = (2^54-1)/2^56 = 0.00111...111[1]000..., and should round to 0 */
mpfr_mul (z, x, y, MPFR_RNDZ);
MPFR_ASSERTN(mpfr_zero_p (z));
/* case rb = 0, sb = 1 */
mpfr_set_str_binary (x, "0.110010011001011110001100100001000001E-1");
mpfr_set_str_binary (y, "0.10100010100010111101");
/* x = 541144371852^37, y = 665789/2^20 */
/* x * y = (2^55-3)/2^57 = 0.00111...111[0]100..., and should round to 0 */
mpfr_mul (z, x, y, MPFR_RNDZ);
MPFR_ASSERTN(mpfr_zero_p (z));
/* case rb = sb = 1 */
mpfr_set_str_binary (x, "0.10100110001001001010001111110010100111E-1");
mpfr_set_str_binary (y, "0.110001010011101001");
/* x = 178394823847/2^39, y = 201961/2^18 */
/* x * y = (2^55-1)/2^57 = 0.00111...111[1]100..., and should round to 0 */
mpfr_mul (z, x, y, MPFR_RNDZ);
MPFR_ASSERTN(mpfr_zero_p (z));
/* similar test for mpfr_mul_2 (we only check rb = sb = 1 here) */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_set_prec (z, 65);
/* 2^67-1 = 193707721 * 761838257287 */
mpfr_set_str_binary (x, "0.1011100010111011111011001001E-1");
mpfr_set_str_binary (y, "0.1011000101100001000110010100010010000111");
mpfr_mul (z, x, y, MPFR_RNDZ);
MPFR_ASSERTN(mpfr_zero_p (z));
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
set_emin (emin);
}
/* bug for RNDF */
static void
bug20170602 (void)
{
mpfr_t x, u, y, yd, yu;
mpfr_init2 (x, 493);
mpfr_init2 (u, 493);
mpfr_init2 (y, 503);
mpfr_init2 (yd, 503);
mpfr_init2 (yu, 503);
mpfr_set_str_binary (x, "0.1111100000000000001111111110000000001111111111111000000000000000000011111111111111111111111000000000000000000001111111111111111111111111111111111111111000000000011111111111111111111000000000011111111111111000000000000001110000000000000000000000000000000000000000011111111111110011111111111100000000000000011111111111111111110000000011111111111111111110011111111111110000000000001111111111111111000000000000000000000000000000000000111111111111111111111111111111011111111111111111111111111111100E44");
mpfr_set_str_binary (u, "0.1110000000000000001111111111111111111111111111111111111000000000111111111111111111111111111111000000000000000000001111111000000000000000011111111111111111111111111111111111111111111111111111111000000000000000011111111111111000000011111111111111111110000000000000001111111111111111111111111111111111111110000000000001111111111111111111111111111111111111000000000000000000000000000000000001111111111111000000000000000000001111111111100000000000000011111111111111111111111111111111111111111111111E35");
mpfr_mul (y, x, u, MPFR_RNDF);
mpfr_mul (yd, x, u, MPFR_RNDD);
mpfr_mul (yu, x, u, MPFR_RNDU);
if (mpfr_cmp (y, yd) != 0 && mpfr_cmp (y, yu) != 0)
{
printf ("RNDF is neither RNDD nor RNDU\n");
printf ("x"); mpfr_dump (x);
printf ("u"); mpfr_dump (u);
printf ("y(RNDF)="); mpfr_dump (y);
printf ("y(RNDD)="); mpfr_dump (yd);
printf ("y(RNDU)="); mpfr_dump (yu);
exit (1);
}
mpfr_clear (x);
mpfr_clear (u);
mpfr_clear (y);
mpfr_clear (yd);
mpfr_clear (yu);
}
/* Test for 1 to 3 limbs. */
static void
small_prec (void)
{
mpfr_exp_t emin, emax;
mpfr_t x, y, z1, z2, zz;
int xq, yq, zq;
mpfr_rnd_t rnd;
mpfr_flags_t flags1, flags2;
int inex1, inex2;
int i, j, r, s, ediff;
emin = mpfr_get_emin ();
emax = mpfr_get_emax ();
/* The mpfr_mul implementation doesn't extend the exponent range,
so that it is OK to reduce it here for the test to make sure that
mpfr_mul_2si can be used. */
set_emin (-1000);
set_emax (1000);
mpfr_inits2 (3 * GMP_NUMB_BITS, x, y, z1, z2, (mpfr_ptr) 0);
mpfr_init2 (zz, 6 * GMP_NUMB_BITS);
for (i = 0; i < 3; i++)
for (j = 0; j < 10000; j++)
{
xq = i * GMP_NUMB_BITS + 1 + randlimb () % GMP_NUMB_BITS;
mpfr_set_prec (x, xq);
yq = i * GMP_NUMB_BITS + 1 + randlimb () % GMP_NUMB_BITS;
mpfr_set_prec (y, yq);
zq = i * GMP_NUMB_BITS + 1 + randlimb () % (GMP_NUMB_BITS-1);
mpfr_set_prec (z1, zq);
mpfr_set_prec (z2, zq);
s = r = randlimb () & 0x7f;
do mpfr_urandomb (x, RANDS); while (mpfr_zero_p (x));
if (s & 1)
mpfr_neg (x, x, MPFR_RNDN);
s >>= 1;
if (s & 1)
{
do mpfr_urandomb (y, RANDS); while (mpfr_zero_p (y));
}
else
{
mpfr_ui_div (y, 1, x, MPFR_RNDN);
mpfr_set_exp (y, 0);
}
s >>= 1;
if (s & 1)
mpfr_neg (y, y, MPFR_RNDN);
s >>= 1;
rnd = RND_RAND_NO_RNDF ();
inex1 = mpfr_mul (zz, x, y, MPFR_RNDN);
MPFR_ASSERTN (inex1 == 0);
if (s == 0)
{
ediff = __gmpfr_emin - MPFR_EXP (x);
mpfr_set_exp (x, __gmpfr_emin);
}
else if (s == 1)
{
ediff = __gmpfr_emax - MPFR_EXP (x) + 1;
mpfr_set_exp (x, __gmpfr_emax);
mpfr_mul_2ui (y, y, 1, MPFR_RNDN);
}
else
ediff = 0;
mpfr_clear_flags ();
inex1 = mpfr_mul_2si (z1, zz, ediff, rnd);
flags1 = __gmpfr_flags;
mpfr_clear_flags ();
inex2 = mpfr_mul (z2, x, y, rnd);
flags2 = __gmpfr_flags;
if (!(mpfr_equal_p (z1, z2) &&
SAME_SIGN (inex1, inex2)
&& flags1 == flags2
))
{
printf ("Error in small_prec on i = %d, j = %d\n", i, j);
printf ("r = 0x%x, xq = %d, yq = %d, zq = %d, rnd = %s\n",
r, xq, yq, zq, mpfr_print_rnd_mode (rnd));
printf ("x = ");
mpfr_dump (x);
printf ("y = ");
mpfr_dump (y);
printf ("ediff = %d\n", ediff);
printf ("zz = ");
mpfr_dump (zz);
printf ("Expected ");
mpfr_dump (z1);
printf ("with inex = %d and flags =", inex1);
flags_out (flags1);
printf ("Got ");
mpfr_dump (z2);
printf ("with inex = %d and flags =", inex2);
flags_out (flags2);
exit (1);
}
}
mpfr_clears (x, y, z1, z2, zz, (mpfr_ptr) 0);
set_emin (emin);
set_emax (emax);
}
/* check ax < __gmpfr_emin with rnd_mode == MPFR_RNDN, rb = 0 and sb <> 0 */
static void
test_underflow2 (void)
{
mpfr_t x, y, z;
mpfr_exp_t emin;
emin = mpfr_get_emin ();
mpfr_set_emin (0);
mpfr_init2 (x, 24);
mpfr_init2 (y, 24);
mpfr_init2 (z, 24);
mpfr_set_ui_2exp (x, 12913, -14, MPFR_RNDN);
mpfr_set_ui_2exp (y, 5197, -13, MPFR_RNDN);
mpfr_clear_underflow ();
/* x*y = 0.0111111111111111111111111[01] thus underflow */
mpfr_mul (z, y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -1) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_set_prec (z, 65);
mpfr_set_str_binary (x, "0.10011101000110111011111100101001111");
mpfr_set_str_binary (y, "0.110100001001000111000011011110011");
mpfr_clear_underflow ();
/* x*y = 0.011111111111111111111111111111111111111111111111111111111111111111[01] thus underflow */
mpfr_mul (z, y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -1) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
mpfr_clear (y);
mpfr_clear (x);
mpfr_clear (z);
mpfr_set_emin (emin);
}
static void
coverage (mpfr_prec_t pmax)
{
mpfr_t a, b, c;
mpfr_prec_t p;
int inex;
for (p = MPFR_PREC_MIN; p <= pmax; p++)
{
mpfr_init2 (a, p);
mpfr_init2 (b, p);
mpfr_init2 (c, p);
/* exercise case b*c = 2^(emin-2), which is just in the middle
between 0 and the smallest positive number 0.5*2^emin */
mpfr_set_ui_2exp (b, 1, mpfr_get_emin (), MPFR_RNDN);
mpfr_set_ui_2exp (c, 1, -2, MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex < 0);
MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
if (p == 1)
goto end_of_loop;
/* case b*c > 2^(emin-2): b = (1-2^(-p))*2^emin,
c = 0.25*(1+2^(1-p)), thus b*c = (1+2^(-p)-2^(1-2p))*2^(emin-2)
should be rounded to 2^(emin-1) for RNDN */
mpfr_nextbelow (b);
mpfr_nextabove (c);
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
/* b = (1-2^(1-p))*2^emin, c = 0.25*(1+2^(1-p)),
thus b*c = (1-2^(2-2p))*2^(emin-2) should be rounded to 0 */
mpfr_nextbelow (b);
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex < 0);
MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
/* special case where b*c is in [nextbelow(0.5*2^emin),0.5*2^emin[ */
if ((p % 2) == 0)
{
/* the middle of the interval [nextbelow(0.5*2^emin),0.5*2^emin[
is (1-2^(-p-1))*2^(emin-1)
= (1-2^(-p/2))*(1+2^(-p/2))*2^(emin-1) */
mpfr_set_si_2exp (b, -1, -p/2, MPFR_RNDN);
mpfr_add_ui (b, b, 1, MPFR_RNDN);
mpfr_set_si_2exp (c, 1, -p/2, MPFR_RNDN);
mpfr_add_ui (c, c, 1, MPFR_RNDN);
MPFR_ASSERTN(mpfr_get_emin () < 0);
mpfr_mul_2si (b, b, (mpfr_get_emin () - 1) / 2, MPFR_RNDN);
mpfr_mul_2si (c, c, (mpfr_get_emin () - 2) / 2, MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDU);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDD);
MPFR_ASSERTN(inex < 0);
MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
}
else /* p is odd:
b = (1-2^(-(p+1)/2))*2^...
c = (1+2^(-(p+1)/2))*2^... */
{
mpfr_set_si_2exp (b, -1, -(p+1)/2, MPFR_RNDN);
mpfr_add_ui (b, b, 1, MPFR_RNDN);
mpfr_set_si_2exp (c, 1, -(p+1)/2, MPFR_RNDN);
mpfr_add_ui (c, c, 1, MPFR_RNDN);
MPFR_ASSERTN(mpfr_get_emin () < 0);
mpfr_mul_2si (b, b, (mpfr_get_emin () - 1) / 2, MPFR_RNDN);
mpfr_mul_2si (c, c, (mpfr_get_emin () - 2) / 2, MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0);
MPFR_ASSERTN(!mpfr_underflow_p ());
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDU);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0);
MPFR_ASSERTN(!mpfr_underflow_p ());
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDD);
MPFR_ASSERTN(inex < 0);
MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0);
MPFR_ASSERTN(mpfr_underflow_p ());
}
if (p <= 2) /* for p=2, 1+2^(-ceil((p+1)/2)) = 1 + 2^(-2) is not
exactly representable */
goto end_of_loop;
/* b = 1-2^(-ceil((p+1)/2))
c = 1+2^(-ceil((p+1)/2))
For p odd, b*c = 1-2^(p+1) should round to 1;
for p even, b*c = 1-2^(p+2) should round to 1 too. */
mpfr_set_si_2exp (b, -1, -(p+2)/2, MPFR_RNDN);
mpfr_add_ui (b, b, 1, MPFR_RNDN);
mpfr_set_si_2exp (c, 1, -(p+2)/2, MPFR_RNDN);
mpfr_add_ui (c, c, 1, MPFR_RNDN);
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
/* For RNDU, b*c should round to 1 */
inex = mpfr_mul (a, b, c, MPFR_RNDU);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
/* For RNDD, b*c should round to 1-2^(-p) */
inex = mpfr_mul (a, b, c, MPFR_RNDD);
MPFR_ASSERTN(inex < 0);
mpfr_nextabove (a);
MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
/* same as above, but near emax, to exercise the case where a carry
produces an overflow */
mpfr_set_si_2exp (b, -1, -(p+2)/2, MPFR_RNDN);
mpfr_add_ui (b, b, 1, MPFR_RNDN);
mpfr_mul_2si (b, b, mpfr_get_emax (), MPFR_RNDN);
mpfr_set_si_2exp (c, 1, -(p+2)/2, MPFR_RNDN);
mpfr_add_ui (c, c, 1, MPFR_RNDN);
/* b*c should round to 2^emax */
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0);
MPFR_ASSERTN(mpfr_overflow_p ());
/* idem for RNDU */
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDU);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0);
MPFR_ASSERTN(mpfr_overflow_p ());
/* For RNDD, b*c should round to (1-2^(-p))*2^emax */
mpfr_clear_flags ();
inex = mpfr_mul (a, b, c, MPFR_RNDD);
MPFR_ASSERTN(inex < 0);
MPFR_ASSERTN(!mpfr_inf_p (a));
MPFR_ASSERTN(!mpfr_overflow_p ());
mpfr_nextabove (a);
MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0);
end_of_loop:
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
}
/* check special underflow case for precision = 64 */
static void
coverage2 (void)
{
mpfr_t a, b, c;
int inex;
mpfr_exp_t emin;
emin = mpfr_get_emin (); /* save emin */
mpfr_set_emin (0);
mpfr_init2 (a, 64);
mpfr_init2 (b, 64);
mpfr_init2 (c, 64);
mpfr_set_str_binary (b, "1111110110100001011100100000100000110110001100100010011010011001E-64"); /* 18276014142440744601/2^64 */
mpfr_set_str_binary (c, "1000000100110010000111000100010010010001000100101010111101010100E-64"); /* 9309534460545511252/2^64 */
/* since 1/2-2^-66 < b0*c0 < 1/2, b0*c0 should be rounded to 1/2 */
inex = mpfr_mul (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, -1) == 0);
MPFR_ASSERTN(inex > 0);
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
mpfr_set_emin (emin); /* restore emin */
}
int
main (int argc, char *argv[])
{
tests_start_mpfr ();
coverage (1024);
coverage2 ();
testall_rndf (9);
check_nans ();
check_exact ();
check_float ();
check53("6.9314718055994530941514e-1", "0.0", MPFR_RNDZ, "0.0");
check53("0.0", "6.9314718055994530941514e-1", MPFR_RNDZ, "0.0");
check_sign();
check53("-4.165000000e4", "-0.00004801920768307322868063274915", MPFR_RNDN,
"2.0");
check53("2.71331408349172961467e-08", "-6.72658901114033715233e-165",
MPFR_RNDZ, "-1.8251348697787782844e-172");
check53("2.71331408349172961467e-08", "-6.72658901114033715233e-165",
MPFR_RNDA, "-1.8251348697787786e-172");
check53("0.31869277231188065", "0.88642843322303122", MPFR_RNDZ,
"2.8249833483992453642e-1");
check("8.47622108205396074254e-01", "3.24039313247872939883e-01", MPFR_RNDU,
28, 45, 2, "0.375");
check("8.47622108205396074254e-01", "3.24039313247872939883e-01", MPFR_RNDA,
28, 45, 2, "0.375");
check("2.63978122803639081440e-01", "6.8378615379333496093e-1", MPFR_RNDN,
34, 23, 31, "0.180504585267044603");
check("1.0", "0.11835170935876249132", MPFR_RNDU, 6, 41, 36,
"0.1183517093595583");
check53("67108865.0", "134217729.0", MPFR_RNDN, "9.007199456067584e15");
check("1.37399642157394197284e-01", "2.28877275604219221350e-01", MPFR_RNDN,
49, 15, 32, "0.0314472340833162888");
check("4.03160720978664954828e-01", "5.854828e-1"
/*"5.85483042917246621073e-01"*/, MPFR_RNDZ,
51, 22, 32, "0.2360436821472831");
check("3.90798504668055102229e-14", "9.85394674650308388664e-04", MPFR_RNDN,
46, 22, 12, "0.385027296503914762e-16");
check("4.58687081072827851358e-01", "2.20543551472118792844e-01", MPFR_RNDN,
49, 3, 2, "0.09375");
check_max();
check_min();
small_prec ();
check_regression ();
test_generic (MPFR_PREC_MIN, 500, 100);
data_check ("data/mulpi", mpfr_mulpi, "mpfr_mulpi");
valgrind20110503 ();
test_underflow (128);
bug20161209 ();
bug20161209a ();
bug20170602 ();
test_underflow2 ();
tests_end_mpfr ();
return 0;
}