/* Test file for mpfr_can_round and mpfr_round_p.
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"
/* Simple cases where err - prec is large enough.
One can get failures as a consequence of r9883. */
static void
test_simple (void)
{
int t[4] = { 2, 3, -2, -3 }; /* test powers of 2 and non-powers of 2 */
int i;
int r1, r2;
for (i = 0; i < 4; i++)
RND_LOOP (r1)
RND_LOOP (r2)
{
mpfr_t b;
int p, err, prec, inex;
int s1, s2;
int expected, got;
p = 12 + (randlimb() % (2 * GMP_NUMB_BITS));
err = p - 3;
prec = 4;
mpfr_init2 (b, p);
inex = mpfr_set_si (b, t[i], MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
got = mpfr_can_round (b, err, (mpfr_rnd_t) r1, (mpfr_rnd_t) r2, prec);
s1 = r1;
s2 = r2;
if (s1 == MPFR_RNDD)
s1 = (t[i] > 0) ? MPFR_RNDZ : MPFR_RNDA;
if (s1 == MPFR_RNDU)
s1 = (t[i] < 0) ? MPFR_RNDZ : MPFR_RNDA;
if (s1 == MPFR_RNDF)
s1 = MPFR_RNDN; /* For s1, RNDF is equivalent to RNDN. */
if (s2 == MPFR_RNDD)
s2 = (t[i] > 0) ? MPFR_RNDZ : MPFR_RNDA;
if (s2 == MPFR_RNDU)
s2 = (t[i] < 0) ? MPFR_RNDZ : MPFR_RNDA;
/* If s1 == s2, we can round.
s1 s2 can round
xxx xxx yes
RNDZ RNDA no
RNDZ RNDN yes
RNDA RNDZ no
RNDA RNDN yes
RNDN RNDZ no
RNDN RNDA no
xxx RNDF yes
*/
expected = 1;
if ((s1 == MPFR_RNDZ && s2 == MPFR_RNDA) ||
(s1 == MPFR_RNDA && s2 == MPFR_RNDZ) ||
(s1 == MPFR_RNDN && s2 == MPFR_RNDZ) ||
(s1 == MPFR_RNDN && s2 == MPFR_RNDA))
expected = 0;
if (!!got != !!expected)
{
printf ("Error in test_simple for i=%d,"
" err=%d r1=%s, r2=%s, p=%d, prec=%d\n", i, err,
mpfr_print_rnd_mode ((mpfr_rnd_t) r1),
mpfr_print_rnd_mode ((mpfr_rnd_t) r2), p, prec);
printf ("b="); mpfr_dump (b);
printf ("expected %d, got %d\n", expected, got);
exit (1);
}
mpfr_clear (b);
}
}
#define MAX_LIMB_SIZE 100
static void
check_round_p (void)
{
mp_limb_t buf[MAX_LIMB_SIZE];
mp_size_t n, i;
mpfr_prec_t p;
mpfr_exp_t err;
int r1, r2;
for (n = 2 ; n <= MAX_LIMB_SIZE ; n++)
{
/* avoid mpn_random which leaks memory */
for (i = 0; i < n; i++)
buf[i] = randlimb ();
/* force the number to be normalized */
buf[n - 1] |= MPFR_LIMB_HIGHBIT;
p = randlimb() % ((n-1) * GMP_NUMB_BITS) + MPFR_PREC_MIN;
err = p + randlimb () % GMP_NUMB_BITS;
r1 = mpfr_round_p (buf, n, err, p);
r2 = mpfr_can_round_raw (buf, n, MPFR_SIGN_POS, err,
MPFR_RNDN, MPFR_RNDZ, p);
if (r1 != r2)
{
printf ("mpfr_round_p(%d) != mpfr_can_round(%d,RNDZ)!\n"
"bn = %ld, err0 = %ld, prec = %lu\n",
r1, r2, (long) n, (long) err, (unsigned long) p);
n_trace ("b", buf, n);
exit (1);
}
/* Same with RNDF: with rnd1=RNDN, rnd2=RNDF is converted to RNDN. */
r1 = mpfr_can_round_raw (buf, n, MPFR_SIGN_POS, err,
MPFR_RNDN, MPFR_RNDN, p);
r2 = mpfr_can_round_raw (buf, n, MPFR_SIGN_POS, err,
MPFR_RNDN, MPFR_RNDF, p);
if (r1 != r2)
{
printf ("mpfr_can_round(%d,RNDN) != mpfr_can_round(%d,RNDF)!\n"
"bn = %ld, err0 = %ld, prec = %lu\n",
r1, r2, (long) n, (long) err, (unsigned long) p);
n_trace ("b", buf, n);
exit (1);
}
/* PZ: disabled those tests for now, since when {buf, n} is exactly
representable in the target precision p, then mpfr_can_round_raw(RNDA)
should give 0, and mpfr_can_round_raw(MPFR_RNDF) should give 1 if the
error is small enough. */
#if 0
/* Same with RNDF: with rnd1=RNDZ, rnd2=RNDF is converted to RNDA. */
r1 = mpfr_can_round_raw (buf, n, MPFR_SIGN_POS, err,
MPFR_RNDZ, MPFR_RNDA, p);
r2 = mpfr_can_round_raw (buf, n, MPFR_SIGN_POS, err,
MPFR_RNDZ, MPFR_RNDF, p);
if (r1 != r2)
{
printf ("mpfr_can_round(%d,RNDA) != mpfr_can_round(%d,RNDF)!\n"
"bn = %ld, err0 = %ld, prec = %lu\n",
r1, r2, (long) n, (long) err, (unsigned long) p);
n_trace ("b", buf, n);
exit (1);
}
/* Same with RNDF: with rnd1=RNDA, rnd2=RNDF is converted to RNDZ. */
r1 = mpfr_can_round_raw (buf, n, MPFR_SIGN_POS, err,
MPFR_RNDA, MPFR_RNDZ, p);
r2 = mpfr_can_round_raw (buf, n, MPFR_SIGN_POS, err,
MPFR_RNDA, MPFR_RNDF, p);
if (r1 != r2)
{
printf ("mpfr_can_round(%d,RNDZ) != mpfr_can_round(%d,RNDF)!\n"
"bn = %ld, err0 = %ld, prec = %lu\n",
r1, r2, (long) n, (long) err, (unsigned long) p);
n_trace ("b", buf, n);
exit (1);
}
#endif
}
}
/* check x=2^i with precision px, error at most 1, and target precision prec */
static void
test_pow2 (mpfr_exp_t i, mpfr_prec_t px, mpfr_rnd_t r1, mpfr_rnd_t r2,
mpfr_prec_t prec)
{
mpfr_t x;
int b, expected_b, b2;
mpfr_init2 (x, px);
mpfr_set_ui_2exp (x, 1, i, MPFR_RNDN);
/* for mpfr_can_round, r1=RNDF is equivalent to r1=RNDN (the sign of the
error is not known) */
b = !!mpfr_can_round (x, i+1, r1, r2, prec);
/* Note: If mpfr_can_round succeeds for both
(r1,r2) = (MPFR_RNDD,MPFR_RNDN) and
(r1,r2) = (MPFR_RNDU,MPFR_RNDN), then it should succeed for
(r1,r2) = (MPFR_RNDN,MPFR_RNDN). So, the condition on prec below
for r1 = MPFR_RNDN should be the most restrictive between those
for r1 = any directed rounding mode.
For r1 like MPFR_RNDA, the unrounded, unknown number may be anyone
in [2^i-1,i]. As both 2^i-1 and 2^i fit on i bits, one cannot round
in any precision >= i bits, hence the condition prec < i; prec = i-1
will work here for r2 = MPFR_RNDN thanks to the even-rounding rule
(and also with rounding ties away from zero). */
expected_b =
MPFR_IS_LIKE_RNDD (r1, MPFR_SIGN_POS) ?
(MPFR_IS_LIKE_RNDU (r2, MPFR_SIGN_POS) ? 0 : prec <= i) :
MPFR_IS_LIKE_RNDU (r1, MPFR_SIGN_POS) ?
(MPFR_IS_LIKE_RNDD (r2, MPFR_SIGN_POS) ? 0 : prec < i) :
(r2 != MPFR_RNDN ? 0 : prec < i);
if (b != expected_b)
{
printf ("Error for x=2^%d, px=%lu, err=%d, r1=%s, r2=%s, prec=%d\n",
(int) i, (unsigned long) px, (int) i + 1,
mpfr_print_rnd_mode (r1), mpfr_print_rnd_mode (r2), (int) prec);
printf ("Expected %d, got %d\n", expected_b, b);
exit (1);
}
if (r1 == MPFR_RNDN && r2 == MPFR_RNDZ)
{
/* Similar test to the one done in src/round_p.c
for MPFR_WANT_ASSERT >= 2. */
b2 = !!mpfr_round_p (MPFR_MANT(x), MPFR_LIMB_SIZE(x), i+1, prec);
if (b2 != b)
{
printf ("Error for x=2^%d, px=%lu, err=%d, prec=%d\n",
(int) i, (unsigned long) px, (int) i + 1, (int) prec);
printf ("mpfr_can_round gave %d, mpfr_round_p gave %d\n", b, b2);
exit (1);
}
}
mpfr_clear (x);
}
static void
check_can_round (void)
{
mpfr_t x, xinf, xsup, yinf, ysup;
int precx, precy, err;
int rnd1, rnd2;
int i, u[3] = { 0, 1, 256 };
int inex;
int expected, got;
int maxerr;
mpfr_inits2 (4 * GMP_NUMB_BITS, x, xinf, xsup, yinf, ysup, (mpfr_ptr) 0);
for (precx = 3 * GMP_NUMB_BITS - 3; precx <= 3 * GMP_NUMB_BITS + 3; precx++)
{
mpfr_set_prec (x, precx);
for (precy = precx - 4; precy <= precx + 4; precy++)
{
mpfr_set_prec (yinf, precy);
mpfr_set_prec (ysup, precy);
for (i = 0; i <= 3; i++)
{
if (i <= 2)
{
/* Test x = 2^(precx - 1) + u */
mpfr_set_ui_2exp (x, 1, precx - 1, MPFR_RNDN);
mpfr_add_ui (x, x, u[i], MPFR_RNDN);
}
else
{
/* Test x = 2^precx - 1 */
mpfr_set_ui_2exp (x, 1, precx, MPFR_RNDN);
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
}
MPFR_ASSERTN (mpfr_get_exp (x) == precx);
maxerr = precy + 3;
if (4 * GMP_NUMB_BITS < maxerr)
maxerr = 4 * GMP_NUMB_BITS;
for (err = precy; err <= maxerr; err++)
{
mpfr_set_ui_2exp (xinf, 1, precx - err, MPFR_RNDN);
inex = mpfr_add (xsup, x, xinf, MPFR_RNDN);
/* Since EXP(x) = precx, and xinf = 2^(precx-err),
x + xinf is exactly representable on 4 * GMP_NUMB_BITS
nbits as long as err <= 4 * GMP_NUMB_BITS */
MPFR_ASSERTN (inex == 0);
inex = mpfr_sub (xinf, x, xinf, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
RND_LOOP (rnd1)
RND_LOOP (rnd2)
{
/* TODO: Test r2 == MPFR_RNDF. The following "continue"
was added while this case had not been specified
yet, but this is no longer the case. */
if (rnd2 == MPFR_RNDF)
continue;
mpfr_set (yinf, MPFR_IS_LIKE_RNDD (rnd1, 1) ?
x : xinf, (mpfr_rnd_t) rnd2);
mpfr_set (ysup, MPFR_IS_LIKE_RNDU (rnd1, 1) ?
x : xsup, (mpfr_rnd_t) rnd2);
expected = !! mpfr_equal_p (yinf, ysup);
got = !! mpfr_can_round (x, err, (mpfr_rnd_t) rnd1,
(mpfr_rnd_t) rnd2, precy);
if (got != expected)
{
printf ("Error in check_can_round on:\n"
"precx=%d, precy=%d, i=%d, err=%d, "
"rnd1=%s, rnd2=%s: expected %d, got %d\n",
precx, precy, i, err,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd1),
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd2),
expected, got);
printf ("x="); mpfr_dump (x);
printf ("yinf="); mpfr_dump (yinf);
printf ("ysup="); mpfr_dump (ysup);
exit (1);
}
}
}
}
}
}
mpfr_clears (x, xinf, xsup, yinf, ysup, (mpfr_ptr) 0);
}
/* test of RNDNA (nearest with ties to away) */
static void
test_rndna (void)
{
mpfr_t x;
int inex;
mpfr_init2 (x, 10);
mpfr_set_str_binary (x, "1111111101"); /* 1021 */
inex = mpfr_prec_round (x, 9, MPFR_RNDNA);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1022) == 0);
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "1111111101"); /* 1021 */
inex = mpfr_prec_round (x, 9, MPFR_RNDN);
MPFR_ASSERTN(inex < 0);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1020) == 0);
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "1111111011"); /* 1019 */
inex = mpfr_prec_round (x, 9, MPFR_RNDNA);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1020) == 0);
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "1111111011"); /* 1019 */
inex = mpfr_prec_round (x, 9, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1020) == 0);
mpfr_clear (x);
}
int
main (void)
{
mpfr_t x;
mpfr_prec_t i, j, k;
int r1, r2;
int n;
tests_start_mpfr ();
test_rndna ();
test_simple ();
/* checks that rounds to nearest sets the last
bit to zero in case of equal distance */
mpfr_init2 (x, 59);
mpfr_set_str_binary (x, "-0.10010001010111000011110010111010111110000000111101100111111E663");
if (mpfr_can_round (x, 54, MPFR_RNDZ, MPFR_RNDZ, 53))
{
printf ("Error (1) in mpfr_can_round\n");
exit (1);
}
mpfr_set_str_binary (x, "-Inf");
if (mpfr_can_round (x, 2000, MPFR_RNDZ, MPFR_RNDZ, 2000))
{
printf ("Error (2) in mpfr_can_round\n");
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_str_binary (x, "0.1011001000011110000110000110001111101011000010001110011000000000");
if (mpfr_can_round (x, 65, MPFR_RNDN, MPFR_RNDN, 54))
{
printf ("Error (3) in mpfr_can_round\n");
exit (1);
}
mpfr_set_prec (x, 137);
mpfr_set_str_binary (x, "-0.10111001101001010110011000110100111010011101101010010100101100001110000100111111011101010110001010111100100101110111100001000010000000000E-97");
if (! mpfr_can_round (x, 132, MPFR_RNDU, MPFR_RNDZ, 128))
{
printf ("Error (4) in mpfr_can_round\n");
exit (1);
}
/* in the following, we can round but cannot determine the inexact flag */
mpfr_set_prec (x, 86);
mpfr_set_str_binary (x, "-0.11100100010011001111011010100111101010011000000000000000000000000000000000000000000000E-80");
if (! mpfr_can_round (x, 81, MPFR_RNDU, MPFR_RNDZ, 44))
{
printf ("Error (5) in mpfr_can_round\n");
exit (1);
}
mpfr_set_prec (x, 62);
mpfr_set_str (x, "0.ff4ca619c76ba69", 16, MPFR_RNDZ);
for (i = 30; i < 99; i++)
for (j = 30; j < 99; j++)
RND_LOOP (r1)
RND_LOOP (r2)
{
/* test for assertions */
mpfr_can_round (x, i, (mpfr_rnd_t) r1, (mpfr_rnd_t) r2, j);
}
test_pow2 (32, 32, MPFR_RNDN, MPFR_RNDN, 32);
test_pow2 (174, 174, MPFR_RNDN, MPFR_RNDN, 174);
test_pow2 (174, 174, MPFR_RNDU, MPFR_RNDN, 174);
test_pow2 (176, 129, MPFR_RNDU, MPFR_RNDU, 174);
test_pow2 (176, 2, MPFR_RNDZ, MPFR_RNDZ, 174);
test_pow2 (176, 2, MPFR_RNDU, MPFR_RNDU, 176);
/* Tests for x = 2^i (E(x) = i+1) with error at most 1 = 2^0. */
for (n = 0; n < 100; n++)
{
/* TODO: Test r2 == MPFR_RNDF (add its support in test_pow2). The
exclusion below was added while this case had not been specified
yet, but this is no longer the case. */
i = (randlimb() % 200) + 4;
for (j = i - 2; j < i + 2; j++)
RND_LOOP (r1)
RND_LOOP (r2)
if (r2 != MPFR_RNDF)
for (k = MPFR_PREC_MIN; k <= i + 2; k++)
test_pow2 (i, k, (mpfr_rnd_t) r1, (mpfr_rnd_t) r2, j);
}
mpfr_clear (x);
check_can_round ();
check_round_p ();
tests_end_mpfr ();
return 0;
}