/* Test file for mpfr_sub1sp.
Copyright 2003-2020 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"
static void check_special (void);
static void check_random (mpfr_prec_t p);
static void check_underflow (mpfr_prec_t p);
static void check_corner (mpfr_prec_t p);
static void
bug20170109 (void)
{
mpfr_t a, b, c;
mpfr_init2 (a, 111);
mpfr_init2 (b, 111);
mpfr_init2 (c, 111);
mpfr_set_str_binary (b, "0.110010010000111111011010101000100010000101101000110000100011010011000100110001100110001010001011100000001101110E1");
mpfr_set_str_binary (c, "0.111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111E-63");
mpfr_sub (a, b, c, MPFR_RNDN);
mpfr_set_str_binary (b, "0.110010010000111111011010101000100010000101101000110000100011001111000100110001100110001010001011100000001101110E1");
MPFR_ASSERTN(mpfr_equal_p (a, b));
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
/* check mpfr_sub1sp1 when:
(1) p = GMP_NUMB_BITS-1, d = GMP_NUMB_BITS and bp[0] = MPFR_LIMB_HIGHBIT
(2) p = 2*GMP_NUMB_BITS-1, d = 2*GMP_NUMB_BITS and b = 1000...000
(3) p = 3*GMP_NUMB_BITS-1, d = 3*GMP_NUMB_BITS and b = 1000...000
*/
static void
test20170208 (void)
{
mpfr_t a, b, c;
int inex;
mpfr_inits2 (GMP_NUMB_BITS - 1, a, b, c, (mpfr_ptr) 0);
/* test (1) */
mpfr_set_ui_2exp (b, 1, GMP_NUMB_BITS, MPFR_RNDN);
mpfr_set_ui_2exp (c, 1, 0, MPFR_RNDN);
inex = mpfr_sub (a, b, c, MPFR_RNDN);
/* b-c = 2^GMP_NUMB_BITS-1 which has GMP_NUMB_BITS bits, thus we should
round to 2^GMP_NUMB_BITS (even rule) */
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, GMP_NUMB_BITS) == 0);
MPFR_ASSERTN(inex > 0);
inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, GMP_NUMB_BITS) == 0);
MPFR_ASSERTN(inex > 0);
mpfr_set_ui_2exp (c, 2, 0, MPFR_RNDN);
mpfr_nextbelow (c);
/* now c = 2 - 2^(1-GMP_NUMB_BITS) */
inex = mpfr_sub (a, b, c, MPFR_RNDN);
/* b-c = 2^GMP_NUMB_BITS-2+2^(1-GMP_NUMB_BITS), which should
round to 2^GMP_NUMB_BITS-2. We check by directly inspecting the bit
field of a, since mpfr_cmp_ui might not work if unsigned long is shorter
than mp_limb_t, and we don't want to use mpfr_add_ui or mpfr_sub_ui
to construct the expected result. */
MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
MPFR_ASSERTN(MPFR_EXP(a) == GMP_NUMB_BITS);
MPFR_ASSERTN(inex < 0);
inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
MPFR_ASSERTN(MPFR_EXP(a) == GMP_NUMB_BITS);
MPFR_ASSERTN(inex < 0);
/* test (2) */
mpfr_set_prec (a, 2 * GMP_NUMB_BITS - 1);
mpfr_set_prec (b, 2 * GMP_NUMB_BITS - 1);
mpfr_set_prec (c, 2 * GMP_NUMB_BITS - 1);
mpfr_set_ui_2exp (b, 1, 2 * GMP_NUMB_BITS, MPFR_RNDN);
mpfr_set_ui_2exp (c, 1, 0, MPFR_RNDN);
inex = mpfr_sub (a, b, c, MPFR_RNDN);
/* b-c = 2^(2*GMP_NUMB_BITS)-1 which has 2*GMP_NUMB_BITS bits, thus we should
round to 2^(2*GMP_NUMB_BITS) (even rule) */
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, 2 * GMP_NUMB_BITS) == 0);
MPFR_ASSERTN(inex > 0);
inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, 2 * GMP_NUMB_BITS) == 0);
MPFR_ASSERTN(inex > 0);
mpfr_set_ui_2exp (c, 2, 0, MPFR_RNDN);
mpfr_nextbelow (c);
/* now c = 2 - 2^(1-2*GMP_NUMB_BITS) */
inex = mpfr_sub (a, b, c, MPFR_RNDN);
/* b-c = 2^(2*GMP_NUMB_BITS)-2+2^(1-2*GMP_NUMB_BITS), which should
round to 2^(2*GMP_NUMB_BITS)-2. We check by directly inspecting the bit
field of a, since mpfr_cmp_ui might not work if unsigned long is shorter
than mp_limb_t, and we don't want to use mpfr_add_ui or mpfr_sub_ui
to construct the expected result. */
MPFR_ASSERTN(MPFR_MANT(a)[1] == (mp_limb_t) -1);
MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
MPFR_ASSERTN(MPFR_EXP(a) == 2 * GMP_NUMB_BITS);
MPFR_ASSERTN(inex < 0);
inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(MPFR_MANT(a)[1] == (mp_limb_t) -1);
MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
MPFR_ASSERTN(MPFR_EXP(a) == 2 * GMP_NUMB_BITS);
MPFR_ASSERTN(inex < 0);
/* test (3) */
mpfr_set_prec (a, 3 * GMP_NUMB_BITS - 1);
mpfr_set_prec (b, 3 * GMP_NUMB_BITS - 1);
mpfr_set_prec (c, 3 * GMP_NUMB_BITS - 1);
mpfr_set_ui_2exp (b, 1, 3 * GMP_NUMB_BITS, MPFR_RNDN);
mpfr_set_ui_2exp (c, 1, 0, MPFR_RNDN);
inex = mpfr_sub (a, b, c, MPFR_RNDN);
/* b-c = 2^(3*GMP_NUMB_BITS)-1 which has 3*GMP_NUMB_BITS bits, thus we should
round to 3^(2*GMP_NUMB_BITS) (even rule) */
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, 3 * GMP_NUMB_BITS) == 0);
MPFR_ASSERTN(inex > 0);
inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, 3 * GMP_NUMB_BITS) == 0);
MPFR_ASSERTN(inex > 0);
mpfr_set_ui_2exp (c, 2, 0, MPFR_RNDN);
mpfr_nextbelow (c);
/* now c = 2 - 2^(1-3*GMP_NUMB_BITS) */
inex = mpfr_sub (a, b, c, MPFR_RNDN);
/* b-c = 2^(3*GMP_NUMB_BITS)-2+2^(1-3*GMP_NUMB_BITS), which should
round to 2^(3*GMP_NUMB_BITS)-2. We check by directly inspecting the bit
field of a, since mpfr_cmp_ui might not work if unsigned long is shorter
than mp_limb_t, and we don't want to use mpfr_add_ui or mpfr_sub_ui
to construct the expected result. */
MPFR_ASSERTN(MPFR_MANT(a)[2] == (mp_limb_t) -1);
MPFR_ASSERTN(MPFR_MANT(a)[1] == (mp_limb_t) -1);
MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
MPFR_ASSERTN(MPFR_EXP(a) == 3 * GMP_NUMB_BITS);
MPFR_ASSERTN(inex < 0);
inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(MPFR_MANT(a)[2] == (mp_limb_t) -1);
MPFR_ASSERTN(MPFR_MANT(a)[1] == (mp_limb_t) -1);
MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
MPFR_ASSERTN(MPFR_EXP(a) == 3 * GMP_NUMB_BITS);
MPFR_ASSERTN(inex < 0);
mpfr_clears (a, b, c, (mpfr_ptr) 0);
}
static void
compare_sub_sub1sp (void)
{
mpfr_t a, b, c, a_ref;
mpfr_prec_t p;
unsigned long d;
int i, inex_ref, inex;
int r;
for (p = 1; p <= 3*GMP_NUMB_BITS; p++)
{
mpfr_inits2 (p, a, b, c, a_ref, (mpfr_ptr) 0);
for (d = 0; d <= p + 2; d++)
{
/* EXP(b) - EXP(c) = d */
for (i = 0; i < 4; i++)
{
/* for i even, b is the smallest number, for b odd the largest */
mpfr_set_ui_2exp (b, 1, d, MPFR_RNDN);
if (i & 1)
{
mpfr_mul_2ui (b, b, 1, MPFR_RNDN);
mpfr_nextbelow (b);
}
mpfr_set_ui_2exp (c, 1, 0, MPFR_RNDN);
if (i & 2)
{
mpfr_mul_2ui (c, c, 1, MPFR_RNDN);
mpfr_nextbelow (c);
}
RND_LOOP_NO_RNDF (r)
{
/* increase the precision of b to ensure sub1sp is not used */
mpfr_prec_round (b, p + 1, MPFR_RNDN);
inex_ref = mpfr_sub (a_ref, b, c, (mpfr_rnd_t) r);
inex = mpfr_prec_round (b, p, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
inex = mpfr_sub1sp (a, b, c, (mpfr_rnd_t) r);
if (inex != inex_ref)
{
printf ("mpfr_sub and mpfr_sub1sp differ for r=%s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
printf ("b="); mpfr_dump (b);
printf ("c="); mpfr_dump (c);
printf ("expected inex=%d and ", inex_ref);
mpfr_dump (a_ref);
printf ("got inex=%d and ", inex);
mpfr_dump (a);
exit (1);
}
MPFR_ASSERTN(mpfr_equal_p (a, a_ref));
}
}
}
mpfr_clears (a, b, c, a_ref, (mpfr_ptr) 0);
}
}
static void
bug20171213 (void)
{
mpfr_t a, b, c;
mpfr_init2 (a, 127);
mpfr_init2 (b, 127);
mpfr_init2 (c, 127);
mpfr_set_str_binary (b, "0.1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E1");
mpfr_set_str_binary (c, "0.1000011010111101100101100110101111111001011001010000110000000000000000000000000000000000000000000000000000000000000000000000000E-74");
mpfr_sub (a, b, c, MPFR_RNDN);
mpfr_set_str_binary (b, "0.1111111111111111111111111111111111111111111111111111111111111111111111111101111001010000100110100110010100000001101001101011110E0");
MPFR_ASSERTN(mpfr_equal_p (a, b));
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
/* generic test for bug20171213:
b = 1.0 with precision p
c = 0.1xxx110...0E-e with precision p, with e >= 1, such that the part 1xxx1 has
exactly p+1-e bits, thus b-c = 0.111..01... is exact on p+1 bits.
Due to the round-to-even rule, b-c should be rounded to 0.111..0.
*/
static void
bug20171213_gen (mpfr_prec_t pmax)
{
mpfr_prec_t p;
mpfr_exp_t e;
mpfr_t a, b, c, d;
for (p = MPFR_PREC_MIN; p <= pmax; p++)
{
for (e = 1; e < p; e++)
{
mpfr_init2 (a, p);
mpfr_init2 (b, p);
mpfr_init2 (c, p);
mpfr_init2 (d, p);
mpfr_set_ui (b, 1, MPFR_RNDN);
mpfr_set_ui_2exp (c, 1, p + 1 - e, MPFR_RNDN); /* c = 2^(p + 1 - e) */
mpfr_sub_ui (c, c, 1, MPFR_RNDN); /* c = 2^(p + 1 - e) - 1 */
mpfr_div_2ui (c, c, p + 1, MPFR_RNDN); /* c = 2^(-e) - 2^(-p-1) */
/* the exact difference is 1 - 2^(-e) + 2^(-p-1) */
mpfr_sub (a, b, c, MPFR_RNDN);
/* check that a = 1 - 2^(-e) */
mpfr_set_ui_2exp (d, 1, e, MPFR_RNDN); /* b = 2^e */
mpfr_sub_ui (d, d, 1, MPFR_RNDN); /* b = 2^e - 1 */
mpfr_div_2ui (d, d, e, MPFR_RNDN); /* b = 1 - 2^(-e) */
if (! mpfr_equal_p (a, d))
{
printf ("bug20171213_gen failed for p=%ld, e=%ld\n",
(long) p, (long) e);
printf ("b="); mpfr_dump (b);
printf ("c="); mpfr_dump (c);
printf ("got a="); mpfr_dump (a);
printf ("expected d="); mpfr_dump (d);
exit (1);
}
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
mpfr_clear (d);
}
}
}
static void
coverage (void)
{
mpfr_t a, b, c, d, u;
int inex;
/* coverage test in mpfr_sub1sp: case d=1, limb > MPFR_LIMB_HIGHBIT, RNDF
and also RNDZ */
mpfr_init2 (a, 3 * GMP_NUMB_BITS);
mpfr_init2 (b, 3 * GMP_NUMB_BITS);
mpfr_init2 (c, 3 * GMP_NUMB_BITS);
mpfr_init2 (d, 3 * GMP_NUMB_BITS);
mpfr_init2 (u, 3 * GMP_NUMB_BITS);
mpfr_set_ui (b, 1, MPFR_RNDN);
mpfr_nextbelow (b); /* b = 1 - 2^(-p) */
mpfr_set_prec (c, GMP_NUMB_BITS);
mpfr_set_ui_2exp (c, 1, -1, MPFR_RNDN);
mpfr_nextbelow (c);
mpfr_nextbelow (c); /* c = 1/2 - 2*2^(-GMP_NUMB_BITS-1) */
mpfr_prec_round (c, 3 * GMP_NUMB_BITS, MPFR_RNDN);
mpfr_nextbelow (c); /* c = 1/2 - 2*2^(-GMP_NUMB_BITS-1) - 2^(-p-1) */
/* b-c = c */
mpfr_sub (a, b, c, MPFR_RNDF);
mpfr_sub (d, b, c, MPFR_RNDD);
mpfr_sub (u, b, c, MPFR_RNDU);
/* check a = d or u */
MPFR_ASSERTN(mpfr_equal_p (a, d) || mpfr_equal_p (a, u));
/* coverage test in mpfr_sub1sp: case d=p, RNDN, sb = 0, significand of b
is even but b<>2^e, (case 1e) */
mpfr_set_prec (a, 3 * GMP_NUMB_BITS);
mpfr_set_prec (b, 3 * GMP_NUMB_BITS);
mpfr_set_prec (c, 3 * GMP_NUMB_BITS);
mpfr_set_ui (b, 1, MPFR_RNDN);
mpfr_nextabove (b);
mpfr_nextabove (b);
mpfr_set_ui_2exp (c, 1, -3 * GMP_NUMB_BITS, MPFR_RNDN);
inex = mpfr_sub (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_equal_p (a, b));
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
mpfr_clear (d);
mpfr_clear (u);
}
/* bug in mpfr_sub1sp1n, made generic */
static void
bug20180217 (mpfr_prec_t pmax)
{
mpfr_t a, b, c;
int inex;
mpfr_prec_t p;
for (p = MPFR_PREC_MIN; p <= pmax; p++)
{
mpfr_init2 (a, p);
mpfr_init2 (b, p);
mpfr_init2 (c, p);
mpfr_set_ui (b, 1, MPFR_RNDN); /* b = 1 */
mpfr_set_ui_2exp (c, 1, -p-1, MPFR_RNDN); /* c = 2^(-p-1) */
/* a - b = 1 - 2^(-p-1) and should be rounded to 1 (case 2f of
mpfr_sub1sp) */
inex = mpfr_sub (a, b, c, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
/* check also when a=b */
mpfr_set_ui (a, 1, MPFR_RNDN);
inex = mpfr_sub (a, a, c, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
/* and when a=c */
mpfr_set_ui (b, 1, MPFR_RNDN); /* b = 1 */
mpfr_set_ui_2exp (a, 1, -p-1, MPFR_RNDN);
inex = mpfr_sub (a, b, a, MPFR_RNDN);
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
}
/* bug in revision 12985 with tlog and GMP_CHECK_RANDOMIZE=1534111552615050
(introduced in revision 12242, does not affect the 4.0 branch) */
static void
bug20180813 (void)
{
mpfr_t a, b, c;
mpfr_init2 (a, 194);
mpfr_init2 (b, 194);
mpfr_init2 (c, 194);
mpfr_set_str_binary (b, "0.10000111101000100000010000100010110111011100110100000101100111000010101000110110010101011101101011110110001000111001000010110010111010010100011011010100001010001110000101000010101110100110001000E7");
mpfr_set_str_binary (c, "0.10000000000000000100001111010001000000100001000101101110111001101000001011001110000101010001101100101010111011010111101100010001110010000101100101110100101000110110101000010100011100001010000101E24");
mpfr_sub (a, b, c, MPFR_RNDN);
mpfr_set_str_binary (b, "-0.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111E23");
MPFR_ASSERTN(mpfr_equal_p (a, b));
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
/* bug in revision 13599 with tatan and GMP_CHECK_RANDOMIZE=1567609230659336:
the values are equal, but the ternary value differs between sub1 and sub1sp
(bug introduced with mpfr_sub1sp2n, does not affect the 4.0 branch) */
static void
bug20190904 (void)
{
mpfr_t a, b, c;
int ret;
mpfr_init2 (a, 128);
mpfr_init2 (b, 128);
mpfr_init2 (c, 128);
mpfr_set_str_binary (b, "0.11001001000011111101101010100010001000010110100011000010001101001100010011000110011000101000101110000000110111000001110011010001E1");
mpfr_set_str_binary (c, "0.10010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010010000000000000000000000E-102");
ret = mpfr_sub (a, b, c, MPFR_RNDN);
mpfr_set_str_binary (b, "0.11001001000011111101101010100010001000010110100011000010001101001100010011000110011000101000101101111111101111000001110011010001E1");
MPFR_ASSERTN(mpfr_equal_p (a, b));
MPFR_ASSERTN(ret > 0);
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
int
main (void)
{
mpfr_prec_t p;
tests_start_mpfr ();
bug20190904 ();
bug20180813 ();
bug20180217 (1024);
coverage ();
compare_sub_sub1sp ();
test20170208 ();
bug20170109 ();
bug20171213 ();
bug20171213_gen (256);
check_special ();
for (p = MPFR_PREC_MIN ; p < 200 ; p++)
{
check_underflow (p);
check_random (p);
check_corner (p);
}
tests_end_mpfr ();
return 0;
}
#define STD_ERROR \
do \
{ \
printf("ERROR: for %s and p=%lu and i=%d:\nY=", \
mpfr_print_rnd_mode ((mpfr_rnd_t) r), (unsigned long) p, i); \
mpfr_dump (y); \
printf ("Z="); mpfr_dump (z); \
printf ("Expected: "); mpfr_dump (x2); \
printf ("Got : "); mpfr_dump (x); \
abort(); \
} \
while (0)
#define STD_ERROR2 \
do \
{ \
printf("ERROR: for %s and p=%lu and i=%d:\nY=", \
mpfr_print_rnd_mode ((mpfr_rnd_t) r), (unsigned long) p, i); \
mpfr_dump (y); \
printf ("Z="); mpfr_dump (z); \
printf ("Expected: "); mpfr_dump (x2); \
printf ("Got : "); mpfr_dump (x); \
printf ("Wrong inexact flag. Expected %d. Got %d\n", \
inexact1, inexact2); \
exit(1); \
} \
while (0)
static void
check_random (mpfr_prec_t p)
{
mpfr_t x,y,z,x2;
int r;
int i, inexact1, inexact2;
mpfr_inits2 (p, x, y, z, x2, (mpfr_ptr) 0);
for (i = 0 ; i < 500 ; i++)
{
mpfr_urandomb (y, RANDS);
mpfr_urandomb (z, RANDS);
if (MPFR_IS_PURE_FP(y) && MPFR_IS_PURE_FP(z))
for(r = 0 ; r < MPFR_RND_MAX ; r++)
{
if (r == MPFR_RNDF)
continue; /* mpfr_sub1 and mpfr_sub1sp could differ,
and inexact makes no sense */
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
}
}
mpfr_clears (x, y, z, x2, (mpfr_ptr) 0);
}
static void
check_special (void)
{
mpfr_t x,y,z,x2;
int r;
mpfr_prec_t p;
int i = -1, inexact1, inexact2;
mpfr_exp_t es;
mpfr_inits (x, y, z, x2, (mpfr_ptr) 0);
for (r = 0 ; r < MPFR_RND_MAX ; r++)
{
if (r == MPFR_RNDF)
continue; /* comparison between sub1 and sub1sp makes no sense here */
p = 53;
mpfr_set_prec(x, 53);
mpfr_set_prec(x2, 53);
mpfr_set_prec(y, 53);
mpfr_set_prec(z, 53);
mpfr_set_str_binary (y,
"0.10110111101101110010010010011011000001101101011011001E31");
mpfr_sub1sp (x, y, y, (mpfr_rnd_t) r);
if (mpfr_cmp_ui(x, 0))
{
printf("Error for x-x with p=%lu. Expected 0. Got:",
(unsigned long) p);
mpfr_dump (x);
exit(1);
}
mpfr_set(z, y, (mpfr_rnd_t) r);
mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp_ui(x, 0))
{
printf("Error for x-y with y=x and p=%lu. Expected 0. Got:",
(unsigned long) p);
mpfr_dump (x);
exit(1);
}
/* diff = 0 */
mpfr_set_str_binary (y,
"0.10110111101101110010010010011011001001101101011011001E31");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
/* Diff = 1 */
mpfr_set_str_binary (y,
"0.10110111101101110010010010011011000001101101011011001E30");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
/* Diff = 2 */
mpfr_set_str_binary (y,
"0.10110111101101110010010010011011000101101101011011001E32");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
/* Diff = 32 */
mpfr_set_str_binary (y,
"0.10110111101101110010010010011011000001101101011011001E63");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
/* Diff = 52 */
mpfr_set_str_binary (y,
"0.10110111101101110010010010011011010001101101011011001E83");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
/* Diff = 53 */
mpfr_set_str_binary (y,
"0.10110111101101110010010010011111000001101101011011001E31");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
/* Diff > 200 */
mpfr_set_str_binary (y,
"0.10110111101101110010010010011011000001101101011011001E331");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.10000000000000000000000000000000000000000000000000000E31");
mpfr_set_str_binary (z,
"0.11111111111111111111111111111111111111111111111111111E30");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.10000000000000000000000000000000000000000000000000000E31");
mpfr_set_str_binary (z,
"0.11111111111111111111111111111111111111111111111111111E29");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.10000000000000000000000000000000000000000000000000000E52");
mpfr_set_str_binary (z,
"0.10000000000010000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.11100000000000000000000000000000000000000000000000000E53");
mpfr_set_str_binary (z,
"0.10000000000000000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(z, y, z, (mpfr_rnd_t) r);
mpfr_set(x, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.10000000000000000000000000000000000000000000000000000E53");
mpfr_set_str_binary (z,
"0.10100000000000000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.10000000000000000000000000000000000000000000000000000E54");
mpfr_set_str_binary (z,
"0.10100000000000000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
p = 63;
mpfr_set_prec(x, p);
mpfr_set_prec(x2, p);
mpfr_set_prec(y, p);
mpfr_set_prec(z, p);
mpfr_set_str_binary (y,
"0.100000000000000000000000000000000000000000000000000000000000000E62");
mpfr_set_str_binary (z,
"0.110000000000000000000000000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
p = 64;
mpfr_set_prec(x, 64);
mpfr_set_prec(x2, 64);
mpfr_set_prec(y, 64);
mpfr_set_prec(z, 64);
mpfr_set_str_binary (y,
"0.1100000000000000000000000000000000000000000000000000000000000000E31");
mpfr_set_str_binary (z,
"0.1111111111111111111111111110000000000000000000000000011111111111E29");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.1000000000000000000000000000000000000000000000000000000000000000E63");
mpfr_set_str_binary (z,
"0.1011000000000000000000000000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.1000000000000000000000000000000000000000000000000000000000000000E63");
mpfr_set_str_binary (z,
"0.1110000000000000000000000000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.10000000000000000000000000000000000000000000000000000000000000E63");
mpfr_set_str_binary (z,
"0.10000000000000000000000000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.1000000000000000000000000000000000000000000000000000000000000000E64");
mpfr_set_str_binary (z,
"0.1010000000000000000000000000000000000000000000000000000000000000E00");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
MPFR_SET_NAN(x);
MPFR_SET_NAN(x2);
mpfr_set_str_binary (y,
"0.1000000000000000000000000000000000000000000000000000000000000000"
"E-1073741823");
mpfr_set_str_binary (z,
"0.1100000000000000000000000000000000000000000000000000000000000000"
"E-1073741823");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
p = 9;
mpfr_set_prec(x, p);
mpfr_set_prec(x2, p);
mpfr_set_prec(y, p);
mpfr_set_prec(z, p);
mpfr_set_str_binary (y, "0.100000000E1");
mpfr_set_str_binary (z, "0.100000000E-8");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
p = 34;
mpfr_set_prec(x, p);
mpfr_set_prec(x2, p);
mpfr_set_prec(y, p);
mpfr_set_prec(z, p);
mpfr_set_str_binary (y, "-0.1011110000111100010111011100110100E-18");
mpfr_set_str_binary (z, "0.1000101010110011010101011110000000E-14");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
p = 124;
mpfr_set_prec(x, p);
mpfr_set_prec(x2, p);
mpfr_set_prec(y, p);
mpfr_set_prec(z, p);
mpfr_set_str_binary (y,
"0.1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E1");
mpfr_set_str_binary (z,
"0.1011111000100111000011001000011101010101101100101010101001000001110100001101110110001110111010000011101001100010111110001100E-31");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
p = 288;
mpfr_set_prec(x, p);
mpfr_set_prec(x2, p);
mpfr_set_prec(y, p);
mpfr_set_prec(z, p);
mpfr_set_str_binary (y,
"0.111000110011000001000111101010111011110011101001101111111110000011100101000001001010110010101010011001010100000001110011110001010101101010001011101110100100001011110100110000101101100011010001001011011010101010000010001101001000110010010111111011110001111101001000101101001100101100101000E80");
mpfr_set_str_binary (z,
"-0.100001111111101001011010001100110010100111001110000110011101001011010100001000000100111011010110110010000000000010101101011000010000110001110010100001100101011100100100001011000100011110000001010101000100011101001000010111100000111000111011001000100100011000100000010010111000000100100111E-258");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
p = 85;
mpfr_set_prec(x, p);
mpfr_set_prec(x2, p);
mpfr_set_prec(y, p);
mpfr_set_prec(z, p);
mpfr_set_str_binary (y,
"0.1111101110100110110110100010101011101001100010100011110110110010010011101100101111100E-4");
mpfr_set_str_binary (z,
"0.1111101110100110110110100010101001001000011000111000011101100101110100001110101010110E-4");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
p = 64;
mpfr_set_prec(x, p); mpfr_set_prec(x2, p);
mpfr_set_prec(y, p); mpfr_set_prec(z, p);
mpfr_set_str_binary (y,
"0.11000000000000000000000000000000"
"00000000000000000000000000000000E1");
mpfr_set_str_binary (z,
"0.10000000000000000000000000000000"
"00000000000000000000000000000001E0");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.11000000000000000000000000000000"
"000000000000000000000000000001E1");
mpfr_set_str_binary (z,
"0.10000000000000000000000000000000"
"00000000000000000000000000000001E0");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
es = mpfr_get_emin ();
set_emin (-1024);
mpfr_set_str_binary (y,
"0.10000000000000000000000000000000"
"000000000000000000000000000000E-1023");
mpfr_set_str_binary (z,
"0.10000000000000000000000000000000"
"00000000000000000000000000000001E-1023");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
mpfr_set_str_binary (y,
"0.10000000000000000000000000000000"
"000000000000000000000000000000E-1023");
mpfr_set_str_binary (z,
"0.1000000000000000000000000000000"
"000000000000000000000000000000E-1023");
inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
if (mpfr_cmp(x, x2))
STD_ERROR;
if (inexact1 != inexact2)
STD_ERROR2;
set_emin (es);
}
mpfr_clears (x, y, z, x2, (mpfr_ptr) 0);
}
static void
check_underflow (mpfr_prec_t p)
{
mpfr_t x, y, z;
int inexact;
mpfr_inits2 (p, x, y, z, (mpfr_ptr) 0);
if (p >= 2) /* we need p >= 2 so that 3 is exact */
{
mpfr_set_ui_2exp (y, 4, mpfr_get_emin () - 2, MPFR_RNDN);
mpfr_set_ui_2exp (z, 3, mpfr_get_emin () - 2, MPFR_RNDN);
inexact = mpfr_sub (x, y, z, MPFR_RNDN);
if (inexact >= 0 || (mpfr_cmp_ui (x, 0) != 0))
{
printf ("4*2^(emin-2) - 3*2^(emin-2) with RNDN failed for p=%ld\n",
(long) p);
printf ("Expected inexact < 0 with x=0\n");
printf ("Got inexact=%d with x=", inexact);
mpfr_dump (x);
exit (1);
}
}
if (p >= 3) /* we need p >= 3 so that 5 is exact */
{
mpfr_set_ui_2exp (y, 5, mpfr_get_emin () - 2, MPFR_RNDN);
mpfr_set_ui_2exp (z, 4, mpfr_get_emin () - 2, MPFR_RNDN);
inexact = mpfr_sub (x, y, z, MPFR_RNDN);
if (inexact >= 0 || (mpfr_cmp_ui (x, 0) != 0))
{
printf ("5*2^(emin-2) - 4*2^(emin-2) with RNDN failed for p=%ld\n",
(long) p);
printf ("Expected inexact < 0 with x=0\n");
printf ("Got inexact=%d with x=", inexact);
mpfr_dump (x);
exit (1);
}
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
/* check corner cases of mpfr_sub1sp in case d = 1 and limb = MPFR_LIMB_HIGHBIT */
static void
check_corner (mpfr_prec_t p)
{
mpfr_t x, y, z;
mpfr_exp_t e;
int inex, odd;
if (p < 4) /* ensures that the initial value of z is > 1 below */
return;
mpfr_inits2 (p, x, y, z, (mpfr_ptr) 0);
mpfr_const_pi (y, MPFR_RNDN);
mpfr_set_ui (z, 2, MPFR_RNDN);
inex = mpfr_sub (z, y, z, MPFR_RNDN); /* z is near pi-2, thus y-z is near 2 */
MPFR_ASSERTN(inex == 0);
for (e = 0; e < p; e++)
{
/* add 2^(-e) to z */
mpfr_mul_2ui (z, z, e, MPFR_RNDN);
inex = mpfr_add_ui (z, z, 1, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
mpfr_div_2ui (z, z, e, MPFR_RNDN);
/* compute x = y - z which should be exact, near 2-2^(-e) */
inex = mpfr_sub (x, y, z, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
MPFR_ASSERTN(mpfr_get_exp (x) == 1);
/* restore initial z */
mpfr_mul_2ui (z, z, e, MPFR_RNDN);
inex = mpfr_sub_ui (z, z, 1, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
mpfr_div_2ui (z, z, e, MPFR_RNDN);
/* subtract 2^(-e) to z */
mpfr_mul_2ui (z, z, e, MPFR_RNDN);
inex = mpfr_sub_ui (z, z, 1, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
mpfr_div_2ui (z, z, e, MPFR_RNDN);
/* ensure last significant bit of z is 0 so that y-z is exact */
odd = mpfr_min_prec (z) == p;
if (odd) /* add one ulp to z */
mpfr_nextabove (z);
/* compute x = y - z which should be exact, near 2+2^(-e) */
inex = mpfr_sub (x, y, z, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
MPFR_ASSERTN(mpfr_get_exp (x) == 2);
/* restore initial z */
if (odd)
mpfr_nextbelow (z);
mpfr_mul_2ui (z, z, e, MPFR_RNDN);
inex = mpfr_add_ui (z, z, 1, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
mpfr_div_2ui (z, z, e, MPFR_RNDN);
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}