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|
/* Test file for mpfr_rint, mpfr_trunc, mpfr_floor, mpfr_ceil, mpfr_round,
mpfr_rint_trunc, mpfr_rint_floor, mpfr_rint_ceil, mpfr_rint_round.
Copyright 2002-2025 Free Software Foundation, Inc.
Contributed by the Pascaline 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/>. */
#include "mpfr-test.h"
#if __MPFR_STDC (199901L)
# include <math.h>
#endif
static void
special (void)
{
mpfr_t x, y;
mpfr_exp_t emax;
mpfr_init (x);
mpfr_init (y);
mpfr_set_nan (x);
mpfr_rint (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_inf (x, 1);
mpfr_rint (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && mpfr_sgn (y) > 0);
mpfr_set_inf (x, -1);
mpfr_rint (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && mpfr_sgn (y) < 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_rint (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS(y));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_rint (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_NEG(y));
/* coverage test */
mpfr_set_prec (x, 2);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_mul_2ui (x, x, mp_bits_per_limb, MPFR_RNDN);
mpfr_rint (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp (y, x) == 0);
/* another coverage test */
emax = mpfr_get_emax ();
set_emax (1);
mpfr_set_prec (x, 3);
mpfr_set_str_binary (x, "1.11E0");
mpfr_set_prec (y, 2);
mpfr_rint (y, x, MPFR_RNDU); /* x rounds to 1.0E1=0.1E2 which overflows */
MPFR_ASSERTN(mpfr_inf_p (y) && mpfr_sgn (y) > 0);
set_emax (emax);
/* yet another */
mpfr_set_prec (x, 97);
mpfr_set_prec (y, 96);
mpfr_set_str_binary (x, "-0.1011111001101111000111011100011100000110110110110000000111010001000101001111101010101011010111100E97");
mpfr_rint (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp (y, x) == 0);
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str_binary (x, "0.10101100000000101001010101111111000000011111010000010E-1");
mpfr_rint (y, x, MPFR_RNDU);
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0);
mpfr_rint (y, x, MPFR_RNDD);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS(y));
mpfr_set_prec (x, 36);
mpfr_set_prec (y, 2);
mpfr_set_str_binary (x, "-11000110101010111111110111001.0000100");
mpfr_rint (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-11E27");
MPFR_ASSERTN(mpfr_cmp (y, x) == 0);
mpfr_set_prec (x, 39);
mpfr_set_prec (y, 29);
mpfr_set_str_binary (x, "-0.100010110100011010001111001001001100111E39");
mpfr_rint (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-0.10001011010001101000111100101E39");
MPFR_ASSERTN(mpfr_cmp (y, x) == 0);
mpfr_set_prec (x, 46);
mpfr_set_prec (y, 32);
mpfr_set_str_binary (x, "-0.1011100110100101000001011111101011001001101001E32");
mpfr_rint (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-0.10111001101001010000010111111011E32");
MPFR_ASSERTN(mpfr_cmp (y, x) == 0);
/* coverage test for mpfr_round */
mpfr_set_prec (x, 3);
mpfr_set_str_binary (x, "1.01E1"); /* 2.5 */
mpfr_set_prec (y, 2);
mpfr_round (y, x);
/* since mpfr_round breaks ties away, should give 3 and not 2 as with
the "round to even" rule */
MPFR_ASSERTN(mpfr_cmp_ui (y, 3) == 0);
/* same test for the function */
(mpfr_round) (y, x);
MPFR_ASSERTN(mpfr_cmp_ui (y, 3) == 0);
mpfr_set_prec (x, 6);
mpfr_set_prec (y, 3);
mpfr_set_str_binary (x, "110.111");
mpfr_round (y, x);
if (mpfr_cmp_ui (y, 7))
{
printf ("Error in round(110.111)\n");
exit (1);
}
/* Bug found by Mark J Watkins */
mpfr_set_prec (x, 84);
mpfr_set_str_binary (x,
"0.110011010010001000000111101101001111111100101110010000000000000" \
"000000000000000000000E32");
mpfr_round (x, x);
if (mpfr_cmp_str (x, "0.1100110100100010000001111011010100000000000000" \
"00000000000000000000000000000000000000E32", 2, MPFR_RNDN))
{
printf ("Rounding error when dest=src\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
#define BASIC_TEST(F,J) \
do \
{ \
int red; \
for (red = 0; red <= 1; red++) \
{ \
int inex1, inex2; \
unsigned int ex_flags, flags; \
\
if (red) \
{ \
set_emin (e); \
set_emax (e); \
} \
\
mpfr_clear_flags (); \
inex1 = mpfr_set_si (y, J, (mpfr_rnd_t) r); \
ex_flags = __gmpfr_flags; \
mpfr_clear_flags (); \
inex2 = mpfr_rint_##F (z, x, (mpfr_rnd_t) r); \
flags = __gmpfr_flags; \
if (! (mpfr_equal_p (y, z) && \
SAME_SIGN (inex1, inex2) && \
flags == ex_flags)) \
{ \
printf ("Basic test failed on mpfr_rint_" #F \
", prec = %d, i = %d, %s\n", prec, s * i, \
mpfr_print_rnd_mode ((mpfr_rnd_t) r)); \
printf ("i.e. x = "); \
mpfr_dump (x); \
if (red) \
printf ("with emin = emax = %d\n", e); \
printf ("Expected "); \
mpfr_dump (y); \
printf ("with inex = %d (or equivalent)\n", inex1); \
printf (" flags:"); \
flags_out (ex_flags); \
printf ("Got "); \
mpfr_dump (z); \
printf ("with inex = %d (or equivalent)\n", inex2); \
printf (" flags:"); \
flags_out (flags); \
exit (1); \
} \
} \
set_emin (emin); \
set_emax (emax); \
} \
while (0)
#define BASIC_TEST2(F,J,INEX) \
do \
{ \
int red; \
for (red = 0; red <= 1; red++) \
{ \
int inex; \
unsigned int ex_flags, flags; \
\
if (red) \
{ \
set_emin (e); \
set_emax (e); \
} \
\
mpfr_clear_flags (); \
inex = mpfr_set_si (y, J, MPFR_RNDN); \
MPFR_ASSERTN (inex == 0 || mpfr_overflow_p ()); \
ex_flags = __gmpfr_flags; \
mpfr_clear_flags (); \
inex = mpfr_##F (z, x); \
if (inex != 0) \
ex_flags |= MPFR_FLAGS_INEXACT; \
flags = __gmpfr_flags; \
if (! (mpfr_equal_p (y, z) && \
inex == (INEX) && \
flags == ex_flags)) \
{ \
printf ("Basic test failed on mpfr_" #F \
", prec = %d, i = %d\n", prec, s * i); \
printf ("i.e. x = "); \
mpfr_dump (x); \
if (red) \
printf ("with emin = emax = %d\n", e); \
printf ("Expected "); \
mpfr_dump (y); \
printf ("with inex = %d\n", (INEX)); \
printf (" flags:"); \
flags_out (ex_flags); \
printf ("Got "); \
mpfr_dump (z); \
printf ("with inex = %d\n", inex); \
printf (" flags:"); \
flags_out (flags); \
exit (1); \
} \
} \
set_emin (emin); \
set_emax (emax); \
} \
while (0)
/* Test mpfr_rint_* on i/4 with |i| between 1 and 72. */
static void
basic_tests (void)
{
mpfr_t x, y, z;
int prec, s, i, r;
mpfr_exp_t emin, emax;
emin = mpfr_get_emin ();
emax = mpfr_get_emax ();
mpfr_init2 (x, 16);
for (prec = MPFR_PREC_MIN; prec <= 7; prec++)
{
mpfr_inits2 (prec, y, z, (mpfr_ptr) 0);
for (s = 1; s >= -1; s -= 2)
for (i = 1; i <= 72; i++)
{
int k, t, u, v, f, e, b;
for (t = i/4, k = 0; t >= 1 << prec; t >>= 1, k++)
;
b = !(t & 1);
t <<= k;
for (u = (i+3)/4, k = 0; u >= 1 << prec; u = (u+1)/2, k++)
;
u <<= k;
v = i < (t+u) << 1 ? t : u;
if (b)
b = i == (t+u) << 1;
f = t == u ? 0 : i % 4 == 0 ? 1 : 2;
mpfr_set_si_2exp (x, s * i, -2, MPFR_RNDN);
e = mpfr_get_exp (x);
RND_LOOP_NO_RNDF (r)
{
BASIC_TEST (trunc, s * (i/4));
BASIC_TEST (floor, s > 0 ? i/4 : - ((i+3)/4));
BASIC_TEST (ceil, s > 0 ? (i+3)/4 : - (i/4));
BASIC_TEST (round, s * ((i+2)/4));
BASIC_TEST (roundeven, s * (i % 8 == 2 ? i/4 : (i+2)/4));
}
BASIC_TEST2 (trunc, s * t, - s * f);
BASIC_TEST2 (floor, s > 0 ? t : - u, - f);
BASIC_TEST2 (ceil, s > 0 ? u : - t, f);
BASIC_TEST2 (round, s * v, v == t ? - s * f : s * f);
BASIC_TEST2 (roundeven, s * (b ? t : v),
b || v == t ? - s * f : s * f);
}
mpfr_clears (y, z, (mpfr_ptr) 0);
}
mpfr_clear (x);
}
#if __MPFR_STDC (199901L)
typedef int (*F2)(mpfr_ptr, mpfr_srcptr);
/* The argument g below will be of type F2 with args (mpfr_ptr, mpfr_srcptr),
except for mpfr_rint, with args (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t). So,
when passing mpfr_rint, we need a cast: "(F2) &mpfr_rint". The cast will
also be needed to compare the pointers: "g == (F2) &mpfr_rint", and that's
all. */
#if defined(__GNUC__)
#pragma GCC diagnostic push
#if __GNUC__ >= 8 || __clang_major__ >= 13
#pragma GCC diagnostic ignored "-Wcast-function-type"
#endif
#endif
static void
test_fct (double (*f)(double), F2 g, const char *s, mpfr_rnd_t r)
{
double d, y;
mpfr_t dd, yy;
mpfr_init2 (dd, 53);
mpfr_init2 (yy, 53);
for (d = -5.0; d <= 5.0; d += 0.25)
{
mpfr_set_d (dd, d, r);
y = (*f)(d);
if (g == (F2) &mpfr_rint)
mpfr_rint (yy, dd, r);
else
(*g)(yy, dd);
mpfr_set_d (dd, y, r);
if (mpfr_cmp (yy, dd))
{
printf ("test_against_libc: incorrect result for %s, rnd = %s,"
" d = %g\ngot ", s, mpfr_print_rnd_mode (r), d);
mpfr_out_str (stdout, 10, 0, yy, MPFR_RNDN);
printf (" instead of %g\n", y);
exit (1);
}
}
mpfr_clear (dd);
mpfr_clear (yy);
}
#define TEST_FCT(F) test_fct (&F, &mpfr_##F, #F, (mpfr_rnd_t) r)
static void
test_against_libc (void)
{
int r = MPFR_RNDN;
(void) r; /* avoid a warning by using r */
#if HAVE_ROUND
TEST_FCT (round);
#endif
#if HAVE_TRUNC
TEST_FCT (trunc);
#endif
#if HAVE_FLOOR
TEST_FCT (floor);
#endif
#if HAVE_CEIL
TEST_FCT (ceil);
#endif
#if HAVE_NEARBYINT
RND_LOOP (r)
if (mpfr_set_machine_rnd_mode ((mpfr_rnd_t) r) == 0)
test_fct (&nearbyint, (F2) &mpfr_rint, "rint", (mpfr_rnd_t) r);
#endif
}
#if defined(__GNUC__)
#pragma GCC diagnostic pop
#endif
#endif
static void
err (const char *str, mp_size_t s, mpfr_ptr x, mpfr_ptr y, mpfr_prec_t p,
mpfr_rnd_t r, int trint, int inexact)
{
printf ("Error: %s\ns = %u, p = %u, r = %s, trint = %d, inexact = %d\nx = ",
str, (unsigned int) s, (unsigned int) p, mpfr_print_rnd_mode (r),
trint, inexact);
mpfr_dump (x);
printf ("y = ");
mpfr_dump (y);
exit (1);
}
static void
coverage_03032011 (void)
{
mpfr_t in, out, cmp;
int status;
int precIn;
char strData[(GMP_NUMB_BITS * 4)+256];
precIn = GMP_NUMB_BITS * 4;
mpfr_init2 (in, precIn);
mpfr_init2 (out, GMP_NUMB_BITS);
mpfr_init2 (cmp, GMP_NUMB_BITS);
/* cmp = "0.1EprecIn+2" */
/* The buffer size is sufficient, as precIn is small in practice. */
sprintf (strData, "0.1E%d", precIn+2);
mpfr_set_str_binary (cmp, strData);
/* in = "0.10...01EprecIn+2" use all (precIn) significand bits */
memset ((void *)strData, '0', precIn+2);
strData[1] = '.';
strData[2] = '1';
sprintf (&strData[precIn+1], "1E%d", precIn+2);
mpfr_set_str_binary (in, strData);
status = mpfr_rint (out, in, MPFR_RNDN);
if ((mpfr_cmp (out, cmp) != 0) || (status >= 0))
{
printf("mpfr_rint error :\n status is %d instead of 0\n", status);
printf(" out value is ");
mpfr_dump(out);
printf(" instead of ");
mpfr_dump(cmp);
exit (1);
}
mpfr_clear (cmp);
mpfr_clear (out);
mpfr_init2 (out, GMP_NUMB_BITS);
mpfr_init2 (cmp, GMP_NUMB_BITS);
/* cmp = "0.10...01EprecIn+2" use all (GMP_NUMB_BITS) significand bits */
strcpy (&strData[GMP_NUMB_BITS+1], &strData[precIn+1]);
mpfr_set_str_binary (cmp, strData);
(MPFR_MANT(in))[2] = MPFR_LIMB_HIGHBIT;
status = mpfr_rint (out, in, MPFR_RNDN);
if ((mpfr_cmp (out, cmp) != 0) || (status <= 0))
{
printf("mpfr_rint error :\n status is %d instead of 0\n", status);
printf(" out value is\n");
mpfr_dump(out);
printf(" instead of\n");
mpfr_dump(cmp);
exit (1);
}
mpfr_clear (cmp);
mpfr_clear (out);
mpfr_clear (in);
}
#define TEST_FUNCTION mpfr_rint_trunc
#define TEST_RANDOM_EMIN -20
#define TEST_RANDOM_ALWAYS_SCALE 1
#define test_generic test_generic_trunc
#include "tgeneric.c"
#define TEST_FUNCTION mpfr_rint_floor
#define TEST_RANDOM_EMIN -20
#define TEST_RANDOM_ALWAYS_SCALE 1
#define test_generic test_generic_floor
#include "tgeneric.c"
#define TEST_FUNCTION mpfr_rint_ceil
#define TEST_RANDOM_EMIN -20
#define TEST_RANDOM_ALWAYS_SCALE 1
#define test_generic test_generic_ceil
#include "tgeneric.c"
#define TEST_FUNCTION mpfr_rint_round
#define TEST_RANDOM_EMIN -20
#define TEST_RANDOM_ALWAYS_SCALE 1
#define test_generic test_generic_round
#include "tgeneric.c"
#define TEST_FUNCTION mpfr_rint_roundeven
#define TEST_RANDOM_EMIN -20
#define TEST_RANDOM_ALWAYS_SCALE 1
#define test_generic test_generic_roundeven
#include "tgeneric.c"
int
main (int argc, char *argv[])
{
mp_size_t s;
mpz_t z;
mpfr_prec_t p;
mpfr_t x, y, t, u, v;
int r;
int inexact, sign_t;
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
mpz_init (z);
mpfr_init (t);
mpfr_init (u);
mpfr_init (v);
mpz_set_ui (z, 1);
/* the code below works for 1 <= MPFR_PREC_MIN <= 2 */
MPFR_ASSERTN(1 <= MPFR_PREC_MIN && MPFR_PREC_MIN <= 2);
for (s = MPFR_PREC_MIN; s < 100; s++)
{
if (s > 1)
{
mpz_mul_2exp (z, z, 1);
if (RAND_BOOL ())
mpz_add_ui (z, z, 1);
}
/* now 2^(s-1) <= z < 2^s */
mpfr_set_prec (x, s);
mpfr_set_prec (t, s);
mpfr_set_prec (u, s);
if (mpfr_set_z (x, z, MPFR_RNDN))
{
#ifndef MPFR_USE_MINI_GMP
gmp_printf ("Error: mpfr_set_z should be exact (z = %Zd, s = %u)\n",
z, (unsigned int) s);
#else /* mini-gmp has no gmp_printf (at least in gmp-6.1.2) */
printf ("mpfr_set_z should be exact\n");
#endif
exit (1);
}
if (RAND_BOOL ())
mpfr_neg (x, x, MPFR_RNDN);
if (RAND_BOOL ())
mpfr_div_2ui (x, x, randlimb () % s, MPFR_RNDN);
for (p = MPFR_PREC_MIN; p < 100; p++)
{
int trint;
mpfr_set_prec (y, p);
mpfr_set_prec (v, p);
RND_LOOP (r)
for (trint = 0; trint < 4; trint++)
{
if (trint == 2)
inexact = mpfr_rint (y, x, (mpfr_rnd_t) r);
else if (trint == 3)
{
if (r != MPFR_RNDN)
continue;
inexact = mpfr_round (y, x);
}
else if (r == MPFR_RNDN)
inexact = (trint ? mpfr_roundeven (y, x) :
mpfr_rint_roundeven (y, x, MPFR_RNDZ));
else if (r == MPFR_RNDZ)
inexact = (trint ? mpfr_trunc (y, x) :
mpfr_rint_trunc (y, x, MPFR_RNDZ));
else if (r == MPFR_RNDU)
inexact = (trint ? mpfr_ceil (y, x) :
mpfr_rint_ceil (y, x, MPFR_RNDU));
else if (r == MPFR_RNDD)
inexact = (trint ? mpfr_floor (y, x) :
mpfr_rint_floor (y, x, MPFR_RNDD));
else
{
MPFR_ASSERTN (r == MPFR_RNDA || r == MPFR_RNDF);
continue;
}
if (mpfr_sub (t, y, x, MPFR_RNDN))
err ("subtraction 1 should be exact", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
sign_t = mpfr_cmp_ui (t, 0);
if (trint != 0 &&
(((inexact == 0) && (sign_t != 0)) ||
((inexact < 0) && (sign_t >= 0)) ||
((inexact > 0) && (sign_t <= 0))))
err ("wrong inexact flag", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
if (inexact == 0)
continue; /* end of the test for exact results */
if (((r == MPFR_RNDD || (r == MPFR_RNDZ && MPFR_IS_POS (x)))
&& inexact > 0) ||
((r == MPFR_RNDU || (r == MPFR_RNDZ && MPFR_IS_NEG (x)))
&& inexact < 0))
err ("wrong rounding direction", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
if (inexact < 0)
{
mpfr_add_ui (v, y, 1, MPFR_RNDU);
if (mpfr_cmp (v, x) <= 0)
err ("representable integer between x and "
"its rounded value", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
}
else
{
mpfr_sub_ui (v, y, 1, MPFR_RNDD);
if (mpfr_cmp (v, x) >= 0)
err ("representable integer between x and "
"its rounded value", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
}
if (r == MPFR_RNDN && trint != 0)
{
int cmp;
if (mpfr_sub (u, v, x, MPFR_RNDN))
err ("subtraction 2 should be exact", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
cmp = mpfr_cmpabs (t, u);
if (cmp > 0)
err ("faithful rounding, but not the nearest integer",
s, x, y, p, (mpfr_rnd_t) r, trint, inexact);
if (cmp < 0)
continue;
/* |t| = |u|: x is the middle of two consecutive
representable integers. */
if (trint == 2)
{
/* halfway case for mpfr_rint in MPFR_RNDN rounding
mode: round to an even integer or significand. */
mpfr_div_2ui (y, y, 1, MPFR_RNDZ);
if (!mpfr_integer_p (y))
err ("halfway case for mpfr_rint, result isn't "
"an even integer", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
if (p > 1)
{
/* For p > 1, if floor(x) and ceil(x) aren't
both representable integers, the significand
must be even. */
mpfr_sub (v, v, y, MPFR_RNDN);
mpfr_abs (v, v, MPFR_RNDN);
if (mpfr_cmp_ui (v, 1) != 0)
{
mpfr_div_2si (y, y, MPFR_EXP (y) -
MPFR_PREC (y) + 1, MPFR_RNDN);
if (!mpfr_integer_p (y))
err ("halfway case for mpfr_rint, "
"significand isn't even", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
}
}
}
else if (trint == 3)
{ /* halfway case for mpfr_round: x must have been
rounded away from zero. */
if ((MPFR_IS_POS (x) && inexact < 0) ||
(MPFR_IS_NEG (x) && inexact > 0))
err ("halfway case for mpfr_round, "
"bad rounding direction", s, x, y, p,
(mpfr_rnd_t) r, trint, inexact);
}
}
}
}
}
mpfr_clear (x);
mpfr_clear (y);
mpz_clear (z);
mpfr_clear (t);
mpfr_clear (u);
mpfr_clear (v);
special ();
basic_tests ();
coverage_03032011 ();
test_generic_trunc (MPFR_PREC_MIN, 300, 20);
test_generic_floor (MPFR_PREC_MIN, 300, 20);
test_generic_ceil (MPFR_PREC_MIN, 300, 20);
test_generic_round (MPFR_PREC_MIN, 300, 20);
test_generic_roundeven (MPFR_PREC_MIN, 300, 20);
#if __MPFR_STDC (199901L)
if (argc > 1 && strcmp (argv[1], "-s") == 0)
test_against_libc ();
#endif
tests_end_mpfr ();
return 0;
}
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