/* tremquo -- test file for mpfr_remquo and mpfr_remainder
Copyright 2007 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.
This file is part of the MPFR Library.
The 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 2.1 of the License, or (at your
option) any later version.
The 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 MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include <stdio.h>
#include <stdlib.h>
#include "mpfr-test.h"
int
main (int argc, char *argv[])
{
mpfr_t x, y, r;
long q[1];
if (argc == 3) /* usage: tremquo x y (rnd=GMP_RNDN implicit) */
{
mpfr_init2 (x, BITS_PER_MP_LIMB);
mpfr_init2 (y, BITS_PER_MP_LIMB);
mpfr_init2 (r, BITS_PER_MP_LIMB);
mpfr_set_str (x, argv[1], 10, GMP_RNDN);
mpfr_set_str (y, argv[2], 10, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
printf ("r=");
mpfr_out_str (stdout, 10, 0, r, GMP_RNDN);
printf (" q=%ld\n", q[0]);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
return 0;
}
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (r);
/* special values */
mpfr_set_nan (x);
mpfr_set_ui (y, 1, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_nan_p (r));
mpfr_set_ui (x, 1, GMP_RNDN);
mpfr_set_nan (y);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_ui (y, 1, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_ui (y, 0, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_POS (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN); /* -0 */
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_NEG (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 17, GMP_RNDN);
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp (r, x) == 0);
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 17, GMP_RNDN);
mpfr_set_ui (y, 0, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_set_ui (y, 17, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_POS (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
mpfr_set_ui (y, 17, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_NEG (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
/* check four possible sign combinations */
mpfr_set_ui (x, 42, GMP_RNDN);
mpfr_set_ui (y, 17, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 8) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_si (x, -42, GMP_RNDN);
mpfr_set_ui (y, 17, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -8) == 0);
MPFR_ASSERTN (q[0] == (long) -2);
mpfr_set_si (x, -42, GMP_RNDN);
mpfr_set_si (y, -17, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -8) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_ui (x, 42, GMP_RNDN);
mpfr_set_si (y, -17, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 8) == 0);
MPFR_ASSERTN (q[0] == (long) -2);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 50);
mpfr_set_ui (x, 42, GMP_RNDN);
mpfr_nextabove (x); /* 42 + 2^(-94) */
mpfr_set_ui (y, 21, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -94) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 100);
mpfr_set_ui (x, 42, GMP_RNDN);
mpfr_nextabove (x); /* 42 + 2^(-44) */
mpfr_set_ui (y, 21, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -44) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 50);
mpfr_set_ui (x, 42, GMP_RNDN);
mpfr_set_ui (y, 21, GMP_RNDN);
mpfr_nextabove (y); /* 21 + 2^(-45) */
mpfr_remquo (r, q, x, y, GMP_RNDN);
/* r should be 42 - 2*(21 + 2^(-45)) = -2^(-44) */
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -44) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 100);
mpfr_set_ui (x, 42, GMP_RNDN);
mpfr_set_ui (y, 21, GMP_RNDN);
mpfr_nextabove (y); /* 21 + 2^(-95) */
mpfr_remquo (r, q, x, y, GMP_RNDN);
/* r should be 42 - 2*(21 + 2^(-95)) = -2^(-94) */
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -94) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
/* exercise large quotient */
mpfr_set_ui_2exp (x, 1, 65, GMP_RNDN);
mpfr_set_ui (y, 1, GMP_RNDN);
/* quotient is 2^65 */
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, 0) == 0);
MPFR_ASSERTN (q[0] % 1073741824L == 0L);
/* another large quotient */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_const_pi (x, GMP_RNDN);
mpfr_mul_2exp (x, x, 63, GMP_RNDN);
mpfr_const_log2 (y, GMP_RNDN);
mpfr_set_prec (r, 10);
mpfr_remquo (r, q, x, y, GMP_RNDN);
/* q should be 41803643793084085130, r should be 605/2048 */
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 605, -11) == 0);
MPFR_ASSERTN ((q[0] > 0) && ((q[0] % 1073741824L) == 733836170L));
/* check cases where quotient is 1.5 +/- eps */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_set_prec (r, 63);
mpfr_set_ui (x, 3, GMP_RNDN);
mpfr_set_ui (y, 2, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
/* x/y = 1.5, quotient should be 2 (even rule), remainder should be -1 */
MPFR_ASSERTN (mpfr_cmp_si (r, -1) == 0);
MPFR_ASSERTN (q[0] == 2L);
mpfr_set_ui (x, 3, GMP_RNDN);
mpfr_nextabove (x); /* 3 + 2^(-63) */
mpfr_set_ui (y, 2, GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
/* x/y = 1.5 + 2^(-64), quo should be 2, r should be -1 + 2^(-63) */
MPFR_ASSERTN (mpfr_add_ui (r, r, 1, GMP_RNDN) == 0);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -63) == 0);
MPFR_ASSERTN (q[0] == 2L);
mpfr_set_ui (x, 3, GMP_RNDN);
mpfr_set_ui (y, 2, GMP_RNDN);
mpfr_nextabove (y); /* 2 + 2^(-63) */
mpfr_remquo (r, q, x, y, GMP_RNDN);
/* x/y = 1.5 - eps, quo should be 1, r should be 1 - 2^(-63) */
MPFR_ASSERTN (mpfr_sub_ui (r, r, 1, GMP_RNDN) == 0);
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -63) == 0);
MPFR_ASSERTN (q[0] == 1L);
/* bug founds by Kaveh Ghazi, 3 May 2007 */
mpfr_set_ui (x, 2, GMP_RNDN);
mpfr_set_ui (y, 3, GMP_RNDN);
mpfr_remainder (r, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -1) == 0);
mpfr_set_si (x, -1, GMP_RNDN);
mpfr_set_ui (y, 1, GMP_RNDN);
mpfr_remainder (r, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, 0) == 0 && MPFR_SIGN (r) < 0);
/* check argument reuse */
mpfr_set_si (x, -1, GMP_RNDN);
mpfr_set_ui (y, 1, GMP_RNDN);
mpfr_remainder (x, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (x, 0) == 0 && MPFR_SIGN (x) < 0);
mpfr_set_ui_2exp (x, 1, mpfr_get_emax () - 1, GMP_RNDN);
mpfr_set_ui_2exp (y, 1, mpfr_get_emin (), GMP_RNDN);
mpfr_remquo (r, q, x, y, GMP_RNDN);
MPFR_ASSERTN (mpfr_zero_p (r) && MPFR_SIGN (r) > 0);
MPFR_ASSERTN (q[0] == 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
tests_end_mpfr ();
return 0;
}
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