/* Test file for mpfr_sqrt.
Copyright 1999, 2001-2017 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
http://www.gnu.org/licenses/ or 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"
#ifdef CHECK_EXTERNAL
static int
test_sqrt (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
{
int res;
int ok = rnd_mode == MPFR_RNDN && mpfr_number_p (b);
if (ok)
{
mpfr_print_raw (b);
}
res = mpfr_sqrt (a, b, rnd_mode);
if (ok)
{
printf (" ");
mpfr_print_raw (a);
printf ("\n");
}
return res;
}
#else
#define test_sqrt mpfr_sqrt
#endif
static void
check3 (const char *as, mpfr_rnd_t rnd_mode, const char *qs)
{
mpfr_t q;
mpfr_init2 (q, 53);
mpfr_set_str1 (q, as);
test_sqrt (q, q, rnd_mode);
if (mpfr_cmp_str1 (q, qs) )
{
printf ("mpfr_sqrt failed for a=%s, rnd_mode=%s\n",
as, mpfr_print_rnd_mode (rnd_mode));
printf ("expected sqrt is %s, got ",qs);
mpfr_out_str (stdout, 10, 0, q, MPFR_RNDN);
putchar ('\n');
exit (1);
}
mpfr_clear (q);
}
static void
check4 (const char *as, mpfr_rnd_t rnd_mode, const char *Qs)
{
mpfr_t q;
mpfr_init2 (q, 53);
mpfr_set_str1 (q, as);
test_sqrt (q, q, rnd_mode);
if (mpfr_cmp_str (q, Qs, 16, MPFR_RNDN))
{
printf ("mpfr_sqrt failed for a=%s, rnd_mode=%s\n",
as, mpfr_print_rnd_mode(rnd_mode));
printf ("expected ");
mpfr_out_str (stdout, 16, 0, q, MPFR_RNDN);
printf ("\ngot %s\n", Qs);
mpfr_clear (q);
exit (1);
}
mpfr_clear (q);
}
static void
check24 (const char *as, mpfr_rnd_t rnd_mode, const char *qs)
{
mpfr_t q;
mpfr_init2 (q, 24);
mpfr_set_str1 (q, as);
test_sqrt (q, q, rnd_mode);
if (mpfr_cmp_str1 (q, qs))
{
printf ("mpfr_sqrt failed for a=%s, prec=24, rnd_mode=%s\n",
as, mpfr_print_rnd_mode(rnd_mode));
printf ("expected sqrt is %s, got ",qs);
mpfr_out_str (stdout, 10, 0, q, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_clear (q);
}
static void
check_diverse (const char *as, mpfr_prec_t p, const char *qs)
{
mpfr_t q;
mpfr_init2 (q, p);
mpfr_set_str1 (q, as);
test_sqrt (q, q, MPFR_RNDN);
if (mpfr_cmp_str1 (q, qs))
{
printf ("mpfr_sqrt failed for a=%s, prec=%lu, rnd_mode=%s\n",
as, (unsigned long) p, mpfr_print_rnd_mode (MPFR_RNDN));
printf ("expected sqrt is %s, got ", qs);
mpfr_out_str (stdout, 10, 0, q, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_clear (q);
}
/* the following examples come from the paper "Number-theoretic Test
Generation for Directed Rounding" from Michael Parks, Table 3 */
static void
check_float (void)
{
check24("70368760954880.0", MPFR_RNDN, "8.388609e6");
check24("281474943156224.0", MPFR_RNDN, "1.6777215e7");
check24("70368777732096.0", MPFR_RNDN, "8.388610e6");
check24("281474909601792.0", MPFR_RNDN, "1.6777214e7");
check24("100216216748032.0", MPFR_RNDN, "1.0010805e7");
check24("120137273311232.0", MPFR_RNDN, "1.0960715e7");
check24("229674600890368.0", MPFR_RNDN, "1.5155019e7");
check24("70368794509312.0", MPFR_RNDN, "8.388611e6");
check24("281474876047360.0", MPFR_RNDN, "1.6777213e7");
check24("91214552498176.0", MPFR_RNDN, "9.550631e6");
check24("70368760954880.0", MPFR_RNDZ, "8.388608e6");
check24("281474943156224.0", MPFR_RNDZ, "1.6777214e7");
check24("70368777732096.0", MPFR_RNDZ, "8.388609e6");
check24("281474909601792.0", MPFR_RNDZ, "1.6777213e7");
check24("100216216748032.0", MPFR_RNDZ, "1.0010805e7");
check24("120137273311232.0", MPFR_RNDZ, "1.0960715e7");
check24("229674600890368.0", MPFR_RNDZ, "1.5155019e7");
check24("70368794509312.0", MPFR_RNDZ, "8.38861e6");
check24("281474876047360.0", MPFR_RNDZ, "1.6777212e7");
check24("91214552498176.0", MPFR_RNDZ, "9.550631e6");
check24("70368760954880.0", MPFR_RNDU, "8.388609e6");
check24("281474943156224.0",MPFR_RNDU, "1.6777215e7");
check24("70368777732096.0", MPFR_RNDU, "8.388610e6");
check24("281474909601792.0", MPFR_RNDU, "1.6777214e7");
check24("100216216748032.0", MPFR_RNDU, "1.0010806e7");
check24("120137273311232.0", MPFR_RNDU, "1.0960716e7");
check24("229674600890368.0", MPFR_RNDU, "1.515502e7");
check24("70368794509312.0", MPFR_RNDU, "8.388611e6");
check24("281474876047360.0", MPFR_RNDU, "1.6777213e7");
check24("91214552498176.0", MPFR_RNDU, "9.550632e6");
check24("70368760954880.0", MPFR_RNDD, "8.388608e6");
check24("281474943156224.0", MPFR_RNDD, "1.6777214e7");
check24("70368777732096.0", MPFR_RNDD, "8.388609e6");
check24("281474909601792.0", MPFR_RNDD, "1.6777213e7");
check24("100216216748032.0", MPFR_RNDD, "1.0010805e7");
check24("120137273311232.0", MPFR_RNDD, "1.0960715e7");
check24("229674600890368.0", MPFR_RNDD, "1.5155019e7");
check24("70368794509312.0", MPFR_RNDD, "8.38861e6");
check24("281474876047360.0", MPFR_RNDD, "1.6777212e7");
check24("91214552498176.0", MPFR_RNDD, "9.550631e6");
/* check that rounding away is just rounding toward plus infinity */
check24("91214552498176.0", MPFR_RNDA, "9.550632e6");
}
static void
special (void)
{
mpfr_t x, y, z;
int inexact;
mpfr_prec_t p;
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
mpfr_set_prec (x, 64);
mpfr_set_str_binary (x, "1010000010100011011001010101010010001100001101011101110001011001E-1");
mpfr_set_prec (y, 32);
test_sqrt (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 2405743844UL))
{
printf ("Error for n^2+n+1/2 with n=2405743843\n");
exit (1);
}
mpfr_set_prec (x, 65);
mpfr_set_str_binary (x, "10100000101000110110010101010100100011000011010111011100010110001E-2");
mpfr_set_prec (y, 32);
test_sqrt (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 2405743844UL))
{
printf ("Error for n^2+n+1/4 with n=2405743843\n");
mpfr_dump (y);
exit (1);
}
mpfr_set_prec (x, 66);
mpfr_set_str_binary (x, "101000001010001101100101010101001000110000110101110111000101100011E-3");
mpfr_set_prec (y, 32);
test_sqrt (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 2405743844UL))
{
printf ("Error for n^2+n+1/4+1/8 with n=2405743843\n");
mpfr_dump (y);
exit (1);
}
mpfr_set_prec (x, 66);
mpfr_set_str_binary (x, "101000001010001101100101010101001000110000110101110111000101100001E-3");
mpfr_set_prec (y, 32);
test_sqrt (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 2405743843UL))
{
printf ("Error for n^2+n+1/8 with n=2405743843\n");
mpfr_dump (y);
exit (1);
}
mpfr_set_prec (x, 27);
mpfr_set_str_binary (x, "0.110100111010101000010001011");
if ((inexact = test_sqrt (x, x, MPFR_RNDZ)) >= 0)
{
printf ("Wrong inexact flag: expected -1, got %d\n", inexact);
exit (1);
}
mpfr_set_prec (x, 2);
for (p=2; p<1000; p++)
{
mpfr_set_prec (z, p);
mpfr_set_ui (z, 1, MPFR_RNDN);
mpfr_nexttoinf (z);
test_sqrt (x, z, MPFR_RNDU);
if (mpfr_cmp_ui_2exp(x, 3, -1))
{
printf ("Error: sqrt(1+ulp(1), up) should give 1.5 (prec=%u)\n",
(unsigned int) p);
printf ("got "); mpfr_print_binary (x); puts ("");
exit (1);
}
}
/* check inexact flag */
mpfr_set_prec (x, 5);
mpfr_set_str_binary (x, "1.1001E-2");
if ((inexact = test_sqrt (x, x, MPFR_RNDN)))
{
printf ("Wrong inexact flag: expected 0, got %d\n", inexact);
exit (1);
}
mpfr_set_prec (x, 2);
mpfr_set_prec (z, 2);
/* checks the sign is correctly set */
mpfr_set_si (x, 1, MPFR_RNDN);
mpfr_set_si (z, -1, MPFR_RNDN);
test_sqrt (z, x, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0) < 0)
{
printf ("Error: square root of 1 gives ");
mpfr_print_binary(z);
putchar('\n');
exit (1);
}
mpfr_set_prec (x, 192);
mpfr_set_prec (z, 160);
mpfr_set_str_binary (z, "0.1011010100000100100100100110011001011100100100000011000111011001011101101101110000110100001000100001100001011000E1");
mpfr_set_prec (x, 160);
test_sqrt(x, z, MPFR_RNDN);
test_sqrt(z, x, MPFR_RNDN);
mpfr_set_prec (x, 53);
mpfr_set_str (x, "8093416094703476.0", 10, MPFR_RNDN);
mpfr_div_2exp (x, x, 1075, MPFR_RNDN);
test_sqrt (x, x, MPFR_RNDN);
mpfr_set_str (z, "1e55596835b5ef@-141", 16, MPFR_RNDN);
if (mpfr_cmp (x, z))
{
printf ("Error: square root of 8093416094703476*2^(-1075)\n");
printf ("expected "); mpfr_dump (z);
printf ("got "); mpfr_dump (x);
exit (1);
}
mpfr_set_prec (x, 33);
mpfr_set_str_binary (x, "0.111011011011110001100111111001000e-10");
mpfr_set_prec (z, 157);
inexact = test_sqrt (z, x, MPFR_RNDN);
mpfr_set_prec (x, 157);
mpfr_set_str_binary (x, "0.11110110101100101111001011100011100011100001101010111011010000100111011000111110100001001011110011111100101110010110010110011001011011010110010000011001101E-5");
if (mpfr_cmp (x, z))
{
printf ("Error: square root (1)\n");
exit (1);
}
if (inexact <= 0)
{
printf ("Error: wrong inexact flag (1)\n");
exit (1);
}
/* case prec(result) << prec(input) */
mpfr_set_prec (z, 2);
for (p = 2; p < 1000; p++)
{
mpfr_set_prec (x, p);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_nextabove (x);
/* 1.0 < x <= 1.5 thus 1 < sqrt(x) <= 1.23 */
inexact = test_sqrt (z, x, MPFR_RNDN);
MPFR_ASSERTN(inexact < 0 && mpfr_cmp_ui (z, 1) == 0);
inexact = test_sqrt (z, x, MPFR_RNDZ);
MPFR_ASSERTN(inexact < 0 && mpfr_cmp_ui (z, 1) == 0);
inexact = test_sqrt (z, x, MPFR_RNDU);
MPFR_ASSERTN(inexact > 0 && mpfr_cmp_ui_2exp (z, 3, -1) == 0);
inexact = test_sqrt (z, x, MPFR_RNDD);
MPFR_ASSERTN(inexact < 0 && mpfr_cmp_ui (z, 1) == 0);
inexact = test_sqrt (z, x, MPFR_RNDA);
MPFR_ASSERTN(inexact > 0 && mpfr_cmp_ui_2exp (z, 3, -1) == 0);
}
/* corner case rw = 0 in rounding to nearest */
mpfr_set_prec (z, GMP_NUMB_BITS - 1);
mpfr_set_prec (y, GMP_NUMB_BITS - 1);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_mul_2exp (y, y, GMP_NUMB_BITS - 1, MPFR_RNDN);
mpfr_nextabove (y);
for (p = 2 * GMP_NUMB_BITS - 1; p <= 1000; p++)
{
mpfr_set_prec (x, p);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_set_exp (x, GMP_NUMB_BITS);
mpfr_add_ui (x, x, 1, MPFR_RNDN);
/* now x = 2^(GMP_NUMB_BITS - 1) + 1 (GMP_NUMB_BITS bits) */
MPFR_ASSERTN (mpfr_mul (x, x, x, MPFR_RNDN) == 0); /* exact */
inexact = test_sqrt (z, x, MPFR_RNDN);
/* even rule: z should be 2^(GMP_NUMB_BITS - 1) */
MPFR_ASSERTN (inexact < 0);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (z, 1, GMP_NUMB_BITS - 1) == 0);
mpfr_nextbelow (x);
/* now x is just below [2^(GMP_NUMB_BITS - 1) + 1]^2 */
inexact = test_sqrt (z, x, MPFR_RNDN);
MPFR_ASSERTN(inexact < 0 &&
mpfr_cmp_ui_2exp (z, 1, GMP_NUMB_BITS - 1) == 0);
mpfr_nextabove (x);
mpfr_nextabove (x);
/* now x is just above [2^(GMP_NUMB_BITS - 1) + 1]^2 */
inexact = test_sqrt (z, x, MPFR_RNDN);
if (mpfr_cmp (z, y))
{
printf ("Error for sqrt(x) in rounding to nearest\n");
printf ("x="); mpfr_dump (x);
printf ("Expected "); mpfr_dump (y);
printf ("Got "); mpfr_dump (z);
exit (1);
}
if (inexact <= 0)
{
printf ("Wrong inexact flag in corner case for p = %lu\n", (unsigned long) p);
exit (1);
}
}
mpfr_set_prec (x, 1000);
mpfr_set_ui (x, 9, MPFR_RNDN);
mpfr_set_prec (y, 10);
inexact = test_sqrt (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 3) || inexact != 0)
{
printf ("Error in sqrt(9:1000) for prec=10\n");
exit (1);
}
mpfr_set_prec (y, GMP_NUMB_BITS);
mpfr_nextabove (x);
inexact = test_sqrt (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 3) || inexact >= 0)
{
printf ("Error in sqrt(9:1000) for prec=%d\n", (int) GMP_NUMB_BITS);
exit (1);
}
mpfr_set_prec (x, 2 * GMP_NUMB_BITS);
mpfr_set_prec (y, GMP_NUMB_BITS);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_nextabove (y);
mpfr_set (x, y, MPFR_RNDN);
inexact = test_sqrt (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 1) || inexact >= 0)
{
printf ("Error in sqrt(1) for prec=%d\n", (int) GMP_NUMB_BITS);
mpfr_dump (y);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
static void
check_inexact (mpfr_prec_t p)
{
mpfr_t x, y, z;
mpfr_rnd_t rnd;
int inexact, sign;
mpfr_init2 (x, p);
mpfr_init2 (y, p);
mpfr_init2 (z, 2*p);
mpfr_urandomb (x, RANDS);
rnd = RND_RAND ();
inexact = test_sqrt (y, x, rnd);
if (mpfr_mul (z, y, y, rnd)) /* exact since prec(z) = 2*prec(y) */
{
printf ("Error: multiplication should be exact\n");
exit (1);
}
mpfr_sub (z, z, x, rnd); /* exact also */
sign = mpfr_cmp_ui (z, 0);
if (((inexact == 0) && (sign)) ||
((inexact > 0) && (sign <= 0)) ||
((inexact < 0) && (sign >= 0)))
{
printf ("Error: wrong inexact flag, expected %d, got %d\n",
sign, inexact);
printf ("x=");
mpfr_print_binary (x);
printf (" rnd=%s\n", mpfr_print_rnd_mode (rnd));
printf ("y="); mpfr_print_binary (y); puts ("");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
static void
check_singular (void)
{
mpfr_t x, got;
mpfr_init2 (x, 100L);
mpfr_init2 (got, 100L);
/* sqrt(NaN) == NaN */
MPFR_SET_NAN (x);
MPFR_ASSERTN (test_sqrt (got, x, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_nan_p (got));
/* sqrt(-1) == NaN */
mpfr_set_si (x, -1L, MPFR_RNDZ);
MPFR_ASSERTN (test_sqrt (got, x, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_nan_p (got));
/* sqrt(+inf) == +inf */
MPFR_SET_INF (x);
MPFR_SET_POS (x);
MPFR_ASSERTN (test_sqrt (got, x, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (got));
/* sqrt(-inf) == NaN */
MPFR_SET_INF (x);
MPFR_SET_NEG (x);
MPFR_ASSERTN (test_sqrt (got, x, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_nan_p (got));
/* sqrt(+0) == +0 */
mpfr_set_si (x, 0L, MPFR_RNDZ);
MPFR_ASSERTN (test_sqrt (got, x, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_number_p (got));
MPFR_ASSERTN (mpfr_cmp_ui (got, 0L) == 0);
MPFR_ASSERTN (MPFR_IS_POS (got));
/* sqrt(-0) == -0 */
mpfr_set_si (x, 0L, MPFR_RNDZ);
MPFR_SET_NEG (x);
MPFR_ASSERTN (test_sqrt (got, x, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_number_p (got));
MPFR_ASSERTN (mpfr_cmp_ui (got, 0L) == 0);
MPFR_ASSERTN (MPFR_IS_NEG (got));
mpfr_clear (x);
mpfr_clear (got);
}
/* check that -1 <= x/sqrt(x^2+s*y^2) <= 1 for rounding to nearest or up
with s = 0 and s = 1 */
static void
test_property1 (mpfr_prec_t p, mpfr_rnd_t r, int s)
{
mpfr_t x, y, z, t;
mpfr_init2 (x, p);
mpfr_init2 (y, p);
mpfr_init2 (z, p);
mpfr_init2 (t, p);
mpfr_urandomb (x, RANDS);
mpfr_mul (z, x, x, r);
if (s)
{
mpfr_urandomb (y, RANDS);
mpfr_mul (t, y, y, r);
mpfr_add (z, z, t, r);
}
mpfr_sqrt (z, z, r);
mpfr_div (z, x, z, r);
/* Note: if both x and y are 0, z is NAN, but the test below will
be false. So, everything is fine. */
if (mpfr_cmp_si (z, -1) < 0 || mpfr_cmp_ui (z, 1) > 0)
{
printf ("Error, -1 <= x/sqrt(x^2+y^2) <= 1 does not hold for r=%s\n",
mpfr_print_rnd_mode (r));
printf ("x="); mpfr_dump (x);
printf ("y="); mpfr_dump (y);
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (t);
}
/* check sqrt(x^2) = x */
static void
test_property2 (mpfr_prec_t p, mpfr_rnd_t r)
{
mpfr_t x, y;
mpfr_init2 (x, p);
mpfr_init2 (y, p);
mpfr_urandomb (x, RANDS);
mpfr_mul (y, x, x, r);
mpfr_sqrt (y, y, r);
if (mpfr_cmp (y, x))
{
printf ("Error, sqrt(x^2) = x does not hold for r=%s\n",
mpfr_print_rnd_mode (r));
printf ("x="); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
/* Bug reported by Fredrik Johansson, occurring when:
- the precision of the result is a multiple of the number of bits
per word (GMP_NUMB_BITS),
- the rounding mode is to nearest (MPFR_RNDN),
- internally, the result has to be rounded up to a power of 2.
*/
static void
bug20160120 (void)
{
mpfr_t x, y;
mpfr_init2 (x, 4 * GMP_NUMB_BITS);
mpfr_init2 (y, GMP_NUMB_BITS);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_nextbelow (x);
mpfr_sqrt (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_check (y));
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0);
mpfr_set_prec (y, 2 * GMP_NUMB_BITS);
mpfr_sqrt (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_check (y));
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0);
mpfr_clear(x);
mpfr_clear(y);
}
#define TEST_FUNCTION test_sqrt
#define TEST_RANDOM_POS 8
#include "tgeneric.c"
int
main (void)
{
mpfr_prec_t p;
int k;
tests_start_mpfr ();
for (p = MPFR_PREC_MIN; p <= 128; p++)
{
test_property1 (p, MPFR_RNDN, 0);
test_property1 (p, MPFR_RNDU, 0);
test_property1 (p, MPFR_RNDA, 0);
test_property1 (p, MPFR_RNDN, 1);
test_property1 (p, MPFR_RNDU, 1);
test_property1 (p, MPFR_RNDA, 1);
test_property2 (p, MPFR_RNDN);
}
check_diverse ("635030154261163106768013773815762607450069292760790610550915652722277604820131530404842415587328", 160, "796887792767063979679855997149887366668464780637");
special ();
check_singular ();
for (p=2; p<200; p++)
for (k=0; k<200; k++)
check_inexact (p);
check_float();
check3 ("-0.0", MPFR_RNDN, "0.0");
check4 ("6.37983013646045901440e+32", MPFR_RNDN, "5.9bc5036d09e0c@13");
check4 ("1.0", MPFR_RNDN, "1");
check4 ("1.0", MPFR_RNDZ, "1");
check4 ("3.725290298461914062500000e-9", MPFR_RNDN, "4@-4");
check4 ("3.725290298461914062500000e-9", MPFR_RNDZ, "4@-4");
check4 ("1190456976439861.0", MPFR_RNDZ, "2.0e7957873529a@6");
check4 ("1219027943874417664.0", MPFR_RNDZ, "4.1cf2af0e6a534@7");
/* the following examples are bugs in Cygnus compiler/system, found by
Fabrice Rouillier while porting mpfr to Windows */
check4 ("9.89438396044940256501e-134", MPFR_RNDU, "8.7af7bf0ebbee@-56");
check4 ("7.86528588050363751914e+31", MPFR_RNDZ, "1.f81fc40f32062@13");
check4 ("0.99999999999999988897", MPFR_RNDN, "f.ffffffffffff8@-1");
check4 ("1.00000000000000022204", MPFR_RNDN, "1");
/* the following examples come from the paper "Number-theoretic Test
Generation for Directed Rounding" from Michael Parks, Table 4 */
check4 ("78652858805036375191418371571712.0", MPFR_RNDN,
"1.f81fc40f32063@13");
check4 ("38510074998589467860312736661504.0", MPFR_RNDN,
"1.60c012a92fc65@13");
check4 ("35318779685413012908190921129984.0", MPFR_RNDN,
"1.51d17526c7161@13");
check4 ("26729022595358440976973142425600.0", MPFR_RNDN,
"1.25e19302f7e51@13");
check4 ("22696567866564242819241453027328.0", MPFR_RNDN,
"1.0ecea7dd2ec3d@13");
check4 ("22696888073761729132924856434688.0", MPFR_RNDN,
"1.0ecf250e8e921@13");
check4 ("36055652513981905145251657416704.0", MPFR_RNDN,
"1.5552f3eedcf33@13");
check4 ("30189856268896404997497182748672.0", MPFR_RNDN,
"1.3853ee10c9c99@13");
check4 ("36075288240584711210898775080960.0", MPFR_RNDN,
"1.556abe212b56f@13");
check4 ("72154663483843080704304789585920.0", MPFR_RNDN,
"1.e2d9a51977e6e@13");
check4 ("78652858805036375191418371571712.0", MPFR_RNDZ,
"1.f81fc40f32062@13");
check4 ("38510074998589467860312736661504.0", MPFR_RNDZ,
"1.60c012a92fc64@13");
check4 ("35318779685413012908190921129984.0", MPFR_RNDZ, "1.51d17526c716@13");
check4 ("26729022595358440976973142425600.0", MPFR_RNDZ, "1.25e19302f7e5@13");
check4 ("22696567866564242819241453027328.0", MPFR_RNDZ,
"1.0ecea7dd2ec3c@13");
check4 ("22696888073761729132924856434688.0", MPFR_RNDZ, "1.0ecf250e8e92@13");
check4 ("36055652513981905145251657416704.0", MPFR_RNDZ,
"1.5552f3eedcf32@13");
check4 ("30189856268896404997497182748672.0", MPFR_RNDZ,
"1.3853ee10c9c98@13");
check4 ("36075288240584711210898775080960.0", MPFR_RNDZ,
"1.556abe212b56e@13");
check4 ("72154663483843080704304789585920.0", MPFR_RNDZ,
"1.e2d9a51977e6d@13");
check4 ("78652858805036375191418371571712.0", MPFR_RNDU,
"1.f81fc40f32063@13");
check4 ("38510074998589467860312736661504.0", MPFR_RNDU,
"1.60c012a92fc65@13");
check4 ("35318779685413012908190921129984.0", MPFR_RNDU,
"1.51d17526c7161@13");
check4 ("26729022595358440976973142425600.0", MPFR_RNDU,
"1.25e19302f7e51@13");
check4 ("22696567866564242819241453027328.0", MPFR_RNDU,
"1.0ecea7dd2ec3d@13");
check4 ("22696888073761729132924856434688.0", MPFR_RNDU,
"1.0ecf250e8e921@13");
check4 ("36055652513981905145251657416704.0", MPFR_RNDU,
"1.5552f3eedcf33@13");
check4 ("30189856268896404997497182748672.0", MPFR_RNDU,
"1.3853ee10c9c99@13");
check4 ("36075288240584711210898775080960.0", MPFR_RNDU,
"1.556abe212b56f@13");
check4 ("72154663483843080704304789585920.0", MPFR_RNDU,
"1.e2d9a51977e6e@13");
check4 ("78652858805036375191418371571712.0", MPFR_RNDD,
"1.f81fc40f32062@13");
check4 ("38510074998589467860312736661504.0", MPFR_RNDD,
"1.60c012a92fc64@13");
check4 ("35318779685413012908190921129984.0", MPFR_RNDD, "1.51d17526c716@13");
check4 ("26729022595358440976973142425600.0", MPFR_RNDD, "1.25e19302f7e5@13");
check4 ("22696567866564242819241453027328.0", MPFR_RNDD,
"1.0ecea7dd2ec3c@13");
check4 ("22696888073761729132924856434688.0", MPFR_RNDD, "1.0ecf250e8e92@13");
check4 ("36055652513981905145251657416704.0", MPFR_RNDD,
"1.5552f3eedcf32@13");
check4 ("30189856268896404997497182748672.0", MPFR_RNDD,
"1.3853ee10c9c98@13");
check4 ("36075288240584711210898775080960.0", MPFR_RNDD,
"1.556abe212b56e@13");
check4 ("72154663483843080704304789585920.0", MPFR_RNDD,
"1.e2d9a51977e6d@13");
/* check that rounding away is just rounding toward plus infinity */
check4 ("72154663483843080704304789585920.0", MPFR_RNDA,
"1.e2d9a51977e6e@13");
test_generic (2, 300, 15);
data_check ("data/sqrt", mpfr_sqrt, "mpfr_sqrt");
bad_cases (mpfr_sqrt, mpfr_sqr, "mpfr_sqrt", 8, -256, 255, 4, 128, 800, 50);
bug20160120 ();
tests_end_mpfr ();
return 0;
}