/* Test file for mpfr_sqrt.
Copyright 1999, 2001, 2002 Free Software Foundation, Inc.
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., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
#include "mpfr-test.h"
#define check(a,r) check3(a,r,-1.0)
int maxulp=0;
void check3 _PROTO((double, mp_rnd_t, double));
void check4 _PROTO((double, mp_rnd_t, char *));
void check24 _PROTO((float, mp_rnd_t, float));
void check_float _PROTO((void));
void special _PROTO((void));
void check_inexact _PROTO((mp_prec_t));
void check_nan _PROTO((void));
void
check3 (double a, mp_rnd_t rnd_mode, double Q)
{
mpfr_t q; double Q2; int ck,u;
ck = (Q!=-1.0); /* if ck=1, then Q is certified correct */
mpfr_init2(q, 53);
mpfr_set_d(q, a, rnd_mode);
#ifdef MPFR_HAVE_FESETROUND
mpfr_set_machine_rnd_mode(rnd_mode);
#endif
mpfr_sqrt(q, q, rnd_mode);
if (ck==0) Q = sqrt(a);
else {
if (Q != sqrt(a) && (!isnan(Q) || !isnan(sqrt(a)))) {
fprintf(stderr, "you've found a bug in your machine's sqrt for x=%1.20e\n", a);
mpfr_clear(q);
exit(1);
}
}
Q2 = mpfr_get_d1 (q);
if (Q!=Q2 && (!isnan(Q) || !isnan(Q2))) {
u = ulp(Q2,Q);
if (ck) {
printf("mpfr_sqrt failed for a=%1.20e, rnd_mode=%s\n",
a, mpfr_print_rnd_mode(rnd_mode));
printf("expected sqrt is %1.20e, got %1.20e (%d ulp)\n",Q,Q2,u);
mpfr_clear(q);
exit(1);
}
else if (u>maxulp || u<-maxulp) {
maxulp = (u>maxulp) ? u : -u;
printf("libm.a differs from mpfr_sqrt for a=%1.20e, rnd_mode=%s\n",
a, mpfr_print_rnd_mode(rnd_mode));
printf("libm.a gives %1.20e, mpfr_sqrt gives %1.20e (%d ulp)\n",Q,Q2,u);
}
}
mpfr_clear(q);
}
void
check4 (double a, mp_rnd_t rnd_mode, char *Q)
{
mpfr_t q, res;
mpfr_init2(q, 53); mpfr_init2(res, 53);
mpfr_set_d(q, a, rnd_mode);
mpfr_sqrt(q, q, rnd_mode);
mpfr_set_str(res, Q, 16, GMP_RNDN);
if (mpfr_cmp(q, res)) {
printf("mpfr_sqrt failed for a=%1.20e, rnd_mode=%s\n",
a, mpfr_print_rnd_mode(rnd_mode));
printf("expected "); mpfr_print_binary(res); putchar('\n');
printf("got "); mpfr_print_binary(q); putchar('\n');
mpfr_clear(q); mpfr_clear(res);
exit(1);
}
mpfr_clear(res);
mpfr_clear(q);
}
void
check24 (float a, mp_rnd_t rnd_mode, float Q)
{
mpfr_t q; float Q2;
mpfr_init2(q, 24);
mpfr_set_d(q, a, rnd_mode);
mpfr_sqrt(q, q, rnd_mode);
Q2 = mpfr_get_d1 (q);
if (Q!=Q2) {
printf("mpfr_sqrt failed for a=%1.10e, prec=24, rnd_mode=%s\n",
a, mpfr_print_rnd_mode(rnd_mode));
printf("expected sqrt is %1.10e, got %1.10e\n",Q,Q2);
exit(1);
}
mpfr_clear(q);
}
/* the following examples come from the paper "Number-theoretic Test
Generation for Directed Rounding" from Michael Parks, Table 3 */
void
check_float (void)
{
float b = 8388608.0; /* 2^23 */
check24(b*8388610.0, GMP_RNDN, 8.388609e6);
check24(b*2.0*16777214.0, GMP_RNDN, 1.6777215e7);
check24(b*8388612.0, GMP_RNDN, 8.388610e6);
check24(b*2.0*16777212.0, GMP_RNDN, 1.6777214e7);
check24(b*11946704.0, GMP_RNDN, 1.0010805e7);
check24(b*14321479.0, GMP_RNDN, 1.0960715e7);
check24(b*2.0*13689673.0, GMP_RNDN, 1.5155019e7);
check24(b*8388614.0, GMP_RNDN, 8.388611e6);
check24(b*2.0*16777210.0, GMP_RNDN, 1.6777213e7);
check24(b*10873622.0, GMP_RNDN, 9.550631e6);
check24(b*8388610.0, GMP_RNDZ, 8.388608e6);
check24(b*2.0*16777214.0, GMP_RNDZ, 1.6777214e7);
check24(b*8388612.0, GMP_RNDZ, 8.388609e6);
check24(b*2.0*16777212.0, GMP_RNDZ, 1.6777213e7);
check24(b*11946704.0, GMP_RNDZ, 1.0010805e7);
check24(b*14321479.0, GMP_RNDZ, 1.0960715e7);
check24(b*2.0*13689673.0, GMP_RNDZ, 1.5155019e7);
check24(b*8388614.0, GMP_RNDZ, 8.38861e6);
check24(b*2.0*16777210.0, GMP_RNDZ, 1.6777212e7);
check24(b*10873622.0, GMP_RNDZ, 9.550631e6);
check24(b*8388610.0, GMP_RNDU, 8.388609e6);
check24(b*2.0*16777214.0, GMP_RNDU, 1.6777215e7);
check24(b*8388612.0, GMP_RNDU, 8.388610e6);
check24(b*2.0*16777212.0, GMP_RNDU, 1.6777214e7);
check24(b*11946704.0, GMP_RNDU, 1.0010806e7);
check24(b*14321479.0, GMP_RNDU, 1.0960716e7);
check24(b*2.0*13689673.0, GMP_RNDU, 1.515502e7);
check24(b*8388614.0, GMP_RNDU, 8.388611e6);
check24(b*2.0*16777210.0, GMP_RNDU, 1.6777213e7);
check24(b*10873622.0, GMP_RNDU, 9.550632e6);
check24(b*8388610.0, GMP_RNDD, 8.388608e6);
check24(b*2.0*16777214.0, GMP_RNDD, 1.6777214e7);
check24(b*8388612.0, GMP_RNDD, 8.388609e6);
check24(b*2.0*16777212.0, GMP_RNDD, 1.6777213e7);
check24(b*11946704.0, GMP_RNDD, 1.0010805e7);
check24(b*14321479.0, GMP_RNDD, 1.0960715e7);
check24(b*2.0*13689673.0, GMP_RNDD, 1.5155019e7);
check24(b*8388614.0, GMP_RNDD, 8.38861e6);
check24(b*2.0*16777210.0, GMP_RNDD, 1.6777212e7);
check24(b*10873622.0, GMP_RNDD, 9.550631e6);
}
void
special (void)
{
mpfr_t x, z;
int inexact;
mp_prec_t p;
mpfr_init (x);
mpfr_init (z);
mpfr_set_prec (x, 27);
mpfr_set_str_raw (x, "0.110100111010101000010001011");
if ((inexact = mpfr_sqrt (x, x, GMP_RNDZ)) >= 0)
{
fprintf (stderr, "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, GMP_RNDN);
mpfr_add_one_ulp (z, GMP_RNDN);
mpfr_sqrt (x, z, GMP_RNDU);
if (mpfr_get_d1 (x) != 1.5)
{
fprintf (stderr, "Error: sqrt(1+ulp(1), up) should give 1.5 (prec=%u)\n", (unsigned) p);
printf ("got "); mpfr_print_binary (x); putchar ('\n');
exit (1);
}
}
/* check inexact flag */
mpfr_set_prec (x, 5);
mpfr_set_str_raw (x, "1.1001E-2");
if ((inexact = mpfr_sqrt (x, x, GMP_RNDN)))
{
fprintf (stderr, "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_d (x, 1.0, GMP_RNDN);
mpfr_set_d (z, -1.0, GMP_RNDN);
mpfr_sqrt (z, x, GMP_RNDN);
if (mpfr_cmp_ui (z, 0) < 0) {
fprintf (stderr, "Error: square root of %e gives %e\n",
mpfr_get_d1 (x), mpfr_get_d1 (z));
exit (1);
}
mpfr_set_prec (x, 192);
mpfr_set_prec (z, 160);
mpfr_set_str_raw (z, "0.1011010100000100100100100110011001011100100100000011000111011001011101101101110000110100001000100001100001011000E1");
mpfr_set_prec (x, 160);
mpfr_sqrt(x, z, GMP_RNDN);
mpfr_sqrt(z, x, GMP_RNDN);
mpfr_clear (x);
mpfr_clear (z);
}
void
check_inexact (mp_prec_t p)
{
mpfr_t x, y, z;
mp_rnd_t rnd;
int inexact, sign;
mpfr_init2 (x, p);
mpfr_init2 (y, p);
mpfr_init2 (z, 2*p);
mpfr_random (x);
rnd = LONG_RAND() % 4;
inexact = mpfr_sqrt (y, x, rnd);
if (mpfr_mul (z, y, y, rnd)) /* exact since prec(z) = 2*prec(y) */
{
fprintf (stderr, "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)))
{
fprintf (stderr, "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); putchar ('\n');
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
void
check_nan (void)
{
mpfr_t x, got;
mpfr_init2 (x, 100L);
mpfr_init2 (got, 100L);
/* sqrt(NaN) == NaN */
MPFR_CLEAR_FLAGS (x);
MPFR_SET_NAN (x);
ASSERT_ALWAYS (mpfr_sqrt (got, x, GMP_RNDZ) == 0); /* exact */
ASSERT_ALWAYS (mpfr_nan_p (got));
/* sqrt(-1) == NaN */
mpfr_set_si (x, -1L, GMP_RNDZ);
ASSERT_ALWAYS (mpfr_sqrt (got, x, GMP_RNDZ) == 0); /* exact */
ASSERT_ALWAYS (mpfr_nan_p (got));
/* sqrt(+inf) == +inf */
MPFR_CLEAR_FLAGS (x);
MPFR_SET_INF (x);
MPFR_SET_POS (x);
ASSERT_ALWAYS (mpfr_sqrt (got, x, GMP_RNDZ) == 0); /* exact */
ASSERT_ALWAYS (mpfr_inf_p (got));
/* sqrt(-inf) == NaN */
MPFR_CLEAR_FLAGS (x);
MPFR_SET_INF (x);
MPFR_SET_NEG (x);
ASSERT_ALWAYS (mpfr_sqrt (got, x, GMP_RNDZ) == 0); /* exact */
ASSERT_ALWAYS (mpfr_nan_p (got));
/* sqrt(-0) == 0 */
mpfr_set_si (x, 0L, GMP_RNDZ);
MPFR_SET_NEG (x);
ASSERT_ALWAYS (mpfr_sqrt (got, x, GMP_RNDZ) == 0); /* exact */
ASSERT_ALWAYS (mpfr_number_p (got));
ASSERT_ALWAYS (mpfr_cmp_ui (got, 0L) == 0);
mpfr_clear (x);
mpfr_clear (got);
}
double five = 5.0;
int
main (void)
{
double a;
mp_prec_t p;
int k;
#ifdef MPFR_HAVE_FESETROUND
int i;
mpfr_test_init ();
/* On Debian potato glibc 2.1.3-18, sqrt() doesn't seem to respect
fesetround. */
{
double a, b;
mpfr_set_machine_rnd_mode (GMP_RNDU);
a = sqrt (five);
mpfr_set_machine_rnd_mode (GMP_RNDD);
b = sqrt (five);
if (a == b)
{
printf ("Tests suppressed, mpfr_set_machine_rnd_mode doesn't affect sqrt()\n");
goto nogood;
}
}
SEED_RAND (time(NULL));
for (i=0;i<100000;i++)
{
a = drand();
if (a < 0.0) a = -a; /* ensures a is positive */
check (a, LONG_RAND() % 4);
}
nogood:
#endif
check_nan ();
for (p=2; p<200; p++)
for (k=0; k<200; k++)
check_inexact (p);
special ();
check_float();
#ifdef HAVE_INFS
check3 (DBL_NAN, GMP_RNDN, DBL_NAN);
check3 (-1.0, GMP_RNDN, DBL_NAN);
check3 (DBL_POS_INF, GMP_RNDN, DBL_POS_INF);
check3 (DBL_NEG_INF, GMP_RNDN, DBL_NAN);
#endif
check3(-0.0, GMP_RNDN, 0.0);
check4(6.37983013646045901440e+32, GMP_RNDN, "5.9bc5036d09e0c@13");
check4(1.0, GMP_RNDN, "1");
check4(1.0, GMP_RNDZ, "1");
check4(3.725290298461914062500000e-9, GMP_RNDN, "4@-4");
check4(3.725290298461914062500000e-9, GMP_RNDZ, "4@-4");
a=1190456976439861.0;
check4(a, GMP_RNDZ, "2.0e7957873529a@6");
check4(1024.0*a, GMP_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, GMP_RNDU, "8.7af7bf0ebbee@-56");
check4(7.86528588050363751914e+31, GMP_RNDZ, "1.f81fc40f32062@13");
check4(0.99999999999999988897, GMP_RNDN, "f.ffffffffffff8@-1");
check4(1.00000000000000022204, GMP_RNDN, "1");
/* the following examples come from the paper "Number-theoretic Test
Generation for Directed Rounding" from Michael Parks, Table 4 */
a = 4503599627370496.0; /* 2^52 */
check4(a*2.0*8732221479794286.0, GMP_RNDN, "1.f81fc40f32063@13");
check4(a*8550954388695124.0, GMP_RNDN, "1.60c012a92fc65@13");
check4(a*7842344481681754.0, GMP_RNDN, "1.51d17526c7161@13");
check4(a*5935035262218600.0, GMP_RNDN, "1.25e19302f7e51@13");
check4(a*5039650445085418.0, GMP_RNDN, "1.0ecea7dd2ec3d@13");
check4(a*5039721545366078.0, GMP_RNDN, "1.0ecf250e8e921@13");
check4(a*8005963117781324.0, GMP_RNDN, "1.5552f3eedcf33@13");
check4(a*6703494707970582.0, GMP_RNDN, "1.3853ee10c9c99@13");
check4(a*8010323124937260.0, GMP_RNDN, "1.556abe212b56f@13");
check4(a*2.0*8010776873384260.0, GMP_RNDN, "1.e2d9a51977e6e@13");
check4(a*2.0*8732221479794286.0, GMP_RNDZ, "1.f81fc40f32062@13");
check4(a*8550954388695124.0, GMP_RNDZ, "1.60c012a92fc64@13");
check4(a*7842344481681754.0, GMP_RNDZ, "1.51d17526c716@13");
check4(a*5935035262218600.0, GMP_RNDZ, "1.25e19302f7e5@13");
check4(a*5039650445085418.0, GMP_RNDZ, "1.0ecea7dd2ec3c@13");
check4(a*5039721545366078.0, GMP_RNDZ, "1.0ecf250e8e92@13");
check4(a*8005963117781324.0, GMP_RNDZ, "1.5552f3eedcf32@13");
check4(a*6703494707970582.0, GMP_RNDZ, "1.3853ee10c9c98@13");
check4(a*8010323124937260.0, GMP_RNDZ, "1.556abe212b56e@13");
check4(a*2.0*8010776873384260.0, GMP_RNDZ, "1.e2d9a51977e6d@13");
check4(a*2.0*8732221479794286.0, GMP_RNDU, "1.f81fc40f32063@13");
check4(a*8550954388695124.0, GMP_RNDU, "1.60c012a92fc65@13");
check4(a*7842344481681754.0, GMP_RNDU, "1.51d17526c7161@13");
check4(a*5935035262218600.0, GMP_RNDU, "1.25e19302f7e51@13");
check4(a*5039650445085418.0, GMP_RNDU, "1.0ecea7dd2ec3d@13");
check4(a*5039721545366078.0, GMP_RNDU, "1.0ecf250e8e921@13");
check4(a*8005963117781324.0, GMP_RNDU, "1.5552f3eedcf33@13");
check4(a*6703494707970582.0, GMP_RNDU, "1.3853ee10c9c99@13");
check4(a*8010323124937260.0, GMP_RNDU, "1.556abe212b56f@13");
check4(a*2.0*8010776873384260.0, GMP_RNDU, "1.e2d9a51977e6e@13");
check4(a*2.0*8732221479794286.0, GMP_RNDD, "1.f81fc40f32062@13");
check4(a*8550954388695124.0, GMP_RNDD, "1.60c012a92fc64@13");
check4(a*7842344481681754.0, GMP_RNDD, "1.51d17526c716@13");
check4(a*5935035262218600.0, GMP_RNDD, "1.25e19302f7e5@13");
check4(a*5039650445085418.0, GMP_RNDD, "1.0ecea7dd2ec3c@13");
check4(a*5039721545366078.0, GMP_RNDD, "1.0ecf250e8e92@13");
check4(a*8005963117781324.0, GMP_RNDD, "1.5552f3eedcf32@13");
check4(a*6703494707970582.0, GMP_RNDD, "1.3853ee10c9c98@13");
check4(a*8010323124937260.0, GMP_RNDD, "1.556abe212b56e@13");
check4(a*2.0*8010776873384260.0, GMP_RNDD, "1.e2d9a51977e6d@13");
return 0;
}
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