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/* Test file for mpfr_atan2u.
Copyright 2021 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"
#define TEST_FUNCTION mpfr_atan2u
#define THREE_ARGS
#include "tgeneric.c"
/* Special cases from IEEE 754-2019 (page 63) */
static void
check_ieee754 (void)
{
mpfr_t x, y, z;
int i;
mpfr_prec_t prec = 2; /* we need at least 2 so that 3/4 is exact */
mpfr_init2 (x, prec);
mpfr_init2 (y, prec);
mpfr_init2 (z, prec);
/* atan2Pi(±0, −0) is ±1 */
mpfr_set_zero (x, -1);
mpfr_set_zero (y, +1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_ui (z, 1) != 0)
{
printf ("Error for atan2u(+0,-0,2)\n");
printf ("expected 1\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_zero (y, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_si (z, -1) != 0)
{
printf ("Error for atan2u(-0,-0,2)\n");
printf ("expected -1\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
/* atan2Pi(±0, +0) is ±0 */
mpfr_set_zero (x, +1);
mpfr_set_zero (y, +1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_NEG(z))
{
printf ("Error for atan2u(+0,+0,2)\n");
printf ("expected +0\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_zero (y, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_POS(z))
{
printf ("Error for atan2u(-0,+0,2)\n");
printf ("expected -0\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
/* atan2Pi(±0, x) is ±1 for x < 0 (including x=-Inf) */
for (i = 0; i < 2; i++)
{
if (i == 0)
mpfr_set_si (x, -1, MPFR_RNDN);
else
mpfr_set_inf (x, -1);
mpfr_set_zero (y, +1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_ui (z, 1) != 0)
{
printf ("Error for atan2u(+0,x,2)\nwith x = ");
mpfr_dump (x);
printf ("expected 1\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_zero (y, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_si (z, -1) != 0)
{
printf ("Error for atan2u(-0,x,2)\nwith x = ");
mpfr_dump (x);
printf ("expected -1\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
}
/* atan2Pi(±0, x) is ±0 for x > 0 (including x=+Inf) */
for (i = 0; i < 2; i++)
{
if (i == 0)
mpfr_set_ui (x, 1, MPFR_RNDN);
else
mpfr_set_inf (x, 1);
mpfr_set_zero (y, +1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_NEG(z))
{
printf ("Error for atan2u(+0,x,2)\nwith x = ");
mpfr_dump (x);
printf ("expected +0\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_zero (y, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_POS(z))
{
printf ("Error for atan2u(-0,x,2)\nwith x = ");
mpfr_dump (x);
printf ("expected -0\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
}
/* atan2Pi(y, ±0) is −½ for y < 0 */
mpfr_set_si (y, -1, MPFR_RNDN);
mpfr_set_zero (x, 1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_si_2exp (z, -1, -1) != 0)
{
printf ("Error for atan2u(-1,+0,2)\n");
printf ("expected -1/2\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_zero (x, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_si_2exp (z, -1, -1) != 0)
{
printf ("Error for atan2u(-1,-0,2)\n");
printf ("expected -1/2\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
/* atan2Pi(y, ±0) is +½ for y > 0 */
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_set_zero (x, 1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_ui_2exp (z, 1, -1) != 0)
{
printf ("Error for atan2u(1,+0,2)\n");
printf ("expected 1/2\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_zero (x, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_ui_2exp (z, 1, -1) != 0)
{
printf ("Error for atan2u(-1,-0,2)\n");
printf ("expected 1/2\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
/* atan2Pi(±y, −∞) is ±1 for finite y > 0 */
mpfr_set_inf (x, -1);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_ui (z, 1) != 0)
{
printf ("Error for atan2u(1,-Inf,2)\n");
printf ("expected 1\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_si (y, -1, MPFR_RNDN);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_si (z, -1) != 0)
{
printf ("Error for atan2u(-1,-Inf,2)\n");
printf ("expected -1\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
/* atan2Pi(±y, +∞) is ±0 for finite y > 0 */
mpfr_set_inf (x, +1);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_NEG(z))
{
printf ("Error for atan2u(1,+Inf,2)\n");
printf ("expected +0\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_si (y, -1, MPFR_RNDN);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_POS(z))
{
printf ("Error for atan2u(-1,+Inf,2)\n");
printf ("expected -0\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
/* atan2Pi(±∞, x) is ±½ for finite x */
for (i = 0; i < 4; i++)
{
if (i == 0)
mpfr_set_ui (x, 1, MPFR_RNDN);
else if (i == 1)
mpfr_set_zero (x, 1);
else if (i == 2)
mpfr_set_zero (x, -1);
else
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_ui_2exp (z, 1, -1) != 0)
{
printf ("Error for atan2u(+Inf,x,2)\nwith x = ");
mpfr_dump (x);
printf ("expected 1/2\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_inf (y, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_si_2exp (z, -1, -1) != 0)
{
printf ("Error for atan2u(-Inf,x,2)\nwith x = ");
mpfr_dump (x);
printf ("expected -1/2\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
}
/* atan2Pi(±∞, −∞) is ±¾ */
mpfr_set_inf (x, -1);
mpfr_set_inf (y, 1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_ui_2exp (z, 3, -2) != 0)
{
printf ("Error for atan2u(+Inf,-Inf,2)\n");
printf ("expected 3/4\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_inf (y, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_si_2exp (z, -3, -2) != 0)
{
printf ("Error for atan2u(+Inf,-Inf,2)\n");
printf ("expected -3/4\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
/* atan2Pi(±∞, +∞) is ±¼ */
mpfr_set_inf (x, 1);
mpfr_set_inf (y, 1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_ui_2exp (z, 1, -2) != 0)
{
printf ("Error for atan2u(+Inf,+Inf,2)\n");
printf ("expected 1/4\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_inf (y, -1);
mpfr_atan2u (z, y, x, 2, MPFR_RNDN);
if (mpfr_cmp_si_2exp (z, -1, -2) != 0)
{
printf ("Error for atan2u(+Inf,+Inf,2)\n");
printf ("expected -1/4\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
/* Special cases from LIA-2 (5.3.9.15) not covered by IEEE 754-2019.
Warning: in LIA-2, the order of arguments is reversed:
arcu (u,x,y) corresponds to atan2u (y,x,u). */
static void
check_lia2 (void)
{
mpfr_t x, y, z;
mpfr_prec_t prec = 9; /* 3*99 must be exactly representable */
unsigned long u;
int r, inex;
mpfr_init2 (x, prec);
mpfr_init2 (y, prec);
mpfr_init2 (z, prec);
/* arcu (u, x, x) = u/8 for x > 0 */
for (u = 1; u < 100; u++)
RND_LOOP (r)
{
mpfr_set_ui (x, 1, MPFR_RNDN); /* exact */
mpfr_set_ui (y, 1, MPFR_RNDN); /* exact */
mpfr_atan2u (z, y, x, u, (mpfr_rnd_t) r);
inex = mpfr_set_ui (x, u, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
inex = mpfr_div_ui (x, x, 8, (mpfr_rnd_t) r);
if ((r != MPFR_RNDF || inex == 0) && !mpfr_equal_p (x, z))
{
printf ("Error: atan2u(1,1,u) != u/8 for u=%lu and rnd=%s\n",
u, mpfr_print_rnd_mode ((mpfr_rnd_t) r));
printf ("got: "); mpfr_dump (z);
exit (1);
}
}
/* arcu (u, x, -x) = -u/8 for x > 0 */
for (u = 1; u < 100; u++)
RND_LOOP (r)
{
mpfr_set_ui (x, 1, MPFR_RNDN); /* exact */
mpfr_set_si (y, -1, MPFR_RNDN); /* exact */
mpfr_atan2u (z, y, x, u, (mpfr_rnd_t) r);
inex = mpfr_set_ui (x, u, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
inex = mpfr_div_si (x, x, -8, (mpfr_rnd_t) r);
if ((r != MPFR_RNDF || inex == 0) && !mpfr_equal_p (x, z))
{
printf ("Error: atan2u(-1,1,u) != -u/8 for u=%lu and rnd=%s\n",
u, mpfr_print_rnd_mode ((mpfr_rnd_t) r));
printf ("got: "); mpfr_dump (z);
exit (1);
}
}
/* arcu (u, x, −x) = 3 · u/8 for x < 0 */
for (u = 1; u < 100; u++)
RND_LOOP (r)
{
mpfr_set_si (x, -1, MPFR_RNDN); /* exact */
mpfr_set_ui (y, 1, MPFR_RNDN); /* exact */
mpfr_atan2u (z, y, x, u, (mpfr_rnd_t) r);
inex = mpfr_set_ui (x, 3 * u, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
inex = mpfr_div_ui (x, x, 8, (mpfr_rnd_t) r);
if ((r != MPFR_RNDF || inex == 0) && !mpfr_equal_p (x, z))
{
printf ("Error: atan2u(1,-1,u) != 3u/8 for u=%lu and rnd=%s\n",
u, mpfr_print_rnd_mode ((mpfr_rnd_t) r));
printf ("got: "); mpfr_dump (z);
exit (1);
}
}
/* arcu (u, x, x) = -3 · u/8 for x < 0 */
for (u = 1; u < 100; u++)
RND_LOOP (r)
{
mpfr_set_si (x, -1, MPFR_RNDN); /* exact */
mpfr_set_si (y, -1, MPFR_RNDN); /* exact */
mpfr_atan2u (z, y, x, u, (mpfr_rnd_t) r);
inex = mpfr_set_ui (x, 3 * u, MPFR_RNDN);
MPFR_ASSERTN(inex == 0);
inex = mpfr_div_si (x, x, -8, (mpfr_rnd_t) r);
if ((r != MPFR_RNDF || inex == 0) && !mpfr_equal_p (x, z))
{
printf ("Error: atan2u(-1,-1,u) != -3u/8 for u=%lu and rnd=%s\n",
u, mpfr_print_rnd_mode ((mpfr_rnd_t) r));
printf ("got: "); mpfr_dump (z);
exit (1);
}
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
static void
check_random (void)
{
mpfr_t x, y, z;
long i, j, B = 20;
unsigned long u;
int r;
mpfr_init2 (x, 53);
mpfr_init2 (y, 53);
mpfr_init2 (z, 53);
/* hard-coded values */
/* first quadrant */
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_ui (y, 42, MPFR_RNDN);
mpfr_atan2u (z, y, x, 360, MPFR_RNDN); /* in degrees */
mpfr_set_str (x, "4.3f6b9d4ccd754p+4", 16, MPFR_RNDN);
if (!mpfr_equal_p (z, x))
{
printf ("Error for atan2u(42,17,360)\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (z);
exit (1);
}
/* second quadrant */
mpfr_set_si (x, -17, MPFR_RNDN);
mpfr_set_ui (y, 42, MPFR_RNDN);
mpfr_atan2u (z, y, x, 360, MPFR_RNDN); /* in degrees */
mpfr_set_str (x, "7.009462b3328acp+4", 16, MPFR_RNDN);
if (!mpfr_equal_p (z, x))
{
printf ("Error for atan2u(42,-17,360)\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (z);
exit (1);
}
/* third quadrant */
mpfr_set_si (x, -17, MPFR_RNDN);
mpfr_set_si (y, -42, MPFR_RNDN);
mpfr_atan2u (z, y, x, 360, MPFR_RNDN); /* in degrees */
mpfr_set_str (x, "-7.009462b3328acp+4", 16, MPFR_RNDN);
if (!mpfr_equal_p (z, x))
{
printf ("Error for atan2u(-42,-17,360)\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (z);
exit (1);
}
/* fourth quadrant */
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_si (y, -42, MPFR_RNDN);
mpfr_atan2u (z, y, x, 360, MPFR_RNDN); /* in degrees */
mpfr_set_str (x, "-4.3f6b9d4ccd754p+4", 16, MPFR_RNDN);
if (!mpfr_equal_p (z, x))
{
printf ("Error for atan2u(-42,17,360)\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (z);
exit (1);
}
/* case u=0 with x > 0 */
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_ui (y, 42, MPFR_RNDN);
mpfr_atan2u (z, y, x, 0, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_NEG(z))
{
printf ("Error for atan2u(42,17,0)\n");
printf ("expected +0\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_si (y, -42, MPFR_RNDN);
mpfr_atan2u (z, y, x, 0, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_POS(z))
{
printf ("Error for atan2u(-42,17,0)\n");
printf ("expected -0\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
/* case u=0 with x < 0 */
mpfr_set_si (x, -17, MPFR_RNDN);
mpfr_set_ui (y, 42, MPFR_RNDN);
mpfr_atan2u (z, y, x, 0, MPFR_RNDN);
if (mpfr_cmp_ui (z, 1) != 0)
{
printf ("Error for atan2u(42,-17,0)\n");
printf ("expected +1\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_set_si (y, -42, MPFR_RNDN);
mpfr_atan2u (z, y, x, 0, MPFR_RNDN);
if (mpfr_cmp_si (z, -1) != 0)
{
printf ("Error for atan2u(-42,-17,0)\n");
printf ("expected -1\n");
printf ("got "); mpfr_dump (z);
exit (1);
}
for (i = -B; i <= B; i++)
{
mpfr_set_si (x, i, MPFR_RNDN);
for (j = -B; j <= B; j++)
{
mpfr_set_si (y, j, MPFR_RNDN);
for (u = 0; u <= B; u++)
RND_LOOP (r)
mpfr_atan2u (z, y, x, u, (mpfr_rnd_t) r);
}
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
/* bug found with GMP_CHECK_RANDOMIZE=1612368173909457 */
static void
bug20210203 (void)
{
/* The "#if" makes sure that 64-bit constants are supported, avoiding
a compilation failure. The "if" makes sure that the constant is
representable in an unsigned long (this would not be the case with
32-bit unsigned long and 64-bit limb). */
#if GMP_NUMB_BITS >= 64 || MPFR_PREC_BITS >= 64
mpfr_t x, y, z;
unsigned long u = 13484982567905493265U;
if (u == 13484982567905493265U)
{
mpfr_init2 (x, 12);
mpfr_init2 (y, 12);
mpfr_init2 (z, 28);
mpfr_set_str_binary (y, "-0.111101100000E-66");
mpfr_set_str_binary (x, "0.111011100000E0");
mpfr_atan2u (z, y, x, u, MPFR_RNDN);
mpfr_set_prec (x, 28);
mpfr_set_str_binary (x, "-0.1111011001001001000110001010E-5");
if (!mpfr_equal_p (z, x))
{
printf ("Error in bug20210203\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
#endif
}
int
main (void)
{
tests_start_mpfr ();
bug20210203 ();
check_ieee754 ();
check_lia2 ();
check_random ();
test_generic (MPFR_PREC_MIN, 100, 100);
tests_end_mpfr ();
return 0;
}
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