path: root/tests/tpow_z.c

/* Test file for mpfr_pow_z -- power function x^z with z a MPZ

Copyright 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao 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 2.1 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.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

#include <stdlib.h>
#include <float.h>
#include <math.h>

#include "mpfr-test.h"

#define ERROR(str) do { printf("Error for "str"\n"); exit (1); } while (0)

static void
check_special (void)
{
  mpfr_t x, y;
  mpz_t  z;
  int res;

  mpfr_init (x);
  mpfr_init (y);
  mpz_init (z);

  /* x^0 = 1 except for NAN */
  mpfr_set_ui (x, 23, GMP_RNDN);
  mpz_set_ui (z, 0);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_cmp_ui (y, 1) != 0)
    ERROR ("23^0");
  mpfr_set_nan (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_nan_p (y) || mpfr_cmp_si (y, 1) != 0)
    ERROR ("NAN^0");
  mpfr_set_inf (x, 1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_cmp_ui (y, 1) != 0)
    ERROR ("INF^0");

  /* sINF^N = INF if s==1 or n even if N > 0*/
  mpz_set_ui (z, 42);
  mpfr_set_inf (x, 1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_inf_p (y) == 0 || mpfr_sgn (y) <= 0)
    ERROR ("INF^42");
  mpfr_set_inf (x, -1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_inf_p (y) == 0 || mpfr_sgn (y) <= 0)
    ERROR ("-INF^42");
  mpz_set_ui (z, 17);
  mpfr_set_inf (x, 1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_inf_p (y) == 0 || mpfr_sgn (y) <= 0)
    ERROR ("INF^17");
  mpfr_set_inf (x, -1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_inf_p (y) == 0 || mpfr_sgn (y) >= 0)
    ERROR ("-INF^17");

  mpz_set_si (z, -42);
  mpfr_set_inf (x, 1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_zero_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("INF^-42");
  mpfr_set_inf (x, -1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_zero_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("-INF^-42");
  mpz_set_si (z, -17);
  mpfr_set_inf (x, 1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_zero_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("INF^-17");
  mpfr_set_inf (x, -1);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_zero_p (y) == 0 || MPFR_SIGN (y) >= 0)
    ERROR ("-INF^-17");

  /* s0^N = +0 if s==+ or n even if N > 0*/
  mpz_set_ui (z, 42);
  MPFR_SET_ZERO (x); MPFR_SET_POS (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_zero_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("+0^42");
  MPFR_SET_NEG (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_zero_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("-0^42");
  mpz_set_ui (z, 17);
  MPFR_SET_POS (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_zero_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("+0^17");
  MPFR_SET_NEG (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_zero_p (y) == 0 || MPFR_SIGN (y) >= 0)
    ERROR ("-0^17");

  mpz_set_si (z, -42);
  MPFR_SET_ZERO (x); MPFR_SET_POS (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_inf_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("+0^-42");
  MPFR_SET_NEG (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_inf_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("-0^-42");
  mpz_set_si (z, -17);
  MPFR_SET_POS (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_inf_p (y) == 0 || MPFR_SIGN (y) <= 0)
    ERROR ("+0^-17");
  MPFR_SET_NEG (x);
  res = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (res != 0 || mpfr_inf_p (y) == 0 || MPFR_SIGN (y) >= 0)
    ERROR ("-0^-17");

  mpz_clear (z);
  mpfr_clear (y);
  mpfr_clear (x);
}

static void
check_integer (mp_prec_t begin, mp_prec_t end, unsigned long max)
{
  mpfr_t x, y1, y2;
  mpz_t z;
  unsigned long i, n;
  mp_prec_t p;
  int res1, res2;
  mp_rnd_t rnd;

  mpfr_inits2 (begin, x, y1, y2, (mpfr_ptr) 0);
  mpz_init (z);
  for (p = begin ; p < end ; p+=4)
    {
      mpfr_set_prec (x, p);
      mpfr_set_prec (y1, p);
      mpfr_set_prec (y2, p);
      for (i = 0 ; i < max ; i++)
        {
          mpz_urandomb (z, RANDS, GMP_NUMB_BITS);
          if ((i & 1) != 0)
            mpz_neg (z, z);
          mpfr_urandomb (x, RANDS);
          mpfr_mul_2ui (x, x, 1, GMP_RNDN); /* 0 <= x < 2 */
          rnd = RND_RAND ();
          if (mpz_fits_slong_p (z))
            {
              n = mpz_get_si (z);
              /* printf ("New test for x=%ld\nCheck Pow_si\n", n); */
              res1 = mpfr_pow_si (y1, x, n, rnd);
              /* printf ("Check pow_z\n"); */
              res2 = mpfr_pow_z  (y2, x, z, rnd);
              if (mpfr_cmp (y1, y2) != 0)
                {
                  printf ("Error for p = %lu, z = %lu, rnd = %s and x = ",
                          p, n, mpfr_print_rnd_mode (rnd));
                  mpfr_dump (x);
                  printf ("Ypowsi = "); mpfr_dump (y1);
                  printf ("Ypowz  = "); mpfr_dump (y2);
                  exit (1);
                }
              if (res1 != res2)
                {
                  printf ("Wrong inexact flags for p = %lu, z = %lu, rnd = %s"
                          " and x = ", p, n, mpfr_print_rnd_mode (rnd));
                  mpfr_dump (x);
                  printf ("Ypowsi(inex = %2d) = ", res1); mpfr_dump (y1);
                  printf ("Ypowz (inex = %2d) = ", res2); mpfr_dump (y2);
                  exit (1);
                }
            }
        } /* for i */
    } /* for p */
  mpfr_clears (x, y1, y2, (mpfr_ptr) 0);
  mpz_clear (z);
}

static void
check_regression (void)
{
  mpfr_t x, y;
  mpz_t  z;
  int res1, res2;

  mpz_init_set_ui (z, 2026876995);
  mpfr_init2 (x, 122);
  mpfr_init2 (y, 122);

  mpfr_set_str_binary (x, "0.10000010010000111101001110100101101010011110011100001111000001001101000110011001001001001011001011010110110110101000111011E1");
  res1 = mpfr_pow_z (y, x, z, GMP_RNDU);
  res2 = mpfr_pow_ui (x, x, 2026876995UL, GMP_RNDU);
  if (mpfr_cmp (x, y) || res1 != res2)
    {
      printf ("Regression (1) tested failed (%d=?%d)\n",res1, res2);
      printf ("pow_ui: "); mpfr_dump (x);
      printf ("pow_z:  "); mpfr_dump (y);

      exit (1);
    }

  mpfr_clear (x);
  mpfr_clear (y);
  mpz_clear (z);
}

/* Bug found by Kevin P. Rauch */
static void
bug20071104 (void)
{
  mpfr_t x, y;
  mpz_t z;
  int inex;

  mpz_init_set_si (z, -2);
  mpfr_inits2 (20, x, y, (mpfr_ptr) 0);
  mpfr_set_ui (x, 0, GMP_RNDN);
  mpfr_nextbelow (x);  /* x = -2^(emin-1) */
  mpfr_clear_flags ();
  inex = mpfr_pow_z (y, x, z, GMP_RNDN);
  if (! mpfr_inf_p (y) || MPFR_SIGN (y) < 0)
    {
      printf ("Error in bug20071104: expected +Inf, got ");
      mpfr_dump (y);
      exit (1);
    }
  if (inex <= 0)
    {
      printf ("Error in bug20071104: bad ternary value (%d)\n", inex);
      exit (1);
    }
  if (__gmpfr_flags != (MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT))
    {
      printf ("Error in bug20071104: bad flags (%u)\n", __gmpfr_flags);
      exit (1);
    }
  mpfr_clears (x, y, (mpfr_ptr) 0);
  mpz_clear (z);
}

static void
check_overflow (void)
{
  mpfr_t a;
  mpz_t z;
  unsigned long n;
  int res;

  mpfr_init2 (a, 53);

  mpfr_set_str_binary (a, "1E10");
  mpz_init_set_ui (z, ULONG_MAX);
  res = mpfr_pow_z (a, a, z, GMP_RNDN);
  if (!MPFR_IS_INF (a) || MPFR_SIGN (a) < 0)
    {
      printf ("Error for (1e10)^ULONG_MAX\n");
      exit (1);
    }

  /* Bug in pow_z.c up to r5109: if x = y (same mpfr_t argument), the
     input argument is negative and not a power of two, z is positive
     and odd, an overflow or underflow occurs, and the temporary result
     res is positive, then the result gets a wrong sign (positive
     instead of negative). */
  mpfr_set_str_binary (a, "-1.1E10");
  n = (ULONG_MAX ^ (ULONG_MAX >> 1)) + 1;
  mpz_set_ui (z, n);
  res = mpfr_pow_z (a, a, z, GMP_RNDN);
  if (!MPFR_IS_INF (a) || MPFR_SIGN (a) > 0)
    {
      printf ("Error for (-1e10)^%lu, expected -Inf,\ngot ", n);
      mpfr_dump (a);
      exit (1);
    }

  mpfr_clear (a);
  mpz_clear (z);
}

/* bug reported by Carl Witty (32-bit architecture) */
static void
bug20080223 (void)
{
  mpfr_t a, exp, answer;

  mpfr_init2 (a, 53);
  mpfr_init2 (exp, 53);
  mpfr_init2 (answer, 53);

  mpfr_set_si (exp, -1073741824, GMP_RNDN);

  mpfr_set_str (a, "1.999999999", 10, GMP_RNDN);
  /* a = 562949953139837/2^48 */
  mpfr_pow (answer, a, exp, GMP_RNDN);
  mpfr_set_str_binary (a, "0.110110101111011001110000111111100011101000111011101E-1073741823");
  MPFR_ASSERTN(mpfr_cmp0 (answer, a) == 0);

  mpfr_clear (a);
  mpfr_clear (exp);
  mpfr_clear (answer);
}

static void
bug20080904 (void)
{
  mpz_t exp;
  mpfr_t a, answer;
  mp_exp_t emin_default;

  mpz_init (exp);
  mpfr_init2 (a, 70);
  mpfr_init2 (answer, 70);

  emin_default = mpfr_get_emin ();
  mpfr_set_emin (MPFR_EMIN_MIN);

  mpz_set_str (exp, "-4eb92f8c7b7bf81e", 16);
  mpfr_set_str_binary (a, "1.110000101110100110100011111000011110111101000011111001111001010011100");

  mpfr_pow_z (answer, a, exp, GMP_RNDN);
  /* The correct result is near 2^(-2^62), so it underflows when
     MPFR_EMIN_MIN > -2^62 (i.e. with 32 and 64 bits machines). */
  mpfr_set_str (a, "AA500C0D7A69275DBp-4632850503556296886", 16, GMP_RNDN);
  MPFR_ASSERTN(mpfr_cmp0 (answer, a) == 0);

  mpfr_set_emin (emin_default);

  mpz_clear (exp);
  mpfr_clear (a);
  mpfr_clear (answer);
}

int
main (void)
{
  tests_start_mpfr ();

  check_special ();

  check_integer (2, 163, 100);
  check_regression ();
  bug20071104 ();
  bug20080223 ();
  bug20080904 ();
  check_overflow ();

  tests_end_mpfr ();
  return 0;
}