path: root/tests/troot.c

/* Test file for mpfr_root (also used for mpfr_rootn_ui).

Copyright 2005-2019 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. */

#ifdef TF
# define TF_IS_MPFR_ROOT 0
#else
# define TF_IS_MPFR_ROOT 1
# define TF mpfr_root
# define _MPFR_NO_DEPRECATED_ROOT
#endif

#include "mpfr-test.h"

#include <time.h>

/* return the cpu time in seconds */
static double
cputime (void)
{
  return (double) clock () / (double) CLOCKS_PER_SEC;
}

#define DEFN(N)                                                         \
  static int root##N (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)        \
  { return TF (y, x, N, rnd); }                                         \
  static int pow##N (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)         \
  { return mpfr_pow_ui (y, x, N, rnd); }

DEFN(2)
DEFN(3)
DEFN(4)
DEFN(5)
DEFN(17)
DEFN(120)

static void
special (void)
{
  mpfr_t x, y;
  int i;

  mpfr_init (x);
  mpfr_init (y);

  /* root(NaN) = NaN */
  mpfr_set_nan (x);
  i = TF (y, x, 17, MPFR_RNDN);
  if (!mpfr_nan_p (y))
    {
      printf ("Error: root(NaN,17) <> NaN\n");
      exit (1);
    }
  MPFR_ASSERTN (i == 0);

  /* root(+Inf) = +Inf */
  mpfr_set_inf (x, 1);
  i = TF (y, x, 42, MPFR_RNDN);
  if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
    {
      printf ("Error: root(+Inf,42) <> +Inf\n");
      exit (1);
    }
  MPFR_ASSERTN (i == 0);

  /* root(-Inf, 17) = -Inf */
  mpfr_set_inf (x, -1);
  i = TF (y, x, 17, MPFR_RNDN);
  if (!mpfr_inf_p (y) || mpfr_sgn (y) > 0)
    {
      printf ("Error: root(-Inf,17) <> -Inf\n");
      exit (1);
    }
  MPFR_ASSERTN (i == 0);

  /* root(-Inf, 42) =  NaN */
  mpfr_set_inf (x, -1);
  i = TF (y, x, 42, MPFR_RNDN);
  if (!mpfr_nan_p (y))
    {
      printf ("Error: root(-Inf,42) <> -Inf\n");
      exit (1);
    }
  MPFR_ASSERTN (i == 0);

  /* root(+/-0, k) = +/-0, with the sign depending on TF.
   * Before calling the function, we set y to NaN with the wrong sign,
   * so that if the code of the function forgets to do something, this
   * will be detected.
   */
  mpfr_set_zero (x, 1);  /* x is +0 */
  MPFR_SET_NAN (y);
  MPFR_SET_NEG (y);
  i = TF (y, x, 17, MPFR_RNDN);
  if (MPFR_NOTZERO (y) || MPFR_IS_NEG (y))
    {
      printf ("Error: root(+0,17) <> +0\n");
      exit (1);
    }
  MPFR_ASSERTN (i == 0);
  MPFR_SET_NAN (y);
  MPFR_SET_NEG (y);
  i = TF (y, x, 42, MPFR_RNDN);
  if (MPFR_NOTZERO (y) || MPFR_IS_NEG (y))
    {
      printf ("Error: root(+0,42) <> +0\n");
      exit (1);
    }
  MPFR_ASSERTN (i == 0);
  mpfr_set_zero (x, -1);  /* x is -0 */
  MPFR_SET_NAN (y);
  MPFR_SET_POS (y);
  i = TF (y, x, 17, MPFR_RNDN);
  if (MPFR_NOTZERO (y) || MPFR_IS_POS (y))
    {
      printf ("Error: root(-0,17) <> -0\n");
      exit (1);
    }
  MPFR_ASSERTN (i == 0);
  MPFR_SET_NAN (y);
  if (TF_IS_MPFR_ROOT)
    MPFR_SET_POS (y);
  else
    MPFR_SET_NEG (y);
  i = TF (y, x, 42, MPFR_RNDN);
  if (MPFR_NOTZERO (y) ||
      (TF_IS_MPFR_ROOT ? MPFR_IS_POS (y) : MPFR_IS_NEG (y)))
    {
      printf ("Error: root(-0,42) <> %c0\n",
              TF_IS_MPFR_ROOT ? '-' : '+');
      exit (1);
    }
  MPFR_ASSERTN (i == 0);

  mpfr_set_prec (x, 53);
  mpfr_set_str (x, "8.39005285514734966412e-01", 10, MPFR_RNDN);
  TF (x, x, 3, MPFR_RNDN);
  if (mpfr_cmp_str1 (x, "9.43166207799662426048e-01"))
    {
      printf ("Error in root3 (1)\n");
      printf ("expected 9.43166207799662426048e-01\n");
      printf ("got      ");
      mpfr_dump (x);
      exit (1);
    }

  mpfr_set_prec (x, 32);
  mpfr_set_prec (y, 32);
  mpfr_set_str_binary (x, "0.10000100001100101001001001011001");
  TF (x, x, 3, MPFR_RNDN);
  mpfr_set_str_binary (y, "0.11001101011000100111000111111001");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in root3 (2)\n");
      exit (1);
    }

  mpfr_set_prec (x, 32);
  mpfr_set_prec (y, 32);
  mpfr_set_str_binary (x, "-0.1100001110110000010101011001011");
  TF (x, x, 3, MPFR_RNDD);
  mpfr_set_str_binary (y, "-0.11101010000100100101000101011001");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in root3 (3)\n");
      exit (1);
    }

  mpfr_set_prec (x, 82);
  mpfr_set_prec (y, 27);
  mpfr_set_str_binary (x, "0.1010001111011101011011000111001011001101100011110110010011011011011010011001100101e-7");
  TF (y, x, 3, MPFR_RNDD);
  mpfr_set_str_binary (x, "0.101011110001110001000100011E-2");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in root3 (4)\n");
      exit (1);
    }

  mpfr_set_prec (x, 204);
  mpfr_set_prec (y, 38);
  mpfr_set_str_binary (x, "0.101000000001101000000001100111111011111001110110100001111000100110100111001101100111110001110001011011010110010011100101111001111100001010010100111011101100000011011000101100010000000011000101001010001001E-5");
  TF (y, x, 3, MPFR_RNDD);
  mpfr_set_str_binary (x, "0.10001001111010011011101000010110110010E-1");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in root3 (5)\n");
      exit (1);
    }

  /* Worst case found on 2006-11-25 */
  mpfr_set_prec (x, 53);
  mpfr_set_prec (y, 53);
  mpfr_set_str_binary (x, "1.0100001101101101001100110001001000000101001101100011E28");
  TF (y, x, 35, MPFR_RNDN);
  mpfr_set_str_binary (x, "1.1100000010110101100011101011000010100001101100100011E0");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in rootn (y, x, 35, MPFR_RNDN) for\n"
              "x = 1.0100001101101101001100110001001000000101001101100011E28\n"
              "Expected ");
      mpfr_dump (x);
      printf ("Got      ");
      mpfr_dump (y);
      exit (1);
    }
  /* Worst cases found on 2006-11-26 */
  mpfr_set_str_binary (x, "1.1111010011101110001111010110000101110000110110101100E17");
  TF (y, x, 36, MPFR_RNDD);
  mpfr_set_str_binary (x, "1.0110100111010001101001010111001110010100111111000010E0");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in rootn (y, x, 36, MPFR_RNDD) for\n"
              "x = 1.1111010011101110001111010110000101110000110110101100E17\n"
              "Expected ");
      mpfr_dump (x);
      printf ("Got      ");
      mpfr_dump (y);
      exit (1);
    }
  mpfr_set_str_binary (x, "1.1100011101101101100010110001000001110001111110010000E23");
  TF (y, x, 36, MPFR_RNDU);
  mpfr_set_str_binary (x, "1.1001010100001110000110111111100011011101110011000100E0");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in rootn (y, x, 36, MPFR_RNDU) for\n"
              "x = 1.1100011101101101100010110001000001110001111110010000E23\n"
              "Expected ");
      mpfr_dump (x);
      printf ("Got      ");
      mpfr_dump (y);
      exit (1);
    }

  /* Check for k = 1 */
  mpfr_set_ui (x, 17, MPFR_RNDN);
  i = TF (y, x, 1, MPFR_RNDN);
  if (mpfr_cmp_ui (x, 17) || i != 0)
    {
      printf ("Error in root for 17^(1/1)\n");
      exit (1);
    }

  mpfr_set_ui (x, 0, MPFR_RNDN);
  i = TF (y, x, 0, MPFR_RNDN);
  if (!MPFR_IS_NAN (y) || i != 0)
    {
      printf ("Error in root for (+0)^(1/0)\n");
      exit (1);
    }
  mpfr_neg (x, x, MPFR_RNDN);
  i = TF (y, x, 0, MPFR_RNDN);
  if (!MPFR_IS_NAN (y) || i != 0)
    {
      printf ("Error in root for (-0)^(1/0)\n");
      exit (1);
    }

  mpfr_set_ui (x, 1, MPFR_RNDN);
  i = TF (y, x, 0, MPFR_RNDN);
  if (!MPFR_IS_NAN (y) || i != 0)
    {
      printf ("Error in root for 1^(1/0)\n");
      exit (1);
    }

  /* Check for k==2 */
  mpfr_set_si (x, -17, MPFR_RNDD);
  i = TF (y, x, 2, MPFR_RNDN);
  if (!MPFR_IS_NAN (y) || i != 0)
    {
      printf ("Error in root for (-17)^(1/2)\n");
      exit (1);
    }

  mpfr_clear (x);
  mpfr_clear (y);
}

/* https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=812779
 * https://bugzilla.gnome.org/show_bug.cgi?id=756960
 * is a GNOME Calculator bug (mpfr_root applied on a negative integer,
 * which is converted to an unsigned integer), but the strange result
 * is also due to a bug in MPFR.
 */
static void
bigint (void)
{
  mpfr_t x, y;

  mpfr_inits2 (64, x, y, (mpfr_ptr) 0);

  mpfr_set_ui (x, 10, MPFR_RNDN);
  if (sizeof (unsigned long) * CHAR_BIT == 64)
    {
      TF (x, x, ULONG_MAX, MPFR_RNDN);
      mpfr_set_ui_2exp (y, 1, -63, MPFR_RNDN);
      mpfr_add_ui (y, y, 1, MPFR_RNDN);
      if (! mpfr_equal_p (x, y))
        {
          printf ("Error in bigint for ULONG_MAX\n");
          printf ("Expected ");
          mpfr_dump (y);
          printf ("Got      ");
          mpfr_dump (x);
          exit (1);
        }
    }

  mpfr_set_ui (x, 10, MPFR_RNDN);
  TF (x, x, 1234567890, MPFR_RNDN);
  mpfr_set_str_binary (y,
    "1.00000000000000000000000000001000000000101011000101000110010001");
  if (! mpfr_equal_p (x, y))
    {
      printf ("Error in bigint for 1234567890\n");
      printf ("Expected ");
      mpfr_dump (y);
      printf ("Got      ");
      mpfr_dump (x);
      exit (1);
    }

  mpfr_clears (x, y, (mpfr_ptr) 0);
}

#define TEST_FUNCTION TF
#define INTEGER_TYPE unsigned long
#define INT_RAND_FUNCTION() \
  (INTEGER_TYPE) (randlimb () & 1 ? randlimb () : randlimb () % 3 + 2)
#include "tgeneric_ui.c"

static void
exact_powers (unsigned long bmax, unsigned long kmax)
{
  long b, k;
  mpz_t z;
  mpfr_t x, y;
  int inex, neg;

  mpz_init (z);
  for (b = 2; b <= bmax; b++)
    for (k = 1; k <= kmax; k++)
      {
        mpz_ui_pow_ui (z, b, k);
        mpfr_init2 (x, mpz_sizeinbase (z, 2));
        mpfr_set_ui (x, b, MPFR_RNDN);
        mpfr_pow_ui (x, x, k, MPFR_RNDN);
        mpz_set_ui (z, b);
        mpfr_init2 (y, mpz_sizeinbase (z, 2));
        for (neg = 0; neg <= 1; neg++)
          {
            inex = TF (y, x, k, MPFR_RNDN);
            if (inex != 0)
              {
                printf ("Error in exact_powers, b=%ld, k=%ld\n", b, k);
                printf ("Expected inex=0, got %d\n", inex);
                exit (1);
              }
            if (neg && (k & 1) == 0)
              {
                if (!MPFR_IS_NAN (y))
                  {
                    printf ("Error in exact_powers, b=%ld, k=%ld\n", b, k);
                    printf ("Expected y=NaN\n");
                    printf ("Got      ");
                    mpfr_out_str (stdout, 10, 0, y, MPFR_RNDN);
                    printf ("\n");
                    exit (1);
                  }
              }
            else if (MPFR_IS_NAN (y) || mpfr_cmp_si (y, b) != 0)
              {
                printf ("Error in exact_powers, b=%ld, k=%ld\n", b, k);
                printf ("Expected y=%ld\n", b);
                printf ("Got      ");
                mpfr_out_str (stdout, 10, 0, y, MPFR_RNDN);
                printf ("\n");
                exit (1);
              }
            mpfr_neg (x, x, MPFR_RNDN);
            b = -b;
          }
        mpfr_clear (x);
        mpfr_clear (y);
      }
  mpz_clear (z);
}

/* Compare root(x,2^h) with pow(x,2^(-h)). */
static void
cmp_pow (void)
{
  mpfr_t x, y1, y2;
  int h;

  mpfr_inits2 (128, x, y1, y2, (mpfr_ptr) 0);

  for (h = 1; h < sizeof (unsigned long) * CHAR_BIT; h++)
    {
      unsigned long k = (unsigned long) 1 << h;
      int i;

      for (i = 0; i < 10; i++)
        {
          mpfr_rnd_t rnd;
          mpfr_flags_t flags1, flags2;
          int inex1, inex2;

          tests_default_random (x, 0, __gmpfr_emin, __gmpfr_emax, 1);
          rnd = RND_RAND_NO_RNDF ();
          mpfr_set_ui_2exp (y1, 1, -h, MPFR_RNDN);
          mpfr_clear_flags ();
          inex1 = mpfr_pow (y1, x, y1, rnd);
          flags1 = __gmpfr_flags;
          mpfr_clear_flags ();
          inex2 = TF (y2, x, k, rnd);
          flags2 = __gmpfr_flags;
          if (!(mpfr_equal_p (y1, y2) && SAME_SIGN (inex1, inex2) &&
                flags1 == flags2))
            {
              printf ("Error in cmp_pow on h=%d, i=%d, rnd=%s\n",
                      h, i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
              printf ("x = ");
              mpfr_dump (x);
              printf ("pow  = ");
              mpfr_dump (y1);
              printf ("with inex = %d, flags =", inex1);
              flags_out (flags1);
              printf ("root = ");
              mpfr_dump (y2);
              printf ("with inex = %d, flags =", inex2);
              flags_out (flags2);
              exit (1);
            }
        }
    }

  mpfr_clears (x, y1, y2, (mpfr_ptr) 0);
}

static void
bug20171214 (void)
{
  mpfr_t x, y;
  int inex;

  mpfr_init2 (x, 805);
  mpfr_init2 (y, 837);
  mpfr_set_ui (x, 1, MPFR_RNDN);
  inex = TF (y, x, 120, MPFR_RNDN);
  MPFR_ASSERTN (inex == 0);
  MPFR_ASSERTN (mpfr_cmp_ui (y, 1) == 0);
  mpfr_set_si (x, -1, MPFR_RNDN);
  inex = TF (y, x, 121, MPFR_RNDN);
  MPFR_ASSERTN (inex == 0);
  MPFR_ASSERTN (mpfr_cmp_si (y, -1) == 0);
  mpfr_clear (x);
  mpfr_clear (y);
}

int
main (int argc, char *argv[])
{
  mpfr_t x;
  int r;
  mpfr_prec_t p;
  unsigned long k;

  if (argc == 3) /* troot prec k */
    {
      double st1, st2;
      unsigned long k;
      int l;
      mpfr_t y;
      p = strtoul (argv[1], NULL, 10);
      k = strtoul (argv[2], NULL, 10);
      mpfr_init2 (x, p);
      mpfr_init2 (y, p);
      mpfr_const_pi (y, MPFR_RNDN);
      TF (x, y, k, MPFR_RNDN); /* to warm up cache */
      st1 = cputime ();
      for (l = 0; cputime () - st1 < 1.0; l++)
        TF (x, y, k, MPFR_RNDN);
      st1 = (cputime () - st1) / l;
      printf ("%-15s took %.2es\n", MAKE_STR(TF), st1);

      /* compare with x^(1/k) = exp(1/k*log(x)) */
      /* first warm up cache */
      mpfr_swap (x, y);
      mpfr_log (y, x, MPFR_RNDN);
      mpfr_div_ui (y, y, k, MPFR_RNDN);
      mpfr_exp (y, y, MPFR_RNDN);

      st2 = cputime ();
      for (l = 0; cputime () - st2 < 1.0; l++)
        {
          mpfr_log (y, x, MPFR_RNDN);
          mpfr_div_ui (y, y, k, MPFR_RNDN);
          mpfr_exp (y, y, MPFR_RNDN);
        }
      st2 = (cputime () - st2) / l;
      printf ("exp(1/k*log(x)) took %.2es\n", st2);

      mpfr_clear (x);
      mpfr_clear (y);
      return 0;
    }

  tests_start_mpfr ();

  bug20171214 ();
  exact_powers (3, 1000);
  special ();
  bigint ();
  cmp_pow ();

  mpfr_init (x);

  for (p = MPFR_PREC_MIN; p < 100; p++)
    {
      mpfr_set_prec (x, p);
      for (r = 0; r < MPFR_RND_MAX; r++)
        {
          mpfr_set_ui (x, 1, MPFR_RNDN);
          k = 2 + randlimb () % 4; /* 2 <= k <= 5 */
          TF (x, x, k, (mpfr_rnd_t) r);
          if (mpfr_cmp_ui (x, 1))
            {
              printf ("Error in rootn[%lu] for x=1, rnd=%s\ngot ",
                      k, mpfr_print_rnd_mode ((mpfr_rnd_t) r));
              mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
              printf ("\n");
              exit (1);
            }
          mpfr_set_si (x, -1, MPFR_RNDN);
          if (k % 2)
            {
              TF (x, x, k, (mpfr_rnd_t) r);
              if (mpfr_cmp_si (x, -1))
                {
                  printf ("Error in rootn[%lu] for x=-1, rnd=%s\ngot ",
                          k, mpfr_print_rnd_mode ((mpfr_rnd_t) r));
                  mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
                  printf ("\n");
                  exit (1);
                }
            }

          if (p >= 5)
            {
              int i;
              for (i = -12; i <= 12; i++)
                {
                  mpfr_set_ui (x, 27, MPFR_RNDN);
                  mpfr_mul_2si (x, x, 3*i, MPFR_RNDN);
                  TF (x, x, 3, MPFR_RNDN);
                  if (mpfr_cmp_si_2exp (x, 3, i))
                    {
                      printf ("Error in rootn[3] for "
                              "x = 27.0 * 2^(%d), rnd=%s\ngot ",
                              3*i, mpfr_print_rnd_mode ((mpfr_rnd_t) r));
                      mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
                      printf ("\ninstead of 3 * 2^(%d)\n", i);
                      exit (1);
                    }
                }
            }
        }
    }
  mpfr_clear (x);

  test_generic_ui (MPFR_PREC_MIN, 200, 30);

  bad_cases (root2, pow2, "rootn[2]", 8, -256, 255, 4, 128, 800, 40);
  bad_cases (root3, pow3, "rootn[3]", 8, -256, 255, 4, 128, 800, 40);
  bad_cases (root4, pow4, "rootn[4]", 8, -256, 255, 4, 128, 800, 40);
  bad_cases (root5, pow5, "rootn[5]", 8, -256, 255, 4, 128, 800, 40);
  bad_cases (root17, pow17, "rootn[17]", 8, -256, 255, 4, 128, 800, 40);
  bad_cases (root120, pow120, "rootn[120]", 8, -256, 255, 4, 128, 800, 40);

  tests_end_mpfr ();
  return 0;
}