path: root/tests/tsqr.c

/* Test file for mpfr_sqr.

Copyright 2004-2019 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
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_sqr
#include "tgeneric.c"

static int
inexact_sign (int x)
{
  return (x < 0) ? -1 : (x > 0);
}

static void
error1 (mpfr_rnd_t rnd, mpfr_prec_t prec,
        mpfr_t in, mpfr_t outmul, mpfr_t outsqr)
{
  printf("ERROR: for %s and prec=%lu\nINPUT=", mpfr_print_rnd_mode(rnd),
         (unsigned long) prec);
  mpfr_dump(in);
  printf("OutputMul="); mpfr_dump(outmul);
  printf("OutputSqr="); mpfr_dump(outsqr);
  exit(1);
}

static void
error2 (mpfr_rnd_t rnd, mpfr_prec_t prec, mpfr_t in, mpfr_t out,
        int inexactmul, int inexactsqr)
{
  printf("ERROR: for %s and prec=%lu\nINPUT=", mpfr_print_rnd_mode(rnd),
         (unsigned long) prec);
  mpfr_dump(in);
  printf("Output="); mpfr_dump(out);
  printf("InexactMul= %d InexactSqr= %d\n", inexactmul, inexactsqr);
  exit(1);
}

static void
check_random (mpfr_prec_t p)
{
  mpfr_t x,y,z;
  int r;
  int i, inexact1, inexact2;

  mpfr_inits2 (p, x, y, z, (mpfr_ptr) 0);
  for(i = 0 ; i < 500 ; i++)
    {
      mpfr_urandomb (x, RANDS);
      if (MPFR_IS_PURE_FP(x))
        RND_LOOP_NO_RNDF (r)
          {
            inexact1 = mpfr_mul (y, x, x, (mpfr_rnd_t) r);
            inexact2 = mpfr_sqr (z, x, (mpfr_rnd_t) r);
            if (mpfr_cmp (y, z))
              error1 ((mpfr_rnd_t) r,p,x,y,z);
            if (inexact_sign (inexact1) != inexact_sign (inexact2))
              error2 ((mpfr_rnd_t) r,p,x,y,inexact1,inexact2);
          }
    }
  mpfr_clears (x, y, z, (mpfr_ptr) 0);
}

static void
check_special (void)
{
  mpfr_t x, y;
  mpfr_exp_t emin;

  mpfr_init (x);
  mpfr_init (y);

  mpfr_set_nan (x);
  mpfr_sqr (y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_nan_p (y));

  mpfr_set_inf (x, 1);
  mpfr_sqr (y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_inf_p (y) && mpfr_sgn (y) > 0);

  mpfr_set_inf (x, -1);
  mpfr_sqr (y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_inf_p (y) && mpfr_sgn (y) > 0);

  mpfr_set_ui (x, 0, MPFR_RNDN);
  mpfr_sqr (y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_zero_p (y));

  emin = mpfr_get_emin ();
  mpfr_set_emin (0);
  mpfr_set_ui (x, 1, MPFR_RNDN);
  mpfr_div_2ui (x, x, 1, MPFR_RNDN);
  MPFR_ASSERTN (!mpfr_zero_p (x));
  mpfr_sqr (y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_zero_p (y));
  mpfr_set_emin (emin);

  mpfr_clear (y);
  mpfr_clear (x);
}

/* check ax < __gmpfr_emin with rnd_mode == MPFR_RNDN, rb = 0 and sb <> 0 */
static void
test_underflow (void)
{
  mpfr_t x, y;
  mpfr_exp_t emin;

  emin = mpfr_get_emin ();
  mpfr_set_emin (0);

  mpfr_init2 (x, 24);
  mpfr_init2 (y, 24);

  mpfr_set_ui_2exp (x, 11863283, -24, MPFR_RNDN);
  /* x^2 = 0.011111111111111111111111101101100111111010101001*2^(-48)
     thus we have an underflow */
  mpfr_clear_underflow ();
  mpfr_sqr (y, x, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_cmp_ui_2exp (y, 1, -1) == 0);
  MPFR_ASSERTN(mpfr_underflow_p ());

  mpfr_set_prec (x, 69);
  mpfr_set_prec (y, 69);
  mpfr_set_str_binary (x, "0.101101010000010011110011001100111111100111011110011001001000010001011");
  mpfr_clear_underflow ();
  mpfr_sqr (y, x, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_cmp_ui_2exp (y, 1, -1) == 0);
  MPFR_ASSERTN(mpfr_underflow_p ());

  mpfr_clear (y);
  mpfr_clear (x);

  mpfr_set_emin (emin);
}

/* Test of a bug seen with GCC 4.5.2 and GMP 5.0.1 on m68k (m68000 target).
     https://sympa.inria.fr/sympa/arc/mpfr/2011-05/msg00003.html
     https://sympa.inria.fr/sympa/arc/mpfr/2011-05/msg00041.html
*/
static void
check_mpn_sqr (void)
{
#if GMP_NUMB_BITS == 32 && __GNU_MP_VERSION >= 5
  /* Note: since we test a low-level bug, src is initialized
     without using a GMP function, just in case. */
  mp_limb_t src[5] =
    { 0x90000000, 0xbaa55f4f, 0x2cbec4d9, 0xfcef3242, 0xda827999 };
  mp_limb_t exd[10] =
    { 0x00000000, 0x31000000, 0xbd4bc59a, 0x41fbe2b5, 0x33471e7e,
      0x90e826a7, 0xbaa55f4f, 0x2cbec4d9, 0xfcef3242, 0xba827999 };
  mp_limb_t dst[10];
  int i;

  mpn_sqr (dst, src, 5);  /* new in GMP 5 */
  for (i = 0; i < 10; i++)
    {
      if (dst[i] != exd[i])
        {
          printf ("Error in check_mpn_sqr\n");
          printf ("exd[%d] = 0x%08lx\n", i, (unsigned long) exd[i]);
          printf ("dst[%d] = 0x%08lx\n", i, (unsigned long) dst[i]);
          printf ("Note: This is not a bug in MPFR, but a bug in"
                  " either GMP or, more\nprobably, in the compiler."
                  " It may cause other tests to fail.\n");
          exit (1);
        }
    }
#endif
}

static void
coverage (mpfr_prec_t pmax)
{
  mpfr_prec_t p;

  for (p = MPFR_PREC_MIN; p <= pmax; p++)
    {
      mpfr_t a, b, c;
      int inex;
      mpfr_exp_t emin;

      mpfr_init2 (a, p);
      mpfr_init2 (b, p);
      mpfr_init2 (c, p);

      /* exercise carry in most significant bits of a, with overflow */
      mpfr_set_ui_2exp (b, 1, mpfr_get_emax (), MPFR_RNDZ);
      mpfr_sqrt (b, b, MPFR_RNDU);
      mpfr_div_2exp (c, b, 1, MPFR_RNDN);
      mpfr_sqr (c, c, MPFR_RNDN);
      mpfr_clear_flags ();
      inex = mpfr_sqr (a, b, MPFR_RNDN);
      /* if EXP(c) > emax-2, there is overflow */
      if (mpfr_get_exp (c) > mpfr_get_emax () - 2)
        {
          MPFR_ASSERTN(inex > 0);
          MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0);
          MPFR_ASSERTN(mpfr_overflow_p ());
        }
      else /* no overflow */
        {
          /* 2^p-1 is a square only for p=1 */
          MPFR_ASSERTN((p == 1 && inex == 0) || (p > 1 && inex < 0));
          MPFR_ASSERTN(!mpfr_overflow_p ());
          mpfr_set_ui_2exp (c, 1, mpfr_get_emax (), MPFR_RNDZ);
          MPFR_ASSERTN(mpfr_equal_p (a, c));
        }

      /* same as above, with RNDU */
      mpfr_set_ui_2exp (b, 1, mpfr_get_emax (), MPFR_RNDZ);
      mpfr_sqrt (b, b, MPFR_RNDU);
      mpfr_div_2exp (c, b, 1, MPFR_RNDN);
      mpfr_sqr (c, c, MPFR_RNDU);
      mpfr_clear_flags ();
      inex = mpfr_sqr (a, b, MPFR_RNDU);
      /* if EXP(c) > emax-2, there is overflow */
      if (mpfr_get_exp (c) > mpfr_get_emax () - 2)
        {
          MPFR_ASSERTN(inex > 0);
          MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0);
          MPFR_ASSERTN(mpfr_overflow_p ());
        }
      else /* no overflow */
        {
          /* 2^p-1 is a square only for p=1 */
          MPFR_ASSERTN((p == 1 && inex == 0) || (p > 1 && inex < 0));
          MPFR_ASSERTN(!mpfr_overflow_p ());
          mpfr_set_ui_2exp (c, 1, mpfr_get_emax (), MPFR_RNDZ);
          MPFR_ASSERTN(mpfr_equal_p (a, c));
        }

      /* exercise trivial overflow */
      mpfr_set_ui_2exp (b, 1, mpfr_get_emax (), MPFR_RNDZ);
      mpfr_sqrt (b, b, MPFR_RNDU);
      mpfr_mul_2exp (b, b, 1, MPFR_RNDN);
      mpfr_clear_flags ();
      inex = mpfr_sqr (a, b, MPFR_RNDN);
      MPFR_ASSERTN(inex > 0);
      MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0);
      MPFR_ASSERTN(mpfr_overflow_p ());

      /* exercise trivial underflow */
      mpfr_set_ui_2exp (b, 1, mpfr_get_emin () - 1, MPFR_RNDZ);
      mpfr_sqrt (b, b, MPFR_RNDU);
      mpfr_div_2exp (b, b, 1, MPFR_RNDN);
      mpfr_clear_flags ();
      inex = mpfr_sqr (a, b, MPFR_RNDN);
      MPFR_ASSERTN(inex < 0);
      MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0);
      MPFR_ASSERTN(mpfr_underflow_p ());

      /* exercise square between 0.5*2^emin and its predecessor (emin even) */
      emin = mpfr_get_emin ();
      mpfr_set_emin (emin + (emin & 1)); /* now emin is even */
      mpfr_set_ui_2exp (b, 1, mpfr_get_emin () - 1, MPFR_RNDN);
      inex = mpfr_sqrt (b, b, MPFR_RNDZ);
      MPFR_ASSERTN(inex != 0); /* sqrt(2) is not exact */
      mpfr_mul_2exp (c, b, 1, MPFR_RNDN);
      mpfr_sqr (c, c, MPFR_RNDN);
      mpfr_clear_flags ();
      inex = mpfr_sqr (a, b, MPFR_RNDN);
      if (mpfr_get_exp (c) < mpfr_get_emin () + 2) /* underflow */
        {
          /* if c > 0.5*2^(emin+1), we should round to 0.5*2^emin */
          if (mpfr_cmp_ui_2exp (c, 1, mpfr_get_emin ()) > 0)
            {
              MPFR_ASSERTN(inex > 0);
              MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0);
              MPFR_ASSERTN(mpfr_underflow_p ());
            }
          else /* we should round to 0 */
            {
              MPFR_ASSERTN(inex < 0);
              MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0);
              MPFR_ASSERTN(mpfr_underflow_p ());
            }
        }
      else
        {
          MPFR_ASSERTN(inex > 0);
          MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0);
          MPFR_ASSERTN(!mpfr_underflow_p ());
        }
      mpfr_set_emin (emin);

      /* exercise exact square root 2^(emin-2) for emin even */
      emin = mpfr_get_emin ();
      mpfr_set_emin (emin + (emin & 1)); /* now emin is even */
      mpfr_set_ui_2exp (b, 1, (mpfr_get_emin () - 2) / 2, MPFR_RNDN);
      inex = mpfr_sqr (a, b, MPFR_RNDN);
      MPFR_ASSERTN(inex < 0);
      MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0);
      MPFR_ASSERTN(mpfr_underflow_p ());
      mpfr_set_emin (emin);

      /* same as above, for RNDU */
      emin = mpfr_get_emin ();
      mpfr_set_emin (emin + (emin & 1)); /* now emin is even */
      mpfr_set_ui_2exp (b, 1, mpfr_get_emin () - 1, MPFR_RNDN);
      inex = mpfr_sqrt (b, b, MPFR_RNDZ);
      MPFR_ASSERTN(inex != 0); /* sqrt(2) is not exact */
      mpfr_mul_2exp (c, b, 1, MPFR_RNDN);
      mpfr_sqr (c, c, MPFR_RNDU);
      mpfr_clear_flags ();
      inex = mpfr_sqr (a, b, MPFR_RNDU);
      MPFR_ASSERTN(inex > 0);
      MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0);
      /* we have underflow if c < 2^(emin+1) */
      if (mpfr_cmp_ui_2exp (c, 1, mpfr_get_emin () + 1) < 0)
        MPFR_ASSERTN(mpfr_underflow_p ());
      else
        MPFR_ASSERTN(!mpfr_underflow_p ());
      mpfr_set_emin (emin);

      mpfr_clear (a);
      mpfr_clear (b);
      mpfr_clear (c);
    }
}

int
main (void)
{
  mpfr_prec_t p;

  tests_start_mpfr ();

  coverage (1024);
  check_mpn_sqr ();
  check_special ();
  test_underflow ();

  for (p = MPFR_PREC_MIN; p < 200; p++)
    check_random (p);

  test_generic (MPFR_PREC_MIN, 200, 15);
  data_check ("data/sqr", mpfr_sqr, "mpfr_sqr");
  bad_cases (mpfr_sqr, mpfr_sqrt, "mpfr_sqr", 8, -256, 255, 4, 128, 800, 50);

  tests_end_mpfr ();
  return 0;
}