path: root/tests/refmpz.c

/* Reference mpz functions.

Copyright 1997, 1999, 2000, 2001, 2002 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP 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 MP 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 MP Library.  If not, see http://www.gnu.org/licenses/.  */

/* always do assertion checking */
#define WANT_ASSERT  1

#include <stdio.h>
#include <stdlib.h> /* for free */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "tests.h"


/* Change this to "#define TRACE(x) x" for some traces. */
#define TRACE(x)


/* FIXME: Shouldn't use plain mpz functions in a reference routine. */
void
refmpz_combit (mpz_ptr r, unsigned long bit)
{
  if (mpz_tstbit (r, bit))
    mpz_clrbit (r, bit);
  else
    mpz_setbit (r, bit);
}


unsigned long
refmpz_hamdist (mpz_srcptr x, mpz_srcptr y)
{
  mp_size_t      xsize, ysize, tsize;
  mp_ptr         xp, yp;
  unsigned long  ret;

  if ((SIZ(x) < 0 && SIZ(y) >= 0)
      || (SIZ(y) < 0 && SIZ(x) >= 0))
    return ULONG_MAX;

  xsize = ABSIZ(x);
  ysize = ABSIZ(y);
  tsize = MAX (xsize, ysize);

  xp = refmpn_malloc_limbs (tsize);
  refmpn_zero (xp, tsize);
  refmpn_copy (xp, PTR(x), xsize);

  yp = refmpn_malloc_limbs (tsize);
  refmpn_zero (yp, tsize);
  refmpn_copy (yp, PTR(y), ysize);

  if (SIZ(x) < 0)
    refmpn_neg (xp, xp, tsize);

  if (SIZ(x) < 0)
    refmpn_neg (yp, yp, tsize);

  ret = refmpn_hamdist (xp, yp, tsize);

  free (xp);
  free (yp);
  return ret;
}


/* (0/b), with mpz b; is 1 if b=+/-1, 0 otherwise */
#define JACOBI_0Z(b)  JACOBI_0LS (PTR(b)[0], SIZ(b))

/* (a/b) effect due to sign of b: mpz/mpz */
#define JACOBI_BSGN_ZZ_BIT1(a, b)   JACOBI_BSGN_SS_BIT1 (SIZ(a), SIZ(b))

/* (a/b) effect due to sign of a: mpz/unsigned-mpz, b odd;
   is (-1/b) if a<0, or +1 if a>=0 */
#define JACOBI_ASGN_ZZU_BIT1(a, b)  JACOBI_ASGN_SU_BIT1 (SIZ(a), PTR(b)[0])

int
refmpz_kronecker (mpz_srcptr a_orig, mpz_srcptr b_orig)
{
  unsigned long  twos;
  mpz_t  a, b;
  int    result_bit1 = 0;

  if (mpz_sgn (b_orig) == 0)
    return JACOBI_Z0 (a_orig);  /* (a/0) */

  if (mpz_sgn (a_orig) == 0)
    return JACOBI_0Z (b_orig);  /* (0/b) */

  if (mpz_even_p (a_orig) && mpz_even_p (b_orig))
    return 0;

  if (mpz_cmp_ui (b_orig, 1) == 0)
    return 1;

  mpz_init_set (a, a_orig);
  mpz_init_set (b, b_orig);

  if (mpz_sgn (b) < 0)
    {
      result_bit1 ^= JACOBI_BSGN_ZZ_BIT1 (a, b);
      mpz_neg (b, b);
    }
  if (mpz_even_p (b))
    {
      twos = mpz_scan1 (b, 0L);
      mpz_tdiv_q_2exp (b, b, twos);
      result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(a)[0]);
    }

  if (mpz_sgn (a) < 0)
    {
      result_bit1 ^= JACOBI_N1B_BIT1 (PTR(b)[0]);
      mpz_neg (a, a);
    }
  if (mpz_even_p (a))
    {
      twos = mpz_scan1 (a, 0L);
      mpz_tdiv_q_2exp (a, a, twos);
      result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(b)[0]);
    }

  for (;;)
    {
      ASSERT (mpz_odd_p (a));
      ASSERT (mpz_odd_p (b));
      ASSERT (mpz_sgn (a) > 0);
      ASSERT (mpz_sgn (b) > 0);

      TRACE (printf ("top\n");
	     mpz_trace (" a", a);
	     mpz_trace (" b", b));

      if (mpz_cmp (a, b) < 0)
	{
	  TRACE (printf ("swap\n"));
	  mpz_swap (a, b);
	  result_bit1 ^= JACOBI_RECIP_UU_BIT1 (PTR(a)[0], PTR(b)[0]);
	}

      if (mpz_cmp_ui (b, 1) == 0)
	break;

      mpz_sub (a, a, b);
      TRACE (printf ("sub\n");
	     mpz_trace (" a", a));
      if (mpz_sgn (a) == 0)
	goto zero;

      twos = mpz_scan1 (a, 0L);
      mpz_fdiv_q_2exp (a, a, twos);
      TRACE (printf ("twos %lu\n", twos);
	     mpz_trace (" a", a));
      result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(b)[0]);
    }

  mpz_clear (a);
  mpz_clear (b);
  return JACOBI_BIT1_TO_PN (result_bit1);

 zero:
  mpz_clear (a);
  mpz_clear (b);
  return 0;
}

/* Same as mpz_kronecker, but ignoring factors of 2 on b */
int
refmpz_jacobi (mpz_srcptr a, mpz_srcptr b)
{
  ASSERT_ALWAYS (mpz_sgn (b) > 0);
  ASSERT_ALWAYS (mpz_odd_p (b));

  return refmpz_kronecker (a, b);
}

/* Legendre symbol via powm. p must be an odd prime. */
int
refmpz_legendre (mpz_srcptr a, mpz_srcptr p)
{
  int res;

  mpz_t r;
  mpz_t e;

  ASSERT_ALWAYS (mpz_sgn (p) > 0);
  ASSERT_ALWAYS (mpz_odd_p (p));

  mpz_init (r);
  mpz_init (e);

  mpz_fdiv_r (r, a, p);

  mpz_set (e, p);
  mpz_sub_ui (e, e, 1);
  mpz_fdiv_q_2exp (e, e, 1);
  mpz_powm (r, r, e, p);

  /* Normalize to a more or less symmetric range around zero */
  if (mpz_cmp (r, e) > 0)
    mpz_sub (r, r, p);

  ASSERT_ALWAYS (mpz_cmpabs_ui (r, 1) <= 0);

  res = mpz_sgn (r);

  mpz_clear (r);
  mpz_clear (e);

  return res;
}


int
refmpz_kronecker_ui (mpz_srcptr a, unsigned long b)
{
  mpz_t  bz;
  int    ret;
  mpz_init_set_ui (bz, b);
  ret = refmpz_kronecker (a, bz);
  mpz_clear (bz);
  return ret;
}

int
refmpz_kronecker_si (mpz_srcptr a, long b)
{
  mpz_t  bz;
  int    ret;
  mpz_init_set_si (bz, b);
  ret = refmpz_kronecker (a, bz);
  mpz_clear (bz);
  return ret;
}

int
refmpz_ui_kronecker (unsigned long a, mpz_srcptr b)
{
  mpz_t  az;
  int    ret;
  mpz_init_set_ui (az, a);
  ret = refmpz_kronecker (az, b);
  mpz_clear (az);
  return ret;
}

int
refmpz_si_kronecker (long a, mpz_srcptr b)
{
  mpz_t  az;
  int    ret;
  mpz_init_set_si (az, a);
  ret = refmpz_kronecker (az, b);
  mpz_clear (az);
  return ret;
}


void
refmpz_pow_ui (mpz_ptr w, mpz_srcptr b, unsigned long e)
{
  mpz_t          s, t;
  unsigned long  i;

  mpz_init_set_ui (t, 1L);
  mpz_init_set (s, b);

  if ((e & 1) != 0)
    mpz_mul (t, t, s);

  for (i = 2; i <= e; i <<= 1)
    {
      mpz_mul (s, s, s);
      if ((i & e) != 0)
	mpz_mul (t, t, s);
    }

  mpz_set (w, t);

  mpz_clear (s);
  mpz_clear (t);
}