mpir/tests/mpz/t-gcd.c

/* Test mpz_gcd, mpz_gcdext, and mpz_gcd_ui.

Copyright 1991, 1993, 1994, 1996, 1997, 2000, 2001, 2002, 2003, 2004, 2005,
2008, 2009, 2012 Free Software Foundation, Inc.

This file is part of the GNU MP Library test suite.

The GNU MP Library test suite is free software; you can redistribute it
and/or modify it under the terms of the GNU 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 test suite 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 General
Public License for more details.

You should have received a copy of the GNU General Public License along with
the GNU MP Library test suite.  If not, see http://www.gnu.org/licenses/.  */

#include <stdio.h>
#include <stdlib.h>

#include "mpir.h"
#include "gmp-impl.h"
#include "tests.h"

void one_test (mpz_t, mpz_t, mpz_t, int);
void debug_mp (mpz_t, int);

static int gcdext_valid_p (const mpz_t, const mpz_t, const mpz_t, const mpz_t);

/* Keep one_test's variables global, so that we don't need
   to reinitialize them for each test.  */
mpz_t gcd1, gcd2, s, temp1, temp2, temp3;

#define MAX_SCHOENHAGE_THRESHOLD HGCD_REDUCE_THRESHOLD

/* Define this to make all operands be large enough for Schoenhage gcd
   to be used.  */
#ifndef WHACK_SCHOENHAGE
#define WHACK_SCHOENHAGE 0
#endif

#if WHACK_SCHOENHAGE
#define MIN_OPERAND_BITSIZE (MAX_SCHOENHAGE_THRESHOLD * GMP_NUMB_BITS)
#else
#define MIN_OPERAND_BITSIZE 1
#endif


void
check_data (void)
{
  static const struct {
    const char *a;
    const char *b;
    const char *want;
  } data[] = {
    /* This tickled a bug in gmp 4.1.2 mpn/x86/k6/gcd_finda.asm. */
    { "0x3FFC000007FFFFFFFFFF00000000003F83FFFFFFFFFFFFFFF80000000000000001",
      "0x1FFE0007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC000000000000000000000001",
      "5" }
  };

  mpz_t  a, b, got, want;
  int    i;

  mpz_inits (a, b, got, want, NULL);

  for (i = 0; i < numberof (data); i++)
    {
      mpz_set_str_or_abort (a, data[i].a, 0);
      mpz_set_str_or_abort (b, data[i].b, 0);
      mpz_set_str_or_abort (want, data[i].want, 0);
      mpz_gcd (got, a, b);
      MPZ_CHECK_FORMAT (got);
      if (mpz_cmp (got, want) != 0)
	{
	  printf    ("mpz_gcd wrong on data[%d]\n", i);
	  printf    (" a  %s\n", data[i].a);
	  printf    (" b  %s\n", data[i].b);
	  mpz_trace (" a", a);
	  mpz_trace (" b", b);
	  mpz_trace (" want", want);
	  mpz_trace (" got ", got);
	  abort ();
	}
    }

  mpz_clears (a, b, got, want, NULL);
}

void
make_chain_operands (mpz_t ref, mpz_t a, mpz_t b, gmp_randstate_t rs, int nb1, int nb2, int chain_len)
{
  mpz_t bs, temp1, temp2;
  int j;

  mpz_inits (bs, temp1, temp2, NULL);

  /* Generate a division chain backwards, allowing otherwise unlikely huge
     quotients.  */

  mpz_set_ui (a, 0);
  mpz_urandomb (bs, rs, 32);
  mpz_urandomb (bs, rs, mpz_get_ui (bs) % nb1 + 1);
  mpz_rrandomb (b, rs, mpz_get_ui (bs));
  mpz_add_ui (b, b, 1);
  mpz_set (ref, b);

  for (j = 0; j < chain_len; j++)
    {
      mpz_urandomb (bs, rs, 32);
      mpz_urandomb (bs, rs, mpz_get_ui (bs) % nb2 + 1);
      mpz_rrandomb (temp2, rs, mpz_get_ui (bs) + 1);
      mpz_add_ui (temp2, temp2, 1);
      mpz_mul (temp1, b, temp2);
      mpz_add (a, a, temp1);

      mpz_urandomb (bs, rs, 32);
      mpz_urandomb (bs, rs, mpz_get_ui (bs) % nb2 + 1);
      mpz_rrandomb (temp2, rs, mpz_get_ui (bs) + 1);
      mpz_add_ui (temp2, temp2, 1);
      mpz_mul (temp1, a, temp2);
      mpz_add (b, b, temp1);
    }

  mpz_clears (bs, temp1, temp2, NULL);
}

/* Test operands from a table of seed data.  This variant creates the operands
   using plain ol' mpz_rrandomb.  This is a hack for better coverage of the gcd
   code, which depends on that the random number generators give the exact
   numbers we expect.  */
void
check_kolmo1 (void)
{
  static const struct {
    unsigned int seed;
    int nb;
    const char *want;
  } data[] = {
    { 59618, 38208, "5"},
    { 76521, 49024, "3"},
    { 85869, 54976, "1"},
    { 99449, 63680, "1"},
    {112453, 72000, "1"}
  };

  gmp_randstate_t rs;
  mpz_t  bs, a, b, want;
  int    i, unb, vnb, nb;

  gmp_randinit_default (rs);

  mpz_inits (bs, a, b, want, NULL);

  for (i = 0; i < numberof (data); i++)
    {
      nb = data[i].nb;

      gmp_randseed_ui (rs, data[i].seed);

      mpz_urandomb (bs, rs, 32);
      unb = mpz_get_ui (bs) % nb;
      mpz_urandomb (bs, rs, 32);
      vnb = mpz_get_ui (bs) % nb;

      mpz_rrandomb (a, rs, unb);
      mpz_rrandomb (b, rs, vnb);

      mpz_set_str_or_abort (want, data[i].want, 0);

      one_test (a, b, want, -1);
    }

  mpz_clears (bs, a, b, want, NULL);
  gmp_randclear (rs);
}

/* Test operands from a table of seed data.  This variant creates the operands
   using a division chain.  This is a hack for better coverage of the gcd
   code, which depends on that the random number generators give the exact
   numbers we expect.  */
void
check_kolmo2 (void)
{
  static const struct {
    unsigned int seed;
    int nb, chain_len;
  } data[] = {
    {  917, 15, 5 },
    { 1032, 18, 6 },
    { 1167, 18, 6 },
    { 1174, 18, 6 },
    { 1192, 18, 6 },
  };

  gmp_randstate_t rs;
  mpz_t  bs, a, b, want;
  int    i;

  gmp_randinit_default (rs);

  mpz_inits (bs, a, b, want, NULL);

  for (i = 0; i < numberof (data); i++)
    {
      gmp_randseed_ui (rs, data[i].seed);
      make_chain_operands (want, a, b, rs, data[i].nb, data[i].nb, data[i].chain_len);
      one_test (a, b, want, -1);
    }

  mpz_clears (bs, a, b, want, NULL);
  gmp_randclear (rs);
}

int
main (int argc, char **argv)
{
  mpz_t op1, op2, ref;
  int i, chain_len;
  gmp_randstate_ptr rands;
  mpz_t bs;
  unsigned long bsi, size_range;
  long int reps = 200;

  tests_start ();

  rands = RANDS;

  mpz_inits (bs, op1, op2, ref, gcd1, gcd2, temp1, temp2, temp3, s, NULL);

  check_data ();
  check_kolmo1 ();
  check_kolmo2 ();

  /* Testcase to exercise the u0 == u1 case in mpn_gcdext_lehmer_n. */
  mpz_set_ui (op2, GMP_NUMB_MAX); /* FIXME: Huge limb doesn't always fit */
  mpz_mul_2exp (op1, op2, 100);
  mpz_add (op1, op1, op2);
  mpz_mul_ui (op2, op2, 2);
  one_test (op1, op2, NULL, -1);

  for (i = 0; i < reps; i++)
    {
      /* Generate plain operands with unknown gcd.  These types of operands
	 have proven to trigger certain bugs in development versions of the
	 gcd code.  The "hgcd->row[3].rsize > M" ASSERT is not triggered by
	 the division chain code below, but that is most likely just a result
	 of that other ASSERTs are triggered before it.  */

      mpz_urandomb (bs, rands, 32);
      size_range = mpz_get_ui (bs) % 17 + 2;

      mpz_urandomb (bs, rands, size_range);
      mpz_rrandomb (op1, rands, mpz_get_ui (bs) + MIN_OPERAND_BITSIZE);
      mpz_urandomb (bs, rands, size_range);
      mpz_rrandomb (op2, rands, mpz_get_ui (bs) + MIN_OPERAND_BITSIZE);

      mpz_urandomb (bs, rands, 8);
      bsi = mpz_get_ui (bs);

      if ((bsi & 0x3c) == 4)
	mpz_mul (op1, op1, op2);	/* make op1 a multiple of op2 */
      else if ((bsi & 0x3c) == 8)
	mpz_mul (op2, op1, op2);	/* make op2 a multiple of op1 */

      if ((bsi & 1) != 0)
	mpz_neg (op1, op1);
      if ((bsi & 2) != 0)
	mpz_neg (op2, op2);

      one_test (op1, op2, NULL, i);

      /* Generate a division chain backwards, allowing otherwise unlikely huge
	 quotients.  */

      mpz_urandomb (bs, rands, 32);
      chain_len = mpz_get_ui (bs) % LOG2C (GMP_NUMB_BITS * MAX_SCHOENHAGE_THRESHOLD);
      mpz_urandomb (bs, rands, 32);
      chain_len = mpz_get_ui (bs) % (1 << chain_len) / 32;

      make_chain_operands (ref, op1, op2, rands, 16, 12, chain_len);

      one_test (op1, op2, ref, i);
    }

  mpz_clears (bs, op1, op2, ref, gcd1, gcd2, temp1, temp2, temp3, s, NULL);

  tests_end ();
  exit (0);
}

void
debug_mp (mpz_t x, int base)
{
  mpz_out_str (stderr, base, x); fputc ('\n', stderr);
}

void
one_test (mpz_t op1, mpz_t op2, mpz_t ref, int i)
{
  /*
  printf ("%d %d %d\n", SIZ (op1), SIZ (op2), ref != NULL ? SIZ (ref) : 0);
  fflush (stdout);
  */

  /*
  fprintf (stderr, "op1=");  debug_mp (op1, -16);
  fprintf (stderr, "op2=");  debug_mp (op2, -16);
  */

  mpz_gcdext (gcd1, s, NULL, op1, op2);
  MPZ_CHECK_FORMAT (gcd1);
  MPZ_CHECK_FORMAT (s);

  if (ref && mpz_cmp (ref, gcd1) != 0)
    {
      fprintf (stderr, "ERROR in test %d\n", i);
      fprintf (stderr, "mpz_gcdext returned incorrect result\n");
      fprintf (stderr, "op1=");                 debug_mp (op1, -16);
      fprintf (stderr, "op2=");                 debug_mp (op2, -16);
      fprintf (stderr, "expected result:\n");   debug_mp (ref, -16);
      fprintf (stderr, "mpz_gcdext returns:\n");debug_mp (gcd1, -16);
      abort ();
    }

  if (!gcdext_valid_p(op1, op2, gcd1, s))
    {
      fprintf (stderr, "ERROR in test %d\n", i);
      fprintf (stderr, "mpz_gcdext returned invalid result\n");
      fprintf (stderr, "op1=");                 debug_mp (op1, -16);
      fprintf (stderr, "op2=");                 debug_mp (op2, -16);
      fprintf (stderr, "mpz_gcdext returns:\n");debug_mp (gcd1, -16);
      fprintf (stderr, "s=");                   debug_mp (s, -16);
      abort ();
    }

  mpz_gcd (gcd2, op1, op2);
  MPZ_CHECK_FORMAT (gcd2);

  if (mpz_cmp (gcd2, gcd1) != 0)
    {
      fprintf (stderr, "ERROR in test %d\n", i);
      fprintf (stderr, "mpz_gcd returned incorrect result\n");
      fprintf (stderr, "op1=");                 debug_mp (op1, -16);
      fprintf (stderr, "op2=");                 debug_mp (op2, -16);
      fprintf (stderr, "expected result:\n");   debug_mp (gcd1, -16);
      fprintf (stderr, "mpz_gcd returns:\n");   debug_mp (gcd2, -16);
      abort ();
    }

  /* This should probably move to t-gcd_ui.c */
  if (mpz_fits_ulong_p (op1) || mpz_fits_ulong_p (op2))
    {
      if (mpz_fits_ulong_p (op1))
	mpz_gcd_ui (gcd2, op2, mpz_get_ui (op1));
      else
	mpz_gcd_ui (gcd2, op1, mpz_get_ui (op2));
      if (mpz_cmp (gcd2, gcd1))
	{
	  fprintf (stderr, "ERROR in test %d\n", i);
	  fprintf (stderr, "mpz_gcd_ui returned incorrect result\n");
	  fprintf (stderr, "op1=");                 debug_mp (op1, -16);
	  fprintf (stderr, "op2=");                 debug_mp (op2, -16);
	  fprintf (stderr, "expected result:\n");   debug_mp (gcd1, -16);
	  fprintf (stderr, "mpz_gcd_ui returns:\n");   debug_mp (gcd2, -16);
	  abort ();
	}
    }

  mpz_gcdext (gcd2, temp1, temp2, op1, op2);
  MPZ_CHECK_FORMAT (gcd2);
  MPZ_CHECK_FORMAT (temp1);
  MPZ_CHECK_FORMAT (temp2);

  mpz_mul (temp1, temp1, op1);
  mpz_mul (temp2, temp2, op2);
  mpz_add (temp1, temp1, temp2);

  if (mpz_cmp (gcd1, gcd2) != 0
      || mpz_cmp (gcd2, temp1) != 0)
    {
      fprintf (stderr, "ERROR in test %d\n", i);
      fprintf (stderr, "mpz_gcdext returned incorrect result\n");
      fprintf (stderr, "op1=");                 debug_mp (op1, -16);
      fprintf (stderr, "op2=");                 debug_mp (op2, -16);
      fprintf (stderr, "expected result:\n");   debug_mp (gcd1, -16);
      fprintf (stderr, "mpz_gcdext returns:\n");debug_mp (gcd2, -16);
      abort ();
    }
}

/* Called when g is supposed to be gcd(a,b), and g = s a + t b, for some t.
   Uses temp1, temp2 and temp3. */
static int
gcdext_valid_p (const mpz_t a, const mpz_t b, const mpz_t g, const mpz_t s)
{
  /* It's not clear that gcd(0,0) is well defined, but we allow it and require that
     gcd(0,0) = 0. */
  if (mpz_sgn (g) < 0)
    return 0;

  if (mpz_sgn (a) == 0)
    {
      /* Must have g == abs (b). Any value for s is in some sense "correct",
	 but it makes sense to require that s == 0. */
      return mpz_cmpabs (g, b) == 0 && mpz_sgn (s) == 0;
    }
  else if (mpz_sgn (b) == 0)
    {
      /* Must have g == abs (a), s == sign (a) */
      return mpz_cmpabs (g, a) == 0 && mpz_cmp_si (s, mpz_sgn (a)) == 0;
    }

  if (mpz_sgn (g) <= 0)
    return 0;

  mpz_tdiv_qr (temp1, temp3, a, g);
  if (mpz_sgn (temp3) != 0)
    return 0;

  mpz_tdiv_qr (temp2, temp3, b, g);
  if (mpz_sgn (temp3) != 0)
    return 0;

  /* Require that 2 |s| < |b/g|, or |s| == 1. */
  if (mpz_cmpabs_ui (s, 1) > 0)
    {
      mpz_mul_2exp (temp3, s, 1);
      if (mpz_cmpabs (temp3, temp2) >= 0)
	return 0;
    }

  /* Compute the other cofactor. */
  mpz_mul(temp2, s, a);
  mpz_sub(temp2, g, temp2);
  mpz_tdiv_qr(temp2, temp3, temp2, b);

  if (mpz_sgn (temp3) != 0)
    return 0;

  /* Require that 2 |t| < |a/g| or |t| == 1*/
  if (mpz_cmpabs_ui (temp2, 1) > 0)
    {
      mpz_mul_2exp (temp2, temp2, 1);
      if (mpz_cmpabs (temp2, temp1) >= 0)
	return 0;
    }
  return 1;
}