t-jac.c

a very popular packet of cryptography tools,it encloses the most common used algorithm and protocols

/* Exercise mpz_*_kronecker_*() and mpz_jacobi() functions. */

/*
Copyright 1999, 2000, 2001, 2002, 2003 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 2.1 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; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA.
*/


/* With no arguments the various Kronecker/Jacobi symbol routines are
   checked against some test data and a lot of derived data.

   To check the test data against PARI-GP, run
   
           t-jac -p | gp -q

   It takes a while because the output from "t-jac -p" is big.


   Enhancements:

   More big test cases than those given by check_squares_zi would be good.  */


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

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


#ifdef _LONG_LONG_LIMB
#define LL(l,ll)  ll
#else
#define LL(l,ll)  l
#endif


int option_pari = 0;


unsigned long
mpz_mod4 (mpz_srcptr z)
{
  mpz_t          m;
  unsigned long  ret;

  mpz_init (m);
  mpz_fdiv_r_2exp (m, z, 2);
  ret = mpz_get_ui (m);
  mpz_clear (m);
  return ret;
}

int
mpz_fits_ulimb_p (mpz_srcptr z)
{
  return (SIZ(z) == 1 || SIZ(z) == 0);
}

mp_limb_t
mpz_get_ulimb (mpz_srcptr z)
{
  if (SIZ(z) == 0)
    return 0;
  else
    return PTR(z)[0];
}


void
try_base (mp_limb_t a, mp_limb_t b, int answer)
{
  int  got;

  if ((b & 1) == 0 || b == 1 || a > b)
    return;

  got = mpn_jacobi_base (a, b, 0);
  if (got != answer)
    {
      printf (LL("mpn_jacobi_base (%lu, %lu) is %d should be %d\n",
                 "mpn_jacobi_base (%llu, %llu) is %d should be %d\n"),
              a, b, got, answer);
      abort ();
    }
}


void
try_zi_ui (mpz_srcptr a, unsigned long b, int answer)
{
  int  got;

  got = mpz_kronecker_ui (a, b);
  if (got != answer)
    {
      printf ("mpz_kronecker_ui (");
      mpz_out_str (stdout, 10, a);
      printf (", %lu) is %d should be %d\n", b, got, answer);
      abort ();
    }
}


void
try_zi_si (mpz_srcptr a, long b, int answer)
{
  int  got;

  got = mpz_kronecker_si (a, b);
  if (got != answer)
    {
      printf ("mpz_kronecker_si (");
      mpz_out_str (stdout, 10, a);
      printf (", %ld) is %d should be %d\n", b, got, answer);
      abort ();
    }
}


void
try_ui_zi (unsigned long a, mpz_srcptr b, int answer)
{
  int  got;

  got = mpz_ui_kronecker (a, b);
  if (got != answer)
    {
      printf ("mpz_ui_kronecker (%lu, ", a);
      mpz_out_str (stdout, 10, b);
      printf (") is %d should be %d\n", got, answer);
      abort ();
    }
}


void
try_si_zi (long a, mpz_srcptr b, int answer)
{
  int  got;

  got = mpz_si_kronecker (a, b);
  if (got != answer)
    {
      printf ("mpz_si_kronecker (%ld, ", a);
      mpz_out_str (stdout, 10, b);
      printf (") is %d should be %d\n", got, answer);
      abort ();
    }
}


/* Don't bother checking mpz_jacobi, since it only differs for b even, and
   we don't have an actual expected answer for it.  tests/devel/try.c does
   some checks though.  */
void
try_zi_zi (mpz_srcptr a, mpz_srcptr b, int answer)
{
  int  got;

  got = mpz_kronecker (a, b);
  if (got != answer)
    {
      printf ("mpz_kronecker (");
      mpz_out_str (stdout, 10, a); 
      printf (", ");
      mpz_out_str (stdout, 10, b);
      printf (") is %d should be %d\n", got, answer);
      abort ();
    }
}


void
try_pari (mpz_srcptr a, mpz_srcptr b, int answer)
{
  printf ("try(");
  mpz_out_str (stdout, 10, a); 
  printf (",");
  mpz_out_str (stdout, 10, b); 
  printf (",%d)\n", answer);
}


void
try_each (mpz_srcptr a, mpz_srcptr b, int answer)
{
  if (option_pari)
    {
      try_pari (a, b, answer);
      return;
    }

  if (mpz_fits_ulimb_p (a) && mpz_fits_ulimb_p (b))
    try_base (mpz_get_ulimb (a), mpz_get_ulimb (b), answer);

  if (mpz_fits_ulong_p (b))
    try_zi_ui (a, mpz_get_ui (b), answer);

  if (mpz_fits_slong_p (b))
    try_zi_si (a, mpz_get_si (b), answer);

  if (mpz_fits_ulong_p (a))
    try_ui_zi (mpz_get_ui (a), b, answer);

  if (mpz_fits_sint_p (a))
    try_si_zi (mpz_get_si (a), b, answer);

  try_zi_zi (a, b, answer);
}        


/* Try (a/b) and (a/-b). */
void
try_pn (mpz_srcptr a, mpz_srcptr b_orig, int answer)
{
  mpz_t  b;

  mpz_init_set (b, b_orig);
  try_each (a, b, answer);

  mpz_neg (b, b);
  if (mpz_sgn (a) < 0)
    answer = -answer;

  try_each (a, b, answer);

  mpz_clear (b);
}


/* Try (a+k*p/b) for various k, using the fact (a/b) is periodic in a with
   period p.  For b>0, p=b if b!=2mod4 or p=4*b if b==2mod4. */

void
try_periodic_num (mpz_srcptr a_orig, mpz_srcptr b, int answer)
{
  mpz_t  a, a_period;
  int    i;

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

  mpz_init_set (a, a_orig);
  mpz_init_set (a_period, b);
  if (mpz_mod4 (b) == 2)
    mpz_mul_ui (a_period, a_period, 4);

  /* don't bother with these tests if they're only going to produce
     even/even */
  if (mpz_even_p (a) && mpz_even_p (b) && mpz_even_p (a_period))
    goto done;

  for (i = 0; i < 10; i++)
    {
      mpz_add (a, a, a_period);
      try_pn (a, b, answer);
    }

  mpz_set (a, a_orig);
  for (i = 0; i < 10; i++)
    {
      mpz_sub (a, a, a_period);
      try_pn (a, b, answer);
    }

 done:
  mpz_clear (a);
  mpz_clear (a_period);
}


/* Try (a/b+k*p) for various k, using the fact (a/b) is periodic in b of
   period p.

                               period p
           a==0,1mod4             a
           a==2mod4              4*a
           a==3mod4 and b odd    4*a
           a==3mod4 and b even   8*a

   In Henri Cohen's book the period is given as 4*a for all a==2,3mod4, but
   a counterexample would seem to be (3/2)=-1 which with (3/14)=+1 doesn't
   have period 4*a (but rather 8*a with (3/26)=-1).  Maybe the plain 4*a is
   to be read as applying to a plain Jacobi symbol with b odd, rather than
   the Kronecker extension to b even. */

void
try_periodic_den (mpz_srcptr a, mpz_srcptr b_orig, int answer)
{
  mpz_t  b, b_period;
  int    i;

  if (mpz_sgn (a) == 0 || mpz_sgn (b_orig) == 0)
    return;

  mpz_init_set (b, b_orig);

  mpz_init_set (b_period, a);
  if (mpz_mod4 (a) == 3 && mpz_even_p (b))
    mpz_mul_ui (b_period, b_period, 8);
  else if (mpz_mod4 (a) >= 2)
    mpz_mul_ui (b_period, b_period, 4);

  /* don't bother with these tests if they're only going to produce
     even/even */
  if (mpz_even_p (a) && mpz_even_p (b) && mpz_even_p (b_period))
    goto done;

  for (i = 0; i < 10; i++)
    {
      mpz_add (b, b, b_period);
      try_pn (a, b, answer);
    }

  mpz_set (b, b_orig);
  for (i = 0; i < 10; i++)
    {
      mpz_sub (b, b, b_period);
      try_pn (a, b, answer);
    }

 done:
  mpz_clear (b);
  mpz_clear (b_period);
}


/* Try (a/b*2^k) for various k. */
void
try_2den (mpz_srcptr a, mpz_srcptr b_orig, int answer)
{
  mpz_t  b;
  int    i;
  int    answer_two;

  /* don't bother when b==0 */
  if (mpz_sgn (b_orig) == 0)
    return;

  mpz_init_set (b, b_orig);

  /* answer_two = (a/2) */
  switch (mpz_fdiv_ui (a, 8)) {
  case 1:
  case 7:
    answer_two = 1;
    break;
  case 3:
  case 5:
    answer_two = -1;
    break;