gen-fac_ui.c

/* Generate mpz_fac_ui data.

Copyright 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 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., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */

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

#include "dumbmp.c"


/* sets x=y*(y+2)*(y+4)*....*(y+2*(z-1))	*/
void
odd_products (mpz_t x, mpz_t y, int z)
{
  mpz_t t;

  mpz_init_set (t, y);
  mpz_set_ui (x, 1);
  for (; z != 0; z--)
    {
      mpz_mul (x, x, t);
      mpz_add_ui (t, t, 2);
    }
  mpz_clear (t);
  return;
}

/* returns 0 on success		*/
int
gen_consts (int numb, int nail, int limb)
{
  mpz_t x, y, z, t;
  unsigned long a, b, first = 1;

  printf ("/* This file is automatically generated by gen-fac_ui.c */\n\n");
  printf ("#if GMP_NUMB_BITS != %d\n", numb);
  printf ("Error , error this data is for %d GMP_NUMB_BITS only\n", numb);
  printf ("#endif\n");
  printf ("#if GMP_LIMB_BITS != %d\n", limb);
  printf ("Error , error this data is for %d GMP_LIMB_BITS only\n", limb);
  printf ("#endif\n");

  printf
    ("/* This table is 0!,1!,2!,3!,...,n! where n! has <= GMP_NUMB_BITS bits */\n");
  printf
    ("#define ONE_LIMB_FACTORIAL_TABLE CNST_LIMB(0x1),CNST_LIMB(0x1),CNST_LIMB(0x2),");
  mpz_init_set_ui (x, 2);
  for (b = 3;; b++)
    {
      mpz_mul_ui (x, x, b);	/* so b!=a       */
      if (mpz_sizeinbase (x, 2) > numb)
	break;
      if (first)
	{
	  first = 0;
	}
      else
	{
	  printf ("),");
	}
      printf ("CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");


  mpz_set_ui (x, 1);
  mpz_mul_2exp (x, x, limb + 1);	/* x=2^(limb+1)        */
  mpz_init (y);
  mpz_set_ui (y, 10000);
  mpz_mul (x, x, y);		/* x=2^(limb+1)*10^4     */
  mpz_set_ui (y, 27182);	/* exp(1)*10^4      */
  mpz_tdiv_q (x, x, y);		/* x=2^(limb+1)/exp(1)        */
  printf ("\n/* is 2^(GMP_LIMB_BITS+1)/exp(1) */\n");
  printf ("#define FAC2OVERE CNST_LIMB(0x");
  mpz_out_str (stdout, 16, x);
  printf (")\n");


  printf
    ("\n/* FACMULn is largest odd x such that x*(x+2)*...*(x+2(n-1))<=2^GMP_NUMB_BITS-1 */\n\n");
  mpz_init (z);
  mpz_init (t);
  for (a = 2; a <= 4; a++)
    {
      mpz_set_ui (x, 1);
      mpz_mul_2exp (x, x, numb);
      mpz_root (x, x, a);
      /* so x is approx sol       */
      if (mpz_even_p (x))
	mpz_sub_ui (x, x, 1);
      mpz_set_ui (y, 1);
      mpz_mul_2exp (y, y, numb);
      mpz_sub_ui (y, y, 1);
      /* decrement x until we are <= real sol     */
      do
	{
	  mpz_sub_ui (x, x, 2);
	  odd_products (t, x, a);
	  if (mpz_cmp (t, y) <= 0)
	    break;
	}
      while (1);
      /* increment x until > real sol     */
      do
	{
	  mpz_add_ui (x, x, 2);
	  odd_products (t, x, a);
	  if (mpz_cmp (t, y) > 0)
	    break;
	}
      while (1);
      /* dec once to get real sol */
      mpz_sub_ui (x, x, 2);
      printf ("#define FACMUL%lu CNST_LIMB(0x", a);
      mpz_out_str (stdout, 16, x);
      printf (")\n");
    }

  return 0;
}

int
main (int argc, char *argv[])
{
  int nail_bits, limb_bits, numb_bits;

  if (argc != 3)
    {
      fprintf (stderr, "Usage: gen-fac_ui limbbits nailbits\n");
      exit (1);
    }
  limb_bits = atoi (argv[1]);
  nail_bits = atoi (argv[2]);
  numb_bits = limb_bits - nail_bits;
  if (limb_bits < 0 || nail_bits < 0 || numb_bits < 0)
    {
      fprintf (stderr, "Invalid limb/nail bits %d,%d\n", limb_bits,
	       nail_bits);
      exit (1);
    }
  gen_consts (numb_bits, nail_bits, limb_bits);
  return 0;
}