Quelle gen-fac.c Sprache: C

/* Generate data for combinatorics: fac_ui, bin_uiui, ...

Copyright 2002, 2011-2016 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 either:

  * 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.

or

  * the GNU General Public License as published by the Free Software
    Foundation; either version 2 of the License, or (at your option) any
    later version.

or both in parallel, as here.

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 General Public License
for more details.

You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library.  If not,
see https://www.gnu.org/licenses/.  */

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

#include "bootstrap.c"

int
mpz_remove_twos (mpz_t x)
{
  mp_bitcnt_t r = mpz_scan1(x, 0);
  mpz_tdiv_q_2exp (x, x, r);
  return r;
}

/* returns 0 on success */
int
gen_consts (unsigned numb, unsigned limb)
{
  mpz_t x, mask, y, last;
  unsigned long a, b;
  unsigned long ofl, ofe;

  printf ("/* This file is automatically generated by gen-fac.c */\n\n");
  printf ("#if GMP_NUMB_BITS != %u\n", numb);
  printf ("Error , error this data is for %u GMP_NUMB_BITS only\n", numb);
  printf ("#endif\n");
#if 0
  printf ("#if GMP_LIMB_BITS != %u\n", limb);
  printf ("Error , error this data is for %u GMP_LIMB_BITS only\n", limb);
  printf ("#endif\n");
#endif

  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");
  mpz_init_set_ui (x, 1);
  mpz_init (last);
  for (b = 2;; b++)
    {
      mpz_mul_ui (x, x, b); /* so b!=a       */
      if (mpz_sizeinbase (x, 2) > numb)
break;
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");

  printf
    ("\n/* This table is 0!,1!,2!/2,3!/2,...,n!/2^sn where n!/2^sn is an */\n");
  printf
    ("/* odd integer for each n, and n!/2^sn has <= GMP_NUMB_BITS bits */\n");
  printf
    ("#define ONE_LIMB_ODD_FACTORIAL_TABLE CNST_LIMB(0x1),CNST_LIMB(0x1),CNST_LIMB(0x1");
  mpz_set_ui (x, 1);
  for (b = 3;; b++)
    {
      for (a = b; (a & 1) == 0; a >>= 1);
      mpz_swap (last, x);
      mpz_mul_ui (x, last, a);
      if (mpz_sizeinbase (x, 2) > numb)
break;
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");
  printf
    ("#define ODD_FACTORIAL_TABLE_MAX CNST_LIMB(0x");
  mpz_out_str (stdout, 16, last);
  printf (")\n");

  ofl = b - 1;
  printf
    ("#define ODD_FACTORIAL_TABLE_LIMIT (%lu)\n", ofl);
  mpz_init (mask);
  mpz_setbit (mask, numb);
  mpz_sub_ui (mask, mask, 1);
  printf
    ("\n/* Previous table, continued, values modulo 2^GMP_NUMB_BITS */\n");
  printf
    ("#define ONE_LIMB_ODD_FACTORIAL_EXTTABLE CNST_LIMB(0x");
  mpz_and (x, x, mask);
  mpz_out_str (stdout, 16, x);
  mpz_init (y);
  mpz_bin_uiui (y, b, b/2);
  b++;
  for (;; b++)
    {
      for (a = b; (a & 1) == 0; a >>= 1);
      if (a == b) {
mpz_divexact_ui (y, y, a/2+1);
mpz_mul_ui (y, y, a);
      } else
mpz_mul_2exp (y, y, 1);
      if (mpz_sizeinbase (y, 2) > numb)
break;
      mpz_mul_ui (x, x, a);
      mpz_and (x, x, mask);
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");
  ofe = b - 1;
  printf
    ("#define ODD_FACTORIAL_EXTTABLE_LIMIT (%lu)\n", ofe);

  printf
    ("\n/* This table is 1!!,3!!,...,(2n+1)!! where (2n+1)!! has <= GMP_NUMB_BITS bits */\n");
  printf
    ("#define ONE_LIMB_ODD_DOUBLEFACTORIAL_TABLE CNST_LIMB(0x1");
  mpz_set_ui (x, 1);
  for (b = 3;; b+=2)
    {
      mpz_swap (last, x);
      mpz_mul_ui (x, last, b);
      if (mpz_sizeinbase (x, 2) > numb)
break;
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");
  printf
    ("#define ODD_DOUBLEFACTORIAL_TABLE_MAX CNST_LIMB(0x");
  mpz_out_str (stdout, 16, last);
  printf (")\n");

  printf
    ("#define ODD_DOUBLEFACTORIAL_TABLE_LIMIT (%lu)\n", b - 2);

  printf
    ("\n/* This table x_1, x_2,... contains values s.t. x_n^n has <= GMP_NUMB_BITS bits */\n");
  printf
    ("#define NTH_ROOT_NUMB_MASK_TABLE (GMP_NUMB_MASK");
  for (b = 2;b <= 8; b++)
    {
      mpz_root (x, mask, b);
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");

  mpz_add_ui (mask, mask, 1);
  printf
    ("\n/* This table contains inverses of odd factorials, modulo 2^GMP_NUMB_BITS */\n");
  printf
    ("\n/* It begins with (2!/2)^-1=1 */\n");
  printf
    ("#define ONE_LIMB_ODD_FACTORIAL_INVERSES_TABLE CNST_LIMB(0x1");
  mpz_set_ui (x, 1);
  for (b = 3;b <= ofe - 2; b++)
    {
      for (a = b; (a & 1) == 0; a >>= 1);
      mpz_mul_ui (x, x, a);
      mpz_invert (y, x, mask);
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, y);
    }
  printf (")\n");

  ofe = (ofe / 16 + 1) * 16;

  printf
    ("\n/* This table contains 2n-popc(2n) for small n */\n");
  printf
    ("\n/* It begins with 2-1=1 (n=1) */\n");
  printf
    ("#define TABLE_2N_MINUS_POPC_2N 1");
  for (b = 4; b <= ofe; b += 2)
    {
      mpz_set_ui (x, b);
      printf (",%lu",b - mpz_popcount (x));
    }
  printf ("\n");
  printf
    ("#define TABLE_LIMIT_2N_MINUS_POPC_2N %lu\n", ofe + 1);

  ofl = (ofl + 1) / 2;
  printf
    ("#define ODD_CENTRAL_BINOMIAL_OFFSET (%lu)\n", ofl);
  printf
    ("\n/* This table contains binomial(2k,k)/2^t */\n");
  printf
    ("\n/* It begins with ODD_CENTRAL_BINOMIAL_TABLE_MIN */\n");
  printf
    ("#define ONE_LIMB_ODD_CENTRAL_BINOMIAL_TABLE ");
  for (b = ofl;; b++)
    {
      mpz_bin_uiui (x, 2 * b, b);
      mpz_remove_twos (x);
      if (mpz_sizeinbase (x, 2) > numb)
break;
      if (b != ofl)
printf ("),");
      printf("CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");

  ofe = b - 1;
  printf
    ("#define ODD_CENTRAL_BINOMIAL_TABLE_LIMIT (%lu)\n", ofe);

  printf
    ("\n/* This table contains the inverses of elements in the previous table. */\n");
  printf
    ("#define ONE_LIMB_ODD_CENTRAL_BINOMIAL_INVERSE_TABLE CNST_LIMB(0x");
  for (b = ofl; b <= ofe; b++)
    {
      mpz_bin_uiui (x, 2 * b, b);
      mpz_remove_twos (x);
      mpz_invert (x, x, mask);
      mpz_out_str (stdout, 16, x);
      if (b != ofe)
printf ("),CNST_LIMB(0x");
    }
  printf (")\n");

  printf
    ("\n/* This table contains the values t in the formula binomial(2k,k)/2^t */\n");
  printf
    ("#define CENTRAL_BINOMIAL_2FAC_TABLE ");
  for (b = ofl; b <= ofe; b++)
    {
      mpz_bin_uiui (x, 2 * b, b);
      printf ("%d", mpz_remove_twos (x));
      if (b != ofe)
printf (",");
    }
  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 limbbits nailbits\n");
      exit (1);
    }
  limb_bits = atoi (argv[1]);
  nail_bits = atoi (argv[2]);
  numb_bits = limb_bits - nail_bits;
  if (limb_bits < 2 || nail_bits < 0 || numb_bits < 1)
    {
      fprintf (stderr, "Invalid limb/nail bits %d,%d\n", limb_bits,
        nail_bits);
      exit (1);
    }
  gen_consts (numb_bits, limb_bits);
  return 0;
}

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