third_party/gmp/gen-trialdivtab.c - RealtimeRoboticsGroup/test - Gitiles

 /* gen-trialdivtab.c

    Contributed to the GNU project by Torbjorn Granlund.

 Copyright 2009, 2012, 2013, 2016, 2018 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/.  */

 /*
   Generate tables for fast, division-free trial division for GMP.

   There is one main table, ptab.  It contains primes, multiplied together, and
   several types of pre-computed inverses.  It refers to tables of the type
   dtab, via the last two indices.  That table contains the individual primes in
   the range, except that the primes are not actually included in the table (see
   the P macro; it sneakingly excludes the primes themselves).  Instead, the
   dtab tables contains tuples for each prime (modular-inverse, limit) used for
   divisibility checks.

   This interface is not intended for division of very many primes, since then
   other algorithms apply.
 */

 #include <stdlib.h>
 #include <stdio.h>
 #include "bootstrap.c"

 int sumspills (mpz_t, mpz_t *, int);
 void mpn_mod_1s_4p_cps (mpz_t [7], mpz_t);

 int limb_bits;

 mpz_t B;

 int
 main (int argc, char *argv[])
 {
   int t, p;
   mpz_t ppp, acc, inv, gmp_numb_max, tmp, Bhalf;
   mpz_t pre[7];
   int i;
   int start_p, end_p, interval_start, interval_end, omitted_p;
   const char *endtok;
   int stop;
   int np, start_idx;

   if (argc < 2)
     {
       fprintf (stderr, "usage: %s bits endprime\n", argv[0]);
       exit (1);
     }

   limb_bits = atoi (argv[1]);

   end_p = 1290;			/* default end prime */
   if (argc == 3)
     end_p = atoi (argv[2]);

   printf ("#if GMP_LIMB_BITS != %d\n", limb_bits);
   printf ("#error This table is for GMP_LIMB_BITS = %d\n", limb_bits);
   printf ("#endif\n\n");

   printf ("#if GMP_NAIL_BITS != 0\n");
   printf ("#error This table does not support nails\n");
   printf ("#endif\n\n");

   for (i = 0; i < 7; i++)
     mpz_init (pre[i]);

   mpz_init (B);
   mpz_setbit (B, limb_bits);
   mpz_init_set (gmp_numb_max, B);
   mpz_sub_ui (gmp_numb_max, gmp_numb_max, 1);

   mpz_init (tmp);
   mpz_init (inv);

   mpz_init (Bhalf);
   mpz_setbit (Bhalf, limb_bits - 1);

   start_p = 3;

   mpz_init_set_ui (ppp, 1);
   mpz_init (acc);
   interval_start = start_p;
   omitted_p = 3;
   interval_end = 0;

 /*  printf ("static struct gmp_primes_dtab gmp_primes_dtab[] = {\n"); */

   printf ("#ifdef WANT_dtab\n");

   for (t = start_p; t <= end_p; t += 2)
     {
       if (! isprime (t))
 	continue;

       mpz_mul_ui (acc, ppp, t);
       stop = mpz_cmp (acc, Bhalf) >= 0;
       if (!stop)
 	{
 	  mpn_mod_1s_4p_cps (pre, acc);
 	  stop = sumspills (acc, pre + 2, 5);
 	}

       if (stop)
 	{
 	  for (p = interval_start; p <= interval_end; p += 2)
 	    {
 	      if (! isprime (p))
 		continue;

 	      printf ("  P(%d,", (int) p);
 	      mpz_invert_ui_2exp (inv, p, limb_bits);
 	      printf ("CNST_LIMB(0x");  mpz_out_str (stdout, 16, inv);  printf ("),");

 	      mpz_tdiv_q_ui (tmp, gmp_numb_max, p);
 	      printf ("CNST_LIMB(0x");  mpz_out_str (stdout, 16, tmp);
 	      printf (")),\n");
 	    }
 	  mpz_set_ui (ppp, t);
 	  interval_start = t;
 	  omitted_p = t;
 	}
       else
 	{
 	  mpz_set (ppp, acc);
 	}
       interval_end = t;
     }
   printf ("#define SMALLEST_OMITTED_PRIME %d\n", (int) omitted_p);
   printf ("#endif\n");

   printf ("#ifdef WANT_ptab\n");

 /*  printf ("static struct gmp_primes_ptab gmp_primes_ptab[] = {\n"); */

   endtok = "";

   mpz_set_ui (ppp, 1);
   interval_start = start_p;
   interval_end = 0;
   np = 0;
   start_idx = 0;
   for (t = start_p; t <= end_p; t += 2)
     {
       if (! isprime (t))
 	continue;

       mpz_mul_ui (acc, ppp, t);

       stop = mpz_cmp (acc, Bhalf) >= 0;
       if (!stop)
 	{
 	  mpn_mod_1s_4p_cps (pre, acc);
 	  stop = sumspills (acc, pre + 2, 5);
 	}

       if (stop)
 	{
 	  mpn_mod_1s_4p_cps (pre, ppp);
 	  printf ("%s", endtok);
 	  printf ("  {CNST_LIMB(0x");  mpz_out_str (stdout, 16, ppp);
 	  printf ("),{CNST_LIMB(0x");  mpz_out_str (stdout, 16, pre[0]);
 	  printf ("),%d", (int) PTR(pre[1])[0]);
 	  for (i = 0; i < 5; i++)
 	    {
 	      printf (",");
 	      printf ("CNST_LIMB(0x");  mpz_out_str (stdout, 16, pre[2 + i]);
 	      printf (")");
 	    }
 	  printf ("},");
 	  printf ("%d,", start_idx);
 	  printf ("%d}", np - start_idx);

 	  endtok = ",\n";
 	  mpz_set_ui (ppp, t);
 	  interval_start = t;
 	  start_idx = np;
 	}
       else
 	{
 	  mpz_set (ppp, acc);
 	}
       interval_end = t;
       np++;
     }

   printf ("\n");
   printf ("#endif\n");

   return 0;
 }

 unsigned long
 mpz_log2 (mpz_t x)
 {
   return mpz_sgn (x) ? mpz_sizeinbase (x, 2) : 0;
 }

 void
 mpn_mod_1s_4p_cps (mpz_t cps[7], mpz_t bparm)
 {
   mpz_t b, bi;
   mpz_t B1modb, B2modb, B3modb, B4modb, B5modb;
   mpz_t t;
   int cnt;

   mpz_init_set (b, bparm);

   cnt = limb_bits - mpz_log2 (b);

   mpz_init (bi);
   mpz_init (t);
   mpz_init (B1modb);
   mpz_init (B2modb);
   mpz_init (B3modb);
   mpz_init (B4modb);
   mpz_init (B5modb);

   mpz_set_ui (t, 1);
   mpz_mul_2exp (t, t, limb_bits - cnt);
   mpz_sub (t, t, b);
   mpz_mul_2exp (t, t, limb_bits);
   mpz_tdiv_q (bi, t, b);		/* bi = B^2/b, except msb */

   mpz_set_ui (t, 1);
   mpz_mul_2exp (t, t, limb_bits);	/* t = B */
   mpz_tdiv_r (B1modb, t, b);

   mpz_mul_2exp (t, B1modb, limb_bits);
   mpz_tdiv_r (B2modb, t, b);

   mpz_mul_2exp (t, B2modb, limb_bits);
   mpz_tdiv_r (B3modb, t, b);

   mpz_mul_2exp (t, B3modb, limb_bits);
   mpz_tdiv_r (B4modb, t, b);

   mpz_mul_2exp (t, B4modb, limb_bits);
   mpz_tdiv_r (B5modb, t, b);

   mpz_set (cps[0], bi);
   mpz_set_ui (cps[1], cnt);
   mpz_tdiv_q_2exp (cps[2], B1modb, 0);
   mpz_tdiv_q_2exp (cps[3], B2modb, 0);
   mpz_tdiv_q_2exp (cps[4], B3modb, 0);
   mpz_tdiv_q_2exp (cps[5], B4modb, 0);
   mpz_tdiv_q_2exp (cps[6], B5modb, 0);

   mpz_clear (b);
   mpz_clear (bi);
   mpz_clear (t);
   mpz_clear (B1modb);
   mpz_clear (B2modb);
   mpz_clear (B3modb);
   mpz_clear (B4modb);
   mpz_clear (B5modb);
 }

 int
 sumspills (mpz_t ppp, mpz_t *a, int n)
 {
   mpz_t s;
   int i, ret;

   mpz_init_set (s, a[0]);

   for (i = 1; i < n; i++)
     {
       mpz_add (s, s, a[i]);
     }
   ret = mpz_cmp (s, B) >= 0;
   mpz_clear (s);

   return ret;
 }
	/* gen-trialdivtab.c

	Contributed to the GNU project by Torbjorn Granlund.

	Copyright 2009, 2012, 2013, 2016, 2018 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/. */

	/*
	Generate tables for fast, division-free trial division for GMP.

	There is one main table, ptab. It contains primes, multiplied together, and
	several types of pre-computed inverses. It refers to tables of the type
	dtab, via the last two indices. That table contains the individual primes in
	the range, except that the primes are not actually included in the table (see
	the P macro; it sneakingly excludes the primes themselves). Instead, the
	dtab tables contains tuples for each prime (modular-inverse, limit) used for
	divisibility checks.

	This interface is not intended for division of very many primes, since then
	other algorithms apply.
	*/

	#include <stdlib.h>
	#include <stdio.h>
	#include "bootstrap.c"

	int sumspills (mpz_t, mpz_t *, int);
	void mpn_mod_1s_4p_cps (mpz_t [7], mpz_t);

	int limb_bits;

	mpz_t B;

	int
	main (int argc, char *argv[])
	{
	int t, p;
	mpz_t ppp, acc, inv, gmp_numb_max, tmp, Bhalf;
	mpz_t pre[7];
	int i;
	int start_p, end_p, interval_start, interval_end, omitted_p;
	const char *endtok;
	int stop;
	int np, start_idx;

	if (argc < 2)
	{
	fprintf (stderr, "usage: %s bits endprime\n", argv[0]);
	exit (1);
	}

	limb_bits = atoi (argv[1]);

	end_p = 1290; /* default end prime */
	if (argc == 3)
	end_p = atoi (argv[2]);

	printf ("#if GMP_LIMB_BITS != %d\n", limb_bits);
	printf ("#error This table is for GMP_LIMB_BITS = %d\n", limb_bits);
	printf ("#endif\n\n");

	printf ("#if GMP_NAIL_BITS != 0\n");
	printf ("#error This table does not support nails\n");
	printf ("#endif\n\n");

	for (i = 0; i < 7; i++)
	mpz_init (pre[i]);

	mpz_init (B);
	mpz_setbit (B, limb_bits);
	mpz_init_set (gmp_numb_max, B);
	mpz_sub_ui (gmp_numb_max, gmp_numb_max, 1);

	mpz_init (tmp);
	mpz_init (inv);

	mpz_init (Bhalf);
	mpz_setbit (Bhalf, limb_bits - 1);

	start_p = 3;

	mpz_init_set_ui (ppp, 1);
	mpz_init (acc);
	interval_start = start_p;
	omitted_p = 3;
	interval_end = 0;

	/* printf ("static struct gmp_primes_dtab gmp_primes_dtab[] = {\n"); */

	printf ("#ifdef WANT_dtab\n");

	for (t = start_p; t <= end_p; t += 2)
	{
	if (! isprime (t))
	continue;

	mpz_mul_ui (acc, ppp, t);
	stop = mpz_cmp (acc, Bhalf) >= 0;
	if (!stop)
	{
	mpn_mod_1s_4p_cps (pre, acc);
	stop = sumspills (acc, pre + 2, 5);
	}

	if (stop)
	{
	for (p = interval_start; p <= interval_end; p += 2)
	{
	if (! isprime (p))
	continue;

	printf (" P(%d,", (int) p);
	mpz_invert_ui_2exp (inv, p, limb_bits);
	printf ("CNST_LIMB(0x"); mpz_out_str (stdout, 16, inv); printf ("),");

	mpz_tdiv_q_ui (tmp, gmp_numb_max, p);
	printf ("CNST_LIMB(0x"); mpz_out_str (stdout, 16, tmp);
	printf (")),\n");
	}
	mpz_set_ui (ppp, t);
	interval_start = t;
	omitted_p = t;
	}
	else
	{
	mpz_set (ppp, acc);
	}
	interval_end = t;
	}
	printf ("#define SMALLEST_OMITTED_PRIME %d\n", (int) omitted_p);
	printf ("#endif\n");

	printf ("#ifdef WANT_ptab\n");

	/* printf ("static struct gmp_primes_ptab gmp_primes_ptab[] = {\n"); */

	endtok = "";

	mpz_set_ui (ppp, 1);
	interval_start = start_p;
	interval_end = 0;
	np = 0;
	start_idx = 0;
	for (t = start_p; t <= end_p; t += 2)
	{
	if (! isprime (t))
	continue;

	mpz_mul_ui (acc, ppp, t);

	stop = mpz_cmp (acc, Bhalf) >= 0;
	if (!stop)
	{
	mpn_mod_1s_4p_cps (pre, acc);
	stop = sumspills (acc, pre + 2, 5);
	}

	if (stop)
	{
	mpn_mod_1s_4p_cps (pre, ppp);
	printf ("%s", endtok);
	printf (" {CNST_LIMB(0x"); mpz_out_str (stdout, 16, ppp);
	printf ("),{CNST_LIMB(0x"); mpz_out_str (stdout, 16, pre[0]);
	printf ("),%d", (int) PTR(pre[1])[0]);
	for (i = 0; i < 5; i++)
	{
	printf (",");
	printf ("CNST_LIMB(0x"); mpz_out_str (stdout, 16, pre[2 + i]);
	printf (")");
	}
	printf ("},");
	printf ("%d,", start_idx);
	printf ("%d}", np - start_idx);

	endtok = ",\n";
	mpz_set_ui (ppp, t);
	interval_start = t;
	start_idx = np;
	}
	else
	{
	mpz_set (ppp, acc);
	}
	interval_end = t;
	np++;
	}

	printf ("\n");
	printf ("#endif\n");

	return 0;
	}

	unsigned long
	mpz_log2 (mpz_t x)
	{
	return mpz_sgn (x) ? mpz_sizeinbase (x, 2) : 0;
	}

	void
	mpn_mod_1s_4p_cps (mpz_t cps[7], mpz_t bparm)
	{
	mpz_t b, bi;
	mpz_t B1modb, B2modb, B3modb, B4modb, B5modb;
	mpz_t t;
	int cnt;

	mpz_init_set (b, bparm);

	cnt = limb_bits - mpz_log2 (b);

	mpz_init (bi);
	mpz_init (t);
	mpz_init (B1modb);
	mpz_init (B2modb);
	mpz_init (B3modb);
	mpz_init (B4modb);
	mpz_init (B5modb);

	mpz_set_ui (t, 1);
	mpz_mul_2exp (t, t, limb_bits - cnt);
	mpz_sub (t, t, b);
	mpz_mul_2exp (t, t, limb_bits);
	mpz_tdiv_q (bi, t, b); /* bi = B^2/b, except msb */

	mpz_set_ui (t, 1);
	mpz_mul_2exp (t, t, limb_bits); /* t = B */
	mpz_tdiv_r (B1modb, t, b);

	mpz_mul_2exp (t, B1modb, limb_bits);
	mpz_tdiv_r (B2modb, t, b);

	mpz_mul_2exp (t, B2modb, limb_bits);
	mpz_tdiv_r (B3modb, t, b);

	mpz_mul_2exp (t, B3modb, limb_bits);
	mpz_tdiv_r (B4modb, t, b);

	mpz_mul_2exp (t, B4modb, limb_bits);
	mpz_tdiv_r (B5modb, t, b);

	mpz_set (cps[0], bi);
	mpz_set_ui (cps[1], cnt);
	mpz_tdiv_q_2exp (cps[2], B1modb, 0);
	mpz_tdiv_q_2exp (cps[3], B2modb, 0);
	mpz_tdiv_q_2exp (cps[4], B3modb, 0);
	mpz_tdiv_q_2exp (cps[5], B4modb, 0);
	mpz_tdiv_q_2exp (cps[6], B5modb, 0);

	mpz_clear (b);
	mpz_clear (bi);
	mpz_clear (t);
	mpz_clear (B1modb);
	mpz_clear (B2modb);
	mpz_clear (B3modb);
	mpz_clear (B4modb);
	mpz_clear (B5modb);
	}

	int
	sumspills (mpz_t ppp, mpz_t *a, int n)
	{
	mpz_t s;
	int i, ret;

	mpz_init_set (s, a[0]);

	for (i = 1; i < n; i++)
	{
	mpz_add (s, s, a[i]);
	}
	ret = mpz_cmp (s, B) >= 0;
	mpz_clear (s);

	return ret;
	}