source/libs/gmp/gmp-src/mpz/primorial_ui.c

   1 /* mpz_primorial_ui(RESULT, N) -- Set RESULT to N# the product of primes <= N.
   2
   3 Contributed to the GNU project by Marco Bodrato.
   4
   5 Copyright 2012 Free Software Foundation, Inc.
   6
   7 This file is part of the GNU MP Library.
   8
   9 The GNU MP Library is free software; you can redistribute it and/or modify
  10 it under the terms of either:
  11
  12   * the GNU Lesser General Public License as published by the Free
  13     Software Foundation; either version 3 of the License, or (at your
  14     option) any later version.
  15
  16 or
  17
  18   * the GNU General Public License as published by the Free Software
  19     Foundation; either version 2 of the License, or (at your option) any
  20     later version.
  21
  22 or both in parallel, as here.
  23
  24 The GNU MP Library is distributed in the hope that it will be useful, but
  25 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  26 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  27 for more details.
  28
  29 You should have received copies of the GNU General Public License and the
  30 GNU Lesser General Public License along with the GNU MP Library.  If not,
  31 see https://www.gnu.org/licenses/.  */
  32
  33 #include "gmp.h"
  34 #include "gmp-impl.h"
  35
  36 /* TODO: Remove duplicated constants / macros / static functions...
  37  */
  38
  39 /*************************************************************/
  40 /* Section macros: common macros, for swing/fac/bin (&sieve) */
  41 /*************************************************************/
  42
  43 #define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I)                \
  44   do {                                                          \
  45     if ((PR) > (MAX_PR)) {                                      \
  46       (VEC)[(I)++] = (PR);                                      \
  47       (PR) = (P);                                               \
  48     } else                                                      \
  49       (PR) *= (P);                                              \
  50   } while (0)
  51
  52 #define LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)                 \
  53     __max_i = (end);                                            \
  54                                                                 \
  55     do {                                                        \
  56       ++__i;                                                    \
  57       if (((sieve)[__index] & __mask) == 0)                     \
  58         {                                                       \
  59           (prime) = id_to_n(__i)
  60
  61 #define LOOP_ON_SIEVE_BEGIN(prime,start,end,off,sieve)          \
  62   do {                                                          \
  63     mp_limb_t __mask, __index, __max_i, __i;                    \
  64                                                                 \
  65     __i = (start)-(off);                                        \
  66     __index = __i / GMP_LIMB_BITS;                              \
  67     __mask = CNST_LIMB(1) << (__i % GMP_LIMB_BITS);             \
  68     __i += (off);                                               \
  69                                                                 \
  70     LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)
  71
  72 #define LOOP_ON_SIEVE_STOP                                      \
  73         }                                                       \
  74       __mask = __mask << 1 | __mask >> (GMP_LIMB_BITS-1);       \
  75       __index += __mask & 1;                                    \
  76     }  while (__i <= __max_i)                                   \
  77
  78 #define LOOP_ON_SIEVE_END                                       \
  79     LOOP_ON_SIEVE_STOP;                                         \
  80   } while (0)
  81
  82 /*********************************************************/
  83 /* Section sieve: sieving functions and tools for primes */
  84 /*********************************************************/
  85
  86 #if 0
  87 static mp_limb_t
  88 bit_to_n (mp_limb_t bit) { return (bit*3+4)|1; }
  89 #endif
  90
  91 /* id_to_n (x) = bit_to_n (x-1) = (id*3+1)|1*/
  92 static mp_limb_t
  93 id_to_n  (mp_limb_t id)  { return id*3+1+(id&1); }
  94
  95 /* n_to_bit (n) = ((n-1)&(-CNST_LIMB(2)))/3U-1 */
  96 static mp_limb_t
  97 n_to_bit (mp_limb_t n) { return ((n-5)|1)/3U; }
  98
  99 #if WANT_ASSERT
 100 static mp_size_t
 101 primesieve_size (mp_limb_t n) { return n_to_bit(n) / GMP_LIMB_BITS + 1; }
 102 #endif
 103
 104 /*********************************************************/
 105 /* Section primorial: implementation                     */
 106 /*********************************************************/
 107
 108 void
 109 mpz_primorial_ui (mpz_ptr x, unsigned long n)
 110 {
 111   static const mp_limb_t table[] = { 1, 1, 2, 6, 6 };
 112
 113   ASSERT (n <= GMP_NUMB_MAX);
 114
 115   if (n < numberof (table))
 116     {
 117       PTR (x)[0] = table[n];
 118       SIZ (x) = 1;
 119     }
 120   else
 121     {
 122       mp_limb_t *sieve, *factors;
 123       mp_size_t size;
 124       mp_limb_t prod;
 125       mp_limb_t j;
 126       TMP_DECL;
 127
 128       size = 1 + n / GMP_NUMB_BITS + n / (2*GMP_NUMB_BITS);
 129       ASSERT (size >= primesieve_size (n));
 130       sieve = MPZ_NEWALLOC (x, size);
 131       size = (gmp_primesieve (sieve, n) + 1) / log_n_max (n) + 1;
 132
 133       TMP_MARK;
 134       factors = TMP_ALLOC_LIMBS (size);
 135
 136       j = 0;
 137
 138       prod = table[numberof (table)-1];
 139
 140       /* Store primes from 5 to n */
 141       {
 142         mp_limb_t prime, max_prod;
 143
 144         max_prod = GMP_NUMB_MAX / n;
 145
 146         LOOP_ON_SIEVE_BEGIN (prime, n_to_bit(numberof (table)), n_to_bit (n), 0, sieve);
 147         FACTOR_LIST_STORE (prime, prod, max_prod, factors, j);
 148         LOOP_ON_SIEVE_END;
 149       }
 150
 151       if (LIKELY (j != 0))
 152         {
 153           factors[j++] = prod;
 154           mpz_prodlimbs (x, factors, j);
 155         }
 156       else
 157         {
 158           PTR (x)[0] = prod;
 159           SIZ (x) = 1;
 160         }
 161
 162       TMP_FREE;
 163     }
 164 }