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+/* mpz_primorial_ui(RESULT, N) -- Set RESULT to N# the product of primes <= N.
+
+Contributed to the GNU project by Marco Bodrato.
+
+Copyright 2012 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 "gmp.h"
+#include "gmp-impl.h"
+
+/* TODO: Remove duplicated constants / macros / static functions...
+ */
+
+/*************************************************************/
+/* Section macros: common macros, for swing/fac/bin (&sieve) */
+/*************************************************************/
+
+#define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I) \
+ do { \
+ if ((PR) > (MAX_PR)) { \
+ (VEC)[(I)++] = (PR); \
+ (PR) = (P); \
+ } else \
+ (PR) *= (P); \
+ } while (0)
+
+#define LOOP_ON_SIEVE_CONTINUE(prime,end,sieve) \
+ __max_i = (end); \
+ \
+ do { \
+ ++__i; \
+ if (((sieve)[__index] & __mask) == 0) \
+ { \
+ (prime) = id_to_n(__i)
+
+#define LOOP_ON_SIEVE_BEGIN(prime,start,end,off,sieve) \
+ do { \
+ mp_limb_t __mask, __index, __max_i, __i; \
+ \
+ __i = (start)-(off); \
+ __index = __i / GMP_LIMB_BITS; \
+ __mask = CNST_LIMB(1) << (__i % GMP_LIMB_BITS); \
+ __i += (off); \
+ \
+ LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)
+
+#define LOOP_ON_SIEVE_STOP \
+ } \
+ __mask = __mask << 1 | __mask >> (GMP_LIMB_BITS-1); \
+ __index += __mask & 1; \
+ } while (__i <= __max_i) \
+
+#define LOOP_ON_SIEVE_END \
+ LOOP_ON_SIEVE_STOP; \
+ } while (0)
+
+/*********************************************************/
+/* Section sieve: sieving functions and tools for primes */
+/*********************************************************/
+
+#if WANT_ASSERT
+static mp_limb_t
+bit_to_n (mp_limb_t bit) { return (bit*3+4)|1; }
+#endif
+
+/* id_to_n (x) = bit_to_n (x-1) = (id*3+1)|1*/
+static mp_limb_t
+id_to_n (mp_limb_t id) { return id*3+1+(id&1); }
+
+/* n_to_bit (n) = ((n-1)&(-CNST_LIMB(2)))/3U-1 */
+static mp_limb_t
+n_to_bit (mp_limb_t n) { return ((n-5)|1)/3U; }
+
+#if WANT_ASSERT
+static mp_size_t
+primesieve_size (mp_limb_t n) { return n_to_bit(n) / GMP_LIMB_BITS + 1; }
+#endif
+
+/*********************************************************/
+/* Section primorial: implementation */
+/*********************************************************/
+
+void
+mpz_primorial_ui (mpz_ptr x, unsigned long n)
+{
+ static const mp_limb_t table[] = { 1, 1, 2, 6, 6 };
+
+ ASSERT (n <= GMP_NUMB_MAX);
+
+ if (n < numberof (table))
+ {
+ PTR (x)[0] = table[n];
+ SIZ (x) = 1;
+ }
+ else
+ {
+ mp_limb_t *sieve, *factors;
+ mp_size_t size;
+ mp_limb_t prod;
+ mp_limb_t j;
+ TMP_DECL;
+
+ size = 1 + n / GMP_NUMB_BITS + n / (2*GMP_NUMB_BITS);
+ ASSERT (size >= primesieve_size (n));
+ sieve = MPZ_NEWALLOC (x, size);
+ size = (gmp_primesieve (sieve, n) + 1) / log_n_max (n) + 1;
+
+ TMP_MARK;
+ factors = TMP_ALLOC_LIMBS (size);
+
+ j = 0;
+
+ prod = table[numberof (table)-1];
+
+ /* Store primes from 5 to n */
+ {
+ mp_limb_t prime, max_prod;
+
+ max_prod = GMP_NUMB_MAX / n;
+
+ LOOP_ON_SIEVE_BEGIN (prime, n_to_bit(numberof (table)), n_to_bit (n), 0, sieve);
+ FACTOR_LIST_STORE (prime, prod, max_prod, factors, j);
+ LOOP_ON_SIEVE_END;
+ }
+
+ if (LIKELY (j != 0))
+ {
+ factors[j++] = prod;
+ mpz_prodlimbs (x, factors, j);
+ }
+ else
+ {
+ PTR (x)[0] = prod;
+ SIZ (x) = 1;
+ }
+
+ TMP_FREE;
+ }
+}