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+/* mpz_primorial_ui(RES, N) -- Set RES to N# the product of primes <= N.
+
+Contributed to the GNU project by Marco Bodrato.
+
+Copyright 2012, 2015, 2016, 2021 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-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)
+
+/*********************************************************/
+/* Section sieve: sieving functions and tools for primes */
+/*********************************************************/
+
+#if WANT_ASSERT
+/* 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; }
+
+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 res, unsigned long n)
+{
+ ASSERT (n <= GMP_NUMB_MAX);
+
+ if (n < 5)
+ {
+ /* The smallest 5 results for primorial are stored */
+ /* in a 15-bits constant (five octal digits) */
+ MPZ_NEWALLOC (res, 1)[0] = (066211 >> (n * 3)) & 7;
+ SIZ (res) = 1;
+ }
+ else
+ {
+ mp_limb_t *sieve, *factors;
+ mp_size_t size, j;
+ mp_limb_t prod;
+ TMP_DECL;
+
+ /* Try to estimate the result size, to avoid */
+ /* resizing, and to initially store the sieve. */
+ size = n / GMP_NUMB_BITS;
+ size = size + (size >> 1) + 1;
+ ASSERT (size >= primesieve_size (n));
+ sieve = MPZ_NEWALLOC (res, size);
+ size = (gmp_primesieve (sieve, n) + 1) / log_n_max (n) + 1;
+
+ TMP_MARK;
+ factors = TMP_ALLOC_LIMBS (size);
+
+ j = 0;
+
+ prod = 6;
+
+ /* Store primes from 5 to n */
+ {
+ mp_limb_t max_prod;
+
+ max_prod = GMP_NUMB_MAX / n;
+
+ /* Loop on sieved primes. */
+ for (mp_limb_t i = 4, *sp = sieve; i < n; i += GMP_LIMB_BITS * 3)
+ for (mp_limb_t b = i, x = ~ *(sp++); x != 0; b += 3, x >>= 1)
+ if (x & 1)
+ {
+ mp_limb_t prime = b | 1;
+ FACTOR_LIST_STORE (prime, prod, max_prod, factors, j);
+ }
+ }
+
+ if (j != 0)
+ {
+ factors[j++] = prod;
+ mpz_prodlimbs (res, factors, j);
+ }
+ else
+ {
+ PTR (res)[0] = prod;
+ SIZ (res) = 1;
+ }
+
+ TMP_FREE;
+ }
+}