--- /dev/null
+/* mpz_fac_ui(result, n) -- Set RESULT to N!.
+
+Copyright (C) 1991, 1993, 1994, 1995 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 the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 2.1 of the License, or (at your
+option) any later version.
+
+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 Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MP Library; see the file COPYING.LIB. If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA. */
+
+#ifdef DBG
+#include <stdio.h>
+#endif
+
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+void
+#if __STDC__
+mpz_fac_ui (mpz_ptr result, unsigned long int n)
+#else
+mpz_fac_ui (result, n)
+ mpz_ptr result;
+ unsigned long int n;
+#endif
+{
+#if SIMPLE_FAC
+
+ /* Be silly. Just multiply the numbers in ascending order. O(n**2). */
+
+ unsigned long int k;
+
+ mpz_set_ui (result, 1L);
+
+ for (k = 2; k <= n; k++)
+ mpz_mul_ui (result, result, k);
+#else
+
+ /* Be smarter. Multiply groups of numbers in ascending order until the
+ product doesn't fit in a limb. Multiply these partial product in a
+ balanced binary tree fashion, to make the operand have as equal sizes
+ as possible. When the operands have about the same size, mpn_mul
+ becomes faster. */
+
+ unsigned long int p, k;
+ mp_limb_t p1, p0;
+
+ /* Stack of partial products, used to make the computation balanced
+ (i.e. make the sizes of the multiplication operands equal). The
+ topmost position of MP_STACK will contain a one-limb partial product,
+ the second topmost will contain a two-limb partial product, and so
+ on. MP_STACK[0] will contain a partial product with 2**t limbs.
+ To compute n! MP_STACK needs to be less than
+ log(n)**2/log(BITS_PER_MP_LIMB), so 30 is surely enough. */
+#define MP_STACK_SIZE 30
+ mpz_t mp_stack[MP_STACK_SIZE];
+
+ /* TOP is an index into MP_STACK, giving the topmost element.
+ TOP_LIMIT_SO_FAR is the largets value it has taken so far. */
+ int top, top_limit_so_far;
+
+ /* Count of the total number of limbs put on MP_STACK so far. This
+ variable plays an essential role in making the compututation balanced.
+ See below. */
+ unsigned int tree_cnt;
+
+ top = top_limit_so_far = -1;
+ tree_cnt = 0;
+ p = 1;
+ for (k = 2; k <= n; k++)
+ {
+ /* Multiply the partial product in P with K. */
+ umul_ppmm (p1, p0, (mp_limb_t) p, (mp_limb_t) k);
+
+ /* Did we get overflow into the high limb, i.e. is the partial
+ product now more than one limb? */
+ if (p1 != 0)
+ {
+ tree_cnt++;
+
+ if (tree_cnt % 2 == 0)
+ {
+ mp_size_t i;
+
+ /* TREE_CNT is even (i.e. we have generated an even number of
+ one-limb partial products), which means that we have a
+ single-limb product on the top of MP_STACK. */
+
+ mpz_mul_ui (mp_stack[top], mp_stack[top], p);
+
+ /* If TREE_CNT is divisable by 4, 8,..., we have two
+ similar-sized partial products with 2, 4,... limbs at
+ the topmost two positions of MP_STACK. Multiply them
+ to form a new partial product with 4, 8,... limbs. */
+ for (i = 4; (tree_cnt & (i - 1)) == 0; i <<= 1)
+ {
+ mpz_mul (mp_stack[top - 1],
+ mp_stack[top], mp_stack[top - 1]);
+ top--;
+ }
+ }
+ else
+ {
+ /* Put the single-limb partial product in P on the stack.
+ (The next time we get a single-limb product, we will
+ multiply the two together.) */
+ top++;
+ if (top > top_limit_so_far)
+ {
+ if (top > MP_STACK_SIZE)
+ abort();
+ /* The stack is now bigger than ever, initialize the top
+ element. */
+ mpz_init_set_ui (mp_stack[top], p);
+ top_limit_so_far++;
+ }
+ else
+ mpz_set_ui (mp_stack[top], p);
+ }
+
+ /* We ignored the last result from umul_ppmm. Put K in P as the
+ first component of the next single-limb partial product. */
+ p = k;
+ }
+ else
+ /* We didn't get overflow in umul_ppmm. Put p0 in P and try
+ with one more value of K. */
+ p = p0; /* bogus if long != mp_limb_t */
+ }
+
+ /* We have partial products in mp_stack[0..top], in descending order.
+ We also have a small partial product in p.
+ Their product is the final result. */
+ if (top < 0)
+ mpz_set_ui (result, p);
+ else
+ mpz_mul_ui (result, mp_stack[top--], p);
+ while (top >= 0)
+ mpz_mul (result, result, mp_stack[top--]);
+
+ /* Free the storage allocated for MP_STACK. */
+ for (top = top_limit_so_far; top >= 0; top--)
+ mpz_clear (mp_stack[top]);
+#endif
+}
projects / ghc-hetmet.git / blobdiff