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1996-09-27 06:29:02 -04:00
/* mpz_fac_ui(result, n) -- Set RESULT to N!.
Copyright (C) 1991 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 General Public License as published by
the Free Software Foundation; either version 2, 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
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with the GNU MP Library; see the file COPYING. If not, write to
the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
#ifdef DBG
#include <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#ifdef __STDC__
mpz_fac_ui (MP_INT *result, unsigned long int n)
mpz_fac_ui (result, n)
MP_INT *result;
unsigned long int n;
/* Be silly. Just multiply the numbers in ascending order. O(n**2). */
mp_limb k;
mpz_set_ui (result, (mp_limb) 1);
for (k = 2; k <= n; k++)
mpz_mul_ui (result, result, k);
/* Be smarter. Multiply groups of numbers in ascending order until the
product doesn't fit in a limb. Multiply these partial products 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.) */
mp_limb k;
mp_limb p1, p0, p;
/* 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
/* 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, p, k);
/* Did we get overflow into the high limb, i.e. is the partial
product now more than one limb? */
if (p1 != 0)
if (tree_cnt % 2 == 0)
mp_size 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]);
/* 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.) */
if (top > top_limit_so_far)
if (top > MP_STACK_SIZE)
/* The stack is now bigger than ever, initialize the top
element. */
mpz_init_set_ui (&mp_stack[top], p);
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;
/* We didn't get overflow in umul_ppmm. Put p0 in P and try
with one more value of K. */
p = p0;
/* We have partial products in mp_stack[], 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);
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]);