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Diffstat (limited to 'contrib/libgmp/mpz/fac_ui.c')
| -rw-r--r-- | contrib/libgmp/mpz/fac_ui.c | 157 |
1 files changed, 157 insertions, 0 deletions
diff --git a/contrib/libgmp/mpz/fac_ui.c b/contrib/libgmp/mpz/fac_ui.c new file mode 100644 index 000000000000..a170060a544e --- /dev/null +++ b/contrib/libgmp/mpz/fac_ui.c @@ -0,0 +1,157 @@ +/* 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 Library General Public License as published by +the Free Software Foundation; either version 2 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 Library General Public +License for more details. + +You should have received a copy of the GNU Library 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 +} |