/* 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 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 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 #endif #include "gmp.h" #include "gmp-impl.h" #include "longlong.h" void #ifdef __STDC__ mpz_fac_ui (MP_INT *result, unsigned long int n) #else mpz_fac_ui (result, n) MP_INT *result; unsigned long int n; #endif { #if SIMPLE_FAC /* 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); #else /* 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 MP_INT 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, p, 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 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; } /* 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 }