1 /* mpz_bin_ui - compute n over k. 2 3 Copyright 1998-2002, 2012, 2013 Free Software Foundation, Inc. 4 5 This file is part of the GNU MP Library. 6 7 The GNU MP Library is free software; you can redistribute it and/or modify 8 it under the terms of either: 9 10 * the GNU Lesser General Public License as published by the Free 11 Software Foundation; either version 3 of the License, or (at your 12 option) any later version. 13 14 or 15 16 * the GNU General Public License as published by the Free Software 17 Foundation; either version 2 of the License, or (at your option) any 18 later version. 19 20 or both in parallel, as here. 21 22 The GNU MP Library is distributed in the hope that it will be useful, but 23 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 24 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 25 for more details. 26 27 You should have received copies of the GNU General Public License and the 28 GNU Lesser General Public License along with the GNU MP Library. If not, 29 see https://www.gnu.org/licenses/. */ 30 31 #include "gmp.h" 32 #include "gmp-impl.h" 33 #include "longlong.h" 34 35 36 /* This is a poor implementation. Look at bin_uiui.c for improvement ideas. 37 In fact consider calling mpz_bin_uiui() when the arguments fit, leaving 38 the code here only for big n. 39 40 The identity bin(n,k) = (-1)^k * bin(-n+k-1,k) can be found in Knuth vol 41 1 section 1.2.6 part G. */ 42 43 44 #define DIVIDE() \ 45 do { \ 46 ASSERT (SIZ(r) > 0); \ 47 MPN_DIVREM_OR_DIVEXACT_1 (PTR(r), PTR(r), (mp_size_t) SIZ(r), kacc); \ 48 SIZ(r) -= (PTR(r)[SIZ(r)-1] == 0); \ 49 } while (0) 50 51 void 52 mpz_bin_ui (mpz_ptr r, mpz_srcptr n, unsigned long int k) 53 { 54 mpz_t ni; 55 mp_limb_t i; 56 mpz_t nacc; 57 mp_limb_t kacc; 58 mp_size_t negate; 59 60 if (SIZ (n) < 0) 61 { 62 /* bin(n,k) = (-1)^k * bin(-n+k-1,k), and set ni = -n+k-1 - k = -n-1 */ 63 mpz_init (ni); 64 mpz_add_ui (ni, n, 1L); 65 mpz_neg (ni, ni); 66 negate = (k & 1); /* (-1)^k */ 67 } 68 else 69 { 70 /* bin(n,k) == 0 if k>n 71 (no test for this under the n<0 case, since -n+k-1 >= k there) */ 72 if (mpz_cmp_ui (n, k) < 0) 73 { 74 SIZ (r) = 0; 75 return; 76 } 77 78 /* set ni = n-k */ 79 mpz_init (ni); 80 mpz_sub_ui (ni, n, k); 81 negate = 0; 82 } 83 84 /* Now wanting bin(ni+k,k), with ni positive, and "negate" is the sign (0 85 for positive, 1 for negative). */ 86 SIZ (r) = 1; PTR (r)[0] = 1; 87 88 /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. In this case it's 89 whether ni+k-k < k meaning ni<k, and if so change to denominator ni+k-k 90 = ni, and new ni of ni+k-ni = k. */ 91 if (mpz_cmp_ui (ni, k) < 0) 92 { 93 unsigned long tmp; 94 tmp = k; 95 k = mpz_get_ui (ni); 96 mpz_set_ui (ni, tmp); 97 } 98 99 kacc = 1; 100 mpz_init_set_ui (nacc, 1L); 101 102 for (i = 1; i <= k; i++) 103 { 104 mp_limb_t k1, k0; 105 106 #if 0 107 mp_limb_t nacclow; 108 int c; 109 110 nacclow = PTR(nacc)[0]; 111 for (c = 0; (((kacc | nacclow) & 1) == 0); c++) 112 { 113 kacc >>= 1; 114 nacclow >>= 1; 115 } 116 mpz_div_2exp (nacc, nacc, c); 117 #endif 118 119 mpz_add_ui (ni, ni, 1L); 120 mpz_mul (nacc, nacc, ni); 121 umul_ppmm (k1, k0, kacc, i << GMP_NAIL_BITS); 122 if (k1 != 0) 123 { 124 /* Accumulator overflow. Perform bignum step. */ 125 mpz_mul (r, r, nacc); 126 SIZ (nacc) = 1; PTR (nacc)[0] = 1; 127 DIVIDE (); 128 kacc = i; 129 } 130 else 131 { 132 /* Save new products in accumulators to keep accumulating. */ 133 kacc = k0 >> GMP_NAIL_BITS; 134 } 135 } 136 137 mpz_mul (r, r, nacc); 138 DIVIDE (); 139 SIZ(r) = (SIZ(r) ^ -negate) + negate; 140 141 mpz_clear (nacc); 142 mpz_clear (ni); 143 } 144