1/* mpz_divexact_gcd -- exact division optimized for GCDs. 2 3 THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE AND ARE ALMOST CERTAIN TO 4 BE SUBJECT TO INCOMPATIBLE CHANGES IN FUTURE GNU MP RELEASES. 5 6Copyright 2000, 2005 Free Software Foundation, Inc. 7 8This file is part of the GNU MP Library. 9 10The GNU MP Library is free software; you can redistribute it and/or modify 11it under the terms of the GNU Lesser General Public License as published by 12the Free Software Foundation; either version 3 of the License, or (at your 13option) any later version. 14 15The GNU MP Library is distributed in the hope that it will be useful, but 16WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 17or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 18License for more details. 19 20You should have received a copy of the GNU Lesser General Public License 21along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 22 23#include "gmp.h" 24#include "gmp-impl.h" 25#include "longlong.h" 26 27 28/* Set q to a/d, expecting d to be from a GCD and therefore usually small. 29 30 The distribution of GCDs of random numbers can be found in Knuth volume 2 31 section 4.5.2 theorem D. 32 33 GCD chance 34 1 60.8% 35 2^k 20.2% (1<=k<32) 36 3*2^k 9.0% (1<=k<32) 37 other 10.1% 38 39 Only the low limb is examined for optimizations, since GCDs bigger than 40 2^32 (or 2^64) will occur very infrequently. 41 42 Future: This could change to an mpn_divexact_gcd, possibly partly 43 inlined, if/when the relevant mpq functions change to an mpn based 44 implementation. */ 45 46 47static void 48mpz_divexact_by3 (mpz_ptr q, mpz_srcptr a) 49{ 50 mp_size_t size = SIZ(a); 51 if (size == 0) 52 { 53 SIZ(q) = 0; 54 return; 55 } 56 else 57 { 58 mp_size_t abs_size = ABS(size); 59 mp_ptr qp; 60 61 MPZ_REALLOC (q, abs_size); 62 63 qp = PTR(q); 64 mpn_divexact_by3 (qp, PTR(a), abs_size); 65 66 abs_size -= (qp[abs_size-1] == 0); 67 SIZ(q) = (size>0 ? abs_size : -abs_size); 68 } 69} 70 71void 72mpz_divexact_gcd (mpz_ptr q, mpz_srcptr a, mpz_srcptr d) 73{ 74 ASSERT (mpz_sgn (d) > 0); 75 76 if (SIZ(d) == 1) 77 { 78 mp_limb_t dl = PTR(d)[0]; 79 int twos; 80 81 if (dl == 1) 82 { 83 if (q != a) 84 mpz_set (q, a); 85 return; 86 } 87 if (dl == 3) 88 { 89 mpz_divexact_by3 (q, a); 90 return; 91 } 92 93 count_trailing_zeros (twos, dl); 94 dl >>= twos; 95 96 if (dl == 1) 97 { 98 mpz_tdiv_q_2exp (q, a, twos); 99 return; 100 } 101 if (dl == 3) 102 { 103 mpz_tdiv_q_2exp (q, a, twos); 104 mpz_divexact_by3 (q, q); 105 return; 106 } 107 } 108 109 mpz_divexact (q, a, d); 110} 111