1 /* gcd_lehmer.c. 2 3 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY 4 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 5 GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE. 6 7 Copyright 2003, 2004, 2005, 2008 Free Software Foundation, Inc. 8 9 This file is part of the GNU MP Library. 10 11 The GNU MP Library is free software; you can redistribute it and/or modify 12 it under the terms of the GNU Lesser General Public License as published by 13 the Free Software Foundation; either version 3 of the License, or (at your 14 option) any later version. 15 16 The GNU MP Library is distributed in the hope that it will be useful, but 17 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 18 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 19 License for more details. 20 21 You should have received a copy of the GNU Lesser General Public License 22 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 23 24 #include "gmp.h" 25 #include "gmp-impl.h" 26 #include "longlong.h" 27 28 /* Use binary algorithm to compute G <-- GCD (U, V) for usize, vsize == 2. 29 Both U and V must be odd. */ 30 static inline mp_size_t 31 gcd_2 (mp_ptr gp, mp_srcptr up, mp_srcptr vp) 32 { 33 mp_limb_t u0, u1, v0, v1; 34 mp_size_t gn; 35 36 u0 = up[0]; 37 u1 = up[1]; 38 v0 = vp[0]; 39 v1 = vp[1]; 40 41 ASSERT (u0 & 1); 42 ASSERT (v0 & 1); 43 44 /* Check for u0 != v0 needed to ensure that argument to 45 * count_trailing_zeros is non-zero. */ 46 while (u1 != v1 && u0 != v0) 47 { 48 unsigned long int r; 49 if (u1 > v1) 50 { 51 u1 -= v1 + (u0 < v0); 52 u0 = (u0 - v0) & GMP_NUMB_MASK; 53 count_trailing_zeros (r, u0); 54 u0 = ((u1 << (GMP_NUMB_BITS - r)) & GMP_NUMB_MASK) | (u0 >> r); 55 u1 >>= r; 56 } 57 else /* u1 < v1. */ 58 { 59 v1 -= u1 + (v0 < u0); 60 v0 = (v0 - u0) & GMP_NUMB_MASK; 61 count_trailing_zeros (r, v0); 62 v0 = ((v1 << (GMP_NUMB_BITS - r)) & GMP_NUMB_MASK) | (v0 >> r); 63 v1 >>= r; 64 } 65 } 66 67 gp[0] = u0, gp[1] = u1, gn = 1 + (u1 != 0); 68 69 /* If U == V == GCD, done. Otherwise, compute GCD (V, |U - V|). */ 70 if (u1 == v1 && u0 == v0) 71 return gn; 72 73 v0 = (u0 == v0) ? ((u1 > v1) ? u1-v1 : v1-u1) : ((u0 > v0) ? u0-v0 : v0-u0); 74 gp[0] = mpn_gcd_1 (gp, gn, v0); 75 76 return 1; 77 } 78 79 /* Temporary storage: n */ 80 mp_size_t 81 mpn_gcd_lehmer_n (mp_ptr gp, mp_ptr ap, mp_ptr bp, mp_size_t n, mp_ptr tp) 82 { 83 /* Relax this requirement, and normalize at the start? Must disallow 84 A = B = 0, though. */ 85 ASSERT(ap[n-1] > 0 || bp[n-1] > 0); 86 87 while (n > 2) 88 { 89 struct hgcd_matrix1 M; 90 mp_limb_t ah, al, bh, bl; 91 mp_limb_t mask; 92 93 mask = ap[n-1] | bp[n-1]; 94 ASSERT (mask > 0); 95 96 if (mask & GMP_NUMB_HIGHBIT) 97 { 98 ah = ap[n-1]; al = ap[n-2]; 99 bh = bp[n-1]; bl = bp[n-2]; 100 } 101 else 102 { 103 int shift; 104 105 count_leading_zeros (shift, mask); 106 ah = MPN_EXTRACT_NUMB (shift, ap[n-1], ap[n-2]); 107 al = MPN_EXTRACT_NUMB (shift, ap[n-2], ap[n-3]); 108 bh = MPN_EXTRACT_NUMB (shift, bp[n-1], bp[n-2]); 109 bl = MPN_EXTRACT_NUMB (shift, bp[n-2], bp[n-3]); 110 } 111 112 /* Try an mpn_nhgcd2 step */ 113 if (mpn_hgcd2 (ah, al, bh, bl, &M)) 114 { 115 n = mpn_hgcd_mul_matrix1_inverse_vector (&M, tp, ap, bp, n); 116 MP_PTR_SWAP (ap, tp); 117 } 118 else 119 { 120 /* mpn_hgcd2 has failed. Then either one of a or b is very 121 small, or the difference is very small. Perform one 122 subtraction followed by one division. */ 123 mp_size_t gn; 124 125 /* Temporary storage n */ 126 n = mpn_gcd_subdiv_step (gp, &gn, ap, bp, n, tp); 127 if (n == 0) 128 return gn; 129 } 130 } 131 132 if (n == 1) 133 { 134 *gp = mpn_gcd_1(ap, 1, bp[0]); 135 return 1; 136 } 137 138 /* Due to the calling convention for mpn_gcd, at most one can be 139 even. */ 140 141 if (! (ap[0] & 1)) 142 MP_PTR_SWAP (ap, bp); 143 144 ASSERT (ap[0] & 1); 145 146 if (bp[0] == 0) 147 { 148 *gp = mpn_gcd_1 (ap, 2, bp[1]); 149 return 1; 150 } 151 else if (! (bp[0] & 1)) 152 { 153 int r; 154 count_trailing_zeros (r, bp[0]); 155 bp[0] = ((bp[1] << (GMP_NUMB_BITS - r)) & GMP_NUMB_MASK) | (bp[0] >> r); 156 bp[1] >>= r; 157 } 158 159 return gcd_2(gp, ap, bp); 160 } 161