1 /* mpz/gcd.c: Calculate the greatest common divisor of two integers.
2
3 Copyright 1991, 1993, 1994, 1996, 2000, 2001, 2002, 2005 Free Software
4 Foundation, Inc.
5
6 This file is part of the GNU MP Library.
7
8 The GNU MP Library is free software; you can redistribute it and/or modify
9 it under the terms of the GNU Lesser General Public License as published by
10 the Free Software Foundation; either version 3 of the License, or (at your
11 option) any later version.
12
13 The GNU MP Library is distributed in the hope that it will be useful, but
14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16 License for more details.
17
18 You should have received a copy of the GNU Lesser General Public License
19 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
20
21 #include "gmp.h"
22 #include "gmp-impl.h"
23 #include "longlong.h"
24 #ifdef BERKELEY_MP
25 #include "mp.h"
26 #endif
27
28
29 void
30 #ifndef BERKELEY_MP
mpz_gcd(mpz_ptr g,mpz_srcptr u,mpz_srcptr v)31 mpz_gcd (mpz_ptr g, mpz_srcptr u, mpz_srcptr v)
32 #else /* BERKELEY_MP */
33 gcd (mpz_srcptr u, mpz_srcptr v, mpz_ptr g)
34 #endif /* BERKELEY_MP */
35 {
36 unsigned long int g_zero_bits, u_zero_bits, v_zero_bits;
37 mp_size_t g_zero_limbs, u_zero_limbs, v_zero_limbs;
38 mp_ptr tp;
39 mp_ptr up = u->_mp_d;
40 mp_size_t usize = ABS (u->_mp_size);
41 mp_ptr vp = v->_mp_d;
42 mp_size_t vsize = ABS (v->_mp_size);
43 mp_size_t gsize;
44 TMP_DECL;
45
46 /* GCD(0, V) == V. */
47 if (usize == 0)
48 {
49 g->_mp_size = vsize;
50 if (g == v)
51 return;
52 if (g->_mp_alloc < vsize)
53 _mpz_realloc (g, vsize);
54 MPN_COPY (g->_mp_d, vp, vsize);
55 return;
56 }
57
58 /* GCD(U, 0) == U. */
59 if (vsize == 0)
60 {
61 g->_mp_size = usize;
62 if (g == u)
63 return;
64 if (g->_mp_alloc < usize)
65 _mpz_realloc (g, usize);
66 MPN_COPY (g->_mp_d, up, usize);
67 return;
68 }
69
70 if (usize == 1)
71 {
72 g->_mp_size = 1;
73 g->_mp_d[0] = mpn_gcd_1 (vp, vsize, up[0]);
74 return;
75 }
76
77 if (vsize == 1)
78 {
79 g->_mp_size = 1;
80 g->_mp_d[0] = mpn_gcd_1 (up, usize, vp[0]);
81 return;
82 }
83
84 TMP_MARK;
85
86 /* Eliminate low zero bits from U and V and move to temporary storage. */
87 while (*up == 0)
88 up++;
89 u_zero_limbs = up - u->_mp_d;
90 usize -= u_zero_limbs;
91 count_trailing_zeros (u_zero_bits, *up);
92 tp = up;
93 up = TMP_ALLOC_LIMBS (usize);
94 if (u_zero_bits != 0)
95 {
96 mpn_rshift (up, tp, usize, u_zero_bits);
97 usize -= up[usize - 1] == 0;
98 }
99 else
100 MPN_COPY (up, tp, usize);
101
102 while (*vp == 0)
103 vp++;
104 v_zero_limbs = vp - v->_mp_d;
105 vsize -= v_zero_limbs;
106 count_trailing_zeros (v_zero_bits, *vp);
107 tp = vp;
108 vp = TMP_ALLOC_LIMBS (vsize);
109 if (v_zero_bits != 0)
110 {
111 mpn_rshift (vp, tp, vsize, v_zero_bits);
112 vsize -= vp[vsize - 1] == 0;
113 }
114 else
115 MPN_COPY (vp, tp, vsize);
116
117 if (u_zero_limbs > v_zero_limbs)
118 {
119 g_zero_limbs = v_zero_limbs;
120 g_zero_bits = v_zero_bits;
121 }
122 else if (u_zero_limbs < v_zero_limbs)
123 {
124 g_zero_limbs = u_zero_limbs;
125 g_zero_bits = u_zero_bits;
126 }
127 else /* Equal. */
128 {
129 g_zero_limbs = u_zero_limbs;
130 g_zero_bits = MIN (u_zero_bits, v_zero_bits);
131 }
132
133 /* Call mpn_gcd. The 2nd argument must not have more bits than the 1st. */
134 vsize = (usize < vsize || (usize == vsize && up[usize-1] < vp[vsize-1]))
135 ? mpn_gcd (vp, vp, vsize, up, usize)
136 : mpn_gcd (vp, up, usize, vp, vsize);
137
138 /* Here G <-- V << (g_zero_limbs*GMP_LIMB_BITS + g_zero_bits). */
139 gsize = vsize + g_zero_limbs;
140 if (g_zero_bits != 0)
141 {
142 mp_limb_t cy_limb;
143 gsize += (vp[vsize - 1] >> (GMP_NUMB_BITS - g_zero_bits)) != 0;
144 if (g->_mp_alloc < gsize)
145 _mpz_realloc (g, gsize);
146 MPN_ZERO (g->_mp_d, g_zero_limbs);
147
148 tp = g->_mp_d + g_zero_limbs;
149 cy_limb = mpn_lshift (tp, vp, vsize, g_zero_bits);
150 if (cy_limb != 0)
151 tp[vsize] = cy_limb;
152 }
153 else
154 {
155 if (g->_mp_alloc < gsize)
156 _mpz_realloc (g, gsize);
157 MPN_ZERO (g->_mp_d, g_zero_limbs);
158 MPN_COPY (g->_mp_d + g_zero_limbs, vp, vsize);
159 }
160
161 g->_mp_size = gsize;
162 TMP_FREE;
163 }
164