1 /* mpz/gcd.c: Calculate the greatest common divisor of two integers.
2
3 Copyright 1991, 1993, 1994, 1996, 2000-2002, 2005, 2010, 2015, 2016
4 Free Software 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 either:
10
11 * the GNU Lesser General Public License as published by the Free
12 Software Foundation; either version 3 of the License, or (at your
13 option) any later version.
14
15 or
16
17 * the GNU General Public License as published by the Free Software
18 Foundation; either version 2 of the License, or (at your option) any
19 later version.
20
21 or both in parallel, as here.
22
23 The GNU MP Library is distributed in the hope that it will be useful, but
24 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
25 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
26 for more details.
27
28 You should have received copies of the GNU General Public License and the
29 GNU Lesser General Public License along with the GNU MP Library. If not,
30 see https://www.gnu.org/licenses/. */
31
32 #include "gmp-impl.h"
33 #include "longlong.h"
34
35
36 void
mpz_gcd(mpz_ptr g,mpz_srcptr u,mpz_srcptr v)37 mpz_gcd (mpz_ptr g, mpz_srcptr u, mpz_srcptr v)
38 {
39 unsigned long int g_zero_bits, u_zero_bits, v_zero_bits;
40 mp_size_t g_zero_limbs, u_zero_limbs, v_zero_limbs;
41 mp_ptr tp;
42 mp_ptr up;
43 mp_size_t usize;
44 mp_ptr vp;
45 mp_size_t vsize;
46 mp_size_t gsize;
47 TMP_DECL;
48
49 up = PTR(u);
50 usize = ABSIZ (u);
51 vp = PTR(v);
52 vsize = ABSIZ (v);
53 /* GCD(0, V) == V. */
54 if (usize == 0)
55 {
56 SIZ (g) = vsize;
57 if (g == v)
58 return;
59 tp = MPZ_NEWALLOC (g, vsize);
60 MPN_COPY (tp, vp, vsize);
61 return;
62 }
63
64 /* GCD(U, 0) == U. */
65 if (vsize == 0)
66 {
67 SIZ (g) = usize;
68 if (g == u)
69 return;
70 tp = MPZ_NEWALLOC (g, usize);
71 MPN_COPY (tp, up, usize);
72 return;
73 }
74
75 if (usize == 1)
76 {
77 SIZ (g) = 1;
78 MPZ_NEWALLOC (g, 1)[0] = mpn_gcd_1 (vp, vsize, up[0]);
79 return;
80 }
81
82 if (vsize == 1)
83 {
84 SIZ(g) = 1;
85 MPZ_NEWALLOC (g, 1)[0] = mpn_gcd_1 (up, usize, vp[0]);
86 return;
87 }
88
89 TMP_MARK;
90
91 /* Eliminate low zero bits from U and V and move to temporary storage. */
92 tp = up;
93 while (*tp == 0)
94 tp++;
95 u_zero_limbs = tp - up;
96 usize -= u_zero_limbs;
97 count_trailing_zeros (u_zero_bits, *tp);
98 up = TMP_ALLOC_LIMBS (usize);
99 if (u_zero_bits != 0)
100 {
101 mpn_rshift (up, tp, usize, u_zero_bits);
102 usize -= up[usize - 1] == 0;
103 }
104 else
105 MPN_COPY (up, tp, usize);
106
107 tp = vp;
108 while (*tp == 0)
109 tp++;
110 v_zero_limbs = tp - vp;
111 vsize -= v_zero_limbs;
112 count_trailing_zeros (v_zero_bits, *tp);
113 vp = TMP_ALLOC_LIMBS (vsize);
114 if (v_zero_bits != 0)
115 {
116 mpn_rshift (vp, tp, vsize, v_zero_bits);
117 vsize -= vp[vsize - 1] == 0;
118 }
119 else
120 MPN_COPY (vp, tp, vsize);
121
122 if (u_zero_limbs > v_zero_limbs)
123 {
124 g_zero_limbs = v_zero_limbs;
125 g_zero_bits = v_zero_bits;
126 }
127 else
128 {
129 g_zero_limbs = u_zero_limbs;
130 if (u_zero_limbs < v_zero_limbs)
131 g_zero_bits = u_zero_bits;
132 else /* Equal. */
133 g_zero_bits = MIN (u_zero_bits, v_zero_bits);
134 }
135
136 /* Call mpn_gcd. The 2nd argument must not have more bits than the 1st. */
137 vsize = (usize < vsize || (usize == vsize && up[usize-1] < vp[vsize-1]))
138 ? mpn_gcd (vp, vp, vsize, up, usize)
139 : mpn_gcd (vp, up, usize, vp, vsize);
140
141 /* Here G <-- V << (g_zero_limbs*GMP_LIMB_BITS + g_zero_bits). */
142 gsize = vsize + g_zero_limbs;
143 if (g_zero_bits != 0)
144 {
145 mp_limb_t cy_limb;
146 gsize += (vp[vsize - 1] >> (GMP_NUMB_BITS - g_zero_bits)) != 0;
147 tp = MPZ_NEWALLOC (g, gsize);
148 MPN_ZERO (tp, g_zero_limbs);
149
150 tp = tp + g_zero_limbs;
151 cy_limb = mpn_lshift (tp, vp, vsize, g_zero_bits);
152 if (cy_limb != 0)
153 tp[vsize] = cy_limb;
154 }
155 else
156 {
157 tp = MPZ_NEWALLOC (g, gsize);
158 MPN_ZERO (tp, g_zero_limbs);
159 MPN_COPY (tp + g_zero_limbs, vp, vsize);
160 }
161
162 SIZ (g) = gsize;
163 TMP_FREE;
164 }
165