root/trunk/etc/bigint/gcd.d

Revision 13, 3.1 kB (checked in by Arcane Jill, 5 years ago)

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1 module etc.bigint.gcd;
2 import etc.bigint.bigint_int;
3
4 /*
5
6 Copyright (c) 2004, Arcane Jill
7
8 All rights reserved. Intellectual Property Me Arse!
9
10 Redistribution and use in source and binary forms, with or without modification, are permitted
11 provided that the following conditions are met:
12
13    * Redistributions of source code must retain the above copyright notice, the phrase
14      "Intellectual Property Me Arse!", this list of conditions, and the following disclaimer.
15    * Redistributions in binary form must reproduce the above copyright notice, the phrase
16      "Intellectual Property Me Arse!", this list of conditions and the following disclaimer
17      in the documentation and/or other materials provided with the distribution.
18    * The name Arcane Jill may not be used to endorse or promote products derived from this
19      software without specific prior written permission.
20
21 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS
22 OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
23 AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER,
24 OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
25 CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
26 SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED, AND ON ANY
27 THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
28 OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
29 OF SUCH DAMAGE.
30
31 */
32
33 /*  ------------------------------------------------------------------------------------
34     Returns the lowest common multiple of a and b
35 */
36 Int lcm(Int a, Int b)
37 {
38     return (a * b) / gcd(a,b);
39 }
40
41 /*  ------------------------------------------------------------------------------------
42     Returns the greatest common divisor of a and b
43 */
44 Int gcd(Int a, Int b)
45 in
46 {
47     assert(a.positive);
48     assert(b.positive);
49 }
50 out(d)
51 {
52     Int x;
53     Int y;
54     assert(d == gcd(a, b, x, y));
55 }
56 body
57 {
58     uint i = ge2(a);
59     uint j = ge2(b);
60     if (i > j) i = j;
61     Int u = a >> i;
62     Int v = b >> i;
63     while (!u.equalsZero())
64     {
65         u = u >> ge2(u);
66         v = v >> ge2(v);
67         if (u >= v) u = u - v;
68         else        v = v - u;
69     }
70     return v << i;
71 }
72
73 /*  ------------------------------------------------------------------------------------
74     Returns the greatest common divisor, d, of a and b
75     and also integers x and y such that a*x + b*y == d
76
77     Note. As currently implemented, this is MUCH slower than gcd()
78     because of the expensive call to divMod.
79 */
80
81 Int gcd(Int a, Int b, out Int x, out Int y)
82 in
83 {
84     assert(a > 0);
85     assert(b > 0);
86 }
87 out(d)
88 {
89     assert(a*x + b*y == d);
90 }
91 body
92 {
93     if (a > b) return gcd(b, a, y, x);
94     Int u = a;
95     Int v = b;
96     Int x1 = Int.ONE;
97     Int y1 = Int.ZERO;
98     Int x2 = Int.ZERO;
99     Int y2 = Int.ONE;
100     while (!u.equalsZero)
101     {
102         Int r;
103         Int q = divMod(v, u, r);
104         x = x2 - q * x1;
105         y = y2 - q * y1;
106         v = u;
107         u = r;
108         x2 = x1;
109         x1 = x;
110         y2 = y1;
111         y1 = y;
112     }
113     x = x2;
114     y = y2;
115     return v;
116 }
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