1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
|
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/**
* Copyright: Eugene Wissner 2016.
* License: $(LINK2 https://www.mozilla.org/en-US/MPL/2.0/,
* Mozilla Public License, v. 2.0).
* Authors: $(LINK2 mailto:belka@caraus.de, Eugene Wissner)
*/
module tanya.container.math;
version (unittest)
{
import std.algorithm.iteration;
}
@nogc:
/**
* Computes $(D_PARAM x) to the power $(D_PARAM y) modulo $(D_PARAM z).
*
* Params:
* x = Base.
* y = Exponent.
* z = Divisor.
*
* Returns: Reminder of the division of $(D_PARAM x) to the power $(D_PARAM y)
* by $(D_PARAM z).
*/
ulong pow(ulong x, ulong y, ulong z) @safe nothrow pure
in
{
assert(z > 0);
}
out (result)
{
assert(result >= 0);
}
body
{
ulong mask = ulong.max / 2 + 1, result;
if (y == 0)
{
return 1 % z;
}
else if (y == 1)
{
return x % z;
}
do
{
auto bit = y & mask;
if (!result && bit)
{
result = x;
continue;
}
result *= result;
if (bit)
{
result *= x;
}
result %= z;
}
while (mask >>= 1);
return result;
}
///
unittest
{
assert(pow(3, 5, 7) == 5);
assert(pow(2, 2, 1) == 0);
assert(pow(3, 3, 3) == 0);
assert(pow(7, 4, 2) == 1);
assert(pow(53, 0, 2) == 1);
assert(pow(53, 1, 3) == 2);
assert(pow(53, 2, 5) == 4);
assert(pow(0, 0, 5) == 1);
assert(pow(0, 5, 5) == 0);
}
/**
* Checks if $(D_PARAM x) is a prime.
*
* Params:
* x = The number should be checked.
*
* Returns: $(D_KEYWORD true) if $(D_PARAM x) is a prime number,
* $(D_KEYWORD false) otherwise.
*/
bool isPseudoprime(ulong x) @safe nothrow pure
{
return pow(2, x - 1, x) == 1;
}
///
unittest
{
uint[30] known = [74623, 74653, 74687, 74699, 74707, 74713, 74717, 74719,
74843, 74747, 74759, 74761, 74771, 74779, 74797, 74821,
74827, 9973, 104729, 15485867, 49979693, 104395303,
593441861, 104729, 15485867, 49979693, 104395303,
593441861, 899809363, 982451653];
known.each!((ref x) => assert(isPseudoprime(x)));
}
|
