-
Notifications
You must be signed in to change notification settings - Fork 0
/
MillerRabin.cs
148 lines (136 loc) · 4.17 KB
/
MillerRabin.cs
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
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
using System.Numerics;
namespace protohackers;
public class MillerRabin
{
/// <summary>
/// Implements the Miller-Rabin primality test algorithm from
/// https://en.wikipedia.org/wiki/Miller-Rabin_primality_test
/// </summary>
/// <param name="n"></param>
/// <param name="k"></param>
/// <returns></returns>
public static bool IsPrime(long n)
{
if (n % 2 == 0 || n < 4)
{
return n == 2 || n == 3;
}
long d = n - 1;
int s = 0;
while(d % 2 == 0)
{
d /= 2;
s++;
}
var rounds = GetRounds(n);
foreach (var a in rounds)
{
long x = ModPow(a, d, n);
if (x == 1 || x == n - 1)
{
continue;
}
for (int i2 = 0; i2 < s; i2++)
{
x = ((x * x) % n);
if (x == n - 1)
{
break;
}
}
if (x != n - 1)
{
return false;
}
}
return true;
}
/// <summary>
/// Implements the Miller-Rabin primality test algorithm from
/// https://en.wikipedia.org/wiki/Miller-Rabin_primality_test
/// </summary>
/// <param name="n"></param>
/// <param name="k"></param>
/// <returns></returns>
public static bool IsPrime(BigInteger n)
{
if (BigInteger.Remainder(n, 2) == 0 || n < 4)
{
return n == 2 || n == 3;
}
BigInteger d = BigInteger.Subtract(n, 1);
int s = 0;
while(BigInteger.Remainder(d, 2) == 0)
{
d = BigInteger.Divide(d, 2);
s++;
}
var rounds = GetRounds(n);
foreach (var a in rounds)
{
BigInteger x = BigInteger.ModPow(a, d, n);
if (x == 1 || x.CompareTo(BigInteger.Subtract(n, 1)) == 0)
{
continue;
}
for (int i2 = 0; i2 < s; i2++)
{
x = BigInteger.Remainder(BigInteger.Multiply(x, x), n);
if (x.CompareTo(BigInteger.Subtract(n, 1)) == 0)
{
break;
}
}
if (x.CompareTo(BigInteger.Subtract(n, 1)) != 0)
{
return false;
}
}
return true;
}
private static long[] GetRounds(long n) => n switch
{
< 2047 => new long[] { 2 },
< 1373653 => new long[] { 2, 3 },
< 9080191 => new long[] { 31, 73 },
< 25326001 => new long[] { 2, 3, 5 },
< 3215031751 => new long[] { 2, 3, 5, 7 },
< 4759123141 => new long[] { 2, 7, 61 },
< 1122004669633 => new long[] { 2, 13, 23, 1662803 },
< 2152302898747 => new long[] { 2, 3, 5, 7, 11 },
< 3474749660383 => new long[] { 2, 3, 5, 7, 11, 13 },
< 341550071728321 => new long[] { 2, 3, 5, 7, 11, 13, 17 },
< 3825123056546413051 => new long[] { 2, 3, 5, 7, 11, 13, 17, 19 },
_ => new long[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 }
};
private static BigInteger[] GetRounds(BigInteger n)
{
if (n.CompareTo(BigInteger.Parse("318665857834031151167461")) < 0)
{
return new BigInteger[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 };
}
if (n.CompareTo(BigInteger.Parse("3317044064679887385961981")) < 0)
{
return new BigInteger[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41 };
}
var rounds = new BigInteger[20];
for (int i = 0; i < 20; i++)
{
rounds[i] = RandomInteger.Next(2, BigInteger.Subtract(n, 2));
}
return rounds;
}
// https://stackoverflow.com/a/5434148/2015348
// https://gist.github.com/bbarry/1068d17b49b0ff98bca5194d275896ed
private static long ModPow(long value, long exponent, long modulus)
{
long result = 1;
while (exponent > 0)
{
if ((exponent & 1) == 1) result = result * value % modulus;
value = value * value % modulus;
exponent >>= 1;
}
return (uint)result;
}
}