librualg 0.29.1

Collection of basic algorithms for everyday development
Documentation 
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

use rand::Rng;

/// The Greatest Common Divisor (GCD)
///```
/// use librualg::math::gcd;
///
/// assert_eq!(gcd(24, 60), 12);
///
/// ```

pub fn gcd(a: u64, b: u64) -> u64{
    match (a, b) {
        (0, b) => b,
        (a, 0) => a,
        (a, b) if a > b => {
            gcd(a % b, b)
        }
        (a, b) => {
            gcd(a, b % a)
        }
    }
}

#[test]
fn test_gcd() {
    assert_eq!(gcd(24, 60), 12);
    assert_eq!(gcd(0, 7), 7);
    assert_eq!(gcd(3, 0), 3);
    assert_eq!(gcd(11, 11), 11);
    assert_eq!(gcd(0, 0), 0);
}

/// The function returns the value of x to the power of y.
///```
/// use librualg::math::pow;
///
/// assert_eq!(pow(2, 20), 1048576);
///
/// ```
pub fn pow(mut value: u64, mut n: u64) -> u64 {
    if n == 0 {
        return 1_u64;
    }
    let mut res = 1;
    while n > 0 {
        if n % 2 != 0 {
            res *= value;
            n -= 1;
        } else {
            value = value * value;
            n >>= 1;
        }
    }
    res
}

#[test]
fn test_pow() {
    assert_eq!(pow(1, 3), 1);
    assert_eq!(pow(0, 3), 0);
    assert_eq!(pow(2, 20), 1048576);
}

/// The function returns the value of x to the power of y by module.
///```
/// use librualg::math::pow_mod;
///
/// assert_eq!(pow_mod(5, 100, 7), 2);
///
/// ```
pub fn pow_mod(mut value: u64, mut n: u64, m: u64) -> u64 {
    if n == 0 {
        return 1_u64;
    }
    let mut res = 1;
    while n > 0 {
        if n % 2 != 0 {
            res = (res * value) % m;
            n -= 1;
        } else {
            value = (value * value) % m;
            n >>= 1;
        }
    }
    res
}

#[test]
fn test_pow_mod() {
    assert_eq!(pow_mod(5, 100, 7), 2);
    assert_eq!(pow_mod(3, 90, 5), 4);
}

/// Checking a Number for Simplicity (Fermat's test)
///```
/// use librualg::math::is_simple;
///
/// assert_eq!(is_simple(157), true);
/// assert_eq!(is_simple(8505), false);
///
/// ```
pub fn is_simple(value: u64) -> bool {
    if value == 2 {
        return true;
    }
    let mut rng = rand::thread_rng();
    for _ in 0..100 {
        let a = rng.gen_range(1, u64::MAX) % (value - 2) + 2;
        if gcd(a, value) != 1 {
            return false;
        }
        if pow_mod(a, value - 1, value) != 1 {
            return false;
        }
    }
    true
}

#[test]
fn test_is_simple() {

    fn generate_simple_numbers(max_value: u64) -> Vec<u64> {
        let mut src = vec![true; max_value as usize + 1];
        let mut dst = Vec::new();
        for i in 2 .. max_value as usize + 1 {
            if src[i] {
                let mut ind = i * i;
                while ind <= max_value as usize {
                    src[ind] = false;
                    ind += i;
                }
                dst.push(i as u64);
            }
        }
        dst
    }

    for value in generate_simple_numbers(1000000) {
        assert_eq!(is_simple(value), true);
    }
    assert_eq!(is_simple(10), false);
    assert_eq!(is_simple(169), false);
    assert_eq!(is_simple(8505), false);
    assert_eq!(is_simple(83521), false);
    assert_eq!(is_simple(34012224), false);
    assert_eq!(is_simple(39916800), false);
}