dashu-ratio 0.6.0

Arbitrary-precision rational math library for Rust. Provides RBig and a relaxed variant for fast computation, with small values inlined on the stack. Exact arithmetic, Diophantine approximation of floats, parsing and formatting in any base including repeating-decimal notation, and conversions to and from other dashu types. Optional serde, rand, num-traits, rkyv, and zeroize.
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
148

use dashu_base::{Approximation::*, Sign::*};
use dashu_ratio::RBig;

mod helper_macros;

#[test]
fn test_simplest_in() {
    assert_eq!(RBig::simplest_in(rbig!(0), rbig!(0)), rbig!(0));
    assert_eq!(RBig::simplest_in(rbig!(-1), rbig!(1)), rbig!(0));
    assert_eq!(RBig::simplest_in(rbig!(-1), rbig!(-1)), rbig!(-1));
    assert_eq!(RBig::simplest_in(rbig!(2 / 7), rbig!(2 / 9)), rbig!(1 / 4));
    assert_eq!(RBig::simplest_in(rbig!(-20 / 7), rbig!(-20 / 9)), rbig!(-5 / 2));
    assert_eq!(RBig::simplest_in(rbig!(5), rbig!(7)), rbig!(6));
    assert_eq!(RBig::simplest_in(rbig!(5), rbig!(6)), rbig!(11 / 2));
}

#[test]
fn test_simplest_from_f32() {
    assert_eq!(RBig::simplest_from_f32(0f32), Some(rbig!(0)));
    assert_eq!(RBig::simplest_from_f32(f32::INFINITY), None);
    assert_eq!(RBig::simplest_from_f32(f32::NEG_INFINITY), None);
    assert_eq!(RBig::simplest_from_f32(f32::NAN), None);

    let cases = [
        // (numerator, denominator)
        // NOTE: make sure each of these numbers fit in a f32
        (1i32, 1u32),
        (2, 1),
        (-3, 1),
        (1, 2),
        (-1, 3),
        (1, 4),
        (-1, 5),
        // convergents of pi
        (22, 7),
        (333, 106),
        (355, 113),
    ];
    for (num, den) in cases {
        let f = num as f32 / den as f32;
        assert_eq!(RBig::simplest_from_f32(f).unwrap(), RBig::from_parts(num.into(), den.into()));
    }
}

#[test]
fn test_simplest_from_f64() {
    assert_eq!(RBig::simplest_from_f64(0f64), Some(rbig!(0)));
    assert_eq!(RBig::simplest_from_f64(f64::INFINITY), None);
    assert_eq!(RBig::simplest_from_f64(f64::NEG_INFINITY), None);
    assert_eq!(RBig::simplest_from_f64(f64::NAN), None);

    let cases = [
        // (numerator, denominator)
        // NOTE: make sure each of these numbers fit in a f64
        (1i64, 1u64),
        (2, 1),
        (-3, 1),
        (1, 2),
        (-1, 3),
        (1, 4),
        (-1, 5),
        // convergents of pi
        (22, 7),
        (333, 106),
        (355, 113),
        (103993, 33102),
        (104348, 33215),
        (208341, 66317),
        (312689, 99532),
        (833719, 265381),
        (1146408, 364913),
        (4272943, 1360120),
        (5419351, 1725033),
        (80143857, 25510582),
        (165707065, 52746197),
        (245850922, 78256779),
    ];
    for (num, den) in cases {
        let f = num as f64 / den as f64;
        assert_eq!(RBig::simplest_from_f64(f).unwrap(), RBig::from_parts(num.into(), den.into()));
    }
}

#[test]
fn test_nearest() {
    // test trivial cases
    assert_eq!(rbig!(0).nearest(&ubig!(1)), Exact(rbig!(0)));
    assert_eq!(rbig!(1).nearest(&ubig!(2)), Exact(rbig!(1)));
    assert_eq!(rbig!(-1).nearest(&ubig!(3)), Exact(rbig!(-1)));

    // test general cases
    let test_cases = [
        // (value, limit, next down, next up, sign of nearest - value)
        (core::f64::consts::PI, 10u64, rbig!(25 / 8), rbig!(22 / 7), Positive),
        (core::f64::consts::PI, 100, rbig!(311 / 99), rbig!(22 / 7), Negative),
        (core::f64::consts::PI, 1000, rbig!(2818 / 897), rbig!(355 / 113), Positive),
        (core::f64::consts::PI, 10000, rbig!(31218 / 9937), rbig!(355 / 113), Positive),
        (
            core::f64::consts::PI,
            100000,
            rbig!(208341 / 66317),
            rbig!(312689 / 99532),
            Positive,
        ),
        (core::f64::consts::SQRT_2, 10, rbig!(7 / 5), rbig!(10 / 7), Negative),
        (core::f64::consts::SQRT_2, 100, rbig!(140 / 99), rbig!(99 / 70), Negative),
        (core::f64::consts::SQRT_2, 1000, rbig!(1393 / 985), rbig!(577 / 408), Negative),
        (
            core::f64::consts::SQRT_2,
            10000,
            rbig!(8119 / 5741),
            rbig!(11482 / 8119),
            Positive,
        ),
        (
            core::f64::consts::SQRT_2,
            100000,
            rbig!(47321 / 33461),
            rbig!(114243 / 80782),
            Positive,
        ),
    ];
    for (value, limit, down, up, cmp) in test_cases {
        let ratio: RBig = value.try_into().unwrap();
        assert_eq!(ratio.next_up(&limit.into()), up.clone());
        assert_eq!(ratio.next_down(&limit.into()), down.clone());
        if cmp == Positive {
            assert_eq!(ratio.nearest(&limit.into()), Inexact(up.clone(), cmp));
        } else {
            assert_eq!(ratio.nearest(&limit.into()), Inexact(down.clone(), cmp));
        }

        let ratio = -ratio;
        assert_eq!(ratio.next_down(&limit.into()), -up.clone());
        assert_eq!(ratio.next_up(&limit.into()), -down.clone());
        if cmp == Positive {
            assert_eq!(ratio.nearest(&limit.into()), Inexact(-up.clone(), -cmp));
        } else {
            assert_eq!(ratio.nearest(&limit.into()), Inexact(-down.clone(), -cmp));
        }
    }
}

#[test]
#[should_panic]
fn test_nearest_zero_limit() {
    let _ = rbig!(1 / 2).nearest(&ubig!(0));
}