computable 0.1.0

Computable real numbers with guaranteed correctness via interval refinement
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
149
150
151
152
153
154
155
156

mod common;

use criterion::{Criterion, black_box, criterion_group, criterion_main};
use num_bigint::BigInt;

use common::{bench_id, bench_id_named, epsilon, precision_bits, verbose};
use computable::{Binary, Computable, pi, pi_bounds_at_precision};

fn bench_pi_refinement(c: &mut Criterion) {
    let mut group = c.benchmark_group("pi/refinement");
    group.sample_size(10);

    for &bits in precision_bits() {
        let eps = epsilon(bits);

        if verbose() {
            let bounds = pi()
                .refine_to_default(eps)
                .expect("pi refinement should succeed");
            eprintln!("[pi/refinement/{bits}] width: {}", bounds.width());
        }

        group.bench_with_input(bench_id(bits), &eps, |b, eps| {
            b.iter(|| {
                black_box(
                    pi().refine_to_default(*eps)
                        .expect("pi refinement should succeed"),
                )
            })
        });
    }

    group.finish();
}

/// Note: unlike other benchmarks where the parameter is an epsilon (2^-bits),
/// here it is passed directly to `pi_bounds_at_precision` as the number of bits
/// of precision to compute via Machin's formula (single-shot, no iterative
/// refinement). The values are the same sweep but the interpretation differs.
fn bench_pi_bounds_at_precision(c: &mut Criterion) {
    let mut group = c.benchmark_group("pi/bounds_at_precision");
    group.sample_size(10);

    for &bits in precision_bits() {
        if verbose() {
            let (lower, upper) = pi_bounds_at_precision(bits);
            eprintln!(
                "[pi/bounds_at_precision/{bits}] width: {}",
                upper.sub(&lower)
            );
        }

        group.bench_with_input(bench_id(bits), &bits, |b, &bits| {
            b.iter(|| black_box(pi_bounds_at_precision(bits)))
        });
    }

    group.finish();
}

fn bench_pi_arithmetic(c: &mut Criterion) {
    let mut group = c.benchmark_group("pi/arithmetic");
    group.sample_size(10);

    for &bits in precision_bits() {
        let eps = epsilon(bits);

        group.bench_with_input(bench_id_named("2pi", bits), &eps, |b, eps| {
            b.iter(|| {
                let two = Computable::constant(Binary::new(BigInt::from(2), BigInt::from(0)));
                black_box(
                    (two * pi())
                        .refine_to_default(*eps)
                        .expect("2pi should succeed"),
                )
            })
        });

        group.bench_with_input(bench_id_named("pi_half", bits), &eps, |b, eps| {
            b.iter(|| {
                let half = Computable::constant(Binary::new(BigInt::from(1), BigInt::from(-1)));
                black_box(
                    (half * pi())
                        .refine_to_default(*eps)
                        .expect("pi/2 should succeed"),
                )
            })
        });

        group.bench_with_input(bench_id_named("pi_sq", bits), &eps, |b, eps| {
            b.iter(|| {
                black_box(
                    (pi() * pi())
                        .refine_to_default(*eps)
                        .expect("pi^2 should succeed"),
                )
            })
        });

        group.bench_with_input(bench_id_named("inv_pi", bits), &eps, |b, eps| {
            b.iter(|| {
                black_box(
                    pi().inv()
                        .refine_to_default(*eps)
                        .expect("1/pi should succeed"),
                )
            })
        });
    }

    group.finish();
}

fn bench_sin_pi(c: &mut Criterion) {
    let mut group = c.benchmark_group("pi/sin_multiples");
    group.sample_size(10);

    for &bits in precision_bits() {
        let eps = epsilon(bits);

        for &multiplier in &[1u64, 2, 10, 100] {
            group.bench_with_input(
                bench_id_named(format!("mul_{multiplier}"), bits),
                &eps,
                |b, eps| {
                    b.iter(|| {
                        let n_pi = if multiplier == 1 {
                            pi()
                        } else {
                            Computable::constant(Binary::new(
                                BigInt::from(multiplier),
                                BigInt::from(0),
                            )) * pi()
                        };
                        black_box(
                            n_pi.sin()
                                .refine_to_default(*eps)
                                .expect("sin(n*pi) should succeed"),
                        )
                    })
                },
            );
        }
    }

    group.finish();
}

criterion_group!(
    benches,
    bench_pi_refinement,
    bench_pi_bounds_at_precision,
    bench_pi_arithmetic,
    bench_sin_pi,
);
criterion_main!(benches);