malachite-float 0.13.0

The arbitrary-precision floating-point type Float, with efficient algorithms partially derived from MPFR.
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

// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.

use crate::test_util::common::rug_float_significant_bits;
use core::cmp::Ordering;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_q::Rational;
use rug::float::Round;
use rug::ops::AssignRound;

pub fn rug_sin_prec_round(x: &rug::Float, prec: u64, rm: Round) -> (rug::Float, Ordering) {
    let mut s = rug::Float::with_val(u32::exact_from(prec), 0);
    let o = s.assign_round(x.sin_ref(), rm);
    (s, o)
}

pub fn rug_sin_prec(x: &rug::Float, prec: u64) -> (rug::Float, Ordering) {
    rug_sin_prec_round(x, prec, Round::Nearest)
}

pub fn rug_sin_round(x: &rug::Float, rm: Round) -> (rug::Float, Ordering) {
    rug_sin_prec_round(x, rug_float_significant_bits(x), rm)
}

pub fn rug_sin(x: &rug::Float) -> rug::Float {
    rug_sin_prec_round(x, rug_float_significant_bits(x), Round::Nearest).0
}

// Computes sin(x) for a Rational x, rounded to `prec` with mode `rm`. The Rational is first
// converted to a rug `Float` with `prec + 128` bits plus its exponent's and its denominator's worth
// of bits. Since sin(x) is close to x for small x, an input that is very close to a short dyadic
// (as a/b can be, to within about 1/b relative) must be carried precisely enough to stay on the
// right side of it, or the ternary value comes out wrong; the cosine oracle needs no such care.
pub fn rug_sin_rational_prec_round(x: &Rational, prec: u64, rm: Round) -> (rug::Float, Ordering) {
    let exponent_bits = if *x == 0u32 {
        0
    } else {
        x.floor_log_base_2_abs().unsigned_abs()
    };
    let denominator_bits = x.denominator_ref().significant_bits();
    let rx = rug::Float::with_val(
        u32::exact_from(prec + 128 + exponent_bits + denominator_bits),
        rug::Rational::exact_from(x),
    );
    let mut s = rug::Float::with_val(u32::exact_from(prec), 0);
    let o = s.assign_round(rx.sin_ref(), rm);
    (s, o)
}

pub fn rug_sin_rational_prec(x: &Rational, prec: u64) -> (rug::Float, Ordering) {
    rug_sin_rational_prec_round(x, prec, Round::Nearest)
}

// `u` must fit in a `u32`, the type rug takes.
pub fn rug_sin_with_period_prec_round(
    x: &rug::Float,
    u: u64,
    prec: u64,
    rm: Round,
) -> (rug::Float, Ordering) {
    let mut s = rug::Float::with_val(u32::exact_from(prec), 0);
    let o = s.assign_round(x.sin_u_ref(u32::exact_from(u)), rm);
    (s, o)
}

pub fn rug_sin_with_period_prec(x: &rug::Float, u: u64, prec: u64) -> (rug::Float, Ordering) {
    rug_sin_with_period_prec_round(x, u, prec, Round::Nearest)
}

// As for `rug_sin_rational_prec_round`, the input carries its denominator's worth of extra bits,
// since the sine of a fraction of a turn close to a short dyadic depends on that closeness.
pub fn rug_sin_with_period_rational_prec_round(
    x: &Rational,
    u: u64,
    prec: u64,
    rm: Round,
) -> (rug::Float, Ordering) {
    let exponent_bits = if *x == 0u32 {
        0
    } else {
        x.floor_log_base_2_abs().unsigned_abs()
    };
    let denominator_bits = x.denominator_ref().significant_bits();
    let rx = rug::Float::with_val(
        u32::exact_from(prec + 128 + exponent_bits + denominator_bits),
        rug::Rational::exact_from(x),
    );
    let mut s = rug::Float::with_val(u32::exact_from(prec), 0);
    let o = s.assign_round(rx.sin_u_ref(u32::exact_from(u)), rm);
    (s, o)
}

pub fn rug_sin_with_period_rational_prec(
    x: &Rational,
    u: u64,
    prec: u64,
) -> (rug::Float, Ordering) {
    rug_sin_with_period_rational_prec_round(x, u, prec, Round::Nearest)
}

pub fn rug_sin_pi_prec_round(x: &rug::Float, prec: u64, rm: Round) -> (rug::Float, Ordering) {
    let mut s = rug::Float::with_val(u32::exact_from(prec), 0);
    let o = s.assign_round(x.sin_pi_ref(), rm);
    (s, o)
}

pub fn rug_sin_pi_rational_prec_round(
    x: &Rational,
    prec: u64,
    rm: Round,
) -> (rug::Float, Ordering) {
    let exponent_bits = if *x == 0u32 {
        0
    } else {
        x.floor_log_base_2_abs().unsigned_abs()
    };
    let denominator_bits = x.denominator_ref().significant_bits();
    let rx = rug::Float::with_val(
        u32::exact_from(prec + 128 + exponent_bits + denominator_bits),
        rug::Rational::exact_from(x),
    );
    let mut s = rug::Float::with_val(u32::exact_from(prec), 0);
    let o = s.assign_round(rx.sin_pi_ref(), rm);
    (s, o)
}