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

// 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_tan_prec_round(x: &rug::Float, prec: u64, rm: Round) -> (rug::Float, Ordering) {
    let mut t = rug::Float::with_val(u32::exact_from(prec), 0);
    let o = t.assign_round(x.tan_ref(), rm);
    (t, o)
}

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

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

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

// As for the sine oracle, the input carries its denominator's worth of extra bits: the tangent of a
// fraction close to a short dyadic depends on that closeness.
pub fn rug_tan_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),
    );
    rug_tan_prec_round(&rx, prec, rm)
}

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

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

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

// As for the other rational oracles, the input carries its denominator's worth of extra bits. `u`
// must fit in a `u32`, the type rug takes.
pub fn rug_tan_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),
    );
    rug_tan_with_period_prec_round(&rx, u, prec, rm)
}

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

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

pub fn rug_tan_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 t = rug::Float::with_val(u32::exact_from(prec), 0);
    let o = t.assign_round(rx.tan_pi_ref(), rm);
    (t, o)
}