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

// Copyright © 2024 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::natural::Natural;
use core::cmp::Ordering;
use malachite_base::named::Named;
use malachite_base::num::arithmetic::traits::DivisibleByPowerOf2;
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::conversion::traits::{
    ConvertibleFrom, ExactFrom, RawMantissaAndExponent, RoundingFrom, SciMantissaAndExponent,
    WrappingFrom,
};
use malachite_base::rounding_modes::RoundingMode;

#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub struct PrimitiveFloatFromNaturalError;

macro_rules! float_impls {
    ($f: ident) => {
        impl<'a> RoundingFrom<&'a Natural> for $f {
            /// Converts a [`Natural`] to a primitive float according to a specified
            /// [`RoundingMode`]. An [`Ordering`] is also returned, indicating whether the returned
            /// value is less than, equal to, or greater than the original value.
            ///
            /// - If the rounding mode is `Floor` or `Down`, the largest float less than or equal to
            ///   the [`Natural`] is returned. If the [`Natural`] is greater than the maximum finite
            ///   float, then the maximum finite float is returned.
            /// - If the rounding mode is `Ceiling` or `Up`, the smallest float greater than or
            ///   equal to the [`Natural`] is returned. If the [`Natural`] is greater than the
            ///   maximum finite float, then positive infinity is returned.
            /// - If the rounding mode is `Nearest`, then the nearest float is returned. If the
            ///   [`Natural`] is exactly between two floats, the float with the zero
            ///   least-significant bit in its representation is selected. If the [`Natural`] is
            ///   greater than the maximum finite float, then the maximum finite float is returned.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(1)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `value.significant_bits()`.
            ///
            /// # Panics
            /// Panics if the rounding mode is `Exact` and `value` cannot be represented exactly.
            ///
            /// # Examples
            /// See [here](super::primitive_float_from_natural#rounding_from).
            fn rounding_from(value: &'a Natural, rm: RoundingMode) -> ($f, Ordering) {
                if *value == 0 {
                    (0.0, Ordering::Equal)
                } else {
                    let (mantissa, exponent, o) = value
                        .sci_mantissa_and_exponent_round(rm)
                        .expect("Value cannot be represented exactly as a float");
                    if let Some(f) =
                        $f::from_sci_mantissa_and_exponent(mantissa, i64::exact_from(exponent))
                    {
                        (f, o)
                    } else {
                        match rm {
                            RoundingMode::Exact => {
                                panic!("Value cannot be represented exactly as an {}", $f::NAME)
                            }
                            RoundingMode::Floor | RoundingMode::Down | RoundingMode::Nearest => {
                                ($f::MAX_FINITE, Ordering::Less)
                            }
                            _ => ($f::INFINITY, Ordering::Greater),
                        }
                    }
                }
            }
        }

        impl<'a> TryFrom<&'a Natural> for $f {
            type Error = PrimitiveFloatFromNaturalError;

            /// Converts a [`Natural`] to a primitive float.
            ///
            /// If the input isn't exactly equal to some float, an error is returned.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(1)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `value.significant_bits()`.
            ///
            /// # Examples
            /// See [here](super::primitive_float_from_natural#try_from).
            fn try_from(value: &'a Natural) -> Result<$f, Self::Error> {
                if *value == 0 {
                    Ok(0.0)
                } else {
                    let (mantissa, exponent, _) = value
                        .sci_mantissa_and_exponent_round(RoundingMode::Exact)
                        .ok_or(PrimitiveFloatFromNaturalError)?;
                    $f::from_sci_mantissa_and_exponent(mantissa, i64::exact_from(exponent))
                        .ok_or(PrimitiveFloatFromNaturalError)
                }
            }
        }

        impl<'a> ConvertibleFrom<&'a Natural> for $f {
            /// Determines whether a [`Natural`] can be exactly converted to a primitive float.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(1)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `value.significant_bits()`.
            ///
            /// # Examples
            /// See [here](super::primitive_float_from_natural#convertible_from).
            fn convertible_from(value: &'a Natural) -> bool {
                if *value == 0 {
                    true
                } else {
                    if let Some((mantissa, exponent, _)) =
                        value.sci_mantissa_and_exponent_round::<$f>(RoundingMode::Exact)
                    {
                        let exponent = i64::exact_from(exponent);
                        if !($f::MIN_EXPONENT..=$f::MAX_EXPONENT).contains(&exponent) {
                            return false;
                        }
                        let (orig_mantissa, orig_exponent) = mantissa.raw_mantissa_and_exponent();
                        orig_exponent == u64::wrapping_from($f::MAX_EXPONENT)
                            && exponent >= $f::MIN_NORMAL_EXPONENT
                            || orig_mantissa.divisible_by_power_of_2(u64::wrapping_from(
                                $f::MIN_NORMAL_EXPONENT - exponent,
                            ))
                    } else {
                        false
                    }
                }
            }
        }
    };
}
apply_to_primitive_floats!(float_impls);