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

//! Decodes a floating-point value into individual parts and error ranges.

use crate::num::dec2flt::float::RawFloat;
use crate::num::FpCategory;

/// Decoded unsigned finite value, such that:
///
/// - The original value equals to `mant * 2^exp`.
///
/// - Any number from `(mant - minus) * 2^exp` to `(mant + plus) * 2^exp` will
///   round to the original value. The range is inclusive only when
///   `inclusive` is `true`.
#[derive(Copy, Clone, Debug, PartialEq, Eq)]
pub struct Decoded {
    /// The scaled mantissa.
    pub mant: u64,
    /// The lower error range.
    pub minus: u64,
    /// The upper error range.
    pub plus: u64,
    /// The shared exponent in base 2.
    pub exp: i16,
    /// True when the error range is inclusive.
    ///
    /// In IEEE 754, this is true when the original mantissa was even.
    pub inclusive: bool,
}

/// Decoded unsigned value.
#[derive(Copy, Clone, Debug, PartialEq, Eq)]
pub enum FullDecoded {
    /// Not-a-number.
    Nan,
    /// Infinities, either positive or negative.
    Infinite,
    /// Zero, either positive or negative.
    Zero,
    /// Finite numbers with further decoded fields.
    Finite(Decoded),
}

/// A floating point type which can be `decode`d.
pub trait DecodableFloat: RawFloat + Copy {
    /// The minimum positive normalized value.
    fn min_pos_norm_value() -> Self;
}

impl DecodableFloat for f32 {
    fn min_pos_norm_value() -> Self {
        f32::MIN_POSITIVE
    }
}

impl DecodableFloat for f64 {
    fn min_pos_norm_value() -> Self {
        f64::MIN_POSITIVE
    }
}

/// Returns a sign (true when negative) and `FullDecoded` value
/// from given floating point number.
pub fn decode<T: DecodableFloat>(v: T) -> (/*negative?*/ bool, FullDecoded) {
    let (mant, exp, sign) = v.integer_decode();
    let even = (mant & 1) == 0;
    let decoded = match v.classify() {
        FpCategory::Nan => FullDecoded::Nan,
        FpCategory::Infinite => FullDecoded::Infinite,
        FpCategory::Zero => FullDecoded::Zero,
        FpCategory::Subnormal => {
            // neighbors: (mant - 2, exp) -- (mant, exp) -- (mant + 2, exp)
            // Float::integer_decode always preserves the exponent,
            // so the mantissa is scaled for subnormals.
            FullDecoded::Finite(Decoded { mant, minus: 1, plus: 1, exp, inclusive: even })
        }
        FpCategory::Normal => {
            let minnorm = <T as DecodableFloat>::min_pos_norm_value().integer_decode();
            if mant == minnorm.0 {
                // neighbors: (maxmant, exp - 1) -- (minnormmant, exp) -- (minnormmant + 1, exp)
                // where maxmant = minnormmant * 2 - 1
                FullDecoded::Finite(Decoded {
                    mant: mant << 2,
                    minus: 1,
                    plus: 2,
                    exp: exp - 2,
                    inclusive: even,
                })
            } else {
                // neighbors: (mant - 1, exp) -- (mant, exp) -- (mant + 1, exp)
                FullDecoded::Finite(Decoded {
                    mant: mant << 1,
                    minus: 1,
                    plus: 1,
                    exp: exp - 1,
                    inclusive: even,
                })
            }
        }
    };
    (sign < 0, decoded)
}