1//! Decodes a floating-point value into individual parts and error ranges.
2
3use crate::num::FpCategory;
4use crate::num::dec2flt::float::RawFloat;
5
6/// Decoded unsigned finite value, such that:
7///
8/// - The original value equals to `mant * 2^exp`.
9///
10/// - Any number from `(mant - minus) * 2^exp` to `(mant + plus) * 2^exp` will
11/// round to the original value. The range is inclusive only when
12/// `inclusive` is `true`.
13#[derive(Copy, Clone, Debug, PartialEq, Eq)]
14pub struct Decoded {
15 /// The scaled mantissa.
16 pub mant: u64,
17 /// The lower error range.
18 pub minus: u64,
19 /// The upper error range.
20 pub plus: u64,
21 /// The shared exponent in base 2.
22 pub exp: i16,
23 /// True when the error range is inclusive.
24 ///
25 /// In IEEE 754, this is true when the original mantissa was even.
26 pub inclusive: bool,
27}
28
29/// Decoded unsigned value.
30#[derive(Copy, Clone, Debug, PartialEq, Eq)]
31pub enum FullDecoded {
32 /// Not-a-number.
33 Nan,
34 /// Infinities, either positive or negative.
35 Infinite,
36 /// Zero, either positive or negative.
37 Zero,
38 /// Finite numbers with further decoded fields.
39 Finite(Decoded),
40}
41
42/// A floating point type which can be `decode`d.
43pub trait DecodableFloat: RawFloat + Copy {
44 /// The minimum positive normalized value.
45 fn min_pos_norm_value() -> Self;
46}
47
48impl DecodableFloat for f32 {
49 fn min_pos_norm_value() -> Self {
50 f32::MIN_POSITIVE
51 }
52}
53
54impl DecodableFloat for f64 {
55 fn min_pos_norm_value() -> Self {
56 f64::MIN_POSITIVE
57 }
58}
59
60/// Returns a sign (true when negative) and `FullDecoded` value
61/// from given floating point number.
62pub fn decode<T: DecodableFloat>(v: T) -> (/*negative?*/ bool, FullDecoded) {
63 let (mant, exp, sign) = v.integer_decode();
64 let even = (mant & 1) == 0;
65 let decoded = match v.classify() {
66 FpCategory::Nan => FullDecoded::Nan,
67 FpCategory::Infinite => FullDecoded::Infinite,
68 FpCategory::Zero => FullDecoded::Zero,
69 FpCategory::Subnormal => {
70 // neighbors: (mant - 2, exp) -- (mant, exp) -- (mant + 2, exp)
71 // Float::integer_decode always preserves the exponent,
72 // so the mantissa is scaled for subnormals.
73 FullDecoded::Finite(Decoded { mant, minus: 1, plus: 1, exp, inclusive: even })
74 }
75 FpCategory::Normal => {
76 let minnorm = <T as DecodableFloat>::min_pos_norm_value().integer_decode();
77 if mant == minnorm.0 {
78 // neighbors: (maxmant, exp - 1) -- (minnormmant, exp) -- (minnormmant + 1, exp)
79 // where maxmant = minnormmant * 2 - 1
80 FullDecoded::Finite(Decoded {
81 mant: mant << 2,
82 minus: 1,
83 plus: 2,
84 exp: exp - 2,
85 inclusive: even,
86 })
87 } else {
88 // neighbors: (mant - 1, exp) -- (mant, exp) -- (mant + 1, exp)
89 FullDecoded::Finite(Decoded {
90 mant: mant << 1,
91 minus: 1,
92 plus: 1,
93 exp: exp - 1,
94 inclusive: even,
95 })
96 }
97 }
98 };
99 (sign < 0, decoded)
100}
101