maryada 0.1.1

No-std binary64 real interval arithmetic conforming to IEEE 1788.1
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
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202

use crate::{
    DecoratedInterval, Decoration, Interval,
    signals::{Signal, SignalSink},
};

/// Encoded length of a bare interval: two binary64 endpoints.
pub const INTERVAL_ENCODED_LEN: usize = 16;
/// Encoded length of a decorated interval: two endpoints and one decoration.
pub const DECORATED_INTERVAL_ENCODED_LEN: usize = 17;

const POSITIVE_INFINITY_BITS: u64 = 0x7ff0_0000_0000_0000;
const NEGATIVE_INFINITY_BITS: u64 = 0xfff0_0000_0000_0000;
const NEGATIVE_ZERO_BITS: u64 = 0x8000_0000_0000_0000;
const POSITIVE_ZERO_BITS: u64 = 0x0000_0000_0000_0000;
const CANONICAL_QUIET_NAN_BITS: u64 = 0x7ff8_0000_0000_0000;

// Level 4 export.

/// Encodes a bare interval using big-endian IEEE 754 endpoint bytes.
pub fn interval_to_be_bytes(x: Interval) -> [u8; INTERVAL_ENCODED_LEN] {
    let mut output = [0_u8; INTERVAL_ENCODED_LEN];
    output[..8].copy_from_slice(&x.inf_raw().to_be_bytes());
    output[8..].copy_from_slice(&x.sup_raw().to_be_bytes());
    output
}

/// Encodes a bare interval using little-endian IEEE 754 endpoint bytes.
pub fn interval_to_le_bytes(x: Interval) -> [u8; INTERVAL_ENCODED_LEN] {
    let mut output = [0_u8; INTERVAL_ENCODED_LEN];
    output[..8].copy_from_slice(&x.inf_raw().to_le_bytes());
    output[8..].copy_from_slice(&x.sup_raw().to_le_bytes());
    output
}

/// Encodes a decorated interval using big-endian endpoint bytes.
///
/// NaI is encoded with two canonical quiet NaNs and the `ill` decoration.
pub fn decorated_interval_to_be_bytes(
    x: DecoratedInterval,
) -> [u8; DECORATED_INTERVAL_ENCODED_LEN] {
    let mut output = [0_u8; DECORATED_INTERVAL_ENCODED_LEN];
    if x.is_nai_raw() {
        let nan = CANONICAL_QUIET_NAN_BITS.to_be_bytes();
        output[..8].copy_from_slice(&nan);
        output[8..16].copy_from_slice(&nan);
        output[16] = Decoration::Ill as u8;
        return output;
    }
    output[..16].copy_from_slice(&interval_to_be_bytes(x.interval_raw()));
    output[16] = x.decoration_raw() as u8;
    output
}

/// Encodes a decorated interval using little-endian endpoint bytes.
///
/// NaI is encoded with two canonical quiet NaNs and the `ill` decoration.
pub fn decorated_interval_to_le_bytes(
    x: DecoratedInterval,
) -> [u8; DECORATED_INTERVAL_ENCODED_LEN] {
    let mut output = [0_u8; DECORATED_INTERVAL_ENCODED_LEN];
    if x.is_nai_raw() {
        let nan = CANONICAL_QUIET_NAN_BITS.to_le_bytes();

        output[..8].copy_from_slice(&nan);
        output[8..16].copy_from_slice(&nan);
        output[16] = Decoration::Ill as u8;

        return output;
    }
    output[..16].copy_from_slice(&interval_to_le_bytes(x.interval_raw()));
    output[16] = x.decoration_raw() as u8;
    output
}

// Level 4 import with InvalidOperand signaling.

/// Decodes a big-endian bare interval.
///
/// Invalid length, bounds, NaNs, or noncanonical signed zeros raise
/// [`Signal::InvalidOperand`] and return the empty interval.
pub fn interval_from_be_bytes<S: SignalSink>(bytes: &[u8], signals: &mut S) -> Interval {
    match decode_interval(bytes, Endian::Big) {
        Some(value) => value,
        None => {
            signals.raise(Signal::InvalidOperand);
            Interval::EMPTY
        }
    }
}

/// Decodes a little-endian bare interval.
///
/// Invalid input raises [`Signal::InvalidOperand`] and returns the empty
/// interval.
pub fn interval_from_le_bytes<S: SignalSink>(bytes: &[u8], signals: &mut S) -> Interval {
    match decode_interval(bytes, Endian::Little) {
        Some(value) => value,
        None => {
            signals.raise(Signal::InvalidOperand);
            Interval::EMPTY
        }
    }
}

/// Decodes a big-endian decorated interval.
///
/// Invalid input raises [`Signal::InvalidOperand`] and returns NaI.
pub fn decorated_interval_from_be_bytes<S: SignalSink>(
    bytes: &[u8],
    signals: &mut S,
) -> DecoratedInterval {
    match decode_decorated(bytes, Endian::Big) {
        Some(value) => value,
        None => {
            signals.raise(Signal::InvalidOperand);
            DecoratedInterval::NAI
        }
    }
}

/// Decodes a little-endian decorated interval.
///
/// Invalid input raises [`Signal::InvalidOperand`] and returns NaI.
pub fn decorated_interval_from_le_bytes<S: SignalSink>(
    bytes: &[u8],
    signals: &mut S,
) -> DecoratedInterval {
    match decode_decorated(bytes, Endian::Little) {
        Some(value) => value,
        None => {
            signals.raise(Signal::InvalidOperand);
            DecoratedInterval::NAI
        }
    }
}

#[derive(Clone, Copy)]
enum Endian {
    Big,
    Little,
}

fn decode_interval(bytes: &[u8], endian: Endian) -> Option<Interval> {
    let bytes: &[u8; INTERVAL_ENCODED_LEN] = bytes.try_into().ok()?;
    let inf_bits = read_u64(&bytes[..8], endian)?;
    let sup_bits = read_u64(&bytes[8..], endian)?;
    decode_interval_bits(inf_bits, sup_bits)
}

fn decode_interval_bits(inf_bits: u64, sup_bits: u64) -> Option<Interval> {
    if inf_bits == POSITIVE_INFINITY_BITS && sup_bits == NEGATIVE_INFINITY_BITS {
        return Some(Interval::EMPTY);
    }
    let inf = f64::from_bits(inf_bits);
    let sup = f64::from_bits(sup_bits);
    if inf.is_nan() || sup.is_nan() || inf > sup || inf == f64::INFINITY || sup == f64::NEG_INFINITY
    {
        return None;
    }
    if inf == 0.0 && inf_bits != NEGATIVE_ZERO_BITS {
        return None;
    }
    if sup == 0.0 && sup_bits != POSITIVE_ZERO_BITS {
        return None;
    }
    Some(Interval::from_valid_bounds(inf, sup))
}

fn decode_decorated(bytes: &[u8], endian: Endian) -> Option<DecoratedInterval> {
    let bytes: &[u8; DECORATED_INTERVAL_ENCODED_LEN] = bytes.try_into().ok()?;
    let inf_bits = read_u64(&bytes[..8], endian)?;
    let sup_bits = read_u64(&bytes[8..16], endian)?;
    let decoration = Decoration::try_from(bytes[16]).ok()?;
    let inf = f64::from_bits(inf_bits);
    let sup = f64::from_bits(sup_bits);
    if decoration == Decoration::Ill {
        return if inf.is_nan() && sup.is_nan() {
            Some(DecoratedInterval::NAI)
        } else {
            None
        };
    }
    if inf.is_nan() || sup.is_nan() {
        return None;
    }
    let interval = decode_interval_bits(inf_bits, sup_bits)?;
    if interval.is_empty_raw() && decoration != Decoration::Trv {
        return None;
    }
    if !interval.is_bounded_raw() && decoration == Decoration::Com {
        return None;
    }
    Some(DecoratedInterval::set_dec_raw(interval, decoration))
}

fn read_u64(bytes: &[u8], endian: Endian) -> Option<u64> {
    let bytes: [u8; 8] = bytes.try_into().ok()?;
    Some(match endian {
        Endian::Big => u64::from_be_bytes(bytes),
        Endian::Little => u64::from_le_bytes(bytes),
    })
}