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

use crate::engine::{
    tables::{self, Exp, Log, Skew},
    Engine, GfElement, ShardsRefMut, GF_MODULUS,
};

// ======================================================================
// Naive - PUBLIC

/// Simple reference implementation of [`Engine`].
///
/// - [`Naive`] is meant for those who want to study
///   the source code to understand [`Engine`].
/// - [`Naive`] also includes some debug assertions
///   which are not present in other implementations.
#[derive(Clone)]
pub struct Naive {
    exp: &'static Exp,
    log: &'static Log,
    skew: &'static Skew,
}

impl Naive {
    /// Creates new [`Naive`], initializing all [tables]
    /// needed for encoding or decoding.
    ///
    /// Currently only difference between encoding/decoding is
    /// [`LogWalsh`] (128 kiB) which is only needed for decoding.
    ///
    /// [`LogWalsh`]: crate::engine::tables::LogWalsh
    pub fn new() -> Self {
        let (exp, log) = tables::initialize_exp_log();
        let skew = tables::initialize_skew();

        Self { exp, log, skew }
    }
}

impl Engine for Naive {
    fn fft(
        &self,
        data: &mut ShardsRefMut,
        pos: usize,
        size: usize,
        truncated_size: usize,
        skew_delta: usize,
    ) {
        debug_assert!(size.is_power_of_two());
        debug_assert!(truncated_size <= size);

        let mut dist = size / 2;
        while dist > 0 {
            let mut r = 0;
            while r < truncated_size {
                let log_m = self.skew[r + dist + skew_delta - 1];
                for i in r..r + dist {
                    let (a, b) = data.dist2_mut(pos + i, dist);

                    // FFT BUTTERFLY

                    if log_m != GF_MODULUS {
                        self.mul_add(a, b, log_m);
                    }
                    Self::xor(b, a);
                }
                r += dist * 2;
            }
            dist /= 2;
        }
    }

    fn ifft(
        &self,
        data: &mut ShardsRefMut,
        pos: usize,
        size: usize,
        truncated_size: usize,
        skew_delta: usize,
    ) {
        debug_assert!(size.is_power_of_two());
        debug_assert!(truncated_size <= size);

        let mut dist = 1;
        while dist < size {
            let mut r = 0;
            while r < truncated_size {
                let log_m = self.skew[r + dist + skew_delta - 1];
                for i in r..r + dist {
                    let (a, b) = data.dist2_mut(pos + i, dist);

                    // IFFT BUTTERFLY

                    Self::xor(b, a);
                    if log_m != GF_MODULUS {
                        self.mul_add(a, b, log_m);
                    }
                }
                r += dist * 2;
            }
            dist *= 2;
        }
    }

    fn mul(&self, x: &mut [u8], log_m: GfElement) {
        let shard_bytes = x.len();
        debug_assert!(shard_bytes & 63 == 0);

        let mut pos = 0;
        while pos < shard_bytes {
            for i in 0..32 {
                let lo = x[pos + i] as GfElement;
                let hi = x[pos + i + 32] as GfElement;
                let prod = tables::mul(lo | (hi << 8), log_m, self.exp, self.log);
                x[pos + i] = prod as u8;
                x[pos + i + 32] = (prod >> 8) as u8;
            }
            pos += 64;
        }
    }

    fn xor(x: &mut [u8], y: &[u8]) {
        let shard_bytes = x.len();
        debug_assert!(shard_bytes & 63 == 0);
        debug_assert_eq!(shard_bytes, y.len());

        for i in 0..shard_bytes {
            x[i] ^= y[i];
        }
    }
}

// ======================================================================
// Naive - IMPL Default

impl Default for Naive {
    fn default() -> Self {
        Self::new()
    }
}

// ======================================================================
// Naive - PRIVATE

impl Naive {
    /// `x[] ^= y[] * log_m`
    fn mul_add(&self, x: &mut [u8], y: &[u8], log_m: GfElement) {
        let shard_bytes = x.len();
        debug_assert!(shard_bytes & 63 == 0);
        debug_assert_eq!(shard_bytes, y.len());

        let mut pos = 0;
        while pos < shard_bytes {
            for i in 0..32 {
                let lo = y[pos + i] as GfElement;
                let hi = y[pos + i + 32] as GfElement;
                let prod = tables::mul(lo | (hi << 8), log_m, self.exp, self.log);
                x[pos + i] ^= prod as u8;
                x[pos + i + 32] ^= (prod >> 8) as u8;
            }
            pos += 64;
        }
    }
}

// ======================================================================
// TESTS

// Engines are tested indirectly via roundtrip tests of HighRate and LowRate.