wgsl-fft 0.3.1

GPU-accelerated FFT using Webgpu compute shaders
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
203
204
205
206
207
208

/// Stockham Radix-4 DIT kernel (derived from Gemini rivalry winner).
///
/// Uniform U: .x = N (transform length), .y = p (stride = 4^stage_index).
/// SRC / DST:  interleaved complex pairs [re₀, im₀, re₁, im₁, …].
/// TWIDDLE:    N complex pairs e^{-2πij/N} for j = 0..N.
///
/// Dispatched log₄N times; each dispatch processes N/4 butterfly groups.
pub const R4_WGSL: &str = r#"
@group(0) @binding(0) var<uniform> U: vec4<u32>;
@group(0) @binding(1) var<storage, read_write> SRC: array<f32>;
@group(0) @binding(2) var<storage, read_write> DST: array<f32>;
@group(0) @binding(3) var<storage, read> TWIDDLE: array<f32>;

fn cmul(a: vec2<f32>, b: vec2<f32>) -> vec2<f32> {
    return vec2<f32>(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x);
}

@compute @workgroup_size(256, 1, 1)
fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
    let tid       = gid.x;
    let batch_id  = gid.y;
    let n         = U.x;
    let p         = U.y;
    let quarter_n = n >> 2u;
    if tid >= quarter_n { return; }

    let four_p = p << 2u;
    let k      = tid % p;
    let j      = tid / p;
    let bo     = batch_id * n * 2u;

    let i0 = j*p + k;
    let i1 = i0 + quarter_n;
    let i2 = i1 + quarter_n;
    let i3 = i2 + quarter_n;

    var x: array<vec2<f32>, 4>;
    x[0] = vec2<f32>(SRC[bo + 2u*i0], SRC[bo + 2u*i0+1u]);
    x[1] = vec2<f32>(SRC[bo + 2u*i1], SRC[bo + 2u*i1+1u]);
    x[2] = vec2<f32>(SRC[bo + 2u*i2], SRC[bo + 2u*i2+1u]);
    x[3] = vec2<f32>(SRC[bo + 2u*i3], SRC[bo + 2u*i3+1u]);

    let stride = quarter_n / p;
    let tw     = k * stride;
    x[1] = cmul(vec2<f32>(TWIDDLE[2u*tw],   TWIDDLE[2u*tw+1u]),   x[1]);
    x[2] = cmul(vec2<f32>(TWIDDLE[4u*tw],   TWIDDLE[4u*tw+1u]),   x[2]);
    x[3] = cmul(vec2<f32>(TWIDDLE[6u*tw],   TWIDDLE[6u*tw+1u]),   x[3]);

    let s02 = x[0] + x[2]; let d02 = x[0] - x[2];
    let s13 = x[1] + x[3]; let d13 = x[1] - x[3];

    let y0 = s02 + s13;
    let y1 = vec2<f32>(d02.x + d13.y, d02.y - d13.x);
    let y2 = s02 - s13;
    let y3 = vec2<f32>(d02.x - d13.y, d02.y + d13.x);

    let d_base = bo + 2u*(j*four_p + k);
    DST[d_base]          = y0.x; DST[d_base+1u]          = y0.y;
    DST[d_base + 2u*p]   = y1.x; DST[d_base + 2u*p+1u]   = y1.y;
    DST[d_base + 4u*p]   = y2.x; DST[d_base + 4u*p+1u]   = y2.y;
    DST[d_base + 6u*p]   = y3.x; DST[d_base + 6u*p+1u]   = y3.y;
}
"#;

/// Stockham Radix-2 DIT kernel — fallback for the final stage when log₂N is odd.
///
/// Uniform U: .x = N, .y = p (stride = 2^(num_r4_stages * 2)).
/// TWIDDLE:   N complex pairs e^{-2πij/N} for j = 0..N.
pub const R2_WGSL: &str = r#"
@group(0) @binding(0) var<uniform> U: vec4<u32>;
@group(0) @binding(1) var<storage, read_write> SRC: array<f32>;
@group(0) @binding(2) var<storage, read_write> DST: array<f32>;
@group(0) @binding(3) var<storage, read> TWIDDLE: array<f32>;

fn cmul(a: vec2<f32>, b: vec2<f32>) -> vec2<f32> {
    return vec2<f32>(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x);
}

@compute @workgroup_size(256, 1, 1)
fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
    let tid      = gid.x;
    let batch_id = gid.y;
    let n        = U.x;
    let p        = U.y;
    let half_n   = n >> 1u;
    if tid >= half_n { return; }

    let two_p = p + p;
    let k     = tid % p;
    let j     = tid / p;
    let bo    = batch_id * n * 2u;

    let i1 = j*p + k;
    let i2 = i1 + half_n;

    let x1 = vec2<f32>(SRC[bo + 2u*i1], SRC[bo + 2u*i1+1u]);
    let x2 = vec2<f32>(SRC[bo + 2u*i2], SRC[bo + 2u*i2+1u]);

    let tw = k * (half_n / p);
    let t  = cmul(vec2<f32>(TWIDDLE[2u*tw], TWIDDLE[2u*tw+1u]), x2);

    let d_base = bo + 2u*(j*two_p + k);
    DST[d_base]          = x1.x + t.x; DST[d_base+1u]          = x1.y + t.y;
    DST[d_base + 2u*p]   = x1.x - t.x; DST[d_base + 2u*p+1u]   = x1.y - t.y;
}
"#;

/// Cooley-Tukey radix-2 DIT FFT shader using vec2<f32> complex pairs.
/// Computes twiddle factors on the fly (no TWIDDLE buffer needed).
/// This matches the pipeline's existing FFT shader format.
///
/// Uniform params: .x = N, .y = stage, .z = direction (0=FFT, 1=IFFT)
/// @binding(0): input_data (storage, read) - array<vec2<f32>>
/// @binding(1): output_data (storage, read_write) - array<vec2<f32>>
pub const COOLEY_TUKEY_R2_WGSL: &str = r#"
struct FftParams {
    n:         u32,
    stage:     u32,
    direction: u32,
    _pad:      u32,
};

@group(0) @binding(0) var<storage, read>       input_data:  array<vec2<f32>>;
@group(0) @binding(1) var<storage, read_write> output_data: array<vec2<f32>>;
@group(0) @binding(2) var<uniform>             params:      FftParams;

fn cmul(a: vec2<f32>, b: vec2<f32>) -> vec2<f32> {
    return vec2<f32>(
        a.x * b.x - a.y * b.y,
        a.x * b.y + a.y * b.x,
    );
}

fn twiddle(k: u32, span: u32, direction: u32) -> vec2<f32> {
    let pi2: f32 = 6.283185307179586;
    let sign = select(-1.0, 1.0, direction == 1u);
    let angle = sign * pi2 * f32(k) / f32(span);
    return vec2<f32>(cos(angle), sin(angle));
}

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
    let i = gid.x;
    if i >= params.n / 2u { return; }

    let span: u32 = 1u << (params.stage + 1u);
    let half: u32 = span >> 1u;
    let group: u32 = i / half;
    let k: u32     = i % half;
    let even: u32  = group * span + k;
    let odd: u32   = even + half;

    let u = input_data[even];
    let v = input_data[odd];
    let w  = twiddle(k, span, params.direction);
    let wv = cmul(w, v);
    output_data[even] = u + wv;
    output_data[odd]  = u - wv;
}
"#;

/// Normalize shader for vec2<f32> format
/// Divides each element by N
/// @binding(0): data (storage, read_write) - array<vec2<f32>>
/// @binding(1): params (uniform) - vec4<u32> where .x = N
pub const NORMALIZE_VEC2_WGSL: &str = r#"
@group(0) @binding(0) var<storage, read_write> data: array<vec2<f32>>;
@group(0) @binding(1) var<uniform> params: vec4<u32>;

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
    let i = gid.x;
    let n = params.x;
    if i >= n { return; }
    let scale = 1.0 / f32(n);
    data[i] = vec2<f32>(data[i].x * scale, data[i].y * scale);
}
"#;

/// Cooley-Tukey radix-2 bit-reversal permutation (vec2<f32> format).
/// Bindings: 0 = src (read), 1 = dst (read_write), 2 = BitRevParams uniform { n, log2_n, _pad0, _pad1 }
pub const BIT_REVERSAL_WGSL: &str = r#"
struct BitRevParams {
    n: u32,
    log2_n: u32,
    _pad0: u32,
    _pad1: u32,
};
@group(0) @binding(0) var<storage, read>       src:    array<vec2<f32>>;
@group(0) @binding(1) var<storage, read_write> dst:    array<vec2<f32>>;
@group(0) @binding(2) var<uniform>             params: BitRevParams;
fn bit_reverse(x: u32, bits: u32) -> u32 {
    var r: u32 = 0u;
    var v: u32 = x;
    for (var i: u32 = 0u; i < bits; i++) {
        r = (r << 1u) | (v & 1u);
        v >>= 1u;
    }
    return r;
}
@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
    let i = gid.x;
    if i >= params.n { return; }
    let j = bit_reverse(i, params.log2_n);
    dst[i] = src[j];
}
"#;