wgsl-fft 0.4.0

GPU-accelerated FFT using Webgpu compute shaders
Documentation 
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/// 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];
}
"#;