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Gaussian Blur: the exact kernel for small blurs runs row by row
The sampled Gaussian (sigma < 3) read every tap through a bounds-checked get, and its vertical pass walked a column per pixel. Taps inside a row are now one slice, and the vertical pass adds whole input rows in 128-pixel tiles. Same f64 sums in the same order: bit-identical output (tested against the per-pixel kernel). Each pass is 15–25% faster.
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@@ -166,6 +166,9 @@ pub fn gaussian_is_exact(sigma_x: f64, sigma_y: f64) -> bool {
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sigma_x.max(sigma_y) < EXACT_SIGMA_BELOW
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}
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/// Pixels per tile of [`gauss_pass`]'s vertical pass.
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const TILE: usize = 128;
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/// One separable pass of a sampled Gaussian (radius 3 sigma) along x or y.
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fn gauss_pass(img: &Image, sigma: f64, vertical: bool, repeat: bool) -> Image {
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// Below 1e-3 the kernel is the identity in f64; tiny sigmas would also make 2σ² underflow to 0 (NaN taps).
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@@ -176,20 +179,65 @@ fn gauss_pass(img: &Image, sigma: f64, vertical: bool, repeat: bool) -> Image {
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let mut k: Vec<f64> = (-r..=r).map(|i| (-((i * i) as f64) / (2.0 * sigma * sigma)).exp()).collect();
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let total: f64 = k.iter().sum();
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k.iter_mut().for_each(|v| *v /= total);
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let w = img.width as usize;
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let (w, h) = (img.width as usize, img.height as usize);
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let mut out = Image::new(img.width, img.height);
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out.rows_mut().for_each(|(y, row)| {
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for x in 0..w {
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let mut acc = [0.0f64; 4];
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for (i, wt) in k.iter().enumerate() {
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let d = i as i64 - r;
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let (sx, sy) = if vertical { (x as i64, y as i64 + d) } else { (x as i64 + d, y as i64) };
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let p = if repeat { img.get_clamped(sx, sy) } else { img.get(sx, sy) };
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for c in 0..4 {
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acc[c] += p[c] as f64 * wt;
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// Every output pixel adds its taps in kernel order, in f64, as a per-pixel loop would: the
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// result is the same to the bit. Taps outside a transparent edge are skipped (adding `+0.0`
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// leaves a sum that started at `+0.0` unchanged).
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if vertical {
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// Row by row: each output row adds whole input rows (contiguous, vectorises), instead of
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// walking a column per pixel (a strided read per tap).
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out.data.par_chunks_mut(w).enumerate().for_each(|(y, row)| {
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// 128 pixels at a time: the f64 sums (4 KB) stay in L1 across the taps.
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for (t, out_tile) in row.chunks_mut(TILE).enumerate() {
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let x0 = t * TILE;
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let mut acc = [[0.0f64; 4]; TILE];
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for (i, &wt) in k.iter().enumerate() {
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let sy = y as i64 + i as i64 - r;
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let sy = if repeat {
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sy.clamp(0, h as i64 - 1)
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} else if sy < 0 || sy >= h as i64 {
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continue;
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} else {
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sy
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};
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let start = sy as usize * w + x0;
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let Some(src) = img.data.get(start..start + out_tile.len()) else { continue };
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for (a, p) in acc.iter_mut().zip(src) {
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for c in 0..4 {
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a[c] += p[c] as f64 * wt;
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}
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}
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}
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for (o, a) in out_tile.iter_mut().zip(acc.iter()) {
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*o = a.map(|v| v as f32);
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}
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}
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row[x] = acc.map(|v| v as f32);
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});
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return out;
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}
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let n = k.len();
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out.data.par_chunks_mut(w).zip(img.data.par_chunks(w)).for_each(|(row, src)| {
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for (x, o) in row.iter_mut().enumerate() {
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let mut acc = [0.0f64; 4];
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// Inside the row: the taps are one slice (no per-tap edge checks).
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if let Some(taps) = x.checked_sub(r as usize).and_then(|x0| src.get(x0..x0 + n)) {
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for (p, wt) in taps.iter().zip(&k) {
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for c in 0..4 {
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acc[c] += p[c] as f64 * wt;
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}
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}
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} else {
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for (i, wt) in k.iter().enumerate() {
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let sx = x as i64 + i as i64 - r;
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let at = if repeat { Some(sx.clamp(0, w as i64 - 1)) } else { Some(sx) };
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let Some(p) = at.and_then(|i| usize::try_from(i).ok()).and_then(|i| src.get(i)) else { continue };
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for c in 0..4 {
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acc[c] += p[c] as f64 * wt;
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}
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}
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}
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*o = acc.map(|v| v as f32);
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}
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});
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out
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@@ -264,6 +312,53 @@ pub fn radial_blur(img: &Image, center: (f64, f64), amount: f64, zoom: bool) ->
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mod tests {
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use super::*;
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/// The sampled Gaussian pass as it was (one pixel at a time, bounds-checked taps): the
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/// row-wise passes must match it to the bit.
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fn gauss_pass_per_pixel(img: &Image, sigma: f64, vertical: bool, repeat: bool) -> Image {
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let r = (sigma * 3.0).ceil() as i64;
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let mut k: Vec<f64> = (-r..=r).map(|i| (-((i * i) as f64) / (2.0 * sigma * sigma)).exp()).collect();
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let total: f64 = k.iter().sum();
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k.iter_mut().for_each(|v| *v /= total);
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let mut out = Image::new(img.width, img.height);
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for y in 0..img.height as i64 {
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for x in 0..img.width as i64 {
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let mut acc = [0.0f64; 4];
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for (i, wt) in k.iter().enumerate() {
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let d = i as i64 - r;
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let (sx, sy) = if vertical { (x, y + d) } else { (x + d, y) };
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let p = if repeat { img.get_clamped(sx, sy) } else { img.get(sx, sy) };
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for c in 0..4 {
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acc[c] += p[c] as f64 * wt;
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}
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}
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out.set(x as u32, y as u32, acc.map(|v| v as f32));
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}
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}
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out
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}
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#[test]
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fn gauss_pass_is_bit_identical_to_the_per_pixel_kernel() {
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// Sizes narrower and shorter than the kernel too (every tap near an edge), with
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// negative, zero and HDR values.
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for (w, h) in [(37, 23), (3, 2), (1, 9), (64, 1)] {
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let mut img = Image::new(w, h);
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for (i, p) in img.data.iter_mut().enumerate() {
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let v = ((i * 7919) % 101) as f32 / 37.0 - 0.6;
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*p = [v, -v * 0.5, if i % 5 == 0 { 0.0 } else { v * 3.0 }, (v + 0.6).min(1.0)];
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}
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for sigma in [0.4, 1.3, 2.9] {
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for vertical in [false, true] {
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for repeat in [false, true] {
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let (a, b) = (gauss_pass(&img, sigma, vertical, repeat), gauss_pass_per_pixel(&img, sigma, vertical, repeat));
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let bits = |i: &Image| i.data.iter().flat_map(|p| p.map(f32::to_bits)).collect::<Vec<_>>();
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assert!(bits(&a) == bits(&b), "{w}×{h} sigma {sigma} vertical {vertical} repeat {repeat}");
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}
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}
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}
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}
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}
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#[test]
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fn gaussian_preserves_mass() {
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let mut img = Image::new(64, 64);
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