// Fold SPLIT per-plane (sum, sum-of-squares) partials into mean and inverse
// standard deviation. One thread handles each plane. Variance uses
// E[x^2] - E[x]^2; max(value, 0) guards against negative rounding residue.
{{ env.wgsl.resourceDeclarations }}

const SPLIT: u32 = {{ split }}u;
const COMBINE_WG: u32 = {{ combineWorkgroupSize }}u;

@compute @workgroup_size(COMBINE_WG, 1, 1)
fn main(@builtin(global_invocation_id) gid: vec3<u32>, @builtin(num_workgroups) nwg: vec3<u32>) {
  let plane = gid.x + gid.y * nwg.x * COMBINE_WG;
  if (plane >= params.planes) {
    return;
  }
  var total = 0.0;
  var total_sq = 0.0;
  let b = plane * SPLIT;
  for (var k = 0u; k < SPLIT; k = k + 1u) {
    total = total + partials[(b + k) * 2u];
    total_sq = total_sq + partials[(b + k) * 2u + 1u];
  }
  let n = f32(params.spatial);
  let mean = total / n;
  let variance = max(total_sq / n - mean * mean, 0.0);
  stats[plane * 2u] = mean;
  stats[plane * 2u + 1u] = inverseSqrt(variance + params.epsilon);
}