{% if usesF16 %}
enable f16;
{% endif %}
{{ env.wgsl.resourceDeclarations }}

// com.microsoft.EmbedLayerNormalization, normalization pass.
//   output = (sum - mean) / sqrt(variance + epsilon) * gamma + beta
// One workgroup owns one (batch, position) row of the summed embedding the
// previous pass left in `output`, and normalizes it in place. The statistics
// accumulate in f32 over the stored tensor-type values.
const HIDDEN: u32 = {{ hidden }}u;
const EPSILON: f32 = {{ epsilon }};
const WG: u32 = {{ workgroupSize }}u;

var<workgroup> partial: array<f32, WG>;

{% macro wgsl_tree_fold_stmt(a, op, idx, svar) %}
{% if op == "max" %}
{{ a }}[{{ idx }}] = max({{ a }}[{{ idx }}], {{ a }}[{{ idx }} + {{ svar }}]);
{%- else %}
{{ a }}[{{ idx }}] = {{ a }}[{{ idx }}] + {{ a }}[{{ idx }} + {{ svar }}];
{%- endif %}
{% endmacro %}
{% macro wgsl_tree_fold(arrays, op="add", idx="lid", wg="WORKGROUP_SIZE", svar="stride", typed=false, form="tail", breakInline=false, bodyInline=false, barrierFirst=false) %}
  var {{ svar }}{{ ": u32 " if typed else " " }}= {{ wg }} / 2u;
  loop {
{% if form == "head" %}
{% if breakInline %}
    if ({{ svar }} == 0u) { break; }
{% else %}
    if ({{ svar }} == 0u) {
      break;
    }
{% endif %}
{% endif %}
{% if bodyInline %}
    if ({{ idx }} < {{ svar }}) { {{ wgsl_tree_fold_stmt(arrays[0], op, idx, svar) }} }
{% else %}
    if ({{ idx }} < {{ svar }}) {
{% for a in arrays %}
      {{ wgsl_tree_fold_stmt(a, op, idx, svar) }}
{% endfor %}
    }
{% endif %}
{% if form == "head" %}
{% if barrierFirst %}
    workgroupBarrier();
    {{ svar }} = {{ svar }} / 2u;
{% else %}
    {{ svar }} = {{ svar }} / 2u;
    workgroupBarrier();
{% endif %}
{% else %}
    workgroupBarrier();
    if ({{ svar }} == 1u) {
      break;
    }
    {{ svar }} = {{ svar }} / 2u;
{% endif %}
  }
{%- endmacro %}

// Reusing partial after this reduction requires a barrier between the read of
// partial[0] and the next write, or the next round can race the prior readers.
{% set trailingBarrier = trailingBarrier is defined and trailingBarrier %}
fn reduce_sum(value: f32, tid: u32) -> f32 {
  partial[tid] = value;
  workgroupBarrier();
{{ wgsl_tree_fold(["partial"], idx="tid", wg="WG", form="head") }}
{% if trailingBarrier %}
  let total = partial[0];
  workgroupBarrier();
  return total;
{% else %}
  return partial[0];
{% endif %}
}


@compute @workgroup_size(WG, 1, 1)
fn main(@builtin(workgroup_id) wg: vec3<u32>,
        @builtin(num_workgroups) nwg: vec3<u32>,
        @builtin(local_invocation_id) lid: vec3<u32>) {
  // 2D-folded row index: wg.y carries the high bits past the
  // maxComputeWorkgroupsPerDimension dispatch limit.
  let token = wg.x + wg.y * nwg.x;
  if (token >= params.tokens) {
    return;
  }
  let tid = lid.x;
  let base = token * HIDDEN;

  var local_sum = 0.0;
  for (var i = tid; i < HIDDEN; i = i + WG) {
    local_sum = local_sum + f32(output[base + i]);
  }
  let mean = reduce_sum(local_sum, tid) / f32(HIDDEN);
  // Separates the mean reduction's read of partial[0] from the variance
  // reduction's writes to the same workgroup array.
  workgroupBarrier();

  var local_sq = 0.0;
  for (var i = tid; i < HIDDEN; i = i + WG) {
    let centred = f32(output[base + i]) - mean;
    local_sq = local_sq + centred * centred;
  }
  let deviation = sqrt(reduce_sum(local_sq, tid) / f32(HIDDEN) + EPSILON);
  workgroupBarrier();

  for (var i = tid; i < HIDDEN; i = i + WG) {
    let centred = f32(output[base + i]) - mean;
    output[base + i] = {{ scalar }}(centred / deviation * f32(gamma[i]) + f32(beta[i]));
  }
}