#include <metal_stdlib>
using namespace metal;
/// Fused RMS normalization + residual addition (bfloat16).
///
/// Computes Gemma4's post-attention / post-FFN ordering:
/// normed[i] = rms_norm(input[i], weight[i], eps)
/// output[i] = residual[i] + normed[i]
///
/// Fuses two separate dispatches (rms_norm_bf16 + elementwise_add_bf16) into
/// one kernel launch per transformer sub-layer. Saves 60-120 dispatches across
/// Gemma4's 30 layers.
///
/// Buffer layout:
/// buffer(0): residual — bfloat [rows * dim] residual stream (unmodified)
/// buffer(1): input — bfloat [rows * dim] sublayer output (to normalize)
/// buffer(2): weight — bfloat [dim] RMS norm learned scale
/// buffer(3): output — bfloat [rows * dim] residual + normed result
/// buffer(4): dim — uint
/// buffer(5): rows — uint
/// buffer(6): eps — float
///
/// Threadgroup: (min(256, next_pow2(dim)), 1, 1) — one threadgroup per row
/// Grid : (rows, 1, 1)
/// Shared mem : tg_size * sizeof(float) for the sum-of-squares reduction
kernel void fused_norm_add_bf16(
device const bfloat* residual [[buffer(0)]],
device const bfloat* input [[buffer(1)]],
device const bfloat* weight [[buffer(2)]],
device bfloat* output [[buffer(3)]],
constant uint& dim [[buffer(4)]],
constant uint& rows [[buffer(5)]],
constant float& eps [[buffer(6)]],
uint row_id [[threadgroup_position_in_grid]],
uint tid [[thread_index_in_threadgroup]],
uint tg_size [[threads_per_threadgroup]],
threadgroup float* shared [[threadgroup(0)]]
) {
if (row_id >= rows) { return; }
const uint base = row_id * dim;
// -------------------------------------------------------------------------
// Phase 1: accumulate partial sum-of-squares over input (not the sum).
//
// We normalize `input` alone — the residual is added after.
// -------------------------------------------------------------------------
float partial_sq = 0.0f;
for (uint i = tid; i < dim; i += tg_size) {
const float v = static_cast<float>(input[base + i]);
partial_sq += v * v;
}
shared[tid] = partial_sq;
threadgroup_barrier(mem_flags::mem_threadgroup);
// Tree reduction to obtain total sum-of-squares.
for (uint stride = tg_size / 2; stride > 0; stride >>= 1) {
if (tid < stride) {
shared[tid] += shared[tid + stride];
}
threadgroup_barrier(mem_flags::mem_threadgroup);
}
// rms_inv = rsqrt(mean(input^2) + eps)
const float rms_inv = rsqrt(shared[0] / float(dim) + eps);
// -------------------------------------------------------------------------
// Phase 2: normalize input, apply weight, add residual, store output.
//
// normed[i] = float(input[i]) * rms_inv * float(weight[i])
// output[i] = bfloat(float(residual[i]) + normed[i])
// -------------------------------------------------------------------------
for (uint i = tid; i < dim; i += tg_size) {
const float normed = static_cast<float>(input[base + i])
* rms_inv
* static_cast<float>(weight[i]);
output[base + i] = bfloat(static_cast<float>(residual[base + i]) + normed);
}
}
/// Fused RMS normalization (no weight) + residual addition (bfloat16).
///
/// Computes:
/// normed[i] = input[i] * rsqrt(mean(input^2) + eps) (no weight scale)
/// output[i] = residual[i] + normed[i]
///
/// Used for V-head norms in Gemma4 that have no learned scale parameter.
///
/// Buffer layout:
/// buffer(0): residual — bfloat [rows * dim]
/// buffer(1): input — bfloat [rows * dim]
/// buffer(2): output — bfloat [rows * dim]
/// buffer(3): dim — uint
/// buffer(4): rows — uint
/// buffer(5): eps — float
///
/// Threadgroup: (min(256, next_pow2(dim)), 1, 1) — one threadgroup per row
/// Grid : (rows, 1, 1)
/// Shared mem : tg_size * sizeof(float) for the reduction
kernel void fused_norm_add_no_weight_bf16(
device const bfloat* residual [[buffer(0)]],
device const bfloat* input [[buffer(1)]],
device bfloat* output [[buffer(2)]],
constant uint& dim [[buffer(3)]],
constant uint& rows [[buffer(4)]],
constant float& eps [[buffer(5)]],
uint row_id [[threadgroup_position_in_grid]],
uint tid [[thread_index_in_threadgroup]],
uint tg_size [[threads_per_threadgroup]],
threadgroup float* shared [[threadgroup(0)]]
) {
if (row_id >= rows) { return; }
const uint base = row_id * dim;
// Phase 1: accumulate partial sum-of-squares over input.
float partial_sq = 0.0f;
for (uint i = tid; i < dim; i += tg_size) {
const float v = static_cast<float>(input[base + i]);
partial_sq += v * v;
}
shared[tid] = partial_sq;
threadgroup_barrier(mem_flags::mem_threadgroup);
// Tree reduction.
for (uint stride = tg_size / 2; stride > 0; stride >>= 1) {
if (tid < stride) {
shared[tid] += shared[tid + stride];
}
threadgroup_barrier(mem_flags::mem_threadgroup);
}
const float rms_inv = rsqrt(shared[0] / float(dim) + eps);
// Phase 2: normalize (no weight), add residual, store output.
for (uint i = tid; i < dim; i += tg_size) {
const float normed = static_cast<float>(input[base + i]) * rms_inv;
output[base + i] = bfloat(static_cast<float>(residual[base + i]) + normed);
}
}