Single-block 8-thread kernel; thread j computes its own 128-dim dot
product, then thread 0 computes block-wide mean/var, then each thread
applies the per-output affine layer-norm. No atomicAdd; reductions are
single-thread (8 elements — negligible cost).
Tests (5/5 on sm_86) assert:
- layer-norm zero-mean output under identity gain
- layer-norm unit-variance output under identity gain
- ln_bias shifts mean uniformly
- ln_gain scales variance (var = gain^2)
- finite output under zero input (variance clamp activates)
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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