scanhorizon

the question

Do the two algebraically identical forms of a selective-SSM scan diverge in floating point at an exact dtype-dependent overflow length?

what came out

The associative scan stays bounded and never overflows, while the divide-out-the-gate form overflows at exactly L*=floor(ln(realmax)/(|A|dt)), matching to the integer (fp16 hits 3 tokens at |A|dt=3). On the M4 GPU Metal's cumprod rounds hotter, so overflow arrives a few positions earlier (174 vs 177).

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