Analyzed lazy fe_sub: on underflow, the unsigned-wrapped value
(a - b + 2^256) differs from (a - b + P) by C = 2^32 + 977.
When multiplied: (a-b+2^256)*x ≠ (a-b)*x mod p (off by x*C mod p).
The P-add-back on underflow is mandatory for correctness.
This is a fundamental difference from 5x52 lazy reduction where
magnitude tracking keeps values representable. With 4x64 fully-packed
limbs, sub MUST add P back, but add CAN skip reduceSelf since values
in [P, 2^256) differ from [0, C) which is handled by mulWide+reduceWide.
Also evaluated:
- WINDOW_G 12→14: only 1.2µs savings for 4x memory (128→512KB).
Not worth it on phones where L1 cache is 128-256KB.
- fe_sqrt optimization: only 831ns overhead over theoretical minimum
of 5.85µs. The addition chain is already near-optimal.
https://claude.ai/code/session_011KVZhDcV2G7idNWEBz12GY
Claude
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