feat: division proof#89
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Mirrors MulUnnormalized.toInt_ex_le; bounds the exponent difference in (-2^e + 1, 2^e - 1) before the post-normalization shift. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Discharge `a.isNaN` case by NaN propagation through ExtRat.div = mul·inv. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Each case uses the same NaN-propagation pattern via ExtRat.div_eq_mul_inv: NaN.inv = NaN, then mul · NaN = NaN, then both branches of the xorSign if/then/else collapse to NaN. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
inv inf = 0, then inf * 0 = NaN closes the inf/inf case via the standard NaN-propagation pipeline. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
The 'rounding-stable-under-perturbation' lemma: if two rationals agree on isNaN, isZero, lower, upper, lowerHalf, and tieBreak classifiers, roundRNE returns the same packed float. This is the abstract property the sticky-bit machinery relies on to bridge the gap between the implementation's truncated-quotient toRat and the true rational quotient. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Document remaining sign-convention reconciliation needed for the non-NaN cases (0/num, etc.). Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
The sign reconciliation for inf/0 is non-trivial because SmtLib's inv(Number 0) returns Infinity false (discarding zero's sign), then the xorSign+neg machinery in SmtLibFunctions.div tries to restore it. Verifying this needs case analysis we defer. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Fix the original `lsb_eq_sticky` statement (which was wrong for the unshifted msb=true case): the lsb of the adjusted significand is `(msb && quot.lsb) || (rem != 0)`. Proved by case-split on quot.msb. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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This PR proves the correctness of the division operation.