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stillwater-sc / universal / 30459701647
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Ran 29 Jul 2026 02:45PM UTC
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29 Jul 2026 02:12PM UTC coverage: 85.232% (+0.003%) from 85.229%
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fix(interval): underflow-safe EFT product enclosure (#1252) (#1253)

* fix(interval): underflow-safe EFT product enclosure (#1252)

The Stage-2 EFT tight path for interval multiplication (#1247) lost containment
when a corner product underflowed into the subnormal range: TwoProduct's roundoff
fma(a,b,-p) underflows below denorm_min and is lost, so sign(e) wrongly reports
"exact" and the endpoint is not widened. interval(1e-160)*interval(1e-160)
returned a zero-width [p,p] that did not contain the true ~1e-320 product --
measured as containment breaks on 100% of subnormal-range products. The overflow
side was already guarded (#1248); this fixes the underflow side.

Replace the per-corner two_prod + tight_lo/tight_hi in operator*= and sqr with an
underflow/overflow-safe interval_detail::prod_enclose(a,b,lo,hi):
  - overflow (!isfinite(p)): outward round
  - safely-normal (|p| >= min * 2^digits, finite residual): direct EFT residual sign
  - exact zero (a==0 || b==0): [0, 0]
  - subnormal/underflow: exact residual sign in a normalized (frexp) domain, where
    ma*mb = P+E is exact in the normal range and (P - ldexp(p,-(ea+eb))) + E has the
    sign of a*b - p without underflow.

TwoSum is exact for finite (incl. subnormal) results, so += / -= are unaffected;
the sum overflow guard in tight_lo/tight_hi stays. Removed the now-unused two_prod
primitive.

Validated (standalone, true int128-mantissa exactness oracle): 0 containment
breaks and 0 spurious widenings of exact products across normal / subnormal /
deep-underflow / exact-subnormal / zero, for both double and float. Regression
added to containment.cpp (subnormal + total-underflow + exact-zero products, and a
subnormal-product fuzz).

gcc + clang: all five interval arithmetic targets PASS.

Resolves #1252
Relates to #1247

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

* test(interval): strengthen subnormal-product regression per CodeRabbit (#1252)

The "subnormal product" case ... (continued)

22 of 22 new or added lines in 1 file covered. (100.0%)

41589 of 48795 relevant lines covered (85.23%)

7166482.32 hits per line

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