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design.md: the affine rounding paragraph names the underflow, overflow and pinning tests

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Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
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Meta Vens 2026-10-04 03:19:06 +02:00
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@ -724,7 +724,14 @@ magnitudes its roundings are relative to (named in the op's comment): at most
`8u S` is needed with `u = 2^-24`, and the factor of two over that is the
allowance for a device whose `+` and `*` are faithful rather than correctly
rounded. `AffineTests.EveryOpEnclosesItsPoints` evaluates the form's set in
double and the function in float32 with no tolerance.
double and the function in float32 with no tolerance. Products and `af_from_iv` also
add `2^-126`, the most an underflow to a subnormal can lose (`TinyOperandsEncloseTheirPoints`).
`af_from_iv` halves its endpoints before it sums and differences them, and `af_range`
scales its terms before it sums them, so endpoints near the float maximum do not overflow
in the middle of the op; a form that overflows anyway gives `af_range` infinite endpoints,
never NaN (`FromIntervalAndRangeHoldAtTheExtremes`). `AbsorptionsArePinned` and
`SnoiseFormCarriesItsDocumentedWidth` pin each absorption and `af_snoise`'s float32 allowance both
ways: the enclosure tests alone cannot see them on a CPU, where float32 is exact.
`af_snoise(centre, axis, radius)` encloses `snoise` over `centre + axis eps + w`,
`|w| <= radius`, from one `snoise_grad`. It returns the narrower of the