feat(floats): executable ULP and absorption for IEEE32Exec#17
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NicolasRouquette wants to merge 1 commit into
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feat(floats): executable ULP and absorption for IEEE32Exec#17NicolasRouquette wants to merge 1 commit into
NicolasRouquette wants to merge 1 commit into
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Add `IEEE32Exec.ulpExp`, an executable unit-in-the-last-place exponent computed directly from the decoded dyadic payload (via `Nat.log2` and the integer exponent selector `fexp32`), and certify it against the real-valued specification: on the finite fragment, `2^(ulpExp x) = ulp32 (toReal x)` (`neuralBpow_ulpExp_eq_ulp32`). Until now the ULP existed only as the real-valued, noncomputable `neuralUlp`/`ulp32`. Also expose the executable absorption test `absorbs a b` (the float32 sum of `a` and `b` equals `a`) and prove it sound against `round32`: when the kernel reports a contribution absorbed, the exact real sum rounds back to `a` (`round32_add_eq_left_of_absorbs`). This is the missing executable primitive and soundness fact that a numerical-adequacy analysis needs, complementing the existing op-level `toReal_*_eq_fp32Round` refinement lemmas.
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Add
IEEE32Exec.ulpExp, an executable unit-in-the-last-place exponent computed directly from the decoded dyadic payload (viaNat.log2and the integer exponent selectorfexp32), and certify it against the real-valued specification: on the finite fragment,2^(ulpExp x) = ulp32 (toReal x)(neuralBpow_ulpExp_eq_ulp32). Until now the ULP existed only as the real-valued, noncomputableneuralUlp/ulp32.Also expose the executable absorption test
absorbs a b(the float32 sum ofaandbequalsa) and prove it sound againstround32: when the kernel reports a contribution absorbed, the exact real sum rounds back toa(round32_add_eq_left_of_absorbs). This is the missing executable primitive and soundness fact that a numerical-adequacy analysis needs, complementing the existing op-leveltoReal_*_eq_fp32Roundrefinement lemmas.