Correctness of word-specialized fused multiply-add dispatch #
Fused multiply-add forms the exact product-plus-addend before one rounding step. The refinements here establish that contract for the binary32, binary64, and reusable small-word kernels.
Accepted kernel results and the generic fallback all agree with Spec.fma, including its
exceptional-value policy. Runtime clients can import FmaWord.Runtime separately.
theorem
FloatLib.Floats.Formats.BinaryInterchange.Model.FmaBackend.generic_eq_spec
{fmt : FloatFormat}
(x y z : Model fmt)
:
Compact generic FMA preserves the public exact-dyadic operation.
theorem
FloatLib.Floats.Formats.BinaryInterchange.Model.FmaBackend.word_eq_spec
{fmt : FloatFormat}
(x y z : Model fmt)
:
Native-word or generic fused multiply-add preserves the logical operation.