Verified scale-aligned binary64 fused multiply-add #
For the accepted normal inputs, shifting the addend significand by the binary64 fraction width places it at the product's scale. Their sum or difference needs at most 107 bits, so two native words hold the exact intermediate value before one nearest-even rounding.
Exact zero, deep cancellation, different scale alignments, and results outside the normal rounder's range use the generic finite kernel. Non-finite operands are handled by the outer arithmetic dispatcher.
Two-word exact arithmetic #
Scale-aligned component semantics #
Refinement of native product rounding #
Native fast-path refinements #
theorem
FloatLib.Floats.Formats.BinaryInterchange.Model.NativeBinary64.fmaFiniteFastImpl_eq
(x y z : Value)
:
The native aligned binary64 FMA path refines the existing exact finite kernel.