Alphabeta Math
AlgorithmAlgorithm: AI-adaptedProof: Not applicablePipeline-generated
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

TwoProduct product and residual computation using fused multiply-add

Definition

For real floating-point a,b compute p=fl(ab), then e=fma(a,b,-p). Return range-failure if the product overflows, the exact FMA residual is nonzero subnormal or overflow, or another operationwise range condition fails; otherwise return (p,e).

Remarks

The separate Finite arithmetic schedules terminate, with early failure counted separately applies to the ordered multiplication and FMA, each returning a finite result or immediate range failure. It gives at most two attempted rounded operations and exactly two on success. Exact recovery under representability of the residual as zero or a normal number is proved in TwoProduct with fused multiply-add returns the exact product residual.

Depends on

Used by

Dependency tree · two levels

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Sources