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Handle multiplication exponent underflow without discarding products that remain representable through their coefficients. Round directly to the destination precision using nearest, ties-to-even rounding, avoiding double rounding through an intermediate wide subnormal. Keep extendedMul's wider result and preserve signed zero on underflow. Preserve fitting subnormal coefficients during narrowing and limit widening normalization to the available exponent range. Use an unsigned distance from the exponent floor for the boundary check and correct the underflow shift direction. Add regressions for multiplication by one, representable squares, halfway rounding, signed zero, subnormal conversions, and a product that previously rounded twice. Fixes libmir#487. AI-Assisted-By: Codex (GPT-6 Astra Medium)
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Fixes #487.
Fpmultiplication currently discards a product when the sum of the operand exponents falls belowlong.min, even when the coefficient makes the result representable. This can turn multiplication by one into zero near the exponent floor.Handle these products by shifting and rounding the coefficient instead of immediately returning zero. Ordinary multiplication rounds directly to its destination precision, avoiding double rounding through an intermediate wide subnormal.
extendedMulretains its wider result, and genuine underflow preserves signed zero.The resulting subnormal values also need to survive conversions between
Fpwidths. Preserve coefficients that already fit when narrowing, and limit normalization when widening to the available exponent range.Regression coverage
Cover multiplication by one, representable squares, halfway rounding with ties to even, signed zero, widening and narrowing subnormals, and a concrete double-rounding counterexample.
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AI-Assisted-By: Codex (GPT-6 Astra Medium)