Article Dans Une Revue Numerische Mathematik Année : 2025

Emulation of the FMA and the correctly-rounded sum of three numbers in rounding-to-nearest floating-point arithmetic

Résumé

We present algorithms that allow to emulate the fused multiply-add (FMA) instruction and the correctly-rounded sum of three numbers (ADD3) in binary floating-point arithmetic, using only rounding-to-nearest floating-point additions, multiplications, and comparisons. We then introduce variants of these algorithms that make it possible to compute the error of an ADD3 or FMA operation.

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hal-04575249 , version 1 (14-05-2024)
hal-04575249 , version 2 (17-03-2025)

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Stef Graillat, Jean-Michel Muller. Emulation of the FMA and the correctly-rounded sum of three numbers in rounding-to-nearest floating-point arithmetic. Numerische Mathematik, 2025, ⟨10.1007/s00211-025-01487-2⟩. ⟨hal-04575249v2⟩
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