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<p>We present algorithms that allow one 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Stef Graillat,
  • Jean-Michel Muller

摘要

We present algorithms that allow one 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.