Accelerating Correctly Rounded Floating-PointDivision when the Divisor is Known in Advance

Jean-Michel Muller; Nicolas Brisebarre; Saurabh Raina

Accelerating Correctly Rounded Floating-PointDivision when the Divisor is Known in Advance

Jean-Michel Muller ^{1, 2} Nicolas Brisebarre ³ Saurabh Raina ¹

1 LIP - Laboratoire de l'Informatique du Parallélisme

2 ARENAIRE - Computer arithmetic

Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme

3 LArAl - Laboratoire d'Arithmétique et d'Algèbre

Abstract : We present techniques for accelerating the floating-point computation of x/y when y is known before x. The proposed algorithms are oriented toward architectures with available fused-mac operations. The goal is to get exactly the same result as with usual division with rounding to nearest. It is known that the advanced computation of 1/y allows performing correctly rounded division in one multiplication plus two fused-macs. We show algorithms that reduce this latency to one multiplication and one fused-mac. This is achieved if a precision of at least n+1 bits is available, where n is the number of mantissa bits in the target format, or if y satisfies some properties that can be easily checked at compile-time. This requires a double-word approximation of 1/y (we also show how to get it). Compilers to accelerate some numerical programs without loss of accuracy can use these techniques.

Keywords : rounded floating-point division fused-mac operation double-word approximation computer arithmetic roundoff error optimising compilers floating point arithmetic

Document type :

Journal articles

Domain :

Computer Science [cs] / Other [cs.OH]

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Contributor : Jean-Michel Muller <>
Submitted on : Monday, July 24, 2006 - 4:27:52 PM
Last modification on : Thursday, February 7, 2019 - 2:25:01 PM
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Accelerating Correctly Rounded Floating-PointDivision when the Divisor is Known in Advance

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Accelerating Correctly Rounded Floating-PointDivision when the Divisor is Known in Advance

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370

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