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
Complete list of metadatas

Cited literature [9 references]  Display  Hide  Download
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00087465
Contributor : Jean-Michel Muller <>
Submitted on : Monday, July 24, 2006 - 4:27:52 PM
Last modification on : Wednesday, November 20, 2019 - 3:10:31 AM
Long-term archiving on : Tuesday, April 6, 2010 - 12:24:15 AM

File

DivIEEETC-aug04.pdf

Identifiers

Collections

INRIA | UNIV-ST-ETIENNE | CNRS | LIP | ENS-LYON | UNIV-LYON1

Citation

Jean-Michel Muller, Nicolas Brisebarre, Saurabh Raina. Accelerating Correctly Rounded Floating-PointDivision when the Divisor is Known in Advance. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2004, 53 (8), pp.1069- 1072. ⟨10.1109/TC.2004.37⟩. ⟨ensl-00087465⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

304

Files downloads

434

Contact

CCSD