Accelerating correctly rounded floating-point division when the divisor is known in advance

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 know...

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Bibliographic Details
Published in:IEEE transactions on computers 2004-08, Vol.53 (8), p.1069-1072
Main Authors: Brisebarre, N., Muller, J.-M., Saurabh Kumar Raina
Format: Article
Language:English
Subjects:
Algorithms
Approximation
compilation optimization
Computation
Computer arithmetic
Computer simulation
Division
division by software
division with fused-mac
Floating point arithmetic
Mathematical analysis
Multiplication
Optimizing compilers
Roundoff errors
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Summary: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.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2004.37