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Double-Residue Modular Range Reduction for Floating-Point Hardware Implementations
March 2006 (vol. 55 no. 3)
pp. 254-267
ASCII Text
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Julio Villalba, Tomas Lang, Mario A. Gonzalez, "Double-Residue Modular Range Reduction for Floating-Point Hardware Implementations," IEEE Transactions on Computers, vol. 55, no. 3, pp. 254-267, March, 2006.
 
 
BibTex
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@article{ 10.1109/TC.2006.38,
author = {Julio Villalba and Tomas Lang and Mario A. Gonzalez},
title = {Double-Residue Modular Range Reduction for Floating-Point Hardware Implementations},
journal ={IEEE Transactions on Computers},
volume = {55},
number = {3},
issn = {0018-9340},
year = {2006},
pages = {254-267},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2006.38},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Double-Residue Modular Range Reduction for Floating-Point Hardware Implementations
IS - 3
SN - 0018-9340
SP254
EP267
EPD - 254-267
A1 - Julio Villalba,
A1 - Tomas Lang,
A1 - Mario A. Gonzalez,
PY - 2006
KW - Range-reduction
KW - elementary function evaluation
KW - floating-point arithmetic.
VL - 55
JA - IEEE Transactions on Computers
ER -
 
In this paper, we present a novel algorithm and the corresponding architecture for performing range reduction, which is a preprocessing task required for the evaluation of some elementary functions such as trigonometric and exponential-based functions. The proposed algorithm introduces a modification to the Modular Range Reduction algorithm which increases the speed of computation and allows us to design an architecture for the floating-point case. The implementation presented admits as an input argument any representable number of the standard single precision IEEE 754 floating-point representation and provides the maximum accuracy to the final result. This supposes a hardware solution to the problem of having an input argument close to a multiple of the constant. A final comparison with other implementations is presented.

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Index Terms:
Range-reduction, elementary function evaluation, floating-point arithmetic.
Citation:
Julio Villalba, Tomas Lang, Mario A. Gonzalez, "Double-Residue Modular Range Reduction for Floating-Point Hardware Implementations," IEEE Transactions on Computers, vol. 55, no. 3, pp. 254-267, March 2006, doi:10.1109/TC.2006.38
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