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An Exponentiation Unit for an OpenGL Lighting Engine
March 2004 (vol. 53 no. 3)
pp. 251-258
ASCII Text
x 
 
David Harris, "An Exponentiation Unit for an OpenGL Lighting Engine," IEEE Transactions on Computers, vol. 53, no. 3, pp. 251-258, March, 2004.
 
 
BibTex
x
 
@article{ 10.1109/TC.2004.1261833,
author = {David Harris},
title = {An Exponentiation Unit for an OpenGL Lighting Engine},
journal ={IEEE Transactions on Computers},
volume = {53},
number = {3},
issn = {0018-9340},
year = {2004},
pages = {251-258},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2004.1261833},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - An Exponentiation Unit for an OpenGL Lighting Engine
IS - 3
SN - 0018-9340
SP251
EP258
EPD - 251-258
A1 - David Harris,
PY - 2004
KW - Powering
KW - exponentiation
KW - computer arithmetic
KW - OpenGL hardware acceleration
KW - table lookups
KW - table complexity
KW - bipartite tables.
VL - 53
JA - IEEE Transactions on Computers
ER -
 

Abstract—The OpenGL geometry pipeline lighting stage requires raising a number in the range [0, 1] to a power between [1, 128] to compute specular reflections and spotlights. The result need only be accurate to a number of bits related to the color depth of the output device. This paper describes a hardware implementation of such an exponentiation unit based on a logarithm lookup table, a multiplier, and an inverse log table. The inputs arrive in IEEE single-precision floating-point format and the output is a floating-point color component in the range [0,1] with 8-10 bits of accuracy. The log lookup table is partitioned into subintervals to reduce table size and each subinterval is computed from a bipartite table to further reduce size. A synthesized design uses 32k gates to achieve 10-bit accuracy with a latency of 9.4 ns in a 180 nm process. Although the system is tailored to the OpenGL application, the same principles can be applied to the design of other exponentiation units.

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Index Terms:
Powering, exponentiation, computer arithmetic, OpenGL hardware acceleration, table lookups, table complexity, bipartite tables.
Citation:
David Harris, "An Exponentiation Unit for an OpenGL Lighting Engine," IEEE Transactions on Computers, vol. 53, no. 3, pp. 251-258, March 2004, doi:10.1109/TC.2004.1261833
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