Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Table-driven implementation of the exponential function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Powering by a Table Look-Up and a Multiplication with Operand Modification
IEEE Transactions on Computers
Approximating Elementary Functions with Symmetric Bipartite Tables
IEEE Transactions on Computers
Arithmetic on the European Logarithmic Microprocessor
IEEE Transactions on Computers - Special issue on computer arithmetic
ASP-DAC '00 Proceedings of the 2000 Asia and South Pacific Design Automation Conference
Numerical computing with IEEE floating point arithmetic
Numerical computing with IEEE floating point arithmetic
A hardware cost minimized fast Phong shader
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
The Symmetric Table Addition Method for Accurate Function Approximation
Journal of VLSI Signal Processing Systems
Function Evaluation by Table Look-up and Addition
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Faithful Bipartite ROM Reciprocal Tables
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Faithful Powering Computation Using Table Look-Up and a Fused Accumulation Tree
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Some Improvements on Multipartite Table Methods
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics)
Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics)
Low-power leading-zero counting and anticipation logic for high-speed floating point units
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Floating-Point Exponentiation Units for Reconfigurable Computing
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
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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.