Proceedings Article10.1109/ARITH.1989.72809
Efficient elementary function generation with multipliers
H.M. Ahmed
- 06 Sep 1989
- pp 52-59
31
TL;DR: The author proposes combining multipliers with these multiplication-free algorithms to construct fast methods of elementary function generation, and demonstrates the idea by combiningmultipliers with the CORDIC algorithm to achieve fast vector rotation.
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Abstract: Virtually all numerical techniques for elementary function generation share the common property of avoiding multiplication by iteratively performing shift operations. However, with the advent of VLSI, multiplier economics are considerably less formidable than before. The author proposes combining multipliers with these multiplication-free algorithms to construct fast methods of elementary function generation. He demonstrates the idea by combining multipliers with the CORDIC algorithm to achieve fast vector rotation. >
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References
A unified algorithm for elementary functions
J. S. Walther
- 18 May 1971
TL;DR: This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arCTanh, In, exp and square-root.
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A Cordic Arithmetic Processor Chip
TL;DR: A monolithic processor computes products, quotients, and several common transcendental functions, based on the well-known principles of "CORDIC," but recourse to a subtle novel corollary results in a scale factor of unity.
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On the design of high performance digital arithmetic units
Paul Michael Farmwald
- 01 Jan 1981
TL;DR: Several new algorithms for use for enhancing the performance of pipelined digital computers have been developed and evaluated and the design of a particular such computer embodying most of these algorithms is discussed in detail--the S-1 Mark IIA.
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Automatic computation of exponentials, logarithms, ratios and square roots
TL;DR: In this paper, it is shown how a relatively simple device can evaluate exponentials, logarithms, ratios and square roots for fraction arguments, employing only shifts, adds, high-speed table lookups, and bit counting.
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Signal processing algorithms and architectures
Hassan Masud Ahmed
- 01 Jan 1982
TL;DR: The goal of the present work is to efficiently map algorithms onto architectures by maintaining a close link with the theoretical basis of a particular signal processing method by exploiting the ability to design a powerful signal processing chip capable of efficiently implementing such popular algorithms as the discrete Fourier transform, ladder filters and associated matrix algebra operations.
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