Proceedings ArticleDOI
A unified algorithm for elementary functions
J. S. Walther
- pp 379-385
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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.Abstract:
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 The basis for the algorithm is coordinate rotation in a linear, circular, or hyperbolic coordinate system depending on which function is to be calculated The only operations required are shifting, adding, subtracting and the recall of prestored constants The limited domain of convergence of the algorithm is calculated, leading to a discussion of the modifications required to extend the domain for floating point calculationsread more
Citations
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Journal ArticleDOI
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.
Journal ArticleDOI
Reciprocation, square root, inverse square root, and some elementary functions using small multipliers
TL;DR: A method is proposed, based on argument reduction and series expansion, that allows fast evaluation of these functions in high precision, and the strength of this method is that the same scheme allows the computation of all these functions.
Journal ArticleDOI
Numerical accuracy and hardware tradeoffs for CORDIC arithmetic for special-purpose processors
Kishore Kota,Joseph R. Cavallaro +1 more
TL;DR: Two approaches for tackling the numerical accuracy problem of fixed-point CORDIC are described and arguments to support the use of such an architecture in certain special-purpose arrays are presented.
Journal ArticleDOI
Orthogonal digital filters for VLSI implementation
S. Rao,Thomas Kailath +1 more
TL;DR: In this paper, an algorithm is developed for the realization of any stable, passive digital rational transfer function in a cascaded interconnection of similar processors with only nearest neighbor links, which is an outgrowth of certain results in stochastic estimation theory, involving in particular, the fast Schur algorithm for lattice filters.
Journal ArticleDOI
High performance rotation architectures based on the radix-4 CORDIC algorithm
TL;DR: The authors present a full radix-4 CORDIC algorithm in rotation mode and circular coordinates and its corresponding selection function, and propose an efficient technique for the compensation of the nonconstant scale factor.
References
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Journal ArticleDOI
The CORDIC Trigonometric Computing Technique
TL;DR: The trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.
Journal ArticleDOI
Decimal-Binary Conversions in CORDIC
TL;DR: The CORDIC conversion technique is sufficiently general to be applied to decimal-binary conversion problems involving other mixed radix systems and other decimal codes.