Initializing RAM-based logarithmic processors

Arnold, Mark G.; Bailey, Thomas A.; Cowles, John; Cupal, J.J.

doi:10.1007/bf00925125

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…As the bibliography of [2] shows, the following series has been given in the literature several times for real z, :…”

Section: Co-transformation Derived From a Truncated Seriesmentioning

confidence: 99%

“…The difficulty faced by an implementor deals with addition and especially subtraction [2] of values represented as logarithms. These two operations require computing functions that represent incrementation and decrement ation of the corresponding real values.…”

Section: Introductionmentioning

confidence: 99%

“…where b > 0 is the base of the logarithms and S, and Db are defined in (1) and (2). In typical modern implementations, b = 2, and in the nineteenth-century literature [ll], b = 10.…”

Section: Introductionmentioning

confidence: 99%

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Arithmetic co-transformations in the real and complex logarithmic number systems

Arnold

Bailey

Cowles

et al.

Proceedings 13th IEEE Sympsoium on Computer Arithmetic

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The real logarithmic number system, which represents a value with a sign bit and a quantized logarithm, can be generalized to create the complex logarithmic number system, which replaces the sign bit with a quantized angle in a log/polar coordinate system. Although multiplication and related operations are easy in both real and complex systems, addition and subtraction are hard, especially when interpolation is used to implement the system. Both real and complex logarithmic arithmetic benefit from the use of co-transformation, which converts an addition or subtraction from a region where interpolation is expensive to a region where it is easier. Two co-transformations that accomplish this goal are introduced. The first is an approximation based on real analysis of the subtraction logarithm. The second is based on simple algebra that applies for both real and complex values and that works for both addition and subtraction.

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“…As the bibliography of [2] shows, the following series has been given in the literature several times for real z, :…”

Section: Co-transformation Derived From a Truncated Seriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%