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

Arnold, Mark G.; Bailey, Thomas A.; Cowles, John; Winkel, M.D.

doi:10.1109/12.709377

Cited by 48 publications

(11 citation statements)

References 23 publications

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“…The LNS addition, however, can be improved further by proposing various implementation methods in order to allow a designer to choose between several solutions, depending on his precision, area and latency requirements. For instance, future versions of FPLibrary will include LNS operators using the cotransformation approach by Arnold et al [2], which should be smaller and more accurate but slower. Our current first-order and second-order approaches to LNS addition will not allow to go much further than single precision (we share this concern with Haselman et al, whose double-precision LNS adder [18] does not even fit in a Virtex-II 2000 FPGA, one of the largest available today).…”

Section: Discussionmentioning

confidence: 99%

A Tool for Unbiased Comparison between Logarithmic and Floating-point Arithmetic

Detrey

Dinechin

2007

J VLSI Sign Process Syst Sign Im

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International audienceFor applications requiring a large dynamic, real numbers may be represented either in floating-point, or in the logarithm number system (LNS). Which system is best for a given application is difficult to know in advance, because the cost and performance of LNS operators depend on the target accuracy in a highly non linear way. Therefore, a comparison of the pros and cons of both number systems in terms of cost, performance and overall accuracy is only relevant on a per-application basis. To make such a comparison possible, two concurrent libraries of parameterized arithmetic operators, targeting recent field-programmable gate arrays, are presented. They are unbiased in the sense that they strive to reflect the state-of-the-art for both number systems. These libraries are freely available at http://www.ens-lyon.fr/LIP/Arenaire/

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Section: Discussionmentioning

confidence: 99%

A Tool for Unbiased Comparison between Logarithmic and Floating-point Arithmetic

Detrey

Dinechin

2007

J VLSI Sign Process Syst Sign Im

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“…Prior implementations have chosen to use consistent addition and subtraction techniques. In other words, prior LNS implementations have used either (1) together with (4), which is the most common choice, or, more rarely some implementations [20,21] have used (2) together with (5). This paper will deviate from this assumption of consistent addition and subtraction techniques in order to explore a novel technique that combines (1) with (5).…”

Section: Basic Addition and Subtractionmentioning

confidence: 90%

“…In other words, the more difficult evaluation of the d b function can always be turned into an evaluation of the s b function of a transformed argument plus an extra term obtained from small tables. The name "cotransformation" was proposed for this technique in [21] because the hardware that implements it uses the unmodified w = min(x, y), z = |x − y| and z s = 0 for LNS addition, but w, z and z s are cotransformed together to beŵ =…”

Section: Techniques For Lns Addition and Subtractionmentioning

confidence: 99%

“…The "Improved Cotransformation" in [24] combines the advantages from [21] and [16] by using z < 0 and by calculating the d b function through the s b as follows:…”

Section: Techniques For Lns Addition and Subtractionmentioning

confidence: 99%

“…Another cotransformation is presented in [21], which is dubbed "Arnold's Cotransformation." It is proven that…”

Section: Techniques For Lns Addition and Subtractionmentioning

confidence: 99%

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A Novel Cotransformation for LNS Subtraction

Vouzis

Collange

Arnold

2008

J Sign Process Syst

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The Logarithmic Number System (LNS) can be considered a simplification of the Floating Point (FP) Number System that assumes the mantissa is always equal to one, and has a binary fixed-point exponent. LNS converts multiplication/division to a single addition/subtraction, which make LNS a very attractive choice for applications where these operations predominate, such as in some signal-processing algorithms. However, for wordlengths greater than 20 bits LNS becomes expensive because of the hardware-demanding LNS operations of addition and subtraction, which are typically important for most signal-processing algorithms. This paper gives an overview of the family of LNS subtraction algorithms called "Cotransformations," and proposes a "Novel Cotransformation Combination" that offers improvements in terms of area and speed without sacrificing accuracy compared to previous methods. The hardware requirements of the proposed method are analyzed mathematically, and the results are verified by using synthesis and simulations.

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Log-Arithmetic, with Single and Dual Base

Benschop¹

2009

Associative Digital Network Theory

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

Cited by 48 publications

References 23 publications

A Tool for Unbiased Comparison between Logarithmic and Floating-point Arithmetic

A Tool for Unbiased Comparison between Logarithmic and Floating-point Arithmetic

A Novel Cotransformation for LNS Subtraction

Log-Arithmetic, with Single and Dual Base

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