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The Denormal Logarithmic Number System (2013)
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BibTeX
@MISC{Arnold13thedenormal,
author = {Mark G. Arnold and Sylvain Collange},
title = {The Denormal Logarithmic Number System},
year = {2013}
}
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Abstract
Abstract—Economical hardware often uses a FiXed-point Number System (FXNS), whose constant absolute precision is acceptable for many signal-processing algorithms. The almostconstant relative precision of the more expensive Floating-Point (FP) number system simplifies design, for example, by eliminating worries about FXNS overflow because the range of FP is much larger than FXNS for the same wordsize; however, primitive FP introduces another problem: underflow. The conventional Signed Logarithmic Number System (SLNS) offers similar range and precision as FP with much better performance (in terms of power, speed and area) for multiplication, division, powers and roots. Moderate-precision addition in SLNS uses table lookup with properties similar to FP (including underflow). This paper proposes a new number system, called the Denormal LNS (DLNS), which is a hybrid of the properties of FXNS and SLNS. The inspiration for DLNS comes from the denormal numbers found in IEEE-754 (that provide better, gradual underflow) and the µ-law often used for speech encoding; the novel DLNS circuit here allows arithmetic to be performed directly on such encoded data. The proposed approach allows customizing the range in which gradual underflow occurs. A wide gradual underflow range acts like FXNS; a narrow one acts like SLNS. Simulation of an FFT application illustrates a moderate gradual underflow decreasing bit-switching activity 15 % compared to underflowfree SLNS, at the cost of increasing application error by 30%. DLNS reduces switching activity 5 % to 20 % more than an abruptly-underflowing SLNS with one-half the error. Synthesis shows the novel circuit primarily consists of traditional SLNS addition and subtraction tables, with additional datapaths that allow the novel ALU to act on conventional SLNS as well as DLNS and mixed data, for a worst-case area overhead of 26%.
Keyphrases
denormal logarithmic number system gradual underflow bit-switching activity application error expensive floating-point conventional slns abstract economical hardware primitive fp subtraction table additional datapaths novel dlns circuit traditional slns addition speech encoding abruptly-underflowing slns fixed-point number system new number system wide gradual underflow range act mixed data almostconstant relative precision constant absolute precision novel alu conventional signed logarithmic number system similar range many signal-processing algorithm number system simplifies design table lookup fft application worst-case area overhead denormal number fxns overflow underflowfree slns moderate-precision addition denormal lns novel circuit
