Now showing 1 - 3 of 3
  • Publication
    A Novel Double Co-Transformation for a Simple and Memory Efficient Logarithmic Number System
    ( 2020-07-01)
    Basir M.S.S.M.
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    To date, co-transformation architecture is typically used in resolving the singularity issue in the logarithmic number system (LNS). The co-transformation was first introduced by Coleman, by using a rule of sign(r1) ≠ sign(r2) which translate the singularity into an argument that can be stored in two identical look-up tables (LUTs) with size of 2k. Recently, a portable 32-bit chipset preferred a small LUT, hitherto a co-transformation architecture is rearranged. This paper presents a novel double co-transformation, by means of first-order co-transformation architecture that covers-0.5 < r < 0 region is extended to r >-1 to replace the triumvirate F, D and E tables occupy by the interpolator. The accuracy settings at the co-transformation is compromised with the worst case error of 0.5 ulp. The outcome revealed a double co-transformation with Lagrange interpolator shows a decline in the total bit by 13% compared to European Logarithmic Microprocessor (ELM). With a simple architecture, the proposed double co-transformation is a promise for a fast LNS system.
  • Publication
    An Investigation of Extended Co-Transformation using Second-Degree Interpolation for Logarithmic Number System
    This paper addresses the proposal of improved logarithmic number system (LNS) with extended co-transformation and memory efficient second-degree Newton interpolator. Since the current interpolation with extension requires 4 look-up tables (LUTs), improvement is proposed to achieve requirement by employing only 3 LUTs with small silicon area. It was found that with the proposed extended co-transformation, a set of interpolation LUT that covered region-1 < r <-0.5 could be eliminated. Results from GNU simulator indicated that the maximum error for the proposed Newton interpolation was 9% lower compared to other current interpolators, although the total memory was unsatisfactory. An Implementation shows an efficient memory for a new LNS system, hence benefited for a dynamic real-time computation
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  • Publication
    A novel double Co-Transformation for a simple and memory efficient logarithmic number system
    To date, co-transformation architecture is typically used in resolving the singularity issue in the logarithmic number system (LNS). The co-transformation was first introduced by Coleman, by using a rule of sign(r 1 ) ≠ sign(r 2 ) which translate the singularity into an argument that can be stored in two identical look-up tables (LUTs) with size of 2k. Recently, a portable 32-bit chipset preferred a small LUT, hitherto a co-transformation architecture is rearranged. This paper presents a novel double co-transformation, by means of first-order co-transformation architecture that covers -0.5 <; r <; 0 region is extended to r > -1 to replace the triumvirate F, D and E tables occupy by the interpolator. The accuracy settings at the co-transformation is compromised with the worst case error of 0.5 ulp. The outcome revealed a double co-transformation with Lagrange interpolator shows a decline in the total bit by 13% compared to European Logarithmic Microprocessor (ELM). With a simple architecture, the proposed double co-transformation is a promise for a fast LNS system.
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