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

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

For 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 ...

Implementation of Floating Point and Logarithmic Number System Arithmetic Unit and Their Comparison for Fpga

Floating point (FP) representation is commonly used to represent real numbers. Some papers have suggested the use of logarithmic number system (LNS) in addition to floating point. In LNS, a real number is represented as a fixed point logarithm. Therefore multiplication and division in LNS are much simpler in comparison to that in FP, so the LNS can be beneficial if addition and subtraction can ...

Precision Arithmetic: A New Floating-Point Arithmetic

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid the excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding r...

Floating-Point Arithmetic

A Floating-Point Unit for Arithmetic Operations

In this paper we present a design for a floating point unit partially compliant with the IEEE 754 floating point standard. The unit fully implements comparisons and partially implements floating-point addition and multiplication. It is fully parametrized and may be used with floating point numbers whose composite fields have widths of any desired length.