Customizing Number Representation and Precision
Olivier Sentieys (TARAN), Daniel Menard (INSA Rennes)

TL;DR
This paper compares fixed-point and floating-point number representations in terms of cost, performance, energy, and accuracy, highlighting that the optimal choice depends on specific application needs, especially in AI and FPGA contexts.
Contribution
It provides a detailed comparison of FxP and FlP representations, analyzing their trade-offs and demonstrating scenarios where low-precision floating-point is advantageous.
Findings
Low-precision floating-point can outperform fixed-point in energy-constrained applications.
The choice between FxP and FlP depends heavily on the specific application requirements.
Both representations have distinct advantages and drawbacks in terms of cost, performance, and accuracy.
Abstract
There is a growing interest in the use of reduced-precision arithmetic, exacerbated by the recent interest in artificial intelligence, especially with deep learning. Most architectures already provide reduced-precision capabilities (e.g., 8-bit integer, 16-bit floating point). In the context of FPGAs, any number format and bit-width can even be considered.In computer arithmetic, the representation of real numbers is a major issue. Fixed-point (FxP) and floating-point (FlP) are the main options to represent reals, both with their advantages and drawbacks. This chapter presents both FxP and FlP number representations, and draws a fair a comparison between their cost, performance and energy, as well as their impact on accuracy during computations.It is shown that the choice between FxP and FlP is not obvious and strongly depends on the application considered. In some cases, low-precision…
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Taxonomy
TopicsNumerical Methods and Algorithms · Cryptography and Residue Arithmetic · Digital Filter Design and Implementation
