Simplified performance evaluation of floating-point formats for implementing intelligent measurement systems

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Abstract
This paper provides a simple method for efficient performance evaluation of floating-point (FP) formats, addressing the challenge of implementing DNN (deep neural network)-based sensor nodes and edge measurement devices. Since resource constraints are imposed in such scenarios, the 32-bit FP format, standardly used for DNN implementation, is unsuitable, and the alternative is found in lower-resolution FP formats which leads to certain performance degradation. Hence, an efficient mechanism for performance evaluation of different FP formats is needed to examine the influence of resolution decreasing. Existing methods utilize the analogy between FP formats and piecewise uniform quantizers (PUQs), using the signal-to-quantization noise ratio (SQNR) of the PUQ to express the performance of FP formats. However, the high complexity of SQNR calculations, involving sum with many terms (e.g. 254 terms for FP formats with an 8-bit exponent), poses a significant challenge. This paper’s main contribution is the significant simplification of the SQNR expression for Gaussian-distributed data, reducing the number of sum terms from 254 to just 5 with minimal accuracy loss, allowing for simple and efficient performance evaluation of FP formats. Major findings include an in-depth analysis of the probability distribution across PUQ segments, a closed-form expression for identifying the highest probability segment, and an evaluation of the SQNR approximation’s accuracy. These findings provide a foundational basis for implementing intelligent DNN-based measurement systems, with applications extending to computing, signal processing, and other fields utilizing FP formats.
Funding Information
  • Ministry of Science, Technological Development and Innovation of the Republic of Serbia (451-03- 65/2024-03/200102)

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