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arXiv · 2605.11546

The Entropy of Floating-Point Numbers

Sultan M. Daniels·Samuel H. D'Ambrosia·Michael R. DeWeese·Anant Sahai
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Abstract

Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a uniformly quantized random variable. Our approximation uncovers a different quantity that provides this link for floating-point quantization. Additionally, we prove that the entropy of a floating-point quantized random variable is approximately unchanged under scaling. Closed-form expressions for the floating-point entropy of common distributions are provided and compared to exact results.

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Sultan M. Daniels, Samuel H. D'Ambrosia, Michael R. DeWeese, Anant Sahai. 2026-09-02. The Entropy of Floating-Point Numbers. https://arxiv.org/abs/2605.11546

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