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Bibliographic Details
Main Authors: Daniels, Sultan, D'Ambrosia, Samuel H., DeWeese, Michael R., Sahai, Anant
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.11546
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author Daniels, Sultan
D'Ambrosia, Samuel H.
DeWeese, Michael R.
Sahai, Anant
author_facet Daniels, Sultan
D'Ambrosia, Samuel H.
DeWeese, Michael R.
Sahai, Anant
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_11546
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The Entropy of Floating-Point Numbers
Daniels, Sultan
D'Ambrosia, Samuel H.
DeWeese, Michael R.
Sahai, Anant
Information Theory
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.
title The Entropy of Floating-Point Numbers
topic Information Theory
url https://arxiv.org/abs/2605.11546