Novel Aspects of IEEE SA P3109 Arithmetic Formats for Machine Learning

# Novel Aspects of IEEE SA P3109 Arithmetic Formats for Machine Learning
Source: [https://arxiv.org/abs/2606.04028](https://arxiv.org/abs/2606.04028)
[View PDF](https://arxiv.org/pdf/2606.04028)

> Abstract:The IEEE P3109 draft standard defines a parameterized family of binary floating\-point formats and associated operations, with a focus on facilitating machine learning\. These formats allow efficient and consistent representation of values in a small number of bits\. The defined formats are parameterized over width and precision in bits, signedness, and the presence of infinities\. Operations are defined by decoding floating\-point values to the set of closed extended reals: the reals augmented with positive and negative infinity and NaN \(Not a Number\)\. Explicit treatment of NaN and infinite operands ensures that only real arithmetic is invoked in operation definitions\. Extensive rounding and saturation modes are defined; stochastic rounding is included\. Operations are exception\-free, accelerating throughput, with exceptional situations communicated through return values, e\.g\., NaN\. Operations on blocks of values sharing a common scale factor are defined in terms of the underlying operations in a uniform manner\. System vendors may describe approximate implementations via a novel scale\-invariant measure, akin to units in the last place, called kappa\-approximation\. Standard function definitions and various other properties are mechanically verified and generated using formal specifications\.

## Submission history

From: Christoph M\. Wintersteiger \[[view email](https://arxiv.org/show-email/110d6528/2606.04028)\] **\[v1\]**Mon, 1 Jun 2026 19:27:39 UTC \(24 KB\)