# Novel Aspects of IEEE SA P3109 Arithmetic Formats for Machine Learning

arXiv: https://arxiv.org/abs/2606.04028 · HTML: https://mlsanity.com/paper/2606.04028/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 14 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [FP8 Formats for Deep Learning](https://mlsanity.com/paper/2209.05433/) (2022)
- [8-bit Numerical Formats for Deep Neural Networks](https://mlsanity.com/paper/2206.02915/) (2022)
- [Adaptive Loss Scaling for Mixed Precision Training](https://mlsanity.com/paper/1910.12385/) (2019)
- [On Stochastic Rounding with Few Random Bits](https://mlsanity.com/paper/2504.20634/) (2025)

## Built on by (most cited first, 1 of 1)

- [Golden Ruler: A Numeric Format Catalog with Bit-Exact Conformance Vectors for FP8, BF16, MXFP4, and Microscaling Formats](https://mlsanity.com/paper/2606.09686/) (2026)

## Abstract (arXiv)

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. Standard function definitions and various other properties are mechanically verified and generated using formal specifications.