{"ID":3053964,"CreatedAt":"2026-06-04T04:41:36.695875263Z","UpdatedAt":"2026-06-04T19:14:31.964469513Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04028","arxiv_id":"2606.04028","title":"Novel Aspects of IEEE SA P3109 Arithmetic Formats for Machine Learning","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.","short_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 pr...","url_abs":"https://arxiv.org/abs/2606.04028","url_pdf":"https://arxiv.org/pdf/2606.04028v1","authors":"[\"Andrew Fitzgibbon\",\"Christoph M. Wintersteiger\",\"Jeffrey Sarnoff\"]","published":"2026-06-01T19:27:39Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}