SIPE: Small Integer Plus Exponent

Lefèvre, Vincent

doi:10.1109/arith.2013.22

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…At the time of writing, a working group is being set up to prepare a standard on arithmetic formats for machine learning. For experimenting with very low precisions even if they are not yet available in hardware, several simulation strategies and tools have been designed (Lefèvre 2013, Rump 2017, Higham and Pranesh 2019, Fasi and Mikaitis 2020.…”

Section: Formats Roundings and Operationsmentioning

confidence: 99%

Floating-point arithmetic

Boldo¹,

Jeannerod²,

Melquiond³

et al. 2023

Acta Numerica

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Floating-point numbers have an intuitive meaning when it comes to physics-based numerical computations, and they have thus become the most common way of approximating real numbers in computers. The IEEE-754 Standard has played a large part in making floating-point arithmetic ubiquitous today, by specifying its semantics in a strict yet useful way as early as 1985. In particular, floating-point operations should be performed as if their results were first computed with an infinite precision and then rounded to the target format. A consequence is that floating-point arithmetic satisfies the ‘standard model’ that is often used for analysing the accuracy of floating-point algorithms. But that is only scraping the surface, and floating-point arithmetic offers much more.In this survey we recall the history of floating-point arithmetic as well as its specification mandated by the IEEE-754 Standard. We also recall what properties it entails and what every programmer should know when designing a floating-point algorithm. We provide various basic blocks that can be implemented with floating-point arithmetic. In particular, one can actually compute the rounding error caused by some floating-point operations, which paves the way to designing more accurate algorithms. More generally, properties of floating-point arithmetic make it possible to extend the accuracy of computations beyond working precision.

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Section: Formats Roundings and Operationsmentioning

confidence: 99%

Floating-point arithmetic

Boldo¹,

Jeannerod²,

Melquiond³

et al. 2023

Acta Numerica

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“…The Sipe [Lefèvre 2013] C library 5 is a header-only tool for experimenting with floating-point algorithms and very low precision. It supports the correctly-rounded basic arithmetic operations, except divisions and square roots, but with fused-multiply-adds (FMA).…”

Section: Related Workmentioning

confidence: 99%

FloatX

Flegar

Scheidegger

Novaković

et al. 2019

ACM Trans. Math. Softw.

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We present FloatX (Float eXtended), a C ++ framework to investigate the effect of leveraging customized floating-point formats in numerical applications. FloatX formats are based on binary IEEE 754 with smaller significand and exponent bit counts specified by the user. Among other properties, FloatX facilitates an incremental transformation of the code, relies on hardware-supported floating-point types as back-end to preserve efficiency, and incurs no storage overhead. The article discusses in detail the design principles, programming interface, and datatype casting rules behind FloatX. Furthermore, it demonstrates FloatX’s usage and benefits via several case studies from well-known numerical dense linear algebra libraries, such as BLAS and LAPACK; the Ginkgo library for sparse linear systems; and two neural network applications related with image processing and text recognition.

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CPFloat: A C Library for Simulating Low-precision Arithmetic

Fasi

Mikaitis

2023

ACM Trans. Math. Softw.

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One can simulate low-precision floating-point arithmetic via software by executing each arithmetic operation in hardware and then rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standard mathematical library functions, but handling subnormals, underflow, and overflow demands special attention, and numerical errors can cause mathematically correct formulae to behave incorrectly in finite arithmetic. Moreover, the ensuing implementations are not necessarily efficient, as the library functions these techniques build upon are typically designed to handle a broad range of cases and may not be optimized for the specific needs of rounding algorithms. CPFloat is a C library for simulating low-precision arithmetics. It offers efficient routines for rounding, performing mathematical computations, and querying properties of the simulated low-precision format. The software exploits the bit-level floating-point representation of the format in which the numbers are stored, and replaces costly library calls with low-level bit manipulations and integer arithmetic. In numerical experiments, the new techniques bring a considerable speedup (typically one order of magnitude or more) over existing alternatives in C, C++, and MATLAB. To our knowledge, CPFloat is currently the most efficient and complete library for experimenting with custom low-precision floating-point arithmetic.

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SIPE: Small Integer Plus Exponent

Cited by 4 publications

References 8 publications

Floating-point arithmetic

Floating-point arithmetic

FloatX

CPFloat: A C Library for Simulating Low-precision Arithmetic

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