Algorithms for stochastically rounded elementary arithmetic operations in IEEE 754 floating-point arithmetic

Fasi, Massimiliano and Mikaitis, Mantas (2020) Algorithms for stochastically rounded elementary arithmetic operations in IEEE 754 floating-point arithmetic. [MIMS Preprint]

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Abstract

We present algorithms for performing the four elementary arithmetic operations (+, -, ×, and ÷) in floating point arithmetic with stochastic rounding, and discuss a few examples where using stochastic rounding may be beneficial. The algorithms require that the hardware be compliant with the IEEE 754 floating-point standard and that a floating-point pseudorandom number generator be available, either in software or in hardware. The goal of these techniques is to emulate operations with stochastic rounding when the underlying hardware does not support this rounding mode, as is the case for most existing CPUs and GPUs. When stochastically rounding double precision operations, the algorithms we propose are on average over 5 times faster than an implementation that uses extended precision. We test our algorithms on various problems where stochastic rounding is expected to bring advantages: harmonic sum, summation of small random numbers, and ordinary differential equation solvers.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Depositing User: Mr Massimiliano Fasi
Date Deposited: 01 Apr 2020 17:26
Last Modified: 01 Apr 2020 17:26
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2758

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