Stochastic Arithmetic as a Model of Granular Computing

Alt, René; Vignes, Jean

doi:10.1002/9780470724163.ch2

Cited by 1 publication

(1 citation statement)

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“…Randomization of rounding can be traced back to the 1950s [24]. Furthermore, a similar idea was also explored in the context of the CESTAC method [25,26] where a program was run multiple times, making random perturbations of the last bit of the result of each elementary operation, and then taking a mean to compute the final result ( [27, p. 486] and references therein).…”

Section: (B) Stochastic Roundingmentioning

confidence: 99%

Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations

Hopkins

Mikaitis

Lester

et al. 2020

Phil. Trans. R. Soc. A.

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Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main reasons are potential improvements in energy efficiency and memory footprint and bandwidth. However, simply switching to lower-precision types typically results in increased numerical errors. We investigate approaches to improving the accuracy of reduced-precision fixedpoint arithmetic types, using examples in an important domain for numerical computation in neuroscience: the solution of Ordinary Differential Equations (ODEs). The Izhikevich neuron model is used to demonstrate that rounding has an important role in producing accurate spike timings from explicit ODE solution algorithms. In particular, fixed-point arithmetic with stochastic rounding consistently results in smaller errors compared to single-precision floating-point and fixed-point arithmetic with roundto-nearest across a range of neuron behaviours and ODE solvers. A computationally much cheaper alternative is also investigated, inspired by the concept of dither that is a widely understood mechanism for providing resolution below the least significant bit (LSB) in digital signal processing. These results will have implications for the solution of ODEs in other subject areas, and should also be directly relevant to the huge range of practical problems that are represented by Partial Differential Equations (PDEs).

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Section: (B) Stochastic Roundingmentioning

confidence: 99%