期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2019.0052
关键词
fixed-point arithmetic; stochastic rounding; Izhikevich neuron model; ordinary differential equation; SpiNNaker; dither
资金
- EPSRC (UK Engineering and Physical Sciences Research Council) [EP/D07908X/1, EP/G015740/1]
- university of Southampton
- university of Cambridge
- university of Sheffield
- ARM Ltd
- Silistix Ltd
- Thales
- EU ICT Flagship Human Brain Project [H2020 785907]
- EU
- Kilburn studentship at the School of Computer Science
- EPSRC [EP/D07908X/1, EP/G015740/1] Funding Source: UKRI
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 fixed-point 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 round-to-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 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. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'.
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