Algorithm-Architecture Codesign George A. Constantinides Circuits and Systems Group Imperial College London August 22, 2017 George A. Constantinides Algorithm-Architecture Codesign
Outline The changing face of computer architecture Implications for numerical compute The early days - multiple word-length paradigm Automatic code refactoring for floating point Algorithm partitioning Conclusion George A. Constantinides Algorithm-Architecture Codesign
Computer Architecture Figure: Intel Core i7 (courtesy of Intel) George A. Constantinides Algorithm-Architecture Codesign
Computer Architecture Figure: Catapult, Intel, AWS, ... George A. Constantinides Algorithm-Architecture Codesign
The Implications for Numerical Compute Opens space for non-standard number representations Floating-point Fixed-point RNS (parallelism) Online Arithmetic (arbitrary precision, overclocking / approximation) ... Ideal: co-synthesis of program and and representation(s) for optimal performance / area / energy Formalisation of specification - rip up rules under the hood! George A. Constantinides Algorithm-Architecture Codesign
The Past Earliest computational use of FPGAs was for DSP Simple control: outer infinite loop, straight-line code Linear arithmetic Signal-to-noise ratio versus worst-case instantaneous error Figure: Biquadratic DFII filter Key observation: no a priori correlation between high-noise quantisation points and low-area quantisation points - multiple precision arithmetic Figure: FCCM 2001: -50% area and +39% speed George A. Constantinides Algorithm-Architecture Codesign
The Present Key observation: interaction between numerical rewrites and classical optimisations, e.g. software pipelining of loops; the rise of HLS Have a play: https://admk.github.io/soap/plot.html Figure: Typical SOAP output George A. Constantinides Algorithm-Architecture Codesign
The Future? Deep (manual) rewrites can lead to radical improvements through hybrid numerical representations Figure: Partitioning between float and fix for CG / MINRES Deep (manual) rewrites can recover high-precision results from low-precision computation Figure: Solve Ax = b in single precision doing the O ( n 3 ) work in half precision George A. Constantinides Algorithm-Architecture Codesign
Conclusion Architecture is in flux - there is an opportunity to seize for pushing the boundaries of numerical compute To make this happen requires cross-disciplinary expertise in: Architecture and HLS Computer arithmetic Numerical analysis Programming languages and formal methods We’re meeting at the right time - let’s shake things up! George A. Constantinides Algorithm-Architecture Codesign
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