Algorithm-Architecture Codesign George A. Constantinides Circuits - - PowerPoint PPT Presentation

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

• ptimal 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(n3) 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