Combining Precision Tuning and Rewriting

Saiki, Brett; Flatt, Oliver; Nandi, Chandrakana; Panchekha, Pavel; Tatlock, Zachary

doi:10.1109/arith51176.2021.00013

Cited by 11 publications

(3 citation statements)

References 5 publications

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“…Hence, the input codes are taken as-is and we do not modify them. However, POP is compatible with other tools for program transformation for numerical accuracy [8,22]. Typically, these tools reorder the computations to make them more accurate in the computer arithmetic.…”

Section: Static Performance and Accuracy Modelmentioning

confidence: 99%

A Study of the Floating-Point Tuning Behaviour on the N-body Problem

Khalifa¹,

Martel²

2021

Preprint

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In this article, we apply a new methodology for precision tuning to the N-body problem. Our technique, implemented in a tool named POP, makes it possible to optimize the numerical data types of a program performing floating-point computations by taking into account the requested accuracy on the results. POP reduces the problem of finding the minimal number of bits needed for each variable of the program to an Integer Linear Problem (ILP) which can be optimally solved in one shot by a classical linear programming solver. The POP tool has been successfully tested on programs implementing several numerical algorithms coming from mathematical libraries and other applicative domains such as IoT. In this work, we demonstrate the efficiency of POP to tune the classical gravitational N-body problem by considering five bodies that interact under gravitational force from one another, subject to Newton's laws of motion. Results on the effect of POP in term of mixed-precision tuning of the N-body example are discussed.

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Section: Static Performance and Accuracy Modelmentioning

confidence: 99%

A Study of the Floating-Point Tuning Behaviour on the N-body Problem

Khalifa¹,

Martel²

2021

Preprint

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“…While these tools do not consider speed, they do sometimes discover rewrites that both increase accuracy and improve runtime [Panchekha et al 2015]. More recently, the Herbie authors have added support for combining rewriting with precision tuning to explore the speed-accuracy trade-off of lower-precision arithmetic [Saiki et al 2021]. Finally, the Stoke tool uses stochastic search over assembly instructions to improve runtime without much reducing accuracy [Schkufza et al 2014].…”

Section: Related Workmentioning

confidence: 99%

“…This is because, while floating-point arithmetic is approximate, most applications tolerate minute errors [Piparo et al 2014]. In fact, a speed-accuracy trade-off is ever-present in numerical software engineering: mixed-and lower-precision floating-point [Chiang et al 2017;Damouche and Martel 2018;Guo and Rubio-González 2018;Rubio-González et al 2013], alternative numerical representations [Behnam and Bojnordi 2020;Darvish Rouhani et al 2020;Wang and Kanwar 2019], quantized or fixed-point arithmetic [Lin et al 2016], rewriting [Saiki et al 2021], and various forms of lossy compression [Ballester-Ripoll et al 2019;Ballester-Ripoll and Pajarola 2015] all promise faster but less accurate programs. In each case, the challenge is helping the numerical software engineer apply the technique and explore the trade-offs available.…”

Section: Introductionmentioning

confidence: 99%

Faster Math Functions, Soundly

Briggs,

Panchekha

2021

Preprint

Self Cite

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Standard library implementations of functions like sin and exp optimize for accuracy, not speed, because they are intended for general-purpose use. But applications tolerate inaccuracy from cancellation, rounding error, and singularities-sometimes even very high error-and many application could tolerate error in function implementations as well. This raises an intriguing possibility: speeding up numerical code by tuning standard function implementations.This paper thus introduces OpTuner, an automatic method for selecting the best implementation of mathematical functions at each use site. OpTuner assembles dozens of implementations for the standard mathematical functions from across the speed-accuracy spectrum. OpTuner then uses error Taylor series and integer linear programming to compute optimal assignments of function implementation to use site and presents the user with a speed-accuracy Pareto curve they can use to speed up their code. In a case study on the POV-Ray ray tracer, OpTuner speeds up a critical computation, leading to a whole program speedup of 9% with no change in the program output (whereas human efforts result in slower code and lower-quality output). On a broader study of 37 standard benchmarks, OpTuner matches 216 implementations to 89 use sites and demonstrates speed-ups of 107% for negligible decreases in accuracy and of up to 438% for error-tolerant applications.

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A Study of the Floating-Point Tuning Behaviour on the N-body Problem

Khalifa

Martel

2021

Computational Science and Its Applications – ICCSA 2021

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Combining Precision Tuning and Rewriting

Cited by 11 publications

References 5 publications

A Study of the Floating-Point Tuning Behaviour on the N-body Problem

A Study of the Floating-Point Tuning Behaviour on the N-body Problem

Faster Math Functions, Soundly

A Study of the Floating-Point Tuning Behaviour on the N-body Problem

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