Verifying bit-manipulations of floating-point

Lee, Wonyeol; Sharma, Rahul; Aiken, Alex

doi:10.1145/2908080.2908107

Cited by 22 publications

(3 citation statements)

References 18 publications

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“…Worst-case analysis of roundoff errors has been an active research area with numerous published approaches [12][13][14][15][16]18,22,33,35,37,38,46,47,50]. Our symbolic affine arithmetic used in PAF (Sect.…”

Section: Related Workmentioning

confidence: 99%

Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations

Constantinides

Dahlqvist

Rakamarić

et al. 2021

Computer Aided Verification

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We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are generally close to being uncorrelated with their generating distribution. Based on these theoretical advances, we propose a model of IEEE floating-point arithmetic for numerical expressions with probabilistic inputs and an algorithm for evaluating this model. Our algorithm provides rigorous bounds to the output and error distributions of arithmetic expressions over random variables, evaluated in the presence of roundoff errors. It keeps track of complex dependencies between random variables using an SMT solver, and is capable of providing sound but tight probabilistic bounds to roundoff errors using symbolic affine arithmetic. We implemented the algorithm in the PAF tool, and evaluated it on FPBench, a standard benchmark suite for the analysis of roundoff errors. Our evaluation shows that PAF computes tighter bounds than current state-of-the-art on almost all benchmarks.

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Section: Related Workmentioning

confidence: 99%

Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations

Constantinides

Dahlqvist

Rakamarić

et al. 2021

Computer Aided Verification

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“…Range reduction typically involves a mix of integer and floating-point computations, so to bound it we use the approach of Lee, Sharma, and Aiken [Lee et al 2016]. In mixed integer-floating point computations the integer values are constant for some range of floating-point values; for example, when rounding a floating-point value to an integer; all of the float values in the range [0.5, 1.5] round to 1.…”

Section: Implementing New Restricted-range Librariesmentioning

confidence: 99%

Faster Math Functions, Soundly

Briggs,

Panchekha

2021

Preprint

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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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“…Unfortunately, this term means different things in the mathematical and programming communities. We use the definition common for programming tools[19,21,23] …”

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confidence: 99%

Toward a Standard Benchmark Format and Suite for Floating-Point Analysis

Damouche

Martel²,

Panchekha³

et al. 2017

Numerical Software Verification

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We introduce FPBench, a standard benchmark format for validation and optimization of numerical accuracy in floating-point computations. FPBench is a first step toward addressing an increasing need in our community for comparisons and combinations of tools from different application domains. To this end, FPBench provides a basic floatingpoint benchmark format and accuracy measures for comparing different tools. The FPBench format and measures allow comparing and composing different floating-point tools. We describe the FPBench format and measures and show that FPBench expresses benchmarks from recent papers in the literature, by building an initial benchmark suite drawn from these papers. We intend for FPBench to grow into a standard benchmark suite for the members of the floating-point tools research community. 3 We are using |S| to denote the number of elements in a set S 4 Where n is the number of arguments. 5 Where N is the number of valid inputs, and n is the number of arguments.

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Verifying bit-manipulations of floating-point

Cited by 22 publications

References 18 publications

Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations

Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations

Faster Math Functions, Soundly

Toward a Standard Benchmark Format and Suite for Floating-Point Analysis

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