DeepAI AI Chat
Log In Sign Up

Sound Approximation of Programs with Elementary Functions

by   Eva Darulova, et al.
Max Planck Institute for Software Systems

Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is, however, not always needed. Unlike arithmetic, where the performance difference between for example single and double precision floating-point arithmetic is relatively small, elementary function calls provide a much richer tradeoff space between accuracy and efficiency. Navigating this space is challenging. First, generating approximations of elementary function calls which are guaranteed to satisfy accuracy error bounds is highly nontrivial. Second, the performance of such approximations generally depends on several parameters which are unintuitive to choose manually, especially for non-experts. We present a fully automated approach and tool which approximates elementary function calls inside small programs while guaranteeing overall user provided error bounds. Our tool leverages existing techniques for roundoff error computation and approximation of individual elementary function calls, and provides automated selection of many parameters. Our experiments show that significant efficiency improvements are possible in exchange for reduced, but guaranteed, accuracy.


page 1

page 2

page 3

page 4


Dandelion: Certified Approximations of Elementary Functions

Elementary function operations such as sin and exp cannot in general be ...

Sound Mixed-Precision Optimization with Rewriting

Finite-precision arithmetic computations face an inherent tradeoff betwe...

Elementary analytic functions in VTC^0

It is known that rational approximations of elementary analytic function...

Bernstein approximation and beyond: proofs by means of elementary probability theory

Bernstein polynomials provide a constructive proof for the Weierstrass a...

Elementary Sets for Logic Programs

By introducing the concepts of a loop and a loop formula, Lin and Zhao s...

Hierarchical Lowrank Arithmetic with Binary Compression

With lowrank approximation the storage requirements for dense data are r...

Accurate Computation of the Log-Sum-Exp and Softmax Functions

Evaluating the log-sum-exp function or the softmax function is a key ste...