An approach to generate correctly rounded math libraries for new floating point variants

Jay P. Lim, Mridul Aanjaneya, John Gustafson, Santosh Nagarakatte

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Given the importance of floating point (FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and posits). These representations do not have correctly rounded math libraries. Further, the use of existing FP libraries for these new representations can produce incorrect results. This paper proposes a novel approach for generating polynomial approximations that can be used to implement correctly rounded math libraries. Existing methods generate polynomials that approximate the real value of an elementary function () and produce wrong results due to approximation errors and rounding errors in the implementation. In contrast, our approach generates polynomials that approximate the correctly rounded value of () (i.e., the value of () rounded to the target representation). It provides more margin to identify efficient polynomials that produce correctly rounded results for all inputs. We frame the problem of generating efficient polynomials that produce correctly rounded results as a linear programming problem. Using our approach, we have developed correctly rounded, yet faster, implementations of elementary functions for multiple target representations.

Original languageEnglish (US)
Article number29
JournalProceedings of the ACM on Programming Languages
Volume5
Issue numberPOPL
DOIs
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Software
  • Safety, Risk, Reliability and Quality

Keywords

  • correctly rounded math libraries
  • floating point
  • posits

Fingerprint

Dive into the research topics of 'An approach to generate correctly rounded math libraries for new floating point variants'. Together they form a unique fingerprint.

Cite this