English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Mainstream math libraries for floating point (FP) do not produce correctlyrounded results for all inputs. In contrast, CR-LIBM and RLIBM providecorrectly rounded implementations for a specific FP representation with onerounding mode. Using such libraries for a representation with a new roundingmode or with different precision will result in wrong results due to doublerounding. This paper proposes a novel method to generate a single polynomialapproximation that produces correctly rounded results for all inputs formultiple rounding modes and multiple precision configurations. To generate acorrectly rounded library for $n$-bits, our key idea is to generate such apolynomial approximation for a representation with $n+2$-bits using the\emph{round-to-odd} mode. We prove that the resulting polynomial approximationwill produce correctly rounded results for all five rounding modes in thestandard and for multiple representations with $k$-bits such that $|E| +1 < k\leq n$, where $|E|$ is the number of exponent bits in the representation.Building on our prior work in the RLIBM project, we also approximate thecorrectly rounded result when we generate the library with $n+2$-bits using theround-to-odd mode. We also generate polynomial approximations by structuring itas a linear programming problem but propose enhancements to polynomialgeneration to handle the round-to-odd mode. Our prototype is the first 32-bitfloat library that produces correctly rounded results with all rounding modesin the IEEE standard for all inputs with a single polynomial approximation. Italso produces correctly rounded results for any FP configuration ranging from10-bits to 32-bits while also being faster than mainstream libraries.

RLIBM-ALL: A Novel Polynomial Approximation Method to Produce Correctly Rounded Results for Multiple Representations and Rounding Modes