Semantics-Preserving DPO-Based Term Graph Rewriting

Term graph rewriting is important as "conceptual implementation" of the execution of functional programs, and of data-flow optimisations in compilers. One way to define term graph transformation rule application is via the well-established and intuitively accessible double-pushout (DPO) approach; we present a new result proving semantics preservation for such DPO-based term graph rewriting.Comment: In Proceedings TERMGRAPH 2018, arXiv:1902.0151

SLEEF: A Portable Vectorized Library of C Standard Mathematical Functions

In this paper, we present techniques used to implement our portable vectorized library of C standard mathematical functions written entirely in C language. In order to make the library portable while maintaining good performance, intrinsic functions of vector extensions are abstracted by inline functions or preprocessor macros. We implemented the functions so that they can use sub-features of vector extensions such as fused multiply-add, mask registers and extraction of mantissa. In order to make computation with SIMD instructions efficient, the library only uses a small number of conditional branches, and all the computation paths are vectorized. We devised a variation of the Payne-Hanek argument reduction for trigonometric functions and a floating point remainder, both of which are suitable for vector computation. We compare the performance of our library to Intel SVML.Comment: in IEEE Transactions on Parallel and Distributed Systems. This is a version with all appendices included in a PDF. Accompanying software can be accessed at https://sleef.org or https://codeocean.com/capsule/686101