New algorithms for improved transcendental functions on IA-64

Abstract

The IA-64 architecture provides new opportunities and challenges for implementing an improved set of transcendental functions. Using several novel polynomial-based table-driven techniques, we are able to provide new algorithms for the transcendental functions. Major improvements include an accuracy level of about 0.6 ulps (units in the last place) and forward trigonometric functions that have a period of 2/spl pi/. The accuracy enhancements are achieved at improved speed, yet without an increase in the table size. In this paper, we highlight the key IA-64 architectural features that influenced our designs, and explain the main ideas used in our new algorithms.