Elementary function evaluation using New Hardware Instruction

Abstract

<p>In this thesis, we present novel fast and accurate hardware/ software implementations of the elementary math functions based on range reduction, e.g. Berner's multiplicative reduction and Gal's accurate table methods. The software implementations are branch free , because the new instructions we are proposing internalize the control flow associated with handling exceptional cases.</p> <p>These methods provide an alternative to common iterative methods of computing reciprocal, square root and reciprocal square root. These methods could be applied to any rationalpower operation. These methods require either the precision available through fused multiply-accumulate instructions or extra working precision in registers. We also extend the range reduction methods to include trigonometric and inverse trigonometric functions.</p> <p>The new hardware instructions enable exception handling at no additional cost in execution time, and scale linearly with increasing superscalar and SIMD widths. Based on reduced instruction, constant counts, and reduced register pressure we would recommend that optimizing compilers always in-line such functions, further improving performance by eliminating function-call overhead.</p> <p>On the Cell/B.E. SPU, we found an overall 234% increase in throughput for the new table-based methods, with increased accuracy.</p> <p>The research reported in the thesis has resulted in a patent application [AESIO], filed jointly with IBM.</p>