Title: Fast Trigonometric Functions using the RLIBM Approach
Author: Sehyeok Park and Santosh Nagarakatte

Abstract:

This paper describes our experience developing polynomial
approximations for trigonometric functions that produce correctly
rounded results for multiple representations and rounding modes using
the RLIBM approach. A key challenge with trigonometric functions
concerns range reduction with π, which reduces a given input in the
domain of a 32-bit float to a small domain. Any rounding error in the
value of π is amplified during range reduction, which can result in
wrong results. We describe our experience implementing fast range
reduction techniques that maintain a large number of bits of π both
with floating-point and integer computations. The resulting
implementations for trigonometric functions are fast and produce
correctly rounded results for all inputs for multiple representations
up to 32-bits with a single implementation.