Approximating trigonometric functions for posits using the CORDIC method

Abstract

Posit is a recently proposed representation for approximating real numbers using a finite number of bits. In contrast to the floating point (FP) representation, posit provides variable precision with a fixed number of total bits (i.e., tapered accuracy). Posit can represent a set of numbers with higher precision than FP and has garnered significant interest in various domains. The posit ecosystem currently does not have a native general-purpose math library. This paper presents our results in developing a math library for posits using the CORDIC method. CORDIC is an iterative algorithm to approximate trigonometric functions by rotating a vector with different angles in each iteration. This paper proposes two extensions to the CORDIC algorithm to account for tapered accuracy with posits that improves precision: (1) fast-forwarding of iterations to start the CORDIC algorithm at a later iteration and (2) the use of a wide accumulator (i.e., the quire data type) to minimize precision loss with accumulation. Our results show that a 32-bit posit implementation of trigonometric functions with our extensions is more accurate than a 32-bit FP implementation.