Intrinsic Compiler Support for Interval Arithmetic

Abstract

Interval arithmetic provides an efficient method for monitoring errors in numerical computations and for solving problems that cannot be efficiently solved with floating-point arithmetic. To support interval arithmetic, several software tools have been developed including interval arithmetic libraries, extended scientific programming languages, and interval-enhanced compilers. The main disadvantage of these software tools is their speed, since interval operations are implemented using function calls. In this paper, compiler support for interval arithmetic is investigated. In particular, the performance benefits of having the compiler inline interval operations to eliminate function call overhead is researched. Interval operations are inlined with the GNU gcc compiler and the performance of interval arithmetic is evaluated on a superscalar architecture. To implement interval operations with compiler support, the compiler produces sequences of instructions that use existing floating point hardware. Simulation results show that the compiler implementation of interval arithmetic is approximately 4 to 5 times faster than a functionally equivalent interval arithmetic software implementation with function call overhead and approximately 1.2 to 1.5 times slower than a dedicated interval arithmetic hardware implementation.