How to Square Floats Accurately and Efficiently on the ST231 Integer Processor

Abstract

We consider the problem of computing IEEE floating-point squares by means of integer arithmetic. We show how to exploit the specific properties of squaring in order to design and implement algorithms that have much lower latency than those for general multiplication, while still guaranteeing correct rounding. Our algorithms are parameterized by the floating-point format, aim at high instruction-level parallelism (ILP) exposure, and cover all rounding modes. We show further that their C implementation for the binary32 format yields efficient codes for targets like the ST231 VLIW integer processor from ST Microelectronics, with a latency at least 1.75x smaller than that of general multiplication in the same context.