Floating-point computation with just enough accuracy

Most mathematical formulae are defined in terms of operations on real numbers, but computers can only operate on numeric values with finite precision and range. Using floating-point values as real numbers does not clearly identify the precision with which each value must be represented. Too little precision yields inaccurate results; too much wastes computational resources. The popularity of multimedia applications has made fast hardware support for low-precision floating-point arithmetic common in Digital Signal Processors (DSPs), SIMD Within A Register (SWAR) instruction set extensions for general purpose processors, and in Graphics Processing Units (GPUs). In this paper, we describe a simple approach by which the speed of these low-precision operations can be speculatively employed to meet user-specified accuracy constraints. Where the native precision(s) yield insufficient accuracy, a simple technique is used to efficiently synthesize enhanced precision using pairs of native values.