Floating-Point Computation with Just Enough Accuracy

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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.