Can One Comparison Replace Two When Checking Integer Bounds?

Efficient Integer Bound Checking: A One-Comparison Approach

A crucial operation in various computational tasks is determining if an integer lies within a specified range. Traditional methods use both greater than and less than operators, resulting in multiple comparisons and potential branches. This can be a noticeable performance overhead, especially in time-sensitive applications.

To address this challenge, a clever trick exists that leverages only one comparison/branch. This technique works by:

• Converting both the integer and the range to unsigned values (a nop for modern computers using twos complement).
• Using a less than operator (<) for an inclusive lower bound and exclusive upper bound, or a less than or equal to operator (<=) for an inclusive upper bound.

If the condition ((unsigned)(number-lower) < (upper-lower)) evaluates to true, the integer is within the range.

One benefit of this approach is that it pre-computes upper-lower, which can be done outside of a loop. This reduces overall computation time. Additionally, it improves branch prediction as the same branch is taken regardless of whether the number is below or above the range.

Real-World Impact:

In a box blur function that restricts pixels to a circle within a square, this method yielded an order of magnitude speedup compared to the traditional >= and <= operators. Code profiling revealed a significant reduction in branching instructions, demonstrating the practical advantages of this optimization technique.

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