Is There a Faster Way to Check if an Integer Falls Within a Given Range?

Fastest Way to Determine if an Integer Is Between Two Integers (Inclusive)

Determining if an integer lies between two other integers is a common operation, and the traditional approach involves using logical AND and inequality comparisons:

x >= start && x <= end

However, is there a faster alternative?

One potential optimization is to use a single comparison/branch. This approach works by converting the number and the lower and upper bounds to unsigned integers and comparing their difference:

if ((unsigned)(number-lower) <= (upper-lower))
    in_range(number);

Why does this work? If the number is below the lower bound, the difference will be negative. If the number is within the range, the difference will be positive and less than or equal to the difference between the upper and lower bounds.

This method has several advantages:

• Reduced branching Instructions (only one comparison needed).
• Improved branch prediction (same branch is taken regardless of the number's position relative to the range).
• Enhanced performance via pre-calculating the difference between upper and lower bounds (minimizing time contributions).

In practice, translating the number and interval to the origin point and testing if the number lies within [0, D], where D = upper - lower, provides the basis for this efficient algorithm. Negative numbers below the lower bound translate to negative values, while numbers above the upper bound translate to values larger than D.

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