How Can Unsigned Integer Conversion Optimize Integer Range Checks?

Determining Integer Range Inclusion with Enhanced Efficiency

Determining whether an integer lies within a specified range is crucial for numerous applications. Traditionally, the approach involves comparing the integer against the range boundaries using logical operators (e.g., >= and <=). However, an optimized technique has emerged, leveraging unsigned integer conversion and a single comparison.

Consider the code snippet:

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

Here, the integer number is converted to an unsigned type using the (unsigned) cast. This conversion flips the sign bit if number is negative, essentially translating the integer line to the origin of the number line.

The term (upper - lower) represents the range difference. When computed outside loops, it becomes a constant value, further optimizing execution speed.

The key insight lies in how unsigned integers are treated. Negative values, when interpreted as unsigned, become larger than positive values. Therefore, if (unsigned)(number - lower) evaluates as negative, number lies below lower. Conversely, if it evaluates as greater than (upper - lower), number exceeds upper.

This method provides several benefits over the traditional approach:

• Reduced branch instructions, improving branch prediction
• Elimination of unnecessary comparisons
• Constant range difference calculation

In real-world scenarios, this optimization can yield significant performance gains, as demonstrated by the speedup observed in the updated code provided. The enhanced code effectively restricts pixels within a circle within a square, a common operation in box blur functions.

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