Integer division is commonly (though not always) defined to be truncating in programming languages, meaning the quotient a / b, when a is not an integer multiple of a, rounds towards 0. In this post, all the quantities under consideration will be non-negative, in which case truncating division is the same as "floor division" (quotient…

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Explores ceiling division techniques for graphics programming, specifically for calculating mipmap sizes. Shows how the standard formula (n + k - 1) / k can cause overflow issues and presents an alternative (n - 1) / k + 1 that avoids this problem. Demonstrates how this optimization applies to texture block calculations in formats like BC1-BC7, where working with sizes-minus-1 throughout the pipeline eliminates bias terms and simplifies hardware implementations.

Ceiling division and mip map sizes