Floor and Ceil Versus Denormals on CPU and GPU

Recently, I dove deep into floating-point numbers and their behavior. Somehow, this topic haunts me in my programming practice since I created Floating-Point Formats Cheatsheet back in 2013 and also released a comprehensive article The Secrets of Floating-Point Numbers in 2024. This time, I would like to focus on one specific question: What is the result of floor(-1.175493930432748e-38) ? Note: Hexadecimal value of our input number is 0x807FFFFD. Floor, ceil, trunc, round To recap, floor, ceil, trunc, round are functions available in the standard library of C, C++, as well as shading languages: HLSL and GLSL. Each of them transforms a floating-point number into an integral floating-point value, but using different rounding rules. Note this is not about a conversion from float to int. The result of these functions is still a float, just having only integral part. When the input is already integral, the value is returned as-is. Otherwise, it gets "snapped" to the nearest integer in a…