GoKawiilRecently, 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 specific direction:
floor - rounding "down" i.e., towards -infinity.
- rounding "down" i.e., towards -infinity. ceil - rounding "up" i.e., towards +infinity.
- rounding "up" i.e., towards +infinity. trunc - rounding towards zero, which we can also explain as truncating the fractional part.
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