Floating points, you sure?

What this C++ floating-point precision question tests

This hard question probes deep knowledge of how C++ handles floating-point representation and comparison. It is the kind of trap that firms like Meta use to separate candidates who understand the language spec from those who rely on intuition alone. The question rewards careful reasoning about IEEE 754 semantics, compiler behavior, and the subtle gaps between what code looks like and what it actually does.

To approach questions like this, you must think through the binary representation of floating-point values, rounding errors introduced by arithmetic, and how equality checks behave when values are not exactly representable. A strong answer shows awareness of precision loss, implicit conversions, and the difference between what a naive reading of the code suggests and what the machine actually executes.

• IEEE 754 single and double precision
• Rounding modes and accumulated error
• Floating-point comparison and identity
• Compiler optimizations and their interaction with floating-point code