sign changes when going from int to float and back

Question

Consider the following code, which is an SSCCE of my actual problem:

#include <iostream>  int roundtrip(int x) {     return int(float(x)); }  int main() {     int a = 2147483583;     int b = 2147483584;     std::cout << a << " -> " << roundtrip(a) << '\n';     std::cout << b << " -> " << roundtrip(b) << '\n'; } 

The output on my computer (Xubuntu 12.04.3 LTS) is:

2147483583 -> 2147483520 2147483584 -> -2147483648 

Note how the positive number b ends up negative after the roundtrip. Is this behavior well-specified? I would have expected int-to-float round-tripping to at least preserve the sign correctly...

Hm, on ideone, the output is different:

2147483583 -> 2147483520 2147483584 -> 2147483647 

Did the g++ team fix a bug in the meantime, or are both outputs perfectly valid?

Answer 1

Your program is invoking undefined behavior because of an overflow in the conversion from floating-point to integer. What you see is only the usual symptom on x86 processors.

The float value nearest to 2147483584 is 2³¹ exactly (the conversion from integer to floating-point usually rounds to the nearest, which can be up, and is up in this case. To be specific, the behavior when converting from integer to floating-point is implementation-defined, most implementations define rounding as being “according to the FPU rounding mode”, and the FPU's default rounding mode is to round to the nearest).

Then, while converting from the float representing 2³¹ to int, an overflow occurs. This overflow is undefined behavior. Some processors raise an exception, others saturate. The IA-32 instruction cvttsd2si typically generated by compilers happens to always return INT_MIN in case of overflow, regardless of whether the float is positive or negative.

You should not rely on this behavior even if you know you are targeting an Intel processor: when targeting x86-64, compilers can emit, for the conversion from floating-point to integer, sequences of instructions that take advantage of the undefined behavior to return results other than what you might otherwise expect for the destination integer type.