std::isinf does not work with -ffast-math. how to check for infinity

Question

Sample code:

#include <iostream>
#include <cmath>
#include <stdint.h>

using namespace std;

static bool my_isnan(double val) {
    union { double f; uint64_t x; } u = { val };
    return (u.x << 1) > (0x7ff0000000000000u << 1);
}

int main() {
    cout << std::isinf(std::log(0.0)) << endl;
    cout << std::isnan(std::sqrt(-1.0)) << endl;
    cout << my_isnan(std::sqrt(-1.0)) << endl;
    cout << __isnan(std::sqrt(-1.0)) << endl;

    return 0;
}

Online compiler.

With -ffast-math, that code prints "0, 0, 1, 1" -- without, it prints "1, 1, 1, 1".

Is that correct? I thought that std::isinf/std::isnan should still work with -ffast-math in these cases.

Also, how can I check for infinity/NaN with -ffast-math? You can see the my_isnan doing this, and it actually works, but that solution is of course very architecture dependent. Also, why does my_isnan work here and std::isnan does not? What about __isnan and __isinf. Do they always work?

With -ffast-math, what is the result of std::sqrt(-1.0) and std::log(0.0). Does it become undefined, or should it be NaN / -Inf?

Related discussions: (GCC) [Bug libstdc++/50724] New: isnan broken by -ffinite-math-only in g++, (Mozilla) Bug 416287 - performance improvement opportunity with isNaN

Answer 1

Note that -ffast-math may make the compiler ignore/violate IEEE specifications, see http://gcc.gnu.org/onlinedocs/gcc-4.8.2/gcc/Optimize-Options.html#Optimize-Options :

This option is not turned on by any -O option besides -Ofast since it can result in incorrect output for programs that depend on an exact implementation of IEEE or ISO rules/specifications for math functions. It may, however, yield faster code for programs that do not require the guarantees of these specifications.

Thus, using -ffast-math you are not guaranteed to see infinity where you should.

In particular, -ffast-math turns on -ffinite-math-only, see http://gcc.gnu.org/wiki/FloatingPointMath which means (from http://gcc.gnu.org/onlinedocs/gcc-4.8.2/gcc/Optimize-Options.html#Optimize-Options )

[...] optimizations for floating-point arithmetic that assume that arguments and results are not NaNs or +-Infs

This means, by enabling the -ffast-math you make a promise to the compiler that your code will never use infinity or NaN, which in turn allows the compiler to optimize the code by, e.g., replacing any calls to isinf or isnan by the constant false (and further optimize from there). If you break your promise to the compiler, the compiler is not required to create correct programs.

Thus the answer quite simple, if your code may have infinities or NaN (which is strongly implied by the fact that you use isinf and isnan), you cannot enable -ffast-math as else you might get incorrect code.

Your implementation of my_isnan works (on some systems) because it directly checks the binary representation of the floating point number. Of course, the processor still might do (some) actual calculations (depending on which optimizations the compiler does), and thus actual NaNs might appear in memory and you can check their binary representation, but as explained above, std::isnan might have been replaced by the constant false. It might equally well happen that the compiler replaces, e.g., sqrt, by some version that doesn't even produce a NaN for input -1. In order to see which optimisations your compiler does, compile to assembler and look at that code.

To make a (not completely unrelated) analogy, if you're telling your compiler your code is in C++ you can not expect it to compile C code correctly and vice-versa (there are actual examples for this, e.g. Can code that is valid in both C and C++ produce different behavior when compiled in each language? ).

It is a bad idea to enable -ffast-math and use my_isnan because this will make everything very machine- and compiler-dependent you don't know what optimizations the compiler does overall, so there might be other hidden problems related to the fact that you are using non-finite maths but tell the compiler otherwise.

A simple fix is to use -ffast-math -fno-finite-math-only which would still give some optimizations.

It also might be that your code looks something like this:

1. filter out all infinities and NaNs
2. do some finite maths on the filtered values (by this I mean maths that is guaranteed to never create infinities or NaNs, this has to be very, very carefully checked)

In this case, you could split up your code and either use optimize #pragma or __attribute__ to turn -ffast-math (respectively -ffinite-math-only and -fno-finite-math-only) on and off selectively for the given pieces of code (however, I remember there being some trouble with some version of GCC related to this) or just split your code into separate files and compile them with different flags. Of course, this also works in more general settings if you can isolate the parts where infinities and NaNs might occur. If you can not isolate these parts, this is a strong indication that you can not use -ffinite-math-only for this code.

Finally, it's important to understand that -ffast-math is not a harmless optimization that simply makes your program faster. It does not only affect the performance of your code but also its correctness (and this on top of all the issues surrounding floating point numbers already, if I remember right William Kahan has a collection of horror stories on his homepage, see also What every programmer should know about floating point arithmetic). In short, you might get faster code, but also wrong or unexpected results (see below for an example). Hence, you should only use such optimizations when you really know what you are doing and you have made absolutely sure, that either

1. the optimizations don't affect the correctness of that particular code, or
2. the errors introduced by the optimization are not critical to the code.

Program code can actually behave quite differently depending on whether this optimization is used or not. In particular it can behave wrong (or at least very contrary to your expectations) when optimizations such as -ffast-math are enabled. Take the following program for example:

#include <iostream>
#include <limits>

int main() {
  double d = 1.0;
  double max = std::numeric_limits<double>::max();
  d /= max;
  d *= max;
  std::cout << d << std::endl;
  return 0;
}

will produce output 1 as expected when compiled without any optimization flag, but using -ffast-math, it will output 0.