Checking if a double (or float) is NaN in C++

According to the IEEE standard, NaN values have the odd property that comparisons involving them are always false. That is, for a float f, f != f will be true only if f is NaN.

Note that, as some comments below have pointed out, not all compilers respect this when optimizing code.

For any compiler which claims to use IEEE floating point, this trick should work. But I can't guarantee that it will work in practice. Check with your compiler, if in doubt.

There is no isnan() function available in current C++ Standard Library. It was introduced in C99 and defined as a macro not a function. Elements of standard library defined by C99 are not part of current C++ standard ISO/IEC 14882:1998 neither its update ISO/IEC 14882:2003.

In 2005 Technical Report 1 was proposed. The TR1 brings compatibility with C99 to C++. In spite of the fact it has never been officially adopted to become C++ standard, many (GCC 4.0+ or Visual C++ 9.0+ C++ implementations do provide TR1 features, all of them or only some (Visual C++ 9.0 does not provide C99 math functions).

If TR1 is available, then cmath includes C99 elements like isnan(), isfinite(), etc. but they are defined as functions, not macros, usually in std::tr1:: namespace, though many implementations (i.e. GCC 4+ on Linux or in XCode on Mac OS X 10.5+) inject them directly to std::, so std::isnan is well defined.

Moreover, some implementations of C++ still make C99 isnan() macro available for C++ (included through cmath or math.h), what may cause more confusions and developers may assume it's a standard behaviour.

A note about Viusal C++, as mentioned above, it does not provide std::isnan neither std::tr1::isnan, but it provides an extension function defined as _isnan() which has been available since Visual C++ 6.0

On XCode, there is even more fun. As mentioned, GCC 4+ defines std::isnan. For older versions of compiler and library form XCode, it seems (here is relevant discussion), haven't had chance to check myself) two functions are defined, __inline_isnand() on Intel and __isnand() on Power PC.

There is also a header-only library present in Boost that have neat tools to deal with floating point datatypes

#include <boost/math/special_functions/fpclassify.hpp>

You get the following functions:

template <class T> bool isfinite(T z);
template <class T> bool isinf(T t);
template <class T> bool isnan(T t);
template <class T> bool isnormal(T t);

If you have time then have a look at whole Math toolkit from Boost, it has many useful tools and is growing quickly.

Also when dealing with floating and non-floating points it might be a good idea to look at the Numeric Conversions.

There is an std::isnan if you compiler supports c99 extensions, but I'm not sure if mingw does.

Here is a small function which should work if your compiler doesn't have the standard function:

bool custom_isnan(double var)
{
    volatile double d = var;
    return d != d;
}

You can use numeric_limits<float>::quiet_NaN( ) defined in the limits standard library to test with. There's a separate constant defined for double.

#include <iostream>
#include <math.h>
#include <limits>

using namespace std;

int main( )
{
   cout << "The quiet NaN for type float is:  "
        << numeric_limits<float>::quiet_NaN( )
        << endl;

   float f_nan = numeric_limits<float>::quiet_NaN();

   if( isnan(f_nan) )
   {
       cout << "Float was Not a Number: " << f_nan << endl;
   }

   return 0;
}

I don't know if this works on all platforms, as I only tested with g++ on Linux.

You can use the isnan() function, but you need to include the C math library.

#include <cmath>

As this function is part of C99, it is not available everywhere. If your vendor does not supply the function, you can also define your own variant for compatibility.

inline bool isnan(double x) {
    return x != x;
}

A possible solution that would not depend on the specific IEEE representation for NaN used would be the following:

template<class T>
bool isnan( T f ) {
    T _nan =  (T)0.0/(T)0.0;
    return 0 == memcmp( (void*)&f, (void*)&_nan, sizeof(T) );
}

It seems to me that the best truly cross-platform approach would be to use a union and to test the bit pattern of the double to check for NaNs.

I have not thoroughly tested this solution, and there may be a more efficient way of working with the bit patterns, but I think that it should work.

#include <stdint.h>
#include <stdio.h>

union NaN
{
    uint64_t bits;
    double num;
};

int main()
{
    //Test if a double is NaN
    double d = 0.0 / 0.0;
    union NaN n;
    n.num = d;
    if((n.bits | 0x800FFFFFFFFFFFFF) == 0xFFFFFFFFFFFFFFFF)
    {
        printf("NaN: %f", d);
    }

    return 0;
}

On x86-64 you can have extremely fast methods for checking for NaN and infinity, which work regardless of -ffast-math compiler option. (f != f, std::isnan, std::isinf always yield false with -ffast-math).

Testing for NaN, infinity and finite numbers can easily be done by checking for maximum exponent. infinity is maximum exponent with zero mantissa, NaN is maximum exponent and non-zero mantissa. The exponent is stored in the next bits after the topmost sign bit, so that we can just left shift to get rid of the sign bit and make the exponent the topmost bits, no masking (operator&) is necessary:

static inline uint64_t load_ieee754_rep(double a) {
    uint64_t r;
    static_assert(sizeof r == sizeof a, "Unexpected sizes.");
    std::memcpy(&r, &a, sizeof a); // Generates movq instruction.
    return r;
}

static inline uint32_t load_ieee754_rep(float a) {
    uint32_t r;
    static_assert(sizeof r == sizeof a, "Unexpected sizes.");
    std::memcpy(&r, &a, sizeof a); // Generates movd instruction.
    return r;
}

constexpr uint64_t inf_double_shl1 = UINT64_C(0xffe0000000000000);
constexpr uint32_t inf_float_shl1 = UINT32_C(0xff000000);

// The shift left removes the sign bit. The exponent moves into the topmost bits,
// so that plain unsigned comparison is enough.
static inline bool isnan2(double a)    { return load_ieee754_rep(a) << 1  > inf_double_shl1; }
static inline bool isinf2(double a)    { return load_ieee754_rep(a) << 1 == inf_double_shl1; }
static inline bool isfinite2(double a) { return load_ieee754_rep(a) << 1  < inf_double_shl1; }
static inline bool isnan2(float a)     { return load_ieee754_rep(a) << 1  > inf_float_shl1; }
static inline bool isinf2(float a)     { return load_ieee754_rep(a) << 1 == inf_float_shl1; }
static inline bool isfinite2(float a)  { return load_ieee754_rep(a) << 1  < inf_float_shl1; }

The std versions of isinf and isfinite load 2 double/float constants from .data segment and in the worst case scenario they can cause 2 data cache misses. The above versions do not load any data, inf_double_shl1 and inf_float_shl1 constants get encoded as immediate operands into the assembly instructions.

Faster isnan2 is just 2 assembly instructions:

bool isnan2(double a) {
    bool r;
    asm(".intel_syntax noprefix"
        "\n\t ucomisd %1, %1"
        "\n\t setp %b0"
        "\n\t .att_syntax prefix"
        : "=g" (r)
        : "x" (a)
        : "cc"
        );
    return r;
}

Uses the fact that ucomisd instruction sets parity flag if any argument is NaN. This is how std::isnan works when no -ffast-math options is specified.

This detects infinity and also NaN in Visual Studio by checking it is within double limits:

//#include <float.h>
double x, y = -1.1; x = sqrt(y);
if (x >= DBL_MIN && x <= DBL_MAX )
    cout << "DETECTOR-2 of errors FAILS" << endl;
else
    cout << "DETECTOR-2 of errors OK" << endl;