The behaviour of floating point division by zero

Consider

#include <iostream>
int main()
{
    double a = 1.0 / 0;
    double b = -1.0 / 0;
    double c = 0.0 / 0;
    std::cout << a << b << c; // to stop compilers from optimising out the code.    
}

I have always thought that a will be +Inf, b will be -Inf, and c will be NaN. But I also hear rumours that strictly speaking the behaviour of floating point division by zero is undefined and therefore the above code cannot considered to be portable C++. (That theoretically obliterates the integrity of my million line plus code stack. Oops.)

Who's correct?

Note I'm happy with implementation defined, but I'm talking about cat-eating, demon-sneezing undefined behaviour here.

C++ standard does not force the IEEE 754 standard, because that depends mostly on hardware architecture.

If the hardware/compiler implement correctly the IEEE 754 standard, the division will provide the expected INF, -INF and NaN, otherwise... it depends.

Undefined means, the compiler implementation decides, and there are many variables to that like the hardware architecture, code generation efficiency, compiler developer laziness, etc..

Source:

The C++ standard state that a division by 0.0 is undefined

> C++ Standard 5.6.4 > > ... If the second operand of / or % is zero the behavior is undefined > > C++ Standard 18.3.2.4 > > ...static constexpr bool is_iec559; > > ...56. True if and only if the type adheres to IEC 559 standard.217 > > ...57. Meaningful for all floating point types.

C++ detection of IEEE754:

The standard library includes a template to detect if IEEE754 is supported or not:

> static constexpr bool is_iec559;

#include <numeric>
bool isFloatIeee754 = std::numeric_limits<float>::is_iec559();

What if IEEE754 is not supported?

It depends, usually a division by 0 trigger a hardware exception and make the application terminate.

Quoting cppreference:

> If the second operand is zero, the behavior is undefined, except that if floating-point division is taking place and the type supports IEEE floating-point arithmetic (see std::numeric_limits::is_iec559), then: > >- if one operand is NaN, the result is NaN > >- dividing a non-zero number by ±0.0 gives the correctly-signed infinity and FE_DIVBYZERO is raised > >- dividing 0.0 by 0.0 gives NaN and FE_INVALID is raised

We are talking about floating-point division here, so it is actually implementation-defined whether double division by zero is undefined.

If std::numeric_limits<double>::is_iec559 is true, and it is "usually true", then the behaviour is well-defined and produces the expected results.

A pretty safe bet would be to plop down a:

static_assert(std::numeric_limits<double>::is_iec559, "Please use IEEE754, you weirdo");

... near your code.

Division by zero both integer and floating point are undefined behavior [expr.mul]p4:

>The binary / operator yields the quotient, and the binary % operator yields the remainder from the division of the first expression by the second. If the second operand of / or % is zero the behavior is undefined. ...

Although implementation can optionally support Annex F which has well defined semantics for floating point division by zero.

We can see from this clang bug report clang sanitizer regards IEC 60559 floating-point division by zero as undefined that even though the macro STDC_IEC_559 is defined, it is being defined by the system headers and at least for clang does not support Annex F and so for clang remains undefined behavior:

> > Annex F of the C standard (IEC 60559 / IEEE 754 support) defines the > > floating-point division by zero, but clang (3.3 and 3.4 Debian snapshot) > > regards it as undefined. This is incorrect: > > Support for Annex F is optional, and we do not support it. > > > #if STDC_IEC_559 > > This macro is being defined by your system headers, not by us; this is > a bug in your system headers. (FWIW, GCC does not fully support Annex > F either, IIRC, so it's not even a Clang-specific bug.)

That bug report and two other bug reports UBSan: Floating point division by zero is not undefined and clang should support Annex F of ISO C (IEC 60559 / IEEE 754) indicate that gcc is conforming to Annex F with respect to floating point divide by zero.

>Though I agree that it isn't up to the C library to define STDC_IEC_559 unconditionally, the problem is specific to clang. GCC does not fully support Annex F, but at least its intent is to support it by default and the division is well-defined with it if the rounding mode isn't changed. Nowadays not supporting IEEE 754 (at least the basic features like the handling of division by zero) is regarded as bad behavior.

This is further support by the gcc Semantics of Floating Point Math in GCC wiki which indicates that -fno-signaling-nans is the default which agrees with the gcc optimizations options documentation which says:

> The default is -fno-signaling-nans.

Interesting to note that UBSan for clang defaults to including float-divide-by-zero under -fsanitize=undefined while gcc does not:

>Detect floating-point division by zero. Unlike other similar options, -fsanitize=float-divide-by-zero is not enabled by -fsanitize=undefined, since floating-point division by zero can be a legitimate way of obtaining infinities and NaNs.

See it live for clang and live for gcc.

Division by 0 is undefined behavior.

From section 5.6 of the C++ standard (C++11):

> The binary / operator yields the quotient, and the binary % operator > yields the remainder from the division of the first expression by the > second. If the second operand of / or % is zero the behavior is > undefined. For integral operands the / operator yields the algebraic > quotient with any fractional part discarded; if the quotient a/b is > representable in the type of the result, (a/b)*b + a%b is equal to a .

No distinction is made between integer and floating point operands for the / operator. The standard only states that dividing by zero is undefined without regard to the operands.

In [expr]/4 we have

> If during the evaluation of an expression, the result is not mathematically defined or not in the range of representable values for its type, the behavior is undefined. [ Note: most existing implementations of C++ ignore integer overflows. Treatment of division by zero, forming a remainder using a zero divisor, and all floating point exceptions vary among machines, and is usually adjustable by a library function. —end note ]

^{Emphasis mine}

So per the standard this is undefined behavior. It does go on to say that some of these cases are actually handled by the implementation and are configurable. So it won't say it is implementation defined but it does let you know that implementations do define some of this behavior.

As to the submitter's question 'Who's correct?', it is perfectly OK to say that both answers are correct. The fact that the C standard describes the behavior as 'undefined' DOES NOT dictate what the underlying hardware actually does; it merely means that if you want your program to be meaningful according to the standard you -may not assume- that the hardware actually implements that operation. But if you happen to be running on hardware that implements the IEEE standard, you will find the operation is in fact implemented, with the results as stipulated by the IEEE standard.

This also depends on the floating point environment.

cppreference has details: http://en.cppreference.com/w/cpp/numeric/fenv (no examples though).

This should be available in most desktop/server C++11 and C99 environments. There are also platform-specific variations that predate the standardization of all this.

I would expect that enabling exceptions makes the code run more slowly, so probably for this reason most platforms that I know of disable exceptions by default.