Why do constant expressions have an exclusion for undefined behavior?

The wording is actually the subject of defect report #1313 which says:

The requirements for constant expressions do not currently, but should, exclude expressions that have undefined behavior, such as pointer arithmetic when the pointers do not point to elements of the same array.

The resolution being the current wording we have now, so this clearly was intended, so what tools does this give us?

Let’s see what happens when we try to create a constexpr variable with an expression that contains undefined behavior, we will use clang for all the following examples. This code (see it live):

constexpr int x = std::numeric_limits<int>::max() + 1 ;

produces the following error:

error: constexpr variable 'x' must be initialized by a constant expression
    constexpr int x = std::numeric_limits<int>::max() + 1 ;
                  ^   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
note: value 2147483648 is outside the range of representable values of type 'int'
    constexpr int x = std::numeric_limits<int>::max() + 1 ;
                                       ^

This code (see it live):

constexpr int x = 1 << 33 ;  // Assuming 32-bit int

produces this error:

error: constexpr variable 'x' must be initialized by a constant expression
    constexpr int x = 1 << 33 ;  // Assuming 32-bit int
             ^   ~~~~~~~
note: shift count 33 >= width of type 'int' (32 bits)
    constexpr int x = 1 << 33 ;  // Assuming 32-bit int
                  ^

and this code which has undefined behavior in a constexpr function:

constexpr const char *str = "Hello World" ;      

constexpr char access( int index )
{
    return str[index] ;
}

int main()
{
    constexpr char ch = access( 20 ) ;
}

produces this error:

error: constexpr variable 'ch' must be initialized by a constant expression
    constexpr char ch = access( 20 ) ;
                   ^    ~~~~~~~~~~~~

 note: cannot refer to element 20 of array of 12 elements in a constant expression
    return str[index] ;
           ^

Well that is useful the compiler can detect undefined behavior in constexpr, or at least what clang believes is undefined. Note, gcc behaves the same except in the case of undefined behavior with right and left shift, gcc will usually produce a warning in these cases but still sees the expression as constant.

We can use this functionality via SFINAE to detect whether an addition expression would cause overflow, the following contrived example was inspired by dyp’s clever answer here:

#include <iostream>
#include <limits>

template <typename T1, typename T2>
struct addIsDefined
{
     template <T1 t1, T2 t2>
     static constexpr bool isDefined()
     {
         return isDefinedHelper<t1,t2>(0) ;
     }

     template <T1 t1, T2 t2, decltype( t1 + t2 ) result = t1+t2>
     static constexpr bool isDefinedHelper(int)
     {
         return true ;
     }

     template <T1 t1, T2 t2>
     static constexpr bool isDefinedHelper(...)
     {
         return false ;
     }
};


int main()
{    
    std::cout << std::boolalpha <<
      addIsDefined<int,int>::isDefined<10,10>() << std::endl ;
    std::cout << std::boolalpha <<
     addIsDefined<int,int>::isDefined<std::numeric_limits<int>::max(),1>() << std::endl ;
    std::cout << std::boolalpha <<
      addIsDefined<unsigned int,unsigned int>::isDefined<std::numeric_limits<unsigned int>::max(),std::numeric_limits<unsigned int>::max()>() << std::endl ;
}

which results in (see it live):

true
false
true

It is not evident that the standard requires this behavior but apparently this comment by Howard Hinnant indicates it indeed is:

[…] and is also constexpr, meaning UB is caught at compile time

Update

Somehow I missed Issue 695 Compile-time calculation errors in constexpr functions which revolves over the wording of section 5 paragraph 4 which used to say (emphasis mine going forward):

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, unless such an expression appears where an integral constant expression is required (5.19 [expr.const]), in which case the program is ill-formed.

and goes on to say:

intended as an acceptable Standardese circumlocution for “evaluated at compile time,” a concept that is not directly defined by the Standard. It is not clear that this formulation adequately covers constexpr functions.

and a later note says:

[…]There is a tension between wanting to diagnose errors at compile time versus not diagnosing errors that will not actually occur at runtime.[…]The consensus of the CWG was that an expression like 1/0 should simply be considered non-constant; any diagnostic would result from the use of the expression in a context requiring a constant expression.

which if I am reading correctly confirms the intention was to be able to diagnose undefined behavior at compile time in the context requiring a constant expression.

We can not definitely say this was the intent but is does strongly suggest it was. The difference in how clang and gcc treat undefined shifts does leave some room for doubt.

I filed a gcc bug report: Right and left shift undefined behavior not an error in a constexpr. Although it seems like this is conforming, it does break SFINAE and we can see from my answer to Is it a conforming compiler extension to treat non-constexpr standard library functions as constexpr? that divergence in implementation observable to SFINAE users seems undesirable to the committee.

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