Can ptrdiff_t represent all subtractions of pointers to elements of the same array object?

Question

For subtraction of pointers i and j to elements of the same array object the note in [expr.add#5] reads:

[ Note: If the value i−j is not in the range of representable values of type std​::​ptrdiff_­t, the behavior is undefined. — end note ]

But given [support.types.layout#2], which states that (emphasis mine):

2. The type ptrdiff_­t is an implementation-defined signed integer type that can hold the difference of two subscripts in an array object, as described in [expr.add].

Is it even possible for the result of i-j not to be in the range of representable values of ptrdiff_t?

PS: I apologize if my question is caused by my poor understanding of the English language.

EDIT: Related: Why is the maximum size of an array "too large"?

Answer 1

Is it even possible for the result of i-j not to be in the range of representable values of ptrdiff_t?

Yes, but it's unlikely.

In fact, [support.types.layout]/2 does not say much except the proper rules about pointers subtraction and ptrdiff_t are defined in [expr.add]. So let us see this section.

[expr.add]/5

When two pointers to elements of the same array object are subtracted, the type of the result is an implementation-defined signed integral type; this type shall be the same type that is defined as std​::​ptrdiff_­t in the <cstddef> header.

First of all, note that the case where i and j are subscript indexes of different arrays is not considered. This allows to treat i-j as P-Q would be where P is a pointer to the element of an array at subscript i and Q is a pointer to the element of the same array at subscript j. In deed, subtracting two pointers to elements of different arrays is undefined behavior:

[expr.add]/5

If the expressions P and Q point to, respectively, elements x[i] and x[j] of the same array object x, the expression P - Q has the value i−j ; otherwise, the behavior is undefined.

As a conclusion, with the notation defined previously, i-j and P-Q are defined to have the same value, with the latter being of type std::ptrdiff_t. But nothing is said about the possibility for this type to hold such a value. This question can, however, be answered with the help of std::numeric_limits; especially, one can detect if an array some_array is too big for std::ptrdiff_t to hold all index differences:

static_assert(std::numeric_limits<std::ptrdiff_t>::max() > sizeof(some_array)/sizeof(some_array[0]),     "some_array is too big, subtracting its first and one-past-the-end element indexes "     "or pointers would lead to undefined behavior as per [expr.add]/5." ); 

Now, on usual target, this would usually not happen as sizeof(std::ptrdiff_t) == sizeof(void*); which means an array would need to be stupidly big for ptrdiff_t to overflow. But there is no guarantee of it.