The Maximum Value of Signed Integer Types

Question

Is the maximum integer value of signed integer types guaranteed to be
(uintmax_t)pow(2, sizeof(TYPE) * CHAR_BIT - 1) - 1
in C and in C++?

Answer 1

No.

Integer types are permitted to have padding bits which do not contribute to the value. For example, a 32-bit signed integer type with 8 padding bits would have a maximum value of 2²³-1, or 16777215, rather than 2³¹-1, or 2147483647.

This is stated explicitly in the C standard. I haven't found similar wording in the C++ standard, but I think C++ also permits integer types to have padding bits.

But very few compilers take advantage of this permission.

To determine the maximum value of an integer type, use the appropriate *_MAX macro defined in <limits.h>, or in C++ use std::numeric_limits<T>::max() as suggested by cdhowie's comment.

(Incidentally, the pow function is not the best way to denote the value you're asking about. It's a floating-point function, and its result may be inexact in some cases.)

Answer 2

It depends what you mean by "maximum integer value".

If you are asking whether it's guaranteed that a specific implementation will support that maximum value, the answer is no.

But if you are asking whether it's guaranteed that no implementation can exceed that maximum value, the answer is yes.

A positive value in a signed integer can have at most n-1 value bits, where n is the number of bits in the data type. So 2 ^n-1-1 is the maximum possible value of a signed integer of n bits.

No implementation can have a higher maximum, but they can have a lower maximum.