Why is unsigned integer overflow defined behavior but signed integer overflow isn't?

Question

Unsigned integer overflow is well defined by both the C and C++ standards. For example, the C99 standard (§6.2.5/9) states

A computatio

Answer 1

First of all, please note that C11 3.4.3, like all examples and foot notes, is not normative text and therefore not relevant to cite!

The relevant text that states that overflow of integers and floats is undefined behavior is this:

C11 6.5/5

If an exceptional condition occurs during the evaluation of an expression (that is, if the result is not mathematically defined or not in the range of representable values for its type), the behavior is undefined.

A clarification regarding the behavior of unsigned integer types specifically can be found here:

C11 6.2.5/9

The range of nonnegative values of a signed integer type is a subrange of the corresponding unsigned integer type, and the representation of the same value in each type is the same. A computation involving unsigned operands can never overflow, because a result that cannot be represented by the resulting unsigned integer type is reduced modulo the number that is one greater than the largest value that can be represented by the resulting type.

This makes unsigned integer types a special case.

Also note that there is an exception if any type is converted to a signed type and the old value can no longer be represented. The behavior is then merely implementation-defined, although a signal may be raised.

C11 6.3.1.3

6.3.1.3 Signed and unsigned integers

When a value with integer type is converted to another integer type other than _Bool, if the value can be represented by the new type, it is unchanged.

Otherwise, if the new type is unsigned, the value is converted by repeatedly adding or subtracting one more than the maximum value that can be represented in the new type until the value is in the range of the new type.

Otherwise, the new type is signed and the value cannot be represented in it; either the result is implementation-defined or an implementation-defined signal is raised.