What happens when I assign a number larger than INT_MAX to an int?

Question

Suppose I assign an eleven digits number to an int, what will happen? I played around with it a little bit and I know it's giving me some other numbers within the int range. How is this new number created?

Answer 1

It is implementation-defined behaviour. This means that your compiler must provide documentation saying what happens in this scenario.

So, consult that documentation to get your answer.

A common way that implementations define it is to truncate the input integer to the number of bits of int (after reinterpreting unsigned as signed if necessary).

C++14 Standard references: [expr.ass]/3, [conv.integral]/3

Answer 2

In C++20, this behavior will still be implementation-defined¹ but the requirements are much stronger than before. This is a side-consequence of the requirement to use two's complement representation for signed integer types coming in C++20.

This kind of conversion is specified by [conv.integral]:

1. A prvalue of an integer type can be converted to a prvalue of another integer type. [...]

2. [...]

3. Otherwise, the result is the unique value of the destination type that is congruent to the source integer modulo 2^N, where N is the width of the destination type.

4. [...]

This behaviour is the same as truncating the representation of the number to the width of the integer type you are assigning to, e.g.:

int32_t u = 0x6881736df7939752;

...will kept the 32 right-most bits, i.e., 0xf7939752, and "copy" these bits to u. In two's complement, this corresponds to -141322414.

_{¹ This will still be implementation-defined because the size of int is implementation-defined. If you assign to, e.g., int32_t, then the behaviour is fully defined.}

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Prior to C++20, there were two different rules for unsigned and signed types:

1. A prvalue of an integer type can be converted to a prvalue of another integer type. [...]
2. If the destination type is unsigned, the resulting value is the least unsigned integer congruent to the source integer (modulo 2ⁿ where n is the number of bits used to represent the unsigned type). [...]
3. If the destination type is signed, the value is unchanged if it can be represented in the destination type; otherwise, the value is implementation-defined.