Why Does Integer Multiplication Lead to Overflow in C ?

Integer Overflow: When Multiplication Leads to Disaster

In C , it's essential to understand integer sizes and types to avoid potential overflows. Let's examine the following code snippet:

long long int n = 2000*2000*2000*2000;    // overflow

long long int n = pow(2000,4);            // works
long long int n = 16000000000000;         // works

Why does the first line result in overflow, while the other two work without issue?

The culprit lies in the way C handles integer literals and arithmetic operations. By default, integer literals are of the smallest type that can hold their value but not smaller than int. In this case, 2000 is an int, typically a 32-bit type.

When performing arithmetic operations, the compiler follows specific rules based on operand types. In this scenario, the multiplication is done with ints, which is the larger of the types involved. However, the assignment is irrelevant as C does not infer types based on destination.

The result of the multiplication, which exceeds the capacity of int, is stored as int, leading to an overflow. This is why the first line triggers an overflow, while the other two do not.

To resolve this issue, we can explicitly specify the type of the constant used in the first line by appending the suffix LL (or ll). This ensures that the literal is treated as a long long int, preventing overflow.

By understanding how integer types and arithmetic operations work in C , we can avoid potential pitfalls and ensure that our code handles data manipulation correctly.

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