math - What are arithmetic underflow and overflow in C?

Question

What do arithmetic underflow and overflow mean in C programming?

Answer 1

Overflow

From http://en.wikipedia.org/wiki/Arithmetic_overflow:

the condition that occurs when a calculation produces a result that is greater in magnitude than that which a given register or storage location can store or represent.

So, for instance:

uint32_t x = 1UL << 31;
x *= 2;  // Overflow!

Note that as @R mentions in a comment below, the C standard suggests:

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.

Of course, this is a fairly idiosyncratic definition of "overflow". Most people would refer to modulo reduction (i.e wrap-around) as "overflow".

Underflow

From http://en.wikipedia.org/wiki/Arithmetic_underflow:

the condition in a computer program that can occur when the true result of a floating point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating point number in the target datatype.

So, for instance:

float x = 1e-30;
x /= 1e20; // Underflow!