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!