Correctly rounded multiplication by arbitrary precision constants

We introduce an algorithm for multiplying a floating-point number x by a constant C that is not exactly representable in floating-point arithmetic. Our algorithm uses a multiplication and a fused multiply and add instruction. We give methods for checking whether, for a given value of C and a given floating-point format, our algorithm returns a correctly rounded result for any x. When it does not, our methods give the values x for which it does not.