Numerical Computing with IEEE Floating Point Arithmetic

A broad overview of numerical computing, in a historical context, with a special focus on the IEEE standard for binary floating point arithmetic. Key ideas are developed step by step, taking the reader from floating point representation, correctly rounded arithmetic, and the IEEE philosophy on exceptions, to an understanding of the crucial concepts of conditioning and stability, explained in a simple yet rigorous context. There are technical details and challenging exercises that go beyond the subjects covered in the text.