Mathematical Conversations

When designing the first computer built at IAS, von Neumann rejected floating-point arithmetic as neither necessary nor convenient. In 1997 William Kahan at Berkeley, who designed the famously accurate algorithms on Hewlett-Packard calculators, said that "floating–point arithmetic becomes an extremely dull subject (of interest only to anal-compulsives) when it is done correctly. It is not being done correctly." I'll describe the history, philosophy, and current practice of arithmetic with real numbers on computers, hopefully to a broader audience than Kahan had in mind.