1 - Floating-Point Arithmetic

Abstract

Roughly speaking, floating-point (FP) arithmetic is the way numerical quantities are handled by the computer. Many different programs rely on FP computations such as control software, weather forecasts, and hybrid systems (embedded systems mixing continuous and discrete behaviors). FP arithmetic corresponds to scientific notation with a limited number of digits for the integer significand. On modern processors, it is specified by the IEEE-754 standard which defines formats, attributes and roundings, exceptional values, and exception handling. FP arithmetic lacks several basic properties of real arithmetic; for example, addition is not associative. FP arithmetic is therefore often considered as strange and unintuitive. This chapter presents some basic knowledge about FP arithmetic, including numbers and their encoding, and operations and rounding. Further readings about FP arithmetic include.