Basic Arithmetic Functions
This chapter examines the properties of the floor, ceiling, and modulus functions, which are central to our formulation of the RTL primitives as well as the floating-point rounding modes. Thus, their definitions and properties are prerequisite to a reading of the subsequent chapters. We also define and investigate the properties of a function that truncates to a specified number of fractional bits, which is related to the floor and is relevant to the analysis of fixed-point encodings, as discussed in Sect. 2.5.