A Simple but Realistic Model of Floating-Point Computation
Warren S. Brown · ACM Transactions on Mathematical Software · 1981
A model of floating-point computation, intended as a basis for efficient portable mathematical software, is presented.The model involves only simple familiar concepts, expressed in a small set of environment parameters.Using these, both a program and its documentation can tailor themselves to the host computer.First, the model numbers, a conventional four-parameter system of floating-point numbers, are introduced.The parameters are the base, the precision, and the minimum and maximum exponents.They must be chosen so that the result of a basic arithmetic operation on model numbers is no less accurate than the result that would be obtained by chopped arithmetic in the model system.Also, the result of a basic operation on operands between model numbers must be bounded by the results of the same operation on the neighboring model numbers.These ideas are summarized in a few fundamental axioms, which enable the machine-independent properties of numerical programs to be stated and proved.The main conclusion is that the model supports conventional, worst case, forward or backward error analyses with only minor qualifications.The model is simple in the sense that its axioms are more easily stated and understood than the detailed operational rules of most floating-point processors.It is realistic in the sense that real computers exhibit most of the forms of behavior (or misbehavior) that it allows, but nearly always conform to its rules.