2.12 An Introduction to Floating-Point Arithmetic

Integer arithmetic does not let you represent fractional numeric values. Therefore, modern CPUs support an approximation of real arithmetic: floating-point arithmetic. A big problem with floating-point arithmetic is that it does not follow the standard rules of algebra. Nevertheless, many programmers apply normal algebraic rules when using floating-point arithmetic. This is a source of defects in many programs. One of the primary goals of this section is to describe the limitations of floating-point arithmetic so you will understand how to use it properly.

Normal algebraic rules apply only to infinite precision arithmetic. Consider the simple statement x := x + 1, where x is an integer. On any modern ...

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