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12.1.4.2 Rule of Float Approximation

Computations with *floats* are only approximate, although they are described as if the results were mathematically accurate. Two mathematically identical expressions may be computationally different because of errors inherent in the floating-point approximation process. The precision of a *float* is not necessarily correlated with the accuracy of that number. For instance, 3.142857142857142857 is a more precise approximation to <PI> than 3.14159, but the latter is more accurate. The precision refers to the number of bits retained in the representation. When an operation combines a *short float* with a *long float*, the result will be a *long float*. Common Lisp functions assume that the accuracy of arguments to them does not exceed their precision. Therefore when two *small floats* are combined, the result is a *small float*. Common Lisp functions never convert automatically from a larger size to a smaller one.

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