12.1.4.3 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.