ANSI Common Lisp 12 Numbers 12.1 Number Concepts 12.1.4 Floating-point Computations
126.96.36.199 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
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.