Emacs version 19 supports floating point numbers, if compiled with the
macro LISP_FLOAT_TYPE defined. The precise range of floating
point numbers is machine-specific; it is the same as the range of the C
data type double on the machine in question.
The printed representation for floating point numbers requires either a decimal point (with at least one digit following), an exponent, or both. For example, `1500.0', `15e2', `15.0e2', `1.5e3', and `.15e4' are five ways of writing a floating point number whose value is 1500. They are all equivalent. You can also use a minus sign to write negative floating point numbers, as in `-1.0'.
Most modern computers support the IEEE floating point standard, which
provides for positive infinity and negative infinity as floating point
values. It also provides for a class of values called NaN or
"not-a-number"; numerical functions return such values in cases where
there is no correct answer. For example, (sqrt -1.0) returns a
NaN. For practical purposes, there's no significant difference between
different NaN values in Emacs Lisp, and there's no rule for precisely
which NaN value should be used in a particular case, so this manual
doesn't try to distinguish them. Emacs Lisp has no read syntax for NaNs
or infinities; perhaps we should create a syntax in the future.
You can use logb to extract the binary exponent of a floating
point number (or estimate the logarithm of an integer):
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