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Floating point numbers are useful for representing numbers that are
not integral. 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 you are using.
The read-syntax 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 Emacs Lisp
doesn't try to distinguish them. Here are the read syntaxes for
these special floating point values:
In addition, the value -0.0 is distinguishable from ordinary
zero in IEEE floating point (although equal and = consider
them equal values).
You can use logb to extract the binary exponent of a floating
point number (or estimate the logarithm of an integer):