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(elisp)Float Basics

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Floating Point Basics
=====================

   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:

positive infinity
     `1.0e+INF'

negative infinity
     `-1.0e+INF'

Not-a-number
     `0.0e+NaN'.

   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):

 - Function: logb number
     This function returns the binary exponent of NUMBER.  More
     precisely, the value is the logarithm of NUMBER base 2, rounded
     down to an integer.

          (logb 10)
               => 3
          (logb 10.0e20)
               => 69