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(cl)Implementation Parameters

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Implementation Parameters
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This package defines several useful constants having to with numbers.

 - Variable: most-positive-fixnum
     This constant equals the largest value a Lisp integer can hold.
     It is typically `2^23-1' or `2^25-1'.

 - Variable: most-negative-fixnum
     This constant equals the smallest (most negative) value a Lisp
     integer can hold.

   The following parameters have to do with floating-point numbers.
This package determines their values by exercising the computer's
floating-point arithmetic in various ways.  Because this operation
might be slow, the code for initializing them is kept in a separate
function that must be called before the parameters can be used.

 - Function: cl-float-limits
     This function makes sure that the Common Lisp floating-point
     parameters like `most-positive-float' have been initialized.
     Until it is called, these parameters will be `nil'.  If this
     version of Emacs does not support floats, the parameters will
     remain `nil'.  If the parameters have already been initialized,
     the function returns immediately.

     The algorithm makes assumptions that will be valid for most modern
     machines, but will fail if the machine's arithmetic is extremely
     unusual, e.g., decimal.

   Since true Common Lisp supports up to four different floating-point
precisions, it has families of constants like
`most-positive-single-float', `most-positive-double-float',
`most-positive-long-float', and so on.  Emacs has only one
floating-point precision, so this package omits the precision word from
the constants' names.

 - Variable: most-positive-float
     This constant equals the largest value a Lisp float can hold.  For
     those systems whose arithmetic supports infinities, this is the
     largest _finite_ value.  For IEEE machines, the value is
     approximately `1.79e+308'.

 - Variable: most-negative-float
     This constant equals the most-negative value a Lisp float can hold.
     (It is assumed to be equal to `(- most-positive-float)'.)

 - Variable: least-positive-float
     This constant equals the smallest Lisp float value greater than
     zero.  For IEEE machines, it is about `4.94e-324' if denormals are
     supported or `2.22e-308' if not.

 - Variable: least-positive-normalized-float
     This constant equals the smallest _normalized_ Lisp float greater
     than zero, i.e., the smallest value for which IEEE denormalization
     will not result in a loss of precision.  For IEEE machines, this
     value is about `2.22e-308'.  For machines that do not support the
     concept of denormalization and gradual underflow, this constant
     will always equal `least-positive-float'.

 - Variable: least-negative-float
     This constant is the negative counterpart of
     `least-positive-float'.

 - Variable: least-negative-normalized-float
     This constant is the negative counterpart of
     `least-positive-normalized-float'.

 - Variable: float-epsilon
     This constant is the smallest positive Lisp float that can be added
     to 1.0 to produce a distinct value.  Adding a smaller number to 1.0
     will yield 1.0 again due to roundoff.  For IEEE machines, epsilon
     is about `2.22e-16'.

 - Variable: float-negative-epsilon
     This is the smallest positive value that can be subtracted from
     1.0 to produce a distinct value.  For IEEE machines, it is about
     `1.11e-16'.