Info Catalog cl: Random Numbers cl: Numbers

cl: Implementation Parameters

 
 8.4 Implementation Parameters
 =============================
 
 This package defines several useful constants having to do with
 floating-point numbers.
 
    It 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 ‘cl-most-positive-float’ have been initialized.
      Until it is called, these parameters will be ‘nil’.  If the
      parameters have already been initialized, the function returns
      immediately.
 
      The algorithm makes assumptions that will be valid for almost all
      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: cl-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: cl-most-negative-float
      This constant equals the most negative value a Lisp float can hold.
      (It is assumed to be equal to ‘(- cl-most-positive-float)’.)
 
  -- Variable: cl-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: cl-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 ‘cl-least-positive-float’.
 
  -- Variable: cl-least-negative-float
      This constant is the negative counterpart of
      ‘cl-least-positive-float’.
 
  -- Variable: cl-least-negative-normalized-float
      This constant is the negative counterpart of
      ‘cl-least-positive-normalized-float’.
 
  -- Variable: cl-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: cl-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’.
 

Info Catalog cl: Random Numbers cl: Numbers