NAME
    abs - absolute value

SYNOPSIS
    abs(x [,eps])

TYPES
    If x is an object of type xx, the function xx_abs has to have
    been defined; this will determine the types for x, eps and
    the returned value.

    For non-object x and eps:

    x           number (real or complex)
    eps         ignored if x is real, nonzero real for complex x,
                defaults to epsilon().

    return      non-negative real

DESCRIPTION
    If x is real, returns the absolute value of x, i.e. x if x >= 0,
    -x if x < 0.

    For complex x with zero real part, returns the absolute value of im(x).

    For other complex x, returns the multiple of eps nearest to the absolute
    value of x, or in the case of two equally near nearest values, the
    the nearest even multiple of eps.  In particular, with eps = 10^-n,
    the result will be the absolute value correct to n decimal places.

EXAMPLE
    ; print abs(3.4), abs(-3.4)
    3.4 3.4

    ; print abs(3+4i, 1e-5), abs(4+5i, 1e-5), abs(4+5i, 1e-10)
    5 6.40312 6.4031242374

LIMITS
    when x is complex, eps != 0

LINK LIBRARY
    NUMBER *qqabs(NUMBER *x)

SEE ALSO
    cmp, epsilon, hypot, norm, near, obj

## Copyright (C) 1999,2021,2023  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:   1994/03/19 01:40:22
## File existed as early as:    1994
##
## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
