NAME
    avercos - inverse versed trigonometric cosine

SYNOPSIS
    avercos(x [,eps])

TYPES
    x		number (real or complex)
    eps		0 < real < 1, defaults to epsilon()

    return	real

DESCRIPTION
    Returns the inverse versed trigonometric cosine of x to a multiple of eps with error less in
    absolute value than .75 * eps.

    This function is sometimes called averc, or arcvercos, is equivalent to:

	avercos(x) = acos(x - 1)

EXAMPLE
    ; print avercos(0), avercos(0.5), avercos(1)
    3.14159265358979323846 2.09439510239319549231 1.57079632679489661923

    ; print avercos(-0.5), avercos(-1)
    3.14159265358979323846-0.96242365011920689499i 3.14159265358979323846-1.31695789692481670863i

    ; print avercos(.5, 1e-5), avercos(.5, 1e-10), avercos(.5, 1e-15), avercos(.5, 1e-20)
    2.0944 2.0943951024 2.094395102393195 2.09439510239319549231

    ; print avercos(5), avercos(5i)
    2.06343706889556054673i 1.76458946334982880901-2.33097465304931241744i

    ; print avercos(5+5i)
    0.90197975146896932949-2.5513216254756988588i

    ; pi = pi(1e-20)
    ; print avercos(pi/6), avercos(pi/3), avercos(4*pi/3)
    2.06735337024267487468 1.52358123506251313372 1.82724307729474887792i

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qavercos_or_NULL(NUMBER *q, NUMBER *epsilon);
    NUMBER *qavercos(NUMBER *q, NUMBER *epsilon);
    COMPLEX *c_avercos(COMPLEX *c, NUMBER *epsilon);

SEE ALSO
    sin, cos, tan, cot, sec, csc
    asin, acos, atan, acot, asec, acsc
    versin, coversin, vercos, covercos
    aversin, acoversin, acovercos
    haversin, hacoversin, havercos, hacovercos
    ahaversin, hacoversin, havercos, ahacovercos
    epsilon

## Copyright (C) 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:	2023/09/05 23:40:24
## File existed as early as:	2023
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/