NAME
    aversin - inverse versed trigonometric sine

SYNOPSIS
    aversin(x [,eps])

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

    return	real

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

    This function is sometimes called avers, or arcversin, is equivalent to:

	aversin(x) = acos(1 - x)

EXAMPLE
    ; print aversin(0), aversin(0.5), aversin(1)
    0 1.04719755119659774615 1.57079632679489661923

    ; print aversin(-0.5), aversin(-1)
    0.96242365011920689498i 1.31695789692481670863i

    ; print aversin(.5, 1e-5), aversin(.5, 1e-10), aversin(.5, 1e-15), aversin(.5, 1e-20)
    1.0472 1.0471975512 1.047197551196598 1.04719755119659774615

    ; print aversin(5), aversin(5i)
    3.14159265358979323846-2.06343706889556054673i 1.37700319023996442947+2.33097465304931241742i

    ; print aversin(5+5i)
    2.23961290212082390892+2.55132162547569885882i

    ; pi = pi(1e-20)
    ; print aversin(pi/6), aversin(pi/3), aversin(4*pi/3)
    1.07423928334711836378 1.61801141852728010475 3.14159265358979323846-1.82724307729474887791i

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qaversin_or_NULL(NUMBER *q, NUMBER *epsilon);
    NUMBER *qaversin(NUMBER *q, NUMBER *epsilon);
    COMPLEX *c_aversin(COMPLEX *c, NUMBER *epsilon);

SEE ALSO
    sin, cos, tan, cot, sec, csc
    asin, acos, atan, acot, asec, acsc
    versin, coversin, vercos, covercos
    acoversin, avercos, 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:	2023/09/03 00:26:24
## 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/