NAME
    ahacoversin - inverse half coversed trigonometric sine

SYNOPSIS
    ahacoversin(x [,eps])

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

    return	number

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

    This function is sometimes called ahacovers, or ahacvs, or archacoversin, is equivalent to:

	ahacoversin(x) = asin(1 - 2*x)

EXAMPLE
    ; print ahacoversin(0), ahacoversin(0.5), ahacoversin(1)
    1.57079632679489661923 0 -1.57079632679489661923

    ; print ahacoversin(-0.5), ahacoversin(-1)
    1.57079632679489661923-1.31695789692481670863i 1.57079632679489661923-1.76274717403908605046i

    ; print ahacoversin(.5, 1e-5), ahacoversin(.5, 1e-10), ahacoversin(.5, 1e-15), ahacoversin(.5, 1e-20)
    0 0 0 0

    ; print ahacoversin(5), ahacoversin(5i)
    -1.57079632679489661923+2.88727095035762068505i 0.09918204387849273625-3.00312524371312921749i

    ; print ahacoversin(5+5i)
    -0.73144212314418701068-3.29254348147605425075i

    ; pi = pi(1e-20)
    ; print ahacoversin(pi/6), ahacoversin(pi/3)
    -0.04721509173238348552 -1.57079632679489661923+0.4311526751624601302i

    ; print ahacoversin(4*pi/3)
    -1.57079632679489661923+2.6869677693029370051i

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qahacoversin(NUMBER *x, NUMBER *eps)
    COMPLEX *c_ahacoversin(COMPLEX *x, NUMBER *eps)

SEE ALSO
    sin, cos, tan, cot, sec, csc
    asin, acos, atan, acot, asec, acsc
    versin, coversin, vercos, covercos
    aversin, acoversin, avercos, acovercos
    haversin, hacoversin, havercos, hacovercos
    ahaversin, 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:	2023/09/24 11:17:28
## 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/