NAME
    asec - inverse trigonometric secant

SYNOPSIS
    asec(x [,eps])

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

    return	real

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

    This function is sometimes called arcsec.

EXAMPLE
    ; print asec(0), asec(0.5), asec(1)
    Error 10453 1.31695789692481670863i 0

    ; print asec(-0.5), asec(-1)
    3.14159265358979323846-1.31695789692481670863i 3.14159265358979323846

    ; print asec(.5, 1e-5), asec(.5, 1e-10), asec(.5, 1e-15), asec(.5, 1e-20)
    1.31695i 1.316957897i 1.316957896924816i 1.31695789692481670863i

    ; print asec(5), asec(5i)
    1.36943840600456582778 1.57079632679489661923+0.19869011034924140647i

    ; print asec(5+5i)
    1.4711326239351014592+0.10033029811220500594i

    ; pi = pi(1e-20)
    ; print asec(pi/6), asec(pi/3)
    1.26327680856656556836i 0.30137360974529145454

    ; print asec(4*pi/3)
    1.32973601406082299099

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qasec(NUMBER *x, NUMBER *eps)
    COMPLEX *c_asec(COMPLEX *c, NUMBER *epsilon)

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

## 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:	1995/11/13 03:49:00
## File existed as early as:	1995
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/