NAME
    havercos - half versed trigonometric cosine

SYNOPSIS
    havercos(x [,eps])

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

    return	number

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

    This function is sometimes called haverc, or haverconsine, is equivalent to:

	havercos(x) = vercos(x) / 2 = (1 + cos(x)) / 2

EXAMPLE
    ; print havercos(1/2), havercos(5/7), havercos(42/7)
    0.93879128094518635806 ~0.87778067335034829924 ~0.98008514332518301028

    ; print havercos(1, 1e-5), havercos(1, 1e-10), havercos(1, 1e-15), havercos(1, 1e-20)
    0.77015 0.77015115295 0.77015115293407 0.7701511529340698587

    ; print havercos(2 + 3i, 1e-5), havercos(2 + 3i, 1e-10)
    -1.594815-4.554615i -1.5948128455-4.5546139469i

    ; pi = pi(1e-20)
    ; print havercos(pi/6), havercos(pi/2), havercos(pi)
    0.93301270189221932338 0.5 0

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qhavercos(NUMBER *x, NUMBER *eps)
    COMPLEX *c_havercos(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, 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:	2023/09/24 11:13:28
## 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/