NAME
    haversin - half versed trigonometric sine

SYNOPSIS
    haversin(x [,eps])

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

    return	number

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

    This function is sometimes called havers, is equivalent to:

	haversin(x) = versin(x) / 2 = (1 - cos(x)) / 2

EXAMPLE
    ; print haversin(1/2), haversin(5/7), haversin(42/7)
    0.06120871905481364194 ~0.12221932664965170076 ~0.01991485667481698972

    ; print haversin(1, 1e-5), haversin(1, 1e-10), haversin(1, 1e-15), haversin(1, 1e-20)
    0.22985 0.22984884705 0.22984884706593 0.2298488470659301413

    ; print haversin(2 + 3i, 1e-5), haversin(2 + 3i, 1e-10)
    2.594815+4.554615i 2.5948128455+4.5546139469i

    ; pi = pi(1e-20)
    ; print haversin(pi/6), haversin(pi/2), haversin(pi)
    0.06698729810778067662 0.5 1

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qhaversin(NUMBER *x, NUMBER *eps)
    COMPLEX *c_haversin(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
    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:	2023/09/24 11:14:48
## 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/