mirror of
https://github.com/lcn2/calc.git
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ab95e47c0a
The trigonometric file files have had several bug fixed.
The EXAMPLE sections of trigonometric file have
been made consistent.
Added these new help files in anticipation of
the code for these new (i.e., to be written) builtin functions:
hacovercos hacoversin havercos haversin
ahacovercos ahacoversin ahavercos ahaversin
82 lines
2.7 KiB
Plaintext
82 lines
2.7 KiB
Plaintext
NAME
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ahavercos - inverse half versed trigonometric cosine
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SYNOPSIS
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ahavercos(x [,eps])
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TYPES
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x number (real or complex)
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eps 0 < real < 1, defaults to epsilon()
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return real
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DESCRIPTION
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Returns the inverse half versed trigonometric cosine of x to a multiple of eps with error less in
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absolute value than .75 * eps.
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This function is sometimes called ahaverc, or archavercos, or archavercosine, is equivalent to:
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ahavercos(x) = acos(2*x - 1)
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EXAMPLE
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; print ahavercos(0), ahavercos(0.5), ahavercos(1)
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3.14159265358979323846 1.57079632679489661923 0
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; print ahavercos(-0.5), ahavercos(-1)
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3.14159265358979323846-1.31695789692481670863i 3.14159265358979323846-1.76274717403908605046i
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; print ahavercos(.5, 1e-5), ahavercos(.5, 1e-10), ahavercos(.5, 1e-15), ahavercos(.5, 1e-20)
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1.5708 1.5707963268 1.570796326794897 1.57079632679489661923
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; print ahavercos(5), ahavercos(5i)
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2.88727095035762068505i 1.66997837067338935548-3.00312524371312921749i
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; print ahavercos(5+5i)
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0.83935420365070960856-3.29254348147605425075i
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; pi = pi(1e-20)
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; print ahavercos(pi/6), ahavercos(pi/3)
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1.52358123506251313372 0.4311526751624601302i
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; print ahavercos(4*pi/3)
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2.6869677693029370051i
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qahavercos_or_NULL(NUMBER *q, NUMBER *epsilon);
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NUMBER *qahavercos(NUMBER *q, NUMBER *epsilon);
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COMPLEX *c_ahavercos(COMPLEX *c, NUMBER *epsilon);
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SEE ALSO
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sin, cos, tan, cot, sec, csc
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asin, acos, atan, acot, asec, acsc
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versin, coversin, vercos, covercos
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aversin, acoversin, avercos, acovercos
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haversin, hacoversin, havercos, hacovercos
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ahaversin, hacoversin, ahacovercos
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epsilon
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## Copyright (C) 2023 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 2023/09/24 11:18:04
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## File existed as early as: 2023
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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