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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
72 lines
2.3 KiB
Plaintext
72 lines
2.3 KiB
Plaintext
NAME
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haversin - half versed trigonometric sine
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SYNOPSIS
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haversin(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 number
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DESCRIPTION
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Calculate the half versed trigonometric sine 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 havers, is equivalent to:
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haversin(x) = versin(x) / 2 = (1 - cos(x)) / 2
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EXAMPLE
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; print haversin(1/2), haversin(5/7), haversin(42/7)
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0.06120871905481364194 ~0.12221932664965170076 ~0.01991485667481698972
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; print haversin(1, 1e-5), haversin(1, 1e-10), haversin(1, 1e-15), haversin(1, 1e-20)
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0.22985 0.22984884705 0.22984884706593 0.2298488470659301413
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; print haversin(2 + 3i, 1e-5), haversin(2 + 3i, 1e-10)
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2.594815+4.554615i 2.5948128455+4.5546139469i
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; pi = pi(1e-20)
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; print haversin(pi/6), haversin(pi/2), haversin(pi)
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0.06698729810778067662 0.5 1
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qhaversin(NUMBER *x, NUMBER *eps)
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COMPLEX *c_haversin(COMPLEX *x, NUMBER *eps)
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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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hacoversin, havercos, hacovercos
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ahaversin, hacoversin, havercos, 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 11:14:48
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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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