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3abedd6713
In cases where the real value to the inverse versed sine and the inverse coversed sine function produces a complex value, the conversion from real to complex was incorrect. Added c_to_q(COMPLEX *c, bool cfree) to make is easier to convert a COMPLEX value that is real (imag part is 0) into a NUMBER and optionally free the COMPLEX value. The func.c code now uses c_to_q(). NOTE: There is a XXX bug marked in the f_aversin() and f_acoversin() that still needs to be fixed.
65 lines
2.0 KiB
Plaintext
65 lines
2.0 KiB
Plaintext
NAME
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aversin - inverse versed trigonometric sine
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SYNOPSIS
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aversin(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 versed 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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The inverse versed sine function is sometimes called avers, sometimes called aver,
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may be defined as:
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aversin(x) = acos(1 - x)
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EXAMPLE
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; print aversin(.5, 1e-5), aversin(.5, 1e-10), aversin(.5, 1e-15), aversin(.5, 1e-20)
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1.0472 1.0471975512 1.047197551196598 1.04719755119659774615
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; print aversin(0), aversin(-5), aversin(2 + 3i)
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0 2.47788873028847500485i 1.87839997632560786916+1.86416154415788242831i
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qaversin_or_NULL(NUMBER *q, NUMBER *epsilon);
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NUMBER *qaversin(NUMBER *q, NUMBER *epsilon);
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COMPLEX *c_aversin(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
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acoversin
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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: 2023/09/03 00:26:24
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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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