88 lines
3.3 KiB
C
88 lines
3.3 KiB
C
/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/* ATAN(X)
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* RETURNS ARC TANGENT OF X
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* DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
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* CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
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*
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* Required kernel function:
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* atan2(y,x)
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*
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* Method:
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* atan(x) = atan2(x,1.0).
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*
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* Special case:
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* if x is NaN, return x itself.
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*
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* Accuracy:
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* 1) If atan2() uses machine PI, then
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*
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* atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
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* and PI is the exact pi rounded to machine precision (see atan2 for
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* details):
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*
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* in decimal:
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* pi = 3.141592653589793 23846264338327 .....
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* 53 bits PI = 3.141592653589793 115997963 ..... ,
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* 56 bits PI = 3.141592653589793 227020265 ..... ,
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*
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* in hexadecimal:
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* pi = 3.243F6A8885A308D313198A2E....
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* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
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* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
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*
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* In a test run with more than 200,000 random arguments on a VAX, the
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* maximum observed error in ulps (units in the last place) was
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* 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))).
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*
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* 2) If atan2() uses true pi, then
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*
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* atan(x) returns the exact atan(x) with error below about 2 ulps.
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*
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* In a test run with more than 1,024,000 random arguments on a VAX, the
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* maximum observed error in ulps (units in the last place) was
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* 0.85 ulps.
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*/
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double atan(x)
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double x;
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{
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double atan2(),one=1.0;
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return(atan2(x,one));
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}
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