74 lines
2.5 KiB
C
74 lines
2.5 KiB
C
/*
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted provided
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* that: (1) source distributions retain this entire copyright notice and
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* comment, and (2) distributions including binaries display the following
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* acknowledgement: ``This product includes software developed by the
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* University of California, Berkeley and its contributors'' in the
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* documentation or other materials provided with the distribution and in
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* all advertising materials mentioning features or use of this software.
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* Neither the name of the University nor the names of its contributors may
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* be used to endorse or promote products derived from this software without
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* specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)atan.c 5.5 (Berkeley) 10/9/90";
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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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