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Annotation of 43BSDTahoe/usr.lib/libm/atan.c, revision 1.1.1.1

1.1       root        1: /*
                      2:  * Copyright (c) 1985 Regents of the University of California.
                      3:  * All rights reserved.
                      4:  *
                      5:  * Redistribution and use in source and binary forms are permitted
                      6:  * provided that the above copyright notice and this paragraph are
                      7:  * duplicated in all such forms and that any documentation,
                      8:  * advertising materials, and other materials related to such
                      9:  * distribution and use acknowledge that the software was developed
                     10:  * by the University of California, Berkeley.  The name of the
                     11:  * University may not be used to endorse or promote products derived
                     12:  * from this software without specific prior written permission.
                     13:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
                     14:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
                     15:  * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
                     16:  *
                     17:  * All recipients should regard themselves as participants in an ongoing
                     18:  * research project and hence should feel obligated to report their
                     19:  * experiences (good or bad) with these elementary function codes, using
                     20:  * the sendbug(8) program, to the authors.
                     21:  */
                     22: 
                     23: #ifndef lint
                     24: static char sccsid[] = "@(#)atan.c     5.3 (Berkeley) 6/30/88";
                     25: #endif /* not lint */
                     26: 
                     27: /* ATAN(X)
                     28:  * RETURNS ARC TANGENT OF X
                     29:  * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
                     30:  * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
                     31:  *
                     32:  * Required kernel function:
                     33:  *     atan2(y,x) 
                     34:  *
                     35:  * Method:                  
                     36:  *     atan(x) = atan2(x,1.0). 
                     37:  *
                     38:  * Special case:
                     39:  *     if x is NaN, return x itself.
                     40:  *
                     41:  * Accuracy:
                     42:  * 1)  If atan2() uses machine PI, then
                     43:  * 
                     44:  *     atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
                     45:  *     and PI is the exact pi rounded to machine precision (see atan2 for
                     46:  *      details):
                     47:  *
                     48:  *     in decimal:
                     49:  *             pi = 3.141592653589793 23846264338327 ..... 
                     50:  *    53 bits   PI = 3.141592653589793 115997963 ..... ,
                     51:  *    56 bits   PI = 3.141592653589793 227020265 ..... ,  
                     52:  *
                     53:  *     in hexadecimal:
                     54:  *             pi = 3.243F6A8885A308D313198A2E....
                     55:  *    53 bits   PI = 3.243F6A8885A30  =  2 * 1.921FB54442D18   error=.276ulps
                     56:  *    56 bits   PI = 3.243F6A8885A308 =  4 * .C90FDAA22168C2    error=.206ulps
                     57:  *     
                     58:  *     In a test run with more than 200,000 random arguments on a VAX, the 
                     59:  *     maximum observed error in ulps (units in the last place) was
                     60:  *     0.86 ulps.      (comparing against (PI/pi)*(exact atan(x))).
                     61:  *
                     62:  * 2)  If atan2() uses true pi, then
                     63:  *
                     64:  *     atan(x) returns the exact atan(x) with error below about 2 ulps.
                     65:  *
                     66:  *     In a test run with more than 1,024,000 random arguments on a VAX, the 
                     67:  *     maximum observed error in ulps (units in the last place) was
                     68:  *     0.85 ulps.
                     69:  */
                     70: 
                     71: double atan(x)
                     72: double x;
                     73: {
                     74:        double atan2(),one=1.0;
                     75:        return(atan2(x,one));
                     76: }

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