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Annotation of 43BSDReno/lib/libm/common_source/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: (1) source distributions retain this entire copyright
                      7:  * notice and comment, and (2) distributions including binaries display
                      8:  * the following acknowledgement:  ``This product includes software
                      9:  * developed by the University of California, Berkeley and its contributors''
                     10:  * in the documentation or other materials provided with the distribution
                     11:  * and in all advertising materials mentioning features or use of this
                     12:  * software. Neither the name of the University nor the names of its
                     13:  * contributors may be used to endorse or promote products derived
                     14:  * from this software without specific prior written permission.
                     15:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
                     16:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
                     17:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
                     18:  *
                     19:  * All recipients should regard themselves as participants in an ongoing
                     20:  * research project and hence should feel obligated to report their
                     21:  * experiences (good or bad) with these elementary function codes, using
                     22:  * the sendbug(8) program, to the authors.
                     23:  */
                     24: 
                     25: #ifndef lint
                     26: static char sccsid[] = "@(#)atan.c     5.4 (Berkeley) 6/1/90";
                     27: #endif /* not lint */
                     28: 
                     29: /* ATAN(X)
                     30:  * RETURNS ARC TANGENT OF X
                     31:  * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
                     32:  * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
                     33:  *
                     34:  * Required kernel function:
                     35:  *     atan2(y,x) 
                     36:  *
                     37:  * Method:                  
                     38:  *     atan(x) = atan2(x,1.0). 
                     39:  *
                     40:  * Special case:
                     41:  *     if x is NaN, return x itself.
                     42:  *
                     43:  * Accuracy:
                     44:  * 1)  If atan2() uses machine PI, then
                     45:  * 
                     46:  *     atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
                     47:  *     and PI is the exact pi rounded to machine precision (see atan2 for
                     48:  *      details):
                     49:  *
                     50:  *     in decimal:
                     51:  *             pi = 3.141592653589793 23846264338327 ..... 
                     52:  *    53 bits   PI = 3.141592653589793 115997963 ..... ,
                     53:  *    56 bits   PI = 3.141592653589793 227020265 ..... ,  
                     54:  *
                     55:  *     in hexadecimal:
                     56:  *             pi = 3.243F6A8885A308D313198A2E....
                     57:  *    53 bits   PI = 3.243F6A8885A30  =  2 * 1.921FB54442D18   error=.276ulps
                     58:  *    56 bits   PI = 3.243F6A8885A308 =  4 * .C90FDAA22168C2    error=.206ulps
                     59:  *     
                     60:  *     In a test run with more than 200,000 random arguments on a VAX, the 
                     61:  *     maximum observed error in ulps (units in the last place) was
                     62:  *     0.86 ulps.      (comparing against (PI/pi)*(exact atan(x))).
                     63:  *
                     64:  * 2)  If atan2() uses true pi, then
                     65:  *
                     66:  *     atan(x) returns the exact atan(x) with error below about 2 ulps.
                     67:  *
                     68:  *     In a test run with more than 1,024,000 random arguments on a VAX, the 
                     69:  *     maximum observed error in ulps (units in the last place) was
                     70:  *     0.85 ulps.
                     71:  */
                     72: 
                     73: double atan(x)
                     74: double x;
                     75: {
                     76:        double atan2(),one=1.0;
                     77:        return(atan2(x,one));
                     78: }

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