Return to atan.c CVS log

Up to [CSRG BSD Unix] / 43BSD / usr.lib / libm

Annotation of 43BSD/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:  * 
                      4:  * Use and reproduction of this software are granted  in  accordance  with
                      5:  * the terms and conditions specified in  the  Berkeley  Software  License
                      6:  * Agreement (in particular, this entails acknowledgement of the programs'
                      7:  * source, and inclusion of this notice) with the additional understanding
                      8:  * that  all  recipients  should regard themselves as participants  in  an
                      9:  * ongoing  research  project and hence should  feel  obligated  to report
                     10:  * their  experiences (good or bad) with these elementary function  codes,
                     11:  * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
                     12:  */
                     13: 
                     14: #ifndef lint
                     15: static char sccsid[] = "@(#)atan.c     1.1 (Berkeley) 8/21/85";
                     16: #endif not lint
                     17: 
                     18: /* ATAN(X)
                     19:  * RETURNS ARC TANGENT OF X
                     20:  * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
                     21:  * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
                     22:  *
                     23:  * Required kernel function:
                     24:  *     atan2(y,x) 
                     25:  *
                     26:  * Method:                  
                     27:  *     atan(x) = atan2(x,1.0). 
                     28:  *
                     29:  * Special case:
                     30:  *     if x is NaN, return x itself.
                     31:  *
                     32:  * Accuracy:
                     33:  * 1)  If atan2() uses machine PI, then
                     34:  * 
                     35:  *     atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
                     36:  *     and PI is the exact pi rounded to machine precision (see atan2 for
                     37:  *      details):
                     38:  *
                     39:  *     in decimal:
                     40:  *             pi = 3.141592653589793 23846264338327 ..... 
                     41:  *    53 bits   PI = 3.141592653589793 115997963 ..... ,
                     42:  *    56 bits   PI = 3.141592653589793 227020265 ..... ,  
                     43:  *
                     44:  *     in hexadecimal:
                     45:  *             pi = 3.243F6A8885A308D313198A2E....
                     46:  *    53 bits   PI = 3.243F6A8885A30  =  2 * 1.921FB54442D18   error=.276ulps
                     47:  *    56 bits   PI = 3.243F6A8885A308 =  4 * .C90FDAA22168C2    error=.206ulps
                     48:  *     
                     49:  *     In a test run with more than 200,000 random arguments on a VAX, the 
                     50:  *     maximum observed error in ulps (units in the last place) was
                     51:  *     0.86 ulps.      (comparing against (PI/pi)*(exact atan(x))).
                     52:  *
                     53:  * 2)  If atan2() uses true pi, then
                     54:  *
                     55:  *     atan(x) returns the exact atan(x) with error below about 2 ulps.
                     56:  *
                     57:  *     In a test run with more than 1,024,000 random arguments on a VAX, the 
                     58:  *     maximum observed error in ulps (units in the last place) was
                     59:  *     0.85 ulps.
                     60:  */
                     61: 
                     62: double atan(x)
                     63: double x;
                     64: {
                     65:        double atan2(),one=1.0;
                     66:        return(atan2(x,one));
                     67: }

This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.