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Annotation of 43BSD/usr.lib/libm/atan.c, revision 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: }

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