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