4.3BSD - /usr/src/usr.lib/libm/atan.c

   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: }

Defined functions

Defined variables