lib/libm/noieee_src/n_atan.c

   1 /*      $NetBSD: n_atan.c,v 1.5 2003/08/07 16:44:50 agc Exp $   */
   2 /*
   3  * Copyright (c) 1985, 1993
   4  *      The Regents of the University of California.  All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  * 2. Redistributions in binary form must reproduce the above copyright
  12  *    notice, this list of conditions and the following disclaimer in the
  13  *    documentation and/or other materials provided with the distribution.
  14  * 3. Neither the name of the University nor the names of its contributors
  15  *    may be used to endorse or promote products derived from this software
  16  *    without specific prior written permission.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  28  * SUCH DAMAGE.
  29  */
  30
  31 #ifndef lint
  32 #if 0
  33 static char sccsid[] = "@(#)atan.c      8.1 (Berkeley) 6/4/93";
  34 #endif
  35 #endif /* not lint */
  36
  37 /* ATAN(X)
  38  * RETURNS ARC TANGENT OF X
  39  * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
  40  * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
  41  *
  42  * Required kernel function:
  43  *      atan2(y,x)
  44  *
  45  * Method:
  46  *      atan(x) = atan2(x,1.0).
  47  *
  48  * Special case:
  49  *      if x is NaN, return x itself.
  50  *
  51  * Accuracy:
  52  * 1)  If atan2() uses machine PI, then
  53  *
  54  *      atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
  55  *      and PI is the exact pi rounded to machine precision (see atan2 for
  56  *      details):
  57  *
  58  *      in decimal:
  59  *              pi = 3.141592653589793 23846264338327 .....
  60  *    53 bits   PI = 3.141592653589793 115997963 ..... ,
  61  *    56 bits   PI = 3.141592653589793 227020265 ..... ,
  62  *
  63  *      in hexadecimal:
  64  *              pi = 3.243F6A8885A308D313198A2E....
  65  *    53 bits   PI = 3.243F6A8885A30  =  2 * 1.921FB54442D18    error=.276ulps
  66  *    56 bits   PI = 3.243F6A8885A308 =  4 * .C90FDAA22168C2    error=.206ulps
  67  *
  68  *      In a test run with more than 200,000 random arguments on a VAX, the
  69  *      maximum observed error in ulps (units in the last place) was
  70  *      0.86 ulps.      (comparing against (PI/pi)*(exact atan(x))).
  71  *
  72  * 2)  If atan2() uses true pi, then
  73  *
  74  *      atan(x) returns the exact atan(x) with error below about 2 ulps.
  75  *
  76  *      In a test run with more than 1,024,000 random arguments on a VAX, the
  77  *      maximum observed error in ulps (units in the last place) was
  78  *      0.85 ulps.
  79  */
  80 #include "mathimpl.h"
  81
  82 double
  83 atan(double x)
  84 {
  85         double one=1.0;
  86         return(atan2(x,one));
  87 }