* 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

atan
defined in line

62;

*never used*
#### Defined variables