ack/lang/basic/lib/atn.c

/*
 * (c) copyright 1983 by the Vrije Universiteit, Amsterdam, The Netherlands.
 *
 *          This product is part of the Amsterdam Compiler Kit.
 *
 * Permission to use, sell, duplicate or disclose this software must be
 * obtained in writing. Requests for such permissions may be sent to
 *
 *      Dr. Andrew S. Tanenbaum
 *      Wiskundig Seminarium
 *      Vrije Universiteit
 *      Postbox 7161
 *      1007 MC Amsterdam
 *      The Netherlands
 *
 */

/* $Header$ */

/* Author: J.W. Stevenson */

/*
	floating-point arctangent

	atan returns the value of the arctangent of its
	argument in the range [-pi/2,pi/2].

	there are no error returns.

	coefficients are #5077 from Hart & Cheney. (19.56D)
*/


static double sq2p1	= 2.414213562373095048802e0;
static double sq2m1	=  .414213562373095048802e0;
static double pio2	= 1.570796326794896619231e0;
static double pio4	=  .785398163397448309615e0;
static double p4	=  .161536412982230228262e2;
static double p3	=  .26842548195503973794141e3;
static double p2	=  .11530293515404850115428136e4;
static double p1	=  .178040631643319697105464587e4;
static double p0	=  .89678597403663861959987488e3;
static double q4	=  .5895697050844462222791e2;
static double q3	=  .536265374031215315104235e3;
static double q2	=  .16667838148816337184521798e4;
static double q1	=  .207933497444540981287275926e4;
static double q0	=  .89678597403663861962481162e3;

/*
	xatan evaluates a series valid in the
	range [-0.414...,+0.414...].
*/

static double
xatan(arg)
double arg;
{
	double argsq;
	double value;

	argsq = arg*arg;
	value = ((((p4*argsq + p3)*argsq + p2)*argsq + p1)*argsq + p0);
	value = value/(((((argsq + q4)*argsq + q3)*argsq + q2)*argsq + q1)*argsq + q0);
	return(value*arg);
}

static double
satan(arg)
double arg;
{
	if(arg < sq2m1)
		return(xatan(arg));
	else if(arg > sq2p1)
		return(pio2 - xatan(1/arg));
	else
		return(pio4 + xatan((arg-1)/(arg+1)));
}


/*
	atan makes its argument positive and
	calls the inner routine satan.
*/

double
_atn(arg)
double arg;
{
	if(arg>0)
		return(satan(arg));
	else
		return(-satan(-arg));
}