harvey/sys/src/libc/port/atan.c

/*
	floating-point arctangent

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

	atan2 returns the arctangent of arg1/arg2
	in the range [-pi,pi].

	there are no error returns.

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

#include <u.h>
#include <libc.h>

#define sq2p1 2.414213562373095048802e0
#define sq2m1  .414213562373095048802e0
#define p4  .161536412982230228262e2
#define p3  .26842548195503973794141e3
#define p2  .11530293515404850115428136e4
#define p1  .178040631643319697105464587e4
#define p0  .89678597403663861959987488e3
#define q4  .5895697050844462222791e2
#define q3  .536265374031215315104235e3
#define q2  .16667838148816337184521798e4
#define q1  .207933497444540981287275926e4
#define q0  .89678597403663861962481162e3


/*
	xatan evaluates a series valid in the
	range [-0.414...,+0.414...]. (tan(pi/8))
 */

static
double
xatan(double arg)
{
	double argsq, 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;
}

/*
	satan reduces its argument (known to be positive)
	to the range [0,0.414...] and calls xatan.
 */

static
double
satan(double arg)
{

	if(arg < sq2m1)
		return xatan(arg);
	if(arg > sq2p1)
		return PIO2 - xatan(1/arg);
	return PIO2/2 + xatan((arg-1)/(arg+1));
}

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

double
atan(double arg)
{

	if(arg > 0)
		return satan(arg);
	return -satan(-arg);
}