eigenmath/arctan.cpp

#include "stdafx.h"
#include "defs.h"

void
eval_arctan(void)
{
	push(cadr(p1));
	eval();
	arctan();
}

void
arctan(void)
{
	double d;

	save();

	p1 = pop();

	if (car(p1) == symbol(TAN)) {
		push(cadr(p1));
		restore();
		return;
	}

	if (isdouble(p1)) {
		errno = 0;
		d = atan(p1->u.d);
		if (errno)
			stop("arctan function error");
		push_double(d);
		restore();
		return;
	}

	if (iszero(p1)) {
		push(zero);
		restore();
		return;
	}

	if (isnegative(p1)) {
		push(p1);
		negate();
		arctan();
		negate();
		restore();
		return;
	}

	// arctan(sin(a) / cos(a)) ?

	if (find(p1, symbol(SIN)) && find(p1, symbol(COS))) {
		push(p1);
		numerator();
		p2 = pop();
		push(p1);
		denominator();
		p3 = pop();
		if (car(p2) == symbol(SIN) && car(p3) == symbol(COS) && equal(cadr(p2), cadr(p3))) {
			push(cadr(p2));
			restore();
			return;
		}
	}

	// arctan(1/sqrt(3)) -> pi/6

	if (car(p1) == symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), -1, 2)) {
		push_rational(1, 6);
		push(symbol(PI));
		multiply();
		restore();
		return;
	}

	// arctan(1) -> pi/4

	if (equaln(p1, 1)) {
		push_rational(1, 4);
		push(symbol(PI));
		multiply();
		restore();
		return;
	}

	// arctan(sqrt(3)) -> pi/3

	if (car(p1) == symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), 1, 2)) {
		push_rational(1, 3);
		push(symbol(PI));
		multiply();
		restore();
		return;
	}

	push_symbol(ARCTAN);
	push(p1);
	list(2);

	restore();
}

#if SELFTEST

static char *s[] = {

	"arctan(x)",
	"arctan(x)",

	"arctan(-x)",
	"-arctan(x)",

	"arctan(0)",
	"0",

	"arctan(tan(x))",
	"x",

	"arctan(1/sqrt(3))-pi/6",	// 30 degrees
	"0",

	"arctan(1)-pi/4",		// 45 degrees
	"0",

	"arctan(sqrt(3))-pi/3",		// 60 degrees
	"0",

	"arctan(a-b)",
	"arctan(a-b)",

	"arctan(b-a)",
	"-arctan(a-b)",

	"arctan(tan(x))",
	"x",
};

void
test_arctan(void)
{
	test(__FILE__, s, sizeof s / sizeof (char *));
}

#endif