pi.cal

早期freebsd实现

/*
 * Copyright (c) 1993 David I. Bell
 * Permission is granted to use, distribute, or modify this source,
 * provided that this copyright notice remains intact.
 *
 * Calculate pi within the specified epsilon using the quartic convergence
 * iteration.
 */

define qpi(epsilon)
{
	local niter, yn, ym, tm, an, am, t, tn, sqrt2, epsilon2, count, digits;
	local bits, bits2;

	if (isnull(epsilon))
		epsilon = epsilon();
	digits = digits(1/epsilon);
	if	(digits <=  8) { niter = 1; epsilon =	1e-8; }
	else if (digits <= 40) { niter = 2; epsilon =  1e-40; }
	else if (digits <= 170) { niter = 3; epsilon = 1e-170; }
	else if (digits <= 693) { niter = 4; epsilon = 1e-693; }
	else {
		niter = 4;
		t = 693;
		while (t < digits) {
			++niter;
			t *= 4;
		}
	}
	epsilon2 = epsilon/(digits/10 + 1);
	digits = digits(1/epsilon2);
	sqrt2 = sqrt(2, epsilon2);
	bits = abs(ilog2(epsilon)) + 1;
	bits2 = abs(ilog2(epsilon2)) + 1;
	yn = sqrt2 - 1;
	an = 6 - 4 * sqrt2;
	tn = 2;
	for (count = 0; count < niter; count++) {
		ym = yn;
		am = an;
		tn *= 4;
		t = sqrt(sqrt(1-ym^4, epsilon2), epsilon2);
		yn = (1-t)/(1+t);
		an = (1+yn)^4*am-tn*yn*(1+yn+yn^2);
		yn = bround(yn, bits2);
		an = bround(an, bits2);
	}
	return (bround(1/an, bits));
}

global lib_debug;
if (lib_debug >= 0) {
    print "qpi(epsilon) defined";
}