program calculate_pi
implicit none
	real :: a, a_new, b, pi, pi_check, t, p
	pi = acos(-1.0)
	a = 1.0
	b = 1.0 / sqrt(2.0)
	t = 1.0 / 4.0
	p = 1.0
	pi_check = (a+b)**2 / (4*t)
	do while (abs(pi - pi_check).gt.1e-22)
	    a_new = (a+b) / 2
	    b = sqrt(a*b)
	    t = t - p * (a-a_new)**2
	    p = 2*p 
	    pi_check = (a+b)**2 / (4*t)
	    a = a_new
	end do
	print "(f0.22, 1x, f0.22, 1x, f0.22)", pi, pi_check, pi-pi_check
end program calculate_pi

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