?from math import *

def f(x):
	return cos(x)
	
a = 0.0; b = 1.0
M = 22
eps = 1.0e-15

n = 1

h=(b-a)/(2.0*n)
I = h*(f(a)+f(b)+4.0*f(a+h))/3.0

j = 1
abserr = abs(I)
print "%2i. iterasjon: I=%1.14f, relativ feil= %e" %(j, I, abserr/abs(I))

while j<M and abserr>eps*abs(I):
	j = j + 1
	Ip = I
	
	n = 2*n; h = (b-a)/(2.0*n)
	
	sumodd = 0.0; x = a + h
	for k in range(1,n+1):
		sumodd = sumodd + f(x)
		x = x + 2*h
		
	sumeven = 0.0
	x = a + 2*h
	for k in range(1,n):
		sumeven = sumeven + f(x)
		x = x + 2*h
		
	I = h*(f(a)+f(b)+2*sumeven+4*sumodd)/3.0
	
	abserr = abs(I-Ip)
	
	print "%2i. iterasjon: I=%1.14f, relativ feil= %e" %(j, I, abserr/abs(I))
	
print "\n%i iterasjoner: I=%1.14f relativ feil=%e " %(j, I, abserr/abs(I))
print "\nEksakt verdi=%1.14f, eksakt relativ feil=%e" %(sin(1.0),abs(sin(1.0)-I)/abs(sin(1.0)))