def compute_pi(nodecimals=0):
"""
Obtain the first nodecimals number of decimals
of pi=3.1415... by aproximation using euler's formula:
pi = infinity_sum( (factorial(n)**2)*(2**(n+1)) / (factorial(2*n +1)) )
http://mathworld.wolfram.com/PiFormulas.html
"""
if not isinstance(nodecimals, int):
raise Exception('The parameter nodecimals must be an integer.')
if nodecimals < 0:
raise Exception('The parameter nodecimals must be positive.')
if nodecimals == 0:
return LongDecimal(ciphers=[3])
nodecimals += 2 # extra precision to avoid rounding up errors
ciphers = [0] * (nodecimals + 1)
pi = LongDecimal(ciphers=ciphers, negative=False)
term = 0
euler_term = LongDecimalEuler(term=term, nodecimals=nodecimals)
while not euler_term.iszero():
pi = pi + euler_term
term += 1
euler_term = LongDecimalEuler(term=term, nodecimals=nodecimals)
pi.setprecision(nodecimals - 2)
return pi
def test_setprecision_with_same_precision(self):
"""
Test that setprecision with the same precision
doesn't change the Long Decimal.
"""
ciphers = [1, 2, 3, 4, 5]
ld = LongDecimal(ciphers=ciphers)
new_precision = len(ciphers) - 1
ld.setprecision(new_precision=new_precision)
self.assertEqual(len(ld), len(ciphers))
self.assertEqual(ld._ciphers, ciphers)
def test_setprecision_with_more_precision(self):
"""
Test setprecision method
when new_precision > current_precision.
"""
ciphers = [1, 2, 3, 4, 5]
ld = LongDecimal(ciphers=ciphers)
new_precision = 5
ld.setprecision(new_precision=new_precision)
self.assertEqual(len(ld), new_precision + 1)
self.assertEqual(ld._ciphers,
ciphers + [0] * (new_precision - len(ciphers) + 1))
def test_setprecision_with_less_precision(self):
"""
Test setprecision method
when new_precision < current_precision.
"""
ciphers = [1, 2, 3, 4, 5]
ld = LongDecimal(ciphers=ciphers)
self.assertEqual(len(ld), len(ciphers))
new_precision = 2
ld.setprecision(new_precision=new_precision)
self.assertEqual(len(ld), new_precision + 1)
self.assertEqual(ld._ciphers, ciphers[:new_precision + 1])