import itertools

def pi(N):
	' 计算pi的值 '
	# step 1: 创建一个奇数序列: 1, 3, 5, 7, 9, ...
	odds_sq = itertools.count(1, 2)
	# step 2: 取该序列的前N项: 1, 3, 5, 7, 9, ..., 2*N-1.
	odds = itertools.takewhile(lambda x: x <= 2*N-1, odds_sq)
	# step 3: 添加正负符号并用4除: 4/1, -4/3, 4/5, -4/7, 4/9, ...
	symbol = itertools.cycle([1, -1])
	sum = 0
	for i in odds:
		sum += 4 * next(symbol) / i
	# step 4: 求和:
	return sum

# 测试:
print(pi(10))
print(pi(100))
print(pi(1000))
print(pi(10000))
assert 3.04 < pi(10) < 3.05
assert 3.13 < pi(100) < 3.14
assert 3.140 < pi(1000) < 3.141
assert 3.1414 < pi(10000) < 3.1415
print('ok')