随机数测试-续：Frequencey test(monobit test), Serial test(two-bit test), Poker test and Runs test

环境

Python version: 3.7.1

代码如下(PseudorandomTest.py)

'''
	Pseudorandom Sequences Tests: 
		1. Frequency test (monobit test)
		2. Serial test (two-bit test)
		3. Poker test
		4. Runs test
		5. Autocorrelation test
	@Author: Notus(hehe_xiao@qq.com)
	@Create: 2019-02-15
	@Update: 2019-02-17
'''

# 1. Frequency test(monobit test)
def monobitTest(num):
	n = len(num)
	n0 = num.count('0')
	n1 = num.count('1')
	X = (n0 - n1) ** 2 / n
	return n, n0, n1, X

# 2. Serial test(two-bit test)
def serialTest(num):
	n = len(num)
	n0 = num.count('0')
	n1 = num.count('1')
	n00 = n01 = n10 = n11 = 0

	for i in range(0, n-1):
		i0 = num[i]
		i1 = num[i+1]
		if i0 == '0':
			if i1 == '0': 
				n00 += 1
			else: 
				n01 += 1
		else:
			if i1 == '0': 
				n10 += 1
			else: 
				n11 += 1
		i += 1

	X = 4 * (n00**2 + n01**2 + n10**2 + n11**2) / (n-1) - 2 * (n0**2 + n1**2) / n + 1
	return n, n00, n01, n10, n11, X	


# 3. Poker test
def pokerTest(num, m):
	n = len(num)
	k = n // m
	if k < 5 * (2 ** m):
		raise ValueError("Error: the value of m is invalid for Poker Test!")

	# ni count list, 0 <= i <= 2**m - 1
	ni_list = [0] * (2 ** m)

	# counting 	
	for b in range(0, n-m, m):
		index = 0
		for c in range(m):
			index = index * 2 + int(num[b + c])
		ni_list[index] += 1

	s = 0
	for i in range(1, 2**m + 1):
		s += ni_list[i - 1] ** 2

	X = (2 ** m) * s / k - k
	return k, ni_list, X


# 4. Runs test
def runsTest(num):
	n = len(num)
	e = {}
	for i in range(1, n + 3):
		e_i = (n - i + 3) / (2 ** (i + 2))
		if e_i >= 5:
			e[i] = e_i
	k = max(e.keys())
	B = [0] * k
	G = [0] * k
	
	def countBG(bit, runLength):
		counts = 0
		contNumbs = 0				# continuous number counts
		for idx in range(n):
			if num[idx] != bit: 
				if contNumbs == runLength:
					counts += 1
				contNumbs = 0
				continue

			contNumbs += 1

			# last block or gap
			if contNumbs == runLength and idx == n - 1: 
				counts += 1 
		return counts

	for i in range(k):
		B[i] = countBG('1', i + 1)
		G[i] = countBG('0', i + 1)

	x1 = x2 = 0
	for i in range(1, k + 1):
		x1 += (B[i-1] - e[i]) ** 2 / e[i]
		x2 += (G[i-1] - e[i]) ** 2 / e[i]
	X = x1 + x2

	return e, k, B, G, X

# 5. Autocorrelation test
# Todo

if __name__ == '__main__':
	num = ('11100' + '01100' + '01000' + '10100' + '11101' + '11100' + '10010' + '01001') * 4
	
	x1 = monobitTest(num)
	print("frequency test: 
n = {}, n0 = {}, n1 = {}, 
X1 = {}
".format(*x1))

	x2 = serialTest(num)
	print("serial test: 
n = {}, n00 = {}, n01 = {}, n10 = {}, n11 = {}, 
X2 = {}
".format(*x2))

	try:
		x3 = pokerTest(num, 3)
	except ValueError as err:
		print(err.args[0])
		sys.exit()
	print("poker test: 
k = {}, ni_list = {} 
X3 = {}
".format(*x3))
	
	x4 = runsTest(num)
	print("runs test: 
e = {}, k = {}, B = {}, G = {} 
X4 = {}".format(*x4))

运行结果

python PseudorandomTest.py
frequency test:
n = 160, n0 = 84, n1 = 76,
X1 = 0.4

serial test:
n = 160, n00 = 44, n01 = 40, n10 = 40, n11 = 35,
X2 = 0.6251572327043959

poker test:
k = 53, ni_list = [5, 10, 6, 4, 12, 3, 6, 7]
X3 = 9.641509433962263

runs test:
e = {1: 20.25, 2: 10.0625, 3: 5.0}, k = 3, B = [25, 4, 5], G = [8, 20, 12]
X4 = 31.791306264856992