Author: Notus(hehe_xiao@qq.com)
Create: 2019-02-18 Update: 2019-02-18
随机数测试：Frequencey test(monobit test), Serial test(two-bit test), Poker test, Runs test and Autocorrelation 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: 2019-02-18 @Version: 1.0'''import math# 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 testdef 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 testdef 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 testdef autocorrelationTest(num, d): n = len(num) if not 1 <= d <= math.floor(n / 2): raise ValueError("Error: d value is invalid!") Ad = 0 for i in range(n - d): Ad += ( int(num[i]) ^ int(num[i + d]) ) X = 2 * (Ad - (n - d) / 2) / math.sqrt(n - d) return Ad, Xif __name__ == '__main__': num = ('11100' + '01100' + '01000' + '10100' + '11101' + '11100' + '10010' + '01001') * 4 x1 = monobitTest(num) print("frequency test: \nn = {}, n0 = {}, n1 = {}, \nX1 = {}\n".format(*x1)) x2 = serialTest(num) print("serial test: \nn = {}, n00 = {}, n01 = {}, n10 = {}, n11 = {}, \nX2 = {}\n".format(*x2)) m = 3 try: x3 = pokerTest(num, m) except ValueError as err: print(err.args[0]) sys.exit() print("poker test: \nk = {}, ni_list = {} \nX3 = {}\n".format(*x3)) x4 = runsTest(num) print("runs test: \ne = {}, k = {}, B = {}, G = {} \nX4 = {}\n".format(*x4)) d = 8 try: x5 = autocorrelationTest(num, d) except ValueError as err: print(err.args[0]) sys.exit() print("Autorcorrelation test: \nA({}) = {} \nX5 = {}".format(d, *x5)) 运行结果
python PseudorandomTest.pyfrequency test:n = 160, n0 = 84, n1 = 76,X1 = 0.4serial test:n = 160, n00 = 44, n01 = 40, n10 = 40, n11 = 35,X2 = 0.6251572327043959poker test:k = 53, ni_list = [5, 10, 6, 4, 12, 3, 6, 7]X3 = 9.641509433962263runs test:e = {1: 20.25, 2: 10.0625, 3: 5.0}, k = 3, B = [25, 4, 5], G = [8, 20, 12]X4 = 31.791306264856992Autorcorrelation test:A(8) = 100X5 = 3.893314107138301