每日一程-10.五种基本随机数测试-续

Author: Notus([email protected])
Create: 2019-02-17
Update: 2019-02-17

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([email protected])
    @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: \nn = {}, n0 = {}, n1 = {}, \nX1 = {}\n".format(*x1))

    x2 = serialTest(num)
    print("serial test: \nn = {}, n00 = {}, n01 = {}, n10 = {}, n11 = {}, \nX2 = {}\n".format(*x2))

    try:
        x3 = pokerTest(num, 3)
    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 = {}".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