# PRNG (Pseudo-Random Number Generator) Test
# PRNG info:
# http://en.wikipedia.org/wiki/Pseudorandom_number_generator
# FB - 201012035
# Compares output distribution of any given PRNG
# w/ an hypothetical True-Random Number Generator (TRNG)
import math
import time
global x
x = time.clock() # seed for the PRNG
# PRNG to test
def prng():
global x
x = math.fmod((x + math.pi) ** 2.0, 1.0)
return x
# combination by recursive method
def c(n, k):
if k == 0: return 1
if n == 0: return 0
return c(n - 1, k - 1) + c(n - 1, k)
### combination by multiplicative method
##def c_(n, k):
## mul = 1.0
## for i in range(k):
## mul = mul * (n - k + i + 1) / (i + 1)
## return mul
# MAIN
n = 20 # number of bits in each trial
print 'Test in progress...'
print
cnk = [] # array to hold bit counts
for k in range(n + 1):
cnk.append(0)
# generate 2**n n-bit pseudo-random numbers
for j in range(2 ** n):
# generate n-bit pseudo-random number and count the 0's in it
# num = ''
ctr = 0
for i in range(n):
b = int(round(prng())) # generate 1 pseudo-random bit
# num += str(b)
if b == 0: ctr += 1
# print num
# increase bit count in the array
cnk[ctr] += 1
print 'Number of bits in each pseudo-random number (n) =', n
print
print 'Comparison of "0" count distributions:'
print ' k', ' c(n,k)', ' actual'
difSum = 0
for k in range(n + 1):
cnk_ = c(n, k)
print '%2d %10d %10d' % (k, cnk_, cnk[k])
difSum += abs(cnk_ - cnk[k])
print
print 'Difference percentage between the distributions:'
print 100 * difSum / (2 ** n)
