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#!/usr/bin/env python
# sp_800_approximate_entropy_test.py
#
# Copyright (C) 2017 David Johnston
# This program is distributed under the terms of the GNU General Public License.
#
# This file is part of sp800_22_tests.
#
# sp800_22_tests is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# sp800_22_tests is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with sp800_22_tests. If not, see <http://www.gnu.org/licenses/>.
from __future__ import print_function
import math
#from scipy.special import gamma, gammainc, gammaincc
from gamma_functions import *
def bits_to_int(bits):
theint = 0
for i in range(len(bits)):
theint = (theint << 1) + bits[i]
return theint
def approximate_entropy_test(bits):
n = len(bits)
m = int(math.floor(math.log(n,2)))-6
if m < 2:
m = 2
if m >3 :
m = 3
print(" n = ",n)
print(" m = ",m)
Cmi = list()
phi_m = list()
for iterm in range(m,m+2):
# Step 1
padded_bits=bits+bits[0:iterm-1]
# Step 2
counts = list()
for i in range(2**iterm):
#print " Pattern #%d of %d" % (i+1,2**iterm)
count = 0
for j in range(n):
if bits_to_int(padded_bits[j:j+iterm]) == i:
count += 1
counts.append(count)
print(" Pattern %d of %d, count = %d" % (i+1,2**iterm, count))
# step 3
Ci = list()
for i in range(2**iterm):
Ci.append(float(counts[i])/float(n))
Cmi.append(Ci)
# Step 4
sum = 0.0
for i in range(2**iterm):
if (Ci[i] > 0.0):
sum += Ci[i]*math.log((Ci[i]/10.0))
phi_m.append(sum)
print(" phi(%d) = %f" % (m,sum))
# Step 5 - let the loop steps 1-4 complete
# Step 6
appen_m = phi_m[0] - phi_m[1]
print(" AppEn(%d) = %f" % (m,appen_m))
chisq = 2*n*(math.log(2) - appen_m)
print(" ChiSquare = ",chisq)
# Step 7
p = gammaincc(2**(m-1),(chisq/2.0))
success = (p >= 0.01)
return (success, p, None)
if __name__ == "__main__":
bits = [1,1,0,0,1,0,0,1,0,0,0,0,1,1,1,1,
1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,
0,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0,
1,1,0,0,0,0,1,0,0,0,1,1,0,1,0,0,
1,1,0,0,0,1,0,0,1,1,0,0,0,1,1,0,
0,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,
1,0,0,0]
success, p, _ = approximate_entropy_test(bits)
print("success =",success)
print("p = ",p)
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