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qrcode.py
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qrcode.py
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#
# QR Code Generator for Python
#
# Copyright (c) 2012 Kazuhiko Arase
#
# URL: http://www.d-project.com/
#
# Licensed under the MIT license:
# http://www.opensource.org/licenses/mit-license.php
#
# The word 'QR Code' is registered trademark of
# DENSO WAVE INCORPORATED
# http://www.denso-wave.com/qrcode/faqpatent-e.html
#
"""QR Code Generator for Python
from qrcode import QRCode, ErrorCorrectLevel
# generate with explicit type number
qr = QRCode()
qr.setTypeNumber(4)
qr.setErrorCorrectLevel(ErrorCorrectLevel.M)
qr.addData('here comes qr!')
qr.make()
# generate with auto type number
# qr = QRCode.getMinimumQRCode('here comes qr!', ErrorCorrectLevel.M)
# create an image
for r in range(qr.getModuleCount() ):
for c in range(qr.getModuleCount() ):
color = black if qr.isDark(r, c) else white
# set pixel ...
"""
class QRCode:
PAD0 = 0xEC
PAD1 = 0x11
def __init__(self):
self.typeNumber = 1
self.errorCorrectLevel = ErrorCorrectLevel.H
self.qrDataList = []
self.modules = []
self.moduleCount = 0
def getTypeNumber(self):
return self.typeNumber
def setTypeNumber(self, typeNumber):
self.typeNumber = typeNumber
def getErrorCorrectLevel(self):
return self.errorCorrectLevel
def setErrorCorrectLevel(self, errorCorrectLevel):
self.errorCorrectLevel = errorCorrectLevel
def clearData(self):
self.qrDataList = []
def addData(self, data):
self.qrDataList.append(QR8BitByte(data) )
def getDataCount(self):
return len(self.qrDataList)
def getData(self, index):
return self.qrDataList[index]
def isDark(self, row, col):
return (self.modules[row][col] if self.modules[row][col] != None
else False)
def getModuleCount(self):
return self.moduleCount
def make(self):
self._make(False, self._getBestMaskPattern() )
def _getBestMaskPattern(self):
minLostPoint = 0
pattern = 0
for i in range(8):
self._make(True, i)
lostPoint = QRUtil.getLostPoint(self)
if i == 0 or minLostPoint > lostPoint:
minLostPoint = lostPoint
pattern = i
return pattern
def _make(self, test, maskPattern):
self.moduleCount = self.typeNumber * 4 + 17
self.modules = [[None] * self.moduleCount
for i in range(self.moduleCount)]
self._setupPositionProbePattern(0, 0)
self._setupPositionProbePattern(self.moduleCount - 7, 0)
self._setupPositionProbePattern(0, self.moduleCount - 7)
self._setupPositionAdjustPattern()
self._setupTimingPattern()
self._setupTypeInfo(test, maskPattern)
if self.typeNumber >= 7:
self._setupTypeNumber(test)
data = QRCode._createData(
self.typeNumber,
self.errorCorrectLevel,
self.qrDataList)
self._mapData(data, maskPattern)
def _mapData(self, data, maskPattern):
rows = list(range(self.moduleCount) )
cols = [col - 1 if col <= 6 else col
for col in range(self.moduleCount - 1, 0, -2)]
maskFunc = QRUtil.getMaskFunction(maskPattern)
byteIndex = 0
bitIndex = 7
for col in cols:
rows.reverse()
for row in rows:
for c in range(2):
if self.modules[row][col - c] == None:
dark = False
if byteIndex < len(data):
dark = ( (data[byteIndex] >> bitIndex) & 1) == 1
if maskFunc(row, col - c):
dark = not dark
self.modules[row][col - c] = dark
bitIndex -= 1
if bitIndex == -1:
byteIndex += 1
bitIndex = 7
def _setupPositionAdjustPattern(self):
pos = QRUtil.getPatternPosition(self.typeNumber)
for row in pos:
for col in pos:
if self.modules[row][col] != None:
continue
for r in range(-2, 3):
for c in range(-2, 3):
self.modules[row + r][col + c] = (
r == -2 or r == 2 or c == -2 or c == 2
or (r == 0 and c == 0) )
def _setupPositionProbePattern(self, row, col):
for r in range(-1, 8):
for c in range(-1, 8):
if (row + r <= -1 or self.moduleCount <= row + r
or col + c <= -1 or self.moduleCount <= col + c):
continue
self.modules[row + r][col + c] = (
(0 <= r and r <= 6 and (c == 0 or c == 6) )
or (0 <= c and c <= 6 and (r == 0 or r == 6) )
or (2 <= r and r <= 4 and 2 <= c and c <= 4) )
def _setupTimingPattern(self):
for r in range(8, self.moduleCount - 8):
if self.modules[r][6] != None:
continue
self.modules[r][6] = r % 2 == 0
for c in range(8, self.moduleCount - 8):
if self.modules[6][c] != None:
continue
self.modules[6][c] = c % 2 == 0
def _setupTypeNumber(self, test):
bits = QRUtil.getBCHTypeNumber(self.typeNumber)
for i in range(18):
self.modules[i // 3][i % 3 + self.moduleCount - 8 - 3] = (
not test and ( (bits >> i) & 1) == 1)
for i in range(18):
self.modules[i % 3 + self.moduleCount - 8 - 3][i // 3] = (
not test and ( (bits >> i) & 1) == 1)
def _setupTypeInfo(self, test, maskPattern):
data = (self.errorCorrectLevel << 3) | maskPattern
bits = QRUtil.getBCHTypeInfo(data)
# vertical
for i in range(15):
mod = not test and ( (bits >> i) & 1) == 1
if i < 6:
self.modules[i][8] = mod
elif i < 8:
self.modules[i + 1][8] = mod
else:
self.modules[self.moduleCount - 15 + i][8] = mod
# horizontal
for i in range(15):
mod = not test and ( (bits >> i) & 1) == 1
if i < 8:
self.modules[8][self.moduleCount - i - 1] = mod
elif i < 9:
self.modules[8][15 - i - 1 + 1] = mod
else:
self.modules[8][15 - i - 1] = mod
# fixed
self.modules[self.moduleCount - 8][8] = not test
@staticmethod
def _createData(typeNumber, errorCorrectLevel, dataArray):
rsBlocks = RSBlock.getRSBlocks(typeNumber, errorCorrectLevel)
buffer = BitBuffer()
for data in dataArray:
buffer.put(data.getMode(), 4)
buffer.put(data.getLength(), data.getLengthInBits(typeNumber) )
data.write(buffer)
totalDataCount = sum(rsBlock.getDataCount()
for rsBlock in rsBlocks)
if buffer.getLengthInBits() > totalDataCount * 8:
raise Exception('code length overflow. (%s > %s)' %
(buffer.getLengthInBits(), totalDataCount * 8) )
# end code
if buffer.getLengthInBits() + 4 <= totalDataCount * 8:
buffer.put(0, 4)
# padding
while buffer.getLengthInBits() % 8 != 0:
buffer.put(False)
# padding
while True:
if buffer.getLengthInBits() >= totalDataCount * 8:
break
buffer.put(QRCode.PAD0, 8)
if buffer.getLengthInBits() >= totalDataCount * 8:
break
buffer.put(QRCode.PAD1, 8)
return QRCode._createBytes(buffer, rsBlocks)
@staticmethod
def _createBytes(buffer, rsBlocks):
offset = 0
maxDcCount = 0
maxEcCount = 0
dcdata = [None] * len(rsBlocks)
ecdata = [None] * len(rsBlocks)
for r in range(len(rsBlocks) ):
dcCount = rsBlocks[r].getDataCount()
ecCount = rsBlocks[r].getTotalCount() - dcCount
maxDcCount = max(maxDcCount, dcCount)
maxEcCount = max(maxEcCount, ecCount)
dcdata[r] = [0] * dcCount
for i in range(len(dcdata[r] ) ):
dcdata[r][i] = 0xff & buffer.getBuffer()[i + offset]
offset += dcCount
rsPoly = QRUtil.getErrorCorrectPolynomial(ecCount)
rawPoly = Polynomial(dcdata[r], rsPoly.getLength() - 1)
modPoly = rawPoly.mod(rsPoly)
ecdata[r] = [0] * (rsPoly.getLength() - 1)
for i in range(len(ecdata[r]) ):
modIndex = i + modPoly.getLength() - len(ecdata[r])
ecdata[r][i] = modPoly.get(modIndex) if modIndex >= 0 else 0
totalCodeCount = sum(rsBlock.getTotalCount()
for rsBlock in rsBlocks)
data = [0] * totalCodeCount
index = 0
for i in range(maxDcCount):
for r in range(len(rsBlocks) ):
if i < len(dcdata[r] ):
data[index] = dcdata[r][i]
index += 1
for i in range(maxEcCount):
for r in range(len(rsBlocks) ):
if i < len(ecdata[r] ):
data[index] = ecdata[r][i]
index += 1
return data
@staticmethod
def getMinimumQRCode(data, errorCorrectLevel):
mode = Mode.MODE_8BIT_BYTE # fixed to 8bit byte
qr = QRCode()
qr.setErrorCorrectLevel(errorCorrectLevel)
qr.addData(data)
length = qr.getData(0).getLength()
for typeNumber in range(1, 11):
if length <= QRUtil.getMaxLength(
typeNumber, mode, errorCorrectLevel):
qr.setTypeNumber(typeNumber)
break
qr.make()
return qr
class Mode:
MODE_NUMBER = 1 << 0
MODE_ALPHA_NUM = 1 << 1
MODE_8BIT_BYTE = 1 << 2
MODE_KANJI = 1 << 3
class ErrorCorrectLevel:
L = 1 # 7%
M = 0 # 15%
Q = 3 # 25%
H = 2 # 30%
class MaskPattern:
PATTERN000 = 0
PATTERN001 = 1
PATTERN010 = 2
PATTERN011 = 3
PATTERN100 = 4
PATTERN101 = 5
PATTERN110 = 6
PATTERN111 = 7
class QRUtil:
@staticmethod
def getPatternPosition(typeNumber):
return QRUtil.PATTERN_POSITION_TABLE[typeNumber - 1]
PATTERN_POSITION_TABLE = [
[],
[6, 18],
[6, 22],
[6, 26],
[6, 30],
[6, 34],
[6, 22, 38],
[6, 24, 42],
[6, 26, 46],
[6, 28, 50],
[6, 30, 54],
[6, 32, 58],
[6, 34, 62],
[6, 26, 46, 66],
[6, 26, 48, 70],
[6, 26, 50, 74],
[6, 30, 54, 78],
[6, 30, 56, 82],
[6, 30, 58, 86],
[6, 34, 62, 90],
[6, 28, 50, 72, 94],
[6, 26, 50, 74, 98],
[6, 30, 54, 78, 102],
[6, 28, 54, 80, 106],
[6, 32, 58, 84, 110],
[6, 30, 58, 86, 114],
[6, 34, 62, 90, 118],
[6, 26, 50, 74, 98, 122],
[6, 30, 54, 78, 102, 126],
[6, 26, 52, 78, 104, 130],
[6, 30, 56, 82, 108, 134],
[6, 34, 60, 86, 112, 138],
[6, 30, 58, 86, 114, 142],
[6, 34, 62, 90, 118, 146],
[6, 30, 54, 78, 102, 126, 150],
[6, 24, 50, 76, 102, 128, 154],
[6, 28, 54, 80, 106, 132, 158],
[6, 32, 58, 84, 110, 136, 162],
[6, 26, 54, 82, 110, 138, 166],
[6, 30, 58, 86, 114, 142, 170]
]
MAX_LENGTH = [
[ [41, 25, 17, 10], [34, 20, 14, 8], [27, 16, 11, 7], [17, 10, 7, 4] ],
[ [77, 47, 32, 20], [63, 38, 26, 16], [48, 29, 20, 12], [34, 20, 14, 8] ],
[ [127, 77, 53, 32], [101, 61, 42, 26], [77, 47, 32, 20], [58, 35, 24, 15] ],
[ [187, 114, 78, 48], [149, 90, 62, 38], [111, 67, 46, 28], [82, 50, 34, 21] ],
[ [255, 154, 106, 65], [202, 122, 84, 52], [144, 87, 60, 37], [106, 64, 44, 27] ],
[ [322, 195, 134, 82], [255, 154, 106, 65], [178, 108, 74, 45], [139, 84, 58, 36] ],
[ [370, 224, 154, 95], [293, 178, 122, 75], [207, 125, 86, 53], [154, 93, 64, 39] ],
[ [461, 279, 192, 118], [365, 221, 152, 93], [259, 157, 108, 66], [202, 122, 84, 52] ],
[ [552, 335, 230, 141], [432, 262, 180, 111], [312, 189, 130, 80], [235, 143, 98, 60] ],
[ [652, 395, 271, 167], [513, 311, 213, 131], [364, 221, 151, 93], [288, 174, 119, 74] ]
]
@staticmethod
def getMaxLength(typeNumber, mode, errorCorrectLevel):
t = typeNumber - 1
e = {
ErrorCorrectLevel.L: 0,
ErrorCorrectLevel.M: 1,
ErrorCorrectLevel.Q: 2,
ErrorCorrectLevel.H: 3
}[errorCorrectLevel]
m = {
Mode.MODE_NUMBER: 0,
Mode.MODE_ALPHA_NUM: 1,
Mode.MODE_8BIT_BYTE: 2,
Mode.MODE_KANJI: 3
}[mode]
return QRUtil.MAX_LENGTH[t][e][m]
@staticmethod
def getErrorCorrectPolynomial(errorCorrectLength):
a = Polynomial([1])
for i in range(errorCorrectLength):
a = a.multiply(Polynomial([1, QRMath.gexp(i)]) )
return a
@staticmethod
def getMaskFunction(maskPattern):
return {
MaskPattern.PATTERN000:
lambda i, j: (i + j) % 2 == 0,
MaskPattern.PATTERN001:
lambda i, j: i % 2 == 0,
MaskPattern.PATTERN010:
lambda i, j: j % 3 == 0,
MaskPattern.PATTERN011:
lambda i, j: (i + j) % 3 == 0,
MaskPattern.PATTERN100:
lambda i, j: (i // 2 + j // 3) % 2 == 0,
MaskPattern.PATTERN101:
lambda i, j: (i * j) % 2 + (i * j) % 3 == 0,
MaskPattern.PATTERN110:
lambda i, j: ( (i * j) % 2 + (i * j) % 3) % 2 == 0,
MaskPattern.PATTERN111:
lambda i, j: ( (i * j) % 3 + (i + j) % 2) % 2 == 0
}[maskPattern]
@staticmethod
def getLostPoint(qrcode):
moduleCount = qrcode.getModuleCount()
lostPoint = 0
# LEVEL1
for row in range(moduleCount):
for col in range(moduleCount):
sameCount = 0
dark = qrcode.isDark(row, col)
for r in range(-1, 2):
if row + r < 0 or moduleCount <= row + r:
continue
for c in range(-1, 2):
if col + c < 0 or moduleCount <= col + c:
continue
if r == 0 and c == 0:
continue
if dark == qrcode.isDark(row + r, col + c):
sameCount += 1
if sameCount > 5:
lostPoint += (3 + sameCount - 5)
# LEVEL2
for row in range(moduleCount - 1):
for col in range(moduleCount - 1):
count = 0
if qrcode.isDark(row, col):
count += 1
if qrcode.isDark(row + 1, col):
count += 1
if qrcode.isDark(row, col + 1):
count += 1
if qrcode.isDark(row + 1, col + 1):
count += 1
if count == 0 or count == 4:
lostPoint += 3
# LEVEL3
for row in range(moduleCount):
for col in range(moduleCount - 6):
if (qrcode.isDark(row, col)
and not qrcode.isDark(row, col + 1)
and qrcode.isDark(row, col + 2)
and qrcode.isDark(row, col + 3)
and qrcode.isDark(row, col + 4)
and not qrcode.isDark(row, col + 5)
and qrcode.isDark(row, col + 6) ):
lostPoint += 40
for col in range(moduleCount):
for row in range(moduleCount - 6):
if (qrcode.isDark(row, col)
and not qrcode.isDark(row + 1, col)
and qrcode.isDark(row + 2, col)
and qrcode.isDark(row + 3, col)
and qrcode.isDark(row + 4, col)
and not qrcode.isDark(row + 5, col)
and qrcode.isDark(row + 6, col) ):
lostPoint += 40
# LEVEL4
darkCount = 0
for col in range(moduleCount):
for row in range(moduleCount):
if qrcode.isDark(row, col):
darkCount += 1
ratio = abs(100 * darkCount // moduleCount // moduleCount - 50) // 5
lostPoint += ratio * 10
return lostPoint
G15 = ( (1 << 10) | (1 << 8) | (1 << 5) | (1 << 4) |
(1 << 2) | (1 << 1) | (1 << 0) )
G18 = ( (1 << 12) | (1 << 11) | (1 << 10) | (1 << 9) |
(1 << 8) | (1 << 5) | (1 << 2) | (1 << 0) )
G15_MASK = (1 << 14) | (1 << 12) | (1 << 10) | (1 << 4) | (1 << 1)
@staticmethod
def getBCHTypeInfo(data):
d = data << 10
while QRUtil.getBCHDigit(d) - QRUtil.getBCHDigit(QRUtil.G15) >= 0:
d ^= (QRUtil.G15 << (QRUtil.getBCHDigit(d) -
QRUtil.getBCHDigit(QRUtil.G15) ) )
return ( (data << 10) | d) ^ QRUtil.G15_MASK
@staticmethod
def getBCHTypeNumber(data):
d = data << 12
while QRUtil.getBCHDigit(d) - QRUtil.getBCHDigit(QRUtil.G18) >= 0:
d ^= (QRUtil.G18 << (QRUtil.getBCHDigit(d) -
QRUtil.getBCHDigit(QRUtil.G18) ) )
return (data << 12) | d
@staticmethod
def getBCHDigit(data):
digit = 0
while data != 0:
digit += 1
data >>= 1
return digit
@staticmethod
def stringToBytes(s):
return [ord(c) & 0xff for c in s]
class QR8BitByte:
def __init__(self, data):
self.mode = Mode.MODE_8BIT_BYTE
self.data = data
def getMode(self):
return self.mode
def getData(self):
return self.data
'''
def write(self, buffer): raise Exception('not implemented.')
def getLength(self): raise Exception('not implemented.')
'''
def write(self, buffer):
data = QRUtil.stringToBytes(self.getData() )
for d in data:
buffer.put(d, 8)
def getLength(self):
return len(QRUtil.stringToBytes(self.getData() ) )
def getLengthInBits(self, type):
if 1 <= type and type < 10: # 1 - 9
return {
Mode.MODE_NUMBER: 10,
Mode.MODE_ALPHA_NUM: 9,
Mode.MODE_8BIT_BYTE: 8,
Mode.MODE_KANJI: 8
}[self.mode]
elif type < 27: # 10 - 26
return {
Mode.MODE_NUMBER: 12,
Mode.MODE_ALPHA_NUM: 11,
Mode.MODE_8BIT_BYTE: 16,
Mode.MODE_KANJI: 10
}[self.mode]
elif type < 41: # 27 - 40
return {
Mode.MODE_NUMBER: 14,
Mode.MODE_ALPHA_NUM: 13,
Mode.MODE_8BIT_BYTE: 16,
Mode.MODE_KANJI: 12
}[self.mode]
else:
raise Exception('type:%s' % type)
class QRMath:
EXP_TABLE = None
LOG_TABLE = None
@staticmethod
def _init():
QRMath.EXP_TABLE = [0] * 256
for i in range(256):
QRMath.EXP_TABLE[i] = (1 << i if i < 8 else
QRMath.EXP_TABLE[i - 4] ^ QRMath.EXP_TABLE[i - 5] ^
QRMath.EXP_TABLE[i - 6] ^ QRMath.EXP_TABLE[i - 8])
QRMath.LOG_TABLE = [0] * 256
for i in range(255):
QRMath.LOG_TABLE[QRMath.EXP_TABLE[i] ] = i
@staticmethod
def glog(n):
if n < 1:
raise Exception('log(%s)' % n)
return QRMath.LOG_TABLE[n]
@staticmethod
def gexp(n):
while n < 0:
n += 255
while n >= 256:
n -= 255
return QRMath.EXP_TABLE[n]
# initialize statics
QRMath._init()
class Polynomial:
def __init__(self, num, shift=0):
offset = 0
length = len(num)
while offset < length and num[offset] == 0:
offset += 1
self.num = num[offset:] + [0] * shift
def get(self, index):
return self.num[index]
def getLength(self):
return len(self.num)
def __repr__(self):
return ','.join( [str(self.get(i) )
for i in range(self.getLength() ) ] )
def toLogString(self):
return ','.join( [str(QRMath.glog(self.get(i) ) )
for i in range(self.getLength() ) ] )
def multiply(self, e):
num = [0] * (self.getLength() + e.getLength() - 1)
for i in range(self.getLength() ):
for j in range(e.getLength() ):
num[i + j] ^= QRMath.gexp(QRMath.glog(self.get(i) ) +
QRMath.glog(e.get(j) ) )
return Polynomial(num)
def mod(self, e):
if self.getLength() - e.getLength() < 0:
return self
ratio = QRMath.glog(self.get(0) ) - QRMath.glog(e.get(0) )
num = self.num[:]
for i in range(e.getLength() ):
num[i] ^= QRMath.gexp(QRMath.glog(e.get(i) ) + ratio)
return Polynomial(num).mod(e)
class RSBlock:
RS_BLOCK_TABLE = [
# L
# M
# Q
# H
# 1
[1, 26, 19],
[1, 26, 16],
[1, 26, 13],
[1, 26, 9],
# 2
[1, 44, 34],
[1, 44, 28],
[1, 44, 22],
[1, 44, 16],
# 3
[1, 70, 55],
[1, 70, 44],
[2, 35, 17],
[2, 35, 13],
# 4
[1, 100, 80],
[2, 50, 32],
[2, 50, 24],
[4, 25, 9],
# 5
[1, 134, 108],
[2, 67, 43],
[2, 33, 15, 2, 34, 16],
[2, 33, 11, 2, 34, 12],
# 6
[2, 86, 68],
[4, 43, 27],
[4, 43, 19],
[4, 43, 15],
# 7
[2, 98, 78],
[4, 49, 31],
[2, 32, 14, 4, 33, 15],
[4, 39, 13, 1, 40, 14],
# 8
[2, 121, 97],
[2, 60, 38, 2, 61, 39],
[4, 40, 18, 2, 41, 19],
[4, 40, 14, 2, 41, 15],
# 9
[2, 146, 116],
[3, 58, 36, 2, 59, 37],
[4, 36, 16, 4, 37, 17],
[4, 36, 12, 4, 37, 13],
# 10
[2, 86, 68, 2, 87, 69],
[4, 69, 43, 1, 70, 44],
[6, 43, 19, 2, 44, 20],
[6, 43, 15, 2, 44, 16]
]
def __init__(self, totalCount, dataCount):
self.totalCount = totalCount
self.dataCount = dataCount
def getDataCount(self):
return self.dataCount
def getTotalCount(self):
return self.totalCount
def __repr__(self):
return ('(total=%s,data=%s)' % (self.totalCount, self.dataCount) )
@staticmethod
def getRSBlocks(typeNumber, errorCorrectLevel):
rsBlock = RSBlock.getRsBlockTable(typeNumber, errorCorrectLevel)
length = len(rsBlock) // 3
list = []
for i in range(length):
count = rsBlock[i * 3 + 0]
totalCount = rsBlock[i * 3 + 1]
dataCount = rsBlock[i * 3 + 2]
list += [RSBlock(totalCount, dataCount)] * count
return list
@staticmethod
def getRsBlockTable(typeNumber, errorCorrectLevel):
return {
ErrorCorrectLevel.L:
RSBlock.RS_BLOCK_TABLE[ (typeNumber - 1) * 4 + 0],
ErrorCorrectLevel.M:
RSBlock.RS_BLOCK_TABLE[ (typeNumber - 1) * 4 + 1],
ErrorCorrectLevel.Q:
RSBlock.RS_BLOCK_TABLE[ (typeNumber - 1) * 4 + 2],
ErrorCorrectLevel.H:
RSBlock.RS_BLOCK_TABLE[ (typeNumber - 1) * 4 + 3]
}[errorCorrectLevel]
class BitBuffer:
def __init__(self, inclements=32):
self.inclements = inclements
self.buffer = [0] * self.inclements
self.length = 0
def getBuffer(self):
return self.buffer
def getLengthInBits(self):
return self.length
def get(self, index):
return ( (self.buffer[index // 8] >> (7 - index % 8) ) & 1) == 1
def putBit(self, bit):
if self.length == len(self.buffer) * 8:
self.buffer += [0] * self.inclements
if bit:
self.buffer[self.length // 8] |= (0x80 >> (self.length % 8) )
self.length += 1
def put(self, num, length):
for i in range(length):
self.putBit( ( (num >> (length - i - 1) ) & 1) == 1)
def __repr__(self):
return ''.join('1' if self.get(i) else '0'
for i in range(self.getLengthInBits() ) )