def field2x_mod(dividend, divisor):
'''uint as polynomial over field[2,x]
>>> field2x_mod(3, 5)
3
>>> field2x_mod(4, 5) # == 4^5
1
>>> field2x_mod(5, 5) # == 5^5
0
>>> field2x_mod(12, 5) # == 12^(5<<1)^5
3
>>> field2x_mod(4, 1) # == 4^(1<<2)
0
'''
## assert dividend >= 0
## assert divisor > 0
dividend = to_uint(dividend, 'dividend')
divisor = to_pint(divisor, 'divisor')
D = divisor.bit_length()
L = dividend.bit_length()
if L <= D*1*8:
return field2x_mod__plain(dividend, divisor)
bs = dividend.to_bytes((L+8-1)//8, 'big')
#assert int.from_bytes(bs, 'big') == dividend
return _field2x_mod__bytes(bs, divisor)
def field2x_divmod(dividend, divisor):
'''uint as polynomial over field[2,x]
>>> field2x_divmod(3, 5)
(0, 3)
>>> field2x_divmod(4, 5) # == 4^5
(1, 1)
>>> field2x_divmod(5, 5) # == 5^5
(1, 0)
>>> field2x_divmod(12, 5) # == 12^(5<<1)^5
(3, 3)
>>> field2x_divmod(4, 1) # == 4^(1<<2)
(4, 0)
'''
## assert dividend >= 0
## assert divisor > 0
dividend = to_uint(dividend, 'dividend')
divisor = to_pint(divisor, 'divisor')
D = divisor.bit_length()
L = dividend.bit_length()
if L <= D*1*8:
return field2x_divmod__plain(dividend, divisor)
bs = dividend.to_bytes((L+8-1)//8, 'big')
return _field2x_divmod__bytes(bs, divisor)
def field2x_invmod(x, M):
x = to_uint(x, 'x')
M = to_pint(M, 'M')
## assert x >= 0
## assert M > 0
x = field2x_mod(x, M)
return field2x_invmod__plain(x, M)
def icut_seq_to(seq, block_size, begin=None, end=None):
block_size = to_pint(block_size, 'block_size')
if begin is None:
begin = 0
if end is None:
end = len(seq)
for i in range(begin, end, block_size):
yield seq[i:i + block_size]
def _icut_to(iterable, block_size, container):
block_size = to_pint(block_size, 'block_size')
if container is None:
container = list
it = iter(iterable)
while True:
c = container(islice(it, block_size))
if not c:
break
yield c
def field2x_divmod__bytes(dividend_in_bytes, divisor, byte_MSB_first):
r'''bytes as uint; uint as polynomial over field[2,x]
>>> field2x_divmod__bytes(b'\x03', 5, True)
(0, 3)
>>> field2x_divmod__bytes(b'\xc0', 5, False)
(0, 3)
>>> field2x_divmod__bytes(b'\x00\x03', 5, True)
(0, 3)
'''
divisor = to_pint(divisor, 'divisor')
#assert divisor > 0
byte_MSB_first = bool(byte_MSB_first)
dividend_in_bytes = std_data_bitorder(dividend_in_bytes, byte_MSB_first)
return _field2x_divmod__bytes(dividend_in_bytes, divisor)
def CRC_generator2exps(generator):
'generator is uint > 0; frame_length = generator.bit_length()-1'
generator = to_pint(generator, 'generator')
#frame_length = generator.bit_length()-1
return uint2expsLE(generator)
def field2x_invmod__bytes(x_in_bytes, M, byte_MSB_first):
M = to_pint(M, 'M')
#assert M > 0
x = field2x_mod__bytes(x_in_bytes, M, byte_MSB_first)
return field2x_invmod__plain(x, M)