def test_cocode():
print("")
for i in range(200):
# Test power map, inveriosn, sign, theta, and conversion to GCode
n1 = randint(0, 0x1fff)
p1 = PLoop(n1)
ccvector = randint(0, 0xffffff)
coc = mat24.vect_to_cocode(ccvector)
cclist = [i for i in range(24) if (ccvector >> i) & 1]
cc1 = Cocode(cclist)
cc2 = Cocode(coc)
if i < 1:
print("\nTesting", GcVector(ccvector), ", cocode =", cc1)
assert cc1 == cc2
u = Parity(mat24.scalar_prod(p1.value, cc1.value))
assert p1 & cc1 == u == cc1 & p1 == u * 1 == u + 0
par = Parity(randint(0, 1))
assert cc1 + par == par + cc1 == cc1.value // 0x800 + par
assert cc1 % 2 == Parity(cc1)
assert len(cc1) == mat24.cocode_weight(cc1.value)
if len(cc1) < 4:
syndrome = mat24.cocode_syndrome(cc1.value)
assert cc1.syndrome().value == syndrome
syn_from_list = sum(1 << i
for i in GcVector(ccvector).syndrome_list())
assert syn_from_list == syndrome
i = randint(0, 23)
assert cc1.syndrome(i).value == mat24.cocode_syndrome(cc1.value, i)
syndrome_list = cc1.syndrome(i).bit_list
assert len(cc1) == len(syndrome_list)
assert syndrome_list == mat24.cocode_to_bit_list(cc1.value, i)
def inv_op_unit(self, tag, d, j):
if tag == 'X':
tag1 = 'X'
d1 = d ^ self.lin_d[0]
j1 = j
sign = (self.sign_XYZ[d] & 1)
sign ^= (self.lin_i[0] >> j) & 1
if self.odd:
cc = m24.vect_to_cocode(1 << j)
sign ^= m24.scalar_prod(d, cc)
elif tag in 'ZY':
s = self.odd ^ (tag == 'Y')
tag1 = 'ZY'[s]
s += 1
d1 = d ^ self.lin_d[s]
j1 = j
sign = (self.sign_XYZ[d] >> s) & 1
sign ^= (self.lin_i[s] >> j) & 1
elif tag == 'T':
tag1 = 'T'
d1 = d
te = self.s_T[d]
so_exp = _as_suboctad(self.f, d)
assert te & 0x3f == so_exp, (hex(te), hex(so_exp))
j1 = j ^ (te & 0x3f)
sign = m24.suboctad_scalar_prod(j, (te >> 8) & 0x3f)
sign ^= (te >> 14) & 1
sign ^= m24.suboctad_weight(j) & self.odd & 1
assert ((te >> 15) ^ self.odd) & 1 == 0
else:
raise ValueError("Illegal tag " + str(tag))
return sign & 1, tag1, d1, j1
def mul_Xp(tag, d, i, g):
eps, pi, rep = g.cocode, g.perm, g.rep
d1 = m24.op_ploop_autpl(d, rep)
i1 = pi[i]
s = d1 >> 12
if eps & 0x800: # if eps is odd:
s ^= m24.scalar_prod(d, m24.vect_to_cocode(1 << i))
s ^= m24.pow_ploop(d, 2) >> 12
return s, tag, d1 & 0x7ff, i1
def __add__(self, other):
if isinstance(other, Cocode):
return Cocode((self.value ^ other.value) & 0xfff)
elif isinstance(other, GcVector):
return Cocode(self.value ^ mat24.vect_to_cocode(other.value))
elif other == 0:
return Cocode(self)
else:
return NotImplemented
def __init__(self, value):
if import_pending:
complete_import()
if isinstance(value, Integral):
self.value = value & 0xfff
elif isinstance(value, Cocode):
self.value = value.value
elif isinstance(value, GcVector):
self.value = mat24.vect_to_cocode(value.value)
elif isinstance(value, XLeech2):
v = value.value
self.value = (mat24.ploop_theta(v >> 12) ^ v) & 0xfff
elif isinstance(value, str):
if len(value) == 1 and value in "reo":
self.value = randint(0, 0xfff)
if "o" in value: self.value |= 0x800
if "e" in value: self.value &= 0x7ff
else:
raise ValueError(ERR_RAND % 'Cocode')
else:
vector = as_vector24(value)
self.value = mat24.vect_to_cocode(vector)
def sign_t_YZ(d, i):
return (m24.scalar_prod(d, m24.vect_to_cocode(1 << i)) ^
(m24.pow_ploop(d, 2)) >> 12)
def sign_t_XY(d, i):
return m24.scalar_prod(d, m24.vect_to_cocode(1 << i))
def mul_Cy(tag, i, j, g):
c = m24.vect_to_cocode((1 << i) + (1 << j))
e = g.pl
s = m24.scalar_prod(e, c)
tag = C - s
return s, tag, i, j
def mul_Ay(tag, i, j, g):
c = m24.vect_to_cocode((1 << i) ^ (1 << j))
e = g.pl
s = m24.scalar_prod(e, c)
if i == j: assert s == 0
return s, tag, i, j
def mul_Zy(tag, d, i, g):
e = g.pl
de = m24.mul_ploop(d, e)
s = m24.scalar_prod(e, m24.vect_to_cocode(1 << i))
s ^= de >> 12
return s, Z, de & 0x7ff, i
def mul_Yy(tag, d, i, g):
e = g.pl & 0xfff
s = m24.scalar_prod(e, m24.vect_to_cocode(1 << i))
s ^= m24.ploop_comm(d, e)
return s, Y, d & 0x7ff, i
def mul_Bx(tag, i, j, g):
c = m24.vect_to_cocode((1 << i) ^ (1 << j))
e = g.pl
s = m24.scalar_prod(e, c)
return s, tag, i, j
def mul_Zx(tag, d, i, g):
e = g.pl
ed = m24.mul_ploop(m24.pow_ploop(e, 3), d)
s = m24.scalar_prod(e, m24.vect_to_cocode(1 << i))
s = (ed >> 12)
return s & 1, Z, ed & 0x7ff, i
def cocode(self):
"""Return number of the cocode word corresponding to the vector.
"""
return mat24.vect_to_cocode(self.value)
def op_xy(v, eps, e, f):
"""Multiply unit vector v with group element
This function multplies a (multiple of a) unit vector v
with the group element
g = d_<eps> * (x_<e>)**(-1) * (y_<f>)**(-1) .
It returns the vector w = v * g. This function uses the same
formula for calculating w = v * g, which is used in the
implementation of the monster group for computing
v = w * g ** (-1).
Input vector v must be given as a tuple as described in class
mmgroup.structures.abstract_mm_rep_space.AbstractMmRepSpace.
Output vector is returned as a tuple of the same shape.
"""
if len(v) == 3:
v = (1,) + v
v_value, v_tag, v_d, v_j = v
parity = (eps >> 11) & 1 # parity of eps
if v_tag == 'X':
w_d = v_d ^ (f & 0x7ff)
sign = v_d >> 12
d = v_d & 0x7ff
c = m24.vect_to_cocode(1 << v_j)
sign += m24.gcode_weight(e ^ f)
sign += m24.gcode_weight(f)
sign += m24.gcode_weight(d) * (parity + 1)
sign += m24.gcode_weight(d ^ e ^ f)
sign += m24.scalar_prod(e, c)
cc = c if parity else 0
cc ^= eps ^ m24.ploop_theta(f) ^ m24.ploop_cap(e, f)
sign += m24.scalar_prod(d, cc)
sign += f >> 12
return (-1)**sign * v_value, 'X', w_d, v_j
elif v_tag in 'YZ':
tau = v_tag == 'Y'
sigma = (tau + parity) & 1
w_tag = "ZY"[sigma]
sign = (v_d >> 12) + ((v_d >> 11) & tau)
w_d = (v_d ^ e ^ (f & ~-sigma)) & 0x7ff
#print("YZ, w_d", hex(w_d), hex(v_d ^ (e & 0x7ff) ^ (f & sigma_1)), err)
# Next we check the sign
d = v_d & 0x7ff
c = m24.vect_to_cocode(1 << v_j)
sign += m24.ploop_cocycle(f, e) * (sigma + 1)
sign += m24.gcode_weight(f) * (sigma)
sign += m24.gcode_weight(d ^ e)
sign += m24.gcode_weight(d ^ e ^ f)
sign += m24.scalar_prod(f, c)
cc = eps ^ m24.ploop_theta(e)
cc ^= m24.ploop_theta(f) * ((sigma ^ 1) & 1)
sign += m24.scalar_prod(d, cc)
sign += (e >> 12) + (f >> 12) * (sigma + 1)
sign += ((e >> 11) & sigma)
return (-1)**sign * v_value, w_tag, w_d, v_j
elif v_tag == 'T':
d = m24.octad_to_gcode(v_d)
w_j = v_j ^ as_suboctad(f, d)
sign = m24.gcode_weight(d ^ e) + m24.gcode_weight(e)
sign += m24.scalar_prod(d, eps)
sign += m24.suboctad_scalar_prod(as_suboctad(e ^ f, d), v_j)
sign += m24.suboctad_weight(v_j) * parity
return (-1)**sign * v_value, 'T', v_d, w_j
elif v_tag in 'BC':
m = v_tag == 'C'
c = m24.vect_to_cocode((1 << v_d) ^ (1 << v_j))
n = m ^ m24.scalar_prod(f, c)
w_tag = "BC"[n]
w_i, w_j = max(v_d, v_j), min(v_d, v_j)
sign = m * parity + m24.scalar_prod(e ^ f, c)
return (-1)**sign * v_value, w_tag, w_i, v_j
elif v_tag == 'A':
w_i, w_j = max(v_d, v_j), min(v_d, v_j)
c = m24.vect_to_cocode((1 << v_d) ^ (1 << v_j))
sign = m24.scalar_prod(f, c)
return (-1)**sign * v_value,'A', w_i, v_j
else:
raise ValueError("Bad tag " + v_tag)
def map_y(y_index):
i, j = (y_index >> 14) & 0x1f, (y_index >> 8) & 0x1f
vect = (1 << i) + (1 << j)
gc = vect_to_cocode(vect)
assert 0 <= gc < 0x800
return gc