def mm_order(g):
w, order = ORDER_VECTOR.copy(), 0
work = mm_vector(15)
while order < 120:
mm_op15_word(w, g.mmdata, len(g.mmdata), 1, work)
order +=1
if mm_op15_compare(w, ORDER_VECTOR) == 0:
return order
raise ValueError("Order computation failed")
def py_check_mm_in_g_x0(g, mode = 0):
"""Check if ``g`` is in the subgroup ``G_x0`` of the monster
If ``g`` is in the subgroup ``G_x0`` of the monster then the
function changes the word representing ``g`` to a (uniquely
defined) word in the generators of the subgroup ``G_x0`` and
returns ``g``.
Otherwise the function does not change ``g`` and returns ``None``.
``g`` must be an instance of class
``mmgroup.mm_group.MMGroupWord``.
"""
global err_in_g_x0_py
err_in_g_x0_py = 0
assert isinstance(g, (MM0, MM))
v = ORDER_VECTOR
w = mm_vector(15)
work = mm_vector(15)
mm_op15_copy(v, w)
res = mm_op15_word(w, g.mmdata, len(g.mmdata), 1, work)
assert res == 0
g1i = find_in_G_x0(w)
if g1i is None:
return None
res = mm_op15_word(w, g1i, len(g1i), 1, work)
assert res == 0
x = np.zeros(0, dtype = np.uint32) if mode & 4 else find_in_Q_x0(w)
if x == None:
return None
g2i = np.array([0x90000000 + (x & 0xfff),
0xB0000000 + ((x >> 12) & 0x1fff)], dtype = np.uint32)
res = mm_op15_word(w, g2i, 2, 1, work)
assert res == 0
g1i = np.append(g1i, g2i)
assert res == 0
if mm_op15_compare(v, w):
#print("vW", v, "\n", w)
err_in_g_x0_py = 9
return None
g._extend(11)
g.length = length = len(g1i)
g.reduced = 0
if mode & 1 == 0:
for i in range(length):
g._data[i] = g1i[length - 1 - i] ^ 0x80000000
else:
for i in range(length):
g._data[i] = g1i[i]
g.reduce()
return g
def reduce_G_x0(g, mode=0):
global reduce_time
va = mm_vector(15, 2)
v, work = va[0].data, va[1].data
r = np.zeros(256, dtype=np.uint32)
g1, n = g.mmdata, len(g.mmdata)
t_start = time.perf_counter()
mm_reduce_load_axis(v, 0)
res = mm_op15_word(v, g1, n, 1, work)
if res < 0: raise ValueError(ERR_GX0 % res)
res = mm_reduce_vector_vp(v, mode, r, work)
if res < 0: raise ValueError(ERR_GX0 % res)
mm_reduce_load_axis(v, 1)
res = mm_op15_word(v, g1, n, 1, work)
if res < 0: raise ValueError(ERR_GX0 % res)
res = mm_reduce_vector_vm(v, r, work)
if res < 0: raise ValueError(ERR_GX0 % res)
reduce_time = time.perf_counter() - t_start
return MM0('a', r[:res])
def check_mm_in_g_x0(g, mode = 0):
global err_in_g_x0_c
assert isinstance(g, (MM0, MM))
w = mm_vector(15)
work = mm_vector(15, 2).ravel()
mode = (mode | 8) & ~2
v = ORDER_VECTOR
mm_op15_copy(v, w)
res = mm_op15_word(w, g.mmdata, len(g.mmdata), 1, work)
assert res == 0
h = np.zeros(11, dtype = np.uint32)
res = mm_order_check_in_Gx0(w, h, mode, work)
if res < 0:
s = "mm_order_check_in_Gx0 failed with error %d"
raise ValueError(s % res)
if res >= 0x100:
err_in_g_x0_c = res
return None
return MM0('a', h[:res])
def reduce_baby_axis(vector, axis=v_start, verbose=0):
v = vector.data
#V = vector.space
work = V()
vA = np.zeros(24 * 4, dtype=np.uint64)
r = np.zeros(120, dtype=np.uint32)
len_r = 0
if verbose: print("Function reduce_baby_axis")
for i in range(5):
vt = mm_reduce_2A_axis_type(v)
assert vt
type = (vt >> 24) & 0xff
vt &= 0xffffff
if verbose:
print("type =", hex(type), ", vt =", hex(vt), ", A(v0) =",
mm_op15_eval_A(v, axis), ", axis =", hex(axis))
if type == 0xA1: # case 10A
v0 = short(v, 3)[0]
v2all = short(v, 1)
v2all = [w ^ v0 for w in v2all]
v4 = find_ortho_short(v2all, axis)
t_types = [0x61]
elif type == 0x63: # case 6C
v2all = span(v, 3, verbose)
v4 = find_ortho_short(v2all, axis)
t_types = [0x41]
elif type == 0x61: # case 6A
v2all = short(v, 5)
v2all = [w ^ vt for w in v2all] # if leech_type(w ^vt) == 4]
v4 = find_ortho_short(v2all, axis)
t_types = [0x41, 0x43]
elif type == 0x43: # case 4C
v2all = radical(v, 1, verbose)
v4 = find_ortho_short(v2all, axis)
t_types = [0x22]
elif type == 0x42: # case 4B
v2all = radical(v, 1, verbose)
v4 = find_ortho_short(v2all, axis)
t_types = [0x22]
elif type == 0x41: # case 4A
v4 = vt
assert leech_type(v4) == 4
t_types = [0x21]
elif type == 0x22: # case 2B
if mm_op15_eval_A(v, axis) in [0, 8]:
v2all = span(v, 4, verbose)
v4 = find_ortho_short(v2all, axis)
t_types = [0x21]
else:
raise ValueError("WTF 2B")
elif type == 0x21: # case 2A
if verbose:
print("v has type 0x21, axis = %s, eval_A = %d" %
(hex(axis), mm_op15_eval_A(v, axis)))
if mm_op15_eval_A(v, axis) == 0:
vt ^= axis
r1 = gen_leech2_reduce_type4(vt, r[len_r:])
assert r1 >= 0
mm_op15_word(v, r[len_r:], r1, 1, work.data)
axis = op_axis(axis, r[len_r:len_r + r1])
len_r += r1
vt = mm_reduce_2A_axis_type(v) & 0xffffff
vt = v_leech2_adjust_sign(v, vt)
vt = gen_leech2_mul(vt, axis)
assert vt & 0xffffff == 0x800000
e = 1 + (vt >> 24)
if verbose: print("e", e)
r[len_r] = 0xD0000003 - e
mm_op15_word(v, r[len_r:], 1, 1, work.data)
axis = op_axis(axis, r[len_r:len_r + 1])
len_r += 1
else:
assert mm_op15_eval_A(v, axis) == 4
vt = mm_reduce_2A_axis_type(v) & 0xffffff
vt = v_leech2_adjust_sign(v, vt)
assert (vt ^ axis) & 0x1ffffff == 0x1000000, (hex(vt), hex(axis))
if verbose:
print("Function reduce_baby_axis terminated successfullly")
return r[:len_r], axis
else:
raise ValueError("WTF1")
r1 = gen_leech2_reduce_type4(v4, r[len_r:])
assert r1 >= 0, (hex(v4), )
mm_op15_word(v, r[len_r:], r1, 1, work.data)
axis = op_axis(axis, r[len_r:len_r + r1])
len_r += r1
ok = False
for e in (1, 2):
mm_op15_t_A(v, e, vA)
t = mm_reduce_2A_axis_type(vA) >> 24
if verbose: print("e", e, hex(t))
if t in t_types:
r[len_r] = 0xD0000003 - e
mm_op15_word(v, r[len_r:], 1, 1, work.data)
axis = op_axis(axis, r[len_r:len_r + 1])
len_r += 1
ok = True
break
if not ok:
raise ValueError("WTF2")
raise ValueError("WTF3")
def reduce_axis(vector, std_axis=1, verbose=0):
v = vector.data
#V = vector.space
work = V()
vA = np.zeros(24 * 4, dtype=np.uint64)
r = np.zeros(120, dtype=np.uint32)
len_r = 0
if verbose: print("Function reduce_axis")
for i in range(5):
vt = mm_reduce_2A_axis_type(v)
assert vt
type = (vt >> 24) & 0xff
vt &= 0xffffff
if verbose: print("type", hex(type))
if type == 0xC3: # case 12C
v2all = radical(v, 7, verbose)
v4 = find_type4(v2all)
t_types = [0x42, 0x61]
elif type == 0xA2: # case 10B
v2all = radical(v, 4, verbose)
v4 = find_type4(v2all)
t_types = [0x42, 0x43]
elif type == 0xA1: # case 10A
v0 = short(v, 3)[0]
v2all = short(v, 1)
v2all = [w ^ v0 for w in v2all]
v4 = find_type4(v2all)
t_types = [0x61]
elif type == 0x82: # case 8B
v2all = short(v, 1)
v2_0 = v2all[0]
v2all = [w ^ v2_0 for w in v2all]
v4 = find_type4(v2all)
t_types = [0x41]
elif type == 0x66: # case 6F
v2all = radical(v, 7, verbose)
v4 = find_type4(v2all)
t_types = [0x43]
elif type == 0x63: # case 6C
v2all = span(v, 3, verbose)
v4 = find_type4(v2all)
t_types = [0x41]
elif type == 0x61: # case 6A
v2all = short(v, 5)
v2all = [w ^ vt for w in v2all]
v4 = find_type4(v2all)
t_types = [0x41]
elif type == 0x43: # case 4C
v2all = radical(v, 1, verbose)
v4 = find_type4(v2all)
t_types = [0x22]
elif type == 0x42: # case 4B
v2all = radical(v, 1, verbose)
v4 = find_type4(v2all)
t_types = [0x22]
elif type == 0x41: # case 4A
v4 = vt
t_types = [0x21]
elif type == 0x22: # case 2B
v2all = span(v, 4, verbose)
v4 = find_type4(v2all)
t_types = [0x21]
elif type == 0x21: # case 2A
if not std_axis:
vt = v_leech2_adjust_sign(v, vt)
if verbose:
print("Function reduce_axis terminated successfullly")
return r[:len_r], vt
r1 = gen_leech2_reduce_type2(vt, r[len_r:])
assert r1 >= 0
mm_op15_word(v, r[len_r:], r1, 1, work.data)
len_r += r1
ind = mm_aux_get_mmv1(15, v, (24 + 3) * 32 + 2)
if (ind != 15 - 2):
r[len_r] = 0xB0000200
mm_op15_word(v, r[len_r:], 1, 1, work.data)
len_r += 1
assert mm_op15_compare(v, V_START.data) == 0
if verbose:
print("Function reduce_axis terminated successfullly")
return r[:len_r], 0x200
else:
raise ValueError("WTF1")
r1 = gen_leech2_reduce_type4(v4, r[len_r:])
assert r1 >= 0
mm_op15_word(v, r[len_r:], r1, 1, work.data)
len_r += r1
ok = False
for e in (1, 2):
mm_op15_t_A(v, e, vA)
t = mm_reduce_2A_axis_type(vA) >> 24
if verbose: print("e", e, hex(t))
if t in t_types:
r[len_r] = 0xD0000003 - e
mm_op15_word(v, r[len_r:], 1, 1, work.data)
len_r += 1
ok = True
break
if not ok:
raise ValueError("WTF2")
raise ValueError("WTF3")