def itransform(entry, direction, width, x):
"""
Inverse transform - we simply reverse the operations in transform.
"""
assert x < 2**width
assert entry < 2**width
return utils.lrot(x, direction + 1, width) ^ entry
def itransform(entry, direction, width, x):
"""
Inverse transform - we simply reverse the operations in transform.
"""
assert x < 2**width
assert entry < 2**width
return utils.lrot(x, direction+1, width)^entry
def hilbert_index(dimension, order, p):
h, e, d = 0, 0, 0
for i in range(order):
l = 0
for x in range(dimension):
b = utils.bitrange(p[dimension - x - 1], order, i, i + 1)
l |= b << x
l = transform(e, d, dimension, l)
w = utils.igraycode(l)
e = e ^ utils.lrot(entry(w), d + 1, dimension)
d = (d + direction(w, dimension) + 1) % dimension
h = (h << dimension) | w
return h
def hilbert_index(dimension, order, p):
h, e, d = 0, 0, 0
for i in range(order):
l = 0
for x in range(dimension):
b = utils.bitrange(p[dimension - x - 1], order, i, i + 1)
l |= b << x
l = transform(e, d, dimension, l)
w = utils.igraycode(l)
e = e ^ utils.lrot(entry(w), d + 1, dimension)
d = (d + direction(w, dimension) + 1) % dimension
h = (h << dimension) | w
return h
def hilbert_index(dimension, order, p):
# Hamilton's paper initialises d to 0, which appears to be an error.
h, e, d = 0, 0, 1
for i in range(order):
l = 0
for x in range(dimension):
b = utils.bitrange(p[x], order, i, i+1)
l |= b<<x
l = transform(e, d, dimension, l)
w = utils.igraycode(l)
e = e ^ utils.lrot(entry(w), d+1, dimension)
d = (d + direction(w, dimension) + 1)%dimension
h = (h<<dimension)|w
return h
def hilbert_point(dimension, order, h):
"""
Convert an index on the Hilbert curve of the specified dimension and
order to a set of point coordinates.
"""
# The bit widths in this function are:
# p[*] - order
# h - order*dimension
# l - dimension
# e - dimension
hwidth = order*dimension
e, d = 0, 0
p = [0]*dimension
for i in range(order):
w = utils.bitrange(h, hwidth, i*dimension, i*dimension+dimension)
l = utils.graycode(w)
l = itransform(e, d, dimension, l)
for j in range(dimension):
b = utils.bitrange(l, dimension, j, j+1)
p[j] = utils.setbit(p[j], order, i, b)
e = e ^ utils.lrot(entry(w), d+1, dimension)
d = (d + direction(w, dimension) + 1)%dimension
return p
def hilbert_point(dimension, order, h):
"""
Convert an index on the Hilbert curve of the specified dimension and
order to a set of point coordinates.
"""
# The bit widths in this function are:
# p[*] - order
# h - order*dimension
# l - dimension
# e - dimension
hwidth = order * dimension
e, d = 0, 0
p = [0] * dimension
for i in range(order):
w = utils.bitrange(h, hwidth, i * dimension, i * dimension + dimension)
l = utils.graycode(w)
l = itransform(e, d, dimension, l)
for j in range(dimension):
b = utils.bitrange(l, dimension, j, j + 1)
p[j] = utils.setbit(p[j], order, i, b)
e = e ^ utils.lrot(entry(w), d + 1, dimension)
d = (d + direction(w, dimension) + 1) % dimension
return p
def rotpair(self, left, right, i, width):
assert utils.rrot(left, i, width) == right
assert utils.lrot(right, i, width) == left
assert utils.lrot(left, i, width) == utils.rrot(left, width-i, width)
def rotpair(self, left, right, i, width):
assert utils.rrot(left, i, width) == right
assert utils.lrot(right, i, width) == left
assert utils.lrot(left, i, width) == utils.rrot(left, width - i, width)