def odd_even_mergesort(self, A):
if len(A) == 1:
return A
if int(log2(len(A))) != log2(len(A)): # accurate to about 2**48
raise ValueError("Length of list must be a power of 2 to odd-even merge sort")
evens = A[::2]
odds = A[1::2]
sorted_evens = self.odd_even_mergesort(evens)
sorted_odds = self.odd_even_mergesort(odds)
return self.odd_even_merge(sorted_evens, sorted_odds)
def odd_even_mergesort(self, A):
if len(A) == 1:
return A
if int(log2(len(A))) != log2(len(A)): # accurate to about 2**48
raise ValueError("Length of list must be a power of 2 to odd-even merge sort")
evens = A[::2]
odds = A[1::2]
sorted_evens = self.odd_even_mergesort(evens)
sorted_odds = self.odd_even_mergesort(odds)
return self.odd_even_merge(sorted_evens, sorted_odds)
def Sorter_(self, equation, polarity=None):
explode = sum(([a] * c for c, a in equation), [])
nterms = len(explode)
explode.extend([False] * (2**ceil(log2(nterms)) - nterms))
def cmp(a, b):
aa, bb = explode[a], explode[b]
explode[a], explode[b] = self.Or(aa, bb, polarity), self.And(aa, bb, polarity)
def merge(lo, hi, r):
step = r * 2
if step < hi - lo:
merge(lo, hi, step)
merge(lo + r, hi, step)
for i in range(lo + r, hi - r, step):
cmp(i, i + r)
else:
cmp(lo, lo + r)
def sort(lo, hi):
if hi - lo >= 1:
mid = lo + ((hi - lo) // 2)
sort(lo, mid)
sort(mid + 1, hi)
merge(lo, hi, 1)
sort(0, len(explode) - 1)
return explode
def build_sorter(self, linear):
if not linear:
return []
sorter_input = []
for coeff, atom in linear.equation:
sorter_input += [atom] * coeff
next_power_of_2 = 2**ceil(log2(len(sorter_input)))
sorter_input += [false] * (next_power_of_2 - len(sorter_input))
return self.odd_even_mergesort(sorter_input)
def build_sorter(self, linear):
if not linear:
return []
sorter_input = []
for coeff, atom in linear.equation:
sorter_input += [atom]*coeff
next_power_of_2 = 2**ceil(log2(len(sorter_input)))
sorter_input += [false]*(next_power_of_2 - len(sorter_input))
return self.odd_even_mergesort(sorter_input)
def test_odd_even_mergesort():
for n in [1, 2, 4, 8]:
A = list(range(1, n + 1))
C = Clauses(n)
S = C.odd_even_mergesort(A)
# Note, the zero-one principle states we only need to test lists of
# 0's and
# 1's. https://en.wikipedia.org/wiki/Sorting_network#Zero-one_principle.
for sol in my_itersolve(C.clauses):
a = [i in sol for i in A]
s = [i in sol for i in S]
assert s == sorted(a, reverse=True)
# TODO: n > 8 takes too long to test all combinations, but maybe we should test
# some random combinations.
assert raises(ValueError,
lambda: Clauses(5).odd_even_mergesort([1, 2, 3, 4, 5]))
# Make sure it works with booleans
for n in [1, 2, 4]:
for item in product(*[[true, false]] * n):
assert list(Clauses(0).odd_even_mergesort(item)) == sorted(
item, reverse=True)
# The most important use-case is extending a non-power of 2 length list
# with false.
for n in range(1, 9):
next_power_of_2 = 2**ceil(log2(n))
assert n <= next_power_of_2
for item in product(*[[true, false]] * (next_power_of_2 - n)):
A = list(range(1, n + 1)) + list(item)
C = Clauses(n)
S = C.odd_even_mergesort(A)
for sol in my_itersolve(C.clauses):
a = [
boolize(i) if isinstance(boolize(i), bool) else i in sol
for i in A
]
s = [
boolize(i) if isinstance(boolize(i), bool) else i in sol
for i in S
]
assert s == sorted(a, reverse=True), (a, s, sol)
def test_odd_even_mergesort():
for n in [1, 2, 4, 8]:
A = list(range(1, n+1))
C = Clauses(n)
S = C.odd_even_mergesort(A)
# Note, the zero-one principle states we only need to test lists of
# 0's and
# 1's. https://en.wikipedia.org/wiki/Sorting_network#Zero-one_principle.
for sol in my_itersolve(C.clauses):
a = [i in sol for i in A]
s = [i in sol for i in S]
assert s == sorted(a, reverse=True)
# TODO: n > 8 takes too long to test all combinations, but maybe we should test
# some random combinations.
assert raises(ValueError, lambda: Clauses(5).odd_even_mergesort([1, 2, 3,
4, 5]))
# Make sure it works with booleans
for n in [1, 2, 4]:
for item in product(*[[true, false]]*n):
assert list(Clauses(0).odd_even_mergesort(item)) == sorted(item, reverse=True)
# The most important use-case is extending a non-power of 2 length list
# with false.
for n in range(1, 9):
next_power_of_2 = 2**ceil(log2(n))
assert n <= next_power_of_2
for item in product(*[[true, false]]*(next_power_of_2 - n)):
A = list(range(1, n + 1)) + list(item)
C = Clauses(n)
S = C.odd_even_mergesort(A)
for sol in my_itersolve(C.clauses):
a = [boolize(i) if isinstance(boolize(i), bool) else
i in sol for i in A]
s = [boolize(i) if isinstance(boolize(i), bool) else
i in sol for i in S]
assert s == sorted(a, reverse=True), (a, s, sol)