def multiply(x, y):
""" Input: positive integers x and y, in binary
output: their product """
xlen = len(x)
ylen = len(y)
print "xlen:ylen :: ", xlen, ylen
n = max(xlen, ylen)
if n == 1:
return str(int(x) * int(y))
m = n/2
xL, xR = x[:m], x[m:]
yL, yR = y[:m], y[m:]
P1 = multiply(xL, yL)
P2 = multiply(xR, yR)
P3 = multiply(binsum(xL, xR), binsum(yL, yR))
# print "P1, P2, P3: ", P1, P2, P3
P4 = binsum(P1, P2)
print "P1, P2, P3, P4: ", P1, P2, P3, P4
print "n, m: ", n, m
a = P1 + ("0" * n)
b = bin_subtract(P3, P4)
b = b + ("0" * m)
result = binsum(a, b)
result = binsum(result, P2)
# print ("maxlen is: ", maxlen)
return result
def two_complement(k):
klen = len(k)
result = []
for i in range(klen):
if int(k[i]) == 0:
result.append('1')
else:
result.append('0')
one = "1"
result = ''.join(result)
result = binsum(result, one)
return result
def bin_subtract(x, y):
""" assumes x and y are binary strings """
xlen = len(x)
ylen = len(y)
diff = abs(xlen - ylen)
z = "0" * diff
# print "Z: ", z
if xlen > ylen:
y = z + y
elif xlen < ylen:
x = z + x
# print "X: ", x
# print "Y: ", y
yc = two_complement(y)
# print "Y 2 complement: ", yc
result = binsum(x, yc)
result = result[1:]
result = result.lstrip("0")
# print "result: ", result
return result
