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adder.py
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adder.py
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from z3 import *
BITLEN = 1 # Number of bits in input
STEPS = 0 # How many steps to take in between input and output layers (e.g. time)
WIDTH = 2 # How many operations/values can be stored in parallel, has to be at least BITLEN * #inputs
# Input variables
x = BitVec('x', BITLEN)
y = BitVec('y', BITLEN)
# Define operations used
pass_func = lambda x: x
op_list = [BitVecRef.__and__, BitVecRef.__or__, BitVecRef.__xor__]
unary_op_list = [BitVecRef.__invert__, pass_func]
for uop in unary_op_list:
op_list.append(lambda x, y : uop(x))
# Chooses a function to use by setting all others to 0
def chooseFunc(i, x, y):
res = 0
for ind, op in enumerate(op_list):
res = If(ind == i, op(x, y), res)
return res
s = Solver()
steps = []
# First step is just the bits of the input padded with constants
firststep = Array("firststep", IntSort(), BitVecSort(1))
for i in range(BITLEN):
firststep = Store(firststep, i * 2, Extract(i, i, x))
firststep = Store(firststep, i * 2 + 1, Extract(i, i, y))
for i in range(BITLEN * 2, WIDTH):
firststep = Store(firststep, i, BitVec("const_0_%d" % i, 1))
steps.append(firststep)
# Generate remaining steps
for i in range(1, STEPS + 2):
final_step = i == STEPS + 1
this_step = Array("finalstep" if final_step else "step_%d" % i, IntSort(), BitVecSort(1))
last_step = steps[-1]
for j in range(BITLEN if final_step else WIDTH):
func_ind = Int("func_%d_%d" % (i,j))
s.add(func_ind >= 0, func_ind < len(op_list))
x_ind = Int("x_%d_%d" % (i,j))
s.add(x_ind >= 0, x_ind < WIDTH)
y_ind = Int("y_%d_%d" % (i,j))
s.add(y_ind >= 0, y_ind < WIDTH)
node = chooseFunc(func_ind, Select(last_step, x_ind), Select(last_step, y_ind))
this_step = Store(this_step, j, node)
steps.append(this_step)
# Set the result to the concatenated bits of the last step
if BITLEN == 1:
result = Select(steps[-1], 0)
else:
result = Concat(*[Select(steps[-1], i) for i in range(BITLEN)])
# Set goal
goal = x ^ y
s.add(ForAll([x, y], goal == result))
print(s)
print(s.check())
print(s.model())