def ref_generator(d, ref, io_sums=False):
circuit = circuit_model.Circuit()
var_inputs = [circuit.var(f'x_{i}', kind='input') for i in range(d)]
var_outputs = [circuit.var(f'y_{i}', kind='output') for i in range(d)]
ref(circuit=circuit, inputs=var_inputs, outputs=var_outputs)
if io_sums:
s = circuit.var('s')
circuit.p_sum(s, var_inputs)
circuit.p_sum(s, var_outputs)
return circuit
def test_refresh(d, ref=simple_ref):
circuit = circuit_model.Circuit()
var_inputs = [circuit.var(f'x_{i}', kind='input') for i in range(d)]
var_outputs = [circuit.var(f'y_{i}', kind='output') for i in range(d)]
ref(circuit=circuit, inputs=var_inputs, outputs=var_outputs)
g = circuit_model.CompGraph(circuit)
x = gen_random_input(d)
inputs = {f'x_{i}': v for i, v in enumerate(x)}
res, _ = g.compute(inputs)
y = [
v for var, v in res.items() if circuit.vars[var].name.startswith('y_')
]
assert (sum(x) % 2) == (sum(y) % 2)
def pini3(d, mat_gen, tmp_sums, strong_bij=False):
c = circuit_model.Circuit()
sx, sy, sz, x, y, z = mul_preamble(d, c, strong_bij)
if tmp_sums:
var_sums = (sx, sy)
else:
var_sums = None
ref_prods = mat_gen(c, x, y, var_sums=var_sums)
# randoms & temps in matrix
r = [{
j: c.var(f'r_{i}_{j}', kind='random' if j < i else 'intermediate')
for j in range(d) if j != i
} for i in range(d)]
for i in range(d):
for j in range(i):
c.assign(r[j][i], r[i][j])
s = [{j: c.var(f's_{i}_{j}')
for j in range(d) if j != i} for i in range(d)]
p = [{
j: [c.var(f'p_{i}_{j}_{k}') for k in range(3)]
for j in range(d) if j != i
} for i in range(d)]
t = [{j: c.var(f't_{i}_{j}') for j in range(d)} for i in range(d)]
for i in range(d):
c.l_prod(t[i][i], ref_prods[i][i])
for j in range(d):
if j != i:
xi, yj = ref_prods[i][j]
# not(x_i)
#nxi = c.var(f'nxi_{i}_{j}')
#c.l_sum(nxi, (xi,))
c.l_sum(s[i][j], (yj, r[i][j]))
c.l_prod(p[i][j][0], (xi, r[i][j]))
c.l_prod(p[i][j][1], (xi, s[i][j]))
c.l_sum(p[i][j][2], (p[i][j][0], r[i][j]))
c.l_sum(t[i][j], (p[i][j][2], p[i][j][1]))
c_var = [[c.var(f'c_{i}_{j}') for j in range(d)] for i in range(d)]
for i in range(d):
c.assign(c_var[i][0], t[i][0])
for j in range(1, d):
c.l_sum(c_var[i][j], (c_var[i][j - 1], t[i][j]))
c.assign(z[i], c_var[i][d - 1])
return c
def BBP15(d, strong_bij=False):
d2 = d - 1
c = circuit_model.Circuit()
_, _, _, x, y, z = mul_preamble(d, c, strong_bij)
# product matrix
p = [[c.var(f'p_{i}_{j}') for j in range(d)] for i in range(d)]
for i, j in it.product(range(d), range(d)):
c.l_prod(p[i][j], (x[i], y[j]))
# randoms & temps in matrix & compression
r = [{
d2 - j: c.var(f'r_{i}_{j}', kind='random')
for j in range(0, d2 - i, 2)
} for i in range(d)]
r2 = {j: c.var(f'r2_{j}', kind='random') for j in range(d2 - 1, 0, -2)}
t = [{
j: [c.var(f't_{i}_{j}_{k}') for k in range(5)]
for j in range(d2, i + 1, -2)
} for i in range(d)]
c_var = [{j: c.var(f'c_{i}_{j}')
for j in range(d2 + 2, i + 1, -2)} for i in range(d)]
for i in range(d):
c.assign(c_var[i][d2 + 2], p[i][i])
for j in range(d2, i + 1, -2):
c.l_sum(t[i][j][0], (r[i][j], p[i][j]))
c.l_sum(t[i][j][1], (t[i][j][0], p[j][i]))
c.l_sum(t[i][j][2], (t[i][j][1], r2[j - 1]))
c.l_sum(t[i][j][3], (t[i][j][2], p[i][j - 1]))
c.l_sum(t[i][j][4], (t[i][j][3], p[j - 1][i]))
c.l_sum(c_var[i][j], (c_var[i][j + 2], t[i][j][4]))
if (i - d2) % 2 != 0:
t[i][i + 1] = [c.var(f't_{i}_{i+1}_0'), c.var(f't_{i}_{i+1}_1')]
c_var[i][i + 1] = c.var(f'c_{i}_{i+1}')
c.l_sum(t[i][i + 1][0], (r[i][i + 1], p[i][i + 1]))
c.l_sum(t[i][i + 1][1], (t[i][i + 1][0], p[i + 1][i]))
c.l_sum(c_var[i][i + 1], (c_var[i][i + 3], t[i][i + 1][1]))
if i % 2 == 1:
c.l_sum(z[i], (c_var[i][i + 1], r2[i]))
else:
c.assign(z[i], c_var[i][i + 1])
else:
for j in range(i - 1, -1, -1):
c_var[i][j + 2] = c.var(f'c_{i}_{j+2}')
c.l_sum(c_var[i][j + 2], (c_var[i][j + 3], r[j][i]))
c.assign(z[i], c_var[i][2])
return c
def pinic(d, mat_gen, tmp_sums, strong_bij=False):
c = circuit_model.Circuit()
x, y, z, shx, shy, shz = mul_preamble(d,
c,
strong_bij=False,
x_kind='intermediate',
x_name='x2')
shx2 = [c.var(f'x_{i}', kind='input') for i in range(d)]
if strong_bij:
for sx, sy in zip(shx2, shy):
c.bij(sx, sy)
x2 = c.var('x', kind='property')
c.bij(x2, x)
refs_gen.bat_ref(c, shx2, shx)
if tmp_sums:
c.p_sum(x, shx2)
bat_mul_inner(d, mat_gen, tmp_sums, c, x, y, z, shx, shy, shz)
return c
def pini1(d, strong_bij=False):
c = circuit_model.Circuit()
sx, sy, sz, x, y, z = mul_preamble(d, c, strong_bij)
# randoms & temps in matrix
r = [{
j: c.var(f'r_{i}_{j}', kind='random' if j < i else 'intermediate')
for j in range(d) if j != i
} for i in range(d)]
for i in range(d):
for j in range(i):
c.assign(r[j][i], r[i][j])
s = [{j: c.var(f's_{i}_{j}')
for j in range(d) if j != i} for i in range(d)]
p = [{
j: [c.var(f'p_{i}_{j}_{k}') for k in range(2)]
for j in range(d) if j != i
} for i in range(d)]
t = [{j: c.var(f't_{i}_{j}') for j in range(d)} for i in range(d)]
for i in range(d):
c.l_prod(t[i][i], (x[i], y[i]))
# not(x_i)
nxi = c.var(f'nxi_{i}')
c.l_sum(nxi, (x[i], ))
for j in range(d):
if j != i:
xi, yj = x[i], y[j]
c.l_sum(s[i][j], (yj, r[i][j]))
c.l_prod(p[i][j][0], (nxi, r[i][j]))
c.l_prod(p[i][j][1], (xi, s[i][j]))
c.l_sum(t[i][j], (p[i][j][0], p[i][j][1]))
c_var = [[c.var(f'c_{i}_{j}') for j in range(d)] for i in range(d)]
for i in range(d):
c.assign(c_var[i][0], t[i][0])
for j in range(1, d):
c.l_sum(c_var[i][j], (c_var[i][j - 1], t[i][j]))
c.assign(z[i], c_var[i][d - 1])
return c
def bat_mul(d, mat_gen, tmp_sums, strong_bij=False):
c = circuit_model.Circuit()
sx, sy, sz, x, y, z = mul_preamble(d, c, strong_bij)
bat_mul_inner(d, mat_gen, tmp_sums, c, sx, sy, sz, x, y, z)
return c
def pini2(d, mat_gen, tmp_sums, strong_bij=False):
d2 = d - 1
c = circuit_model.Circuit()
sx, sy, sz, x, y, z = mul_preamble(d, c, strong_bij)
if tmp_sums:
var_sums = (sx, sy)
else:
var_sums = None
ref_prods = mat_gen(c, x, y, var_sums=var_sums)
# product matrix
s1 = [c.var(f's1_{i}', kind='random') for i in range(d)]
s = [{j: c.var(f's_{i}_{j}') for j in range(i + 1, d)} for i in range(d)]
u = [{
j: [c.var(f's_{i}_{j}_{k}') for k in range(2)]
for j in range(i + 1, d)
} for i in range(d)]
p = [{
j: [c.var(f's_{i}_{j}_{k}') for k in range(4)]
for j in range(i + 1, d)
} for i in range(d)]
for i in range(d):
for j in range(i + 1, d):
c.l_sum(s[i][j], (s1[i], s1[j]))
xi, yj = ref_prods[i][j]
xj, yi = ref_prods[j][i]
c.l_sum(u[i][j][0], (yj, s[i][j]))
c.l_sum(u[i][j][1], (xj, s[i][j]))
c.l_prod(p[i][j][0], (xi, s[i][j]))
c.l_prod(p[i][j][1], (xi, u[i][j][0]))
c.l_prod(p[i][j][2], (yi, s[i][j]))
c.l_prod(p[i][j][3], (yi, u[i][j][1]))
# randoms & temps in matrix & compression
r = [{
d2 - j: c.var(f'r_{i}_{j}', kind='random')
for j in range(0, d2 - i, 2)
} for i in range(d)]
r2 = {j: c.var(f'r2_{j}', kind='random') for j in range(d2 - 1, 0, -2)}
t = [{
j: [c.var(f't_{i}_{j}_{k}') for k in range(9)]
for j in range(d2, i + 1, -2)
} for i in range(d)]
c_var = [{j: c.var(f'c_{i}_{j}')
for j in range(d2 + 2, i + 1, -2)} for i in range(d)]
for i in range(d):
pi = c.var(f'p_{i}_{i}')
c.l_prod(pi, ref_prods[i][i])
c.assign(c_var[i][d2 + 2], pi)
for j in range(d2, i + 1, -2):
c.l_sum(t[i][j][0], (r[i][j], p[i][j][0]))
c.l_sum(t[i][j][1], (t[i][j][0], p[i][j][1]))
c.l_sum(t[i][j][2], (t[i][j][1], p[i][j][2]))
c.l_sum(t[i][j][3], (t[i][j][2], p[i][j][3]))
c.l_sum(t[i][j][4], (t[i][j][3], r2[j - 1]))
c.l_sum(t[i][j][5], (t[i][j][4], p[i][j - 1][0]))
c.l_sum(t[i][j][6], (t[i][j][5], p[i][j - 1][1]))
c.l_sum(t[i][j][7], (t[i][j][6], p[i][j - 1][2]))
c.l_sum(t[i][j][8], (t[i][j][7], p[i][j - 1][3]))
c.l_sum(c_var[i][j], (c_var[i][j + 2], t[i][j][8]))
if (i - d2) % 2 != 0:
t[i][i + 1] = [c.var(f't_{i}_{i+1}_{k}') for k in range(4)]
c_var[i][i + 1] = c.var(f'c_{i}_{i+1}')
c.l_sum(t[i][i + 1][0], (r[i][i + 1], p[i][i + 1][0]))
c.l_sum(t[i][i + 1][1], (t[i][i + 1][0], p[i][i + 1][1]))
c.l_sum(t[i][i + 1][2], (t[i][i + 1][1], p[i][i + 1][2]))
c.l_sum(t[i][i + 1][3], (t[i][i + 1][2], p[i][i + 1][3]))
c.l_sum(c_var[i][i + 1], (c_var[i][i + 3], t[i][i + 1][3]))
if i % 2 == 1:
c.l_sum(z[i], (c_var[i][i + 1], r2[i]))
else:
c.assign(z[i], c_var[i][i + 1])
else:
for j in range(i - 1, -1, -1):
c_var[i][j + 2] = c.var(f'c_{i}_{j+2}')
c.l_sum(c_var[i][j + 2], (c_var[i][j + 3], r[j][i]))
c.assign(z[i], c_var[i][2])
return c
def test_refresh(d, ref=simple_ref):
circuit = circuit_model.Circuit()
var_inputs = [circuit.var(f'x_{i}', kind='input') for i in range(d)]
var_outputs = [circuit.var(f'y_{i}', kind='output') for i in range(d)]
ref(circuit=circuit, inputs=var_inputs, outputs=var_outputs)
g = circuit_model.CompGraph(circuit)
x = gen_random_input(d)
inputs = {f'x_{i}': v for i, v in enumerate(x)}
res, _ = g.compute(inputs)
y = [
v for var, v in res.items() if circuit.vars[var].name.startswith('y_')
]
assert (sum(x) % 2) == (sum(y) % 2)
if __name__ == '__main__':
import sys
try:
d = int(sys.argv[1])
except IndexError:
d = 3
for ref_name, ref_f in refs.items():
#for ref_name, ref_f in ():
print(f'---- {ref_name}, d={d} ----')
circuit = circuit_model.Circuit()
var_inputs = [circuit.var(f'x_{i}', kind='input') for i in range(d)]
ref_f(circuit, var_inputs, out_name='y')
print(circuit)
for _ in range(100):
test_refresh(d, ref_f)