The multiplication and subtraction circuits were found by djb using GNU
Superoptimizer, and the addition circuit is derived from the subtraction
one by hand. They depend on a different representation: -1 is now (1, 1)
rather than (1, 0), and the latter becomes undefined.
The following Python program checks that the circuits work:
values = [0, 1, -1]
def toBits(v):
if v == 0:
return 0, 0
elif v == 1:
return 0, 1
elif v == -1:
return 1, 1
else:
raise ValueError(v)
def mul((s1, a1), (s2, a2)):
return ((s1 ^ s2) & a1 & a2, a1 & a2)
def add((s1, a1), (s2, a2)):
t = s1 ^ a2
return (t & (s2 ^ a1), (a1 ^ a2) | (t ^ s2))
def sub((s1, a1), (s2, a2)):
t = a1 ^ a2
return ((s1 ^ a2) & (t ^ s2), t | (s1 ^ s2))
def fromBits((s, a)):
if s == 0 and a == 0:
return 0
if s == 0 and a == 1:
return 1
if s == 1 and a == 1:
return -1
else:
raise ValueError((s, a))
def wrap(v):
if v == 2:
return -1
elif v == -2:
return 1
else:
return v
for v1 in values:
for v2 in values:
print v1, v2
result = fromBits(mul(toBits(v1), toBits(v2)))
if result != v1 * v2:
raise ValueError((v1, v2, result))
result = fromBits(add(toBits(v1), toBits(v2)))
if result != wrap(v1 + v2):
raise ValueError((v1, v2, result))
result = fromBits(sub(toBits(v1), toBits(v2)))
if result != wrap(v1 - v2):
raise ValueError((v1, v2, result))
Change-Id: Ie1a4ca5a82c2651057efc62330eca6fdd9878122
Reviewed-on: https://boringssl-review.googlesource.com/c/34344
Reviewed-by: David Benjamin <davidben@google.com>
eadef4730e