On Thu, Oct 19, 2023 at 03:30:33PM +0800, Shung-Hsi Yu wrote: > On Wed, Oct 18, 2023 at 09:24:05PM -0700, Andrii Nakryiko wrote: > > Add tests that validate correctness and completeness of BPF verifier's > > register range bounds. > > Nitpick: in abstract-interpretation-speak, completeness seems to mean > something different. I believe what we're trying to check here is > soundness[1], again, in abstraction-interpretation-speak), so using > completeness here may be misleading to some. (I'll leave explanation to > other that understand this concept better than I do, rather than making an > ill attempt that would probably just make things worst) > > > The main bulk is a lot of auto-generated tests based on a small set of > > seed values for lower and upper 32 bits of full 64-bit values. > > Currently we validate only range vs const comparisons, but the idea is > > to start validating range over range comparisons in subsequent patch set. > > CC Langston Barrett who had previously send kunit-based tnum checks[2] a > while back. If this patch is merged, perhaps we can consider adding > validation for tnum as well in the future using similar framework. > > More comments below > > > When setting up initial register ranges we treat registers as one of > > u64/s64/u32/s32 numeric types, and then independently perform conditional > > comparisons based on a potentially different u64/s64/u32/s32 types. This > > tests lots of tricky cases of deriving bounds information across > > different numeric domains. > > > > Given there are lots of auto-generated cases, we guard them behind > > SLOW_TESTS=1 envvar requirement, and skip them altogether otherwise. > > With current full set of upper/lower seed value, all supported > > comparison operators and all the combinations of u64/s64/u32/s32 number > > domains, we get about 7.7 million tests, which run in about 35 minutes > > on my local qemu instance. So it's something that can be run manually > > for exhaustive check in a reasonable time, and perhaps as a nightly CI > > test, but certainly is too slow to run as part of a default test_progs run. > > FWIW an alternative approach that speeds things up is to use model checkers > like Z3 or CBMC. On my laptop, using Z3 to validate tnum_add() against *all* > possible inputs takes less than 1.3 seconds[3] (based on code from [1] > paper, but I somehow lost the link to their GitHub repository). Found it. For reference, code used in "Sound, Precise, and Fast Abstract Interpretation with Tristate Numbers"[1] can be found at https://github.com/bpfverif/tnums-cgo22/blob/main/verification/tnum.py Below is a truncated form of the above that only check tnum_add(), requires a package called python3-z3 on most distros: #!/usr/bin/python3 from uuid import uuid4 from z3 import And, BitVec, BitVecRef, BitVecVal, Implies, prove SIZE = 64 # Working with 64-bit integers class Tnum: """A model of tristate number use in Linux kernel's BPF verifier. https://github.com/torvalds/linux/blob/v5.18/kernel/bpf/tnum.c """ val: BitVecRef mask: BitVecRef def __init__(self, val=None, mask=None): uid = uuid4() # Ensure that the BitVec are uniq, required by the Z3 solver self.val = BitVec(f'Tnum-val-{uid}', bv=SIZE) if val is None else val self.mask = BitVec(f'Tnum-mask-{uid}', bv=SIZE) if mask is None else mask def contains(self, bitvec: BitVecRef): # Simplified version of tnum_in() # https://github.com/torvalds/linux/blob/v5.18/kernel/bpf/tnum.c#L167-L173 return (~self.mask & bitvec) == self.val def wellformed(self): # Bit cannot be set in both val and mask, such tnum is not valid return self.val & self.mask == BitVecVal(0, bv=SIZE) # The function that we want to check def tnum_add(a: Tnum, b: Tnum): # Unmodified tnum_add() # https://github.com/torvalds/linux/blob/v5.18/kernel/bpf/tnum.c#L62-L72 sm = a.mask + b.mask sv = a.val + b.val sigma = sm + sv chi = sigma ^ sv mu = chi | a.mask | b.mask return Tnum(sv & ~mu, mu) t1 = Tnum() t2 = Tnum() x = BitVec('x', bv=SIZE) # Any possible 64-bit value y = BitVec('y', bv=SIZE) # same as above # Condition that needs to hold before we move forward to check tnum_add() premises = And( t1.wellformed(), # t1 and t2 is wellformed t2.wellformed(), t1.contains(x), # x is within t1, and y is within t2 t2.contains(y), ) # This ask Z3 solver to prove that tnum_add() work as intended prove( Implies( # Assuming that t1 and t2 is wellformed, x is within t1, and y is # within t2 premises, # Below is what we'd like to check. Namely, for any random x whos # value is within t1, and any random y whos value is within t2, # (x+y) is always within the tnum produced by tnum_add(t1, t2) tnum_add(t1, t2).contains(x+y), ) ) > One of the potential issue with [3] is that Z3Py is written in Python. So > there's the large over head of translating the C-implementation into Python > using Z3Py APIs each time we changed relevant code. This overhead could > potentially be removed with CBMC, which understand C, and we had a > precedence of using CBMC[4] within the kernel source code, though it was > later removed[5] due because SRCU changes are still happening too fast for > the format tests to keep up, so it looks like CBMC is not a silver-bullet. > > I really meant to look into the CMBC approach for verification of ranges and > tnum, but fails to allocate time for it, so far. > > Shung-Hsi > > > ... > > 1: https://people.cs.rutgers.edu/~sn349/papers/cgo-2022.pdf > 2: https://lore.kernel.org/bpf/20220430215727.113472-1-langston.barrett@xxxxxxxxx/ > 3: https://gist.github.com/shunghsiyu/a63e08e6231553d1abdece4aef29f70e > 4: https://lore.kernel.org/all/1485295229-14081-3-git-send-email-paulmck@xxxxxxxxxxxxxxxxxx/ Also forgot to add the link to the removal of SRCU formal-verification tests 5: https://lore.kernel.org/all/20230717182337.1098991-2-paulmck@xxxxxxxxxx/
