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This patch improves the precison of the scalar(32)_min_max_add and
scalar(32)_min_max_sub functions, which update the u(32)min/u(32)_max
ranges for the BPF_ADD and BPF_SUB instructions. We discovered this more
precise operator using a technique we are developing for automatically
synthesizing functions for updating tnums and ranges.
According to the BPF ISA [1], "Underflow and overflow are allowed during
arithmetic operations, meaning the 64-bit or 32-bit value will wrap".
Our patch leverages the wrap-around semantics of unsigned overflow and
underflow to improve precision.
Below is an example of our patch for scalar_min_max_add; the idea is
analogous for all four functions.
There are three cases to consider when adding two u64 ranges [dst_umin,
dst_umax] and [src_umin, src_umax]. Consider a value x in the range
[dst_umin, dst_umax] and another value y in the range [src_umin,
src_umax].
(a) No overflow: No addition x + y overflows. This occurs when even the
largest possible sum, i.e., dst_umax + src_umax <= U64_MAX.
(b) Partial overflow: Some additions x + y overflow. This occurs when
the largest possible sum overflows (dst_umax + src_umax > U64_MAX), but
the smallest possible sum does not overflow (dst_umin + src_umin <=
U64_MAX).
(c) Full overflow: All additions x + y overflow. This occurs when both
the smallest possible sum and the largest possible sum overflow, i.e.,
both (dst_umin + src_umin) and (dst_umax + src_umax) are > U64_MAX.
The current implementation conservatively sets the output bounds to
unbounded, i.e, [umin=0, umax=U64_MAX], whenever there is *any*
possibility of overflow, i.e, in cases (b) and (c). Otherwise it
computes tight bounds as [dst_umin + src_umin, dst_umax + src_umax]:
if (check_add_overflow(*dst_umin, src_reg->umin_value, dst_umin) ||
check_add_overflow(*dst_umax, src_reg->umax_value, dst_umax)) {
*dst_umin = 0;
*dst_umax = U64_MAX;
}
Our synthesis-based technique discovered a more precise operator.
Particularly, in case (c), all possible additions x + y overflow and
wrap around according to eBPF semantics, and the computation of the
output range as [dst_umin + src_umin, dst_umax + src_umax] continues to
work. Only in case (b), do we need to set the output bounds to
unbounded, i.e., [0, U64_MAX].
Case (b) can be checked by seeing if the minimum possible sum does *not*
overflow and the maximum possible sum *does* overflow, and when that
happens, we set the output to unbounded:
min_overflow = check_add_overflow(*dst_umin, src_reg->umin_value, dst_umin);
max_overflow = check_add_overflow(*dst_umax, src_reg->umax_value, dst_umax);
if (!min_overflow && max_overflow) {
*dst_umin = 0;
*dst_umax = U64_MAX;
}
Below is an example eBPF program and the corresponding log from the
verifier.
The current implementation of scalar_min_max_add() sets r3's bounds to
[0, U64_MAX] at instruction 5: (0f) r3 += r3, due to conservative
overflow handling.
0: R1=ctx() R10=fp0
0: (b7) r4 = 0 ; R4_w=0
1: (87) r4 = -r4 ; R4_w=scalar()
2: (18) r3 = 0xa000000000000000 ; R3_w=0xa000000000000000
4: (4f) r3 |= r4 ; R3_w=scalar(smin=0xa000000000000000,smax=-1,umin=0xa000000000000000,var_off=(0xa000000000000000; 0x5fffffffffffffff)) R4_w=scalar()
5: (0f) r3 += r3 ; R3_w=scalar()
6: (b7) r0 = 1 ; R0_w=1
7: (95) exit
With our patch, r3's bounds after instruction 5 are set to a much more
precise [0x4000000000000000,0xfffffffffffffffe].
...
5: (0f) r3 += r3 ; R3_w=scalar(umin=0x4000000000000000,umax=0xfffffffffffffffe)
6: (b7) r0 = 1 ; R0_w=1
7: (95) exit
The logic for scalar32_min_max_add is analogous. For the
scalar(32)_min_max_sub functions, the reasoning is similar but applied
to detecting underflow instead of overflow.
We verified the correctness of the new implementations using Agni [3,4].
We since also discovered that a similar technique has been used to
calculate output ranges for unsigned interval addition and subtraction
in Hacker's Delight [2].
[1] https://docs.kernel.org/bpf/standardization/instruction-set.html
[2] Hacker's Delight Ch.4-2, Propagating Bounds through Add’s and Subtract’s
[3] https://github.com/bpfverif/agni
[4] https://people.cs.rutgers.edu/~sn349/papers/sas24-preprint.pdf
Co-developed-by: Matan Shachnai <m.shachnai@rutgers.edu>
Signed-off-by: Matan Shachnai <m.shachnai@rutgers.edu>
Co-developed-by: Srinivas Narayana <srinivas.narayana@rutgers.edu>
Signed-off-by: Srinivas Narayana <srinivas.narayana@rutgers.edu>
Co-developed-by: Santosh Nagarakatte <santosh.nagarakatte@rutgers.edu>
Signed-off-by: Santosh Nagarakatte <santosh.nagarakatte@rutgers.edu>
Signed-off-by: Harishankar Vishwanathan <harishankar.vishwanathan@gmail.com>
Acked-by: Eduard Zingerman <eddyz87@gmail.com>
Link: https://lore.kernel.org/r/20250623040359.343235-2-harishankar.vishwanathan@gmail.com
Signed-off-by: Alexei Starovoitov <ast@kernel.org>