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This patch implements range tracking (interval analysis) for BPF_DIV and
BPF_MOD operations when the divisor is a constant, covering both signed
and unsigned variants.
While LLVM typically optimizes integer division and modulo by constants
into multiplication and shift sequences, this optimization is less
effective for the BPF target when dealing with 64-bit arithmetic.
Currently, the verifier does not track bounds for scalar division or
modulo, treating the result as "unbounded". This leads to false positive
rejections for safe code patterns.
For example, the following code (compiled with -O2):
```c
int test(struct pt_regs *ctx) {
char buffer[6] = {1};
__u64 x = bpf_ktime_get_ns();
__u64 res = x % sizeof(buffer);
char value = buffer[res];
bpf_printk("res = %llu, val = %d", res, value);
return 0;
}
```
Generates a raw `BPF_MOD64` instruction:
```asm
; __u64 res = x % sizeof(buffer);
1: 97 00 00 00 06 00 00 00 r0 %= 0x6
; char value = buffer[res];
2: 18 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 r1 = 0x0 ll
4: 0f 01 00 00 00 00 00 00 r1 += r0
5: 91 14 00 00 00 00 00 00 r4 = *(s8 *)(r1 + 0x0)
```
Without this patch, the verifier fails with "math between map_value
pointer and register with unbounded min value is not allowed" because
it cannot deduce that `r0` is within [0, 5].
According to the BPF instruction set[1], the instruction's offset field
(`insn->off`) is used to distinguish between signed (`off == 1`) and
unsigned division (`off == 0`). Moreover, we also follow the BPF division
and modulo runtime behavior (semantics) to handle special cases, such as
division by zero and signed division overflow.
- UDIV: dst = (src != 0) ? (dst / src) : 0
- SDIV: dst = (src == 0) ? 0 : ((src == -1 && dst == LLONG_MIN) ? LLONG_MIN : (dst / src))
- UMOD: dst = (src != 0) ? (dst % src) : dst
- SMOD: dst = (src == 0) ? dst : ((src == -1 && dst == LLONG_MIN) ? 0: (dst s% src))
Here is the overview of the changes made in this patch (See the code comments
for more details and examples):
1. For BPF_DIV: Firstly check whether the divisor is zero. If so, set the
destination register to zero (matching runtime behavior).
For non-zero constant divisors: goto `scalar(32)?_min_max_(u|s)div` functions.
- General cases: compute the new range by dividing max_dividend and
min_dividend by the constant divisor.
- Overflow case (SIGNED_MIN / -1) in signed division: mark the result
as unbounded if the dividend is not a single number.
2. For BPF_MOD: Firstly check whether the divisor is zero. If so, leave the
destination register unchanged (matching runtime behavior).
For non-zero constant divisors: goto `scalar(32)?_min_max_(u|s)mod` functions.
- General case: For signed modulo, the result's sign matches the
dividend's sign. And the result's absolute value is strictly bounded
by `min(abs(dividend), abs(divisor) - 1)`.
- Special care is taken when the divisor is SIGNED_MIN. By casting
to unsigned before negation and subtracting 1, we avoid signed
overflow and correctly calculate the maximum possible magnitude
(`res_max_abs` in the code).
- "Small dividend" case: If the dividend is already within the possible
result range (e.g., [-2, 5] % 10), the operation is an identity
function, and the destination register remains unchanged.
3. In `scalar(32)?_min_max_(u|s)(div|mod)` functions: After updating current
range, reset other ranges and tnum to unbounded/unknown.
e.g., in `scalar_min_max_sdiv`, signed 64-bit range is updated. Then reset
unsigned 64-bit range and 32-bit range to unbounded, and tnum to unknown.
Exception: in BPF_MOD's "small dividend" case, since the result remains
unchanged, we do not reset other ranges/tnum.
4. Also updated existing selftests based on the expected BPF_DIV and
BPF_MOD behavior.
[1] https://www.kernel.org/doc/Documentation/bpf/standardization/instruction-set.rst
Co-developed-by: Shenghao Yuan <shenghaoyuan0928@163.com>
Signed-off-by: Shenghao Yuan <shenghaoyuan0928@163.com>
Co-developed-by: Tianci Cao <ziye@zju.edu.cn>
Signed-off-by: Tianci Cao <ziye@zju.edu.cn>
Signed-off-by: Yazhou Tang <tangyazhou518@outlook.com>
Tested-by: syzbot@syzkaller.appspotmail.com
Link: https://lore.kernel.org/r/20260119085458.182221-2-tangyazhou@zju.edu.cn
Signed-off-by: Alexei Starovoitov <ast@kernel.org>
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