linux/kernel
Yazhou Tang 44fdd581d2 bpf: Add range tracking for BPF_DIV and BPF_MOD
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>
2026-01-20 16:41:53 -08:00
..
bpf bpf: Add range tracking for BPF_DIV and BPF_MOD 2026-01-20 16:41:53 -08:00
cgroup cgroup: Eliminate cgrp_ancestor_storage in cgroup_root 2026-01-07 15:11:03 -10:00
configs hung_task: panic when there are more than N hung tasks at the same time 2025-11-12 10:00:14 -08:00
debug kdb: Adapt kdb_msg_write to work with NBCON consoles 2025-10-24 12:56:20 +02:00
dma dma-mapping fixes for Linux 6.19: 2025-12-11 08:14:23 +09:00
entry rseq: Switch to TIF_RSEQ if supported 2025-11-04 08:35:37 +01:00
events Fix perf swevent hrtimer deinit regression. 2026-01-11 06:55:27 -10:00
futex Futex changes for v6.19: 2025-12-10 17:21:30 +09:00
gcov gcov: add support for GCC 15 2025-11-09 21:19:44 -08:00
irq treewide: Update email address 2026-01-11 06:09:11 -10:00
kcsan Kernel Concurrency Sanitizer (KCSAN) updates for v6.18 2025-10-02 08:31:44 -07:00
livepatch livepatching changes for 6.19 2025-12-03 13:46:48 -08:00
liveupdate mm: memfd_luo: add CONFIG_SHMEM dependency 2025-12-10 16:07:44 -08:00
locking RCU pull request for v6.19 2025-12-03 12:18:07 -08:00
module Significant patch series in this pull request: 2025-12-06 14:01:20 -08:00
power PM: hibernate: Fix crash when freeing invalid crypto compressor 2026-01-05 19:12:56 +01:00
printk soc: driver updates for 6.19 2025-12-05 17:29:04 -08:00
rcu RCU pull request for v6.19 2025-12-03 12:18:07 -08:00
sched Merge git://git.kernel.org/pub/scm/linux/kernel/git/bpf/bpf after rc5 2026-01-14 15:22:01 -08:00
time treewide: Update email address 2026-01-11 06:09:11 -10:00
trace bpf: Add __force annotations to silence sparse warnings 2026-01-16 14:21:11 -08:00
unwind unwind_user/x86: Teach FP unwind about start of function 2025-10-29 10:29:58 +01:00
.gitignore kheaders: rebuild kheaders_data.tar.xz when a file is modified within a minute 2025-06-24 20:30:37 +09:00
acct.c act: use credential guards in acct_write_process() 2025-11-04 12:36:49 +01:00
async.c
audit_fsnotify.c VFS/audit: introduce kern_path_parent() for audit 2025-09-23 12:37:35 +02:00
audit_tree.c mount-related stuff for this cycle 2025-10-03 10:19:44 -07:00
audit_watch.c VFS/audit: introduce kern_path_parent() for audit 2025-09-23 12:37:35 +02:00
audit.c audit: fix skb leak when audit rate limit is exceeded 2025-09-10 19:55:00 -04:00
audit.h audit: fix comment misindentation in audit.h 2025-10-22 19:28:06 -04:00
auditfilter.c audit: Use kzalloc() instead of kmalloc()/memset() in audit_krule_to_data() 2025-11-07 16:38:34 -05:00
auditsc.c audit: merge loops in __audit_inode_child() 2025-11-07 16:50:42 -05:00
backtracetest.c
bounds.c x86/asm: Remove ANNOTATE_DATA_SPECIAL usage 2025-12-03 16:53:19 +01:00
capability.c capability: Remove unused has_capability 2025-03-07 22:03:09 -06:00
cfi.c cfi: Move BPF CFI types and helpers to generic code 2025-07-31 18:23:53 -07:00
compat.c
configs.c
context_tracking.c context_tracking: Make RCU watch ct_kernel_exit_state() warning 2025-03-04 18:44:29 -08:00
cpu_pm.c syscore: Pass context data to callbacks 2025-11-14 10:01:52 +01:00
cpu.c cpu: Make atomic hotplug callbacks run with interrupts disabled on UP 2025-12-10 15:49:11 +09:00
crash_core_test.c crash: add KUnit tests for crash_exclude_mem_range 2025-09-13 17:32:55 -07:00
crash_core.c crash: fix crashkernel resource shrink 2025-11-15 10:52:01 -08:00
crash_dump_dm_crypt.c crash_dump: retrieve dm crypt keys in kdump kernel 2025-05-21 10:48:21 -07:00
crash_reserve.c crash: let architecture decide crash memory export to iomem_resource 2025-11-12 10:00:15 -08:00
cred.c kernel-6.19-rc1.cred 2025-12-01 13:45:41 -08:00
delayacct.c delayacct: remove redundant code and adjust indentation 2025-05-27 19:40:33 -07:00
dma.c
elfcorehdr.c
exec_domain.c
exit.c Significant patch series in this pull request: 2025-12-06 14:01:20 -08:00
exit.h
extable.c
fail_function.c
fork.c Significant patch series in this pull request: 2025-12-06 14:01:20 -08:00
freezer.c freezer: Clarify that only cgroup1 freezer uses PM freezer 2025-10-30 20:10:27 +01:00
gen_kheaders.sh kheaders: make it possible to override TAR 2025-08-06 10:23:36 +09:00
groups.c
hung_task.c hung_task: add hung_task_sys_info sysctl to dump sys info on task-hung 2025-11-20 14:03:43 -08:00
iomem.c mm/memremap: Pass down MEMREMAP_* flags to arch_memremap_wb() 2025-02-21 15:05:38 +01:00
irq_work.c kasan: make kasan_record_aux_stack_noalloc() the default behaviour 2025-01-13 22:40:36 -08:00
jump_label.c jump_label: Use RCU in all users of __module_text_address(). 2025-03-10 11:54:46 +01:00
kallsyms_internal.h
kallsyms_selftest.c kallsyms: use kmalloc_array() instead of kmalloc() 2025-09-28 11:36:14 -07:00
kallsyms_selftest.h
kallsyms.c kallsyms: Fix wrong "big" kernel symbol type read from procfs 2025-11-24 16:56:24 +01:00
kcmp.c kcmp: improve performance adding an unlikely hint to task comparisons 2025-02-21 10:25:33 +01:00
Kconfig.freezer
Kconfig.hz kernel: Fix "select" wording on HZ_250 description 2025-02-21 09:20:30 +01:00
Kconfig.kexec liveupdate: kho: move to kernel/liveupdate 2025-11-27 14:24:33 -08:00
Kconfig.locks
Kconfig.preempt softirq: Allow to drop the softirq-BKL lock on PREEMPT_RT 2025-09-17 16:25:41 +02:00
kcov.c kcov: use write memory barrier after memcpy() in kcov_move_area() 2025-09-13 17:32:44 -07:00
kexec_core.c kernel/kexec: fix IMA when allocation happens in CMA area 2025-12-23 11:23:14 -08:00
kexec_elf.c kexec: initialize ELF lowest address to ULONG_MAX 2025-03-16 22:30:47 -07:00
kexec_file.c x86/kexec: carry forward the boot DTB on kexec 2025-09-13 17:32:43 -07:00
kexec_internal.h kexec: enable CMA based contiguous allocation 2025-08-02 12:01:38 -07:00
kexec.c kexec: enable CMA based contiguous allocation 2025-08-02 12:01:38 -07:00
kheaders.c kheaders: Simplify attribute through __BIN_ATTR_SIMPLE_RO() 2024-12-24 09:46:49 +01:00
kprobes.c kprobes: Add missing kerneldoc for __get_insn_slot 2025-07-15 18:45:34 +09:00
kstack_erase.c sysctl: remove __user qualifier from stack_erasing_sysctl buffer argument 2025-11-27 15:44:53 +01:00
ksyms_common.c
ksysfs.c kexec: move sysfs entries to /sys/kernel/kexec 2025-11-27 14:24:42 -08:00
kthread.c kthread: Warn if mm_struct lacks user_ns in kthread_use_mm() 2025-12-24 21:32:58 +01:00
latencytop.c treewide: const qualify ctl_tables where applicable 2025-01-28 13:48:37 +01:00
Makefile liveupdate: kho: move to kernel/liveupdate 2025-11-27 14:24:33 -08:00
module_signature.c
notifier.c reboot: move reboot_notifier_list to kernel/reboot.c 2024-11-05 17:12:31 -08:00
nscommon.c ns: rename is_initial_namespace() 2025-11-11 10:01:31 +01:00
nsproxy.c nsproxy: fix free_nsproxy() and simplify create_new_namespaces() 2025-11-14 13:10:38 +01:00
nstree.c nstree: fix kernel-doc comments for internal functions 2025-11-14 13:10:38 +01:00
padata.c padata: remove __padata_list_init() 2025-11-14 18:15:49 +08:00
panic.c Significant patch series in this pull request: 2025-12-06 14:01:20 -08:00
params.c params: Replace deprecated strcpy() with strscpy() and memcpy() 2025-08-16 21:47:25 +02:00
pid_namespace.c pid: rely on common reference count behavior 2025-11-11 10:01:32 +01:00
pid_sysctl.h treewide: const qualify ctl_tables where applicable 2025-01-28 13:48:37 +01:00
pid.c ns: drop custom reference count initialization for initial namespaces 2025-11-11 10:01:32 +01:00
profile.c
ptrace.c rseq: Introduce struct rseq_data 2025-11-04 08:30:50 +01:00
range.c
reboot.c - The 7 patch series "powerpc/crash: use generic crashkernel 2025-04-01 10:06:52 -07:00
regset.c
relay.c relay: update relay to use mmap_prepare 2025-11-16 17:28:11 -08:00
resource_kunit.c
resource.c Reinstate "resource: avoid unnecessary lookups in find_next_iomem_res()" 2025-11-27 14:24:45 -08:00
rseq.c rseq: Switch to fast path processing on exit to user 2025-11-04 08:34:39 +01:00
scftorture.c scftorture: Handle NULL argument passed to scf_add_to_free_list(). 2024-11-14 16:09:51 -08:00
scs.c scs: fix a wrong parameter in __scs_magic 2025-11-12 10:00:13 -08:00
seccomp.c Performance events updates for v6.18: 2025-09-30 11:11:21 -07:00
signal.c signal: Move MMCID exit out of sighand lock 2025-11-25 19:45:40 +01:00
smp.c smp: Introduce a helper function to check for pending IPIs 2025-11-19 18:06:50 +01:00
smpboot.c sched/smp: Use the SMP version of idle_thread_set_boot_cpu() 2025-06-13 08:47:20 +02:00
smpboot.h
softirq.c softirq: Allow to drop the softirq-BKL lock on PREEMPT_RT 2025-09-17 16:25:41 +02:00
stacktrace.c
static_call_inline.c Modules changes for 6.15-rc1 2025-03-30 15:44:36 -07:00
static_call.c
stop_machine.c sched/core: Fix migrate_swap() vs. hotplug 2025-07-01 15:02:03 +02:00
sys_ni.c uprobes/x86: Add uprobe syscall to speed up uprobe 2025-08-21 20:09:20 +02:00
sys.c Patch series in this pull request: 2025-10-02 18:44:54 -07:00
sysctl-test.c sysctl: move u8 register test to lib/test_sysctl.c 2025-04-14 14:13:41 +02:00
sysctl.c sysctl: Wrap do_proc_douintvec with the public function proc_douintvec_conv 2025-11-27 15:45:38 +01:00
task_work.c task_work: Fix NMI race condition 2025-10-29 10:29:54 +01:00
taskstats.c fdget(), more trivial conversions 2024-11-03 01:28:06 -05:00
torture.c torture: Delay CPU-hotplug operations until boot completes 2025-08-14 15:26:30 -07:00
tracepoint.c tracepoint: Print the function symbol when tracepoint_debug is set 2025-03-21 15:30:10 -04:00
tsacct.c pid: change bacct_add_tsk() to use task_ppid_nr_ns() 2025-08-19 13:38:20 +02:00
ucount.c ucount: use atomic_long_try_cmpxchg() in atomic_long_inc_below() 2025-08-02 12:01:38 -07:00
uid16.c
uid16.h
umh.c treewide: const qualify ctl_tables where applicable 2025-01-28 13:48:37 +01:00
up.c
user_namespace.c ns: move ns type into struct ns_common 2025-09-25 09:23:54 +02:00
user-return-notifier.c
user.c ns: drop custom reference count initialization for initial namespaces 2025-11-11 10:01:32 +01:00
utsname_sysctl.c treewide: const qualify ctl_tables where applicable 2025-01-28 13:48:37 +01:00
utsname.c namespace-6.18-rc1 2025-09-29 11:20:29 -07:00
vhost_task.c vhost: Take a reference on the task in struct vhost_task. 2025-09-21 17:44:20 -04:00
vmcore_info.c vmcoreinfo: track and log recoverable hardware errors 2025-11-27 14:24:44 -08:00
watch_queue.c watch_queue: Use local kmap in post_one_notification() 2025-11-19 12:17:28 +01:00
watchdog_buddy.c watchdog: fix opencoded cpumask_next_wrap() in watchdog_next_cpu() 2025-07-31 11:28:03 -04:00
watchdog_perf.c watchdog: skip checks when panic is in progress 2025-09-13 17:32:53 -07:00
watchdog.c Significant patch series in this pull request: 2025-12-06 14:01:20 -08:00
workqueue_internal.h
workqueue.c workqueue: Don't rely on wq->rescuer to stop rescuer 2025-11-21 09:45:36 -10:00