consider C program represented in eBPF:
int filter(int arg)
{
    int a, b, c, *ptr;

    if (arg == 1)
        ptr = &a;
    else if (arg == 2)
        ptr = &b;
    else
        ptr = &c;

    *ptr = 0;
    return 0;
}
eBPF verifier has to follow all possible paths through the program
to recognize that '*ptr = 0' instruction would be safe to execute
in all situations.
It's doing it by picking a path towards the end and observes changes
to registers and stack at every insn until it reaches bpf_exit.
Then it comes back to one of the previous branches and goes towards
the end again with potentially different values in registers.
When program has a lot of branches, the number of possible combinations
of branches is huge, so verifer has a hard limit of walking no more
than 32k instructions. This limit can be reached and complex (but valid)
programs could be rejected. Therefore it's important to recognize equivalent
verifier states to prune this depth first search.

Basic idea can be illustrated by the program (where .. are some eBPF insns):
    1: ..
    2: if (rX == rY) goto 4
    3: ..
    4: ..
    5: ..
    6: bpf_exit
In the first pass towards bpf_exit the verifier will walk insns: 1, 2, 3, 4, 5, 6
Since insn#2 is a branch the verifier will remember its state in verifier stack
to come back to it later.
Since insn#4 is marked as 'branch target', the verifier will remember its state
in explored_states[4] linked list.
Once it reaches insn#6 successfully it will pop the state recorded at insn#2 and
will continue.
Without search pruning optimization verifier would have to walk 4, 5, 6 again,
effectively simulating execution of insns 1, 2, 4, 5, 6
With search pruning it will check whether state at #4 after jumping from #2
is equivalent to one recorded in explored_states[4] during first pass.
If there is an equivalent state, verifier can prune the search at #4 and declare
this path to be safe as well.
In other words two states at #4 are equivalent if execution of 1, 2, 3, 4 insns
and 1, 2, 4 insns produces equivalent registers and stack.

Signed-off-by: Alexei Starovoitov <ast@plumgrid.com>
Signed-off-by: David S. Miller <davem@davemloft.net>