docs/bpf: Add description of register liveness tracking algorithm

registers it may hold).  They must all be safe for the branch to be pruned.

This is implemented in states_equal().

Some technical details about state pruning implementation could be found below.

Register liveness tracking

--------------------------

In order to make state pruning effective, liveness state is tracked for each

register and stack slot. The basic idea is to track which registers and stack

slots are actually used during subseqeuent execution of the program, until

program exit is reached. Registers and stack slots that were never used could be

removed from the cached state thus making more states equivalent to a cached

state. This could be illustrated by the following program::

  0: call bpf_get_prandom_u32()

  1: r1 = 0

  2: if r0 == 0 goto +1

  3: r0 = 1

  --- checkpoint ---

  4: r0 = r1

  5: exit

Suppose that a state cache entry is created at instruction #4 (such entries are

also called "checkpoints" in the text below). The verifier could reach the

instruction with one of two possible register states:

* r0 = 1, r1 = 0

* r0 = 0, r1 = 0

However, only the value of register ``r1`` is important to successfully finish

verification. The goal of the liveness tracking algorithm is to spot this fact

and figure out that both states are actually equivalent.

Data structures

~~~~~~~~~~~~~~~

Liveness is tracked using the following data structures::

  enum bpf_reg_liveness {

	REG_LIVE_NONE = 0,

	REG_LIVE_READ32 = 0x1,

	REG_LIVE_READ64 = 0x2,

	REG_LIVE_READ = REG_LIVE_READ32 | REG_LIVE_READ64,

	REG_LIVE_WRITTEN = 0x4,

	REG_LIVE_DONE = 0x8,

  };

  struct bpf_reg_state {

 	...

	struct bpf_reg_state *parent;

 	...

	enum bpf_reg_liveness live;

 	...

  };

  struct bpf_stack_state {

	struct bpf_reg_state spilled_ptr;

	...

  };

  struct bpf_func_state {

	struct bpf_reg_state regs[MAX_BPF_REG];

        ...

	struct bpf_stack_state *stack;

  }

  struct bpf_verifier_state {

	struct bpf_func_state *frame[MAX_CALL_FRAMES];

	struct bpf_verifier_state *parent;

        ...

  }

* ``REG_LIVE_NONE`` is an initial value assigned to ``->live`` fields upon new

  verifier state creation;

* ``REG_LIVE_WRITTEN`` means that the value of the register (or stack slot) is

  defined by some instruction verified between this verifier state's parent and

  verifier state itself;

* ``REG_LIVE_READ{32,64}`` means that the value of the register (or stack slot)

  is read by a some child state of this verifier state;

* ``REG_LIVE_DONE`` is a marker used by ``clean_verifier_state()`` to avoid

  processing same verifier state multiple times and for some sanity checks;

* ``->live`` field values are formed by combining ``enum bpf_reg_liveness``

  values using bitwise or.

Register parentage chains

~~~~~~~~~~~~~~~~~~~~~~~~~

In order to propagate information between parent and child states, a *register

parentage chain* is established. Each register or stack slot is linked to a

corresponding register or stack slot in its parent state via a ``->parent``

pointer. This link is established upon state creation in ``is_state_visited()``

and might be modified by ``set_callee_state()`` called from

``__check_func_call()``.

The rules for correspondence between registers / stack slots are as follows:

* For the current stack frame, registers and stack slots of the new state are

  linked to the registers and stack slots of the parent state with the same

  indices.

* For the outer stack frames, only caller saved registers (r6-r9) and stack

  slots are linked to the registers and stack slots of the parent state with the

  same indices.

* When function call is processed a new ``struct bpf_func_state`` instance is

  allocated, it encapsulates a new set of registers and stack slots. For this

  new frame, parent links for r6-r9 and stack slots are set to nil, parent links

  for r1-r5 are set to match caller r1-r5 parent links.

This could be illustrated by the following diagram (arrows stand for

``->parent`` pointers)::

      ...                    ; Frame #0, some instructions

  --- checkpoint #0 ---

  1 : r6 = 42                ; Frame #0

  --- checkpoint #1 ---

  2 : call foo()             ; Frame #0

      ...                    ; Frame #1, instructions from foo()

  --- checkpoint #2 ---

      ...                    ; Frame #1, instructions from foo()

  --- checkpoint #3 ---

      exit                   ; Frame #1, return from foo()

  3 : r1 = r6                ; Frame #0  <- current state

             +-------------------------------+-------------------------------+

             |           Frame #0            |           Frame #1            |

  Checkpoint +-------------------------------+-------------------------------+

  #0         | r0 | r1-r5 | r6-r9 | fp-8 ... |

             +-------------------------------+

                ^    ^       ^       ^

                |    |       |       |

  Checkpoint +-------------------------------+

  #1         | r0 | r1-r5 | r6-r9 | fp-8 ... |

             +-------------------------------+

                     ^       ^       ^

                     |_______|_______|_______________

                             |       |               |

               nil  nil      |       |               |      nil     nil

                |    |       |       |               |       |       |

  Checkpoint +-------------------------------+-------------------------------+

  #2         | r0 | r1-r5 | r6-r9 | fp-8 ... | r0 | r1-r5 | r6-r9 | fp-8 ... |

             +-------------------------------+-------------------------------+

                             ^       ^               ^       ^       ^

               nil  nil      |       |               |       |       |

                |    |       |       |               |       |       |

  Checkpoint +-------------------------------+-------------------------------+

  #3         | r0 | r1-r5 | r6-r9 | fp-8 ... | r0 | r1-r5 | r6-r9 | fp-8 ... |

             +-------------------------------+-------------------------------+

                             ^       ^

               nil  nil      |       |

                |    |       |       |

  Current    +-------------------------------+

  state      | r0 | r1-r5 | r6-r9 | fp-8 ... |

             +-------------------------------+

                             \

                               r6 read mark is propagated via these links

                               all the way up to checkpoint #1.

                               The checkpoint #1 contains a write mark for r6

                               because of instruction (1), thus read propagation

                               does not reach checkpoint #0 (see section below).

Liveness marks tracking

~~~~~~~~~~~~~~~~~~~~~~~

For each processed instruction, the verifier tracks read and written registers

and stack slots. The main idea of the algorithm is that read marks propagate

back along the state parentage chain until they hit a write mark, which 'screens

off' earlier states from the read. The information about reads is propagated by

function ``mark_reg_read()`` which could be summarized as follows::

  mark_reg_read(struct bpf_reg_state *state, ...):

      parent = state->parent

      while parent:

          if state->live & REG_LIVE_WRITTEN:

              break

          if parent->live & REG_LIVE_READ64:

              break

          parent->live |= REG_LIVE_READ64

          state = parent

          parent = state->parent

Notes:

* The read marks are applied to the **parent** state while write marks are

  applied to the **current** state. The write mark on a register or stack slot

  means that it is updated by some instruction in the straight-line code leading

  from the parent state to the current state.

* Details about REG_LIVE_READ32 are omitted.

* Function ``propagate_liveness()`` (see section :ref:`read_marks_for_cache_hits`)

  might override the first parent link. Please refer to the comments in the

  ``propagate_liveness()`` and ``mark_reg_read()`` source code for further

  details.

Because stack writes could have different sizes ``REG_LIVE_WRITTEN`` marks are

applied conservatively: stack slots are marked as written only if write size

corresponds to the size of the register, e.g. see function ``save_register_state()``.

Consider the following example::

  0: (*u64)(r10 - 8) = 0   ; define 8 bytes of fp-8

  --- checkpoint #0 ---

  1: (*u32)(r10 - 8) = 1   ; redefine lower 4 bytes

  2: r1 = (*u32)(r10 - 8)  ; read lower 4 bytes defined at (1)

  3: r2 = (*u32)(r10 - 4)  ; read upper 4 bytes defined at (0)

As stated above, the write at (1) does not count as ``REG_LIVE_WRITTEN``. Should

it be otherwise, the algorithm above wouldn't be able to propagate the read mark

from (3) to checkpoint #0.

Once the ``BPF_EXIT`` instruction is reached ``update_branch_counts()`` is

called to update the ``->branches`` counter for each verifier state in a chain

of parent verifier states. When the ``->branches`` counter reaches zero the

verifier state becomes a valid entry in a set of cached verifier states.

Each entry of the verifier states cache is post-processed by a function

``clean_live_states()``. This function marks all registers and stack slots

without ``REG_LIVE_READ{32,64}`` marks as ``NOT_INIT`` or ``STACK_INVALID``.

Registers/stack slots marked in this way are ignored in function ``stacksafe()``

called from ``states_equal()`` when a state cache entry is considered for

equivalence with a current state.

Now it is possible to explain how the example from the beginning of the section

works::

  0: call bpf_get_prandom_u32()

  1: r1 = 0

  2: if r0 == 0 goto +1

  3: r0 = 1

  --- checkpoint[0] ---

  4: r0 = r1

  5: exit

* At instruction #2 branching point is reached and state ``{ r0 == 0, r1 == 0, pc == 4 }``

  is pushed to states processing queue (pc stands for program counter).

* At instruction #4:

  * ``checkpoint[0]`` states cache entry is created: ``{ r0 == 1, r1 == 0, pc == 4 }``;

  * ``checkpoint[0].r0`` is marked as written;

  * ``checkpoint[0].r1`` is marked as read;

* At instruction #5 exit is reached and ``checkpoint[0]`` can now be processed

  by ``clean_live_states()``. After this processing ``checkpoint[0].r0`` has a

  read mark and all other registers and stack slots are marked as ``NOT_INIT``

  or ``STACK_INVALID``

* The state ``{ r0 == 0, r1 == 0, pc == 4 }`` is popped from the states queue

  and is compared against a cached state ``{ r1 == 0, pc == 4 }``, the states

  are considered equivalent.

.. _read_marks_for_cache_hits:

Read marks propagation for cache hits

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Another point is the handling of read marks when a previously verified state is

found in the states cache. Upon cache hit verifier must behave in the same way

as if the current state was verified to the program exit. This means that all

read marks, present on registers and stack slots of the cached state, must be

propagated over the parentage chain of the current state. Example below shows

why this is important. Function ``propagate_liveness()`` handles this case.

Consider the following state parentage chain (S is a starting state, A-E are

derived states, -> arrows show which state is derived from which)::

                   r1 read

            <-------------                A[r1] == 0

                                          C[r1] == 0

      S ---> A ---> B ---> exit           E[r1] == 1

      |

      ` ---> C ---> D

      |

      ` ---> E      ^

                    |___   suppose all these

             ^           states are at insn #Y

             |

      suppose all these

    states are at insn #X

* Chain of states ``S -> A -> B -> exit`` is verified first.

* While ``B -> exit`` is verified, register ``r1`` is read and this read mark is

  propagated up to state ``A``.

* When chain of states ``C -> D`` is verified the state ``D`` turns out to be

  equivalent to state ``B``.

* The read mark for ``r1`` has to be propagated to state ``C``, otherwise state

  ``C`` might get mistakenly marked as equivalent to state ``E`` even though

  values for register ``r1`` differ between ``C`` and ``E``.

Understanding eBPF verifier messages

====================================