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Compute may-live registers before each instruction in the program.
The register is live before the instruction I if it is read by I or
some instruction S following I during program execution and is not
overwritten between I and S.
This information would be used in the next patch as a hint in
func_states_equal().
Use a simple algorithm described in [1] to compute this information:
- define the following:
- I.use : a set of all registers read by instruction I;
- I.def : a set of all registers written by instruction I;
- I.in : a set of all registers that may be alive before I execution;
- I.out : a set of all registers that may be alive after I execution;
- I.successors : a set of instructions S that might immediately
follow I for some program execution;
- associate separate empty sets 'I.in' and 'I.out' with each instruction;
- visit each instruction in a postorder and update corresponding
'I.in' and 'I.out' sets as follows:
I.out = U [S.in for S in I.successors]
I.in = (I.out / I.def) U I.use
(where U stands for set union, / stands for set difference)
- repeat the computation while I.{in,out} changes for any instruction.
On implementation side keep things as simple, as possible:
- check_cfg() already marks instructions EXPLORED in post-order,
modify it to save the index of each EXPLORED instruction in a vector;
- represent I.{in,out,use,def} as bitmasks;
- don't split the program into basic blocks and don't maintain the
work queue, instead:
- do fixed-point computation by visiting each instruction;
- maintain a simple 'changed' flag if I.{in,out} for any instruction
change;
Measurements show that even such simplistic implementation does not
add measurable verification time overhead (for selftests, at-least).
Note on check_cfg() ex_insn_beg/ex_done change:
To avoid out of bounds access to env->cfg.insn_postorder array,
it should be guaranteed that instruction transitions to EXPLORED state
only once. Previously this was not the fact for incorrect programs
with direct calls to exception callbacks.
The 'align' selftest needs adjustment to skip computed insn/live
registers printout. Otherwise it matches lines from the live registers
printout.
[1] https://en.wikipedia.org/wiki/Live-variable_analysis
Signed-off-by: Eduard Zingerman <eddyz87@gmail.com>
Link: https://lore.kernel.org/r/20250304195024.2478889-4-eddyz87@gmail.com
Signed-off-by: Alexei Starovoitov <ast@kernel.org>
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