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Computes liveness information for each op in each block.
tfp.experimental.auto_batching.liveness.liveness_analysis( graph, live_out )
A "live" variable is one that this analysis cannot prove will not be read later in the execution of the program: https://en.wikipedia.org/wiki/Live_variable_analysis.
Note that the semantics assumed by this analysis is that the control
flow graph being analyzed does not use variable stacks internally,
but they will only be used to implement the function sequence when
function calls are lowered. For this reason, a write (as from
FunctionCallOp) is treated as killing a variable,
even though the downstream virtual machine pushes the outputs of
PrimOp. This semantics is also why
The algorithm is to traverse the blocks in the CFG in reverse order, computing the in-block liveness map and the set of variables that are live into the entry of each block.
Within a block, proceed down the instructions in reverse order, updating the live variable set as each instruction is stepped over, and recording (a copy of) it. The set of variables that are live out of the last instruction of a block is the union of the variables that are live into the blocks to which control may be transferred (plus anything the terminator instruction itself may read).
As coded, this assumes that all control transfers go later in the CFG. Supporting loops will require equation solving.
As coded, crashes in the presence of
The latter two limitations amount to requiring this liveness
analysis only be used before lowering function calls, and that the
body of every
Function analyzed be loop-free. Ergo, all recursive
computations must cross
FunctionCallOp boundaries in any program
to which this is applied.
ControlFlowGraphon which to perform liveness analysis.
live_out: A Python list of
str. The set of variables that are live on exit from this
LivenessInfotuple. Each of these has three fields:
strvariable names live into the block;
live_out_instructionsgives a list parallel to the
Block's instructions list, of variables live out of that instruction; and
strvariable names live out of the block.
ValueError: If an invalid instruction is encountered, or if trying to do liveness analysis in the presence of IndirectGotoOp or of backward control transfers.