Speling.
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@@ -8,8 +8,8 @@
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//!
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//! The primary consumer of the liveness analysis is the SSA coloring pass which goes through each
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//! EBB and assigns a register to the defined values. This algorithm needs to maintain a set of the
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//! curently live values as it is iterating down the instructions in the EBB. It asks the following
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//! questions:
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//! currently live values as it is iterating down the instructions in the EBB. It asks the
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//! following questions:
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//!
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//! - What is the set of live values at the entry to the EBB?
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//! - When moving past a use of a value, is that value still alive in the EBB, or was that the last
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@@ -18,7 +18,7 @@
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//!
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//! The set of `LiveRange` instances can answer these questions through their `def_local_end` and
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//! `livein_local_end` queries. The coloring algorithm visits EBBs in a topological order of the
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//! dominator tree, so it can compute the set of live values at the begining of an EBB by starting
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//! dominator tree, so it can compute the set of live values at the beginning of an EBB by starting
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//! from the set of live values at the dominating branch instruction and filtering it with
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//! `livein_local_end`. These sets do not need to be stored in the liveness analysis.
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//!
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@@ -32,11 +32,11 @@
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//! A number of different liveness analysis algorithms exist, so it is worthwhile to look at a few
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//! alternatives.
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//!
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//! ## Dataflow equations
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//! ## Data-flow equations
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//!
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//! The classic *live variables analysis* that you will find in all compiler books from the
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//! previous century does not depend on SSA form. It is typically implemented by iteratively
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//! solving dataflow equations on bitvectors of variables. The result is a live-out bitvector of
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//! solving data-flow equations on bit-vectors of variables. The result is a live-out bit-vector of
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//! variables for every basic block in the program.
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//!
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//! This algorithm has some disadvantages that makes us look elsewhere:
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@@ -44,18 +44,18 @@
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//! - Quadratic memory use. We need a bit per variable per basic block in the function.
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//! - Sparse representation. In practice, the majority of SSA values never leave their basic block,
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//! and those that do span basic blocks rarely span a large number of basic blocks. This makes
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//! the bitvectors quite sparse.
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//! - Traditionally, the dataflow equations were solved for real program *variables* which does not
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//! include temporaries used in evaluating expressions. We have an SSA form program which blurs
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//! the distinction between temporaries and variables. This makes the quadratic memory problem
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//! worse because there are many more SSA values than there was variables in the original
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//! the bit-vectors quite sparse.
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//! - Traditionally, the data-flow equations were solved for real program *variables* which does
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//! not include temporaries used in evaluating expressions. We have an SSA form program which
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//! blurs the distinction between temporaries and variables. This makes the quadratic memory
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//! problem worse because there are many more SSA values than there was variables in the original
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//! program, and we don't know a priori which SSA values leave their basic block.
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//! - Missing last-use information. For values that are not live-out of a basic block, we would
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//! need to store information about the last use in the block somewhere. LLVM stores this
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//! information as a 'kill bit' on the last use in the IR. Maintaining these kill bits has been a
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//! source of problems for LLVM's register allocator.
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//!
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//! Dataflow equations can detect when a variable is used uninitialized, and they can handle
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//! Data-flow equations can detect when a variable is used uninitialized, and they can handle
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//! multiple definitions of the same variable. We don't need this generality since we already have
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//! a program in SSA form.
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//!
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@@ -83,7 +83,7 @@
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//! The iterative SSA form reconstruction can be skipped if the depth-first search only encountered
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//! one SSA value.
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//!
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//! This algorithm has some advantages compared to the dataflow equations:
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//! This algorithm has some advantages compared to the data-flow equations:
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//!
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//! - The live ranges of local virtual registers are computed very quickly without ever traversing
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//! the CFG. The memory needed to store these live ranges is independent of the number of basic
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@@ -106,11 +106,11 @@
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//! was presented at CGO 2008:
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//!
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//! > Boissinot, B., Hack, S., Grund, D., de Dinechin, B. D., & Rastello, F. (2008). *Fast Liveness
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//! Checking for SSA-Form Programs.* CGO.
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//! Checking for SSA-Form Programs.* CGO.
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//!
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//! This analysis uses a global precomputation that only depends on the CFG of the function. It
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//! This analysis uses a global pre-computation that only depends on the CFG of the function. It
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//! then allows liveness queries for any (value, program point) pair. Each query traverses the use
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//! chain of the value and performs lookups in the precomputed bitvectors.
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//! chain of the value and performs lookups in the precomputed bit-vectors.
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//!
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//! I did not seriously consider this analysis for Cretonne because:
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//!
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@@ -118,8 +118,8 @@
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//! - Popular variables like the `this` pointer in a C++ method can have very large use chains.
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//! Traversing such a long use chain on every liveness lookup has the potential for some nasty
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//! quadratic behavior in unfortunate cases.
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//! - It says "fast" in the title, but the paper only claims to be 16% faster than a dataflow based
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//! approach, which isn't that impressive.
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//! - It says "fast" in the title, but the paper only claims to be 16% faster than a data-flow
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//! based approach, which isn't that impressive.
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//!
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//! Nevertheless, the property of only depending in the CFG structure is very useful. If Cretonne
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//! gains use chains, this approach would be worth a proper evaluation.
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@@ -171,7 +171,7 @@
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//! - Related values should be stored on the same cache line. The current sparse set implementation
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//! does a decent job of that.
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//! - For global values, the list of live-in intervals is very likely to fit on a single cache
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//! line. These lists are very likely ot be found in L2 cache at least.
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//! line. These lists are very likely to be found in L2 cache at least.
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//!
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//! There is some room for improvement.
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@@ -271,10 +271,10 @@ impl Liveness {
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self.worklist.push(ebb);
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}
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// The worklist contains those EBBs where we have learned that the value needs to be
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// The work list contains those EBBs where we have learned that the value needs to be
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// live-in.
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//
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// This algorithm bcomes a depth-first traversal up the CFG, enumerating all paths through
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// This algorithm becomes a depth-first traversal up the CFG, enumerating all paths through
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// the CFG from the existing live range to `ebb`.
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//
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// Extend the live range as we go. The live range itself also serves as a visited set since
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