enhancement done the trivial way; by extending inputs and truncating outputs
which is addequate for targets with little or no support for integer arithmetic
on integer types less than 32 bits.
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These are two related changes (one in llvm, one in clang).
LLVM:
- rename address_safety => sanitize_address (the enum value is the same, so we preserve binary compatibility with old bitcode)
- rename thread_safety => sanitize_thread
- rename no_uninitialized_checks -> sanitize_memory
CLANG:
- add __attribute__((no_sanitize_address)) as a synonym for __attribute__((no_address_safety_analysis))
- add __attribute__((no_sanitize_thread))
- add __attribute__((no_sanitize_memory))
for S in address thread memory
If -fsanitize=S is present and __attribute__((no_sanitize_S)) is not
set llvm attribute sanitize_S
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@176075 91177308-0d34-0410-b5e6-96231b3b80d8
This is a common pattern with dyn_cast and similar constructs, when the
PHI no longer depends on the select it can often be turned into a simpler
construct or even get hoisted out of the loop.
PR15340.
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The 'nobuiltin' attribute is applied to call sites to indicate that LLVM should
not treat the callee function as a built-in function. I.e., it shouldn't try to
replace that function with different code.
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Storing the load/store instructions with the values
and inspect them using Alias Analysis to make sure
they don't alias, since the GEP pointer operand doesn't
take the offset into account.
Trying hard to not add any extra cost to loads and stores
that don't overlap on global values, AA is *only* calculated
if all of the previous attempts failed.
Using biggest vector register size as the stride for the
vectorization access, as we're being conservative and
the cost model (which calculates the real vectorization
factor) is only run after the legalization phase.
We might re-think this relationship in the future, but
for now, I'd rather be safe than sorry.
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This patch makes asan instrument memory accesses with unusual sizes (e.g. 5 bytes or 10 bytes), e.g. long double or
packed structures.
Instrumentation is done with two 1-byte checks
(first and last bytes) and if the error is found
__asan_report_load_n(addr, real_size) or
__asan_report_store_n(addr, real_size)
is called.
Also, call these two new functions in memset/memcpy
instrumentation.
asan-rt part will follow.
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This fixes PR15289. This bug was introduced (recently) in r175215; collecting
all std::vector references for candidate pairs to delete at once is invalid
because subsequent lookups in the owning DenseMap could invalidate the
references.
bugpoint was able to reduce a useful test case. Unfortunately, because whether
or not this asserts depends on memory layout, this test case will sometimes
appear to produce valid output. Nevertheless, running under valgrind will
reveal the error.
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(or (bool?A:B),(bool?C:D)) --> (bool?(or A,C):(or B,D))
By the time the OR is visited, both the SELECTs have been visited and not
optimized and the OR itself hasn't been transformed so we do this transform in
the hopes that the new ORs will be optimized.
The transform is explicitly disabled for vector-selects until "codegen matures
to handle them better".
Patch by Muhammad Tauqir!
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Several functions and variable names used the term 'tree' to refer
to what is actually a DAG. Correcting this mistake will, hopefully,
prevent confusion in the future.
No functionality change intended.
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It enables to work with a smaller constant, which is target friendly for those which can compare to immediates.
It also avoids inserting a shift in favor of a trunc, which can be free on some targets.
This used to work until LLVM-3.1, but regressed with the 3.2 release.
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For some basic blocks, it is possible to generate many candidate pairs for
relatively few pairable instructions. When many (tens of thousands) of these pairs
are generated for a single instruction group, the time taken to generate and
rank the different vectorization plans can become quite large. As a result, we now
cap the number of candidate pairs within each instruction group. This is done by
closing out the group once the threshold is reached (set now at 3000 pairs).
Although this will limit the overall compile-time impact, this may not be the best
way to achieve this result. It might be better, for example, to prune excessive
candidate pairs after the fact the prevent the generation of short, but highly-connected
groups. We can experiment with this in the future.
This change reduces the overall compile-time slowdown of the csa.ll test case in
PR15222 to ~5x. If 5x is still considered too large, a lower limit can be
used as the default.
This represents a functionality change, but only for very large inputs
(thus, there is no regression test).
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All instances of std::multimap have now been replaced by
DenseMap<K, std::vector<V> >, and this yields a speedup of 5% on the
csa.ll test case from PR15222.
No functionality change intended.
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This is another commit on the road to removing std::multimap from
BBVectorize. This gives an ~1% speedup on the csa.ll test case
in PR15222.
No functionality change intended.
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It's possible (e.g. after an LTO build) that an internal global may be used for
debugging purposes. If that's the case appending a '.b' to it makes it hard to
find that variable. Steal the name from the old GV before deleting it so that
they can find that variable again.
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When building the pairable-instruction dependency map, don't search
past the last pairable instruction. For large blocks that have been
divided into multiple instruction groups, searching past the last
instruction in each group is very wasteful. This gives a 32% speedup
on the csa.ll test case from PR15222 (when using 50 instructions
in each group).
No functionality change intended.
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This map is queried only for instructions in pairs of pairable
instructions; so make sure that only pairs of pairable
instructions are added to the map. This gives a 3.5% speedup
on the csa.ll test case from PR15222.
No functionality change intended.
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This eliminates one more linear search over a range of
std::multimap entries. This gives a 22% speedup on the
csa.ll test case from PR15222.
No functionality change intended.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@174893 91177308-0d34-0410-b5e6-96231b3b80d8
This flag makes asan use a small (<2G) offset for 64-bit asan shadow mapping.
On x86_64 this saves us a register, thus achieving ~2/3 of the
zero-base-offset's benefits in both performance and code size.
Thanks Jakub Jelinek for the idea.
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This removes the last of the linear searches over ranges of std::multimap
iterators, giving a 7% speedup on the doduc.bc input from PR15222.
No functionality change intended.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@174859 91177308-0d34-0410-b5e6-96231b3b80d8
This is another cleanup aimed at eliminating linear searches
in ranges of std::multimap.
No functionality change intended.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@174858 91177308-0d34-0410-b5e6-96231b3b80d8
Profiling suggests that getInstructionTypes is performance-sensitive,
this cleans up some double-casting in that function in favor of
using dyn_cast.
No functionality change intended.
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By itself, this does not have much of an effect, but only because in the default
configuration the full cycle checks are used only for small problem sizes.
This is part of a general cleanup of uses of iteration over std::multimap
ranges only for the purpose of checking membership.
No functionality change intended.
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Handle chains in which the same offset is used for both loads and
stores to the same array.
Fixes rdar://11410078.
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This reverts r171041. This was a nice idea that didn't work out well.
Clang warnings need to be associated with warning groups so that they can
be selectively disabled, promoted to errors, etc. This simplistic patch didn't
allow for that. Enhancing it to provide some way for the backend to specify
a front-end warning type seems like overkill for the few uses of this, at
least for now.
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This is a follow-up to the cost-model change in r174713 which splits
the cost of a memory operation between the address computation and the
actual memory access. In r174713, this cost is always added to the
memory operation cost, and so BBVectorize will do the same.
Currently, this new cost function is used only by ARM, and I don't
have any ARM test cases for BBVectorize. Assistance in generating some
good ARM test cases for BBVectorize would be greatly appreciated!
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isn't using the default calling convention. However, if the transformation is
from a call to inline IR, then the calling convention doesn't matter.
rdar://13157990
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Adds a function to target transform info to query for the cost of address
computation. The cost model analysis pass now also queries this interface.
The code in LoopVectorize adds the cost of address computation as part of the
memory instruction cost calculation. Only there, we know whether the instruction
will be scalarized or not.
Increase the penality for inserting in to D registers on swift. This becomes
necessary because we now always assume that address computation has a cost and
three is a closer value to the architecture.
radar://13097204
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We don't want too many classes in a pass and the classes obscure the details. I
was going a little overboard with object modeling here. Replace classes by
generic code that handles both loads and stores.
No functionality change intended.
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1. Moved a comment from ObjCARCOpts.cpp -> ObjCARCContract.cpp.
2. Removed a comment from ObjCARCOpts.cpp that was already moved to
ObjCARCAliasAnalysis.h/.cpp.
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Introduce a helper class that computes the cost of memory access instructions.
No functionality change intended.
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In the loop vectorizer cost model, we used to ignore stores/loads of a pointer
type when computing the widest type within a loop. This meant that if we had
only stores/loads of pointers in a loop we would return a widest type of 8bits
(instead of 32 or 64 bit) and therefore a vector factor that was too big.
Now, if we see a consecutive store/load of pointers we use the size of a pointer
(from data layout).
This problem occured in SingleSource/Benchmarks/Shootout-C++/hash.cpp (reduced
test case is the first test in vector_ptr_load_store.ll).
radar://13139343
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says, but that's a defect (to be filed). "Cls::purevfn()" is still an odr use.
Also fixes a bug in the previous patch that caused us to not mark the function
referenced just because we didn't want to mark it odr used.
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the SCEV vector size in LoopStrengthReduce. It is observed that
the BaseRegs vector size is 4 in most cases,
and elements are frequently copied when it is initialized as
SmallVector<const SCEV *, 2> BaseRegs.
Our benchmark results show that the compilation time performance
improved by ~0.5%.
Patch by Wan Xiaofei.
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This is a re-worked version of r174048.
Given source IR:
call void @llvm.dbg.declare(metadata !{i32* %argc.addr}, metadata !14), !dbg !15
we used to generate
call void @llvm.dbg.declare(metadata !27, metadata !28), !dbg !29!27 = metadata !{null}
With this patch, we will correctly generate
call void @llvm.dbg.declare(metadata !{i32* %argc.addr}, metadata !27), !dbg !28
Looking up %argc.addr in ValueMap will return null, since %argc.addr is already
correctly set up, we can use identity mapping.
rdar://problem/13089880
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reference to a pointer, so that it can handle the case where DataLayout
is not available and behave conservatively.
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There are still places which treat the Attribute object as a collection of
attributes. I'm systematically removing them.
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Given source IR:
call void @llvm.dbg.declare(metadata !{i32* %argc.addr}, metadata !14), !dbg !15
we used to generate
call void @llvm.dbg.declare(metadata !27, metadata !28), !dbg !29!27 = metadata !{null}
With this patch, we will correctly generate
call void @llvm.dbg.declare(metadata !{i32* %argc.addr}, metadata !27), !dbg !28
Looking up %argc.addr in ValueMap will return null, since %argc.addr is already
correctly set up, we can use identity mapping.
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actually have DEBUG statements. Also changed raw_ostream in said header
to be a forward declaration (removing an include).
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This was missed since whenever I was including ObjCARCAliasAnalysis.h, I
was including ObjCARC.h before it which included these includes
(resulting in no compilation breakage).
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This also required adding 2x headers Dependency Analysis.h/Provenance Analysis.h
and a .cpp file DependencyAnalysis.cpp to unentangle the dependencies inbetween
ObjCARCContract and ObjCARCOpts.
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Because BBVectorize may significantly shorten a loop body, unroll
again after vectorization. This is especially important when using
runtime or partial unrolling.
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It is way too slow. Change the default option value to 0.
Always do exact shadow propagation for unsigned ICmp with constants, it is
cheap (under 1% cpu time) and required for correctness.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173682 91177308-0d34-0410-b5e6-96231b3b80d8
When flipping the pair of subvectors that form a vector, if the
vector length is 2, we can use the SK_Reverse shuffle kind to get
more-accurate cost information. Also we can use the SK_ExtractSubvector
shuffle kind to get accurate subvector extraction costs.
The current cost model implementations don't yet seem complex enough
for this to make a difference (thus, there are no test cases with this
commit), but it should help in future.
Depending on how the various targets optimize and combine shuffles in
practice, we might be able to get more-accurate costs by combining the
costs of multiple shuffle kinds. For example, the cost of flipping the
subvector pairs could be modeled as two extractions and two subvector
insertions. These changes, however, should probably be motivated
by specific test cases.
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This name change does the following:
1. Causes the function name to use proper ARC terminology.
2. Makes it clear what the function truly does.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173609 91177308-0d34-0410-b5e6-96231b3b80d8
In the future, AttributeWithIndex won't be used anymore. Besides, it exposes the
internals of the AttributeSet to outside users, which isn't goodness.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173602 91177308-0d34-0410-b5e6-96231b3b80d8
In the future, AttributeWithIndex won't be used anymore. Besides, it exposes the
internals of the AttributeSet to outside users, which isn't goodness.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173601 91177308-0d34-0410-b5e6-96231b3b80d8
In the future, AttributeWithIndex won't be used anymore. Besides, it exposes the
internals of the AttributeSet to outside users, which isn't goodness.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173600 91177308-0d34-0410-b5e6-96231b3b80d8
The 'getSlot' function and its ilk allow introspection into the AttributeSet
class. However, that class should be opaque. Allow access through accessor
methods instead.
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Only for integers, pointers, and vectors of those. No floats.
Instrumentation seems very heavy, and may need to be replaced
with some approximation in the future.
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loops over instructions in the basic block or the use-def list of the
value, neither of which are really efficient when repeatedly querying
about values in the same basic block.
What's more, we already know that the CondBB is small, and so we can do
a much more efficient test by counting the uses in CondBB, and seeing if
those account for all of the uses.
Finally, we shouldn't blanket fail on any such instruction, instead we
should conservatively assume that those instructions are part of the
cost.
Note that this actually fixes a bug in the pass because
isUsedInBasicBlock has a really terrible bug in it. I'll fix that in my
next commit, but the fix for it would make this code suddenly take the
compile time hit I thought it already was taking, so I wanted to go
ahead and migrate this code to a faster & better pattern.
The bug in isUsedInBasicBlock was also causing other tests to test the
wrong thing entirely: for example we weren't actually disabling
speculation for floating point operations as intended (and tested), but
the test passed because we failed to speculate them due to the
isUsedInBasicBlock failure.
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Original commit message:
Plug TTI into the speculation logic, giving it a real cost interface
that can be specialized by targets.
The goal here is not to be more aggressive, but to just be more accurate
with very obvious cases. There are instructions which are known to be
truly free and which were not being modeled as such in this code -- see
the regression test which is distilled from an inner loop of zlib.
Everywhere the TTI cost model is insufficiently conservative I've added
explicit checks with FIXME comments to go add proper modelling of these
cost factors.
If this causes regressions, the likely solution is to make TTI even more
conservative in its cost estimates, but test cases will help here.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173357 91177308-0d34-0410-b5e6-96231b3b80d8
that can be specialized by targets.
The goal here is not to be more aggressive, but to just be more accurate
with very obvious cases. There are instructions which are known to be
truly free and which were not being modeled as such in this code -- see
the regression test which is distilled from an inner loop of zlib.
Everywhere the TTI cost model is insufficiently conservative I've added
explicit checks with FIXME comments to go add proper modelling of these
cost factors.
If this causes regressions, the likely solution is to make TTI even more
conservative in its cost estimates, but test cases will help here.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173342 91177308-0d34-0410-b5e6-96231b3b80d8
a cost fuction that seems both a bit ad-hoc and also poorly suited to
evaluating constant expressions.
Notably, it is missing any support for trivial expressions such as
'inttoptr'. I could fix this routine, but it isn't clear to me all of
the constraints its other users are operating under.
The core protection that seems relevant here is avoiding the formation
of a select instruction wich a further chain of select operations in
a constant expression operand. Just explicitly encode that constraint.
Also, update the comments and organization here to make it clear where
this needs to go -- this should be driven off of real cost measurements
which take into account the number of constants expressions and the
depth of the constant expression tree.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173340 91177308-0d34-0410-b5e6-96231b3b80d8
terms of cost rather than hoisting a single instruction.
This does *not* change the cost model! We still set the cost threshold
at 1 here, it's just that we track it by accumulating cost rather than
by storing an instruction.
The primary advantage is that we no longer leave no-op intrinsics in the
basic block. For example, this will now move both debug info intrinsics
and a single instruction, instead of only moving the instruction and
leaving a basic block with nothing bug debug info intrinsics in it, and
those intrinsics now no longer ordered correctly with the hoisted value.
Instead, we now splice the entire conditional basic block's instruction
sequence.
This also places the code for checking the safety of hoisting next to
the code computing the cost.
Currently, the only observable side-effect of this change is that debug
info intrinsics are no longer abandoned. I'm not sure how to craft
a test case for this, and my real goal was the refactoring, but I'll
talk to Dave or Eric about how to add a test case for this.
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Previously, the code would scan the PHI nodes and build up a small
setvector of candidate value pairs in phi nodes to go and rewrite. Once
certain the rewrite could be performed, the code walks the set, and for
each one re-scans the entire PHI node list looking for nodes to rewrite
operands.
Instead, scan the PHI nodes once to check for hazards, and then scan it
a second time to rewrite the operands to selects. No set vector, and
a max of two scans.
The only downside is that we might form identical selects, but
instcombine or anything else should fold those easily, and it seems
unlikely to happen often.
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pretty in doxygen, adding some of the details actually present in
a classic example where this matters (a loop from gzip and many other
compression algorithms), and a cautionary note about the risks inherent
in the transform. This has come up on the mailing lists recently, and
I suspect folks reading this code could benefit from going and looking
at the MI pass that can really deal with these issues.
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This does the right thing unless the multiplication overflows, but the old code
didn't handle that case either.
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used uninitialized, since it fails to understand that Array is only used when
SingleValue is not, and outputs a warning. It also seems generally safer given
that the constructor is non-trivial and has plenty of early exits.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173242 91177308-0d34-0410-b5e6-96231b3b80d8
SSPStrong applies a heuristic to insert stack protectors in these situations:
* A Protector is required for functions which contain an array, regardless of
type or length.
* A Protector is required for functions which contain a structure/union which
contains an array, regardless of type or length. Note, there is no limit to
the depth of nesting.
* A protector is required when the address of a local variable (i.e., stack
based variable) is exposed. (E.g., such as through a local whose address is
taken as part of the RHS of an assignment or a local whose address is taken as
part of a function argument.)
This patch implements the SSPString attribute to be equivalent to
SSPRequired. This will change in a subsequent patch.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173230 91177308-0d34-0410-b5e6-96231b3b80d8
Collections of attributes are handled via the AttributeSet class now. This
finally frees us up to make significant changes to how attributes are structured.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173228 91177308-0d34-0410-b5e6-96231b3b80d8
The method PerformCodePlacement was doing too much (i.e. 3x loops, lots of
different checking). This refactoring separates the analysis section of the
method into a separate function while leaving the actual code placement and
analysis preparation in PerformCodePlacement.
*NOTE* Really this part of ObjCARC should be refactored out of the main pass
class into its own seperate class/struct. But, it is not time to make that
change yet though (don't want to make such an invasive change without fixing all
of the bugs first).
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Use the AttributeSet when we're talking about more than one attribute. Add a
function that adds a single attribute. No functionality change intended.
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generic function calls and intrinsics. This is somewhat overlapping with
an existing intrinsic cost method, but that one seems targetted at
vector intrinsics. I'll merge them or separate their names and use cases
in a separate commit.
This sinks the test of 'callIsSmall' down into TTI where targets can
control it. The whole thing feels very hack-ish to me though. I've left
a FIXME comment about the fundamental design problem this presents. It
isn't yet clear to me what the users of this function *really* care
about. I'll have to do more analysis to figure that out. Putting this
here at least provides it access to proper analysis pass tools and other
such. It also allows us to more cleanly implement the baseline cost
interfaces in TTI.
With this commit, it is now theoretically possible to simplify much of
the inline cost analysis's handling of calls by calling through to this
interface. That conversion will have to happen in subsequent commits as
it requires more extensive restructuring of the inline cost analysis.
The CodeMetrics class is now really only in the business of running over
a block of code and aggregating the metrics on that block of code, with
the actual cost evaluation done entirely in terms of TTI.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173148 91177308-0d34-0410-b5e6-96231b3b80d8
This is more code to isolate the use of the Attribute class to that of just
holding one attribute instead of a collection of attributes.
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is free. The whole CodeMetrics API should probably be reworked more, but
this is enough to allow deleting the duplicate code there for computing
whether an instruction is free.
All of the passes using this have been updated to pull in TTI and hand
it to the CodeMetrics stuff. Further, a dead CodeMetrics API
(analyzeFunction) is nuked for lack of users.
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a dynamic analysis done on each call to the routine. However, now it can
use the standard pass infrastructure to reference other analyses,
instead of a silly setter method. This will become more interesting as
I teach it about more analysis passes.
This updates the two inliner passes to use the inline cost analysis.
Doing so highlights how utterly redundant these two passes are. Either
we should find a cheaper way to do always inlining, or we should merge
the two and just fiddle with the thresholds to get the desired behavior.
I'm leaning increasingly toward the latter as it would also remove the
Inliner sub-class split.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@173030 91177308-0d34-0410-b5e6-96231b3b80d8
We ignore the cpu frontend and focus on pipeline utilization. We do this because we
don't have a good way to estimate the loop body size at the IR level.
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This separates the check for "too few elements to run the vector loop" from the
"memory overlap" check, giving a lot nicer code and allowing to skip the memory
checks when we're not going to execute the vector code anyways. We still leave
the decision of whether to emit the memory checks as branches or setccs, but it
seems to be doing a good job. If ugly code pops up we may want to emit them as
separate blocks too. Small speedup on MultiSource/Benchmarks/MallocBench/espresso.
Most of this is legwork to allow multiple bypass blocks while updating PHIs,
dominators and loop info.
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Further encapsulation of the Attribute object. Don't allow direct access to the
Attribute object as an aggregate.
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Because the Attribute class is going to stop representing a collection of
attributes, limit the use of it as an aggregate in favor of using AttributeSet.
This replaces some of the uses for querying the function attributes.
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Specifically according to the semantics of ARC -fno-objc-arc-exception simply
states that it is expected that the unwind path out of a call *MAY* not release
objects. Thus we can have the situation where a release gets moved into a catch
block which we ignore when we remove a retain/release pair resulting in (even
though we assume the program is exiting anyways) the cleanup code path
potentially blowing up before program exit.
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some optimization opportunities (in the enclosing supper-expressions).
rule 1. (-0.0 - X ) * Y => -0.0 - (X * Y)
if expression "-0.0 - X" has only one reference.
rule 2. (0.0 - X ) * Y => -0.0 - (X * Y)
if expression "0.0 - X" has only one reference, and
the instruction is marked "noSignedZero".
2. Eliminate negation (The compiler was already able to handle these
opt if the 0.0s are replaced with -0.0.)
rule 3: (0.0 - X) * (0.0 - Y) => X * Y
rule 4: (0.0 - X) * C => X * -C
if the expr is flagged "noSignedZero".
3.
Rule 5: (X*Y) * X => (X*X) * Y
if X!=Y and the expression is flagged with "UnsafeAlgebra".
The purpose of this transformation is two-fold:
a) to form a power expression (of X).
b) potentially shorten the critical path: After transformation, the
latency of the instruction Y is amortized by the expression of X*X,
and therefore Y is in a "less critical" position compared to what it
was before the transformation.
4. Remove the InstCombine code about simplifiying "X * select".
The reasons are following:
a) The "select" is somewhat architecture-dependent, therefore the
higher level optimizers are not able to precisely predict if
the simplification really yields any performance improvement
or not.
b) The "select" operator is bit complicate, and tends to obscure
optimization opportunities. It is btter to keep it as low as
possible in expr tree, and let CodeGen to tackle the optimization.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@172551 91177308-0d34-0410-b5e6-96231b3b80d8
---------------------------------------------------------------------------
C_A: reassociation is allowed
C_R: reciprocal of a constant C is appropriate, which means
- 1/C is exact, or
- reciprocal is allowed and 1/C is neither a special value nor a denormal.
-----------------------------------------------------------------------------
rule1: (X/C1) / C2 => X / (C2*C1) (if C_A)
=> X * (1/(C2*C1)) (if C_A && C_R)
rule 2: X*C1 / C2 => X * (C1/C2) if C_A
rule 3: (X/Y)/Z = > X/(Y*Z) (if C_A && at least one of Y and Z is symbolic value)
rule 4: Z/(X/Y) = > (Z*Y)/X (similar to rule3)
rule 5: C1/(X*C2) => (C1/C2) / X (if C_A)
rule 6: C1/(X/C2) => (C1*C2) / X (if C_A)
rule 7: C1/(C2/X) => (C1/C2) * X (if C_A)
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