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llvm-project/polly/lib/Analysis/DependenceInfo.cpp

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//===- DependenceInfo.cpp - Calculate dependency information for a Scop. --===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// Calculate the data dependency relations for a Scop using ISL.
//
// The integer set library (ISL) from Sven, has a integrated dependency analysis
// to calculate data dependences. This pass takes advantage of this and
// calculate those dependences a Scop.
//
// The dependences in this pass are exact in terms that for a specific read
// statement instance only the last write statement instance is returned. In
// case of may writes a set of possible write instances is returned. This
// analysis will never produce redundant dependences.
//
//===----------------------------------------------------------------------===//
//
#include "polly/DependenceInfo.h"
#include "polly/LinkAllPasses.h"
#include "polly/Options.h"
#include "polly/ScopInfo.h"
#include "polly/Support/GICHelper.h"
#include "llvm/Support/Debug.h"
#include <isl/aff.h>
#include <isl/ctx.h>
#include <isl/flow.h>
#include <isl/map.h>
#include <isl/options.h>
#include <isl/schedule.h>
#include <isl/set.h>
#include <isl/union_map.h>
#include <isl/union_set.h>
using namespace polly;
using namespace llvm;
#define DEBUG_TYPE "polly-dependence"
static cl::opt<int> OptComputeOut(
"polly-dependences-computeout",
cl::desc("Bound the dependence analysis by a maximal amount of "
"computational steps (0 means no bound)"),
cl::Hidden, cl::init(500000), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<bool> LegalityCheckDisabled(
"disable-polly-legality", cl::desc("Disable polly legality check"),
cl::Hidden, cl::init(false), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<bool>
UseReductions("polly-dependences-use-reductions",
cl::desc("Exploit reductions in dependence analysis"),
cl::Hidden, cl::init(true), cl::ZeroOrMore,
cl::cat(PollyCategory));
enum AnalysisType { VALUE_BASED_ANALYSIS, MEMORY_BASED_ANALYSIS };
static cl::opt<enum AnalysisType> OptAnalysisType(
"polly-dependences-analysis-type",
cl::desc("The kind of dependence analysis to use"),
cl::values(clEnumValN(VALUE_BASED_ANALYSIS, "value-based",
"Exact dependences without transitive dependences"),
clEnumValN(MEMORY_BASED_ANALYSIS, "memory-based",
"Overapproximation of dependences")),
cl::Hidden, cl::init(VALUE_BASED_ANALYSIS), cl::ZeroOrMore,
cl::cat(PollyCategory));
static cl::opt<Dependences::AnalysisLevel> OptAnalysisLevel(
"polly-dependences-analysis-level",
cl::desc("The level of dependence analysis"),
cl::values(clEnumValN(Dependences::AL_Statement, "statement-wise",
"Statement-level analysis"),
clEnumValN(Dependences::AL_Reference, "reference-wise",
"Memory reference level analysis that distinguish"
" accessed references in the same statement"),
clEnumValN(Dependences::AL_Access, "access-wise",
"Memory reference level analysis that distinguish"
" access instructions in the same statement")),
cl::Hidden, cl::init(Dependences::AL_Statement), cl::ZeroOrMore,
cl::cat(PollyCategory));
//===----------------------------------------------------------------------===//
/// Tag the @p Relation domain with @p TagId
static __isl_give isl_map *tag(__isl_take isl_map *Relation,
__isl_take isl_id *TagId) {
isl_space *Space = isl_map_get_space(Relation);
Space = isl_space_drop_dims(Space, isl_dim_out, 0,
isl_map_dim(Relation, isl_dim_out));
Space = isl_space_set_tuple_id(Space, isl_dim_out, TagId);
isl_multi_aff *Tag = isl_multi_aff_domain_map(Space);
Relation = isl_map_preimage_domain_multi_aff(Relation, Tag);
return Relation;
}
/// Tag the @p Relation domain with either MA->getArrayId() or
/// MA->getId() based on @p TagLevel
static __isl_give isl_map *tag(__isl_take isl_map *Relation, MemoryAccess *MA,
Dependences::AnalysisLevel TagLevel) {
if (TagLevel == Dependences::AL_Reference)
return tag(Relation, MA->getArrayId().release());
if (TagLevel == Dependences::AL_Access)
return tag(Relation, MA->getId().release());
// No need to tag at the statement level.
return Relation;
}
/// Collect information about the SCoP @p S.
static void collectInfo(Scop &S, isl_union_map *&Read,
isl_union_map *&MustWrite, isl_union_map *&MayWrite,
isl_union_map *&ReductionTagMap,
isl_union_set *&TaggedStmtDomain,
Dependences::AnalysisLevel Level) {
isl_space *Space = S.getParamSpace().release();
Read = isl_union_map_empty(isl_space_copy(Space));
MustWrite = isl_union_map_empty(isl_space_copy(Space));
MayWrite = isl_union_map_empty(isl_space_copy(Space));
ReductionTagMap = isl_union_map_empty(isl_space_copy(Space));
isl_union_map *StmtSchedule = isl_union_map_empty(Space);
SmallPtrSet<const ScopArrayInfo *, 8> ReductionArrays;
if (UseReductions)
for (ScopStmt &Stmt : S)
for (MemoryAccess *MA : Stmt)
if (MA->isReductionLike())
ReductionArrays.insert(MA->getScopArrayInfo());
for (ScopStmt &Stmt : S) {
for (MemoryAccess *MA : Stmt) {
isl_set *domcp = Stmt.getDomain().release();
isl_map *accdom = MA->getAccessRelation().release();
accdom = isl_map_intersect_domain(accdom, domcp);
if (ReductionArrays.count(MA->getScopArrayInfo())) {
// Wrap the access domain and adjust the schedule accordingly.
//
// An access domain like
// Stmt[i0, i1] -> MemAcc_A[i0 + i1]
// will be transformed into
// [Stmt[i0, i1] -> MemAcc_A[i0 + i1]] -> MemAcc_A[i0 + i1]
//
// We collect all the access domains in the ReductionTagMap.
// This is used in Dependences::calculateDependences to create
// a tagged Schedule tree.
ReductionTagMap =
isl_union_map_add_map(ReductionTagMap, isl_map_copy(accdom));
accdom = isl_map_range_map(accdom);
} else {
accdom = tag(accdom, MA, Level);
if (Level > Dependences::AL_Statement) {
isl_map *StmtScheduleMap = Stmt.getSchedule().release();
assert(StmtScheduleMap &&
"Schedules that contain extension nodes require special "
"handling.");
isl_map *Schedule = tag(StmtScheduleMap, MA, Level);
StmtSchedule = isl_union_map_add_map(StmtSchedule, Schedule);
}
}
if (MA->isRead())
Read = isl_union_map_add_map(Read, accdom);
else if (MA->isMayWrite())
MayWrite = isl_union_map_add_map(MayWrite, accdom);
else
MustWrite = isl_union_map_add_map(MustWrite, accdom);
}
if (!ReductionArrays.empty() && Level == Dependences::AL_Statement)
StmtSchedule =
isl_union_map_add_map(StmtSchedule, Stmt.getSchedule().release());
}
StmtSchedule = isl_union_map_intersect_params(
StmtSchedule, S.getAssumedContext().release());
TaggedStmtDomain = isl_union_map_domain(StmtSchedule);
ReductionTagMap = isl_union_map_coalesce(ReductionTagMap);
Read = isl_union_map_coalesce(Read);
MustWrite = isl_union_map_coalesce(MustWrite);
MayWrite = isl_union_map_coalesce(MayWrite);
}
/// Fix all dimension of @p Zero to 0 and add it to @p user
static isl_stat fixSetToZero(__isl_take isl_set *Zero, void *user) {
isl_union_set **User = (isl_union_set **)user;
for (unsigned i = 0; i < isl_set_dim(Zero, isl_dim_set); i++)
Zero = isl_set_fix_si(Zero, isl_dim_set, i, 0);
*User = isl_union_set_add_set(*User, Zero);
return isl_stat_ok;
}
/// Compute the privatization dependences for a given dependency @p Map
///
/// Privatization dependences are widened original dependences which originate
/// or end in a reduction access. To compute them we apply the transitive close
/// of the reduction dependences (which maps each iteration of a reduction
/// statement to all following ones) on the RAW/WAR/WAW dependences. The
/// dependences which start or end at a reduction statement will be extended to
/// depend on all following reduction statement iterations as well.
/// Note: "Following" here means according to the reduction dependences.
///
/// For the input:
///
/// S0: *sum = 0;
/// for (int i = 0; i < 1024; i++)
/// S1: *sum += i;
/// S2: *sum = *sum * 3;
///
/// we have the following dependences before we add privatization dependences:
///
/// RAW:
/// { S0[] -> S1[0]; S1[1023] -> S2[] }
/// WAR:
/// { }
/// WAW:
/// { S0[] -> S1[0]; S1[1024] -> S2[] }
/// RED:
/// { S1[i0] -> S1[1 + i0] : i0 >= 0 and i0 <= 1022 }
///
/// and afterwards:
///
/// RAW:
/// { S0[] -> S1[i0] : i0 >= 0 and i0 <= 1023;
/// S1[i0] -> S2[] : i0 >= 0 and i0 <= 1023}
/// WAR:
/// { }
/// WAW:
/// { S0[] -> S1[i0] : i0 >= 0 and i0 <= 1023;
/// S1[i0] -> S2[] : i0 >= 0 and i0 <= 1023}
/// RED:
/// { S1[i0] -> S1[1 + i0] : i0 >= 0 and i0 <= 1022 }
///
/// Note: This function also computes the (reverse) transitive closure of the
/// reduction dependences.
void Dependences::addPrivatizationDependences() {
isl_union_map *PrivRAW, *PrivWAW, *PrivWAR;
// The transitive closure might be over approximated, thus could lead to
// dependency cycles in the privatization dependences. To make sure this
// will not happen we remove all negative dependences after we computed
// the transitive closure.
TC_RED = isl_union_map_transitive_closure(isl_union_map_copy(RED), nullptr);
// FIXME: Apply the current schedule instead of assuming the identity schedule
// here. The current approach is only valid as long as we compute the
// dependences only with the initial (identity schedule). Any other
// schedule could change "the direction of the backward dependences" we
// want to eliminate here.
isl_union_set *UDeltas = isl_union_map_deltas(isl_union_map_copy(TC_RED));
isl_union_set *Universe = isl_union_set_universe(isl_union_set_copy(UDeltas));
isl_union_set *Zero = isl_union_set_empty(isl_union_set_get_space(Universe));
isl_union_set_foreach_set(Universe, fixSetToZero, &Zero);
isl_union_map *NonPositive = isl_union_set_lex_le_union_set(UDeltas, Zero);
TC_RED = isl_union_map_subtract(TC_RED, NonPositive);
TC_RED = isl_union_map_union(
TC_RED, isl_union_map_reverse(isl_union_map_copy(TC_RED)));
TC_RED = isl_union_map_coalesce(TC_RED);
isl_union_map **Maps[] = {&RAW, &WAW, &WAR};
isl_union_map **PrivMaps[] = {&PrivRAW, &PrivWAW, &PrivWAR};
for (unsigned u = 0; u < 3; u++) {
isl_union_map **Map = Maps[u], **PrivMap = PrivMaps[u];
*PrivMap = isl_union_map_apply_range(isl_union_map_copy(*Map),
isl_union_map_copy(TC_RED));
*PrivMap = isl_union_map_union(
*PrivMap, isl_union_map_apply_range(isl_union_map_copy(TC_RED),
isl_union_map_copy(*Map)));
*Map = isl_union_map_union(*Map, *PrivMap);
}
isl_union_set_free(Universe);
}
static __isl_give isl_union_flow *buildFlow(__isl_keep isl_union_map *Snk,
__isl_keep isl_union_map *Src,
__isl_keep isl_union_map *MaySrc,
__isl_keep isl_schedule *Schedule) {
isl_union_access_info *AI;
AI = isl_union_access_info_from_sink(isl_union_map_copy(Snk));
if (MaySrc)
AI = isl_union_access_info_set_may_source(AI, isl_union_map_copy(MaySrc));
if (Src)
AI = isl_union_access_info_set_must_source(AI, isl_union_map_copy(Src));
AI = isl_union_access_info_set_schedule(AI, isl_schedule_copy(Schedule));
auto Flow = isl_union_access_info_compute_flow(AI);
DEBUG(if (!Flow) dbgs() << "last error: "
<< isl_ctx_last_error(isl_schedule_get_ctx(Schedule))
<< '\n';);
return Flow;
}
/// Compute exact WAR dependences
/// We need exact WAR dependences. That is, if there are
/// dependences of the form:
/// must-W2 (sink) <- must-W1 (sink) <- R (source)
/// We wish to generate *ONLY*:
/// { R -> W1 },
/// NOT:
/// { R -> W2, R -> W1 }
///
/// However, in the case of may-writes, we do *not* wish to allow
/// may-writes to block must-writes. This makes sense, since perhaps the
/// may-write will not happen. In that case, the exact dependence will
/// be the (read -> must-write).
/// Example:
/// must-W2 (sink) <- may-W1 (sink) <- R (source)
/// We wish to generate:
/// { R-> W1, R -> W2 }
///
/// We use the fact that may dependences are not allowed to flow
/// through a must source. That way, reads will be stopped by intermediate
/// must-writes.
/// However, may-sources may not interfere with one another. Hence, reads
/// will not block each other from generating dependences.
///
/// Write (Sink) <- MustWrite (Must-Source) <- Read (MaySource) is
/// present, then the dependence
/// { Write <- Read }
/// is not tracked.
///
/// We would like to specify the Must-Write as kills, source as Read
/// and sink as Write.
/// ISL does not have the functionality currently to support "kills".
/// Use the Must-Source as a way to specify "kills".
/// The drawback is that we will have both
/// { Write <- MustWrite, Write <- Read }
///
/// We need to filter this to track only { Write <- Read }.
///
/// Filtering { Write <- Read } from WAROverestimated:
/// --------------------------------------------------
/// isl_union_flow_get_full_may_dependence gives us dependences of the form
/// WAROverestimated = { Read+MustWrite -> [Write -> MemoryAccess]}
///
/// We need to intersect the domain with Read to get only
/// Read dependences.
/// Read = { Read -> MemoryAccess }
///
///
/// 1. Construct:
/// WARMemAccesses = { Read+Write -> [Read+Write -> MemoryAccess] }
/// This takes a Read+Write from WAROverestimated and maps it to the
/// corresponding wrapped memory access from WAROverestimated.
///
/// 2. Apply WARMemAcesses to the domain of WAR Overestimated to give:
/// WAR = { [Read+Write -> MemoryAccess] -> [Write -> MemoryAccess] }
///
/// WAR is in a state where we can intersect with Read, since they
/// have the same structure.
///
/// 3. Intersect this with a wrapped Read. Read is wrapped
/// to ensure the domains look the same.
/// WAR = WAR \intersect (wrapped Read)
/// WAR = { [Read -> MemoryAccesss] -> [Write -> MemoryAccess] }
///
/// 4. Project out the memory access in the domain to get
/// WAR = { Read -> Write }
static isl_union_map *buildWAR(isl_union_map *Write, isl_union_map *MustWrite,
isl_union_map *Read, isl_schedule *Schedule) {
isl_union_flow *Flow = buildFlow(Write, MustWrite, Read, Schedule);
auto *WAROverestimated = isl_union_flow_get_full_may_dependence(Flow);
// 1. Constructing WARMemAccesses
// WarMemAccesses = { Read+Write -> [Write -> MemAccess] }
// Range factor of range product
// { Read+Write -> MemAcesss }
// Domain projection
// { [Read+Write -> MemAccess] -> Read+Write }
// Reverse
// { Read+Write -> [Read+Write -> MemAccess] }
auto WARMemAccesses = isl_union_map_copy(WAROverestimated);
WARMemAccesses = isl_union_map_range_factor_range(WAROverestimated);
WARMemAccesses = isl_union_map_domain_map(WARMemAccesses);
WARMemAccesses = isl_union_map_reverse(WARMemAccesses);
// 2. Apply to get domain tagged with memory accesses
isl_union_map *WAR =
isl_union_map_apply_domain(WAROverestimated, WARMemAccesses);
// 3. Intersect with Read to extract only reads
auto ReadWrapped = isl_union_map_wrap(isl_union_map_copy(Read));
WAR = isl_union_map_intersect_domain(WAR, ReadWrapped);
// 4. Project out memory accesses to get usual style dependences
WAR = isl_union_map_range_factor_domain(WAR);
WAR = isl_union_map_domain_factor_domain(WAR);
isl_union_flow_free(Flow);
return WAR;
}
void Dependences::calculateDependences(Scop &S) {
isl_union_map *Read, *MustWrite, *MayWrite, *ReductionTagMap;
isl_schedule *Schedule;
isl_union_set *TaggedStmtDomain;
DEBUG(dbgs() << "Scop: \n" << S << "\n");
collectInfo(S, Read, MustWrite, MayWrite, ReductionTagMap, TaggedStmtDomain,
Level);
bool HasReductions = !isl_union_map_is_empty(ReductionTagMap);
DEBUG(dbgs() << "Read: " << Read << '\n';
dbgs() << "MustWrite: " << MustWrite << '\n';
dbgs() << "MayWrite: " << MayWrite << '\n';
dbgs() << "ReductionTagMap: " << ReductionTagMap << '\n';
dbgs() << "TaggedStmtDomain: " << TaggedStmtDomain << '\n';);
Schedule = S.getScheduleTree().release();
if (!HasReductions) {
isl_union_map_free(ReductionTagMap);
// Tag the schedule tree if we want fine-grain dependence info
if (Level > AL_Statement) {
auto TaggedMap =
isl_union_set_unwrap(isl_union_set_copy(TaggedStmtDomain));
auto Tags = isl_union_map_domain_map_union_pw_multi_aff(TaggedMap);
Schedule = isl_schedule_pullback_union_pw_multi_aff(Schedule, Tags);
}
} else {
isl_union_map *IdentityMap;
isl_union_pw_multi_aff *ReductionTags, *IdentityTags, *Tags;
// Extract Reduction tags from the combined access domains in the given
// SCoP. The result is a map that maps each tagged element in the domain to
// the memory location it accesses. ReductionTags = {[Stmt[i] ->
// Array[f(i)]] -> Stmt[i] }
ReductionTags =
isl_union_map_domain_map_union_pw_multi_aff(ReductionTagMap);
// Compute an identity map from each statement in domain to itself.
// IdentityTags = { [Stmt[i] -> Stmt[i] }
IdentityMap = isl_union_set_identity(isl_union_set_copy(TaggedStmtDomain));
IdentityTags = isl_union_pw_multi_aff_from_union_map(IdentityMap);
Tags = isl_union_pw_multi_aff_union_add(ReductionTags, IdentityTags);
// By pulling back Tags from Schedule, we have a schedule tree that can
// be used to compute normal dependences, as well as 'tagged' reduction
// dependences.
Schedule = isl_schedule_pullback_union_pw_multi_aff(Schedule, Tags);
}
DEBUG(dbgs() << "Read: " << Read << "\n";
dbgs() << "MustWrite: " << MustWrite << "\n";
dbgs() << "MayWrite: " << MayWrite << "\n";
dbgs() << "Schedule: " << Schedule << "\n");
isl_union_map *StrictWAW = nullptr;
{
IslMaxOperationsGuard MaxOpGuard(IslCtx.get(), OptComputeOut);
RAW = WAW = WAR = RED = nullptr;
isl_union_map *Write = isl_union_map_union(isl_union_map_copy(MustWrite),
isl_union_map_copy(MayWrite));
// We are interested in detecting reductions that do not have intermediate
// computations that are captured by other statements.
//
// Example:
// void f(int *A, int *B) {
// for(int i = 0; i <= 100; i++) {
//
// *-WAR (S0[i] -> S0[i + 1] 0 <= i <= 100)------------*
// | |
// *-WAW (S0[i] -> S0[i + 1] 0 <= i <= 100)------------*
// | |
// v |
// S0: *A += i; >------------------*-----------------------*
// |
// if (i >= 98) { WAR (S0[i] -> S1[i]) 98 <= i <= 100
// |
// S1: *B = *A; <--------------*
// }
// }
// }
//
// S0[0 <= i <= 100] has a reduction. However, the values in
// S0[98 <= i <= 100] is captured in S1[98 <= i <= 100].
// Since we allow free reordering on our reduction dependences, we need to
// remove all instances of a reduction statement that have data dependences
// originating from them.
// In the case of the example, we need to remove S0[98 <= i <= 100] from
// our reduction dependences.
//
// When we build up the WAW dependences that are used to detect reductions,
// we consider only **Writes that have no intermediate Reads**.
//
// `isl_union_flow_get_must_dependence` gives us dependences of the form:
// (sink <- must_source).
//
// It *will not give* dependences of the form:
// 1. (sink <- ... <- may_source <- ... <- must_source)
// 2. (sink <- ... <- must_source <- ... <- must_source)
//
// For a detailed reference on ISL's flow analysis, see:
// "Presburger Formulas and Polyhedral Compilation" - Approximate Dataflow
// Analysis.
//
// Since we set "Write" as a must-source, "Read" as a may-source, and ask
// for must dependences, we get all Writes to Writes that **do not flow
// through a Read**.
//
// ScopInfo::checkForReductions makes sure that if something captures
// the reduction variable in the same basic block, then it is rejected
// before it is even handed here. This makes sure that there is exactly
// one read and one write to a reduction variable in a Statement.
// Example:
// void f(int *sum, int A[N], int B[N]) {
// for (int i = 0; i < N; i++) {
// *sum += A[i]; < the store and the load is not tagged as a
// B[i] = *sum; < reduction-like access due to the overlap.
// }
// }
isl_union_flow *Flow = buildFlow(Write, Write, Read, Schedule);
StrictWAW = isl_union_flow_get_must_dependence(Flow);
isl_union_flow_free(Flow);
if (OptAnalysisType == VALUE_BASED_ANALYSIS) {
Flow = buildFlow(Read, MustWrite, MayWrite, Schedule);
RAW = isl_union_flow_get_may_dependence(Flow);
isl_union_flow_free(Flow);
Flow = buildFlow(Write, MustWrite, MayWrite, Schedule);
WAW = isl_union_flow_get_may_dependence(Flow);
isl_union_flow_free(Flow);
WAR = buildWAR(Write, MustWrite, Read, Schedule);
isl_union_map_free(Write);
isl_schedule_free(Schedule);
} else {
isl_union_flow *Flow;
Flow = buildFlow(Read, nullptr, Write, Schedule);
RAW = isl_union_flow_get_may_dependence(Flow);
isl_union_flow_free(Flow);
Flow = buildFlow(Write, nullptr, Read, Schedule);
WAR = isl_union_flow_get_may_dependence(Flow);
isl_union_flow_free(Flow);
Flow = buildFlow(Write, nullptr, Write, Schedule);
WAW = isl_union_flow_get_may_dependence(Flow);
isl_union_flow_free(Flow);
isl_union_map_free(Write);
isl_schedule_free(Schedule);
}
isl_union_map_free(MustWrite);
isl_union_map_free(MayWrite);
isl_union_map_free(Read);
RAW = isl_union_map_coalesce(RAW);
WAW = isl_union_map_coalesce(WAW);
WAR = isl_union_map_coalesce(WAR);
// End of max_operations scope.
}
if (isl_ctx_last_error(IslCtx.get()) == isl_error_quota) {
isl_union_map_free(RAW);
isl_union_map_free(WAW);
isl_union_map_free(WAR);
isl_union_map_free(StrictWAW);
RAW = WAW = WAR = StrictWAW = nullptr;
isl_ctx_reset_error(IslCtx.get());
}
// Drop out early, as the remaining computations are only needed for
// reduction dependences or dependences that are finer than statement
// level dependences.
if (!HasReductions && Level == AL_Statement) {
RED = isl_union_map_empty(isl_union_map_get_space(RAW));
TC_RED = isl_union_map_empty(isl_union_set_get_space(TaggedStmtDomain));
isl_union_set_free(TaggedStmtDomain);
isl_union_map_free(StrictWAW);
return;
}
isl_union_map *STMT_RAW, *STMT_WAW, *STMT_WAR;
STMT_RAW = isl_union_map_intersect_domain(
isl_union_map_copy(RAW), isl_union_set_copy(TaggedStmtDomain));
STMT_WAW = isl_union_map_intersect_domain(
isl_union_map_copy(WAW), isl_union_set_copy(TaggedStmtDomain));
STMT_WAR =
isl_union_map_intersect_domain(isl_union_map_copy(WAR), TaggedStmtDomain);
DEBUG({
dbgs() << "Wrapped Dependences:\n";
dump();
dbgs() << "\n";
});
// To handle reduction dependences we proceed as follows:
// 1) Aggregate all possible reduction dependences, namely all self
// dependences on reduction like statements.
// 2) Intersect them with the actual RAW & WAW dependences to the get the
// actual reduction dependences. This will ensure the load/store memory
// addresses were __identical__ in the two iterations of the statement.
// 3) Relax the original RAW, WAW and WAR dependences by subtracting the
// actual reduction dependences. Binary reductions (sum += A[i]) cause
// the same, RAW, WAW and WAR dependences.
// 4) Add the privatization dependences which are widened versions of
// already present dependences. They model the effect of manual
// privatization at the outermost possible place (namely after the last
// write and before the first access to a reduction location).
// Step 1)
RED = isl_union_map_empty(isl_union_map_get_space(RAW));
for (ScopStmt &Stmt : S) {
for (MemoryAccess *MA : Stmt) {
if (!MA->isReductionLike())
continue;
isl_set *AccDomW = isl_map_wrap(MA->getAccessRelation().release());
isl_map *Identity =
isl_map_from_domain_and_range(isl_set_copy(AccDomW), AccDomW);
RED = isl_union_map_add_map(RED, Identity);
}
}
// Step 2)
RED = isl_union_map_intersect(RED, isl_union_map_copy(RAW));
RED = isl_union_map_intersect(RED, StrictWAW);
if (!isl_union_map_is_empty(RED)) {
// Step 3)
RAW = isl_union_map_subtract(RAW, isl_union_map_copy(RED));
WAW = isl_union_map_subtract(WAW, isl_union_map_copy(RED));
WAR = isl_union_map_subtract(WAR, isl_union_map_copy(RED));
// Step 4)
addPrivatizationDependences();
}
DEBUG({
dbgs() << "Final Wrapped Dependences:\n";
dump();
dbgs() << "\n";
});
// RED_SIN is used to collect all reduction dependences again after we
// split them according to the causing memory accesses. The current assumption
// is that our method of splitting will not have any leftovers. In the end
// we validate this assumption until we have more confidence in this method.
isl_union_map *RED_SIN = isl_union_map_empty(isl_union_map_get_space(RAW));
// For each reduction like memory access, check if there are reduction
// dependences with the access relation of the memory access as a domain
// (wrapped space!). If so these dependences are caused by this memory access.
// We then move this portion of reduction dependences back to the statement ->
// statement space and add a mapping from the memory access to these
// dependences.
for (ScopStmt &Stmt : S) {
for (MemoryAccess *MA : Stmt) {
if (!MA->isReductionLike())
continue;
isl_set *AccDomW = isl_map_wrap(MA->getAccessRelation().release());
isl_union_map *AccRedDepU = isl_union_map_intersect_domain(
isl_union_map_copy(TC_RED), isl_union_set_from_set(AccDomW));
if (isl_union_map_is_empty(AccRedDepU)) {
isl_union_map_free(AccRedDepU);
continue;
}
isl_map *AccRedDep = isl_map_from_union_map(AccRedDepU);
RED_SIN = isl_union_map_add_map(RED_SIN, isl_map_copy(AccRedDep));
AccRedDep = isl_map_zip(AccRedDep);
AccRedDep = isl_set_unwrap(isl_map_domain(AccRedDep));
setReductionDependences(MA, AccRedDep);
}
}
assert(isl_union_map_is_equal(RED_SIN, TC_RED) &&
"Intersecting the reduction dependence domain with the wrapped access "
"relation is not enough, we need to loosen the access relation also");
isl_union_map_free(RED_SIN);
RAW = isl_union_map_zip(RAW);
WAW = isl_union_map_zip(WAW);
WAR = isl_union_map_zip(WAR);
RED = isl_union_map_zip(RED);
TC_RED = isl_union_map_zip(TC_RED);
DEBUG({
dbgs() << "Zipped Dependences:\n";
dump();
dbgs() << "\n";
});
RAW = isl_union_set_unwrap(isl_union_map_domain(RAW));
WAW = isl_union_set_unwrap(isl_union_map_domain(WAW));
WAR = isl_union_set_unwrap(isl_union_map_domain(WAR));
RED = isl_union_set_unwrap(isl_union_map_domain(RED));
TC_RED = isl_union_set_unwrap(isl_union_map_domain(TC_RED));
DEBUG({
dbgs() << "Unwrapped Dependences:\n";
dump();
dbgs() << "\n";
});
RAW = isl_union_map_union(RAW, STMT_RAW);
WAW = isl_union_map_union(WAW, STMT_WAW);
WAR = isl_union_map_union(WAR, STMT_WAR);
RAW = isl_union_map_coalesce(RAW);
WAW = isl_union_map_coalesce(WAW);
WAR = isl_union_map_coalesce(WAR);
RED = isl_union_map_coalesce(RED);
TC_RED = isl_union_map_coalesce(TC_RED);
DEBUG(dump());
}
bool Dependences::isValidSchedule(Scop &S,
StatementToIslMapTy *NewSchedule) const {
if (LegalityCheckDisabled)
return true;
isl_union_map *Dependences = getDependences(TYPE_RAW | TYPE_WAW | TYPE_WAR);
isl_space *Space = S.getParamSpace().release();
isl_union_map *Schedule = isl_union_map_empty(Space);
isl_space *ScheduleSpace = nullptr;
for (ScopStmt &Stmt : S) {
isl_map *StmtScat;
if (NewSchedule->find(&Stmt) == NewSchedule->end())
StmtScat = Stmt.getSchedule().release();
else
StmtScat = isl_map_copy((*NewSchedule)[&Stmt]);
assert(StmtScat &&
"Schedules that contain extension nodes require special handling.");
if (!ScheduleSpace)
ScheduleSpace = isl_space_range(isl_map_get_space(StmtScat));
Schedule = isl_union_map_add_map(Schedule, StmtScat);
}
Dependences =
isl_union_map_apply_domain(Dependences, isl_union_map_copy(Schedule));
Dependences = isl_union_map_apply_range(Dependences, Schedule);
isl_set *Zero = isl_set_universe(isl_space_copy(ScheduleSpace));
for (unsigned i = 0; i < isl_set_dim(Zero, isl_dim_set); i++)
Zero = isl_set_fix_si(Zero, isl_dim_set, i, 0);
isl_union_set *UDeltas = isl_union_map_deltas(Dependences);
isl_set *Deltas = isl_union_set_extract_set(UDeltas, ScheduleSpace);
isl_union_set_free(UDeltas);
isl_map *NonPositive = isl_set_lex_le_set(Deltas, Zero);
bool IsValid = isl_map_is_empty(NonPositive);
isl_map_free(NonPositive);
return IsValid;
}
// Check if the current scheduling dimension is parallel.
//
// We check for parallelism by verifying that the loop does not carry any
// dependences.
//
// Parallelism test: if the distance is zero in all outer dimensions, then it
// has to be zero in the current dimension as well.
//
// Implementation: first, translate dependences into time space, then force
// outer dimensions to be equal. If the distance is zero in the current
// dimension, then the loop is parallel. The distance is zero in the current
// dimension if it is a subset of a map with equal values for the current
// dimension.
bool Dependences::isParallel(isl_union_map *Schedule, isl_union_map *Deps,
isl_pw_aff **MinDistancePtr) const {
isl_set *Deltas, *Distance;
isl_map *ScheduleDeps;
unsigned Dimension;
bool IsParallel;
Deps = isl_union_map_apply_range(Deps, isl_union_map_copy(Schedule));
Deps = isl_union_map_apply_domain(Deps, isl_union_map_copy(Schedule));
if (isl_union_map_is_empty(Deps)) {
isl_union_map_free(Deps);
return true;
}
ScheduleDeps = isl_map_from_union_map(Deps);
Dimension = isl_map_dim(ScheduleDeps, isl_dim_out) - 1;
for (unsigned i = 0; i < Dimension; i++)
ScheduleDeps = isl_map_equate(ScheduleDeps, isl_dim_out, i, isl_dim_in, i);
Deltas = isl_map_deltas(ScheduleDeps);
Distance = isl_set_universe(isl_set_get_space(Deltas));
// [0, ..., 0, +] - All zeros and last dimension larger than zero
for (unsigned i = 0; i < Dimension; i++)
Distance = isl_set_fix_si(Distance, isl_dim_set, i, 0);
Distance = isl_set_lower_bound_si(Distance, isl_dim_set, Dimension, 1);
Distance = isl_set_intersect(Distance, Deltas);
IsParallel = isl_set_is_empty(Distance);
if (IsParallel || !MinDistancePtr) {
isl_set_free(Distance);
return IsParallel;
}
Distance = isl_set_project_out(Distance, isl_dim_set, 0, Dimension);
Distance = isl_set_coalesce(Distance);
// This last step will compute a expression for the minimal value in the
// distance polyhedron Distance with regards to the first (outer most)
// dimension.
*MinDistancePtr = isl_pw_aff_coalesce(isl_set_dim_min(Distance, 0));
return false;
}
static void printDependencyMap(raw_ostream &OS, __isl_keep isl_union_map *DM) {
if (DM)
OS << DM << "\n";
else
OS << "n/a\n";
}
void Dependences::print(raw_ostream &OS) const {
OS << "\tRAW dependences:\n\t\t";
printDependencyMap(OS, RAW);
OS << "\tWAR dependences:\n\t\t";
printDependencyMap(OS, WAR);
OS << "\tWAW dependences:\n\t\t";
printDependencyMap(OS, WAW);
OS << "\tReduction dependences:\n\t\t";
printDependencyMap(OS, RED);
OS << "\tTransitive closure of reduction dependences:\n\t\t";
printDependencyMap(OS, TC_RED);
}
void Dependences::dump() const { print(dbgs()); }
void Dependences::releaseMemory() {
isl_union_map_free(RAW);
isl_union_map_free(WAR);
isl_union_map_free(WAW);
isl_union_map_free(RED);
isl_union_map_free(TC_RED);
RED = RAW = WAR = WAW = TC_RED = nullptr;
for (auto &ReductionDeps : ReductionDependences)
isl_map_free(ReductionDeps.second);
ReductionDependences.clear();
}
__isl_give isl_union_map *Dependences::getDependences(int Kinds) const {
assert(hasValidDependences() && "No valid dependences available");
isl_space *Space = isl_union_map_get_space(RAW);
isl_union_map *Deps = isl_union_map_empty(Space);
if (Kinds & TYPE_RAW)
Deps = isl_union_map_union(Deps, isl_union_map_copy(RAW));
if (Kinds & TYPE_WAR)
Deps = isl_union_map_union(Deps, isl_union_map_copy(WAR));
if (Kinds & TYPE_WAW)
Deps = isl_union_map_union(Deps, isl_union_map_copy(WAW));
if (Kinds & TYPE_RED)
Deps = isl_union_map_union(Deps, isl_union_map_copy(RED));
if (Kinds & TYPE_TC_RED)
Deps = isl_union_map_union(Deps, isl_union_map_copy(TC_RED));
Deps = isl_union_map_coalesce(Deps);
Deps = isl_union_map_detect_equalities(Deps);
return Deps;
}
bool Dependences::hasValidDependences() const {
return (RAW != nullptr) && (WAR != nullptr) && (WAW != nullptr);
}
__isl_give isl_map *
Dependences::getReductionDependences(MemoryAccess *MA) const {
return isl_map_copy(ReductionDependences.lookup(MA));
}
void Dependences::setReductionDependences(MemoryAccess *MA, isl_map *D) {
assert(ReductionDependences.count(MA) == 0 &&
"Reduction dependences set twice!");
ReductionDependences[MA] = D;
}
const Dependences &
DependenceAnalysis::Result::getDependences(Dependences::AnalysisLevel Level) {
if (Dependences *d = D[Level].get())
return *d;
return recomputeDependences(Level);
}
const Dependences &DependenceAnalysis::Result::recomputeDependences(
Dependences::AnalysisLevel Level) {
D[Level].reset(new Dependences(S.getSharedIslCtx(), Level));
D[Level]->calculateDependences(S);
return *D[Level];
}
DependenceAnalysis::Result
DependenceAnalysis::run(Scop &S, ScopAnalysisManager &SAM,
ScopStandardAnalysisResults &SAR) {
return {S, {}};
}
AnalysisKey DependenceAnalysis::Key;
PreservedAnalyses
DependenceInfoPrinterPass::run(Scop &S, ScopAnalysisManager &SAM,
ScopStandardAnalysisResults &SAR,
SPMUpdater &U) {
auto &DI = SAM.getResult<DependenceAnalysis>(S, SAR);
if (auto d = DI.D[OptAnalysisLevel].get()) {
d->print(OS);
return PreservedAnalyses::all();
}
// Otherwise create the dependences on-the-fly and print them
Dependences D(S.getSharedIslCtx(), OptAnalysisLevel);
D.calculateDependences(S);
D.print(OS);
return PreservedAnalyses::all();
}
const Dependences &
DependenceInfo::getDependences(Dependences::AnalysisLevel Level) {
if (Dependences *d = D[Level].get())
return *d;
return recomputeDependences(Level);
}
const Dependences &
DependenceInfo::recomputeDependences(Dependences::AnalysisLevel Level) {
D[Level].reset(new Dependences(S->getSharedIslCtx(), Level));
D[Level]->calculateDependences(*S);
return *D[Level];
}
bool DependenceInfo::runOnScop(Scop &ScopVar) {
S = &ScopVar;
return false;
}
/// Print the dependences for the given SCoP to @p OS.
void polly::DependenceInfo::printScop(raw_ostream &OS, Scop &S) const {
if (auto d = D[OptAnalysisLevel].get()) {
d->print(OS);
return;
}
// Otherwise create the dependences on-the-fly and print it
Dependences D(S.getSharedIslCtx(), OptAnalysisLevel);
D.calculateDependences(S);
D.print(OS);
}
void DependenceInfo::getAnalysisUsage(AnalysisUsage &AU) const {
AU.addRequiredTransitive<ScopInfoRegionPass>();
AU.setPreservesAll();
}
char DependenceInfo::ID = 0;
Pass *polly::createDependenceInfoPass() { return new DependenceInfo(); }
INITIALIZE_PASS_BEGIN(DependenceInfo, "polly-dependences",
"Polly - Calculate dependences", false, false);
INITIALIZE_PASS_DEPENDENCY(ScopInfoRegionPass);
INITIALIZE_PASS_END(DependenceInfo, "polly-dependences",
"Polly - Calculate dependences", false, false)
//===----------------------------------------------------------------------===//
const Dependences &
DependenceInfoWrapperPass::getDependences(Scop *S,
Dependences::AnalysisLevel Level) {
auto It = ScopToDepsMap.find(S);
if (It != ScopToDepsMap.end())
if (It->second) {
if (It->second->getDependenceLevel() == Level)
return *It->second.get();
}
return recomputeDependences(S, Level);
}
const Dependences &DependenceInfoWrapperPass::recomputeDependences(
Scop *S, Dependences::AnalysisLevel Level) {
std::unique_ptr<Dependences> D(new Dependences(S->getSharedIslCtx(), Level));
D->calculateDependences(*S);
auto Inserted = ScopToDepsMap.insert(std::make_pair(S, std::move(D)));
return *Inserted.first->second;
}
bool DependenceInfoWrapperPass::runOnFunction(Function &F) {
auto &SI = *getAnalysis<ScopInfoWrapperPass>().getSI();
for (auto &It : SI) {
assert(It.second && "Invalid SCoP object!");
recomputeDependences(It.second.get(), Dependences::AL_Access);
}
return false;
}
void DependenceInfoWrapperPass::print(raw_ostream &OS, const Module *M) const {
for (auto &It : ScopToDepsMap) {
assert((It.first && It.second) && "Invalid Scop or Dependence object!\n");
It.second->print(OS);
}
}
void DependenceInfoWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
AU.addRequiredTransitive<ScopInfoWrapperPass>();
AU.setPreservesAll();
}
char DependenceInfoWrapperPass::ID = 0;
Pass *polly::createDependenceInfoWrapperPassPass() {
return new DependenceInfoWrapperPass();
}
INITIALIZE_PASS_BEGIN(
DependenceInfoWrapperPass, "polly-function-dependences",
"Polly - Calculate dependences for all the SCoPs of a function", false,
false)
INITIALIZE_PASS_DEPENDENCY(ScopInfoWrapperPass);
INITIALIZE_PASS_END(
DependenceInfoWrapperPass, "polly-function-dependences",
"Polly - Calculate dependences for all the SCoPs of a function", false,
false)
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