Induction variable analysis (with unit tests).

Rationale:
Induction variable analysis forms the basis of a wide
variety of compiler optimizations. This implementation
finds induction variables using the elegant SSA-based
algorithm defined by [Gerlek et al.].

Change-Id: I79b8dce33ffb8b283c179699a8dff5bd196f75b2

1 files changed, 514 insertions, 0 deletions

diff --git a/compiler/optimizing/induction_var_analysis_test.cc b/compiler/optimizing/induction_var_analysis_test.cc
new file mode 100644
index 0000000000..2093e3355d
--- /dev/null
+++ b/compiler/optimizing/induction_var_analysis_test.cc
@@ -0,0 +1,514 @@
+/*
+ * Copyright (C) 2015 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include <regex>
+
+#include "base/arena_allocator.h"
+#include "builder.h"
+#include "gtest/gtest.h"
+#include "induction_var_analysis.h"
+#include "nodes.h"
+#include "optimizing_unit_test.h"
+
+namespace art {
+
+/**
+ * Fixture class for the InductionVarAnalysis tests.
+ */
+class InductionVarAnalysisTest : public testing::Test {
+ public:
+  InductionVarAnalysisTest() : pool_(), allocator_(&pool_) {
+    graph_ = CreateGraph(&allocator_);
+  }
+
+  ~InductionVarAnalysisTest() { }
+
+  // Builds single for-loop at depth d.
+  void BuildForLoop(int d, int n) {
+    ASSERT_LT(d, n);
+    loop_preheader_[d] = new (&allocator_) HBasicBlock(graph_);
+    graph_->AddBlock(loop_preheader_[d]);
+    loop_header_[d] = new (&allocator_) HBasicBlock(graph_);
+    graph_->AddBlock(loop_header_[d]);
+    loop_preheader_[d]->AddSuccessor(loop_header_[d]);
+    if (d < (n - 1)) {
+      BuildForLoop(d + 1, n);
+    }
+    loop_body_[d] = new (&allocator_) HBasicBlock(graph_);
+    graph_->AddBlock(loop_body_[d]);
+    loop_body_[d]->AddSuccessor(loop_header_[d]);
+    if (d < (n - 1)) {
+      loop_header_[d]->AddSuccessor(loop_preheader_[d + 1]);
+      loop_header_[d + 1]->AddSuccessor(loop_body_[d]);
+    } else {
+      loop_header_[d]->AddSuccessor(loop_body_[d]);
+    }
+  }
+
+  // Builds a n-nested loop in CFG where each loop at depth 0 <= d < n
+  // is defined as "for (int i_d = 0; i_d < 100; i_d++)". Tests can further
+  // populate the loop with instructions to set up interesting scenarios.
+  void BuildLoopNest(int n) {
+    ASSERT_LE(n, 10);
+    graph_->SetNumberOfVRegs(n + 2);
+
+    // Build basic blocks with entry, nested loop, exit.
+    entry_ = new (&allocator_) HBasicBlock(graph_);
+    graph_->AddBlock(entry_);
+    BuildForLoop(0, n);
+    exit_ = new (&allocator_) HBasicBlock(graph_);
+    graph_->AddBlock(exit_);
+    entry_->AddSuccessor(loop_preheader_[0]);
+    loop_header_[0]->AddSuccessor(exit_);
+    graph_->SetEntryBlock(entry_);
+    graph_->SetExitBlock(exit_);
+
+    // Provide entry and exit instructions.
+    // 0 : parameter
+    // 1 : constant 0
+    // 2 : constant 1
+    // 3 : constant 100
+    parameter_ = new (&allocator_)
+        HParameterValue(0, Primitive::kPrimNot, true);
+    entry_->AddInstruction(parameter_);
+    constant0_ = new (&allocator_) HConstant(Primitive::kPrimInt);
+    entry_->AddInstruction(constant0_);
+    constant1_ = new (&allocator_) HConstant(Primitive::kPrimInt);
+    entry_->AddInstruction(constant1_);
+    constant100_ = new (&allocator_) HConstant(Primitive::kPrimInt);
+    entry_->AddInstruction(constant100_);
+    exit_->AddInstruction(new (&allocator_) HExit());
+    induc_ = new (&allocator_) HLocal(n);
+    entry_->AddInstruction(induc_);
+    entry_->AddInstruction(new (&allocator_) HStoreLocal(induc_, constant0_));
+    tmp_ = new (&allocator_) HLocal(n + 1);
+    entry_->AddInstruction(tmp_);
+    entry_->AddInstruction(new (&allocator_) HStoreLocal(tmp_, constant100_));
+
+    // Provide loop instructions.
+    for (int d = 0; d < n; d++) {
+      basic_[d] = new (&allocator_) HLocal(d);
+      entry_->AddInstruction(basic_[d]);
+      loop_preheader_[d]->AddInstruction(
+           new (&allocator_) HStoreLocal(basic_[d], constant0_));
+      HInstruction* load = new (&allocator_)
+          HLoadLocal(basic_[d], Primitive::kPrimInt);
+      loop_header_[d]->AddInstruction(load);
+      HInstruction* compare = new (&allocator_)
+          HGreaterThanOrEqual(load, constant100_);
+      loop_header_[d]->AddInstruction(compare);
+      loop_header_[d]->AddInstruction(new (&allocator_) HIf(compare));
+      load = new (&allocator_) HLoadLocal(basic_[d], Primitive::kPrimInt);
+      loop_body_[d]->AddInstruction(load);
+      increment_[d] = new (&allocator_)
+          HAdd(Primitive::kPrimInt, load, constant1_);
+      loop_body_[d]->AddInstruction(increment_[d]);
+      loop_body_[d]->AddInstruction(
+               new (&allocator_) HStoreLocal(basic_[d], increment_[d]));
+      loop_body_[d]->AddInstruction(new (&allocator_) HGoto());
+    }
+  }
+
+  // Builds if-statement at depth d.
+  void BuildIf(int d, HBasicBlock** ifT, HBasicBlock **ifF) {
+    HBasicBlock* cond = new (&allocator_) HBasicBlock(graph_);
+    HBasicBlock* ifTrue = new (&allocator_) HBasicBlock(graph_);
+    HBasicBlock* ifFalse = new (&allocator_) HBasicBlock(graph_);
+    graph_->AddBlock(cond);
+    graph_->AddBlock(ifTrue);
+    graph_->AddBlock(ifFalse);
+    // Conditional split.
+    loop_header_[d]->ReplaceSuccessor(loop_body_[d], cond);
+    cond->AddSuccessor(ifTrue);
+    cond->AddSuccessor(ifFalse);
+    ifTrue->AddSuccessor(loop_body_[d]);
+    ifFalse->AddSuccessor(loop_body_[d]);
+    cond->AddInstruction(new (&allocator_) HIf(parameter_));
+    *ifT = ifTrue;
+    *ifF = ifFalse;
+  }
+
+  // Inserts instruction right before increment at depth d.
+  HInstruction* InsertInstruction(HInstruction* instruction, int d) {
+    loop_body_[d]->InsertInstructionBefore(instruction, increment_[d]);
+    return instruction;
+  }
+
+  // Inserts local load at depth d.
+  HInstruction* InsertLocalLoad(HLocal* local, int d) {
+    return InsertInstruction(
+        new (&allocator_) HLoadLocal(local, Primitive::kPrimInt), d);
+  }
+
+  // Inserts local store at depth d.
+  HInstruction* InsertLocalStore(HLocal* local, HInstruction* rhs, int d) {
+    return InsertInstruction(new (&allocator_) HStoreLocal(local, rhs), d);
+  }
+
+  // Inserts an array store with given local as subscript at depth d to
+  // enable tests to inspect the computed induction at that point easily.
+  HInstruction* InsertArrayStore(HLocal* subscript, int d) {
+    HInstruction* load = InsertInstruction(
+        new (&allocator_) HLoadLocal(subscript, Primitive::kPrimInt), d);
+    return InsertInstruction(new (&allocator_) HArraySet(
+        parameter_, load, constant0_, Primitive::kPrimInt, 0), d);
+  }
+
+  // Returns loop information of loop at depth d.
+  HLoopInformation* GetLoopInfo(int d) {
+    return loop_body_[d]->GetLoopInformation();
+  }
+
+  // Performs InductionVarAnalysis (after proper set up).
+  void PerformInductionVarAnalysis() {
+    ASSERT_TRUE(graph_->TryBuildingSsa());
+    iva_ = new (&allocator_) HInductionVarAnalysis(graph_);
+    iva_->Run();
+  }
+
+  // General building fields.
+  ArenaPool pool_;
+  ArenaAllocator allocator_;
+  HGraph* graph_;
+  HInductionVarAnalysis* iva_;
+
+  // Fixed basic blocks and instructions.
+  HBasicBlock* entry_;
+  HBasicBlock* exit_;
+  HInstruction* parameter_;  // "this"
+  HInstruction* constant0_;
+  HInstruction* constant1_;
+  HInstruction* constant100_;
+  HLocal* induc_;  // "vreg_n", the "k"
+  HLocal* tmp_;    // "vreg_n+1"
+
+  // Loop specifics.
+  HBasicBlock* loop_preheader_[10];
+  HBasicBlock* loop_header_[10];
+  HBasicBlock* loop_body_[10];
+  HInstruction* increment_[10];
+  HLocal* basic_[10];  // "vreg_d", the "i_d"
+};
+
+//
+// The actual InductionVarAnalysis tests.
+//
+
+TEST_F(InductionVarAnalysisTest, ProperLoopSetup) {
+  // Setup:
+  // for (int i_0 = 0; i_0 < 100; i_0++) {
+  //   ..
+  //     for (int i_9 = 0; i_9 < 100; i_9++) {
+  //     }
+  //   ..
+  // }
+  BuildLoopNest(10);
+  ASSERT_TRUE(graph_->TryBuildingSsa());
+  ASSERT_EQ(entry_->GetLoopInformation(), nullptr);
+  for (int d = 0; d < 1; d++) {
+    ASSERT_EQ(loop_preheader_[d]->GetLoopInformation(),
+              (d == 0) ? nullptr
+                       : loop_header_[d - 1]->GetLoopInformation());
+    ASSERT_NE(loop_header_[d]->GetLoopInformation(), nullptr);
+    ASSERT_NE(loop_body_[d]->GetLoopInformation(), nullptr);
+    ASSERT_EQ(loop_header_[d]->GetLoopInformation(),
+              loop_body_[d]->GetLoopInformation());
+  }
+  ASSERT_EQ(exit_->GetLoopInformation(), nullptr);
+}
+
+TEST_F(InductionVarAnalysisTest, FindBasicInductionVar) {
+  // Setup:
+  // for (int i = 0; i < 100; i++) {
+  //    a[i] = 0;
+  // }
+  BuildLoopNest(1);
+  HInstruction* store = InsertArrayStore(basic_[0], 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "((2:Constant) * i + (1:Constant))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+  EXPECT_STREQ(
+      "((2:Constant) * i + ((1:Constant) + (2:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), increment_[0]).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindDerivedInductionVarAdd) {
+  // Setup:
+  // for (int i = 0; i < 100; i++) {
+  //    k = 100 + i;
+  //    a[k] = 0;
+  // }
+  BuildLoopNest(1);
+  HInstruction *add = InsertInstruction(
+      new (&allocator_) HAdd(
+          Primitive::kPrimInt, constant100_, InsertLocalLoad(basic_[0], 0)), 0);
+  InsertLocalStore(induc_, add, 0);
+  HInstruction* store = InsertArrayStore(induc_, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "((2:Constant) * i + ((3:Constant) + (1:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindDerivedInductionVarSub) {
+  // Setup:
+  // for (int i = 0; i < 100; i++) {
+  //    k = 100 - i;
+  //    a[k] = 0;
+  // }
+  BuildLoopNest(1);
+  HInstruction *sub = InsertInstruction(
+      new (&allocator_) HSub(
+          Primitive::kPrimInt, constant100_, InsertLocalLoad(basic_[0], 0)), 0);
+  InsertLocalStore(induc_, sub, 0);
+  HInstruction* store = InsertArrayStore(induc_, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "(( - (2:Constant)) * i + ((3:Constant) - (1:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindDerivedInductionVarMul) {
+  // Setup:
+  // for (int i = 0; i < 100; i++) {
+  //    k = 100 * i;
+  //    a[k] = 0;
+  // }
+  BuildLoopNest(1);
+  HInstruction *mul = InsertInstruction(
+      new (&allocator_) HMul(
+          Primitive::kPrimInt, constant100_, InsertLocalLoad(basic_[0], 0)), 0);
+  InsertLocalStore(induc_, mul, 0);
+  HInstruction* store = InsertArrayStore(induc_, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "(((3:Constant) * (2:Constant)) * i + ((3:Constant) * (1:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindDerivedInductionVarNeg) {
+  // Setup:
+  // for (int i = 0; i < 100; i++) {
+  //    k = - i;
+  //    a[k] = 0;
+  // }
+  BuildLoopNest(1);
+  HInstruction *neg = InsertInstruction(
+      new (&allocator_) HNeg(
+          Primitive::kPrimInt, InsertLocalLoad(basic_[0], 0)), 0);
+  InsertLocalStore(induc_, neg, 0);
+  HInstruction* store = InsertArrayStore(induc_, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "(( - (2:Constant)) * i + ( - (1:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindChainInduction) {
+  // Setup:
+  // k = 0;
+  // for (int i = 0; i < 100; i++) {
+  //    k = k + 100;
+  //    a[k] = 0;
+  //    k = k - 1;
+  //    a[k] = 0;
+  // }
+  BuildLoopNest(1);
+  HInstruction *add = InsertInstruction(
+      new (&allocator_) HAdd(
+          Primitive::kPrimInt, InsertLocalLoad(induc_, 0), constant100_), 0);
+  InsertLocalStore(induc_, add, 0);
+  HInstruction* store1 = InsertArrayStore(induc_, 0);
+  HInstruction *sub = InsertInstruction(
+      new (&allocator_) HSub(
+          Primitive::kPrimInt, InsertLocalLoad(induc_, 0), constant1_), 0);
+  InsertLocalStore(induc_, sub, 0);
+  HInstruction* store2 = InsertArrayStore(induc_, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "(((3:Constant) - (2:Constant)) * i + ((1:Constant) + (3:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), store1->InputAt(1)).c_str());
+  EXPECT_STREQ(
+      "(((3:Constant) - (2:Constant)) * i + "
+      "(((1:Constant) + (3:Constant)) - (2:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), store2->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindTwoWayBasicInduction) {
+  // Setup:
+  // k = 0;
+  // for (int i = 0; i < 100; i++) {
+  //    if () k = k + 1;
+  //    else  k = k + 1;
+  //    a[k] = 0;
+  // }
+  BuildLoopNest(1);
+  HBasicBlock* ifTrue;
+  HBasicBlock* ifFalse;
+  BuildIf(0, &ifTrue, &ifFalse);
+  // True-branch.
+  HInstruction* load1 = new (&allocator_)
+      HLoadLocal(induc_, Primitive::kPrimInt);
+  ifTrue->AddInstruction(load1);
+  HInstruction* inc1 = new (&allocator_)
+      HAdd(Primitive::kPrimInt, load1, constant1_);
+  ifTrue->AddInstruction(inc1);
+  ifTrue->AddInstruction(new (&allocator_) HStoreLocal(induc_, inc1));
+  // False-branch.
+  HInstruction* load2 = new (&allocator_)
+      HLoadLocal(induc_, Primitive::kPrimInt);
+  ifFalse->AddInstruction(load2);
+  HInstruction* inc2 = new (&allocator_)
+        HAdd(Primitive::kPrimInt, load2, constant1_);
+  ifFalse->AddInstruction(inc2);
+  ifFalse->AddInstruction(new (&allocator_) HStoreLocal(induc_, inc2));
+  // Merge over a phi.
+  HInstruction* store = InsertArrayStore(induc_, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "((2:Constant) * i + ((1:Constant) + (2:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindTwoWayDerivedInduction) {
+  // Setup:
+  // for (int i = 0; i < 100; i++) {
+  //    if () k = i + 1;
+  //    else  k = i + 1;
+  //    a[k] = 0;
+  // }
+  BuildLoopNest(1);
+  HBasicBlock* ifTrue;
+  HBasicBlock* ifFalse;
+  BuildIf(0, &ifTrue, &ifFalse);
+  // True-branch.
+  HInstruction* load1 = new (&allocator_)
+      HLoadLocal(basic_[0], Primitive::kPrimInt);
+  ifTrue->AddInstruction(load1);
+  HInstruction* inc1 = new (&allocator_)
+      HAdd(Primitive::kPrimInt, load1, constant1_);
+  ifTrue->AddInstruction(inc1);
+  ifTrue->AddInstruction(new (&allocator_) HStoreLocal(induc_, inc1));
+  // False-branch.
+  HInstruction* load2 = new (&allocator_)
+      HLoadLocal(basic_[0], Primitive::kPrimInt);
+  ifFalse->AddInstruction(load2);
+  HInstruction* inc2 = new (&allocator_)
+        HAdd(Primitive::kPrimInt, load2, constant1_);
+  ifFalse->AddInstruction(inc2);
+  ifFalse->AddInstruction(new (&allocator_) HStoreLocal(induc_, inc2));
+  // Merge over a phi.
+  HInstruction* store = InsertArrayStore(induc_, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "((2:Constant) * i + ((1:Constant) + (2:Constant)))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindFirstOrderWrapAroundInduction) {
+  // Setup:
+  // k = 0;
+  // for (int i = 0; i < 100; i++) {
+  //    a[k] = 0;
+  //    k = 100 - i;
+  // }
+  BuildLoopNest(1);
+  HInstruction* store = InsertArrayStore(induc_, 0);
+  HInstruction *sub = InsertInstruction(
+      new (&allocator_) HSub(
+          Primitive::kPrimInt, constant100_, InsertLocalLoad(basic_[0], 0)), 0);
+  InsertLocalStore(induc_, sub, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "wrap((1:Constant), "
+      "(( - (2:Constant)) * i + ((3:Constant) - (1:Constant))))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindSecondOrderWrapAroundInduction) {
+  // Setup:
+  // k = 0;
+  // t = 100;
+  // for (int i = 0; i < 100; i++) {
+  //    a[k] = 0;
+  //    k = t;
+  //    t = 100 - i;
+  // }
+  BuildLoopNest(1);
+  HInstruction* store = InsertArrayStore(induc_, 0);
+  InsertLocalStore(induc_, InsertLocalLoad(tmp_, 0), 0);
+  HInstruction *sub = InsertInstruction(
+       new (&allocator_) HSub(
+           Primitive::kPrimInt, constant100_, InsertLocalLoad(basic_[0], 0)), 0);
+  InsertLocalStore(tmp_, sub, 0);
+  PerformInductionVarAnalysis();
+
+  EXPECT_STREQ(
+      "wrap((1:Constant), wrap((3:Constant), "
+      "(( - (2:Constant)) * i + ((3:Constant) - (1:Constant)))))",
+      iva_->InductionToString(GetLoopInfo(0), store->InputAt(1)).c_str());
+}
+
+TEST_F(InductionVarAnalysisTest, FindDeepLoopInduction) {
+  // Setup:
+  // k = 0;
+  // for (int i_0 = 0; i_0 < 100; i_0++) {
+  //   ..
+  //     for (int i_9 = 0; i_9 < 100; i_9++) {
+  //       k = 1 + k;
+  //       a[k] = 0;
+  //     }
+  //   ..
+  // }
+  BuildLoopNest(10);
+  HInstruction *inc = InsertInstruction(
+      new (&allocator_) HAdd(
+          Primitive::kPrimInt, constant1_, InsertLocalLoad(induc_, 9)), 9);
+  InsertLocalStore(induc_, inc, 9);
+  HInstruction* store = InsertArrayStore(induc_, 9);
+  PerformInductionVarAnalysis();
+
+  // Match exact number of constants, but be less strict on phi number,
+  // since that depends on the SSA building phase.
+  std::regex r("\\(\\(2:Constant\\) \\* i \\+ "
+               "\\(\\(2:Constant\\) \\+ \\(\\d+:Phi\\)\\)\\)");
+
+  for (int d = 0; d < 10; d++) {
+    if (d == 9) {
+      EXPECT_TRUE(std::regex_match(
+          iva_->InductionToString(GetLoopInfo(d), store->InputAt(1)), r));
+    } else {
+      EXPECT_STREQ(
+          "",
+          iva_->InductionToString(GetLoopInfo(d), store->InputAt(1)).c_str());
+    }
+    EXPECT_STREQ(
+        "((2:Constant) * i + ((1:Constant) + (2:Constant)))",
+        iva_->InductionToString(GetLoopInfo(d), increment_[d]).c_str());
+  }
+}
+
+}  // namespace art