Improved range analysis (and thus BCE) around min/max/abs intrinsics.
Rationale:
Inspection of some typical bit set utilities revealed that we
were missing obvious cases where two or more array lengths
were combined using a min.
Change-Id: I3e6463f221c793aaa1d592d4caabef0511754ae9
Test: test-art-host-run-test-620-checker-bce-intrinsics
diff --git a/compiler/optimizing/induction_var_range.cc b/compiler/optimizing/induction_var_range.cc
index 7cc8b1e..235793d 100644
--- a/compiler/optimizing/induction_var_range.cc
+++ b/compiler/optimizing/induction_var_range.cc
@@ -58,22 +58,90 @@
}
/**
- * An upper bound a * (length / a) + b, where a >= 1, can be conservatively rewritten as length + b
- * because length >= 0 is true. This makes it more likely the bound is useful to clients.
+ * Detects an instruction that is >= 0. As long as the value is carried by
+ * a single instruction, arithmetic wrap-around cannot occur.
*/
-static InductionVarRange::Value SimplifyMax(InductionVarRange::Value v) {
- int64_t value;
- if (v.is_known &&
- v.a_constant >= 1 &&
- v.instruction->IsDiv() &&
- v.instruction->InputAt(0)->IsArrayLength() &&
- IsIntAndGet(v.instruction->InputAt(1), &value) && v.a_constant == value) {
- return InductionVarRange::Value(v.instruction->InputAt(0), 1, v.b_constant);
+static bool IsGEZero(HInstruction* instruction) {
+ DCHECK(instruction != nullptr);
+ if (instruction->IsArrayLength()) {
+ return true;
+ } else if (instruction->IsInvokeStaticOrDirect()) {
+ switch (instruction->AsInvoke()->GetIntrinsic()) {
+ case Intrinsics::kMathMinIntInt:
+ case Intrinsics::kMathMinLongLong:
+ // Instruction MIN(>=0, >=0) is >= 0.
+ return IsGEZero(instruction->InputAt(0)) &&
+ IsGEZero(instruction->InputAt(1));
+ case Intrinsics::kMathAbsInt:
+ case Intrinsics::kMathAbsLong:
+ // Instruction ABS(x) is >= 0.
+ return true;
+ default:
+ break;
+ }
+ }
+ int64_t value = -1;
+ return IsIntAndGet(instruction, &value) && value >= 0;
+}
+
+/** Hunts "under the hood" for a suitable instruction at the hint. */
+static bool IsMaxAtHint(
+ HInstruction* instruction, HInstruction* hint, /*out*/HInstruction** suitable) {
+ if (instruction->IsInvokeStaticOrDirect()) {
+ switch (instruction->AsInvoke()->GetIntrinsic()) {
+ case Intrinsics::kMathMinIntInt:
+ case Intrinsics::kMathMinLongLong:
+ // For MIN(x, y), return most suitable x or y as maximum.
+ return IsMaxAtHint(instruction->InputAt(0), hint, suitable) ||
+ IsMaxAtHint(instruction->InputAt(1), hint, suitable);
+ default:
+ break;
+ }
+ } else {
+ *suitable = instruction;
+ while (instruction->IsArrayLength() ||
+ instruction->IsNullCheck() ||
+ instruction->IsNewArray()) {
+ instruction = instruction->InputAt(0);
+ }
+ return instruction == hint;
+ }
+ return false;
+}
+
+/** Post-analysis simplification of a minimum value that makes the bound more useful to clients. */
+static InductionVarRange::Value SimplifyMin(InductionVarRange::Value v) {
+ if (v.is_known && v.a_constant == 1 && v.b_constant <= 0) {
+ // If a == 1, instruction >= 0 and b <= 0, just return the constant b.
+ // No arithmetic wrap-around can occur.
+ if (IsGEZero(v.instruction)) {
+ return InductionVarRange::Value(v.b_constant);
+ }
}
return v;
}
-/** Helper method to test for a constant value. */
+/** Post-analysis simplification of a maximum value that makes the bound more useful to clients. */
+static InductionVarRange::Value SimplifyMax(InductionVarRange::Value v, HInstruction* hint) {
+ if (v.is_known && v.a_constant >= 1) {
+ // An upper bound a * (length / a) + b, where a >= 1, can be conservatively rewritten as
+ // length + b because length >= 0 is true.
+ int64_t value;
+ if (v.instruction->IsDiv() &&
+ v.instruction->InputAt(0)->IsArrayLength() &&
+ IsIntAndGet(v.instruction->InputAt(1), &value) && v.a_constant == value) {
+ return InductionVarRange::Value(v.instruction->InputAt(0), 1, v.b_constant);
+ }
+ // If a == 1, the most suitable one suffices as maximum value.
+ HInstruction* suitable = nullptr;
+ if (v.a_constant == 1 && IsMaxAtHint(v.instruction, hint, &suitable)) {
+ return InductionVarRange::Value(suitable, 1, v.b_constant);
+ }
+ }
+ return v;
+}
+
+/** Tests for a constant value. */
static bool IsConstantValue(InductionVarRange::Value v) {
return v.is_known && v.a_constant == 0;
}
@@ -97,7 +165,7 @@
}
}
-/** Helper method to insert an instruction. */
+/** Inserts an instruction. */
static HInstruction* Insert(HBasicBlock* block, HInstruction* instruction) {
DCHECK(block != nullptr);
DCHECK(block->GetLastInstruction() != nullptr) << block->GetBlockId();
@@ -106,7 +174,7 @@
return instruction;
}
-/** Helper method to obtain loop's control instruction. */
+/** Obtains loop's control instruction. */
static HInstruction* GetLoopControl(HLoopInformation* loop) {
DCHECK(loop != nullptr);
return loop->GetHeader()->GetLastInstruction();
@@ -150,9 +218,14 @@
chase_hint_ = chase_hint;
bool in_body = context->GetBlock() != loop->GetHeader();
int64_t stride_value = 0;
- *min_val = GetVal(info, trip, in_body, /* is_min */ true);
- *max_val = SimplifyMax(GetVal(info, trip, in_body, /* is_min */ false));
+ *min_val = SimplifyMin(GetVal(info, trip, in_body, /* is_min */ true));
+ *max_val = SimplifyMax(GetVal(info, trip, in_body, /* is_min */ false), chase_hint);
*needs_finite_test = NeedsTripCount(info, &stride_value) && IsUnsafeTripCount(trip);
+ chase_hint_ = nullptr;
+ // Retry chasing constants for wrap-around (merge sensitive).
+ if (!min_val->is_known && info->induction_class == HInductionVarAnalysis::kWrapAround) {
+ *min_val = SimplifyMin(GetVal(info, trip, in_body, /* is_min */ true));
+ }
return true;
}
@@ -175,7 +248,7 @@
needs_taken_test)
&& (stride_value == -1 ||
stride_value == 0 ||
- stride_value == 1); // avoid wrap-around anomalies.
+ stride_value == 1); // avoid arithmetic wrap-around anomalies.
}
void InductionVarRange::GenerateRange(HInstruction* context,
@@ -302,7 +375,8 @@
return true;
}
}
- // Try range analysis on the invariant, but only on proper range to avoid wrap-around anomalies.
+ // Try range analysis on the invariant, only accept a proper range
+ // to avoid arithmetic wrap-around anomalies.
Value min_val = GetVal(info, nullptr, /* in_body */ true, /* is_min */ true);
Value max_val = GetVal(info, nullptr, /* in_body */ true, /* is_min */ false);
if (IsConstantValue(min_val) &&
@@ -450,25 +524,26 @@
HInductionVarAnalysis::InductionInfo* trip,
bool in_body,
bool is_min) const {
- // Stop chasing the instruction at constant or hint.
- int64_t value;
- if (IsIntAndGet(instruction, &value) && CanLongValueFitIntoInt(value)) {
- return Value(static_cast<int32_t>(value));
- } else if (instruction == chase_hint_) {
- return Value(instruction, 1, 0);
- }
- // Special cases when encountering a single instruction that denotes trip count in the
- // loop-body: min is 1 and, when chasing constants, max of safe trip-count is max int
- if (in_body && trip != nullptr && instruction == trip->op_a->fetch) {
+ // Special case when chasing constants: single instruction that denotes trip count in the
+ // loop-body is minimal 1 and maximal, with safe trip-count, max int,
+ if (chase_hint_ == nullptr && in_body && trip != nullptr && instruction == trip->op_a->fetch) {
if (is_min) {
return Value(1);
- } else if (chase_hint_ == nullptr && !IsUnsafeTripCount(trip)) {
+ } else if (!IsUnsafeTripCount(trip)) {
return Value(std::numeric_limits<int32_t>::max());
}
}
- // Chase the instruction a bit deeper into the HIR tree, so that it becomes more likely
- // range analysis will compare the same instructions as terminal nodes.
- if (instruction->IsAdd()) {
+ // Unless at a constant or hint, chase the instruction a bit deeper into the HIR tree, so that
+ // it becomes more likely range analysis will compare the same instructions as terminal nodes.
+ int64_t value;
+ if (IsIntAndGet(instruction, &value) && CanLongValueFitIntoInt(value)) {
+ // Proper constant reveals best information.
+ return Value(static_cast<int32_t>(value));
+ } else if (instruction == chase_hint_) {
+ // At hint, fetch is represented by itself.
+ return Value(instruction, 1, 0);
+ } else if (instruction->IsAdd()) {
+ // Incorporate suitable constants in the chased value.
if (IsIntAndGet(instruction->InputAt(0), &value) && CanLongValueFitIntoInt(value)) {
return AddValue(Value(static_cast<int32_t>(value)),
GetFetch(instruction->InputAt(1), trip, in_body, is_min));
@@ -477,14 +552,14 @@
Value(static_cast<int32_t>(value)));
}
} else if (instruction->IsArrayLength()) {
- // Return extreme values when chasing constants. Otherwise, chase deeper.
+ // Exploit length properties when chasing constants or chase into a new array declaration.
if (chase_hint_ == nullptr) {
return is_min ? Value(0) : Value(std::numeric_limits<int32_t>::max());
} else if (instruction->InputAt(0)->IsNewArray()) {
return GetFetch(instruction->InputAt(0)->InputAt(0), trip, in_body, is_min);
}
} else if (instruction->IsTypeConversion()) {
- // Since analysis is 32-bit (or narrower) we allow a widening along the path.
+ // Since analysis is 32-bit (or narrower), chase beyond widening along the path.
if (instruction->AsTypeConversion()->GetInputType() == Primitive::kPrimInt &&
instruction->AsTypeConversion()->GetResultType() == Primitive::kPrimLong) {
return GetFetch(instruction->InputAt(0), trip, in_body, is_min);
@@ -506,6 +581,7 @@
!IsUnsafeTripCount(next_trip)) {
return GetVal(next_info, next_trip, next_in_body, is_min);
}
+ // Fetch is represented by itself.
return Value(instruction, 1, 0);
}
@@ -870,10 +946,11 @@
HInstruction* opb = nullptr;
switch (info->induction_class) {
case HInductionVarAnalysis::kInvariant:
- // Invariants.
+ // Invariants (note that even though is_min does not impact code generation for
+ // invariants, some effort is made to keep this parameter consistent).
switch (info->operation) {
case HInductionVarAnalysis::kAdd:
- case HInductionVarAnalysis::kXor:
+ case HInductionVarAnalysis::kXor: // no proper is_min for second arg
case HInductionVarAnalysis::kLT:
case HInductionVarAnalysis::kLE:
case HInductionVarAnalysis::kGT:
diff --git a/test/620-checker-bce-intrinsics/expected.txt b/test/620-checker-bce-intrinsics/expected.txt
new file mode 100644
index 0000000..b0aad4d
--- /dev/null
+++ b/test/620-checker-bce-intrinsics/expected.txt
@@ -0,0 +1 @@
+passed
diff --git a/test/620-checker-bce-intrinsics/info.txt b/test/620-checker-bce-intrinsics/info.txt
new file mode 100644
index 0000000..a868845
--- /dev/null
+++ b/test/620-checker-bce-intrinsics/info.txt
@@ -0,0 +1 @@
+Test on bounds check elimination in loops using intrinsics.
diff --git a/test/620-checker-bce-intrinsics/src/Main.java b/test/620-checker-bce-intrinsics/src/Main.java
new file mode 100644
index 0000000..afc3c65
--- /dev/null
+++ b/test/620-checker-bce-intrinsics/src/Main.java
@@ -0,0 +1,285 @@
+/*
+ * Copyright (C) 2016 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.
+ */
+
+/**
+ * Tests on bounds check elimination in loops that use intrinsics.
+ * All bounds checks below should be statically eliminated.
+ */
+public class Main {
+
+ /// CHECK-START: int Main.oneArray(int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop:B\d+>> outer_loop:none
+ //
+ /// CHECK-START: int Main.oneArray(int[]) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int oneArray(int[] a) {
+ int x = 0;
+ for (int i = 0; i < a.length; i++) {
+ x += a[i];
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.oneArrayAbs(int[], int) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop:B\d+>> outer_loop:none
+ //
+ /// CHECK-START: int Main.oneArrayAbs(int[], int) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int oneArrayAbs(int[] a, int lo) {
+ int x = 0;
+ for (int i = Math.abs(lo); i < a.length; i++) {
+ x += a[i];
+ }
+ return x;
+ }
+
+
+ /// CHECK-START: int Main.twoArrays(int[], int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop>> outer_loop:none
+ //
+ /// CHECK-START: int Main.twoArrays(int[], int[]) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int twoArrays(int[] a, int[] b) {
+ int x = 0;
+ for (int i = 0; i < Math.min(a.length, b.length); i++) {
+ x += a[i] + b[i];
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.threeArrays(int[], int[], int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop>> outer_loop:none
+ //
+ /// CHECK-START: int Main.threeArrays(int[], int[], int[]) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int threeArrays(int[] a, int[] b, int[] c) {
+ int x = 0;
+ for (int i = 0; i < Math.min(Math.min(a.length, b.length), c.length); i++) {
+ x += a[i] + b[i] + c[i];
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.fourArrays(int[], int[], int[], int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop>> outer_loop:none
+ //
+ /// CHECK-START: int Main.fourArrays(int[], int[], int[], int[]) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int fourArrays(int[] a, int[] b, int[] c, int[] d) {
+ int x = 0;
+ for (int i = 0; i < Math.min(Math.min(a.length, b.length), Math.min(c.length, d.length)); i++) {
+ x += a[i] + b[i] + c[i] + d[i];
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.oneArrayWithCleanup(int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop1:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop2:B\d+>> outer_loop:none
+ //
+ /// CHECK-EVAL: "<<Loop1>>" != "<<Loop2>>"
+ //
+ /// CHECK-START: int Main.oneArrayWithCleanup(int[]) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int oneArrayWithCleanup(int[] a) {
+ int x = 0;
+ int n = Math.min(4, a.length);
+ for (int i = 0; i < n; i++) {
+ x += a[i];
+ }
+ for (int i = n; i < a.length; i++) {
+ x += a[i] * 10;
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.twoArraysWithCleanup(int[], int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop1:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop1>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop2:B\d+>> outer_loop:none
+ //
+ /// CHECK-EVAL: "<<Loop1>>" != "<<Loop2>>"
+ //
+ /// CHECK-START: int Main.twoArraysWithCleanup(int[], int[]) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int twoArraysWithCleanup(int[] a, int[] b) {
+ int x = 0;
+ int n = Math.min(a.length, b.length);
+ for (int i = n - 1; i >= 0; i--) {
+ x += a[i] + b[i];
+ }
+ for (int i = n; i < a.length; i++) {
+ x += a[i];
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.threeArraysWithCleanup(int[], int[], int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop1:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop1>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop1>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop2:B\d+>> outer_loop:none
+ //
+ /// CHECK-EVAL: "<<Loop1>>" != "<<Loop2>>"
+ //
+ /// CHECK-START: int Main.threeArraysWithCleanup(int[], int[], int[]) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int threeArraysWithCleanup(int[] a, int[] b, int[] c) {
+ int x = 0;
+ int n = Math.min(a.length, Math.min(b.length, c.length));
+ for (int i = n - 1; i >= 0; i--) {
+ x += a[i] + b[i] + c[i];
+ }
+ for (int i = n; i < a.length; i++) {
+ x += a[i];
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.altLoopLogic(int[], int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop>> outer_loop:none
+ //
+ /// CHECK-START: int Main.altLoopLogic(int[], int[]) BCE (after)
+ /// CHECK-NOT: BoundsCheck
+ /// CHECK-NOT: Deoptimize
+ static int altLoopLogic(int[] a, int[] b) {
+ int x = 0;
+ int n = Math.min(a.length, b.length);
+ for (int i = n; i-- > 0;) {
+ x += a[i] + b[i];
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.hiddenMin(int[], int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop>> outer_loop:none
+ //
+ /// CHECK-START: int Main.hiddenMin(int[], int[]) BCE (after)
+ //
+ // TODO: make this so
+ static int hiddenMin(int[] a, int[] b) {
+ int x = 0;
+ for (int i = 0; i < a.length && i < b.length; i++) {
+ x += a[i] + b[i];
+ }
+ return x;
+ }
+
+ /// CHECK-START: int Main.hiddenMinWithCleanup(int[], int[]) BCE (before)
+ /// CHECK-DAG: BoundsCheck loop:<<Loop1:B\d+>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop1>> outer_loop:none
+ /// CHECK-DAG: BoundsCheck loop:<<Loop2:B\d+>> outer_loop:none
+ //
+ /// CHECK-EVAL: "<<Loop1>>" != "<<Loop2>>"
+ //
+ /// CHECK-START: int Main.hiddenMinWithCleanup(int[], int[]) BCE (after)
+ //
+ // TODO: make this so
+ static int hiddenMinWithCleanup(int[] a, int[] b) {
+ int x = 0;
+ int i = 0;
+ for (; i < a.length && i < b.length; i++) {
+ x += a[i] + b[i];
+ }
+ for (; i < a.length; i++) {
+ x += a[i];
+ }
+ return x;
+ }
+
+ public static void main(String[] args) {
+ int[] a = { 1, 2, 3, 4, 5 };
+ int[] b = { 6, 7, 8, 9, 4, 2 };
+ int[] c = { 1, 2, 3 };
+ int[] d = { 8, 5, 3, 2 };
+
+ expectEquals(15, oneArray(a));
+ expectEquals(36, oneArray(b));
+ expectEquals(6, oneArray(c));
+ expectEquals(18, oneArray(d));
+
+ expectEquals(5, oneArrayAbs(a, -4));
+ expectEquals(15, oneArrayAbs(a, 0));
+ expectEquals(5, oneArrayAbs(a, 4));
+
+ expectEquals(30, twoArrays(a, a));
+ expectEquals(49, twoArrays(a, b));
+ expectEquals(12, twoArrays(a, c));
+ expectEquals(28, twoArrays(a, d));
+
+ expectEquals(45, threeArrays(a, a, a));
+ expectEquals(33, threeArrays(a, b, c));
+ expectEquals(58, threeArrays(a, b, d));
+ expectEquals(28, threeArrays(a, c, d));
+
+ expectEquals(60, fourArrays(a, a, a, a));
+ expectEquals(49, fourArrays(a, b, c, d));
+
+ expectEquals(60, oneArrayWithCleanup(a));
+ expectEquals(90, oneArrayWithCleanup(b));
+ expectEquals(6, oneArrayWithCleanup(c));
+ expectEquals(18, oneArrayWithCleanup(d));
+
+ expectEquals(30, twoArraysWithCleanup(a, a));
+ expectEquals(49, twoArraysWithCleanup(a, b));
+ expectEquals(21, twoArraysWithCleanup(a, c));
+ expectEquals(33, twoArraysWithCleanup(a, d));
+
+ expectEquals(45, threeArraysWithCleanup(a, a, a));
+ expectEquals(42, threeArraysWithCleanup(a, b, c));
+ expectEquals(63, threeArraysWithCleanup(a, b, d));
+ expectEquals(37, threeArraysWithCleanup(a, c, d));
+
+ expectEquals(30, altLoopLogic(a, a));
+ expectEquals(49, altLoopLogic(a, b));
+ expectEquals(12, altLoopLogic(a, c));
+ expectEquals(28, altLoopLogic(a, d));
+
+ expectEquals(30, hiddenMin(a, a));
+ expectEquals(49, hiddenMin(a, b));
+ expectEquals(12, hiddenMin(a, c));
+ expectEquals(28, hiddenMin(a, d));
+
+ expectEquals(30, hiddenMinWithCleanup(a, a));
+ expectEquals(49, hiddenMinWithCleanup(a, b));
+ expectEquals(21, hiddenMinWithCleanup(a, c));
+ expectEquals(33, hiddenMinWithCleanup(a, d));
+
+ System.out.println("passed");
+ }
+
+ private static void expectEquals(int expected, int result) {
+ if (expected != result) {
+ throw new Error("Expected: " + expected + ", found: " + result);
+ }
+ }
+}
