blob: 99805928e4f7d0d9cc4e7d426d701cade7b80f81 [file] [log] [blame]
/*
* 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 "code_generator_utils.h"
#include <android-base/logging.h>
#include "nodes.h"
namespace art HIDDEN {
void CalculateMagicAndShiftForDivRem(int64_t divisor, bool is_long,
int64_t* magic, int* shift) {
// It does not make sense to calculate magic and shift for zero divisor.
DCHECK_NE(divisor, 0);
/* Implementation according to H.S.Warren's "Hacker's Delight" (Addison Wesley, 2002)
* Chapter 10 and T.Grablund, P.L.Montogomery's "Division by Invariant Integers Using
* Multiplication" (PLDI 1994).
* The magic number M and shift S can be calculated in the following way:
* Let nc be the most positive value of numerator(n) such that nc = kd - 1,
* where divisor(d) >= 2.
* Let nc be the most negative value of numerator(n) such that nc = kd + 1,
* where divisor(d) <= -2.
* Thus nc can be calculated like:
* nc = exp + exp % d - 1, where d >= 2 and exp = 2^31 for int or 2^63 for long
* nc = -exp + (exp + 1) % d, where d >= 2 and exp = 2^31 for int or 2^63 for long
*
* So the shift p is the smallest p satisfying
* 2^p > nc * (d - 2^p % d), where d >= 2
* 2^p > nc * (d + 2^p % d), where d <= -2.
*
* The magic number M is calculated by
* M = (2^p + d - 2^p % d) / d, where d >= 2
* M = (2^p - d - 2^p % d) / d, where d <= -2.
*
* Notice that p is always bigger than or equal to 32 (resp. 64), so we just return 32 - p
* (resp. 64 - p) as the shift number S.
*/
int64_t p = is_long ? 63 : 31;
const uint64_t exp = is_long ? (UINT64_C(1) << 63) : (UINT32_C(1) << 31);
// Initialize the computations.
uint64_t abs_d = (divisor >= 0) ? divisor : -divisor;
uint64_t sign_bit = is_long ? static_cast<uint64_t>(divisor) >> 63 :
static_cast<uint32_t>(divisor) >> 31;
uint64_t tmp = exp + sign_bit;
uint64_t abs_nc = tmp - 1 - (tmp % abs_d);
uint64_t quotient1 = exp / abs_nc;
uint64_t remainder1 = exp % abs_nc;
uint64_t quotient2 = exp / abs_d;
uint64_t remainder2 = exp % abs_d;
/*
* To avoid handling both positive and negative divisor, "Hacker's Delight"
* introduces a method to handle these 2 cases together to avoid duplication.
*/
uint64_t delta;
do {
p++;
quotient1 = 2 * quotient1;
remainder1 = 2 * remainder1;
if (remainder1 >= abs_nc) {
quotient1++;
remainder1 = remainder1 - abs_nc;
}
quotient2 = 2 * quotient2;
remainder2 = 2 * remainder2;
if (remainder2 >= abs_d) {
quotient2++;
remainder2 = remainder2 - abs_d;
}
delta = abs_d - remainder2;
} while (quotient1 < delta || (quotient1 == delta && remainder1 == 0));
*magic = (divisor > 0) ? (quotient2 + 1) : (-quotient2 - 1);
if (!is_long) {
*magic = static_cast<int>(*magic);
}
*shift = is_long ? p - 64 : p - 32;
}
bool IsBooleanValueOrMaterializedCondition(HInstruction* cond_input) {
return !cond_input->IsCondition() || !cond_input->IsEmittedAtUseSite();
}
// A helper class to group functions analyzing if values are non-negative
// at the point of use. The class keeps some context used by the functions.
// The class is not supposed to be used directly or its instances to be kept.
// The main function using it is HasNonNegativeInputAt.
// If you want to use the class methods you need to become a friend of the class.
class UnsignedUseAnalyzer {
private:
explicit UnsignedUseAnalyzer(ArenaAllocator* allocator)
: seen_values_(allocator->Adapter(kArenaAllocCodeGenerator)) {
}
bool IsNonNegativeUse(HInstruction* target_user, HInstruction* value);
bool IsComparedValueNonNegativeInBlock(HInstruction* value,
HCondition* cond,
HBasicBlock* target_block);
ArenaSet<HInstruction*> seen_values_;
friend bool HasNonNegativeInputAt(HInstruction* instr, size_t i);
};
// Check that the value compared with a non-negavite value is
// non-negative in the specified basic block.
bool UnsignedUseAnalyzer::IsComparedValueNonNegativeInBlock(HInstruction* value,
HCondition* cond,
HBasicBlock* target_block) {
DCHECK(cond->HasInput(value));
// To simplify analysis, we require:
// 1. The condition basic block and target_block to be different.
// 2. The condition basic block to end with HIf.
// 3. HIf to use the condition.
if (cond->GetBlock() == target_block ||
!cond->GetBlock()->EndsWithIf() ||
cond->GetBlock()->GetLastInstruction()->InputAt(0) != cond) {
return false;
}
// We need to find a successor basic block of HIf for the case when instr is non-negative.
// If the successor dominates target_block, instructions in target_block see a non-negative value.
HIf* if_instr = cond->GetBlock()->GetLastInstruction()->AsIf();
HBasicBlock* successor = nullptr;
switch (cond->GetCondition()) {
case kCondGT:
case kCondGE: {
if (cond->GetLeft() == value) {
// The expression is v > A or v >= A.
// If A is non-negative, we need the true successor.
if (IsNonNegativeUse(cond, cond->GetRight())) {
successor = if_instr->IfTrueSuccessor();
} else {
return false;
}
} else {
DCHECK_EQ(cond->GetRight(), value);
// The expression is A > v or A >= v.
// If A is non-negative, we need the false successor.
if (IsNonNegativeUse(cond, cond->GetLeft())) {
successor = if_instr->IfFalseSuccessor();
} else {
return false;
}
}
break;
}
case kCondLT:
case kCondLE: {
if (cond->GetLeft() == value) {
// The expression is v < A or v <= A.
// If A is non-negative, we need the false successor.
if (IsNonNegativeUse(cond, cond->GetRight())) {
successor = if_instr->IfFalseSuccessor();
} else {
return false;
}
} else {
DCHECK_EQ(cond->GetRight(), value);
// The expression is A < v or A <= v.
// If A is non-negative, we need the true successor.
if (IsNonNegativeUse(cond, cond->GetLeft())) {
successor = if_instr->IfTrueSuccessor();
} else {
return false;
}
}
break;
}
default:
return false;
}
DCHECK_NE(successor, nullptr);
return successor->Dominates(target_block);
}
// Check the value used by target_user is non-negative.
bool UnsignedUseAnalyzer::IsNonNegativeUse(HInstruction* target_user, HInstruction* value) {
DCHECK(target_user->HasInput(value));
// Prevent infinitive recursion which can happen when the value is an induction variable.
if (!seen_values_.insert(value).second) {
return false;
}
// Check if the value is always non-negative.
if (IsGEZero(value)) {
return true;
}
for (const HUseListNode<HInstruction*>& use : value->GetUses()) {
HInstruction* user = use.GetUser();
if (user == target_user) {
continue;
}
// If the value is compared with some non-negative value, this can guarantee the value to be
// non-negative at its use.
// JFYI: We're not using HTypeConversion to bind the new information because it would
// increase the complexity of optimizations: HTypeConversion can create a dependency
// which does not exist in the input program, for example:
// between two uses, 1st - cmp, 2nd - target_user.
if (user->IsCondition()) {
// The condition must dominate target_user to guarantee that the value is always checked
// before it is used by target_user.
if (user->GetBlock()->Dominates(target_user->GetBlock()) &&
IsComparedValueNonNegativeInBlock(value, user->AsCondition(), target_user->GetBlock())) {
return true;
}
}
// TODO The value is non-negative if it is used as an array index before.
// TODO The value is non-negative if it is initialized by a positive number and all of its
// modifications keep the value non-negative, for example the division operation.
}
return false;
}
bool HasNonNegativeInputAt(HInstruction* instr, size_t i) {
UnsignedUseAnalyzer analyzer(instr->GetBlock()->GetGraph()->GetAllocator());
return analyzer.IsNonNegativeUse(instr, instr->InputAt(i));
}
bool HasNonNegativeOrMinIntInputAt(HInstruction* instr, size_t i) {
HInstruction* input = instr->InputAt(i);
return input->IsAbs() ||
IsInt64Value(input, DataType::MinValueOfIntegralType(input->GetType())) ||
HasNonNegativeInputAt(instr, i);
}
} // namespace art