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SPIRV-Tools/source/opt/loop_dependence.cpp
dan sinclair eda2cfbe12
Cleanup includes. (#1795) 
This Cl cleans up the include paths to be relative to the top level
directory. Various include-what-you-use fixes have been added.
2018-08-03 15:06:09 -04:00

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// Copyright (c) 2018 Google LLC.
//
// 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 "source/opt/loop_dependence.h"
#include <functional>
#include <memory>
#include <numeric>
#include <string>
#include <utility>
#include <vector>
#include "source/opt/instruction.h"
#include "source/opt/scalar_analysis.h"
#include "source/opt/scalar_analysis_nodes.h"
namespace spvtools {
namespace opt {
using SubscriptPair = std::pair<SENode*, SENode*>;
namespace {
// Calculate the greatest common divisor of a & b using Stein's algorithm.
// https://en.wikipedia.org/wiki/Binary_GCD_algorithm
int64_t GreatestCommonDivisor(int64_t a, int64_t b) {
// Simple cases
if (a == b) {
return a;
} else if (a == 0) {
return b;
} else if (b == 0) {
return a;
}
// Both even
if (a % 2 == 0 && b % 2 == 0) {
return 2 * GreatestCommonDivisor(a / 2, b / 2);
}
// Even a, odd b
if (a % 2 == 0 && b % 2 == 1) {
return GreatestCommonDivisor(a / 2, b);
}
// Odd a, even b
if (a % 2 == 1 && b % 2 == 0) {
return GreatestCommonDivisor(a, b / 2);
}
// Both odd, reduce the larger argument
if (a > b) {
return GreatestCommonDivisor((a - b) / 2, b);
} else {
return GreatestCommonDivisor((b - a) / 2, a);
}
}
// Check if node is affine, ie in the form: a0*i0 + a1*i1 + ... an*in + c
// and contains only the following types of nodes: SERecurrentNode, SEAddNode
// and SEConstantNode
bool IsInCorrectFormForGCDTest(SENode* node) {
bool children_ok = true;
if (auto add_node = node->AsSEAddNode()) {
for (auto child : add_node->GetChildren()) {
children_ok &= IsInCorrectFormForGCDTest(child);
}
}
bool this_ok = node->AsSERecurrentNode() || node->AsSEAddNode() ||
node->AsSEConstantNode();
return children_ok && this_ok;
}
// If |node| is an SERecurrentNode then returns |node| or if |node| is an
// SEAddNode returns a vector of SERecurrentNode that are its children.
std::vector<SERecurrentNode*> GetAllTopLevelRecurrences(SENode* node) {
auto nodes = std::vector<SERecurrentNode*>{};
if (auto recurrent_node = node->AsSERecurrentNode()) {
nodes.push_back(recurrent_node);
}
if (auto add_node = node->AsSEAddNode()) {
for (auto child : add_node->GetChildren()) {
auto child_nodes = GetAllTopLevelRecurrences(child);
nodes.insert(nodes.end(), child_nodes.begin(), child_nodes.end());
}
}
return nodes;
}
// If |node| is an SEConstantNode then returns |node| or if |node| is an
// SEAddNode returns a vector of SEConstantNode that are its children.
std::vector<SEConstantNode*> GetAllTopLevelConstants(SENode* node) {
auto nodes = std::vector<SEConstantNode*>{};
if (auto recurrent_node = node->AsSEConstantNode()) {
nodes.push_back(recurrent_node);
}
if (auto add_node = node->AsSEAddNode()) {
for (auto child : add_node->GetChildren()) {
auto child_nodes = GetAllTopLevelConstants(child);
nodes.insert(nodes.end(), child_nodes.begin(), child_nodes.end());
}
}
return nodes;
}
bool AreOffsetsAndCoefficientsConstant(
const std::vector<SERecurrentNode*>& nodes) {
for (auto node : nodes) {
if (!node->GetOffset()->AsSEConstantNode() ||
!node->GetOffset()->AsSEConstantNode()) {
return false;
}
}
return true;
}
// Fold all SEConstantNode that appear in |recurrences| and |constants| into a
// single integer value.
int64_t CalculateConstantTerm(const std::vector<SERecurrentNode*>& recurrences,
const std::vector<SEConstantNode*>& constants) {
int64_t constant_term = 0;
for (auto recurrence : recurrences) {
constant_term +=
recurrence->GetOffset()->AsSEConstantNode()->FoldToSingleValue();
}
for (auto constant : constants) {
constant_term += constant->FoldToSingleValue();
}
return constant_term;
}
int64_t CalculateGCDFromCoefficients(
const std::vector<SERecurrentNode*>& recurrences, int64_t running_gcd) {
for (SERecurrentNode* recurrence : recurrences) {
auto coefficient = recurrence->GetCoefficient()->AsSEConstantNode();
running_gcd = GreatestCommonDivisor(
running_gcd, std::abs(coefficient->FoldToSingleValue()));
}
return running_gcd;
}
// Compare 2 fractions while first normalizing them, e.g. 2/4 and 4/8 will both
// be simplified to 1/2 and then determined to be equal.
bool NormalizeAndCompareFractions(int64_t numerator_0, int64_t denominator_0,
int64_t numerator_1, int64_t denominator_1) {
auto gcd_0 =
GreatestCommonDivisor(std::abs(numerator_0), std::abs(denominator_0));
auto gcd_1 =
GreatestCommonDivisor(std::abs(numerator_1), std::abs(denominator_1));
auto normalized_numerator_0 = numerator_0 / gcd_0;
auto normalized_denominator_0 = denominator_0 / gcd_0;
auto normalized_numerator_1 = numerator_1 / gcd_1;
auto normalized_denominator_1 = denominator_1 / gcd_1;
return normalized_numerator_0 == normalized_numerator_1 &&
normalized_denominator_0 == normalized_denominator_1;
}
} // namespace
bool LoopDependenceAnalysis::GetDependence(const Instruction* source,
const Instruction* destination,
DistanceVector* distance_vector) {
// Start off by finding and marking all the loops in |loops_| that are
// irrelevant to the dependence analysis.
MarkUnsusedDistanceEntriesAsIrrelevant(source, destination, distance_vector);
Instruction* source_access_chain = GetOperandDefinition(source, 0);
Instruction* destination_access_chain = GetOperandDefinition(destination, 0);
auto num_access_chains =
(source_access_chain->opcode() == SpvOpAccessChain) +
(destination_access_chain->opcode() == SpvOpAccessChain);
// If neither is an access chain, then they are load/store to a variable.
if (num_access_chains == 0) {
if (source_access_chain != destination_access_chain) {
// Not the same location, report independence
return true;
} else {
// Accessing the same variable
for (auto& entry : distance_vector->GetEntries()) {
entry = DistanceEntry();
}
return false;
}
}
// If only one is an access chain, it could be accessing a part of a struct
if (num_access_chains == 1) {
auto source_is_chain = source_access_chain->opcode() == SpvOpAccessChain;
auto access_chain =
source_is_chain ? source_access_chain : destination_access_chain;
auto variable =
source_is_chain ? destination_access_chain : source_access_chain;
auto location_in_chain = GetOperandDefinition(access_chain, 0);
if (variable != location_in_chain) {
// Not the same location, report independence
return true;
} else {
// Accessing the same variable
for (auto& entry : distance_vector->GetEntries()) {
entry = DistanceEntry();
}
return false;
}
}
// If the access chains aren't collecting from the same structure there is no
// dependence.
Instruction* source_array = GetOperandDefinition(source_access_chain, 0);
Instruction* destination_array =
GetOperandDefinition(destination_access_chain, 0);
// Nested access chains are not supported yet, bail out.
if (source_array->opcode() == SpvOpAccessChain ||
destination_array->opcode() == SpvOpAccessChain) {
for (auto& entry : distance_vector->GetEntries()) {
entry = DistanceEntry();
}
return false;
}
if (source_array != destination_array) {
PrintDebug("Proved independence through different arrays.");
return true;
}
// To handle multiple subscripts we must get every operand in the access
// chains past the first.
std::vector<Instruction*> source_subscripts = GetSubscripts(source);
std::vector<Instruction*> destination_subscripts = GetSubscripts(destination);
auto sets_of_subscripts =
PartitionSubscripts(source_subscripts, destination_subscripts);
auto first_coupled = std::partition(
std::begin(sets_of_subscripts), std::end(sets_of_subscripts),
[](const std::set<std::pair<Instruction*, Instruction*>>& set) {
return set.size() == 1;
});
// Go through each subscript testing for independence.
// If any subscript results in independence, we prove independence between the
// load and store.
// If we can't prove independence we store what information we can gather in
// a DistanceVector.
for (auto it = std::begin(sets_of_subscripts); it < first_coupled; ++it) {
auto source_subscript = std::get<0>(*(*it).begin());
auto destination_subscript = std::get<1>(*(*it).begin());
SENode* source_node = scalar_evolution_.SimplifyExpression(
scalar_evolution_.AnalyzeInstruction(source_subscript));
SENode* destination_node = scalar_evolution_.SimplifyExpression(
scalar_evolution_.AnalyzeInstruction(destination_subscript));
// Check the loops are in a form we support.
auto subscript_pair = std::make_pair(source_node, destination_node);
const Loop* loop = GetLoopForSubscriptPair(subscript_pair);
if (loop) {
if (!IsSupportedLoop(loop)) {
PrintDebug(
"GetDependence found an unsupported loop form. Assuming <=> for "
"loop.");
DistanceEntry* distance_entry =
GetDistanceEntryForSubscriptPair(subscript_pair, distance_vector);
if (distance_entry) {
distance_entry->direction = DistanceEntry::Directions::ALL;
}
continue;
}
}
// If either node is simplified to a CanNotCompute we can't perform any
// analysis so must assume <=> dependence and return.
if (source_node->GetType() == SENode::CanNotCompute ||
destination_node->GetType() == SENode::CanNotCompute) {
// Record the <=> dependence if we can get a DistanceEntry
PrintDebug(
"GetDependence found source_node || destination_node as "
"CanNotCompute. Abandoning evaluation for this subscript.");
DistanceEntry* distance_entry =
GetDistanceEntryForSubscriptPair(subscript_pair, distance_vector);
if (distance_entry) {
distance_entry->direction = DistanceEntry::Directions::ALL;
}
continue;
}
// We have no induction variables so can apply a ZIV test.
if (IsZIV(subscript_pair)) {
PrintDebug("Found a ZIV subscript pair");
if (ZIVTest(subscript_pair)) {
PrintDebug("Proved independence with ZIVTest.");
return true;
}
}
// We have only one induction variable so should attempt an SIV test.
if (IsSIV(subscript_pair)) {
PrintDebug("Found a SIV subscript pair.");
if (SIVTest(subscript_pair, distance_vector)) {
PrintDebug("Proved independence with SIVTest.");
return true;
}
}
// We have multiple induction variables so should attempt an MIV test.
if (IsMIV(subscript_pair)) {
PrintDebug("Found a MIV subscript pair.");
if (GCDMIVTest(subscript_pair)) {
PrintDebug("Proved independence with the GCD test.");
auto current_loops = CollectLoops(source_node, destination_node);
for (auto current_loop : current_loops) {
auto distance_entry =
GetDistanceEntryForLoop(current_loop, distance_vector);
distance_entry->direction = DistanceEntry::Directions::NONE;
}
return true;
}
}
}
for (auto it = first_coupled; it < std::end(sets_of_subscripts); ++it) {
auto coupled_instructions = *it;
std::vector<SubscriptPair> coupled_subscripts{};
for (const auto& elem : coupled_instructions) {
auto source_subscript = std::get<0>(elem);
auto destination_subscript = std::get<1>(elem);
SENode* source_node = scalar_evolution_.SimplifyExpression(
scalar_evolution_.AnalyzeInstruction(source_subscript));
SENode* destination_node = scalar_evolution_.SimplifyExpression(
scalar_evolution_.AnalyzeInstruction(destination_subscript));
coupled_subscripts.push_back({source_node, destination_node});
}
auto supported = true;
for (const auto& subscript : coupled_subscripts) {
auto loops = CollectLoops(std::get<0>(subscript), std::get<1>(subscript));
auto is_subscript_supported =
std::all_of(std::begin(loops), std::end(loops),
[this](const Loop* l) { return IsSupportedLoop(l); });
supported = supported && is_subscript_supported;
}
if (DeltaTest(coupled_subscripts, distance_vector)) {
return true;
}
}
// We were unable to prove independence so must gather all of the direction
// information we found.
PrintDebug(
"Couldn't prove independence.\n"
"All possible direction information has been collected in the input "
"DistanceVector.");
return false;
}
bool LoopDependenceAnalysis::ZIVTest(
const std::pair<SENode*, SENode*>& subscript_pair) {
auto source = std::get<0>(subscript_pair);
auto destination = std::get<1>(subscript_pair);
PrintDebug("Performing ZIVTest");
// If source == destination, dependence with direction = and distance 0.
if (source == destination) {
PrintDebug("ZIVTest found EQ dependence.");
return false;
} else {
PrintDebug("ZIVTest found independence.");
// Otherwise we prove independence.
return true;
}
}
bool LoopDependenceAnalysis::SIVTest(
const std::pair<SENode*, SENode*>& subscript_pair,
DistanceVector* distance_vector) {
DistanceEntry* distance_entry =
GetDistanceEntryForSubscriptPair(subscript_pair, distance_vector);
if (!distance_entry) {
PrintDebug(
"SIVTest could not find a DistanceEntry for subscript_pair. Exiting");
}
SENode* source_node = std::get<0>(subscript_pair);
SENode* destination_node = std::get<1>(subscript_pair);
int64_t source_induction_count = CountInductionVariables(source_node);
int64_t destination_induction_count =
CountInductionVariables(destination_node);
// If the source node has no induction variables we can apply a
// WeakZeroSrcTest.
if (source_induction_count == 0) {
PrintDebug("Found source has no induction variable.");
if (WeakZeroSourceSIVTest(
source_node, destination_node->AsSERecurrentNode(),
destination_node->AsSERecurrentNode()->GetCoefficient(),
distance_entry)) {
PrintDebug("Proved independence with WeakZeroSourceSIVTest.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
}
}
// If the destination has no induction variables we can apply a
// WeakZeroDestTest.
if (destination_induction_count == 0) {
PrintDebug("Found destination has no induction variable.");
if (WeakZeroDestinationSIVTest(
source_node->AsSERecurrentNode(), destination_node,
source_node->AsSERecurrentNode()->GetCoefficient(),
distance_entry)) {
PrintDebug("Proved independence with WeakZeroDestinationSIVTest.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
}
}
// We now need to collect the SERecurrentExpr nodes from source and
// destination. We do not handle cases where source or destination have
// multiple SERecurrentExpr nodes.
std::vector<SERecurrentNode*> source_recurrent_nodes =
source_node->CollectRecurrentNodes();
std::vector<SERecurrentNode*> destination_recurrent_nodes =
destination_node->CollectRecurrentNodes();
if (source_recurrent_nodes.size() == 1 &&
destination_recurrent_nodes.size() == 1) {
PrintDebug("Found source and destination have 1 induction variable.");
SERecurrentNode* source_recurrent_expr = *source_recurrent_nodes.begin();
SERecurrentNode* destination_recurrent_expr =
*destination_recurrent_nodes.begin();
// If the coefficients are identical we can apply a StrongSIVTest.
if (source_recurrent_expr->GetCoefficient() ==
destination_recurrent_expr->GetCoefficient()) {
PrintDebug("Found source and destination share coefficient.");
if (StrongSIVTest(source_node, destination_node,
source_recurrent_expr->GetCoefficient(),
distance_entry)) {
PrintDebug("Proved independence with StrongSIVTest");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
}
}
// If the coefficients are of equal magnitude and opposite sign we can
// apply a WeakCrossingSIVTest.
if (source_recurrent_expr->GetCoefficient() ==
scalar_evolution_.CreateNegation(
destination_recurrent_expr->GetCoefficient())) {
PrintDebug("Found source coefficient = -destination coefficient.");
if (WeakCrossingSIVTest(source_node, destination_node,
source_recurrent_expr->GetCoefficient(),
distance_entry)) {
PrintDebug("Proved independence with WeakCrossingSIVTest");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
}
}
}
return false;
}
bool LoopDependenceAnalysis::StrongSIVTest(SENode* source, SENode* destination,
SENode* coefficient,
DistanceEntry* distance_entry) {
PrintDebug("Performing StrongSIVTest.");
// If both source and destination are SERecurrentNodes we can perform tests
// based on distance.
// If either source or destination contain value unknown nodes or if one or
// both are not SERecurrentNodes we must attempt a symbolic test.
std::vector<SEValueUnknown*> source_value_unknown_nodes =
source->CollectValueUnknownNodes();
std::vector<SEValueUnknown*> destination_value_unknown_nodes =
destination->CollectValueUnknownNodes();
if (source_value_unknown_nodes.size() > 0 ||
destination_value_unknown_nodes.size() > 0) {
PrintDebug(
"StrongSIVTest found symbolics. Will attempt SymbolicStrongSIVTest.");
return SymbolicStrongSIVTest(source, destination, coefficient,
distance_entry);
}
if (!source->AsSERecurrentNode() || !destination->AsSERecurrentNode()) {
PrintDebug(
"StrongSIVTest could not simplify source and destination to "
"SERecurrentNodes so will exit.");
distance_entry->direction = DistanceEntry::Directions::ALL;
return false;
}
// Build an SENode for distance.
std::pair<SENode*, SENode*> subscript_pair =
std::make_pair(source, destination);
const Loop* subscript_loop = GetLoopForSubscriptPair(subscript_pair);
SENode* source_constant_term =
GetConstantTerm(subscript_loop, source->AsSERecurrentNode());
SENode* destination_constant_term =
GetConstantTerm(subscript_loop, destination->AsSERecurrentNode());
if (!source_constant_term || !destination_constant_term) {
PrintDebug(
"StrongSIVTest could not collect the constant terms of either source "
"or destination so will exit.");
return false;
}
SENode* constant_term_delta =
scalar_evolution_.SimplifyExpression(scalar_evolution_.CreateSubtraction(
destination_constant_term, source_constant_term));
// Scalar evolution doesn't perform division, so we must fold to constants and
// do it manually.
// We must check the offset delta and coefficient are constants.
int64_t distance = 0;
SEConstantNode* delta_constant = constant_term_delta->AsSEConstantNode();
SEConstantNode* coefficient_constant = coefficient->AsSEConstantNode();
if (delta_constant && coefficient_constant) {
int64_t delta_value = delta_constant->FoldToSingleValue();
int64_t coefficient_value = coefficient_constant->FoldToSingleValue();
PrintDebug(
"StrongSIVTest found delta value and coefficient value as constants "
"with values:\n"
"\tdelta value: " +
ToString(delta_value) +
"\n\tcoefficient value: " + ToString(coefficient_value) + "\n");
// Check if the distance is not integral to try to prove independence.
if (delta_value % coefficient_value != 0) {
PrintDebug(
"StrongSIVTest proved independence through distance not being an "
"integer.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
} else {
distance = delta_value / coefficient_value;
PrintDebug("StrongSIV test found distance as " + ToString(distance));
}
} else {
// If we can't fold delta and coefficient to single values we can't produce
// distance.
// As a result we can't perform the rest of the pass and must assume
// dependence in all directions.
PrintDebug("StrongSIVTest could not produce a distance. Must exit.");
distance_entry->distance = DistanceEntry::Directions::ALL;
return false;
}
// Next we gather the upper and lower bounds as constants if possible. If
// distance > upper_bound - lower_bound we prove independence.
SENode* lower_bound = GetLowerBound(subscript_loop);
SENode* upper_bound = GetUpperBound(subscript_loop);
if (lower_bound && upper_bound) {
PrintDebug("StrongSIVTest found bounds.");
SENode* bounds = scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateSubtraction(upper_bound, lower_bound));
if (bounds->GetType() == SENode::SENodeType::Constant) {
int64_t bounds_value = bounds->AsSEConstantNode()->FoldToSingleValue();
PrintDebug(
"StrongSIVTest found upper_bound - lower_bound as a constant with "
"value " +
ToString(bounds_value));
// If the absolute value of the distance is > upper bound - lower bound
// then we prove independence.
if (llabs(distance) > llabs(bounds_value)) {
PrintDebug(
"StrongSIVTest proved independence through distance escaping the "
"loop bounds.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DISTANCE;
distance_entry->direction = DistanceEntry::Directions::NONE;
distance_entry->distance = distance;
return true;
}
}
} else {
PrintDebug("StrongSIVTest was unable to gather lower and upper bounds.");
}
// Otherwise we can get a direction as follows
// { < if distance > 0
// direction = { = if distance == 0
// { > if distance < 0
PrintDebug(
"StrongSIVTest could not prove independence. Gathering direction "
"information.");
if (distance > 0) {
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DISTANCE;
distance_entry->direction = DistanceEntry::Directions::LT;
distance_entry->distance = distance;
return false;
}
if (distance == 0) {
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DISTANCE;
distance_entry->direction = DistanceEntry::Directions::EQ;
distance_entry->distance = 0;
return false;
}
if (distance < 0) {
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DISTANCE;
distance_entry->direction = DistanceEntry::Directions::GT;
distance_entry->distance = distance;
return false;
}
// We were unable to prove independence or discern any additional information
// Must assume <=> direction.
PrintDebug(
"StrongSIVTest was unable to determine any dependence information.");
distance_entry->direction = DistanceEntry::Directions::ALL;
return false;
}
bool LoopDependenceAnalysis::SymbolicStrongSIVTest(
SENode* source, SENode* destination, SENode* coefficient,
DistanceEntry* distance_entry) {
PrintDebug("Performing SymbolicStrongSIVTest.");
SENode* source_destination_delta = scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateSubtraction(source, destination));
// By cancelling out the induction variables by subtracting the source and
// destination we can produce an expression of symbolics and constants. This
// expression can be compared to the loop bounds to find if the offset is
// outwith the bounds.
std::pair<SENode*, SENode*> subscript_pair =
std::make_pair(source, destination);
const Loop* subscript_loop = GetLoopForSubscriptPair(subscript_pair);
if (IsProvablyOutsideOfLoopBounds(subscript_loop, source_destination_delta,
coefficient)) {
PrintDebug(
"SymbolicStrongSIVTest proved independence through loop bounds.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
}
// We were unable to prove independence or discern any additional information.
// Must assume <=> direction.
PrintDebug(
"SymbolicStrongSIVTest was unable to determine any dependence "
"information.");
distance_entry->direction = DistanceEntry::Directions::ALL;
return false;
}
bool LoopDependenceAnalysis::WeakZeroSourceSIVTest(
SENode* source, SERecurrentNode* destination, SENode* coefficient,
DistanceEntry* distance_entry) {
PrintDebug("Performing WeakZeroSourceSIVTest.");
std::pair<SENode*, SENode*> subscript_pair =
std::make_pair(source, destination);
const Loop* subscript_loop = GetLoopForSubscriptPair(subscript_pair);
// Build an SENode for distance.
SENode* destination_constant_term =
GetConstantTerm(subscript_loop, destination);
SENode* delta = scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateSubtraction(source, destination_constant_term));
// Scalar evolution doesn't perform division, so we must fold to constants and
// do it manually.
int64_t distance = 0;
SEConstantNode* delta_constant = delta->AsSEConstantNode();
SEConstantNode* coefficient_constant = coefficient->AsSEConstantNode();
if (delta_constant && coefficient_constant) {
PrintDebug(
"WeakZeroSourceSIVTest folding delta and coefficient to constants.");
int64_t delta_value = delta_constant->FoldToSingleValue();
int64_t coefficient_value = coefficient_constant->FoldToSingleValue();
// Check if the distance is not integral.
if (delta_value % coefficient_value != 0) {
PrintDebug(
"WeakZeroSourceSIVTest proved independence through distance not "
"being an integer.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
} else {
distance = delta_value / coefficient_value;
PrintDebug(
"WeakZeroSourceSIVTest calculated distance with the following "
"values\n"
"\tdelta value: " +
ToString(delta_value) +
"\n\tcoefficient value: " + ToString(coefficient_value) +
"\n\tdistance: " + ToString(distance) + "\n");
}
} else {
PrintDebug(
"WeakZeroSourceSIVTest was unable to fold delta and coefficient to "
"constants.");
}
// If we can prove the distance is outside the bounds we prove independence.
SEConstantNode* lower_bound =
GetLowerBound(subscript_loop)->AsSEConstantNode();
SEConstantNode* upper_bound =
GetUpperBound(subscript_loop)->AsSEConstantNode();
if (lower_bound && upper_bound) {
PrintDebug("WeakZeroSourceSIVTest found bounds as SEConstantNodes.");
int64_t lower_bound_value = lower_bound->FoldToSingleValue();
int64_t upper_bound_value = upper_bound->FoldToSingleValue();
if (!IsWithinBounds(llabs(distance), lower_bound_value,
upper_bound_value)) {
PrintDebug(
"WeakZeroSourceSIVTest proved independence through distance escaping "
"the loop bounds.");
PrintDebug(
"Bound values were as follow\n"
"\tlower bound value: " +
ToString(lower_bound_value) +
"\n\tupper bound value: " + ToString(upper_bound_value) +
"\n\tdistance value: " + ToString(distance) + "\n");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DISTANCE;
distance_entry->direction = DistanceEntry::Directions::NONE;
distance_entry->distance = distance;
return true;
}
} else {
PrintDebug(
"WeakZeroSourceSIVTest was unable to find lower and upper bound as "
"SEConstantNodes.");
}
// Now we want to see if we can detect to peel the first or last iterations.
// We get the FirstTripValue as GetFirstTripInductionNode() +
// GetConstantTerm(destination)
SENode* first_trip_SENode =
scalar_evolution_.SimplifyExpression(scalar_evolution_.CreateAddNode(
GetFirstTripInductionNode(subscript_loop),
GetConstantTerm(subscript_loop, destination)));
// If source == FirstTripValue, peel_first.
if (first_trip_SENode) {
PrintDebug("WeakZeroSourceSIVTest built first_trip_SENode.");
if (first_trip_SENode->AsSEConstantNode()) {
PrintDebug(
"WeakZeroSourceSIVTest has found first_trip_SENode as an "
"SEConstantNode with value: " +
ToString(first_trip_SENode->AsSEConstantNode()->FoldToSingleValue()) +
"\n");
}
if (source == first_trip_SENode) {
// We have found that peeling the first iteration will break dependency.
PrintDebug(
"WeakZeroSourceSIVTest has found peeling first iteration will break "
"dependency");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::PEEL;
distance_entry->peel_first = true;
return false;
}
} else {
PrintDebug("WeakZeroSourceSIVTest was unable to build first_trip_SENode");
}
// We get the LastTripValue as GetFinalTripInductionNode(coefficient) +
// GetConstantTerm(destination)
SENode* final_trip_SENode =
scalar_evolution_.SimplifyExpression(scalar_evolution_.CreateAddNode(
GetFinalTripInductionNode(subscript_loop, coefficient),
GetConstantTerm(subscript_loop, destination)));
// If source == LastTripValue, peel_last.
if (final_trip_SENode) {
PrintDebug("WeakZeroSourceSIVTest built final_trip_SENode.");
if (first_trip_SENode->AsSEConstantNode()) {
PrintDebug(
"WeakZeroSourceSIVTest has found final_trip_SENode as an "
"SEConstantNode with value: " +
ToString(final_trip_SENode->AsSEConstantNode()->FoldToSingleValue()) +
"\n");
}
if (source == final_trip_SENode) {
// We have found that peeling the last iteration will break dependency.
PrintDebug(
"WeakZeroSourceSIVTest has found peeling final iteration will break "
"dependency");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::PEEL;
distance_entry->peel_last = true;
return false;
}
} else {
PrintDebug("WeakZeroSourceSIVTest was unable to build final_trip_SENode");
}
// We were unable to prove independence or discern any additional information.
// Must assume <=> direction.
PrintDebug(
"WeakZeroSourceSIVTest was unable to determine any dependence "
"information.");
distance_entry->direction = DistanceEntry::Directions::ALL;
return false;
}
bool LoopDependenceAnalysis::WeakZeroDestinationSIVTest(
SERecurrentNode* source, SENode* destination, SENode* coefficient,
DistanceEntry* distance_entry) {
PrintDebug("Performing WeakZeroDestinationSIVTest.");
// Build an SENode for distance.
std::pair<SENode*, SENode*> subscript_pair =
std::make_pair(source, destination);
const Loop* subscript_loop = GetLoopForSubscriptPair(subscript_pair);
SENode* source_constant_term = GetConstantTerm(subscript_loop, source);
SENode* delta = scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateSubtraction(destination, source_constant_term));
// Scalar evolution doesn't perform division, so we must fold to constants and
// do it manually.
int64_t distance = 0;
SEConstantNode* delta_constant = delta->AsSEConstantNode();
SEConstantNode* coefficient_constant = coefficient->AsSEConstantNode();
if (delta_constant && coefficient_constant) {
PrintDebug(
"WeakZeroDestinationSIVTest folding delta and coefficient to "
"constants.");
int64_t delta_value = delta_constant->FoldToSingleValue();
int64_t coefficient_value = coefficient_constant->FoldToSingleValue();
// Check if the distance is not integral.
if (delta_value % coefficient_value != 0) {
PrintDebug(
"WeakZeroDestinationSIVTest proved independence through distance not "
"being an integer.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
} else {
distance = delta_value / coefficient_value;
PrintDebug(
"WeakZeroDestinationSIVTest calculated distance with the following "
"values\n"
"\tdelta value: " +
ToString(delta_value) +
"\n\tcoefficient value: " + ToString(coefficient_value) +
"\n\tdistance: " + ToString(distance) + "\n");
}
} else {
PrintDebug(
"WeakZeroDestinationSIVTest was unable to fold delta and coefficient "
"to constants.");
}
// If we can prove the distance is outside the bounds we prove independence.
SEConstantNode* lower_bound =
GetLowerBound(subscript_loop)->AsSEConstantNode();
SEConstantNode* upper_bound =
GetUpperBound(subscript_loop)->AsSEConstantNode();
if (lower_bound && upper_bound) {
PrintDebug("WeakZeroDestinationSIVTest found bounds as SEConstantNodes.");
int64_t lower_bound_value = lower_bound->FoldToSingleValue();
int64_t upper_bound_value = upper_bound->FoldToSingleValue();
if (!IsWithinBounds(llabs(distance), lower_bound_value,
upper_bound_value)) {
PrintDebug(
"WeakZeroDestinationSIVTest proved independence through distance "
"escaping the loop bounds.");
PrintDebug(
"Bound values were as follows\n"
"\tlower bound value: " +
ToString(lower_bound_value) +
"\n\tupper bound value: " + ToString(upper_bound_value) +
"\n\tdistance value: " + ToString(distance));
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DISTANCE;
distance_entry->direction = DistanceEntry::Directions::NONE;
distance_entry->distance = distance;
return true;
}
} else {
PrintDebug(
"WeakZeroDestinationSIVTest was unable to find lower and upper bound "
"as SEConstantNodes.");
}
// Now we want to see if we can detect to peel the first or last iterations.
// We get the FirstTripValue as GetFirstTripInductionNode() +
// GetConstantTerm(source)
SENode* first_trip_SENode = scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateAddNode(GetFirstTripInductionNode(subscript_loop),
GetConstantTerm(subscript_loop, source)));
// If destination == FirstTripValue, peel_first.
if (first_trip_SENode) {
PrintDebug("WeakZeroDestinationSIVTest built first_trip_SENode.");
if (first_trip_SENode->AsSEConstantNode()) {
PrintDebug(
"WeakZeroDestinationSIVTest has found first_trip_SENode as an "
"SEConstantNode with value: " +
ToString(first_trip_SENode->AsSEConstantNode()->FoldToSingleValue()) +
"\n");
}
if (destination == first_trip_SENode) {
// We have found that peeling the first iteration will break dependency.
PrintDebug(
"WeakZeroDestinationSIVTest has found peeling first iteration will "
"break dependency");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::PEEL;
distance_entry->peel_first = true;
return false;
}
} else {
PrintDebug(
"WeakZeroDestinationSIVTest was unable to build first_trip_SENode");
}
// We get the LastTripValue as GetFinalTripInductionNode(coefficient) +
// GetConstantTerm(source)
SENode* final_trip_SENode =
scalar_evolution_.SimplifyExpression(scalar_evolution_.CreateAddNode(
GetFinalTripInductionNode(subscript_loop, coefficient),
GetConstantTerm(subscript_loop, source)));
// If destination == LastTripValue, peel_last.
if (final_trip_SENode) {
PrintDebug("WeakZeroDestinationSIVTest built final_trip_SENode.");
if (final_trip_SENode->AsSEConstantNode()) {
PrintDebug(
"WeakZeroDestinationSIVTest has found final_trip_SENode as an "
"SEConstantNode with value: " +
ToString(final_trip_SENode->AsSEConstantNode()->FoldToSingleValue()) +
"\n");
}
if (destination == final_trip_SENode) {
// We have found that peeling the last iteration will break dependency.
PrintDebug(
"WeakZeroDestinationSIVTest has found peeling final iteration will "
"break dependency");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::PEEL;
distance_entry->peel_last = true;
return false;
}
} else {
PrintDebug(
"WeakZeroDestinationSIVTest was unable to build final_trip_SENode");
}
// We were unable to prove independence or discern any additional information.
// Must assume <=> direction.
PrintDebug(
"WeakZeroDestinationSIVTest was unable to determine any dependence "
"information.");
distance_entry->direction = DistanceEntry::Directions::ALL;
return false;
}
bool LoopDependenceAnalysis::WeakCrossingSIVTest(
SENode* source, SENode* destination, SENode* coefficient,
DistanceEntry* distance_entry) {
PrintDebug("Performing WeakCrossingSIVTest.");
// We currently can't handle symbolic WeakCrossingSIVTests. If either source
// or destination are not SERecurrentNodes we must exit.
if (!source->AsSERecurrentNode() || !destination->AsSERecurrentNode()) {
PrintDebug(
"WeakCrossingSIVTest found source or destination != SERecurrentNode. "
"Exiting");
distance_entry->direction = DistanceEntry::Directions::ALL;
return false;
}
// Build an SENode for distance.
SENode* offset_delta =
scalar_evolution_.SimplifyExpression(scalar_evolution_.CreateSubtraction(
destination->AsSERecurrentNode()->GetOffset(),
source->AsSERecurrentNode()->GetOffset()));
// Scalar evolution doesn't perform division, so we must fold to constants and
// do it manually.
int64_t distance = 0;
SEConstantNode* delta_constant = offset_delta->AsSEConstantNode();
SEConstantNode* coefficient_constant = coefficient->AsSEConstantNode();
if (delta_constant && coefficient_constant) {
PrintDebug(
"WeakCrossingSIVTest folding offset_delta and coefficient to "
"constants.");
int64_t delta_value = delta_constant->FoldToSingleValue();
int64_t coefficient_value = coefficient_constant->FoldToSingleValue();
// Check if the distance is not integral or if it has a non-integral part
// equal to 1/2.
if (delta_value % (2 * coefficient_value) != 0 &&
static_cast<float>(delta_value % (2 * coefficient_value)) /
static_cast<float>(2 * coefficient_value) !=
0.5) {
PrintDebug(
"WeakCrossingSIVTest proved independence through distance escaping "
"the loop bounds.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DIRECTION;
distance_entry->direction = DistanceEntry::Directions::NONE;
return true;
} else {
distance = delta_value / (2 * coefficient_value);
}
if (distance == 0) {
PrintDebug("WeakCrossingSIVTest found EQ dependence.");
distance_entry->dependence_information =
DistanceEntry::DependenceInformation::DISTANCE;
distance_entry->direction = DistanceEntry::Directions::EQ;
distance_entry->distance = 0;
return false;
}
} else {
PrintDebug(
"WeakCrossingSIVTest was unable to fold offset_delta and coefficient "
"to constants.");
}
// We were unable to prove independence or discern any additional information.
// Must assume <=> direction.
PrintDebug(
"WeakCrossingSIVTest was unable to determine any dependence "
"information.");
distance_entry->direction = DistanceEntry::Directions::ALL;
return false;
}
// Perform the GCD test if both, the source and the destination nodes, are in
// the form a0*i0 + a1*i1 + ... an*in + c.
bool LoopDependenceAnalysis::GCDMIVTest(
const std::pair<SENode*, SENode*>& subscript_pair) {
auto source = std::get<0>(subscript_pair);
auto destination = std::get<1>(subscript_pair);
// Bail out if source/destination is in an unexpected form.
if (!IsInCorrectFormForGCDTest(source) ||
!IsInCorrectFormForGCDTest(destination)) {
return false;
}
auto source_recurrences = GetAllTopLevelRecurrences(source);
auto dest_recurrences = GetAllTopLevelRecurrences(destination);
// Bail out if all offsets and coefficients aren't constant.
if (!AreOffsetsAndCoefficientsConstant(source_recurrences) ||
!AreOffsetsAndCoefficientsConstant(dest_recurrences)) {
return false;
}
// Calculate the GCD of all coefficients.
auto source_constants = GetAllTopLevelConstants(source);
int64_t source_constant =
CalculateConstantTerm(source_recurrences, source_constants);
auto dest_constants = GetAllTopLevelConstants(destination);
int64_t destination_constant =
CalculateConstantTerm(dest_recurrences, dest_constants);
int64_t delta = std::abs(source_constant - destination_constant);
int64_t running_gcd = 0;
running_gcd = CalculateGCDFromCoefficients(source_recurrences, running_gcd);
running_gcd = CalculateGCDFromCoefficients(dest_recurrences, running_gcd);
return delta % running_gcd != 0;
}
using PartitionedSubscripts =
std::vector<std::set<std::pair<Instruction*, Instruction*>>>;
PartitionedSubscripts LoopDependenceAnalysis::PartitionSubscripts(
const std::vector<Instruction*>& source_subscripts,
const std::vector<Instruction*>& destination_subscripts) {
PartitionedSubscripts partitions{};
auto num_subscripts = source_subscripts.size();
// Create initial partitions with one subscript pair per partition.
for (size_t i = 0; i < num_subscripts; ++i) {
partitions.push_back({{source_subscripts[i], destination_subscripts[i]}});
}
// Iterate over the loops to create all partitions
for (auto loop : loops_) {
int64_t k = -1;
for (size_t j = 0; j < partitions.size(); ++j) {
auto& current_partition = partitions[j];
// Does |loop| appear in |current_partition|
auto it = std::find_if(
current_partition.begin(), current_partition.end(),
[loop,
this](const std::pair<Instruction*, Instruction*>& elem) -> bool {
auto source_recurrences =
scalar_evolution_.AnalyzeInstruction(std::get<0>(elem))
->CollectRecurrentNodes();
auto destination_recurrences =
scalar_evolution_.AnalyzeInstruction(std::get<1>(elem))
->CollectRecurrentNodes();
source_recurrences.insert(source_recurrences.end(),
destination_recurrences.begin(),
destination_recurrences.end());
auto loops_in_pair = CollectLoops(source_recurrences);
auto end_it = loops_in_pair.end();
return std::find(loops_in_pair.begin(), end_it, loop) != end_it;
});
auto has_loop = it != current_partition.end();
if (has_loop) {
if (k == -1) {
k = j;
} else {
// Add |partitions[j]| to |partitions[k]| and discard |partitions[j]|
partitions[static_cast<size_t>(k)].insert(current_partition.begin(),
current_partition.end());
current_partition.clear();
}
}
}
}
// Remove empty (discarded) partitions
partitions.erase(
std::remove_if(
partitions.begin(), partitions.end(),
[](const std::set<std::pair<Instruction*, Instruction*>>& partition) {
return partition.empty();
}),
partitions.end());
return partitions;
}
Constraint* LoopDependenceAnalysis::IntersectConstraints(
Constraint* constraint_0, Constraint* constraint_1,
const SENode* lower_bound, const SENode* upper_bound) {
if (constraint_0->AsDependenceNone()) {
return constraint_1;
} else if (constraint_1->AsDependenceNone()) {
return constraint_0;
}
// Both constraints are distances. Either the same distance or independent.
if (constraint_0->AsDependenceDistance() &&
constraint_1->AsDependenceDistance()) {
auto dist_0 = constraint_0->AsDependenceDistance();
auto dist_1 = constraint_1->AsDependenceDistance();
if (*dist_0->GetDistance() == *dist_1->GetDistance()) {
return constraint_0;
} else {
return make_constraint<DependenceEmpty>();
}
}
// Both constraints are points. Either the same point or independent.
if (constraint_0->AsDependencePoint() && constraint_1->AsDependencePoint()) {
auto point_0 = constraint_0->AsDependencePoint();
auto point_1 = constraint_1->AsDependencePoint();
if (*point_0->GetSource() == *point_1->GetSource() &&
*point_0->GetDestination() == *point_1->GetDestination()) {
return constraint_0;
} else {
return make_constraint<DependenceEmpty>();
}
}
// Both constraints are lines/distances.
if ((constraint_0->AsDependenceDistance() ||
constraint_0->AsDependenceLine()) &&
(constraint_1->AsDependenceDistance() ||
constraint_1->AsDependenceLine())) {
auto is_distance_0 = constraint_0->AsDependenceDistance() != nullptr;
auto is_distance_1 = constraint_1->AsDependenceDistance() != nullptr;
auto a0 = is_distance_0 ? scalar_evolution_.CreateConstant(1)
: constraint_0->AsDependenceLine()->GetA();
auto b0 = is_distance_0 ? scalar_evolution_.CreateConstant(-1)
: constraint_0->AsDependenceLine()->GetB();
auto c0 =
is_distance_0
? scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateNegation(
constraint_0->AsDependenceDistance()->GetDistance()))
: constraint_0->AsDependenceLine()->GetC();
auto a1 = is_distance_1 ? scalar_evolution_.CreateConstant(1)
: constraint_1->AsDependenceLine()->GetA();
auto b1 = is_distance_1 ? scalar_evolution_.CreateConstant(-1)
: constraint_1->AsDependenceLine()->GetB();
auto c1 =
is_distance_1
? scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateNegation(
constraint_1->AsDependenceDistance()->GetDistance()))
: constraint_1->AsDependenceLine()->GetC();
if (a0->AsSEConstantNode() && b0->AsSEConstantNode() &&
c0->AsSEConstantNode() && a1->AsSEConstantNode() &&
b1->AsSEConstantNode() && c1->AsSEConstantNode()) {
auto constant_a0 = a0->AsSEConstantNode()->FoldToSingleValue();
auto constant_b0 = b0->AsSEConstantNode()->FoldToSingleValue();
auto constant_c0 = c0->AsSEConstantNode()->FoldToSingleValue();
auto constant_a1 = a1->AsSEConstantNode()->FoldToSingleValue();
auto constant_b1 = b1->AsSEConstantNode()->FoldToSingleValue();
auto constant_c1 = c1->AsSEConstantNode()->FoldToSingleValue();
// a & b can't both be zero, otherwise it wouldn't be line.
if (NormalizeAndCompareFractions(constant_a0, constant_b0, constant_a1,
constant_b1)) {
// Slopes are equal, either parallel lines or the same line.
if (constant_b0 == 0 && constant_b1 == 0) {
if (NormalizeAndCompareFractions(constant_c0, constant_a0,
constant_c1, constant_a1)) {
return constraint_0;
}
return make_constraint<DependenceEmpty>();
} else if (NormalizeAndCompareFractions(constant_c0, constant_b0,
constant_c1, constant_b1)) {
// Same line.
return constraint_0;
} else {
// Parallel lines can't intersect, report independence.
return make_constraint<DependenceEmpty>();
}
} else {
// Lines are not parallel, therefore, they must intersect.
// Calculate intersection.
if (upper_bound->AsSEConstantNode() &&
lower_bound->AsSEConstantNode()) {
auto constant_lower_bound =
lower_bound->AsSEConstantNode()->FoldToSingleValue();
auto constant_upper_bound =
upper_bound->AsSEConstantNode()->FoldToSingleValue();
auto up = constant_b1 * constant_c0 - constant_b0 * constant_c1;
// Both b or both a can't be 0, so down is never 0
// otherwise would have entered the parallel line section.
auto down = constant_b1 * constant_a0 - constant_b0 * constant_a1;
auto x_coord = up / down;
int64_t y_coord = 0;
int64_t arg1 = 0;
int64_t const_b_to_use = 0;
if (constant_b1 != 0) {
arg1 = constant_c1 - constant_a1 * x_coord;
y_coord = arg1 / constant_b1;
const_b_to_use = constant_b1;
} else if (constant_b0 != 0) {
arg1 = constant_c0 - constant_a0 * x_coord;
y_coord = arg1 / constant_b0;
const_b_to_use = constant_b0;
}
if (up % down == 0 &&
arg1 % const_b_to_use == 0 && // Coordinates are integers.
constant_lower_bound <=
x_coord && // x_coord is within loop bounds.
x_coord <= constant_upper_bound &&
constant_lower_bound <=
y_coord && // y_coord is within loop bounds.
y_coord <= constant_upper_bound) {
// Lines intersect at integer coordinates.
return make_constraint<DependencePoint>(
scalar_evolution_.CreateConstant(x_coord),
scalar_evolution_.CreateConstant(y_coord),
constraint_0->GetLoop());
} else {
return make_constraint<DependenceEmpty>();
}
} else {
// Not constants, bail out.
return make_constraint<DependenceNone>();
}
}
} else {
// Not constants, bail out.
return make_constraint<DependenceNone>();
}
}
// One constraint is a line/distance and the other is a point.
if ((constraint_0->AsDependencePoint() &&
(constraint_1->AsDependenceLine() ||
constraint_1->AsDependenceDistance())) ||
(constraint_1->AsDependencePoint() &&
(constraint_0->AsDependenceLine() ||
constraint_0->AsDependenceDistance()))) {
auto point_0 = constraint_0->AsDependencePoint() != nullptr;
auto point = point_0 ? constraint_0->AsDependencePoint()
: constraint_1->AsDependencePoint();
auto line_or_distance = point_0 ? constraint_1 : constraint_0;
auto is_distance = line_or_distance->AsDependenceDistance() != nullptr;
auto a = is_distance ? scalar_evolution_.CreateConstant(1)
: line_or_distance->AsDependenceLine()->GetA();
auto b = is_distance ? scalar_evolution_.CreateConstant(-1)
: line_or_distance->AsDependenceLine()->GetB();
auto c =
is_distance
? scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateNegation(
line_or_distance->AsDependenceDistance()->GetDistance()))
: line_or_distance->AsDependenceLine()->GetC();
auto x = point->GetSource();
auto y = point->GetDestination();
if (a->AsSEConstantNode() && b->AsSEConstantNode() &&
c->AsSEConstantNode() && x->AsSEConstantNode() &&
y->AsSEConstantNode()) {
auto constant_a = a->AsSEConstantNode()->FoldToSingleValue();
auto constant_b = b->AsSEConstantNode()->FoldToSingleValue();
auto constant_c = c->AsSEConstantNode()->FoldToSingleValue();
auto constant_x = x->AsSEConstantNode()->FoldToSingleValue();
auto constant_y = y->AsSEConstantNode()->FoldToSingleValue();
auto left_hand_side = constant_a * constant_x + constant_b * constant_y;
if (left_hand_side == constant_c) {
// Point is on line, return point
return point_0 ? constraint_0 : constraint_1;
} else {
// Point not on line, report independence (empty constraint).
return make_constraint<DependenceEmpty>();
}
} else {
// Not constants, bail out.
return make_constraint<DependenceNone>();
}
}
return nullptr;
}
// Propagate constraints function as described in section 5 of Practical
// Dependence Testing, Goff, Kennedy, Tseng, 1991.
SubscriptPair LoopDependenceAnalysis::PropagateConstraints(
const SubscriptPair& subscript_pair,
const std::vector<Constraint*>& constraints) {
SENode* new_first = subscript_pair.first;
SENode* new_second = subscript_pair.second;
for (auto& constraint : constraints) {
// In the paper this is a[k]. We're extracting the coefficient ('a') of a
// recurrent expression with respect to the loop 'k'.
SENode* coefficient_of_recurrent =
scalar_evolution_.GetCoefficientFromRecurrentTerm(
new_first, constraint->GetLoop());
// In the paper this is a'[k].
SENode* coefficient_of_recurrent_prime =
scalar_evolution_.GetCoefficientFromRecurrentTerm(
new_second, constraint->GetLoop());
if (constraint->GetType() == Constraint::Distance) {
DependenceDistance* as_distance = constraint->AsDependenceDistance();
// In the paper this is a[k]*d
SENode* rhs = scalar_evolution_.CreateMultiplyNode(
coefficient_of_recurrent, as_distance->GetDistance());
// In the paper this is a[k] <- 0
SENode* zeroed_coefficient =
scalar_evolution_.BuildGraphWithoutRecurrentTerm(
new_first, constraint->GetLoop());
// In the paper this is e <- e - a[k]*d.
new_first = scalar_evolution_.CreateSubtraction(zeroed_coefficient, rhs);
new_first = scalar_evolution_.SimplifyExpression(new_first);
// In the paper this is a'[k] - a[k].
SENode* new_child = scalar_evolution_.SimplifyExpression(
scalar_evolution_.CreateSubtraction(coefficient_of_recurrent_prime,
coefficient_of_recurrent));
// In the paper this is a'[k]'i[k].
SERecurrentNode* prime_recurrent =
scalar_evolution_.GetRecurrentTerm(new_second, constraint->GetLoop());
if (!prime_recurrent) continue;
// As we hash the nodes we need to create a new node when we update a
// child.
SENode* new_recurrent = scalar_evolution_.CreateRecurrentExpression(
constraint->GetLoop(), prime_recurrent->GetOffset(), new_child);
// In the paper this is a'[k] <- a'[k] - a[k].
new_second = scalar_evolution_.UpdateChildNode(
new_second, prime_recurrent, new_recurrent);
}
}
new_second = scalar_evolution_.SimplifyExpression(new_second);
return std::make_pair(new_first, new_second);
}
bool LoopDependenceAnalysis::DeltaTest(
const std::vector<SubscriptPair>& coupled_subscripts,
DistanceVector* dv_entry) {
std::vector<Constraint*> constraints(loops_.size());
std::vector<bool> loop_appeared(loops_.size());
std::generate(std::begin(constraints), std::end(constraints),
[this]() { return make_constraint<DependenceNone>(); });
// Separate SIV and MIV subscripts
std::vector<SubscriptPair> siv_subscripts{};
std::vector<SubscriptPair> miv_subscripts{};
for (const auto& subscript_pair : coupled_subscripts) {
if (IsSIV(subscript_pair)) {
siv_subscripts.push_back(subscript_pair);
} else {
miv_subscripts.push_back(subscript_pair);
}
}
// Delta Test
while (!siv_subscripts.empty()) {
std::vector<bool> results(siv_subscripts.size());
std::vector<DistanceVector> current_distances(
siv_subscripts.size(), DistanceVector(loops_.size()));
// Apply SIV test to all SIV subscripts, report independence if any of them
// is independent
std::transform(
std::begin(siv_subscripts), std::end(siv_subscripts),
std::begin(current_distances), std::begin(results),
[this](SubscriptPair& p, DistanceVector& d) { return SIVTest(p, &d); });
if (std::accumulate(std::begin(results), std::end(results), false,
std::logical_or<bool>{})) {
return true;
}
// Derive new constraint vector.
std::vector<std::pair<Constraint*, size_t>> all_new_constrants{};
for (size_t i = 0; i < siv_subscripts.size(); ++i) {
auto loop = GetLoopForSubscriptPair(siv_subscripts[i]);
auto loop_id =
std::distance(std::begin(loops_),
std::find(std::begin(loops_), std::end(loops_), loop));
loop_appeared[loop_id] = true;
auto distance_entry = current_distances[i].GetEntries()[loop_id];
if (distance_entry.dependence_information ==
DistanceEntry::DependenceInformation::DISTANCE) {
// Construct a DependenceDistance.
auto node = scalar_evolution_.CreateConstant(distance_entry.distance);
all_new_constrants.push_back(
{make_constraint<DependenceDistance>(node, loop), loop_id});
} else {
// Construct a DependenceLine.
const auto& subscript_pair = siv_subscripts[i];
SENode* source_node = std::get<0>(subscript_pair);
SENode* destination_node = std::get<1>(subscript_pair);
int64_t source_induction_count = CountInductionVariables(source_node);
int64_t destination_induction_count =
CountInductionVariables(destination_node);
SENode* a = nullptr;
SENode* b = nullptr;
SENode* c = nullptr;
if (destination_induction_count != 0) {
a = destination_node->AsSERecurrentNode()->GetCoefficient();
c = scalar_evolution_.CreateNegation(
destination_node->AsSERecurrentNode()->GetOffset());
} else {
a = scalar_evolution_.CreateConstant(0);
c = scalar_evolution_.CreateNegation(destination_node);
}
if (source_induction_count != 0) {
b = scalar_evolution_.CreateNegation(
source_node->AsSERecurrentNode()->GetCoefficient());
c = scalar_evolution_.CreateAddNode(
c, source_node->AsSERecurrentNode()->GetOffset());
} else {
b = scalar_evolution_.CreateConstant(0);
c = scalar_evolution_.CreateAddNode(c, source_node);
}
a = scalar_evolution_.SimplifyExpression(a);
b = scalar_evolution_.SimplifyExpression(b);
c = scalar_evolution_.SimplifyExpression(c);
all_new_constrants.push_back(
{make_constraint<DependenceLine>(a, b, c, loop), loop_id});
}
}
// Calculate the intersection between the new and existing constraints.
std::vector<Constraint*> intersection = constraints;
for (const auto& constraint_to_intersect : all_new_constrants) {
auto loop_id = std::get<1>(constraint_to_intersect);
auto loop = loops_[loop_id];
intersection[loop_id] = IntersectConstraints(
intersection[loop_id], std::get<0>(constraint_to_intersect),
GetLowerBound(loop), GetUpperBound(loop));
}
// Report independence if an empty constraint (DependenceEmpty) is found.
auto first_empty =
std::find_if(std::begin(intersection), std::end(intersection),
[](Constraint* constraint) {
return constraint->AsDependenceEmpty() != nullptr;
});
if (first_empty != std::end(intersection)) {
return true;
}
std::vector<SubscriptPair> new_siv_subscripts{};
std::vector<SubscriptPair> new_miv_subscripts{};
auto equal =
std::equal(std::begin(constraints), std::end(constraints),
std::begin(intersection),
[](Constraint* a, Constraint* b) { return *a == *b; });
// If any constraints have changed, propagate them into the rest of the
// subscripts possibly creating new ZIV/SIV subscripts.
if (!equal) {
std::vector<SubscriptPair> new_subscripts(miv_subscripts.size());
// Propagate constraints into MIV subscripts
std::transform(std::begin(miv_subscripts), std::end(miv_subscripts),
std::begin(new_subscripts),
[this, &intersection](SubscriptPair& subscript_pair) {
return PropagateConstraints(subscript_pair,
intersection);
});
// If a ZIV subscript is returned, apply test, otherwise, update untested
// subscripts.
for (auto& subscript : new_subscripts) {
if (IsZIV(subscript) && ZIVTest(subscript)) {
return true;
} else if (IsSIV(subscript)) {
new_siv_subscripts.push_back(subscript);
} else {
new_miv_subscripts.push_back(subscript);
}
}
}
// Set new constraints and subscripts to test.
std::swap(siv_subscripts, new_siv_subscripts);
std::swap(miv_subscripts, new_miv_subscripts);
std::swap(constraints, intersection);
}
// Create the dependence vector from the constraints.
for (size_t i = 0; i < loops_.size(); ++i) {
// Don't touch entries for loops that weren't tested.
if (loop_appeared[i]) {
auto current_constraint = constraints[i];
auto& current_distance_entry = (*dv_entry).GetEntries()[i];
if (auto dependence_distance =
current_constraint->AsDependenceDistance()) {
if (auto constant_node =
dependence_distance->GetDistance()->AsSEConstantNode()) {
current_distance_entry.dependence_information =
DistanceEntry::DependenceInformation::DISTANCE;
current_distance_entry.distance = constant_node->FoldToSingleValue();
if (current_distance_entry.distance == 0) {
current_distance_entry.direction = DistanceEntry::Directions::EQ;
} else if (current_distance_entry.distance < 0) {
current_distance_entry.direction = DistanceEntry::Directions::GT;
} else {
current_distance_entry.direction = DistanceEntry::Directions::LT;
}
}
} else if (auto dependence_point =
current_constraint->AsDependencePoint()) {
auto source = dependence_point->GetSource();
auto destination = dependence_point->GetDestination();
if (source->AsSEConstantNode() && destination->AsSEConstantNode()) {
current_distance_entry = DistanceEntry(
source->AsSEConstantNode()->FoldToSingleValue(),
destination->AsSEConstantNode()->FoldToSingleValue());
}
}
}
}
// Test any remaining MIV subscripts and report independence if found.
std::vector<bool> results(miv_subscripts.size());
std::transform(std::begin(miv_subscripts), std::end(miv_subscripts),
std::begin(results),
[this](const SubscriptPair& p) { return GCDMIVTest(p); });
return std::accumulate(std::begin(results), std::end(results), false,
std::logical_or<bool>{});
}
} // namespace opt
} // namespace spvtools
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