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test_memdependency.cpp
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#include <gtest/gtest.h>
#include <test/cpp/tensorexpr/test_base.h>
#include <torch/csrc/jit/tensorexpr/bounds_overlap.h>
#include <torch/csrc/jit/tensorexpr/ir.h>
#include <torch/csrc/jit/tensorexpr/ir_printer.h>
#include <torch/csrc/jit/tensorexpr/ir_simplifier.h>
#include <torch/csrc/jit/tensorexpr/loopnest.h>
#include <torch/csrc/jit/tensorexpr/mem_dependency_checker.h>
#include <torch/csrc/jit/tensorexpr/tensor.h>
namespace torch {
namespace jit {
using namespace torch::jit::tensorexpr;
// Test helper function used to determine if two regions of a buffer have an
// overlap. No Overlap & partial overlap is obvious. Contains means A is
// larger and fully encloses B, while ContainedOrEqual is the reverse. Equal
// ranges are ContainedOrEqual.
TEST(MemDependency, BoundOverlap) {
KernelScope kernel_scope;
using namespace analysis;
auto CB = [](int s, int e) { return Bound(new IntImm(s), new IntImm(e)); };
// Sanity check 3 overlap cases.
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(0, 0), CB(0, 0)));
ASSERT_EQ(PartialOverlap, boundOverlap(CB(0, 3), CB(2, 5)));
ASSERT_EQ(NoOverlap, boundOverlap(CB(0, 0), CB(1, 1)));
// Partial overlap works in either order.
ASSERT_EQ(PartialOverlap, boundOverlap(CB(0, 10), CB(7, 14)));
ASSERT_EQ(PartialOverlap, boundOverlap(CB(7, 14), CB(0, 10)));
// Total Overlap works when one bound encloses the other, and returns which.
ASSERT_EQ(Contains, boundOverlap(CB(2, 15), CB(7, 9)));
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(2, 15), CB(0, 16)));
// Total overlap works when the bounds are an identical range, returns
// ContainedOrEqual.
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(2, 15), CB(2, 15)));
// Total overlap when only one end of the bound matches.
ASSERT_EQ(Contains, boundOverlap(CB(2, 15), CB(2, 10)));
ASSERT_EQ(Contains, boundOverlap(CB(2, 15), CB(3, 15)));
ASSERT_EQ(Contains, boundOverlap(CB(0, 10), CB(0, 9)));
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(2, 10), CB(2, 15)));
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(3, 15), CB(2, 15)));
// No overlap when a < b.
ASSERT_EQ(NoOverlap, boundOverlap(CB(0, 2), CB(5, 10)));
ASSERT_EQ(NoOverlap, boundOverlap(CB(2, 2), CB(3, 3)));
ASSERT_EQ(NoOverlap, boundOverlap(CB(100, 120), CB(130, 130)));
// No overlap when a > b.
ASSERT_EQ(NoOverlap, boundOverlap(CB(5, 10), CB(0, 2)));
ASSERT_EQ(NoOverlap, boundOverlap(CB(3, 3), CB(2, 2)));
ASSERT_EQ(NoOverlap, boundOverlap(CB(130, 130), CB(100, 120)));
// No overlap when adjacent.
ASSERT_EQ(NoOverlap, boundOverlap(CB(0, 100), CB(101, 120)));
ASSERT_EQ(NoOverlap, boundOverlap(CB(2, 3), CB(0, 1)));
// Partial overlap when middle bounds match.
ASSERT_EQ(PartialOverlap, boundOverlap(CB(0, 100), CB(100, 120)));
ASSERT_EQ(PartialOverlap, boundOverlap(CB(0, 2), CB(2, 4)));
ASSERT_EQ(PartialOverlap, boundOverlap(CB(100, 120), CB(0, 100)));
ASSERT_EQ(PartialOverlap, boundOverlap(CB(2, 3), CB(1, 2)));
// Total overlap when one bound is single length over one end of the other.
ASSERT_EQ(Contains, boundOverlap(CB(2, 15), CB(15, 15)));
ASSERT_EQ(Contains, boundOverlap(CB(2, 15), CB(2, 2)));
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(2, 2), CB(2, 15)));
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(15, 15), CB(2, 15)));
}
TEST(MemDependency, BoundOverlapSymbolic) {
KernelScope kernel_scope;
VarHandle x("x", kInt);
VarHandle y("y", kInt);
VarHandle z("z", kInt);
VarHandle w("w", kInt);
using namespace analysis;
auto CB = [](ExprHandle s, ExprHandle e) {
return Bound(s.node(), e.node());
};
// Sanity check cases where the start and end is symbolic but the diff is
// constant.
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(x, x), CB(x, x)));
ASSERT_EQ(PartialOverlap, boundOverlap(CB(x, x + 3), CB(x + 2, x + 5)));
ASSERT_EQ(NoOverlap, boundOverlap(CB(x, x), CB(x + 1, x + 1)));
// We can't infer the sign of y, so cannot tell whether adding y is larger or
// smaller than y/2.
ASSERT_EQ(PartialOverlap, boundOverlap(CB(x, x + y), CB(x, x + y / 2)));
// No information about this bound, have to take the most conservative option:
// there may be an overlap.
ASSERT_EQ(PartialOverlap, boundOverlap(CB(x, y), CB(z, w)));
// Math on opaque terms works.
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(x + w, y - z), CB(x + w, y - z)));
// Even requiring simplification.
ASSERT_EQ(ContainedOrEqual, boundOverlap(CB(x - w - w, y), CB(x - w * 2, y)));
}
// Tests the helper function for overlap of multi dimensional indices bounds.
// This uses boundOverlap on each dimension and return the "lowest" kind of
// overlap.
TEST(MemDependency, BoundOverlapMultiDim) {
KernelScope kernel_scope;
using namespace analysis;
auto CB = [](int s, int e) { return Bound(new IntImm(s), new IntImm(e)); };
// Sanity check one dimensional cases.
ASSERT_EQ(ContainedOrEqual, overlaps({CB(0, 0)}, {CB(0, 0)}));
ASSERT_EQ(NoOverlap, overlaps({CB(0, 2)}, {CB(5, 10)}));
ASSERT_EQ(PartialOverlap, overlaps({CB(0, 100)}, {CB(100, 120)}));
// Total overlap in 3 dims.
ASSERT_EQ(
ContainedOrEqual,
overlaps({CB(0, 2), CB(0, 5), CB(0, 4)}, {CB(0, 2), CB(0, 5), CB(0, 4)}));
ASSERT_EQ(
ContainedOrEqual,
overlaps(
{CB(0, 2), CB(0, 5), CB(0, 4)}, {CB(0, 2), CB(0, 5), CB(0, 10)}));
// Total overlap in 2 dims, no overlap in another.
ASSERT_EQ(
NoOverlap,
overlaps(
{CB(0, 2), CB(0, 5), CB(0, 4)}, {CB(0, 2), CB(0, 5), CB(5, 10)}));
// Total overlap in 2 dims, partial overlap in another.
ASSERT_EQ(
PartialOverlap,
overlaps(
{CB(0, 2), CB(0, 5), CB(0, 5)}, {CB(0, 2), CB(0, 5), CB(5, 10)}));
// This case is most important, so verify the overlap in any dim. (dim 2)
ASSERT_EQ(
PartialOverlap,
overlaps({CB(0, 2), CB(0, 5), CB(0, 5)}, {CB(0, 2), CB(2, 6), CB(0, 5)}));
// Dim 1.
ASSERT_EQ(
PartialOverlap,
overlaps({CB(0, 2), CB(0, 5), CB(0, 5)}, {CB(1, 3), CB(0, 5), CB(0, 5)}));
// Total overlap in 1 dim, partial in 2.
ASSERT_EQ(
PartialOverlap,
overlaps(
{CB(0, 2), CB(0, 5), CB(0, 5)}, {CB(2, 6), CB(0, 5), CB(5, 10)}));
// Total overlap, partial overlap, no overlap.
ASSERT_EQ(
NoOverlap,
overlaps(
{CB(0, 2), CB(0, 5), CB(0, 5)}, {CB(2, 6), CB(11, 15), CB(0, 5)}));
// Total overlap (B) in 2 dims, total overlap (A) in another.
ASSERT_EQ(
Contains,
overlaps({CB(0, 2), CB(0, 5), CB(0, 4)}, {CB(0, 2), CB(0, 3), CB(0, 4)}));
// Total overlap (A) in 2 dims, total overlap (B) in another.
ASSERT_EQ(
Contains,
overlaps(
{CB(0, 12), CB(0, 15), CB(0, 4)}, {CB(0, 2), CB(0, 3), CB(0, 14)}));
// Total (B), No Overlap, Total (A).
ASSERT_EQ(
NoOverlap,
overlaps(
{CB(0, 2), CB(0, 5), CB(0, 5)}, {CB(0, 6), CB(11, 15), CB(1, 2)}));
}
// Test the helper we use to subtract bounds: returns the regions(s) of A which
// remain after removing the region of B.
TEST(MemDependency, BoundSubtract) {
KernelScope kernel_scope;
using namespace analysis;
auto CB = [](int s, int e) { return Bound(new IntImm(s), new IntImm(e)); };
auto EQ = [](const IndexBounds& x, const IndexBounds& y) {
return indexBoundsEquals(x, y);
};
// One element subtract.
ASSERT_EQ(subtractBound(CB(0, 0), CB(0, 0)).size(), 0);
ASSERT_EQ(subtractBound(CB(5, 5), CB(5, 5)).size(), 0);
// No Overlap.
ASSERT_TRUE(EQ(subtractBound(CB(5, 5), CB(2, 2)), {CB(5, 5)}));
ASSERT_TRUE(EQ(subtractBound(CB(5, 5), CB(0, 4)), {CB(5, 5)}));
// one side overlap.
ASSERT_TRUE(EQ(subtractBound(CB(1, 5), CB(4, 7)), {CB(1, 3)}));
ASSERT_TRUE(EQ(subtractBound(CB(0, 5), CB(5, 7)), {CB(0, 4)}));
ASSERT_TRUE(EQ(subtractBound(CB(4, 5), CB(1, 4)), {CB(5, 5)}));
ASSERT_TRUE(EQ(subtractBound(CB(1, 5), CB(0, 4)), {CB(5, 5)}));
// both sides overlap.
ASSERT_TRUE(EQ(subtractBound(CB(1, 5), CB(0, 7)), {}));
ASSERT_TRUE(EQ(subtractBound(CB(5, 5), CB(5, 7)), {}));
// internal overlap.
ASSERT_TRUE(EQ(subtractBound(CB(1, 5), CB(2, 3)), {CB(1, 1), CB(4, 5)}));
ASSERT_TRUE(EQ(subtractBound(CB(0, 5), CB(2, 4)), {CB(0, 1), CB(5, 5)}));
}
TEST(MemDependency, BoundSubtractSymbolic) {
KernelScope kernel_scope;
VarHandle x("x", kInt);
VarHandle y("y", kInt);
VarHandle z("z", kInt);
VarHandle w("w", kInt);
using namespace analysis;
auto CB = [](ExprHandle s, ExprHandle e) {
return Bound(s.node(), e.node());
};
auto EQ = [](const IndexBounds& x, const IndexBounds& y) {
return indexBoundsEquals(x, y);
};
// One element subtract.
ASSERT_TRUE(EQ(subtractBound(CB(x, x), CB(x, x)), {}));
ASSERT_TRUE(EQ(subtractBound(CB(x + 1, x + 1), CB(x + 1, x + 1)), {}));
ASSERT_TRUE(EQ(subtractBound(CB(x * 2, x * 2), CB(x * 2, x * 2)), {}));
// Subtract constant range low.
ASSERT_TRUE(
EQ(subtractBound(CB(x, x + 10), CB(x, x + 4)), {CB(x + 5, x + 10)}));
// Subtract constant range high.
ASSERT_TRUE(
EQ(subtractBound(CB(x, x + 10), CB(x + 6, x + 12)), {CB(x, x + 5)}));
// Subtract constant range total overlap.
ASSERT_TRUE(EQ(subtractBound(CB(x, x + 10), CB(x, x + 10)), {}));
ASSERT_TRUE(EQ(subtractBound(CB(x + 2, x + 10), CB(x, x + 12)), {}));
// Subtract constant range internal.
ASSERT_TRUE(
EQ(subtractBound(CB(x, x + 10), CB(x + 3, x + 7)),
{CB(x, x + 2), CB(x + 8, x + 10)}));
// Size is inferable but not constant, only works with a single var.
ASSERT_TRUE(EQ(subtractBound(CB(0, x), CB(0, x * 2)), {}));
ASSERT_TRUE(EQ(subtractBound(CB(0, x * 2), CB(0, x - 1)), {CB(x, x * 2)}));
// Size is not inferable.
ASSERT_TRUE(EQ(subtractBound(CB(x, y), CB(z, w)), {CB(x, y)}));
ASSERT_TRUE(EQ(subtractBound(CB(x, y), CB(x, z)), {CB(x, y)}));
ASSERT_TRUE(EQ(subtractBound(CB(x, y), CB(0, x)), {CB(x, y)}));
ASSERT_TRUE(EQ(subtractBound(CB(x, x), CB(0, 0)), {CB(x, x)}));
}
// Tests the helper function that does subtraction, but for multi dimensional
// indices bounds.
TEST(MemDependency, BoundSubtractMultiDim) {
KernelScope kernel_scope;
using namespace analysis;
auto CB = [](int s, int e) { return Bound(new IntImm(s), new IntImm(e)); };
auto EQ = [](std::vector<IndexBounds> x, std::vector<IndexBounds> y) {
if (x.size() != y.size()) {
return false;
}
for (auto i = 0; i < x.size(); ++i) {
if (!indexBoundsEquals(x[i], y[i])) {
return false;
}
}
return true;
};
// sanity check one dimension.
ASSERT_TRUE(EQ(subtractIndicesBounds({CB(0, 9)}, {CB(0, 9)}), {}));
ASSERT_TRUE(EQ(subtractIndicesBounds({CB(3, 9)}, {CB(0, 12)}), {}));
ASSERT_TRUE(
EQ(subtractIndicesBounds({CB(0, 12)}, {CB(0, 9)}), {{CB(10, 12)}}));
ASSERT_TRUE(
EQ(subtractIndicesBounds({CB(0, 12)}, {CB(3, 12)}), {{CB(0, 2)}}));
ASSERT_TRUE(EQ(
subtractIndicesBounds({CB(0, 9)}, {CB(1, 8)}), {{CB(0, 0)}, {CB(9, 9)}}));
// Multi dim total overlap.
ASSERT_TRUE(EQ(
subtractIndicesBounds({CB(0, 9), CB(0, 2)}, {CB(0, 9), CB(0, 2)}), {}));
ASSERT_TRUE(EQ(
subtractIndicesBounds({CB(0, 9), CB(0, 2)}, {CB(0, 10), CB(0, 20)}), {}));
// Mutli dim one way partial in dim 1.
ASSERT_TRUE(
EQ(subtractIndicesBounds({CB(0, 9), CB(0, 2)}, {CB(0, 3), CB(0, 2)}),
{{CB(4, 9), CB(0, 2)}}));
// Mutli dim one way partial in dim 2.
ASSERT_TRUE(
EQ(subtractIndicesBounds({CB(0, 9), CB(0, 20)}, {CB(0, 9), CB(0, 10)}),
{{CB(0, 9), CB(11, 20)}}));
// Partial overlap in 2 dims.
ASSERT_TRUE(
EQ(subtractIndicesBounds({CB(0, 5), CB(0, 5)}, {CB(2, 8), CB(2, 8)}),
{{CB(0, 1), CB(0, 5)}, {CB(2, 5), CB(0, 1)}}));
// Partial overlap in 3 dims.
ASSERT_TRUE(
EQ(subtractIndicesBounds(
{CB(0, 5), CB(0, 5), CB(0, 5)}, {CB(2, 8), CB(2, 8), CB(2, 8)}),
{{CB(0, 1), CB(0, 5), CB(0, 5)},
{CB(2, 5), CB(0, 1), CB(0, 5)},
{CB(2, 5), CB(2, 5), CB(0, 1)}}));
}
// Tests the multi dimensional subtraction code for bounds that cannot be fully
// materialized.
TEST(MemDependency, BoundSubtractMultiDimSymbolic) {
KernelScope kernel_scope;
VarHandle x("x", kInt);
VarHandle y("y", kInt);
using namespace analysis;
auto CB = [](ExprHandle s, ExprHandle e) {
return Bound(s.node(), e.node());
};
auto EQ = [](std::vector<IndexBounds> x, std::vector<IndexBounds> y) {
if (x.size() != y.size()) {
return false;
}
for (auto i = 0; i < x.size(); ++i) {
if (!indexBoundsEquals(x[i], y[i])) {
return false;
}
}
return true;
};
// Cannot determine overlaps.
ASSERT_TRUE(EQ(subtractIndicesBounds({CB(x, x)}, {CB(0, 0)}), {{CB(x, x)}}));
// Various total Overlaps.
ASSERT_TRUE(EQ(
subtractIndicesBounds({CB(x, x), CB(x, x)}, {CB(x, x), CB(x, x)}), {}));
ASSERT_TRUE(EQ(
subtractIndicesBounds({CB(x, y), CB(x, y)}, {CB(x, y), CB(x, y)}), {}));
ASSERT_TRUE(EQ(
subtractIndicesBounds({CB(x, x), CB(y, y)}, {CB(x, x), CB(y, y)}), {}));
ASSERT_TRUE(EQ(
subtractIndicesBounds({CB(0, x), CB(0, y)}, {CB(0, x), CB(0, y)}), {}));
// one-way overlap in first dim.
ASSERT_TRUE(
EQ(subtractIndicesBounds({CB(0, x), CB(0, y)}, {CB(0, x - 5), CB(0, y)}),
{{CB(x - 4, x), CB(0, y)}}));
// second dim.
ASSERT_TRUE(
EQ(subtractIndicesBounds({CB(0, x), CB(0, y)}, {CB(0, x), CB(5, y)}),
{{CB(0, x), CB(0, 4)}}));
// Internal overlap in first dim.
ASSERT_TRUE(
EQ(subtractIndicesBounds({CB(0, x), CB(0, y)}, {CB(2, x - 5), CB(0, y)}),
{{CB(0, 1), CB(0, y)}, {CB(x - 4, x), CB(0, y)}}));
// second dim.
ASSERT_TRUE(EQ(
subtractIndicesBounds({CB(0, x), CB(0, y)}, {CB(0, x), CB(10, y - 10)}),
{{CB(0, x), CB(0, 9)}, {CB(0, x), CB(y - 9, y)}}));
// Overlap in both dimensions.
ASSERT_TRUE(
EQ(subtractIndicesBounds(
{CB(0, x), CB(0, y)}, {CB(5, x - 5), CB(10, y - 10)}),
{
{CB(0, 4), CB(0, y)},
{CB(x - 4, x), CB(0, y)},
{CB(0, x), CB(0, 9)},
{CB(0, x), CB(y - 9, y)},
}));
}
// Simple check that the analyzer does anything at all...
TEST(MemDependency, MemDependencyCheckerSimple) {
KernelScope kernel_scope;
BufHandle a("A", {1}, kInt);
BufHandle b("B", {1}, kInt);
analysis::MemDependencyChecker analyzer;
/*
* A[0] = 3;
* B[0] = A[0] + 1;
*/
Store* aStore = Store::make(a, {0}, 3, 1);
Store* bStore = Store::make(b, {0}, Add::make(Load::make(a, {0}, 1), 1), 1);
Stmt* stmt = Block::make({aStore, bStore});
stmt->accept(&analyzer);
ASSERT_TRUE(analyzer.dependsDirectly(bStore, aStore));
ASSERT_FALSE(analyzer.dependsIndirectly(aStore, bStore));
// sanity check, but anything that depends directly must depend indirectly.
ASSERT_TRUE(analyzer.dependsIndirectly(bStore, aStore));
}
// Check that there is a difference between direct and indirect dependence.
TEST(MemDependency, MemDependencyCheckerMultiStmt) {
KernelScope kernel_scope;
BufHandle a("A", {1}, kInt);
BufHandle b("B", {1}, kInt);
BufHandle c("C", {1}, kInt);
analysis::MemDependencyChecker analyzer;
/*
* A[0] = 3;
* B[0] = A[0];
* C[0] = B[0] + 1;
*/
Store* aStore = Store::make(a, {0}, 3, 1);
Store* bStore = Store::make(b, {0}, Load::make(a, {0}, 1), 1);
Store* cStore = Store::make(c, {0}, Add::make(Load::make(b, {0}, 1), 1), 1);
Stmt* stmt = Block::make({aStore, bStore, cStore});
stmt->accept(&analyzer);
// C depends on A indirectly.
ASSERT_FALSE(analyzer.dependsDirectly(cStore, aStore));
ASSERT_TRUE(analyzer.dependsIndirectly(cStore, aStore));
// C depends on B directly, which depends on A directly.
ASSERT_TRUE(analyzer.dependsDirectly(cStore, bStore));
ASSERT_TRUE(analyzer.dependsDirectly(bStore, aStore));
// Dependency goes top to bottom only.
ASSERT_FALSE(analyzer.dependsIndirectly(bStore, cStore));
ASSERT_FALSE(analyzer.dependsIndirectly(aStore, bStore));
ASSERT_FALSE(analyzer.dependsIndirectly(aStore, cStore));
}
// Verify that we do filter writes that are totally overlapped by later writes.
TEST(MemDependency, MemDependencyCheckerOverlap) {
KernelScope kernel_scope;
BufHandle a("A", {1}, kInt);
BufHandle b("B", {1}, kInt);
analysis::MemDependencyChecker analyzer;
/*
* A[0] = 3;
* A[0] = 6;
* B[0] = A[0] + 1;
*/
Store* aStore = Store::make(a, {0}, 3, 1);
Store* a2Store = Store::make(a, {0}, 6, 1);
Store* bStore = Store::make(b, {0}, Add::make(Load::make(a, {0}, 1), 1), 1);
Stmt* stmt = Block::make({aStore, a2Store, bStore});
stmt->accept(&analyzer);
// B store depends on second A store but not first since it is completely
// overlapped.
ASSERT_TRUE(analyzer.dependsIndirectly(bStore, a2Store));
ASSERT_FALSE(analyzer.dependsIndirectly(bStore, aStore));
// No dependency between either A store.
ASSERT_FALSE(analyzer.dependsIndirectly(aStore, a2Store));
ASSERT_FALSE(analyzer.dependsIndirectly(a2Store, aStore));
}
// Verify that bounds match loop iterations, and that dependencies progress
// across loop scopes.
TEST(MemDependency, MemDependencyCheckerLoop) {
KernelScope kernel_scope;
BufHandle a("A", {1}, kInt);
BufHandle b("B", {1}, kInt);
VarHandle x("x", kInt);
using namespace analysis;
MemDependencyChecker analyzer;
/*
* for (int x = 0; x < 10; ++x) {
* A[x] = x;
* }
* B[0] = A[0] + 1;
*/
Store* aStore = Store::make(a, {x}, x, 1);
Stmt* loop = For::make(x, 0, 10, aStore);
Store* bStore = Store::make(b, {0}, Add::make(Load::make(a, {4}, 1), 1), 1);
Stmt* stmt = Block::make({loop, bStore});
stmt->accept(&analyzer);
// Same A->B dependency.
ASSERT_TRUE(analyzer.dependsDirectly(bStore, aStore));
// B depends on the loop.
ASSERT_TRUE(analyzer.dependsDirectly(bStore, loop));
// A is in the loop but does not depend on any loop iteration.
ASSERT_FALSE(analyzer.dependsIndirectly(aStore, loop));
auto aStoreAccess = analyzer.accessFor(aStore);
ASSERT_NE(aStoreAccess, nullptr);
// It should have bounds covering the range of x: 0 <= x < 10.
ASSERT_TRUE(indexBoundsEquals(
aStoreAccess->bounds(), {Bound(new IntImm(0), new IntImm(9))}));
}
// Reductions should promote dependencies as well.
TEST(MemDependency, MemDependencyCheckerLoopReduce) {
KernelScope kernel_scope;
BufHandle a("A", {10}, kInt);
BufHandle b("B", {10}, kInt);
VarHandle x("x", kInt);
using namespace analysis;
MemDependencyChecker analyzer;
/*
* A[0] = 0;
* for (int x = 0; x < 10; ++x) {
* A[0] = A[x] + 1;
* }
* B[0] = A[0];
*/
Store* aInit = Store::make(a, {0}, 0, 1);
ExprHandle reduce =
ExprHandle(Sum()(a.node(), ExprHandle(1), {x.node()}, {x.node()}));
Store* aReduce = Store::make(a, {0}, reduce, 1);
Stmt* loop = For::make(x, 0, 10, aReduce);
Store* bStore = Store::make(b, {0}, Load::make(a, {0}, 1), 1);
Stmt* stmt = Block::make({aInit, loop, bStore});
stmt->accept(&analyzer);
// B -> A.
ASSERT_TRUE(analyzer.dependsDirectly(bStore, aReduce));
// B depends indirectly on the intializer of A, since the reduction depends
// on it.
ASSERT_FALSE(analyzer.dependsDirectly(bStore, aInit));
ASSERT_TRUE(analyzer.dependsIndirectly(bStore, aInit));
ASSERT_TRUE(analyzer.dependsDirectly(aReduce, aInit));
// B depends on the loop.
ASSERT_TRUE(analyzer.dependsDirectly(bStore, loop));
// A is in the loop and depends on other iterations.
ASSERT_TRUE(analyzer.dependsDirectly(aReduce, loop));
// The loop contents depend on the initializer too.
ASSERT_TRUE(analyzer.dependsDirectly(loop, aInit));
// Find loads within the reduction:
auto reduceLoads = NodeFinder<Load>::find(reduce.node());
// Pull out the access for the load inside the loop.
for (auto* load : reduceLoads) {
auto loopLoad = analyzer.accessFor(load);
// It should have 10 element long bounds.
ASSERT_TRUE(indexBoundsEquals(
loopLoad->bounds(), {Bound(new IntImm(0), new IntImm(9))}));
}
}
// Lowering a reduction doesn't affect dependency analysis.
TEST(MemDependency, MemDependencyCheckerLoopReduceExpanded) {
KernelScope kernel_scope;
BufHandle a("A", {10}, kInt);
BufHandle b("B", {10}, kInt);
VarHandle x("x", kInt);
using namespace analysis;
MemDependencyChecker analyzer;
/*
* A[0] = 0;
* for (int x = 0; x < 10; ++x) {
* A[0] = A[x] + 1;
* }
* B[0] = A[0];
*/
Store* aInit = Store::make(a, {0}, 0, 1);
ExprHandle aLoad = Load::make(a, {x}, 1);
Store* aReduce = Store::make(a, {0}, Add::make(aLoad, 1));
Stmt* loop = For::make(x, 0, 10, aReduce);
Store* bStore = Store::make(b, {0}, Load::make(a, {0}, 1), 1);
Stmt* stmt = Block::make({aInit, loop, bStore});
stmt->accept(&analyzer);
// B -> A.
ASSERT_TRUE(analyzer.dependsDirectly(bStore, aReduce));
// B depends indirectly on the intializer of A, since the reduction depends
// on it.
ASSERT_FALSE(analyzer.dependsDirectly(bStore, aInit));
ASSERT_TRUE(analyzer.dependsIndirectly(bStore, aInit));
ASSERT_TRUE(analyzer.dependsDirectly(aReduce, aInit));
// B depends on the loop.
ASSERT_TRUE(analyzer.dependsDirectly(bStore, loop));
// A is in the loop and depends on other iterations.
ASSERT_TRUE(analyzer.dependsDirectly(aReduce, loop));
// The loop contents depend on the initializer too.
ASSERT_TRUE(analyzer.dependsDirectly(loop, aInit));
// Pull out the access for the store inside the loop.
auto loopLoad = analyzer.accessFor(aLoad.node());
// It should have 10 element long bounds.
ASSERT_TRUE(indexBoundsEquals(
loopLoad->bounds(), {Bound(new IntImm(0), new IntImm(9))}));
}
// Can determine dependencies of outputs, through to inputs.
TEST(MemDependency, MemDependencyCheckerInputsOutputs) {
KernelScope kernel_scope;
BufHandle a("A", {10}, kInt);
BufHandle b("B", {10}, kInt);
VarHandle x("x", kInt);
// initialize analyzer with inputs and outputs.
analysis::MemDependencyChecker analyzer({a}, {b});
// Here's a Relu.
/*
* for (int x = 0; x < 10; ++x) {
* B[x] = Max(A[x], 0);
* }
*/
ExprHandle aLoad = Load::make(a, {x}, 1);
Store* bStore = Store::make(b, {x}, Max::make(aLoad, 0, true), 1);
Stmt* loop = For::make(x, 0, 10, bStore);
Stmt* stmt = Block::make({loop});
stmt->accept(&analyzer);
// Output depends indirectly on input.
ASSERT_TRUE(analyzer.dependsIndirectly(b.node(), a.node()));
// aLoad depends directly on the input A.
ASSERT_TRUE(analyzer.dependsDirectly(aLoad.node(), a.node()));
// bStore therefore depends directly on the input A.
ASSERT_TRUE(analyzer.dependsDirectly(bStore, a.node()));
// The output depends directly on the store.
ASSERT_TRUE(analyzer.dependsDirectly(b.node(), bStore));
// Check AccessInfo based overloads.
auto input = analyzer.input(a.node());
auto output = analyzer.output(b.node());
// Output depends indirectly on input.
ASSERT_TRUE(analyzer.dependsIndirectly(output, input));
// Not directly.
ASSERT_FALSE(analyzer.dependsDirectly(output, input));
// Not in reverse order.
ASSERT_FALSE(analyzer.dependsIndirectly(input, output));
// output -> bStore -> bLoad -> input.
auto storeAccess = analyzer.accessFor(bStore);
auto loadAccess = analyzer.accessFor(aLoad.node());
ASSERT_TRUE(analyzer.dependsDirectly(output, storeAccess));
ASSERT_TRUE(analyzer.dependsDirectly(loadAccess, input));
}
// Can tell if an output does not depend on an input.
TEST(MemDependency, MemDependencyCheckerOutputDoesntDepend) {
KernelScope kernel_scope;
BufHandle a("A", {10}, kInt);
BufHandle b("B", {10}, kInt);
VarHandle x("x", kInt);
// initialize analyzer with inputs and outputs.
analysis::MemDependencyChecker analyzer({a}, {b});
// Here's a dumb Relu.
/*
* for (int x = 0; x < 10; ++x) {
* B[x] = Max(x, 0);
* }
*/
Store* bStore = Store::make(b, {x}, Max::make(x, 0, true), 1);
Stmt* loop = For::make(x, 0, 10, bStore);
Stmt* stmt = Block::make({loop});
stmt->accept(&analyzer);
// Output does not depend indirectly on input.
ASSERT_FALSE(analyzer.dependsIndirectly(b.node(), a.node()));
// The output still depends directly on the store.
ASSERT_TRUE(analyzer.dependsDirectly(b.node(), bStore));
// Check AccessInfo based overloads.
auto input = analyzer.input(a.node());
auto output = analyzer.output(b.node());
// Output does not depend indirectly on input.
ASSERT_FALSE(analyzer.dependsIndirectly(output, input));
}
// Verify different loop extents produce accesses with different bounds, and
// that later accesses find dependencies that overlap their entire bound range.
TEST(MemDependency, MemDependencyCheckerLoopBounds) {
KernelScope kernel_scope;
BufHandle a("A", {10}, kInt);
BufHandle b("B", {10}, kInt);
BufHandle c("C", {10}, kInt);
VarHandle x("x", kInt);
using namespace analysis;
MemDependencyChecker analyzer({a}, {c});
// This enables using the execution order of the loops to determine if some
// loops are self dependent or not.
analyzer.allowLoopExecutionOrderAnalysis();
/*
* for (int x = 1; x < 10; ++x) {
* B[x] = A[x];
* }
* for (int x = 1; x < 9; ++x) {
* B[x] = B[x] * 2;
* }
* for (int x = 3; x < 4; ++x) {
* C[x] = A[x];
* }
* for (int x = 0; x < 10; ++x) {
* C[x] = B[x];
* }
*/
std::vector<Stmt*> stmts(
{For::make(x, 1, 10, Store::make(b, {x}, Load::make(a, {x}, 1), 1)),
For::make(
x,
1,
9,
Store::make(b, {x}, Mul::make(Load::make(b, {x}, 1), 2), 1)),
For::make(x, 3, 4, Store::make(c, {x}, Load::make(a, {x}, 1), 1)),
For::make(x, 0, 10, Store::make(c, {x}, Load::make(b, {x}, 1), 1))});
Stmt* stmt = Block::make(stmts);
stmt->accept(&analyzer);
auto input = analyzer.input(a.node());
auto output = analyzer.output(c.node());
// sanity check Output -> Input.
ASSERT_TRUE(analyzer.dependsIndirectly(output, input));
// Check the For loop dependencies:
// Last write to C depends on both writes to B since they contain the last
// write to at least one element.
ASSERT_TRUE(analyzer.dependsIndirectly(stmts[3], stmts[1]));
ASSERT_TRUE(analyzer.dependsIndirectly(stmts[3], stmts[0]));
// The last write to C does not depend on the other write to C.
ASSERT_FALSE(analyzer.dependsIndirectly(stmts[3], stmts[2]));
auto CB = [](int s, int e) { return Bound(new IntImm(s), new IntImm(e)); };
auto EQ = [](const IndexBounds& x, const IndexBounds& y) {
return indexBoundsEquals(x, y);
};
/* 0. Input: A[(0, 9)] - dependents: 1 5
* 1. Load: A[(1, 9)] - depends on: 0 - dependents: 2
* 2. Store: B[(1, 9)] - depends on: 1 - dependents: 3 7
* 3. Load: B[(1, 8)] - depends on: 2 - dependents: 4
* 4. Store: B[(1, 8)] - depends on: 3 - dependents: 7
* 5. Load: A[(3, 3)] - depends on: 0 - dependents: 6
* 6. Store: C[(3, 3)] - depends on: 5
* 7. Load: B[(0, 9)] - depends on: 2 4 - dependents: 8
* 8. Store: C[(0, 9)] - depends on: 7 - dependents: 9
* 9. Output: C[(0, 9)] - depends on: 8
*/
// Now let's look at the bounds of each access.
// There are 9 accesses in this Stmt, so this is exhaustive, we wont do this
// much.
auto history = analyzer.getHistory();
ASSERT_EQ(history.size(), 10);
const Var* aVar = a.node()->base_handle();
const Var* bVar = b.node()->base_handle();
const Var* cVar = c.node()->base_handle();
// The first access is the input A.
ASSERT_EQ(history[0]->type(), AccessType::Input);
ASSERT_EQ(history[0]->var(), aVar);
// It has the bounds of the producing Input.
ASSERT_TRUE(EQ(history[0]->bounds(), {CB(0, 9)}));
// sanity check the input we retrieved earlier matches.
ASSERT_EQ(history[0], input);
// The second access is the load of A in the first loop.
ASSERT_EQ(history[1]->type(), AccessType::Load);
ASSERT_EQ(history[1]->var(), aVar);
// It has the bounds of the loop, i.e. start == 1.
ASSERT_TRUE(EQ(history[1]->bounds(), {CB(1, 9)}));
// It reads from A, so it should have a dependency on the last write to this
// range - with is the input.
ASSERT_EQ(history[1]->dependencies().size(), 1);
ASSERT_TRUE(history[1]->hasDependency(history[0]));
// The third access is the store into B in the first loop.
ASSERT_EQ(history[2]->type(), AccessType::Store);
ASSERT_EQ(history[2]->var(), bVar);
// It also has the bounds of the loop, i.e. start == 1.
ASSERT_TRUE(EQ(history[2]->bounds(), {CB(1, 9)}));
// The previous load is in its RHS, so it depends on it.
ASSERT_EQ(history[2]->dependencies().size(), 1);
ASSERT_TRUE(history[2]->hasDependency(history[1]));
// The third access is the load from B in the second loop.
ASSERT_EQ(history[3]->type(), AccessType::Load);
ASSERT_EQ(history[3]->var(), bVar);
// It has the bounds of the second loop, i.e. >= 1 < 9.
ASSERT_TRUE(EQ(history[3]->bounds(), {CB(1, 8)}));
// It reads from B in a smaller range, so should depend on the previous
// store.
ASSERT_EQ(history[3]->dependencies().size(), 1);
ASSERT_TRUE(history[3]->hasDependency(history[2]));
// The fourth: the store to B in the second loop.
ASSERT_EQ(history[4]->type(), AccessType::Store);
ASSERT_EQ(history[4]->var(), bVar);
// It also has the bounds of the second loop.
ASSERT_TRUE(EQ(history[4]->bounds(), {CB(1, 8)}));
// The previous load is in its RHS, so it depends on it as before.
ASSERT_EQ(history[4]->dependencies().size(), 1);
ASSERT_TRUE(history[4]->hasDependency(history[3]));
// The fifth access is the load is from the 3rd loop, and skips previous B
// accesses.
ASSERT_EQ(history[5]->type(), AccessType::Load);
ASSERT_EQ(history[5]->var(), aVar);
// It has the bounds of the third loop: >= 3 < 4.
ASSERT_TRUE(EQ(history[5]->bounds(), {CB(3, 3)}));
// It depends on the last thing to write to A, which is the A input.
ASSERT_EQ(history[5]->dependencies().size(), 1);
ASSERT_TRUE(history[5]->hasDependency(history[0]));
// Sixth: the store into the output C.
ASSERT_EQ(history[6]->type(), AccessType::Store);
ASSERT_EQ(history[6]->var(), cVar);
// It also has the bounds of the third loop.
ASSERT_TRUE(EQ(history[6]->bounds(), {CB(3, 3)}));
// The previous load is in its RHS, so it depends on it as always.
ASSERT_EQ(history[6]->dependencies().size(), 1);
ASSERT_TRUE(history[6]->hasDependency(history[5]));
// The seventh access is the load of B in the fourth loop.
ASSERT_EQ(history[7]->type(), AccessType::Load);
ASSERT_EQ(history[7]->var(), bVar);
// It has the bounds of the final loop, >= 0 < 10
ASSERT_TRUE(EQ(history[7]->bounds(), {CB(0, 9)}));
// The bounds of this read are larger than the bounds of the previous write,
// so it depends on both previous Stores to B.
ASSERT_EQ(history[7]->dependencies().size(), 2);
ASSERT_TRUE(history[7]->hasDependency(history[2]));
ASSERT_TRUE(history[7]->hasDependency(history[4]));
// Eight: the final store into the output C.
ASSERT_EQ(history[8]->type(), AccessType::Store);
ASSERT_EQ(history[8]->var(), cVar);
// It also has the bounds of the final loop.
ASSERT_TRUE(EQ(history[8]->bounds(), {CB(0, 9)}));
// The previous load is in its RHS, so it depends on it as always.
ASSERT_EQ(history[8]->dependencies().size(), 1);
ASSERT_TRUE(history[8]->hasDependency(history[7]));
// The last access represents the output Buf.
ASSERT_EQ(history[9]->type(), AccessType::Output);
ASSERT_EQ(history[9]->var(), cVar);
// It has the bounds of the output Buf.
ASSERT_TRUE(EQ(history[9]->bounds(), {CB(0, 9)}));
// sanity check the input we retrieved earlier matches.
ASSERT_EQ(history[9], output);
// It depends on the last write to C only.
ASSERT_EQ(history[9]->dependencies().size(), 1);
ASSERT_TRUE(history[9]->hasDependency(history[8]));
}
// Verify that we can still infer bounds when the loop var is offset.
TEST(MemDependency, MemDependencyCheckerLoopBoundsIndexShift) {
KernelScope kernel_scope;
BufHandle a("A", {10}, kInt);
BufHandle b("B", {10}, kInt);
VarHandle x("x", kInt);
using namespace analysis;
MemDependencyChecker analyzer({a}, {b});
// This enables using the execution order of the loops to determine if some
// loops are self dependent or not.
analyzer.allowLoopExecutionOrderAnalysis();
/*
* for (int x = 1; x < 10; x++) {
* A[x] = A[x - 1];
* }
* for (int x = 0; x < 9; x++) {
* A[x] = A[x + 1];
* }
* for (int x = 0; x < 9; x++) {
* A[9 - x] = A[8 - x];
* }
* for (int x = 0; x < 10; x++) {
* A[x] = A[9 - x];
* }
* for (int x = 0; x < 10; x++) {
* B[x] = A[x];
* }
*/
Stmt* stmt = Block::make(
{For::make(x, 1, 10, Store::make(a, {x}, Load::make(a, {x - 1}, 1), 1)),
For::make(x, 0, 9, Store::make(a, {x}, Load::make(a, {x + 1}, 1), 1)),
For::make(
x,
0,
9,
Store::make(
a,
{ExprHandle(9) - x},
Load::make(a, {ExprHandle(8) - x}, 1),
1)),
For::make(
x,
0,
10,
Store::make(a, {x}, Load::make(a, {ExprHandle(9) - x}, 1), 1)),
For::make(x, 0, 10, Store::make(b, {x}, Load::make(a, {x}, 1), 1))});
stmt->accept(&analyzer);
// Sanity check output depends on Input.
ASSERT_TRUE(analyzer.dependsIndirectly(b.node(), a.node()));
auto CB = [](int s, int e) { return Bound(new IntImm(s), new IntImm(e)); };
auto EQ = [](const IndexBounds& x, const IndexBounds& y) {
return indexBoundsEquals(x, y);
};
/* 0. Input: A[(0, 9)] - dependents: 1
* 1. Load: A[(0, 8)] - depends on: 0 2 - dependents: 2
* 2. Store: A[(1, 9)] - depends on: 1 - dependents: 1 3
* 3. Load: A[(1, 9)] - depends on: 2 - dependents: 4
* 4. Store: A[(0, 8)] - depends on: 3 - dependents: 5 7
* 5. Load: A[(0, 8)] - depends on: 4 - dependents: 6
* 6. Store: A[(1, 9)] - depends on: 5 - dependents: 7
* 7. Load: A[(0, 9)] - depends on: 4 6 8 - dependents: 8
* 8. Store: A[(0, 9)] - depends on: 7 - dependents: 7 9
* 9. Load: A[(0, 9)] - depends on: 8 - dependents: 10
* 10. Store: B[(0, 9)] - depends on: 9 - dependents: 11
* 11. Output: B[(0, 9)] - depends on: 10
*/
// Now let's look at the bounds of each access.
auto history = analyzer.getHistory();
ASSERT_EQ(history.size(), 12);
const Var* aVar = a.node()->base_handle();
const Var* bVar = b.node()->base_handle();