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The product of two chrec's can always be represented as a chrec.
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git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@141066 91177308-0d34-0410-b5e6-96231b3b80d8
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@nlewycky
nlewycky committed Oct 4, 2011
1 parent 6744a17 commit e97728e
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Showing 3 changed files with 239 additions and 39 deletions.
8 changes: 8 additions & 0 deletions include/llvm/Analysis/ScalarEvolution.h
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Original file line number Diff line number Diff line change
Expand Up @@ -588,6 +588,14 @@ namespace llvm {
Ops.push_back(RHS);
return getMulExpr(Ops, Flags);
}
const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
SmallVector<const SCEV *, 3> Ops;
Ops.push_back(Op0);
Ops.push_back(Op1);
Ops.push_back(Op2);
return getMulExpr(Ops, Flags);
}
const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
const Loop *L, SCEV::NoWrapFlags Flags);
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104 changes: 72 additions & 32 deletions lib/Analysis/ScalarEvolution.cpp
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Expand Up @@ -1812,6 +1812,38 @@ const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
return S;
}

static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
uint64_t k = i*j;
if (j > 1 && k / j != i) Overflow = true;
return k;
}

/// Compute the result of "n choose k", the binomial coefficient. If an
/// intermediate computation overflows, Overflow will be set and the return will
/// be garbage. Overflow is not cleared on absense of overflow.
static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
// We use the multiplicative formula:
// n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
// At each iteration, we take the n-th term of the numeral and divide by the
// (k-n)th term of the denominator. This division will always produce an
// integral result, and helps reduce the chance of overflow in the
// intermediate computations. However, we can still overflow even when the
// final result would fit.

if (n == 0 || n == k) return 1;
if (k > n) return 0;

if (k > n/2)
k = n-k;

uint64_t r = 1;
for (uint64_t i = 1; i <= k; ++i) {
r = umul_ov(r, n-(i-1), Overflow);
r /= i;
}
return r;
}

/// getMulExpr - Get a canonical multiply expression, or something simpler if
/// possible.
const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
Expand Down Expand Up @@ -1987,53 +2019,61 @@ const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
for (unsigned OtherIdx = Idx+1;
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
++OtherIdx) {
bool Retry = false;
if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
// {A,+,B}<L> * {C,+,D}<L> --> {A*C,+,A*D + B*C + B*D,+,2*B*D}<L>
//
// {A,+,B} * {C,+,D} = A+It*B * C+It*D = A*C + (A*D + B*C)*It + B*D*It^2
// Given an equation of the form x + y*It + z*It^2 (above), we want to
// express it in terms of {X,+,Y,+,Z}.
// {X,+,Y,+,Z} = X + Y*It + Z*(It^2 - It)/2.
// Rearranging, X = x, Y = y+z, Z = 2z.
// {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
// = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
// choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
// ]]],+,...up to x=2n}.
// Note that the arguments to choose() are always integers with values
// known at compile time, never SCEV objects.
//
// x = A*C, y = (A*D + B*C), z = B*D.
// Therefore X = A*C, Y = A*D + B*C + B*D and Z = 2*B*D.
// The implementation avoids pointless extra computations when the two
// addrec's are of different length (mathematically, it's equivalent to
// an infinite stream of zeros on the right).
bool OpsModified = false;
for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
++OtherIdx)
if (const SCEVAddRecExpr *OtherAddRec =
dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
if (OtherAddRec->getLoop() == AddRecLoop) {
const SCEV *A = AddRec->getStart();
const SCEV *B = AddRec->getStepRecurrence(*this);
const SCEV *C = OtherAddRec->getStart();
const SCEV *D = OtherAddRec->getStepRecurrence(*this);
const SCEV *NewStart = getMulExpr(A, C);
const SCEV *BD = getMulExpr(B, D);
const SCEV *NewStep = getAddExpr(getMulExpr(A, D),
getMulExpr(B, C), BD);
const SCEV *NewSecondOrderStep =
getMulExpr(BD, getConstant(BD->getType(), 2));

// This can happen when AddRec or OtherAddRec have >3 operands.
// TODO: support these add-recs.
if (isLoopInvariant(NewStart, AddRecLoop) &&
isLoopInvariant(NewStep, AddRecLoop) &&
isLoopInvariant(NewSecondOrderStep, AddRecLoop)) {
SmallVector<const SCEV *, 3> AddRecOps;
AddRecOps.push_back(NewStart);
AddRecOps.push_back(NewStep);
AddRecOps.push_back(NewSecondOrderStep);
bool Overflow = false;
Type *Ty = AddRec->getType();
bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
SmallVector<const SCEV*, 7> AddRecOps;
for (int x = 0, xe = AddRec->getNumOperands() +
OtherAddRec->getNumOperands() - 1;
x != xe && !Overflow; ++x) {
const SCEV *Term = getConstant(Ty, 0);
for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
z < ze && !Overflow; ++z) {
uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
uint64_t Coeff;
if (LargerThan64Bits)
Coeff = umul_ov(Coeff1, Coeff2, Overflow);
else
Coeff = Coeff1*Coeff2;
const SCEV *CoeffTerm = getConstant(Ty, Coeff);
const SCEV *Term1 = AddRec->getOperand(y-z);
const SCEV *Term2 = OtherAddRec->getOperand(z);
Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
}
}
AddRecOps.push_back(Term);
}
if (!Overflow) {
const SCEV *NewAddRec = getAddRecExpr(AddRecOps,
AddRec->getLoop(),
SCEV::FlagAnyWrap);
if (Ops.size() == 2) return NewAddRec;
Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
Retry = true;
OpsModified = true;
}
}
if (Retry)
if (OpsModified)
return getMulExpr(Ops);
}
}
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166 changes: 159 additions & 7 deletions unittests/Analysis/ScalarEvolutionTest.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -8,20 +8,35 @@
//===----------------------------------------------------------------------===//

#include <llvm/Analysis/ScalarEvolutionExpressions.h>
#include <llvm/Analysis/LoopInfo.h>
#include <llvm/GlobalVariable.h>
#include <llvm/Constants.h>
#include <llvm/LLVMContext.h>
#include <llvm/Module.h>
#include <llvm/PassManager.h>
#include <llvm/ADT/SmallVector.h>
#include "gtest/gtest.h"

namespace llvm {
namespace {

TEST(ScalarEvolutionsTest, SCEVUnknownRAUW) {
// We use this fixture to ensure that we clean up ScalarEvolution before
// deleting the PassManager.
class ScalarEvolutionsTest : public testing::Test {
protected:
ScalarEvolutionsTest() : M("", Context), SE(*new ScalarEvolution) {}
~ScalarEvolutionsTest() {
// Manually clean up, since we allocated new SCEV objects after the
// pass was finished.
SE.releaseMemory();
}
LLVMContext Context;
Module M("world", Context);
Module M;
PassManager PM;
ScalarEvolution &SE;
};

TEST_F(ScalarEvolutionsTest, SCEVUnknownRAUW) {
FunctionType *FTy = FunctionType::get(Type::getVoidTy(Context),
std::vector<Type *>(), false);
Function *F = cast<Function>(M.getOrInsertFunction("f", FTy));
Expand All @@ -35,8 +50,6 @@ TEST(ScalarEvolutionsTest, SCEVUnknownRAUW) {
Value *V2 = new GlobalVariable(M, Ty, false, GlobalValue::ExternalLinkage, Init, "V2");

// Create a ScalarEvolution and "run" it so that it gets initialized.
PassManager PM;
ScalarEvolution &SE = *new ScalarEvolution();
PM.add(&SE);
PM.run(M);

Expand Down Expand Up @@ -72,10 +85,149 @@ TEST(ScalarEvolutionsTest, SCEVUnknownRAUW) {
EXPECT_EQ(cast<SCEVUnknown>(M0->getOperand(1))->getValue(), V0);
EXPECT_EQ(cast<SCEVUnknown>(M1->getOperand(1))->getValue(), V0);
EXPECT_EQ(cast<SCEVUnknown>(M2->getOperand(1))->getValue(), V0);
}

TEST_F(ScalarEvolutionsTest, SCEVMultiplyAddRecs) {
Type *Ty = Type::getInt32Ty(Context);
SmallVector<Type *, 10> Types;
Types.append(10, Ty);
FunctionType *FTy = FunctionType::get(Type::getVoidTy(Context), Types, false);
Function *F = cast<Function>(M.getOrInsertFunction("f", FTy));
BasicBlock *BB = BasicBlock::Create(Context, "entry", F);
ReturnInst::Create(Context, 0, BB);

// Create a ScalarEvolution and "run" it so that it gets initialized.
PM.add(&SE);
PM.run(M);

// It's possible to produce an empty loop through the default constructor,
// but you can't add any blocks to it without a LoopInfo pass.
Loop L;
const_cast<std::vector<BasicBlock*>&>(L.getBlocks()).push_back(BB);

Function::arg_iterator AI = F->arg_begin();
SmallVector<const SCEV *, 5> A;
A.push_back(SE.getSCEV(&*AI++));
A.push_back(SE.getSCEV(&*AI++));
A.push_back(SE.getSCEV(&*AI++));
A.push_back(SE.getSCEV(&*AI++));
A.push_back(SE.getSCEV(&*AI++));
const SCEV *A_rec = SE.getAddRecExpr(A, &L, SCEV::FlagAnyWrap);

SmallVector<const SCEV *, 5> B;
B.push_back(SE.getSCEV(&*AI++));
B.push_back(SE.getSCEV(&*AI++));
B.push_back(SE.getSCEV(&*AI++));
B.push_back(SE.getSCEV(&*AI++));
B.push_back(SE.getSCEV(&*AI++));
const SCEV *B_rec = SE.getAddRecExpr(B, &L, SCEV::FlagAnyWrap);

/* Spot check that we perform this transformation:
{A0,+,A1,+,A2,+,A3,+,A4} * {B0,+,B1,+,B2,+,B3,+,B4} =
{A0*B0,+,
A1*B0 + A0*B1 + A1*B1,+,
A2*B0 + 2A1*B1 + A0*B2 + 2A2*B1 + 2A1*B2 + A2*B2,+,
A3*B0 + 3A2*B1 + 3A1*B2 + A0*B3 + 3A3*B1 + 6A2*B2 + 3A1*B3 + 3A3*B2 +
3A2*B3 + A3*B3,+,
A4*B0 + 4A3*B1 + 6A2*B2 + 4A1*B3 + A0*B4 + 4A4*B1 + 12A3*B2 + 12A2*B3 +
4A1*B4 + 6A4*B2 + 12A3*B3 + 6A2*B4 + 4A4*B3 + 4A3*B4 + A4*B4,+,
5A4*B1 + 10A3*B2 + 10A2*B3 + 5A1*B4 + 20A4*B2 + 30A3*B3 + 20A2*B4 +
30A4*B3 + 30A3*B4 + 20A4*B4,+,
15A4*B2 + 20A3*B3 + 15A2*B4 + 60A4*B3 + 60A3*B4 + 90A4*B4,+,
35A4*B3 + 35A3*B4 + 140A4*B4,+,
70A4*B4}
*/

const SCEVAddRecExpr *Product =
dyn_cast<SCEVAddRecExpr>(SE.getMulExpr(A_rec, B_rec));
ASSERT_TRUE(Product);
ASSERT_EQ(Product->getNumOperands(), 9u);

SmallVector<const SCEV *, 16> Sum;
Sum.push_back(SE.getMulExpr(A[0], B[0]));
EXPECT_EQ(Product->getOperand(0), SE.getAddExpr(Sum));
Sum.clear();

// SCEV produces different an equal but different expression for these.
// Re-enable when PR11052 is fixed.
#if 0
Sum.push_back(SE.getMulExpr(A[1], B[0]));
Sum.push_back(SE.getMulExpr(A[0], B[1]));
Sum.push_back(SE.getMulExpr(A[1], B[1]));
EXPECT_EQ(Product->getOperand(1), SE.getAddExpr(Sum));
Sum.clear();

Sum.push_back(SE.getMulExpr(A[2], B[0]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 2), A[1], B[1]));
Sum.push_back(SE.getMulExpr(A[0], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 2), A[2], B[1]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 2), A[1], B[2]));
Sum.push_back(SE.getMulExpr(A[2], B[2]));
EXPECT_EQ(Product->getOperand(2), SE.getAddExpr(Sum));
Sum.clear();

Sum.push_back(SE.getMulExpr(A[3], B[0]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[2], B[1]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[1], B[2]));
Sum.push_back(SE.getMulExpr(A[0], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[3], B[1]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 6), A[2], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[1], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[3], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[2], B[3]));
Sum.push_back(SE.getMulExpr(A[3], B[3]));
EXPECT_EQ(Product->getOperand(3), SE.getAddExpr(Sum));
Sum.clear();

Sum.push_back(SE.getMulExpr(A[4], B[0]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[3], B[1]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 6), A[2], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[1], B[3]));
Sum.push_back(SE.getMulExpr(A[0], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[4], B[1]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 12), A[3], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 12), A[2], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[1], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 6), A[4], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 12), A[3], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 6), A[2], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[4], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[3], B[4]));
Sum.push_back(SE.getMulExpr(A[4], B[4]));
EXPECT_EQ(Product->getOperand(4), SE.getAddExpr(Sum));
Sum.clear();

Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 5), A[4], B[1]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 10), A[3], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 10), A[2], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 5), A[1], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 20), A[4], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 30), A[3], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 20), A[2], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 30), A[4], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 30), A[3], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 20), A[4], B[4]));
EXPECT_EQ(Product->getOperand(5), SE.getAddExpr(Sum));
Sum.clear();

Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 15), A[4], B[2]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 20), A[3], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 15), A[2], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 60), A[4], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 60), A[3], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 90), A[4], B[4]));
EXPECT_EQ(Product->getOperand(6), SE.getAddExpr(Sum));
Sum.clear();

Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 35), A[4], B[3]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 35), A[3], B[4]));
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 140), A[4], B[4]));
EXPECT_EQ(Product->getOperand(7), SE.getAddExpr(Sum));
Sum.clear();
#endif

// Manually clean up, since we allocated new SCEV objects after the
// pass was finished.
SE.releaseMemory();
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 70), A[4], B[4]));
EXPECT_EQ(Product->getOperand(8), SE.getAddExpr(Sum));
}

} // end anonymous namespace
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