mirror of
https://github.com/c64scene-ar/llvm-6502.git
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The product of two chrec's can always be represented as a chrec.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@141066 91177308-0d34-0410-b5e6-96231b3b80d8
This commit is contained in:
Nick Lewycky
parent
6744a17dcf
commit
e97728ecf8
@ -588,6 +588,14 @@ namespace llvm {
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Ops.push_back(RHS);
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return getMulExpr(Ops, Flags);
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}
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const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
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SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
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SmallVector<const SCEV *, 3> Ops;
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Ops.push_back(Op0);
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Ops.push_back(Op1);
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Ops.push_back(Op2);
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return getMulExpr(Ops, Flags);
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}
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const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
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const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
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const Loop *L, SCEV::NoWrapFlags Flags);
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@ -1812,6 +1812,38 @@ const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
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return S;
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}
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static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
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uint64_t k = i*j;
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if (j > 1 && k / j != i) Overflow = true;
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return k;
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}
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/// Compute the result of "n choose k", the binomial coefficient. If an
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/// intermediate computation overflows, Overflow will be set and the return will
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/// be garbage. Overflow is not cleared on absense of overflow.
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static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
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// We use the multiplicative formula:
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// n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
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// At each iteration, we take the n-th term of the numeral and divide by the
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// (k-n)th term of the denominator. This division will always produce an
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// integral result, and helps reduce the chance of overflow in the
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// intermediate computations. However, we can still overflow even when the
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// final result would fit.
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if (n == 0 || n == k) return 1;
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if (k > n) return 0;
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if (k > n/2)
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k = n-k;
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uint64_t r = 1;
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for (uint64_t i = 1; i <= k; ++i) {
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r = umul_ov(r, n-(i-1), Overflow);
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r /= i;
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}
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return r;
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}
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/// getMulExpr - Get a canonical multiply expression, or something simpler if
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/// possible.
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const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
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@ -1987,53 +2019,61 @@ const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
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for (unsigned OtherIdx = Idx+1;
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OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
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++OtherIdx) {
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bool Retry = false;
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if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
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// {A,+,B}<L> * {C,+,D}<L> --> {A*C,+,A*D + B*C + B*D,+,2*B*D}<L>
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// {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
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// = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
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// choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
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// ]]],+,...up to x=2n}.
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// Note that the arguments to choose() are always integers with values
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// known at compile time, never SCEV objects.
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//
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// {A,+,B} * {C,+,D} = A+It*B * C+It*D = A*C + (A*D + B*C)*It + B*D*It^2
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// Given an equation of the form x + y*It + z*It^2 (above), we want to
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// express it in terms of {X,+,Y,+,Z}.
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// {X,+,Y,+,Z} = X + Y*It + Z*(It^2 - It)/2.
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// Rearranging, X = x, Y = y+z, Z = 2z.
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//
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// x = A*C, y = (A*D + B*C), z = B*D.
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// Therefore X = A*C, Y = A*D + B*C + B*D and Z = 2*B*D.
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// The implementation avoids pointless extra computations when the two
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// addrec's are of different length (mathematically, it's equivalent to
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// an infinite stream of zeros on the right).
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bool OpsModified = false;
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for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
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++OtherIdx)
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if (const SCEVAddRecExpr *OtherAddRec =
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dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
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if (OtherAddRec->getLoop() == AddRecLoop) {
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const SCEV *A = AddRec->getStart();
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const SCEV *B = AddRec->getStepRecurrence(*this);
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const SCEV *C = OtherAddRec->getStart();
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const SCEV *D = OtherAddRec->getStepRecurrence(*this);
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const SCEV *NewStart = getMulExpr(A, C);
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const SCEV *BD = getMulExpr(B, D);
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const SCEV *NewStep = getAddExpr(getMulExpr(A, D),
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getMulExpr(B, C), BD);
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const SCEV *NewSecondOrderStep =
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getMulExpr(BD, getConstant(BD->getType(), 2));
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// This can happen when AddRec or OtherAddRec have >3 operands.
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// TODO: support these add-recs.
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if (isLoopInvariant(NewStart, AddRecLoop) &&
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isLoopInvariant(NewStep, AddRecLoop) &&
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isLoopInvariant(NewSecondOrderStep, AddRecLoop)) {
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SmallVector<const SCEV *, 3> AddRecOps;
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AddRecOps.push_back(NewStart);
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AddRecOps.push_back(NewStep);
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AddRecOps.push_back(NewSecondOrderStep);
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bool Overflow = false;
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Type *Ty = AddRec->getType();
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bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
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SmallVector<const SCEV*, 7> AddRecOps;
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for (int x = 0, xe = AddRec->getNumOperands() +
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OtherAddRec->getNumOperands() - 1;
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x != xe && !Overflow; ++x) {
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const SCEV *Term = getConstant(Ty, 0);
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for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
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uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
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for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
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ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
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z < ze && !Overflow; ++z) {
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uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
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uint64_t Coeff;
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if (LargerThan64Bits)
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Coeff = umul_ov(Coeff1, Coeff2, Overflow);
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else
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Coeff = Coeff1*Coeff2;
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const SCEV *CoeffTerm = getConstant(Ty, Coeff);
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const SCEV *Term1 = AddRec->getOperand(y-z);
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const SCEV *Term2 = OtherAddRec->getOperand(z);
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Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
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}
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}
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AddRecOps.push_back(Term);
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}
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if (!Overflow) {
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const SCEV *NewAddRec = getAddRecExpr(AddRecOps,
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AddRec->getLoop(),
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SCEV::FlagAnyWrap);
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if (Ops.size() == 2) return NewAddRec;
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Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
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Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
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Retry = true;
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OpsModified = true;
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}
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}
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if (Retry)
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if (OpsModified)
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return getMulExpr(Ops);
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}
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}
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@ -8,20 +8,35 @@
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//===----------------------------------------------------------------------===//
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#include <llvm/Analysis/ScalarEvolutionExpressions.h>
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#include <llvm/Analysis/LoopInfo.h>
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#include <llvm/GlobalVariable.h>
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#include <llvm/Constants.h>
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#include <llvm/LLVMContext.h>
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#include <llvm/Module.h>
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#include <llvm/PassManager.h>
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#include <llvm/ADT/SmallVector.h>
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#include "gtest/gtest.h"
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namespace llvm {
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namespace {
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TEST(ScalarEvolutionsTest, SCEVUnknownRAUW) {
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// We use this fixture to ensure that we clean up ScalarEvolution before
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// deleting the PassManager.
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class ScalarEvolutionsTest : public testing::Test {
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protected:
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ScalarEvolutionsTest() : M("", Context), SE(*new ScalarEvolution) {}
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~ScalarEvolutionsTest() {
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// Manually clean up, since we allocated new SCEV objects after the
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// pass was finished.
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SE.releaseMemory();
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}
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LLVMContext Context;
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Module M("world", Context);
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Module M;
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PassManager PM;
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ScalarEvolution &SE;
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};
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TEST_F(ScalarEvolutionsTest, SCEVUnknownRAUW) {
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FunctionType *FTy = FunctionType::get(Type::getVoidTy(Context),
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std::vector<Type *>(), false);
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Function *F = cast<Function>(M.getOrInsertFunction("f", FTy));
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@ -35,8 +50,6 @@ TEST(ScalarEvolutionsTest, SCEVUnknownRAUW) {
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Value *V2 = new GlobalVariable(M, Ty, false, GlobalValue::ExternalLinkage, Init, "V2");
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// Create a ScalarEvolution and "run" it so that it gets initialized.
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PassManager PM;
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ScalarEvolution &SE = *new ScalarEvolution();
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PM.add(&SE);
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PM.run(M);
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@ -72,10 +85,149 @@ TEST(ScalarEvolutionsTest, SCEVUnknownRAUW) {
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EXPECT_EQ(cast<SCEVUnknown>(M0->getOperand(1))->getValue(), V0);
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EXPECT_EQ(cast<SCEVUnknown>(M1->getOperand(1))->getValue(), V0);
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EXPECT_EQ(cast<SCEVUnknown>(M2->getOperand(1))->getValue(), V0);
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}
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// Manually clean up, since we allocated new SCEV objects after the
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// pass was finished.
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SE.releaseMemory();
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TEST_F(ScalarEvolutionsTest, SCEVMultiplyAddRecs) {
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Type *Ty = Type::getInt32Ty(Context);
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SmallVector<Type *, 10> Types;
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Types.append(10, Ty);
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FunctionType *FTy = FunctionType::get(Type::getVoidTy(Context), Types, false);
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Function *F = cast<Function>(M.getOrInsertFunction("f", FTy));
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BasicBlock *BB = BasicBlock::Create(Context, "entry", F);
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ReturnInst::Create(Context, 0, BB);
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// Create a ScalarEvolution and "run" it so that it gets initialized.
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PM.add(&SE);
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PM.run(M);
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// It's possible to produce an empty loop through the default constructor,
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// but you can't add any blocks to it without a LoopInfo pass.
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Loop L;
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const_cast<std::vector<BasicBlock*>&>(L.getBlocks()).push_back(BB);
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Function::arg_iterator AI = F->arg_begin();
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SmallVector<const SCEV *, 5> A;
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A.push_back(SE.getSCEV(&*AI++));
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A.push_back(SE.getSCEV(&*AI++));
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A.push_back(SE.getSCEV(&*AI++));
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A.push_back(SE.getSCEV(&*AI++));
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A.push_back(SE.getSCEV(&*AI++));
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const SCEV *A_rec = SE.getAddRecExpr(A, &L, SCEV::FlagAnyWrap);
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SmallVector<const SCEV *, 5> B;
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B.push_back(SE.getSCEV(&*AI++));
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B.push_back(SE.getSCEV(&*AI++));
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B.push_back(SE.getSCEV(&*AI++));
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B.push_back(SE.getSCEV(&*AI++));
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B.push_back(SE.getSCEV(&*AI++));
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const SCEV *B_rec = SE.getAddRecExpr(B, &L, SCEV::FlagAnyWrap);
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/* Spot check that we perform this transformation:
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{A0,+,A1,+,A2,+,A3,+,A4} * {B0,+,B1,+,B2,+,B3,+,B4} =
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{A0*B0,+,
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A1*B0 + A0*B1 + A1*B1,+,
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A2*B0 + 2A1*B1 + A0*B2 + 2A2*B1 + 2A1*B2 + A2*B2,+,
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A3*B0 + 3A2*B1 + 3A1*B2 + A0*B3 + 3A3*B1 + 6A2*B2 + 3A1*B3 + 3A3*B2 +
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3A2*B3 + A3*B3,+,
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A4*B0 + 4A3*B1 + 6A2*B2 + 4A1*B3 + A0*B4 + 4A4*B1 + 12A3*B2 + 12A2*B3 +
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4A1*B4 + 6A4*B2 + 12A3*B3 + 6A2*B4 + 4A4*B3 + 4A3*B4 + A4*B4,+,
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5A4*B1 + 10A3*B2 + 10A2*B3 + 5A1*B4 + 20A4*B2 + 30A3*B3 + 20A2*B4 +
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30A4*B3 + 30A3*B4 + 20A4*B4,+,
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15A4*B2 + 20A3*B3 + 15A2*B4 + 60A4*B3 + 60A3*B4 + 90A4*B4,+,
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35A4*B3 + 35A3*B4 + 140A4*B4,+,
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70A4*B4}
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*/
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const SCEVAddRecExpr *Product =
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dyn_cast<SCEVAddRecExpr>(SE.getMulExpr(A_rec, B_rec));
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ASSERT_TRUE(Product);
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ASSERT_EQ(Product->getNumOperands(), 9u);
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SmallVector<const SCEV *, 16> Sum;
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Sum.push_back(SE.getMulExpr(A[0], B[0]));
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EXPECT_EQ(Product->getOperand(0), SE.getAddExpr(Sum));
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Sum.clear();
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// SCEV produces different an equal but different expression for these.
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// Re-enable when PR11052 is fixed.
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#if 0
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Sum.push_back(SE.getMulExpr(A[1], B[0]));
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Sum.push_back(SE.getMulExpr(A[0], B[1]));
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Sum.push_back(SE.getMulExpr(A[1], B[1]));
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EXPECT_EQ(Product->getOperand(1), SE.getAddExpr(Sum));
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Sum.clear();
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Sum.push_back(SE.getMulExpr(A[2], B[0]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 2), A[1], B[1]));
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Sum.push_back(SE.getMulExpr(A[0], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 2), A[2], B[1]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 2), A[1], B[2]));
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Sum.push_back(SE.getMulExpr(A[2], B[2]));
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EXPECT_EQ(Product->getOperand(2), SE.getAddExpr(Sum));
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Sum.clear();
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Sum.push_back(SE.getMulExpr(A[3], B[0]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[2], B[1]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[1], B[2]));
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Sum.push_back(SE.getMulExpr(A[0], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[3], B[1]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 6), A[2], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[1], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[3], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 3), A[2], B[3]));
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Sum.push_back(SE.getMulExpr(A[3], B[3]));
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EXPECT_EQ(Product->getOperand(3), SE.getAddExpr(Sum));
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Sum.clear();
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Sum.push_back(SE.getMulExpr(A[4], B[0]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[3], B[1]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 6), A[2], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[1], B[3]));
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Sum.push_back(SE.getMulExpr(A[0], B[4]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[4], B[1]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 12), A[3], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 12), A[2], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[1], B[4]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 6), A[4], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 12), A[3], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 6), A[2], B[4]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[4], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 4), A[3], B[4]));
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Sum.push_back(SE.getMulExpr(A[4], B[4]));
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EXPECT_EQ(Product->getOperand(4), SE.getAddExpr(Sum));
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Sum.clear();
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 5), A[4], B[1]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 10), A[3], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 10), A[2], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 5), A[1], B[4]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 20), A[4], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 30), A[3], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 20), A[2], B[4]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 30), A[4], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 30), A[3], B[4]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 20), A[4], B[4]));
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EXPECT_EQ(Product->getOperand(5), SE.getAddExpr(Sum));
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Sum.clear();
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 15), A[4], B[2]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 20), A[3], B[3]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 15), A[2], B[4]));
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Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 60), A[4], B[3]));
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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
|
||||
|
||||
Sum.push_back(SE.getMulExpr(SE.getConstant(Ty, 70), A[4], B[4]));
|
||||
EXPECT_EQ(Product->getOperand(8), SE.getAddExpr(Sum));
|
||||
}
|
||||
|
||||
} // end anonymous namespace
|
||||
|
||||
Loading…
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Reference in New Issue
Block a user