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//===- ScalarEvolutionNormalization.cpp - See below -----------------------===//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// This file implements utilities for working with "normalized" expressions.
// See the comments at the top of ScalarEvolutionNormalization.h for details.
#include "llvm/Analysis/ScalarEvolutionNormalization.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
using namespace llvm;
/// TransformKind - Different types of transformations that
/// TransformForPostIncUse can do.
enum TransformKind {
/// Normalize - Normalize according to the given loops.
/// Denormalize - Perform the inverse transform on the expression with the
/// given loop set.
namespace {
struct NormalizeDenormalizeRewriter
: public SCEVRewriteVisitor<NormalizeDenormalizeRewriter> {
const TransformKind Kind;
// NB! Pred is a function_ref. Storing it here is okay only because
// we're careful about the lifetime of NormalizeDenormalizeRewriter.
const NormalizePredTy Pred;
NormalizeDenormalizeRewriter(TransformKind Kind, NormalizePredTy Pred,
ScalarEvolution &SE)
: SCEVRewriteVisitor<NormalizeDenormalizeRewriter>(SE), Kind(Kind),
Pred(Pred) {}
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr);
} // namespace
const SCEV *
NormalizeDenormalizeRewriter::visitAddRecExpr(const SCEVAddRecExpr *AR) {
SmallVector<const SCEV *, 8> Operands;
transform(AR->operands(), std::back_inserter(Operands),
[&](const SCEV *Op) { return visit(Op); });
if (!Pred(AR))
return SE.getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagAnyWrap);
// Normalization and denormalization are fancy names for decrementing and
// incrementing a SCEV expression with respect to a set of loops. Since
// Pred(AR) has returned true, we know we need to normalize or denormalize AR
// with respect to its loop.
if (Kind == Denormalize) {
// Denormalization / "partial increment" is essentially the same as \c
// SCEVAddRecExpr::getPostIncExpr. Here we use an explicit loop to make the
// symmetry with Normalization clear.
for (int i = 0, e = Operands.size() - 1; i < e; i++)
Operands[i] = SE.getAddExpr(Operands[i], Operands[i + 1]);
} else {
assert(Kind == Normalize && "Only two possibilities!");
// Normalization / "partial decrement" is a bit more subtle. Since
// incrementing a SCEV expression (in general) changes the step of the SCEV
// expression as well, we cannot use the step of the current expression.
// Instead, we have to use the step of the very expression we're trying to
// compute!
// We solve the issue by recursively building up the result, starting from
// the "least significant" operand in the add recurrence:
// Base case:
// Single operand add recurrence. It's its own normalization.
// N-operand case:
// {S_{N-1},+,S_{N-2},+,...,+,S_0} = S
// Since the step recurrence of S is {S_{N-2},+,...,+,S_0}, we know its
// normalization by induction. We subtract the normalized step
// recurrence from S_{N-1} to get the normalization of S.
for (int i = Operands.size() - 2; i >= 0; i--)
Operands[i] = SE.getMinusSCEV(Operands[i], Operands[i + 1]);
return SE.getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagAnyWrap);
const SCEV *llvm::normalizeForPostIncUse(const SCEV *S,
const PostIncLoopSet &Loops,
ScalarEvolution &SE,
bool CheckInvertible) {
if (Loops.empty())
return S;
auto Pred = [&](const SCEVAddRecExpr *AR) {
return Loops.count(AR->getLoop());
const SCEV *Normalized =
NormalizeDenormalizeRewriter(Normalize, Pred, SE).visit(S);
const SCEV *Denormalized = denormalizeForPostIncUse(Normalized, Loops, SE);
// If the normalized expression isn't invertible.
if (CheckInvertible && Denormalized != S)
return nullptr;
return Normalized;
const SCEV *llvm::normalizeForPostIncUseIf(const SCEV *S, NormalizePredTy Pred,
ScalarEvolution &SE) {
return NormalizeDenormalizeRewriter(Normalize, Pred, SE).visit(S);
const SCEV *llvm::denormalizeForPostIncUse(const SCEV *S,
const PostIncLoopSet &Loops,
ScalarEvolution &SE) {
if (Loops.empty())
return S;
auto Pred = [&](const SCEVAddRecExpr *AR) {
return Loops.count(AR->getLoop());
return NormalizeDenormalizeRewriter(Denormalize, Pred, SE).visit(S);