llvm/lib/Analysis/ScalarEvolutionNormalization.cpp

   1 //===- ScalarEvolutionNormalization.cpp - See below -----------------------===//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8 //
   9 // This file implements utilities for working with "normalized" expressions.
  10 // See the comments at the top of ScalarEvolutionNormalization.h for details.
  11 //
  12 //===----------------------------------------------------------------------===//
  13
  14 #include "llvm/Analysis/ScalarEvolutionNormalization.h"
  15 #include "llvm/Analysis/LoopInfo.h"
  16 #include "llvm/Analysis/ScalarEvolution.h"
  17 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
  18 using namespace llvm;
  19
  20 /// TransformKind - Different types of transformations that
  21 /// TransformForPostIncUse can do.
  22 enum TransformKind {
  23   /// Normalize - Normalize according to the given loops.
  24   Normalize,
  25   /// Denormalize - Perform the inverse transform on the expression with the
  26   /// given loop set.
  27   Denormalize
  28 };
  29
  30 namespace {
  31 struct NormalizeDenormalizeRewriter
  32     : public SCEVRewriteVisitor<NormalizeDenormalizeRewriter> {
  33   const TransformKind Kind;
  34
  35   // NB! Pred is a function_ref.  Storing it here is okay only because
  36   // we're careful about the lifetime of NormalizeDenormalizeRewriter.
  37   const NormalizePredTy Pred;
  38
  39   NormalizeDenormalizeRewriter(TransformKind Kind, NormalizePredTy Pred,
  40                                ScalarEvolution &SE)
  41       : SCEVRewriteVisitor<NormalizeDenormalizeRewriter>(SE), Kind(Kind),
  42         Pred(Pred) {}
  43   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr);
  44 };
  45 } // namespace
  46
  47 const SCEV *
  48 NormalizeDenormalizeRewriter::visitAddRecExpr(const SCEVAddRecExpr *AR) {
  49   SmallVector<const SCEV *, 8> Operands;
  50
  51   transform(AR->operands(), std::back_inserter(Operands),
  52             [&](const SCEV *Op) { return visit(Op); });
  53
  54   if (!Pred(AR))
  55     return SE.getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagAnyWrap);
  56
  57   // Normalization and denormalization are fancy names for decrementing and
  58   // incrementing a SCEV expression with respect to a set of loops.  Since
  59   // Pred(AR) has returned true, we know we need to normalize or denormalize AR
  60   // with respect to its loop.
  61
  62   if (Kind == Denormalize) {
  63     // Denormalization / "partial increment" is essentially the same as \c
  64     // SCEVAddRecExpr::getPostIncExpr.  Here we use an explicit loop to make the
  65     // symmetry with Normalization clear.
  66     for (int i = 0, e = Operands.size() - 1; i < e; i++)
  67       Operands[i] = SE.getAddExpr(Operands[i], Operands[i + 1]);
  68   } else {
  69     assert(Kind == Normalize && "Only two possibilities!");
  70
  71     // Normalization / "partial decrement" is a bit more subtle.  Since
  72     // incrementing a SCEV expression (in general) changes the step of the SCEV
  73     // expression as well, we cannot use the step of the current expression.
  74     // Instead, we have to use the step of the very expression we're trying to
  75     // compute!
  76     //
  77     // We solve the issue by recursively building up the result, starting from
  78     // the "least significant" operand in the add recurrence:
  79     //
  80     // Base case:
  81     //   Single operand add recurrence.  It's its own normalization.
  82     //
  83     // N-operand case:
  84     //   {S_{N-1},+,S_{N-2},+,...,+,S_0} = S
  85     //
  86     //   Since the step recurrence of S is {S_{N-2},+,...,+,S_0}, we know its
  87     //   normalization by induction.  We subtract the normalized step
  88     //   recurrence from S_{N-1} to get the normalization of S.
  89
  90     for (int i = Operands.size() - 2; i >= 0; i--)
  91       Operands[i] = SE.getMinusSCEV(Operands[i], Operands[i + 1]);
  92   }
  93
  94   return SE.getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagAnyWrap);
  95 }
  96
  97 const SCEV *llvm::normalizeForPostIncUse(const SCEV *S,
  98                                          const PostIncLoopSet &Loops,
  99                                          ScalarEvolution &SE,
 100                                          bool CheckInvertible) {
 101   if (Loops.empty())
 102     return S;
 103   auto Pred = [&](const SCEVAddRecExpr *AR) {
 104     return Loops.count(AR->getLoop());
 105   };
 106   const SCEV *Normalized =
 107       NormalizeDenormalizeRewriter(Normalize, Pred, SE).visit(S);
 108   const SCEV *Denormalized = denormalizeForPostIncUse(Normalized, Loops, SE);
 109   // If the normalized expression isn't invertible.
 110   if (CheckInvertible && Denormalized != S)
 111     return nullptr;
 112   return Normalized;
 113 }
 114
 115 const SCEV *llvm::normalizeForPostIncUseIf(const SCEV *S, NormalizePredTy Pred,
 116                                            ScalarEvolution &SE) {
 117   return NormalizeDenormalizeRewriter(Normalize, Pred, SE).visit(S);
 118 }
 119
 120 const SCEV *llvm::denormalizeForPostIncUse(const SCEV *S,
 121                                            const PostIncLoopSet &Loops,
 122                                            ScalarEvolution &SE) {
 123   if (Loops.empty())
 124     return S;
 125   auto Pred = [&](const SCEVAddRecExpr *AR) {
 126     return Loops.count(AR->getLoop());
 127   };
 128   return NormalizeDenormalizeRewriter(Denormalize, Pred, SE).visit(S);
 129 }