ScalarEvolution: Add URem support

In LLVM IR the following code:

    %r = urem <ty> %t, %b

is equivalent to:

    %q = udiv <ty> %t, %b
    %s = mul <ty> nuw %q, %b
    %r = sub <ty> nuw %t, %q ; (t / b) * b + (t % b) = t

As UDiv, Mul and Sub are already supported by SCEV, URem can be
implemented with minimal effort this way.

Note: While SRem and SDiv are also related this way, SCEV does not
provides SDiv yet.

llvm-svn: 306695

1 files changed, 26 insertions, 0 deletions

diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
index 73a95ec405c..80bbc8b05e2 100644
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -2935,6 +2935,29 @@ const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
   return getOrCreateMulExpr(Ops, Flags);
 }
 
+/// Represents an unsigned remainder expression based on unsigned division.
+const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
+                                         const SCEV *RHS) {
+  assert(getEffectiveSCEVType(LHS->getType()) ==
+         getEffectiveSCEVType(RHS->getType()) &&
+         "SCEVURemExpr operand types don't match!");
+
+  // TODO:
+  //  - short circuit '%a = %x urem %x --> 0' (why is it not done for udiv?)
+  //  - short circuit '%a = %x urem 0 --> %a' (same as for udiv)
+  //  - update upper-bound and lower-bound cache for the final result
+  //    (or improve how subtraction is estimated)
+
+  // Short-circuit easy cases
+  if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
+    if (RHSC->getValue()->equalsInt(1))
+      return getZero(LHS->getType()); // X urem 1 --> 0
+
+  const SCEV *UDiv = getUDivExpr(LHS, RHS);
+  const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
+  return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
+}
+
 /// Get a canonical unsigned division expression, or something simpler if
 /// possible.
 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
@@ -4095,6 +4118,7 @@ static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
   case Instruction::Sub:
   case Instruction::Mul:
   case Instruction::UDiv:
+  case Instruction::URem:
   case Instruction::And:
   case Instruction::Or:
   case Instruction::AShr:
@@ -5416,6 +5440,8 @@ const SCEV *ScalarEvolution::createSCEV(Value *V) {
     }
     case Instruction::UDiv:
       return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
+    case Instruction::URem:
+      return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
     case Instruction::Sub: {
       SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
       if (BO->Op)