Fix PR2088. Use modulo linear equation solver to compute loop iteration

count.


git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@53810 91177308-0d34-0410-b5e6-96231b3b80d8

lib/Analysis/ScalarEvolution.cpp

@@ -78,6 +78,8 @@
 #include "llvm/Support/MathExtras.h"
 #include "llvm/Support/Streams.h"
 #include "llvm/ADT/Statistic.h"
+//TMP:
+#include "llvm/Support/Debug.h"
 #include <ostream>
 #include <algorithm>
 #include <cmath>
@@ -2461,6 +2463,53 @@ SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
   return UnknownValue;
 }
 
+/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
+/// following equation:
+///
+///     A * X = B (mod N)
+///
+/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
+/// A and B isn't important.
+///
+/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
+static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
+                                               ScalarEvolution &SE) {
+  uint32_t BW = A.getBitWidth();
+  assert(BW == B.getBitWidth() && "Bit widths must be the same.");
+  assert(A != 0 && "A must be non-zero.");
+
+  // 1. D = gcd(A, N)
+  //
+  // The gcd of A and N may have only one prime factor: 2. The number of
+  // trailing zeros in A is its multiplicity
+  uint32_t Mult2 = A.countTrailingZeros();
+  // D = 2^Mult2
+
+  // 2. Check if B is divisible by D.
+  //
+  // B is divisible by D if and only if the multiplicity of prime factor 2 for B
+  // is not less than multiplicity of this prime factor for D.
+  if (B.countTrailingZeros() < Mult2)
+    return new SCEVCouldNotCompute();
+
+  // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
+  // modulo (N / D).
+  //
+  // (N / D) may need BW+1 bits in its representation.  Hence, we'll use this
+  // bit width during computations.
+  APInt AD = A.lshr(Mult2).zext(BW + 1);  // AD = A / D
+  APInt Mod(BW + 1, 0);
+  Mod.set(BW - Mult2);  // Mod = N / D
+  APInt I = AD.multiplicativeInverse(Mod);
+
+  // 4. Compute the minimum unsigned root of the equation:
+  // I * (B / D) mod (N / D)
+  APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
+
+  // The result is guaranteed to be less than 2^BW so we may truncate it to BW
+  // bits.
+  return SE.getConstant(Result.trunc(BW));
+}
 
 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
 /// given quadratic chrec {L,+,M,+,N}.  This returns either the two roots (which
@@ -2533,36 +2582,36 @@ SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
     return UnknownValue;
 
   if (AddRec->isAffine()) {
-    // If this is an affine expression the execution count of this branch is
-    // equal to:
+    // If this is an affine expression, the execution count of this branch is
+    // the minimum unsigned root of the following equation:
     //
-    //     (0 - Start/Step)    iff   Start % Step == 0
+    //     Start + Step*N = 0 (mod 2^BW)
     //
+    // equivalent to:
+    //
+    //             Step*N = -Start (mod 2^BW)
+    //
+    // where BW is the common bit width of Start and Step.
+
     // Get the initial value for the loop.
     SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
     if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
-    SCEVHandle Step = AddRec->getOperand(1);
 
-    Step = getSCEVAtScope(Step, L->getParentLoop());
+    SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
 
-    // Figure out if Start % Step == 0.
-    // FIXME: We should add DivExpr and RemExpr operations to our AST.
     if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
-      if (StepC->getValue()->equalsInt(1))      // N % 1 == 0
-        return SE.getNegativeSCEV(Start);  // 0 - Start/1 == -Start
-      if (StepC->getValue()->isAllOnesValue())  // N % -1 == 0
-        return Start;                   // 0 - Start/-1 == Start
+      // For now we handle only constant steps.
 
-      // Check to see if Start is divisible by SC with no remainder.
-      if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
-        ConstantInt *StartCC = StartC->getValue();
-        Constant *StartNegC = ConstantExpr::getNeg(StartCC);
-        Constant *Rem = ConstantExpr::getURem(StartNegC, StepC->getValue());
-        if (Rem->isNullValue()) {
-          Constant *Result = ConstantExpr::getUDiv(StartNegC,StepC->getValue());
-          return SE.getUnknown(Result);
-        }
-      }
+      // First, handle unitary steps.
+      if (StepC->getValue()->equalsInt(1))      // 1*N = -Start (mod 2^BW), so:
+        return SE.getNegativeSCEV(Start);       //   N = -Start (as unsigned)
+      if (StepC->getValue()->isAllOnesValue())  // -1*N = -Start (mod 2^BW), so:
+        return Start;                           //    N = Start (as unsigned)
+
+      // Then, try to solve the above equation provided that Start is constant.
+      if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
+        return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
+                                            -StartC->getValue()->getValue(),SE);
     }
   } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of