[SCEV] Simplify/generalize howFarToZero solving.

[efriedma]

Summary

Make SolveLinEquationWithOverflow take the start as a SCEV, so we can solve more cases. With that implemented, get rid of the unnecessary special case for powers of two.

The additional functionality probably isn't particularly useful, but it might help a little for certain cases involving pointer arithmetic.

[sanjoy]

LGTM

lib/Analysis/ScalarEvolution.cpp

7037

Can't we keep this same assert using getScalarTypeInBits?

lib/Analysis/ScalarEvolution.cpp

 /// 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 const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
+static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *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)
+  if (SE.GetMinTrailingZeros(B) < Mult2)
     return SE.getCouldNotCompute();
 
   // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
   // modulo (N / D).
   //
   // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
   // (N / D) in general. The inverse itself always fits into BW bits, though,
   // so we immediately truncate it.
   APInt AD = A.lshr(Mult2).zext(BW + 1);  // AD = A / D
   APInt Mod(BW + 1, 0);
   Mod.setBit(BW - Mult2);  // Mod = N / D
   APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
 
   // 4. Compute the minimum unsigned root of the equation:
   // I * (B / D) mod (N / D)
   // To simplify the computation, we factor out the divide by D:
   // (I * B mod N) / D
-  APInt Result = (I * B).lshr(Mult2);
-
-  return SE.getConstant(Result);
+  const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
+  return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
 }
 
 /// Find the roots of the quadratic equation for the given quadratic chrec
 /// {L,+,M,+,N}.  This returns either the two roots (which might be the same) or
 /// two SCEVCouldNotCompute objects.
 ///
 static Optional<std::pair<const SCEVConstant *,const SCEVConstant *>>
 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
       // If Distance + 1 doesn't overflow, we can compute the maximum distance
       // as "unsigned_max(Distance + 1) - 1".
       ConstantRange CR = getUnsignedRange(DistancePlusOne);
       MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
     }
     return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
   }
 
-  // As a special case, handle the instance where Step is a positive power of
-  // two. In this case, determining whether Step divides Distance evenly can be
-  // done by counting and comparing the number of trailing zeros of Step and
-  // Distance.
-  if (!CountDown) {
-    const APInt &StepV = StepC->getAPInt();
-    // StepV.isPowerOf2() returns true if StepV is an positive power of two.  It
-    // also returns true if StepV is maximally negative (eg, INT_MIN), but that
-    // case is not handled as this code is guarded by !CountDown.
-    if (StepV.isPowerOf2() &&
-        GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
-      // Here we've constrained the equation to be of the form
-      //
-      //   2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W)  ... (0)
-      //
-      // where we're operating on a W bit wide integer domain and k is
-      // non-negative.  The smallest unsigned solution for X is the trip count.
-      //
-      // (0) is equivalent to:
-      //
-      //      2^(N + k) * Distance' - 2^N * X = L * 2^W
-      // <=>  2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
-      // <=>  2^k * Distance' - X = L * 2^(W - N)
-      // <=>  2^k * Distance'     = L * 2^(W - N) + X    ... (1)
-      //
-      // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
-      // by 2^(W - N).
-      //
-      // <=>  X = 2^k * Distance' URem 2^(W - N)   ... (2)
-      //
-      // E.g. say we're solving
-      //
-      //   2 * Val = 2 * X  (in i8)   ... (3)
-      //
-      // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
-      //
-      // Note: It is tempting to solve (3) by setting X = Val, but Val is not
-      // necessarily the smallest unsigned value of X that satisfies (3).
-      // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
-      // is i8 1, not i8 -127
-
-      const auto *Limit = getUDivExactExpr(Distance, Step);
-      return ExitLimit(Limit, Limit, false, Predicates);
-    }
-  }
-
   // If the condition controls loop exit (the loop exits only if the expression
   // is true) and the addition is no-wrap we can use unsigned divide to
   // compute the backedge count.  In this case, the step may not divide the
   // distance, but we don't care because if the condition is "missed" the loop
   // will have undefined behavior due to wrapping.
   if (ControlsExit && AddRec->hasNoSelfWrap() &&
       loopHasNoAbnormalExits(AddRec->getLoop())) {
     const SCEV *Exact =
         getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
     return ExitLimit(Exact, Exact, false, Predicates);
   }
 
-  // Then, try to solve the above equation provided that Start is constant.
-  if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
-    const SCEV *E = SolveLinEquationWithOverflow(
-        StepC->getValue()->getValue(), -StartC->getValue()->getValue(), *this);
-    return ExitLimit(E, E, false, Predicates);
-  }
-  return getCouldNotCompute();
-}
+  // Solve the general equation.
+      StepC->getAPInt(), getNegativeSCEV(Start), *this);
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
   // Loops that look like: while (X == 0) are very strange indeed.  We don't
   // handle them yet except for the trivial case.  This could be expanded in the
   // future as needed.
 
   // If the value is a constant, check to see if it is known to be non-zero

test/Analysis/ScalarEvolution/sext-inreg.ll

entry:
   br i1 %t0, label %bb, label %return
 
 bb:
   %i.01 = phi i64 [ 0, %entry ], [ %indvar.next, %bb ]
   %t1 = shl i64 %i.01, 7
   %t2 = ashr i64 %t1, 7
 ; CHECK: %t2 = ashr i64 %t1, 7
 ; CHECK-NEXT: sext i57 {0,+,199}<%bb> to i64
-; CHECK-NOT: i57
+; CHECK-SAME: Exits: (sext i57 (199 * (trunc i64 (-1 + (2780916192016515319 * %n)) to i57)) to i64)
 ; CHECK: %s2 = ashr i64 %s1, 5
 ; CHECK-NEXT: sext i59 {0,+,199}<%bb> to i64
-; CHECK-NOT: i59
+; CHECK-SAME: Exits: (sext i59 (199 * (trunc i64 (-1 + (2780916192016515319 * %n)) to i59)) to i64)
   %s1 = shl i64 %i.01, 5
   %s2 = ashr i64 %s1, 5
   %t3 = getelementptr i64, i64* %x, i64 %i.01
   store i64 0, i64* %t3, align 1
   %indvar.next = add i64 %i.01, 199
   %exitcond = icmp eq i64 %indvar.next, %n
   br i1 %exitcond, label %return, label %bb
 
 return:
         %p = phi i64 [ 0, %entry ], [ %t2, %bb ]
         %q = phi i64 [ 0, %entry ], [ %s2, %bb ]
         %v = xor i64 %p, %q
   ret i64 %v
 }

test/Analysis/ScalarEvolution/trip-count-pow2.ll

loop:
   %i = phi i32 [ 0, %entry ], [ %i.next, %loop ]
   %i.next = add i32 %i, 96
   %t = icmp ne i32 %i.next, %s
   br i1 %t, label %loop, label %exit
 exit:
   ret void
 
 ; CHECK-LABEL: @test3
-; CHECK: Loop %loop: Unpredictable backedge-taken count.
-; CHECK: Loop %loop: Unpredictable max backedge-taken count.
+; CHECK: Loop %loop: backedge-taken count is ((-32 + (32 * %n)) /u 32)
+; CHECK: Loop %loop: max backedge-taken count is ((-32 + (32 * %n)) /u 32)
+}
+
+define void @test4(i32 %n) {
+entry:
+  %s = mul i32 %n, 4
+  br label %loop
+loop:
+  %i = phi i32 [ 0, %entry ], [ %i.next, %loop ]
+  %i.next = add i32 %i, 12
+  %t = icmp ne i32 %i.next, %s
+  br i1 %t, label %loop, label %exit
+exit:
+  ret void
+
+; CHECK-LABEL: @test4
+; CHECK: Loop %loop: backedge-taken count is ((-4 + (-1431655764 * %n)) /u 4)
+; CHECK: Loop %loop: max backedge-taken count is ((-4 + (-1431655764 * %n)) /u 4)
+}
+
+define void @test5(i32 %n) {
+entry:
+  %s = mul i32 %n, 4
+  br label %loop
+loop:
+  %i = phi i32 [ %s, %entry ], [ %i.next, %loop ]
+  %i.next = add i32 %i, -4
+  %t = icmp ne i32 %i.next, 0
+  br i1 %t, label %loop, label %exit
+exit:
+  ret void
+
+; CHECK-LABEL: @test5
+; CHECK: Loop %loop: backedge-taken count is ((-4 + (4 * %n)) /u 4)
+; CHECK: Loop %loop: max backedge-taken count is ((-4 + (4 * %n)) /u 4)
 }