[InstSimplify] Fold x*C1/C2 <= x (PR48744)

We can fold x*C1/C2 <= x to true if C1 <= C2. This is valid even
if the multiplication is not nuw: https://alive2.llvm.org/ce/z/vULors

The multiplication or division can be replaced by shifts. We don't
handle the case where both are shifts, as that should get folded
away by InstCombine.

Author: nikic

llvm/lib/Analysis/InstructionSimplify.cpp

@@ -2901,6 +2901,28 @@ static Value *simplifyICmpWithBinOpOnLHS(
       return getTrue(ITy);
   }
 
+  // (x*C1)/C2 <= x for C1 <= C2.
+  // This holds even if the multiplication overflows: Assume that x != 0 and
+  // arithmetic is modulo M. For overflow to occur we must have C1 >= M/x and
+  // thus C2 >= M/x. It follows that (x*C1)/C2 <= (M-1)/C2 <= ((M-1)*x)/M < x.
+  //
+  // Additionally, either the multiplication and division might be represented
+  // as shifts:
+  // (x*C1)>>C2 <= x for C1 < 2**C2.
+  // (x<<C1)/C2 <= x for 2**C1 < C2.
+  const APInt *C1, *C2;
+  if ((match(LBO, m_UDiv(m_Mul(m_Specific(RHS), m_APInt(C1)), m_APInt(C2))) &&
+       C1->ule(*C2)) ||
+      (match(LBO, m_LShr(m_Mul(m_Specific(RHS), m_APInt(C1)), m_APInt(C2))) &&
+       C1->ule(APInt(C2->getBitWidth(), 1) << *C2)) ||
+      (match(LBO, m_UDiv(m_Shl(m_Specific(RHS), m_APInt(C1)), m_APInt(C2))) &&
+       (APInt(C1->getBitWidth(), 1) << *C1).ule(*C2))) {
+    if (Pred == ICmpInst::ICMP_UGT)
+      return getFalse(ITy);
+    if (Pred == ICmpInst::ICMP_ULE)
+      return getTrue(ITy);
+  }
+
   return nullptr;
 }
 

llvm/test/Transforms/InstSimplify/icmp.ll

@@ -39,10 +39,7 @@ define i1 @poison2(i32 %x) {
 
 define i1 @mul_div_cmp_smaller(i8 %x) {
 ; CHECK-LABEL: @mul_div_cmp_smaller(
-; CHECK-NEXT:    [[MUL:%.*]] = mul i8 [[X:%.*]], 3
-; CHECK-NEXT:    [[DIV:%.*]] = udiv i8 [[MUL]], 4
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i8 [[DIV]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 true
 ;
   %mul = mul i8 %x, 3
   %div = udiv i8 %mul, 4
@@ -52,10 +49,7 @@ define i1 @mul_div_cmp_smaller(i8 %x) {
 
 define i1 @mul_div_cmp_equal(i8 %x) {
 ; CHECK-LABEL: @mul_div_cmp_equal(
-; CHECK-NEXT:    [[MUL:%.*]] = mul i8 [[X:%.*]], 3
-; CHECK-NEXT:    [[DIV:%.*]] = udiv i8 [[MUL]], 3
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i8 [[DIV]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 true
 ;
   %mul = mul i8 %x, 3
   %div = udiv i8 %mul, 3
@@ -78,10 +72,7 @@ define i1 @mul_div_cmp_greater(i8 %x) {
 }
 define i1 @mul_div_cmp_ugt(i8 %x) {
 ; CHECK-LABEL: @mul_div_cmp_ugt(
-; CHECK-NEXT:    [[MUL:%.*]] = mul i8 [[X:%.*]], 3
-; CHECK-NEXT:    [[DIV:%.*]] = udiv i8 [[MUL]], 4
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ugt i8 [[DIV]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 false
 ;
   %mul = mul i8 %x, 3
   %div = udiv i8 %mul, 4
@@ -133,10 +124,7 @@ define i1 @mul_div_cmp_wrong_operand(i8 %x, i8 %y) {
 
 define i1 @mul_lshr_cmp_smaller(i8 %x) {
 ; CHECK-LABEL: @mul_lshr_cmp_smaller(
-; CHECK-NEXT:    [[MUL:%.*]] = mul i8 [[X:%.*]], 3
-; CHECK-NEXT:    [[DIV:%.*]] = lshr i8 [[MUL]], 2
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i8 [[DIV]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 true
 ;
   %mul = mul i8 %x, 3
   %div = lshr i8 %mul, 2
@@ -146,10 +134,7 @@ define i1 @mul_lshr_cmp_smaller(i8 %x) {
 
 define i1 @mul_lshr_cmp_equal(i8 %x) {
 ; CHECK-LABEL: @mul_lshr_cmp_equal(
-; CHECK-NEXT:    [[MUL:%.*]] = mul i8 [[X:%.*]], 4
-; CHECK-NEXT:    [[DIV:%.*]] = lshr i8 [[MUL]], 2
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i8 [[DIV]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 true
 ;
   %mul = mul i8 %x, 4
   %div = lshr i8 %mul, 2
@@ -172,10 +157,7 @@ define i1 @mul_lshr_cmp_greater(i8 %x) {
 
 define i1 @shl_div_cmp_smaller(i8 %x) {
 ; CHECK-LABEL: @shl_div_cmp_smaller(
-; CHECK-NEXT:    [[MUL:%.*]] = shl i8 [[X:%.*]], 2
-; CHECK-NEXT:    [[DIV:%.*]] = udiv i8 [[MUL]], 5
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i8 [[DIV]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 true
 ;
   %mul = shl i8 %x, 2
   %div = udiv i8 %mul, 5
@@ -185,10 +167,7 @@ define i1 @shl_div_cmp_smaller(i8 %x) {
 
 define i1 @shl_div_cmp_equal(i8 %x) {
 ; CHECK-LABEL: @shl_div_cmp_equal(
-; CHECK-NEXT:    [[MUL:%.*]] = shl i8 [[X:%.*]], 2
-; CHECK-NEXT:    [[DIV:%.*]] = udiv i8 [[MUL]], 4
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i8 [[DIV]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 true
 ;
   %mul = shl i8 %x, 2
   %div = udiv i8 %mul, 4