diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -6460,6 +6460,11 @@
   unsigned Width = Lower.getBitWidth();
   const APInt *C;
   switch (II.getIntrinsicID()) {
+  case Intrinsic::ctpop:
+    // Maximum of set bits is the bit width.
+    assert(Lower == 0 && "Expected lower bound to be zero");
+    Upper = Width + 1;
+    break;
   case Intrinsic::uadd_sat:
     // uadd.sat(x, C) produces [C, UINT_MAX].
     if (match(II.getOperand(0), m_APInt(C)) ||
diff --git a/llvm/test/Transforms/InstSimplify/compare.ll b/llvm/test/Transforms/InstSimplify/compare.ll
--- a/llvm/test/Transforms/InstSimplify/compare.ll
+++ b/llvm/test/Transforms/InstSimplify/compare.ll
@@ -2073,9 +2073,7 @@
 
 define i1 @ctpop_sgt_bitwidth(i11 %x) {
 ; CHECK-LABEL: @ctpop_sgt_bitwidth(
-; CHECK-NEXT:    [[POP:%.*]] = call i11 @llvm.ctpop.i11(i11 [[X:%.*]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i11 [[POP]], 11
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 false
 ;
   %pop = call i11 @llvm.ctpop.i11(i11 %x)
   %cmp = icmp sgt i11 %pop, 11
@@ -2084,9 +2082,7 @@
 
 define i1 @ctpop_sle_minus1(i11 %x) {
 ; CHECK-LABEL: @ctpop_sle_minus1(
-; CHECK-NEXT:    [[POP:%.*]] = call i11 @llvm.ctpop.i11(i11 [[X:%.*]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sle i11 [[POP]], -1
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 false
 ;
   %pop = call i11 @llvm.ctpop.i11(i11 %x)
   %cmp = icmp sle i11 %pop, -1
@@ -2095,15 +2091,15 @@
 
 define i1 @ctpop_ugt_bitwidth(i73 %x) {
 ; CHECK-LABEL: @ctpop_ugt_bitwidth(
-; CHECK-NEXT:    [[POP:%.*]] = call i73 @llvm.ctpop.i73(i73 [[X:%.*]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ugt i73 [[POP]], 73
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 false
 ;
   %pop = call i73 @llvm.ctpop.i73(i73 %x)
   %cmp = icmp ugt i73 %pop, 73
   ret i1 %cmp
 }
 
+; Negative test - does not simplify, but instcombine could reduce this.
+
 define i1 @ctpop_ugt_bitwidth_minus1(i73 %x) {
 ; CHECK-LABEL: @ctpop_ugt_bitwidth_minus1(
 ; CHECK-NEXT:    [[POP:%.*]] = call i73 @llvm.ctpop.i73(i73 [[X:%.*]])
@@ -2117,9 +2113,7 @@
 
 define <2 x i1> @ctpop_sgt_bitwidth_splat(<2 x i13> %x) {
 ; CHECK-LABEL: @ctpop_sgt_bitwidth_splat(
-; CHECK-NEXT:    [[POP:%.*]] = call <2 x i13> @llvm.ctpop.v2i13(<2 x i13> [[X:%.*]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt <2 x i13> [[POP]], <i13 13, i13 13>
-; CHECK-NEXT:    ret <2 x i1> [[CMP]]
+; CHECK-NEXT:    ret <2 x i1> zeroinitializer
 ;
   %pop = call <2 x i13> @llvm.ctpop.v2i13(<2 x i13> %x)
   %cmp = icmp sgt <2 x i13> %pop, <i13 13, i13 13>
@@ -2128,9 +2122,7 @@
 
 define i1 @ctpop_ult_plus1_bitwidth(i11 %x) {
 ; CHECK-LABEL: @ctpop_ult_plus1_bitwidth(
-; CHECK-NEXT:    [[POP:%.*]] = call i11 @llvm.ctpop.i11(i11 [[X:%.*]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i11 [[POP]], 12
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 true
 ;
   %pop = call i11 @llvm.ctpop.i11(i11 %x)
   %cmp = icmp ult i11 %pop, 12
@@ -2139,9 +2131,7 @@
 
 define i1 @ctpop_ne_big_bitwidth(i73 %x) {
 ; CHECK-LABEL: @ctpop_ne_big_bitwidth(
-; CHECK-NEXT:    [[POP:%.*]] = call i73 @llvm.ctpop.i73(i73 [[X:%.*]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ne i73 [[POP]], 75
-; CHECK-NEXT:    ret i1 [[CMP]]
+; CHECK-NEXT:    ret i1 true
 ;
   %pop = call i73 @llvm.ctpop.i73(i73 %x)
   %cmp = icmp ne i73 %pop, 75
@@ -2150,15 +2140,15 @@
 
 define <2 x i1> @ctpop_slt_bitwidth_plus1_splat(<2 x i13> %x) {
 ; CHECK-LABEL: @ctpop_slt_bitwidth_plus1_splat(
-; CHECK-NEXT:    [[POP:%.*]] = call <2 x i13> @llvm.ctpop.v2i13(<2 x i13> [[X:%.*]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp slt <2 x i13> [[POP]], <i13 14, i13 14>
-; CHECK-NEXT:    ret <2 x i1> [[CMP]]
+; CHECK-NEXT:    ret <2 x i1> <i1 true, i1 true>
 ;
   %pop = call <2 x i13> @llvm.ctpop.v2i13(<2 x i13> %x)
   %cmp = icmp slt <2 x i13> %pop, <i13 14, i13 14>
   ret <2 x i1> %cmp
 }
 
+; Negative test - does not simplify, but instcombine could reduce this.
+
 define <2 x i1> @ctpop_slt_bitwidth_splat(<2 x i13> %x) {
 ; CHECK-LABEL: @ctpop_slt_bitwidth_splat(
 ; CHECK-NEXT:    [[POP:%.*]] = call <2 x i13> @llvm.ctpop.v2i13(<2 x i13> [[X:%.*]])