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
@@ -580,6 +580,11 @@
   return false;
 }
 
+// TODO: cmpExcludesZero misses many cases where `RHS` is non-constant but
+// we still have enough information about `RHS` to conclude non-zero. For
+// example Pred=EQ, RHS=isKnownNonZero. cmpExcludesZero is called in loops
+// so the extra compile time may not be worth it, but possibly a second API
+// should be created for use outside of loops.
 static bool cmpExcludesZero(CmpInst::Predicate Pred, const Value *RHS) {
   // v u> y implies v != 0.
   if (Pred == ICmpInst::ICMP_UGT)
@@ -2900,12 +2905,38 @@
     return (XKnown.countMaxTrailingZeros() + YKnown.countMaxTrailingZeros()) <
            BitWidth;
   }
-  case Instruction::Select:
+  case Instruction::Select: {
     // (C ? X : Y) != 0 if X != 0 and Y != 0.
-    if (isKnownNonZero(I->getOperand(1), DemandedElts, Depth, Q) &&
-        isKnownNonZero(I->getOperand(2), DemandedElts, Depth, Q))
+
+    // First check if the arm is non-zero using `isKnownNonZero`. If that fails,
+    // then see if the select condition implies the arm is non-zero. For example
+    // (X != 0 ? X : Y), we know the true arm is non-zero as the `X` "return" is
+    // dominated by `X != 0`.
+    auto SelectArmIsNonZero = [&](bool IsTrueArm) {
+      Value *Op;
+      Op = IsTrueArm ? I->getOperand(1) : I->getOperand(2);
+      // Op is trivially non-zero.
+      if (isKnownNonZero(Op, DemandedElts, Depth, Q))
+        return true;
+
+      // The condition of the select dominates the true/false arm. Check if the
+      // condition implies that a given arm is non-zero.
+      Value *X;
+      CmpInst::Predicate Pred;
+      if (!match(I->getOperand(0), m_c_ICmp(Pred, m_Specific(Op), m_Value(X))))
+        return false;
+
+      if (!IsTrueArm)
+        Pred = ICmpInst::getInversePredicate(Pred);
+
+      return cmpExcludesZero(Pred, X);
+    };
+
+    if (SelectArmIsNonZero(/* IsTrueArm */ true) &&
+        SelectArmIsNonZero(/* IsTrueArm */ false))
       return true;
     break;
+  }
   case Instruction::PHI: {
     auto *PN = cast<PHINode>(I);
     if (Q.IIQ.UseInstrInfo && isNonZeroRecurrence(PN))
diff --git a/llvm/test/Analysis/ValueTracking/select-known-non-zero-const.ll b/llvm/test/Analysis/ValueTracking/select-known-non-zero-const.ll
--- a/llvm/test/Analysis/ValueTracking/select-known-non-zero-const.ll
+++ b/llvm/test/Analysis/ValueTracking/select-known-non-zero-const.ll
@@ -4,11 +4,7 @@
 declare void @llvm.assume(i1)
 define <2 x i1> @select_v_ne_z(<2 x i8> %v, <2 x i8> %yy) {
 ; CHECK-LABEL: @select_v_ne_z(
-; CHECK-NEXT:    [[Y:%.*]] = or <2 x i8> [[YY:%.*]], <i8 1, i8 1>
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ne <2 x i8> [[V:%.*]], zeroinitializer
-; CHECK-NEXT:    [[S:%.*]] = select <2 x i1> [[CMP]], <2 x i8> [[V]], <2 x i8> [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq <2 x i8> [[S]], zeroinitializer
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> zeroinitializer
 ;
   %y = or <2 x i8> %yy, <i8 1, i8 1>
   %cmp = icmp ne <2 x i8> %v, zeroinitializer
@@ -38,10 +34,7 @@
 ; CHECK-LABEL: @select_v_eq_nz(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 44, [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -55,10 +48,7 @@
 ; CHECK-LABEL: @inv_select_v_ugt_nz(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ugt i8 14, [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -72,10 +62,7 @@
 ; CHECK-LABEL: @inv_select_v_ugt_fail(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ugt i8 -2, [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -87,11 +74,7 @@
 
 define <2 x i1> @select_v_ult(<2 x i8> %v, <2 x i8> %C, <2 x i8> %yy) {
 ; CHECK-LABEL: @select_v_ult(
-; CHECK-NEXT:    [[Y:%.*]] = or <2 x i8> [[YY:%.*]], <i8 1, i8 1>
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ult <2 x i8> [[C:%.*]], [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select <2 x i1> [[CMP]], <2 x i8> [[V]], <2 x i8> [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq <2 x i8> [[S]], zeroinitializer
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> zeroinitializer
 ;
   %y = or <2 x i8> %yy, <i8 1, i8 1>
   %cmp = icmp ult <2 x i8> %C, %v
@@ -102,11 +85,7 @@
 
 define <2 x i1> @select_v_uge_nz(<2 x i8> %v, <2 x i8> %yy) {
 ; CHECK-LABEL: @select_v_uge_nz(
-; CHECK-NEXT:    [[Y:%.*]] = or <2 x i8> [[YY:%.*]], <i8 1, i8 1>
-; CHECK-NEXT:    [[CMP:%.*]] = icmp uge <2 x i8> [[V:%.*]], <i8 1, i8 1>
-; CHECK-NEXT:    [[S:%.*]] = select <2 x i1> [[CMP]], <2 x i8> [[V]], <2 x i8> [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq <2 x i8> [[S]], zeroinitializer
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> zeroinitializer
 ;
   %y = or <2 x i8> %yy, <i8 1, i8 1>
   %cmp = icmp uge <2 x i8> %v, <i8 1, i8 1>
@@ -119,10 +98,7 @@
 ; CHECK-LABEL: @inv_select_v_ule(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i8 [[V:%.*]], 4
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -136,10 +112,7 @@
 ; CHECK-LABEL: @select_v_sgt_nonneg(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i8 [[V:%.*]], 0
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -170,10 +143,7 @@
 ; CHECK-LABEL: @inv_select_v_sgt_neg(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i8 [[V:%.*]], -1
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -187,10 +157,7 @@
 ; CHECK-LABEL: @inv_select_v_sgt_nonneg_nz(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i8 99, [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -204,10 +171,7 @@
 ; CHECK-LABEL: @select_v_slt_nonneg(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i8 0, [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -238,10 +202,7 @@
 ; CHECK-LABEL: @select_v_slt_neg(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i8 [[V:%.*]], -1
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -255,10 +216,7 @@
 ; CHECK-LABEL: @select_v_sge_nonneg_nz(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sge i8 [[V:%.*]], 1
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -272,10 +230,7 @@
 ; CHECK-LABEL: @select_v_sge_neg(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sge i8 -3, [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -289,10 +244,7 @@
 ; CHECK-LABEL: @inv_select_v_sge_z(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sge i8 [[V:%.*]], 0
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -306,10 +258,7 @@
 ; CHECK-LABEL: @inv_select_v_sge_fail(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sge i8 [[V:%.*]], -44
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -323,10 +272,7 @@
 ; CHECK-LABEL: @select_v_sle_neg(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sle i8 [[V:%.*]], -1
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -340,10 +286,7 @@
 ; CHECK-LABEL: @select_v_sle_nonneg_nz(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sle i8 1, [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -374,10 +317,7 @@
 ; CHECK-LABEL: @inv_select_v_sle_nonneg(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sle i8 [[V:%.*]], 0
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
diff --git a/llvm/test/Analysis/ValueTracking/select-known-non-zero.ll b/llvm/test/Analysis/ValueTracking/select-known-non-zero.ll
--- a/llvm/test/Analysis/ValueTracking/select-known-non-zero.ll
+++ b/llvm/test/Analysis/ValueTracking/select-known-non-zero.ll
@@ -6,10 +6,7 @@
 ; CHECK-LABEL: @select_v_ne_z(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ne i8 [[V:%.*]], 0
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -103,10 +100,7 @@
 ; CHECK-LABEL: @select_v_ult(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i8 [[C:%.*]], [[V:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[V]], i8 [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -141,10 +135,7 @@
 ; CHECK-LABEL: @inv_select_v_ule(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i8 [[V:%.*]], [[C:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
@@ -347,10 +338,7 @@
 ; CHECK-LABEL: @inv_select_v_sge_z(
 ; CHECK-NEXT:    [[YNZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[YNZ]])
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sge i8 [[V:%.*]], 0
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[CMP]], i8 [[Y]], i8 [[V]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[S]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %ynz = icmp ne i8 %y, 0
   call void @llvm.assume(i1 %ynz)
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
@@ -729,10 +729,7 @@
 
 define i1 @select6(i32 %x) {
 ; CHECK-LABEL: @select6(
-; CHECK-NEXT:    [[C:%.*]] = icmp sgt i32 [[X:%.*]], 0
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[C]], i32 [[X]], i32 4
-; CHECK-NEXT:    [[C2:%.*]] = icmp eq i32 [[S]], 0
-; CHECK-NEXT:    ret i1 [[C2]]
+; CHECK-NEXT:    ret i1 false
 ;
   %c = icmp sgt i32 %x, 0
   %s = select i1 %c, i32 %x, i32 4