diff --git a/llvm/lib/CodeGen/SelectionDAG/SelectionDAG.cpp b/llvm/lib/CodeGen/SelectionDAG/SelectionDAG.cpp
--- a/llvm/lib/CodeGen/SelectionDAG/SelectionDAG.cpp
+++ b/llvm/lib/CodeGen/SelectionDAG/SelectionDAG.cpp
@@ -5065,14 +5065,95 @@
                                [](ConstantSDNode *C) { return !C->isZero(); }))
     return true;
 
-  // TODO: Recognize more cases here.
+  // TODO: Recognize more cases here. Most of the cases are also incomplete to
+  // some degree.
   switch (Op.getOpcode()) {
-  default: break;
+  default:
+    break;
+
   case ISD::OR:
-    if (isKnownNeverZero(Op.getOperand(1), Depth + 1) ||
-        isKnownNeverZero(Op.getOperand(0), Depth + 1))
+    return isKnownNeverZero(Op.getOperand(1), Depth + 1) ||
+           isKnownNeverZero(Op.getOperand(0), Depth + 1);
+
+  case ISD::VSELECT:
+  case ISD::SELECT:
+    return isKnownNeverZero(Op.getOperand(1), Depth + 1) &&
+           isKnownNeverZero(Op.getOperand(2), Depth + 1);
+
+  case ISD::SHL:
+    if (Op->getFlags().hasNoSignedWrap() || Op->getFlags().hasNoUnsignedWrap())
+      return isKnownNeverZero(Op.getOperand(0), Depth + 1);
+
+    // 1 << X is never zero. TODO: This can be expanded if we can bound X.
+    // The expression is really !Known.One[BitWidth-MaxLog2(Known):0].isZero()
+    if (computeKnownBits(Op.getOperand(0), Depth + 1).One[0])
+      return true;
+    break;
+
+  case ISD::UADDSAT:
+  case ISD::UMAX:
+    return isKnownNeverZero(Op.getOperand(1), Depth + 1) ||
+           isKnownNeverZero(Op.getOperand(0), Depth + 1);
+
+  case ISD::UMIN:
+    return isKnownNeverZero(Op.getOperand(1), Depth + 1) &&
+           isKnownNeverZero(Op.getOperand(0), Depth + 1);
+
+  case ISD::ROTL:
+  case ISD::ROTR:
+  case ISD::BITREVERSE:
+  case ISD::BSWAP:
+  case ISD::CTPOP:
+  case ISD::ABS:
+    return isKnownNeverZero(Op.getOperand(0), Depth + 1);
+
+  case ISD::SRA:
+  case ISD::SRL:
+    if (Op->getFlags().hasExact())
+      return isKnownNeverZero(Op.getOperand(0), Depth + 1);
+    // Signed >> X is never zero. TODO: This can be expanded if we can bound X.
+    // The expression is really
+    // !Known.One[SignBit:SignBit-(BitWidth-MaxLog2(Known))].isZero()
+    if (computeKnownBits(Op.getOperand(0), Depth + 1).isNegative())
       return true;
     break;
+
+  case ISD::UDIV:
+  case ISD::SDIV:
+    // div exact can only produce a zero if the dividend is zero.
+    // TODO: For udiv this is also true if Op1 u<= Op0
+    if (Op->getFlags().hasExact())
+      return isKnownNeverZero(Op.getOperand(0), Depth + 1);
+    break;
+
+  case ISD::ADD:
+    if (Op->getFlags().hasNoUnsignedWrap())
+      if (isKnownNeverZero(Op.getOperand(1), Depth + 1) ||
+          isKnownNeverZero(Op.getOperand(0), Depth + 1))
+        return true;
+    // TODO: There are a lot more cases we can prove for add.
+    break;
+
+  case ISD::SUB: {
+    if (isNullConstant(Op.getOperand(0)))
+      return isKnownNeverZero(Op.getOperand(1), Depth + 1);
+
+    std::optional<bool> ne =
+        KnownBits::ne(computeKnownBits(Op.getOperand(0), Depth + 1),
+                      computeKnownBits(Op.getOperand(1), Depth + 1));
+    return ne && *ne;
+  }
+
+  case ISD::MUL:
+    if (Op->getFlags().hasNoSignedWrap() || Op->getFlags().hasNoUnsignedWrap())
+      if (isKnownNeverZero(Op.getOperand(1), Depth + 1) &&
+          isKnownNeverZero(Op.getOperand(0), Depth + 1))
+        return true;
+    break;
+
+  case ISD::ZERO_EXTEND:
+  case ISD::SIGN_EXTEND:
+    return isKnownNeverZero(Op.getOperand(0), Depth + 1);
   }
 
   return computeKnownBits(Op, Depth).isNonZero();
diff --git a/llvm/test/CodeGen/X86/divrem-by-select.ll b/llvm/test/CodeGen/X86/divrem-by-select.ll
--- a/llvm/test/CodeGen/X86/divrem-by-select.ll
+++ b/llvm/test/CodeGen/X86/divrem-by-select.ll
@@ -67,20 +67,16 @@
 ; CHECK-X64-V4:       # %bb.0:
 ; CHECK-X64-V4-NEXT:    vpsllq $63, %xmm0, %xmm0
 ; CHECK-X64-V4-NEXT:    vpmovq2m %xmm0, %k1
-; CHECK-X64-V4-NEXT:    vpbroadcastq {{.*#+}} xmm0 = [1,1]
-; CHECK-X64-V4-NEXT:    vpbroadcastq {{\.?LCPI[0-9]+_[0-9]+}}(%rip), %xmm0 {%k1}
-; CHECK-X64-V4-NEXT:    vpextrq $1, %xmm0, %rcx
-; CHECK-X64-V4-NEXT:    vpextrq $1, %xmm1, %rax
-; CHECK-X64-V4-NEXT:    xorl %edx, %edx
-; CHECK-X64-V4-NEXT:    divq %rcx
-; CHECK-X64-V4-NEXT:    movq %rax, %rcx
-; CHECK-X64-V4-NEXT:    vmovq %xmm0, %rsi
-; CHECK-X64-V4-NEXT:    vmovq %xmm1, %rax
-; CHECK-X64-V4-NEXT:    xorl %edx, %edx
-; CHECK-X64-V4-NEXT:    divq %rsi
+; CHECK-X64-V4-NEXT:    vpextrq $1, %xmm1, %rdx
+; CHECK-X64-V4-NEXT:    movabsq $-3689348814741910323, %rax # imm = 0xCCCCCCCCCCCCCCCD
+; CHECK-X64-V4-NEXT:    mulxq %rax, %rcx, %rcx
 ; CHECK-X64-V4-NEXT:    vmovq %rcx, %xmm0
-; CHECK-X64-V4-NEXT:    vmovq %rax, %xmm1
-; CHECK-X64-V4-NEXT:    vpunpcklqdq {{.*#+}} xmm0 = xmm1[0],xmm0[0]
+; CHECK-X64-V4-NEXT:    vmovq %xmm1, %rdx
+; CHECK-X64-V4-NEXT:    mulxq %rax, %rax, %rax
+; CHECK-X64-V4-NEXT:    vmovq %rax, %xmm2
+; CHECK-X64-V4-NEXT:    vpunpcklqdq {{.*#+}} xmm0 = xmm2[0],xmm0[0]
+; CHECK-X64-V4-NEXT:    vpsrlq $3, %xmm0, %xmm1 {%k1}
+; CHECK-X64-V4-NEXT:    vmovdqa %xmm1, %xmm0
 ; CHECK-X64-V4-NEXT:    retq
 
   ;; Fails at the moment because `10` is even so there is no common
@@ -115,23 +111,23 @@
 ;
 ; CHECK-X64-V4-LABEL: udiv_indentity_non_zero:
 ; CHECK-X64-V4:       # %bb.0:
-; CHECK-X64-V4-NEXT:    vpsllq $63, %xmm0, %xmm0
-; CHECK-X64-V4-NEXT:    vpmovq2m %xmm0, %k1
-; CHECK-X64-V4-NEXT:    vpcmpeqd %xmm0, %xmm0, %xmm0
-; CHECK-X64-V4-NEXT:    vpbroadcastq {{.*#+}} xmm3 = [1,1]
-; CHECK-X64-V4-NEXT:    vpsubq %xmm0, %xmm2, %xmm3 {%k1}
-; CHECK-X64-V4-NEXT:    vpextrq $1, %xmm3, %rcx
+; CHECK-X64-V4-NEXT:    vpcmpeqd %xmm3, %xmm3, %xmm3
+; CHECK-X64-V4-NEXT:    vpsubq %xmm3, %xmm2, %xmm2
+; CHECK-X64-V4-NEXT:    vpextrq $1, %xmm2, %rcx
 ; CHECK-X64-V4-NEXT:    vpextrq $1, %xmm1, %rax
 ; CHECK-X64-V4-NEXT:    xorl %edx, %edx
 ; CHECK-X64-V4-NEXT:    divq %rcx
 ; CHECK-X64-V4-NEXT:    movq %rax, %rcx
-; CHECK-X64-V4-NEXT:    vmovq %xmm3, %rsi
+; CHECK-X64-V4-NEXT:    vmovq %xmm2, %rsi
 ; CHECK-X64-V4-NEXT:    vmovq %xmm1, %rax
 ; CHECK-X64-V4-NEXT:    xorl %edx, %edx
 ; CHECK-X64-V4-NEXT:    divq %rsi
+; CHECK-X64-V4-NEXT:    vpsllq $63, %xmm0, %xmm0
+; CHECK-X64-V4-NEXT:    vpmovq2m %xmm0, %k1
 ; CHECK-X64-V4-NEXT:    vmovq %rcx, %xmm0
-; CHECK-X64-V4-NEXT:    vmovq %rax, %xmm1
-; CHECK-X64-V4-NEXT:    vpunpcklqdq {{.*#+}} xmm0 = xmm1[0],xmm0[0]
+; CHECK-X64-V4-NEXT:    vmovq %rax, %xmm2
+; CHECK-X64-V4-NEXT:    vpunpcklqdq {{.*#+}} xmm1 {%k1} = xmm2[0],xmm0[0]
+; CHECK-X64-V4-NEXT:    vmovdqa %xmm1, %xmm0
 ; CHECK-X64-V4-NEXT:    retq
   %non_zero = add nsw nuw <2 x i64> %y, <i64 1, i64 1>
   %d = select <2 x i1> %c, <2 x i64> %non_zero, <2 x i64> <i64 1, i64 1>
diff --git a/llvm/test/CodeGen/X86/known-never-zero.ll b/llvm/test/CodeGen/X86/known-never-zero.ll
--- a/llvm/test/CodeGen/X86/known-never-zero.ll
+++ b/llvm/test/CodeGen/X86/known-never-zero.ll
@@ -47,9 +47,7 @@
 ; CHECK-NEXT:    testb $1, %dil
 ; CHECK-NEXT:    movl $122, %eax
 ; CHECK-NEXT:    cmovnel %esi, %eax
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %y = or i32 %x, 1
   %z = select i1 %c, i32 %y, i32 122
@@ -85,9 +83,7 @@
 ; CHECK-NEXT:    movl $123, %eax
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    shll %cl, %eax
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %z = shl i32 123, %x
   %r = call i32 @llvm.cttz.i32(i32 %z, i1 false)
@@ -101,9 +97,7 @@
 ; CHECK-NEXT:    orl $256, %esi # imm = 0x100
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    shll %cl, %esi
-; CHECK-NEXT:    bsfl %esi, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %esi, %eax
 ; CHECK-NEXT:    retq
   %y = or i32 %yy, 256
   %z = shl nsw i32 %y, %x
@@ -118,9 +112,7 @@
 ; CHECK-NEXT:    orl $256, %esi # imm = 0x100
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    shll %cl, %esi
-; CHECK-NEXT:    bsfl %esi, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %esi, %eax
 ; CHECK-NEXT:    retq
   %y = or i32 %yy, 256
   %z = shl nuw i32 %y, %x
@@ -153,9 +145,7 @@
 ; CHECK-NEXT:    incl %edi
 ; CHECK-NEXT:    movl $-1, %eax
 ; CHECK-NEXT:    cmovnel %edi, %eax
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %z = call i32 @llvm.uadd.sat.i32(i32 %x, i32 1)
   %r = call i32 @llvm.cttz.i32(i32 %z, i1 false)
@@ -190,9 +180,7 @@
 ; CHECK-NEXT:    shll %cl, %eax
 ; CHECK-NEXT:    cmpl %eax, %edi
 ; CHECK-NEXT:    cmoval %edi, %eax
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %yy = shl nuw i32 4, %y
   %z = call i32 @llvm.umax.i32(i32 %x, i32 %yy)
@@ -228,9 +216,7 @@
 ; CHECK-NEXT:    addl $4, %esi
 ; CHECK-NEXT:    cmpl %esi, %eax
 ; CHECK-NEXT:    cmovbl %eax, %esi
-; CHECK-NEXT:    bsfl %esi, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %esi, %eax
 ; CHECK-NEXT:    retq
   %x = shl nuw i32 4, %xx
   %y = add nuw nsw i32 %yy, 4
@@ -371,9 +357,7 @@
 ; CHECK-NEXT:    orl $256, %esi # imm = 0x100
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    sarl %cl, %esi
-; CHECK-NEXT:    bsfl %esi, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %esi, %eax
 ; CHECK-NEXT:    retq
   %y = or i32 %yy, 256
   %z = ashr exact i32 %y, %x
@@ -407,9 +391,7 @@
 ; CHECK-NEXT:    movl $-2147360405, %eax # imm = 0x8001E16B
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    shrl %cl, %eax
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %z = lshr i32 2147606891, %x
   %r = call i32 @llvm.cttz.i32(i32 %z, i1 false)
@@ -423,9 +405,7 @@
 ; CHECK-NEXT:    orl $256, %esi # imm = 0x100
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    shrl %cl, %esi
-; CHECK-NEXT:    bsfl %esi, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %esi, %eax
 ; CHECK-NEXT:    retq
   %y = or i32 %yy, 256
   %z = lshr exact i32 %y, %x
@@ -459,9 +439,7 @@
 ; CHECK-NEXT:    orl $64, %eax
 ; CHECK-NEXT:    xorl %edx, %edx
 ; CHECK-NEXT:    divl %esi
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %x = or i32 %xx, 64
   %z = udiv exact i32 %x, %y
@@ -495,9 +473,7 @@
 ; CHECK-NEXT:    orl $64, %eax
 ; CHECK-NEXT:    cltd
 ; CHECK-NEXT:    idivl %esi
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %x = or i32 %xx, 64
   %z = sdiv exact i32 %x, %y
@@ -529,9 +505,7 @@
 ; CHECK:       # %bb.0:
 ; CHECK-NEXT:    orl $1, %edi
 ; CHECK-NEXT:    addl %esi, %edi
-; CHECK-NEXT:    bsfl %edi, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %edi, %eax
 ; CHECK-NEXT:    retq
   %x = or i32 %xx, 1
   %z = add nuw i32 %x, %y
@@ -565,9 +539,7 @@
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    shll %cl, %eax
 ; CHECK-NEXT:    negl %eax
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %x = shl nuw nsw i32 256, %xx
   %z = sub i32 0, %x
@@ -582,9 +554,7 @@
 ; CHECK-NEXT:    orl $64, %eax
 ; CHECK-NEXT:    andl $-65, %edi
 ; CHECK-NEXT:    subl %eax, %edi
-; CHECK-NEXT:    bsfl %edi, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %edi, %eax
 ; CHECK-NEXT:    retq
   %x = or i32 %xx, 64
   %y = and i32 %xx, -65
@@ -745,9 +715,7 @@
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    shll %cl, %eax
 ; CHECK-NEXT:    movzwl %ax, %eax
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %x = shl nuw nsw i16 256, %xx
   %z = zext i16 %x to i32
@@ -780,9 +748,7 @@
 ; CHECK-NEXT:    # kill: def $cl killed $cl killed $ecx
 ; CHECK-NEXT:    shll %cl, %eax
 ; CHECK-NEXT:    cwtl
-; CHECK-NEXT:    bsfl %eax, %ecx
-; CHECK-NEXT:    movl $32, %eax
-; CHECK-NEXT:    cmovnel %ecx, %eax
+; CHECK-NEXT:    rep bsfl %eax, %eax
 ; CHECK-NEXT:    retq
   %x = shl nuw nsw i16 256, %xx
   %z = sext i16 %x to i32