diff --git a/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp b/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
@@ -1337,6 +1337,19 @@
     if (Instruction *Res = processUGT_ADDCST_ADD(Cmp, A, B, CI2, CI, *this))
       return Res;
 
+  Value *X;
+  // icmp slt (and (sub 0, X), X), 0 --> icmp eq (X, CI)
+  // icmp sgt (and (sub 0, X), X), -1 --> icmp ne (X, CI)
+  if (match(Op0, m_OneUse(m_And(m_Sub(m_Zero(), m_Value(X)), m_Deferred(X))))) {
+    Constant *CI = ConstantInt::get(
+        X->getType(),
+        APInt::getSignedMinValue(X->getType()->getScalarSizeInBits()));
+    if (Pred == ICmpInst::ICMP_SLT && match(Op1, m_Zero()))
+      return new ICmpInst(ICmpInst::ICMP_EQ, X, CI);
+    if (Pred == ICmpInst::ICMP_SGT && match(Op1, m_AllOnes()))
+      return new ICmpInst(ICmpInst::ICMP_NE, X, CI);
+  }
+
   // icmp(phi(C1, C2, ...), C) -> phi(icmp(C1, C), icmp(C2, C), ...).
   Constant *C = dyn_cast<Constant>(Op1);
   if (!C)
diff --git a/llvm/test/Transforms/InstCombine/fold-signbit-test-power2.ll b/llvm/test/Transforms/InstCombine/fold-signbit-test-power2.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/fold-signbit-test-power2.ll
@@ -0,0 +1,23 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt < %s -passes=instcombine -S | FileCheck %s
+define i1 @pow2_or_zero1(i8 %x) {
+; CHECK-LABEL: @pow2_or_zero1(
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[X:%.*]], -128
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %negx = sub i8 0, %x
+  %pow2_or_zero = and i8 %negx, %x
+  %cmp = icmp slt i8 %pow2_or_zero, 0
+  ret i1 %cmp
+}
+
+define i1 @pow2_or_zero2(i8 %x) {
+; CHECK-LABEL: @pow2_or_zero2(
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ne i8 [[X:%.*]], -128
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %negx = sub i8 0, %x
+  %pow2_or_zero = and i8 %negx, %x
+  %cmp = icmp sgt i8 %pow2_or_zero, -1
+  ret i1 %cmp
+}
diff --git a/llvm/test/Transforms/InstCombine/minmax-of-xor-x.ll b/llvm/test/Transforms/InstCombine/minmax-of-xor-x.ll
--- a/llvm/test/Transforms/InstCombine/minmax-of-xor-x.ll
+++ b/llvm/test/Transforms/InstCombine/minmax-of-xor-x.ll
@@ -134,9 +134,7 @@
 
 define i8 @smax_xor_pow2_neg(i8 %x, i8 %y) {
 ; CHECK-LABEL: @smax_xor_pow2_neg(
-; CHECK-NEXT:    [[NY:%.*]] = sub i8 0, [[Y:%.*]]
-; CHECK-NEXT:    [[YP2:%.*]] = and i8 [[NY]], [[Y]]
-; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i8 [[YP2]], 0
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[Y:%.*]], -128
 ; CHECK-NEXT:    br i1 [[CMP]], label [[NEG:%.*]], label [[POS:%.*]]
 ; CHECK:       neg:
 ; CHECK-NEXT:    [[R:%.*]] = and i8 [[X:%.*]], 127