Index: llvm/include/llvm/Analysis/ValueTracking.h
===================================================================
--- llvm/include/llvm/Analysis/ValueTracking.h
+++ llvm/include/llvm/Analysis/ValueTracking.h
@@ -275,6 +275,19 @@
   /// floating-point mode for the function interprets denormals as zero.
   bool isKnownNeverLogicalZero(const Function &F, Type *Ty) const;
 
+  /// Return true if we can prove that the analyzed floating-point value is
+  /// either NaN or never less than -0.0.
+  ///
+  ///      NaN --> true
+  ///       +0 --> true
+  ///       -0 --> true
+  ///   x > +0 --> true
+  ///   x < -0 --> false
+  bool cannotBeOrderedLessThanZero() const {
+    const FPClassTest OrderedNegMask = fcNegSubnormal | fcNegNormal | fcNegInf;
+    return (KnownFPClasses & OrderedNegMask) == fcNone;
+  }
+
   KnownFPClass &operator|=(const KnownFPClass &RHS) {
     KnownFPClasses = KnownFPClasses | RHS.KnownFPClasses;
 
Index: llvm/unittests/Analysis/ValueTrackingTest.cpp
===================================================================
--- llvm/unittests/Analysis/ValueTrackingTest.cpp
+++ llvm/unittests/Analysis/ValueTrackingTest.cpp
@@ -1616,6 +1616,59 @@
   expectKnownFPClass(fcAllFlags, std::nullopt, A7);
 }
 
+TEST_F(ComputeKnownFPClassTest, CannotBeOrderedLessThanZero) {
+  parseAssembly("define float @test(float %arg) {\n"
+                "  %A = fmul float %arg, %arg"
+                "  ret float %A\n"
+                "}\n");
+
+  Type *FPTy = Type::getDoubleTy(M->getContext());
+  const DataLayout &DL = M->getDataLayout();
+
+  EXPECT_TRUE(
+      computeKnownFPClass(ConstantFP::getZero(FPTy, /*Negative=*/false), DL)
+          .cannotBeOrderedLessThanZero());
+  EXPECT_TRUE(
+      computeKnownFPClass(ConstantFP::getZero(FPTy, /*Negative=*/true), DL)
+          .cannotBeOrderedLessThanZero());
+
+  EXPECT_TRUE(computeKnownFPClass(ConstantFP::getInfinity(FPTy, false), DL)
+                  .cannotBeOrderedLessThanZero());
+  EXPECT_FALSE(computeKnownFPClass(ConstantFP::getInfinity(FPTy, true), DL)
+                   .cannotBeOrderedLessThanZero());
+
+  EXPECT_TRUE(computeKnownFPClass(ConstantFP::get(FPTy, 1.0), DL)
+                  .cannotBeOrderedLessThanZero());
+  EXPECT_FALSE(computeKnownFPClass(ConstantFP::get(FPTy, -1.0), DL)
+                   .cannotBeOrderedLessThanZero());
+
+  EXPECT_TRUE(
+      computeKnownFPClass(
+          ConstantFP::get(FPTy, APFloat::getSmallest(FPTy->getFltSemantics(),
+                                                     /*Negative=*/false)),
+          DL)
+          .cannotBeOrderedLessThanZero());
+  EXPECT_FALSE(
+      computeKnownFPClass(
+          ConstantFP::get(FPTy, APFloat::getSmallest(FPTy->getFltSemantics(),
+                                                     /*Negative=*/true)),
+          DL)
+          .cannotBeOrderedLessThanZero());
+
+  EXPECT_TRUE(
+      computeKnownFPClass(ConstantFP::getQNaN(FPTy, /*Negative=*/false), DL)
+          .cannotBeOrderedLessThanZero());
+  EXPECT_TRUE(
+      computeKnownFPClass(ConstantFP::getQNaN(FPTy, /*Negative=*/true), DL)
+          .cannotBeOrderedLessThanZero());
+  EXPECT_TRUE(
+      computeKnownFPClass(ConstantFP::getSNaN(FPTy, /*Negative=*/false), DL)
+          .cannotBeOrderedLessThanZero());
+  EXPECT_TRUE(
+      computeKnownFPClass(ConstantFP::getSNaN(FPTy, /*Negative=*/true), DL)
+          .cannotBeOrderedLessThanZero());
+}
+
 TEST_F(ValueTrackingTest, isNonZeroRecurrence) {
   parseAssembly(R"(
     define i1 @test(i8 %n, i8 %r) {