Index: llvm/lib/Analysis/ValueTracking.cpp
===================================================================
--- llvm/lib/Analysis/ValueTracking.cpp
+++ llvm/lib/Analysis/ValueTracking.cpp
@@ -4472,6 +4472,13 @@
     break;
   }
   case Instruction::FMul: {
+    // X * X is always non-negative or a NaN.
+    if (Op->getOperand(0) == Op->getOperand(1))
+      Known.knownNot(fcNegative);
+
+    if ((InterestedClasses & fcNan) != fcNan)
+      break;
+
     KnownFPClass KnownLHS, KnownRHS;
     computeKnownFPClass(Op->getOperand(1), DemandedElts,
                         fcNan | fcInf | fcZero | fcSubnormal, KnownRHS,
Index: llvm/test/Transforms/Attributor/nofpclass-nan-fmul.ll
===================================================================
--- llvm/test/Transforms/Attributor/nofpclass-nan-fmul.ll
+++ llvm/test/Transforms/Attributor/nofpclass-nan-fmul.ll
@@ -164,6 +164,36 @@
   ret float %fmul
 }
 
+define float @ret_fmul_square(float %arg) #0 {
+; CHECK-LABEL: define nofpclass(ninf nzero nsub nnorm) float @ret_fmul_square
+; CHECK-SAME: (float [[ARG:%.*]]) #[[ATTR0]] {
+; CHECK-NEXT:    [[FMUL:%.*]] = fmul float [[ARG]], [[ARG]]
+; CHECK-NEXT:    ret float [[FMUL]]
+;
+  %fmul = fmul float %arg, %arg
+  ret float %fmul
+}
+
+define float @ret_fmul_square_nnan(float nofpclass(nan) %arg) #0 {
+; CHECK-LABEL: define nofpclass(ninf nzero nsub nnorm) float @ret_fmul_square_nnan
+; CHECK-SAME: (float nofpclass(nan) [[ARG:%.*]]) #[[ATTR0]] {
+; CHECK-NEXT:    [[FMUL:%.*]] = fmul float [[ARG]], [[ARG]]
+; CHECK-NEXT:    ret float [[FMUL]]
+;
+  %fmul = fmul float %arg, %arg
+  ret float %fmul
+}
+
+define float @ret_fmul_square_nnan_nzero(float nofpclass(nan zero) %arg) #0 {
+; CHECK-LABEL: define nofpclass(nan ninf nzero nsub nnorm) float @ret_fmul_square_nnan_nzero
+; CHECK-SAME: (float nofpclass(nan zero) [[ARG:%.*]]) #[[ATTR0]] {
+; CHECK-NEXT:    [[FMUL:%.*]] = fmul float [[ARG]], [[ARG]]
+; CHECK-NEXT:    ret float [[FMUL]]
+;
+  %fmul = fmul float %arg, %arg
+  ret float %fmul
+}
+
 attributes #0 = { "denormal-fp-math"="ieee,ieee" }
 attributes #1 = { "denormal-fp-math"="ieee,preserve-sign" }
 attributes #2 = { "denormal-fp-math"="ieee,positive-zero" }