Index: llvm/lib/Analysis/ValueTracking.cpp
===================================================================
--- llvm/lib/Analysis/ValueTracking.cpp
+++ llvm/lib/Analysis/ValueTracking.cpp
@@ -4457,6 +4457,22 @@
 
     break;
   }
+  case Instruction::FMul: {
+    KnownFPClass KnownLHS, KnownRHS;
+    computeKnownFPClass(Op->getOperand(1), DemandedElts, fcNan | fcInf,
+                        KnownRHS, Depth + 1, Q, TLI);
+    if (KnownRHS.isKnownNeverNaN() && KnownRHS.isKnownNeverInfinity()) {
+      computeKnownFPClass(Op->getOperand(0), DemandedElts, fcNan | fcInf,
+                          KnownLHS, Depth + 1, Q, TLI);
+
+      // Zero multiplied with infinity produces NaN.
+      // FIXME: If neither side can be zero fmul never produces NaN.
+      if (KnownLHS.isKnownNeverNaN() && KnownLHS.isKnownNeverInfinity())
+        Known.knownNot(fcNan);
+    }
+
+    break;
+  }
   case Instruction::SIToFP:
   case Instruction::UIToFP: {
     // Cannot produce nan
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
@@ -22,7 +22,7 @@
 }
 
 define float @ret_fmul_nonan_noinf__nonan_noinf(float nofpclass(nan inf) %arg0, float nofpclass(nan inf) %arg1) {
-; CHECK-LABEL: define float @ret_fmul_nonan_noinf__nonan_noinf
+; CHECK-LABEL: define nofpclass(nan) float @ret_fmul_nonan_noinf__nonan_noinf
 ; CHECK-SAME: (float nofpclass(nan inf) [[ARG0:%.*]], float nofpclass(nan inf) [[ARG1:%.*]]) #[[ATTR0]] {
 ; CHECK-NEXT:    [[FMUL:%.*]] = fmul float [[ARG0]], [[ARG1]]
 ; CHECK-NEXT:    ret float [[FMUL]]
Index: llvm/unittests/Analysis/ValueTrackingTest.cpp
===================================================================
--- llvm/unittests/Analysis/ValueTrackingTest.cpp
+++ llvm/unittests/Analysis/ValueTrackingTest.cpp
@@ -1575,6 +1575,23 @@
   expectKnownFPClass(fcAllFlags, std::nullopt, A5);
 }
 
+TEST_F(ComputeKnownFPClassTest, FMul) {
+  parseAssembly(
+      "define float @test(float nofpclass(nan inf) %nnan.ninf, float nofpclass(nan) %nnan, float nofpclass(qnan) %no.qnan, float %unknown) {\n"
+      "  %A = fmul float %nnan.ninf, %nnan.ninf"
+      "  %A2 = fmul float %nnan.ninf, %nnan"
+      "  %A3 = fmul float %nnan, %nnan.ninf"
+      "  %A4 = fmul float %nnan.ninf, %no.qnan"
+      "  %A5 = fmul float %nnan, %nnan"
+      "  ret float %A\n"
+      "}\n");
+  expectKnownFPClass(fcFinite | fcInf, std::nullopt, A);
+  expectKnownFPClass(fcAllFlags, std::nullopt, A2);
+  expectKnownFPClass(fcAllFlags, std::nullopt, A3);
+  expectKnownFPClass(fcAllFlags, std::nullopt, A4);
+  expectKnownFPClass(fcAllFlags, std::nullopt, A5);
+}
+
 TEST_F(ValueTrackingTest, isNonZeroRecurrence) {
   parseAssembly(R"(
     define i1 @test(i8 %n, i8 %r) {