diff --git a/llvm/lib/Support/APFloat.cpp b/llvm/lib/Support/APFloat.cpp
--- a/llvm/lib/Support/APFloat.cpp
+++ b/llvm/lib/Support/APFloat.cpp
@@ -2226,9 +2226,16 @@
   }
 
   // If this is a truncation, perform the shift before we narrow the storage.
-  if (shift < 0 && (isFiniteNonZero() || category==fcNaN))
+  if (shift < 0 && (isFiniteNonZero() || category==fcNaN)) {
     lostFraction = shiftRight(significandParts(), oldPartCount, -shift);
 
+    // If we are truncating a denormal, the lostFraction is not relevant when
+    // normalizing, but it can't be lfExactlyZero or lfMoreThanHalf, otherwise
+    // it would return incorrect result if the significand is zero after shift
+    if (isDenormal())
+      lostFraction = lfLessThanHalf;
+  }
+
   // Fix the storage so it can hold to new value.
   if (newPartCount > oldPartCount) {
     // The new type requires more storage; make it available.
diff --git a/llvm/test/Transforms/InstSimplify/ConstProp/cast.ll b/llvm/test/Transforms/InstSimplify/ConstProp/cast.ll
--- a/llvm/test/Transforms/InstSimplify/ConstProp/cast.ll
+++ b/llvm/test/Transforms/InstSimplify/ConstProp/cast.ll
@@ -79,21 +79,17 @@
   ret float %b
 }
 
-; FIXME: This should be 0.0.
-
 define float @trunc_denorm_lost_fraction1() {
 ; CHECK-LABEL: @trunc_denorm_lost_fraction1(
-; CHECK-NEXT:    ret float 0x36A0000000000000
+; CHECK-NEXT:    ret float 0.000000e+00
 ;
   %b = fptrunc double 0x0000000010000001 to float
   ret float %b
 }
 
-; FIXME: This should be 0.0.
-
 define float @trunc_denorm_lost_fraction2() {
 ; CHECK-LABEL: @trunc_denorm_lost_fraction2(
-; CHECK-NEXT:    ret float 0x36A0000000000000
+; CHECK-NEXT:    ret float 0.000000e+00
 ;
   %b = fptrunc double 0x000000001fffffff to float
   ret float %b
@@ -107,11 +103,9 @@
   ret float %b
 }
 
-; FIXME: This should be -0.0.
-
 define float @trunc_denorm_lost_fraction4() {
 ; CHECK-LABEL: @trunc_denorm_lost_fraction4(
-; CHECK-NEXT:    ret float 0xB6A0000000000000
+; CHECK-NEXT:    ret float -0.000000e+00
 ;
   %b = fptrunc double 0x8000000010000001 to float
   ret float %b
diff --git a/llvm/unittests/ADT/APFloatTest.cpp b/llvm/unittests/ADT/APFloatTest.cpp
--- a/llvm/unittests/ADT/APFloatTest.cpp
+++ b/llvm/unittests/ADT/APFloatTest.cpp
@@ -1859,6 +1859,32 @@
   EXPECT_EQ(0x7fc00000, test.bitcastToAPInt());
   EXPECT_TRUE(losesInfo);
   EXPECT_EQ(status, APFloat::opOK);
+
+  // Test that subnormals are handled correctly in double to float conversion
+  test = APFloat(APFloat::IEEEdouble(), "0x0.0000010000000p-1022");
+  test.convert(APFloat::IEEEsingle(), APFloat::rmNearestTiesToEven, &losesInfo);
+  EXPECT_EQ(0.0f, test.convertToFloat());
+  EXPECT_TRUE(losesInfo);
+
+  test = APFloat(APFloat::IEEEdouble(), "0x0.0000010000001p-1022");
+  test.convert(APFloat::IEEEsingle(), APFloat::rmNearestTiesToEven, &losesInfo);
+  EXPECT_EQ(0.0f, test.convertToFloat());
+  EXPECT_TRUE(losesInfo);
+
+  test = APFloat(APFloat::IEEEdouble(), "-0x0.0000010000001p-1022");
+  test.convert(APFloat::IEEEsingle(), APFloat::rmNearestTiesToEven, &losesInfo);
+  EXPECT_EQ(0.0f, test.convertToFloat());
+  EXPECT_TRUE(losesInfo);
+
+  test = APFloat(APFloat::IEEEdouble(), "0x0.0000020000000p-1022");
+  test.convert(APFloat::IEEEsingle(), APFloat::rmNearestTiesToEven, &losesInfo);
+  EXPECT_EQ(0.0f, test.convertToFloat());
+  EXPECT_TRUE(losesInfo);
+
+  test = APFloat(APFloat::IEEEdouble(), "0x0.0000020000001p-1022");
+  test.convert(APFloat::IEEEsingle(), APFloat::rmNearestTiesToEven, &losesInfo);
+  EXPECT_EQ(0.0f, test.convertToFloat());
+  EXPECT_TRUE(losesInfo);
 }
 
 TEST(APFloatTest, PPCDoubleDouble) {