Index: llvm/lib/Analysis/ConstantFolding.cpp
===================================================================
--- llvm/lib/Analysis/ConstantFolding.cpp
+++ llvm/lib/Analysis/ConstantFolding.cpp
@@ -3183,6 +3183,12 @@
         break;
       }
 
+      case LibFunc_atan:
+      case LibFunc_atanf:
+      case LibFunc_atanl:
+        return !Op.isDenormal();
+
+
       case LibFunc_asinl:
       case LibFunc_asin:
       case LibFunc_asinf:
@@ -3248,6 +3254,21 @@
         return Op0.isNaN() || Op1.isNaN() ||
                (!Op0.isInfinity() && !Op1.isZero());
 
+      case LibFunc_atan2:
+      case LibFunc_atan2f:
+      case LibFunc_atan2l: {
+        // atan2 can fail if the result underflows. Notice the magnitude of
+        // result is atan(Op0/Op1) and atan(x) approaches x at 0.
+        // Op0/Op1/2 is a conservative lowerbound for the result magnitue-wise
+        // If this bound is denormalized or rounds to 0, we return false.
+        auto Two = APFloat(2.0);
+        bool ignore;
+        Two.convert(Op0.getSemantics(), APFloat::rmNearestTiesToEven, &ignore);
+        auto ResLowerBound = Op0 / Op1 / Two;
+        return !ResLowerBound.isDenormal() &&
+               !(!Op0.isZero() && ResLowerBound.isZero());
+      }
+
       default:
         break;
       }
Index: llvm/test/Transforms/EarlyCSE/atan.ll
===================================================================
--- /dev/null
+++ llvm/test/Transforms/EarlyCSE/atan.ll
@@ -0,0 +1,112 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -early-cse -S < %s | FileCheck %s
+
+define float @callatan0() {
+; CHECK-LABEL: @callatan0(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float -0.000000e+00
+;
+entry:
+  %call = call float @atanf(float -0.0)
+  ret float %call
+}
+
+define float @callatanInf() {
+; CHECK-LABEL: @callatanInf(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CALL:%.*]] = call float @atanf(float 0x7FF0000000000000)
+; CHECK-NEXT:    ret float [[CALL]]
+;
+entry:
+  %call = call float @atanf(float 0x7FF0000000000000)
+  ret float %call
+}
+
+define float @callatanNaN() {
+; CHECK-LABEL: @callatanNaN(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CALL:%.*]] = call float @atanf(float 0x7FF8000000000000)
+; CHECK-NEXT:    ret float [[CALL]]
+;
+entry:
+  %call = call float @atanf(float 0x7FF8000000000000)
+  ret float %call
+}
+
+define float @callatanDenorm() {
+; CHECK-LABEL: @callatanDenorm(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CALL:%.*]] = call float @atanf(float 0x37A16C2000000000)
+; CHECK-NEXT:    ret float 0x37A16C2000000000
+;
+entry:
+  %call = call float @atanf(float 0x37A16C2000000000)
+  ret float %call
+}
+
+define float @callatan2_00() {
+; CHECK-LABEL: @callatan2_00(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float -0.000000e+00
+;
+entry:
+  %call = call float @atan2f(float -0.0, float 0.0)
+  ret float %call
+}
+
+define float @callatan2_x0() {
+; CHECK-LABEL: @callatan2_x0(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 0x3FF921FB60000000
+;
+entry:
+  %call = call float @atan2f(float 1.0, float -0.000000e+00)
+  ret float %call
+}
+
+define float @callatan2_0x() {
+; CHECK-LABEL: @callatan2_0x(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float -0.000000e+00
+;
+entry:
+  %call = call float @atan2f(float -0.0, float 1.0)
+  ret float %call
+}
+
+define float @callatan2_xx() {
+; CHECK-LABEL: @callatan2_xx(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 0xBFE921FB60000000
+;
+entry:
+  %call = call float @atan2f(float -1.0, float 1.0)
+  ret float %call
+}
+
+define float @callatan2_denorm() {
+; CHECK-LABEL: @callatan2_denorm(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CALL:%.*]] = call float @atan2f(float 0x39B4484C00000000, float 1.000000e+10)
+; CHECK-NEXT:    ret float 0x37A16C2000000000
+;
+entry:
+  %call = call float @atan2f(float 0x39B4484C00000000, float 1.0e+10)
+  ret float %call
+}
+
+define float @callatan2_flush_to_zero() {
+; CHECK-LABEL: @callatan2_flush_to_zero(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CALL:%.*]] = call float @atan2f(float 0x39B4484C00000000, float 0x4415AF1D80000000)
+; CHECK-NEXT:    ret float 0.000000e+00
+;
+entry:
+  %call = call float @atan2f(float 0x39B4484C00000000, float 0x4415AF1D80000000)
+  ret float %call
+}
+
+declare dso_local float @atanf(float) #0
+declare dso_local float @atan2f(float, float) #0
+
+attributes #0 = { nofree nounwind willreturn }
\ No newline at end of file
Index: llvm/test/Transforms/InstSimplify/ConstProp/math-1.ll
===================================================================
--- llvm/test/Transforms/InstSimplify/ConstProp/math-1.ll
+++ llvm/test/Transforms/InstSimplify/ConstProp/math-1.ll
@@ -22,7 +22,6 @@
 declare double @atan(double) #0
 define double @f_atan() {
 ; CHECK-LABEL: @f_atan(
-; CHECK-NEXT:    [[RES:%.*]] = tail call fast double @atan(double 1.000000e+00)
 ; CHECK-NEXT:    ret double 0x3FE921FB
 ;
   %res = tail call fast double @atan(double 1.0)
Index: llvm/test/Transforms/InstSimplify/ConstProp/math-2.ll
===================================================================
--- llvm/test/Transforms/InstSimplify/ConstProp/math-2.ll
+++ llvm/test/Transforms/InstSimplify/ConstProp/math-2.ll
@@ -4,7 +4,6 @@
 declare double @atan2(double, double) #0
 define double @f_atan2() {
 ; CHECK-LABEL: @f_atan2(
-; CHECK-NEXT:    [[RES:%.*]] = tail call fast double @atan2(double 1.000000e+00, double 2.000000e+00)
 ; CHECK-NEXT:    ret double 0x3FDDAC6{{.+}}
 ;
   %res = tail call fast double @atan2(double 1.0, double 2.0)