diff --git a/llvm/lib/Target/NVPTX/NVPTXISelLowering.cpp b/llvm/lib/Target/NVPTX/NVPTXISelLowering.cpp
--- a/llvm/lib/Target/NVPTX/NVPTXISelLowering.cpp
+++ b/llvm/lib/Target/NVPTX/NVPTXISelLowering.cpp
@@ -553,20 +553,29 @@
   // These map to corresponding instructions for f32/f64. f16 must be
   // promoted to f32. v2f16 is expanded to f16, which is then promoted
   // to f32.
-  for (const auto &Op : {ISD::FDIV, ISD::FREM, ISD::FSQRT, ISD::FSIN, ISD::FCOS,
-                         ISD::FABS, ISD::FMINNUM, ISD::FMAXNUM}) {
+  for (const auto &Op :
+       {ISD::FDIV, ISD::FREM, ISD::FSQRT, ISD::FSIN, ISD::FCOS, ISD::FABS}) {
     setOperationAction(Op, MVT::f16, Promote);
     setOperationAction(Op, MVT::f32, Legal);
     setOperationAction(Op, MVT::f64, Legal);
     setOperationAction(Op, MVT::v2f16, Expand);
   }
-  // max.f16 is supported on sm_80+.
-  if (STI.allowFP16Math() && STI.getSmVersion() >= 80 &&
-      STI.getPTXVersion() >= 70) {
-    setOperationAction(ISD::FMINNUM, MVT::f16, Legal);
-    setOperationAction(ISD::FMAXNUM, MVT::f16, Legal);
-    setOperationAction(ISD::FMINNUM, MVT::v2f16, Legal);
-    setOperationAction(ISD::FMAXNUM, MVT::v2f16, Legal);
+  // max.f16, max.f16x2 and max.NaN are supported on sm_80+.
+  auto GetMinMaxAction = [&](LegalizeAction NotSm80Action) {
+    bool IsAtLeastSm80 = STI.getSmVersion() >= 80 && STI.getPTXVersion() >= 70;
+    return IsAtLeastSm80 ? Legal : NotSm80Action;
+  };
+  for (const auto &Op : {ISD::FMINNUM, ISD::FMAXNUM}) {
+    setFP16OperationAction(Op, MVT::f16, GetMinMaxAction(Promote), Promote);
+    setOperationAction(Op, MVT::f32, Legal);
+    setOperationAction(Op, MVT::f64, Legal);
+    setFP16OperationAction(Op, MVT::v2f16, GetMinMaxAction(Expand), Expand);
+  }
+  for (const auto &Op : {ISD::FMINIMUM, ISD::FMAXIMUM}) {
+    setFP16OperationAction(Op, MVT::f16, GetMinMaxAction(Expand), Expand);
+    setOperationAction(Op, MVT::f32, GetMinMaxAction(Expand));
+    setOperationAction(Op, MVT::f64, GetMinMaxAction(Expand));
+    setFP16OperationAction(Op, MVT::v2f16, GetMinMaxAction(Expand), Expand);
   }
 
   // No FEXP2, FLOG2.  The PTX ex2 and log2 functions are always approximate.
diff --git a/llvm/lib/Target/NVPTX/NVPTXInstrInfo.td b/llvm/lib/Target/NVPTX/NVPTXInstrInfo.td
--- a/llvm/lib/Target/NVPTX/NVPTXInstrInfo.td
+++ b/llvm/lib/Target/NVPTX/NVPTXInstrInfo.td
@@ -868,6 +868,8 @@
 
 defm FMIN : F3<"min", fminnum>;
 defm FMAX : F3<"max", fmaxnum>;
+defm FMINNAN : F3<"min.NaN", fminimum>;
+defm FMAXNAN : F3<"max.NaN", fmaximum>;
 
 defm FABS  : F2<"abs", fabs>;
 defm FNEG  : F2<"neg", fneg>;
diff --git a/llvm/test/CodeGen/NVPTX/fminimum-fmaximum.ll b/llvm/test/CodeGen/NVPTX/fminimum-fmaximum.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/CodeGen/NVPTX/fminimum-fmaximum.ll
@@ -0,0 +1,92 @@
+; RUN: llc < %s -march=nvptx | FileCheck %s --check-prefixes=CHECK,CHECK-NONAN
+; RUN: llc < %s -march=nvptx -mcpu=sm_80 | FileCheck %s --check-prefixes=CHECK,CHECK-NAN
+
+; ---- minimum ----
+
+; CHECK-LABEL: minimum_half
+define half @minimum_half(half %a) #0 {
+  ; CHECK-NONAN: setp
+  ; CHECK-NONAN: selp.b16
+  ; CHECK-NAN: min.NaN.f16
+  %p = fcmp ult half %a, 0.0
+  %x = select i1 %p, half %a, half 0.0
+  ret half %x
+}
+
+; CHECK-LABEL: minimum_float
+define float @minimum_float(float %a) #0 {
+  ; CHECK-NONAN: setp
+  ; CHECK-NONAN: selp.f32
+  ; CHECK-NAN: min.NaN.f32
+  %p = fcmp ult float %a, 0.0
+  %x = select i1 %p, float %a, float 0.0
+  ret float %x
+}
+
+; CHECK-LABEL: minimum_double
+define double @minimum_double(double %a) #0 {
+  ; CHECK-NONAN: setp
+  ; CHECK-NONAN: selp.f64
+  ; CHECK-NAN: min.NaN.f64
+  %p = fcmp ult double %a, 0.0
+  %x = select i1 %p, double %a, double 0.0
+  ret double %x
+}
+
+; CHECK-LABEL: minimum_v2half
+define <2 x half> @minimum_v2half(<2 x half> %a, <2 x half> %b) #0 {
+  ; CHECK-NONAN-DAG: setp
+  ; CHECK-NONAN-DAG: setp
+  ; CHECK-NONAN-DAG: selp.b16
+  ; CHECK-NONAN-DAG: selp.b16
+  ; CHECK-NAN: min.NaN.f16x2
+  %p = fcmp ult <2 x half> %a, zeroinitializer
+  %x = select <2 x i1> %p, <2 x half> %a, <2 x half> zeroinitializer
+  ret <2 x half> %x
+}
+
+; ---- maximum ----
+
+; CHECK-LABEL: maximum_half
+define half @maximum_half(half %a) #0 {
+  ; CHECK-NONAN: setp
+  ; CHECK-NONAN: selp.b16
+  ; CHECK-NAN: max.NaN.f16
+  %p = fcmp ugt half %a, 0.0
+  %x = select i1 %p, half %a, half 0.0
+  ret half %x
+}
+
+; CHECK-LABEL: maximum_float
+define float @maximum_float(float %a) #0 {
+  ; CHECK-NONAN: setp
+  ; CHECK-NONAN: selp.f32
+  ; CHECK-NAN: max.NaN.f32
+  %p = fcmp ugt float %a, 0.0
+  %x = select i1 %p, float %a, float 0.0
+  ret float %x
+}
+
+; CHECK-LABEL: maximum_double
+define double @maximum_double(double %a) #0 {
+  ; CHECK-NONAN: setp
+  ; CHECK-NONAN: selp.f64
+  ; CHECK-NAN: max.NaN.f64
+  %p = fcmp ugt double %a, 0.0
+  %x = select i1 %p, double %a, double 0.0
+  ret double %x
+}
+
+; CHECK-LABEL: maximum_v2half
+define <2 x half> @maximum_v2half(<2 x half> %a, <2 x half> %b) #0 {
+  ; CHECK-NONAN-DAG: setp
+  ; CHECK-NONAN-DAG: setp
+  ; CHECK-NONAN-DAG: selp.b16
+  ; CHECK-NONAN-DAG: selp.b16
+  ; CHECK-NAN: max.NaN.f16x2
+  %p = fcmp ugt <2 x half> %a, zeroinitializer
+  %x = select <2 x i1> %p, <2 x half> %a, <2 x half> zeroinitializer
+  ret <2 x half> %x
+}
+
+attributes #0 = { "no-signed-zeros-fp-math"="true" }