diff --git a/llvm/lib/Analysis/ConstantFolding.cpp b/llvm/lib/Analysis/ConstantFolding.cpp
index 4bece85d3cfbf..743ce92a5c1ea 100644
--- a/llvm/lib/Analysis/ConstantFolding.cpp
+++ b/llvm/lib/Analysis/ConstantFolding.cpp
@@ -2008,7 +2008,9 @@ bool llvm::canConstantFoldCallTo(const CallBase *Call, const Function *F) {
            Name == "log10f" || Name == "logb" || Name == "logbf" ||
            Name == "log1p" || Name == "log1pf";
   case 'n':
-    return Name == "nearbyint" || Name == "nearbyintf";
+    return Name == "nearbyint" || Name == "nearbyintf" || Name == "nextafter" ||
+           Name == "nextafterf" || Name == "nexttoward" ||
+           Name == "nexttowardf";
   case 'p':
     return Name == "pow" || Name == "powf";
   case 'r':
@@ -3174,6 +3176,57 @@ static Constant *evaluateCompare(const APFloat &Op1, const APFloat &Op2,
   return nullptr;
 }
 
+/// Returns the first NaN in the operand list if it exists, preserving the NaN
+/// payload if possible. Returns nullptr if no NaNs are in the list.
+static Constant *TryConstantFoldNaN(ArrayRef<APFloat> Operands,
+                                    const Type *RetTy) {
+  assert(RetTy != nullptr);
+  for (const APFloat &Op : Operands) {
+    if (Op.isNaN()) {
+      bool Unused;
+      APFloat Ret(Op);
+      Ret.convert(RetTy->getFltSemantics(), detail::rmNearestTiesToEven,
+                  &Unused);
+      return ConstantFP::get(RetTy->getContext(), Ret);
+    }
+  }
+  return nullptr;
+}
+
+static Constant *ConstantFoldNextToward(const APFloat &Op0, const APFloat &Op1,
+                                        const Type *RetTy) {
+  assert(RetTy != nullptr);
+  if (Constant *RetNaN = TryConstantFoldNaN({Op0, Op1}, RetTy))
+    return RetNaN;
+
+  // Recall that the second argument of nexttoward is always a long double,
+  // so we may need to promote the first argument for comparisons to be valid.
+  bool LosesInfo;
+  APFloat PromotedOp0(Op0);
+  PromotedOp0.convert(Op1.getSemantics(), detail::rmNearestTiesToEven,
+                      &LosesInfo);
+  assert(!LosesInfo && "Unexpected lossy promotion");
+  const APFloat::cmpResult Result = PromotedOp0.compare(Op1);
+  assert(Result != APFloat::cmpUnordered && "Unexpected NaN");
+
+  // When equal, the standard says we must return the second argument.
+  // This allows nice behavior such as nexttoward(0.0, -0.0) = -0.0 and
+  // nexttoward(-0.0, 0.0) = 0.0
+  if (Result == detail::cmpEqual) {
+    APFloat Ret(Op1);
+    Ret.convert(RetTy->getFltSemantics(), detail::rmNearestTiesToEven,
+                &LosesInfo);
+    return ConstantFP::get(RetTy->getContext(), Ret);
+  }
+
+  APFloat Next(Op0);
+  Next.next(/*nextDown=*/Result == APFloat::cmpGreaterThan);
+  const bool DidOverflow = !Op0.isInfinity() && Next.isInfinity();
+  if (Next.isZero() || Next.isDenormal() || DidOverflow)
+    return nullptr;
+  return ConstantFP::get(RetTy->getContext(), Next);
+}
+
 static Constant *ConstantFoldLibCall2(StringRef Name, Type *Ty,
                                       ArrayRef<Constant *> Operands,
                                       const TargetLibraryInfo *TLI) {
@@ -3233,6 +3286,13 @@ static Constant *ConstantFoldLibCall2(StringRef Name, Type *Ty,
     if (TLI->has(Func))
       return ConstantFoldBinaryFP(atan2, Op1V, Op2V, Ty);
     break;
+  case LibFunc_nextafter:
+  case LibFunc_nextafterf:
+  case LibFunc_nexttoward:
+  case LibFunc_nexttowardf:
+    if (TLI->has(Func)) {
+      return ConstantFoldNextToward(Op1V, Op2V, Ty);
+    }
   }
 
   return nullptr;
@@ -4685,6 +4745,14 @@ bool llvm::isMathLibCallNoop(const CallBase *Call,
         // may occur, so allow for that possibility.
         return !Op0.isZero() || !Op1.isZero();
 
+      case LibFunc_nextafter:
+      case LibFunc_nextafterf:
+      case LibFunc_nextafterl:
+      case LibFunc_nexttoward:
+      case LibFunc_nexttowardf:
+      case LibFunc_nexttowardl: {
+        return ConstantFoldNextToward(Op0, Op1, F->getReturnType()) != nullptr;
+      }
       default:
         break;
       }
diff --git a/llvm/test/Transforms/InstCombine/constant-fold-nextafter.ll b/llvm/test/Transforms/InstCombine/constant-fold-nextafter.ll
new file mode 100644
index 0000000000000..63d0821279f7d
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/constant-fold-nextafter.ll
@@ -0,0 +1,255 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 6
+; RUN: cat %S/floating-point-constants.ll %s | opt -passes=instcombine -S | FileCheck %s
+
+define double @nextafter_up_direction() {
+; CHECK-LABEL: define double @nextafter_up_direction() {
+; CHECK-NEXT:    ret double 0x3FF0000000000001
+;
+  %next = call double @nextafter(double 1.0, double 2.0)
+  ret double %next
+}
+
+define float @nextafterf_up_direction() {
+; CHECK-LABEL: define float @nextafterf_up_direction() {
+; CHECK-NEXT:    ret float 0x3FF0000020000000
+;
+  %next = call float @nextafterf(float 1.0, float 2.0)
+  ret float %next
+}
+
+define double @nextafter_down_direction() {
+; CHECK-LABEL: define double @nextafter_down_direction() {
+; CHECK-NEXT:    ret double 0x3FEFFFFFFFFFFFFF
+;
+  %next = call double @nextafter(double 1.0, double 0.0)
+  ret double %next
+}
+
+define float @nextafterf_down_direction() {
+; CHECK-LABEL: define float @nextafterf_down_direction() {
+; CHECK-NEXT:    ret float 0x3FEFFFFFE0000000
+;
+  %next = call float @nextafterf(float 1.0, float 0.0)
+  ret float %next
+}
+
+define double @nextafter_equal_args() {
+; CHECK-LABEL: define double @nextafter_equal_args() {
+; CHECK-NEXT:    ret double 1.000000e+00
+;
+  %next = call double @nextafter(double 1.0, double 1.0)
+  ret double %next
+}
+
+define float @nextafterf_equal_args() {
+; CHECK-LABEL: define float @nextafterf_equal_args() {
+; CHECK-NEXT:    ret float 1.000000e+00
+;
+  %next = call float @nextafterf(float 1.0, float 1.0)
+  ret float %next
+}
+
+define double @nextafter_pos_zero_neg_zero() {
+; CHECK-LABEL: define double @nextafter_pos_zero_neg_zero() {
+; CHECK-NEXT:    ret double -0.000000e+00
+;
+  %next = call double @nextafter(double 0.0, double -0.0)
+  ret double %next
+}
+
+define float @nextafterf_pos_zero_neg_zero() {
+; CHECK-LABEL: define float @nextafterf_pos_zero_neg_zero() {
+; CHECK-NEXT:    ret float -0.000000e+00
+;
+  %next = call float @nextafterf(float 0.0, float -0.0)
+  ret float %next
+}
+
+define double @nextafter_neg_zero_pos_zero() {
+; CHECK-LABEL: define double @nextafter_neg_zero_pos_zero() {
+; CHECK-NEXT:    ret double 0.000000e+00
+;
+  %next = call double @nextafter(double -0.0, double 0.0)
+  ret double %next
+}
+
+define float @nextafterf_neg_zero_pos_zero() {
+; CHECK-LABEL: define float @nextafterf_neg_zero_pos_zero() {
+; CHECK-NEXT:    ret float 0.000000e+00
+;
+  %next = call float @nextafterf(float -0.0, float 0.0)
+  ret float %next
+}
+
+define double @nextafter_nan_with_payload() {
+; CHECK-LABEL: define double @nextafter_nan_with_payload() {
+; CHECK-NEXT:    ret double 0x7FF8000000000001
+;
+  %tmp1 = load i64, ptr @dbl_nan
+  %tmp2 = or i64 %tmp1, 1
+  %nan_with_payload = bitcast i64 %tmp2 to double
+  %next = call double @nextafter(double %nan_with_payload, double 1.0)
+  ret double %next
+
+}
+
+define float @nextafterf_nan_with_payload() {
+; CHECK-LABEL: define float @nextafterf_nan_with_payload() {
+; CHECK-NEXT:    ret float 0x7FF8000020000000
+;
+  %tmp1 = load i32, ptr @flt_nan
+  %tmp2 = or i32 %tmp1, 1
+  %nan_with_payload = bitcast i32 %tmp2 to float
+  %next = call float @nextafterf(float %nan_with_payload, float 1.0)
+  ret float %next
+}
+
+define double @nextafter_pos_overflow () {
+; CHECK-LABEL: define double @nextafter_pos_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nextafter(double 0x7FEFFFFFFFFFFFFF, double 0x7FF0000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %arg1 = load double, ptr @dbl_pos_max
+  %arg2 = load double, ptr @dbl_pos_infinity
+  %next = call double @nextafter(double %arg1, double %arg2)
+  ret double %next
+}
+
+define float @nextafterf_pos_overflow() {
+; CHECK-LABEL: define float @nextafterf_pos_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nextafterf(float 0x47EFFFFFE0000000, float 0x7FF0000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %arg1 = load float, ptr @flt_pos_max
+  %arg2 = load float, ptr @flt_pos_infinity
+  %next = call float @nextafterf(float %arg1, float %arg2)
+  ret float %next
+}
+
+define double @nextafter_neg_overflow() {
+; CHECK-LABEL: define double @nextafter_neg_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nextafter(double 0xFFEFFFFFFFFFFFFF, double 0xFFF0000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %arg1 = load double, ptr @dbl_neg_max
+  %arg2 = load double, ptr @dbl_neg_infinity
+  %next = call double @nextafter(double %arg1, double %arg2)
+  ret double %next
+}
+
+define float @nextafterf_neg_overflow() {
+; CHECK-LABEL: define float @nextafterf_neg_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nextafterf(float 0xC7EFFFFFE0000000, float 0xFFF0000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %arg1 = load float, ptr @flt_neg_max
+  %arg2 = load float, ptr @flt_neg_infinity
+  %next = call float @nextafterf(float %arg1, float %arg2)
+  ret float %next
+}
+
+define double @nextafter_zero_from_above() {
+; CHECK-LABEL: define double @nextafter_zero_from_above() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nextafter(double 4.940660e-324, double 0.000000e+00)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %arg = load double, ptr @dbl_pos_min_subnormal
+  %next = call double @nextafter(double %arg, double 0.0)
+  ret double %next
+}
+
+define float @nextafterf_zero_from_above() {
+; CHECK-LABEL: define float @nextafterf_zero_from_above() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nextafterf(float 0x36A0000000000000, float 0.000000e+00)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %arg = load float, ptr @flt_pos_min_subnormal
+  %next = call float @nextafterf(float %arg, float 0.0)
+  ret float %next
+}
+
+define double @nextafter_zero_from_below() {
+; CHECK-LABEL: define double @nextafter_zero_from_below() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nextafter(double -4.940660e-324, double 0.000000e+00)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %arg = load double, ptr @dbl_neg_min_subnormal
+  %next = call double @nextafter(double %arg, double 0.0)
+  ret double %next
+}
+
+define float @nextafterf_zero_from_below() {
+; CHECK-LABEL: define float @nextafterf_zero_from_below() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nextafterf(float 0xB6A0000000000000, float 0.000000e+00)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %arg = load float, ptr @flt_neg_min_subnormal
+  %next = call float @nextafterf(float %arg, float 0.0)
+  ret float %next
+}
+
+define double @nextafter_subnormal() {
+; CHECK-LABEL: define double @nextafter_subnormal() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nextafter(double 4.940660e-324, double 0x7FF0000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %subnormal = load double, ptr @dbl_pos_min_subnormal
+  %infinity = load double, ptr @dbl_pos_infinity
+  %next = call double @nextafter(double %subnormal, double %infinity)
+  ret double %next
+}
+
+define float @nextafterf_subnormal() {
+; CHECK-LABEL: define float @nextafterf_subnormal() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nextafterf(float 0x36A0000000000000, float 0x7FF0000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %subnormal = load float, ptr @flt_pos_min_subnormal
+  %infinity = load float, ptr @flt_pos_infinity
+  %next = call float @nextafterf(float %subnormal, float %infinity)
+  ret float %next
+}
+
+define double @nextafter_poison() {
+; CHECK-LABEL: define double @nextafter_poison() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nextafter(double poison, double 1.000000e+00)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %next = call double @nextafter(double poison, double 1.0)
+  ret double %next
+}
+
+define double @nextafterf_poison() {
+; CHECK-LABEL: define double @nextafterf_poison() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nextafterf(float poison, float 1.000000e+00)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %next = call double @nextafterf(float poison, float 1.0)
+  ret double %next
+}
+
+define double @nextafter_subnormal_readnone() {
+; CHECK-LABEL: define double @nextafter_subnormal_readnone() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nextafter(double 4.940660e-324, double 0x7FF0000000000000) #[[ATTR1:[0-9]+]]
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %subnormal = load double, ptr @dbl_pos_min_subnormal
+  %infinity = load double, ptr @dbl_pos_infinity
+  %next = call double @nextafter(double %subnormal, double %infinity) readnone
+  ret double %next
+}
+
+define float @nextafterf_subnormal_readnone() {
+; CHECK-LABEL: define float @nextafterf_subnormal_readnone() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nextafterf(float 0x36A0000000000000, float 0x7FF0000000000000) #[[ATTR1]]
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %subnormal = load float, ptr @flt_pos_min_subnormal
+  %infinity = load float, ptr @flt_pos_infinity
+  %next = call float @nextafterf(float %subnormal, float %infinity) readnone
+  ret float %next
+}
+
+declare double @nextafter(double, double) #0
+declare float @nextafterf(float, float) #0
+attributes #0 = { willreturn memory(errnomem: write) }
diff --git a/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-fp128.ll b/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-fp128.ll
new file mode 100644
index 0000000000000..c387563c68f9c
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-fp128.ll
@@ -0,0 +1,276 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 6
+; RUN: cat %S/floating-point-constants.ll %s | opt -passes=instcombine -S | FileCheck %s
+
+define double @nexttoward_up_direction() {
+; CHECK-LABEL: define double @nexttoward_up_direction() {
+; CHECK-NEXT:    ret double 0x3FF0000000000001
+;
+  %arg = fpext double 2.0 to fp128
+  %next = call double @nexttoward(double 1.0, fp128 %arg)
+  ret double %next
+}
+
+define float @nexttowardf_up_direction() {
+; CHECK-LABEL: define float @nexttowardf_up_direction() {
+; CHECK-NEXT:    ret float 0x3FF0000020000000
+;
+  %arg = fpext float 2.0 to fp128
+  %next = call float @nexttowardf(float 1.0, fp128 %arg)
+  ret float %next
+}
+
+define double @nexttoward_down_direction() {
+; CHECK-LABEL: define double @nexttoward_down_direction() {
+; CHECK-NEXT:    ret double 0x3FEFFFFFFFFFFFFF
+;
+  %arg = fpext double 0.0 to fp128
+  %next = call double @nexttoward(double 1.0, fp128 %arg)
+  ret double %next
+}
+
+define float @nexttowardf_down_direction() {
+; CHECK-LABEL: define float @nexttowardf_down_direction() {
+; CHECK-NEXT:    ret float 0x3FEFFFFFE0000000
+;
+  %arg = fpext float 0.0 to fp128
+  %next = call float @nexttowardf(float 1.0, fp128 %arg)
+  ret float %next
+}
+
+define double @nexttoward_equal_args() {
+; CHECK-LABEL: define double @nexttoward_equal_args() {
+; CHECK-NEXT:    ret double 1.000000e+00
+;
+  %arg = fpext double 1.0 to fp128
+  %next = call double @nexttoward(double 1.0, fp128 %arg)
+  ret double %next
+}
+
+define float @nexttowardf_equal_args() {
+; CHECK-LABEL: define float @nexttowardf_equal_args() {
+; CHECK-NEXT:    ret float 1.000000e+00
+;
+  %arg = fpext float 1.0 to fp128
+  %next = call float @nexttowardf(float 1.0, fp128 %arg)
+  ret float %next
+}
+
+define double @nexttoward_pos_zero_neg_zero() {
+; CHECK-LABEL: define double @nexttoward_pos_zero_neg_zero() {
+; CHECK-NEXT:    ret double -0.000000e+00
+;
+  %neg_zero_ext = fpext double -0.0 to fp128
+  %next = call double @nexttoward(double 0.0, fp128 %neg_zero_ext)
+  ret double %next
+}
+
+define float @nexttowardf_pos_zero_neg_zero() {
+; CHECK-LABEL: define float @nexttowardf_pos_zero_neg_zero() {
+; CHECK-NEXT:    ret float -0.000000e+00
+;
+  %neg_zero_ext = fpext float -0.0 to fp128
+  %next = call float @nexttowardf(float 0.0, fp128 %neg_zero_ext)
+  ret float %next
+}
+
+define double @nexttoward_neg_zero_pos_zero() {
+; CHECK-LABEL: define double @nexttoward_neg_zero_pos_zero() {
+; CHECK-NEXT:    ret double 0.000000e+00
+;
+  %pos_zero_ext = fpext double 0.0 to fp128
+  %next = call double @nexttoward(double -0.0, fp128 %pos_zero_ext)
+  ret double %next
+}
+
+define float @nexttowardf_neg_zero_pos_zero() {
+; CHECK-LABEL: define float @nexttowardf_neg_zero_pos_zero() {
+; CHECK-NEXT:    ret float 0.000000e+00
+;
+  %pos_zero_ext = fpext float 0.0 to fp128
+  %next = call float @nexttowardf(float -0.0, fp128 %pos_zero_ext)
+  ret float %next
+}
+
+define double @nexttoward_nan_with_payload() {
+; CHECK-LABEL: define double @nexttoward_nan_with_payload() {
+; CHECK-NEXT:    ret double 0x7FF8000000000001
+;
+  %tmp1 = load i64, ptr @dbl_nan
+  %tmp2 = or i64 %tmp1, 1
+  %nan_with_payload = bitcast i64 %tmp2 to double
+  %dummy_arg = fpext double 1.0 to fp128
+  %next = call double @nexttoward(double %nan_with_payload, fp128 %dummy_arg)
+  ret double %next
+}
+
+define float @nexttowardf_nan_with_payload() {
+; CHECK-LABEL: define float @nexttowardf_nan_with_payload() {
+; CHECK-NEXT:    ret float 0x7FF8000020000000
+;
+  %tmp1 = load i32, ptr @flt_nan
+  %tmp2 = or i32 %tmp1, 1
+  %nan_with_payload = bitcast i32 %tmp2 to float
+  %dummy_arg = fpext float 1.0 to fp128
+  %next = call float @nexttowardf(float %nan_with_payload, fp128 %dummy_arg)
+  ret float %next
+}
+
+define double @nexttoward_pos_overflow() {
+; CHECK-LABEL: define double @nexttoward_pos_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 0x7FEFFFFFFFFFFFFF, fp128 0xL00000000000000007FFF000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %pos_max = load double, ptr @dbl_pos_max
+  %pos_inf = load double, ptr @dbl_pos_infinity
+  %ext_pos_inf = fpext double %pos_inf to fp128
+  %next = call double @nexttoward(double %pos_max, fp128 %ext_pos_inf)
+  ret double %next
+}
+
+define float @nexttowardf_pos_overflow () {
+; CHECK-LABEL: define float @nexttowardf_pos_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0x47EFFFFFE0000000, fp128 0xL00000000000000007FFF000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %pos_max = load float, ptr @flt_pos_max
+  %pos_inf = load float, ptr @flt_pos_infinity
+  %ext_pos_inf = fpext float %pos_inf to fp128
+  %next = call float @nexttowardf(float %pos_max, fp128 %ext_pos_inf)
+  ret float %next
+}
+
+define double @nexttoward_neg_overflow() {
+; CHECK-LABEL: define double @nexttoward_neg_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 0xFFEFFFFFFFFFFFFF, fp128 0xL0000000000000000FFFF000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %neg_max = load double, ptr @dbl_neg_max
+  %neg_inf = load double, ptr @dbl_neg_infinity
+  %ext_neg_inf = fpext double %neg_inf to fp128
+  %next = call double @nexttoward(double %neg_max, fp128 %ext_neg_inf)
+  ret double %next
+}
+
+define float @nexttowardf_neg_overflow() {
+; CHECK-LABEL: define float @nexttowardf_neg_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0xC7EFFFFFE0000000, fp128 0xL0000000000000000FFFF000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %neg_max = load float, ptr @flt_neg_max
+  %neg_inf = load float, ptr @flt_neg_infinity
+  %ext_neg_inf = fpext float %neg_inf to fp128
+  %next = call float @nexttowardf(float %neg_max, fp128 %ext_neg_inf)
+  ret float %next
+}
+
+define double @nexttoward_zero_from_above() {
+; CHECK-LABEL: define double @nexttoward_zero_from_above() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 4.940660e-324, fp128 0xL00000000000000000000000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %subnormal = load double, ptr @dbl_pos_min_subnormal
+  %zero = fpext double 0.0 to fp128
+  %next = call double @nexttoward(double %subnormal, fp128 %zero)
+  ret double %next
+}
+
+define float @nexttowardf_zero_from_above() {
+; CHECK-LABEL: define float @nexttowardf_zero_from_above() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0x36A0000000000000, fp128 0xL00000000000000000000000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %min_subnormal = load float, ptr @flt_pos_min_subnormal
+  %zero = fpext float 0.0 to fp128
+  %next = call float @nexttowardf(float %min_subnormal, fp128 %zero)
+  ret float %next
+}
+
+define double @nexttoward_zero_from_below() {
+; CHECK-LABEL: define double @nexttoward_zero_from_below() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double -4.940660e-324, fp128 0xL00000000000000000000000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %subnormal = load double, ptr @dbl_neg_min_subnormal
+  %zero = fpext double 0.0 to fp128
+  %next = call double @nexttoward(double %subnormal, fp128 %zero)
+  ret double %next
+}
+
+define float @nexttowardf_zero_from_below() {
+; CHECK-LABEL: define float @nexttowardf_zero_from_below() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0xB6A0000000000000, fp128 0xL00000000000000000000000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %min_subnormal = load float, ptr @flt_neg_min_subnormal
+  %zero = fpext float 0.0 to fp128
+  %next = call float @nexttowardf(float %min_subnormal, fp128 %zero)
+  ret float %next
+}
+
+define double @nexttoward_subnormal() {
+; CHECK-LABEL: define double @nexttoward_subnormal() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 4.940660e-324, fp128 0xL00000000000000003FFF000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %subnormal = load double, ptr @dbl_pos_min_subnormal
+  %target = fpext double 1.0 to fp128
+  %next = call double @nexttoward(double %subnormal, fp128 %target)
+  ret double %next
+}
+
+define float @nexttowardf_subnormal() {
+; CHECK-LABEL: define float @nexttowardf_subnormal() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0x36A0000000000000, fp128 0xL00000000000000003FFF000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %subnormal = load float, ptr @flt_pos_min_subnormal
+  %target = fpext float 1.0 to fp128
+  %next = call float @nexttowardf(float %subnormal, fp128 %target)
+  ret float %next
+}
+
+define double @nexttoward_poison() {
+; CHECK-LABEL: define double @nexttoward_poison() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double poison, fp128 0xL00000000000000003FFF000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %dummy_arg = fpext double 1.0 to fp128
+  %next = call double @nexttoward(double poison, fp128 %dummy_arg)
+  ret double %next
+}
+
+define float @nexttowardf_poison() {
+; CHECK-LABEL: define float @nexttowardf_poison() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float poison, fp128 0xL00000000000000003FFF000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %dummy_arg = fpext double 1.0 to fp128
+  %next = call float @nexttowardf(float poison, fp128 %dummy_arg)
+  ret float %next
+}
+
+define double @nexttoward_subnormal_readnone() {
+; CHECK-LABEL: define double @nexttoward_subnormal_readnone() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 4.940660e-324, fp128 0xL00000000000000003FFF000000000000) #[[ATTR1:[0-9]+]]
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %subnormal = load double, ptr @dbl_pos_min_subnormal
+  %target = fpext double 1.0 to fp128
+  %next = call double @nexttoward(double %subnormal, fp128 %target) readnone
+  ret double %next
+}
+
+define float @nexttowardf_subnormal_readnone() {
+; CHECK-LABEL: define float @nexttowardf_subnormal_readnone() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0x36A0000000000000, fp128 0xL00000000000000003FFF000000000000) #[[ATTR1]]
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %subnormal = load float, ptr @flt_pos_min_subnormal
+  %target = fpext float 1.0 to fp128
+  %next = call float @nexttowardf(float %subnormal, fp128 %target) readnone
+  ret float %next
+}
+
+declare double @nexttoward(double, fp128) #0
+declare float @nexttowardf(float, fp128) #0
+attributes #0 = { willreturn memory(errnomem: write) }
diff --git a/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-ppc-fp128.ll b/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-ppc-fp128.ll
new file mode 100644
index 0000000000000..f029adfcf5d30
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-ppc-fp128.ll
@@ -0,0 +1,112 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 6
+; RUN: cat %S/floating-point-constants.ll %s | opt -passes=instcombine -S | FileCheck %s
+
+define double @nexttoward_up_direction() {
+; CHECK-LABEL: define double @nexttoward_up_direction() {
+; CHECK-NEXT:    ret double 0x3FF0000000000001
+;
+  %arg = fpext double 2.0 to ppc_fp128
+  %next = call double @nexttoward(double 1.0, ppc_fp128 %arg)
+  ret double %next
+}
+
+define float @nexttowardf_up_direction() {
+; CHECK-LABEL: define float @nexttowardf_up_direction() {
+; CHECK-NEXT:    ret float 0x3FF0000020000000
+;
+  %arg = fpext float 2.0 to ppc_fp128
+  %next = call float @nexttowardf(float 1.0, ppc_fp128 %arg)
+  ret float %next
+}
+
+define double @nexttoward_down_direction() {
+; CHECK-LABEL: define double @nexttoward_down_direction() {
+; CHECK-NEXT:    ret double 0x3FEFFFFFFFFFFFFF
+;
+  %arg = fpext double 0.0 to ppc_fp128
+  %next = call double @nexttoward(double 1.0, ppc_fp128 %arg)
+  ret double %next
+}
+
+define float @nexttowardf_down_direction() {
+; CHECK-LABEL: define float @nexttowardf_down_direction() {
+; CHECK-NEXT:    ret float 0x3FEFFFFFE0000000
+;
+  %arg = fpext float 0.0 to ppc_fp128
+  %next = call float @nexttowardf(float 1.0, ppc_fp128 %arg)
+  ret float %next
+}
+
+define double @nexttoward_pos_overflow() {
+; CHECK-LABEL: define double @nexttoward_pos_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 0x7FEFFFFFFFFFFFFF, ppc_fp128 0xM7FF00000000000000000000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %pos_max = load double, ptr @dbl_pos_max
+  %pos_inf = load double, ptr @dbl_pos_infinity
+  %ext_pos_inf = fpext double %pos_inf to ppc_fp128
+  %next = call double @nexttoward(double %pos_max, ppc_fp128 %ext_pos_inf)
+  ret double %next
+}
+
+define float @nexttowardf_pos_overflow () {
+; CHECK-LABEL: define float @nexttowardf_pos_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0x47EFFFFFE0000000, ppc_fp128 0xM7FF00000000000000000000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %pos_max = load float, ptr @flt_pos_max
+  %pos_inf = load float, ptr @flt_pos_infinity
+  %ext_pos_inf = fpext float %pos_inf to ppc_fp128
+  %next = call float @nexttowardf(float %pos_max, ppc_fp128 %ext_pos_inf)
+  ret float %next
+}
+
+define double @nexttoward_neg_overflow() {
+; CHECK-LABEL: define double @nexttoward_neg_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 0xFFEFFFFFFFFFFFFF, ppc_fp128 0xMFFF00000000000000000000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %neg_max = load double, ptr @dbl_neg_max
+  %neg_inf = load double, ptr @dbl_neg_infinity
+  %ext_neg_inf = fpext double %neg_inf to ppc_fp128
+  %next = call double @nexttoward(double %neg_max, ppc_fp128 %ext_neg_inf)
+  ret double %next
+}
+
+define float @nexttowardf_neg_overflow() {
+; CHECK-LABEL: define float @nexttowardf_neg_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0xC7EFFFFFE0000000, ppc_fp128 0xMFFF00000000000000000000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %neg_max = load float, ptr @flt_neg_max
+  %neg_inf = load float, ptr @flt_neg_infinity
+  %ext_neg_inf = fpext float %neg_inf to ppc_fp128
+  %next = call float @nexttowardf(float %neg_max, ppc_fp128 %ext_neg_inf)
+  ret float %next
+}
+
+define double @nexttoward_subnormal() {
+; CHECK-LABEL: define double @nexttoward_subnormal() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 4.940660e-324, ppc_fp128 0xM3FF00000000000000000000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %subnormal = load double, ptr @dbl_pos_min_subnormal
+  %target = fpext double 1.0 to ppc_fp128
+  %next = call double @nexttoward(double %subnormal, ppc_fp128 %target)
+  ret double %next
+}
+
+define float @nexttowardf_subnormal() {
+; CHECK-LABEL: define float @nexttowardf_subnormal() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0x36A0000000000000, ppc_fp128 0xM3FF00000000000000000000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %subnormal = load float, ptr @flt_pos_min_subnormal
+  %target = fpext float 1.0 to ppc_fp128
+  %next = call float @nexttowardf(float %subnormal, ppc_fp128 %target)
+  ret float %next
+}
+
+declare double @nexttoward(double, ppc_fp128) #0
+declare float @nexttowardf(float, ppc_fp128) #0
+attributes #0 = { willreturn memory(errnomem: write) }
diff --git a/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-x86-fp80.ll b/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-x86-fp80.ll
new file mode 100644
index 0000000000000..84a29fe0deb10
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/constant-fold-nexttoward-x86-fp80.ll
@@ -0,0 +1,112 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 6
+; RUN: cat %S/floating-point-constants.ll %s | opt -passes=instcombine -S | FileCheck %s
+
+define double @nexttoward_up_direction() {
+; CHECK-LABEL: define double @nexttoward_up_direction() {
+; CHECK-NEXT:    ret double 0x3FF0000000000001
+;
+  %arg = fpext double 2.0 to x86_fp80
+  %next = call double @nexttoward(double 1.0, x86_fp80 %arg)
+  ret double %next
+}
+
+define float @nexttowardf_up_direction() {
+; CHECK-LABEL: define float @nexttowardf_up_direction() {
+; CHECK-NEXT:    ret float 0x3FF0000020000000
+;
+  %arg = fpext float 2.0 to x86_fp80
+  %next = call float @nexttowardf(float 1.0, x86_fp80 %arg)
+  ret float %next
+}
+
+define double @nexttoward_down_direction() {
+; CHECK-LABEL: define double @nexttoward_down_direction() {
+; CHECK-NEXT:    ret double 0x3FEFFFFFFFFFFFFF
+;
+  %arg = fpext double 0.0 to x86_fp80
+  %next = call double @nexttoward(double 1.0, x86_fp80 %arg)
+  ret double %next
+}
+
+define float @nexttowardf_down_direction() {
+; CHECK-LABEL: define float @nexttowardf_down_direction() {
+; CHECK-NEXT:    ret float 0x3FEFFFFFE0000000
+;
+  %arg = fpext float 0.0 to x86_fp80
+  %next = call float @nexttowardf(float 1.0, x86_fp80 %arg)
+  ret float %next
+}
+
+define double @nexttoward_pos_overflow () {
+; CHECK-LABEL: define double @nexttoward_pos_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 0x7FEFFFFFFFFFFFFF, x86_fp80 0xK7FFF8000000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %pos_max = load double, ptr @dbl_pos_max
+  %pos_inf = load double, ptr @dbl_pos_infinity
+  %ext_pos_inf = fpext double %pos_inf to x86_fp80
+  %next = call double @nexttoward(double %pos_max, x86_fp80 %ext_pos_inf)
+  ret double %next
+}
+
+define float @nexttowardf_pos_overflow() {
+; CHECK-LABEL: define float @nexttowardf_pos_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0x47EFFFFFE0000000, x86_fp80 0xK7FFF8000000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %pos_max = load float, ptr @flt_pos_max
+  %pos_inf = load float, ptr @flt_pos_infinity
+  %ext_pos_inf = fpext float %pos_inf to x86_fp80
+  %next = call float @nexttowardf(float %pos_max, x86_fp80 %ext_pos_inf)
+  ret float %next
+}
+
+define double @nexttoward_neg_overflow() {
+; CHECK-LABEL: define double @nexttoward_neg_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 0xFFEFFFFFFFFFFFFF, x86_fp80 0xKFFFF8000000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %neg_max = load double, ptr @dbl_neg_max
+  %neg_inf = load double, ptr @dbl_neg_infinity
+  %ext_neg_inf = fpext double %neg_inf to x86_fp80
+  %next = call double @nexttoward(double %neg_max, x86_fp80 %ext_neg_inf)
+  ret double %next
+}
+
+define float @nexttowardf_neg_overflow() {
+; CHECK-LABEL: define float @nexttowardf_neg_overflow() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0xC7EFFFFFE0000000, x86_fp80 0xKFFFF8000000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %neg_max = load float, ptr @flt_neg_max
+  %neg_inf = load float, ptr @flt_neg_infinity
+  %ext_neg_inf = fpext float %neg_inf to x86_fp80
+  %next = call float @nexttowardf(float %neg_max, x86_fp80 %ext_neg_inf)
+  ret float %next
+}
+
+define double @nexttoward_subnormal() {
+; CHECK-LABEL: define double @nexttoward_subnormal() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call double @nexttoward(double 4.940660e-324, x86_fp80 0xK3FFF8000000000000000)
+; CHECK-NEXT:    ret double [[NEXT]]
+;
+  %subnormal = load double, ptr @dbl_pos_min_subnormal
+  %target = fpext double 1.0 to x86_fp80
+  %next = call double @nexttoward(double %subnormal, x86_fp80 %target)
+  ret double %next
+}
+
+define float @nexttowardf_subnormal() {
+; CHECK-LABEL: define float @nexttowardf_subnormal() {
+; CHECK-NEXT:    [[NEXT:%.*]] = call float @nexttowardf(float 0x36A0000000000000, x86_fp80 0xK3FFF8000000000000000)
+; CHECK-NEXT:    ret float [[NEXT]]
+;
+  %subnormal = load float, ptr @flt_pos_min_subnormal
+  %target = fpext float 1.0 to x86_fp80
+  %next = call float @nexttowardf(float %subnormal, x86_fp80 %target)
+  ret float %next
+}
+
+declare double @nexttoward(double, x86_fp80) #0
+declare float @nexttowardf(float, x86_fp80) #0
+attributes #0 = { willreturn memory(errnomem: write) }
diff --git a/llvm/test/Transforms/InstCombine/floating-point-constants.ll b/llvm/test/Transforms/InstCombine/floating-point-constants.ll
new file mode 100644
index 0000000000000..5d135b0aaebaa
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/floating-point-constants.ll
@@ -0,0 +1,48 @@
+; RUN: true
+; Constants for edge case float testing.
+
+; Generated with:
+; clang -S -emit-llvm floating-point-constants.c
+;
+; // floating-point-constants.c
+; #include <math.h>
+; #include <float.h>
+;
+; const float flt_nan = NAN;
+; const float flt_pos_min_subnormal = FLT_TRUE_MIN;
+; const float flt_pos_min_normal = FLT_MIN;
+; const float flt_pos_max = FLT_MAX;
+; const float flt_pos_infinity = INFINITY;
+; const float flt_neg_min_subnormal = -FLT_TRUE_MIN;
+; const float flt_neg_min_normal = -FLT_MIN;
+; const float flt_neg_max = -FLT_MAX;
+; const float flt_neg_infinity = -INFINITY;
+;
+; const double dbl_nan = NAN;
+; const double dbl_pos_min_subnormal = DBL_TRUE_MIN;
+; const double dbl_pos_min_normal = DBL_MIN;
+; const double dbl_pos_max = DBL_MAX;
+; const double dbl_pos_infinity = INFINITY;
+; const double dbl_neg_min_subnormal = -DBL_TRUE_MIN;
+; const double dbl_neg_min_normal = -DBL_MIN;
+; const double dbl_neg_max = -DBL_MAX;
+; const double dbl_neg_infinity = -INFINITY;
+
+@flt_nan = dso_local constant float 0x7FF8000000000000, align 4
+@flt_pos_min_subnormal = dso_local constant float 0x36A0000000000000, align 4
+@flt_pos_min_normal = dso_local constant float 0x3810000000000000, align 4
+@flt_pos_max = dso_local constant float 0x47EFFFFFE0000000, align 4
+@flt_pos_infinity = dso_local constant float 0x7FF0000000000000, align 4
+@flt_neg_min_subnormal = dso_local constant float 0xB6A0000000000000, align 4
+@flt_neg_min_normal = dso_local constant float 0xB810000000000000, align 4
+@flt_neg_max = dso_local constant float 0xC7EFFFFFE0000000, align 4
+@flt_neg_infinity = dso_local constant float 0xFFF0000000000000, align 4
+@dbl_nan = dso_local constant double 0x7FF8000000000000, align 8
+@dbl_pos_min_subnormal = dso_local constant double 4.940660e-324, align 8
+@dbl_pos_min_normal = dso_local constant double 0x10000000000000, align 8
+@dbl_pos_max = dso_local constant double 0x7FEFFFFFFFFFFFFF, align 8
+@dbl_pos_infinity = dso_local constant double 0x7FF0000000000000, align 8
+@dbl_neg_min_subnormal = dso_local constant double -4.940660e-324, align 8
+@dbl_neg_min_normal = dso_local constant double 0x8010000000000000, align 8
+@dbl_neg_max = dso_local constant double 0xFFEFFFFFFFFFFFFF, align 8
+@dbl_neg_infinity = dso_local constant double 0xFFF0000000000000, align 8