diff --git a/clang/lib/AST/Interp/InterpBuiltin.cpp b/clang/lib/AST/Interp/InterpBuiltin.cpp
--- a/clang/lib/AST/Interp/InterpBuiltin.cpp
+++ b/clang/lib/AST/Interp/InterpBuiltin.cpp
@@ -9,6 +9,7 @@
 #include "Interp.h"
 #include "PrimType.h"
 #include "clang/Basic/Builtins.h"
+#include "clang/Basic/TargetInfo.h"
 
 namespace clang {
 namespace interp {
@@ -59,6 +60,67 @@
   return true;
 }
 
+static bool interp__builtin_nan(InterpState &S, CodePtr OpPC,
+                                const InterpFrame *Frame, const Function *F,
+                                bool Signaling) {
+  const Pointer &Arg = getParam<Pointer>(Frame, 0);
+
+  if (!CheckLoad(S, OpPC, Arg))
+    return false;
+
+  assert(Arg.getFieldDesc()->isPrimitiveArray());
+
+  // Convert the given string to an integer using StringRef's API.
+  llvm::APInt Fill;
+  std::string Str;
+  assert(Arg.getNumElems() >= 1);
+  for (unsigned I = 0;; ++I) {
+    const Pointer &Elem = Arg.atIndex(I);
+
+    if (!CheckLoad(S, OpPC, Elem))
+      return false;
+
+    if (Elem.deref<int8_t>() == 0)
+      break;
+
+    Str += Elem.deref<char>();
+  }
+
+  // Treat empty strings as if they were zero.
+  if (Str.empty())
+    Fill = llvm::APInt(32, 0);
+  else if (StringRef(Str).getAsInteger(0, Fill))
+    return false;
+
+  const llvm::fltSemantics &TargetSemantics =
+      S.getCtx().getFloatTypeSemantics(F->getDecl()->getReturnType());
+
+  Floating Result;
+  if (S.getCtx().getTargetInfo().isNan2008()) {
+    if (Signaling)
+      Result = Floating(
+          llvm::APFloat::getSNaN(TargetSemantics, /*Negative=*/false, &Fill));
+    else
+      Result = Floating(
+          llvm::APFloat::getQNaN(TargetSemantics, /*Negative=*/false, &Fill));
+  } else {
+    // Prior to IEEE 754-2008, architectures were allowed to choose whether
+    // the first bit of their significand was set for qNaN or sNaN. MIPS chose
+    // a different encoding to what became a standard in 2008, and for pre-
+    // 2008 revisions, MIPS interpreted sNaN-2008 as qNan and qNaN-2008 as
+    // sNaN. This is now known as "legacy NaN" encoding.
+    if (Signaling)
+      Result = Floating(
+          llvm::APFloat::getQNaN(TargetSemantics, /*Negative=*/false, &Fill));
+    else
+      Result = Floating(
+          llvm::APFloat::getSNaN(TargetSemantics, /*Negative=*/false, &Fill));
+  }
+
+  S.Stk.push<Floating>(Result);
+  return true;
+}
+
 bool InterpretBuiltin(InterpState &S, CodePtr OpPC, const Function *F) {
   InterpFrame *Frame = S.Current;
   APValue Dummy;
@@ -72,7 +134,24 @@
   case Builtin::BI__builtin_strcmp:
     if (interp__builtin_strcmp(S, OpPC, Frame))
       return Ret<PT_Sint32>(S, OpPC, Dummy);
-    return false;
+    break;
+  case Builtin::BI__builtin_nan:
+  case Builtin::BI__builtin_nanf:
+  case Builtin::BI__builtin_nanl:
+  case Builtin::BI__builtin_nanf16:
+  case Builtin::BI__builtin_nanf128:
+    if (interp__builtin_nan(S, OpPC, Frame, F, /*Signaling=*/false))
+      return Ret<PT_Float>(S, OpPC, Dummy);
+    break;
+  case Builtin::BI__builtin_nans:
+  case Builtin::BI__builtin_nansf:
+  case Builtin::BI__builtin_nansl:
+  case Builtin::BI__builtin_nansf16:
+  case Builtin::BI__builtin_nansf128:
+    if (interp__builtin_nan(S, OpPC, Frame, F, /*Signaling=*/true))
+      return Ret<PT_Float>(S, OpPC, Dummy);
+    break;
+
   default:
     return false;
   }
diff --git a/clang/test/AST/Interp/builtin-functions.cpp b/clang/test/AST/Interp/builtin-functions.cpp
--- a/clang/test/AST/Interp/builtin-functions.cpp
+++ b/clang/test/AST/Interp/builtin-functions.cpp
@@ -1,5 +1,8 @@
 // RUN: %clang_cc1 -fexperimental-new-constant-interpreter %s -verify
 // RUN: %clang_cc1 -verify=ref %s -Wno-constant-evaluated
+// RUN: %clang_cc1 -std=c++20 -fexperimental-new-constant-interpreter %s -verify
+// RUN: %clang_cc1 -std=c++20 -verify=ref %s -Wno-constant-evaluated
+
 
 namespace strcmp {
   constexpr char kFoobar[6] = {'f','o','o','b','a','r'};
@@ -34,3 +37,26 @@
                                                                         // ref-error {{not an integral constant}} \
                                                                         // ref-note {{dereferenced one-past-the-end}}
 }
+
+namespace nan {
+  constexpr double NaN1 = __builtin_nan("");
+
+  /// The current interpreter does not accept this, but it should.
+  constexpr float NaN2 = __builtin_nans([](){return "0xAE98";}()); // ref-error {{must be initialized by a constant expression}}
+
+  constexpr double NaN3 = __builtin_nan("foo"); // expected-error {{must be initialized by a constant expression}} \
+                                                // ref-error {{must be initialized by a constant expression}}
+  constexpr float NaN4 = __builtin_nanf("");
+  constexpr long double NaN5 = __builtin_nanf128("");
+
+  /// FIXME: This should be accepted by the current interpreter as well.
+  constexpr char f[] = {'0', 'x', 'A', 'E', '\0'};
+  constexpr double NaN6 = __builtin_nan(f); // ref-error {{must be initialized by a constant expression}}
+
+  /// FIXME: Current interpreter misses diagnostics.
+  constexpr char f2[] = {'0', 'x', 'A', 'E'}; /// No trailing 0 byte.
+  constexpr double NaN7 = __builtin_nan(f2); // ref-error {{must be initialized by a constant expression}} \
+                                             // expected-error {{must be initialized by a constant expression}} \
+                                             // expected-note {{read of dereferenced one-past-the-end pointer}} \
+                                             // expected-note {{in call to}}
+}