diff --git a/clang/docs/LanguageExtensions.rst b/clang/docs/LanguageExtensions.rst
--- a/clang/docs/LanguageExtensions.rst
+++ b/clang/docs/LanguageExtensions.rst
@@ -4660,6 +4660,7 @@
 * ``__builtin_ffs``
 * ``__builtin_ffsl``
 * ``__builtin_ffsll``
+* ``__builtin_fmax``
 * ``__builtin_fpclassify``
 * ``__builtin_inf``
 * ``__builtin_isinf``
diff --git a/clang/lib/AST/ExprConstant.cpp b/clang/lib/AST/ExprConstant.cpp
--- a/clang/lib/AST/ExprConstant.cpp
+++ b/clang/lib/AST/ExprConstant.cpp
@@ -14023,6 +14023,24 @@
     Result.copySign(RHS);
     return true;
   }
+
+  case Builtin::BI__builtin_fmax:
+  case Builtin::BI__builtin_fmaxf:
+  case Builtin::BI__builtin_fmaxl:
+  case Builtin::BI__builtin_fmaxf16:
+  case Builtin::BI__builtin_fmaxf128: {
+    // TODO: Handle sNaN.
+    APFloat RHS(0.);
+    if (!EvaluateFloat(E->getArg(0), Result, Info) ||
+        !EvaluateFloat(E->getArg(1), RHS, Info))
+      return false;
+    // When comparing zeroes, return +0.0 if one of the zeroes is positive.
+    if (Result.isZero() && RHS.isZero() && Result.isNegative())
+      Result = RHS;
+    else if (Result.isNaN() || RHS > Result)
+      Result = RHS;
+    return true;
+  }
   }
 }
 
diff --git a/clang/test/Sema/constant-builtins-fmax.cpp b/clang/test/Sema/constant-builtins-fmax.cpp
new file mode 100644
--- /dev/null
+++ b/clang/test/Sema/constant-builtins-fmax.cpp
@@ -0,0 +1,54 @@
+// RUN: %clang_cc1 -fsyntax-only -verify %s
+// expected-no-diagnostics
+
+constexpr double NaN = __builtin_nan("");
+constexpr double Inf = __builtin_inf();
+constexpr double NegInf = -__builtin_inf();
+
+#define FMAX_TEST_SIMPLE(T, FUNC)                           \
+    static_assert(T(6.7890) == FUNC(T(1.2345), T(6.7890))); \
+    static_assert(T(6.7890) == FUNC(T(6.7890), T(1.2345)));
+
+#define FMAX_TEST_NAN(T, FUNC)                          \
+    static_assert(Inf == FUNC(NaN, Inf));               \
+    static_assert(NegInf == FUNC(NegInf, NaN));         \
+    static_assert(0.0 == FUNC(NaN, 0.0));               \
+    static_assert(-0.0 == FUNC(-0.0, NaN));             \
+    static_assert(T(-1.2345) == FUNC(NaN, T(-1.2345))); \
+    static_assert(T(1.2345) == FUNC(T(1.2345), NaN));   \
+    static_assert(__builtin_isnan(FUNC(NaN, NaN)));
+
+#define FMAX_TEST_INF(T, FUNC)                  \
+    static_assert(Inf == FUNC(NegInf, Inf));    \
+    static_assert(Inf == FUNC(Inf, 0.0));       \
+    static_assert(Inf == FUNC(-0.0, Inf));      \
+    static_assert(Inf == FUNC(Inf, T(1.2345))); \
+    static_assert(Inf == FUNC(T(-1.2345), Inf));
+
+#define FMAX_TEST_NEG_INF(T, FUNC)                         \
+    static_assert(Inf == FUNC(Inf, NegInf));               \
+    static_assert(0.0 == FUNC(NegInf, 0.0));               \
+    static_assert(-0.0 == FUNC(-0.0, NegInf));             \
+    static_assert(T(-1.2345) == FUNC(NegInf, T(-1.2345))); \
+    static_assert(T(1.2345) == FUNC(T(1.2345), NegInf));
+
+#define FMAX_TEST_BOTH_ZERO(T, FUNC)       \
+    static_assert(__builtin_copysign(1.0, FUNC(0.0, 0.0)) == 1.0);  \
+    static_assert(__builtin_copysign(1.0, FUNC(-0.0, 0.0)) == 1.0);  \
+    static_assert(__builtin_copysign(1.0, FUNC(0.0, -0.0)) == 1.0);  \
+    static_assert(__builtin_copysign(1.0, FUNC(-0.0, -0.0)) == -1.0);
+
+#define LIST_FMAX_TESTS(T, FUNC) \
+    FMAX_TEST_SIMPLE(T, FUNC)    \
+    FMAX_TEST_NAN(T, FUNC)       \
+    FMAX_TEST_INF(T, FUNC)       \
+    FMAX_TEST_NEG_INF(T, FUNC)   \
+    FMAX_TEST_BOTH_ZERO(T, FUNC)
+
+LIST_FMAX_TESTS(double, __builtin_fmax)
+LIST_FMAX_TESTS(float, __builtin_fmaxf)
+LIST_FMAX_TESTS((long double), __builtin_fmaxl)
+LIST_FMAX_TESTS(__fp16, __builtin_fmaxf16)
+#ifdef __FLOAT128__
+LIST_FMAX_TESTS(__float128, __builtin_fmaxf128)
+#endif