diff --git a/include/fmt/format.h b/include/fmt/format.h
index 51d830a2..eefc727d 100644
--- a/include/fmt/format.h
+++ b/include/fmt/format.h
@@ -2164,31 +2164,34 @@ FMT_CONSTEXPR20 auto write_float(OutputIt out, const DecimalFP& fp,
   }
 }
 
-template <typename T, FMT_ENABLE_IF(std::is_floating_point<T>::value)>
-FMT_CONSTEXPR20 bool isinf(T value) {
-  if (is_constant_evaluated()) {
-#if defined(__cpp_if_constexpr)
-    if constexpr (std::numeric_limits<double>::is_iec559) {
-      auto bits = bit_cast<uint64_t>(static_cast<double>(value));
-      return (bits & exponent_mask<double>()) &&
-             !(bits & ((uint64_t(1) << num_significand_bits<double>()) - 1));
-    }
+#ifdef __SIZEOF_FLOAT128__
+using float128 = __float128;
+#else
+using float128 = void;
 #endif
-  }
-  return std::isinf(value);
+template <typename T> using is_float128 = std::is_same<T, float128>;
+
+template <typename T, FMT_ENABLE_IF(std::is_floating_point<T>::value &&
+                                    !is_float128<T>::value)>
+FMT_CONSTEXPR20 bool isfinite(T value) {
+  if (is_constant_evaluated()) return value - value == 0;
+  return std::isfinite(value);
+}
+template <typename T, FMT_ENABLE_IF(is_float128<T>::value)>
+constexpr bool isfinite(T value) {
+  return value - value == 0;  // std::isfinite doesn't support __float128.
 }
 
-template <typename T, FMT_ENABLE_IF(std::is_floating_point<T>::value)>
-FMT_CONSTEXPR20 bool isfinite(T value) {
-  if (is_constant_evaluated()) {
-#if defined(__cpp_if_constexpr)
-    if constexpr (std::numeric_limits<double>::is_iec559) {
-      auto bits = detail::bit_cast<uint64_t>(static_cast<double>(value));
-      return (bits & exponent_mask<double>()) != exponent_mask<double>();
-    }
-#endif
-  }
-  return std::isfinite(value);
+template <typename T, FMT_ENABLE_IF(std::is_floating_point<T>::value &&
+                                    !is_float128<T>::value)>
+FMT_CONSTEXPR20 bool isinf(T value) {
+  if (is_constant_evaluated()) return !isfinite(value) && value == value;
+  return std::isinf(value);
+}
+template <typename T, FMT_ENABLE_IF(is_float128<T>::value)>
+constexpr bool isinf(T value) {
+  // std::isinf doesn't support __float128.
+  return !isfinite(value) && value == value;
 }
 
 template <typename T, FMT_ENABLE_IF(std::is_floating_point<T>::value)>
@@ -2201,7 +2204,7 @@ FMT_INLINE FMT_CONSTEXPR bool signbit(T value) {
     }
 #endif
   }
-  return std::signbit(value);
+  return std::signbit(static_cast<double>(value));
 }
 
 template <typename Char, typename OutputIt, typename T,
diff --git a/test/format-test.cc b/test/format-test.cc
index 87116133..8c0056e6 100644
--- a/test/format-test.cc
+++ b/test/format-test.cc
@@ -66,6 +66,27 @@ TEST(uint128_test, minus) {
   EXPECT_EQ(n - 2, 40);
 }
 
+template <typename Float> void check_isfinite() {
+  using fmt::detail::isfinite;
+  EXPECT_TRUE(isfinite(Float(0.0)));
+  EXPECT_TRUE(isfinite(Float(42.0)));
+  EXPECT_TRUE(isfinite(Float(-42.0)));
+  EXPECT_TRUE(isfinite(Float(fmt::detail::max_value<double>())));
+  // Use double because std::numeric_limits is broken for __float128.
+  using limits = std::numeric_limits<double>;
+  EXPECT_FALSE(isfinite(Float(limits::infinity())));
+  EXPECT_FALSE(isfinite(Float(-limits::infinity())));
+  EXPECT_FALSE(isfinite(Float(limits::quiet_NaN())));
+  EXPECT_FALSE(isfinite(Float(-limits::quiet_NaN())));
+}
+
+TEST(float_test, isfinite) {
+  check_isfinite<double>();
+#ifdef __SIZEOF_FLOAT128__
+  check_isfinite<fmt::detail::float128>();
+#endif
+}
+
 struct uint32_pair {
   uint32_t u[2];
 };