diff --git a/libc/test/src/math/smoke/TotalOrderTest.h b/libc/test/src/math/smoke/TotalOrderTest.h
@@ -0,0 +1,138 @@
+//===-- Utility class to test different flavors of totalorder ---*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LIBC_TEST_SRC_MATH_SMOKE_TOTALORDERTEST_H
+#define LIBC_TEST_SRC_MATH_SMOKE_TOTALORDERTEST_H
+
+#include "test/UnitTest/FEnvSafeTest.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+template <typename T>
+class TotalOrderTestTemplate : public LIBC_NAMESPACE::testing::FEnvSafeTest {
+
+  DECLARE_SPECIAL_CONSTANTS(T)
+
+public:
+  typedef int (*TotalOrderFunc)(const T *, const T *);
+
+  bool funcWrapper(TotalOrderFunc func, T x, T y) { return func(&x, &y) != 0; }
+
+  void testXLesserThanY(TotalOrderFunc func) {
+    EXPECT_TRUE(funcWrapper(func, neg_inf, inf));
+
+    EXPECT_TRUE(funcWrapper(func, T(0.0), T(0.1)));
+    EXPECT_TRUE(funcWrapper(func, T(0.0), T(123.38)));
+
+    EXPECT_TRUE(funcWrapper(func, T(-0.1), T(0.0)));
+    EXPECT_TRUE(funcWrapper(func, T(-123.38), T(0.0)));
+
+    EXPECT_TRUE(funcWrapper(func, T(-0.1), T(0.1)));
+    EXPECT_TRUE(funcWrapper(func, T(-123.38), T(123.38)));
+  }
+
+  void testXGreaterThanY(TotalOrderFunc func) {
+    EXPECT_FALSE(funcWrapper(func, inf, neg_inf));
+
+    EXPECT_FALSE(funcWrapper(func, T(0.0), T(-0.1)));
+    EXPECT_FALSE(funcWrapper(func, T(0.0), T(-123.38)));
+
+    EXPECT_FALSE(funcWrapper(func, T(0.1), T(0.0)));
+    EXPECT_FALSE(funcWrapper(func, T(123.38), T(0.0)));
+
+    EXPECT_FALSE(funcWrapper(func, T(0.1), T(-0.1)));
+    EXPECT_FALSE(funcWrapper(func, T(123.38), T(-123.38)));
+  }
+
+  void testXEqualToY(TotalOrderFunc func) {
+    EXPECT_TRUE(funcWrapper(func, inf, inf));
+    EXPECT_TRUE(funcWrapper(func, neg_inf, neg_inf));
+
+    EXPECT_TRUE(funcWrapper(func, T(-0.0), T(0.0)));
+    EXPECT_FALSE(funcWrapper(func, T(0.0), T(-0.0)));
+
+    EXPECT_TRUE(funcWrapper(func, T(0.0), T(0.0)));
+    EXPECT_TRUE(funcWrapper(func, T(-0.0), T(-0.0)));
+    EXPECT_TRUE(funcWrapper(func, T(0.1), T(0.1)));
+    EXPECT_TRUE(funcWrapper(func, T(-0.1), T(-0.1)));
+    EXPECT_TRUE(funcWrapper(func, T(123.38), T(123.38)));
+    EXPECT_TRUE(funcWrapper(func, T(-123.38), T(-123.38)));
+  }
+
+  void testSingleNaN(TotalOrderFunc func) {
+    EXPECT_TRUE(funcWrapper(func, neg_aNaN, T(0.0)));
+    EXPECT_TRUE(funcWrapper(func, neg_aNaN, T(0.1)));
+    EXPECT_TRUE(funcWrapper(func, neg_aNaN, T(123.38)));
+
+    EXPECT_FALSE(funcWrapper(func, T(0.0), neg_aNaN));
+    EXPECT_FALSE(funcWrapper(func, T(0.1), neg_aNaN));
+    EXPECT_FALSE(funcWrapper(func, T(123.38), neg_aNaN));
+
+    EXPECT_TRUE(funcWrapper(func, T(0.0), aNaN));
+    EXPECT_TRUE(funcWrapper(func, T(0.1), aNaN));
+    EXPECT_TRUE(funcWrapper(func, T(123.38), aNaN));
+
+    EXPECT_FALSE(funcWrapper(func, aNaN, T(0.0)));
+    EXPECT_FALSE(funcWrapper(func, aNaN, T(0.1)));
+    EXPECT_FALSE(funcWrapper(func, aNaN, T(123.38)));
+  }
+
+  void testNaNSigns(TotalOrderFunc func) {
+    EXPECT_TRUE(funcWrapper(func, neg_aNaN, aNaN));
+    EXPECT_TRUE(funcWrapper(func, neg_aNaN, sNaN));
+    EXPECT_TRUE(funcWrapper(func, neg_sNaN, aNaN));
+    EXPECT_TRUE(funcWrapper(func, neg_sNaN, sNaN));
+
+    EXPECT_FALSE(funcWrapper(func, aNaN, neg_aNaN));
+    EXPECT_FALSE(funcWrapper(func, aNaN, neg_sNaN));
+    EXPECT_FALSE(funcWrapper(func, sNaN, neg_aNaN));
+    EXPECT_FALSE(funcWrapper(func, sNaN, neg_sNaN));
+  }
+
+  void testQuietVsSignalingNaN(TotalOrderFunc func) {
+    EXPECT_TRUE(funcWrapper(func, neg_aNaN, neg_sNaN));
+    EXPECT_FALSE(funcWrapper(func, neg_sNaN, neg_aNaN));
+    EXPECT_TRUE(funcWrapper(func, sNaN, aNaN));
+    EXPECT_FALSE(funcWrapper(func, aNaN, sNaN));
+  }
+
+  void testNaNPayloads(TotalOrderFunc func) {
+    T qnan_123 = FPBits::quiet_nan(Sign::POS, 0x123).get_val();
+    T neg_qnan_123 = FPBits::quiet_nan(Sign::NEG, 0x123).get_val();
+    T snan_123 = FPBits::signaling_nan(Sign::POS, 0x123).get_val();
+    T neg_snan_123 = FPBits::signaling_nan(Sign::NEG, 0x123).get_val();
+
+    EXPECT_TRUE(funcWrapper(func, aNaN, aNaN));
+    EXPECT_TRUE(funcWrapper(func, sNaN, sNaN));
+    EXPECT_TRUE(funcWrapper(func, aNaN, qnan_123));
+    EXPECT_TRUE(funcWrapper(func, sNaN, snan_123));
+    EXPECT_FALSE(funcWrapper(func, qnan_123, aNaN));
+    EXPECT_FALSE(funcWrapper(func, snan_123, sNaN));
+
+    EXPECT_TRUE(funcWrapper(func, neg_aNaN, neg_aNaN));
+    EXPECT_TRUE(funcWrapper(func, neg_sNaN, neg_sNaN));
+    EXPECT_FALSE(funcWrapper(func, neg_aNaN, neg_qnan_123));
+    EXPECT_FALSE(funcWrapper(func, neg_sNaN, neg_snan_123));
+    EXPECT_TRUE(funcWrapper(func, neg_qnan_123, neg_aNaN));
+    EXPECT_TRUE(funcWrapper(func, neg_snan_123, neg_sNaN));
+  }
+};
+
+#define LIST_TOTALORDER_TESTS(T, func)                                         \
+  using LlvmLibcTotalOrderTest = TotalOrderTestTemplate<T>;                    \
+  TEST_F(LlvmLibcTotalOrderTest, XLesserThanY) { testXLesserThanY(&func); }    \
+  TEST_F(LlvmLibcTotalOrderTest, XGreaterThanY) { testXGreaterThanY(&func); }  \
+  TEST_F(LlvmLibcTotalOrderTest, XEqualToY) { testXEqualToY(&func); }          \
+  TEST_F(LlvmLibcTotalOrderTest, SingleNaN) { testSingleNaN(&func); }          \
+  TEST_F(LlvmLibcTotalOrderTest, NaNSigns) { testNaNSigns(&func); }            \
+  TEST_F(LlvmLibcTotalOrderTest, QuietVsSignalingNaN) {                        \
+    testQuietVsSignalingNaN(&func);                                            \
+  }                                                                            \
+  TEST_F(LlvmLibcTotalOrderTest, NaNPayloads) { testNaNPayloads(&func); }
+
+#endif // LIBC_TEST_SRC_MATH_SMOKE_TOTALORDERTEST_H
diff --git a/libc/test/src/math/smoke/totalorderf16_test.cpp b/libc/test/src/math/smoke/totalorderf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for totalorderf16 ---------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "TotalOrderTest.h"
+
+#include "src/math/totalorderf16.h"
+
+LIST_TOTALORDER_TESTS(float16, LIBC_NAMESPACE::totalorderf16)
diff --git a/libc/test/src/math/smoke/totalordermagf16_test.cpp b/libc/test/src/math/smoke/totalordermagf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for totalordermagf16 ------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "TotalOrderMagTest.h"
+
+#include "src/math/totalordermagf16.h"
+
+LIST_TOTALORDERMAG_TESTS(float16, LIBC_NAMESPACE::totalordermagf16)