diff --git a/libc/test/UnitTest/FPMatcher.h b/libc/test/UnitTest/FPMatcher.h
@@ -102,8 +102,10 @@ template <typename T> struct FPTest : public Test {
   const T inf = FPBits::inf(Sign::POS).get_val();                              \
   const T neg_inf = FPBits::inf(Sign::NEG).get_val();                          \
   const T min_normal = FPBits::min_normal().get_val();                         \
-  const T max_normal = FPBits::max_normal().get_val();                         \
-  const T min_denormal = FPBits::min_subnormal().get_val();                    \
+  const T max_normal = FPBits::max_normal(Sign::POS).get_val();                \
+  const T neg_max_normal = FPBits::max_normal(Sign::NEG).get_val();            \
+  const T min_denormal = FPBits::min_subnormal(Sign::POS).get_val();           \
+  const T neg_min_denormal = FPBits::min_subnormal(Sign::NEG).get_val();       \
   const T max_denormal = FPBits::max_subnormal().get_val();
 
 #define EXPECT_FP_EQ(expected, actual)                                         \

diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
@@ -1614,6 +1614,90 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+add_fp_unittest(
+  nextdown_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextdown_test.cpp
+  HDRS
+    NextDownTest.h
+  DEPENDS
+    libc.include.math
+    libc.src.math.nextdown
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  nextdownf_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextdownf_test.cpp
+  HDRS
+    NextDownTest.h
+  DEPENDS
+    libc.include.math
+    libc.src.math.nextdownf
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  nextdownf128_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextdownf128_test.cpp
+  HDRS
+    NextDownTest.h
+  DEPENDS
+    libc.include.math
+    libc.src.math.nextdownf128
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  nextup_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextup_test.cpp
+  HDRS
+    NextUpTest.h
+  DEPENDS
+    libc.include.math
+    libc.src.math.nextup
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  nextupf_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextupf_test.cpp
+  HDRS
+    NextUpTest.h
+  DEPENDS
+    libc.include.math
+    libc.src.math.nextupf
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  nextupf128_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextupf128_test.cpp
+  HDRS
+    NextUpTest.h
+  DEPENDS
+    libc.include.math
+    libc.src.math.nextupf128
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
 # TODO(lntue): The current implementation of fputil::general::fma<float> is only
 # correctly rounded for the default rounding mode round-to-nearest tie-to-even.
 add_fp_unittest(

diff --git a/libc/test/src/math/smoke/NextDownTest.h b/libc/test/src/math/smoke/NextDownTest.h
@@ -0,0 +1,43 @@
+//===-- Utility class to test different flavors of nextdown -----*- 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 LLVM_LIBC_TEST_SRC_MATH_NEXTDOWNTEST_H
+#define LLVM_LIBC_TEST_SRC_MATH_NEXTDOWNTEST_H
+
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+template <typename T>
+class NextDownTestTemplate : public LIBC_NAMESPACE::testing::Test {
+
+  DECLARE_SPECIAL_CONSTANTS(T)
+
+public:
+  typedef T (*NextDownFunc)(T);
+
+  void testNaN(NextDownFunc func) { ASSERT_FP_EQ(func(aNaN), aNaN); }
+
+  void testBoundaries(NextDownFunc func) {
+    ASSERT_FP_EQ(zero, func(min_denormal));
+
+    ASSERT_FP_EQ(neg_min_denormal, func(zero));
+    ASSERT_FP_EQ(neg_min_denormal, func(neg_zero));
+
+    ASSERT_FP_EQ(neg_max_normal, func(neg_max_normal));
+    ASSERT_FP_EQ(neg_inf, func(neg_inf));
+
+    ASSERT_FP_EQ(max_normal, func(inf));
+  }
+};
+
+#define LIST_NEXTDOWN_TESTS(T, func)                                           \
+  using LlvmLibcNextDownTest = NextDownTestTemplate<T>;                        \
+  TEST_F(LlvmLibcNextDownTest, TestNaN) { testNaN(&func); }                    \
+  TEST_F(LlvmLibcNextDownTest, TestBoundaries) { testBoundaries(&func); }
+
+#endif // LLVM_LIBC_TEST_SRC_MATH_NEXTDOWNTEST_H
diff --git a/libc/test/src/math/smoke/NextUpTest.h b/libc/test/src/math/smoke/NextUpTest.h
@@ -0,0 +1,43 @@
+//===-- Utility class to test different flavors of nextup -------*- 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 LLVM_LIBC_TEST_SRC_MATH_NEXTUPTEST_H
+#define LLVM_LIBC_TEST_SRC_MATH_NEXTUPTEST_H
+
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+template <typename T>
+class NextUpTestTemplate : public LIBC_NAMESPACE::testing::Test {
+
+  DECLARE_SPECIAL_CONSTANTS(T)
+
+public:
+  typedef T (*NextUpFunc)(T);
+
+  void testNaN(NextUpFunc func) { ASSERT_FP_EQ(func(aNaN), aNaN); }
+
+  void testBoundaries(NextUpFunc func) {
+    ASSERT_FP_EQ(neg_zero, func(neg_min_denormal));
+
+    ASSERT_FP_EQ(min_denormal, func(zero));
+    ASSERT_FP_EQ(min_denormal, func(neg_zero));
+
+    ASSERT_FP_EQ(max_normal, func(max_normal));
+    ASSERT_FP_EQ(inf, func(inf));
+
+    ASSERT_FP_EQ(neg_max_normal, func(neg_inf));
+  }
+};
+
+#define LIST_NEXTUP_TESTS(T, func)                                             \
+  using LlvmLibcNextUpTest = NextUpTestTemplate<T>;                            \
+  TEST_F(LlvmLibcNextUpTest, TestNaN) { testNaN(&func); }                      \
+  TEST_F(LlvmLibcNextUpTest, TestBoundaries) { testBoundaries(&func); }
+
+#endif // LLVM_LIBC_TEST_SRC_MATH_NEXTUPTEST_H
diff --git a/libc/test/src/math/smoke/nextdown_test.cpp b/libc/test/src/math/smoke/nextdown_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextdown --------------------------------------------===//
+//
+// 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 "NextDownTest.h"
+
+#include "src/math/nextdown.h"
+
+LIST_NEXTDOWN_TESTS(double, LIBC_NAMESPACE::nextdown)
diff --git a/libc/test/src/math/smoke/nextdownf128_test.cpp b/libc/test/src/math/smoke/nextdownf128_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextdownf128 ----------------------------------------===//
+//
+// 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 "NextDownTest.h"
+
+#include "src/math/nextdownf128.h"
+
+LIST_NEXTDOWN_TESTS(float128, LIBC_NAMESPACE::nextdownf128)
diff --git a/libc/test/src/math/smoke/nextdownf_test.cpp b/libc/test/src/math/smoke/nextdownf_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextdownf -------------------------------------------===//
+//
+// 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 "NextDownTest.h"
+
+#include "src/math/nextdownf.h"
+
+LIST_NEXTDOWN_TESTS(float, LIBC_NAMESPACE::nextdownf)
diff --git a/libc/test/src/math/smoke/nextup_test.cpp b/libc/test/src/math/smoke/nextup_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextup ----------------------------------------------===//
+//
+// 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 "NextUpTest.h"
+
+#include "src/math/nextup.h"
+
+LIST_NEXTUP_TESTS(double, LIBC_NAMESPACE::nextup)
diff --git a/libc/test/src/math/smoke/nextupf128_test.cpp b/libc/test/src/math/smoke/nextupf128_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextupf128 ------------------------------------------===//
+//
+// 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 "NextUpTest.h"
+
+#include "src/math/nextupf128.h"
+
+LIST_NEXTUP_TESTS(float128, LIBC_NAMESPACE::nextupf128)
diff --git a/libc/test/src/math/smoke/nextupf_test.cpp b/libc/test/src/math/smoke/nextupf_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextupf ---------------------------------------------===//
+//
+// 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 "NextUpTest.h"
+
+#include "src/math/nextupf.h"
+
+LIST_NEXTUP_TESTS(float, LIBC_NAMESPACE::nextupf)