diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
@@ -2541,8 +2541,10 @@ add_fp_unittest(
   HDRS
     NextAfterTest.h
   DEPENDS
+    libc.hdr.fenv_macros
     libc.src.math.nextafter
-    libc.src.__support.FPUtil.basic_operations
+    libc.src.__support.CPP.bit
+    libc.src.__support.FPUtil.fenv_impl
     libc.src.__support.FPUtil.fp_bits
 )
 
@@ -2555,8 +2557,10 @@ add_fp_unittest(
   HDRS
     NextAfterTest.h
   DEPENDS
+    libc.hdr.fenv_macros
     libc.src.math.nextafterf
-    libc.src.__support.FPUtil.basic_operations
+    libc.src.__support.CPP.bit
+    libc.src.__support.FPUtil.fenv_impl
     libc.src.__support.FPUtil.fp_bits
 )
 
@@ -2569,8 +2573,26 @@ add_fp_unittest(
   HDRS
     NextAfterTest.h
   DEPENDS
+    libc.hdr.fenv_macros
     libc.src.math.nextafterl
-    libc.src.__support.FPUtil.basic_operations
+    libc.src.__support.CPP.bit
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+)
+
+add_fp_unittest(
+  nextafterf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextafterf16_test.cpp
+  HDRS
+    NextAfterTest.h
+  DEPENDS
+    libc.hdr.fenv_macros
+    libc.src.math.nextafterf16
+    libc.src.__support.CPP.bit
+    libc.src.__support.FPUtil.fenv_impl
     libc.src.__support.FPUtil.fp_bits
 )
 
@@ -2583,8 +2605,10 @@ add_fp_unittest(
   HDRS
     NextAfterTest.h
   DEPENDS
+    libc.hdr.fenv_macros
     libc.src.math.nextafterf128
-    libc.src.__support.FPUtil.basic_operations
+    libc.src.__support.CPP.bit
+    libc.src.__support.FPUtil.fenv_impl
     libc.src.__support.FPUtil.fp_bits
 )
 
@@ -2599,8 +2623,10 @@ if(NOT LIBC_TARGET_OS_IS_GPU)
     HDRS
       NextTowardTest.h
     DEPENDS
+      libc.hdr.fenv_macros
       libc.src.math.nexttoward
-      libc.src.__support.FPUtil.basic_operations
+      libc.src.__support.CPP.bit
+      libc.src.__support.FPUtil.fenv_impl
       libc.src.__support.FPUtil.fp_bits
   )
 
@@ -2613,8 +2639,10 @@ if(NOT LIBC_TARGET_OS_IS_GPU)
     HDRS
       NextTowardTest.h
     DEPENDS
+      libc.hdr.fenv_macros
       libc.src.math.nexttowardf
-      libc.src.__support.FPUtil.basic_operations
+      libc.src.__support.CPP.bit
+      libc.src.__support.FPUtil.fenv_impl
       libc.src.__support.FPUtil.fp_bits
   )
 endif()
@@ -2628,8 +2656,26 @@ add_fp_unittest(
   HDRS
     NextTowardTest.h
   DEPENDS
+    libc.hdr.fenv_macros
     libc.src.math.nexttowardl
-    libc.src.__support.FPUtil.basic_operations
+    libc.src.__support.CPP.bit
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+)
+
+add_fp_unittest(
+  nexttowardf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nexttowardf16_test.cpp
+  HDRS
+    NextTowardTest.h
+  DEPENDS
+    libc.hdr.fenv_macros
+    libc.src.math.nexttowardf16
+    libc.src.__support.CPP.bit
+    libc.src.__support.FPUtil.fenv_impl
     libc.src.__support.FPUtil.fp_bits
 )
 
@@ -2643,7 +2689,6 @@ add_fp_unittest(
     NextDownTest.h
   DEPENDS
     libc.src.math.nextdown
-    libc.src.__support.FPUtil.manipulation_functions
 )
 
 add_fp_unittest(
@@ -2656,7 +2701,6 @@ add_fp_unittest(
     NextDownTest.h
   DEPENDS
     libc.src.math.nextdownf
-    libc.src.__support.FPUtil.manipulation_functions
 )
 
 add_fp_unittest(
@@ -2669,7 +2713,18 @@ add_fp_unittest(
     NextDownTest.h
   DEPENDS
     libc.src.math.nextdownl
-    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  nextdownf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextdownf16_test.cpp
+  HDRS
+    NextDownTest.h
+  DEPENDS
+    libc.src.math.nextdownf16
 )
 
 add_fp_unittest(
@@ -2682,7 +2737,6 @@ add_fp_unittest(
     NextDownTest.h
   DEPENDS
     libc.src.math.nextdownf128
-    libc.src.__support.FPUtil.manipulation_functions
 )
 
 add_fp_unittest(
@@ -2695,7 +2749,6 @@ add_fp_unittest(
     NextUpTest.h
   DEPENDS
     libc.src.math.nextup
-    libc.src.__support.FPUtil.manipulation_functions
 )
 
 add_fp_unittest(
@@ -2708,7 +2761,6 @@ add_fp_unittest(
     NextUpTest.h
   DEPENDS
     libc.src.math.nextupf
-    libc.src.__support.FPUtil.manipulation_functions
 )
 
 add_fp_unittest(
@@ -2721,7 +2773,18 @@ add_fp_unittest(
     NextUpTest.h
   DEPENDS
     libc.src.math.nextupl
-    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  nextupf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nextupf16_test.cpp
+  HDRS
+    NextUpTest.h
+  DEPENDS
+    libc.src.math.nextupf16
 )
 
 add_fp_unittest(
@@ -2734,7 +2797,6 @@ add_fp_unittest(
     NextUpTest.h
   DEPENDS
     libc.src.math.nextupf128
-    libc.src.__support.FPUtil.manipulation_functions
 )
 
 # TODO(lntue): The current implementation of fputil::general::fma<float> is only

diff --git a/libc/test/src/math/smoke/NextAfterTest.h b/libc/test/src/math/smoke/NextAfterTest.h
@@ -9,15 +9,15 @@
 #ifndef LLVM_LIBC_TEST_SRC_MATH_NEXTAFTERTEST_H
 #define LLVM_LIBC_TEST_SRC_MATH_NEXTAFTERTEST_H
 
-#include "hdr/math_macros.h"
 #include "src/__support/CPP/bit.h"
-#include "src/__support/CPP/type_traits.h"
-#include "src/__support/FPUtil/BasicOperations.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FPBits.h"
 #include "test/UnitTest/FEnvSafeTest.h"
 #include "test/UnitTest/FPMatcher.h"
 #include "test/UnitTest/Test.h"
 
+#include "hdr/fenv_macros.h"
+
 // TODO: Strengthen errno,exception checks and remove these assert macros
 // after new matchers/test fixtures are added
 #define ASSERT_FP_EQ_WITH_EXCEPTION(result, expected, expected_exception)      \
@@ -181,7 +181,7 @@ class NextAfterTestTemplate : public LIBC_NAMESPACE::testing::FEnvSafeTest {
     result_bits = FPBits(result);
     ASSERT_EQ(result_bits.get_biased_exponent(), x_bits.get_biased_exponent());
     ASSERT_EQ(result_bits.get_mantissa(),
-              x_bits.get_mantissa() + StorageType(1));
+              static_cast<StorageType>(x_bits.get_mantissa() + StorageType(1)));
 
     x = -x;
 
@@ -195,7 +195,7 @@ class NextAfterTestTemplate : public LIBC_NAMESPACE::testing::FEnvSafeTest {
     result_bits = FPBits(result);
     ASSERT_EQ(result_bits.get_biased_exponent(), x_bits.get_biased_exponent());
     ASSERT_EQ(result_bits.get_mantissa(),
-              x_bits.get_mantissa() + StorageType(1));
+              static_cast<StorageType>(x_bits.get_mantissa() + StorageType(1)));
   }
 };
 

diff --git a/libc/test/src/math/smoke/NextTowardTest.h b/libc/test/src/math/smoke/NextTowardTest.h
@@ -9,16 +9,15 @@
 #ifndef LLVM_LIBC_TEST_SRC_MATH_NEXTTOWARDTEST_H
 #define LLVM_LIBC_TEST_SRC_MATH_NEXTTOWARDTEST_H
 
-#include "hdr/fenv_macros.h"
-#include "hdr/math_macros.h"
 #include "src/__support/CPP/bit.h"
-#include "src/__support/CPP/type_traits.h"
-#include "src/__support/FPUtil/BasicOperations.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FPBits.h"
 #include "test/UnitTest/FEnvSafeTest.h"
 #include "test/UnitTest/FPMatcher.h"
 #include "test/UnitTest/Test.h"
 
+#include "hdr/fenv_macros.h"
+
 // TODO: Strengthen errno,exception checks and remove these assert macros
 // after new matchers/test fixtures are added
 #define ASSERT_FP_EQ_WITH_EXCEPTION(result, expected, expected_exception)      \
@@ -194,7 +193,7 @@ class NextTowardTestTemplate : public LIBC_NAMESPACE::testing::FEnvSafeTest {
     result_bits = FPBits(result);
     ASSERT_EQ(result_bits.get_biased_exponent(), x_bits.get_biased_exponent());
     ASSERT_EQ(result_bits.get_mantissa(),
-              x_bits.get_mantissa() + StorageType(1));
+              static_cast<StorageType>(x_bits.get_mantissa() + StorageType(1)));
 
     x = -x;
 
@@ -208,7 +207,7 @@ class NextTowardTestTemplate : public LIBC_NAMESPACE::testing::FEnvSafeTest {
     result_bits = FPBits(result);
     ASSERT_EQ(result_bits.get_biased_exponent(), x_bits.get_biased_exponent());
     ASSERT_EQ(result_bits.get_mantissa(),
-              x_bits.get_mantissa() + StorageType(1));
+              static_cast<StorageType>(x_bits.get_mantissa() + StorageType(1)));
   }
 };
 

diff --git a/libc/test/src/math/smoke/nextafterf16_test.cpp b/libc/test/src/math/smoke/nextafterf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextafterf16 ----------------------------------------===//
+//
+// 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 "NextAfterTest.h"
+
+#include "src/math/nextafterf16.h"
+
+LIST_NEXTAFTER_TESTS(float16, LIBC_NAMESPACE::nextafterf16)
diff --git a/libc/test/src/math/smoke/nextdownf16_test.cpp b/libc/test/src/math/smoke/nextdownf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextdownf16 -----------------------------------------===//
+//
+// 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/nextdownf16.h"
+
+LIST_NEXTDOWN_TESTS(float16, LIBC_NAMESPACE::nextdownf16)
diff --git a/libc/test/src/math/smoke/nexttowardf16_test.cpp b/libc/test/src/math/smoke/nexttowardf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nexttowardf16 ---------------------------------------===//
+//
+// 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 "NextTowardTest.h"
+
+#include "src/math/nexttowardf16.h"
+
+LIST_NEXTTOWARD_TESTS(float16, LIBC_NAMESPACE::nexttowardf16)
diff --git a/libc/test/src/math/smoke/nextupf16_test.cpp b/libc/test/src/math/smoke/nextupf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for nextupf16 -------------------------------------------===//
+//
+// 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/nextupf16.h"
+
+LIST_NEXTUP_TESTS(float16, LIBC_NAMESPACE::nextupf16)