diff --git a/libc/src/math/generic/llogbf16.cpp b/libc/src/math/generic/llogbf16.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of llogbf16 function -------------------------------===//
+//
+// 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 "src/math/llogbf16.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(long, llogbf16, (float16 x)) {
+  return fputil::intlogb<long>(x);
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/logbf16.cpp b/libc/src/math/generic/logbf16.cpp
@@ -0,0 +1,17 @@
+//===-- Implementation of logbf16 function --------------------------------===//
+//
+// 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 "src/math/logbf16.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float16, logbf16, (float16 x)) { return fputil::logb(x); }
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/modff16.cpp b/libc/src/math/generic/modff16.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of modff16 function --------------------------------===//
+//
+// 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 "src/math/modff16.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float16, modff16, (float16 x, float16 *iptr)) {
+  return fputil::modf(x, *iptr);
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/ilogbf16.h b/libc/src/math/ilogbf16.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for ilogbf16 ----------------------*- 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_SRC_MATH_ILOGBF16_H
+#define LLVM_LIBC_SRC_MATH_ILOGBF16_H
+
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE {
+
+int ilogbf16(float16 x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_ILOGBF16_H
diff --git a/libc/src/math/llogbf16.h b/libc/src/math/llogbf16.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for llogbf16 ----------------------*- 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_SRC_MATH_LLOGBF16_H
+#define LLVM_LIBC_SRC_MATH_LLOGBF16_H
+
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE {
+
+long llogbf16(float16 x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_LLOGBF16_H
diff --git a/libc/src/math/logbf16.h b/libc/src/math/logbf16.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for logbf16 -----------------------*- 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_SRC_MATH_LOGBF16_H
+#define LLVM_LIBC_SRC_MATH_LOGBF16_H
+
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE {
+
+float16 logbf16(float16 x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_LOGBF16_H
diff --git a/libc/src/math/modff16.h b/libc/src/math/modff16.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for modff16 -----------------------*- 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_SRC_MATH_MODFF16_H
+#define LLVM_LIBC_SRC_MATH_MODFF16_H
+
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE {
+
+float16 modff16(float16 x, float16 *iptr);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_MODFF16_H
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
@@ -1091,6 +1091,18 @@ add_fp_unittest(
     libc.src.math.frexpl
 )
 
+add_fp_unittest(
+  frexpf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    frexpf16_test.cpp
+  HDRS
+    FrexpTest.h
+  DEPENDS
+    libc.src.math.frexpf16
+)
+
 add_fp_unittest(
   frexpf128_test
   SUITE
@@ -1353,7 +1365,7 @@ add_fp_unittest(
     ILogbTest.h
   DEPENDS
     libc.src.math.ilogb
-    libc.src.__support.CPP.limits
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.manipulation_functions
 )
@@ -1368,7 +1380,7 @@ add_fp_unittest(
     ILogbTest.h
   DEPENDS
     libc.src.math.ilogbf
-    libc.src.__support.CPP.limits
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.manipulation_functions
 )
@@ -1383,7 +1395,22 @@ add_fp_unittest(
     ILogbTest.h
   DEPENDS
     libc.src.math.ilogbl
-    libc.src.__support.CPP.limits
+    libc.src.__support.CPP.algorithm
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  ilogbf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    ilogbf16_test.cpp
+  HDRS
+    ILogbTest.h
+  DEPENDS
+    libc.src.math.ilogbf16
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.manipulation_functions
 )
@@ -1398,7 +1425,7 @@ add_fp_unittest(
     ILogbTest.h
   DEPENDS
     libc.src.math.ilogbf128
-    libc.src.__support.CPP.limits
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.manipulation_functions
 )
@@ -1413,7 +1440,7 @@ add_fp_unittest(
     ILogbTest.h
   DEPENDS
     libc.src.math.llogb
-    libc.src.__support.CPP.limits
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.manipulation_functions
 )
@@ -1428,7 +1455,7 @@ add_fp_unittest(
     ILogbTest.h
   DEPENDS
     libc.src.math.llogbf
-    libc.src.__support.CPP.limits
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.manipulation_functions
 )
@@ -1443,7 +1470,22 @@ add_fp_unittest(
     ILogbTest.h
   DEPENDS
     libc.src.math.llogbl
-    libc.src.__support.CPP.limits
+    libc.src.__support.CPP.algorithm
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  llogbf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    llogbf16_test.cpp
+  HDRS
+    ILogbTest.h
+  DEPENDS
+    libc.src.math.llogbf16
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.manipulation_functions
 )
@@ -1458,7 +1500,7 @@ add_fp_unittest(
     ILogbTest.h
   DEPENDS
     libc.src.math.llogbf128
-    libc.src.__support.CPP.limits
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.manipulation_functions
 )
@@ -1529,8 +1571,11 @@ add_fp_unittest(
     libc-math-smoke-tests
   SRCS
     logb_test.cpp
+  HDRS
+    LogbTest.h
   DEPENDS
     libc.src.math.logb
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.manipulation_functions
 )
 
@@ -1540,8 +1585,11 @@ add_fp_unittest(
     libc-math-smoke-tests
   SRCS
     logbf_test.cpp
+  HDRS
+    LogbTest.h
   DEPENDS
     libc.src.math.logbf
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.manipulation_functions
 )
 
@@ -1555,6 +1603,21 @@ add_fp_unittest(
     LogbTest.h
   DEPENDS
     libc.src.math.logbl
+    libc.src.__support.CPP.algorithm
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_fp_unittest(
+  logbf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    logbf16_test.cpp
+  HDRS
+    LogbTest.h
+  DEPENDS
+    libc.src.math.logbf16
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.manipulation_functions
 )
 
@@ -1564,8 +1627,11 @@ add_fp_unittest(
     libc-math-smoke-tests
   SRCS
     logbf128_test.cpp
+  HDRS
+    LogbTest.h
   DEPENDS
     libc.src.math.logbf128
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.manipulation_functions
 )
 
@@ -1579,6 +1645,7 @@ add_fp_unittest(
     ModfTest.h
   DEPENDS
     libc.src.math.modf
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.basic_operations
     libc.src.__support.FPUtil.nearest_integer_operations
 )
@@ -1593,6 +1660,7 @@ add_fp_unittest(
     ModfTest.h
   DEPENDS
     libc.src.math.modff
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.basic_operations
     libc.src.__support.FPUtil.nearest_integer_operations
 )
@@ -1607,6 +1675,22 @@ add_fp_unittest(
     ModfTest.h
   DEPENDS
     libc.src.math.modfl
+    libc.src.__support.CPP.algorithm
+    libc.src.__support.FPUtil.basic_operations
+    libc.src.__support.FPUtil.nearest_integer_operations
+)
+
+add_fp_unittest(
+  modff16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    modff16_test.cpp
+  HDRS
+    ModfTest.h
+  DEPENDS
+    libc.src.math.modff16
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.basic_operations
     libc.src.__support.FPUtil.nearest_integer_operations
 )
@@ -1621,6 +1705,7 @@ add_fp_unittest(
     ModfTest.h
   DEPENDS
     libc.src.math.modff128
+    libc.src.__support.CPP.algorithm
     libc.src.__support.FPUtil.basic_operations
     libc.src.__support.FPUtil.nearest_integer_operations
 )

diff --git a/libc/test/src/math/smoke/FrexpTest.h b/libc/test/src/math/smoke/FrexpTest.h
@@ -6,7 +6,6 @@
 //
 //===----------------------------------------------------------------------===//
 
-#include "src/__support/FPUtil/BasicOperations.h"
 #include "test/UnitTest/FEnvSafeTest.h"
 #include "test/UnitTest/FPMatcher.h"
 #include "test/UnitTest/Test.h"

diff --git a/libc/test/src/math/smoke/ILogbTest.h b/libc/test/src/math/smoke/ILogbTest.h
@@ -9,7 +9,7 @@
 #ifndef LLVM_LIBC_TEST_SRC_MATH_ILOGBTEST_H
 #define LLVM_LIBC_TEST_SRC_MATH_ILOGBTEST_H
 
-#include "src/__support/CPP/limits.h" // INT_MAX
+#include "src/__support/CPP/algorithm.h"
 #include "src/__support/FPUtil/FPBits.h"
 #include "src/__support/FPUtil/ManipulationFunctions.h"
 #include "test/UnitTest/FEnvSafeTest.h"
@@ -76,10 +76,12 @@ class LlvmLibcILogbTest : public LIBC_NAMESPACE::testing::FEnvSafeTest {
   void test_subnormal_range(Func func) {
     constexpr StorageType MIN_SUBNORMAL = FPBits::min_subnormal().uintval();
     constexpr StorageType MAX_SUBNORMAL = FPBits::max_subnormal().uintval();
-    constexpr StorageType COUNT = 10'001;
-    constexpr StorageType STEP = (MAX_SUBNORMAL - MIN_SUBNORMAL) / COUNT;
+    constexpr int COUNT = 10'001;
+    constexpr StorageType STEP = LIBC_NAMESPACE::cpp::max(
+        static_cast<StorageType>((MAX_SUBNORMAL - MIN_SUBNORMAL) / COUNT),
+        StorageType(1));
     for (StorageType v = MIN_SUBNORMAL; v <= MAX_SUBNORMAL; v += STEP) {
-      FPBits x_bits = FPBits(v);
+      FPBits x_bits(v);
       if (x_bits.is_zero() || x_bits.is_inf_or_nan())
         continue;
 
@@ -94,10 +96,12 @@ class LlvmLibcILogbTest : public LIBC_NAMESPACE::testing::FEnvSafeTest {
   void test_normal_range(Func func) {
     constexpr StorageType MIN_NORMAL = FPBits::min_normal().uintval();
     constexpr StorageType MAX_NORMAL = FPBits::max_normal().uintval();
-    constexpr StorageType COUNT = 10'001;
-    constexpr StorageType STEP = (MAX_NORMAL - MIN_NORMAL) / COUNT;
+    constexpr int COUNT = 10'001;
+    constexpr StorageType STEP = LIBC_NAMESPACE::cpp::max(
+        static_cast<StorageType>((MAX_NORMAL - MIN_NORMAL) / COUNT),
+        StorageType(1));
     for (StorageType v = MIN_NORMAL; v <= MAX_NORMAL; v += STEP) {
-      FPBits x_bits = FPBits(v);
+      FPBits x_bits(v);
       if (x_bits.is_zero() || x_bits.is_inf_or_nan())
         continue;
 

diff --git a/libc/test/src/math/smoke/LogbTest.h b/libc/test/src/math/smoke/LogbTest.h
@@ -6,6 +6,7 @@
 //
 //===----------------------------------------------------------------------===//
 
+#include "src/__support/CPP/algorithm.h"
 #include "src/__support/FPUtil/ManipulationFunctions.h"
 #include "test/UnitTest/FEnvSafeTest.h"
 #include "test/UnitTest/FPMatcher.h"
@@ -69,10 +70,12 @@ class LogbTest : public LIBC_NAMESPACE::testing::FEnvSafeTest {
 
   void testRange(LogbFunc func) {
     using StorageType = typename FPBits::StorageType;
-    constexpr StorageType COUNT = 100'000;
-    constexpr StorageType STEP = STORAGE_MAX / COUNT;
-    for (StorageType i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
-      FPBits x_bits = FPBits(v);
+    constexpr int COUNT = 100'000;
+    constexpr StorageType STEP = LIBC_NAMESPACE::cpp::max(
+        static_cast<StorageType>(STORAGE_MAX / COUNT), StorageType(1));
+    StorageType v = 0;
+    for (int i = 0; i <= COUNT; ++i, v += STEP) {
+      FPBits x_bits(v);
       if (x_bits.is_zero() || x_bits.is_inf_or_nan())
         continue;
 

diff --git a/libc/test/src/math/smoke/ModfTest.h b/libc/test/src/math/smoke/ModfTest.h
@@ -6,6 +6,7 @@
 //
 //===----------------------------------------------------------------------===//
 
+#include "src/__support/CPP/algorithm.h"
 #include "src/__support/FPUtil/BasicOperations.h"
 #include "src/__support/FPUtil/NearestIntegerOperations.h"
 #include "test/UnitTest/FEnvSafeTest.h"
@@ -83,10 +84,12 @@ class ModfTest : public LIBC_NAMESPACE::testing::FEnvSafeTest {
   }
 
   void testRange(ModfFunc func) {
-    constexpr StorageType COUNT = 100'000;
-    constexpr StorageType STEP = STORAGE_MAX / COUNT;
-    for (StorageType i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
-      FPBits x_bits = FPBits(v);
+    constexpr int COUNT = 100'000;
+    constexpr StorageType STEP = LIBC_NAMESPACE::cpp::max(
+        static_cast<StorageType>(STORAGE_MAX / COUNT), StorageType(1));
+    StorageType v = 0;
+    for (int i = 0; i <= COUNT; ++i, v += STEP) {
+      FPBits x_bits(v);
       if (x_bits.is_zero() || x_bits.is_inf_or_nan())
         continue;
 

diff --git a/libc/test/src/math/smoke/frexpf16_test.cpp b/libc/test/src/math/smoke/frexpf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for frexpf16 --------------------------------------------===//
+//
+// 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 "FrexpTest.h"
+
+#include "src/math/frexpf16.h"
+
+LIST_FREXP_TESTS(float16, LIBC_NAMESPACE::frexpf16);
diff --git a/libc/test/src/math/smoke/ilogbf16_test.cpp b/libc/test/src/math/smoke/ilogbf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for ilogbf16 --------------------------------------------===//
+//
+// 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 "ILogbTest.h"
+
+#include "src/math/ilogbf16.h"
+
+LIST_INTLOGB_TESTS(int, float16, LIBC_NAMESPACE::ilogbf16);
diff --git a/libc/test/src/math/smoke/llogbf16_test.cpp b/libc/test/src/math/smoke/llogbf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for llogbf16 --------------------------------------------===//
+//
+// 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 "ILogbTest.h"
+
+#include "src/math/llogbf16.h"
+
+LIST_INTLOGB_TESTS(long, float16, LIBC_NAMESPACE::llogbf16);
diff --git a/libc/test/src/math/smoke/logbf16_test.cpp b/libc/test/src/math/smoke/logbf16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for logbf16 ---------------------------------------------===//
+//
+// 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 "LogbTest.h"
+
+#include "src/math/logbf16.h"
+
+LIST_LOGB_TESTS(float16, LIBC_NAMESPACE::logbf16)
diff --git a/libc/test/src/math/smoke/modff16_test.cpp b/libc/test/src/math/smoke/modff16_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for modff16 ---------------------------------------------===//
+//
+// 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 "ModfTest.h"
+
+#include "src/math/modff16.h"
+
+LIST_MODF_TESTS(float16, LIBC_NAMESPACE::modff16)