[libc][math][c23] Add {frexp,ilogb,llogb,logb,modf}f16 C23 math functions (#94758)

Part of #93566.

31 files changed, 480 insertions, 36 deletions

diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index ee86822..50e0a6d 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -516,12 +516,17 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.fminimum_magf16
     libc.src.math.fminimum_mag_numf16
     libc.src.math.fminimum_numf16
+    libc.src.math.frexpf16
     libc.src.math.fromfpf16
     libc.src.math.fromfpxf16
+    libc.src.math.ilogbf16
+    libc.src.math.llogbf16
     libc.src.math.llrintf16
     libc.src.math.llroundf16
+    libc.src.math.logbf16
     libc.src.math.lrintf16
     libc.src.math.lroundf16
+    libc.src.math.modff16
     libc.src.math.nanf16
     libc.src.math.nearbyintf16
     libc.src.math.nextafterf16
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index c4b3b1a..31ad0bc 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -549,12 +549,17 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.fminimum_mag_numf16
     libc.src.math.fminimum_numf16
     libc.src.math.fmodf16
+    libc.src.math.frexpf16
     libc.src.math.fromfpf16
     libc.src.math.fromfpxf16
+    libc.src.math.ilogbf16
+    libc.src.math.llogbf16
     libc.src.math.llrintf16
     libc.src.math.llroundf16
+    libc.src.math.logbf16
     libc.src.math.lrintf16
     libc.src.math.lroundf16
+    libc.src.math.modff16
     libc.src.math.nanf16
     libc.src.math.nearbyintf16
     libc.src.math.nextafterf16
diff --git a/libc/docs/c23.rst b/libc/docs/c23.rst
index 71232cc..fec9b24 100644
--- a/libc/docs/c23.rst
+++ b/libc/docs/c23.rst
@@ -50,7 +50,7 @@ Additions:
   * issignaling
   * issubnormal
   * iszero
-  * llogb*
+  * llogb* |check|
   * pown*
   * powr*
   * rootn*
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
index 43f63e91..3e122fb 100644
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -160,7 +160,7 @@ Basic Operations
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | fmul             | N/A              | |check|         |                        | N/A                  |                        | 7.12.14.3              | F.10.11                    |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| frexp            | |check|          | |check|         | |check|                |                      | |check|                | 7.12.6.7               | F.10.3.7                   |
+| frexp            | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.6.7               | F.10.3.7                   |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | fromfp           | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.9.10              | F.10.6.10                  |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
@@ -168,23 +168,23 @@ Basic Operations
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | fsub             | N/A              |                 |                        | N/A                  |                        | 7.12.14.2              | F.10.11                    |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| ilogb            | |check|          | |check|         | |check|                |                      | |check|                | 7.12.6.8               | F.10.3.8                   |
+| ilogb            | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.6.8               | F.10.3.8                   |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | ldexp            | |check|          | |check|         | |check|                |                      | |check|                | 7.12.6.9               | F.10.3.9                   |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| llogb            | |check|          | |check|         | |check|                |                      | |check|                | 7.12.6.10              | F.10.3.10                  |
+| llogb            | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.6.10              | F.10.3.10                  |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | llrint           | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.9.5               | F.10.6.5                   |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | llround          | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.9.7               | F.10.6.7                   |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| logb             | |check|          | |check|         | |check|                |                      | |check|                | 7.12.6.17              | F.10.3.17                  |
+| logb             | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.6.17              | F.10.3.17                  |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | lrint            | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.9.5               | F.10.6.5                   |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | lround           | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.9.7               | F.10.6.7                   |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| modf             | |check|          | |check|         | |check|                |                      | |check|                | 7.12.6.18              | F.10.3.18                  |
+| modf             | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.6.18              | F.10.3.18                  |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | nan              | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.11.2              | F.10.8.2                   |
 +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/spec/spec.td b/libc/spec/spec.td
index 056a314..7e1283e 100644
--- a/libc/spec/spec.td
+++ b/libc/spec/spec.td
@@ -115,6 +115,7 @@ def IntPtr : PtrType<IntType>;
 def RestrictedIntPtr : RestrictedPtrType<IntType>;
 def FloatPtr : PtrType<FloatType>;
 def DoublePtr : PtrType<DoubleType>;
+def Float16Ptr : PtrType<Float16Type>;
 def Float128Ptr : PtrType<Float128Type>;
 def UnsignedCharPtr : PtrType<UnsignedCharType>;
 
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index ac16041..b5b6dbc 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -487,6 +487,7 @@ def StdC : StandardSpec<"stdc"> {
           FunctionSpec<"frexp", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<IntPtr>]>,
           FunctionSpec<"frexpf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<IntPtr>]>,
           FunctionSpec<"frexpl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<IntPtr>]>,
+          GuardedFunctionSpec<"frexpf16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>, ArgSpec<IntPtr>], "LIBC_TYPES_HAS_FLOAT16">,
           GuardedFunctionSpec<"frexpf128", RetValSpec<Float128Type>, [ArgSpec<Float128Type>, ArgSpec<IntPtr>], "LIBC_TYPES_HAS_FLOAT128">,
 
           FunctionSpec<"fromfp", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<IntType>, ArgSpec<UnsignedIntType>]>,
@@ -519,11 +520,13 @@ def StdC : StandardSpec<"stdc"> {
           FunctionSpec<"ilogb", RetValSpec<IntType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"ilogbf", RetValSpec<IntType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"ilogbl", RetValSpec<IntType>, [ArgSpec<LongDoubleType>]>,
+          GuardedFunctionSpec<"ilogbf16", RetValSpec<IntType>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
           GuardedFunctionSpec<"ilogbf128", RetValSpec<IntType>, [ArgSpec<Float128Type>], "LIBC_TYPES_HAS_FLOAT128">,
 
           FunctionSpec<"llogb", RetValSpec<LongType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"llogbf", RetValSpec<LongType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"llogbl", RetValSpec<LongType>, [ArgSpec<LongDoubleType>]>,
+          GuardedFunctionSpec<"llogbf16", RetValSpec<LongType>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
           GuardedFunctionSpec<"llogbf128", RetValSpec<LongType>, [ArgSpec<Float128Type>], "LIBC_TYPES_HAS_FLOAT128">,
 
           FunctionSpec<"ldexp", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<IntType>]>,
@@ -546,11 +549,13 @@ def StdC : StandardSpec<"stdc"> {
           FunctionSpec<"logb", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"logbf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"logbl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>]>,
+          GuardedFunctionSpec<"logbf16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
           GuardedFunctionSpec<"logbf128", RetValSpec<Float128Type>, [ArgSpec<Float128Type>], "LIBC_TYPES_HAS_FLOAT128">,
 
           FunctionSpec<"modf", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoublePtr>]>,
           FunctionSpec<"modff", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatPtr>]>,
           FunctionSpec<"modfl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoublePtr>]>,
+          GuardedFunctionSpec<"modff16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>, ArgSpec<Float16Ptr>], "LIBC_TYPES_HAS_FLOAT16">,
           GuardedFunctionSpec<"modff128", RetValSpec<Float128Type>, [ArgSpec<Float128Type>, ArgSpec<Float128Ptr>], "LIBC_TYPES_HAS_FLOAT128">,
 
           FunctionSpec<"cos", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
diff --git a/libc/src/__support/FPUtil/CMakeLists.txt b/libc/src/__support/FPUtil/CMakeLists.txt
index 01ca425..1744f8c 100644
--- a/libc/src/__support/FPUtil/CMakeLists.txt
+++ b/libc/src/__support/FPUtil/CMakeLists.txt
@@ -217,6 +217,7 @@ add_header_library(
     .nearest_integer_operations
     .normal_float
     libc.hdr.math_macros
+    libc.src.__support.CPP.algorithm
     libc.src.__support.CPP.bit
     libc.src.__support.CPP.limits
     libc.src.__support.CPP.type_traits
diff --git a/libc/src/__support/FPUtil/ManipulationFunctions.h b/libc/src/__support/FPUtil/ManipulationFunctions.h
index a289c2e..f695b83 100644
--- a/libc/src/__support/FPUtil/ManipulationFunctions.h
+++ b/libc/src/__support/FPUtil/ManipulationFunctions.h
@@ -16,6 +16,7 @@
 #include "rounding_mode.h"
 
 #include "hdr/math_macros.h"
+#include "src/__support/CPP/algorithm.h"
 #include "src/__support/CPP/bit.h"
 #include "src/__support/CPP/limits.h" // INT_MAX, INT_MIN
 #include "src/__support/CPP/type_traits.h"
@@ -102,7 +103,7 @@ intlogb(U x) {
     return IntLogbConstants<T>::T_MAX;
   }
 
-  DyadicFloat<FPBits<U>::STORAGE_LEN> normal(bits.get_val());
+  DyadicFloat<cpp::max(FPBits<U>::STORAGE_LEN, 32)> normal(bits.get_val());
   int exponent = normal.get_unbiased_exponent();
   // The C standard does not specify the return value when an exponent is
   // out of int range. However, XSI conformance required that INT_MAX or
@@ -138,7 +139,7 @@ LIBC_INLINE constexpr T logb(T x) {
     return FPBits<T>::inf().get_val();
   }
 
-  DyadicFloat<FPBits<T>::STORAGE_LEN> normal(bits.get_val());
+  DyadicFloat<cpp::max(FPBits<T>::STORAGE_LEN, 32)> normal(bits.get_val());
   return static_cast<T>(normal.get_unbiased_exponent());
 }
 
diff --git a/libc/src/__support/FPUtil/NormalFloat.h b/libc/src/__support/FPUtil/NormalFloat.h
index 8bc1fec..33529d5 100644
--- a/libc/src/__support/FPUtil/NormalFloat.h
+++ b/libc/src/__support/FPUtil/NormalFloat.h
@@ -110,9 +110,11 @@ template <typename T> struct NormalFloat {
       if (shift <= FPBits<T>::FRACTION_LEN + 1) {
         // Generate a subnormal number. Might lead to loss of precision.
         // We round to nearest and round halfway cases to even.
-        const StorageType shift_out_mask = (StorageType(1) << shift) - 1;
+        const StorageType shift_out_mask =
+            static_cast<StorageType>(StorageType(1) << shift) - 1;
         const StorageType shift_out_value = mantissa & shift_out_mask;
-        const StorageType halfway_value = StorageType(1) << (shift - 1);
+        const StorageType halfway_value =
+            static_cast<StorageType>(StorageType(1) << (shift - 1));
         result.set_biased_exponent(0);
         result.set_mantissa(mantissa >> shift);
         StorageType new_mantissa = result.get_mantissa();
@@ -135,7 +137,8 @@ template <typename T> struct NormalFloat {
       }
     }
 
-    result.set_biased_exponent(exponent + FPBits<T>::EXP_BIAS);
+    result.set_biased_exponent(
+        static_cast<StorageType>(exponent + FPBits<T>::EXP_BIAS));
     result.set_mantissa(mantissa);
     return result.get_val();
   }
@@ -155,7 +158,7 @@ private:
     // Normalize subnormal numbers.
     if (bits.is_subnormal()) {
       unsigned shift = evaluate_normalization_shift(bits.get_mantissa());
-      mantissa = StorageType(bits.get_mantissa()) << shift;
+      mantissa = static_cast<StorageType>(bits.get_mantissa() << shift);
       exponent = 1 - FPBits<T>::EXP_BIAS - shift;
     } else {
       exponent = bits.get_biased_exponent() - FPBits<T>::EXP_BIAS;
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index 68b8924..f8582d8 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -191,6 +191,7 @@ add_math_entrypoint_object(fmodf128)
 add_math_entrypoint_object(frexp)
 add_math_entrypoint_object(frexpf)
 add_math_entrypoint_object(frexpl)
+add_math_entrypoint_object(frexpf16)
 add_math_entrypoint_object(frexpf128)
 
 add_math_entrypoint_object(fromfp)
@@ -211,11 +212,13 @@ add_math_entrypoint_object(hypotf)
 add_math_entrypoint_object(ilogb)
 add_math_entrypoint_object(ilogbf)
 add_math_entrypoint_object(ilogbl)
+add_math_entrypoint_object(ilogbf16)
 add_math_entrypoint_object(ilogbf128)
 
 add_math_entrypoint_object(llogb)
 add_math_entrypoint_object(llogbf)
 add_math_entrypoint_object(llogbl)
+add_math_entrypoint_object(llogbf16)
 add_math_entrypoint_object(llogbf128)
 
 add_math_entrypoint_object(ldexp)
@@ -238,6 +241,7 @@ add_math_entrypoint_object(logf)
 add_math_entrypoint_object(logb)
 add_math_entrypoint_object(logbf)
 add_math_entrypoint_object(logbl)
+add_math_entrypoint_object(logbf16)
 add_math_entrypoint_object(logbf128)
 
 add_math_entrypoint_object(llrint)
@@ -267,6 +271,7 @@ add_math_entrypoint_object(lroundf128)
 add_math_entrypoint_object(modf)
 add_math_entrypoint_object(modff)
 add_math_entrypoint_object(modfl)
+add_math_entrypoint_object(modff16)
 add_math_entrypoint_object(modff128)
 
 add_math_entrypoint_object(nan)
diff --git a/libc/src/math/frexpf16.h b/libc/src/math/frexpf16.h
new file mode 100644
index 0000000..dc1898c
--- /dev/null
+++ b/libc/src/math/frexpf16.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for frexpf16 ----------------------*- 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_FREXPF16_H
+#define LLVM_LIBC_SRC_MATH_FREXPF16_H
+
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE {
+
+float16 frexpf16(float16 x, int *exp);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_FREXPF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 4f94468..caaa0ac 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1302,6 +1302,19 @@ add_entrypoint_object(
 )
 
 add_entrypoint_object(
+  frexpf16
+  SRCS
+    frexpf16.cpp
+  HDRS
+    ../frexpf16.h
+  COMPILE_OPTIONS
+    -O3
+  DEPENDS
+    libc.src.__support.macros.properties.types
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_entrypoint_object(
   frexpf128
   SRCS
     frexpf128.cpp
@@ -1351,6 +1364,19 @@ add_entrypoint_object(
 )
 
 add_entrypoint_object(
+  ilogbf16
+  SRCS
+    ilogbf16.cpp
+  HDRS
+    ../ilogbf16.h
+  COMPILE_OPTIONS
+    -O3
+  DEPENDS
+    libc.src.__support.macros.properties.types
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_entrypoint_object(
   ilogbf128
   SRCS
     ilogbf128.cpp
@@ -1400,6 +1426,19 @@ add_entrypoint_object(
 )
 
 add_entrypoint_object(
+  llogbf16
+  SRCS
+    llogbf16.cpp
+  HDRS
+    ../llogbf16.h
+  COMPILE_OPTIONS
+    -O3
+  DEPENDS
+    libc.src.__support.macros.properties.types
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_entrypoint_object(
   llogbf128
   SRCS
     llogbf128.cpp
@@ -1673,6 +1712,19 @@ add_entrypoint_object(
 )
 
 add_entrypoint_object(
+  logbf16
+  SRCS
+    logbf16.cpp
+  HDRS
+    ../logbf16.h
+  COMPILE_OPTIONS
+    -O3
+  DEPENDS
+    libc.src.__support.macros.properties.types
+    libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_entrypoint_object(
   logbf128
   SRCS
     logbf128.cpp
@@ -1681,6 +1733,7 @@ add_entrypoint_object(
   COMPILE_OPTIONS
     -O3
   DEPENDS
+    libc.src.__support.macros.properties.types
     libc.src.__support.FPUtil.manipulation_functions
 )
 
@@ -1721,6 +1774,19 @@ add_entrypoint_object(
 )
 
 add_entrypoint_object(
+  modff16
+  SRCS
+    modff16.cpp
+  HDRS
+    ../modff16.h
+  DEPENDS
+    libc.src.__support.macros.properties.types
+    libc.src.__support.FPUtil.manipulation_functions
+  COMPILE_OPTIONS
+    -O3
+)
+
+add_entrypoint_object(
   modff128
   SRCS
     modff128.cpp
diff --git a/libc/src/math/generic/frexpf16.cpp b/libc/src/math/generic/frexpf16.cpp
new file mode 100644
index 0000000..2d29c07
--- /dev/null
+++ b/libc/src/math/generic/frexpf16.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of frexpf16 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/frexpf16.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float16, frexpf16, (float16 x, int *exp)) {
+  return fputil::frexp(x, *exp);
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/ilogbf16.cpp b/libc/src/math/generic/ilogbf16.cpp
new file mode 100644
index 0000000..87e43f8
--- /dev/null
+++ b/libc/src/math/generic/ilogbf16.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of ilogbf16 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/ilogbf16.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(int, ilogbf16, (float16 x)) {
+  return fputil::intlogb<int>(x);
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/llogbf16.cpp b/libc/src/math/generic/llogbf16.cpp
new file mode 100644
index 0000000..b7a21b9
--- /dev/null
+++ 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
new file mode 100644
index 0000000..52eb9ac
--- /dev/null
+++ 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
new file mode 100644
index 0000000..50cc5b5
--- /dev/null
+++ 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
new file mode 100644
index 0000000..4884a14
--- /dev/null
+++ 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
new file mode 100644
index 0000000..267ae41
--- /dev/null
+++ 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
new file mode 100644
index 0000000..8082e06
--- /dev/null
+++ 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
new file mode 100644
index 0000000..a3017c5
--- /dev/null
+++ 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
index cc0e00a..84aa76c 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -1092,6 +1092,18 @@ add_fp_unittest(
 )
 
 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
     libc-math-smoke-tests
@@ -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
index e9e4964..fc2313a 100644
--- 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
index 05f906b..3315ac2 100644
--- 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 @@ public:
   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 @@ public:
   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
index 4938fcf..0bb6e12 100644
--- 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 @@ public:
 
   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
index 85db2d6..6226e5d 100644
--- 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 @@ public:
   }
 
   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
new file mode 100644
index 0000000..4d5492c
--- /dev/null
+++ 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
new file mode 100644
index 0000000..e046709
--- /dev/null
+++ 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
new file mode 100644
index 0000000..8907681
--- /dev/null
+++ 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
new file mode 100644
index 0000000..cfc1a05
--- /dev/null
+++ 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
new file mode 100644
index 0000000..7093377
--- /dev/null
+++ 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)