[libc][math][c23] Add f16sqrt{,l,f128} C23 math functions (#96642)

Part of #95250.

24 files changed, 352 insertions, 124 deletions

diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 8a26536..ea89f8b 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -510,6 +510,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.f16div
     libc.src.math.f16divf
     libc.src.math.f16fmaf
+    libc.src.math.f16sqrt
     libc.src.math.f16sqrtf
     libc.src.math.fabsf16
     libc.src.math.fdimf16
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index e1922ca..9f67dea 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -543,7 +543,9 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.f16fma
     libc.src.math.f16fmaf
     libc.src.math.f16fmal
+    libc.src.math.f16sqrt
     libc.src.math.f16sqrtf
+    libc.src.math.f16sqrtl
     libc.src.math.fabsf16
     libc.src.math.fdimf16
     libc.src.math.floorf16
@@ -596,8 +598,9 @@ if(LIBC_TYPES_HAS_FLOAT16)
   if(LIBC_TYPES_HAS_FLOAT128)
     list(APPEND TARGET_LIBM_ENTRYPOINTS
       # math.h C23 mixed _Float16 and _Float128 entrypoints
-      libc.src.math.f16fmaf128
       libc.src.math.f16divf128
+      libc.src.math.f16fmaf128
+      libc.src.math.f16sqrtf128
     )
   endif()
 endif()
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
index 1bc75a9..3ca7bf9 100644
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -292,7 +292,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | fma       | |check|          | |check|         |                        |                      |                        | 7.12.13.1              | F.10.10.1                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| f16sqrt   | |check|          |                 |                        | N/A                  |                        | 7.12.14.6              | F.10.11                    |
+| f16sqrt   | |check|\*        | |check|\*       | |check|\*              | N/A                  | |check|                | 7.12.14.6              | F.10.11                    |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | fsqrt     | N/A              |                 |                        | N/A                  |                        | 7.12.14.6              | F.10.11                    |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/spec/llvm_libc_ext.td b/libc/spec/llvm_libc_ext.td
index ed1a17e..74a90a4 100644
--- a/libc/spec/llvm_libc_ext.td
+++ b/libc/spec/llvm_libc_ext.td
@@ -60,6 +60,10 @@ def LLVMLibcExt : StandardSpec<"llvm_libc_ext"> {
           GuardedFunctionSpec<"f16div", RetValSpec<Float16Type>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>], "LIBC_TYPES_HAS_FLOAT16">,
           GuardedFunctionSpec<"f16divf", RetValSpec<Float16Type>, [ArgSpec<FloatType>, ArgSpec<FloatType>], "LIBC_TYPES_HAS_FLOAT16">,
           GuardedFunctionSpec<"f16divl", RetValSpec<Float16Type>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>], "LIBC_TYPES_HAS_FLOAT16">,
+
+          GuardedFunctionSpec<"f16sqrt", RetValSpec<Float16Type>, [ArgSpec<DoubleType>], "LIBC_TYPES_HAS_FLOAT16">,
+          GuardedFunctionSpec<"f16sqrtf", RetValSpec<Float16Type>, [ArgSpec<FloatType>], "LIBC_TYPES_HAS_FLOAT16">,
+          GuardedFunctionSpec<"f16sqrtl", RetValSpec<Float16Type>, [ArgSpec<LongDoubleType>], "LIBC_TYPES_HAS_FLOAT16">,
       ]
   >;
 
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index 481515a..6e59062 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -731,7 +731,7 @@ def StdC : StandardSpec<"stdc"> {
 
           GuardedFunctionSpec<"f16divf128", RetValSpec<Float16Type>, [ArgSpec<Float128Type>, ArgSpec<Float128Type>], "LIBC_TYPES_HAS_FLOAT16_AND_FLOAT128">,
 
-          GuardedFunctionSpec<"f16sqrtf", RetValSpec<Float16Type>, [ArgSpec<FloatType>], "LIBC_TYPES_HAS_FLOAT16">,
+          GuardedFunctionSpec<"f16sqrtf128", RetValSpec<Float16Type>, [ArgSpec<Float128Type>], "LIBC_TYPES_HAS_FLOAT16_AND_FLOAT128">,
       ]
   >;
 
diff --git a/libc/src/__support/FPUtil/generic/CMakeLists.txt b/libc/src/__support/FPUtil/generic/CMakeLists.txt
index bd8af98..fb49fd0 100644
--- a/libc/src/__support/FPUtil/generic/CMakeLists.txt
+++ b/libc/src/__support/FPUtil/generic/CMakeLists.txt
@@ -8,6 +8,7 @@ add_header_library(
     libc.src.__support.common
     libc.src.__support.CPP.bit
     libc.src.__support.CPP.type_traits
+    libc.src.__support.FPUtil.dyadic_float
     libc.src.__support.FPUtil.fenv_impl
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.rounding_mode
diff --git a/libc/src/__support/FPUtil/generic/sqrt.h b/libc/src/__support/FPUtil/generic/sqrt.h
index d6e894f..1b71379 100644
--- a/libc/src/__support/FPUtil/generic/sqrt.h
+++ b/libc/src/__support/FPUtil/generic/sqrt.h
@@ -14,7 +14,7 @@
 #include "src/__support/CPP/type_traits.h"
 #include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/FPUtil/dyadic_float.h"
 #include "src/__support/common.h"
 #include "src/__support/uint128.h"
 
@@ -78,16 +78,14 @@ sqrt(InType x) {
     return x86::sqrt(x);
   } else {
     // IEEE floating points formats.
-    using OutFPBits = typename fputil::FPBits<OutType>;
-    using OutStorageType = typename OutFPBits::StorageType;
-    using InFPBits = typename fputil::FPBits<InType>;
+    using OutFPBits = FPBits<OutType>;
+    using InFPBits = FPBits<InType>;
     using InStorageType = typename InFPBits::StorageType;
+    using DyadicFloat =
+        DyadicFloat<cpp::bit_ceil(static_cast<size_t>(InFPBits::STORAGE_LEN))>;
+
     constexpr InStorageType ONE = InStorageType(1) << InFPBits::FRACTION_LEN;
     constexpr auto FLT_NAN = OutFPBits::quiet_nan().get_val();
-    constexpr int EXTRA_FRACTION_LEN =
-        InFPBits::FRACTION_LEN - OutFPBits::FRACTION_LEN;
-    constexpr InStorageType EXTRA_FRACTION_MASK =
-        (InStorageType(1) << EXTRA_FRACTION_LEN) - 1;
 
     InFPBits bits(x);
 
@@ -135,6 +133,7 @@ sqrt(InType x) {
       InStorageType y = ONE;
       InStorageType r = x_mant - ONE;
 
+      // TODO: Reduce iteration count to OutFPBits::FRACTION_LEN + 2 or + 3.
       for (InStorageType current_bit = ONE >> 1; current_bit;
            current_bit >>= 1) {
         r <<= 1;
@@ -146,91 +145,19 @@ sqrt(InType x) {
       }
 
       // We compute one more iteration in order to round correctly.
-      bool lsb = (y & (InStorageType(1) << EXTRA_FRACTION_LEN)) !=
-                 0;    // Least significant bit
-      bool rb = false; // Round bit
       r <<= 2;
-      InStorageType tmp = (y << 2) + 1;
+      y <<= 2;
+      InStorageType tmp = y + 1;
       if (r >= tmp) {
         r -= tmp;
-        rb = true;
-      }
-
-      bool sticky = false;
-
-      if constexpr (EXTRA_FRACTION_LEN > 0) {
-        sticky = rb || (y & EXTRA_FRACTION_MASK) != 0;
-        rb = (y & (InStorageType(1) << (EXTRA_FRACTION_LEN - 1))) != 0;
-      }
-
-      // Remove hidden bit and append the exponent field.
-      x_exp = ((x_exp >> 1) + OutFPBits::EXP_BIAS);
-
-      OutStorageType y_out = static_cast<OutStorageType>(
-          ((y - ONE) >> EXTRA_FRACTION_LEN) |
-          (static_cast<OutStorageType>(x_exp) << OutFPBits::FRACTION_LEN));
-
-      if constexpr (EXTRA_FRACTION_LEN > 0) {
-        if (x_exp >= OutFPBits::MAX_BIASED_EXPONENT) {
-          switch (quick_get_round()) {
-          case FE_TONEAREST:
-          case FE_UPWARD:
-            return OutFPBits::inf().get_val();
-          default:
-            return OutFPBits::max_normal().get_val();
-          }
-        }
-
-        if (x_exp <
-            -OutFPBits::EXP_BIAS - OutFPBits::SIG_LEN + EXTRA_FRACTION_LEN) {
-          switch (quick_get_round()) {
-          case FE_UPWARD:
-            return OutFPBits::min_subnormal().get_val();
-          default:
-            return OutType(0.0);
-          }
-        }
-
-        if (x_exp <= 0) {
-          int underflow_extra_fraction_len = EXTRA_FRACTION_LEN - x_exp + 1;
-          InStorageType underflow_extra_fraction_mask =
-              (InStorageType(1) << underflow_extra_fraction_len) - 1;
-
-          rb = (y & (InStorageType(1) << (underflow_extra_fraction_len - 1))) !=
-               0;
-          OutStorageType subnormal_mant =
-              static_cast<OutStorageType>(y >> underflow_extra_fraction_len);
-          lsb = (subnormal_mant & 1) != 0;
-          sticky = sticky || (y & underflow_extra_fraction_mask) != 0;
-
-          switch (quick_get_round()) {
-          case FE_TONEAREST:
-            if (rb && (lsb || sticky))
-              ++subnormal_mant;
-            break;
-          case FE_UPWARD:
-            if (rb || sticky)
-              ++subnormal_mant;
-            break;
-          }
-
-          return cpp::bit_cast<OutType>(subnormal_mant);
-        }
-      }
-
-      switch (quick_get_round()) {
-      case FE_TONEAREST:
-        // Round to nearest, ties to even
-        if (rb && (lsb || (r != 0)))
-          ++y_out;
-        break;
-      case FE_UPWARD:
-        if (rb || (r != 0) || sticky)
-          ++y_out;
-        break;
+        // Rounding bit.
+        y |= 2;
       }
+      // Sticky bit.
+      y |= static_cast<unsigned int>(r != 0);
 
-      return cpp::bit_cast<OutType>(y_out);
+      DyadicFloat yd(Sign::POS, (x_exp >> 1) - 2 - InFPBits::FRACTION_LEN, y);
+      return yd.template as<OutType, /*ShouldSignalExceptions=*/true>();
     }
   }
 }
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index fb0d971..4777f66 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -109,7 +109,10 @@ add_math_entrypoint_object(f16fmaf)
 add_math_entrypoint_object(f16fmal)
 add_math_entrypoint_object(f16fmaf128)
 
+add_math_entrypoint_object(f16sqrt)
 add_math_entrypoint_object(f16sqrtf)
+add_math_entrypoint_object(f16sqrtl)
+add_math_entrypoint_object(f16sqrtf128)
 
 add_math_entrypoint_object(fabs)
 add_math_entrypoint_object(fabsf)
diff --git a/libc/src/math/f16sqrt.h b/libc/src/math/f16sqrt.h
new file mode 100644
index 0000000..f1134ac
--- /dev/null
+++ b/libc/src/math/f16sqrt.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for f16sqrt -----------------------*- 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_F16SQRT_H
+#define LLVM_LIBC_SRC_MATH_F16SQRT_H
+
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE {
+
+float16 f16sqrt(double x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_F16SQRT_H
diff --git a/libc/src/math/f16sqrtf128.h b/libc/src/math/f16sqrtf128.h
new file mode 100644
index 0000000..61a6ce9
--- /dev/null
+++ b/libc/src/math/f16sqrtf128.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for f16sqrtf128 -------------------*- 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_F16SQRTF128_H
+#define LLVM_LIBC_SRC_MATH_F16SQRTF128_H
+
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE {
+
+float16 f16sqrtf128(float128 x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_F16SQRTF128_H
diff --git a/libc/src/math/f16sqrtl.h b/libc/src/math/f16sqrtl.h
new file mode 100644
index 0000000..fd3c55f
--- /dev/null
+++ b/libc/src/math/f16sqrtl.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for f16sqrtl ----------------------*- 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_F16SQRTL_H
+#define LLVM_LIBC_SRC_MATH_F16SQRTL_H
+
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE {
+
+float16 f16sqrtl(long double x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_F16SQRTL_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 0e4893c..7dd6c48 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3881,6 +3881,19 @@ add_entrypoint_object(
 )
 
 add_entrypoint_object(
+  f16sqrt
+  SRCS
+    f16sqrt.cpp
+  HDRS
+    ../f16sqrt.h
+  DEPENDS
+    libc.src.__support.macros.properties.types
+    libc.src.__support.FPUtil.sqrt
+  COMPILE_OPTIONS
+    -O3
+)
+
+add_entrypoint_object(
   f16sqrtf
   SRCS
     f16sqrtf.cpp
@@ -3892,3 +3905,29 @@ add_entrypoint_object(
   COMPILE_OPTIONS
     -O3
 )
+
+add_entrypoint_object(
+  f16sqrtl
+  SRCS
+    f16sqrtl.cpp
+  HDRS
+    ../f16sqrtl.h
+  DEPENDS
+    libc.src.__support.macros.properties.types
+    libc.src.__support.FPUtil.sqrt
+  COMPILE_OPTIONS
+    -O3
+)
+
+add_entrypoint_object(
+  f16sqrtf128
+  SRCS
+    f16sqrtf128.cpp
+  HDRS
+    ../f16sqrtf128.h
+  DEPENDS
+    libc.src.__support.macros.properties.types
+    libc.src.__support.FPUtil.sqrt
+  COMPILE_OPTIONS
+    -O3
+)
diff --git a/libc/src/math/generic/f16sqrt.cpp b/libc/src/math/generic/f16sqrt.cpp
new file mode 100644
index 0000000..9d5f081
--- /dev/null
+++ b/libc/src/math/generic/f16sqrt.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of f16sqrt 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/f16sqrt.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float16, f16sqrt, (double x)) {
+  return fputil::sqrt<float16>(x);
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/f16sqrtf128.cpp b/libc/src/math/generic/f16sqrtf128.cpp
new file mode 100644
index 0000000..11a1e82
--- /dev/null
+++ b/libc/src/math/generic/f16sqrtf128.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of f16sqrtf128 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/f16sqrtf128.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float16, f16sqrtf128, (float128 x)) {
+  return fputil::sqrt<float16>(x);
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/f16sqrtl.cpp b/libc/src/math/generic/f16sqrtl.cpp
new file mode 100644
index 0000000..2aaac9a
--- /dev/null
+++ b/libc/src/math/generic/f16sqrtl.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of f16sqrtl 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/f16sqrtl.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float16, f16sqrtl, (long double x)) {
+  return fputil::sqrt<float16>(x);
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index 061feea..1326d08 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -1259,9 +1259,10 @@ add_fp_unittest(
     libc-math-unittests
   SRCS
     sqrtf_test.cpp
+  HDRS
+    SqrtTest.h
   DEPENDS
     libc.src.math.sqrtf
-    libc.src.__support.FPUtil.fp_bits
 )
 
 add_fp_unittest(
@@ -1271,9 +1272,10 @@ add_fp_unittest(
     libc-math-unittests
   SRCS
     sqrt_test.cpp
+  HDRS
+    SqrtTest.h
   DEPENDS
     libc.src.math.sqrt
-    libc.src.__support.FPUtil.fp_bits
 )
 
 add_fp_unittest(
@@ -1283,9 +1285,10 @@ add_fp_unittest(
     libc-math-unittests
   SRCS
     sqrtl_test.cpp
+  HDRS
+    SqrtTest.h
   DEPENDS
     libc.src.math.sqrtl
-    libc.src.__support.FPUtil.fp_bits
 )
 
 add_fp_unittest(
@@ -1295,9 +1298,10 @@ add_fp_unittest(
     libc-math-unittests
   SRCS
     generic_sqrtf_test.cpp
+  HDRS
+    SqrtTest.h
   DEPENDS
     libc.src.math.sqrtf
-    libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.generic.sqrt
   COMPILE_OPTIONS
     -O3
@@ -1310,9 +1314,10 @@ add_fp_unittest(
     libc-math-unittests
   SRCS
     generic_sqrt_test.cpp
+  HDRS
+    SqrtTest.h
   DEPENDS
     libc.src.math.sqrt
-    libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.generic.sqrt
   COMPILE_OPTIONS
     -O3
@@ -1325,9 +1330,10 @@ add_fp_unittest(
     libc-math-unittests
   SRCS
     generic_sqrtl_test.cpp
+  HDRS
+    SqrtTest.h
   DEPENDS
     libc.src.math.sqrtl
-    libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.generic.sqrt
   COMPILE_OPTIONS
     -O3
@@ -1986,6 +1992,32 @@ add_fp_unittest(
     libc.src.stdlib.srand
 )
 
+add_fp_unittest(
+  f16sqrt_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    f16sqrt_test.cpp
+  HDRS
+    SqrtTest.h
+  DEPENDS
+    libc.src.math.f16sqrt
+)
+
+add_fp_unittest(
+  f16sqrtl_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    f16sqrtl_test.cpp
+  HDRS
+    SqrtTest.h
+  DEPENDS
+    libc.src.math.f16sqrtl
+)
+
 add_subdirectory(generic)
 add_subdirectory(smoke)
 
diff --git a/libc/test/src/math/SqrtTest.h b/libc/test/src/math/SqrtTest.h
index 1c422e2..770cc94 100644
--- a/libc/test/src/math/SqrtTest.h
+++ b/libc/test/src/math/SqrtTest.h
@@ -6,51 +6,36 @@
 //
 //===----------------------------------------------------------------------===//
 
-#include "src/__support/CPP/bit.h"
 #include "test/UnitTest/FEnvSafeTest.h"
 #include "test/UnitTest/FPMatcher.h"
 #include "test/UnitTest/Test.h"
 #include "utils/MPFRWrapper/MPFRUtils.h"
 
-#include "hdr/math_macros.h"
-
 namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
 
-template <typename T>
+template <typename OutType, typename InType>
 class SqrtTest : public LIBC_NAMESPACE::testing::FEnvSafeTest {
 
-  DECLARE_SPECIAL_CONSTANTS(T)
+  DECLARE_SPECIAL_CONSTANTS(InType)
 
   static constexpr StorageType HIDDEN_BIT =
-      StorageType(1) << LIBC_NAMESPACE::fputil::FPBits<T>::FRACTION_LEN;
+      StorageType(1) << LIBC_NAMESPACE::fputil::FPBits<InType>::FRACTION_LEN;
 
 public:
-  typedef T (*SqrtFunc)(T);
-
-  void test_special_numbers(SqrtFunc func) {
-    ASSERT_FP_EQ(aNaN, func(aNaN));
-    ASSERT_FP_EQ(inf, func(inf));
-    ASSERT_FP_EQ(aNaN, func(neg_inf));
-    ASSERT_FP_EQ(0.0, func(0.0));
-    ASSERT_FP_EQ(-0.0, func(-0.0));
-    ASSERT_FP_EQ(aNaN, func(T(-1.0)));
-    ASSERT_FP_EQ(T(1.0), func(T(1.0)));
-    ASSERT_FP_EQ(T(2.0), func(T(4.0)));
-    ASSERT_FP_EQ(T(3.0), func(T(9.0)));
-  }
+  using SqrtFunc = OutType (*)(InType);
 
   void test_denormal_values(SqrtFunc func) {
     for (StorageType mant = 1; mant < HIDDEN_BIT; mant <<= 1) {
-      FPBits denormal(T(0.0));
+      FPBits denormal(zero);
       denormal.set_mantissa(mant);
-      T x = denormal.get_val();
+      InType x = denormal.get_val();
       EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
     }
 
     constexpr StorageType COUNT = 200'001;
     constexpr StorageType STEP = HIDDEN_BIT / COUNT;
     for (StorageType i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
-      T x = LIBC_NAMESPACE::cpp::bit_cast<T>(v);
+      InType x = FPBits(i).get_val();
       EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
     }
   }
@@ -59,17 +44,21 @@ public:
     constexpr StorageType COUNT = 200'001;
     constexpr StorageType STEP = STORAGE_MAX / COUNT;
     for (StorageType i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
-      T x = LIBC_NAMESPACE::cpp::bit_cast<T>(v);
-      if (isnan(x) || (x < 0)) {
+      FPBits x_bits(v);
+      InType x = x_bits.get_val();
+      if (x_bits.is_nan() || (x < 0))
         continue;
-      }
       EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
     }
   }
 };
 
 #define LIST_SQRT_TESTS(T, func)                                               \
-  using LlvmLibcSqrtTest = SqrtTest<T>;                                        \
-  TEST_F(LlvmLibcSqrtTest, SpecialNumbers) { test_special_numbers(&func); }    \
+  using LlvmLibcSqrtTest = SqrtTest<T, T>;                                     \
+  TEST_F(LlvmLibcSqrtTest, DenormalValues) { test_denormal_values(&func); }    \
+  TEST_F(LlvmLibcSqrtTest, NormalRange) { test_normal_range(&func); }
+
+#define LIST_NARROWING_SQRT_TESTS(OutType, InType, func)                       \
+  using LlvmLibcSqrtTest = SqrtTest<OutType, InType>;                          \
   TEST_F(LlvmLibcSqrtTest, DenormalValues) { test_denormal_values(&func); }    \
   TEST_F(LlvmLibcSqrtTest, NormalRange) { test_normal_range(&func); }
diff --git a/libc/test/src/math/f16sqrt_test.cpp b/libc/test/src/math/f16sqrt_test.cpp
new file mode 100644
index 0000000..759b388
--- /dev/null
+++ b/libc/test/src/math/f16sqrt_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for f16sqrt ---------------------------------------------===//
+//
+// 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 "SqrtTest.h"
+
+#include "src/math/f16sqrt.h"
+
+LIST_NARROWING_SQRT_TESTS(float16, double, LIBC_NAMESPACE::f16sqrt)
diff --git a/libc/test/src/math/f16sqrtl_test.cpp b/libc/test/src/math/f16sqrtl_test.cpp
new file mode 100644
index 0000000..4e069bc
--- /dev/null
+++ b/libc/test/src/math/f16sqrtl_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for f16sqrtl --------------------------------------------===//
+//
+// 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 "SqrtTest.h"
+
+#include "src/math/f16sqrtl.h"
+
+LIST_NARROWING_SQRT_TESTS(float16, long double, LIBC_NAMESPACE::f16sqrtl)
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index e3d8a14..a1b4a03 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -3735,6 +3735,18 @@ add_fp_unittest(
 )
 
 add_fp_unittest(
+  f16sqrt_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    f16sqrt_test.cpp
+  HDRS
+    SqrtTest.h
+  DEPENDS
+    libc.src.math.f16sqrt
+)
+
+add_fp_unittest(
   f16sqrtf_test
   SUITE
     libc-math-smoke-tests
@@ -3747,6 +3759,30 @@ add_fp_unittest(
 )
 
 add_fp_unittest(
+  f16sqrtl_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    f16sqrtl_test.cpp
+  HDRS
+    SqrtTest.h
+  DEPENDS
+    libc.src.math.f16sqrtl
+)
+
+add_fp_unittest(
+  f16sqrtf128_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    f16sqrtf128_test.cpp
+  HDRS
+    SqrtTest.h
+  DEPENDS
+    libc.src.math.f16sqrtf128
+)
+
+add_fp_unittest(
   sin_test
   SUITE
     libc-math-smoke-tests
diff --git a/libc/test/src/math/smoke/f16sqrt_test.cpp b/libc/test/src/math/smoke/f16sqrt_test.cpp
new file mode 100644
index 0000000..759b388
--- /dev/null
+++ b/libc/test/src/math/smoke/f16sqrt_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for f16sqrt ---------------------------------------------===//
+//
+// 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 "SqrtTest.h"
+
+#include "src/math/f16sqrt.h"
+
+LIST_NARROWING_SQRT_TESTS(float16, double, LIBC_NAMESPACE::f16sqrt)
diff --git a/libc/test/src/math/smoke/f16sqrtf128_test.cpp b/libc/test/src/math/smoke/f16sqrtf128_test.cpp
new file mode 100644
index 0000000..31c99486
--- /dev/null
+++ b/libc/test/src/math/smoke/f16sqrtf128_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for f16sqrtf128 -----------------------------------------===//
+//
+// 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 "SqrtTest.h"
+
+#include "src/math/f16sqrtf128.h"
+
+LIST_NARROWING_SQRT_TESTS(float16, float128, LIBC_NAMESPACE::f16sqrtf128)
diff --git a/libc/test/src/math/smoke/f16sqrtl_test.cpp b/libc/test/src/math/smoke/f16sqrtl_test.cpp
new file mode 100644
index 0000000..4e069bc
--- /dev/null
+++ b/libc/test/src/math/smoke/f16sqrtl_test.cpp
@@ -0,0 +1,13 @@
+//===-- Unittests for f16sqrtl --------------------------------------------===//
+//
+// 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 "SqrtTest.h"
+
+#include "src/math/f16sqrtl.h"
+
+LIST_NARROWING_SQRT_TESTS(float16, long double, LIBC_NAMESPACE::f16sqrtl)
diff --git a/libc/utils/MPFRWrapper/MPFRUtils.cpp b/libc/utils/MPFRWrapper/MPFRUtils.cpp
index 0bfe499..9a0e498 100644
--- a/libc/utils/MPFRWrapper/MPFRUtils.cpp
+++ b/libc/utils/MPFRWrapper/MPFRUtils.cpp
@@ -810,6 +810,12 @@ template void explain_unary_operation_single_output_error(Operation op, float16,
 template void explain_unary_operation_single_output_error(Operation op, float,
                                                           float16, double,
                                                           RoundingMode);
+template void explain_unary_operation_single_output_error(Operation op, double,
+                                                          float16, double,
+                                                          RoundingMode);
+template void explain_unary_operation_single_output_error(Operation op,
+                                                          long double, float16,
+                                                          double, RoundingMode);
 #endif
 
 template <typename T>
@@ -1015,6 +1021,11 @@ template bool compare_unary_operation_single_output(Operation, float16, float16,
                                                     double, RoundingMode);
 template bool compare_unary_operation_single_output(Operation, float, float16,
                                                     double, RoundingMode);
+template bool compare_unary_operation_single_output(Operation, double, float16,
+                                                    double, RoundingMode);
+template bool compare_unary_operation_single_output(Operation, long double,
+                                                    float16, double,
+                                                    RoundingMode);
 #endif
 
 template <typename T>