[libc][math][c23] Add rsqrtf16() function

libc/config/linux/aarch64/entrypoints.txt

@@ -735,6 +735,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.rintf16
     libc.src.math.roundevenf16
     libc.src.math.roundf16
+    libc.src.math.rsqrtf16
     libc.src.math.scalblnf16
     libc.src.math.scalbnf16
     libc.src.math.setpayloadf16

libc/config/linux/riscv/entrypoints.txt

@@ -749,6 +749,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.rintf16
     libc.src.math.roundevenf16
     libc.src.math.roundf16
+    libc.src.math.rsqrtf16
     libc.src.math.scalblnf16
     libc.src.math.scalbnf16
     libc.src.math.setpayloadf16

libc/config/linux/x86_64/entrypoints.txt

@@ -784,6 +784,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.rintf16
     libc.src.math.roundevenf16
     libc.src.math.roundf16
+    libc.src.math.rsqrtf16
     libc.src.math.scalblnf16
     libc.src.math.scalbnf16
     libc.src.math.setpayloadf16

libc/docs/headers/math/index.rst

@@ -255,6 +255,7 @@ Basic Operations
 Higher Math Functions
 =====================
 
+
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+----------++------------+------------------------+----------------------------+
 | <Func>    | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | <Func_bf16> (bfloat16) | C23 Definition Section | C23 Error Handling Section |
 +===========+==================+=================+========================+======================+========================+========================+========================+============================+
@@ -342,7 +343,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
 | rootn     |                  |                 |                        |                      |                        |                        | 7.12.7.8               | F.10.4.8                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
-| rsqrt     |                  |                 |                        |                      |                        |                        | 7.12.7.9               | F.10.4.9                   |
+| rsqrt     |                  |                 |                        | |check|              |                        |                        | 7.12.7.9               | F.10.4.9                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
 | sin       | |check|          | |check|         |                        | |check|              |                        |                        | 7.12.4.6               | F.10.1.6                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
@@ -363,6 +364,7 @@ Higher Math Functions
 | tgamma    |                  |                 |                        |                      |                        |                        | 7.12.8.4               | F.10.5.4                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
 
+
 Legends:
 
 * |check| : correctly rounded for all 4 rounding modes.

libc/include/math.yaml

@@ -2349,6 +2349,13 @@ functions:
     return_type: long double
     arguments:
       - type: long double
+  - name: rsqrtf16
+    standards:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
+    guard: LIBC_TYPES_HAS_FLOAT16
   - name: scalbln
     standards:
       - stdc

libc/shared/math.h

@@ -53,4 +53,6 @@
 #include "math/ldexpf128.h"
 #include "math/ldexpf16.h"
 
+#include "math/rsqrtf16.h"
+
 #endif // LLVM_LIBC_SHARED_MATH_H

libc/shared/math/rsqrtf16.h

@@ -0,0 +1,29 @@
+//===-- Shared rsqrtf16 function -------------------------------*- 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_SHARED_MATH_RSQRTF16_H
+#define LLVM_LIBC_SHARED_MATH_RSQRTF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "shared/libc_common.h"
+#include "src/__support/math/rsqrtf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::rsqrtf16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_RSQRTF16_H

libc/src/__support/math/CMakeLists.txt

@@ -109,6 +109,22 @@ add_header_library(
     libc.src.__support.macros.properties.types
 )
 
+
+add_header_library(
+  rsqrtf16
+  HDRS
+    rsqrtf16.h
+  DEPENDS
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.manipulation_functions
+    libc.src.__support.macros.optimization
+    libc.src.__support.macros.properties.types
+)
+
 add_header_library(
   asin_utils
   HDRS

libc/src/__support/math/rsqrtf16.h

@@ -0,0 +1,83 @@
+//===-- Implementation header for rsqrtf16 ----------------------*- 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___SUPPORT_MATH_RSQRTF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_RSQRTF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace math {
+
+LIBC_INLINE static constexpr float16 rsqrtf16(float16 x) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+
+  const uint16_t x_u = xbits.uintval();
+  const uint16_t x_abs = x_u & 0x7fff;
+  const uint16_t x_sign = x_u >> 15;
+
+  // x is NaN
+  if (LIBC_UNLIKELY(xbits.is_nan())) {
+    if (xbits.is_signaling_nan()) {
+      fputil::raise_except_if_required(FE_INVALID);
+      return FPBits::quiet_nan().get_val();
+    }
+    return x;
+  }
+
+  // |x| = 0
+  if (LIBC_UNLIKELY(x_abs == 0x0)) {
+    fputil::raise_except_if_required(FE_DIVBYZERO);
+    fputil::set_errno_if_required(ERANGE);
+    return FPBits::inf(Sign::POS).get_val();
+  }
+
+  // -inf <= x < 0
+  if (LIBC_UNLIKELY(x_sign == 1)) {
+    fputil::raise_except_if_required(FE_INVALID);
+    fputil::set_errno_if_required(EDOM);
+    return FPBits::quiet_nan().get_val();
+  }
+
+  // x = +inf => rsqrt(x) = 0
+  if (LIBC_UNLIKELY(xbits.is_inf()))
+    return FPBits::zero().get_val();
+
+  // TODO: add integer based implementation when LIBC_TARGET_CPU_HAS_FPU_FLOAT
+  // is not defined
+  float result = 1.0f / fputil::sqrt<float>(fputil::cast<float>(x));
+
+  // Targeted post-corrections to ensure correct rounding in half for specific
+  // mantissa patterns
+  const uint16_t half_mantissa = x_abs & 0x3ff;
+  if (LIBC_UNLIKELY(half_mantissa == 0x011F)) {
+    result = fputil::multiply_add(result, 0x1.0p-21f, result);
+  } else if (LIBC_UNLIKELY(half_mantissa == 0x0313)) {
+    result = fputil::multiply_add(result, -0x1.0p-21f, result);
+  }
+
+  return fputil::cast<float16>(result);
+}
+
+} // namespace math
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_RSQRTF16_H

libc/src/math/CMakeLists.txt

@@ -516,6 +516,8 @@ add_math_entrypoint_object(roundevenf16)
 add_math_entrypoint_object(roundevenf128)
 add_math_entrypoint_object(roundevenbf16)
 
+add_math_entrypoint_object(rsqrtf16)
+
 add_math_entrypoint_object(scalbln)
 add_math_entrypoint_object(scalblnf)
 add_math_entrypoint_object(scalblnl)

libc/src/math/generic/CMakeLists.txt

@@ -973,7 +973,7 @@ add_entrypoint_object(
 )
 
 add_entrypoint_object(
-    roundevenbf16
+  roundevenbf16
   SRCS
     roundevenbf16.cpp
   HDRS
@@ -988,6 +988,17 @@ add_entrypoint_object(
     ROUND_OPT
 )
 
+add_entrypoint_object(
+  rsqrtf16
+  SRCS
+    rsqrtf16.cpp
+  HDRS
+    ../rsqrtf16.h
+  DEPENDS
+    libc.src.__support.math.rsqrtf16
+    libc.src.errno.errno
+)
+
 add_entrypoint_object(
   lround
   SRCS

libc/src/math/generic/rsqrtf16.cpp

@@ -0,0 +1,15 @@
+//===-- Half-precision rsqrt 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/rsqrtf16.h"
+#include "src/__support/math/rsqrtf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(float16, rsqrtf16, (float16 x)) { return math::rsqrtf16(x); }
+} // namespace LIBC_NAMESPACE_DECL

libc/src/math/rsqrtf16.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for rsqrtf16 ----------------------*- 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_RSQRTF16_H
+#define LLVM_LIBC_SRC_MATH_RSQRTF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 rsqrtf16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_RSQRTF16_H

libc/test/shared/CMakeLists.txt

@@ -48,4 +48,6 @@ add_fp_unittest(
     libc.src.__support.math.ldexpf
     libc.src.__support.math.ldexpf128
     libc.src.__support.math.ldexpf16
+    libc.src.__support.math.rsqrtf16
+
 )

libc/test/shared/shared_math_test.cpp

@@ -17,6 +17,8 @@ TEST(LlvmLibcSharedMathTest, AllFloat16) {
 
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::acoshf16(1.0f16));
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::acospif16(1.0f16));
+  EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::rsqrtf16(1.0f16));
+
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::asinf16(0.0f16));
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::asinhf16(0.0f16));
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::atanf16(0.0f16));

libc/test/src/math/CMakeLists.txt

@@ -1678,6 +1678,17 @@ add_fp_unittest(
     libc.src.math.sqrtl
 )
 
+add_fp_unittest(
+  rsqrtf16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    rsqrtf16_test.cpp
+  DEPENDS
+    libc.src.math.rsqrtf16
+)
+
 add_fp_unittest(
   sqrtf16_test
   NEED_MPFR

libc/test/src/math/rsqrtf16_test.cpp

@@ -0,0 +1,42 @@
+//===-- Exhaustive test for rsqrtf16 --------------------------------------===//
+//
+// 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/rsqrtf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcRsqrtf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+// Range: [0, Inf]
+static constexpr uint16_t POS_START = 0x0000U;
+static constexpr uint16_t POS_STOP = 0x7c00U;
+
+// Range: [-Inf, 0]
+static constexpr uint16_t NEG_START = 0x8000U;
+static constexpr uint16_t NEG_STOP = 0xfc00U;
+
+TEST_F(LlvmLibcRsqrtf16Test, PositiveRange) {
+  for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Rsqrt, x,
+                                   LIBC_NAMESPACE::rsqrtf16(x), 0.5);
+  }
+}
+
+TEST_F(LlvmLibcRsqrtf16Test, NegativeRange) {
+  for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Rsqrt, x,
+                                   LIBC_NAMESPACE::rsqrtf16(x), 0.5);
+  }
+}

libc/test/src/math/smoke/CMakeLists.txt

@@ -3502,6 +3502,17 @@ add_fp_unittest(
     libc.src.math.sqrtl
 )
 
+add_fp_unittest(
+  rsqrtf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    rsqrtf16_test.cpp
+  DEPENDS
+    libc.src.math.rsqrtf16
+    libc.hdr.errno_macros
+)
+
 add_fp_unittest(
   sqrtf16_test
   SUITE