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

libc/config/linux/x86_64/entrypoints.txt

@@ -740,6 +740,7 @@ 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

@@ -333,7 +333,7 @@ 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                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/include/math.yaml

@@ -2237,6 +2237,13 @@ 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/src/math/CMakeLists.txt

@@ -467,6 +467,8 @@ add_math_entrypoint_object(roundevenl)
 add_math_entrypoint_object(roundevenf16)
 add_math_entrypoint_object(roundevenf128)
 
+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

@@ -955,6 +955,25 @@ add_entrypoint_object(
     libc.src.__support.FPUtil.nearest_integer_operations
 )
 
+add_entrypoint_object(
+  rsqrtf16
+  SRCS
+  rsqrtf16.cpp
+  HDRS
+    ../rsqrtf16.h
+  DEPENDS
+    libc.hdr.errno_macros
+    libc.hdr.fenv_macros
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.fma
+    libc.src.__support.FPUtil.manipulation_functions
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.macros.optimization
+    libc.src.__support.macros.properties.types  
+)
+
 add_entrypoint_object(
   lround
   SRCS

libc/src/math/generic/rsqrtf16.cpp

@@ -0,0 +1,120 @@
+//===-- 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 "hdr/errno_macros.h"
+#include "hdr/fenv_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FMA.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(float16, rsqrtf16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+  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 fputil::cast<float16>(0.0f);
+  }
+
+  // x is valid, estimate the result
+  // Range reduction:
+  // x can be expressed as m*2^e, where e - int exponent and m - mantissa
+  // rsqrtf16(x) = rsqrtf16(m*2^e)
+  // rsqrtf16(m*2^e) = 1/sqrt(m) * 1/sqrt(2^e) = 1/sqrt(m) * 1/2^(e/2)
+  // 1/sqrt(m) * 1/2^(e/2) = 1/sqrt(m) * 2^(-e/2)
+
+  float xf = x;
+  int exponent;
+  float mantissa = fputil::frexp(xf, exponent);
+
+  float result;
+  int exp_floored = -(exponent >> 1);
+
+  if (mantissa == 0.5f) {
+    // When mantissa is 0.5f, x was a power of 2 (or subnormal that normalizes this way).
+    // 1/sqrt(0.5f) = sqrt(2.0f) = 0x1.6a09e6p0f
+    // If exponent is odd (exponent = 2k + 1):
+    //   rsqrt(x) = (1/sqrt(0.5)) * 2^(-(2k+1)/2) = sqrt(2) * 2^(-k-0.5)
+    //            = sqrt(2) * 2^(-k) * (1/sqrt(2)) = 2^(-k)
+    //   exp_floored = -((2k+1)>>1) = -(k) = -k
+    //   So result = ldexp(1.0f, exp_floored)
+    // If exponent is even (exponent = 2k):
+    //   rsqrt(x) = (1/sqrt(0.5)) * 2^(-2k/2) = sqrt(2) * 2^(-k)
+    //   exp_floored = -((2k)>>1) = -(k) = -k
+    //   So result = ldexp(sqrt(2.0f), exp_floored)
+    if (exponent & 1) {
+      result = fputil::ldexp(1.0f, exp_floored);
+    } else {
+      constexpr float SQRT_2_F = 0x1.6a09e6p0f; // sqrt(2.0f)
+      result = fputil::ldexp(SQRT_2_F, exp_floored);
+    }
+  } else {
+    // 6-degree polynomial generated using Sollya
+    // P = fpminimax(1/sqrt(x), [|0,1,2,3,4,5|], [|SG...|], [0.5, 1]);
+    float interm = fputil::polyeval(
+        mantissa, 0x1.9c81c4p1f, -0x1.e2c57cp2f, 0x1.91e8bp3f,
+        -0x1.899954p3f, 0x1.9edcp2f, -0x1.6bd93cp0f);
+
+    // Apply one Newton-Raphson iteration to refine the approximation of
+    // 1/sqrt(mantissa) y_new = y_old * (1.5 - 0.5 * mantissa * y_old^2) Using
+    // fputil::fma for potential precision benefits in the factor calculation  
+    float interm_sq = interm * interm;
+    float factor = fputil::fma<float>(-0.5f * mantissa, interm_sq, 1.5f);
+    float interm_refined = interm * factor;
+
+    // Apply a second Newton-Raphson iteration
+    // y_new = y_old * (1.5 - 0.5 * mantissa * y_old^2)
+    float interm_refined_sq = interm_refined * interm_refined;
+    float factor2 =
+        fputil::fma<float>(-0.5f * mantissa, interm_refined_sq, 1.5f);
+    float interm_refined2 = interm_refined * factor2;
+
+    result = fputil::ldexp(interm_refined2, exp_floored);
+    if (exponent & 1) {
+      const float ONE_OVER_SQRT2 = 0x1.6a09e6p-1f;
+      result = fputil::fma<float>(result, ONE_OVER_SQRT2, 0.0f);
+    }
+  }
+
+  return fputil::cast<float16>(result);
+}
+} // 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/src/math/CMakeLists.txt

@@ -1560,6 +1560,17 @@ 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

@@ -2958,6 +2958,17 @@ add_fp_unittest(
     libc.src.math.sqrtl
 )
 
+add_fp_unittest(
+  rsqrtf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    rsqrtf16_test.cpp
+  DEPENDS
+    libc.src.errno.errno
+    libc.src.math.rsqrtf16
+)
+
 add_fp_unittest(
   sqrtf16_test
   SUITE

libc/test/src/math/smoke/rsqrtf16_test.cpp

@@ -0,0 +1,37 @@
+//===-- Unittests 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/errno/libc_errno.h"
+#include "src/math/rsqrtf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcRsqrtf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+TEST_F(LlvmLibcRsqrtf16Test, SpecialNumbers) {
+  LIBC_NAMESPACE::libc_errno = 0;
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::rsqrtf16(aNaN));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::rsqrtf16(sNaN), FE_INVALID);
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(inf, LIBC_NAMESPACE::rsqrtf16(0.0f));
+  EXPECT_MATH_ERRNO(ERANGE);
+
+  EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::rsqrtf16(1.0f));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(0.0f, LIBC_NAMESPACE::rsqrtf16(inf));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::rsqrtf16(neg_inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::rsqrtf16(-2.0f));
+  EXPECT_MATH_ERRNO(EDOM);
+}

libc/utils/MPFRWrapper/MPCommon.cpp

@@ -366,6 +366,12 @@ MPFRNumber MPFRNumber::rint(mpfr_rnd_t rnd) const {
   return result;
 }
 
+MPFRNumber MPFRNumber::rsqrt() const {
+  MPFRNumber result(*this);
+  mpfr_rec_sqrt(result.value, value, mpfr_rounding);
+  return result;
+}
+
 MPFRNumber MPFRNumber::mod_2pi() const {
   MPFRNumber result(0.0, 1280);
   MPFRNumber _2pi(0.0, 1280);

libc/utils/MPFRWrapper/MPCommon.h

@@ -216,6 +216,7 @@ class MPFRNumber {
   bool round_to_long(long &result) const;
   bool round_to_long(mpfr_rnd_t rnd, long &result) const;
   MPFRNumber rint(mpfr_rnd_t rnd) const;
+  MPFRNumber rsqrt() const;
   MPFRNumber mod_2pi() const;
   MPFRNumber mod_pi_over_2() const;
   MPFRNumber mod_pi_over_4() const;

libc/utils/MPFRWrapper/MPFRUtils.cpp

@@ -86,6 +86,8 @@ unary_operation(Operation op, InputType input, unsigned int precision,
     return mpfrInput.round();
   case Operation::RoundEven:
     return mpfrInput.roundeven();
+  case Operation::Rsqrt:
+    return mpfrInput.rsqrt();
   case Operation::Sin:
     return mpfrInput.sin();
   case Operation::Sinpi:

libc/utils/MPFRWrapper/MPFRUtils.h

@@ -55,6 +55,7 @@ enum class Operation : int {
   ModPIOver4,
   Round,
   RoundEven,
+  Rsqrt,
   Sin,
   Sinpi,
   Sinh,