[libc][math][c23] Implement C23 math function asinpif16

libc/config/linux/aarch64/entrypoints.txt

@@ -656,6 +656,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
   list(APPEND TARGET_LIBM_ENTRYPOINTS
     # math.h C23 _Float16 entrypoints
     # libc.src.math.acoshf16
+    libc.src.math.asinpif16
     libc.src.math.canonicalizef16
     libc.src.math.ceilf16
     libc.src.math.copysignf16

libc/config/linux/x86_64/entrypoints.txt

@@ -690,6 +690,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.acospif16
     libc.src.math.asinf16
     libc.src.math.asinhf16
+    libc.src.math.asinpif16
     libc.src.math.atanf16
     libc.src.math.atanhf16
     libc.src.math.canonicalizef16

libc/docs/headers/math/index.rst

@@ -259,7 +259,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | asinh     | |check|          |                 |                        | |check|              |                        | 7.12.5.2               | F.10.2.2                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| asinpi    |                  |                 |                        |                      |                        | 7.12.4.9               | F.10.1.9                   |
+| asinpi    |                  |                 |                        | |check|              |                        | 7.12.4.9               | F.10.1.9                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | atan      | |check|          | 1 ULP           |                        | |check|              |                        | 7.12.4.3               | F.10.1.3                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/include/math.yaml

@@ -85,6 +85,13 @@ functions:
     return_type: double
     arguments:
       - type: double
+  - name: asinpif16
+    standards:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
+    guard: LIBC_TYPES_HAS_FLOAT16
   - name: atan2
     standards:
       - stdc

libc/src/math/CMakeLists.txt

@@ -58,6 +58,8 @@ add_math_entrypoint_object(asinh)
 add_math_entrypoint_object(asinhf)
 add_math_entrypoint_object(asinhf16)
 
+add_math_entrypoint_object(asinpif16)
+
 add_math_entrypoint_object(atan)
 add_math_entrypoint_object(atanf)
 add_math_entrypoint_object(atanf16)

libc/src/math/asinpif16.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for asinpif16 ---------------------*- 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_ASINPIF16_H
+#define LLVM_LIBC_SRC_MATH_ASINPIF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 asinpif16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ASINPIF16_H

libc/src/math/generic/CMakeLists.txt

@@ -4001,6 +4001,25 @@ add_entrypoint_object(
     libc.src.__support.macros.properties.types
 )
 
+add_entrypoint_object(
+  asinpif16
+  SRCS
+    asinpif16.cpp
+  HDRS
+    ../asinpif16.h
+  DEPENDS
+    libc.hdr.errno_macros
+    libc.hdr.fenv_macros
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.except_value_utils
+    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.sqrt
+    libc.src.__support.macros.optimization
+)
+
 add_entrypoint_object(
   atanhf
   SRCS

libc/src/math/generic/asinpif16.cpp

@@ -0,0 +1,151 @@
+//===-- Half-precision asinpif16(x) 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/asinpif16.h"
+#include "hdr/errno_macros.h"
+#include "hdr/fenv_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_ASINPIF16_EXCEPTS = 3;
+
+static constexpr fputil::ExceptValues<float16, N_ASINPIF16_EXCEPTS>
+    ASINPIF16_EXCEPTS{{
+        // (input_hex, RZ_output_hex, RU_offset, RD_offset, RN_offset)
+        // x = 0.0, asinfpi(0.0) = 0.0
+        {0x0000, 0x0000, 0, 0, 0},
+
+        // x = 0x1.004p-3, asinpif16(x) = 0x1.47p-5 (RZ)
+        {0x3001U, 0x291cU, 1U, 0U, 1U},
+        // x = 0x1.0bp-1, asinpif16(x) = 0x1.658p-3 (RZ)
+        {0x382cU, 0x3196U, 1U, 0U, 0U},
+    }};
+
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+LLVM_LIBC_FUNCTION(float16, asinpif16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+
+  FPBits xbits(x);
+  uint16_t x_uint = xbits.uintval();
+  bool is_neg = static_cast<bool>(x_uint >> 15);
+  float16 x_abs = is_neg ? -x : x;
+
+  auto signed_result = [is_neg](auto r) -> auto { return is_neg ? -r : r; };
+
+  if (LIBC_UNLIKELY(x_abs > 1.0f16)) {
+    // aspinf16(NaN) = NaN
+    if (xbits.is_nan()) {
+      if (xbits.is_signaling_nan()) {
+        fputil::raise_except_if_required(FE_INVALID);
+        return FPBits::quiet_nan().get_val();
+      }
+      return x;
+    }
+
+    // 1 < |x| <= +/-inf
+    fputil::raise_except_if_required(FE_INVALID);
+    fputil::set_errno_if_required(EDOM);
+
+    return FPBits::quiet_nan().get_val();
+  }
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+  // exceptional values
+  if (auto r = ASINPIF16_EXCEPTS.lookup(x_uint); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+  // the coefficients for the polynomial approximation of asin(x)/pi in the
+  // range [0, 0.5] extracted using python-sympy
+  //
+  // Python code to generate the coefficients:
+  //  > from sympy import *
+  //  > import math
+  //  > x = symbols('x')
+  //  > print(series(asin(x)/math.pi, x, 0, 21))
+  //
+  // OUTPUT:
+  //
+  // 0.318309886183791*x + 0.0530516476972984*x**3 + 0.0238732414637843*x**5 +
+  // 0.0142102627760621*x**7 + 0.00967087327815336*x**9 +
+  // 0.00712127941391293*x**11 + 0.00552355646848375*x**13 +
+  // 0.00444514782463692*x**15 + 0.00367705242846804*x**17 +
+  // 0.00310721681820837*x**19 + O(x**21)
+  //
+  // it's very accurate in the range [0, 0.5] and has a maximum error of
+  // 0.0000000000000001 in the range [0, 0.5].
+  static constexpr double POLY_COEFFS[10] = {
+      0x1.45f306dc9c889p-2, // x^1
+      0x1.b2995e7b7b5fdp-5, // x^3
+      0x1.8723a1d588a36p-6, // x^5
+      0x1.d1a452f20430dp-7, // x^7
+      0x1.3ce52a3a09f61p-7, // x^9
+      0x1.d2b33e303d375p-8, // x^11
+      0x1.69fde663c674fp-8, // x^13
+      0x1.235134885f19bp-8, // x^15
+  };
+  // polynomial evaluation using horner's method
+  // work only for |x| in [0, 0.5]
+  auto asinpi_polyeval = [](double x) -> double {
+    return x * fputil::polyeval(x * x, POLY_COEFFS[0], POLY_COEFFS[1],
+                                POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4],
+                                POLY_COEFFS[5], POLY_COEFFS[6], POLY_COEFFS[7]);
+  };
+
+  // if |x| <= 0.5:
+  if (LIBC_UNLIKELY(x_abs <= 0.5f16)) {
+    // Use polynomial approximation of asin(x)/pi in the range [0, 0.5]
+    double result = asinpi_polyeval(fputil::cast<double>(x_abs));
+    return fputil::cast<float16>(signed_result(result));
+  }
+
+  // If |x| > 0.5, we need to use the range reduction method:
+  //    y = asin(x) => x = sin(y)
+  //      because: sin(a) = cos(pi/2 - a)
+  //      therefore:
+  //    x = cos(pi/2 - y)
+  //      let z = pi/2 - y,
+  //    x = cos(z)
+  //      becuase: cos(2a) = 1 - 2 * sin^2(a), z = 2a, a = z/2
+  //      therefore:
+  //    cos(z) = 1 - 2 * sin^2(z/2)
+  //    sin(z/2) = sqrt((1 - cos(z))/2)
+  //    sin(z/2) = sqrt((1 - x)/2)
+  //      let u = (1 - x)/2
+  //      then:
+  //    sin(z/2) = sqrt(u)
+  //    z/2 = asin(sqrt(u))
+  //    z = 2 * asin(sqrt(u))
+  //    pi/2 - y = 2 * asin(sqrt(u))
+  //    y = pi/2 - 2 * asin(sqrt(u))
+  //    y/pi = 1/2 - 2 * asin(sqrt(u))/pi
+  //
+  // Finally, we can write:
+  //   asinpi(x) = 1/2 - 2 * asinpi(sqrt(u))
+  //     where u = (1 - x) /2
+  //             = 0.5 - 0.5 * x
+  //             = multiply_add(-0.5, x, 0.5)
+
+  double u = fputil::multiply_add(-0.5, fputil::cast<double>(x_abs), 0.5);
+  double asinpi_sqrt_u = asinpi_polyeval(fputil::sqrt<double>(u));
+  double result = fputil::multiply_add(-2.0, asinpi_sqrt_u, 0.5);
+
+  return fputil::cast<float16>(signed_result(result));
+}
+
+} // namespace LIBC_NAMESPACE_DECL

libc/test/src/math/CMakeLists.txt

@@ -2267,6 +2267,17 @@ add_fp_unittest(
     libc.src.math.asinf16  
 )
 
+add_fp_unittest(
+  asinpif16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    asinpif16_test.cpp
+  DEPENDS
+    libc.src.math.asinpif16
+)
+
 add_fp_unittest(
   acosf_test
   NEED_MPFR

libc/test/src/math/asinpif16_test.cpp

@@ -0,0 +1,40 @@
+//===-- Exhaustive test for asinpif16 -------------------------------------===//
+//
+// 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/asinpif16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcAsinpif16Test = 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(LlvmLibcAsinpif16Test, PositiveRange) {
+  for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asinpi, x,
+                                   LIBC_NAMESPACE::asinpif16(x), 0.5f);
+  }
+}
+
+TEST_F(LlvmLibcAsinpif16Test, NegativeRange) {
+  for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asinpi, x,
+                                   LIBC_NAMESPACE::asinpif16(x), 0.5);
+  }
+}

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

@@ -3982,6 +3982,20 @@ add_fp_unittest(
     libc.src.math.asinhf16
 )
 
+add_fp_unittest(
+  asinpif16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    asinpif16_test.cpp
+  DEPENDS
+  libc.src.math.asinpif16  
+    libc.src.errno.errno
+    libc.src.math.fabs
+    libc.src.__support.FPUtil.fp_bits
+)
+
 add_fp_unittest(
   acoshf_test
   SUITE