[libc][math][c23] Add asinf16() function

libc/config/linux/x86_64/entrypoints.txt

@@ -642,6 +642,7 @@ endif()
 if(LIBC_TYPES_HAS_FLOAT16)
   list(APPEND TARGET_LIBM_ENTRYPOINTS
     # math.h C23 _Float16 entrypoints
+    libc.src.math.asinf16
     libc.src.math.canonicalizef16
     libc.src.math.ceilf16
     libc.src.math.copysignf16

libc/docs/headers/math/index.rst

@@ -256,7 +256,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | acospi    |                  |                 |                        |                      |                        | 7.12.4.8               | F.10.1.8                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| asin      | |check|          |                 |                        |                      |                        | 7.12.4.2               | F.10.1.2                   |
+| asin      | |check|          |                 |                        | |check|              |                        | 7.12.4.2               | F.10.1.2                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | asinh     | |check|          |                 |                        |                      |                        | 7.12.5.2               | F.10.2.2                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/include/math.yaml

@@ -32,6 +32,13 @@ functions:
     return_type: float
     arguments:
       - type: float
+  - name: asinf16
+    standards:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
+    guard: LIBC_TYPES_HAS_FLOAT16
   - name: asinhf
     standards:
       - stdc

libc/src/math/CMakeLists.txt

@@ -49,6 +49,7 @@ add_math_entrypoint_object(asin)
 add_math_entrypoint_object(asinf)
 add_math_entrypoint_object(asinh)
 add_math_entrypoint_object(asinhf)
+add_math_entrypoint_object(asinf16)
 
 add_math_entrypoint_object(atan)
 add_math_entrypoint_object(atanf)

libc/src/math/asinf16.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for asinf16 -----------------------*- 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_ASINF16_H
+#define LLVM_LIBC_SRC_MATH_ASINF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 asinf16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ASINF16_H

libc/src/math/generic/CMakeLists.txt

@@ -4598,6 +4598,25 @@ add_entrypoint_object(
     ${libc_opt_high_flag}
 )
 
+add_entrypoint_object(
+  asinf16
+  SRCS
+    asinf16.cpp
+  HDRS
+    ../asinf16.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.multiply_add
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.sqrt
+    libc.src.__support.macros.optimization
+    libc.src.__support.macros.properties.types  
+)
+
 add_entrypoint_object(
   acosf
   SRCS

libc/src/math/generic/asinf16.cpp

@@ -0,0 +1,122 @@
+//===-- Half-precision asinf16(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/asinf16.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/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Generated by Sollya using the following command:
+// > round(pi/2, D, RN);
+static constexpr float PI_2 = 0x1.921fb54442d18p0f;
+
+LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+  float xf = x;
+
+  float xsq = xf * xf;
+
+  // |x| <= 0x1p-1, |x| <= 0.5
+  if (x_abs <= 0x3800) {
+    // asinf16(+/-0) = +/-0
+    if (LIBC_UNLIKELY(x_abs == 0))
+      return x;
+
+    // Exhaustive tests show that,
+    // for |x| <= 0x1.878p-9, when:
+    // x > 0, and rounding upward, or
+    // x < 0, and rounding downward, then,
+    // asin(x) = x * 2^-11 + x
+    // else, in other rounding modes,
+    // asin(x) = x
+    if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) {
+      int rounding = fputil::quick_get_round();
+
+      if ((xbits.is_pos() && rounding == FE_UPWARD) ||
+          (xbits.is_neg() && rounding == FE_DOWNWARD))
+        return fputil::cast<float16>(fputil::multiply_add(xf, 0x1.0p-11f, xf));
+      return x;
+    }
+
+    // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
+    // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+    float result =
+        fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
+                         0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+    return fputil::cast<float16>(xf * result);
+  }
+
+  // |x| > 1, asinf16(x) = NaN
+  if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
+    fputil::set_errno_if_required(EDOM);
+    fputil::raise_except_if_required(FE_INVALID);
+
+    return FPBits::quiet_nan().get_val();
+  }
+
+  // When |x| > 0.5, assume that 0.5 < |x| <= 1,
+  //
+  // Step-by-step range-reduction proof:
+  // 1:  Let y = asin(x), such that, x = sin(y)
+  // 2:  From complimentary angle identity:
+  //       x = sin(y) = cos(pi/2 - y)
+  // 3:  Let z = pi/2 - y, such that x = cos(z)
+  // 4:  From double angle formula; cos(2A) = 1 - sin^2(A):
+  //       z = 2A, z/2 = A
+  //       cos(z) = 1 - 2 * sin^2(z/2)
+  // 5:  Make sin(z/2) subject of the formula:
+  //       sin(z/2) = sqrt((1 - cos(z))/2)
+  // 6:  Recall [3]; x = cos(z). Therefore:
+  //       sin(z/2) = sqrt((1 - x)/2)
+  // 7:  Let u = (1 - x)/2
+  // 8:  Therefore:
+  //       asin(sqrt(u)) = z/2
+  //       2 * asin(sqrt(u)) = z
+  // 9:  Recall [3], z = pi/2 - y. Therefore:
+  //       y = pi/2 - z
+  //       y = pi/2 - 2 * arcsin(sqrt(u))
+  // 10: Recall [1], y = asin(x). Therefore:
+  //       asin(x) = pi/2 - 2 * asin(sqrt(u))
+  //
+  // WHY?
+  // 11: Recall [7], u = (1 - x)/2
+  // 12: Since 0.5 < x <= 1, therefore:
+  //       0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
+  //
+  // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
+  // Step [10] as `sqrt(u)` is in range.
+
+  // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0
+  float xf_abs = (xf < 0 ? -xf : xf);
+  float sign = (xbits.uintval() >> 15 == 1 ? -1.0 : 1.0);
+  float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
+  float u_sqrt = fputil::sqrt<float>(u);
+
+  // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
+  // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+  float asin_sqrt_u =
+      u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
+                                0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+
+  return fputil::cast<float16>(sign *
+                               fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2));
+}
+
+} // namespace LIBC_NAMESPACE_DECL

libc/test/src/math/CMakeLists.txt

@@ -2186,6 +2186,17 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+add_fp_unittest(
+  asinf16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    asinf16_test.cpp
+  DEPENDS
+    libc.src.math.asinf16  
+)
+
 add_fp_unittest(
   acosf_test
   NEED_MPFR

libc/test/src/math/asinf16_test.cpp

@@ -0,0 +1,42 @@
+//===-- Exhaustive test for asinf16 ---------------------------------------===//
+//
+// 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/asinf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcAsinf16Test = 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(LlvmLibcAsinf16Test, PositiveRange) {
+  for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x,
+                                   LIBC_NAMESPACE::asinf16(x), 0.5);
+  }
+}
+
+TEST_F(LlvmLibcAsinf16Test, NegativeRange) {
+  for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x,
+                                   LIBC_NAMESPACE::asinf16(x), 0.5);
+  }
+}

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

@@ -3954,6 +3954,17 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+add_fp_unittest(
+  asinf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    asinf16_test.cpp
+  DEPENDS
+    libc.src.errno.errno
+    libc.src.math.asinf16  
+)
+
 add_fp_unittest(
   acosf_test
   SUITE

libc/test/src/math/smoke/asinf16_test.cpp

@@ -0,0 +1,37 @@
+//===-- Unittests for asinf16 ---------------------------------------------===//
+//
+//
+// 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/asinf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcAsinf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+TEST_F(LlvmLibcAsinf16Test, SpecialNumbers) {
+  LIBC_NAMESPACE::libc_errno = 0;
+
+  EXPECT_FP_EQ(zero, LIBC_NAMESPACE::asinf16(zero));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::asinf16(neg_zero));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(neg_inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(2.0f));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(-2.0f));
+  EXPECT_MATH_ERRNO(EDOM);
+}