[libc][math][c23] Add acosf16() function

libc/config/linux/x86_64/entrypoints.txt

@@ -648,6 +648,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
   list(APPEND TARGET_LIBM_ENTRYPOINTS
     # math.h C23 _Float16 entrypoints
     libc.src.math.asinf16
+    libc.src.math.acosf16
     libc.src.math.canonicalizef16
     libc.src.math.ceilf16
     libc.src.math.copysignf16

libc/docs/headers/math/index.rst

@@ -250,7 +250,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | <Func>    | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section |
 +===========+==================+=================+========================+======================+========================+========================+============================+
-| acos      | |check|          |                 |                        |                      |                        | 7.12.4.1               | F.10.1.1                   |
+| acos      | |check|          |                 |                        | |check|              |                        | 7.12.4.1               | F.10.1.1                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | acosh     | |check|          |                 |                        |                      |                        | 7.12.5.1               | F.10.2.1                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/include/math.yaml

@@ -14,6 +14,13 @@ functions:
     return_type: float
     arguments:
       - type: float
+  - name: acosf16
+    standards:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
+    guard: LIBC_TYPES_HAS_FLOAT16
   - name: acoshf
     standards:
       - stdc

libc/src/math/CMakeLists.txt

@@ -42,6 +42,8 @@ endfunction()
 
 add_math_entrypoint_object(acos)
 add_math_entrypoint_object(acosf)
+add_math_entrypoint_object(acosf16)
+
 add_math_entrypoint_object(acosh)
 add_math_entrypoint_object(acoshf)
 

libc/src/math/acosf16.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for acosf16 -----------------------*- 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_ACOSF16_H
+#define LLVM_LIBC_SRC_MATH_ACOSF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 acosf16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ACOSF16_H

libc/src/math/generic/CMakeLists.txt

@@ -4034,6 +4034,26 @@ add_entrypoint_object(
     .inv_trigf_utils
 )
 
+add_entrypoint_object(
+  acosf16
+  SRCS
+    acosf16.cpp
+  HDRS
+    ../acosf16.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
+    libc.src.__support.macros.properties.types  
+)
+
 add_entrypoint_object(
   atanf
   SRCS

libc/src/math/generic/acosf16.cpp

@@ -0,0 +1,147 @@
+//===-- Half-precision acosf16(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/acosf16.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 {
+
+// Generated by Sollya using the following command:
+// > round(pi/2, SG, RN);
+// > round(pi, SG, RN);
+static constexpr float PI_2 = 0x1.921fb6p0f;
+static constexpr float PI = 0x1.921fb6p1f;
+
+static constexpr size_t N_EXCEPTS = 2;
+
+static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    {0xacaf, 0x3e93, 1, 0, 0},
+    {0xb874, 0x4052, 1, 0, 1},
+}};
+
+LLVM_LIBC_FUNCTION(float16, acosf16, (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| > 0x1p0, |x| > 1, or x is NaN.
+  if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
+    // acosf16(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();
+  }
+
+  float xf = x;
+
+  // Handle exceptional values
+  if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+
+  // |x| == 0x1p0, x is 1 or -1
+  // if x is (-)1, return pi, else
+  // if x is (+)1, return 0
+  if (LIBC_UNLIKELY(x_abs == 0x3c00))
+    return fputil::cast<float16>(x_sign ? PI : 0.0f);
+
+  float xsq = xf * xf;
+
+  // |x| <= 0x1p-1, |x| <= 0.5
+  if (x_abs <= 0x3800) {
+    // if x is 0, return pi/2
+    if (LIBC_UNLIKELY(x_abs == 0))
+      return fputil::cast<float16>(PI_2);
+
+    // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
+    // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
+    // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+    float interm =
+        fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
+                         0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+    return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_2));
+  }
+
+  // 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 * asin(sqrt(u))
+  // 10: Recall [1], y = asin(x). Therefore:
+  //       asin(x) = pi/2 - 2 * asin(sqrt(u))
+  // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
+  //     Therefore:
+  //       acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u)))
+  //       acos(x) = 2 * asin(sqrt(u))
+  //
+  // THE RANGE REDUCTION, HOW?
+  // 12: Recall [7], u = (1 - x)/2
+  // 13: 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 [11] as `sqrt(u)` is in range.
+  // When -1 < x <= -0.5, the identity:
+  //       acos(x) = pi - acos(-x)
+  // allows us to compute for the negative x value (lhs)
+  // with a positive x value instead (rhs).
+
+  float xf_abs = (xf < 0 ? -xf : xf);
+  float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
+  float sqrt_u = fputil::sqrt<float>(u);
+
+  // Degree-6 minimax 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 =
+      sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
+                                0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+
+  return fputil::cast<float16>(
+      x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
+}
+} // namespace LIBC_NAMESPACE_DECL

libc/test/src/math/CMakeLists.txt

@@ -2210,6 +2210,17 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+add_fp_unittest(
+  acosf16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    acosf16_test.cpp
+  DEPENDS
+    libc.src.math.acosf16  
+)
+
 add_fp_unittest(
   atanf_test
   NEED_MPFR

libc/test/src/math/acosf16_test.cpp

@@ -0,0 +1,42 @@
+//===-- Exhaustive test for acosf16 ---------------------------------------===//
+//
+// 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/acosf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcAcosf16Test = 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(LlvmLibcAcosf16Test, PositiveRange) {
+  for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
+                                   LIBC_NAMESPACE::acosf16(x), 0.5);
+  }
+}
+
+TEST_F(LlvmLibcAcosf16Test, NegativeRange) {
+  for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
+                                   LIBC_NAMESPACE::acosf16(x), 0.5);
+  }
+}

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

@@ -3980,6 +3980,17 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+add_fp_unittest(
+  acosf16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    acosf16_test.cpp
+  DEPENDS
+    libc.src.errno.errno
+    libc.src.math.acosf16  
+)
+
 add_fp_unittest(
   atanf_test
   SUITE

libc/test/src/math/smoke/acosf16_test.cpp

@@ -0,0 +1,39 @@
+//===-- Unittests for acosf16 ---------------------------------------------===//
+//
+//
+// 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/acosf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcAcosf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+TEST_F(LlvmLibcAcosf16Test, SpecialNumbers) {
+  LIBC_NAMESPACE::libc_errno = 0;
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(aNaN));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::acosf16(sNaN), FE_INVALID);
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(zero, LIBC_NAMESPACE::acosf16(1.0f));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(neg_inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(2.0f));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(-2.0f));
+  EXPECT_MATH_ERRNO(EDOM);
+}