[libc][math][c23] Add acospif16() function

libc/config/linux/x86_64/entrypoints.txt

@@ -658,6 +658,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     # math.h C23 _Float16 entrypoints
     libc.src.math.acosf16
     libc.src.math.acoshf16
+    libc.src.math.acospif16
     libc.src.math.asinf16
     libc.src.math.asinhf16
     libc.src.math.canonicalizef16

libc/docs/headers/math/index.rst

@@ -253,7 +253,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | acosh     | |check|          |                 |                        | |check|              |                        | 7.12.5.1               | F.10.2.1                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| acospi    |                  |                 |                        |                      |                        | 7.12.4.8               | F.10.1.8                   |
+| acospi    |                  |                 |                        | |check|              |                        | 7.12.4.8               | F.10.1.8                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | asin      | |check|          |                 |                        | |check|              |                        | 7.12.4.2               | F.10.1.2                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/include/math.yaml

@@ -34,6 +34,13 @@ functions:
     arguments:
       - type: _Float16
     guard: LIBC_TYPES_HAS_FLOAT16
+    name: acospif16
+    standards:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
+    guard: LIBC_TYPES_HAS_FLOAT16
   - name: asin
     standards:
       - stdc

libc/src/math/CMakeLists.txt

@@ -43,6 +43,7 @@ endfunction()
 add_math_entrypoint_object(acos)
 add_math_entrypoint_object(acosf)
 add_math_entrypoint_object(acosf16)
+add_math_entrypoint_object(acospif16)
 
 add_math_entrypoint_object(acosh)
 add_math_entrypoint_object(acoshf)

libc/src/math/acospif16.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for acospif16 ---------------------*- 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_ACOSPIF16_H
+#define LLVM_LIBC_SRC_MATH_ACOSPIF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 acospif16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ACOSPIF16_H

libc/src/math/generic/CMakeLists.txt

@@ -4112,6 +4112,25 @@ add_entrypoint_object(
     libc.src.__support.macros.properties.types  
 )
 
+add_entrypoint_object(
+  acospif16
+  SRCS
+    acospif16.cpp
+  HDRS
+    ../acospif16.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_header_library(
   atan_utils
   HDRS

libc/src/math/generic/acospif16.cpp

@@ -0,0 +1,134 @@
+//===-- Half-precision acospi 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/acospif16.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 {
+
+LLVM_LIBC_FUNCTION(float16, acospif16, (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)) {
+    // acospif16(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();
+  }
+
+  // |x| == 0x1p0, x is 1 or -1
+  // if x is (-)1, return 1
+  // if x is (+)1, return 0
+  if (LIBC_UNLIKELY(x_abs == 0x3c00))
+    return fputil::cast<float16>(x_sign ? 1.0f : 0.0f);
+
+  float xf = x;
+  float xsq = xf * xf;
+
+  // Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya
+  // with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0,
+  // 0.5]);
+  constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f,
+                                    0x1.897e36p-6f, 0x1.9efafcp-7f,
+                                    0x1.06d884p-6f};
+  // |x| <= 0x1p-1, |x| <= 0.5
+  if (x_abs <= 0x3800) {
+    // if x is 0, return 0.5
+    if (LIBC_UNLIKELY(x_abs == 0))
+      return fputil::cast<float16>(0.5f);
+
+    // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then
+    //            acospi(x) = 0.5 - asin(x)/pi
+    float interm =
+        fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2],
+                         POLY_COEFFS[3], POLY_COEFFS[4]);
+
+    return fputil::cast<float16>(fputil::multiply_add(-xf, interm, 0.5f));
+  }
+
+  // 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 - 2 * 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))
+  //       acospi(x) = 2 * (asin(sqrt(u)) / pi)
+  //
+  // 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)
+  //       acospi(x) = 1 - acos(-x)/pi
+  // 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);
+
+  float asin_sqrt_u =
+      sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1],
+                                POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]);
+
+  // Same as acos(x), but devided the expression with pi
+  return fputil::cast<float16>(
+      x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f)
+             : 2.0f * asin_sqrt_u);
+}
+} // namespace LIBC_NAMESPACE_DECL

libc/test/src/math/CMakeLists.txt

@@ -2269,6 +2269,17 @@ add_fp_unittest(
     libc.src.math.acosf16  
 )
 
+add_fp_unittest(
+  acospif16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    acospif16_test.cpp
+  DEPENDS
+    libc.src.math.acospif16  
+)
+
 add_fp_unittest(
   atanf_test
   NEED_MPFR

libc/test/src/math/acospif16_test.cpp

@@ -0,0 +1,42 @@
+//===-- Exhaustive test for acospif16 -------------------------------------===//
+//
+// 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/acospif16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcAcospif16Test = 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(LlvmLibcAcospif16Test, PositiveRange) {
+  for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acospi, x,
+                                   LIBC_NAMESPACE::acospif16(x), 0.5);
+  }
+}
+
+TEST_F(LlvmLibcAcospif16Test, NegativeRange) {
+  for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acospi, x,
+                                   LIBC_NAMESPACE::acospif16(x), 0.5);
+  }
+}

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

@@ -4040,6 +4040,17 @@ add_fp_unittest(
     libc.src.math.acosf16  
 )
 
+add_fp_unittest(
+  acospif16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    acospif16_test.cpp
+  DEPENDS
+    libc.src.errno.errno
+    libc.src.math.acospif16  
+)
+
 add_fp_unittest(
   atanf_test
   SUITE

libc/test/src/math/smoke/acospif16_test.cpp

@@ -0,0 +1,38 @@
+//===-- Unittests for acospif16 -------------------------------------------===//
+//
+// 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/acospif16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcAcospif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+TEST_F(LlvmLibcAcospif16Test, SpecialNumbers) {
+  LIBC_NAMESPACE::libc_errno = 0;
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(aNaN));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::acospif16(sNaN),
+                              FE_INVALID);
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(zero, LIBC_NAMESPACE::acospif16(1.0f));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(neg_inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(2.0f));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(-2.0f));
+  EXPECT_MATH_ERRNO(EDOM);
+}

libc/utils/MPFRWrapper/MPCommon.cpp

@@ -70,6 +70,23 @@ MPFRNumber MPFRNumber::acosh() const {
   return result;
 }
 
+MPFRNumber MPFRNumber::acospi() const {
+  MPFRNumber result(*this);
+
+#if MPFR_VERSION_MAJOR > 4 ||                                                  \
+    (MPFR_VERSION_MAJOR == 4 && MPFR_VERSION_MINOR >= 2)
+  mpfr_acospi(result.value, value, mpfr_rounding);
+  return result;
+#else
+  MPFRNumber value_acos(0.0, 1280);
+  mpfr_acos(value_acos.value, value, MPFR_RNDN);
+  MPFRNumber value_pi(0.0, 1280);
+  mpfr_const_pi(value_pi.value, MPFR_RNDN);
+  mpfr_div(result.value, value_acos.value, value_pi.value, mpfr_rounding);
+  return result;
+#endif
+}
+
 MPFRNumber MPFRNumber::add(const MPFRNumber &b) const {
   MPFRNumber result(*this);
   mpfr_add(result.value, value, b.value, mpfr_rounding);

libc/utils/MPFRWrapper/MPCommon.h

@@ -181,6 +181,7 @@ class MPFRNumber {
   MPFRNumber abs() const;
   MPFRNumber acos() const;
   MPFRNumber acosh() const;
+  MPFRNumber acospi() const;
   MPFRNumber add(const MPFRNumber &b) const;
   MPFRNumber asin() const;
   MPFRNumber asinh() const;

libc/utils/MPFRWrapper/MPFRUtils.cpp

@@ -32,6 +32,8 @@ unary_operation(Operation op, InputType input, unsigned int precision,
     return mpfrInput.acos();
   case Operation::Acosh:
     return mpfrInput.acosh();
+  case Operation::Acospi:
+    return mpfrInput.acospi();
   case Operation::Asin:
     return mpfrInput.asin();
   case Operation::Asinh:

libc/utils/MPFRWrapper/MPFRUtils.h

@@ -28,6 +28,7 @@ enum class Operation : int {
   Abs,
   Acos,
   Acosh,
+  Acospi,
   Asin,
   Asinh,
   Atan,