[libc][math][c23] Implement C23 math function atanpif16

libc/config/linux/x86_64/entrypoints.txt

@@ -705,6 +705,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.asinhf16
     libc.src.math.atanf16
     libc.src.math.atanhf16
+    libc.src.math.atanpif16
     libc.src.math.canonicalizef16
     libc.src.math.ceilf16
     libc.src.math.copysignf16

libc/docs/headers/math/index.rst

@@ -269,7 +269,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | atanh     | |check|          |                 |                        | |check|              |                        | 7.12.5.3               | F.10.2.3                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| atanpi    |                  |                 |                        |                      |                        | 7.12.4.10              | F.10.1.10                  |
+| atanpi    |                  |                 |                        | |check|              |                        | 7.12.4.10              | F.10.1.10                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | cbrt      | |check|          | |check|         |                        |                      |                        | 7.12.7.1               | F.10.4.1                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/include/math.yaml

@@ -134,6 +134,13 @@ functions:
     arguments:
       - type: float
   - name: atanhf16
+    standatds:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
+    guard: LIBC_TYPES_HAS_FLOAT16
+  - name: atanpif16
     standards:
       - stdc
     return_type: _Float16

libc/src/math/CMakeLists.txt

@@ -71,6 +71,8 @@ add_math_entrypoint_object(atanh)
 add_math_entrypoint_object(atanhf)
 add_math_entrypoint_object(atanhf16)
 
+add_math_entrypoint_object(atanpif16)
+
 add_math_entrypoint_object(canonicalize)
 add_math_entrypoint_object(canonicalizef)
 add_math_entrypoint_object(canonicalizel)

libc/src/math/atanpif16.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for atanpif16 ---------------------*- 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_ATANPIF16_H
+#define LLVM_LIBC_SRC_MATH_ATANPIF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 atanpif16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ASINF16_H

libc/src/math/generic/CMakeLists.txt

@@ -3951,6 +3951,23 @@ add_entrypoint_object(
     libc.src.__support.macros.properties.types
 )
 
+add_entrypoint_object(
+  atanpif16
+  SRCS
+    atanpif16.cpp
+  HDRS
+    ../atanpif16.h
+  DEPENDS
+    libc.hdr.errno_macros
+    libc.hdr.fenv_macros
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.sqrt
+)
+
 add_entrypoint_object(
   asinf
   SRCS

libc/src/math/generic/atanpif16.cpp

@@ -0,0 +1,155 @@
+//===-- Half-precision atanpi 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/atanpif16.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"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Using Python's SymPy library, we can obtain the polynomial approximation of
+// arctan(x)/pi. The steps are as follows:
+//  >>> from sympy import *
+//  >>> import math
+//  >>> x = symbols('x')
+//  >>> print(series(atan(x)/math.pi, x, 0, 17))
+//
+// Output:
+// 0.318309886183791*x - 0.106103295394597*x**3 + 0.0636619772367581*x**5 -
+// 0.0454728408833987*x**7 + 0.0353677651315323*x**9 - 0.0289372623803446*x**11
+// + 0.0244853758602916*x**13 - 0.0212206590789194*x**15 + O(x**17)
+//
+// We will assign this 19-degree Taylor polynomial as g(x). This polynomial
+// approximation is accurate for arctan(x)/pi when |x| is in the range [0, 0.5].
+//
+//
+// To compute arctan(x) for all real x, we divide the domain into the following
+// cases:
+//
+// * Case 1: |x| <= 0.5
+//      In this range, the direct polynomial approximation is used:
+//      arctan(x)/pi = sign(x) * g(|x|)
+//      or equivalently, arctan(x) = sign(x) * pi * g(|x|).
+//
+// * Case 2: 0.5 < |x| <= 1
+//      We use the double-angle identity for the tangent function, specifically:
+//        arctan(x) = 2 * arctan(x / (1 + sqrt(1 + x^2))).
+//      Applying this, we have:
+//        arctan(x)/pi = sign(x) * 2 * arctan(x')/pi,
+//        where x' = |x| / (1 + sqrt(1 + x^2)).
+//        Thus, arctan(x)/pi = sign(x) * 2 * g(x')
+//
+//      When |x| is in (0.5, 1], the value of x' will always fall within the
+//      interval [0.207, 0.414], which is within the accurate range of g(x).
+//
+// * Case 3: |x| > 1
+//      For values of |x| greater than 1, we use the reciprocal transformation
+//      identity:
+//        arctan(x) = pi/2 - arctan(1/x) for x > 0.
+//      For any x (real number), this generalizes to:
+//        arctan(x)/pi = sign(x) * (1/2 - arctan(1/|x|)/pi).
+//      Then, using g(x) for arctan(1/|x|)/pi:
+//        arctan(x)/pi = sign(x) * (1/2 - g(1/|x|)).
+//
+//      Note that if 1/|x| still falls outside the
+//      g(x)'s primary range of accuracy (i.e., if 0.5 < 1/|x| <= 1), the rule
+//      from Case 2 must be applied recursively to 1/|x|.
+
+LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+
+  FPBits xbits(x);
+  bool is_neg = xbits.is_neg();
+
+  auto signed_result = [is_neg](double r) -> float16 {
+    return fputil::cast<float16>(is_neg ? -r : r);
+  };
+
+  if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {
+    if (xbits.is_nan()) {
+      return x;
+    }
+    // atanpi(±∞) = ±0.5
+    return signed_result(0.5);
+  }
+
+  if (LIBC_UNLIKELY(xbits.is_zero())) {
+    return x;
+  }
+
+  double x_abs = fputil::cast<double>(xbits.abs().get_val());
+
+  if (LIBC_UNLIKELY(x_abs == 1.0)) {
+    return signed_result(0.25);
+  }
+
+  // polynomial coefficients for atan(x)/pi taylor series
+  // generated using sympy: series(atan(x)/pi, x, 0, 17)
+  constexpr double POLY_COEFFS[] = {
+      0x1.45f306dc9c889p-2,  // x^1:   1/pi
+      -0x1.b2995e7b7b60bp-4, // x^3:  -1/(3*pi)
+      0x1.04c26be3b06ccp-4,  // x^5:   1/(5*pi)
+      -0x1.7483758e69c08p-5, // x^7:  -1/(7*pi)
+      0x1.21bb945252403p-5,  // x^9:   1/(9*pi)
+      -0x1.da1bace3cc68ep-6, // x^11: -1/(11*pi)
+      0x1.912b1c2336cf2p-6,  // x^13:  1/(13*pi)
+      -0x1.5bade52f95e7p-6,  // x^15: -1/(15*pi)
+  };
+
+  // evaluate atan(x)/pi using polynomial approximation, valid for |x| <= 0.5
+  constexpr auto atanpi_eval = [](double x) -> double {
+    double xx = x * x;
+    return x * fputil::polyeval(xx, POLY_COEFFS[0], POLY_COEFFS[1],
+                                POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4],
+                                POLY_COEFFS[5], POLY_COEFFS[6], POLY_COEFFS[7]);
+  };
+
+  // Case 1: |x| <= 0.5 - Direct polynomial evaluation
+  if (LIBC_LIKELY(x_abs <= 0.5)) {
+    double result = atanpi_eval(x_abs);
+    return signed_result(result);
+  }
+
+  // case 2: 0.5 < |x| <= 1 - use double-angle reduction
+  // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))
+  // so atanpi(x) = 2 * atanpi(x') where x' = x / (1 + sqrt(1 + x^2))
+  if (x_abs <= 1.0) {
+    double x2 = x_abs * x_abs;
+    double sqrt_term = fputil::sqrt<double>(1.0 + x2);
+    double x_prime = x_abs / (1.0 + sqrt_term);
+    double result = 2.0 * atanpi_eval(x_prime);
+    return signed_result(result);
+  }
+
+  // case 3: |x| > 1 - use reciprocal transformation
+  // atan(x) = pi/2 - atan(1/x) for x > 0
+  // so atanpi(x) = 1/2 - atanpi(1/x)
+  double x_recip = 1.0 / x_abs;
+  double result;
+
+  // if 1/|x| > 0.5, we need to apply Case 2 transformation to 1/|x|
+  if (x_recip > 0.5) {
+    double xx_recip = x_recip * x_recip;
+    double sqrt_term = fputil::sqrt<double>(1.0 + xx_recip);
+    double x_prime = x_recip / (1.0 + sqrt_term);
+    result = fputil::multiply_add(-2.0, atanpi_eval(x_prime), 0.5);
+  } else {
+    // direct evaluation since 1/|x| <= 0.5
+    result = 0.5 - atanpi_eval(x_recip);
+  }
+
+  return signed_result(result);
+}
+
+} // namespace LIBC_NAMESPACE_DECL

libc/test/src/math/CMakeLists.txt

@@ -2169,6 +2169,17 @@ add_fp_unittest(
     libc.src.math.atanhf16
 )
 
+add_fp_unittest(
+  atanpif16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    atanpif16_test.cpp
+  DEPENDS
+    libc.src.math.atanpif16
+)
+
 add_fp_unittest(
   fmul_test
   NEED_MPFR

libc/test/src/math/atanpif16_test.cpp

@@ -0,0 +1,41 @@
+//===-- Exhaustive test for atanpif16 -------------------------------------===//
+//
+// 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/atanpif16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcAtanpif16Test = 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(LlvmLibcAtanpif16Test, PositiveRange) {
+  for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atanpi, x,
+                                   LIBC_NAMESPACE::atanpif16(x), 0.5);
+  }
+}
+
+TEST_F(LlvmLibcAtanpif16Test, NegativeRange) {
+  for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atanpi, x,
+                                   LIBC_NAMESPACE::atanpif16(x), 0.5);
+  }
+}
+

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

@@ -3965,6 +3965,18 @@ add_fp_unittest(
     libc.src.__support.FPUtil.cast
 )
 
+add_fp_unittest(
+  atanpif16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    atanpif16_test.cpp
+  DEPENDS
+    libc.src.math.atanpif16
+    libc.src.errno.errno
+)
+
 add_fp_unittest(
   asinhf_test
   SUITE

libc/test/src/math/smoke/atanpif16_test.cpp

@@ -0,0 +1,66 @@
+//===-- Unittests for atanpif16 -------------------------------------------===//
+//
+// 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/atanpif16.h"
+#include "test/UnitTest/FPMatcher.h"
+
+using LlvmLibcAtanpif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+TEST_F(LlvmLibcAtanpif16Test, SpecialNumbers) {
+  // zero
+  EXPECT_FP_EQ(zero, LIBC_NAMESPACE::atanpif16(zero));
+  EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::atanpif16(neg_zero));
+
+  // NaN inputs
+  EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+               LIBC_NAMESPACE::atanpif16(FPBits::quiet_nan().get_val()));
+
+  EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+               LIBC_NAMESPACE::atanpif16(FPBits::signaling_nan().get_val()));
+
+  // infinity inputs -> should return +/-0.5
+  EXPECT_FP_EQ(0.5f16, LIBC_NAMESPACE::atanpif16(inf));
+  EXPECT_FP_EQ(-0.5f16, LIBC_NAMESPACE::atanpif16(neg_inf));
+}
+
+TEST_F(LlvmLibcAtanpif16Test, SymmetryProperty) {
+  // Test that atanpi(-x) = -atanpi(x)
+  constexpr float16 TEST_VALS[] = {0.1f16,  0.25f16, 0.5f16,   0.75f16,
+                                   1.0f16,  1.5f16,  2.0f16,   5.0f16,
+                                   10.0f16, 50.0f16, 100.0f16, 1000.0f16};
+
+  for (float16 x : TEST_VALS) {
+    FPBits neg_x_bits(x);
+    neg_x_bits.set_sign(Sign::NEG);
+    float16 neg_x = neg_x_bits.get_val();
+
+    float16 pos_result = LIBC_NAMESPACE::atanpif16(x);
+    float16 neg_result = LIBC_NAMESPACE::atanpif16(neg_x);
+
+    EXPECT_FP_EQ(pos_result, FPBits(neg_result).abs().get_val());
+  }
+}
+
+TEST_F(LlvmLibcAtanpif16Test, MonotonicityProperty) {
+  // Test that atanpi is monotonically increasing
+  constexpr float16 TEST_VALS[] = {-1000.0f16, -100.0f16, -10.0f16, -2.0f16,
+                                   -1.0f16,    -0.5f16,   -0.1f16,  0.0f16,
+                                   0.1f16,     0.5f16,    1.0f16,   2.0f16,
+                                   10.0f16,    100.0f16,  1000.0f16};
+
+  for (size_t i = 0; i < sizeof(TEST_VALS) / sizeof(TEST_VALS[0]) - 1; ++i) {
+    float16 x1 = TEST_VALS[i];
+    float16 x2 = TEST_VALS[i + 1];
+    float16 result1 = LIBC_NAMESPACE::atanpif16(x1);
+    float16 result2 = LIBC_NAMESPACE::atanpif16(x2);
+
+    EXPECT_TRUE(result1 < result2);
+  }
+}
+