[libc] [llvm] [libc][math] Refactored atanpif16 to header only (PR #184316)

via llvm-commits llvm-commits at lists.llvm.org
Sat Mar 14 14:29:18 PDT 2026


https://github.com/abhijeetsharma200 updated https://github.com/llvm/llvm-project/pull/184316

>From 5aeec726e1384b8e370e114b51dff7c9f0e09d6e Mon Sep 17 00:00:00 2001
From: Abhijeet Sharma <abhijeetsharma2002 at gmail.com>
Date: Tue, 3 Mar 2026 11:40:16 +0100
Subject: [PATCH 1/5] Refactored atanpif16 to header only

---
 libc/shared/math.h                            |   1 +
 libc/shared/math/atanpif16.h                  |  29 ++++
 libc/src/__support/math/CMakeLists.txt        |  16 ++
 libc/src/__support/math/atanpif16.h           | 120 +++++++++++++++
 libc/src/math/generic/CMakeLists.txt          |  11 +-
 libc/src/math/generic/atanpif16.cpp           | 143 +-----------------
 libc/test/shared/CMakeLists.txt               |   1 +
 libc/test/shared/shared_math_test.cpp         |   1 +
 .../llvm-project-overlay/libc/BUILD.bazel     |  21 +++
 9 files changed, 192 insertions(+), 151 deletions(-)
 create mode 100644 libc/shared/math/atanpif16.h
 create mode 100644 libc/src/__support/math/atanpif16.h

diff --git a/libc/shared/math.h b/libc/shared/math.h
index a7d735ffa1746..bb1153a94b134 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -33,6 +33,7 @@
 #include "math/atanf16.h"
 #include "math/atanhf.h"
 #include "math/atanhf16.h"
+#include "math/atanpif16.h"
 #include "math/bf16add.h"
 #include "math/bf16addf.h"
 #include "math/bf16addf128.h"
diff --git a/libc/shared/math/atanpif16.h b/libc/shared/math/atanpif16.h
new file mode 100644
index 0000000000000..c79c2979b32e5
--- /dev/null
+++ b/libc/shared/math/atanpif16.h
@@ -0,0 +1,29 @@
+//===-- Shared atanpif16 function -------------------------------*- 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_SHARED_MATH_ATANPIF16_H
+#define LLVM_LIBC_SHARED_MATH_ATANPIF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "shared/libc_common.h"
+#include "src/__support/math/atanpif16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::atanpif16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_ATANPIF16_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 3bb8e76a54bfb..18bcb7224761e 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -331,6 +331,22 @@ add_header_library(
     libc.src.__support.macros.optimization
 )
 
+add_header_library(
+  atanpif16
+  HDRS
+    atanpif16.h
+  DEPENDS
+    libc.hdr.fenv_macros
+    libc.include.llvm-libc-macros.float16_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
+)
+
 add_header_library(
   asinf
   HDRS
diff --git a/libc/src/__support/math/atanpif16.h b/libc/src/__support/math/atanpif16.h
new file mode 100644
index 0000000000000..1638a1ac8c31e
--- /dev/null
+++ b/libc/src/__support/math/atanpif16.h
@@ -0,0 +1,120 @@
+//===-- 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___SUPPORT_MATH_ATANPIF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ATANPIF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#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 {
+namespace math {
+
+LIBC_INLINE constexpr 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()) {
+      if (xbits.is_signaling_nan()) {
+        fputil::raise_except_if_required(FE_INVALID);
+        return FPBits::quiet_nan().get_val();
+      }
+      return x;
+    }
+    // atanpi(+-inf) = +-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);
+
+  // evaluate atan(x)/pi using polynomial approximation, valid for |x| <= 0.5
+  constexpr auto atanpi_eval = [](double x) -> double {
+    // polynomial coefficients for atan(x)/pi taylor series
+    // generated using sympy: series(atan(x)/pi, x, 0, 17)
+    constexpr static 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)
+    };
+    double x_sq = x * x;
+    return x * fputil::polyeval(x_sq, 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 x_abs_sq = x_abs * x_abs;
+    double sqrt_term = fputil::sqrt<double>(1.0 + x_abs_sq);
+    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 x_recip_sq = x_recip * x_recip;
+    double sqrt_term = fputil::sqrt<double>(1.0 + x_recip_sq);
+    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 math
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ATANPIF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index f8ec25be61d12..851689b48955a 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4041,16 +4041,7 @@ add_entrypoint_object(
   HDRS
     ../atanpif16.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
+    libc.src.__support.math.atanpif16
 )
 
 add_entrypoint_object(
diff --git a/libc/src/math/generic/atanpif16.cpp b/libc/src/math/generic/atanpif16.cpp
index c54087c7165fe..c6b7355ebc8f1 100644
--- a/libc/src/math/generic/atanpif16.cpp
+++ b/libc/src/math/generic/atanpif16.cpp
@@ -7,151 +7,12 @@
 //===----------------------------------------------------------------------===//
 
 #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"
-#include "src/__support/macros/optimization.h"
+#include "src/__support/math/atanpif16.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 degree-15 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()) {
-      if (xbits.is_signaling_nan()) {
-        fputil::raise_except_if_required(FE_INVALID);
-        return FPBits::quiet_nan().get_val();
-      }
-      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);
-
-  // evaluate atan(x)/pi using polynomial approximation, valid for |x| <= 0.5
-  constexpr auto atanpi_eval = [](double x) -> double {
-    // polynomial coefficients for atan(x)/pi taylor series
-    // generated using sympy: series(atan(x)/pi, x, 0, 17)
-    constexpr static 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)
-    };
-    double x_sq = x * x;
-    return x * fputil::polyeval(x_sq, 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 x_abs_sq = x_abs * x_abs;
-    double sqrt_term = fputil::sqrt<double>(1.0 + x_abs_sq);
-    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 x_recip_sq = x_recip * x_recip;
-    double sqrt_term = fputil::sqrt<double>(1.0 + x_recip_sq);
-    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);
+  return math::atanpif16(x);
 }
 
 } // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/shared/CMakeLists.txt b/libc/test/shared/CMakeLists.txt
index a04a15cdabcb7..4912ccd3d9ae6 100644
--- a/libc/test/shared/CMakeLists.txt
+++ b/libc/test/shared/CMakeLists.txt
@@ -30,6 +30,7 @@ add_fp_unittest(
     libc.src.__support.math.atanf16
     libc.src.__support.math.atanhf
     libc.src.__support.math.atanhf16
+    libc.src.__support.math.atanpif16
     libc.src.__support.math.bf16add
     libc.src.__support.math.bf16addf
     libc.src.__support.math.bf16addl
diff --git a/libc/test/shared/shared_math_test.cpp b/libc/test/shared/shared_math_test.cpp
index 460449e4fcb2e..07167b624ac3f 100644
--- a/libc/test/shared/shared_math_test.cpp
+++ b/libc/test/shared/shared_math_test.cpp
@@ -26,6 +26,7 @@ TEST(LlvmLibcSharedMathTest, AllFloat16) {
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::asinpif16(0.0f16));
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::atanf16(0.0f16));
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::atanhf16(0.0f16));
+  EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::atanpif16(0.0f16));
   EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::cosf16(0.0f16));
   EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::coshf16(0.0f16));
   EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::cospif16(0.0f16));
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 87d1d88e971bf..2d2c58e375b57 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -3036,6 +3036,22 @@ libc_support_library(
     ],
 )
 
+libc_support_library(
+    name = "__support_math_atanpif16",
+    hdrs = ["src/__support/math/atanpif16.h"],
+    deps = [
+        ":__support_fputil_cast",
+        ":__support_fputil_fenv_impl",
+        ":__support_fputil_fp_bits",
+        ":__support_fputil_multiply_add",
+        ":__support_fputil_polyeval",
+        ":__support_fputil_sqrt",
+        ":__support_macros_optimization",
+        ":hdr_fenv_macros",
+        ":llvm_libc_macros_float16_macros",
+    ],
+)
+
 libc_support_library(
     name = "__support_math_bf16add",
     hdrs = ["src/__support/math/bf16add.h"],
@@ -6009,6 +6025,11 @@ libc_math_function(
     ],
 )
 
+libc_math_function(
+    name = "atanpif16",
+    additional_deps = [":__support_math_atanpif16"],
+)
+
 libc_math_function(
     name = "bf16add",
     additional_deps = [":__support_math_bf16add"],

>From 02c9a206a3cd360350c12827ca495b0ee5ec6ab9 Mon Sep 17 00:00:00 2001
From: Abhijeet Sharma <abhijeetsharma2002 at gmail.com>
Date: Tue, 3 Mar 2026 11:54:47 +0100
Subject: [PATCH 2/5] Fixed failing test

---
 libc/src/__support/math/atanpif16.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/libc/src/__support/math/atanpif16.h b/libc/src/__support/math/atanpif16.h
index 1638a1ac8c31e..8734e655151dd 100644
--- a/libc/src/__support/math/atanpif16.h
+++ b/libc/src/__support/math/atanpif16.h
@@ -96,7 +96,7 @@ LIBC_INLINE constexpr float16 atanpif16(float16 x) {
   // 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;
+  double result = 0.0;
 
   // if 1/|x| > 0.5, we need to apply Case 2 transformation to 1/|x|
   if (x_recip > 0.5) {

>From 7efb9003b8f6eed88dd6ef06f5bea50b74042218 Mon Sep 17 00:00:00 2001
From: Abhijeet Sharma <abhijeetsharma2002 at gmail.com>
Date: Mon, 9 Mar 2026 12:12:18 +0100
Subject: [PATCH 3/5] fixes as per code review

---
 libc/src/__support/math/CMakeLists.txt            | 2 ++
 libc/src/__support/math/atanpif16.h               | 2 +-
 utils/bazel/llvm-project-overlay/libc/BUILD.bazel | 2 +-
 3 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 18bcb7224761e..9f4573849ec83 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -336,6 +336,7 @@ add_header_library(
   HDRS
     atanpif16.h
   DEPENDS
+    libc.hdr.errno_macros
     libc.hdr.fenv_macros
     libc.include.llvm-libc-macros.float16_macros
     libc.src.__support.FPUtil.cast
@@ -344,6 +345,7 @@ add_header_library(
     libc.src.__support.FPUtil.multiply_add
     libc.src.__support.FPUtil.polyeval
     libc.src.__support.FPUtil.sqrt
+    libc.src.__support.macros.config
     libc.src.__support.macros.optimization
 )
 
diff --git a/libc/src/__support/math/atanpif16.h b/libc/src/__support/math/atanpif16.h
index 8734e655151dd..4573509182276 100644
--- a/libc/src/__support/math/atanpif16.h
+++ b/libc/src/__support/math/atanpif16.h
@@ -25,7 +25,7 @@
 namespace LIBC_NAMESPACE_DECL {
 namespace math {
 
-LIBC_INLINE constexpr float16 atanpif16(float16 x) {
+LIBC_INLINE float16 atanpif16(float16 x) {
   using FPBits = fputil::FPBits<float16>;
 
   FPBits xbits(x);
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 2d2c58e375b57..df69947b7d24d 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -3046,8 +3046,8 @@ libc_support_library(
         ":__support_fputil_multiply_add",
         ":__support_fputil_polyeval",
         ":__support_fputil_sqrt",
+        ":__support_macros_config",
         ":__support_macros_optimization",
-        ":hdr_fenv_macros",
         ":llvm_libc_macros_float16_macros",
     ],
 )

>From 201f8a99cf980fa12b7247ec11a4b4640810eec8 Mon Sep 17 00:00:00 2001
From: Abhijeet Sharma <abhijeetsharma2002 at gmail.com>
Date: Mon, 9 Mar 2026 21:15:45 +0100
Subject: [PATCH 4/5] fixed failing bazel build

---
 utils/bazel/llvm-project-overlay/libc/BUILD.bazel | 1 +
 1 file changed, 1 insertion(+)

diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index df69947b7d24d..f08f43f857832 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -3048,6 +3048,7 @@ libc_support_library(
         ":__support_fputil_sqrt",
         ":__support_macros_config",
         ":__support_macros_optimization",
+        ":hdr_fenv_macros",
         ":llvm_libc_macros_float16_macros",
     ],
 )

>From 03799ab3bf6d0c9c2b8273c4317144d5caa57a52 Mon Sep 17 00:00:00 2001
From: Abhijeet Sharma <abhijeetsharma2002 at gmail.com>
Date: Sat, 14 Mar 2026 22:28:13 +0100
Subject: [PATCH 5/5] fixes as per code review

---
 libc/src/__support/math/CMakeLists.txt |  1 -
 libc/src/__support/math/atanpif16.h    | 48 ++++++++++++++++++++++++++
 2 files changed, 48 insertions(+), 1 deletion(-)

diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 6063b8dbe41d9..0f1d461b4ecf7 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -336,7 +336,6 @@ add_header_library(
   HDRS
     atanpif16.h
   DEPENDS
-    libc.hdr.errno_macros
     libc.hdr.fenv_macros
     libc.include.llvm-libc-macros.float16_macros
     libc.src.__support.FPUtil.cast
diff --git a/libc/src/__support/math/atanpif16.h b/libc/src/__support/math/atanpif16.h
index 4573509182276..e0eaff6678fc5 100644
--- a/libc/src/__support/math/atanpif16.h
+++ b/libc/src/__support/math/atanpif16.h
@@ -25,6 +25,54 @@
 namespace LIBC_NAMESPACE_DECL {
 namespace math {
 
+// 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 degree-15 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|.
+
 LIBC_INLINE float16 atanpif16(float16 x) {
   using FPBits = fputil::FPBits<float16>;
 



More information about the llvm-commits mailing list