From 1c1135b3fccf59537243fc365e83a568f77273ae Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Thu, 24 Jul 2025 11:49:03 +0300
Subject: [PATCH 01/20] feat: add the implementatio of `atanpif16`

---
 libc/src/math/CMakeLists.txt         |   2 +
 libc/src/math/atanpif16.h            |  22 ++++
 libc/src/math/generic/CMakeLists.txt |  17 +++
 libc/src/math/generic/atanpif16.cpp  | 155 +++++++++++++++++++++++++++
 4 files changed, 196 insertions(+)
 create mode 100644 libc/src/math/atanpif16.h
 create mode 100644 libc/src/math/generic/atanpif16.cpp

diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index d177ff79141c0..033aa2396b86b 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -67,6 +67,8 @@ add_math_entrypoint_object(atan2f128)
 add_math_entrypoint_object(atanh)
 add_math_entrypoint_object(atanhf)
 
+add_math_entrypoint_object(atanpif16)
+
 add_math_entrypoint_object(canonicalize)
 add_math_entrypoint_object(canonicalizef)
 add_math_entrypoint_object(canonicalizel)
diff --git a/libc/src/math/atanpif16.h b/libc/src/math/atanpif16.h
new file mode 100644
index 0000000000000..14dc150014578
--- /dev/null
+++ b/libc/src/math/atanpif16.h
@@ -0,0 +1,22 @@
+//===-- 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
+
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index adbed5b2de48c..421d8163ea792 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4029,6 +4029,23 @@ add_entrypoint_object(
     libc.src.__support.macros.optimization
 )
 
+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_object_library(
   inv_trigf_utils
   HDRS
diff --git a/libc/src/math/generic/atanpif16.cpp b/libc/src/math/generic/atanpif16.cpp
new file mode 100644
index 0000000000000..e7ab0a48ca2ab
--- /dev/null
+++ b/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, 21))
+//
+// 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 +
+// 0.0187241109519877*x**17 - 0.01675315190441*x**19 + O(x**21)
+//
+// 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());
+
+  // Polynomial coefficients for atan(x)/pi Taylor series
+  // Generated using SymPy: series(atan(x)/pi, x, 0, 21)
+  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)
+      0x1.32c69d0bde9e8p-6,  // x^17:  1/(17*pi)
+      -0x1.127bcfe232f8cp-6, // x^19: -1/(19*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],
+                                POLY_COEFFS[8], POLY_COEFFS[9]);
+  };
+
+  // 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 x_recip2 = x_recip * x_recip;
+    double sqrt_term = fputil::sqrt<double>(1.0 + x_recip2);
+    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

From 1a5d472cde4fb58887ddcf3d1e9bd73fc0b763b0 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Thu, 24 Jul 2025 11:49:16 +0300
Subject: [PATCH 02/20] add entries

---
 libc/config/linux/x86_64/entrypoints.txt | 1 +
 libc/include/math.yaml                   | 6 ++++++
 2 files changed, 7 insertions(+)

diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 73dfeae1a2c94..1585f803229b6 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -664,6 +664,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.acoshf16
     libc.src.math.asinf16
     libc.src.math.asinhf16
+    libc.src.math.atanpif16
     libc.src.math.canonicalizef16
     libc.src.math.ceilf16
     libc.src.math.copysignf16
diff --git a/libc/include/math.yaml b/libc/include/math.yaml
index fef829422244d..06a67fdb44a9c 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -113,6 +113,12 @@ functions:
     return_type: float
     arguments:
       - type: float
+  - name: atanpif16
+    standards:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
   - name: canonicalize
     standards:
       - stdc

From 926937077156306fe3ddbb3137e8416ab01160e8 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Thu, 24 Jul 2025 12:45:34 +0300
Subject: [PATCH 03/20] add unit tests for `atanpif16`

---
 libc/src/math/generic/atanpif16.cpp         | 16 ++---
 libc/test/src/math/smoke/CMakeLists.txt     | 12 ++++
 libc/test/src/math/smoke/atanpif16_test.cpp | 66 +++++++++++++++++++++
 3 files changed, 86 insertions(+), 8 deletions(-)
 create mode 100644 libc/test/src/math/smoke/atanpif16_test.cpp

diff --git a/libc/src/math/generic/atanpif16.cpp b/libc/src/math/generic/atanpif16.cpp
index e7ab0a48ca2ab..0ca0c534d1658 100644
--- a/libc/src/math/generic/atanpif16.cpp
+++ b/libc/src/math/generic/atanpif16.cpp
@@ -91,8 +91,8 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
 
   double x_abs = fputil::cast<double>(xbits.abs().get_val());
 
-  // Polynomial coefficients for atan(x)/pi Taylor series
-  // Generated using SymPy: series(atan(x)/pi, x, 0, 21)
+  // polynomial coefficients for atan(x)/pi taylor series
+  // generated using sympy: series(atan(x)/pi, x, 0, 21)
   constexpr double POLY_COEFFS[] = {
       0x1.45f306dc9c889p-2,  // x^1:   1/pi
       -0x1.b2995e7b7b60bp-4, // x^3:  -1/(3*pi)
@@ -121,9 +121,9 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
     return signed_result(result);
   }
 
-  // Case 2: 0.5 < |x| <= 1 - Use double-angle reduction
+  // 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))
+  // 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);
@@ -132,16 +132,16 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
     return signed_result(result);
   }
 
-  // Case 3: |x| > 1 - Use reciprocal transformation
+  // 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)
+  // 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_recip2 = x_recip * x_recip;
-    double sqrt_term = fputil::sqrt<double>(1.0 + x_recip2);
+    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 {
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index 223d1933bca38..2461478e2ffb5 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -3947,6 +3947,18 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+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
diff --git a/libc/test/src/math/smoke/atanpif16_test.cpp b/libc/test/src/math/smoke/atanpif16_test.cpp
new file mode 100644
index 0000000000000..e0f3ce5f52392
--- /dev/null
+++ b/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);
+  }
+}

From bdae5140992b134249ef8331ab91c4f0dda6f2ca Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Thu, 24 Jul 2025 12:53:13 +0300
Subject: [PATCH 04/20] add exhaustive test for `atanpif16`

---
 libc/test/src/math/CMakeLists.txt     | 11 ++++++++
 libc/test/src/math/atanpif16_test.cpp | 40 +++++++++++++++++++++++++++
 libc/utils/MPFRWrapper/MPCommon.cpp   |  6 ++++
 libc/utils/MPFRWrapper/MPCommon.h     |  1 +
 libc/utils/MPFRWrapper/MPFRUtils.cpp  |  2 ++
 libc/utils/MPFRWrapper/MPFRUtils.h    |  1 +
 6 files changed, 61 insertions(+)
 create mode 100644 libc/test/src/math/atanpif16_test.cpp

diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index 7ee8b86135557..b17c7bc50fa42 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -2143,6 +2143,17 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+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
diff --git a/libc/test/src/math/atanpif16_test.cpp b/libc/test/src/math/atanpif16_test.cpp
new file mode 100644
index 0000000000000..2c24b5048a2fb
--- /dev/null
+++ b/libc/test/src/math/atanpif16_test.cpp
@@ -0,0 +1,40 @@
+//===-- 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);
+  }
+}
\ No newline at end of file
diff --git a/libc/utils/MPFRWrapper/MPCommon.cpp b/libc/utils/MPFRWrapper/MPCommon.cpp
index ac8cde2f97221..5bb95df02fcf0 100644
--- a/libc/utils/MPFRWrapper/MPCommon.cpp
+++ b/libc/utils/MPFRWrapper/MPCommon.cpp
@@ -106,6 +106,12 @@ MPFRNumber MPFRNumber::atanh() const {
   return result;
 }
 
+MPFRNumber MPFRNumber::atanpi() const {
+  MPFRNumber result(*this);
+  mpfr_atanpi(result.value, value, mpfr_rounding);
+  return result;
+}
+
 MPFRNumber MPFRNumber::cbrt() const {
   MPFRNumber result(*this);
   mpfr_cbrt(result.value, value, mpfr_rounding);
diff --git a/libc/utils/MPFRWrapper/MPCommon.h b/libc/utils/MPFRWrapper/MPCommon.h
index eaa512e30bc86..6888fcfad1329 100644
--- a/libc/utils/MPFRWrapper/MPCommon.h
+++ b/libc/utils/MPFRWrapper/MPCommon.h
@@ -187,6 +187,7 @@ class MPFRNumber {
   MPFRNumber atan() const;
   MPFRNumber atan2(const MPFRNumber &b);
   MPFRNumber atanh() const;
+  MPFRNumber atanpi() const;
   MPFRNumber cbrt() const;
   MPFRNumber ceil() const;
   MPFRNumber cos() const;
diff --git a/libc/utils/MPFRWrapper/MPFRUtils.cpp b/libc/utils/MPFRWrapper/MPFRUtils.cpp
index 4a033dbc2049b..cb65f080192b8 100644
--- a/libc/utils/MPFRWrapper/MPFRUtils.cpp
+++ b/libc/utils/MPFRWrapper/MPFRUtils.cpp
@@ -40,6 +40,8 @@ unary_operation(Operation op, InputType input, unsigned int precision,
     return mpfrInput.atan();
   case Operation::Atanh:
     return mpfrInput.atanh();
+  case Operation::Atanpi:
+    return mpfrInput.atanpi();
   case Operation::Cbrt:
     return mpfrInput.cbrt();
   case Operation::Ceil:
diff --git a/libc/utils/MPFRWrapper/MPFRUtils.h b/libc/utils/MPFRWrapper/MPFRUtils.h
index bc65f87c6b5ab..a650a09428f18 100644
--- a/libc/utils/MPFRWrapper/MPFRUtils.h
+++ b/libc/utils/MPFRWrapper/MPFRUtils.h
@@ -32,6 +32,7 @@ enum class Operation : int {
   Asinh,
   Atan,
   Atanh,
+  Atanpi,
   Cbrt,
   Ceil,
   Cos,

From 3d0becae259c11c1f6b9f5b1eb82cfa96c09bc7d Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Thu, 24 Jul 2025 12:55:58 +0300
Subject: [PATCH 05/20] improve `atanpif16` implementation

---
 libc/src/math/generic/atanpif16.cpp | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/libc/src/math/generic/atanpif16.cpp b/libc/src/math/generic/atanpif16.cpp
index 0ca0c534d1658..985cf3738614e 100644
--- a/libc/src/math/generic/atanpif16.cpp
+++ b/libc/src/math/generic/atanpif16.cpp
@@ -23,13 +23,12 @@ namespace LIBC_NAMESPACE_DECL {
 //  >>> from sympy import *
 //  >>> import math
 //  >>> x = symbols('x')
-//  >>> print(series(atan(x)/math.pi, x, 0, 21))
+//  >>> 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 +
-// 0.0187241109519877*x**17 - 0.01675315190441*x**19 + O(x**21)
+// + 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].
@@ -86,13 +85,17 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
   }
 
   if (LIBC_UNLIKELY(xbits.is_zero())) {
-    return x; //
+    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, 21)
+  // 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)
@@ -102,8 +105,6 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
       -0x1.da1bace3cc68ep-6, // x^11: -1/(11*pi)
       0x1.912b1c2336cf2p-6,  // x^13:  1/(13*pi)
       -0x1.5bade52f95e7p-6,  // x^15: -1/(15*pi)
-      0x1.32c69d0bde9e8p-6,  // x^17:  1/(17*pi)
-      -0x1.127bcfe232f8cp-6, // x^19: -1/(19*pi)
   };
 
   // evaluate atan(x)/pi using polynomial approximation, valid for |x| <= 0.5
@@ -111,8 +112,7 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
     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],
-                                POLY_COEFFS[8], POLY_COEFFS[9]);
+                                POLY_COEFFS[5], POLY_COEFFS[6], POLY_COEFFS[7]);
   };
 
   // Case 1: |x| <= 0.5 - Direct polynomial evaluation

From 2499fc92c872e0fa5555db041cd83b209156d8ba Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 25 Jul 2025 12:59:05 +0300
Subject: [PATCH 06/20] formatting

---
 libc/src/math/atanpif16.h                   | 1 -
 libc/test/src/math/smoke/atanpif16_test.cpp | 1 -
 2 files changed, 2 deletions(-)

diff --git a/libc/src/math/atanpif16.h b/libc/src/math/atanpif16.h
index 14dc150014578..8f2391a6e47e5 100644
--- a/libc/src/math/atanpif16.h
+++ b/libc/src/math/atanpif16.h
@@ -19,4 +19,3 @@ float16 atanpif16(float16 x);
 } // namespace LIBC_NAMESPACE_DECL
 
 #endif // LLVM_LIBC_SRC_MATH_ASINF16_H
-
diff --git a/libc/test/src/math/smoke/atanpif16_test.cpp b/libc/test/src/math/smoke/atanpif16_test.cpp
index e0f3ce5f52392..f1cb1ec4ef3b3 100644
--- a/libc/test/src/math/smoke/atanpif16_test.cpp
+++ b/libc/test/src/math/smoke/atanpif16_test.cpp
@@ -29,7 +29,6 @@ TEST_F(LlvmLibcAtanpif16Test, SpecialNumbers) {
   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,

From 5d0880036612a0180e2c1fd9cce66ac73108cffe Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 25 Jul 2025 12:59:11 +0300
Subject: [PATCH 07/20] fix conflicts

---
 libc/include/math.yaml               | 2 ++
 libc/src/math/generic/CMakeLists.txt | 2 +-
 2 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/libc/include/math.yaml b/libc/include/math.yaml
index 4e08fd74dccc3..539e42c0bbecb 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -134,12 +134,14 @@ 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
     arguments:
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 280493bed92e7..d1f375256d236 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3931,7 +3931,7 @@ add_entrypoint_object(
     libc.src.__support.macros.optimization
 )
 
-add_object_library(
+add_entrypoint_object(
   atanhf16
   SRCS
     atanhf16.cpp

From c8ffe9b33af5d7473912de22a0792e39910507a0 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 25 Jul 2025 13:00:45 +0300
Subject: [PATCH 08/20] fix conflcts

---
 libc/src/math/generic/CMakeLists.txt | 12 ------------
 1 file changed, 12 deletions(-)

diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index d1f375256d236..603c91cd99598 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3968,18 +3968,6 @@ add_entrypoint_object(
     libc.src.__support.FPUtil.sqrt
 )
 
-add_object_library(
-  inv_trigf_utils
-  HDRS
-    inv_trigf_utils.h
-  SRCS
-    inv_trigf_utils.cpp
-  DEPENDS
-    libc.src.__support.FPUtil.multiply_add
-    libc.src.__support.FPUtil.polyeval
-    libc.src.__support.common
-)
-
 add_entrypoint_object(
   asinf
   SRCS

From 1e3a59fb5cc47db941e0a3b2e2399c87e9dd4cd9 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 25 Jul 2025 13:03:18 +0300
Subject: [PATCH 09/20] missed blank line

---
 libc/test/src/math/atanpif16_test.cpp | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/libc/test/src/math/atanpif16_test.cpp b/libc/test/src/math/atanpif16_test.cpp
index 2c24b5048a2fb..9e5606afe1fbc 100644
--- a/libc/test/src/math/atanpif16_test.cpp
+++ b/libc/test/src/math/atanpif16_test.cpp
@@ -37,4 +37,5 @@ TEST_F(LlvmLibcAtanpif16Test, NegativeRange) {
     EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atanpi, x,
                                    LIBC_NAMESPACE::atanpif16(x), 0.5);
   }
-}
\ No newline at end of file
+}
+

From e06c286f16f154a47dae6d310f6f088279ec4eea Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 25 Jul 2025 13:04:16 +0300
Subject: [PATCH 10/20] missed blank line

---
 libc/test/src/math/smoke/atanpif16_test.cpp | 1 +
 1 file changed, 1 insertion(+)

diff --git a/libc/test/src/math/smoke/atanpif16_test.cpp b/libc/test/src/math/smoke/atanpif16_test.cpp
index f1cb1ec4ef3b3..ca12b3ad8d040 100644
--- a/libc/test/src/math/smoke/atanpif16_test.cpp
+++ b/libc/test/src/math/smoke/atanpif16_test.cpp
@@ -63,3 +63,4 @@ TEST_F(LlvmLibcAtanpif16Test, MonotonicityProperty) {
     EXPECT_TRUE(result1 < result2);
   }
 }
+

From fad9a76bbf3b796b151470c87b2011b3ce22d0b1 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 25 Jul 2025 14:19:40 +0300
Subject: [PATCH 11/20] check `atanpi` in float16

---
 libc/docs/headers/math/index.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/libc/docs/headers/math/index.rst b/libc/docs/headers/math/index.rst
index 9679c4a6c807f..d5fb397342d4f 100644
--- a/libc/docs/headers/math/index.rst
+++ b/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                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

From 5d9362a75d1a0c277bc3629800957315a5e1538c Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Thu, 7 Aug 2025 21:07:03 +0300
Subject: [PATCH 12/20] fix format

---
 libc/test/src/math/atanpif16_test.cpp | 1 -
 1 file changed, 1 deletion(-)

diff --git a/libc/test/src/math/atanpif16_test.cpp b/libc/test/src/math/atanpif16_test.cpp
index 9e5606afe1fbc..38771f0147d60 100644
--- a/libc/test/src/math/atanpif16_test.cpp
+++ b/libc/test/src/math/atanpif16_test.cpp
@@ -38,4 +38,3 @@ TEST_F(LlvmLibcAtanpif16Test, NegativeRange) {
                                    LIBC_NAMESPACE::atanpif16(x), 0.5);
   }
 }
-

From a5f5f1c11d79160fc9acdeafa85df3df86c33028 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 8 Aug 2025 14:14:29 +0300
Subject: [PATCH 13/20] fix atanpi mpfr number

---
 libc/utils/MPFRWrapper/MPCommon.cpp | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/libc/utils/MPFRWrapper/MPCommon.cpp b/libc/utils/MPFRWrapper/MPCommon.cpp
index dab53eaa28abe..3b1827298ccb5 100644
--- a/libc/utils/MPFRWrapper/MPCommon.cpp
+++ b/libc/utils/MPFRWrapper/MPCommon.cpp
@@ -125,8 +125,17 @@ MPFRNumber MPFRNumber::atanh() const {
 
 MPFRNumber MPFRNumber::atanpi() const {
   MPFRNumber result(*this);
-  mpfr_atanpi(result.value, value, mpfr_rounding);
+#if 0 && (MPFR_VERSION >= MPFR_VERSION_NUM(4, 2, 0))
+   mpfr_asinpi(result.value, value, mpfr_rounding);
+   return result;
+#else
+  MPFRNumber value_atan(0.0, 1280);
+  mpfr_atan(value_atan.value, value, MPFR_RNDN);
+  MPFRNumber value_pi(0.0, 1280);
+  mpfr_const_pi(value_pi.value, MPFR_RNDN);
+  mpfr_div(result.value, value_atan.value, value_pi.value, mpfr_rounding);
   return result;
+#endif
 }
 
 MPFRNumber MPFRNumber::cbrt() const {

From cefc0752c6fed7f88b1fb80d6892f134880d98c5 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 8 Aug 2025 14:14:49 +0300
Subject: [PATCH 14/20] improvements

---
 libc/src/math/generic/atanpif16.cpp         | 19 +++++++++++--------
 libc/test/src/math/smoke/atanpif16_test.cpp | 18 ++++++++----------
 2 files changed, 19 insertions(+), 18 deletions(-)

diff --git a/libc/src/math/generic/atanpif16.cpp b/libc/src/math/generic/atanpif16.cpp
index 985cf3738614e..4db8be09bfd27 100644
--- a/libc/src/math/generic/atanpif16.cpp
+++ b/libc/src/math/generic/atanpif16.cpp
@@ -15,6 +15,7 @@
 #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 {
 
@@ -78,21 +79,23 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
 
   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())) {
+  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)) {
+  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)
@@ -109,8 +112,8 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
 
   // 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],
+    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]);
   };
@@ -140,8 +143,8 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
 
   // 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_sq_recip = x_recip * x_recip;
+    double sqrt_term = fputil::sqrt<double>(1.0 + x_sq_recip);
     double x_prime = x_recip / (1.0 + sqrt_term);
     result = fputil::multiply_add(-2.0, atanpi_eval(x_prime), 0.5);
   } else {
diff --git a/libc/test/src/math/smoke/atanpif16_test.cpp b/libc/test/src/math/smoke/atanpif16_test.cpp
index ca12b3ad8d040..5accb5d34193a 100644
--- a/libc/test/src/math/smoke/atanpif16_test.cpp
+++ b/libc/test/src/math/smoke/atanpif16_test.cpp
@@ -6,10 +6,11 @@
 //
 //===----------------------------------------------------------------------===//
 
-#include "src/errno/libc_errno.h"
+#include "src/__support/libc_errno.h"
 #include "src/math/atanpif16.h"
 #include "test/UnitTest/FPMatcher.h"
 
+using LIBC_NAMESPACE::cpp::array;
 using LlvmLibcAtanpif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
 
 TEST_F(LlvmLibcAtanpif16Test, SpecialNumbers) {
@@ -21,8 +22,7 @@ TEST_F(LlvmLibcAtanpif16Test, SpecialNumbers) {
   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()));
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::atanpif16(aNaN));
 
   // infinity inputs -> should return +/-0.5
   EXPECT_FP_EQ(0.5f16, LIBC_NAMESPACE::atanpif16(inf));
@@ -49,12 +49,11 @@ TEST_F(LlvmLibcAtanpif16Test, SymmetryProperty) {
 
 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) {
+  constexpr array<float16, 15> 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 < TEST_VALS.size() - 1; ++i) {
     float16 x1 = TEST_VALS[i];
     float16 x2 = TEST_VALS[i + 1];
     float16 result1 = LIBC_NAMESPACE::atanpif16(x1);
@@ -63,4 +62,3 @@ TEST_F(LlvmLibcAtanpif16Test, MonotonicityProperty) {
     EXPECT_TRUE(result1 < result2);
   }
 }
-

From 0da444c2e7857e5fc727595cc46ec72aee1f1774 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 8 Aug 2025 14:15:01 +0300
Subject: [PATCH 15/20] add missed depends

---
 libc/src/math/generic/CMakeLists.txt | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 603c91cd99598..b1fb6aa562288 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3960,12 +3960,14 @@ add_entrypoint_object(
   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.polyeval
-    libc.src.__support.FPUtil.cast
     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(

From 669c7e06dfbfdc5cf1866af4f6557f9a0f755927 Mon Sep 17 00:00:00 2001
From: Mohamed Emad <hulxxv@gmail.com>
Date: Fri, 15 Aug 2025 10:42:01 +0300
Subject: [PATCH 16/20] fix: wrong condition in mpfr

---
 libc/utils/MPFRWrapper/MPCommon.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/libc/utils/MPFRWrapper/MPCommon.cpp b/libc/utils/MPFRWrapper/MPCommon.cpp
index 3b1827298ccb5..9f20f18217fa0 100644
--- a/libc/utils/MPFRWrapper/MPCommon.cpp
+++ b/libc/utils/MPFRWrapper/MPCommon.cpp
@@ -125,7 +125,7 @@ MPFRNumber MPFRNumber::atanh() const {
 
 MPFRNumber MPFRNumber::atanpi() const {
   MPFRNumber result(*this);
-#if 0 && (MPFR_VERSION >= MPFR_VERSION_NUM(4, 2, 0))
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(4, 2, 0))
    mpfr_asinpi(result.value, value, mpfr_rounding);
    return result;
 #else

From 5b69a72ea218afeef0c86831b5dae7b89977aef5 Mon Sep 17 00:00:00 2001
From: Mohamed Emad <hulxxv@gmail.com>
Date: Fri, 15 Aug 2025 10:48:01 +0300
Subject: [PATCH 17/20] formatting

---
 libc/utils/MPFRWrapper/MPCommon.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/libc/utils/MPFRWrapper/MPCommon.cpp b/libc/utils/MPFRWrapper/MPCommon.cpp
index 9f20f18217fa0..6463c0f7672cb 100644
--- a/libc/utils/MPFRWrapper/MPCommon.cpp
+++ b/libc/utils/MPFRWrapper/MPCommon.cpp
@@ -126,8 +126,8 @@ MPFRNumber MPFRNumber::atanh() const {
 MPFRNumber MPFRNumber::atanpi() const {
   MPFRNumber result(*this);
 #if (MPFR_VERSION >= MPFR_VERSION_NUM(4, 2, 0))
-   mpfr_asinpi(result.value, value, mpfr_rounding);
-   return result;
+  mpfr_asinpi(result.value, value, mpfr_rounding);
+  return result;
 #else
   MPFRNumber value_atan(0.0, 1280);
   mpfr_atan(value_atan.value, value, MPFR_RNDN);

From 0a234b66237ff77d1a9d222c6b6412c685c09620 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Fri, 15 Aug 2025 14:36:05 +0300
Subject: [PATCH 18/20] fix  `MPFRNumber::atanpi()`

---
 libc/utils/MPFRWrapper/MPCommon.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/libc/utils/MPFRWrapper/MPCommon.cpp b/libc/utils/MPFRWrapper/MPCommon.cpp
index 6463c0f7672cb..8a164b8dc25ad 100644
--- a/libc/utils/MPFRWrapper/MPCommon.cpp
+++ b/libc/utils/MPFRWrapper/MPCommon.cpp
@@ -125,8 +125,8 @@ MPFRNumber MPFRNumber::atanh() const {
 
 MPFRNumber MPFRNumber::atanpi() const {
   MPFRNumber result(*this);
-#if (MPFR_VERSION >= MPFR_VERSION_NUM(4, 2, 0))
-  mpfr_asinpi(result.value, value, mpfr_rounding);
+#if MPFR_VERSION >= MPFR_VERSION_NUM(4, 2, 0)
+  mpfr_atanpi(result.value, value, mpfr_rounding);
   return result;
 #else
   MPFRNumber value_atan(0.0, 1280);

From ed38cadf40d8c51e821df6624c78c0c902c51c61 Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Tue, 2 Sep 2025 20:09:41 +0300
Subject: [PATCH 19/20] use `cpp::array` instead of regular array

---
 libc/test/src/math/smoke/atanpif16_test.cpp | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/libc/test/src/math/smoke/atanpif16_test.cpp b/libc/test/src/math/smoke/atanpif16_test.cpp
index 5accb5d34193a..9eb1005a5c171 100644
--- a/libc/test/src/math/smoke/atanpif16_test.cpp
+++ b/libc/test/src/math/smoke/atanpif16_test.cpp
@@ -31,9 +31,9 @@ TEST_F(LlvmLibcAtanpif16Test, SpecialNumbers) {
 
 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};
+  constexpr array<float16, 12> 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);

From c5493aae7f8e07c14b067da41fa012c732f71cde Mon Sep 17 00:00:00 2001
From: hulxv <hulxxv@gmail.com>
Date: Tue, 2 Sep 2025 20:13:32 +0300
Subject: [PATCH 20/20] enhancements

---
 libc/src/math/generic/atanpif16.cpp | 35 ++++++++++++++---------------
 libc/utils/MPFRWrapper/MPCommon.cpp |  4 ++--
 2 files changed, 19 insertions(+), 20 deletions(-)

diff --git a/libc/src/math/generic/atanpif16.cpp b/libc/src/math/generic/atanpif16.cpp
index 4db8be09bfd27..c54087c7165fe 100644
--- a/libc/src/math/generic/atanpif16.cpp
+++ b/libc/src/math/generic/atanpif16.cpp
@@ -31,7 +31,7 @@ namespace LIBC_NAMESPACE_DECL {
 // 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
+// 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].
 //
 //
@@ -97,21 +97,20 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
   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 {
+    // 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],
@@ -128,8 +127,8 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
   // 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_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);
@@ -143,8 +142,8 @@ LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
 
   // if 1/|x| > 0.5, we need to apply Case 2 transformation to 1/|x|
   if (x_recip > 0.5) {
-    double x_sq_recip = x_recip * x_recip;
-    double sqrt_term = fputil::sqrt<double>(1.0 + x_sq_recip);
+    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 {
diff --git a/libc/utils/MPFRWrapper/MPCommon.cpp b/libc/utils/MPFRWrapper/MPCommon.cpp
index 8a164b8dc25ad..1255559ebe115 100644
--- a/libc/utils/MPFRWrapper/MPCommon.cpp
+++ b/libc/utils/MPFRWrapper/MPCommon.cpp
@@ -129,9 +129,9 @@ MPFRNumber MPFRNumber::atanpi() const {
   mpfr_atanpi(result.value, value, mpfr_rounding);
   return result;
 #else
-  MPFRNumber value_atan(0.0, 1280);
+  MPFRNumber value_atan(0.0, mpfr_precision * 3);
   mpfr_atan(value_atan.value, value, MPFR_RNDN);
-  MPFRNumber value_pi(0.0, 1280);
+  MPFRNumber value_pi(0.0, mpfr_precision * 3);
   mpfr_const_pi(value_pi.value, MPFR_RNDN);
   mpfr_div(result.value, value_atan.value, value_pi.value, mpfr_rounding);
   return result;