[libc][math] Refactor acoshf16 implementation to header-only in src/__support/math folder. (#148568)

Part of #147386

in preparation for:
https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450

8 files changed, 176 insertions, 109 deletions

diff --git a/libc/shared/math.h b/libc/shared/math.h
index 33fe235..e3c674c 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -15,6 +15,7 @@
 #include "math/acosf.h"
 #include "math/acosf16.h"
 #include "math/acoshf.h"
+#include "math/acoshf16.h"
 #include "math/erff.h"
 #include "math/exp.h"
 #include "math/exp10.h"
diff --git a/libc/shared/math/acoshf16.h b/libc/shared/math/acoshf16.h
new file mode 100644
index 0000000..2f0bc6e
--- /dev/null
+++ b/libc/shared/math/acoshf16.h
@@ -0,0 +1,29 @@
+//===-- Shared acoshf16 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_ACOSHF16_H
+#define LLVM_LIBC_SHARED_MATH_ACOSHF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+#include "shared/libc_common.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/math/acoshf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acoshf16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOSHF16_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index b0e562f..9a8a4d1 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -80,6 +80,22 @@ add_header_library(
 )
 
 add_header_library(
+  acoshf16
+  HDRS
+    acoshf16.h
+  DEPENDS
+    .acoshf_utils
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.except_value_utils
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.sqrt
+    libc.src.__support.macros.optimization
+)
+
+add_header_library(
   asin_utils
   HDRS
     asin_utils.h
diff --git a/libc/src/__support/math/acoshf16.h b/libc/src/__support/math/acoshf16.h
new file mode 100644
index 0000000..15e7f6a
--- /dev/null
+++ b/libc/src/__support/math/acoshf16.h
@@ -0,0 +1,123 @@
+//===-- Implementation header for acoshf16 ----------------------*- 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_ACOSHF_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "acoshf_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+static constexpr float16 acoshf16(float16 x) {
+
+  using namespace acoshf_internal;
+  constexpr size_t N_EXCEPTS = 2;
+  constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSHF16_EXCEPTS{{
+      // (input, RZ output, RU offset, RD offset, RN offset)
+      // x = 0x1.6dcp+1, acoshf16(x) = 0x1.b6p+0 (RZ)
+      {0x41B7, 0x3ED8, 1, 0, 0},
+      // x = 0x1.39p+0, acoshf16(x) = 0x1.4f8p-1 (RZ)
+      {0x3CE4, 0x393E, 1, 0, 1},
+  }};
+
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+  uint16_t x_u = xbits.uintval();
+
+  // Check for NaN input first.
+  if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {
+    if (xbits.is_signaling_nan()) {
+      fputil::raise_except_if_required(FE_INVALID);
+      return FPBits::quiet_nan().get_val();
+    }
+    if (xbits.is_neg()) {
+      fputil::set_errno_if_required(EDOM);
+      fputil::raise_except_if_required(FE_INVALID);
+      return FPBits::quiet_nan().get_val();
+    }
+    return x;
+  }
+
+  // Domain error for inputs less than 1.0.
+  if (LIBC_UNLIKELY(x <= 1.0f)) {
+    if (x == 1.0f)
+      return FPBits::zero().get_val();
+    fputil::set_errno_if_required(EDOM);
+    fputil::raise_except_if_required(FE_INVALID);
+    return FPBits::quiet_nan().get_val();
+  }
+
+  if (auto r = ACOSHF16_EXCEPTS.lookup(xbits.uintval());
+      LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+
+  float xf = x;
+  // High-precision polynomial approximation for inputs close to 1.0
+  // ([1, 1.25)).
+  //
+  // Brief derivation:
+  // 1. Expand acosh(1 + delta) using Taylor series around delta=0:
+  //    acosh(1 + delta) ≈ sqrt(2 * delta) * [1 - delta/12 + 3*delta^2/160
+  //                     - 5*delta^3/896 + 35*delta^4/18432 + ...]
+  // 2. Truncate the series to fit accurately for delta in [0, 0.25].
+  // 3. Polynomial coefficients (from sollya) used here are:
+  //    P(delta) ≈ 1 - 0x1.555556p-4 * delta + 0x1.333334p-6 * delta^2
+  //               - 0x1.6db6dcp-8 * delta^3 + 0x1.f1c71cp-10 * delta^4
+  // 4. The Sollya commands used to generate these coefficients were:
+  //      > display = hexadecimal;
+  //      > round(1/12, SG, RN);
+  //      > round(3/160, SG, RN);
+  //      > round(5/896, SG, RN);
+  //      > round(35/18432, SG, RN);
+  //      With hexadecimal display mode enabled, the outputs were:
+  //      0x1.555556p-4
+  //      0x1.333334p-6
+  //      0x1.6db6dcp-8
+  //      0x1.f1c71cp-10
+  // 5. The maximum absolute error, estimated using:
+  //      dirtyinfnorm(acosh(1 + x) - sqrt(2*x) * P(x), [0, 0.25])
+  //    is:
+  //      0x1.d84281p-22
+  if (LIBC_UNLIKELY(x_u < 0x3D00U)) {
+    float delta = xf - 1.0f;
+    float sqrt_2_delta = fputil::sqrt<float>(2.0 * delta);
+    float pe = fputil::polyeval(delta, 0x1p+0f, -0x1.555556p-4f, 0x1.333334p-6f,
+                                -0x1.6db6dcp-8f, 0x1.f1c71cp-10f);
+    float approx = sqrt_2_delta * pe;
+    return fputil::cast<float16>(approx);
+  }
+
+  // acosh(x) = log(x + sqrt(x^2 - 1))
+  float sqrt_term = fputil::sqrt<float>(fputil::multiply_add(xf, xf, -1.0f));
+  float result = static_cast<float>(log_eval(xf + sqrt_term));
+
+  return fputil::cast<float16>(result);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 86baf2b..408f99e 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3878,18 +3878,8 @@ add_entrypoint_object(
   HDRS
     ../acoshf16.h
   DEPENDS
-    .explogxf
-    libc.hdr.errno_macros
-    libc.hdr.fenv_macros
-    libc.src.__support.FPUtil.cast
-    libc.src.__support.FPUtil.except_value_utils
-    libc.src.__support.FPUtil.fenv_impl
-    libc.src.__support.FPUtil.fp_bits
-    libc.src.__support.FPUtil.multiply_add
-    libc.src.__support.FPUtil.polyeval
-    libc.src.__support.FPUtil.sqrt
-    libc.src.__support.macros.optimization
-    libc.src.__support.macros.properties.types
+    libc.src.__support.math.acoshf16
+    libc.src.errno.errno
 )
 
 add_entrypoint_object(
diff --git a/libc/src/math/generic/acoshf16.cpp b/libc/src/math/generic/acoshf16.cpp
index 96ca956..bb3a91f 100644
--- a/libc/src/math/generic/acoshf16.cpp
+++ b/libc/src/math/generic/acoshf16.cpp
@@ -7,105 +7,10 @@
 //===----------------------------------------------------------------------===//
 
 #include "src/math/acoshf16.h"
-#include "explogxf.h"
-#include "hdr/errno_macros.h"
-#include "hdr/fenv_macros.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/cast.h"
-#include "src/__support/FPUtil/except_value_utils.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/sqrt.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h"
+#include "src/__support/math/acoshf16.h"
 
 namespace LIBC_NAMESPACE_DECL {
 
-static constexpr size_t N_EXCEPTS = 2;
-static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSHF16_EXCEPTS{{
-    // (input, RZ output, RU offset, RD offset, RN offset)
-    // x = 0x1.6dcp+1, acoshf16(x) = 0x1.b6p+0 (RZ)
-    {0x41B7, 0x3ED8, 1, 0, 0},
-    // x = 0x1.39p+0, acoshf16(x) = 0x1.4f8p-1 (RZ)
-    {0x3CE4, 0x393E, 1, 0, 1},
-}};
-
-LLVM_LIBC_FUNCTION(float16, acoshf16, (float16 x)) {
-  using namespace acoshf_internal;
-  using FPBits = fputil::FPBits<float16>;
-  FPBits xbits(x);
-  uint16_t x_u = xbits.uintval();
-
-  // Check for NaN input first.
-  if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {
-    if (xbits.is_signaling_nan()) {
-      fputil::raise_except_if_required(FE_INVALID);
-      return FPBits::quiet_nan().get_val();
-    }
-    if (xbits.is_neg()) {
-      fputil::set_errno_if_required(EDOM);
-      fputil::raise_except_if_required(FE_INVALID);
-      return FPBits::quiet_nan().get_val();
-    }
-    return x;
-  }
-
-  // Domain error for inputs less than 1.0.
-  if (LIBC_UNLIKELY(x <= 1.0f)) {
-    if (x == 1.0f)
-      return FPBits::zero().get_val();
-    fputil::set_errno_if_required(EDOM);
-    fputil::raise_except_if_required(FE_INVALID);
-    return FPBits::quiet_nan().get_val();
-  }
-
-  if (auto r = ACOSHF16_EXCEPTS.lookup(xbits.uintval());
-      LIBC_UNLIKELY(r.has_value()))
-    return r.value();
-
-  float xf = x;
-  // High-precision polynomial approximation for inputs close to 1.0
-  // ([1, 1.25)).
-  //
-  // Brief derivation:
-  // 1. Expand acosh(1 + delta) using Taylor series around delta=0:
-  //    acosh(1 + delta) ≈ sqrt(2 * delta) * [1 - delta/12 + 3*delta^2/160
-  //                     - 5*delta^3/896 + 35*delta^4/18432 + ...]
-  // 2. Truncate the series to fit accurately for delta in [0, 0.25].
-  // 3. Polynomial coefficients (from sollya) used here are:
-  //    P(delta) ≈ 1 - 0x1.555556p-4 * delta + 0x1.333334p-6 * delta^2
-  //               - 0x1.6db6dcp-8 * delta^3 + 0x1.f1c71cp-10 * delta^4
-  // 4. The Sollya commands used to generate these coefficients were:
-  //      > display = hexadecimal;
-  //      > round(1/12, SG, RN);
-  //      > round(3/160, SG, RN);
-  //      > round(5/896, SG, RN);
-  //      > round(35/18432, SG, RN);
-  //      With hexadecimal display mode enabled, the outputs were:
-  //      0x1.555556p-4
-  //      0x1.333334p-6
-  //      0x1.6db6dcp-8
-  //      0x1.f1c71cp-10
-  // 5. The maximum absolute error, estimated using:
-  //      dirtyinfnorm(acosh(1 + x) - sqrt(2*x) * P(x), [0, 0.25])
-  //    is:
-  //      0x1.d84281p-22
-  if (LIBC_UNLIKELY(x_u < 0x3D00U)) {
-    float delta = xf - 1.0f;
-    float sqrt_2_delta = fputil::sqrt<float>(2.0 * delta);
-    float pe = fputil::polyeval(delta, 0x1p+0f, -0x1.555556p-4f, 0x1.333334p-6f,
-                                -0x1.6db6dcp-8f, 0x1.f1c71cp-10f);
-    float approx = sqrt_2_delta * pe;
-    return fputil::cast<float16>(approx);
-  }
-
-  // acosh(x) = log(x + sqrt(x^2 - 1))
-  float sqrt_term = fputil::sqrt<float>(fputil::multiply_add(xf, xf, -1.0f));
-  float result = static_cast<float>(log_eval(xf + sqrt_term));
-
-  return fputil::cast<float16>(result);
-}
+LLVM_LIBC_FUNCTION(float16, acoshf16, (float16 x)) { return math::acoshf16(x); }
 
 } // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/shared/CMakeLists.txt b/libc/test/shared/CMakeLists.txt
index a402d6e..89b607d 100644
--- a/libc/test/shared/CMakeLists.txt
+++ b/libc/test/shared/CMakeLists.txt
@@ -11,6 +11,7 @@ add_fp_unittest(
     libc.src.__support.math.acosf
     libc.src.__support.math.acosf16
     libc.src.__support.math.acoshf
+    libc.src.__support.math.acoshf16
     libc.src.__support.math.erff
     libc.src.__support.math.exp
     libc.src.__support.math.exp10
diff --git a/libc/test/shared/shared_math_test.cpp b/libc/test/shared/shared_math_test.cpp
index 25555b8..8d3cebd 100644
--- a/libc/test/shared/shared_math_test.cpp
+++ b/libc/test/shared/shared_math_test.cpp
@@ -14,6 +14,8 @@
 TEST(LlvmLibcSharedMathTest, AllFloat16) {
   int exponent;
 
+  EXPECT_FP_EQ(0x0p+0f, LIBC_NAMESPACE::shared::acoshf16(1.0f));
+
   EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::exp10f16(0.0f16));
 
   EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::expf16(0.0f16));