[libc] [llvm] [libc][math][c23] Add atan2f16 function (PR #183531)

[Xinlong Chen via llvm-commits]

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@@ -0,0 +1,107 @@
+//===-- Implementation header for atan2f16 ----------------------*- 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_ATAN2F16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ATAN2F16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "inv_trigf_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+LIBC_INLINE float16 atan2f16(float16 y, float16 x) {
+  using namespace inv_trigf_utils_internal;
+  using FPBits = fputil::FPBits<float16>;
+
+  constexpr double IS_NEG[2] = {1.0, -1.0};
+  constexpr double PI = 0x1.921fb54442d18p+1;
+  constexpr double PI_OVER_2 = 0x1.921fb54442d18p+0;
+  constexpr double PI_OVER_4 = 0x1.921fb54442d18p-1;
+  constexpr double THREE_PI_OVER_4 = 0x1.2d97c7f3321d2p+1;
+
+  // const_term[x_sign][recip]; recip = (|x| < |y|)
+  constexpr double CONST_TERM[2][2] = {
+      {0.0, -PI_OVER_2},
+      {-PI, PI_OVER_2},
+  };
+
+  FPBits x_bits(x), y_bits(y);
+  bool x_sign = x_bits.sign().is_neg();
+  bool y_sign = y_bits.sign().is_neg();
+  x_bits.set_sign(Sign::POS);
+  y_bits.set_sign(Sign::POS);
+  uint16_t x_abs = x_bits.uintval();
+  uint16_t y_abs = y_bits.uintval();
+  uint16_t max_abs = x_abs > y_abs ? x_abs : y_abs;
+  uint16_t min_abs = x_abs <= y_abs ? x_abs : y_abs;
+
+  if (LIBC_UNLIKELY(max_abs >= 0x7c00U || min_abs == 0)) {
+    if (x_bits.is_nan() || y_bits.is_nan()) {
+      if (x_bits.is_signaling_nan() || y_bits.is_signaling_nan())
+        fputil::raise_except_if_required(FE_INVALID);
+      return FPBits::quiet_nan().get_val();
+    }
+    size_t x_except = (x_abs == 0) ? 0 : (x_abs == 0x7c00U ? 2 : 1);
+    size_t y_except = (y_abs == 0) ? 0 : (y_abs == 0x7c00U ? 2 : 1);
+    constexpr double EXCEPTS[3][3][2] = {
+        {{0.0, PI}, {0.0, PI}, {0.0, PI}},
+        {{PI_OVER_2, PI_OVER_2}, {0.0, 0.0}, {0.0, PI}},
+        {{PI_OVER_2, PI_OVER_2},
+         {PI_OVER_2, PI_OVER_2},
+         {PI_OVER_4, THREE_PI_OVER_4}},
+    };
+    double r = IS_NEG[y_sign] * EXCEPTS[y_except][x_except][x_sign];
+    return fputil::cast<float16>(r);
+  }
+
+  bool recip = x_abs < y_abs;
+  double final_sign = IS_NEG[x_sign ^ y_sign ^ recip];
+  double const_term = CONST_TERM[x_sign][recip];
+
+  // atan2(y,x) = final_sign * (const_term + atan(n/d)),
+  //   where n = min(|x|,|y|), d = max(|x|,|y|), so 0 <= n/d <= 1.
+  //
+  // To compute atan(n/d), we use a lookup table with 16 equally-spaced knots:
+  //   idx = round(16 * n/d),  so  |n/d - idx/16| <= 1/32.
+  //   q_d = n/d - idx/16.
+  // Then by the atan addition formula:
+  //   atan(n/d) = atan(idx/16) + q_d * Q(q_d)
+  // where Q(q_d) approximates
+  //   [atan(idx/16 + q_d) - atan(idx/16)] / q_d
+  // via atan_eval(q_d, idx) from inv_trigf_utils.
+  double n = static_cast<double>(FPBits(min_abs).get_val());
+  double d = static_cast<double>(FPBits(max_abs).get_val());
+  double q_d = n / d;
+
+  double k_d = fputil::nearest_integer(q_d * 0x1.0p4);
+  int idx = static_cast<int>(k_d);
+  q_d = fputil::multiply_add(k_d, -0x1.0p-4, q_d);
+
+  double p = atan_eval(q_d, static_cast<unsigned>(idx));
+  double r = final_sign *
+             fputil::multiply_add(q_d, p, const_term + ATAN_K_OVER_16[idx]);
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Xinlong-Chen wrote:

done

https://github.com/llvm/llvm-project/pull/183531