[libc-commits] [libc] [llvm] [libc][math][c23] Add acosbf16 math function (PR #184633)

[via libc-commits]

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@@ -0,0 +1,94 @@
+//===-- Implementation header for acosbf16 ----------------------*- 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_ACOSBF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSBF16_H
+
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/bfloat16.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/inv_trigf_utils.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace math {
+
+LIBC_INLINE bfloat16 acosbf16(bfloat16 x) {
+  // Generated by Sollya using the following command:
+  // > display = hexadecimal;
+  // > round(pi/2, SG, RN);
+  constexpr float PI_2 = 0x1.921fb6p0f;
+  // > round(pi, SG, RN);
+  constexpr float PI = 0x1.921fb6p1;
+
+  using FPBits = fputil::FPBits<bfloat16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+  bool sign = (x_u >> 15);
+  float xf = x;
+
+  float xf_abs = (xf < 0 ? -xf : xf);
+  float x_sq = xf_abs * xf_abs;
+
+  // case 1: x <= 0.5
+  if (x_abs <= 0x3F00) {
+    // |x| = {0}
+    if (LIBC_UNLIKELY(x_abs == 0))
+      return fputil::cast<bfloat16>(PI_2);
+
+    float xp = fputil::cast<float>(inv_trigf_utils_internal::asin_eval(x_sq));
+    float result = xf * fputil::multiply_add(x_sq, xp, 1.0f);
+    return fputil::cast<bfloat16>(PI_2 - result);
+  }
+
+  // case 2: 0.5< |x|<= 1.0
+  if (x_abs <= 0x3F80) {
+    // |x| = {1}
+    if (x_abs == 0x3F80) {
+      if (sign)
+        return fputil::cast<bfloat16>(PI);
+      else
+        return fputil::cast<bfloat16>(0.0f);
+    }
+
+    // using reduction for acos:
+    // acos(|x|) = 2*asin(sqrt((1 - |x|)/2)),
+    // and acos(x) = acos(|x|) for x >= 0, pi - acos(|x|) for x < 0
+    float t = fputil::multiply_add<float>(xf_abs, -0.5f, 0.5f);
+    float t_sqrt = fputil::sqrt<float>(t);
+    float tp = fputil::cast<float>(inv_trigf_utils_internal::asin_eval(t));
+    float asin_sqrt_t = t_sqrt * (fputil::multiply_add(t, tp, 1.0f));
+
+    return fputil::cast<bfloat16>(
+        (sign) ? fputil::multiply_add(asin_sqrt_t, -2.0f, PI)
+               : 2 * asin_sqrt_t);
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lntue wrote:

`2.0f`

https://github.com/llvm/llvm-project/pull/184633