[libc-commits] [libc] [llvm] [libc][math][c23] Add atanbf16 function (PR #184019)

[via libc-commits]

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@@ -0,0 +1,109 @@
+//===-- bfloat16 precision atanbf16(x) 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.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ATANBF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ATANBF16_H
+
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.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"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+LIBC_INLINE bfloat16 atanbf16(bfloat16 x) {
+  // Generated by Sollya using the following command:
+  // > display = hexadecimal;
+  // > round(pi/2, SG, RN);
+  constexpr float PI_2 = 0x1.921fb6p0f;
+
+  using FPBits = fputil::FPBits<bfloat16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+  bool x_sign = x_u >> 15;
+  float sign = (x_sign ? -1.0f : 1.0f);
+
+  // |x| is +/-inf or NaN
+  if (LIBC_UNLIKELY(x_abs >= 0x7F80)) {
+    // 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;
+    }
+    // atanbf16(+/-inf) = +/-pi/2
+    return fputil::cast<bfloat16>(sign * PI_2);
+  }
+
+  // atanbf16(+/-0) = +/-0
+  if (LIBC_UNLIKELY(x_abs == 0))
+    return x;
+
+  float xf = x;
+  float x_sq = xf * xf;
+
+  // |x| <= 1
+  // Taylor series -> [x - x^3/3 + x^5/5 - x^7/7 ...]
+  // x * [1 - x^2/3 + x^4/5 - x^6/7...] -> x * P(x)
+  // atan(x) = x * poly(x^2)
+  // atan(x)/x = poly(x^2)
+
+  // Degree 14 polynomial of atan(x) generated using Sollya with command :
+  // > display = hexadecimal ;
+  // > P = fpminimax(atan(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|SG, SG,
+  // SG..SG|], [0, 1]);
+  //
+  // absolute error for the polynomial given by:
+  // dirtyinfnorm(atan(x) - x * P(x), [0, 1]) gives
+  // error ~ 0x1.482168p-24
+  // worst case error for it being ~ 0x1.dcf750p-23
+  // satisfying -> error < worst_case
+  if (x_abs <= 0x3f80) {
+    float result = fputil::polyeval(
+        x_sq, 0x1.fffffcp-1f, -0x1.55519ep-2f, 0x1.98f6a8p-3f, -0x1.1f0a92p-3f,
+        0x1.95b654p-4f, -0x1.e65492p-5f, 0x1.8c0c36p-6f, -0x1.32316ep-8f);
+    return fputil::cast<bfloat16>(xf * result);
+  }
+
+  // If |x| > 1:
+  // atan(x) = sign(x) * (pi/2 - atan(1/|x|))
+  // Since 1/|x| < 1, we can use the same polynomial.
+  float x_inv_sq = 1.0f / x_sq;
+  float x_inv = fputil::sqrt<float>(x_inv_sq);
+
+  // Degree 14 polynomial of atan(1/|x|) generated using Sollya with command :
+  // > display = hexadecimal ;
+  // > P = fpminimax(atan(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|SG, SG, SG...
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lntue wrote:

Polynomial is the same as the other branch.  Create an array and use it in both cases.

https://github.com/llvm/llvm-project/pull/184019