Function Atanh

tensorflow/compiler/xla/client/lib/math.cc:1232–1250

atanh(x) = 0.5 * log((1 + x) / (1 - x)) if abs(x) <= 1 atanh(x) = nan otherwise

// atanh(x) = 0.5 * log((1 + x) / (1 - x)) if abs(x) <= 1
// atanh(x) = nan                          otherwise
XlaOp Atanh(XlaOp x) {
  XlaBuilder* b = x.builder();
  auto do_it = [&](XlaOp x) -> StatusOr<XlaOp> {
    TF_ASSIGN_OR_RETURN(auto shape, b->GetShape(x));
    auto naive_result = (Log1p(x) - Log1p(-x)) * ScalarLike(x, 0.5);

    // TODO(jlebar): For now, we ignore the nan edge case for complex inputs,
    // because we don't yet have exhaustive tests for complex trig functions.
    if (primitive_util::IsComplexType(shape.element_type())) {
      return naive_result;
    }

    auto nan = FullLike(x, std::numeric_limits<float>::quiet_NaN());
    return Select(Gt(Abs(x), ScalarLike(x, 1)), nan, naive_result);
  };
  return DoWithUpcastToF32(x, {BF16}, [&](XlaOp x) {  //
    return b->ReportErrorOrReturn(do_it(x));
  });
}

// Cosh(x) = (e^x + e^-x) / 2
//         = e^(x + log(1/2)) + e^(-x + log(1/2)).