1 #ifndef STAN_MATH_PRIM_FUN_ATANH_HPP
2 #define STAN_MATH_PRIM_FUN_ATANH_HPP
3 
4 #include <stan/math/prim/core.hpp>
5 #include <stan/math/prim/err.hpp>
6 #include <stan/math/prim/meta.hpp>
7 #include <stan/math/prim/fun/copysign.hpp>
8 #include <stan/math/prim/fun/is_nan.hpp>
9 #include <stan/math/prim/fun/log.hpp>
10 #include <stan/math/prim/functor/apply_scalar_unary.hpp>
11 #include <cmath>
12 #include <complex>
13 
14 namespace stan {
15 namespace math {
16 
17 /**
18  * Return the inverse hyperbolic tangent of the specified value.
19  * An argument of -1 returns negative infinity and an argument of 1
20  * returns infinity.
21  * Returns nan for nan argument.
22  *
23  * @param[in] x Argument.
24  * @return Inverse hyperbolic tangent of the argument.
25  * @throw std::domain_error If argument is not in [-1, 1].
26  */
atanh(double x)27 inline double atanh(double x) {
28   if (is_nan(x)) {
29     return x;
30   } else {
31     check_bounded("atanh", "x", x, -1.0, 1.0);
32     return std::atanh(x);
33   }
34 }
35 
36 /**
37  * Integer version of atanh.
38  *
39  * @param[in] x Argument.
40  * @return Inverse hyperbolic tangent of the argument.
41  * @throw std::domain_error If argument is less than 1.
42  */
atanh(int x)43 inline double atanh(int x) {
44   check_bounded("atanh", "x", x, -1, 1);
45   return std::atanh(x);
46 }
47 
48 /**
49  * Structure to wrap atanh() so it can be vectorized.
50  */
51 struct atanh_fun {
52   /**
53    * Return the inverse hyperbolic tangent of the specified argument.
54    *
55    * @tparam T type of argument
56    * @param x argument
57    * @return Inverse hyperbolic tangent of the argument.
58    */
59   template <typename T>
funstan::math::atanh_fun60   static inline T fun(const T& x) {
61     return atanh(x);
62   }
63 };
64 
65 /**
66  * Return the elementwise application of <code>atanh()</code> to
67  * specified argument container.  The return type promotes the
68  * underlying scalar argument type to double if it is an integer,
69  * and otherwise is the argument type.
70  *
71  * @tparam T type of container
72  * @param x container
73  * @return Elementwise atanh of members of container.
74  */
75 template <
76     typename T, require_not_var_matrix_t<T>* = nullptr,
77     require_all_not_nonscalar_prim_or_rev_kernel_expression_t<T>* = nullptr>
atanh(const T & x)78 inline auto atanh(const T& x) {
79   return apply_scalar_unary<atanh_fun, T>::apply(x);
80 }
81 
82 namespace internal {
83 /**
84  * Return the hyperbolic arc tangent of the complex argument.
85  *
86  * @tparam V value type of argument
87  * @param[in] z argument
88  * @return hyperbolic arc tangent of the argument
89  */
90 template <typename V>
complex_atanh(const std::complex<V> & z)91 inline std::complex<V> complex_atanh(const std::complex<V>& z) {
92   std::complex<double> y_d = atanh(value_of_rec(z));
93   V one(1);
94   auto y = 0.5 * (log(one + z) - log(one - z));
95   return copysign(y, y_d);
96 }
97 }  // namespace internal
98 
99 }  // namespace math
100 }  // namespace stan
101 
102 #endif
103