1 #ifndef STAN_MATH_REV_FUN_LOG2_HPP
2 #define STAN_MATH_REV_FUN_LOG2_HPP
3 
4 #include <stan/math/rev/meta.hpp>
5 #include <stan/math/rev/core.hpp>
6 #include <stan/math/prim/fun/log2.hpp>
7 #include <stan/math/prim/fun/constants.hpp>
8 
9 namespace stan {
10 namespace math {
11 
12 /**
13  * Returns the base 2 logarithm of the specified variable (C99).
14  *
15  * See log2() for the double-based version.
16  *
17  * The derivative is
18  *
19  * \f$\frac{d}{dx} \log_2 x = \frac{1}{x \log 2}\f$.
20  *
21    \f[
22    \mbox{log2}(x) =
23    \begin{cases}
24      \textrm{NaN} & \mbox{if } x < 0 \\
25      \log_2(x) & \mbox{if } x\geq 0 \\[6pt]
26      \textrm{NaN} & \mbox{if } x = \textrm{NaN}
27    \end{cases}
28    \f]
29 
30    \f[
31    \frac{\partial\, \mbox{log2}(x)}{\partial x} =
32    \begin{cases}
33      \textrm{NaN} & \mbox{if } x < 0 \\
34      \frac{1}{x\ln2} & \mbox{if } x\geq 0 \\[6pt]
35      \textrm{NaN} & \mbox{if } x = \textrm{NaN}
36    \end{cases}
37    \f]
38  *
39  * @tparam T Arithmetic or a type inheriting from `EigenBase`.
40  * @param a The variable.
41  * @return Base 2 logarithm of the variable.
42  */
43 template <typename T, require_stan_scalar_or_eigen_t<T>* = nullptr>
log2(const var_value<T> & a)44 inline auto log2(const var_value<T>& a) {
45   return make_callback_var(log2(a.val()), [a](auto& vi) mutable {
46     as_array_or_scalar(a.adj()) += as_array_or_scalar(vi.adj())
47                                    / (LOG_TWO * as_array_or_scalar(a.val()));
48   });
49 }
50 
51 }  // namespace math
52 }  // namespace stan
53 #endif
54