Cleanup documentation for C functions

jfalcou · Jun 27, 2024 · d325269 · d325269
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diff --git a/include/eve/module/bessel/regular/cyl_bessel_i0.hpp b/include/eve/module/bessel/regular/cyl_bessel_i0.hpp
@@ -27,12 +27,12 @@ namespace eve
   //! @addtogroup bessel
   //! @{
   //!   @var cyl_bessel_i0
-  //!   @brief Computes the modified Bessel function of the first kind,
+  //!   @brief `elementwise_callable` object computing the modified Bessel function of the first kind,
   //!   \f$ I_0(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau}\,\mathrm{d}\tau\f$.
   //!
   //!   It is the solution of \f$ x^{2}y''+xy'-x^2y=0\f$ for which \f$ y(0) = 0\f$.
   //!
-  //!   **Defined in header**
+  //!   @groupheader{Header file}
   //!
   //!   @code
   //!   #include <eve/module/bessel.hpp>
@@ -43,21 +43,33 @@ namespace eve
   //!   @code
   //!   namespace eve
   //!   {
-  //!     template<eve::floating_value T> constexpr T cyl_bessel_i0(T x) noexcept;
+  //!      // Regular overload
+  //!      constexpr auto cyl_bessel_i0(floating_value auto x)                          noexcept; // 1
+  //!
+  //!      // Lanes masking
+  //!      constexpr auto cyl_bessel_i0[conditional_expr auto c](floating_value auto x) noexcept; // 2
+  //!      constexpr auto cyl_bessel_i0[logical_value auto m](floating_value auto x)    noexcept; // 2
   //!   }
   //!   @endcode
   //!
   //!   **Parameters**
   //!
   //!     * `x`: positive [floating argument](@ref eve::floating_value).
+  //!     * `c`: [Conditional expression](@ref conditional_expr) masking the operation.
+  //!     * `m`: [Logical value](@ref logical) masking the operation.
   //!
   //!    **Return value**
   //!
-  //!    The value of \f$ \displaystyle I_0(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau}
-  //!    \,\mathrm{d}\tau\f$ is returned.
+  //!      1. The value of \f$ \displaystyle I_0(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau}
+  //!         \,\mathrm{d}\tau\f$ is returned.
+  //!      2. [The operation is performed conditionnaly](@ref conditional).
   //!
-  //!   @groupheader{Example}
+  //!  @groupheader{External references}
+  //!   *  [C++ standard reference](https://en.cppreference.com/w/cpp/numeric/special_functions/cyl_bessel_i)
+  //!   *  [Wikipedia](https://en.wikipedia.org/wiki/Bessel_function)
+  //!   *  [DLMF](https://dlmf.nist.gov/10.25)
   //!
+  //!   @groupheader{Example}
   //!   @godbolt{doc/bessel/regular/cyl_bessel_i0.cpp}
   //! @}
   //================================================================================================

diff --git a/include/eve/module/bessel/regular/cyl_bessel_i1.hpp b/include/eve/module/bessel/regular/cyl_bessel_i1.hpp
@@ -27,12 +27,12 @@ namespace eve
   //! @addtogroup bessel
   //! @{
   //!   @var cyl_bessel_i1
-  //!   @brief Computes  the modified Bessel function of the first kind,
+  //!   @brief `elementwise_callable` object computing the modified Bessel function of the first kind,
   //!   \f$ I_1(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau}\cos\tau\,\mathrm{d}\tau\f$.
   //!
   //!   It is the solution of  \f$ x^{2}y''+xy'-(1+x^2)y=0\f$ for which \f$ y(0) = 0\f$.
   //!
-  //!   **Defined in header**
+  //!   @groupheader{Header file}
   //!
   //!   @code
   //!   #include <eve/module/bessel.hpp>
@@ -43,21 +43,33 @@ namespace eve
   //!   @code
   //!   namespace eve
   //!   {
-  //!     template<eve::floating_value T> constexpr T cyl_bessel_i1(T x) noexcept;
+  //!      // Regular overload
+  //!      constexpr auto cyl_bessel_i1(floating_value auto x)                          noexcept; // 1
+  //!
+  //!      // Lanes masking
+  //!      constexpr auto cyl_bessel_i1[conditional_expr auto c](floating_value auto x) noexcept; // 2
+  //!      constexpr auto cyl_bessel_i1[logical_value auto m](floating_value auto x)    noexcept; // 2
   //!   }
   //!   @endcode
   //!
   //!   **Parameters**
   //!
-  //!   * `x` : [Floating argument](@ref eve::floating_value).
+  //!     * `x`: [Floating argument](@ref eve::floating_value).
+  //!     * `c`: [Conditional expression](@ref conditional_expr) masking the operation.
+  //!     * `m`: [Logical value](@ref logical) masking the operation.
   //!
   //!   **Return value**
   //!
-  //!   The value of  \f$ \displaystyle I_1(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau}
-  //!   \cos\tau\,\mathrm{d}\tau\f$ is returned.
+  //!      1. The value of  \f$ \displaystyle I_1(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau}
+  //!        \cos\tau\,\mathrm{d}\tau\f$ is returned.
+  //!      2. [The operation is performed conditionnaly](@ref conditional).
   //!
-  //!   @groupheader{Example}
+  //!  @groupheader{External references}
+  //!   *  [C++ standard reference](https://en.cppreference.com/w/cpp/numeric/special_functions/cyl_bessel_i)
+  //!   *  [Wikipedia](https://en.wikipedia.org/wiki/Bessel_function)
+  //!   *  [DLMF](https://dlmf.nist.gov/10.25)
   //!
+  //!   @groupheader{Example}
   //!   @godbolt{doc/bessel/regular/cyl_bessel_i1.cpp}
   //! @}
   //================================================================================================

diff --git a/include/eve/module/bessel/regular/cyl_bessel_in.hpp b/include/eve/module/bessel/regular/cyl_bessel_in.hpp
@@ -28,13 +28,13 @@ namespace eve
   //! @addtogroup bessel
   //! @{
   //!   @var cyl_bessel_in
-  //!   @brief Computes  the modified Bessel functions of the first kind,
+  //!   @brief `elementwise_callable` object computing the modified Bessel functions of the first kind,
   //!   \f$ I_{n}(x)=\left(\frac12z\right)^n\sum_{k=0}^{\infty}{\frac{(x^2/4)^k}
   //!   {k!\,\Gamma (k+n +1)}}\f$.
   //!
   //!   It is the solution of \f$ x^{2}y''+xy'+(x^2-n^2)y=0\f$ for which \f$ y(0) = 0\f$.
   //!
-  //!   **Defined in header**
+  //!   @groupheader{Header file}
   //!
   //!   @code
   //!   #include <eve/module/bessel.hpp>
@@ -45,20 +45,32 @@ namespace eve
   //!   @code
   //!   namespace eve
   //!   {
-  //!    template< eve::value N, eve::floating_value T >
-  //!    constexpr T cyl_bessel_in(N n, T x) noexcept;
+  //!      // Regular overload
+  //!      constexpr auto cyl_bessel_in(value auto n, floating_value auto x)                          noexcept; // 1
+  //!
+  //!      // Lanes masking
+  //!      constexpr auto cyl_bessel_in[conditional_expr auto c](value auto n, floating_value auto x) noexcept; // 2
+  //!      constexpr auto cyl_bessel_in[logical_value auto m](value auto n, floating_value auto x)    noexcept; // 2
   //!   }
   //!   @endcode
   //!
   //!   **Parameters**
   //!
-  //!     * `n`:  order of the function (non necessarily integral),
+  //!     * `n`: order of the function (non necessarily integral),
   //!     * `x`: [ floating argument](@ref eve::floating_value).
+  //!     * `c`: [Conditional expression](@ref conditional_expr) masking the operation.
+  //!     * `m`: [Logical value](@ref logical) masking the operation.
   //!
   //!   **Return value**
   //!
-  //!   The value of \f$\displaystyle I_{n}(x)=\left(\frac12z\right)^n\sum_{k=0}^{\infty}
-  //!   {\frac{(x^2/4)^k}{k!\,\Gamma (k+n +1)}}\f$ is returned.
+  //!      1. The value of \f$\displaystyle I_{n}(x)=\left(\frac12z\right)^n\sum_{k=0}^{\infty}
+  //!         {\frac{(x^2/4)^k}{k!\,\Gamma (k+n +1)}}\f$ is returned.
+  //!      2. [The operation is performed conditionnaly](@ref conditional).
+  //!
+  //!  @groupheader{External references}
+  //!   *  [C++ standard reference](https://en.cppreference.com/w/cpp/numeric/special_functions/cyl_bessel_i)
+  //!   *  [Wikipedia](https://en.wikipedia.org/wiki/Bessel_function)
+  //!   *  [DLMF](https://dlmf.nist.gov/10.2)
   //!
   //!   @groupheader{Example}
   //!

diff --git a/include/eve/module/bessel/regular/cyl_bessel_j0.hpp b/include/eve/module/bessel/regular/cyl_bessel_j0.hpp
@@ -27,13 +27,13 @@ namespace eve
   //! @addtogroup bessel
   //! @{
   //!   @var cyl_bessel_j0
-  //!   @brief Computes  the Bessel function of the first kind,
+  //!   @brief `elementwise_callable` object computing the Bessel function of the first kind,
   //!   \f$ J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau)
   //!   \,\mathrm {d} \tau \f$.
   //!
   //!   It is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$.
   //!
-  //!   **Defined in header**
+  //!   @groupheader{Header file}
   //!
   //!   @code
   //!   #include <eve/module/bessel.hpp>
@@ -44,21 +44,33 @@ namespace eve
   //!   @code
   //!   namespace eve
   //!   {
-  //!     template<eve::floating_value T> constexpr T cyl_bessel_j0(T x) noexcept;
+  //!      // Regular overload
+  //!      constexpr auto cyl_bessel_j0(floating_value auto x)                          noexcept; // 1
+  //!
+  //!      // Lanes masking
+  //!      constexpr auto cyl_bessel_j0[conditional_expr auto c](floating_value auto x) noexcept; // 2
+  //!      constexpr auto cyl_bessel_j0[logical_value auto m]floating_(value auto x)    noexcept; // 2
   //!   }
   //!   @endcode
   //!
   //!   **Parameters**
   //!
-  //!   * `x` :  [ordered floating argument](@ref eve::floating_value).
+  //!     * `x`: positive [floating argument](@ref eve::floating_value).
+  //!     * `c`: [Conditional expression](@ref conditional_expr) masking the operation.
+  //!     * `m`: [Logical value](@ref logical) masking the operation.
   //!
   //!   **Return value**
   //!
-  //!   The value of \f$ \displaystyle J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau )
-  //!   \,\mathrm {d} \tau \f$ is returned.
+  //!     1. The value of \f$ \displaystyle J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau )
+  //!        \,\mathrm {d} \tau \f$ is returned.
+  //!     2. [The operation is performed conditionnaly](@ref conditional).
   //!
-  //!   @groupheader{Example}
+  //!  @groupheader{External references}
+  //!   *  [C++ standard reference](https://en.cppreference.com/w/cpp/numeric/special_functions/cyl_bessel_i)
+  //!   *  [Wikipedia](https://en.wikipedia.org/wiki/Bessel_function)
+  //!   *  [DLMF](https://dlmf.nist.gov/10.2)
   //!
+  //!   @groupheader{Example}
   //!   @godbolt{doc/bessel/regular/cyl_bessel_j0.cpp}
   //! @}
   //================================================================================================

diff --git a/include/eve/module/bessel/regular/cyl_bessel_j1.hpp b/include/eve/module/bessel/regular/cyl_bessel_j1.hpp
@@ -27,12 +27,12 @@ namespace eve
   //! @addtogroup bessel
   //! @{
   //!   @var cyl_bessel_j1
-  //!   @brief Computes the Bessel function of the first kind,
+  //!   @brief `elementwise_callable` object computing the Bessel function of the first kind,
   //!   \f$ J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )\,\mathrm {d} \tau \f$.
   //!
   //!   It is the solution of \f$ x^{2}y''+xy'+(x^2-1)y=0\f$ for which \f$ y(0) = 0\f$.
   //!
-  //!   **Defined in header**
+  //!   @groupheader{Header file}
   //!
   //!   @code
   //!   #include <eve/module/bessel.hpp>
@@ -43,18 +43,31 @@ namespace eve
   //!   @code
   //!   namespace eve
   //!   {
-  //!     template<eve::floating_value T> constexpr T cyl_bessel_j1(T x) noexcept;
+  //!      // Regular overload
+  //!      constexpr auto cyl_bessel_j1(floating_value auto x)                          noexcept; // 1
+  //!
+  //!      // Lanes masking
+  //!      constexpr auto cyl_bessel_j1[conditional_expr auto c](floating_value auto x) noexcept; // 2
+  //!      constexpr auto cyl_bessel_j1[logical_value auto m](floating_value auto x)    noexcept; // 2
   //!   }
   //!   @endcode
   //!
   //!   **Parameters**
-  //!
-  //!   * `x`: [floating argument](@ref eve::floating_value).
+ //!
+  //!     * `x`: positive [floating argument](@ref eve::floating_value).
+  //!     * `c`: [Conditional expression](@ref conditional_expr) masking the operation.
+  //!     * `m`: [Logical value](@ref logical) masking the operation.
   //!
   //!   **Return value**
   //!
-  //!   The value of \f$ \displaystyle J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )
-  //!   \,\mathrm {d} \tau \f$ is returned.
+  //!     1. The value of \f$ \displaystyle J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )
+  //!       \,\mathrm {d} \tau \f$ is returned.
+  //!     2. [The operation is performed conditionnaly](@ref conditional).
+  //!
+  //!  @groupheader{External references}
+  //!   *  [C++ standard reference](https://en.cppreference.com/w/cpp/numeric/special_functions/cyl_bessel_j)
+  //!   *  [Wikipedia](https://en.wikipedia.org/wiki/Bessel_function)
+  //!   *  [DLMF](https://dlmf.nist.gov/10.2)
   //!
   //!   @groupheader{Example}
   //!

diff --git a/include/eve/module/bessel/regular/cyl_bessel_jn.hpp b/include/eve/module/bessel/regular/cyl_bessel_jn.hpp
@@ -29,14 +29,14 @@ namespace eve
   //! @addtogroup bessel
   //! @{
   //!   @var cyl_bessel_jn
-  //!   @brief Computes the Bessel functions of the first kind,
+  //!   @brief `elementwise_callable` object computing the Bessel functions of the first kind,
   //!   \f$ J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}}
   //!   {\left({x \over 2}\right)}^{2p+n }\f$.
   //!
   //!   It is the solution of \f$ x^{2}y''+xy'+(x^2-n^2)y=0\f$ for which
   //!   \f$ y(0) = 0\f$ if \f$n \ne 0\f$ else \f$1\f$.
   //!
-  //!   **Defined in header**
+  //!   @groupheader{Header file}
   //!
   //!   @code
   //!   #include <eve/module/bessel.hpp>
@@ -47,22 +47,34 @@ namespace eve
   //!   @code
   //!   namespace eve
   //!   {
-  //!     template<eve::value N, eve::floating_value T> constexpr T cyl_bessel_jn(T x) noexcept;
+  //!      // Regular overload
+  //!      constexpr auto cyl_bessel_jn(value auto n, floating_value auto x)                          noexcept; // 1
+  //!
+  //!      // Lanes masking
+  //!      constexpr auto cyl_bessel_jn[conditional_expr auto c](value auto n, floating_value auto x) noexcept; // 2
+  //!      constexpr auto cyl_bessel_jn[logical_value auto m](value auto n, floating_value auto x)    noexcept; // 2
   //!   }
   //!   @endcode
   //!
   //!   **Parameters**
   //!
-  //!   * `n`: order of the function (not necessarily integral)
-  //!   * `x`: [floating argument](@ref eve::floating_value).
+  //!     * `n`: order of the function (not necessarily integral)
+  //!     * `x`: [floating argument](@ref eve::floating_value).
+  //!     * `c`: [Conditional expression](@ref conditional_expr) masking the operation.
+  //!     * `m`: [Logical value](@ref logical) masking the operation.
   //!
   //!   **Return value**
   //!
-  //!   The value of \f$\displaystyle J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}}
-  //!   {\left({x \over 2}\right)}^{2p+n }\f$ is returned.
+  //!      1. The value of \f$\displaystyle J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}}
+  //!        {\left({x \over 2}\right)}^{2p+n }\f$ is returned.
+  //!      2. [The operation is performed conditionnaly](@ref conditional).
   //!
-  //!  @groupheader{Example}
+  //!  @groupheader{External references}
+  //!   *  [C++ standard reference](https://en.cppreference.com/w/cpp/numeric/special_functions/cyl_bessel_j)
+  //!   *  [Wikipedia](https://en.wikipedia.org/wiki/Bessel_function)
+  //!   *  [DLMF](https://dlmf.nist.gov/10.2)
   //!
+  //!  @groupheader{Example}
   //!  @godbolt{doc/bessel/regular/cyl_bessel_jn.cpp}
   //! @}
   //================================================================================================

diff --git a/include/eve/module/bessel/regular/cyl_bessel_k0.hpp b/include/eve/module/bessel/regular/cyl_bessel_k0.hpp
@@ -27,13 +27,13 @@ namespace eve
   //! @addtogroup bessel
   //! @{
   //!   @var cyl_bessel_k0
-  //!   @brief Computes the modified Bessel function of the second kind,
+  //!   @brief `elementwise_callable` object computing the modified Bessel function of the second kind,
   //!   \f$ K_0(x)=\int_{0}^{\infty}\frac{\cos(x\tau)}
   //!   {\sqrt{\tau^2+1}}\,\mathrm{d}\tau\f$.
   //!
   //!   It is a solution \f$ x^{2}y''+xy'-x^2y=0\f$ for which \f$ y(0) = \infty\f$.
   //!
-  //!   **Defined in header**
+  //!   @groupheader{Header file}
   //!
   //!   @code
   //!   #include <eve/module/bessel.hpp>
@@ -44,21 +44,33 @@ namespace eve
   //!   @code
   //!   namespace eve
   //!   {
-  //!     template< eve::floating_value T > constexpr T cyl_bessel_k0(T x) noexcept;
+  //!      // Regular overload
+  //!      constexpr auto cyl_bessel_k0(floating_value auto x)                          noexcept; // 1
+  //!
+  //!      // Lanes masking
+  //!      constexpr auto cyl_bessel_k0[conditional_expr auto c](floating_value auto x) noexcept; // 2
+  //!      constexpr auto cyl_bessel_k0[logical_value auto m](floating_value auto x)    noexcept; // 2
   //!   }
   //!   @endcode
   //!
   //!   **Parameters**
   //!
-  //!   * `x`: [floating argument](@ref eve::floating_value).
+  //!     * `x`: positive [floating argument](@ref eve::floating_value).
+  //!     * `c`: [Conditional expression](@ref conditional_expr) masking the operation.
+  //!     * `m`: [Logical value](@ref logical) masking the operation.
   //!
   //!   **Return value**
   //!
-  //!   The value of \f$ \displaystyle K_0(x)=\int_{0}^{\infty}\frac{\cos(x\tau)}
-  //!   {\sqrt{\tau^2+1}}\,\mathrm{d}\tau\f$ is returned.
+  //!     1. The value of \f$ \displaystyle K_0(x)=\int_{0}^{\infty}\frac{\cos(x\tau)}
+  //!       {\sqrt{\tau^2+1}}\,\mathrm{d}\tau\f$ is returned.
+  //!     2. [The operation is performed conditionnaly](@ref conditional).
   //!
-  //!   @groupheader{Example}
+  //!  @groupheader{External references}
+  //!   *  [C++ standard reference](https://en.cppreference.com/w/cpp/numeric/special_functions/cyl_bessel_i)
+  //!   *  [Wikipedia](https://en.wikipedia.org/wiki/Bessel_function)
+  //!   *  [DLMF](https://dlmf.nist.gov/10.2)
   //!
+  //!   @groupheader{Example}
   //!   @godbolt{doc/bessel/regular/cyl_bessel_k0.cpp}
   //! @}
   //================================================================================================