Cayley/bessel4

include/kyosu/functions.hpp

@@ -54,6 +54,13 @@
 #include <kyosu/functions/cyl_bessel_j1.hpp>
 #include <kyosu/functions/cyl_bessel_jn.hpp>
 #include <kyosu/functions/cyl_bessel_y0.hpp>
+#include <kyosu/functions/cyl_bessel_y1.hpp>
+#include <kyosu/functions/cyl_bessel_yn.hpp>
+#include <kyosu/functions/cyl_bessel_h1n.hpp>
+#include <kyosu/functions/cyl_bessel_h2n.hpp>
+#include <kyosu/functions/cyl_bessel_k0.hpp>
+#include <kyosu/functions/cyl_bessel_k1.hpp>
+#include <kyosu/functions/cyl_bessel_kn.hpp>
 #include <kyosu/functions/dec.hpp>
 #include <kyosu/functions/deta.hpp>
 #include <kyosu/functions/digamma.hpp>

include/kyosu/functions/cyl_bessel_h1n.hpp

@@ -0,0 +1,77 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright: KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/bessel.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_cyl_bessel_h1n: eve::elementwise
+  {
+    using callable_tag_type = callable_cyl_bessel_h1n;
+
+    KYOSU_DEFERS_CALLABLE(cyl_bessel_h1n_);
+
+    template<eve::ordered_value N, eve::floating_ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, N n, T const& z) noexcept
+    {
+      using e_t = eve::element_type_t<T>;
+      return complex(cyl_bessel_jn(n, z), cyl_bessel_yn(n, z));
+    }
+
+    template<typename N, typename T>
+    KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1) const noexcept
+    -> decltype(eve::tag_invoke(*this, target0, target1))
+    {
+      return eve::tag_invoke(*this, target0, target1);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_cyl_bessel_h1n(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @brief Computes the Bessel/Hankel functions of the third kind ,
+//!   \f$ H_n^{(1)}\f$.
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h1n(int n, T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto cyl_bessel_h1n(int n, T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z`: Value to process.
+//!
+//!   **Return value**
+//!
+//!     * return  \f$H_n^{(1)}(z)\f$.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/cyl_bessel_h1n.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_cyl_bessel_h1n cyl_bessel_h1n = {};
+}

include/kyosu/functions/cyl_bessel_h2n.hpp

@@ -0,0 +1,77 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright: KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/bessel.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_cyl_bessel_h2n: eve::elementwise
+  {
+    using callable_tag_type = callable_cyl_bessel_h1n;
+
+    KYOSU_DEFERS_CALLABLE(cyl_bessel_h2n_);
+
+    template<eve::ordered_value N, eve::floating_ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, N n, T const& z) noexcept
+    {
+      using e_t = eve::element_type_t<T>;
+      return complex(cyl_bessel_jn(n, z), -cyl_bessel_yn(n, z));
+    }
+
+    template<typename N, typename T>
+    KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1) const noexcept
+    -> decltype(eve::tag_invoke(*this, target0, target1))
+    {
+      return eve::tag_invoke(*this, target0, target1);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_cyl_bessel_h2n(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @brief Computes the Bessel/Hankel functions of the third kind ,
+//!   \f$ H_n^{(2)}\f$.
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h2n(int n, T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto cyl_bessel_h2n(int n, T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z`: Value to process.
+//!
+//!   **Return value**
+//!
+//!     * return  \f$H_n^{(2)}(z)\f$.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/cyl_bessel_h2n.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_cyl_bessel_h2n cyl_bessel_h2n = {};
+}

include/kyosu/functions/cyl_bessel_k0.hpp

@@ -0,0 +1,73 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright: KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/bessel.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_cyl_bessel_k0: eve::elementwise
+  {
+    using callable_tag_type = callable_cyl_bessel_k0;
+
+    KYOSU_DEFERS_CALLABLE(cyl_bessel_k0_);
+
+    template<eve::floating_ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept { return eve::cyl_bessel_k0(v); }
+
+    template<typename T>
+    KYOSU_FORCEINLINE auto operator()(T const& target) const noexcept -> decltype(eve::tag_invoke(*this, target))
+    {
+      return eve::tag_invoke(*this, target);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_cyl_bessel_k0(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var cyl_bessel_k0
+//!   @brief Computes  the Bessel function of the second kind,
+//!   \f$ K_0(x)\f$ extended to the complex plane and cayley_dickson values.
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_k0(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto cyl_bessel_k0(T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z`: Value to process.
+//!
+//!   **Return value**
+//!
+//!     * return the cylindrical \f$K_0(z)\f$.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/cyl_bessel_k0.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_cyl_bessel_k0 cyl_bessel_k0 = {};
+}

include/kyosu/functions/cyl_bessel_k1.hpp

@@ -0,0 +1,73 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright: KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/bessel.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_cyl_bessel_k1: eve::elementwise
+  {
+    using callable_tag_type = callable_cyl_bessel_k1;
+
+    KYOSU_DEFERS_CALLABLE(cyl_bessel_k1_);
+
+    template<eve::floating_ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept { return eve::cyl_bessel_k1(v); }
+
+    template<typename T>
+    KYOSU_FORCEINLINE auto operator()(T const& target) const noexcept -> decltype(eve::tag_invoke(*this, target))
+    {
+      return eve::tag_invoke(*this, target);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_cyl_bessel_k1(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var cyl_bessel_k1
+//!   @brief Computes  the Bessel function of the second kind,
+//!   \f$ K_1(x)\f$ extended to the complex plane and cayley_dickson values.
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_k1(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto cyl_bessel_k1(T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z`: Value to process.
+//!
+//!   **Return value**
+//!
+//!     * return the cylindrical \f$K_1(z)\f$.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/cyl_bessel_k1.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_cyl_bessel_k1 cyl_bessel_k1 = {};
+}

include/kyosu/functions/cyl_bessel_kn.hpp

@@ -0,0 +1,79 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright: KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/bessel.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_cyl_bessel_kn: eve::elementwise
+  {
+    using callable_tag_type = callable_cyl_bessel_kn;
+
+    KYOSU_DEFERS_CALLABLE(cyl_bessel_kn_);
+
+    template<eve::ordered_value N, eve::floating_ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, N n, T const& v) noexcept { return eve::cyl_bessel_kn(n, v); }
+
+    template<typename N, typename T>
+    KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1) const noexcept
+    -> decltype(eve::tag_invoke(*this, target0, target1))
+    {
+      return eve::tag_invoke(*this, target0, target1);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_cyl_bessel_kn(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @brief Computes 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$.
+//!
+//!   In the real field, it is the solution of \f$ 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$1\f$.
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T>                                constexpr auto cyl_bessel_kn(int n, T z) noexcept;
+//!      template<eve::floating_ordered_value N, eve::floating_ordered_value T>     constexpr T    cyl_bessel_kn(N n, T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z`: Value to process.
+//!
+//!   **Return value**
+//!
+//!     * return the cylindrical \f$J_n(z)\f$.
+//!
+//!  @warning Up to now the cayley_dickson versions have only been imlemented dor scalar int values of n.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/cyl_bessel_kn.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_cyl_bessel_kn cyl_bessel_kn = {};
+}