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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,34 @@ | ||
| //====================================================================================================================== | ||
| /* | ||
| Kyosu - Complex Without Complexes | ||
| Copyright : KYOSU Contributors & Maintainers | ||
| SPDX-License-Identifier: BSL-1.0 | ||
| */ | ||
| //====================================================================================================================== | ||
| #pragma once | ||
|
|
||
| auto cayley_extend(auto f, auto z, auto... rs) | ||
| { | ||
| auto p = kyosu::pure(z); | ||
| auto az = kyosu::abs(p); | ||
| auto c = f(kyosu::complex(kyosu::real(z), az), rs...); | ||
| return kyosu::real(c) + kyosu::ipart(c)*kyosu::sign(p); | ||
| } | ||
|
|
||
| auto cayley_extend_rev(auto f, auto z1, auto z2) | ||
| { | ||
| auto p = kyosu::pure(z2); | ||
| auto az2 = kyosu::abs(p); | ||
| auto c = f(z1, kyosu::complex(kyosu::real(z2), az2)); | ||
| return kyosu::real(c) + kyosu::ipart(c)*kyosu::sign(p); | ||
| } | ||
|
|
||
| auto cayley_extend2(auto f, auto z, auto... rs) | ||
| { | ||
| auto p = kyosu::pure(z); | ||
| auto az = kyosu::abs(p); | ||
| auto [c1, c2] = f(kyosu::complex(kyosu::real(z), az), rs...); | ||
| auto s = kyosu::sign(p); | ||
| return kumi::tuple{ kyosu::real(c1) + kyosu::ipart(c1)*s | ||
| , kyosu::real(c2) + kyosu::ipart(c2)*s}; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,76 @@ | ||
| //====================================================================================================================== | ||
| /* | ||
| 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_i0: eve::elementwise | ||
| { | ||
| using callable_tag_type = callable_cyl_bessel_i0; | ||
|
|
||
| KYOSU_DEFERS_CALLABLE(cyl_bessel_i0_); | ||
|
|
||
| template<eve::floating_ordered_value T> | ||
| static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept { return eve::cyl_bessel_i0(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_i0(T&&...)> operator()(T&&... x) const | ||
| requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete; | ||
| }; | ||
| } | ||
|
|
||
| namespace kyosu | ||
| { | ||
| //====================================================================================================================== | ||
| //! @addtogroup functions | ||
| //! @{ | ||
| //! @var cyl_bessel_i0 | ||
| //! @brief Computes the Bessel function of the first kind, | ||
| //! \f$ J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau) | ||
| //! \,\mathrm {d} \tau \f$ extended to the complex plane and cayley_dickson values. | ||
| //! | ||
| //! In the real field, it is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$. | ||
| //! | ||
| //! @code | ||
| //! #include <kyosu/functions.hpp> | ||
| //! @endcode | ||
| //! | ||
| //! @groupheader{Callable Signatures} | ||
| //! | ||
| //! @code | ||
| //! namespace kyosu | ||
| //! { | ||
| //! template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_i0(T z) noexcept; | ||
| //! template<eve::floating_ordered_value T> constexpr T cyl_bessel_i0(T z) noexcept; | ||
| //! } | ||
| //! @endcode | ||
| //! | ||
| //! **Parameters** | ||
| //! | ||
| //! * `z`: Value to process. | ||
| //! | ||
| //! **Return value** | ||
| //! | ||
| //! * return the cylindrical \f$J_0(z)\f$. | ||
| //! | ||
| //! @groupheader{Example} | ||
| //! | ||
| //! @godbolt{doc/cyl_bessel_i0.cpp} | ||
| //! @} | ||
| //====================================================================================================================== | ||
| inline constexpr tags::callable_cyl_bessel_i0 cyl_bessel_i0 = {}; | ||
| } |
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