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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,162 @@ | ||
| //====================================================================================================================== | ||
| /* | ||
| Kyosu - Complex Without Complexes | ||
| Copyright : KYOSU Contributors & Maintainers | ||
| SPDX-License-Identifier: BSL-1.0 | ||
| */ | ||
| //====================================================================================================================== | ||
| #pragma once | ||
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| namespace kyosu::_ | ||
| { | ||
| ///////////////////////////////// | ||
| // contains implementations of | ||
| // sph_bessel_h1_0 | ||
| // sph_bessel_h1_1 | ||
| // sph_bessel_h2_0 | ||
| // sph_bessel_h2_1 | ||
| // sph_bessel_h1n | ||
| // sph_bessel_h2n | ||
| // sph_bessel_h12n | ||
| ///////////////////////////////// | ||
| // utilities | ||
| // sb_h1_0 | ||
| // sb_h1_1 | ||
| // sb_h2_0 | ||
| // sb_h2_1 | ||
| // sb_h1n | ||
| // sb_h2n | ||
| // sb_h12n | ||
| //////////////////////////////// | ||
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| //===------------------------------------------------------------------------------------------- | ||
| //===------------------------------------------------------------------------------------------- | ||
| // spherical bessel of the third kind | ||
| //===------------------------------------------------------------------------------------------- | ||
| //===------------------------------------------------------------------------------------------- | ||
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| template<eve::integral_scalar_value N, typename Z> KYOSU_FORCEINLINE | ||
| auto sb_h2n(N n, Z z) noexcept | ||
| { | ||
| auto imzlt0 = eve::is_ltz(imag(z)); | ||
| z = if_else(imzlt0, z, -z); | ||
| using u_t = eve::underlying_type_t<Z>; | ||
| auto i = complex(u_t(0), u_t(1)); | ||
| auto rz = rec(z); | ||
| auto miz = mulmi(z); | ||
| auto h0 = if_else(imzlt0, i*exp(miz), -i*exp(-miz))*rz; | ||
| if(n == 0) return h0; | ||
| auto h1 = if_else(imzlt0, (rz+i),(rz-i))*h0 ; | ||
| if(n == 1) return if_else(imzlt0,h1, -h1); | ||
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| auto h2 = h1; | ||
| for(int i=1; i < n; ++i) | ||
| { | ||
| auto f = (2*i+1)*rz; | ||
| h2 = f*h1-h0; | ||
| h0 = h1; | ||
| h1 = h2; | ||
| } | ||
| return if_else(imzlt0, h2, eve::sign_alternate(u_t(n))*h2); | ||
| } | ||
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| template<eve::integral_scalar_value N, typename Z> KYOSU_FORCEINLINE | ||
| auto sb_h1n(N n, Z z) noexcept | ||
| { | ||
| using u_t = eve::underlying_type_t<Z>; | ||
| return eve::sign_alternate(u_t(n))*sph_bessel_h2n(n, -z); | ||
| } | ||
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| template<typename Z> KYOSU_FORCEINLINE | ||
| auto sb_h2_0(Z z) noexcept | ||
| { | ||
| return sb_h2n(0, z); | ||
| } | ||
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| template<typename Z> KYOSU_FORCEINLINE | ||
| auto sb_h2_1(Z z) noexcept | ||
| { | ||
| return sb_h2n(1, z); | ||
| } | ||
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| template<typename Z> KYOSU_FORCEINLINE | ||
| auto sb_h1n(int n, Z z) noexcept | ||
| { | ||
| using u_t = eve::underlying_type_t<Z>; | ||
| return eve::sign_alternate(u_t(n))*sph_bessel_h2n(n, -z); | ||
| } | ||
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| template<typename Z> KYOSU_FORCEINLINE | ||
| auto sb_h1_0(Z z) noexcept | ||
| { | ||
| return sb_h2_0(-z); | ||
| } | ||
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| template<typename Z> KYOSU_FORCEINLINE | ||
| auto sb_h1_1(Z z) noexcept | ||
| { | ||
| return -sb_h2_1(-z); | ||
| } | ||
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| //===------------------------------------------------------------------------------------------- | ||
| // sph_bessel_h1n | ||
| //===------------------------------------------------------------------------------------------- | ||
| template<typename Z> | ||
| auto dispatch(eve::tag_of<kyosu::sph_bessel_h1n>, int n, Z z) noexcept | ||
| { | ||
| if constexpr(concepts::complex<Z>) | ||
| { | ||
| EVE_ASSERT(n >= 0, "spherical functions need positive order"); | ||
| return sb_h1n(n, z); | ||
| } | ||
| else | ||
| { | ||
| return cayley_extend_rev(sph_bessel_h1n, n, z); | ||
| } | ||
| } | ||
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| template<typename Z> | ||
| auto dispatch(eve::tag_of<kyosu::sph_bessel_h1_0>, Z z) noexcept | ||
| { | ||
| return sb_h1_0(z); | ||
| } | ||
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| template<typename Z> | ||
| auto dispatch(eve::tag_of<kyosu::sph_bessel_h1_1>, Z z) noexcept | ||
| { | ||
| return sb_h1_1(z); | ||
| } | ||
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| //===------------------------------------------------------------------------------------------- | ||
| // sph_bessel_h2n | ||
| //===------------------------------------------------------------------------------------------- | ||
| template<eve::integral_scalar_value N, typename Z> | ||
| auto dispatch(eve::tag_of<kyosu::sph_bessel_h2n>, N n, Z z) noexcept | ||
| { | ||
| EVE_ASSERT(n >= 0, "spherical functions need positive order"); | ||
| if constexpr(concepts::complex<Z>) | ||
| { | ||
| return sb_h2n(n, z); | ||
| } | ||
| else | ||
| { | ||
| return cayley_extend_rev(sph_bessel_h2n, n, z); | ||
| } | ||
| } | ||
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| template<typename Z> | ||
| auto dispatch(eve::tag_of<kyosu::sph_bessel_h2_0>, Z z) noexcept | ||
| { | ||
| return sb_h2n(0, z); | ||
| } | ||
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| template<typename Z> | ||
| auto dispatch(eve::tag_of<kyosu::sph_bessel_h2_1>, Z z) noexcept | ||
| { | ||
| return sb_h2n(1, z); | ||
| } | ||
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| } |
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