some docs impoved + doc tests

include/kyosu/functions/cyl_bessel_h1.hpp

@@ -58,7 +58,7 @@ namespace kyosu
 //! @addtogroup functions
 //! @{
 //!   @var cyl_bessel_h1
-//!   @brief Computes the Bessel functions of the third  kind \f$H^{(1)\f$ and \f$H^{(2)}\f$,
+//!   @brief Computes the Bessel functions of the third  kind  \f$H^{(1)}\f$,
 //!
 //!   @code
 //!   #include <kyosu/functions.hpp>
@@ -87,16 +87,16 @@ namespace kyosu
 //!
 //!     * `nu`: scalar floating order of the function.
 //!     * `z`: Value to process.
-//!     * `h1s: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively)
+//!     * `h1s: range able to contain `n = int(abs(nu))+1` complex values (of type complex_t<T> or Z respectively)
 //!
 //!   **Return value**
 //!
-//!     * returns  \f$\{H^{(1)}_\nu(z)\}f$.
+//!     * returns  \f$H^{(1)}_\nu(z)\f$.
 //!
 //!   *Ouput values
 //!
-//!     * on output (if present) h1s contains the values of   \f$((H^{(1)}_{\vu_0+i})_{i = 0\cdot n}\f$;
-//!       where \f$\vu_0\f$ is the fractional part of $\vu\f$
+//!     * on output (if present) h1s contains the values of   \f$ (H^{(1)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \f$;
+//!       where \f$ \nu_0 \f$ is the fractional part of \f$\nu\f$ and \f$\epsilon\f$ is the sign of  \f$ \nu\f$.
 //!
 //!  @groupheader{Example}
 //!

include/kyosu/functions/cyl_bessel_h12.hpp

@@ -44,7 +44,7 @@ namespace kyosu
 //! @addtogroup functions
 //! @{
 //!   @var cyl_bessel_h12
-//!   @brief Computes the Bessel functions of the third  kind \f$H^{(1)\f$ and \f$H^{(2)}\f$,
+//!   @brief Computes the Bessel functions of the third  kind \f$ H^{(1)} \f$ and \f$ H^{(2)} \f$,
 //!
 //!   @code
 //!   #include <kyosu/functions.hpp>
@@ -67,17 +67,17 @@ namespace kyosu
 //!
 //!     * `n`: scalar floating order of the function.
 //!     * `z`: Value to process.
-//!     * `h1s: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively)
-//!     * `h2s: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively)
+//!     * `h1s: range able to contain  `n = int(abs(nu))+1` complex values (of type complex_t<T> or Z respectively)
+//!     * `h2s: range able to contain  `n = int(abs(nu))+1` complex values (of type complex_t<T> or Z respectively)
 //!
 //!   **Return value**
 //!
-//!     * returns the kumi pair \f$\{J_\nu(z), Y_\nu(z)\}f$.
+//!     * returns the kumi pair \f$ \{ H^{(1)}_\nu(z). H^{(2)}_\nu(z) \} \f$.
 //!
 //!   *Ouput values
 //!
-//!     * on output h1s contains the values of   \f$((H^{1}_{\vu_0+i})_{i = 0\cdot \vu}\f$, where \f$\vu_0\f$ is the fractional part of $\vu\f$
-//!     * on output h2s contains the values of   \f$((H^{2}_{\vu_0+i})_{i = 0\cdot \vu}\f$, where \f$\vu_0\f$ is the fractional part of $\vu\f$
+//!     * on output (if present) h1s and h2s contains the values of   \f$ (H^{(1\|2)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \f$
+//!       respectively,  where \f$ \nu_0 \f$ is the fractional part of \f$\nu\f$ and \f$\epsilon\f$ is the sign of  \f$ \nu\f$.
 //!
 //!  @groupheader{Example}
 //!

include/kyosu/functions/cyl_bessel_h1_0.hpp

@@ -21,7 +21,7 @@ namespace kyosu::tags
     template<eve::floating_ordered_value T>
     static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
     {
-      auto fn = callable_cyl_bessel_h1_0{}; 
+      auto fn = callable_cyl_bessel_h1_0{};
       return fn(complex(v));
     }
 
@@ -55,7 +55,7 @@ namespace kyosu
 //!   namespace kyosu
 //!   {
 //!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h1_0(T z) noexcept;
-//!      template<eve::floating_ordered_value T>     constexpr T    cyl_bessel_h1_0(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto cyl_bessel_h1_0(T z) noexcept;
 //!   }
 //!   @endcode
 //!

include/kyosu/functions/cyl_bessel_h1_1.hpp

@@ -55,7 +55,7 @@ namespace kyosu
 //!   namespace kyosu
 //!   {
 //!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h1_1(T z) noexcept;
-//!      template<eve::floating_ordered_value T>     constexpr T    cyl_bessel_h1_1(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto cyl_bessel_h1_1(T z) noexcept;
 //!   }
 //!   @endcode
 //!

include/kyosu/functions/cyl_bessel_h2.hpp

@@ -58,7 +58,7 @@ namespace kyosu
 //! @addtogroup functions
 //! @{
 //!   @var cyl_bessel_h2
-//!   @brief Computes the Bessel functions of the third  kind \f$H^{(2)\f$ and \f$H^{(2)}\f$,
+//!   @brief Computes the Bessel functions of the third  kind \f$ H^{(2)}_\nu \f$,
 //!
 //!   @code
 //!   #include <kyosu/functions.hpp>
@@ -87,16 +87,16 @@ namespace kyosu
 //!
 //!     * `nu`: scalar floating order of the function.
 //!     * `z`: Value to process.
-//!     * `h2s: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively)
+//!     * `h2s: range able to contain `n = int(abs(nu))+1` complex values (of type complex_t<T> or Z respectively)
 //!
 //!   **Return value**
 //!
-//!     * returns  \f$\{H^{(2)}_\nu(z)\}f$.
+//!     * returns  \f$H^{(2)}_\nu(z)\f$.
 //!
 //!   *Ouput values
 //!
-//!     * on output (if present) h2s contains the values of   \f$((H^{(2)}_{\vu_0+i})_{i = 0\cdot n}\f$;
-//!       where \f$\vu_0\f$ is the fractional part of $\vu\f$
+//!     * on output (if present) h2s contains the values of   \f$ (H^{(2)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \f$, 
+//!       where \f$ \nu_0 \f$ is the fractional part of \f$\nu\f$ and \f$\epsilon\f$ is the sign of  \f$ \nu\f$.
 //!
 //!  @groupheader{Example}
 //!

include/kyosu/functions/cyl_bessel_i.hpp

@@ -73,19 +73,31 @@ namespace kyosu
 //!      constexpr auto cyl_bessel_i(N nu, T z) noexcept;
 //!
 //!      template<eve::floating_ordered_value, eve::floating_ordered_value T>
-//!      constexpr T    cyl_bessel_i(N n, T z) noexcept;
+//!      constexpr T    cyl_bessel_i(N nu, T z) noexcept;
+//!
+//!      template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T, Range R>
+//!      constexpr auto cyl_bessel_i(N nu, T z, R & is) noexcept;
+//!
+//!      template<eve::floating_ordered_value, eve::floating_ordered_value T, Range R>
+//!      constexpr T    cyl_bessel_i(N nu, T z, R& is) noexcept;
 //!   }
 //!   @endcode
 //!
 //!   **Parameters**
 //!
 //!     * `nu`: order of the function.
 //!     * `z`: Value to process.
+//!     * `is`: Ouput range able to contain `n = int(abs(nu))+1` complex values (of type complex_t<T> or Z respectively)
 //!
 //!   **Return value**
 //!
 //!     * returns \f$I_\nu(z)\f$.
 //!
+//!   *Ouput values
+//!
+//!     * on output (if present) 1s contains the values of   \f$ (I^{(1)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \f$;
+//!       where \f$ \nu_0 \f$ is the fractional part of \f$\nu\f$ and \f$\epsilon\f$ is the sign of  \f$ \nu\f$.
+//!
 //!  @groupheader{Example}
 //!
 //!  @godbolt{doc/cyl_bessel_i.cpp}

include/kyosu/functions/sph_bessel_h1_0.hpp

@@ -1,4 +1,4 @@
-//======================================================================================================================
+ //======================================================================================================================
 /*
   Kyosu - Complex Without Complexes
   Copyright: KYOSU Contributors & Maintainers

test/doc/cyl_bessel_h1.cpp

@@ -0,0 +1,20 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  auto v = 0.0;
+  std::cout << "z                    " << z << std::endl;
+  for(int n=0; n <= 3; ++n)
+  {
+    auto h1 = kyosu::cyl_bessel_h1(v, z);
+    std::cout << "v                  " << v  << std::endl;
+    std::cout << "yl_bessel_h1(v, z) " << h1 << std::endl;
+    v = v+0.25;
+  }
+  return 0;
+}

test/doc/cyl_bessel_h12.cpp

@@ -0,0 +1,20 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  auto v = 3.3;
+  std::cout << "z                    " << z << std::endl;
+  std::vector<decltype(z)> h1(4), h2(4);
+  kyosu::cyl_bessel_h12(v, z, h1, h2);
+  for(int n=0; n <= 3; ++n)
+  {
+    std::cout << "h1[" << n << "] = " << h1[n] << std::endl;
+    std::cout << "h2[" << n << "] = " << h2[n] << std::endl;
+  }
+  return 0;
+}

test/doc/cyl_bessel_h1_0.cpp

@@ -0,0 +1,13 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  std::cout << "z " << z << std::endl;
+  std::cout << "cyl_bessel_h1_0(z) " << kyosu::cyl_bessel_h1_0(z) << std::endl;
+  return 0;
+}

test/doc/cyl_bessel_h1_1.cpp

@@ -0,0 +1,13 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  std::cout << "z " << z << std::endl;
+  std::cout << "cyl_bessel_h1_1(z) " << kyosu::cyl_bessel_h1_1(z) << std::endl;
+  return 0;
+}

test/doc/cyl_bessel_h2.cpp

@@ -0,0 +1,20 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  auto v = 0.0;
+  std::cout << "z                    " << z << std::endl;
+  for(int n=0; n <= 3; ++n)
+  {
+    auto h2 = kyosu::cyl_bessel_h2(v, z);
+    std::cout << "v                  " << v  << std::endl;
+    std::cout << "yl_bessel_h2(v, z) " << h2 << std::endl;
+    v = v+0.25;
+  }
+  return 0;
+}

test/doc/cyl_bessel_h2_0.cpp

@@ -0,0 +1,13 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  std::cout << "z " << z << std::endl;
+  std::cout << "cyl_bessel_h2_0(z) " << kyosu::cyl_bessel_h2_0(z) << std::endl;
+  return 0;
+}

test/doc/cyl_bessel_h2_1.cpp

@@ -0,0 +1,13 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  std::cout << "z " << z << std::endl;
+  std::cout << "cyl_bessel_h2_1(z) " << kyosu::cyl_bessel_h2_1(z) << std::endl;
+  return 0;
+}

test/doc/cyl_bessel_i.cpp

@@ -0,0 +1,19 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  auto v = 3.3;
+  std::cout << "z                    " << z << std::endl;
+  std::vector<decltype(z)> is(4);
+  kyosu::cyl_bessel_i(v, z, is);
+  for(int n=0; n <= 3; ++n)
+  {
+    std::cout << "is[" << n << "] = " << is[n] << std::endl;
+  }
+  return 0;
+}

test/doc/cyl_bessel_j.cpp

@@ -0,0 +1,19 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  auto v = 3.3;
+  std::cout << "z                    " << z << std::endl;
+  std::vector<decltype(z)> js(4);
+  kyosu::cyl_bessel_j(v, z, js);
+  for(int n=0; n <= 3; ++n)
+  {
+    std::cout << "js[" << n << "] = " << js[n] << std::endl;
+  }
+  return 0;
+}

test/doc/cyl_bessel_k.cpp

@@ -0,0 +1,19 @@
+#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+
+int main()
+{
+  std::cout.precision(16);
+  using w_t = eve::wide<double, eve::fixed<2>>;
+  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
+  auto v = 3.3;
+  std::cout << "z                    " << z << std::endl;
+  std::vector<decltype(z)> ks(4);
+  kyosu::cyl_bessel_k(v, z, ks);
+  for(int n=0; n <= 3; ++n)
+  {
+    std::cout << "ks[" << n << "] = " << ks[n] << std::endl;
+  }
+  return 0;
+}