diff --git a/include/kyosu/complex/acospi.hpp b/include/kyosu/complex/acospi.hpp
new file mode 100644
index 00000000..c3bed466
--- /dev/null
+++ b/include/kyosu/complex/acospi.hpp
@@ -0,0 +1,80 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/math.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_acospi : eve::elementwise
+  {
+    using callable_tag_type = callable_acospi;
+
+    KYOSU_DEFERS_CALLABLE(acospi_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_acospi{};
+      return fn(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_acospi(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var acospi
+//!   @brief Computes the arc cosine of the argument times \f$\pi\f$.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto acospi(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto acospi(T z) noexcept;  //2
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//! **Return value**
+//!
+//!   1. a real input z is treated as if to_complex(z) was entered.
+//!
+//!   2. Returns `pi(as(z))*acos(z)`
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/acospi.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_acospi acospi = {};
+}
diff --git a/include/kyosu/complex/acotpi.hpp b/include/kyosu/complex/acotpi.hpp
new file mode 100644
index 00000000..28c0f444
--- /dev/null
+++ b/include/kyosu/complex/acotpi.hpp
@@ -0,0 +1,80 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/math.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_acotpi : eve::elementwise
+  {
+    using callable_tag_type = callable_acotpi;
+
+    KYOSU_DEFERS_CALLABLE(acotpi_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_acotpi{};
+      return fn(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_acotpi(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var acotpi
+//!   @brief Computes the arc cotangent of the argument times \f$\pi\f$.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto acotpi(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto acotpi(T z) noexcept;  //2
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//! **Return value**
+//!
+//!   1. a real input z is treated as if to_complex(z) was entered.
+//!
+//!   2. Returns `pi(as(z))*acot(z)`
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/acotpi.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_acotpi acotpi = {};
+}
diff --git a/include/kyosu/complex/acscpi.hpp b/include/kyosu/complex/acscpi.hpp
new file mode 100644
index 00000000..f260d088
--- /dev/null
+++ b/include/kyosu/complex/acscpi.hpp
@@ -0,0 +1,80 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/math.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_acscpi : eve::elementwise
+  {
+    using callable_tag_type = callable_acscpi;
+
+    KYOSU_DEFERS_CALLABLE(acscpi_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_acscpi{};
+      return fn(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_acscpi(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var acscpi
+//!   @brief Computes the arc cosecant of the argument times \f$\pi\f$.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto acscpi(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto acscpi(T z) noexcept;  //2
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//! **Return value**
+//!
+//!   1. a real input z is treated as if to_complex(z) was entered.
+//!
+//!   2. Returns `pi(as(z))*acsc(z)`
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/acscpi.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_acscpi acscpi = {};
+}
diff --git a/include/kyosu/complex/asecpi.hpp b/include/kyosu/complex/asecpi.hpp
new file mode 100644
index 00000000..9e368c70
--- /dev/null
+++ b/include/kyosu/complex/asecpi.hpp
@@ -0,0 +1,80 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/math.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_asecpi : eve::elementwise
+  {
+    using callable_tag_type = callable_asecpi;
+
+    KYOSU_DEFERS_CALLABLE(asecpi_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_asecpi{};
+      return fn(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_asecpi(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var asecpi
+//!   @brief Computes the arc secant of the argument times \f$\pi\f$.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto asecpi(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto asecpi(T z) noexcept;  //2
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//! **Return value**
+//!
+//!   1. a real input z is treated as if to_complex(z) was entered.
+//!
+//!   2. Returns `pi(as(z))*asec(z)`
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/asecpi.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_asecpi asecpi = {};
+}
diff --git a/include/kyosu/complex/asinpi.hpp b/include/kyosu/complex/asinpi.hpp
new file mode 100644
index 00000000..62156b09
--- /dev/null
+++ b/include/kyosu/complex/asinpi.hpp
@@ -0,0 +1,80 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/math.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_asinpi : eve::elementwise
+  {
+    using callable_tag_type = callable_asinpi;
+
+    KYOSU_DEFERS_CALLABLE(asinpi_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_asinpi{};
+      return fn(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_asinpi(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var asinpi
+//!   @brief Computes the arc sine of the argument times \f$\pi\f$.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto asinpi(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto asinpi(T z) noexcept;  //2
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//! **Return value**
+//!
+//!   1. a real input z is treated as if to_complex(z) was entered.
+//!
+//!   2. Returns `pi(as(z))*asin(z)`
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/asinpi.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_asinpi asinpi = {};
+}
diff --git a/include/kyosu/complex/atanpi.hpp b/include/kyosu/complex/atanpi.hpp
new file mode 100644
index 00000000..2fe9bcdd
--- /dev/null
+++ b/include/kyosu/complex/atanpi.hpp
@@ -0,0 +1,80 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/math.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_atanpi : eve::elementwise
+  {
+    using callable_tag_type = callable_atanpi;
+
+    KYOSU_DEFERS_CALLABLE(atanpi_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_atanpi{};
+      return fn(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_atanpi(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var atanpi
+//!   @brief Computes the arc tangent of the argument times \f$\pi\f$.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto atanpi(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto atanpi(T z) noexcept;  //2
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//! **Return value**
+//!
+//!   1. a real input z is treated as if to_complex(z) was entered.
+//!
+//!   2. Returns `pi(as(z))*atan(z)`
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/atanpi.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_atanpi atanpi = {};
+}
diff --git a/include/kyosu/functions.hpp b/include/kyosu/functions.hpp
index 79d6629e..2197a603 100644
--- a/include/kyosu/functions.hpp
+++ b/include/kyosu/functions.hpp
@@ -75,6 +75,7 @@
 #include <kyosu/functions/pow_abs.hpp>
 #include <kyosu/functions/powm1.hpp>
 #include <kyosu/functions/pure.hpp>
+#include <kyosu/functions/radinpi.hpp>
 #include <kyosu/functions/real.hpp>
 #include <kyosu/functions/rec.hpp>
 #include <kyosu/functions/reldist.hpp>
@@ -105,16 +106,22 @@
 #include <kyosu/complex/acos.hpp>
 #include <kyosu/complex/acosh.hpp>
 #include <kyosu/complex/acot.hpp>
+#include <kyosu/complex/acospi.hpp>
 #include <kyosu/complex/acoth.hpp>
+#include <kyosu/complex/acotpi.hpp>
 #include <kyosu/complex/acsc.hpp>
 #include <kyosu/complex/acsch.hpp>
+#include <kyosu/complex/acscpi.hpp>
 #include <kyosu/complex/arg.hpp>
 #include <kyosu/complex/asec.hpp>
 #include <kyosu/complex/asech.hpp>
+#include <kyosu/complex/asecpi.hpp>
 #include <kyosu/complex/asin.hpp>
 #include <kyosu/complex/asinh.hpp>
+#include <kyosu/complex/asinpi.hpp>
 #include <kyosu/complex/atan.hpp>
 #include <kyosu/complex/atanh.hpp>
+#include <kyosu/complex/atanpi.hpp>
 #include <kyosu/complex/is_imag.hpp>
 #include <kyosu/complex/polar.hpp>
 #include <kyosu/functions/from_polar.hpp>
diff --git a/include/kyosu/functions/radinpi.hpp b/include/kyosu/functions/radinpi.hpp
new file mode 100644
index 00000000..6e828357
--- /dev/null
+++ b/include/kyosu/functions/radinpi.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>
+
+namespace kyosu::tags
+{
+  struct callable_radinpi : eve::elementwise
+  {
+    using callable_tag_type = callable_radinpi;
+
+    KYOSU_DEFERS_CALLABLE(radinpi_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept { return T(0); }//eve::radinpi(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_radinpi(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var radinpi
+//!   @brief Computes the parameter divided by \f$\pi\f$.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T> constexpr as_real_t<T> radinpi(T z) noexcept;
+//!      template<eve::ordered_value T>              constexpr T            radinpi(T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z` : Value to process.
+//!
+//!   **Return value**
+//!
+//!     Returns  argument divided by \f$\pi\f$.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/radinpi.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_radinpi radinpi = {};
+}
diff --git a/include/kyosu/types/impl/arithmetic.hpp b/include/kyosu/types/impl/arithmetic.hpp
index dd44931c..cc11562b 100644
--- a/include/kyosu/types/impl/arithmetic.hpp
+++ b/include/kyosu/types/impl/arithmetic.hpp
@@ -239,4 +239,14 @@ namespace kyosu::_
       return res;
     }
   }
+
+  template<typename C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::radinpi> const&, C c) noexcept
+  {
+    using u_t =  eve::element_type_t<C>;
+    return c*eve::inv_pi(eve::as<u_t>()); ;
+  }
+
+
 }
diff --git a/include/kyosu/types/impl/complex/invtrig.hpp b/include/kyosu/types/impl/complex/invtrig.hpp
index cbc70246..10d88a22 100644
--- a/include/kyosu/types/impl/complex/invtrig.hpp
+++ b/include/kyosu/types/impl/complex/invtrig.hpp
@@ -537,4 +537,47 @@ namespace kyosu::_
   {
     return kyosu::atanh(kyosu::rec(a0));
   }
+
+  template<kyosu::concepts::complex C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::acospi> const&, C const& a0) noexcept
+  {
+    return kyosu::radinpi(kyosu::acos(a0));
+  }
+
+  template<kyosu::concepts::complex C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::acotpi> const&, C const& a0) noexcept
+  {
+    return kyosu::radinpi(kyosu::acot(a0));
+  }
+
+  template<kyosu::concepts::complex C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::acscpi> const&, C const& a0) noexcept
+  {
+    return kyosu::radinpi(kyosu::acsc(a0));
+  }
+
+  template<kyosu::concepts::complex C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::asecpi> const&, C const& a0) noexcept
+  {
+    return kyosu::radinpi(kyosu::asec(a0));
+  }
+
+  template<kyosu::concepts::complex C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::asinpi> const&, C const& a0) noexcept
+  {
+    return kyosu::radinpi(kyosu::asin(a0));
+  }
+
+  template<kyosu::concepts::complex C>
+  KYOSU_FORCEINLINE constexpr
+  auto dispatch(eve::tag_of<kyosu::atanpi> const&, C const& a0) noexcept
+  {
+    return kyosu::radinpi(kyosu::atan(a0));
+  }
+
 }
diff --git a/test/unit/complex/acospi.cpp b/test/unit/complex/acospi.cpp
new file mode 100644
index 00000000..1c3ade37
--- /dev/null
+++ b/test/unit/complex/acospi.cpp
@@ -0,0 +1,39 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#include <kyosu/kyosu.hpp>
+#include <test.hpp>
+#include <complex>
+
+TTS_CASE_WITH( "Check behavior of acospi on scalar"
+        , tts::bunch<kyosu::scalar_real_types>
+        , tts::generate( tts::randoms(-10, 10), tts::randoms(-10, 10))
+        )
+  <typename T>(T const& a0, T const& a1 )
+{
+  using e_t = typename T::value_type;
+  auto inv_pi = eve::inv_pi(eve::as<e_t>());
+  for(size_t i = 0; i < a0.size(); ++i)
+  {
+    auto e = a0[i];
+    auto f = a1[i];
+    auto z = kyosu::to_complex(e, f);
+    TTS_RELATIVE_EQUAL(kyosu::acospi(z),  inv_pi*kyosu::acos(z), 1.0e-6);
+  }
+};
+
+TTS_CASE_WITH( "Check behavior of acospi on wide"
+             , kyosu::simd_real_types
+             , tts::generate( tts::between(-10, 10)
+                            , tts::between(-10, 10))
+             )
+  <typename T>(T const& a0, T const& a1 )
+{
+  auto inv_pi = eve::inv_pi(eve::as(a0));
+  auto z = kyosu::to_complex(a0, a1);
+  TTS_RELATIVE_EQUAL(kyosu::acospi(z), inv_pi*kyosu::acos(z), 1.0e-6);
+};
diff --git a/test/unit/complex/acotpi.cpp b/test/unit/complex/acotpi.cpp
new file mode 100644
index 00000000..99dfc1e7
--- /dev/null
+++ b/test/unit/complex/acotpi.cpp
@@ -0,0 +1,36 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#include <kyosu/kyosu.hpp>
+#include <test.hpp>
+#include <complex>
+
+TTS_CASE_WITH ( "Check behavior of acotpi on scalar"
+              , tts::bunch<kyosu::scalar_real_types>
+              , tts::generate( tts::randoms(-10, 10)
+                             , tts::randoms(-10, 10)
+                             )
+              )
+  <typename T>(T const& a0, T const& a1 )
+{
+  for(size_t i = 0; i < a0.size(); ++i)
+  {
+    auto z = kyosu::to_complex(a0[i], a1[i]);
+    TTS_RELATIVE_EQUAL(kyosu::acotpi(z),  kyosu::atanpi(kyosu::rec(z)), 1.0e-5);
+  }
+};
+
+TTS_CASE_WITH( "Check behavior of acot on wide"
+             , kyosu::simd_real_types
+             , tts::generate( tts::randoms(-10, 10)
+                            , tts::randoms(-10, 10))
+             )
+  <typename T>(T const& a0, T const&  a1)
+{
+  auto z = kyosu::to_complex(a0, a1);
+  TTS_RELATIVE_EQUAL(kyosu::acotpi(z), kyosu::atanpi(kyosu::rec(z)), 1.0e-5);
+};
diff --git a/test/unit/complex/acscpi.cpp b/test/unit/complex/acscpi.cpp
new file mode 100644
index 00000000..4eb9877c
--- /dev/null
+++ b/test/unit/complex/acscpi.cpp
@@ -0,0 +1,36 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#include <kyosu/kyosu.hpp>
+#include <test.hpp>
+#include <complex>
+
+TTS_CASE_WITH ( "Check behavior of acscpi on scalar"
+              , tts::bunch<kyosu::scalar_real_types>
+              , tts::generate( tts::randoms(-10, 10)
+                             , tts::randoms(-10, 10)
+                             )
+              )
+  <typename T>(T const& a0, T const& a1 )
+{
+  for(size_t i = 0; i < a0.size(); ++i)
+  {
+    auto z = kyosu::to_complex(a0[i], a1[i]);
+    TTS_RELATIVE_EQUAL(kyosu::acscpi(z),  kyosu::asinpi(kyosu::rec(z)), 1.0e-5);
+  }
+};
+
+TTS_CASE_WITH( "Check behavior of acsc on wide"
+             , kyosu::simd_real_types
+             , tts::generate( tts::randoms(-10, 10)
+                            , tts::randoms(-10, 10))
+             )
+  <typename T>(T const& a0, T const&  a1)
+{
+  auto z = kyosu::to_complex(a0, a1);
+  TTS_RELATIVE_EQUAL(kyosu::acscpi(z), kyosu::asinpi(kyosu::rec(z)), 1.0e-5);
+};
diff --git a/test/unit/complex/asecpi.cpp b/test/unit/complex/asecpi.cpp
new file mode 100644
index 00000000..0b0ef736
--- /dev/null
+++ b/test/unit/complex/asecpi.cpp
@@ -0,0 +1,36 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#include <kyosu/kyosu.hpp>
+#include <test.hpp>
+#include <complex>
+
+TTS_CASE_WITH ( "Check behavior of acscpi on scalar"
+              , tts::bunch<kyosu::scalar_real_types>
+              , tts::generate( tts::randoms(-10, 10)
+                             , tts::randoms(-10, 10)
+                             )
+              )
+  <typename T>(T const& a0, T const& a1 )
+{
+  for(size_t i = 0; i < a0.size(); ++i)
+  {
+    auto z = kyosu::to_complex(a0[i], a1[i]);
+    TTS_RELATIVE_EQUAL(kyosu::asecpi(z),  kyosu::acospi(kyosu::rec(z)), 1.0e-5);
+  }
+};
+
+TTS_CASE_WITH( "Check behavior of acsc on wide"
+             , kyosu::simd_real_types
+             , tts::generate( tts::randoms(-10, 10)
+                            , tts::randoms(-10, 10))
+             )
+  <typename T>(T const& a0, T const&  a1)
+{
+  auto z = kyosu::to_complex(a0, a1);
+  TTS_RELATIVE_EQUAL(kyosu::asecpi(z), kyosu::acospi(kyosu::rec(z)), 1.0e-5);
+};
diff --git a/test/unit/complex/asinpi.cpp b/test/unit/complex/asinpi.cpp
new file mode 100644
index 00000000..60d27158
--- /dev/null
+++ b/test/unit/complex/asinpi.cpp
@@ -0,0 +1,39 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#include <kyosu/kyosu.hpp>
+#include <test.hpp>
+#include <complex>
+
+TTS_CASE_WITH( "Check behavior of asinpi on scalar"
+        , tts::bunch<kyosu::scalar_real_types>
+        , tts::generate( tts::randoms(-10, 10), tts::randoms(-10, 10))
+        )
+  <typename T>(T const& a0, T const& a1 )
+{
+  using e_t = typename T::value_type;
+ auto inv_pi = eve::inv_pi(eve::as<e_t>());
+  for(size_t i = 0; i < a0.size(); ++i)
+  {
+     auto e = a0[i];
+     auto f = a1[i];
+     auto z = kyosu::to_complex(e, f);
+     TTS_RELATIVE_EQUAL(kyosu::asinpi(z),  inv_pi*kyosu::asin(z), 1.0e-6);
+  }
+};
+
+TTS_CASE_WITH( "Check behavior of asinpi on wide"
+             , kyosu::simd_real_types
+             , tts::generate( tts::between(-10, 10)
+                            , tts::between(-10, 10))
+             )
+  <typename T>(T const& a0, T const& a1 )
+{
+  auto inv_pi = eve::inv_pi(eve::as(a0));
+  auto z = kyosu::to_complex(a0, a1);
+  TTS_RELATIVE_EQUAL(kyosu::asinpi(z), inv_pi*kyosu::asin(z), 1.0e-6);
+};
diff --git a/test/unit/complex/atanpi.cpp b/test/unit/complex/atanpi.cpp
new file mode 100644
index 00000000..1e17f823
--- /dev/null
+++ b/test/unit/complex/atanpi.cpp
@@ -0,0 +1,39 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright : KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#include <kyosu/kyosu.hpp>
+#include <test.hpp>
+#include <complex>
+
+TTS_CASE_WITH ( "Check behavior of atanpi on scalar"
+              , tts::bunch<kyosu::scalar_real_types>
+              , tts::generate( tts::randoms(-10, 10)
+                             , tts::randoms(-10, 10)
+                             )
+              )
+  <typename T>(T const& a0, T const& a1 )
+{
+  using e_t = typename T::value_type;
+  auto inv_pi = eve::inv_pi(eve::as<e_t>());
+  for(size_t i = 0; i < a0.size(); ++i)
+  {
+    auto z = kyosu::to_complex(a0[i], a1[i]);
+    TTS_RELATIVE_EQUAL(kyosu::atanpi(z),  inv_pi*kyosu::atan(z), 1.0e-5);
+  }
+};
+
+TTS_CASE_WITH( "Check behavior of atan on wide"
+             , kyosu::simd_real_types
+             , tts::generate( tts::randoms(-10, 10)
+                            , tts::randoms(-10, 10))
+             )
+  <typename T>(T const& a0, T const&  a1)
+{
+  auto inv_pi = eve::inv_pi(eve::as(a0));
+  auto z = kyosu::to_complex(a0, a1);
+  TTS_RELATIVE_EQUAL(kyosu::atanpi(z), inv_pi*kyosu::atan(z), 1.0e-5);
+};