Complex inverse trigonometry

include/kyosu/complex/acos.hpp

@@ -0,0 +1,97 @@
+//======================================================================================================================
+/*
+  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_acos : eve::elementwise
+  {
+    using callable_tag_type = callable_acos;
+
+    KYOSU_DEFERS_CALLABLE(acos_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_acos{};
+      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_acos(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var acos
+//!   @brief Computes the acosine of the argument.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto acos(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto acos(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 [elementwise](@ref glossary_elementwise) the complex principal value
+//!      of the arc cosine of the input.
+//!      Branch cuts exist outside the interval \f$[-1, +1]\f$ along the real axis.
+//!
+//!      * for every z: eve::acos(eve::conj(z)) == eve::conj(std::acos(z))
+//!      * If z is \f$\pm0\f$, the result is \f$\pi/2\f$
+//!      * If z is \f$i NaN\f$, the result is \f$\pi/2+ i NaN\f$
+//!      * If z is \f$x+i\infty\f$ (for any finite x), the result is \f$\pi/2-i\infty\f$
+//!      * If z is \f$x+i NaN\f$ (for any nonzero finite x), the result is \f$NaN+i NaN\f$.
+//!      * If z is \f$-\infty+i y\f$ (for any positive finite y), the result is \f$\pi-i\infty\f$
+//!      * If z is \f$+\infty+i y\f$ (for any positive finite y), the result is \f$+0-i\infty\f$
+//!      * If z is \f$-\infty+i +\infty\f$, the result is \f$3\pi/4-i\infty\f$
+//!      * If z is \f$\infty+i +\infty\f$, the result is \f$\pi/4-i\infty\f$
+//!      * If z is \f$\pm\infty+i NaN\f$, the result is \f$NaN \pm i\infty\f$ (the sign
+//!        of the imaginary part is unspecified)
+//!      * If z is \f$NaN+i y\f$ (for any finite y), the result is \f$NaN+i NaN\f$
+//!      * If z is \f$NaN+i\infty\f$, the result is \f$NaN-i\infty\f$
+//!      * If z is \f$NaN+i NaN\f$, the result is \f$NaN+i NaN\f$
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/acos.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_acos acos = {};
+}

include/kyosu/complex/acosh.hpp

@@ -0,0 +1,96 @@
+//======================================================================================================================
+/*
+  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_acosh : eve::elementwise
+  {
+    using callable_tag_type = callable_acosh;
+
+    KYOSU_DEFERS_CALLABLE(acosh_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_acosh{};
+      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_acosh(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var acosh
+//!   @brief Computes the acoshine of the argument.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto acosh(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto acosh(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 the complex arc hyperbolic sine of z, in the range of a half-strip mathematically
+//!       unbounded along the real axis and in the interval  \f$i\times[-\pi/2, \pi/2]\f$ along
+//!       the imaginary axis.
+//!
+//!         * for every z: eve::acosh(eve::conj(z)) == eve::conj(std::acosh(z))
+//!         * for every z: eve::acosh(-z) == -eve::acosh(z)
+//!         * If z is \f$+0\f$, the result is \f$+0\f$
+//!         * If z is \f$NaN\f$, the result is \f$NaN\f$
+//!         * If z is \f$+1\f$, the result is \f$+\infty\f$
+//!         * If z is \f$x+i \infty\f$ (for any finite positive x), the result is \f$+0,\pi/2\f$
+//!         * If z is \f$x+i NaN\f$ (for any finite nonzero x),  the result is \f$NaN+i NaN\f$
+//!         * If z is \f$+\infty+i y\f$ (for any finite positive y),  the result is \f$i \pi/2\f$
+//!         * If z is \f$+\infty+i \infty\f$, the result is \f$i \pi/2\f$
+//!         * If z is \f$+\infty+i NaN\f$,  the result is \f$i NaN\f$
+//!         * If z is \f$NaN+i y\f$ (for any finite y), the result is \f$NaN+i NaN\f$
+//!         * If z is \f$NaN+i \infty\f$, the result is \f$i \pi/2\f$ (the sign of the real part is unspecified)
+//!         * If z is \f$NaN+i NaN\f$,  the result is \f$NaN+i NaN\f$
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/acosh.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_acosh acosh = {};
+}

include/kyosu/complex/acot.hpp

@@ -0,0 +1,81 @@
+//======================================================================================================================
+/*
+  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_acot : eve::elementwise
+  {
+    using callable_tag_type = callable_acot;
+
+    KYOSU_DEFERS_CALLABLE(acot_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_acot{};
+      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_acot(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var acot
+//!   @brief Computes the acotine of the argument.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto acot(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto acot(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 [elementwise](@ref glossary_elementwise) the complex principal value
+//!      of the arc cotangent of the input as the arc tangent of the inverse of the input.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/acot.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_acot acot = {};
+}

include/kyosu/complex/acoth.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_acoth : eve::elementwise
+  {
+    using callable_tag_type = callable_acoth;
+
+    KYOSU_DEFERS_CALLABLE(acoth_);
+
+    template<eve::ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, T const& v) noexcept
+    {
+      auto fn = callable_acoth{};
+      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_acoth(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var acoth
+//!   @brief Computes the acothine of the argument.
+//!
+//!   **Defined in Header**
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<eve::ordered_value T>       constexpr auto acoth(T z) noexcept;  //1
+//!      template<kyosu::concepts::complex T> constexpr auto acoth(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 the complex arc hyperbolic cotangent of z, computed as \f$\mathop{\mathrm{atanh}}(1/z)\f$.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/acoth.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_acoth acoth = {};
+}