tests doc and corrections

include/eve/module/elliptic/am.hpp

@@ -68,10 +68,7 @@ namespace eve
 //!   **Parameters**
 //!
 //!     * `u`: argument.
-//!     * `m`: amplitude parameter (\f$0\le m\le 1).
-//!     * `alpha `: modular angle in radian.
-//!     * `tol': accuracy tolerance (by defaut [epsilon](@ref eve::epsilon).
-//!     * `k`: elliptic modulus (eccentricity) .
+//!     * `x`: amplitude parameter (\f$0\le m\le 1).
 //!     * `c`: [Conditional expression](@ref eve::conditional_expr) masking the operation.
 //!     * `l`: [Logical value](@ref eve::logical_value) masking the operation.
 //!
@@ -90,9 +87,9 @@ namespace eve
 
 //!  @groupheader{External references}
 //!   *  [C++ standard reference: am](https://en.cppreference.com/w/cpp/numeric/special_functions/am)
-//!   *  [DLMF: Jacobi Amplitude](https://dlmf.nist.gov/22.16)
-//!   *  [Wolfram MathWorld: Jacobi Amplitude](https://mathworld.wolfram.com/JacobiAmplitude.html)
-//!   *  [Wikipedia: Jacobi elliptic functions](https://en.wikipedia.org/wiki/Jacobi_elliptic_functions)
+//!   *  [DLMF: Jacobi zeta](https://dlmf.nist.gov/22.16)
+//!   *  [Wolfram MathWorld: Jacobi Zeta Function](https://mathworld.wolfram.com/JacobiZetaFunction.html)
+//!   *  [Boost: jacobi_zeta](https://beta.boost.org/doc/libs/1_84_0/libs/math/doc/html/math_toolkit/ellint/jacobi_zeta.html)
 //!
 //!  @groupheader{Example}
 //!  @godbolt{doc/elliptic/am.cpp}
@@ -150,7 +147,7 @@ namespace eve
           {
             phi = average(phi, asin(c[n]*sin(phi)/a[n]) );
           }
-          return phi;
+          return if_else(is_infinite(u) && is_eqz(k), u, phi);
         };
 
       T r;

include/eve/module/elliptic/heuman_lambda.hpp

@@ -37,7 +37,7 @@ namespace eve
 //! @addtogroup elliptic
 //! @{
 //!   @var heuman_lambda
-//!   @brief `elementwise_callable` object computing the  Jacobi's sn, cn and dn function simultaneously.
+//!   @brief `elementwise_callable` object computing the  Heuman lambda function.
 //!
 //!   @groupheader{Header file}
 //!
@@ -53,11 +53,6 @@ namespace eve
 //!      // Regular overload
 //!      constexpr auto heuman_lambda(floating_value auto u, floating_value auto x)                  noexcept; // 1
 //!
-//!      //Semantic modifiers
-//!      constexpr auto heuman_lambda[modular](floating_value auto u, floating_value auto alpha)     noexcept; // 1
-//!      constexpr auto heuman_lambda[eccentric(floating_value auto u, floating_value auto k)        noexcept; // 1
-//!      constexpr auto heuman_lambda[threshold = tol](floating_value auto u, floating_value auto x) noexcept; // 1
-//!
 //!      // Lanes masking
 //!      constexpr auto heuman_lambda[conditional_expr auto c](/*any of the above overloads*/)       noexcept; // 2
 //!      constexpr auto heuman_lambda[logical_value autolm](/*any of the above overloads*/)          noexcept; // 2
@@ -67,30 +62,19 @@ namespace eve
 //!   **Parameters**
 //!
 //!     * `u`: argument.
-//!     * `m`: amplitude parameter (\f$0\le m\le 1).
-//!     * `alpha `: modular angle in radian.
-//!     * `tol': accuracy tolerance (by defaut [epsilon](@ref eve::epsilon).
-//!     * `k`: elliptic modulus (eccentricity) .
+//!     * `x`: amplitude parameter (\f$0\le m\le 1\f$).
 //!     * `c`: [Conditional expression](@ref eve::conditional_expr) masking the operation.
 //!     * `l`: [Logical value](@ref eve::logical_value) masking the operation.
 //!
 //!   **Return value**
 //!
-//!      1. return a `kumi::tuple` containing `sn``cn` and `dn` values. Take care that the meaning of the second parameters
-//!         depends on the option used (see note below).
+//!      1. return the Heuman lambda value
 //!      2. [The operation is performed conditionally](@ref conditional)
 //!
-//! @note
-//!   * \f$\alpha\f$ is named the modular angle given in radian (modular option).
-//!   * \f$ k = \sin\alpha \f$ is named the elliptic modulus or eccentricity (eccentric option).
-//!   * \f$ m = k^2 = \sin^2\alpha\f$ is named the parameter (no option).
-//!   Each of the above three quantities is completely determined by any of the others (given that they are non-negative).
-//!   Thus, they can be used interchangeably (give the right option).
-
 //!  @groupheader{External references}
-//!   *  [DLMF: Jacobian Elliptic](https://dlmf.nist.gov/22.2)
-//!   *  [Wolfram MathWorld: Jacobi Elliptic Functions](https://mathworld.wolfram.com/JacobiEllipticFunctions.html)
-//!   *  [Wikipedia: Jacobi elliptic functions](https://en.wikipedia.org/wiki/heuman_lambda_functions)
+//!   *  [Wolfram MathWorld: Heuman lambda Function](https://mathworld.wolfram.com/HeumanLambdaFunction.html)
+//!   *  [Wikipedia: Heuman Lambda functions](https://en.wikipedia.org/wiki/heuman_lambda_functions)
+//!   *  [Boost: Heuman lambda](https://www.boost.org/doc/libs/1_73_0/libs/math/doc/html/math_toolkit/ellint/heuman_lambda.html)
 //!
 //!  @groupheader{Example}
 //!  @godbolt{doc/elliptic/heuman_lambda.cpp}

include/eve/module/elliptic/jacobi_elliptic.hpp

@@ -65,10 +65,7 @@ namespace eve
 //!   **Parameters**
 //!
 //!     * `u`: argument.
-//!     * `m`: amplitude parameter (\f$0\le m\le 1).
-//!     * `alpha `: modular angle in radian.
-//!     * `tol': accuracy tolerance (by defaut [epsilon](@ref eve::epsilon).
-//!     * `k`: elliptic modulus (eccentricity) .
+//!     * `m`: amplitude parameter (\f$0\le m\le 1\f$).
 //!     * `c`: [Conditional expression](@ref eve::conditional_expr) masking the operation.
 //!     * `l`: [Logical value](@ref eve::logical_value) masking the operation.
 //!
@@ -78,13 +75,6 @@ namespace eve
 //!         depends on the option used (see note below).
 //!      2. [The operation is performed conditionally](@ref conditional)
 //!
-//! @note
-//!   * \f$\alpha\f$ is named the modular angle given in radian (modular option).
-//!   * \f$ k = \sin\alpha \f$ is named the elliptic modulus or eccentricity (eccentric option).
-//!   * \f$ m = k^2 = \sin^2\alpha\f$ is named the parameter (no option).
-//!   Each of the above three quantities is completely determined by any of the others (given that they are non-negative).
-//!   Thus, they can be used interchangeably (give the right option).
-
 //!  @groupheader{External references}
 //!   *  [DLMF: Jacobian Elliptic](https://dlmf.nist.gov/22.2)
 //!   *  [Wolfram MathWorld: Jacobi Elliptic Functions](https://mathworld.wolfram.com/JacobiEllipticFunctions.html)

include/eve/module/elliptic/jacobi_zeta.hpp

@@ -37,7 +37,7 @@ namespace eve
 //! @addtogroup elliptic
 //! @{
 //!   @var jacobi_zeta
-//!   @brief `elementwise_callable` object computing the  Jacobi's sn, cn and dn function simultaneously.
+//!   @brief `elementwise_callable` object computing the  Jacobi Zeta function.
 //!
 //!   @groupheader{Header file}
 //!
@@ -62,26 +62,15 @@ namespace eve
 //!   **Parameters**
 //!
 //!     * `u`: argument.
-//!     * `m`: amplitude parameter (\f$0\le m\le 1).
-//!     * `alpha `: modular angle in radian.
-//!     * `tol': accuracy tolerance (by defaut [epsilon](@ref eve::epsilon).
-//!     * `k`: elliptic modulus (eccentricity) .
+//!     * `x`: amplitude parameter (\f$0\le x\le 1\f$).
 //!     * `c`: [Conditional expression](@ref eve::conditional_expr) masking the operation.
 //!     * `l`: [Logical value](@ref eve::logical_value) masking the operation.
 //!
 //!   **Return value**
 //!
-//!      1. return a `kumi::tuple` containing `sn``cn` and `dn` values. Take care that the meaning of the second parameters
-//!         depends on the option used (see note below).
+//!      1. return the jacobi zeta value.
 //!      2. [The operation is performed conditionally](@ref conditional)
 //!
-//! @note
-//!   * \f$\alpha\f$ is named the modular angle given in radian (modular option).
-//!   * \f$ k = \sin\alpha \f$ is named the elliptic modulus or eccentricity (eccentric option).
-//!   * \f$ m = k^2 = \sin^2\alpha\f$ is named the parameter (no option).
-//!   Each of the above three quantities is completely determined by any of the others (given that they are non-negative).
-//!   Thus, they can be used interchangeably (give the right option).
-
 //!  @groupheader{External references}
 //!   *  [DLMF: Jacobian Elliptic](https://dlmf.nist.gov/22.2)
 //!   *  [Wolfram MathWorld: Jacobi Elliptic Functions](https://mathworld.wolfram.com/JacobiEllipticFunctions.html)

test/doc/elliptic/heuman_lambda.cpp

@@ -1,12 +1,6 @@
 // revision 1
 #include <eve/module/elliptic.hpp>
 #include <iostream>
-#if __has_include(<boost/math/special_functions/heuman_lambda.hpp>)
-#include <boost/math/special_functions/heuman_lambda.hpp>
-#define EVE_HAS_BOOST
-#endif
-
-auto hl = [](auto x, auto y) -> decltype(x) { return boost::math::heuman_lambda(y, x); };
 
 eve::wide wf{0.9, 0.2, 0.75, 0.5};
 eve::wide wphi{0.8, 1.0e-30, 0.5, 0.1};
@@ -16,7 +10,6 @@ int main(){
    std::cout << "<- wphi = " << wphi << "\n";
 
    std::cout << "-> heuman_lambda(wphi, wf)               = " << eve::heuman_lambda(wphi, wf) << "\n";
-   std::cout << "-> hl           (wphi, wf)               = " << eve::detail::map(hl, wphi, wf) << "\n";
    std::cout << "-> heuman_lambda[ignore_last(2)](wphi,wf)= " << eve::heuman_lambda[eve::ignore_last(2)](wphi, wf) << "\n";
    std::cout << "-> heuman_lambda[wf != 1.0](wphi,wf)     = " << eve::heuman_lambda[wf != -1.0f](wphi, wf) << "\n";
    std::cout << "-> heuman_lambda(pio_2[lower], wf)       = " << eve::heuman_lambda(eve::pio_2[eve::lower](eve::as(wphi)), wf) << '\n';

test/doc/elliptic/jacobi_zeta.cpp

@@ -1,12 +1,6 @@
 // revision 1
 #include <eve/module/elliptic.hpp>
 #include <iostream>
-#if __has_include(<boost/math/special_functions/heuman_lambda.hpp>)
-#include <boost/math/special_functions/jacobi_zeta.hpp>
-#define EVE_HAS_BOOST
-#endif
-
-auto jz = [](auto x, auto y) -> decltype(x) { return boost::math::jacobi_zeta(y, x); };
 
 eve::wide wf{1.0, 0.0, 0.75, 0.5};
 eve::wide wphi{1.0, 1.0e-30, 0.5, 0.0};
@@ -16,7 +10,6 @@ int main(){
    std::cout << "<- wphi = " << wphi << "\n";
 
    std::cout << "-> jacobi_zeta(wphi, wf)               = " << eve::jacobi_zeta(wphi, wf) << "\n";
-   std::cout << "-> jz           (wphi, wf)             = " << eve::detail::map(jz, wphi, wf) << "\n";
    std::cout << "-> jacobi_zeta[ignore_last(2)](wphi,wf)= " << eve::jacobi_zeta[eve::ignore_last(2)](wphi, wf) << "\n";
    std::cout << "-> jacobi_zeta[wf != 1.0](wphi,wf)     = " << eve::jacobi_zeta[wf != -1.0f](wphi, wf) << "\n";
    std::cout << "-> jacobi_zeta(pio_2[lower], wf)       = " << eve::jacobi_zeta(eve::pio_2[eve::lower](eve::as(wphi)), wf) << '\n';

test/unit/module/elliptic/heuman_lambda.cpp

@@ -11,7 +11,7 @@
 #include <eve/module/elliptic.hpp>
 #include <eve/module/math.hpp>
 
-TTS_CASE_TPL ( "Check jacobi_elliptic over real"
+TTS_CASE_TPL ( "Check heuman_lambda over real"
              , eve::test::scalar::ieee_reals
              )
   <typename T>(tts::type<T>)