jfalcou · jfalcou · Dec 15, 2024 · Dec 14, 2024 · Dec 15, 2024
diff --git a/include/kyosu/functions/abs.hpp b/include/kyosu/functions/abs.hpp
@@ -69,6 +69,9 @@ namespace kyosu
 //!       The modulus is the square root of the sum of the squares of the absolute value of each component.
 //!    2. With the raw option no provision is made to enhance accuracy and avoid overflows
 //!
+//!  @groupheader{External references}
+//!   *  [C++ standard reference: complex abs](https://en.cppreference.com/w/cpp/numeric/complex/abs)
+//!
 //!  @groupheader{Example}
 //!  @godbolt{doc/abs.cpp}
 //======================================================================================================================

diff --git a/include/kyosu/functions/beta.hpp b/include/kyosu/functions/beta.hpp
@@ -65,7 +65,6 @@ namespace kyosu
 //!   *  [Wolfram MathWorld: Beta Function](https://mathworld.wolfram.com/BetaFunction.html)
 //!
 //!  @groupheader{Example}
-//!
 //!  @godbolt{doc/beta.cpp}
 //======================================================================================================================
   inline constexpr auto beta = eve::functor<beta_t>;

diff --git a/include/kyosu/functions/deta.hpp b/include/kyosu/functions/deta.hpp
@@ -61,8 +61,10 @@ namespace kyosu
 //!
 //!   Returns the Dirichlet sum \f$  \displaystyle \sum_{n = 0}^\infty \frac{(-1)^n}{(kn+1)^z}\f$
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Dirichlet series](https://en.wikipedia.org/wiki/Dirichlet_series)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/deta.cpp}
 //======================================================================================================================
   inline constexpr auto deta = eve::functor<deta_t>;

diff --git a/include/kyosu/functions/digamma.hpp b/include/kyosu/functions/digamma.hpp
@@ -57,8 +57,10 @@ namespace kyosu
 //!
 //!     The value of the Digamma function: \f$\frac{\Gamma'(z)}{\Gamma(z)}\f$ is returned.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Digamma function](https://en.wikipedia.org/wiki/Digamma_function)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/digamma.cpp}
 //======================================================================================================================
   inline constexpr auto digamma = eve::functor<digamma_t>;

diff --git a/include/kyosu/functions/erf.hpp b/include/kyosu/functions/erf.hpp
@@ -62,8 +62,12 @@ namespace kyosu
 //!
 //!   * The value of the error function is returned.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Erf](https://mathworld.wolfram.com/Erf.html)
+//!   *  [DLMF: Error Functions](https://dlmf.nist.gov/7.2#i)
+//!   *  [Wikipedia: Error Function](https://en.wikipedia.org/wiki/Error_function)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/erf.cpp}
 //======================================================================================================================
   inline constexpr auto erf = eve::functor<erf_t>;

diff --git a/include/kyosu/functions/erfcx.hpp b/include/kyosu/functions/erfcx.hpp
@@ -74,8 +74,10 @@ namespace kyosu
 //!
 //!   2. The value of the normalized complementary error function is returned.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Error function](https://en.wikipedia.org/wiki/Error_function)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/erfcx.cpp}
 //======================================================================================================================
   inline constexpr auto erfcx = eve::functor<erfcx_t>;

diff --git a/include/kyosu/functions/erfi.hpp b/include/kyosu/functions/erfi.hpp
@@ -77,8 +77,12 @@ namespace kyosu
 //!
 //!   Returns the imaginary error function \f$ \displaystyle \mathrm{erfi}(z) = -i\mathrm{erf}(iz)\f$
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Erfi](https://mathworld.wolfram.com/Erfi.html)
+//!   *  [DLMF](https://dlmf.nist.gov/7.1)
+//!   *  [Wikipedia: Error Function](https://en.wikipedia.org/wiki/Error_function)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/erfi.cpp}
 //======================================================================================================================
   inline constexpr auto erfi = eve::functor<erfi_t>;

diff --git a/include/kyosu/functions/faddeeva.hpp b/include/kyosu/functions/faddeeva.hpp
@@ -56,8 +56,11 @@ namespace kyosu
 //!
 //!   Returns \f$e^{-z^2}\mathrm{erfc}(-iz)\f$ the scaled complex complementary error function
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [DLMF: Error Functions](https://dlmf.nist.gov/7.21)
+//!   *  [Wikipedia: Faddeeva function](https://en.wikipedia.org/wiki/Faddeeva_function)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/faddeeva.cpp}
 //======================================================================================================================
   inline constexpr auto faddeeva = eve::functor<faddeeva_t>;

diff --git a/include/kyosu/functions/horner.hpp b/include/kyosu/functions/horner.hpp
@@ -109,9 +109,10 @@ namespace kyosu
 //!        *  If x is scalar, the polynomials are all computed at the same point
 //!        *  If x is simd, the nth polynomial is computed on the nth value of x
 //!
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method)
 //!
 //!  @groupheader{Example}
-//!
 //!  @godbolt{doc/horner.cpp}
 //======================================================================================================================
   inline constexpr auto horner = eve::functor<horner_t>;

diff --git a/include/kyosu/functions/lambda.hpp b/include/kyosu/functions/lambda.hpp
@@ -74,8 +74,11 @@ namespace kyosu
 //!
 //!    Returns the Dirichlet sum \f$  \displaystyle \sum_0^\infty \frac{1}{(2n+1)^z}\f$
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Dirichlet lambda](https://mathworld.wolfram.com/DirichletLambdaFunction.html)
+//!   *  [Wikipedia: Dirichlet series](https://en.wikipedia.org/wiki/Dirichlet_series)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/lambda.cpp}
 //======================================================================================================================
   inline constexpr auto lambda = eve::functor<lambda_t>;

diff --git a/include/kyosu/functions/lbeta.hpp b/include/kyosu/functions/lbeta.hpp
@@ -57,8 +57,10 @@ namespace kyosu
 //!
 //!    `log(beta(x, y))`.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Beta Function](https://mathworld.wolfram.com/BetaFunction.html)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/lbeta.cpp}
 //======================================================================================================================
   inline constexpr auto lbeta = eve::functor<lbeta_t>;

diff --git a/include/kyosu/functions/lerp.hpp b/include/kyosu/functions/lerp.hpp
@@ -62,6 +62,9 @@ namespace kyosu
 //!
 //!    @see slerp for better unitary quaternion (spheroidal) interpolation.
 //!
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Linear interpolation](https://en.wikipedia.org/wiki/Linear_interpolation)
+//!
 //!  @groupheader{Example}
 //!
 //!  @godbolt{doc/lerp.cpp}

diff --git a/include/kyosu/functions/log.hpp b/include/kyosu/functions/log.hpp
@@ -98,8 +98,12 @@ namespace kyosu
 //!
 //!   3. `log(z)` is semantically equivalent to `log(abs(z)) + sign(pure(z)) * arg(z)`
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Logarithm](https://mathworld.wolfram.com/Logarithm.html)
+//!   *  [DLMF: Logarithm](https://dlmf.nist.gov/4.2)
+//!   *  [Wikipedia: Logarithm](https://en.wikipedia.org/wiki/Logarithm)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/log.cpp}
 //======================================================================================================================
   inline constexpr auto log = eve::functor<log_t>;

diff --git a/include/kyosu/functions/log10.hpp b/include/kyosu/functions/log10.hpp
@@ -75,9 +75,11 @@ namespace kyosu
 //!   1.  a real typed input z is treated as if `complex(z)` was entered.
 //!   2.  returns [log](@ref kyosu::log)(z)/log_10(as(z)).
 //!
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Common Logarithm](https://mathworld.wolfram.com/CommonLogarithm.html)
+//!   *  [Wikipedia: Logarithm](https://en.wikipedia.org/wiki/Logarithm)
 //!
 //!  @groupheader{Example}
-//!
 //!  @godbolt{doc/log10.cpp}
 //======================================================================================================================
   inline constexpr auto log10 = eve::functor<log10_t>;

diff --git a/include/kyosu/functions/log2.hpp b/include/kyosu/functions/log2.hpp
@@ -78,8 +78,10 @@ namespace kyosu
 //!   1.  a real typed input z is treated as if `complex(z)` was entered.
 //!   2.  returns [log](@ref kyosu::log)(z)/log_2(as(z)).
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Binary Logarithm](https://en.wikipedia.org/wiki/Binary_logarithm)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/log2.cpp}
 //======================================================================================================================
   inline constexpr auto log2 = eve::functor<log2_t>;

diff --git a/include/kyosu/functions/lpnorm.hpp b/include/kyosu/functions/lpnorm.hpp
@@ -60,8 +60,10 @@ namespace kyosu
 //!
 //!     Returns \f$ \left(\sum_{i = 0}^n |x_i|^p\right)^{\frac1p} \f$.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Error Function](https://en.wikipedia.org/wiki/Lp_space)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/lpnorm.cpp}
 //======================================================================================================================
   inline constexpr auto lpnorm = eve::functor<lpnorm_t>;

diff --git a/include/kyosu/functions/lrising_factorial.hpp b/include/kyosu/functions/lrising_factorial.hpp
@@ -57,8 +57,11 @@ namespace kyosu
 //!      \f$\displaystyle \log\left(\frac{\Gamma(a+x)}{\Gamma(a)}\right)\f$ is returned.
 //!      If all iputs are real typed they are reated as complex ones.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Rising Factorial](https://mathworld.wolfram.com/RisingFactorial.html)
+//!   *  [Wikipedia: Error Function](https://en.wikipedia.org/wiki/Falling_and_rising_factorials)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/lrising_factorial.cpp}
 //======================================================================================================================
   inline constexpr auto lrising_factorial = eve::functor<lrising_factorial_t>;

diff --git a/include/kyosu/functions/manhattan.hpp b/include/kyosu/functions/manhattan.hpp
@@ -63,8 +63,10 @@ namespace kyosu
 //!
 //!  @note This is NOT `lpnorm(1, x0, xs...)` which is the \f$l_1\f$ norm of \f$l_2\f$ norm of its arguments.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: L1 norm](https://mathworld.wolfram.com/L1-Norm.html)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/manhattan.cpp}
 //======================================================================================================================
   inline constexpr auto manhattan = eve::functor<manhattan_t>;

diff --git a/include/kyosu/functions/pow.hpp b/include/kyosu/functions/pow.hpp
@@ -101,6 +101,10 @@ namespace kyosu
 //!      4. pow can accept an integral typed second parameter,  in this case it is the russian peasant algorithm
 //!         that is used (feasible as every monogen ideals are commutative).
 //!
+//!  @groupheader{External references}
+//!   *  [C++ standard reference: complex pow](https://en.cppreference.com/w/cpp/numeric/complex/pow)
+//!   *  [Wolfram MathWorld: Power](https://mathworld.wolfram.com/Power.html)
+//!
 //!  @groupheader{Example}
 //!
 //!  @godbolt{doc/pow.cpp}

diff --git a/include/kyosu/functions/reverse_horner.hpp b/include/kyosu/functions/reverse_horner.hpp
@@ -113,9 +113,10 @@ namespace kyosu
 //!        *  If x is scalar, the polynomials are all computed at the same point
 //!        *  If x is simd, the nth polynomial is computed on the nth value of x
 //!
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method)
 //!
 //!  @groupheader{Example}
-//!
 //!  @godbolt{doc/reverse_horner.cpp}
 //======================================================================================================================
   inline constexpr auto reverse_horner = eve::functor<reverse_horner_t>;

diff --git a/include/kyosu/functions/rising_factorial.hpp b/include/kyosu/functions/rising_factorial.hpp
@@ -56,8 +56,11 @@ namespace kyosu
 //!
 //!      \f$\displaystyle \frac{\Gamma(a+x)}{\Gamma(a)}\f$ is returned.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Rising Factorial](https://mathworld.wolfram.com/RisingFactorial.html)
+//!   *  [Wikipedia: Error Function](https://en.wikipedia.org/wiki/Falling_and_rising_factorials)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/rising_factorial.cpp}
 //======================================================================================================================
   inline constexpr auto rising_factorial = eve::functor<rising_factorial_t>;

diff --git a/include/kyosu/functions/sec.hpp b/include/kyosu/functions/sec.hpp
@@ -56,8 +56,10 @@ namespace kyosu
 //!
 //!    Returns the secant of the argument.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld](https://mathworld.wolfram.com/Secant.html)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/sec.cpp}
 //======================================================================================================================
   inline constexpr auto sec = eve::functor<sec_t>;

diff --git a/include/kyosu/functions/sin.hpp b/include/kyosu/functions/sin.hpp
@@ -70,8 +70,12 @@ namespace kyosu
 //!       where \f$I_z = \frac{\underline{z}}{|\underline{z}|}\f$ and
 //!        \f$\underline{z}\f$ is the [pure](@ref kyosu::imag ) part of \f$z\f$.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [C++ standard reference: complex sin](https://en.cppreference.com/w/cpp/numeric/complex/sin)
+//!   *  [Wolfram MathWorld: Sinine](https://mathworld.wolfram.com/Sine.html)
+//!   *  [Wikipedia: sinus](https://fr.wikipedia.org/wiki/sinus)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/sin.cpp}
 //======================================================================================================================
   inline constexpr auto sin = eve::functor<sin_t>;

diff --git a/include/kyosu/functions/sinc.hpp b/include/kyosu/functions/sinc.hpp
@@ -66,8 +66,11 @@ namespace kyosu
 //!
 //!     Returns the sine cardinal of the argument.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wikipedia](https://fr.wikipedia.org/wiki/Sinus_cardinal)
+//!   *  [Wolfram MathWorld](https://mathworld.wolfram.com/SineCardinalFunction.html)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/sinc.cpp}
 //======================================================================================================================
   inline constexpr auto sinc = eve::functor<sinc_t>;

diff --git a/include/kyosu/functions/sinh.hpp b/include/kyosu/functions/sinh.hpp
@@ -103,6 +103,11 @@ namespace kyosu
 //!
 //!   3. Is semantically equivalent to (exp(z)-exp(-z))/2.
 //!
+//!  @groupheader{External references}
+//!   *  [C++ standard reference: complex sinh](https://en.cppreference.com/w/cpp/numeric/complex/sinh)
+//!   *  [Wolfram MathWorld: Hyperbolic Sine](https://mathworld.wolfram.com/HyperbolicSine.html)
+//!   *  [Wikipedia: hyperbolic functions](https://en.wikipedia.org/wiki/Hyperbolic_functions)
+//!
 //!  @groupheader{Example}
 //!
 //!  @godbolt{doc/sinh.cpp}

diff --git a/include/kyosu/functions/sqrt.hpp b/include/kyosu/functions/sqrt.hpp
@@ -75,6 +75,11 @@ namespace kyosu
 //!
 //!     2. Returns a square root of z.
 //!
+//!  @groupheader{External references}
+//!   *  [C++ standard reference: complex cosh](https://en.cppreference.com/w/cpp/numeric/complex/sqrt)
+//!   *  [Wolfram MathWorld: Square Root](https://mathworld.wolfram.com/SquareRoot.html)
+//!   *  [Wikipedia: Square root](https://en.wikipedia.org/wiki/Square_root)
+//!
 //!  @groupheader{Example}
 //!
 //!  @godbolt{doc/sqrt.cpp}

diff --git a/include/kyosu/functions/tan.hpp b/include/kyosu/functions/tan.hpp
@@ -68,8 +68,12 @@ namespace kyosu
 //!     3. Returns \f$-I_z\, \tanh(I_z\; z)\f$ if \f$z\f$ is not zero else \f$\tan(z_0)\f$, where \f$I_z = \frac{\underline{z}}{|\underline{z}|}\f$ and
 //!         \f$\underline{z}\f$ is the [pure](@ref kyosu::imag ) part of \f$z\f$.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [C++ standard reference: complex tan](https://en.cppreference.com/w/cpp/numeric/complex/tan)
+//!   *  [Wolfram MathWorld: Tangent](https://mathworld.wolfram.com/Tangent.html)
+//!   *  [Wikipedia: tangent](https://fr.wikipedia.org/wiki/tangent)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/tan.cpp}
 //======================================================================================================================
   inline constexpr auto tan = eve::functor<tan_t>;

diff --git a/include/kyosu/functions/tgamma.hpp b/include/kyosu/functions/tgamma.hpp
@@ -57,8 +57,11 @@ namespace kyosu
 //!
 //!     Returns \f$\Gamma(z)\f$.
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wolfram MathWorld: Gamma Function](https://mathworld.wolfram.com/GammaFunction.html)
+//!   *  [Wikipedia: Gamma function](https://en.wikipedia.org/wiki/Gamma_function)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/tgamma.cpp}
 //======================================================================================================================
   inline constexpr auto tgamma = eve::functor<tgamma_t>;

diff --git a/include/kyosu/functions/zeta.hpp b/include/kyosu/functions/zeta.hpp
@@ -69,8 +69,10 @@ namespace kyosu
 //!
 //!   Returns the Dirichlet zeta sum: \f$  \displaystyle \sum_0^\infty \frac{1}{(n+1)^z}\f$
 //!
-//!  @groupheader{Example}
+//!  @groupheader{External references}
+//!   *  [Wikipedia: Dirichlet series](https://en.wikipedia.org/wiki/Dirichlet_series)
 //!
+//!  @groupheader{Example}
 //!  @godbolt{doc/zeta.cpp}
 //======================================================================================================================
   inline constexpr auto zeta = eve::functor<zeta_t>;