diff --git a/group__complex.html b/group__complex.html new file mode 100644 index 00000000..c6e08e91 --- /dev/null +++ b/group__complex.html @@ -0,0 +1,154 @@ + + + + + + + + +kyosu: Complex + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
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+Variables
+
Complex
+
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+ + + + + + + + +

+Variables

constexpr tags::callable_from_polar kyosu::from_polar = {}
 Callable object computing a complex from its polar coordinates.
 
constexpr tags::callable_to_polar kyosu::to_polar = {}
 Callable object computing the polar coordinates from a complex.
 
+
+
+ + + + + + + + + + diff --git a/group__complex_gac49e8cf76fe002ef3d3e480fb80217ff.html b/group__complex_gac49e8cf76fe002ef3d3e480fb80217ff.html new file mode 100644 index 00000000..7acce905 --- /dev/null +++ b/group__complex_gac49e8cf76fe002ef3d3e480fb80217ff.html @@ -0,0 +1,180 @@ + + + + + + + + +kyosu: kyosu::to_polar + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
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+ +

◆ to_polar

+ +
+
+ + + + + +
+ + + + +
kyosu::to_polar = {}
+ 		+inlineconstexpr
+
+ +

Callable object computing the polar coordinates from a complex.

+

This function is the reciprocal of from_polar

+

Defined in header

+
#include eve/module/quaternion.hpp>`
+

Callable Signatures

+
namespace eve
+
{
+
auto to_polar( auto q) const noexcept;
+
}
+
kyosu::to_polar
constexpr tags::callable_to_polar to_polar
Callable object computing the polar coordinates from a complex.
Definition: to_polar.hpp:86
+

Parameters

+

q : quaternion

+

Return value

+

a tuple containing in this order rho, 'theta': the modulus and the argument in radian of the complex input

+
+

+Example

+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga467a58e50ffba284e333fac35f5cc93c.html b/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html similarity index 71% rename from group__functions_ga467a58e50ffba284e333fac35f5cc93c.html rename to group__complex_gad70670d8278d34dc0f0faf883a48eab8.html index 7bd278d7..09bcbd74 100644 --- a/group__functions_ga467a58e50ffba284e333fac35f5cc93c.html +++ b/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html @@ -6,7 +6,7 @@ -kyosu: kyosu::to_complex +kyosu: kyosu::from_polar @@ -96,7 +96,7 @@
@@ -122,8 +122,8 @@
- -

◆ to_complex

+ +

◆ from_polar

@@ -132,7 +132,7 @@

- +
kyosu::to_complex = {}kyosu::from_polar = {}
@@ -142,27 +142,24 @@

-

Constructs a kyosu::complex.

-

Defined in Header

-
#include <kyosu/functions.hpp>
+

Callable object computing a complex from its polar coordinates.

+

This function is the reciprocal of from_polar

+

Defined in header

+
#include eve/module/quaternion.hpp>`

Callable Signatures

-
namespace kyosu
+
namespace eve
{
-
template<eve::ordered_value T> constexpr auto to_complex(T r) noexcept;
-
template<eve::ordered_value T> constexpr auto to_complex(T r, T i) noexcept;
-
-
template<kyosu::concepts::cayley_dickson T> constexpr T to_complex(T z) noexcept;
+
auto from_polar( auto rho, auto theta) const noexcept;
}
-
kyosu::to_complex
constexpr tags::callable_to_complex to_complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:72
-
kyosu
Main KYOSU namespace.
Definition: acos.hpp:14
+
kyosu::from_polar
constexpr tags::callable_from_polar from_polar
Callable object computing a complex from its polar coordinates.
Definition: from_polar.hpp:91

Parameters

-
    -
  • z : Complex value.
    • -
  • r, i : Real and imaginary part sued to construct a kyosu::complex..
    • -
+

rho : modulus rho : argument.

Return value

-

Returns a kyosu::complex constructed from its arguments.

-

Example

+

the complex number associated.

+
Note
: a negative rho is not an error but is treated as {-rho, theta+pi}.
+
+

+Example

diff --git a/group__functions.html b/group__functions.html index 6bfc5074..6bae5d46 100644 --- a/group__functions.html +++ b/group__functions.html @@ -196,9 +196,15 @@ constexpr tags::callable_average kyosu::average = {}  Computes the average of the two parameters.
  +constexpr tags::callable_beta kyosu::beta = {} + Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\).
+  constexpr tags::callable_ceil kyosu::ceil = {}  Computes the ceil value.
  +constexpr tags::callable_complex kyosu::complex = {} + Constructs a kyosu::complex.
+  constexpr tags::callable_conj kyosu::conj = {}  Computes the conjugate value.
  @@ -235,12 +241,31 @@ constexpr tags::callable_dec kyosu::dec = {}  decrements the argument by 1.
  +constexpr tags::callable_deta kyosu::deta = {} + Computes the Dirichlet sums \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(kn+1)^z}\).
+  +constexpr tags::callable_digamma kyosu::digamma = {} + Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\).
+  constexpr tags::callable_dist kyosu::dist = {}  Computes the distance between the two parameters.
  constexpr tags::callable_dot kyosu::dot = {}  Computes elementwise the dot product of the coordinates of the corresponding element.
  +constexpr tags::callable_erf kyosu::erf = {} + Computes the error function: \( \displaystyle + \mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\) or its analytic continuation in the complex plane.
+  +constexpr tags::callable_erfcx kyosu::erfcx = {} + Computes the normalized complementary error function \( \displaystyle \mbox{erfcx}(x) = e^{x^2} \mbox{erfc}(x)\).
+  +constexpr tags::callable_erfi kyosu::erfi = {} + Callable object computing The imaginary error function \( \displaystyle \mathrm{erfi}(z) = -i\mathrm{erf}(iz)\).
+  +constexpr tags::callable_eta kyosu::eta = {} + Computes the Dirichlet sum \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\). Sometimes this function is for obvious reasons called the alternative \(\zeta\) function .
+  constexpr tags::callable_exp kyosu::exp = {}  Computes the exponential of the argument.
  @@ -265,6 +290,9 @@ constexpr tags::callable_expx2 kyosu::expx2 = {}  Computes the exponential of the squared argument.
  +constexpr tags::callable_faddeeva kyosu::faddeeva = {} + Callable object computing \(e^{-z^2}\mathrm{erfc}(-iz)\) the scaled complex error func.
+  constexpr tags::callable_floor kyosu::floor = {}  Computes the floor value.
  @@ -337,6 +365,15 @@ constexpr tags::callable_kpart kyosu::kpart = {}  Extracts the \(k\) part of a value.
  +constexpr tags::callable_lambda kyosu::lambda = {} + Callable object computing The Dirichlet \( \displaystyle \lambda(z) = \sum_0^\infty \frac{1}{(2n+1)^z}\).
+  +constexpr tags::callable_lbeta kyosu::lbeta = {} + Computes the natural logarithm of the lbeta function.
+  +constexpr tags::callable_ldiv kyosu::ldiv = {} + Computes the left division of the two parameters.
+  constexpr tags::callable_lerp kyosu::lerp = {}  Computes the linear interpolation.
  @@ -355,10 +392,19 @@ constexpr tags::callable_log_abs kyosu::log_abs = {}  Computes the natural logarithm of the absolute value of the argument.
  +constexpr tags::callable_log_abs_gamma kyosu::log_abs_gamma = {} + Computes the log of the modulus of the \(\Gamma\) function of the parameter.
+  +constexpr tags::callable_log_gamma kyosu::log_gamma = {} + Computes the log of the \(\Gamma\) function of the parameter.
+  constexpr tags::callable_lpnorm kyosu::lpnorm = {}  Callable object computing the lpnorm operation \( \left(\sum_{i = 0}^n |x_i|^p\right)^{\frac1p} \).
  +constexpr tags::callable_lrising_factorial kyosu::lrising_factorial = {} + Computes the lrising_factorial function: \(\log\frac{\Gamma(x+y)}{\Gamma(x)}\).
+  constexpr tags::callable_manhattan kyosu::manhattan = {}  Callable object computing the manhattan operation.
  @@ -386,9 +432,15 @@ constexpr tags::callable_powm1 kyosu::powm1 = {}  Computes the computing the powm1 operation \(x^y-1\).
  +constexpr tags::callable_proj kyosu::proj = {} + Callable object computing proj(x), the projection of the cayley_dickson number z onto the (hyper) Riemann sphere.
+  constexpr tags::callable_purepart kyosu::purepart = {}  Extracts the pure part of a value.
  +constexpr tags::callable_quaternion kyosu::quaternion = {} + Constructs a kyosu::quaternion.
+  constexpr tags::callable_radinpi kyosu::radinpi = {}  Computes the parameter divided by \(\pi\).
  @@ -401,6 +453,9 @@ constexpr tags::callable_reldist kyosu::reldist = {}  Computes the relative distance between the two parameters.
  +constexpr tags::callable_rising_factorial kyosu::rising_factorial = {} + Computes the rising_factorial function: \(\frac{\Gamma(x+y)}{\Gamma(x)}\).
+  constexpr tags::callable_sec kyosu::sec = {}  Computes the secant of the argument.
  @@ -455,15 +510,15 @@ constexpr tags::callable_tanpi kyosu::tanpi = {}  Computes the tangent of the argument in \(\pi\) mutiples.
  -constexpr tags::callable_to_complex kyosu::to_complex = {} - Constructs a kyosu::complex.
-  -constexpr tags::callable_to_quaternion kyosu::to_quaternion = {} - Constructs a kyosu::quaternion.
-  +constexpr tags::callable_tgamma kyosu::tgamma = {} + Computes the tgammaolute value of the parameter.
+  constexpr tags::callable_trunc kyosu::trunc = {}  Computes the trunc value.
  +constexpr tags::callable_zeta kyosu::zeta = {} + Computes the Riemann \(\zeta\) \( \displaystyle \sum_0^\infty \frac{1}{(n+1)^z}\).
+ 

diff --git a/group__functions_ga013ae7a04bb6a995c81537ab9c4396b4.html b/group__functions_ga013ae7a04bb6a995c81537ab9c4396b4.html index 94bf338a..9019b921 100644 --- a/group__functions_ga013ae7a04bb6a995c81537ab9c4396b4.html +++ b/group__functions_ga013ae7a04bb6a995c81537ab9c4396b4.html @@ -166,14 +166,14 @@

Example

int main()
{
using kyosu::manhattan;
-
using kyosu::complex;
-
using kyosu::quaternion;
+
using kyosu::complex_t;
+
using kyosu::quaternion_t;
using e_t = float;
-
using c_t = complex<float>;
-
using q_t = quaternion<float>;
+
using c_t = kyosu::complex_t<float>;
+
using q_t = kyosu::quaternion_t<float>;
using we_t = eve::wide<float, eve::fixed<2>>;
-
using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
-
using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
+
using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
+
using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
std::cout << "Real: "<< "\n";
e_t e0(1);
@@ -202,8 +202,8 @@

Example

return 0;
}
kyosu::manhattan
constexpr tags::callable_manhattan manhattan
Callable object computing the manhattan operation.
Definition: manhattan.hpp:75
-
kyosu::quaternion
cayley_dickson< T, 4 > quaternion
Type alias for quaternion numbers.
Definition: quaternion.hpp:26
-
kyosu::complex
cayley_dickson< T, 2 > complex
Type alias for complex numbers.
Definition: complex.hpp:26
+
kyosu::quaternion_t
as_cayley_dickson_n_t< 4, T > quaternion_t
Type alias for quaternion numbers.
Definition: quaternion.hpp:27
+
kyosu::complex_t
as_cayley_dickson_n_t< 2, T > complex_t
Type alias for complex numbers.
Definition: complex.hpp:27
diff --git a/group__functions_ga057662e8933c9837bb4bbb5ffb2822f0.html b/group__functions_ga057662e8933c9837bb4bbb5ffb2822f0.html index 0b3bcd8a..ecea7ee8 100644 --- a/group__functions_ga057662e8933c9837bb4bbb5ffb2822f0.html +++ b/group__functions_ga057662e8933c9837bb4bbb5ffb2822f0.html @@ -168,33 +168,33 @@

Example

int main()
{
using kyosu::kpart;
-
using kyosu::complex;
-
using kyosu::quaternion;
+
using kyosu::complex_t;
+
using kyosu::quaternion_t;
std::cout << "Real: ";
float f = 72.9f;
std::cout << f << " -> " << kpart(f) << "\n";
std::cout << "Complex: ";
-
auto z = complex<float>(3.5f,-2.9f);
+
auto z = kyosu::complex_t<float>(3.5f,-2.9f);
std::cout << z << " -> " << kpart(z) << "\n";
std::cout << "Quaternion: ";
-
auto q = quaternion<double>(1.,2.,3.,4.);
+
auto q = kyosu::quaternion_t<double>(1.,2.,3.,4.);
std::cout << q << " -> " << kpart(q) << " => ";
kpart(q) = 42.7;
std::cout << q << "\n";
std::cout << "SIMD: ";
-
eve::wide<quaternion<double>, eve::fixed<2>> wz(quaternion<double>(1.3,-3.7,4.2,-7.8));
+
eve::wide<kyosu::quaternion_t<double>, eve::fixed<2>> wz(kyosu::quaternion_t<double>(1.3,-3.7,4.2,-7.8));
std::cout << wz << " -> " << kpart(wz) << " => ";
kpart(wz) = eve::wide<double, eve::fixed<2>>{13.37,63.24};
std::cout << wz << "\n";
return 0;
}
-
kyosu::quaternion
cayley_dickson< T, 4 > quaternion
Type alias for quaternion numbers.
Definition: quaternion.hpp:26
-
kyosu::complex
cayley_dickson< T, 2 > complex
Type alias for complex numbers.
Definition: complex.hpp:26
+
kyosu::quaternion_t
as_cayley_dickson_n_t< 4, T > quaternion_t
Type alias for quaternion numbers.
Definition: quaternion.hpp:27
+
kyosu::complex_t
as_cayley_dickson_n_t< 2, T > complex_t
Type alias for complex numbers.
Definition: complex.hpp:27
diff --git a/group__functions_ga0704e6ec9b43b3f6a8864e38b566f795.html b/group__functions_ga0704e6ec9b43b3f6a8864e38b566f795.html index c4bec057..2ab94bab 100644 --- a/group__functions_ga0704e6ec9b43b3f6a8864e38b566f795.html +++ b/group__functions_ga0704e6ec9b43b3f6a8864e38b566f795.html @@ -159,11 +159,33 @@

-
  • a real input z is treated as if to_complex(z) was entered.
    • +
  • a real input z is treated as if complex(z) was entered.
  • Returns elementwise the complex principal value of the arc cotangent of the input as the arc tangent of the inverse of the input.

    • Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> acot(zc) = " << kyosu::acot(zc)<< std::endl
    +
    << "-> acot(ref2) = " << kyosu::acot(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga0ae8f99de8716a46dd7de3ff990602bb.html b/group__functions_ga0ae8f99de8716a46dd7de3ff990602bb.html index 2488b0e9..9b73399b 100644 --- a/group__functions_ga0ae8f99de8716a46dd7de3ff990602bb.html +++ b/group__functions_ga0ae8f99de8716a46dd7de3ff990602bb.html @@ -160,7 +160,51 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::exp2;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    we_t we = we_t(e);
    +
    std::cout << e << " -> " << exp2(e) << "\n";
    +
    std::cout << we << " -> " << exp2(we) << "\n";
    +
    std::cout << exp2(c_t(e))<< "\n";
    +
    std::cout << exp2(q_t(e))<< "\n";
    +
    std::cout << exp2(wc_t(e))<< "\n";
    +
    std::cout << exp2(wq_t(e))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    wc_t wc = wc_t(c);
    +
    std::cout << c << " -> " << exp2(c) << "\n";
    +
    std::cout << wc << " -> " << exp2(wc) << "\n";
    +
    std::cout << exp2(q_t(c))<< "\n";
    +
    std::cout << exp2(wq_t(c))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    wq_t wq = wq_t(q);
    +
    std::cout << q << " -> " << exp2(q) << "\n";
    +
    std::cout << wq << " -> " << exp2(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga0d165215c9a5f3f78feab4b70874f436.html b/group__functions_ga0d165215c9a5f3f78feab4b70874f436.html index fd6ce203..08f665f3 100644 --- a/group__functions_ga0d165215c9a5f3f78feab4b70874f436.html +++ b/group__functions_ga0d165215c9a5f3f78feab4b70874f436.html @@ -160,7 +160,51 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::cotpi;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    we_t we = we_t(e);
    +
    std::cout << e << " -> " << cotpi(e) << "\n";
    +
    std::cout << we << " -> " << cotpi(we) << "\n";
    +
    std::cout << cotpi(c_t(e))<< "\n";
    +
    std::cout << cotpi(q_t(e))<< "\n";
    +
    std::cout << cotpi(wc_t(e))<< "\n";
    +
    std::cout << cotpi(wq_t(e))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    wc_t wc = wc_t(c);
    +
    std::cout << c << " -> " << cotpi(c) << "\n";
    +
    std::cout << wc << " -> " << cotpi(wc) << "\n";
    +
    std::cout << cotpi(q_t(c))<< "\n";
    +
    std::cout << cotpi(wq_t(c))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    wq_t wq = wq_t(q);
    +
    std::cout << q << " -> " << cotpi(q) << "\n";
    +
    std::cout << wq << " -> " << cotpi(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga0e8c3f00c6f3777a5a14320c7b1a31da.html b/group__functions_ga0e8c3f00c6f3777a5a14320c7b1a31da.html new file mode 100644 index 00000000..2f617419 --- /dev/null +++ b/group__functions_ga0e8c3f00c6f3777a5a14320c7b1a31da.html @@ -0,0 +1,203 @@ + + + + + + + + +kyosu: kyosu::log_gamma + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
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    +
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    + +

    ◆ log_gamma

    + +
    +
    + + + + + +
    + + + + +
    kyosu::log_gamma = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the log of the \(\Gamma\) function of the parameter.

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<kyosu::concepts::complex T> constexpr T log_gamma(T z) noexcept;
    +
    template<eve::floatingordered_value T> constexpr T log_gamma(T z) noexcept;
    +
    }
    +
    kyosu::log_gamma
    constexpr tags::callable_log_gamma log_gamma
    Computes the log of the function of the parameter.
    Definition: log_gamma.hpp:74
    +
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14
    +

    Parameters

    +
      +
    • z : Value to process.
      • +
    +

    Return value

    +

    Returns \(\log(\Gamma(z))\). If z is floating the result is as if complex(z) was used in the call.

    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> log_gamma(zc) = " << kyosu::log_gamma(zc)<< std::endl
    +
    << "-> log_gamma(ref2) = " << kyosu::log_gamma(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga1410062f3325c9a4b687d12f5ae53f55.html b/group__functions_ga1410062f3325c9a4b687d12f5ae53f55.html index f7316155..5c738e45 100644 --- a/group__functions_ga1410062f3325c9a4b687d12f5ae53f55.html +++ b/group__functions_ga1410062f3325c9a4b687d12f5ae53f55.html @@ -160,7 +160,60 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::is_denormal;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using eve::as;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<4>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<4>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<4>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    e_t nan = eve::nan(as(e));
    +
    e_t inf = eve::inf(as(e));
    +
    e_t zer = eve::zero(as(e));
    +
    e_t mind= eve::mindenormal(as(e));
    +
    we_t we = we_t(e, zer, nan, mind);
    +
    std::cout << e << " -> " << is_denormal(e) << "\n";
    +
    std::cout << we << " -> " << is_denormal(we) << "\n";
    +
    std::cout << is_denormal(c_t(e))<< "\n";
    +
    std::cout << is_denormal(q_t(e))<< "\n";
    +
    std::cout << is_denormal(kyosu::complex(we))<< "\n";
    +
    std::cout << is_denormal(kyosu::quaternion(we))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    c_t d(0.0f, mind);
    +
    wc_t wc = wc_t(c, zer, nan, d);
    +
    std::cout << c << " -> " << is_denormal(c) << "\n";
    +
    std::cout << wc << " -> " << is_denormal(wc) << "\n";
    +
    std::cout << is_denormal(kyosu::complex(wc))<< "\n";;
    +
    std::cout << is_denormal(kyosu::quaternion(wc))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, mind, 3.2f);
    +
    q_t r(3.5f, nan, inf, zer);
    +
    wq_t wq = wq_t(q, zer, nan, r);
    +
    std::cout << q << " -> " << is_denormal(q) << "\n";
    +
    std::cout << wq << " -> " << is_denormal(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    kyosu::quaternion
    constexpr tags::callable_quaternion quaternion
    Constructs a kyosu::quaternion.
    Definition: to_quaternion.hpp:72
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga1658a3b3d9e67c35d2a85233572770ed.html b/group__functions_ga1658a3b3d9e67c35d2a85233572770ed.html new file mode 100644 index 00000000..43da4f93 --- /dev/null +++ b/group__functions_ga1658a3b3d9e67c35d2a85233572770ed.html @@ -0,0 +1,224 @@ + + + + + + + + +kyosu: kyosu::lbeta + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
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    + +

    ◆ lbeta

    + +
    +
    + + + + + +
    + + + + +
    kyosu::lbeta = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the natural logarithm of the lbeta function.

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template< eve::floating_ordered_value T, eve::floating_ordered_value U >
    +
    auto lbeta(T x,U y) noexcept; //1
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto lbeta(eve::complex_t<T> x, U y) noexcept; //2
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto lbeta(T x, eve::complex_t<U> y) noexcept; //2
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto lbeta(eve::complex_t<T> x, eve::complex_t<U> y) noexcept; //2
    +
    }
    +
    kyosu::lbeta
    constexpr tags::callable_lbeta lbeta
    Computes the natural logarithm of the lbeta function.
    Definition: lbeta.hpp:83
    +
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14
    +

    Parameters

    +
      +
    • x,y : Values to process.
      • +
    +

    Return value

    +

    log(beta(x, y).

    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::lbeta;
    +
    using kyosu::complex_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using we_t = eve::wide<float, eve::fixed<2>>;
    +
    using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
    +
    +
    std::cout << "Real: "<< "\n";
    +
    e_t e0(1);
    +
    e_t e1(2);
    +
    std::cout << e0 << ", " << e1 << " -> " << lbeta(e0, e1) << "\n";
    +
    std::cout << e0 << ", " << e0 << " -> " << lbeta(e0, e0) << "\n";
    +
    we_t we0(e0);
    +
    we_t we1(e1);
    +
    std::cout << we0 << ", " << we1 << " -> " << lbeta(we0, we1) << "\n";
    +
    +
    std::cout << "Complex: "<< "\n";
    +
    c_t c0(1, 5);
    +
    c_t c1(5, 9);
    +
    std::cout << c0 << ", " << c1 << " -> " << lbeta(c0, c1) << "\n";
    +
    std::cout << c0 << ", " << c0 << " -> " << lbeta(c0, c0) << "\n";
    +
    wc_t wc0(c0, c1);
    +
    wc_t wc1(c1, c1);
    +
    std::cout << wc0 << ", " << wc1 << " -> " << lbeta(wc0, wc1) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga1b78fa57857ad714ce5f0e6e3ace5db9.html b/group__functions_ga1b78fa57857ad714ce5f0e6e3ace5db9.html index c7750592..4fec7133 100644 --- a/group__functions_ga1b78fa57857ad714ce5f0e6e3ace5db9.html +++ b/group__functions_ga1b78fa57857ad714ce5f0e6e3ace5db9.html @@ -167,11 +167,11 @@

    Example

    int main()
    {
    using kyosu::minus;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    using e_t = float;
    -
    using c_t = complex<float>;
    -
    using q_t = quaternion<float>;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    @@ -196,8 +196,8 @@

    Example

    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga23d96b11ec047300319b6b8ccfa07765.html b/group__functions_ga23d96b11ec047300319b6b8ccfa07765.html index 716dc145..e11ddc9d 100644 --- a/group__functions_ga23d96b11ec047300319b6b8ccfa07765.html +++ b/group__functions_ga23d96b11ec047300319b6b8ccfa07765.html @@ -169,14 +169,14 @@

    Example

    int main()
    {
    using kyosu::reldist;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    using e_t = float;
    -
    using c_t = complex<float>;
    -
    using q_t = quaternion<float>;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    using we_t = eve::wide<float, eve::fixed<2>>;
    -
    using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
    -
    using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
    +
    using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
    +
    using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
    std::cout << "Real: "<< "\n";
    e_t e0(1);
    @@ -206,8 +206,8 @@

    Example

    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga265f03cd0d4edaaecd88fbcfc3346644.html b/group__functions_ga265f03cd0d4edaaecd88fbcfc3346644.html index df1a18c5..bc0adba1 100644 --- a/group__functions_ga265f03cd0d4edaaecd88fbcfc3346644.html +++ b/group__functions_ga265f03cd0d4edaaecd88fbcfc3346644.html @@ -167,11 +167,11 @@

    Example

    int main()
    {
    using kyosu::dec;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    using e_t = float;
    -
    using c_t = complex<float>;
    -
    using q_t = quaternion<float>;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    @@ -196,8 +196,8 @@

    Example

    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga29021b202d2832d1e6863d7402e25b79.html b/group__functions_ga29021b202d2832d1e6863d7402e25b79.html index 4b5e960d..20962252 100644 --- a/group__functions_ga29021b202d2832d1e6863d7402e25b79.html +++ b/group__functions_ga29021b202d2832d1e6863d7402e25b79.html @@ -160,7 +160,52 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::expx2;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    we_t we = we_t(e);
    +
    std::cout << e << " -> " << expx2(e) << "\n";
    +
    std::cout << we << " -> " << expx2(we) << "\n";
    +
    std::cout << expx2(c_t(e))<< "\n";
    +
    std::cout << expx2(q_t(e))<< "\n";
    +
    std::cout << expx2(wc_t(e))<< "\n";
    +
    std::cout << expx2(wq_t(e))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    wc_t wc = wc_t(c);
    +
    std::cout << c << " -> " << expx2(c) << "\n";
    +
    std::cout << wc << " -> " << expx2(wc) << "\n";
    +
    std::cout << expx2(q_t(c))<< "\n";
    +
    std::cout << expx2(wq_t(c))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    wq_t wq = wq_t(q);
    +
    std::cout << q << " -> " << expx2(q) << "\n";
    +
    std::cout << wq << " -> " << expx2(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::expx2
    constexpr tags::callable_expx2 expx2
    Computes the exponential of the squared argument.
    Definition: expx2.hpp:73
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga2cccab7b0cb7548aabfcd581a6c98fa6.html b/group__functions_ga2cccab7b0cb7548aabfcd581a6c98fa6.html index 9f4e6a51..6b119296 100644 --- a/group__functions_ga2cccab7b0cb7548aabfcd581a6c98fa6.html +++ b/group__functions_ga2cccab7b0cb7548aabfcd581a6c98fa6.html @@ -167,26 +167,26 @@

    Example

    int main()
    {
    using kyosu::floor;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    std::cout << "Real: ";
    std::cout << 72.9f << " -> " << floor(72.9f) << "\n";
    std::cout << "Complex: ";
    -
    std::cout << complex<float>(3.5f,-2.9f) << " -> " << floor(complex<float>(3.5f,-2.9f)) << "\n";
    +
    std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << floor(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
    std::cout << "Quaternion: ";
    -
    std::cout << quaternion<double>(1.,2.,3.,4.) << " -> " << floor(quaternion<double>(1.,2.,3.,4.)) << "\n";
    +
    std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << floor(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
    std::cout << "SIMD: ";
    -
    using wc_t = eve::wide<complex<double>, eve::fixed<2>>;
    -
    std::cout << wc_t(complex<double>(1.3,-3.7)) << " -> " << floor(wc_t(complex<double>(1.3,-3.7))) << "\n";
    +
    using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
    +
    std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << floor(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga2ddfc28eca2aadd941d5fc5e991a5fde.html b/group__functions_ga2ddfc28eca2aadd941d5fc5e991a5fde.html new file mode 100644 index 00000000..39c034a9 --- /dev/null +++ b/group__functions_ga2ddfc28eca2aadd941d5fc5e991a5fde.html @@ -0,0 +1,190 @@ + + + + + + + + +kyosu: kyosu::rising_factorial + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    kyosu v0.1.0 +
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    ◆ rising_factorial

    + +
    +
    + + + + + +
    + + + + +
    kyosu::rising_factorial = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the rising_factorial function: \(\frac{\Gamma(x+y)}{\Gamma(x)}\).

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template< eve::floating_ordered_value T, eve::floating_ordered_value U >
    +
    auto rising_factorial(T x,U y) noexcept; //1
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto rising_factorial(eve::complex_t<T> x, U y) noexcept; //2
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto rising_factorial(T x, eve::complex_t<U> y) noexcept; //2
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto rising_factorial(eve::complex_t<T> x, eve::complex_t<U> y) noexcept; //2
    +
    }
    +
    kyosu::rising_factorial
    constexpr tags::callable_rising_factorial rising_factorial
    Computes the rising_factorial function: .
    Definition: rising_factorial.hpp:83
    +
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14
    +

    Parameters

    +
      +
    • x,y : Values to process.
      • +
    +

    Return value

    +

    Computes the Rising Factorial function i.e. \(\frac{\Gamma(x+y)}{\Gamma(x)}\).

    +

    Example

    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga398aa088354c3b9d0a0a1b5d6b7145f9.html b/group__functions_ga398aa088354c3b9d0a0a1b5d6b7145f9.html index 0ffd870e..40b54924 100644 --- a/group__functions_ga398aa088354c3b9d0a0a1b5d6b7145f9.html +++ b/group__functions_ga398aa088354c3b9d0a0a1b5d6b7145f9.html @@ -160,7 +160,51 @@

    log(z). If z is an ordered value log returns a complex typed value.

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::log;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    we_t we = we_t(e);
    +
    std::cout << e << " -> " << log(e) << "\n";
    +
    std::cout << we << " -> " << log(we) << "\n";
    +
    std::cout << log(c_t(e))<< "\n";
    +
    std::cout << log(q_t(e))<< "\n";
    +
    std::cout << log(wc_t(e))<< "\n";
    +
    std::cout << log(wq_t(e))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    wc_t wc = wc_t(c);
    +
    std::cout << c << " -> " << log(c) << "\n";
    +
    std::cout << wc << " -> " << log(wc) << "\n";
    +
    std::cout << log(q_t(c))<< "\n";
    +
    std::cout << log(wq_t(c))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    wq_t wq = wq_t(q);
    +
    std::cout << q << " -> " << log(q) << "\n";
    +
    std::cout << wq << " -> " << log(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga3c49606902ab917444da4ac9ed3003ce.html b/group__functions_ga3c49606902ab917444da4ac9ed3003ce.html index 5a64af7b..497bfb78 100644 --- a/group__functions_ga3c49606902ab917444da4ac9ed3003ce.html +++ b/group__functions_ga3c49606902ab917444da4ac9ed3003ce.html @@ -169,14 +169,14 @@

    Example

    int main()
    {
    using kyosu::dist;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    using e_t = float;
    -
    using c_t = complex<float>;
    -
    using q_t = quaternion<float>;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    using we_t = eve::wide<float, eve::fixed<2>>;
    -
    using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
    -
    using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
    +
    using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
    +
    using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
    std::cout << "Real: "<< "\n";
    e_t e0(1);
    @@ -206,8 +206,8 @@

    Example

    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga3d9e6e28fb334f64bbe3c1b60f28d15b.html b/group__functions_ga3d9e6e28fb334f64bbe3c1b60f28d15b.html index 38dd734f..bd332014 100644 --- a/group__functions_ga3d9e6e28fb334f64bbe3c1b60f28d15b.html +++ b/group__functions_ga3d9e6e28fb334f64bbe3c1b60f28d15b.html @@ -167,14 +167,14 @@

    Example

    int main()
    {
    using kyosu::lpnorm;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    using e_t = float;
    -
    using c_t = complex<float>;
    -
    using q_t = quaternion<float>;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    using we_t = eve::wide<float, eve::fixed<2>>;
    -
    using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
    -
    using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
    +
    using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
    +
    using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
    std::cout << "Real: "<< "\n";
    e_t e0(1);
    @@ -203,8 +203,8 @@

    Example

    return 0;
    }
    kyosu::lpnorm
    constexpr tags::callable_lpnorm lpnorm
    Callable object computing the lpnorm operation .
    Definition: lpnorm.hpp:77
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga3e5656e4788dbebd4450758cba9dab9d.html b/group__functions_ga3e5656e4788dbebd4450758cba9dab9d.html index ad15d265..43aead7a 100644 --- a/group__functions_ga3e5656e4788dbebd4450758cba9dab9d.html +++ b/group__functions_ga3e5656e4788dbebd4450758cba9dab9d.html @@ -160,7 +160,59 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::is_not_infinite;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using eve::as;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<4>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<4>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<4>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    e_t nan = eve::nan(as(e));
    +
    e_t inf = eve::inf(as(e));
    +
    e_t zer = eve::zero(as(e));
    +
    we_t we = we_t(e, zer, nan, inf);
    +
    std::cout << e << " -> " << is_not_infinite(e) << "\n";
    +
    std::cout << we << " -> " << is_not_infinite(we) << "\n";
    +
    std::cout << is_not_infinite(c_t(e))<< "\n";
    +
    std::cout << is_not_infinite(q_t(e))<< "\n";
    +
    std::cout << is_not_infinite(kyosu::complex(we))<< "\n";
    +
    std::cout << is_not_infinite(kyosu::quaternion(we))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    c_t d(0.0f, inf);
    +
    wc_t wc = wc_t(c, zer, nan, d);
    +
    std::cout << c << " -> " << is_not_infinite(c) << "\n";
    +
    std::cout << wc << " -> " << is_not_infinite(wc) << "\n";
    +
    std::cout << is_not_infinite(kyosu::complex(wc))<< "\n";;
    +
    std::cout << is_not_infinite(kyosu::quaternion(wc))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    q_t r(3.5f, nan, inf, zer);
    +
    wq_t wq = wq_t(q, zer, nan, r);
    +
    std::cout << q << " -> " << is_not_infinite(q) << "\n";
    +
    std::cout << wq << " -> " << is_not_infinite(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    kyosu::quaternion
    constexpr tags::callable_quaternion quaternion
    Constructs a kyosu::quaternion.
    Definition: to_quaternion.hpp:72
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga40c963ecefcdeba9487598d5ef9bf874.html b/group__functions_ga40c963ecefcdeba9487598d5ef9bf874.html index 6ab1a382..06304f8c 100644 --- a/group__functions_ga40c963ecefcdeba9487598d5ef9bf874.html +++ b/group__functions_ga40c963ecefcdeba9487598d5ef9bf874.html @@ -159,11 +159,33 @@

    -
  • a real input z is treated as if to_complex(z) was entered.
    • +
  • a real input z is treated as if complex(z) was entered.
  • Returns elementwise \(\mathop{\mathrm{asin}}(1/z)\).

    • Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> acsc(zc) = " << kyosu::acsc(zc)<< std::endl
    +
    << "-> acsc(ref2) = " << kyosu::acsc(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga42fce115bbd07cb330a84af0213c656d.html b/group__functions_ga42fce115bbd07cb330a84af0213c656d.html index ad5df5a2..928ea48c 100644 --- a/group__functions_ga42fce115bbd07cb330a84af0213c656d.html +++ b/group__functions_ga42fce115bbd07cb330a84af0213c656d.html @@ -149,9 +149,10 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T log1p(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr as_complex_t<T> log1p(T z) noexcept;
    +
    template<eve::ordered_value T> constexpr complex_t<T> log1p(T z) noexcept;
    }
    kyosu::log1p
    constexpr tags::callable_log1p log1p
    Computes the natural logarithm of the argument plus 1.
    Definition: log1p.hpp:78
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14

    Parameters

      @@ -160,7 +161,50 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::log1p;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<2>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<2>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<2>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      we_t we = we_t(e);
      +
      std::cout << e << " -> " << log1p(e) << "\n";
      +
      std::cout << we << " -> " << log1p(we) << "\n";
      +
      std::cout << log1p(c_t(e))<< "\n";
      +
      std::cout << log1p(q_t(e))<< "\n";
      +
      std::cout << log1p(wc_t(e))<< "\n";
      +
      std::cout << log1p(wq_t(e))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      wc_t wc = wc_t(c);
      +
      std::cout << c << " -> " << log1p(c) << "\n";
      +
      std::cout << wc << " -> " << log1p(wc) << "\n";
      +
      std::cout << log1p(q_t(c))<< "\n";
      +
      std::cout << log1p(wq_t(c))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      wq_t wq = wq_t(q);
      +
      std::cout << q << " -> " << log1p(q) << "\n";
      +
      std::cout << wq << " -> " << log1p(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      diff --git a/group__functions_ga441cd97a80d870b01cf6cd1ace7238e7.html b/group__functions_ga441cd97a80d870b01cf6cd1ace7238e7.html index f163e099..a94b8c22 100644 --- a/group__functions_ga441cd97a80d870b01cf6cd1ace7238e7.html +++ b/group__functions_ga441cd97a80d870b01cf6cd1ace7238e7.html @@ -160,7 +160,59 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::is_not_finite;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using eve::as;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<4>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<4>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<4>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      e_t nan = eve::nan(as(e));
      +
      e_t inf = eve::inf(as(e));
      +
      e_t zer = eve::zero(as(e));
      +
      we_t we = we_t(e, zer, nan, inf);
      +
      std::cout << e << " -> " << is_not_finite(e) << "\n";
      +
      std::cout << we << " -> " << is_not_finite(we) << "\n";
      +
      std::cout << is_not_finite(c_t(e))<< "\n";
      +
      std::cout << is_not_finite(q_t(e))<< "\n";
      +
      std::cout << is_not_finite(kyosu::complex(we))<< "\n";
      +
      std::cout << is_not_finite(kyosu::quaternion(we))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      c_t d(0.0f, inf);
      +
      wc_t wc = wc_t(c, zer, nan, d);
      +
      std::cout << c << " -> " << is_not_finite(c) << "\n";
      +
      std::cout << wc << " -> " << is_not_finite(wc) << "\n";
      +
      std::cout << is_not_finite(kyosu::complex(wc))<< "\n";;
      +
      std::cout << is_not_finite(kyosu::quaternion(wc))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      q_t r(3.5f, nan, inf, zer);
      +
      wq_t wq = wq_t(q, zer, nan, r);
      +
      std::cout << q << " -> " << is_not_finite(q) << "\n";
      +
      std::cout << wq << " -> " << is_not_finite(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex
      constexpr tags::callable_complex complex
      Constructs a kyosu::complex.
      Definition: to_complex.hpp:70
      +
      kyosu::quaternion
      constexpr tags::callable_quaternion quaternion
      Constructs a kyosu::quaternion.
      Definition: to_quaternion.hpp:72
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga45677fbbb676a8b5287c2c0c0ab5deae.html b/group__functions_ga45677fbbb676a8b5287c2c0c0ab5deae.html index 94edb383..1e58f1d6 100644 --- a/group__functions_ga45677fbbb676a8b5287c2c0c0ab5deae.html +++ b/group__functions_ga45677fbbb676a8b5287c2c0c0ab5deae.html @@ -160,7 +160,59 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::is_not_real;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using eve::as;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<4>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<4>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<4>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      e_t nan = eve::nan(as(e));
      +
      e_t inf = eve::inf(as(e));
      +
      e_t zer = eve::zero(as(e));
      +
      we_t we = we_t(e, zer, nan, inf);
      +
      std::cout << e << " -> " << is_not_real(e) << "\n";
      +
      std::cout << we << " -> " << is_not_real(we) << "\n";
      +
      std::cout << is_not_real(c_t(e))<< "\n";
      +
      std::cout << is_not_real(q_t(e))<< "\n";
      +
      std::cout << is_not_real(kyosu::complex(we))<< "\n";
      +
      std::cout << is_not_real(kyosu::quaternion(we))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      c_t d(0.0f, inf);
      +
      wc_t wc = wc_t(c, zer, nan, d);
      +
      std::cout << c << " -> " << is_not_real(c) << "\n";
      +
      std::cout << wc << " -> " << is_not_real(wc) << "\n";
      +
      std::cout << is_not_real(kyosu::complex(wc))<< "\n";;
      +
      std::cout << is_not_real(kyosu::quaternion(wc))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      q_t r(3.5f, nan, inf, zer);
      +
      wq_t wq = wq_t(q, zer, nan, r);
      +
      std::cout << q << " -> " << is_not_real(q) << "\n";
      +
      std::cout << wq << " -> " << is_not_real(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex
      constexpr tags::callable_complex complex
      Constructs a kyosu::complex.
      Definition: to_complex.hpp:70
      +
      kyosu::quaternion
      constexpr tags::callable_quaternion quaternion
      Constructs a kyosu::quaternion.
      Definition: to_quaternion.hpp:72
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga4c6ee3532d93a937aaa603ba4699b3ed.html b/group__functions_ga4c6ee3532d93a937aaa603ba4699b3ed.html index 0975c1b0..a375549b 100644 --- a/group__functions_ga4c6ee3532d93a937aaa603ba4699b3ed.html +++ b/group__functions_ga4c6ee3532d93a937aaa603ba4699b3ed.html @@ -167,26 +167,26 @@

      Example

      int main()
      {
      using kyosu::frac;
      -
      using kyosu::complex;
      -
      using kyosu::quaternion;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      std::cout << "Real: ";
      std::cout << 72.9f << " -> " << frac(72.9f) << "\n";
      std::cout << "Complex: ";
      -
      std::cout << complex<float>(3.5f,-2.9f) << " -> " << frac(complex<float>(3.5f,-2.9f)) << "\n";
      +
      std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << frac(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
      std::cout << "Quaternion: ";
      -
      std::cout << quaternion<double>(1.,2.,3.,4.) << " -> " << frac(quaternion<double>(1.,2.,3.,4.)) << "\n";
      +
      std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << frac(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
      std::cout << "SIMD: ";
      -
      using wc_t = eve::wide<complex<double>, eve::fixed<2>>;
      -
      std::cout << wc_t(complex<double>(1.3,-3.7)) << " -> " << frac(wc_t(complex<double>(1.3,-3.7))) << "\n";
      +
      using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
      +
      std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << frac(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
      return 0;
      }
      -
      kyosu::quaternion
      cayley_dickson< T, 4 > quaternion
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:26
      -
      kyosu::complex
      cayley_dickson< T, 2 > complex
      Type alias for complex numbers.
      Definition: complex.hpp:26
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      diff --git a/group__functions_ga4f655a16c878099303a59697347bce41.html b/group__functions_ga4f655a16c878099303a59697347bce41.html index 6dfa9830..56af3cce 100644 --- a/group__functions_ga4f655a16c878099303a59697347bce41.html +++ b/group__functions_ga4f655a16c878099303a59697347bce41.html @@ -168,50 +168,43 @@

      Example

      int main()
      {
      using kyosu::is_unitary;
      -
      using kyosu::complex;
      -
      using kyosu::quaternion;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      using e_t = float;
      -
      using c_t = complex<float>;
      -
      using q_t = quaternion<float>;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      using we_t = eve::wide<e_t, eve::fixed<2>>;
      using wc_t = eve::wide<c_t, eve::fixed<2>>;
      using wq_t = eve::wide<q_t, eve::fixed<2>>;
      std::cout << "Real: \n";
      -
      e_t e(72.9f);
      +
      e_t e(2.9f);
      we_t we = we_t(e);
      -
      e_t ue = kyosu::sign(e);
      -
      we_t uwe = kyosu::sign(we);
      std::cout << e << " -> " << is_unitary(e) << "\n";
      std::cout << we << " -> " << is_unitary(we) << "\n";
      -
      std::cout << ue << " -> " << is_unitary(ue) << "\n";
      -
      std::cout << uwe << " -> " << is_unitary(uwe) << "\n";
      +
      std::cout << is_unitary(c_t(e))<< "\n";
      +
      std::cout << is_unitary(q_t(e))<< "\n";
      +
      std::cout << is_unitary(wc_t(e))<< "\n";
      +
      std::cout << is_unitary(wq_t(e))<< "\n";
      std::cout << "Complex: \n";
      c_t c(3.5f,-2.9f);
      wc_t wc = wc_t(c);
      -
      c_t uc = kyosu::sign(c);
      -
      wc_t uwc = kyosu::sign(wc);
      std::cout << c << " -> " << is_unitary(c) << "\n";
      std::cout << wc << " -> " << is_unitary(wc) << "\n";
      -
      std::cout << uc << " -> " << is_unitary(uc) << "\n";
      -
      std::cout << uwc << " -> " << is_unitary(uwc) << "\n";
      +
      std::cout << is_unitary(q_t(c))<< "\n";
      +
      std::cout << is_unitary(wq_t(c))<< "\n";
      std::cout << "Quaternion: \n";
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      wq_t wq = wq_t(q);
      -
      q_t uq = kyosu::sign(q);
      -
      wq_t uwq = kyosu::sign(wq);
      std::cout << q << " -> " << is_unitary(q) << "\n";
      std::cout << wq << " -> " << is_unitary(wq) << "\n";
      -
      std::cout << uq << " -> " << is_unitary(uq) << "\n";
      -
      std::cout << uwq << " -> " << is_unitary(uwq) << "\n";
      return 0;
      }
      -
      kyosu::sign
      constexpr tags::callable_sign sign
      Computes tne normalized value z/abs(z) if z is not zero else 0.
      Definition: sign.hpp:75
      -
      kyosu::quaternion
      cayley_dickson< T, 4 > quaternion
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:26
      -
      kyosu::complex
      cayley_dickson< T, 2 > complex
      Type alias for complex numbers.
      Definition: complex.hpp:26
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      diff --git a/group__functions_ga5354d486ec4fca0c8261639b8ccfffd7.html b/group__functions_ga5354d486ec4fca0c8261639b8ccfffd7.html index 7f34d687..8e809bc7 100644 --- a/group__functions_ga5354d486ec4fca0c8261639b8ccfffd7.html +++ b/group__functions_ga5354d486ec4fca0c8261639b8ccfffd7.html @@ -167,11 +167,11 @@

      Example

      int main()
      {
      using kyosu::inc;
      -
      using kyosu::complex;
      -
      using kyosu::quaternion;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      using e_t = float;
      -
      using c_t = complex<float>;
      -
      using q_t = quaternion<float>;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      using we_t = eve::wide<e_t, eve::fixed<2>>;
      using wc_t = eve::wide<c_t, eve::fixed<2>>;
      using wq_t = eve::wide<q_t, eve::fixed<2>>;
      @@ -196,8 +196,8 @@

      Example

      return 0;
      }
      -
      kyosu::quaternion
      cayley_dickson< T, 4 > quaternion
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:26
      -
      kyosu::complex
      cayley_dickson< T, 2 > complex
      Type alias for complex numbers.
      Definition: complex.hpp:26
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      diff --git a/group__functions_ga56c1f717912fdf18ae43c1051719cea3.html b/group__functions_ga56c1f717912fdf18ae43c1051719cea3.html index 38527450..e95650ce 100644 --- a/group__functions_ga56c1f717912fdf18ae43c1051719cea3.html +++ b/group__functions_ga56c1f717912fdf18ae43c1051719cea3.html @@ -159,13 +159,35 @@

      -
    • a real input z is treated as if to_complex(z) was entered.
      • +
    • a real input z is treated as if complex(z) was entered.

    • Returns the elementwise the complex principal value of the arc sine of the input in the range of a strip unbounded along the imaginary axis and in the interval \([-\pi/2, \pi/2]\) along the real axis.

      special cases are handled as if the operation was implemented by \(-i \mathrm{asinh}(i z)\)

      • Example

      -

      Defined in Header

      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> asin(zc) = " << kyosu::asin(zc)<< std::endl
      +
      << "-> asin(ref2) = " << kyosu::asin(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +

      Defined in Header

      #include <kyosu/functions.hpp>

      Callable Signatures

      namespace kyosu
      @@ -179,13 +201,34 @@

      Example

    Return value

      -
    1. a real input z is treated as if to_complex(z) was entered.
      2. -

    2. Returns the elementwise the complex principal value of the arc sine of the input in the range of a strip unbounded along the imaginary axis and in the interval \([-\pi/2, \pi/2]\) along the real axis.

      +
    3. a real input z is treated as if complex(z) was entered.
      4. +

    4. Returns elementwise the complex principal value of the arc sine of the input in the range of a strip unbounded along the imaginary axis and in the interval \([-\pi/2, \pi/2]\) along the real axis.

      special cases are handled as if the operation was implemented by \(-i \mathrm{asinh}(i z)\)

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> asin(zc) = " << kyosu::asin(zc)<< std::endl
    +
    << "-> asin(ref2) = " << kyosu::asin(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    diff --git a/group__functions_ga57a5e1064f03073d3e81144181f6ac71.html b/group__functions_ga57a5e1064f03073d3e81144181f6ac71.html index 68296361..4d525b77 100644 --- a/group__functions_ga57a5e1064f03073d3e81144181f6ac71.html +++ b/group__functions_ga57a5e1064f03073d3e81144181f6ac71.html @@ -167,26 +167,26 @@

    Example

    int main()
    {
    using kyosu::trunc;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    std::cout << "Real: ";
    std::cout << 72.9f << " -> " << trunc(72.9f) << "\n";
    std::cout << "Complex: ";
    -
    std::cout << complex<float>(3.5f,-2.9f) << " -> " << trunc(complex<float>(3.5f,-2.9f)) << "\n";
    +
    std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << trunc(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
    std::cout << "Quaternion: ";
    -
    std::cout << quaternion<double>(1.,2.,3.,4.) << " -> " << trunc(quaternion<double>(1.,2.,3.,4.)) << "\n";
    +
    std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << trunc(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
    std::cout << "SIMD: ";
    -
    using wc_t = eve::wide<complex<double>, eve::fixed<2>>;
    -
    std::cout << wc_t(complex<double>(1.3,-3.7)) << " -> " << trunc(wc_t(complex<double>(1.3,-3.7))) << "\n";
    +
    using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
    +
    std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << trunc(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga5ed3799fdd8b66d17a274669dcf3319b.html b/group__functions_ga5ed3799fdd8b66d17a274669dcf3319b.html index 8bfd03f8..933496a8 100644 --- a/group__functions_ga5ed3799fdd8b66d17a274669dcf3319b.html +++ b/group__functions_ga5ed3799fdd8b66d17a274669dcf3319b.html @@ -160,7 +160,59 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::is_eqz;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using eve::as;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<4>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<4>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<4>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    e_t nan = eve::nan(as(e));
    +
    e_t inf = eve::inf(as(e));
    +
    e_t zer = eve::zero(as(e));
    +
    we_t we = we_t(e, zer, nan, inf);
    +
    std::cout << e << " -> " << is_eqz(e) << "\n";
    +
    std::cout << we << " -> " << is_eqz(we) << "\n";
    +
    std::cout << is_eqz(c_t(e))<< "\n";
    +
    std::cout << is_eqz(q_t(e))<< "\n";
    +
    std::cout << is_eqz(kyosu::complex(we))<< "\n";
    +
    std::cout << is_eqz(kyosu::quaternion(we))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    c_t d(0.0f, inf);
    +
    wc_t wc = wc_t(c, zer, nan, d);
    +
    std::cout << c << " -> " << is_eqz(c) << "\n";
    +
    std::cout << wc << " -> " << is_eqz(wc) << "\n";
    +
    std::cout << is_eqz(kyosu::complex(wc))<< "\n";;
    +
    std::cout << is_eqz(kyosu::quaternion(wc))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    q_t r(3.5f, nan, inf, zer);
    +
    wq_t wq = wq_t(q, zer, nan, r);
    +
    std::cout << q << " -> " << is_eqz(q) << "\n";
    +
    std::cout << wq << " -> " << is_eqz(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    kyosu::quaternion
    constexpr tags::callable_quaternion quaternion
    Constructs a kyosu::quaternion.
    Definition: to_quaternion.hpp:72
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga6061b321a4cb255fbbcae1992d42aafa.html b/group__functions_ga6061b321a4cb255fbbcae1992d42aafa.html index 4dfe01b0..ea53567f 100644 --- a/group__functions_ga6061b321a4cb255fbbcae1992d42aafa.html +++ b/group__functions_ga6061b321a4cb255fbbcae1992d42aafa.html @@ -160,7 +160,51 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::csch;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    we_t we = we_t(e);
    +
    std::cout << e << " -> " << csch(e) << "\n";
    +
    std::cout << we << " -> " << csch(we) << "\n";
    +
    std::cout << csch(c_t(e))<< "\n";
    +
    std::cout << csch(q_t(e))<< "\n";
    +
    std::cout << csch(wc_t(e))<< "\n";
    +
    std::cout << csch(wq_t(e))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    wc_t wc = wc_t(c);
    +
    std::cout << c << " -> " << csch(c) << "\n";
    +
    std::cout << wc << " -> " << csch(wc) << "\n";
    +
    std::cout << csch(q_t(c))<< "\n";
    +
    std::cout << csch(wq_t(c))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    wq_t wq = wq_t(q);
    +
    std::cout << q << " -> " << csch(q) << "\n";
    +
    std::cout << wq << " -> " << csch(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga61fefac92fc13470ee246ab0a77a8008.html b/group__functions_ga61fefac92fc13470ee246ab0a77a8008.html index 4fad76b8..3c36de3c 100644 --- a/group__functions_ga61fefac92fc13470ee246ab0a77a8008.html +++ b/group__functions_ga61fefac92fc13470ee246ab0a77a8008.html @@ -169,14 +169,14 @@

    Example

    int main()
    {
    using kyosu::average;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    using e_t = float;
    -
    using c_t = complex<float>;
    -
    using q_t = quaternion<float>;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    using we_t = eve::wide<float, eve::fixed<2>>;
    -
    using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
    -
    using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
    +
    using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
    +
    using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
    std::cout << "Real: "<< "\n";
    e_t e0(1);
    @@ -213,8 +213,8 @@

    Example

    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga64844c4bb1523fd1a5bfc288ec1186df.html b/group__functions_ga64844c4bb1523fd1a5bfc288ec1186df.html new file mode 100644 index 00000000..6869886c --- /dev/null +++ b/group__functions_ga64844c4bb1523fd1a5bfc288ec1186df.html @@ -0,0 +1,203 @@ + + + + + + + + +kyosu: kyosu::faddeeva + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
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    +
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    +
    +
    +
    +
    + +
    + +

    ◆ faddeeva

    + +
    +
    + + + + + +
    + + + + +
    kyosu::faddeeva = {}
    +     		+inlineconstexpr
    +
    + +

    Callable object computing \(e^{-z^2}\mathrm{erfc}(-iz)\) the scaled complex error func.

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<eve::ordered_value T> constexpr auto faddeeva(T z) noexcept; //1
    +
    template<kyosu::concepts::complex T> constexpr auto faddeeva(T z) noexcept; //2
    +
    }
    +
    kyosu::faddeeva
    constexpr tags::callable_faddeeva faddeeva
    Callable object computing the scaled complex error func.
    Definition: faddeeva.hpp:77
    +
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14
    +

    Parameters

    +
      +
    • z : Value to process.
      • +
    +

    Return value

    +

    Returns \(e^{-z^2}\mathrm{erfc}(-iz)\) the scaled complex error function

    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> faddeeva(zc) = " << kyosu::faddeeva(zc)<< std::endl
    +
    << "-> faddeeva(ref2) = " << kyosu::faddeeva(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga64a0550a46270d01b31593e38a364f72.html b/group__functions_ga64a0550a46270d01b31593e38a364f72.html new file mode 100644 index 00000000..9fd73f64 --- /dev/null +++ b/group__functions_ga64a0550a46270d01b31593e38a364f72.html @@ -0,0 +1,227 @@ + + + + + + + + +kyosu: kyosu::beta + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
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    +
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    +
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    +
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    +
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    +
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    +
    + +
    + +

    ◆ beta

    + +
    +
    + + + + + +
    + + + + +
    kyosu::beta = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\).

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template< eve::floating_ordered_value T, eve::floating_ordered_value U >
    +
    auto beta(T x,U y) noexcept; //1
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto beta(eve::complex_t<T> x, U y) noexcept; //2
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto beta(T x, eve::complex_t<U> y) noexcept; //2
    +
    +
    template< eve::floating_value T, eve::floating_value U >
    +
    auto beta(eve::complex_t<T> x, eve::complex_t<U> y) noexcept; //2
    +
    }
    +
    kyosu::beta
    constexpr tags::callable_beta beta
    Computes the beta function: .
    Definition: beta.hpp:84
    +
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14
    +

    Parameters

    +
      +
    • x,y : Values to process.
      • +
    +

    Return value

    +
      +
    1. \(\displaystyle \mathbf{B}(x,y) = \int_0^1 t^{x-1}(1-t)^{y-1}\mbox{d}t\)
      2. +
    2. The complex \(\displaystyle \mathbb{B}(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) is returned.
      3. +
    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::beta;
    +
    using kyosu::complex_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using we_t = eve::wide<float, eve::fixed<2>>;
    +
    using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
    +
    +
    std::cout << "Real: "<< "\n";
    +
    e_t e0(1);
    +
    e_t e1(2);
    +
    std::cout << e0 << ", " << e1 << " -> " << beta(e0, e1) << "\n";
    +
    std::cout << e0 << ", " << e0 << " -> " << beta(e0, e0) << "\n";
    +
    we_t we0(e0);
    +
    we_t we1(e1);
    +
    std::cout << we0 << ", " << we1 << " -> " << beta(we0, we1) << "\n";
    +
    +
    std::cout << "Complex: "<< "\n";
    +
    c_t c0(1, 5);
    +
    c_t c1(5, 9);
    +
    std::cout << c0 << ", " << c1 << " -> " << beta(c0, c1) << "\n";
    +
    std::cout << c0 << ", " << c0 << " -> " << beta(c0, c0) << "\n";
    +
    wc_t wc0(c0, c1);
    +
    wc_t wc1(c1, c1);
    +
    std::cout << wc0 << ", " << wc1 << " -> " << beta(wc0, wc1) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga6658defe6cc879802872ceb5e92749a9.html b/group__functions_ga6658defe6cc879802872ceb5e92749a9.html index 475135f3..a1b23f1f 100644 --- a/group__functions_ga6658defe6cc879802872ceb5e92749a9.html +++ b/group__functions_ga6658defe6cc879802872ceb5e92749a9.html @@ -160,7 +160,51 @@

    exp(z*z).

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::expx2;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    we_t we = we_t(e);
    +
    std::cout << e << " -> " << expx2(e) << "\n";
    +
    std::cout << we << " -> " << expx2(we) << "\n";
    +
    std::cout << expx2(c_t(e))<< "\n";
    +
    std::cout << expx2(q_t(e))<< "\n";
    +
    std::cout << expx2(wc_t(e))<< "\n";
    +
    std::cout << expx2(wq_t(e))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    wc_t wc = wc_t(c);
    +
    std::cout << c << " -> " << expx2(c) << "\n";
    +
    std::cout << wc << " -> " << expx2(wc) << "\n";
    +
    std::cout << expx2(q_t(c))<< "\n";
    +
    std::cout << expx2(wq_t(c))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    wq_t wq = wq_t(q);
    +
    std::cout << q << " -> " << expx2(q) << "\n";
    +
    std::cout << wq << " -> " << expx2(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga686170a43d13c97096af719b7c0e7fda.html b/group__functions_ga686170a43d13c97096af719b7c0e7fda.html index fac0ca02..8e2af145 100644 --- a/group__functions_ga686170a43d13c97096af719b7c0e7fda.html +++ b/group__functions_ga686170a43d13c97096af719b7c0e7fda.html @@ -160,7 +160,59 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::is_nan;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using eve::as;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<4>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<4>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<4>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    e_t nan = eve::nan(as(e));
    +
    e_t inf = eve::inf(as(e));
    +
    e_t zer = eve::zero(as(e));
    +
    we_t we = we_t(e, zer, nan, inf);
    +
    std::cout << e << " -> " << is_nan(e) << "\n";
    +
    std::cout << we << " -> " << is_nan(we) << "\n";
    +
    std::cout << is_nan(c_t(e))<< "\n";
    +
    std::cout << is_nan(q_t(e))<< "\n";
    +
    std::cout << is_nan(kyosu::complex(we))<< "\n";
    +
    std::cout << is_nan(kyosu::quaternion(we))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    c_t d(0.0f, inf);
    +
    wc_t wc = wc_t(c, zer, nan, d);
    +
    std::cout << c << " -> " << is_nan(c) << "\n";
    +
    std::cout << wc << " -> " << is_nan(wc) << "\n";
    +
    std::cout << is_nan(kyosu::complex(wc))<< "\n";;
    +
    std::cout << is_nan(kyosu::quaternion(wc))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    q_t r(3.5f, nan, inf, zer);
    +
    wq_t wq = wq_t(q, zer, nan, r);
    +
    std::cout << q << " -> " << is_nan(q) << "\n";
    +
    std::cout << wq << " -> " << is_nan(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    kyosu::quaternion
    constexpr tags::callable_quaternion quaternion
    Constructs a kyosu::quaternion.
    Definition: to_quaternion.hpp:72
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga6caf1752927065dfc9ab769d9b00676a.html b/group__functions_ga6caf1752927065dfc9ab769d9b00676a.html new file mode 100644 index 00000000..9d15f2e6 --- /dev/null +++ b/group__functions_ga6caf1752927065dfc9ab769d9b00676a.html @@ -0,0 +1,203 @@ + + + + + + + + +kyosu: kyosu::digamma + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
    Loading...
    +
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    +
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    +
    +
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    +
    + +
    + +

    ◆ digamma

    + +
    +
    + + + + + +
    + + + + +
    kyosu::digamma = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\).

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<kyosu::concepts::complex T> constexpr T digamma(T z) noexcept;
    +
    template<eve::floatingordered_value T> constexpr T digamma(T z) noexcept;
    +
    }
    +
    kyosu::digamma
    constexpr tags::callable_digamma digamma
    Computes the Digamma function i.e. the logarithmic derivative of the .
    Definition: digamma.hpp:73
    +
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14
    +

    Parameters

    +
      +
    • z : Value to process.
      • +
    +

    Return value

    +

    The value of the Digamma function: \(\frac{\Gamma'(z)}{\Gamma(z)}\) is returned.

    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> digamma(zc) = " << kyosu::digamma(zc)<< std::endl
    +
    << "-> digamma(ref2) = " << kyosu::digamma(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga6d65485712648eb40b8dc0453d9c3baf.html b/group__functions_ga6d65485712648eb40b8dc0453d9c3baf.html index 3b329c22..a86956fd 100644 --- a/group__functions_ga6d65485712648eb40b8dc0453d9c3baf.html +++ b/group__functions_ga6d65485712648eb40b8dc0453d9c3baf.html @@ -165,20 +165,20 @@

    Example

    int main()
    {
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    -
    auto c = complex<float>(3.5f,-2.9f);
    -
    auto q = quaternion<float>(1.f,2.f,3.f,4.f);
    +
    auto c = kyosu::complex_t<float>(3.5f,-2.9f);
    +
    auto q = kyosu::quaternion_t<float>(1.f,2.f,3.f,4.f);
    auto t = 1.0f;
    auto r = kyosu::if_else(t > 2.0f, q, c);
    std::cout << r << std::endl;
    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga6ead34ff89aeb18c2380188af5f83dcd.html b/group__functions_ga6ead34ff89aeb18c2380188af5f83dcd.html index b6b0c44b..e65c5992 100644 --- a/group__functions_ga6ead34ff89aeb18c2380188af5f83dcd.html +++ b/group__functions_ga6ead34ff89aeb18c2380188af5f83dcd.html @@ -167,31 +167,31 @@

    Example

    int main()
    {
    using kyosu::sqr;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    std::cout << "Real: "<< "\n";
    std::cout << 72.9f << " -> " << sqr(72.9f) << "\n";
    std::cout << 72.9f << " -> " << (72.9f)*(72.9f) << "\n";
    std::cout << "Complex: "<< "\n";
    -
    std::cout << complex<float>(3.5f,-2.9f) << " -> " << sqr(complex<float>(3.5f,-2.9f)) << "\n";
    -
    std::cout << complex<float>(3.5f,-2.9f) << " -> " << (complex<float>(3.5f,-2.9f))*(complex<float>(3.5f,-2.9f)) << "\n";
    +
    std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << sqr(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
    +
    std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << (kyosu::complex_t<float>(3.5f,-2.9f))*(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
    std::cout << "Quaternion: "<< "\n";
    -
    std::cout << quaternion<double>(1.1,2.2,-3.3,4.4) << " -> " << sqr(quaternion<double>(1.1,2.2,-3.3,4.4)) << "\n";
    -
    std::cout << quaternion<double>(1.1,2.2,-3.3,4.4) << " -> " << (quaternion<double>(1.1,2.2,-3.3,4.4))*(quaternion<double>(1.1,2.2,-3.3,4.4))<< "\n";
    +
    std::cout << kyosu::quaternion_t<double>(1.1,2.2,-3.3,4.4) << " -> " << sqr(kyosu::quaternion_t<double>(1.1,2.2,-3.3,4.4)) << "\n";
    +
    std::cout << kyosu::quaternion_t<double>(1.1,2.2,-3.3,4.4) << " -> " << (kyosu::quaternion_t<double>(1.1,2.2,-3.3,4.4))*(kyosu::quaternion_t<double>(1.1,2.2,-3.3,4.4))<< "\n";
    std::cout << "SIMD: ";
    -
    using wc_t = eve::wide<complex<double>, eve::fixed<2>>;
    -
    std::cout << wc_t(complex<double>(1.3,-3.7)) << " -> " << sqr(wc_t(complex<double>(1.3,-3.7))) << "\n";
    -
    std::cout << wc_t(complex<double>(1.3,-3.7)) << " -> " << (wc_t(complex<double>(1.3,-3.7)))*(wc_t(complex<double>(1.3,-3.7)))<< "\n";
    +
    using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
    +
    std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << sqr(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
    +
    std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << (wc_t(kyosu::complex_t<double>(1.3,-3.7)))*(wc_t(kyosu::complex_t<double>(1.3,-3.7)))<< "\n";
    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga72bd8b3dcf975e0e9bb4e5e83df4f4a0.html b/group__functions_ga72bd8b3dcf975e0e9bb4e5e83df4f4a0.html index 7c7a1588..548fe667 100644 --- a/group__functions_ga72bd8b3dcf975e0e9bb4e5e83df4f4a0.html +++ b/group__functions_ga72bd8b3dcf975e0e9bb4e5e83df4f4a0.html @@ -159,11 +159,33 @@

    -
  • a real input z is treated as if to_complex(z) was entered.
    • +
  • a real input z is treated as if complex(z) was entered.
  • Returns the complex arc hyperbolic cotangent of z, computed as \(\mathop{\mathrm{atanh}}(1/z)\).

    • Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> acoth(zc) = " << kyosu::acoth(zc)<< std::endl
    +
    << "-> acoth(ref2) = " << kyosu::acoth(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga738d6a61ebf48d0bacd80f958d1b590b.html b/group__functions_ga738d6a61ebf48d0bacd80f958d1b590b.html new file mode 100644 index 00000000..761f4462 --- /dev/null +++ b/group__functions_ga738d6a61ebf48d0bacd80f958d1b590b.html @@ -0,0 +1,206 @@ + + + + + + + + +kyosu: kyosu::erfcx + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
    Loading...
    +
    Searching...
    +
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    +
    +
    +
    +
    + +
    + +

    ◆ erfcx

    + +
    +
    + + + + + +
    + + + + +
    kyosu::erfcx = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the normalized complementary error function \( \displaystyle \mbox{erfcx}(x) = e^{x^2} \mbox{erfc}(x)\).

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<eve::ordered_value T> constexpr auto erfcx(T z) noexcept; //1
    +
    template<kyosu::concepts::complex T> constexpr auto erfcx(T z) noexcept; //2
    +
    }
    +
    kyosu::erfcx
    constexpr tags::callable_erfcx erfcx
    Computes the normalized complementary error function .
    Definition: erfcx.hpp:79
    +
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14
    +

    Parameters

    +
      +
    • z : Value to process.
      • +
    +

    Return value

    +
      +
    1. a real input z is treated as if complex(z) was entered.
      2. +
    2. The value of the normalized complementary error function is returned.
      3. +
    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> erfcx(zc) = " << kyosu::erfcx(zc)<< std::endl
    +
    << "-> erfcx(ref2) = " << kyosu::erfcx(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga783725b137881f9e6e60e1f9b3bae9fc.html b/group__functions_ga783725b137881f9e6e60e1f9b3bae9fc.html index f743f875..4b01f66b 100644 --- a/group__functions_ga783725b137881f9e6e60e1f9b3bae9fc.html +++ b/group__functions_ga783725b137881f9e6e60e1f9b3bae9fc.html @@ -160,7 +160,51 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::cot;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    we_t we = we_t(e);
    +
    std::cout << e << " -> " << cot(e) << "\n";
    +
    std::cout << we << " -> " << cot(we) << "\n";
    +
    std::cout << cot(c_t(e))<< "\n";
    +
    std::cout << cot(q_t(e))<< "\n";
    +
    std::cout << cot(wc_t(e))<< "\n";
    +
    std::cout << cot(wq_t(e))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    wc_t wc = wc_t(c);
    +
    std::cout << c << " -> " << cot(c) << "\n";
    +
    std::cout << wc << " -> " << cot(wc) << "\n";
    +
    std::cout << cot(q_t(c))<< "\n";
    +
    std::cout << cot(wq_t(c))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    wq_t wq = wq_t(q);
    +
    std::cout << q << " -> " << cot(q) << "\n";
    +
    std::cout << wq << " -> " << cot(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga7859bd9f30d2ef73a22fc8d114faea47.html b/group__functions_ga7859bd9f30d2ef73a22fc8d114faea47.html index 6884420b..c3fd5986 100644 --- a/group__functions_ga7859bd9f30d2ef73a22fc8d114faea47.html +++ b/group__functions_ga7859bd9f30d2ef73a22fc8d114faea47.html @@ -159,13 +159,35 @@

    -
  • a real input z is treated as if to_complex(z) was entered.
    • +
  • a real input z is treated as if complex(z) was entered.

  • Returns the elementwise the complex principal value of the arc tangent of the input in the range of a strip unbounded along the imaginary axis and in the interval \([-\pi/2, \pi/2]\) along the real axis.

    special cases are handled as if the operation was implemented by \(-i \mathrm{atanh}(i z)\)

    • Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> atan(zc) = " << kyosu::atan(zc)<< std::endl
    +
    << "-> atan(ref2) = " << kyosu::atan(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga788b51ca9d3366567828c74d46f12168.html b/group__functions_ga788b51ca9d3366567828c74d46f12168.html index 67304c68..6c1f27bd 100644 --- a/group__functions_ga788b51ca9d3366567828c74d46f12168.html +++ b/group__functions_ga788b51ca9d3366567828c74d46f12168.html @@ -160,7 +160,51 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::cos;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<2>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<2>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<2>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    we_t we = we_t(e);
    +
    std::cout << e << " -> " << cos(e) << "\n";
    +
    std::cout << we << " -> " << cos(we) << "\n";
    +
    std::cout << cos(c_t(e))<< "\n";
    +
    std::cout << cos(q_t(e))<< "\n";
    +
    std::cout << cos(wc_t(e))<< "\n";
    +
    std::cout << cos(wq_t(e))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    wc_t wc = wc_t(c);
    +
    std::cout << c << " -> " << cos(c) << "\n";
    +
    std::cout << wc << " -> " << cos(wc) << "\n";
    +
    std::cout << cos(q_t(c))<< "\n";
    +
    std::cout << cos(wq_t(c))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    wq_t wq = wq_t(q);
    +
    std::cout << q << " -> " << cos(q) << "\n";
    +
    std::cout << wq << " -> " << cos(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga7ab67d971ae8c2c4d99fe414d6085116.html b/group__functions_ga7ab67d971ae8c2c4d99fe414d6085116.html index 546aea99..c56b8209 100644 --- a/group__functions_ga7ab67d971ae8c2c4d99fe414d6085116.html +++ b/group__functions_ga7ab67d971ae8c2c4d99fe414d6085116.html @@ -160,7 +160,59 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::is_nez;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    using eve::as;
    +
    using e_t = float;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    +
    using we_t = eve::wide<e_t, eve::fixed<4>>;
    +
    using wc_t = eve::wide<c_t, eve::fixed<4>>;
    +
    using wq_t = eve::wide<q_t, eve::fixed<4>>;
    +
    +
    std::cout << "Real: \n";
    +
    e_t e(2.9f);
    +
    e_t nan = eve::nan(as(e));
    +
    e_t inf = eve::inf(as(e));
    +
    e_t zer = eve::zero(as(e));
    +
    we_t we = we_t(e, zer, nan, inf);
    +
    std::cout << e << " -> " << is_nez(e) << "\n";
    +
    std::cout << we << " -> " << is_nez(we) << "\n";
    +
    std::cout << is_nez(c_t(e))<< "\n";
    +
    std::cout << is_nez(q_t(e))<< "\n";
    +
    std::cout << is_nez(kyosu::complex(we))<< "\n";
    +
    std::cout << is_nez(kyosu::quaternion(we))<< "\n";
    +
    +
    std::cout << "Complex: \n";
    +
    c_t c(3.5f,-2.9f);
    +
    c_t d(0.0f, inf);
    +
    wc_t wc = wc_t(c, zer, nan, d);
    +
    std::cout << c << " -> " << is_nez(c) << "\n";
    +
    std::cout << wc << " -> " << is_nez(wc) << "\n";
    +
    std::cout << is_nez(kyosu::complex(wc))<< "\n";;
    +
    std::cout << is_nez(kyosu::quaternion(wc))<< "\n";
    +
    +
    std::cout << "Quaternion: \n";
    +
    q_t q(3.5f,-2.9f, 2.1f, 3.2f);
    +
    q_t r(3.5f, nan, inf, zer);
    +
    wq_t wq = wq_t(q, zer, nan, r);
    +
    std::cout << q << " -> " << is_nez(q) << "\n";
    +
    std::cout << wq << " -> " << is_nez(wq) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    kyosu::quaternion
    constexpr tags::callable_quaternion quaternion
    Constructs a kyosu::quaternion.
    Definition: to_quaternion.hpp:72
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    diff --git a/group__functions_ga7ad40bb479ce858eed855c2819c4ab22.html b/group__functions_ga7ad40bb479ce858eed855c2819c4ab22.html new file mode 100644 index 00000000..34bf45e6 --- /dev/null +++ b/group__functions_ga7ad40bb479ce858eed855c2819c4ab22.html @@ -0,0 +1,203 @@ + + + + + + + + +kyosu: kyosu::eta + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
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    + +

    ◆ eta

    + +
    +
    + + + + + +
    + + + + +
    kyosu::eta = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the Dirichlet sum \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\). Sometimes this function is for obvious reasons called the alternative \(\zeta\) function .

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<unsigned_scalar_value K, eve::ordered_value T> constexpr auto eta(K, k, T z) noexcept; //1
    +
    template<unsigned_scalar_value K, kyosu::concepts::complex T> constexpr auto eta(K, k, T z) noexcept; //2
    +
    }
    +
    kyosu::eta
    constexpr tags::callable_eta eta
    Computes the Dirichlet sum . Sometimes this function is for obvious reasons called the alternative f...
    Definition: eta.hpp:78
    +
    kyosu
    Main KYOSU namespace.
    Definition: acos.hpp:14
    +

    Parameters

    +
      +
    • z : Vcomplex or real value to process.
      • +
    +

    Return value

    +

    Returns the Dirichlet alternating zeta function: sum \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\)

    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    +
    using wide_ft = eve::wide <float, eve::fixed<4>>;
    +
    wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
    +
    wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
    +
    wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
    +
    auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
    +
    +
    std::cout
    +
    << "---- simd" << std::endl
    +
    << "<- zc = " << zc << std::endl
    +
    << "-> eta(zc) = " << kyosu::eta(zc)<< std::endl
    +
    << "-> eta(ref2) = " << kyosu::eta(ref2) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga7bde9020d5e1ce1e69cdb7b011ef0a7d.html b/group__functions_ga7bde9020d5e1ce1e69cdb7b011ef0a7d.html index 39be402a..da26af2f 100644 --- a/group__functions_ga7bde9020d5e1ce1e69cdb7b011ef0a7d.html +++ b/group__functions_ga7bde9020d5e1ce1e69cdb7b011ef0a7d.html @@ -169,14 +169,14 @@

    Example

    int main()
    {
    using kyosu::is_not_equal;
    -
    using kyosu::complex;
    -
    using kyosu::quaternion;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    using e_t = float;
    -
    using c_t = complex<float>;
    -
    using q_t = quaternion<float>;
    +
    using c_t = kyosu::complex_t<float>;
    +
    using q_t = kyosu::quaternion_t<float>;
    using we_t = eve::wide<float, eve::fixed<2>>;
    -
    using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
    -
    using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
    +
    using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
    +
    using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
    std::cout << "Real: "<< "\n";
    e_t e0(1);
    @@ -207,8 +207,8 @@

    Example

    return 0;
    }
    -
    kyosu::quaternion
    cayley_dickson< T, 4 > quaternion
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:26
    -
    kyosu::complex
    cayley_dickson< T, 2 > complex
    Type alias for complex numbers.
    Definition: complex.hpp:26
    +
    kyosu::quaternion_t
    as_cayley_dickson_n_t< 4, T > quaternion_t
    Type alias for quaternion numbers.
    Definition: quaternion.hpp:27
    +
    kyosu::complex_t
    as_cayley_dickson_n_t< 2, T > complex_t
    Type alias for complex numbers.
    Definition: complex.hpp:27
    diff --git a/group__functions_ga80a14005a373e1fd513a765281accdb8.html b/group__functions_ga80a14005a373e1fd513a765281accdb8.html index 78663461..640e2921 100644 --- a/group__functions_ga80a14005a373e1fd513a765281accdb8.html +++ b/group__functions_ga80a14005a373e1fd513a765281accdb8.html @@ -159,7 +159,7 @@

    -
  • a real input z is treated as if to_complex(z) was entered.
    • +
  • a real input z is treated as if complex(z) was entered.
  • 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 \(i\times[-\pi/2, \pi/2]\) along the imaginary axis.
    • for every z: eve::atanh(eve::conj(z)) == eve::conj(std::atanh(z))
    • for every z: eve::atanh(-z) == -eve::atanh(z)
      • @@ -178,7 +178,29 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> atanh(zc) = " << kyosu::atanh(zc)<< std::endl
      +
      << "-> atanh(ref2) = " << kyosu::atanh(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga80b0877803d92aafcb11e1c641f7f0fd.html b/group__functions_ga80b0877803d92aafcb11e1c641f7f0fd.html new file mode 100644 index 00000000..5921862b --- /dev/null +++ b/group__functions_ga80b0877803d92aafcb11e1c641f7f0fd.html @@ -0,0 +1,214 @@ + + + + + + + + +kyosu: kyosu::deta + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + +
      + + + + + + + + +
      +
      kyosu v0.1.0 +
      +
      Complex Without Complexes
      +
      + +   + + + + +
      +
      +
      + + + + +
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      ◆ deta

      + +
      +
      + + + + + +
      + + + + +
      kyosu::deta = {}
      +       		+inlineconstexpr
      +
      + +

      Computes the Dirichlet sums \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(kn+1)^z}\).

      +

      Defined in Header

      +
      #include <kyosu/functions.hpp>
      +

      Callable Signatures

      +
      namespace kyosu
      +
      {
      +
      template<unsigned_scalar_value K, eve::ordered_value T> constexpr auto deta(K, k, T z) noexcept; //1
      +
      template<unsigned_scalar_value K, kyosu::concepts::complex T> constexpr auto deta(K, k, T z) noexcept; //2
      +
      }
      +
      kyosu::deta
      constexpr tags::callable_deta deta
      Computes the Dirichlet sums .
      Definition: deta.hpp:78
      +
      kyosu
      Main KYOSU namespace.
      Definition: acos.hpp:14
      +

      Parameters

      +
        +
      • k : scalar unsigned value, parameter of the sum.
        • +
      • z : Vcomplex or real value to process.
        • +
      +

      Return value

      +

      Returns the Dirichlet sum \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(kn+1)^z}\)

      +

      Example

      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::deta;
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.6f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      auto z = kyosu::complex_t<double>(1.0, 0.0);
      +
      auto zf= kyosu::complex_t<float >(1.0, 0.0);
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- z = " << z << std::endl
      +
      << "-> deta(1, z) = " << deta(1u, z) << std::endl
      +
      << "-> deta(2, z) = " << deta(2u, z) << std::endl
      +
      << "-> deta(3, z) = " << deta(3u, z) << std::endl
      +
      << "-> deta(2, 0.2)= " << deta(2u, 0.2)<< std::endl
      +
      << "-> deta(1, 0.2)= " << deta(1u, 0.2)<< std::endl
      +
      << "-> deta(1, z) = " << deta(1u, zf) << std::endl
      +
      << "-> deta(2, z) = " << deta(2u, zf) << std::endl
      +
      << "-> deta(3, z) = " << deta(3u, zf) << std::endl
      +
      << "-> deta(2, 0.2)= " << deta(2u, 0.2f)<< std::endl
      +
      << "-> deta(1, 0.2)= " << deta(1u, 0.2f)<< std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> deta(1, zc) = " << deta(1u, zc)<< std::endl;
      +
      return 0;
      +
      }
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      +
      +
      +
      +
      + + + + + + + + + + diff --git a/group__functions_ga842342e7ca73ffdcaa7ca9141e45d56f.html b/group__functions_ga842342e7ca73ffdcaa7ca9141e45d56f.html index a9a09b8f..0c1e84f5 100644 --- a/group__functions_ga842342e7ca73ffdcaa7ca9141e45d56f.html +++ b/group__functions_ga842342e7ca73ffdcaa7ca9141e45d56f.html @@ -168,33 +168,33 @@

      Example

      int main()
      {
      using kyosu::jpart;
      -
      using kyosu::complex;
      -
      using kyosu::quaternion;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      std::cout << "Real: ";
      float f = 72.9f;
      std::cout << f << " -> " << jpart(f) << "\n";
      std::cout << "Complex: ";
      -
      auto z = complex<float>(3.5f,-2.9f);
      +
      auto z = kyosu::complex_t<float>(3.5f,-2.9f);
      std::cout << z << " -> " << jpart(z) << "\n";
      std::cout << "Quaternion: ";
      -
      auto q = quaternion<double>(1.,2.,3.,4.);
      +
      auto q = kyosu::quaternion_t<double>(1.,2.,3.,4.);
      std::cout << q << " -> " << jpart(q) << " => ";
      jpart(q) = 42.7;
      std::cout << q << "\n";
      std::cout << "SIMD: ";
      -
      eve::wide<quaternion<double>, eve::fixed<2>> wz(quaternion<double>(1.3,-3.7,4.2,-7.8));
      +
      eve::wide<kyosu::quaternion_t<double>, eve::fixed<2>> wz(kyosu::quaternion_t<double>(1.3,-3.7,4.2,-7.8));
      std::cout << wz << " -> " << jpart(wz) << " => ";
      jpart(wz) = eve::wide<double, eve::fixed<2>>{13.37,63.24};
      std::cout << wz << "\n";
      return 0;
      }
      -
      kyosu::quaternion
      cayley_dickson< T, 4 > quaternion
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:26
      -
      kyosu::complex
      cayley_dickson< T, 2 > complex
      Type alias for complex numbers.
      Definition: complex.hpp:26
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      diff --git a/group__functions_ga87e87a2d786aa520b7a6f37208f369bc.html b/group__functions_ga87e87a2d786aa520b7a6f37208f369bc.html new file mode 100644 index 00000000..a605cb7a --- /dev/null +++ b/group__functions_ga87e87a2d786aa520b7a6f37208f369bc.html @@ -0,0 +1,205 @@ + + + + + + + + +kyosu: kyosu::lambda + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + +
      + + + + + + + + +
      +
      kyosu v0.1.0 +
      +
      Complex Without Complexes
      +
      + +   + + + + +
      +
      +
      + + + + +
      +
      + +
      +
      +
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      + +

      ◆ lambda

      + +
      +
      + + + + + +
      + + + + +
      kyosu::lambda = {}
      +       		+inlineconstexpr
      +
      + +

      Callable object computing The Dirichlet \( \displaystyle \lambda(z) = \sum_0^\infty \frac{1}{(2n+1)^z}\).

      +

      This function can be extended to the whole complex plane as \(\lambda(z) = \zeta(z)(1-2^{-x})\) (where \(\zeta\) is the Riemann zeta function). It coincides with the serie where the serie converges. However for z = 1 the result is \(\infty\).

      +

      Defined in Header

      +
      #include <kyosu/functions.hpp>
      +

      Callable Signatures

      +
      namespace kyosu
      +
      {
      +
      template<unsigned_scalar_value K, eve::ordered_value T> constexpr auto lambda(K, k, T z) noexcept; //1
      +
      template<unsigned_scalar_value K, kyosu::concepts::complex T> constexpr auto lambda(K, k, T z) noexcept; //2
      +
      }
      +
      kyosu::lambda
      constexpr tags::callable_lambda lambda
      Callable object computing The Dirichlet .
      Definition: lambda.hpp:81
      +
      kyosu
      Main KYOSU namespace.
      Definition: acos.hpp:14
      +

      Parameters

      +
        +
      • z : Vcomplex or real value to process.
        • +
      +

      Return value

      +

      Returns the Dirichlet sum \( \displaystyle \sum_0^\infty \frac{1}{(2n+1)^z}\)

      +

      Example

      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "<- ref2 = " << ref2 << std::endl
      +
      << "-> lambda(zc) = " << kyosu::lambda(zc)<< std::endl
      +
      << "-> lambda(ref2) = " << kyosu::lambda(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      +
      +
      +
      +
      + + + + + + + + + + diff --git a/group__functions_ga8be5621ef70c215de54eb8683578fa60.html b/group__functions_ga8be5621ef70c215de54eb8683578fa60.html index 76d8e37f..1d07ee85 100644 --- a/group__functions_ga8be5621ef70c215de54eb8683578fa60.html +++ b/group__functions_ga8be5621ef70c215de54eb8683578fa60.html @@ -160,7 +160,51 @@

      log(abs(z)).

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::log_abs;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<2>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<2>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<2>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      we_t we = we_t(e);
      +
      std::cout << e << " -> " << log_abs(e) << "\n";
      +
      std::cout << we << " -> " << log_abs(we) << "\n";
      +
      std::cout << log_abs(c_t(e))<< "\n";
      +
      std::cout << log_abs(q_t(e))<< "\n";
      +
      std::cout << log_abs(wc_t(e))<< "\n";
      +
      std::cout << log_abs(wq_t(e))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      wc_t wc = wc_t(c);
      +
      std::cout << c << " -> " << log_abs(c) << "\n";
      +
      std::cout << wc << " -> " << log_abs(wc) << "\n";
      +
      std::cout << log_abs(q_t(c))<< "\n";
      +
      std::cout << log_abs(wq_t(c))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      wq_t wq = wq_t(q);
      +
      std::cout << q << " -> " << log_abs(q) << "\n";
      +
      std::cout << wq << " -> " << log_abs(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga8d6f64b6ed68055ef05917557d2e60b6.html b/group__functions_ga8d6f64b6ed68055ef05917557d2e60b6.html index d7874bd1..b18b70a4 100644 --- a/group__functions_ga8d6f64b6ed68055ef05917557d2e60b6.html +++ b/group__functions_ga8d6f64b6ed68055ef05917557d2e60b6.html @@ -167,27 +167,27 @@

      Example

      int main()
      {
      using kyosu::conj;
      -
      using kyosu::complex;
      -
      using kyosu::quaternion;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      std::cout << "Real: ";
      std::cout << 72.9f << " -> " << conj(72.9f) << "\n";
      std::cout << "Complex: ";
      -
      std::cout << complex<float>(3.5f,-2.9f) << " -> " << conj(complex<float>(3.5f,-2.9f)) << "\n";
      +
      std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << conj(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
      std::cout << "Quaternion: ";
      -
      std::cout << quaternion<double>(1.,2.,3.,4.) << " -> " << conj(quaternion<double>(1.,2.,3.,4.)) << "\n";
      +
      std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << conj(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
      std::cout << "SIMD: ";
      -
      using wc_t = eve::wide<complex<double>, eve::fixed<2>>;
      -
      std::cout << wc_t(complex<double>(1.3,-3.7)) << " -> " << conj(wc_t(complex<double>(1.3,-3.7))) << "\n";
      +
      using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
      +
      std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << conj(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
      return 0;
      }
      kyosu::conj
      constexpr tags::callable_conj conj
      Computes the conjugate value.
      Definition: conj.hpp:75
      -
      kyosu::quaternion
      cayley_dickson< T, 4 > quaternion
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:26
      -
      kyosu::complex
      cayley_dickson< T, 2 > complex
      Type alias for complex numbers.
      Definition: complex.hpp:26
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      diff --git a/group__functions_ga8e2d2c2ba91d22a96ff3603b42e4760d.html b/group__functions_ga8e2d2c2ba91d22a96ff3603b42e4760d.html index e55d2d14..0b6933d2 100644 --- a/group__functions_ga8e2d2c2ba91d22a96ff3603b42e4760d.html +++ b/group__functions_ga8e2d2c2ba91d22a96ff3603b42e4760d.html @@ -160,7 +160,60 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::is_not_denormal;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using eve::as;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<4>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<4>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<4>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      e_t nan = eve::nan(as(e));
      +
      e_t inf = eve::inf(as(e));
      +
      e_t zer = eve::zero(as(e));
      +
      e_t mind= eve::mindenormal(as(e));
      +
      we_t we = we_t(e, zer, nan, mind);
      +
      std::cout << e << " -> " << is_not_denormal(e) << "\n";
      +
      std::cout << we << " -> " << is_not_denormal(we) << "\n";
      +
      std::cout << is_not_denormal(c_t(e))<< "\n";
      +
      std::cout << is_not_denormal(q_t(e))<< "\n";
      +
      std::cout << is_not_denormal(kyosu::complex(we))<< "\n";
      +
      std::cout << is_not_denormal(kyosu::quaternion(we))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      c_t d(0.0f, mind);
      +
      wc_t wc = wc_t(c, zer, nan, d);
      +
      std::cout << c << " -> " << is_not_denormal(c) << "\n";
      +
      std::cout << wc << " -> " << is_not_denormal(wc) << "\n";
      +
      std::cout << is_not_denormal(kyosu::complex(wc))<< "\n";;
      +
      std::cout << is_not_denormal(kyosu::quaternion(wc))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, mind, 3.2f);
      +
      q_t r(3.5f, nan, inf, zer);
      +
      wq_t wq = wq_t(q, zer, nan, r);
      +
      std::cout << q << " -> " << is_not_denormal(q) << "\n";
      +
      std::cout << wq << " -> " << is_not_denormal(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex
      constexpr tags::callable_complex complex
      Constructs a kyosu::complex.
      Definition: to_complex.hpp:70
      +
      kyosu::quaternion
      constexpr tags::callable_quaternion quaternion
      Constructs a kyosu::quaternion.
      Definition: to_quaternion.hpp:72
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga8e88be0e83296a515c882ad40e828386.html b/group__functions_ga8e88be0e83296a515c882ad40e828386.html index 71b6cb22..daa472d9 100644 --- a/group__functions_ga8e88be0e83296a515c882ad40e828386.html +++ b/group__functions_ga8e88be0e83296a515c882ad40e828386.html @@ -161,7 +161,30 @@

      Example

      -

      Defined in Header

      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> imag(zc) = " << kyosu::imag(zc)<< std::endl
      +
      << "-> imag(ref2) = " << kyosu::imag(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      kyosu::imag
      constexpr tags::callable_ipart imag
      Alias for ipart.
      Definition: ipart.hpp:81
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +

      Defined in Header

      #include <kyosu/functions.hpp>

      Callable Signatures

      namespace kyosu
      @@ -177,7 +200,28 @@

      Example

      Return value

      Returns the imaginary part of its argument. For real inputs, the call returns 0. It is an alias of imag.

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> imag(zc) = " << kyosu::imag(zc)<< std::endl
      +
      << "-> imag(ref2) = " << kyosu::imag(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      diff --git a/group__functions_ga8febd271f0bc94c5fb1d12cd5644778b.html b/group__functions_ga8febd271f0bc94c5fb1d12cd5644778b.html index a720153e..ee5d35a3 100644 --- a/group__functions_ga8febd271f0bc94c5fb1d12cd5644778b.html +++ b/group__functions_ga8febd271f0bc94c5fb1d12cd5644778b.html @@ -167,26 +167,26 @@

      Example

      int main()
      {
      using kyosu::nearest;
      -
      using kyosu::complex;
      -
      using kyosu::quaternion;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      std::cout << "Real: ";
      std::cout << 72.9f << " -> " << nearest(72.9f) << "\n";
      std::cout << "Complex: ";
      -
      std::cout << complex<float>(3.5f,-2.9f) << " -> " << nearest(complex<float>(3.5f,-2.9f)) << "\n";
      +
      std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << nearest(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
      std::cout << "Quaternion: ";
      -
      std::cout << quaternion<double>(1.,2.,3.,4.) << " -> " << nearest(quaternion<double>(1.,2.,3.,4.)) << "\n";
      +
      std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << nearest(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
      std::cout << "SIMD: ";
      -
      using wc_t = eve::wide<complex<double>, eve::fixed<2>>;
      -
      std::cout << wc_t(complex<double>(1.3,-3.7)) << " -> " << nearest(wc_t(complex<double>(1.3,-3.7))) << "\n";
      +
      using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
      +
      std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << nearest(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
      return 0;
      }
      -
      kyosu::quaternion
      cayley_dickson< T, 4 > quaternion
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:26
      -
      kyosu::complex
      cayley_dickson< T, 2 > complex
      Type alias for complex numbers.
      Definition: complex.hpp:26
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      diff --git a/group__functions_ga9187d90d21bff228986d00b254bcb818.html b/group__functions_ga9187d90d21bff228986d00b254bcb818.html index 77efea84..778a26bf 100644 --- a/group__functions_ga9187d90d21bff228986d00b254bcb818.html +++ b/group__functions_ga9187d90d21bff228986d00b254bcb818.html @@ -159,11 +159,33 @@

      -
    • a real input z is treated as if to_complex(z) was entered.
      • +
    • a real input z is treated as if complex(z) was entered.
    • Returns elementwise \(\mathop{\mathrm{acos}}(1/z)\).

      • Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> asec(zc) = " << kyosu::asec(zc)<< std::endl
      +
      << "-> asec(ref2) = " << kyosu::asec(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga926e8d9f232cf45c07fe4f2a23353bb9.html b/group__functions_ga926e8d9f232cf45c07fe4f2a23353bb9.html new file mode 100644 index 00000000..4d210cc2 --- /dev/null +++ b/group__functions_ga926e8d9f232cf45c07fe4f2a23353bb9.html @@ -0,0 +1,190 @@ + + + + + + + + +kyosu: kyosu::lrising_factorial + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + +
      + + + + + + + + +
      +
      kyosu v0.1.0 +
      +
      Complex Without Complexes
      +
      + +   + + + + +
      +
      +
      + + + + +
      +
      + +
      +
      +
      + +
      + +
      +
      + + +
      +
      +
      +
      +
      +
      Loading...
      +
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      +
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      +
      +
      +
      +
      + +
      + +

      ◆ lrising_factorial

      + +
      +
      + + + + + +
      + + + + +
      kyosu::lrising_factorial = {}
      +       		+inlineconstexpr
      +
      + +

      Computes the lrising_factorial function: \(\log\frac{\Gamma(x+y)}{\Gamma(x)}\).

      +

      Defined in Header

      +
      #include <kyosu/functions.hpp>
      +

      Callable Signatures

      +
      namespace kyosu
      +
      {
      +
      template< eve::floating_ordered_value T, eve::floating_ordered_value U >
      +
      auto lrising_factorial(T x,U y) noexcept; //1
      +
      +
      template< eve::floating_value T, eve::floating_value U >
      +
      auto lrising_factorial(eve::complex_t<T> x, U y) noexcept; //2
      +
      +
      template< eve::floating_value T, eve::floating_value U >
      +
      auto lrising_factorial(T x, eve::complex_t<U> y) noexcept; //2
      +
      +
      template< eve::floating_value T, eve::floating_value U >
      +
      auto lrising_factorial(eve::complex_t<T> x, eve::complex_t<U> y) noexcept; //2
      +
      }
      +
      kyosu::lrising_factorial
      constexpr tags::callable_lrising_factorial lrising_factorial
      Computes the lrising_factorial function: .
      Definition: lrising_factorial.hpp:83
      +
      kyosu
      Main KYOSU namespace.
      Definition: acos.hpp:14
      +

      Parameters

      +
        +
      • x,y : Values to process.
        • +
      +

      Return value

      +

      Computes the Rising Factorial function i.e. \(\log\frac{\Gamma(x+y)}{\Gamma(x)}\).

      +

      Example

      +
      +
      +
      +
      +
      + + + + + + + + + + diff --git a/group__functions_ga92c4c9260b24c8171caca5c014ad4298.html b/group__functions_ga92c4c9260b24c8171caca5c014ad4298.html index 076463be..efc31439 100644 --- a/group__functions_ga92c4c9260b24c8171caca5c014ad4298.html +++ b/group__functions_ga92c4c9260b24c8171caca5c014ad4298.html @@ -159,11 +159,33 @@

      -
    • a real input z is treated as if to_complex(z) was entered.
      • +
    • a real input z is treated as if complex(z) was entered.
    • Returns pi(as(z))*asin(z)

      • Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> asinpi(zc) = " << kyosu::asinpi(zc)<< std::endl
      +
      << "-> asinpi(ref2) = " << kyosu::asinpi(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga97d21d58bdd2678e7dacea216758a5a8.html b/group__functions_ga97d21d58bdd2678e7dacea216758a5a8.html index 6afe491c..32fc7264 100644 --- a/group__functions_ga97d21d58bdd2678e7dacea216758a5a8.html +++ b/group__functions_ga97d21d58bdd2678e7dacea216758a5a8.html @@ -160,7 +160,59 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::is_real;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using eve::as;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<4>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<4>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<4>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      e_t nan = eve::nan(as(e));
      +
      e_t inf = eve::inf(as(e));
      +
      e_t zer = eve::zero(as(e));
      +
      we_t we = we_t(e, zer, nan, inf);
      +
      std::cout << e << " -> " << is_real(e) << "\n";
      +
      std::cout << we << " -> " << is_real(we) << "\n";
      +
      std::cout << is_real(c_t(e))<< "\n";
      +
      std::cout << is_real(q_t(e))<< "\n";
      +
      std::cout << is_real(kyosu::complex(we))<< "\n";
      +
      std::cout << is_real(kyosu::quaternion(we))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      c_t d(0.0f, inf);
      +
      wc_t wc = wc_t(c, zer, nan, d);
      +
      std::cout << c << " -> " << is_real(c) << "\n";
      +
      std::cout << wc << " -> " << is_real(wc) << "\n";
      +
      std::cout << is_real(kyosu::complex(wc))<< "\n";;
      +
      std::cout << is_real(kyosu::quaternion(wc))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      q_t r(3.5f, nan, inf, zer);
      +
      wq_t wq = wq_t(q, zer, nan, r);
      +
      std::cout << q << " -> " << is_real(q) << "\n";
      +
      std::cout << wq << " -> " << is_real(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex
      constexpr tags::callable_complex complex
      Constructs a kyosu::complex.
      Definition: to_complex.hpp:70
      +
      kyosu::quaternion
      constexpr tags::callable_quaternion quaternion
      Constructs a kyosu::quaternion.
      Definition: to_quaternion.hpp:72
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga9c043e0de4393e03663a8b017f3776d1.html b/group__functions_ga9c043e0de4393e03663a8b017f3776d1.html index 5075fe15..d41ffa65 100644 --- a/group__functions_ga9c043e0de4393e03663a8b017f3776d1.html +++ b/group__functions_ga9c043e0de4393e03663a8b017f3776d1.html @@ -160,7 +160,59 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::is_infinite;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using eve::as;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<4>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<4>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<4>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      e_t nan = eve::nan(as(e));
      +
      e_t inf = eve::inf(as(e));
      +
      e_t zer = eve::zero(as(e));
      +
      we_t we = we_t(e, zer, nan, inf);
      +
      std::cout << e << " -> " << is_infinite(e) << "\n";
      +
      std::cout << we << " -> " << is_infinite(we) << "\n";
      +
      std::cout << is_infinite(c_t(e))<< "\n";
      +
      std::cout << is_infinite(q_t(e))<< "\n";
      +
      std::cout << is_infinite(kyosu::complex(we))<< "\n";
      +
      std::cout << is_infinite(kyosu::quaternion(we))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      c_t d(0.0f, inf);
      +
      wc_t wc = wc_t(c, zer, nan, d);
      +
      std::cout << c << " -> " << is_infinite(c) << "\n";
      +
      std::cout << wc << " -> " << is_infinite(wc) << "\n";
      +
      std::cout << is_infinite(kyosu::complex(wc))<< "\n";;
      +
      std::cout << is_infinite(kyosu::quaternion(wc))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      q_t r(3.5f, nan, inf, zer);
      +
      wq_t wq = wq_t(q, zer, nan, r);
      +
      std::cout << q << " -> " << is_infinite(q) << "\n";
      +
      std::cout << wq << " -> " << is_infinite(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex
      constexpr tags::callable_complex complex
      Constructs a kyosu::complex.
      Definition: to_complex.hpp:70
      +
      kyosu::quaternion
      constexpr tags::callable_quaternion quaternion
      Constructs a kyosu::quaternion.
      Definition: to_quaternion.hpp:72
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_ga9c08281f95af17445823ff698486d24b.html b/group__functions_ga9c08281f95af17445823ff698486d24b.html index 0ba20ffe..d4bdd79e 100644 --- a/group__functions_ga9c08281f95af17445823ff698486d24b.html +++ b/group__functions_ga9c08281f95af17445823ff698486d24b.html @@ -160,7 +160,51 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::exp10;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<2>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<2>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<2>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      we_t we = we_t(e);
      +
      std::cout << e << " -> " << exp10(e) << "\n";
      +
      std::cout << we << " -> " << exp10(we) << "\n";
      +
      std::cout << exp10(c_t(e))<< "\n";
      +
      std::cout << exp10(q_t(e))<< "\n";
      +
      std::cout << exp10(wc_t(e))<< "\n";
      +
      std::cout << exp10(wq_t(e))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      wc_t wc = wc_t(c);
      +
      std::cout << c << " -> " << exp10(c) << "\n";
      +
      std::cout << wc << " -> " << exp10(wc) << "\n";
      +
      std::cout << exp10(q_t(c))<< "\n";
      +
      std::cout << exp10(wq_t(c))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      wq_t wq = wq_t(q);
      +
      std::cout << q << " -> " << exp10(q) << "\n";
      +
      std::cout << wq << " -> " << exp10(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_gaa2dcdb1644aa5086e764ee6de919ad93.html b/group__functions_gaa2dcdb1644aa5086e764ee6de919ad93.html index 41b4a779..89e7d360 100644 --- a/group__functions_gaa2dcdb1644aa5086e764ee6de919ad93.html +++ b/group__functions_gaa2dcdb1644aa5086e764ee6de919ad93.html @@ -170,14 +170,14 @@

      Example

      int main()
      {
      using kyosu::dot;
      -
      using kyosu::complex;
      -
      using kyosu::quaternion;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      using e_t = float;
      -
      using c_t = complex<float>;
      -
      using q_t = quaternion<float>;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      using we_t = eve::wide<float, eve::fixed<2>>;
      -
      using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
      -
      using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
      +
      using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
      +
      using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
      std::cout << "Real: "<< "\n";
      e_t e0(1);
      @@ -208,8 +208,8 @@

      Example

      return 0;
      }
      -
      kyosu::quaternion
      cayley_dickson< T, 4 > quaternion
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:26
      -
      kyosu::complex
      cayley_dickson< T, 2 > complex
      Type alias for complex numbers.
      Definition: complex.hpp:26
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      diff --git a/group__functions_gaa370bac6943c4ab923e63d86dcea41ea.html b/group__functions_gaa370bac6943c4ab923e63d86dcea41ea.html index 2e1a5490..db601327 100644 --- a/group__functions_gaa370bac6943c4ab923e63d86dcea41ea.html +++ b/group__functions_gaa370bac6943c4ab923e63d86dcea41ea.html @@ -160,7 +160,29 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 0.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> is_imag(zc) = " << kyosu::is_imag(zc)<< std::endl
      +
      << "-> is_imag(ref2) = " << kyosu::is_imag(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_gaa3f0aecf42f2a0c04ae456b4c604551f.html b/group__functions_gaa3f0aecf42f2a0c04ae456b4c604551f.html index 1fafd62d..8c027c6d 100644 --- a/group__functions_gaa3f0aecf42f2a0c04ae456b4c604551f.html +++ b/group__functions_gaa3f0aecf42f2a0c04ae456b4c604551f.html @@ -159,11 +159,33 @@

      -
    • a real input z is treated as if to_complex(z) was entered.
      • +
    • a real input z is treated as if complex(z) was entered.
    • Returns pi(as(z))*acot(z)

      • Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      +
      using wide_ft = eve::wide <float, eve::fixed<4>>;
      +
      wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
      +
      wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
      +
      wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
      +
      auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
      +
      +
      std::cout
      +
      << "---- simd" << std::endl
      +
      << "<- zc = " << zc << std::endl
      +
      << "-> acotpi(zc) = " << kyosu::acotpi(zc)<< std::endl
      +
      << "-> acotpi(ref2) = " << kyosu::acotpi(ref2) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_gaa608876852fffef8d90a4f7280ff4549.html b/group__functions_gaa608876852fffef8d90a4f7280ff4549.html index dd669f3b..534ba8ef 100644 --- a/group__functions_gaa608876852fffef8d90a4f7280ff4549.html +++ b/group__functions_gaa608876852fffef8d90a4f7280ff4549.html @@ -160,7 +160,52 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::cos;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<2>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<2>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<2>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      we_t we = we_t(e);
      +
      std::cout << e << " -> " << cos(e) << "\n";
      +
      std::cout << we << " -> " << cos(we) << "\n";
      +
      std::cout << cos(c_t(e))<< "\n";
      +
      std::cout << cos(q_t(e))<< "\n";
      +
      std::cout << cos(wc_t(e))<< "\n";
      +
      std::cout << cos(wq_t(e))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      wc_t wc = wc_t(c);
      +
      std::cout << c << " -> " << cos(c) << "\n";
      +
      std::cout << wc << " -> " << cos(wc) << "\n";
      +
      std::cout << cos(q_t(c))<< "\n";
      +
      std::cout << cos(wq_t(c))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      wq_t wq = wq_t(q);
      +
      std::cout << q << " -> " << cos(q) << "\n";
      +
      std::cout << wq << " -> " << cos(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::cos
      constexpr tags::callable_cos cos
      Computes the cosine of the argument.
      Definition: cos.hpp:73
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_gaa651f9b616ad1022127142bf9cdc68e8.html b/group__functions_gaa651f9b616ad1022127142bf9cdc68e8.html index 9350c0b1..969dd842 100644 --- a/group__functions_gaa651f9b616ad1022127142bf9cdc68e8.html +++ b/group__functions_gaa651f9b616ad1022127142bf9cdc68e8.html @@ -160,7 +160,51 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::coth;
      +
      using kyosu::complex_t;
      +
      using kyosu::quaternion_t;
      +
      using e_t = float;
      +
      using c_t = kyosu::complex_t<float>;
      +
      using q_t = kyosu::quaternion_t<float>;
      +
      using we_t = eve::wide<e_t, eve::fixed<2>>;
      +
      using wc_t = eve::wide<c_t, eve::fixed<2>>;
      +
      using wq_t = eve::wide<q_t, eve::fixed<2>>;
      +
      +
      std::cout << "Real: \n";
      +
      e_t e(2.9f);
      +
      we_t we = we_t(e);
      +
      std::cout << e << " -> " << coth(e) << "\n";
      +
      std::cout << we << " -> " << coth(we) << "\n";
      +
      std::cout << coth(c_t(e))<< "\n";
      +
      std::cout << coth(q_t(e))<< "\n";
      +
      std::cout << coth(wc_t(e))<< "\n";
      +
      std::cout << coth(wq_t(e))<< "\n";
      +
      +
      std::cout << "Complex: \n";
      +
      c_t c(3.5f,-2.9f);
      +
      wc_t wc = wc_t(c);
      +
      std::cout << c << " -> " << coth(c) << "\n";
      +
      std::cout << wc << " -> " << coth(wc) << "\n";
      +
      std::cout << coth(q_t(c))<< "\n";
      +
      std::cout << coth(wq_t(c))<< "\n";
      +
      +
      std::cout << "Quaternion: \n";
      +
      q_t q(3.5f,-2.9f, 2.1f, 3.2f);
      +
      wq_t wq = wq_t(q);
      +
      std::cout << q << " -> " << coth(q) << "\n";
      +
      std::cout << wq << " -> " << coth(wq) << "\n";
      +
      +
      return 0;
      +
      }
      +
      kyosu::quaternion_t
      as_cayley_dickson_n_t< 4, T > quaternion_t
      Type alias for quaternion numbers.
      Definition: quaternion.hpp:27
      +
      kyosu::complex_t
      as_cayley_dickson_n_t< 2, T > complex_t
      Type alias for complex numbers.
      Definition: complex.hpp:27
      +
      diff --git a/group__functions_gaa67951f7f8d8489a34dd23928f747757.html b/group__functions_gaa67951f7f8d8489a34dd23928f747757.html index e7d58f9c..49c5968c 100644 --- a/group__functions_gaa67951f7f8d8489a34dd23928f747757.html +++ b/group__functions_gaa67951f7f8d8489a34dd23928f747757.html @@ -159,7 +159,7 @@

      -
    • a real input z is treated as if to_complex(z) was entered.
      • +
    • a real input z is treated as if complex(z) was entered.
    • 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 \(i\times[-\pi/2, \pi/2]\) 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)
        • @@ -178,7 +178,29 @@

        Example

        -
        +
        #include <kyosu/kyosu.hpp>
        +
        #include <eve/wide.hpp>
        +
        #include <iostream>
        +
        +
        int main()
        +
        {
        +
        +
        using wide_ft = eve::wide <float, eve::fixed<4>>;
        +
        wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
        +
        wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
        +
        wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
        +
        auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
        +
        +
        std::cout
        +
        << "---- simd" << std::endl
        +
        << "<- zc = " << zc << std::endl
        +
        << "-> acosh(zc) = " << kyosu::acosh(zc)<< std::endl
        +
        << "-> acosh(ref2) = " << kyosu::acosh(ref2) << std::endl;
        +
        +
        return 0;
        +
        }
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        +
        diff --git a/group__functions_gaa683fad544774c6d87efc39b424f78e0.html b/group__functions_gaa683fad544774c6d87efc39b424f78e0.html index 01b508ee..71906e48 100644 --- a/group__functions_gaa683fad544774c6d87efc39b424f78e0.html +++ b/group__functions_gaa683fad544774c6d87efc39b424f78e0.html @@ -160,7 +160,51 @@

        Example

        -
        +
        #include <kyosu/kyosu.hpp>
        +
        #include <eve/wide.hpp>
        +
        #include <iostream>
        +
        +
        int main()
        +
        {
        +
        using kyosu::cospi;
        +
        using kyosu::complex_t;
        +
        using kyosu::quaternion_t;
        +
        using e_t = float;
        +
        using c_t = kyosu::complex_t<float>;
        +
        using q_t = kyosu::quaternion_t<float>;
        +
        using we_t = eve::wide<e_t, eve::fixed<2>>;
        +
        using wc_t = eve::wide<c_t, eve::fixed<2>>;
        +
        using wq_t = eve::wide<q_t, eve::fixed<2>>;
        +
        +
        std::cout << "Real: \n";
        +
        e_t e(2.9f);
        +
        we_t we = we_t(e);
        +
        std::cout << e << " -> " << cospi(e) << "\n";
        +
        std::cout << we << " -> " << cospi(we) << "\n";
        +
        std::cout << cospi(c_t(e))<< "\n";
        +
        std::cout << cospi(q_t(e))<< "\n";
        +
        std::cout << cospi(wc_t(e))<< "\n";
        +
        std::cout << cospi(wq_t(e))<< "\n";
        +
        +
        std::cout << "Complex: \n";
        +
        c_t c(3.5f,-2.9f);
        +
        wc_t wc = wc_t(c);
        +
        std::cout << c << " -> " << cospi(c) << "\n";
        +
        std::cout << wc << " -> " << cospi(wc) << "\n";
        +
        std::cout << cospi(q_t(c))<< "\n";
        +
        std::cout << cospi(wq_t(c))<< "\n";
        +
        +
        std::cout << "Quaternion: \n";
        +
        q_t q(3.5f,-2.9f, 2.1f, 3.2f);
        +
        wq_t wq = wq_t(q);
        +
        std::cout << q << " -> " << cospi(q) << "\n";
        +
        std::cout << wq << " -> " << cospi(wq) << "\n";
        +
        +
        return 0;
        +
        }
        +
        kyosu::quaternion_t
        as_cayley_dickson_n_t< 4, T > quaternion_t
        Type alias for quaternion numbers.
        Definition: quaternion.hpp:27
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        +
        diff --git a/group__functions_gaa9d12dd4e1420039046c737ddd3240be.html b/group__functions_gaa9d12dd4e1420039046c737ddd3240be.html index 55fbb32e..3716db3c 100644 --- a/group__functions_gaa9d12dd4e1420039046c737ddd3240be.html +++ b/group__functions_gaa9d12dd4e1420039046c737ddd3240be.html @@ -169,8 +169,8 @@

        Example

        int main()
        {
        using kyosu::real;
        -
        using kyosu::complex;
        -
        using kyosu::quaternion;
        +
        using kyosu::complex_t;
        +
        using kyosu::quaternion_t;
        std::cout << "Real: ";
        float f = 72.9f;
        @@ -179,27 +179,27 @@

        Example

        std::cout << f << "\n";
        std::cout << "Complex: ";
        -
        auto z = complex<float>(3.5f,-2.9f);
        +
        auto z = kyosu::complex_t<float>(3.5f,-2.9f);
        std::cout << z << " -> " << real(z) << " => ";
        real(z) = 11.23f;
        std::cout << z << "\n";
        std::cout << "Quaternion: ";
        -
        auto q = quaternion<double>(1.,2.,3.,4.);
        +
        auto q = kyosu::quaternion_t<double>(1.,2.,3.,4.);
        std::cout << q << " -> " << real(q) << " => ";
        real(q) = 42.7;
        std::cout << q << "\n";
        std::cout << "SIMD: ";
        -
        eve::wide<complex<double>, eve::fixed<2>> wz(complex<double>(1.3,-3.7));
        +
        eve::wide<kyosu::complex_t<double>, eve::fixed<2>> wz(kyosu::complex_t<double>(1.3,-3.7));
        std::cout << wz << " -> " << real(wz) << " => ";
        real(wz) = eve::wide<double, eve::fixed<2>>{13.37,63.24};
        std::cout << wz << "\n";
        return 0;
        }
        -
        kyosu::quaternion
        cayley_dickson< T, 4 > quaternion
        Type alias for quaternion numbers.
        Definition: quaternion.hpp:26
        -
        kyosu::complex
        cayley_dickson< T, 2 > complex
        Type alias for complex numbers.
        Definition: complex.hpp:26
        +
        kyosu::quaternion_t
        as_cayley_dickson_n_t< 4, T > quaternion_t
        Type alias for quaternion numbers.
        Definition: quaternion.hpp:27
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        diff --git a/group__functions_gaae7085c537556dd281121a349ffb2b93.html b/group__functions_gaae7085c537556dd281121a349ffb2b93.html index dabcf945..e6e949a9 100644 --- a/group__functions_gaae7085c537556dd281121a349ffb2b93.html +++ b/group__functions_gaae7085c537556dd281121a349ffb2b93.html @@ -160,7 +160,51 @@

        Example

        -
        +
        #include <kyosu/kyosu.hpp>
        +
        #include <eve/wide.hpp>
        +
        #include <iostream>
        +
        +
        int main()
        +
        {
        +
        using kyosu::cscpi;
        +
        using kyosu::complex_t;
        +
        using kyosu::quaternion_t;
        +
        using e_t = float;
        +
        using c_t = kyosu::complex_t<float>;
        +
        using q_t = kyosu::quaternion_t<float>;
        +
        using we_t = eve::wide<e_t, eve::fixed<2>>;
        +
        using wc_t = eve::wide<c_t, eve::fixed<2>>;
        +
        using wq_t = eve::wide<q_t, eve::fixed<2>>;
        +
        +
        std::cout << "Real: \n";
        +
        e_t e(2.9f);
        +
        we_t we = we_t(e);
        +
        std::cout << e << " -> " << cscpi(e) << "\n";
        +
        std::cout << we << " -> " << cscpi(we) << "\n";
        +
        std::cout << cscpi(c_t(e))<< "\n";
        +
        std::cout << cscpi(q_t(e))<< "\n";
        +
        std::cout << cscpi(wc_t(e))<< "\n";
        +
        std::cout << cscpi(wq_t(e))<< "\n";
        +
        +
        std::cout << "Complex: \n";
        +
        c_t c(3.5f,-2.9f);
        +
        wc_t wc = wc_t(c);
        +
        std::cout << c << " -> " << cscpi(c) << "\n";
        +
        std::cout << wc << " -> " << cscpi(wc) << "\n";
        +
        std::cout << cscpi(q_t(c))<< "\n";
        +
        std::cout << cscpi(wq_t(c))<< "\n";
        +
        +
        std::cout << "Quaternion: \n";
        +
        q_t q(3.5f,-2.9f, 2.1f, 3.2f);
        +
        wq_t wq = wq_t(q);
        +
        std::cout << q << " -> " << cscpi(q) << "\n";
        +
        std::cout << wq << " -> " << cscpi(wq) << "\n";
        +
        +
        return 0;
        +
        }
        +
        kyosu::quaternion_t
        as_cayley_dickson_n_t< 4, T > quaternion_t
        Type alias for quaternion numbers.
        Definition: quaternion.hpp:27
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        +
        diff --git a/group__functions_gaafed3076d5ce6fbfa0bfa53301927ae3.html b/group__functions_gaafed3076d5ce6fbfa0bfa53301927ae3.html index dd15a03e..304f1690 100644 --- a/group__functions_gaafed3076d5ce6fbfa0bfa53301927ae3.html +++ b/group__functions_gaafed3076d5ce6fbfa0bfa53301927ae3.html @@ -159,11 +159,33 @@

        -
      • a real input z is treated as if to_complex(z) was entered.
        • +
      • a real input z is treated as if complex(z) was entered.
      • Returns elementwise \(\mathop{\mathrm{acosh}}(1/z)\).

        • Example

        -
        +
        #include <kyosu/kyosu.hpp>
        +
        #include <eve/wide.hpp>
        +
        #include <iostream>
        +
        +
        int main()
        +
        {
        +
        +
        using wide_ft = eve::wide <float, eve::fixed<4>>;
        +
        wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
        +
        wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
        +
        wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
        +
        auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
        +
        +
        std::cout
        +
        << "---- simd" << std::endl
        +
        << "<- zc = " << zc << std::endl
        +
        << "-> asech(zc) = " << kyosu::asech(zc)<< std::endl
        +
        << "-> asech(ref2) = " << kyosu::asech(ref2) << std::endl;
        +
        +
        return 0;
        +
        }
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        +
        diff --git a/group__functions_gab07fa9f73fd002dccfcb769a87bee81c.html b/group__functions_gab07fa9f73fd002dccfcb769a87bee81c.html index 07014d89..90c065b3 100644 --- a/group__functions_gab07fa9f73fd002dccfcb769a87bee81c.html +++ b/group__functions_gab07fa9f73fd002dccfcb769a87bee81c.html @@ -159,11 +159,33 @@

        -
      • a real input z is treated as if to_complex(z) was entered.
        • +
      • a real input z is treated as if complex(z) was entered.
      • Returns pi(as(z))*atan(z)

        • Example

        -
        +
        #include <kyosu/kyosu.hpp>
        +
        #include <eve/wide.hpp>
        +
        #include <iostream>
        +
        +
        int main()
        +
        {
        +
        +
        using wide_ft = eve::wide <float, eve::fixed<4>>;
        +
        wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
        +
        wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
        +
        wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
        +
        auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
        +
        +
        std::cout
        +
        << "---- simd" << std::endl
        +
        << "<- zc = " << zc << std::endl
        +
        << "-> atanpi(zc) = " << kyosu::atanpi(zc)<< std::endl
        +
        << "-> atanpi(ref2) = " << kyosu::atanpi(ref2) << std::endl;
        +
        +
        return 0;
        +
        }
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        +
        diff --git a/group__functions_gab0f1c35d5251d1f6db39bec53d8960b6.html b/group__functions_gab0f1c35d5251d1f6db39bec53d8960b6.html index a23c14db..8fda8cae 100644 --- a/group__functions_gab0f1c35d5251d1f6db39bec53d8960b6.html +++ b/group__functions_gab0f1c35d5251d1f6db39bec53d8960b6.html @@ -167,11 +167,11 @@

        Example

        int main()
        {
        using kyosu::expm1;
        -
        using kyosu::complex;
        -
        using kyosu::quaternion;
        +
        using kyosu::complex_t;
        +
        using kyosu::quaternion_t;
        using e_t = float;
        -
        using c_t = complex<float>;
        -
        using q_t = quaternion<float>;
        +
        using c_t = kyosu::complex_t<float>;
        +
        using q_t = kyosu::quaternion_t<float>;
        using we_t = eve::wide<e_t, eve::fixed<2>>;
        using wc_t = eve::wide<c_t, eve::fixed<2>>;
        using wq_t = eve::wide<q_t, eve::fixed<2>>;
        @@ -202,8 +202,8 @@

        Example

        return 0;
        }
        -
        kyosu::quaternion
        cayley_dickson< T, 4 > quaternion
        Type alias for quaternion numbers.
        Definition: quaternion.hpp:26
        -
        kyosu::complex
        cayley_dickson< T, 2 > complex
        Type alias for complex numbers.
        Definition: complex.hpp:26
        +
        kyosu::quaternion_t
        as_cayley_dickson_n_t< 4, T > quaternion_t
        Type alias for quaternion numbers.
        Definition: quaternion.hpp:27
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        diff --git a/group__functions_ga4169785cc523f33d0cb1f8615f1d1323.html b/group__functions_gab1054201f9cf583c8723b683ac50abce.html similarity index 72% rename from group__functions_ga4169785cc523f33d0cb1f8615f1d1323.html rename to group__functions_gab1054201f9cf583c8723b683ac50abce.html index 84f6fbcd..d0d89497 100644 --- a/group__functions_ga4169785cc523f33d0cb1f8615f1d1323.html +++ b/group__functions_gab1054201f9cf583c8723b683ac50abce.html @@ -6,7 +6,7 @@ -kyosu: kyosu::to_quaternion +kyosu: kyosu::ldiv @@ -96,7 +96,7 @@
        @@ -122,8 +122,8 @@
        - -

        ◆ to_quaternion

        + +

        ◆ ldiv

        @@ -132,7 +132,7 @@

        - +
        kyosu::to_quaternion = {}kyosu::ldiv = {}
        @@ -142,26 +142,25 @@

        -

        Constructs a kyosu::quaternion.

        +

        Computes the left division of the two parameters.

        Defined in Header

        #include <kyosu/functions.hpp>

        Callable Signatures

        -
        namespace kyosu
        -
        {
        -
        template<eve::ordered_value T> constexpr auto to_quaternion(T r) noexcept;
        -
        template<eve::ordered_value T> constexpr auto to_quaternion(T r, T i) noexcept;
        -
        -
        template<kyosu::concepts::cayley_dickson T> constexpr T to_quaternion(T z) noexcept;
        -
        }
        -
        kyosu::to_quaternion
        constexpr tags::callable_to_quaternion to_quaternion
        Constructs a kyosu::quaternion.
        Definition: to_quaternion.hpp:72
        +
        namespace kyosu
        +
        {
        +
        template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto ldiv(T0 z0, T1, z1) noexcept;
        +
        template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto ldiv(T0 z0, T1, z1) noexcept;
        +
        template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto ldiv(T0 z0, T1, z1) noexcept;
        +
        template<eve::ordered_value T0, ordered_value T1> > constexpr auto ldiv(T0 z0, T1, z1) noexcept;
        +
        ! }
        +
        kyosu::ldiv
        constexpr tags::callable_ldiv ldiv
        Computes the left division of the two parameters.
        Definition: ldiv.hpp:78
        kyosu
        Main KYOSU namespace.
        Definition: acos.hpp:14

        Parameters

          -
        • z : Quaternion value.
          • -
        • r, i : Real and imaginary part sued to construct a kyosu::quaternion..
          • +
        • z0, z1 : Values to process.

        Return value

        -

        Returns a kyosu::quaternion constructed from its arguments.

        +

        Returns the left division of the two arguments. This function not equivalent to z1/z0 as soon as multiplication is not commutative.

        Example

        diff --git a/group__functions_gab4f4ec4acf88c38ee4101b3c6b69058f.html b/group__functions_gab4f4ec4acf88c38ee4101b3c6b69058f.html index 019af953..a25764eb 100644 --- a/group__functions_gab4f4ec4acf88c38ee4101b3c6b69058f.html +++ b/group__functions_gab4f4ec4acf88c38ee4101b3c6b69058f.html @@ -159,11 +159,33 @@

        -
      • a real input z is treated as if to_complex(z) was entered.
        • +
      • a real input z is treated as if complex(z) was entered.
      • Returns pi(as(z))*acsc(z)

        • Example

        -
        +
        #include <kyosu/kyosu.hpp>
        +
        #include <eve/wide.hpp>
        +
        #include <iostream>
        +
        +
        int main()
        +
        {
        +
        +
        using wide_ft = eve::wide <float, eve::fixed<4>>;
        +
        wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
        +
        wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
        +
        wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
        +
        auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
        +
        +
        std::cout
        +
        << "---- simd" << std::endl
        +
        << "<- zc = " << zc << std::endl
        +
        << "-> acscpi(zc) = " << kyosu::acscpi(zc)<< std::endl
        +
        << "-> acscpi(ref2) = " << kyosu::acscpi(ref2) << std::endl;
        +
        +
        return 0;
        +
        }
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        +

        diff --git a/group__functions_gabe0cc0a4ddad9387b7e6bc13e6b3bcfd.html b/group__functions_gabe0cc0a4ddad9387b7e6bc13e6b3bcfd.html index e8581c88..760db85f 100644 --- a/group__functions_gabe0cc0a4ddad9387b7e6bc13e6b3bcfd.html +++ b/group__functions_gabe0cc0a4ddad9387b7e6bc13e6b3bcfd.html @@ -160,7 +160,29 @@

        imag(z), real(z)).

        Example

        -
        +
        #include <kyosu/kyosu.hpp>
        +
        #include <eve/wide.hpp>
        +
        #include <iostream>
        +
        +
        int main()
        +
        {
        +
        +
        using wide_ft = eve::wide <float, eve::fixed<4>>;
        +
        wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
        +
        wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
        +
        wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
        +
        auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
        +
        +
        std::cout
        +
        << "---- simd" << std::endl
        +
        << "<- zc = " << zc << std::endl
        +
        << "-> arg(zc) = " << kyosu::arg(zc)<< std::endl
        +
        << "-> arg(ref2) = " << kyosu::arg(ref2) << std::endl;
        +
        +
        return 0;
        +
        }
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        +
        diff --git a/group__functions_gabe8cd1a34e2b6559105a1c6c101d52f7.html b/group__functions_gabe8cd1a34e2b6559105a1c6c101d52f7.html index 18c1cde2..c8b09085 100644 --- a/group__functions_gabe8cd1a34e2b6559105a1c6c101d52f7.html +++ b/group__functions_gabe8cd1a34e2b6559105a1c6c101d52f7.html @@ -149,9 +149,10 @@

        namespace kyosu
        {
        template<kyosu::concepts::cayley_dickson T> constexpr T log10(T z) noexcept;
        -
        template<eve::ordered_value T> constexpr as_complex_t<T> log10(T z) noexcept;
        +
        template<eve::ordered_value T> constexpr complex_t<T> log10(T z) noexcept;
        }
        kyosu::log10
        constexpr tags::callable_log10 log10
        Computes the base 10 logarithm of the argument.
        Definition: log10.hpp:78
        +
        kyosu::complex_t
        as_cayley_dickson_n_t< 2, T > complex_t
        Type alias for complex numbers.
        Definition: complex.hpp:27
        kyosu
        Main KYOSU namespace.
        Definition: acos.hpp:14

        Parameters

          @@ -160,7 +161,50 @@

          log10(z). If z is an ordered value log10 returns a complex typed value.

          Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using kyosu::log10;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          +
          using e_t = float;
          +
          using c_t = kyosu::complex_t<float>;
          +
          using q_t = kyosu::quaternion_t<float>;
          +
          using we_t = eve::wide<e_t, eve::fixed<2>>;
          +
          using wc_t = eve::wide<c_t, eve::fixed<2>>;
          +
          using wq_t = eve::wide<q_t, eve::fixed<2>>;
          +
          +
          std::cout << "Real: \n";
          +
          e_t e(2.9f);
          +
          we_t we = we_t(e);
          +
          std::cout << e << " -> " << log10(e) << "\n";
          +
          std::cout << we << " -> " << log10(we) << "\n";
          +
          std::cout << log10(c_t(e))<< "\n";
          +
          std::cout << log10(q_t(e))<< "\n";
          +
          std::cout << log10(wc_t(e))<< "\n";
          +
          std::cout << log10(wq_t(e))<< "\n";
          +
          +
          std::cout << "Complex: \n";
          +
          c_t c(3.5f,-2.9f);
          +
          wc_t wc = wc_t(c);
          +
          std::cout << c << " -> " << log10(c) << "\n";
          +
          std::cout << wc << " -> " << log10(wc) << "\n";
          +
          std::cout << log10(q_t(c))<< "\n";
          +
          std::cout << log10(wq_t(c))<< "\n";
          +
          +
          std::cout << "Quaternion: \n";
          +
          q_t q(3.5f,-2.9f, 2.1f, 3.2f);
          +
          wq_t wq = wq_t(q);
          +
          std::cout << q << " -> " << log10(q) << "\n";
          +
          std::cout << wq << " -> " << log10(wq) << "\n";
          +
          +
          return 0;
          +
          }
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          diff --git a/group__functions_gabfab93a2a2b4f527d3c69eeb13856d2c.html b/group__functions_gabfab93a2a2b4f527d3c69eeb13856d2c.html index c7fcb38a..489801e5 100644 --- a/group__functions_gabfab93a2a2b4f527d3c69eeb13856d2c.html +++ b/group__functions_gabfab93a2a2b4f527d3c69eeb13856d2c.html @@ -169,14 +169,14 @@

          Example

          int main()
          {
          using kyosu::is_equal;
          -
          using kyosu::complex;
          -
          using kyosu::quaternion;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          using e_t = float;
          -
          using c_t = complex<float>;
          -
          using q_t = quaternion<float>;
          +
          using c_t = kyosu::complex_t<float>;
          +
          using q_t = kyosu::quaternion_t<float>;
          using we_t = eve::wide<float, eve::fixed<2>>;
          -
          using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
          -
          using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
          +
          using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
          +
          using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
          std::cout << "Real: "<< "\n";
          e_t e0(1);
          @@ -207,8 +207,8 @@

          Example

          return 0;
          }
          -
          kyosu::quaternion
          cayley_dickson< T, 4 > quaternion
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:26
          -
          kyosu::complex
          cayley_dickson< T, 2 > complex
          Type alias for complex numbers.
          Definition: complex.hpp:26
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          diff --git a/group__functions_gac01bdb4384827ce21ddddedd19f8b032.html b/group__functions_gac01bdb4384827ce21ddddedd19f8b032.html new file mode 100644 index 00000000..cb2b5cea --- /dev/null +++ b/group__functions_gac01bdb4384827ce21ddddedd19f8b032.html @@ -0,0 +1,203 @@ + + + + + + + + +kyosu: kyosu::erfi + + + + + + + + + + + + + + + + + + + + + + + + + + +
          + +
          + + + + + + + + +
          +
          kyosu v0.1.0 +
          +
          Complex Without Complexes
          +
          + +   + + + + +
          +
          +
          + + + + +
          +
          + +
          +
          +
          + +
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          Loading...
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          + +
          + +

          ◆ erfi

          + +
          +
          + + + + + +
          + + + + +
          kyosu::erfi = {}
          +           		+inlineconstexpr
          +
          + +

          Callable object computing The imaginary error function \( \displaystyle \mathrm{erfi}(z) = -i\mathrm{erf}(iz)\).

          +

          Defined in Header

          +
          #include <kyosu/functions.hpp>
          +

          Callable Signatures

          +
          namespace kyosu
          +
          {
          +
          template<eve::ordered_value T> constexpr auto erfi(T z) noexcept; //1
          +
          template<kyosu::concepts::complex T> constexpr auto erfi(T z) noexcept; //2
          +
          }
          +
          kyosu::erfi
          constexpr tags::callable_erfi erfi
          Callable object computing The imaginary error function .
          Definition: erfi.hpp:79
          +
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14
          +

          Parameters

          +
            +
          • z : Vcomplex or real value to process.
            • +
          +

          Return value

          +

          Returns the imaginary error function \( \displaystyle \mathrm{erfi}(z) = -i\mathrm{erf}(iz)\)

          +

          Example

          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> erfi(zc) = " << kyosu::erfi(zc)<< std::endl
          +
          << "-> erfi(ref2) = " << kyosu::erfi(ref2) << std::endl;
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          +
          +
          +
          +
          + + + + + + + + + + diff --git a/group__functions_gac2c1a89f5526dbb4d7e64e2fe8fe698a.html b/group__functions_gac2c1a89f5526dbb4d7e64e2fe8fe698a.html index 46d2736b..4ce36765 100644 --- a/group__functions_gac2c1a89f5526dbb4d7e64e2fe8fe698a.html +++ b/group__functions_gac2c1a89f5526dbb4d7e64e2fe8fe698a.html @@ -159,11 +159,33 @@

          -
        • a real input z is treated as if to_complex(z) was entered.
          • +
        • a real input z is treated as if complex(z) was entered.
        • Returns elementwise \(\mathop{\mathrm{asinh}}(1/z)\).

          • Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> acsch(zc) = " << kyosu::acsch(zc)<< std::endl
          +
          << "-> acsch(ref2) = " << kyosu::acsch(ref2) << std::endl;
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          diff --git a/group__functions_gac91bff00b4c1a3c8e0b249a07bd6c080.html b/group__functions_gac91bff00b4c1a3c8e0b249a07bd6c080.html index 13b3c88e..7b2c1aa7 100644 --- a/group__functions_gac91bff00b4c1a3c8e0b249a07bd6c080.html +++ b/group__functions_gac91bff00b4c1a3c8e0b249a07bd6c080.html @@ -160,7 +160,59 @@

          Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using kyosu::is_not_nan;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          +
          using eve::as;
          +
          using e_t = float;
          +
          using c_t = kyosu::complex_t<float>;
          +
          using q_t = kyosu::quaternion_t<float>;
          +
          using we_t = eve::wide<e_t, eve::fixed<4>>;
          +
          using wc_t = eve::wide<c_t, eve::fixed<4>>;
          +
          using wq_t = eve::wide<q_t, eve::fixed<4>>;
          +
          +
          std::cout << "Real: \n";
          +
          e_t e(2.9f);
          +
          e_t nan = eve::nan(as(e));
          +
          e_t inf = eve::inf(as(e));
          +
          e_t zer = eve::zero(as(e));
          +
          we_t we = we_t(e, zer, nan, inf);
          +
          std::cout << e << " -> " << is_not_nan(e) << "\n";
          +
          std::cout << we << " -> " << is_not_nan(we) << "\n";
          +
          std::cout << is_not_nan(c_t(e))<< "\n";
          +
          std::cout << is_not_nan(q_t(e))<< "\n";
          +
          std::cout << is_not_nan(kyosu::complex(we))<< "\n";
          +
          std::cout << is_not_nan(kyosu::quaternion(we))<< "\n";
          +
          +
          std::cout << "Complex: \n";
          +
          c_t c(3.5f,-2.9f);
          +
          c_t d(0.0f, inf);
          +
          wc_t wc = wc_t(c, zer, nan, d);
          +
          std::cout << c << " -> " << is_not_nan(c) << "\n";
          +
          std::cout << wc << " -> " << is_not_nan(wc) << "\n";
          +
          std::cout << is_not_nan(kyosu::complex(wc))<< "\n";;
          +
          std::cout << is_not_nan(kyosu::quaternion(wc))<< "\n";
          +
          +
          std::cout << "Quaternion: \n";
          +
          q_t q(3.5f,-2.9f, 2.1f, 3.2f);
          +
          q_t r(3.5f, nan, inf, zer);
          +
          wq_t wq = wq_t(q, zer, nan, r);
          +
          std::cout << q << " -> " << is_not_nan(q) << "\n";
          +
          std::cout << wq << " -> " << is_not_nan(wq) << "\n";
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex
          constexpr tags::callable_complex complex
          Constructs a kyosu::complex.
          Definition: to_complex.hpp:70
          +
          kyosu::quaternion
          constexpr tags::callable_quaternion quaternion
          Constructs a kyosu::quaternion.
          Definition: to_quaternion.hpp:72
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          diff --git a/group__functions_gaca9f3f8f0c75ddbff90aab0785d7a23f.html b/group__functions_gaca9f3f8f0c75ddbff90aab0785d7a23f.html index 36b22362..8241ba36 100644 --- a/group__functions_gaca9f3f8f0c75ddbff90aab0785d7a23f.html +++ b/group__functions_gaca9f3f8f0c75ddbff90aab0785d7a23f.html @@ -160,7 +160,59 @@

          Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using kyosu::is_finite;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          +
          using eve::as;
          +
          using e_t = float;
          +
          using c_t = kyosu::complex_t<float>;
          +
          using q_t = kyosu::quaternion_t<float>;
          +
          using we_t = eve::wide<e_t, eve::fixed<4>>;
          +
          using wc_t = eve::wide<c_t, eve::fixed<4>>;
          +
          using wq_t = eve::wide<q_t, eve::fixed<4>>;
          +
          +
          std::cout << "Real: \n";
          +
          e_t e(2.9f);
          +
          e_t nan = eve::nan(as(e));
          +
          e_t inf = eve::inf(as(e));
          +
          e_t zer = eve::zero(as(e));
          +
          we_t we = we_t(e, zer, nan, inf);
          +
          std::cout << e << " -> " << is_finite(e) << "\n";
          +
          std::cout << we << " -> " << is_finite(we) << "\n";
          +
          std::cout << is_finite(c_t(e))<< "\n";
          +
          std::cout << is_finite(q_t(e))<< "\n";
          +
          std::cout << is_finite(kyosu::complex(we))<< "\n";
          +
          std::cout << is_finite(kyosu::quaternion(we))<< "\n";
          +
          +
          std::cout << "Complex: \n";
          +
          c_t c(3.5f,-2.9f);
          +
          c_t d(0.0f, inf);
          +
          wc_t wc = wc_t(c, zer, nan, d);
          +
          std::cout << c << " -> " << is_finite(c) << "\n";
          +
          std::cout << wc << " -> " << is_finite(wc) << "\n";
          +
          std::cout << is_finite(kyosu::complex(wc))<< "\n";;
          +
          std::cout << is_finite(kyosu::quaternion(wc))<< "\n";
          +
          +
          std::cout << "Quaternion: \n";
          +
          q_t q(3.5f,-2.9f, 2.1f, 3.2f);
          +
          q_t r(3.5f, nan, inf, zer);
          +
          wq_t wq = wq_t(q, zer, nan, r);
          +
          std::cout << q << " -> " << is_finite(q) << "\n";
          +
          std::cout << wq << " -> " << is_finite(wq) << "\n";
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex
          constexpr tags::callable_complex complex
          Constructs a kyosu::complex.
          Definition: to_complex.hpp:70
          +
          kyosu::quaternion
          constexpr tags::callable_quaternion quaternion
          Constructs a kyosu::quaternion.
          Definition: to_quaternion.hpp:72
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          diff --git a/group__functions_gacb0340f73510f30b99ad37fa82c22e8f.html b/group__functions_gacb0340f73510f30b99ad37fa82c22e8f.html new file mode 100644 index 00000000..55840d5b --- /dev/null +++ b/group__functions_gacb0340f73510f30b99ad37fa82c22e8f.html @@ -0,0 +1,207 @@ + + + + + + + + +kyosu: kyosu::erf + + + + + + + + + + + + + + + + + + + + + + + + + + +
          + +
          + + + + + + + + +
          +
          kyosu v0.1.0 +
          +
          Complex Without Complexes
          +
          + +   + + + + +
          +
          +
          + + + + +
          +
          + +
          +
          +
          + +
          + +
          +
          + + +
          +
          +
          +
          +
          +
          Loading...
          +
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          +
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          +
          +
          +
          +
          + +
          + +

          ◆ erf

          + +
          +
          + + + + + +
          + + + + +
          kyosu::erf = {}
          +           		+inlineconstexpr
          +
          + +

          Computes the error function: \( \displaystyle + \mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\) or its analytic continuation in the complex plane.

          +

          Defined in Header

          +
          #include <kyosu/functions.hpp>
          +

          Callable Signatures

          +
          namespace kyosu
          +
          {
          +
          template<eve::ordered_value T> constexpr auto erf(T z) noexcept; //1
          +
          template<kyosu::concepts::complex T> constexpr auto erf(T z) noexcept; //2
          +
          }
          +
          kyosu::erf
          constexpr tags::callable_erf erf
          Computes the error function: or its analytic continuation in the complex plane.
          Definition: erf.hpp:80
          +
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14
          +

          Parameters

          +
            +
          • z : Value to process.
            • +
          +

          Return value

          +
            +
          1. a real input z is treated as if complex(z) was entered.
            2. +
          2. The value of the error function in the complex plane is returned
            3. +
          +

          Example

          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> erf(zc) = " << kyosu::erf(zc)<< std::endl
          +
          << "-> erf(ref2) = " << kyosu::erf(ref2) << std::endl;
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          +
          +
          +
          +
          + + + + + + + + + + diff --git a/group__functions_gacde87320a89a08d11a584bcc29d9aef6.html b/group__functions_gacde87320a89a08d11a584bcc29d9aef6.html index f5a149f9..838148dd 100644 --- a/group__functions_gacde87320a89a08d11a584bcc29d9aef6.html +++ b/group__functions_gacde87320a89a08d11a584bcc29d9aef6.html @@ -159,7 +159,7 @@

          -
        • a real input z is treated as if to_complex(z) was entered.
          • +
        • a real input z is treated as if complex(z) was entered.
        • Returns elementwise the complex principal value of the arc cosine of the input. Branch cuts exist outside the interval \([-1, +1]\) along the real axis.

          Return value

            -
          1. a real input z is treated as if to_complex(z) was entered.
            2. +
          2. a real input z is treated as if complex(z) was entered.
          3. Returns elementwise the complex principal value of the arc cosine of the input. Branch cuts exist outside the interval \([-1, +1]\) along the real axis.
            • for every z: eve::acos(eve::conj(z)) == eve::conj(std::acos(z))
            • If z is \(\pm0\), the result is \(\pi/2\)
              • @@ -211,7 +233,28 @@

              Example

          Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> acos(zc) = " << kyosu::acos(zc)<< std::endl
          +
          << "-> acos(ref2) = " << kyosu::acos(ref2) << std::endl;
          +
          +
          return 0;
          +
          }
          +
          diff --git a/group__functions_gad00c7ec9930289364786f5004c212c9b.html b/group__functions_gad00c7ec9930289364786f5004c212c9b.html new file mode 100644 index 00000000..dbf78c3c --- /dev/null +++ b/group__functions_gad00c7ec9930289364786f5004c212c9b.html @@ -0,0 +1,203 @@ + + + + + + + + +kyosu: kyosu::log_abs_gamma + + + + + + + + + + + + + + + + + + + + + + + + + + +
          + +
          + + + + + + + + +
          +
          kyosu v0.1.0 +
          +
          Complex Without Complexes
          +
          + +   + + + + +
          +
          +
          + + + + +
          +
          + +
          +
          +
          + +
          + +
          +
          + + +
          +
          +
          +
          +
          +
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          +
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          +
          +
          + +
          + +

          ◆ log_abs_gamma

          + +
          +
          + + + + + +
          + + + + +
          kyosu::log_abs_gamma = {}
          +           		+inlineconstexpr
          +
          + +

          Computes the log of the modulus of the \(\Gamma\) function of the parameter.

          +

          Defined in Header

          +
          #include <kyosu/functions.hpp>
          +

          Callable Signatures

          +
          namespace kyosu
          +
          {
          +
          template<kyosu::concepts::complex T> constexpr T log_abs_gamma(T z) noexcept;
          +
          template<eve::floatingordered_value T> constexpr T log_abs_gamma(T z) noexcept;
          +
          }
          +
          kyosu::log_abs_gamma
          constexpr tags::callable_log_abs_gamma log_abs_gamma
          Computes the log of the modulus of the function of the parameter.
          Definition: log_abs_gamma.hpp:76
          +
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14
          +

          Parameters

          +
            +
          • z : Value to process.
            • +
          +

          Return value

          +

          Returns \(\log(|\Gamma(z)|)\). If z is floating the result is as if complex(z) was used in the call.

          +

          Example

          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> log_abs_gamma(zc) = " << kyosu::log_abs_gamma(zc)<< std::endl
          +
          << "-> log_abs_gamma(ref2) = " << kyosu::log_abs_gamma(ref2) << std::endl;
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          +
          +
          +
          +
          + + + + + + + + + + diff --git a/group__functions_gad4e960a6cb254cdd741323efc8efa3a0.html b/group__functions_gad4e960a6cb254cdd741323efc8efa3a0.html index 0f04d7cd..f75b8c34 100644 --- a/group__functions_gad4e960a6cb254cdd741323efc8efa3a0.html +++ b/group__functions_gad4e960a6cb254cdd741323efc8efa3a0.html @@ -168,26 +168,26 @@

          Example

          int main()
          {
          using kyosu::conj;
          -
          using kyosu::complex;
          -
          using kyosu::quaternion;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          std::cout << "Real: ";
          std::cout << 72.9f << " -> " << conj(72.9f) << "\n";
          std::cout << "Complex: ";
          -
          std::cout << complex<float>(3.5f,-2.9f) << " -> " << conj(complex<float>(3.5f,-2.9f)) << "\n";
          +
          std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << conj(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
          std::cout << "Quaternion: ";
          -
          std::cout << quaternion<double>(1.,2.,3.,4.) << " -> " << conj(quaternion<double>(1.,2.,3.,4.)) << "\n";
          +
          std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << conj(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
          std::cout << "SIMD: ";
          -
          using wc_t = eve::wide<complex<double>, eve::fixed<2>>;
          -
          std::cout << wc_t(complex<double>(1.3,-3.7)) << " -> " << conj(wc_t(complex<double>(1.3,-3.7))) << "\n";
          +
          using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
          +
          std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << conj(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
          return 0;
          }
          -
          kyosu::quaternion
          cayley_dickson< T, 4 > quaternion
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:26
          -
          kyosu::complex
          cayley_dickson< T, 2 > complex
          Type alias for complex numbers.
          Definition: complex.hpp:26
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          diff --git a/group__functions_gad726f439fb9920c055c094631185d449.html b/group__functions_gad726f439fb9920c055c094631185d449.html index 433917a6..8fc002d1 100644 --- a/group__functions_gad726f439fb9920c055c094631185d449.html +++ b/group__functions_gad726f439fb9920c055c094631185d449.html @@ -167,11 +167,11 @@

          Example

          int main()
          {
          using kyosu::exp;
          -
          using kyosu::complex;
          -
          using kyosu::quaternion;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          using e_t = float;
          -
          using c_t = complex<float>;
          -
          using q_t = quaternion<float>;
          +
          using c_t = kyosu::complex_t<float>;
          +
          using q_t = kyosu::quaternion_t<float>;
          using we_t = eve::wide<e_t, eve::fixed<2>>;
          using wc_t = eve::wide<c_t, eve::fixed<2>>;
          using wq_t = eve::wide<q_t, eve::fixed<2>>;
          @@ -202,8 +202,8 @@

          Example

          return 0;
          }
          -
          kyosu::quaternion
          cayley_dickson< T, 4 > quaternion
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:26
          -
          kyosu::complex
          cayley_dickson< T, 2 > complex
          Type alias for complex numbers.
          Definition: complex.hpp:26
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          diff --git a/group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html b/group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html new file mode 100644 index 00000000..a72917be --- /dev/null +++ b/group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html @@ -0,0 +1,203 @@ + + + + + + + + +kyosu: kyosu::complex + + + + + + + + + + + + + + + + + + + + + + + + + + +
          + +
          + + + + + + + + +
          +
          kyosu v0.1.0 +
          +
          Complex Without Complexes
          +
          + +   + + + + +
          +
          +
          + + + + +
          +
          + +
          +
          +
          + +
          + +
          +
          + + +
          +
          +
          +
          +
          +
          Loading...
          +
          Searching...
          +
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          +
          +
          +
          +
          + +
          + +

          ◆ complex

          + +
          +
          + + + + + +
          + + + + +
          kyosu::complex = {}
          +           		+inlineconstexpr
          +
          + +

          Constructs a kyosu::complex.

          +

          Defined in Header

          +
          #include <kyosu/functions.hpp>
          +

          Callable Signatures

          +
          namespace kyosu
          +
          {
          +
          template<eve::ordered_value T> constexpr auto complex(T r, T i = 0) noexcept;
          +
          template<kyosu::concepts::cayley_dickson T> constexpr T complex(T z) noexcept;
          +
          }
          +
          kyosu::complex
          constexpr tags::callable_complex complex
          Constructs a kyosu::complex.
          Definition: to_complex.hpp:70
          +
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14
          +

          Parameters

          +
            +
          • z : Complex value.
            • +
          • r, i : Real and imaginary part sued to construct a kyosu::complex..
            • +
          +

          Return value

          +

          Returns a kyosu::complex constructed from its arguments.

          +

          Example

          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using kyosu::complex;
          +
          +
          std::cout << "Real: ";
          +
          std::cout << "complex(72.9f) -> " << complex(72.9f) << "\n";
          +
          +
          std::cout << "Complex: ";
          +
          std::cout << "complex(3.5f, 2.9f) -> " << complex(3.5f,-2.9f) << "\n";
          +
          +
          std::cout << "SIMD complex: ";
          +
          using w_t = eve::wide<double, eve::fixed<2>>;
          +
          w_t a(3.5f,-2.9f), b(1.0, -3.0);
          +
          std::cout << "complex(a, b) -> " << complex(a, b) << "\n";
          +
          +
          return 0;
          +
          }
          +
          +
          +
          +
          +
          + + + + + + + + + + diff --git a/group__functions_gae6df724ac822c7361d9ea9252e62d0a4.html b/group__functions_gae6df724ac822c7361d9ea9252e62d0a4.html new file mode 100644 index 00000000..d057e6a7 --- /dev/null +++ b/group__functions_gae6df724ac822c7361d9ea9252e62d0a4.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::quaternion + + + + + + + + + + + + + + + + + + + + + + + + + + +
          + +
          + + + + + + + + +
          +
          kyosu v0.1.0 +
          +
          Complex Without Complexes
          +
          + +   + + + + +
          +
          +
          + + + + +
          +
          + +
          +
          +
          + +
          + +
          +
          + + +
          +
          +
          +
          +
          +
          Loading...
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          +
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          +
          +
          +
          +
          + +
          + +

          ◆ quaternion

          + +
          +
          + + + + + +
          + + + + +
          kyosu::quaternion = {}
          +           		+inlineconstexpr
          +
          + +

          Constructs a kyosu::quaternion.

          +

          Defined in Header

          +
          #include <kyosu/functions.hpp>
          +

          Callable Signatures

          +
          namespace kyosu
          +
          {
          +
          template<eve::ordered_value T> constexpr auto quaternion(T r, T i = 0, T j = 0, T k = 0) noexcept;
          +
          template<eve::ordered_value T> constexpr auto quaternion(complex_t<T> c0, complex_t<T> c1 = 0) noexcept;
          +
          template<kyosu::concepts::cayley_dickson T> constexpr T quaternion(T z) noexcept;
          +
          }
          +
          kyosu::quaternion
          constexpr tags::callable_quaternion quaternion
          Constructs a kyosu::quaternion.
          Definition: to_quaternion.hpp:72
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14
          +

          Parameters

          +
            +
          • z : Quaternion value.
            • +
          • c0,c1 : Complex values generates the quaternion c0+j*conj(c1) i.e. real(c0+i*imag(c1)+j*real(1)+k*imag(c1)
            • +
          • r, i, j, k : Real and unreal parts sued to construct a kyosu::quaternion from its components
            • +
          +

          Return value

          +

          Returns a kyosu::quaternion constructed from its arguments.

          +

          Example

          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using kyosu::complex;
          +
          using kyosu::quaternion;
          +
          +
          std::cout << "Real: ";
          +
          std::cout << "quaternion(72.9f) -> " << quaternion(72.9f) << "\n";
          +
          +
          std::cout << "Complex: ";
          +
          std::cout << "quaternion(3.5f, 2.9f) -> " << quaternion(3.5f,-2.9f) << "\n";
          +
          +
          std::cout << "Quaternion: ";
          +
          std::cout << "quaternion(1.0, 2.0, 3.0, 4.0) -> " << quaternion(1.,2.,3.,4.) << "\n";
          +
          auto c0 = complex(1.0, 2.3);
          +
          auto c1 = complex(-4.0, -1.5);
          +
          std::cout << "c0 = " << c0 << "\n";
          +
          std::cout << "c1 = " << c1 << "\n";
          +
          std::cout << "quaternion(c0, c1) -> " << quaternion(c0, c1) << "\n";
          +
          +
          std::cout << "SIMD quaternion: \n";
          +
          using w_t = eve::wide<double, eve::fixed<2>>;
          +
          w_t a(3.5f,-2.9f), b(1.0, -3.0);
          +
          std::cout << "a = " << a << "\n";
          +
          std::cout << "b = " << b << "\n";
          +
          std::cout << "quaternion(a, b) -> " << quaternion(a, b) << "\n";
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex
          constexpr tags::callable_complex complex
          Constructs a kyosu::complex.
          Definition: to_complex.hpp:70
          +
          +
          +
          +
          +
          + + + + + + + + + + diff --git a/group__functions_gae8a89a63722b9cdec2f2d4daf58bf025.html b/group__functions_gae8a89a63722b9cdec2f2d4daf58bf025.html index ae07914e..a568919e 100644 --- a/group__functions_gae8a89a63722b9cdec2f2d4daf58bf025.html +++ b/group__functions_gae8a89a63722b9cdec2f2d4daf58bf025.html @@ -167,11 +167,11 @@

          Example

          int main()
          {
          using kyosu::oneminus;
          -
          using kyosu::complex;
          -
          using kyosu::quaternion;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          using e_t = float;
          -
          using c_t = complex<float>;
          -
          using q_t = quaternion<float>;
          +
          using c_t = kyosu::complex_t<float>;
          +
          using q_t = kyosu::quaternion_t<float>;
          using we_t = eve::wide<e_t, eve::fixed<2>>;
          using wc_t = eve::wide<c_t, eve::fixed<2>>;
          using wq_t = eve::wide<q_t, eve::fixed<2>>;
          @@ -196,8 +196,8 @@

          Example

          return 0;
          }
          -
          kyosu::quaternion
          cayley_dickson< T, 4 > quaternion
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:26
          -
          kyosu::complex
          cayley_dickson< T, 2 > complex
          Type alias for complex numbers.
          Definition: complex.hpp:26
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          diff --git a/group__functions_gae97bce0027166d1321885e92abb15836.html b/group__functions_gae97bce0027166d1321885e92abb15836.html new file mode 100644 index 00000000..392b9374 --- /dev/null +++ b/group__functions_gae97bce0027166d1321885e92abb15836.html @@ -0,0 +1,216 @@ + + + + + + + + +kyosu: kyosu::proj + + + + + + + + + + + + + + + + + + + + + + + + + + +
          + +
          + + + + + + + + +
          +
          kyosu v0.1.0 +
          +
          Complex Without Complexes
          +
          + +   + + + + +
          +
          +
          + + + + +
          +
          + +
          +
          +
          + +
          + +
          +
          + + +
          +
          +
          +
          +
          +
          Loading...
          +
          Searching...
          +
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          +
          +
          +
          +
          + +
          + +

          ◆ proj

          + +
          +
          + + + + + +
          + + + + +
          kyosu::proj = {}
          +           		+inlineconstexpr
          +
          + +

          Callable object computing proj(x), the projection of the cayley_dickson number z onto the (hyper) Riemann sphere.

          +

          Defined in Header

          +
          #include <kyosu/functions.hpp>
          +

          Callable Signatures

          +
          namespace kyosu
          +
          {
          +
          template<kyosu::concepts::cayley_dickson T> constexpr T proj(T z) noexcept;
          +
          template<eve::ordered_value T> constexpr T proj(T z) noexcept;
          +
          }
          +
          kyosu::proj
          constexpr tags::callable_proj proj
          Callable object computing proj(x), the projection of the cayley_dickson number z onto the (hyper) Rie...
          Definition: proj.hpp:78
          +
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14
          +

          Parameters

          +
            +
          • z : Value to projugate.
            • +
          +

          Return value

          +

          For most z, std::proj(z)==z, but all infinities, even the numbers where one component is infinite and the other is NaN, become positive real infinity, (inf, 0.0...) or (inf, -0.0...). The sign of the pure (zero) components is the signs of the components of pure(z). 

          For floating inputs the call returns a complex number.
+

          Example

          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using kyosu::proj;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          +
          auto inf = eve::inf(eve::as<float>());
          +
          +
          std::cout << "Real: \n";
          +
          std::cout << " " << 72.9f << " -> " << proj(72.9f) << "\n";
          +
          std::cout << " " << inf << " -> " << proj(inf) << "\n";
          +
          std::cout << " " << -inf << " -> " << proj(-inf) << "\n";
          +
          +
          std::cout << "Complex: \n";
          +
          std::cout << " " << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << proj(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
          +
          std::cout << " " << kyosu::complex_t<float>(3.5f,inf) << " -> " << proj(kyosu::complex_t<float>(3.5f,inf)) << "\n";
          +
          std::cout << " " << kyosu::complex_t<float>(3.5f,-inf) << " -> " << proj(kyosu::complex_t<float>(3.5f,-inf)) << "\n";
          +
          std::cout << " " << kyosu::complex_t<float>(inf,-2.9f) << " -> " << proj(kyosu::complex_t<float>(inf,-2.9f)) << "\n";
          +
          std::cout << " " << kyosu::complex_t<float>(inf, 2.9f) << " -> " << proj(kyosu::complex_t<float>(inf,2.9f)) << "\n";
          +
          +
          std::cout << "Quaternion: \n";
          +
          std::cout << " " << kyosu::quaternion_t<double>(1.f,2.f,3.f,4.f) << " -> " << proj(kyosu::quaternion_t<double>(1.f,2.f,3.f,4.f)) << "\n";
          +
          std::cout << " " << kyosu::quaternion_t<double>(-1.f,inf,3.f,-4.f) << " -> " << proj(kyosu::quaternion_t<double>(-1.f,inf,3.f,-4.f)) << "\n";
          +
          +
          using T = eve::wide < float, eve::fixed < 2 > >;
          +
          using c_t = kyosu::quaternion_t<T>;
          +
          auto g = c_t(32, 44, 55, 34);
          +
          std::cout << g << std::endl;
          +
          return 0;
          +
          }
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          +
          +
          +
          +
          + + + + + + + + + + diff --git a/group__functions_gaecbb072c068e6effd78aa84c6e65b329.html b/group__functions_gaecbb072c068e6effd78aa84c6e65b329.html index 0d5084c9..153d6f66 100644 --- a/group__functions_gaecbb072c068e6effd78aa84c6e65b329.html +++ b/group__functions_gaecbb072c068e6effd78aa84c6e65b329.html @@ -160,7 +160,51 @@

          Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using kyosu::csc;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          +
          using e_t = float;
          +
          using c_t = kyosu::complex_t<float>;
          +
          using q_t = kyosu::quaternion_t<float>;
          +
          using we_t = eve::wide<e_t, eve::fixed<2>>;
          +
          using wc_t = eve::wide<c_t, eve::fixed<2>>;
          +
          using wq_t = eve::wide<q_t, eve::fixed<2>>;
          +
          +
          std::cout << "Real: \n";
          +
          e_t e(2.9f);
          +
          we_t we = we_t(e);
          +
          std::cout << e << " -> " << csc(e) << "\n";
          +
          std::cout << we << " -> " << csc(we) << "\n";
          +
          std::cout << csc(c_t(e))<< "\n";
          +
          std::cout << csc(q_t(e))<< "\n";
          +
          std::cout << csc(wc_t(e))<< "\n";
          +
          std::cout << csc(wq_t(e))<< "\n";
          +
          +
          std::cout << "Complex: \n";
          +
          c_t c(3.5f,-2.9f);
          +
          wc_t wc = wc_t(c);
          +
          std::cout << c << " -> " << csc(c) << "\n";
          +
          std::cout << wc << " -> " << csc(wc) << "\n";
          +
          std::cout << csc(q_t(c))<< "\n";
          +
          std::cout << csc(wq_t(c))<< "\n";
          +
          +
          std::cout << "Quaternion: \n";
          +
          q_t q(3.5f,-2.9f, 2.1f, 3.2f);
          +
          wq_t wq = wq_t(q);
          +
          std::cout << q << " -> " << csc(q) << "\n";
          +
          std::cout << wq << " -> " << csc(wq) << "\n";
          +
          +
          return 0;
          +
          }
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          diff --git a/group__functions_gaee536feee7876ba344199903c2852962.html b/group__functions_gaee536feee7876ba344199903c2852962.html index 557cebca..8c43ec7c 100644 --- a/group__functions_gaee536feee7876ba344199903c2852962.html +++ b/group__functions_gaee536feee7876ba344199903c2852962.html @@ -159,11 +159,34 @@

          -
        • a real input z is treated as if to_complex(z) was entered.
          • +
        • a real input z is treated as if complex(z) was entered.
        • Returns pi(as(z))*asec(z)

          • Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> asech(zc) = " << kyosu::asech(zc)<< std::endl
          +
          << "-> asech(ref2) = " << kyosu::asech(ref2) << std::endl;
          +
          +
          return 0;
          +
          }
          +
          kyosu::asech
          constexpr tags::callable_asech asech
          Computes the hyperbolic arcsecant of the argument.
          Definition: asech.hpp:79
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          diff --git a/group__functions_gaee913dc7298d2917743440e9d056d971.html b/group__functions_gaee913dc7298d2917743440e9d056d971.html index c482ccbe..e284b0aa 100644 --- a/group__functions_gaee913dc7298d2917743440e9d056d971.html +++ b/group__functions_gaee913dc7298d2917743440e9d056d971.html @@ -161,7 +161,34 @@

          Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using kyosu::abs;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          +
          +
          std::cout << "Real: ";
          +
          std::cout << 72.9f << " -> " << abs(72.9f) << "\n";
          +
          +
          std::cout << "Complex: ";
          +
          std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << abs(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
          +
          +
          std::cout << "Quaternion: ";
          +
          std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << abs(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
          +
          +
          std::cout << "SIMD: ";
          +
          using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
          +
          std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << abs(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
          +
          +
          return 0;
          +
          }
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          diff --git a/group__functions_gaf0240aea3dcf4428abd35906e94323e7.html b/group__functions_gaf0240aea3dcf4428abd35906e94323e7.html index 0c9afd42..5f7e7c56 100644 --- a/group__functions_gaf0240aea3dcf4428abd35906e94323e7.html +++ b/group__functions_gaf0240aea3dcf4428abd35906e94323e7.html @@ -166,14 +166,14 @@

          Example

          int main()
          {
          using kyosu::hypot;
          -
          using kyosu::complex;
          -
          using kyosu::quaternion;
          +
          using kyosu::complex_t;
          +
          using kyosu::quaternion_t;
          using e_t = float;
          -
          using c_t = complex<float>;
          -
          using q_t = quaternion<float>;
          +
          using c_t = kyosu::complex_t<float>;
          +
          using q_t = kyosu::quaternion_t<float>;
          using we_t = eve::wide<float, eve::fixed<2>>;
          -
          using wc_t = eve::wide<complex<float>, eve::fixed<2>>;
          -
          using wq_t = eve::wide<quaternion<float>, eve::fixed<2>>;
          +
          using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
          +
          using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
          std::cout << "Real: "<< "\n";
          e_t e0(1);
          @@ -202,8 +202,8 @@

          Example

          return 0;
          }
          kyosu::hypot
          constexpr tags::callable_hypot hypot
          Callable object computing the hypot operation.
          Definition: hypot.hpp:75
          -
          kyosu::quaternion
          cayley_dickson< T, 4 > quaternion
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:26
          -
          kyosu::complex
          cayley_dickson< T, 2 > complex
          Type alias for complex numbers.
          Definition: complex.hpp:26
          +
          kyosu::quaternion_t
          as_cayley_dickson_n_t< 4, T > quaternion_t
          Type alias for quaternion numbers.
          Definition: quaternion.hpp:27
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          diff --git a/group__functions_gaf0517a14ea9458fd0698d804b465d366.html b/group__functions_gaf0517a14ea9458fd0698d804b465d366.html new file mode 100644 index 00000000..ea6d07e6 --- /dev/null +++ b/group__functions_gaf0517a14ea9458fd0698d804b465d366.html @@ -0,0 +1,200 @@ + + + + + + + + +kyosu: kyosu::zeta + + + + + + + + + + + + + + + + + + + + + + + + + + +
          + +
          + + + + + + + + +
          +
          kyosu v0.1.0 +
          +
          Complex Without Complexes
          +
          + +   + + + + +
          +
          +
          + + + + +
          +
          + +
          +
          +
          + +
          + +
          +
          + + +
          +
          +
          +
          +
          +
          Loading...
          +
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          +
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          +
          +
          +
          +
          + +
          + +

          ◆ zeta

          + +
          +
          + + + + + +
          + + + + +
          kyosu::zeta = {}
          +           		+inlineconstexpr
          +
          + +

          Computes the Riemann \(\zeta\) \( \displaystyle \sum_0^\infty \frac{1}{(n+1)^z}\).

          +

          Defined in Header

          +
          #include <kyosu/functions.hpp>
          +

          Callable Signatures

          +
          namespace kyosu
          +
          {
          +
          template<unsigned_scalar_value K, eve::ordered_value T> constexpr auto zeta(K, k, T z) noexcept; //1
          +
          template<unsigned_scalar_value K, kyosu::concepts::complex T> constexpr auto zeta(K, k, T z) noexcept; //2
          +
          }
          +
          kyosu::zeta
          constexpr tags::callable_zeta zeta
          Computes the Riemann .
          Definition: zeta.hpp:78
          +
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14
          +

          Parameters

          +
            +
          • k : scalar unsigned value, parameter of the sum.
            • +
          • z : Vcomplex or real value to process.
            • +
          +

          Return value

          +

          Returns the Dirichlet alternating zzeta function: sum \( \displaystyle \sum_0^\infty \frac{1}{(n+1)^z}\)

          +

          Example

          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> zeta(zc) = " << kyosu::zeta(zc) << std::endl
          +
          << "-> zeta(ref1) = " << kyosu::zeta(ref1) << std::endl;
          +
          return 0;
          +
          }
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          +
          +
          +
          +
          + + + + + + + + + + diff --git a/group__functions_gaf0f1fa52661fc9f3b89a02a76d001794.html b/group__functions_gaf0f1fa52661fc9f3b89a02a76d001794.html index aedf46c5..9f93a417 100644 --- a/group__functions_gaf0f1fa52661fc9f3b89a02a76d001794.html +++ b/group__functions_gaf0f1fa52661fc9f3b89a02a76d001794.html @@ -159,11 +159,33 @@

          -
        • a real input z is treated as if to_complex(z) was entered.
          • +
        • a real input z is treated as if complex(z) was entered.
        • Returns pi(as(z))*acos(z)

          • Example

          -
          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> acospi(zc) = " << kyosu::acospi(zc)<< std::endl
          +
          << "-> acospi(ref2) = " << kyosu::acospi(ref2) << std::endl;
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          diff --git a/group__functions_gaf57c0dd30eab1c6bf0a4c81c849307d5.html b/group__functions_gaf57c0dd30eab1c6bf0a4c81c849307d5.html new file mode 100644 index 00000000..7d3b242e --- /dev/null +++ b/group__functions_gaf57c0dd30eab1c6bf0a4c81c849307d5.html @@ -0,0 +1,203 @@ + + + + + + + + +kyosu: kyosu::tgamma + + + + + + + + + + + + + + + + + + + + + + + + + + +
          + +
          + + + + + + + + +
          +
          kyosu v0.1.0 +
          +
          Complex Without Complexes
          +
          + +   + + + + +
          +
          +
          + + + + +
          +
          + +
          +
          +
          + +
          + +
          +
          + + +
          +
          +
          +
          +
          +
          Loading...
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          +
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          +
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          +
          +
          + +
          + +

          ◆ tgamma

          + +
          +
          + + + + + +
          + + + + +
          kyosu::tgamma = {}
          +           		+inlineconstexpr
          +
          + +

          Computes the tgammaolute value of the parameter.

          +

          Defined in Header

          +
          #include <kyosu/functions.hpp>
          +

          Callable Signatures

          +
          namespace kyosu
          +
          {
          +
          template<kyosu::concepts::complex T> constexpr T tgamma(T z) noexcept;
          +
          template<eve::floatingordered_value T> constexpr T tgamma(T z) noexcept;
          +
          }
          +
          kyosu::tgamma
          constexpr tags::callable_tgamma tgamma
          Computes the tgammaolute value of the parameter.
          Definition: tgamma.hpp:75
          +
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14
          +

          Parameters

          +
            +
          • z : Value to process.
            • +
          +

          Return value

          +

          Returns \(\Gamma(z)\). If z is floating the result is as if complex(z) was used in the call.

          +

          Example

          +
          #include <kyosu/kyosu.hpp>
          +
          #include <eve/wide.hpp>
          +
          #include <iostream>
          +
          +
          int main()
          +
          {
          +
          +
          using wide_ft = eve::wide <float, eve::fixed<4>>;
          +
          wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
          +
          wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
          +
          wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
          +
          auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
          +
          +
          std::cout
          +
          << "---- simd" << std::endl
          +
          << "<- zc = " << zc << std::endl
          +
          << "-> tgamma(zc) = " << kyosu::tgamma(zc)<< std::endl
          +
          << "-> tgamma(ref2) = " << kyosu::tgamma(ref2) << std::endl;
          +
          +
          return 0;
          +
          }
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          +
          +
          +
          +
          +
          + + + + + + + + + + diff --git a/group__functions_gafb007a0b170f27331d8aa088e9f8f0b0.html b/group__functions_gafb007a0b170f27331d8aa088e9f8f0b0.html index 4c350cba..e35431c6 100644 --- a/group__functions_gafb007a0b170f27331d8aa088e9f8f0b0.html +++ b/group__functions_gafb007a0b170f27331d8aa088e9f8f0b0.html @@ -149,9 +149,10 @@

          namespace kyosu
          {
          template<kyosu::concepts::cayley_dickson T> constexpr T log2(T z) noexcept;
          -
          template<eve::ordered_value T> constexpr as_complex_t<T> log2(T z) noexcept;
          +
          template<eve::ordered_value T> constexpr complex_t<T> log2(T z) noexcept;
          }
          kyosu::log2
          constexpr tags::callable_log2 log2
          Computes the base 2 logarithm of the argument.
          Definition: log2.hpp:78
          +
          kyosu::complex_t
          as_cayley_dickson_n_t< 2, T > complex_t
          Type alias for complex numbers.
          Definition: complex.hpp:27
          kyosu
          Main KYOSU namespace.
          Definition: acos.hpp:14

          Parameters

            @@ -160,7 +161,50 @@

            log2(z). If z is an ordered value log2 returns a complex typed value.

            Example

            -
            +
            #include <kyosu/kyosu.hpp>
            +
            #include <eve/wide.hpp>
            +
            #include <iostream>
            +
            +
            int main()
            +
            {
            +
            using kyosu::log2;
            +
            using kyosu::complex_t;
            +
            using kyosu::quaternion_t;
            +
            using e_t = float;
            +
            using c_t = kyosu::complex_t<float>;
            +
            using q_t = kyosu::quaternion_t<float>;
            +
            using we_t = eve::wide<e_t, eve::fixed<2>>;
            +
            using wc_t = eve::wide<c_t, eve::fixed<2>>;
            +
            using wq_t = eve::wide<q_t, eve::fixed<2>>;
            +
            +
            std::cout << "Real: \n";
            +
            e_t e(2.9f);
            +
            we_t we = we_t(e);
            +
            std::cout << e << " -> " << log2(e) << "\n";
            +
            std::cout << we << " -> " << log2(we) << "\n";
            +
            std::cout << log2(c_t(e))<< "\n";
            +
            std::cout << log2(q_t(e))<< "\n";
            +
            std::cout << log2(wc_t(e))<< "\n";
            +
            std::cout << log2(wq_t(e))<< "\n";
            +
            +
            std::cout << "Complex: \n";
            +
            c_t c(3.5f,-2.9f);
            +
            wc_t wc = wc_t(c);
            +
            std::cout << c << " -> " << log2(c) << "\n";
            +
            std::cout << wc << " -> " << log2(wc) << "\n";
            +
            std::cout << log2(q_t(c))<< "\n";
            +
            std::cout << log2(wq_t(c))<< "\n";
            +
            +
            std::cout << "Quaternion: \n";
            +
            q_t q(3.5f,-2.9f, 2.1f, 3.2f);
            +
            wq_t wq = wq_t(q);
            +
            std::cout << q << " -> " << log2(q) << "\n";
            +
            std::cout << wq << " -> " << log2(wq) << "\n";
            +
            +
            return 0;
            +
            }
            +
            kyosu::quaternion_t
            as_cayley_dickson_n_t< 4, T > quaternion_t
            Type alias for quaternion numbers.
            Definition: quaternion.hpp:27
            +
            diff --git a/group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html b/group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html index d3d5e735..0f12d720 100644 --- a/group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html +++ b/group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html @@ -159,7 +159,7 @@

            -
          • a real input z is treated as if to_complex(z) was entered.
            • +
          • a real input z is treated as if complex(z) was entered.
          • Returns the complex arc hyperbolic sine of z, with branch cuts outside the interval \(i\times[-\pi/2, \pi/2]\) along the imaginary axis.
            • for every z: eve::asinh(eve::conj(z)) == eve::conj(std::asinh(z))
            • for every z: eve::asinh(-z) == -eve::asinh(z)
              • @@ -177,7 +177,29 @@

              Example

              -
              +
              #include <kyosu/kyosu.hpp>
              +
              #include <eve/wide.hpp>
              +
              #include <iostream>
              +
              +
              int main()
              +
              {
              +
              +
              using wide_ft = eve::wide <float, eve::fixed<4>>;
              +
              wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
              +
              wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
              +
              wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
              +
              auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
              +
              +
              std::cout
              +
              << "---- simd" << std::endl
              +
              << "<- zc = " << zc << std::endl
              +
              << "-> asinh(zc) = " << kyosu::asinh(zc)<< std::endl
              +
              << "-> asinh(ref2) = " << kyosu::asinh(ref2) << std::endl;
              +
              +
              return 0;
              +
              }
              +
              kyosu::complex_t
              as_cayley_dickson_n_t< 2, T > complex_t
              Type alias for complex numbers.
              Definition: complex.hpp:27
              +
              diff --git a/group__quaternion.html b/group__quaternion.html index 3745d642..c57697cf 100644 --- a/group__quaternion.html +++ b/group__quaternion.html @@ -142,6 +142,9 @@ constexpr tags::callable_from_euler kyosu::from_euler = {}  Callable object computing a quaternion from its euler representation.
                +constexpr tags::callable_from_multipolar kyosu::from_multipolar = {} + Callable object computing a quaternion from its multipolar representation.
              +  constexpr tags::callable_from_rotation_matrix kyosu::from_rotation_matrix = {}  Callable object computing a quaternion from its rotation_matrix representation.
                @@ -151,12 +154,36 @@ constexpr tags::callable_from_spherical kyosu::from_spherical = {}  Callable object computing a quaternion from its spherical representation.
                +constexpr tags::callable_rot_angle kyosu::rot_angle = {} + Callable object computing the normalized angle of rotation defined by a quaternion.
              +  +constexpr tags::callable_rot_axis kyosu::rot_axis = {} + Callable object computing the normalized axis of rotation defined by a quaternion.
              +  +constexpr tags::callable_rotate_vec kyosu::rotate_vec = {} + Callable object rotating an \(\mathbb{R}^3\) vector using a quaternion.
              +  +constexpr tags::callable_to_angle_axis kyosu::to_angle_axis = {} + Callable object computing the angle_axis coordinates from a quaternion.
              +  +constexpr tags::callable_to_cylindrical kyosu::to_cylindrical = {} + Callable object computing the cylindrical coordinates from a quaternion.
              +  constexpr tags::callable_to_euler kyosu::to_euler = {}  Callable object computing euler angles from a quaternion.
                +constexpr tags::callable_to_multipolar kyosu::to_multipolar = {} + Callable object computing the multipolar coordinates from a quaternion.
              +  constexpr tags::callable_to_rotation_matrix kyosu::to_rotation_matrix = {}  Callable object computing a quaternion from its to_rotation_matrix representation.
                +constexpr tags::callable_to_semipolar kyosu::to_semipolar = {} + Callable object computing the semipolar coordinates from a quaternion.
              +  +constexpr tags::callable_to_spherical kyosu::to_spherical = {} + Callable object computing the spherical coordinates from a quaternion.
              +  diff --git a/group__quaternion_ga31804ee3fdb4a806efea330cf1e20898.html b/group__quaternion_ga31804ee3fdb4a806efea330cf1e20898.html new file mode 100644 index 00000000..43bd22dc --- /dev/null +++ b/group__quaternion_ga31804ee3fdb4a806efea330cf1e20898.html @@ -0,0 +1,180 @@ + + + + + + + + +kyosu: kyosu::to_angle_axis + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
              +
              Loading...
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              Searching...
              +
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              +
              +
              +
              +
              + +
              + +

              ◆ to_angle_axis

              + +
              +
              + + + + + +
              + + + + +
              kyosu::to_angle_axis = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object computing the angle_axis coordinates from a quaternion.

              +

              This function is the reciprocal of from_angle_axis

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto to_angle_axis( auto q) const noexcept;
              +
              }
              +
              kyosu::to_angle_axis
              constexpr tags::callable_to_angle_axis to_angle_axis
              Callable object computing the angle_axis coordinates from a quaternion.
              Definition: to_angle_axis.hpp:85
              +

              Parameters

              +

              q : quaternion

              +

              Return value

              +

              a tuple containing in this order rho1, 'theta1', rho2 'theta2': the moduli and the angles in radian of the angle_axis \(\mathbb{R}^4\) coordinates

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__quaternion_ga3519a64d1cbe848507cc57a05b5ed1b3.html b/group__quaternion_ga3519a64d1cbe848507cc57a05b5ed1b3.html new file mode 100644 index 00000000..b5bcd053 --- /dev/null +++ b/group__quaternion_ga3519a64d1cbe848507cc57a05b5ed1b3.html @@ -0,0 +1,180 @@ + + + + + + + + +kyosu: kyosu::to_semipolar + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
              +
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              +
              + +
              + +

              ◆ to_semipolar

              + +
              +
              + + + + + +
              + + + + +
              kyosu::to_semipolar = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object computing the semipolar coordinates from a quaternion.

              +

              This function is the reciprocal of from_semipolar

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto to_semipolar( auto q) const noexcept;
              +
              }
              +
              kyosu::to_semipolar
              constexpr tags::callable_to_semipolar to_semipolar
              Callable object computing the semipolar coordinates from a quaternion.
              Definition: to_semipolar.hpp:86
              +

              Parameters

              +

              q : quaternion

              +

              Return value

              +

              a tuple containing in this order rho1, 'theta1', h1 'h2': the components of the semipolar parametrisation of \(\mathbb{R}^4\) coordinates

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__quaternion_ga47b1fa117c5671882a31b65c997660d7.html b/group__quaternion_ga47b1fa117c5671882a31b65c997660d7.html new file mode 100644 index 00000000..aa30721d --- /dev/null +++ b/group__quaternion_ga47b1fa117c5671882a31b65c997660d7.html @@ -0,0 +1,180 @@ + + + + + + + + +kyosu: kyosu::rot_angle + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
              +
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              +
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              +
              +
              + +
              + +

              ◆ rot_angle

              + +
              +
              + + + + + +
              + + + + +
              kyosu::rot_angle = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object computing the normalized angle of rotation defined by a quaternion.

              +

              This function is the reciprocal of from_polar

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto rot_angle( auto q) const noexcept;
              +
              }
              +
              kyosu::rot_angle
              constexpr tags::callable_rot_angle rot_angle
              Callable object computing the normalized angle of rotation defined by a quaternion.
              Definition: rot_angle.hpp:83
              +

              Parameters

              +

              q : quaternion

              +

              Return value

              +

              the rotation angle in radian

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__quaternion_ga943f811be2981809d36a4f31f52b0025.html b/group__quaternion_ga943f811be2981809d36a4f31f52b0025.html index ac5278c5..2cc151e7 100644 --- a/group__quaternion_ga943f811be2981809d36a4f31f52b0025.html +++ b/group__quaternion_ga943f811be2981809d36a4f31f52b0025.html @@ -161,7 +161,7 @@

              +

              Example

              #include <eve/module/quaternion.hpp>
              #include <eve/wide.hpp>
              diff --git a/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html b/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html new file mode 100644 index 00000000..e0cc9854 --- /dev/null +++ b/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html @@ -0,0 +1,180 @@ + + + + + + + + +kyosu: kyosu::rot_axis + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
              +
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              +
              +
              + +
              + +

              ◆ rot_axis

              + +
              +
              + + + + + +
              + + + + +
              kyosu::rot_axis = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object computing the normalized axis of rotation defined by a quaternion.

              +

              This function is the reciprocal of from_polar

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto rot_axis( auto q) const noexcept;
              +
              }
              +
              kyosu::rot_axis
              constexpr tags::callable_rot_axis rot_axis
              Callable object computing the normalized axis of rotation defined by a quaternion.
              Definition: rot_axis.hpp:84
              +

              Parameters

              +

              q : quaternion

              +

              Return value

              +

              a span containing the three coordinates of the axis if the quaternion is zero {1, 0, 0} is returned

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + +
              + + + + + + diff --git a/group__quaternion_gaa82e66812fcb0f8af20b07a448752561.html b/group__quaternion_gaa82e66812fcb0f8af20b07a448752561.html new file mode 100644 index 00000000..c9ce5223 --- /dev/null +++ b/group__quaternion_gaa82e66812fcb0f8af20b07a448752561.html @@ -0,0 +1,180 @@ + + + + + + + + +kyosu: kyosu::to_cylindrical + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
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              +
              + +
              + +

              ◆ to_cylindrical

              + +
              +
              + + + + + +
              + + + + +
              kyosu::to_cylindrical = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object computing the cylindrical coordinates from a quaternion.

              +

              This function is the reciprocal of from_cylindrical

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto to_cylindrical( auto q) const noexcept;
              +
              }
              +
              kyosu::to_cylindrical
              constexpr tags::callable_to_cylindrical to_cylindrical
              Callable object computing the cylindrical coordinates from a quaternion.
              Definition: to_cylindrical.hpp:86
              +

              Parameters

              +

              q : quaternion

              +

              Return value

              +

              a tuple containing in this order rho1, 'theta1', h1 'h2': the components of the cylindrical parametrisation of \(\mathbb{R}^4\) coordinates

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html b/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html new file mode 100644 index 00000000..edfea2c4 --- /dev/null +++ b/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html @@ -0,0 +1,180 @@ + + + + + + + + +kyosu: kyosu::to_spherical + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
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              +
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              +
              +
              + +
              + +

              ◆ to_spherical

              + +
              +
              + + + + + +
              + + + + +
              kyosu::to_spherical = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object computing the spherical coordinates from a quaternion.

              +

              This function is the reciprocal of from_spherical

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto to_spherical( auto q) const noexcept;
              +
              }
              +
              kyosu::to_spherical
              constexpr tags::callable_to_spherical to_spherical
              Callable object computing the spherical coordinates from a quaternion.
              Definition: to_spherical.hpp:86
              +

              Parameters

              +

              q : quaternion

              +

              Return value

              +

              a tuple containing in this order rho, 'theta', ph1 'ph2': the components of the spherical parametrisation of \(\mathbb{R}^4\) coordinates

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__quaternion_gadcb9029f90743da06cc952f8fe8120f0.html b/group__quaternion_gadcb9029f90743da06cc952f8fe8120f0.html new file mode 100644 index 00000000..93ca7a3a --- /dev/null +++ b/group__quaternion_gadcb9029f90743da06cc952f8fe8120f0.html @@ -0,0 +1,197 @@ + + + + + + + + +kyosu: kyosu::from_multipolar + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
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              +
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              +
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              +
              +
              + +
              + +

              ◆ from_multipolar

              + +
              +
              + + + + + +
              + + + + +
              constexpr tags::callable_from_multipolar kyosu::from_multipolar = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object computing a quaternion from its multipolar representation.

              +

              This function build quaternions in a way similar to the way polar builds complex numbers from a multipolar representation of an \(\mathbb{R}^4\) element.

              +

              from_multipolar the two \(\mathbb{C}\) components of the quaternion are given in polar coordinates

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto from_multipolar( auto rho1, auto theta1 auto rho2, auto theta2) const noexcept;
              +
              }
              +
              kyosu::from_multipolar
              constexpr tags::callable_from_multipolar from_multipolar
              Callable object computing a quaternion from its multipolar representation.
              Definition: from_multipolar.hpp:97
              +

              Parameters

              +

              rho1, rho2: the moduli 'theta1', 'theta2': the angles in radian

              +

              Return value

              +

              the quaternion value

              +
              +

              +Example

              +

              This function build quaternions in a way similar to the way polar builds complex numbers from a multipolar representation of an \(\mathbb{R}^4\) element.

              +

              from_multipolar the two \(\mathbb{C}\) components of the quaternion are given in polar coordinates

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto from_multipolar( auto rho1, auto theta1 auto rho2, auto theta2) const noexcept;
              +
              }
              +

              Parameters

              +

              rho1, rho2: the moduli 'theta1', 'theta2': the angles in radian

              +

              Return value

              +

              the quaternion value

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__quaternion_gae984161c55fda44efe7d7f9b274334c6.html b/group__quaternion_gae984161c55fda44efe7d7f9b274334c6.html new file mode 100644 index 00000000..f96a0c72 --- /dev/null +++ b/group__quaternion_gae984161c55fda44efe7d7f9b274334c6.html @@ -0,0 +1,180 @@ + + + + + + + + +kyosu: kyosu::to_multipolar + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
              +
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              +
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              +
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              +
              +
              + +
              + +

              ◆ to_multipolar

              + +
              +
              + + + + + +
              + + + + +
              kyosu::to_multipolar = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object computing the multipolar coordinates from a quaternion.

              +

              This function is the reciprocal of from_multipolar

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto to_multipolar( auto q) const noexcept;
              +
              }
              +
              kyosu::to_multipolar
              constexpr tags::callable_to_multipolar to_multipolar
              Callable object computing the multipolar coordinates from a quaternion.
              Definition: to_multipolar.hpp:86
              +

              Parameters

              +

              q : quaternion

              +

              Return value

              +

              a tuple containing in this order rho1, 'theta1', rho2 'theta2': the moduli and the angles in radian of the multipolar \(\mathbb{R}^4\) coordinates

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html b/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html new file mode 100644 index 00000000..237e32e2 --- /dev/null +++ b/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html @@ -0,0 +1,179 @@ + + + + + + + + +kyosu: kyosu::rotate_vec + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
              +
              Loading...
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              +
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              +
              +
              +
              +
              + +
              + +

              ◆ rotate_vec

              + +
              +
              + + + + + +
              + + + + +
              kyosu::rotate_vec = {}
              +               		+inlineconstexpr
              +
              + +

              Callable object rotating an \(\mathbb{R}^3\) vector using a quaternion.

              +

              Defined in header

              +
              #include eve/module/quaternion.hpp>`
              +

              Callable Signatures

              +
              namespace eve
              +
              {
              +
              auto rotate_vec( auto q) const noexcept;
              +
              }
              +
              kyosu::rotate_vec
              constexpr tags::callable_rotate_vec rotate_vec
              Callable object rotating an vector using a quaternion.
              Definition: rotate_vec.hpp:105
              +

              Parameters

              +

              q: quaternion defining the rotation. x: span of 3 elements to rotate

              +

              Return value

              +

              the span rotated by q

              +
              +

              +Example

              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__types.html b/group__types.html index e3b00b30..efd73058 100644 --- a/group__types.html +++ b/group__types.html @@ -133,14 +133,18 @@ - - - - - - - - + + + + + + + + + + + +

              Typedefs

              template<typename T >
              using kyosu::complex = cayley_dickson< T, 2 >
               Type alias for complex numbers.
               
              template<typename T >
              using kyosu::quaternion = cayley_dickson< T, 4 >
               Type alias for quaternion numbers.
               
              template<typename T >
              using kyosu::complex_t = as_cayley_dickson_n_t< 2, T >
               Type alias for complex numbers.
               
              template<typename T >
              using kyosu::octonion_t = as_cayley_dickson_n_t< 8, T >
               Type alias for quaternion numbers.
               
              template<typename T >
              using kyosu::quaternion_t = as_cayley_dickson_n_t< 4, T >
               Type alias for quaternion numbers.
               
              diff --git a/group__types_ga0fb102adb92b2be024f398e2ac5dd5cd.html b/group__types_ga0fb102adb92b2be024f398e2ac5dd5cd.html new file mode 100644 index 00000000..de1481bf --- /dev/null +++ b/group__types_ga0fb102adb92b2be024f398e2ac5dd5cd.html @@ -0,0 +1,159 @@ + + + + + + + + +kyosu: kyosu::quaternion_t + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
              +
              Loading...
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              +
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              +
              +
              +
              +
              + +
              + +

              ◆ quaternion_t

              + +
              +
              +
              +template<typename T >
              + + + + +
              kyosu::quaternion_t
              +
              + +

              Type alias for quaternion numbers.

              +

              Quaternion numbers are implemented as Caley-dickson numbers of dimension 4.

              + +
              +
              +
              +
              + + + + + + + + + + diff --git a/group__types_gad699121c78ba21aef370db14abdd67ec.html b/group__types_ga642e4c9da3267bde80011f41e698ba76.html similarity index 93% rename from group__types_gad699121c78ba21aef370db14abdd67ec.html rename to group__types_ga642e4c9da3267bde80011f41e698ba76.html index 20429f91..e67b5414 100644 --- a/group__types_gad699121c78ba21aef370db14abdd67ec.html +++ b/group__types_ga642e4c9da3267bde80011f41e698ba76.html @@ -6,7 +6,7 @@ -kyosu: kyosu::complex +kyosu: kyosu::complex_t @@ -96,7 +96,7 @@
              @@ -122,8 +122,8 @@
              - -

              ◆ complex

              + +

              ◆ complex_t

              @@ -131,7 +131,7 @@

              - kyosu::complex + kyosu::complex_t

              diff --git a/group__types_gaaa8536022a04b81b80cfe47246a4897f.html b/group__types_gaa3272e84862798bbb6561c13620c165b.html similarity index 93% rename from group__types_gaaa8536022a04b81b80cfe47246a4897f.html rename to group__types_gaa3272e84862798bbb6561c13620c165b.html index 403bc59f..f516db41 100644 --- a/group__types_gaaa8536022a04b81b80cfe47246a4897f.html +++ b/group__types_gaa3272e84862798bbb6561c13620c165b.html @@ -6,7 +6,7 @@ -kyosu: kyosu::quaternion +kyosu: kyosu::octonion_t @@ -96,7 +96,7 @@
              @@ -122,8 +122,8 @@
              - -

              ◆ quaternion

              + +

              ◆ octonion_t

              @@ -131,7 +131,7 @@

              - kyosu::quaternion + kyosu::octonion_t

              diff --git a/namespacekyosu.html b/namespacekyosu.html index 4dc7d26f..a83f84db 100644 --- a/namespacekyosu.html +++ b/namespacekyosu.html @@ -148,14 +148,18 @@ using as_real_t = typename as_real< T >::type  Compute the real type associated to a Cayley-Dickson-like type.
                -template<typename T > -using complex = cayley_dickson< T, 2 > - Type alias for complex numbers.
              -  -template<typename T > -using quaternion = cayley_dickson< T, 4 > - Type alias for quaternion numbers.
              -  +template<typename T > +using complex_t = as_cayley_dickson_n_t< 2, T > + Type alias for complex numbers.
              +  +template<typename T > +using octonion_t = as_cayley_dickson_n_t< 8, T > + Type alias for quaternion numbers.
              +  +template<typename T > +using quaternion_t = as_cayley_dickson_n_t< 4, T > + Type alias for quaternion numbers.
              +  @@ -324,9 +328,15 @@ + + + + + + @@ -363,6 +373,12 @@ + + + + + + @@ -373,6 +389,19 @@ + + + + + + + + + + + + @@ -397,6 +426,9 @@ + + + @@ -415,6 +447,12 @@ + + + + + + @@ -490,6 +528,15 @@ + + + + + + + + + @@ -508,10 +555,19 @@ + + + + + + + + + @@ -539,9 +595,15 @@ + + + + + + @@ -554,6 +616,18 @@ + + + + + + + + + + + + @@ -608,21 +682,39 @@ - - - + + + + + + + + + - - - + + + + + + + + + + + + + + +

              Functions

              constexpr tags::callable_average average = {}
               Computes the average of the two parameters.
               
              constexpr tags::callable_beta beta = {}
               Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\).
               
              constexpr tags::callable_ceil ceil = {}
               Computes the ceil value.
               
              constexpr tags::callable_complex complex = {}
               Constructs a kyosu::complex.
               
              constexpr tags::callable_conj conj = {}
               Computes the conjugate value.
               
              constexpr tags::callable_dec dec = {}
               decrements the argument by 1.
               
              constexpr tags::callable_deta deta = {}
               Computes the Dirichlet sums \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(kn+1)^z}\).
               
              constexpr tags::callable_digamma digamma = {}
               Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\).
               
              template<typename T >
              constexpr unsigned int dimension_v = *implementation-defined*
               Obtains the number of dimensions of the algebra containing a given type.
              constexpr tags::callable_dot dot = {}
               Computes elementwise the dot product of the coordinates of the corresponding element.
               
              constexpr tags::callable_erf erf = {}
               Computes the error function: \( \displaystyle + \mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\) or its analytic continuation in the complex plane.
               
              constexpr tags::callable_erfcx erfcx = {}
               Computes the normalized complementary error function \( \displaystyle \mbox{erfcx}(x) = e^{x^2} \mbox{erfc}(x)\).
               
              constexpr tags::callable_erfi erfi = {}
               Callable object computing The imaginary error function \( \displaystyle \mathrm{erfi}(z) = -i\mathrm{erf}(iz)\).
               
              constexpr tags::callable_eta eta = {}
               Computes the Dirichlet sum \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\). Sometimes this function is for obvious reasons called the alternative \(\zeta\) function .
               
              constexpr tags::callable_exp exp = {}
               Computes the exponential of the argument.
               
              constexpr tags::callable_expx2 expx2 = {}
               Computes the exponential of the squared argument.
               
              constexpr tags::callable_faddeeva faddeeva = {}
               Callable object computing \(e^{-z^2}\mathrm{erfc}(-iz)\) the scaled complex error func.
               
              constexpr tags::callable_floor floor = {}
               Computes the floor value.
               
              constexpr tags::callable_from_euler from_euler = {}
               Callable object computing a quaternion from its euler representation.
               
              constexpr tags::callable_from_multipolar from_multipolar = {}
               Callable object computing a quaternion from its multipolar representation.
               
              constexpr tags::callable_from_polar from_polar = {}
               Callable object computing a complex from its polar coordinates.
               
              constexpr tags::callable_from_rotation_matrix from_rotation_matrix = {}
               Callable object computing a quaternion from its rotation_matrix representation.
               
              constexpr tags::callable_kpart kpart = {}
               Extracts the \(k\) part of a value.
               
              constexpr tags::callable_lambda lambda = {}
               Callable object computing The Dirichlet \( \displaystyle \lambda(z) = \sum_0^\infty \frac{1}{(2n+1)^z}\).
               
              constexpr tags::callable_lbeta lbeta = {}
               Computes the natural logarithm of the lbeta function.
               
              constexpr tags::callable_ldiv ldiv = {}
               Computes the left division of the two parameters.
               
              constexpr tags::callable_lerp lerp = {}
               Computes the linear interpolation.
               
              constexpr tags::callable_log_abs log_abs = {}
               Computes the natural logarithm of the absolute value of the argument.
               
              constexpr tags::callable_log_abs_gamma log_abs_gamma = {}
               Computes the log of the modulus of the \(\Gamma\) function of the parameter.
               
              constexpr tags::callable_log_gamma log_gamma = {}
               Computes the log of the \(\Gamma\) function of the parameter.
               
              constexpr tags::callable_lpnorm lpnorm = {}
               Callable object computing the lpnorm operation \( \left(\sum_{i = 0}^n |x_i|^p\right)^{\frac1p} \).
               
              constexpr tags::callable_lrising_factorial lrising_factorial = {}
               Computes the lrising_factorial function: \(\log\frac{\Gamma(x+y)}{\Gamma(x)}\).
               
              constexpr tags::callable_manhattan manhattan = {}
               Callable object computing the manhattan operation.
               
              constexpr tags::callable_powm1 powm1 = {}
               Computes the computing the powm1 operation \(x^y-1\).
               
              constexpr tags::callable_proj proj = {}
               Callable object computing proj(x), the projection of the cayley_dickson number z onto the (hyper) Riemann sphere.
               
              constexpr tags::callable_purepart purepart = {}
               Extracts the pure part of a value.
               
              constexpr tags::callable_quaternion quaternion = {}
               Constructs a kyosu::quaternion.
               
              constexpr tags::callable_radinpi radinpi = {}
               Computes the parameter divided by \(\pi\).
               
              constexpr tags::callable_reldist reldist = {}
               Computes the relative distance between the two parameters.
               
              constexpr tags::callable_rising_factorial rising_factorial = {}
               Computes the rising_factorial function: \(\frac{\Gamma(x+y)}{\Gamma(x)}\).
               
              constexpr tags::callable_rot_angle rot_angle = {}
               Callable object computing the normalized angle of rotation defined by a quaternion.
               
              constexpr tags::callable_rot_axis rot_axis = {}
               Callable object computing the normalized axis of rotation defined by a quaternion.
               
              constexpr tags::callable_rotate_vec rotate_vec = {}
               Callable object rotating an \(\mathbb{R}^3\) vector using a quaternion.
               
              constexpr tags::callable_sec sec = {}
               Computes the secant of the argument.
               
              constexpr tags::callable_tanpi tanpi = {}
               Computes the tangent of the argument in \(\pi\) mutiples.
               
              constexpr tags::callable_to_complex to_complex = {}
               Constructs a kyosu::complex.
               
              constexpr tags::callable_tgamma tgamma = {}
               Computes the tgammaolute value of the parameter.
               
              constexpr tags::callable_to_angle_axis to_angle_axis = {}
               Callable object computing the angle_axis coordinates from a quaternion.
               
              constexpr tags::callable_to_cylindrical to_cylindrical = {}
               Callable object computing the cylindrical coordinates from a quaternion.
               
              constexpr tags::callable_to_euler to_euler = {}
               Callable object computing euler angles from a quaternion.
               
              constexpr tags::callable_to_quaternion to_quaternion = {}
               Constructs a kyosu::quaternion.
               
              constexpr tags::callable_to_multipolar to_multipolar = {}
               Callable object computing the multipolar coordinates from a quaternion.
               
              constexpr tags::callable_to_polar to_polar = {}
               Callable object computing the polar coordinates from a complex.
               
              constexpr tags::callable_to_rotation_matrix to_rotation_matrix = {}
               Callable object computing a quaternion from its to_rotation_matrix representation.
               
              constexpr tags::callable_to_semipolar to_semipolar = {}
               Callable object computing the semipolar coordinates from a quaternion.
               
              constexpr tags::callable_to_spherical to_spherical = {}
               Callable object computing the spherical coordinates from a quaternion.
               
              constexpr tags::callable_trunc trunc = {}
               Computes the trunc value.
               
              constexpr tags::callable_zeta zeta = {}
               Computes the Riemann \(\zeta\) \( \displaystyle \sum_0^\infty \frac{1}{(n+1)^z}\).
               
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