From bee67c9283a1a1924c08725a3e8c49686119cbd3 Mon Sep 17 00:00:00 2001 From: jfalcou Date: Sat, 30 Sep 2023 14:57:22 +0000 Subject: [PATCH] deploy: a53fe914c58b8088af1e80d77fa5c128047916da --- group__complex.html | 2 +- ...ex_gac49e8cf76fe002ef3d3e480fb80217ff.html | 8 +- ...ex_gad70670d8278d34dc0f0faf883a48eab8.html | 13 +- group__functions.html | 94 ++++--- ...ns_ga013ae7a04bb6a995c81537ab9c4396b4.html | 7 +- ...ns_ga047b3d79d00d4907df04ec98f2a0fada.html | 16 +- ...ns_ga054a9a0efe44dd5dcc9bb675b0f9e89d.html | 2 +- ...ns_ga057662e8933c9837bb4bbb5ffb2822f0.html | 6 +- ...ns_ga0704e6ec9b43b3f6a8864e38b566f795.html | 6 +- ...ns_ga0ae8f99de8716a46dd7de3ff990602bb.html | 4 +- ...ns_ga0d165215c9a5f3f78feab4b70874f436.html | 8 +- ...ns_ga0e8c3f00c6f3777a5a14320c7b1a31da.html | 2 +- ...ns_ga1410062f3325c9a4b687d12f5ae53f55.html | 4 +- ...ns_ga1658a3b3d9e67c35d2a85233572770ed.html | 2 +- ...ns_ga1b78fa57857ad714ce5f0e6e3ace5db9.html | 4 +- ...ns_ga1e253b4aba99259dbb98d891247c2a38.html | 27 +- 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group__functions_ga8e242553caca873ace58560327d8bd4e.html create mode 100644 group__functions_ga8f4895e6ad347a36555c231f430684eb.html create mode 100644 group__functions_gaa1c85fe49012f1d7bdabbfe0fe1abaf4.html create mode 100644 group__functions_gab64d320c3bacdf74f8a860ca960df8c2.html create mode 100644 group__functions_gac24fb66ef0ba0fd8adb3c596264f24e8.html create mode 100644 group__functions_gac828b36348f592f5f2d891bd546ee733.html rename group__quaternion_gaeb24f578562330d825ff8f68da4b9252.html => group__functions_gaeb24f578562330d825ff8f68da4b9252.html (89%) create mode 100644 group__quaternion_gadc8b483ae153b0e6d1eb4d7ece78660d.html diff --git a/group__complex.html b/group__complex.html index c6e08e91..968bf9bc 100644 --- a/group__complex.html +++ b/group__complex.html @@ -131,7 +131,7 @@

Variables

constexpr tags::callable_from_polar kyosu::from_polar = {} - Callable object computing a complex from its polar coordinates.
+ Callable object computing a complex or a general Cayley-Dickson from a polar representation.
  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 index b36644f5..9ecde6ed 100644 --- a/group__complex_gac49e8cf76fe002ef3d3e480fb80217ff.html +++ b/group__complex_gac49e8cf76fe002ef3d3e480fb80217ff.html @@ -149,12 +149,12 @@

Callable Signatures

namespace eve
{
-
template<eve::ordered_value T> constexpr auto arg(T z) noexcept; //1
+
template<eve::floating_ordered_value T> constexpr auto arg(T z) noexcept; //1
template<kyosu::concepts::complex T> constexpr auto atan(T z) noexcept; //2
template<kyosu::concepts::cayley_dickson T> constexpr auto argy(T z) noexcept; //3
}
-
kyosu::atan
constexpr tags::callable_atan atan
Computes the inverse hyperbolic tangent of the argument.
Definition: atan.hpp:86
-
kyosu::arg
constexpr tags::callable_arg arg
complex number argument.
Definition: arg.hpp:79
+
kyosu::atan
constexpr tags::callable_atan atan
Computes the arctangent of the argument.
Definition: atan.hpp:86
+
kyosu::arg
constexpr tags::callable_arg arg
argument.
Definition: arg.hpp:78

Parameters

q : cayley dickson value

Return value

@@ -164,7 +164,7 @@

+

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
diff --git a/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html b/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html index d4c2243c..59fd67a0 100644 --- a/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html +++ b/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html @@ -142,26 +142,29 @@

-

Callable object computing a complex from its polar coordinates.

+

Callable object computing a complex or a general Cayley-Dickson from a polar representation.

This function is the reciprocal of from_polar

Defined in header

#include eve/module/quaternion.hpp>`

Callable Signatures

namespace eve
{
-
template<eve::ordered_value T0, eve::ordered_value T1>,
+
template<eve::floating_ordered_value T0, eve::floating_ordered_value T1>,
auto from_polar( T0 rho, T1 theta) const noexcept; // 1
-
template<eve::ordered_value T0, eve::ordered_value T1, kyosu::concepts::cayley_dickson C>,
+
template<eve::floating_ordered_value T0, eve::floating_ordered_value T1, kyosu::concepts::cayley_dickson C>,
auto from_polar( T0 rho, T1 theta, C iz) const noexcept; // 2
}
-
kyosu::from_polar
constexpr tags::callable_from_polar from_polar
Callable object computing a complex from its polar coordinates.
Definition: from_polar.hpp:102
+
kyosu::from_polar
constexpr tags::callable_from_polar from_polar
Callable object computing a complex or a general Cayley-Dickson from a polar representation.
Definition: from_polar.hpp:106

Parameters

-

rho : modulus. theta : argument. ‘iz’ : unitary cayley dickson value.

+

rho : modulus.

+

theta : argument.

+

‘iz’ : unitary cayley dickson value.

Return value

  1. the complex number rho*exp(i*theta).
  2. the cayley_dickson value rho*exp(iz*theta).
+
Note
the entries constitue a proper polar representation if rho is non-negative and if iz present it must be pure unitary with non-negative jpart. However the formula is taken anyway.

Example

#include <kyosu/kyosu.hpp>
diff --git a/group__functions.html b/group__functions.html index 5abadd08..5b7f9ff0 100644 --- a/group__functions.html +++ b/group__functions.html @@ -143,7 +143,7 @@  Computes the inverse hyperbolic cosine of the argument.
  constexpr tags::callable_acospi kyosu::acospi = {} - Computes the arc cosine of the argument times \(\pi\).
+ Computes the arc cosine of the argument in \(\pi\) multiples.
  constexpr tags::callable_acot kyosu::acot = {}  Computes the arc cotangent of the argument.
@@ -152,7 +152,7 @@  Computes the inverse hyperbolic cotangent of the argument.
  constexpr tags::callable_acotpi kyosu::acotpi = {} - Computes the arc cotangent of the argument times \(\pi\).
+ Computes the arc cotangent of the argument in \(\pi\) multiples.
  constexpr tags::callable_acsc kyosu::acsc = {}  Computes the arccosecant of the argument.
@@ -161,47 +161,53 @@  Computes the inverse hyperbolic cosecant of the argument.
  constexpr tags::callable_acscpi kyosu::acscpi = {} - Computes the arc cosecant of the argument times \(\pi\).
+ Computes the arc cosecant of the argume!nt in \(\pi\) multiples.
  constexpr tags::callable_arg kyosu::arg = {} - complex number argument.
+ argument.
  constexpr tags::callable_asec kyosu::asec = {}  Computes the arcsecant of the argument.
  constexpr tags::callable_asech kyosu::asech = {} - Computes the hyperbolic arcsecant of the argument.
+ Computes the inverse hyperbolic secant of the argument.
  constexpr tags::callable_asecpi kyosu::asecpi = {} - Computes the arc secant of the argument times \(\pi\).
+ Computes the arc secant of the argument in \(\pi\) multiples.
  constexpr tags::callable_asin kyosu::asin = {}  Computes the arcsine of the argument.
  constexpr tags::callable_asinh kyosu::asinh = {} - Computes the asinhine of the argument.
+ Computes the inverse hyperbolic sine of the argument.
  constexpr tags::callable_asinpi kyosu::asinpi = {} - Computes the arc sine of the argument times \(\pi\).
+ Computes the arc sine of the argument in \(\pi\) multiples.
  +constexpr tags::callable_associator kyosu::associator = {} + Computes the associator of the three parameters.
+  constexpr tags::callable_atan kyosu::atan = {} - Computes the inverse hyperbolic tangent of the argument.
+ Computes the arctangent of the argument.
  constexpr tags::callable_atanh kyosu::atanh = {}  Computes the inverse hyperbolic tangent of the argument.
  constexpr tags::callable_atanpi kyosu::atanpi = {} - Computes the arc tangent of the argument times \(\pi\).
+ Computes the arc tangent of the argument in \(\pi\) multiples.
  constexpr tags::callable_average kyosu::average = {}  Computes the average of the two parameters.
  constexpr tags::callable_beta kyosu::beta = {} - Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\).
+ Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) for real or complex entries.
  constexpr tags::callable_ceil kyosu::ceil = {}  Computes the ceil value.
  +constexpr tags::callable_commutator kyosu::commutator = {} + Computes the commutator of the two parameters.
+  constexpr tags::callable_complex kyosu::complex = {}  Constructs a kyosu::complex.
  @@ -218,7 +224,7 @@  Computes the hyperbolic cosine of the argument.
  constexpr tags::callable_cospi kyosu::cospi = {} - Computes the cosine of the argument in \(\pi\) mutiples.
+ Computes the cosine from the argument in \(\pi\) multiples.
  constexpr tags::callable_cot kyosu::cot = {}  Computes the cotangent of the argument.
@@ -227,25 +233,25 @@  Computes the hyperbolic cotangent of the argument.
  constexpr tags::callable_cotpi kyosu::cotpi = {} - Computes the cotangent of the argument in \(\pi\) mutiples.
+ Computes the cotangent from the argument in \(\pi\) multiples.
  constexpr tags::callable_csc kyosu::csc = {}  Computes the cosecant of the argument.
  constexpr tags::callable_csch kyosu::csch = {} - Computes the hyperbolic cscant of the argument.
+ Computes the hyperbolic cosecant of the argument.
  constexpr tags::callable_cscpi kyosu::cscpi = {} - Computes the cosecant of the argument in \(\pi\) mutiples.
+ Computes the cosecant from the argument in \(\pi\) multiples.
  constexpr tags::callable_dec kyosu::dec = {}  decrements the argument by 1.
  constexpr tags::callable_deta kyosu::deta = {} - Computes the Dirichlet sums \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(kn+1)^z}\).
+ Computes the Dirichlet sums \( \displaystyle \sum_{n = 0}^\infty \frac{(-1)^n}{(kn+1)^z}\).
  constexpr tags::callable_digamma kyosu::digamma = {} - Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\).
+ Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\) function.
  constexpr tags::callable_dist kyosu::dist = {}  Computes the distance between the two parameters.
@@ -276,13 +282,13 @@  Computes the base 2 exponential of the argument.
  constexpr tags::callable_exp_i kyosu::exp_i = {} - Computes the exponential of the argument times i.
+ Computes the exponential of i times the argument.
  constexpr tags::callable_exp_ipi kyosu::exp_ipi = {} - Computes the exponential of the argument times i.
+ Computes the exponential of \(i\pi\) times the argument.
  constexpr tags::callable_expm1 kyosu::expm1 = {} - Computes the expm1onential of the argument minus 1.
+ Computes the exponential of the argument minus 1.
  constexpr tags::callable_expmx2 kyosu::expmx2 = {}  Computes the exponential of the opposite of the squared argument.
@@ -299,18 +305,25 @@ constexpr tags::callable_frac kyosu::frac = {}  Computes the frac value.
  +constexpr tags::callable_from_angle_axis kyosu::from_angle_axis = {} + Callable object computing a quaternion from its angle_axis representation.
+  constexpr tags::callable_hypot kyosu::hypot = {}  Callable object computing the hypot operation.
  constexpr tags::callable_if_else kyosu::if_else = {}  Select a value between two arguments based on a logical mask.
  -constexpr tags::callable_ipart kyosu::imag = {} - Alias for ipart.
-  + +constexpr tags::callable_ipart kyosu::imag = {} + Alias for ipart.
+  constexpr tags::callable_inc kyosu::inc = {}  Increments the argument.
  +constexpr tags::callable_ipart kyosu::ipart = {} + Extracts the imaginary part of a value.
+  constexpr tags::callable_is_denormal kyosu::is_denormal = {}  test if the parameter is denormal.
  @@ -318,13 +331,13 @@  retuen true if and only if the two parameters are equal.
  constexpr tags::callable_is_eqz kyosu::is_eqz = {} - test the parameter for zero equality.
+ test the parameter for equality to zero.
  constexpr tags::callable_is_finite kyosu::is_finite = {}  test if the parameter is finite.
  constexpr tags::callable_is_pure kyosu::is_imag = {} - test if the parameter real part is zero.
+ alias of is_pure
  constexpr tags::callable_is_infinite kyosu::is_infinite = {}  test if the parameter is infinite.
@@ -339,7 +352,7 @@  test if the parameter is not denormal.
  constexpr tags::callable_is_not_equal kyosu::is_not_equal = {} - retuen true if and only if the two parameters are equal.
+ return true if and only if the two parameters are not equal.
  constexpr tags::callable_is_not_finite kyosu::is_not_finite = {}  test if the parameter is not finite.
@@ -348,7 +361,7 @@  test if the parameter is not infinite.
  constexpr tags::callable_is_not_nan kyosu::is_not_nan = {} - test if the parameter is not_nan.
+ test if the parameter is not a Nan.
  constexpr tags::callable_is_not_real kyosu::is_not_real = {}  test if the parameter is not_real.
@@ -380,6 +393,15 @@ constexpr tags::callable_lerp kyosu::lerp = {}  Computes the linear interpolation.
  +constexpr tags::callable_lipart kyosu::lipart = {} + Extracts the li (sixth) part of a value.
+  +constexpr tags::callable_ljpart kyosu::ljpart = {} + Extracts the lj (seventh) part of a value.
+  +constexpr tags::callable_lkpart kyosu::lkpart = {} + Extracts the lk (eighth) part of a value.
+  constexpr tags::callable_log kyosu::log = {}  Computes the natural logarithm of the argument.
  @@ -401,6 +423,9 @@ constexpr tags::callable_log_gamma kyosu::log_gamma = {}  Computes the log of the \(\Gamma\) function of the parameter.
  +constexpr tags::callable_lpart kyosu::lpart = {} + Extracts the l (fifth) part of a value.
+  constexpr tags::callable_lpnorm kyosu::lpnorm = {}  Callable object computing the lpnorm operation \( \left(\sum_{i = 0}^n |x_i|^p\right)^{\frac1p} \).
@@ -418,7 +443,7 @@  Computes the nearest value.
  constexpr tags::callable_oneminus kyosu::oneminus = {} - Computes the value 1 minus the argument.
+ Computes the value one minus the argument.
  constexpr tags::callable_pow kyosu::pow = {}  Computes the computing the pow operation \(x^y\).
@@ -435,6 +460,9 @@ 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_pure kyosu::pure = {} + Extracts the imaginary part of a value.
+  constexpr tags::callable_quaternion kyosu::quaternion = {}  Constructs a kyosu::quaternion.
  @@ -460,7 +488,7 @@  Computes the hyperbolic secant of the argument.
  constexpr tags::callable_secpi kyosu::secpi = {} - Computes the secant of the argument in \(\pi\) mutiples.
+ Computes the secant of the argument in \(\pi\) multiples.
  constexpr tags::callable_sign kyosu::sign = {}  Computes tne normalized value z/abs(z) if z is not zero else 0.
@@ -481,10 +509,10 @@  Computes simultaneously the hyperbolic sine and cosine of the argument.
  constexpr tags::callable_sinpi kyosu::sinpi = {} - Computes the sine of the argument in \(\pi\) mutiples.
+ Computes the sine of the argument in \(\pi\) multiples.
  constexpr tags::callable_sinpicospi kyosu::sinpicospi = {} - Computes simultaneously the sine and cosine of the argument in \(\pi\) mutiples.
+ Computes simultaneously the sine and cosine of the argument in \(\pi\) multiples.
  constexpr tags::callable_slerp kyosu::slerp = {}  Computes the spherical interpolation between unitary quaternions.
@@ -505,7 +533,7 @@  Computes the hyperbolic tangent of the argument.
  constexpr tags::callable_tanpi kyosu::tanpi = {} - Computes the tangent of the argument in \(\pi\) mutiples.
+ Computes the tangent of the argument in \(\pi\) multiples.
  constexpr tags::callable_tgamma kyosu::tgamma = {}  Computes the tgammaolute value of the parameter.
@@ -514,7 +542,7 @@  Computes the trunc value.
  constexpr tags::callable_zeta kyosu::zeta = {} - Computes the Riemann \(\zeta\) \( \displaystyle \sum_0^\infty \frac{1}{(n+1)^z}\).
+ Computes the Riemann \( \displaystyle\zeta(z)=\sum_0^\infty \frac{1}{(n+1)^z}\).
 
diff --git a/group__functions_ga013ae7a04bb6a995c81537ab9c4396b4.html b/group__functions_ga013ae7a04bb6a995c81537ab9c4396b4.html index dfcad214..76150055 100644 --- a/group__functions_ga013ae7a04bb6a995c81537ab9c4396b4.html +++ b/group__functions_ga013ae7a04bb6a995c81537ab9c4396b4.html @@ -148,16 +148,16 @@

Callable Signatures

namespace kyosu
{
-
template< floating_value P, typename ... Ts>
-
auto operator()(Ts ... zi ) const noexcept
+
template< floating_value P, typename ... Ts> auto manhattan(Ts ... zi ) const noexcept
! }
+
kyosu::manhattan
constexpr tags::callable_manhattan manhattan
Callable object computing the manhattan operation.
Definition: manhattan.hpp:74
kyosu
Main KYOSU namespace.
Definition: beta.hpp:13

Parameters

  • zi... : Values to process.

Return value

-

Returns the sum of the absolute values of all elements of all zi.

+

Returns elementwise the sum of the absolute values of all elements of each zi.

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
@@ -201,7 +201,6 @@

Example

return 0;
}
-
kyosu::manhattan
constexpr tags::callable_manhattan manhattan
Callable object computing the manhattan operation.
Definition: manhattan.hpp:75
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_ga047b3d79d00d4907df04ec98f2a0fada.html b/group__functions_ga047b3d79d00d4907df04ec98f2a0fada.html index bf0332b3..5f04250b 100644 --- a/group__functions_ga047b3d79d00d4907df04ec98f2a0fada.html +++ b/group__functions_ga047b3d79d00d4907df04ec98f2a0fada.html @@ -146,21 +146,18 @@

#include <kyosu/functions.hpp>

Callable Signatures

-
namespace kyosu
-
{
-
template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto powm1(T0 z0, T1, z1) noexcept;
-
template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto powm1(T0 z0, T1, z1) noexcept;
-
template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto powm1(T0 z0, T1, z1) noexcept;
-
template<eve::ordered_value T0, ordered_value T1> > constexpr auto powm1(T0 z0, T1, z1) noexcept;
-
! }
-
kyosu::powm1
constexpr tags::callable_powm1 powm1
Computes the computing the powm1 operation .
Definition: powm1.hpp:78
+
namespace kyosu
+
{
+
constexpr auto average(auto z0, auto, z1) noexcept;
+
}
+
kyosu::average
constexpr tags::callable_average average
Computes the average of the two parameters.
Definition: average.hpp:74
kyosu
Main KYOSU namespace.
Definition: beta.hpp:13

Parameters

  • z0, z1 : Values to process.

Return value

-

the call is semantically equivalent to eve::exp(z1*eve::log(z0))-1

+

the call is semantically equivalent to dec(eve::pow(z0, z1))

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
@@ -213,6 +210,7 @@

Example

return 0;
}
+
kyosu::powm1
constexpr tags::callable_powm1 powm1
Computes the computing the powm1 operation .
Definition: powm1.hpp:75
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_ga054a9a0efe44dd5dcc9bb675b0f9e89d.html b/group__functions_ga054a9a0efe44dd5dcc9bb675b0f9e89d.html index cb8b5825..3b156e72 100644 --- a/group__functions_ga054a9a0efe44dd5dcc9bb675b0f9e89d.html +++ b/group__functions_ga054a9a0efe44dd5dcc9bb675b0f9e89d.html @@ -149,7 +149,7 @@

namespace kyosu
{
template<kyosu::concepts::cayley_dickson T> constexpr T rec(T z) noexcept;
-
template<eve::ordered_value T> constexpr T rec(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T rec(T z) noexcept;
}
kyosu::rec
constexpr tags::callable_rec rec
Computes the inverse of the argument.
Definition: rec.hpp:73
kyosu
Main KYOSU namespace.
Definition: beta.hpp:13
diff --git a/group__functions_ga057662e8933c9837bb4bbb5ffb2822f0.html b/group__functions_ga057662e8933c9837bb4bbb5ffb2822f0.html index 2c95869f..8a9d2027 100644 --- a/group__functions_ga057662e8933c9837bb4bbb5ffb2822f0.html +++ b/group__functions_ga057662e8933c9837bb4bbb5ffb2822f0.html @@ -150,16 +150,16 @@

{

template<kyosu::concepts::cayley_dickson T> constexpr auto& kpart(T& z) noexcept;
template<kyosu::concepts::cayley_dickson T> constexpr auto kpart(T const& z) noexcept;
-
template<eve::ordered_value T> constexpr T kpart(T const& z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T kpart(T const& z) noexcept;
}
-
kyosu::kpart
constexpr tags::callable_kpart kpart
Extracts the part of a value.
Definition: kpart.hpp:78
+
kyosu::kpart
constexpr tags::callable_kpart kpart
Extracts the part of a value.
Definition: kpart.hpp:80
kyosu
Main KYOSU namespace.
Definition: beta.hpp:13

Parameters

  • z : Original value.

Return value

-

Returns the \(k\) part of its argument. For real and complex inputs, the call returns 0.

+

Returns the \(k\) part of its argument. For real and complex inputs, the call returns 0. Its the fourth coefficient in the z representation and so is 0 for complex and floating.

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
diff --git a/group__functions_ga0704e6ec9b43b3f6a8864e38b566f795.html b/group__functions_ga0704e6ec9b43b3f6a8864e38b566f795.html index 1860a97b..a30a0bbb 100644 --- a/group__functions_ga0704e6ec9b43b3f6a8864e38b566f795.html +++ b/group__functions_ga0704e6ec9b43b3f6a8864e38b566f795.html @@ -148,7 +148,7 @@

Callable Signatures

namespace kyosu
{
-
template<eve::ordered_value T> constexpr auto acot(T z) noexcept; //1
+
template<eve::floating_ordered_value T> constexpr auto acot(T z) noexcept; //1
template<kyosu::concepts::complex T> constexpr auto acot(T z) noexcept; //2
template<kyosu::concepts::cayley_dickson T> constexpr auto acot(T z) noexcept; //3
}
@@ -160,9 +160,9 @@

-
  • A real type input z calls eve::acot(z); and so returns the same type as input.
    • +
  • A real type input z calls eve::acot(z); and so returns the same type as the input.
  • Returns elementwise the complex principal value of the arc cotangent of the input as the arc tangent of the inverse of the input.
    • -
  • Returns \(I_z \mathrm{acoth}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).
    • +
  • Returns \(I_z \mathrm{acoth}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).

    • Example

    #include <kyosu/kyosu.hpp>
    diff --git a/group__functions_ga0ae8f99de8716a46dd7de3ff990602bb.html b/group__functions_ga0ae8f99de8716a46dd7de3ff990602bb.html index bd8b8ef1..ba473506 100644 --- a/group__functions_ga0ae8f99de8716a46dd7de3ff990602bb.html +++ b/group__functions_ga0ae8f99de8716a46dd7de3ff990602bb.html @@ -148,8 +148,8 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexp2r T exp2(T z) noexcept;
    -
    template<eve::ordered_value T> constexp2r T exp2(T z) noexcept;
    +
    template<kyosu::concepts::cayley_dickson T> constexpr T exp2(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T exp2(T z) noexcept;
    }
    kyosu::exp2
    constexpr tags::callable_exp2 exp2
    Computes the base 2 exponential of the argument.
    Definition: exp2.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    diff --git a/group__functions_ga0d165215c9a5f3f78feab4b70874f436.html b/group__functions_ga0d165215c9a5f3f78feab4b70874f436.html index 680b4e6e..828ec8c8 100644 --- a/group__functions_ga0d165215c9a5f3f78feab4b70874f436.html +++ b/group__functions_ga0d165215c9a5f3f78feab4b70874f436.html @@ -142,23 +142,23 @@

    -

    Computes the cotangent of the argument in \(\pi\) mutiples.

    +

    Computes the cotangent from the argument in \(\pi\) multiples.

    Defined in Header

    #include <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T cotpi(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T cotpi(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T cotpi(T z) noexcept;
    }
    -
    kyosu::cotpi
    constexpr tags::callable_cotpi cotpi
    Computes the cotangent of the argument in mutiples.
    Definition: cotpi.hpp:73
    +
    kyosu::cotpi
    constexpr tags::callable_cotpi cotpi
    Computes the cotangent from the argument in multiples.
    Definition: cotpi.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns the cotangent of the argument in \(\pi\) mutiples.

    +

    Returns the cotangent from the argument in \(\pi\) multiples.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga0e8c3f00c6f3777a5a14320c7b1a31da.html b/group__functions_ga0e8c3f00c6f3777a5a14320c7b1a31da.html index d2d8cd62..f3aecf63 100644 --- a/group__functions_ga0e8c3f00c6f3777a5a14320c7b1a31da.html +++ b/group__functions_ga0e8c3f00c6f3777a5a14320c7b1a31da.html @@ -149,7 +149,7 @@

    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;
    +
    template<eve::floating_ordered_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: beta.hpp:13
    diff --git a/group__functions_ga1410062f3325c9a4b687d12f5ae53f55.html b/group__functions_ga1410062f3325c9a4b687d12f5ae53f55.html index 38b37730..f3fd3cfd 100644 --- a/group__functions_ga1410062f3325c9a4b687d12f5ae53f55.html +++ b/group__functions_ga1410062f3325c9a4b687d12f5ae53f55.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr auto is_denormal(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto is_denormal(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto is_denormal(T z) noexcept;
    }
    kyosu::is_denormal
    constexpr tags::callable_is_denormal is_denormal
    test if the parameter is denormal.
    Definition: is_denormal.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    @@ -158,7 +158,7 @@

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga1658a3b3d9e67c35d2a85233572770ed.html b/group__functions_ga1658a3b3d9e67c35d2a85233572770ed.html index 5fd32029..60dd5319 100644 --- a/group__functions_ga1658a3b3d9e67c35d2a85233572770ed.html +++ b/group__functions_ga1658a3b3d9e67c35d2a85233572770ed.html @@ -167,7 +167,7 @@

    beta(x, y).

    +

    log(beta(x, y).

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga1b78fa57857ad714ce5f0e6e3ace5db9.html b/group__functions_ga1b78fa57857ad714ce5f0e6e3ace5db9.html index 6b64e97b..dbbed89e 100644 --- a/group__functions_ga1b78fa57857ad714ce5f0e6e3ace5db9.html +++ b/group__functions_ga1b78fa57857ad714ce5f0e6e3ace5db9.html @@ -149,13 +149,13 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T minus(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T minus(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T minus(T z) noexcept;
    }
    kyosu::minus
    constexpr tags::callable_minus minus
    Computes the opposite value.
    Definition: minus.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

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

    Return value

    Returns the opposite of its argument.

    diff --git a/group__functions_ga1e253b4aba99259dbb98d891247c2a38.html b/group__functions_ga1e253b4aba99259dbb98d891247c2a38.html index 08aff3ab..ff9b2b57 100644 --- a/group__functions_ga1e253b4aba99259dbb98d891247c2a38.html +++ b/group__functions_ga1e253b4aba99259dbb98d891247c2a38.html @@ -148,17 +148,36 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpr T sinh(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T sinh(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto sinh(T z) noexcept; //1
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto sinh(T z) noexcept; //2
    }
    -
    kyosu::sinh
    constexpr tags::callable_sinh sinh
    Computes the hyperbolic sine of the argument.
    Definition: sinh.hpp:73
    +
    kyosu::sinh
    constexpr tags::callable_sinh sinh
    Computes the hyperbolic sine of the argument.
    Definition: sinh.hpp:92
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns the hyperbolic sine of the argument.

    +
      +
    1. Returns the hyperbolic sine of the argument.
      2. +
    2. Returns elementwise the complex value of the hyperbolic sine of the input.
        +
      • for every z: eve::sinh(kyosu::conj(z)) == kyosu::conj(std::sinh(z))
        • +
      • for every z: kyosu::sinh(-z) == -kyosu::sinh(z)
        • +
      • If z is \(+0\), the result is \(+0\)
        • +
      • If z is \(i \infty\), the result is \(i NaN\) (the sign of the real part is unspecified)
        • +
      • If z is \(i NaN\), the result is \(NaN\)
        • +
      • If z is \(x+i \infty\) (for any positive finite x), the result is \(NaN+i NaN\)
        • +
      • If z is \(x+i NaN\) (for any positive finite x), the result is \(NaN+i NaN\)
        • +
      • If z is \(+\infty\), the result is \(+\infty\)
        • +
      • If z is \(+\infty+i y\) (for any positive finite y), the result is \(\infty\times e^{iy}\)
        • +
      • If z is \(+\infty+i \infty\), the result is \(\pm \infty+i NaN\) (the sign of the real part is unspecified)
        • +
      • If z is \(+\infty+i NaN\), the result is \(\pm \infty+i NaN\) (the sign of the real part is unspecified)
        • +
      • If z is \(NaN\), the result is \(NaN\)
        • +
      • If z is \(NaN+i y\) (for any finite nonzero y), the result is \(NaN+i NaN\)
        • +
      +
      3. +
    3. Is semantically equivalent to (exp(z)-exp(-z))/2.
      4. +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga23d96b11ec047300319b6b8ccfa07765.html b/group__functions_ga23d96b11ec047300319b6b8ccfa07765.html index 0e4c5f91..adf90508 100644 --- a/group__functions_ga23d96b11ec047300319b6b8ccfa07765.html +++ b/group__functions_ga23d96b11ec047300319b6b8ccfa07765.html @@ -148,12 +148,9 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto reldist(T0 z0, T1, z1) noexcept;
    -
    template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto reldist(T0 z0, T1, z1) noexcept;
    -
    template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto reldist(T0 z0, T1, z1) noexcept;
    -
    template<eve::ordered_value T0, ordered_value T1> > constexpr auto reldist(T0 z0, T1, z1) noexcept;
    +
    constexpr auto reldist(auto z0, auto, z1) noexcept;
    ! }
    -
    kyosu::reldist
    constexpr tags::callable_reldist reldist
    Computes the relative distance between the two parameters.
    Definition: reldist.hpp:80
    +
    kyosu::reldist
    constexpr tags::callable_reldist reldist
    Computes the relative distance between the two parameters.
    Definition: reldist.hpp:77
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      diff --git a/group__functions_ga25372aaebdff2ad59971a9fee778ba0f.html b/group__functions_ga25372aaebdff2ad59971a9fee778ba0f.html index 00a1be60..b6d61c04 100644 --- a/group__functions_ga25372aaebdff2ad59971a9fee778ba0f.html +++ b/group__functions_ga25372aaebdff2ad59971a9fee778ba0f.html @@ -146,21 +146,48 @@

      #include <kyosu/functions.hpp>

    Callable Signatures

    -
    namespace kyosu
    -
    {
    -
    template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto pow(T0 z0, T1, z1) noexcept;
    -
    template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto pow(T0 z0, T1, z1) noexcept;
    -
    template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto pow(T0 z0, T1, z1) noexcept;
    -
    template<eve::ordered_value T0, ordered_value T1> > constexpr auto pow(T0 z0, T1, z1) noexcept;
    -
    ! }
    -
    kyosu::pow
    constexpr tags::callable_pow pow
    Computes the computing the pow operation .
    Definition: pow.hpp:77
    +
    namespace kyosu
    +
    {
    +
    constexpr auto pow(auto z0, auto, z1) noexcept; \\123
    +
    constexpr auto pow(auto z0, eve::integral_value n) noexcept; \\4
    +
    }
    +
    kyosu::pow
    constexpr tags::callable_pow pow
    Computes the computing the pow operation .
    Definition: pow.hpp:113
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z0, z1 : Values to process.
    -

    Return value

    -

    the call is semantically equivalent to eve::exp(z1*eve::log(z0))

    +

    Return value

      +
    1. if both parameters are floating the call will act as if they were converted to complex before call
      2. +
    2. if both parameters are floating or complex. The ieee specification are taken:
      + In particular we have (IEC 60559):
        +
      • pow(+0, y), where y is a negative odd integer, returns \(+\infty\)
        • +
      • pow(-0, y), where y is a negative odd integer, returns \(-\infty\)
        • +
      • pow( \(\pm0\), y), where y is negative, finite, and is an even integer or a non-integer, returns \(+\infty\)
        • +
      • pow( \(\pm0\), \(-\infty\)) returns \(+\infty\)
        • +
      • pow(+0, y), where y is a positive odd integer, returns +0
        • +
      • pow(-0, y), where y is a positive odd integer, returns -0
        • +
      • pow( \(\pm0\), y), where y is positive non-integer or a positive even integer, returns +0
        • +
      • pow(-1, \(\pm\infty\)) returns 1
        • +
      • pow(+1, y) returns 1 for any y, even when y is NaN
        • +
      • pow(x, \(\pm0\)) returns 1 for any x, even when x is NaN
        • +
      • pow(x, y) returns NaN if x is finite and less than 0 and y is finite and non-integer.
        • +
      • pow(x, \(-\infty\)) returns \(+\infty\) for any |x|<1
        • +
      • pow(x, \(-\infty\)) returns +0 for any |x|>1
        • +
      • pow(x, \(+\infty\)) returns +0 for any |x|<1
        • +
      • pow(x, \(+\infty\)) returns \(+\infty\) for any |x|>1
        • +
      • pow( \(-\infty\), y) returns -0 if y is a negative odd integer
        • +
      • pow( \(-\infty\), y) returns +0 if y is a negative non-integer or even integer
        • +
      • pow( \(-\infty\), y) returns \(-\infty\) if y is a positive odd integer
        • +
      • pow( \(-\infty\), y) returns \(+\infty\) if y is a positive non-integer or even integer
        • +
      • pow( \(+\infty\), y) returns +0 for any y less than 0
        • +
      • pow( \(+\infty\), y) returns \(+\infty\) for any y greater than 0
        • +
      • except where specified above, if any argument is NaN, NaN is returned
        • +
      +
      3. +
    3. if any parameter as a dimensionnality greater yhan 2, the call is semantically equivalent to kyosu::exp(z1*eve::log(z0))
      4. +
    4. pow can accept an integral typed second parameter, in this case it is the russian peasant algorithm that is used.
      5. +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga265f03cd0d4edaaecd88fbcfc3346644.html b/group__functions_ga265f03cd0d4edaaecd88fbcfc3346644.html index dbfaae5a..939c35a3 100644 --- a/group__functions_ga265f03cd0d4edaaecd88fbcfc3346644.html +++ b/group__functions_ga265f03cd0d4edaaecd88fbcfc3346644.html @@ -144,12 +144,12 @@

    #declude <kyosu/functions.hpp>
    +
    #include <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T dec(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T dec(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T dec(T z) noexcept;
    }
    kyosu::dec
    constexpr tags::callable_dec dec
    decrements the argument by 1.
    Definition: dec.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    diff --git a/group__functions_ga26c8821ba25972647692322f5236a370.html b/group__functions_ga26c8821ba25972647692322f5236a370.html index 271ad52d..40c4580e 100644 --- a/group__functions_ga26c8821ba25972647692322f5236a370.html +++ b/group__functions_ga26c8821ba25972647692322f5236a370.html @@ -148,17 +148,22 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpr T sin(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T sin(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto sin(T z) noexcept; //1
    +
    template<kyosu::concepts::complex T> constexpr auto sin(T z) noexcept; //2
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto sin(T z) noexcept; //3
    }
    -
    kyosu::sin
    constexpr tags::callable_sin sin
    Computes the sine of the argument.
    Definition: sin.hpp:73
    +
    kyosu::sin
    constexpr tags::callable_sin sin
    Computes the sine of the argument.
    Definition: sin.hpp:80
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns the sine of the argument.

    +
      +
    1. Returns the sine of the argument.
      2. +
    2. The behavior of this function is equivalent to \(-i*\sinh(i*z)\).
      3. +
    3. Returns \(-I_z\cosh(I_z\; z)\) if \(z\) is not zero else \(\sin(z_0)\), where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).
      4. +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga29021b202d2832d1e6863d7402e25b79.html b/group__functions_ga29021b202d2832d1e6863d7402e25b79.html index f4d2e2ae..5f34097a 100644 --- a/group__functions_ga29021b202d2832d1e6863d7402e25b79.html +++ b/group__functions_ga29021b202d2832d1e6863d7402e25b79.html @@ -148,8 +148,8 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpmx2r T expmx2(T z) noexcept;
    -
    template<eve::ordered_value T> constexpmx2r T expmx2(T z) noexcept;
    +
    template<kyosu::concepts::cayley_dickson T> constexpr T expmx2(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T expmx2(T z) noexcept;
    }
    kyosu::expmx2
    constexpr tags::callable_expmx2 expmx2
    Computes the exponential of the opposite of the squared argument.
    Definition: expmx2.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    diff --git a/group__functions_ga297cbe86ab12760ec934f76879f805d0.html b/group__functions_ga297cbe86ab12760ec934f76879f805d0.html index 3f81873f..3292bbb6 100644 --- a/group__functions_ga297cbe86ab12760ec934f76879f805d0.html +++ b/group__functions_ga297cbe86ab12760ec934f76879f805d0.html @@ -148,18 +148,17 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpr as_real_t<T> sqr_abs(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T sqr_abs(T z) noexcept;
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto sqr_abs(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto sqr_abs(T z) noexcept;
    }
    kyosu::sqr_abs
    constexpr tags::callable_sqr_abs sqr_abs
    Computes the squared absolute value of the parameter.
    Definition: sqr_abs.hpp:72
    -
    kyosu::as_real_t
    typename as_real< T >::type as_real_t
    Compute the real type associated to a Cayley-Dickson-like type.
    Definition: traits.hpp:79
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns the squared modulus of its argument.

    +

    Returns the squared modulus of its argument, a floating value.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga2cccab7b0cb7548aabfcd581a6c98fa6.html b/group__functions_ga2cccab7b0cb7548aabfcd581a6c98fa6.html index 8e0e4675..f61f1514 100644 --- a/group__functions_ga2cccab7b0cb7548aabfcd581a6c98fa6.html +++ b/group__functions_ga2cccab7b0cb7548aabfcd581a6c98fa6.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T floor(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T floor(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T floor(T z) noexcept;
    }
    kyosu::floor
    constexpr tags::callable_floor floor
    Computes the floor value.
    Definition: floor.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    @@ -158,7 +158,7 @@

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga2f8614d64bb1b781e4496b56b0accfa1.html b/group__functions_ga2f8614d64bb1b781e4496b56b0accfa1.html index fc99d715..0bfe75c1 100644 --- a/group__functions_ga2f8614d64bb1b781e4496b56b0accfa1.html +++ b/group__functions_ga2f8614d64bb1b781e4496b56b0accfa1.html @@ -148,17 +148,22 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpr T tan(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T tan(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T tan(T z) noexcept; //1
    +
    template<kyosu::concepts::complex T> constexpr T tan(T z) noexcept; //2
    +
    template<kyosu::concepts::cayley_dickson T> constexpr T tan(T z) noexcept; //3
    }
    -
    kyosu::tan
    constexpr tags::callable_tan tan
    Computes the tangent of the argument.
    Definition: tan.hpp:73
    +
    kyosu::tan
    constexpr tags::callable_tan tan
    Computes the tangent of the argument.
    Definition: tan.hpp:79
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns the tangent of the argument.

    +
      +
    1. Returns eve::tan(z)
      2. +
    2. The behavior of this function is equivalent to \(-i\tanh(i\; z)\).
      3. +
    3. Returns \(-I_z\,; \tanh(I_z\; z)\) if \(z\) is not zero else \(\tan(z_0)\), where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).
      4. +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga308a170dbf61d3a4aba52d975abf902e.html b/group__functions_ga308a170dbf61d3a4aba52d975abf902e.html index d5bf0fef..9f2c72e8 100644 --- a/group__functions_ga308a170dbf61d3a4aba52d975abf902e.html +++ b/group__functions_ga308a170dbf61d3a4aba52d975abf902e.html @@ -148,8 +148,8 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpr T sec(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T sec(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto sec(T z) noexcept;
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto sec(T z) noexcept;
    }
    kyosu::sec
    constexpr tags::callable_sec sec
    Computes the secant of the argument.
    Definition: sec.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    diff --git a/group__functions_ga398aa088354c3b9d0a0a1b5d6b7145f9.html b/group__functions_ga398aa088354c3b9d0a0a1b5d6b7145f9.html index 8c449182..d859d052 100644 --- a/group__functions_ga398aa088354c3b9d0a0a1b5d6b7145f9.html +++ b/group__functions_ga398aa088354c3b9d0a0a1b5d6b7145f9.html @@ -148,17 +148,38 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constlogr T log(T z) noexcept;
    -
    template<eve::ordered_value T> constlogr T log(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T log(T z) noexcept; //1
    +
    template<kyosu::concepts::complex T> constexpr T log(T z) noexcept; //2
    +
    template<kyosu::concepts::cayley_dickson T> constexpr T log(T z) noexcept; //2
    }
    -
    kyosu::log
    constexpr tags::callable_log log
    Computes the natural logarithm of the argument.
    Definition: log.hpp:78
    +
    kyosu::log
    constexpr tags::callable_log log
    Computes the natural logarithm of the argument.
    Definition: log.hpp:101
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

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

    +
      +
    1. a real typed input z is treated as if kyosu::complex(z) was entered.
      2. +
    2. Returns elementwise the natural logarithm of the input in the range of a strip in the interval \(i\times[-\pi, \pi]\) along the imaginary axis and mathematically unbounded along the real axis. .
        +
      • The function is continuous onto the branch cut along the negative real axis, taking into account the sign of imaginary part
        • +
      • for every z: kyosu::log(kyosu::conj(z)) == kyosu::conj(kyosu::log(z))
        • +
      • If z is \(-0\), the result is \(-\infty+i \pi \)
        • +
      • If z is \(+0\), the result is \(-\infty\)
        • +
      • If z is \(x+i \infty\) (for any finite x), the result is \(+\infty+i \pi/2\)
        • +
      • If z is \(x+i NaN\) (for any finite x), the result is \(NaN+i NaN\)
        • +
      • If z is \(-\infty+i y\) (for any finite positive y), the result is \(+\infty+i \pi \)
        • +
      • If z is \(+\infty+i y\) (for any finite positive y), the result is \(+\infty\)
        • +
      • If z is \(-\infty+i \infty\), the result is \(+\infty+i 3\pi/4\)
        • +
      • If z is \(+\infty+i \infty\), the result is \(+\infty+i \pi/4\)
        • +
      • If z is \(\pm\infty+i NaN\), the result is \(+\infty+i NaN\)
        • +
      • If z is \(NaN+i y\) (for any finite y), the result is \(NaN+i NaN\)
        • +
      • If z is \(NaN+i \infty\), the result is \(+\infty+i NaN\)
        • +
      • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)
        • +
      +
      3. +
    3. log(z) is semantically equivalent to log(abs(z))+sign(pure(z))*arg(z)
      4. +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga3aa2bb7847bd2885618e263ed0f0cd82.html b/group__functions_ga3aa2bb7847bd2885618e263ed0f0cd82.html index 23fb3ef9..11a85df2 100644 --- a/group__functions_ga3aa2bb7847bd2885618e263ed0f0cd82.html +++ b/group__functions_ga3aa2bb7847bd2885618e263ed0f0cd82.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr auto sinhcosh(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto sinhcosh(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto sinhcosh(T z) noexcept;
    }
    kyosu::sinhcosh
    constexpr tags::callable_sinhcosh sinhcosh
    Computes simultaneously the hyperbolic sine and cosine of the argument.
    Definition: sinhcosh.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    diff --git a/group__functions_ga3aeaaaa9878d7ab2378c1bd62dd7b34a.html b/group__functions_ga3aeaaaa9878d7ab2378c1bd62dd7b34a.html new file mode 100644 index 00000000..d0574e51 --- /dev/null +++ b/group__functions_ga3aeaaaa9878d7ab2378c1bd62dd7b34a.html @@ -0,0 +1,220 @@ + + + + + + + + +kyosu: kyosu::ipart + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
    Loading...
    +
    Searching...
    +
    No Matches
    +
    +
    +
    +
    + +
    + +

    ◆ ipart

    + +
    +
    + + + + + +
    + + + + +
    kyosu::ipart = {}
    +     		+inlineconstexpr
    +
    + +

    Extracts the imaginary part of a value.

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto& ipart(T& z) noexcept;
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto ipart(T const& z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T ipart(T const& z) noexcept;
    +
    }
    +
    kyosu::ipart
    constexpr tags::callable_ipart ipart
    Extracts the imaginary part of a value.
    Definition: ipart.hpp:82
    +
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    +

    Parameters

    +
      +
    • z : Original value.
      • +
    +

    Return value

    +

    Returns the second part of its argument.

    +

    For real inputs, the call returns 0.

    +

    For complex inputs it is the imaginary part.

    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::ipart;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    +
    std::cout << "Real: ";
    +
    float f = 72.9f;
    +
    std::cout << f << " -> " << ipart(f) << "\n";
    +
    +
    std::cout << "Complex: ";
    +
    auto z = kyosu::complex_t<float>(3.5f,-2.9f);
    +
    std::cout << z << " -> " << ipart(z) << " => ";
    +
    ipart(z) = 11.23f;
    +
    std::cout << z << "\n";
    +
    +
    std::cout << "Quaternion: ";
    +
    auto q = kyosu::quaternion_t<double>(1.,2.,3.,4.);
    +
    std::cout << q << " -> " << ipart(q) << " => ";
    +
    ipart(q) = 42.7;
    +
    std::cout << q << "\n";
    +
    +
    std::cout << "SIMD: ";
    +
    eve::wide<kyosu::complex_t<double>, eve::fixed<2>> wz(kyosu::complex_t<double>(1.3,-3.7));
    +
    std::cout << wz << " -> " << ipart(wz) << " => ";
    +
    ipart(wz) = eve::wide<double, eve::fixed<2>>{13.37,63.24};
    +
    std::cout << wz << "\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 3b4ec425..c80b5f8f 100644 --- a/group__functions_ga3c49606902ab917444da4ac9ed3003ce.html +++ b/group__functions_ga3c49606902ab917444da4ac9ed3003ce.html @@ -146,21 +146,18 @@

    #include <kyosu/functions.hpp>

    Callable Signatures

    -
    namespace kyosu
    -
    {
    -
    template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto dist(T0 z0, T1, z1) noexcept;
    -
    template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto dist(T0 z0, T1, z1) noexcept;
    -
    template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto dist(T0 z0, T1, z1) noexcept;
    -
    template<eve::ordered_value T0, ordered_value T1> > constexpr auto dist(T0 z0, T1, z1) noexcept;
    -
    ! }
    -
    kyosu::dist
    constexpr tags::callable_dist dist
    Computes the distance between the two parameters.
    Definition: dist.hpp:78
    +
    namespace kyosu
    +
    {
    +
    constexpr auto dist(auto z0, auto z1) noexcept;
    +
    }
    +
    kyosu::dist
    constexpr tags::callable_dist dist
    Computes the distance between the two parameters.
    Definition: dist.hpp:76
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      -
    • z0, z1 : Value to process.
      • +
    • z0, z1 : Values to process.

    Return value

    -

    Returns the distance between the two arguments computed as the absolute value of the arguments difference.

    +

    Returns the distance between the two arguments computed as the absolute value of the arguments difference. Arguments can be a mix of floting or Cayley-Dicson values.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga3d9e6e28fb334f64bbe3c1b60f28d15b.html b/group__functions_ga3d9e6e28fb334f64bbe3c1b60f28d15b.html index 30d5bdfb..b4c78d7e 100644 --- a/group__functions_ga3d9e6e28fb334f64bbe3c1b60f28d15b.html +++ b/group__functions_ga3d9e6e28fb334f64bbe3c1b60f28d15b.html @@ -149,16 +149,17 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template< floating_value P, typename T, typename ... Ts>
    -
    auto operator()(P p, T z,Ts ... zs ) const noexcept
    +
    template< floating_value P, typename T, typename ... Ts> auto lpnorm(P p, T z,Ts ... zs ) const noexcept
    ! }
    +
    kyosu::lpnorm
    constexpr tags::callable_lpnorm lpnorm
    Callable object computing the lpnorm operation .
    Definition: lpnorm.hpp:77
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      -
    • z, zs... : Values to process.
      • +
    • p: : positive floating ordered value
      • +
    • zs... : Values to process.

    Return value

    -

    Returns \( \left(\sum_{i = 0}^n//! |x_i|^p\right)^{\frac1p} \).

    +

    Returns \( \left(\sum_{i = 0}^n |x_i|^p\right)^{\frac1p} \).

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    @@ -202,7 +203,6 @@

    Example

    return 0;
    }
    -
    kyosu::lpnorm
    constexpr tags::callable_lpnorm lpnorm
    Callable object computing the lpnorm operation .
    Definition: lpnorm.hpp:77
    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 c3ad8da4..7444a394 100644 --- a/group__functions_ga3e5656e4788dbebd4450758cba9dab9d.html +++ b/group__functions_ga3e5656e4788dbebd4450758cba9dab9d.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr auto is_not_infinite(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto is_not_infinite(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto is_not_infinite(T z) noexcept;
    }
    kyosu::is_not_infinite
    constexpr tags::callable_is_not_infinite is_not_infinite
    test if the parameter is not infinite.
    Definition: is_not_infinite.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    @@ -158,7 +158,7 @@

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga40c963ecefcdeba9487598d5ef9bf874.html b/group__functions_ga40c963ecefcdeba9487598d5ef9bf874.html index 84ce635a..85cb7445 100644 --- a/group__functions_ga40c963ecefcdeba9487598d5ef9bf874.html +++ b/group__functions_ga40c963ecefcdeba9487598d5ef9bf874.html @@ -148,7 +148,7 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<eve::ordered_value T> constexpr auto acsc(T z) noexcept; //1
    +
    template<eve::floating_ordered_value T> constexpr auto acsc(T z) noexcept; //1
    template<kyosu::concepts::cayley_dickson T> constexpr auto acsc(T z) noexcept; //2
    }
    kyosu::acsc
    constexpr tags::callable_acsc acsc
    Computes the arccosecant of the argument.
    Definition: acsc.hpp:79
    @@ -159,7 +159,7 @@

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

    • Example

    diff --git a/group__functions_ga42fce115bbd07cb330a84af0213c656d.html b/group__functions_ga42fce115bbd07cb330a84af0213c656d.html index 2b3d1662..6162e8c1 100644 --- a/group__functions_ga42fce115bbd07cb330a84af0213c656d.html +++ b/group__functions_ga42fce115bbd07cb330a84af0213c656d.html @@ -148,10 +148,10 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpr T log1p(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr complex_t<T> log1p(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr complex_t<T> log1p(T z) noexcept; //1
    +
    template<kyosu::concepts::cayley_dickson T> constexpr T log1p(T z) noexcept; //2
    }
    -
    kyosu::log1p
    constexpr tags::callable_log1p log1p
    Computes the natural logarithm of the argument plus 1.
    Definition: log1p.hpp:78
    +
    kyosu::log1p
    constexpr tags::callable_log1p log1p
    Computes the natural logarithm of the argument plus 1.
    Definition: log1p.hpp:81
    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: beta.hpp:13

    Parameters

    @@ -159,7 +159,11 @@

    +
  • a real typed input z is treated as if kyosu::complex(z) was entered.
    + For real and complex entries provision are made to get better precision near z = 0.
    • +
  • returns log(1+z).
    • +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga441cd97a80d870b01cf6cd1ace7238e7.html b/group__functions_ga441cd97a80d870b01cf6cd1ace7238e7.html index 77aaa838..7327bd1e 100644 --- a/group__functions_ga441cd97a80d870b01cf6cd1ace7238e7.html +++ b/group__functions_ga441cd97a80d870b01cf6cd1ace7238e7.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr auto is_not_finite(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto is_not_finite(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto is_not_finite(T z) noexcept;
    }
    kyosu::is_not_finite
    constexpr tags::callable_is_not_finite is_not_finite
    test if the parameter is not finite.
    Definition: is_not_finite.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    @@ -158,7 +158,7 @@

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga45677fbbb676a8b5287c2c0c0ab5deae.html b/group__functions_ga45677fbbb676a8b5287c2c0c0ab5deae.html index 0cd7fa5b..fcfc1321 100644 --- a/group__functions_ga45677fbbb676a8b5287c2c0c0ab5deae.html +++ b/group__functions_ga45677fbbb676a8b5287c2c0c0ab5deae.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr auto is_not_real(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto is_not_real(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto is_not_real(T z) noexcept;
    }
    kyosu::is_not_real
    constexpr tags::callable_is_not_real is_not_real
    test if the parameter is not_real.
    Definition: is_not_real.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    @@ -158,7 +158,7 @@

    pure part is not zero.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_ga46ff71e1e2cf6bbbeb771eeb0885f3b6.html b/group__functions_ga46ff71e1e2cf6bbbeb771eeb0885f3b6.html index 068eb3e5..fd9f0f58 100644 --- a/group__functions_ga46ff71e1e2cf6bbbeb771eeb0885f3b6.html +++ b/group__functions_ga46ff71e1e2cf6bbbeb771eeb0885f3b6.html @@ -148,12 +148,12 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<eve::ordered_value T> constexpr auto acos(T z) noexcept; //1
    +
    template<eve::floating_ordered_value T> constexpr auto acos(T z) noexcept; //1
    template<kyosu::concepts::complex T> constexpr auto atan(T z) noexcept; //2
    template<kyosu::concepts::cayley_dickson T> constexpr auto acos(T z) noexcept; //3
    }
    -
    kyosu::acos
    constexpr tags::callable_acos acos
    Computes the acosine of the argument.
    Definition: acos.hpp:100
    -
    kyosu::atan
    constexpr tags::callable_atan atan
    Computes the inverse hyperbolic tangent of the argument.
    Definition: atan.hpp:86
    +
    kyosu::acos
    constexpr tags::callable_acos acos
    Computes the acosine of the argument.
    Definition: acos.hpp:101
    +
    kyosu::atan
    constexpr tags::callable_atan atan
    Computes the arctangent of the argument.
    Definition: atan.hpp:86
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      @@ -161,9 +161,9 @@

      -
    • a real input z is treated as if complex(z) was entered.
      • +
    • a real typed input z is treated as if kyosu::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.
        -
      • for every z: eve::acos(eve::conj(z)) == eve::conj(std::acos(z))
        • +
      • for every z: kyosu::acos( kyosu::conj(z) ) == kyosu::conj(kyosu::acos(z))
      • If z is \(\pm0\), the result is \(\pi/2\)
      • If z is \(i NaN\), the result is \(\pi/2+ i NaN\)
      • If z is \(x+i\infty\) (for any finite x), the result is \(\pi/2-i\infty\)
        • @@ -178,7 +178,7 @@

        pure part of \(z\). template<kyosu::concepts::cayley_dickson T> constexpr T cosh(T z) noexcept; }

        Example

        #include <kyosu/kyosu.hpp>
        diff --git a/group__functions_ga4c6ee3532d93a937aaa603ba4699b3ed.html b/group__functions_ga4c6ee3532d93a937aaa603ba4699b3ed.html index b4577932..47f653fa 100644 --- a/group__functions_ga4c6ee3532d93a937aaa603ba4699b3ed.html +++ b/group__functions_ga4c6ee3532d93a937aaa603ba4699b3ed.html @@ -149,7 +149,7 @@

        namespace kyosu
        {
        template<kyosu::concepts::cayley_dickson T> constexpr T frac(T z) noexcept;
        -
        template<eve::ordered_value T> constexpr T frac(T z) noexcept;
        +
        template<eve::floating_ordered_value T> constexpr T frac(T z) noexcept;
        }
        kyosu::frac
        constexpr tags::callable_frac frac
        Computes the frac value.
        Definition: frac.hpp:73
        kyosu
        Main KYOSU namespace.
        Definition: beta.hpp:13
        @@ -158,7 +158,7 @@

        Example

        #include <kyosu/kyosu.hpp>
        #include <eve/wide.hpp>
        diff --git a/group__functions_ga4f655a16c878099303a59697347bce41.html b/group__functions_ga4f655a16c878099303a59697347bce41.html index adb4eda1..3c6cd159 100644 --- a/group__functions_ga4f655a16c878099303a59697347bce41.html +++ b/group__functions_ga4f655a16c878099303a59697347bce41.html @@ -149,7 +149,7 @@

        namespace kyosu
        {
        template<kyosu::concepts::cayley_dickson T> constexpr auto is_unitary(T z) noexcept;
        -
        template<eve::ordered_value T> constexpr auto is_unitary(T z) noexcept;
        +
        template<eve::floating_ordered_value T> constexpr auto is_unitary(T z) noexcept;
        }
        kyosu::is_unitary
        constexpr tags::callable_is_unitary is_unitary
        test if the parameter is unitary (absolute value one).
        Definition: is_unitary.hpp:74
        kyosu
        Main KYOSU namespace.
        Definition: beta.hpp:13
        @@ -158,7 +158,7 @@

        Note
        As for now is_unitary accepts almost equality (will change when decorators will be at hand in kyosu)

        Example

        #include <kyosu/kyosu.hpp>
        diff --git a/group__functions_ga4f764df12120f10236ef0c746e9ed6ff.html b/group__functions_ga4f764df12120f10236ef0c746e9ed6ff.html index a1c8d62d..c32a686b 100644 --- a/group__functions_ga4f764df12120f10236ef0c746e9ed6ff.html +++ b/group__functions_ga4f764df12120f10236ef0c746e9ed6ff.html @@ -148,7 +148,7 @@

        Callable Signatures

        namespace kyosu
        {
        -
        template<eve::ordered_value T> constexpr auto atanh(T z) noexcept; //1
        +
        template<eve::floating_ordered_value T> constexpr auto atanh(T z) noexcept; //1
        template<kyosu::concepts::complex T> constexpr auto atanh(T z) noexcept; //2
        template<kyosu::concepts::cayley_dickson T> constexpr auto atanh(T z) noexcept; //3
        }
        @@ -160,10 +160,10 @@

        -
      • 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)
          • +
        • a real input z is treated as if kyosu::complex(z) was entered.
          • +
        • Returns the complex inverse hyperbolic tangent 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: kyosu::atanh( kyosu::conj(z)) == kyosu::conj(kyosu::atanh(z)
            • +
          • for every z: kyosu::atanh(-z) == -kyosu::atanh(z)
          • If z is \(+0\), the result is \(+0\)
          • If z is \(NaN\), the result is \(NaN\)
          • If z is \(+1\), the result is \(+\infty\)
            • diff --git a/group__functions_ga5354d486ec4fca0c8261639b8ccfffd7.html b/group__functions_ga5354d486ec4fca0c8261639b8ccfffd7.html index 8c7aaa3a..a2a2ca83 100644 --- a/group__functions_ga5354d486ec4fca0c8261639b8ccfffd7.html +++ b/group__functions_ga5354d486ec4fca0c8261639b8ccfffd7.html @@ -149,7 +149,7 @@

            namespace kyosu
            {
            template<kyosu::concepts::cayley_dickson T> constexpr T inc(T z) noexcept;
            -
            template<eve::ordered_value T> constexpr T inc(T z) noexcept;
            +
            template<eve::floating_ordered_value T> constexpr T inc(T z) noexcept;
            }
            kyosu::inc
            constexpr tags::callable_inc inc
            Increments the argument.
            Definition: inc.hpp:72
            kyosu
            Main KYOSU namespace.
            Definition: beta.hpp:13
            diff --git a/group__functions_ga57a5e1064f03073d3e81144181f6ac71.html b/group__functions_ga57a5e1064f03073d3e81144181f6ac71.html index e02aafa9..280f3190 100644 --- a/group__functions_ga57a5e1064f03073d3e81144181f6ac71.html +++ b/group__functions_ga57a5e1064f03073d3e81144181f6ac71.html @@ -149,7 +149,7 @@

            namespace kyosu
            {
            template<kyosu::concepts::cayley_dickson T> constexpr T trunc(T z) noexcept;
            -
            template<eve::ordered_value T> constexpr T trunc(T z) noexcept;
            +
            template<eve::floating_ordered_value T> constexpr T trunc(T z) noexcept;
            }
            kyosu::trunc
            constexpr tags::callable_trunc trunc
            Computes the trunc value.
            Definition: trunc.hpp:73
            kyosu
            Main KYOSU namespace.
            Definition: beta.hpp:13
            diff --git a/group__functions_ga5ed3799fdd8b66d17a274669dcf3319b.html b/group__functions_ga5ed3799fdd8b66d17a274669dcf3319b.html index f732c0d9..d0d794bd 100644 --- a/group__functions_ga5ed3799fdd8b66d17a274669dcf3319b.html +++ b/group__functions_ga5ed3799fdd8b66d17a274669dcf3319b.html @@ -142,16 +142,16 @@

            -

            test the parameter for zero equality.

            +

            test the parameter for equality to zero.

            Defined in Header

            #include <kyosu/functions.hpp>

            Callable Signatures

            namespace kyosu
            {
            template<kyosu::concepts::cayley_dickson T> constexpr auto is_eqz(T z) noexcept;
            -
            template<eve::ordered_value T> constexpr auto is_eqz(T z) noexcept;
            +
            template<eve::floating_ordered_value T> constexpr auto is_eqz(T z) noexcept;
            }
            -
            kyosu::is_eqz
            constexpr tags::callable_is_eqz is_eqz
            test the parameter for zero equality.
            Definition: is_eqz.hpp:72
            +
            kyosu::is_eqz
            constexpr tags::callable_is_eqz is_eqz
            test the parameter for equality to zero.
            Definition: is_eqz.hpp:72
            kyosu
            Main KYOSU namespace.
            Definition: beta.hpp:13

            Parameters

              diff --git a/group__functions_ga6061b321a4cb255fbbcae1992d42aafa.html b/group__functions_ga6061b321a4cb255fbbcae1992d42aafa.html index 21c2a8b6..cd0ddb0f 100644 --- a/group__functions_ga6061b321a4cb255fbbcae1992d42aafa.html +++ b/group__functions_ga6061b321a4cb255fbbcae1992d42aafa.html @@ -142,23 +142,23 @@

              -

              Computes the hyperbolic cscant of the argument.

              +

              Computes the hyperbolic cosecant of the argument.

              Defined in Header

              #include <kyosu/functions.hpp>

              Callable Signatures

              namespace kyosu
              {
              template<kyosu::concepts::cayley_dickson T> constexpr T csch(T z) noexcept;
              -
              template<eve::ordered_value T> constexpr T csch(T z) noexcept;
              +
              template<eve::floating_ordered_value T> constexpr T csch(T z) noexcept;
              }
              -
              kyosu::csch
              constexpr tags::callable_csch csch
              Computes the hyperbolic cscant of the argument.
              Definition: csch.hpp:73
              +
              kyosu::csch
              constexpr tags::callable_csch csch
              Computes the hyperbolic cosecant of the argument.
              Definition: csch.hpp:73
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

              • z : Value to process.

              Return value

              -

              Returns the hyperbolic cscant of the argument.

              +

              Returns the hyperbolic cosecant of the argument.

              Example

              #include <kyosu/kyosu.hpp>
              #include <eve/wide.hpp>
              diff --git a/group__functions_ga606d275eaf727424c499a9ddb6a09cd6.html b/group__functions_ga606d275eaf727424c499a9ddb6a09cd6.html index 25f7a842..f60d80c0 100644 --- a/group__functions_ga606d275eaf727424c499a9ddb6a09cd6.html +++ b/group__functions_ga606d275eaf727424c499a9ddb6a09cd6.html @@ -142,23 +142,23 @@

              -

              Computes the secant of the argument in \(\pi\) mutiples.

              +

              Computes the secant of the argument in \(\pi\) multiples.

              Defined in Header

              #include <kyosu/functions.hpp>

              Callable Signatures

              namespace kyosu
              {
              -
              template<kyosu::concepts::cayley_dickson T> constexpr T secpi(T z) noexcept;
              -
              template<eve::ordered_value T> constexpr T secpi(T z) noexcept;
              +
              template<kyosu::concepts::cayley_dickson T> constexpr auto secpi(T z) noexcept;
              +
              template<eve::floating_ordered_value T> constexpr auto secpi(T z) noexcept;
              }
              -
              kyosu::secpi
              constexpr tags::callable_secpi secpi
              Computes the secant of the argument in mutiples.
              Definition: secpi.hpp:73
              +
              kyosu::secpi
              constexpr tags::callable_secpi secpi
              Computes the secant of the argument in multiples.
              Definition: secpi.hpp:73
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

              • z : Value to process.

              Return value

              -

              Returns the secant of the argument in \(\pi\) mutiples.

              +

              Returns the secant of the argument in \(\pi\) multiples.

              Example

              #include <kyosu/kyosu.hpp>
              #include <eve/wide.hpp>
              diff --git a/group__functions_ga61fefac92fc13470ee246ab0a77a8008.html b/group__functions_ga61fefac92fc13470ee246ab0a77a8008.html index 00477305..6220cbce 100644 --- a/group__functions_ga61fefac92fc13470ee246ab0a77a8008.html +++ b/group__functions_ga61fefac92fc13470ee246ab0a77a8008.html @@ -146,21 +146,18 @@

              #include <kyosu/functions.hpp>

              Callable Signatures

              -
              namespace kyosu
              -
              {
              -
              template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto average(T0 z0, T1, z1) noexcept;
              -
              template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto average(T0 z0, T1, z1) noexcept;
              -
              template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto average(T0 z0, T1, z1) noexcept;
              -
              template<eve::ordered_value T0, ordered_value T1> > constexpr auto average(T0 z0, T1, z1) noexcept;
              -
              ! }
              -
              kyosu::average
              constexpr tags::callable_average average
              Computes the average of the two parameters.
              Definition: average.hpp:77
              +
              namespace kyosu
              +
              {
              +
              constexpr auto average(auto z0, auto, z1) noexcept;
              +
              }
              +
              kyosu::average
              constexpr tags::callable_average average
              Computes the average of the two parameters.
              Definition: average.hpp:74
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

                -
              • z0, z1 : Value to process.
                • +
              • z0, z1 : Value to process. Can be a mix of complex and real floating values and complex values.

              Return value

              -

              Returns the average of the two arguments .

              +

              Returns the arithmetic mean of the two arguments.

              Example

              #include <kyosu/kyosu.hpp>
              #include <eve/wide.hpp>
              diff --git a/group__functions_ga64a0550a46270d01b31593e38a364f72.html b/group__functions_ga64a0550a46270d01b31593e38a364f72.html index 5bff04c8..4a489aea 100644 --- a/group__functions_ga64a0550a46270d01b31593e38a364f72.html +++ b/group__functions_ga64a0550a46270d01b31593e38a364f72.html @@ -142,34 +142,24 @@

              -

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

              +

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

              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
              +
              auto beta(auto x, auto y) noexcept;
              }
              -
              kyosu::beta
              constexpr tags::callable_beta beta
              Computes the beta function: .
              Definition: beta.hpp:84
              +
              kyosu::beta
              constexpr tags::callable_beta beta
              Computes the beta function: for real or complex entries.
              Definition: beta.hpp:76
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

                -
              • x,y : Values to process.
                • +
              • x,y : Values to process. Can be a mix of complex and real floating values and complex values.

              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. +
              3. If x and y are real typed values returns \(\displaystyle \mathbf{B}(x,y) = \int_0^1 t^{x-1}(1-t)^{y-1}\mbox{d}t\)
                4. +
              4. The complex value \(\displaystyle \mathbb{B}(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) is returned.

              Example

              #include <kyosu/kyosu.hpp>
              diff --git a/group__functions_ga660e094a5a7d9c646c30eeb9273ef80a.html b/group__functions_ga660e094a5a7d9c646c30eeb9273ef80a.html index 7154a08e..059e5267 100644 --- a/group__functions_ga660e094a5a7d9c646c30eeb9273ef80a.html +++ b/group__functions_ga660e094a5a7d9c646c30eeb9273ef80a.html @@ -146,14 +146,11 @@

              #include <kyosu/functions.hpp>

              Callable Signatures

              -
              namespace kyosu
              -
              {
              -
              template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto slerp(T0 z0, T1, z1, auto eve::ordered_value t) noexcept;
              -
              template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto slerp(T0 z0, T1, z1, auto eve::ordered_value t) noexcept;
              -
              template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto slerp(T0 z0, T1, z1, auto eve::ordered_value t) noexcept;
              -
              template<eve::ordered_value T0, ordered_value T1> > constexpr auto slerp(T0 z0, T1, z1, auto eve::ordered_value t) noexcept;
              -
              ! }
              -
              kyosu::slerp
              constexpr tags::callable_slerp slerp
              Computes the spherical interpolation between unitary quaternions.
              Definition: slerp.hpp:82
              +
              namespace kyosu
              +
              {
              +
              constexpr auto lerp(auto z0, auto, z1, floating_ordered_value t) noexcept;
              +
              }
              +
              kyosu::lerp
              constexpr tags::callable_lerp lerp
              Computes the linear interpolation.
              Definition: lerp.hpp:80
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

                @@ -221,6 +218,7 @@

                Example

                return 0;
                }
                +
                kyosu::slerp
                constexpr tags::callable_slerp slerp
                Computes the spherical interpolation between unitary quaternions.
                Definition: slerp.hpp:79
                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_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_ga6658defe6cc879802872ceb5e92749a9.html b/group__functions_ga6658defe6cc879802872ceb5e92749a9.html index 0da03914..01f5d721 100644 --- a/group__functions_ga6658defe6cc879802872ceb5e92749a9.html +++ b/group__functions_ga6658defe6cc879802872ceb5e92749a9.html @@ -148,8 +148,8 @@

                Callable Signatures

                namespace kyosu
                {
                -
                template<kyosu::concepts::cayley_dickson T> constexpx2r T expx2(T z) noexcept;
                -
                template<eve::ordered_value T> constexpx2r T expx2(T z) noexcept;
                +
                template<kyosu::concepts::cayley_dickson T> constexpr T expx2(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr T expx2(T z) noexcept;
                }
                kyosu::expx2
                constexpr tags::callable_expx2 expx2
                Computes the exponential of the squared argument.
                Definition: expx2.hpp:73
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                diff --git a/group__functions_ga680756a6a228206f45212247b16d5961.html b/group__functions_ga680756a6a228206f45212247b16d5961.html index 3184b5fb..79351aa4 100644 --- a/group__functions_ga680756a6a228206f45212247b16d5961.html +++ b/group__functions_ga680756a6a228206f45212247b16d5961.html @@ -142,23 +142,23 @@

                -

                Computes the tangent of the argument in \(\pi\) mutiples.

                +

                Computes the tangent of the argument in \(\pi\) multiples.

                Defined in Header

                #include <kyosu/functions.hpp>

                Callable Signatures

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexpr T tanpi(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr T tanpi(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr T tanpi(T z) noexcept;
                }
                -
                kyosu::tanpi
                constexpr tags::callable_tanpi tanpi
                Computes the tangent of the argument in mutiples.
                Definition: tanpi.hpp:73
                +
                kyosu::tanpi
                constexpr tags::callable_tanpi tanpi
                Computes the tangent of the argument in multiples.
                Definition: tanpi.hpp:73
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                • z : Value to process.

                Return value

                -

                Returns the tangent of the argument in \(\pi\) mutiples.

                +

                Returns the tangent of the argument in \(\pi\) multiples.

                Example

                #include <kyosu/kyosu.hpp>
                #include <eve/wide.hpp>
                diff --git a/group__functions_ga686170a43d13c97096af719b7c0e7fda.html b/group__functions_ga686170a43d13c97096af719b7c0e7fda.html index 72ee9023..a5d86f3f 100644 --- a/group__functions_ga686170a43d13c97096af719b7c0e7fda.html +++ b/group__functions_ga686170a43d13c97096af719b7c0e7fda.html @@ -149,7 +149,7 @@

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexpr auto is_nan(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr auto is_nan(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr auto is_nan(T z) noexcept;
                }
                kyosu::is_nan
                constexpr tags::callable_is_nan is_nan
                test if the parameter is nan.
                Definition: is_nan.hpp:72
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                @@ -158,7 +158,7 @@

                Example

                #include <kyosu/kyosu.hpp>
                #include <eve/wide.hpp>
                diff --git a/group__functions_ga8e88be0e83296a515c882ad40e828386.html b/group__functions_ga6a75cd107789510275cb469d917ea79b.html similarity index 66% rename from group__functions_ga8e88be0e83296a515c882ad40e828386.html rename to group__functions_ga6a75cd107789510275cb469d917ea79b.html index 4597ed74..8f67c4b6 100644 --- a/group__functions_ga8e88be0e83296a515c882ad40e828386.html +++ b/group__functions_ga6a75cd107789510275cb469d917ea79b.html @@ -6,7 +6,7 @@ -kyosu: kyosu::imag +kyosu: kyosu::pure @@ -96,7 +96,7 @@
                @@ -122,8 +122,8 @@
                - -

                ◆ imag

                + +

                ◆ pure

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

                - +
                kyosu::imag = {}kyosu::pure = {}
                @@ -142,24 +142,23 @@

                -

                Alias for ipart.

                -

                Extracts the imaginary part of a value.

                +

                Extracts the imaginary part of a value.

                Defined in Header

                #include <kyosu/functions.hpp>

                Callable Signatures

                namespace kyosu
                {
                -
                template<kyosu::concepts::cayley_dickson T> constexpr auto& ipart(T& z) noexcept;
                -
                template<kyosu::concepts::cayley_dickson T> constexpr auto ipart(T const& z) noexcept;
                -
                template<eve::ordered_value T> constexpr T ipart(T const& z) noexcept;
                +
                template<kyosu::concepts::cayley_dickson T> constexpr auto pure(T const& z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr T pure(T const& z) noexcept;
                }
                +
                kyosu::pure
                constexpr tags::callable_pure pure
                Extracts the imaginary part of a value.
                Definition: pure.hpp:77
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                • z : Original value.

                Return value

                -

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

                +

                Returns the pure (also called 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>
                @@ -177,50 +176,13 @@

                Example

                std::cout
                << "---- simd" << std::endl
                << "<- zc = " << zc << std::endl
                -
                << "-> imag(zc) = " << kyosu::imag(zc)<< std::endl
                -
                << "-> imag(ref2) = " << kyosu::imag(ref2) << 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::imag
                constexpr tags::callable_ipart imag
                Alias for ipart.
                Definition: ipart.hpp:85
                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
                -
                {
                -
                template<kyosu::concepts::cayley_dickson T> constexpr auto& pure(T& z) noexcept;
                -
                template<kyosu::concepts::cayley_dickson T> constexpr auto pure(T const& z) noexcept;
                -
                template<eve::ordered_value T> constexpr T pure(T const& z) noexcept;
                -
                }
                -

                Parameters

                -
                  -
                • z : Original value.
                  • -
                -

                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_ga6caf1752927065dfc9ab769d9b00676a.html b/group__functions_ga6caf1752927065dfc9ab769d9b00676a.html index f046e837..7999dac7 100644 --- a/group__functions_ga6caf1752927065dfc9ab769d9b00676a.html +++ b/group__functions_ga6caf1752927065dfc9ab769d9b00676a.html @@ -142,20 +142,20 @@

                -

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

                +

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

                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;
                +
                template<eve::floating_ordered_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::digamma
                constexpr tags::callable_digamma digamma
                Computes the Digamma function i.e. the logarithmic derivative of the function.
                Definition: digamma.hpp:73
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                  -
                • z : Value to process.
                  • +
                • z : real or complex value to process.

                Return value

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

                diff --git a/group__functions_ga6d65485712648eb40b8dc0453d9c3baf.html b/group__functions_ga6d65485712648eb40b8dc0453d9c3baf.html index 9f49be4e..73e572d6 100644 --- a/group__functions_ga6d65485712648eb40b8dc0453d9c3baf.html +++ b/group__functions_ga6d65485712648eb40b8dc0453d9c3baf.html @@ -148,10 +148,9 @@

                Callable Signatures

                namespace kyosu
                {
                -
                template<eve::value T, eve::value U, eve::value V>
                -
                constexpr auto if_else(T x, U, y, V z ) noexcept;
                +
                template<eve::value T, eve::value U, eve::value V> constexpr auto if_else(T x, U, y, V z ) noexcept;
                }
                -
                kyosu::if_else
                constexpr tags::callable_if_else if_else
                Select a value between two arguments based on a logical mask.
                Definition: if_else.hpp:66
                +
                kyosu::if_else
                constexpr tags::callable_if_else if_else
                Select a value between two arguments based on a logical mask.
                Definition: if_else.hpp:65
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                  diff --git a/group__functions_ga6e37d60fa6fa7ac76d0c5d9c8417d854.html b/group__functions_ga6e37d60fa6fa7ac76d0c5d9c8417d854.html index ee8a913e..6fcc3ba3 100644 --- a/group__functions_ga6e37d60fa6fa7ac76d0c5d9c8417d854.html +++ b/group__functions_ga6e37d60fa6fa7ac76d0c5d9c8417d854.html @@ -149,7 +149,7 @@

                  Callable Signatures

                  namespace kyosu
                  {
                  -
                  template<eve::ordered_value T> constexpr auto acsch(T z) noexcept; //1
                  +
                  template<eve::floating_ordered_value T> constexpr auto acsch(T z) noexcept; //1
                  template<kyosu::concepts::cayley_dickson T> constexpr auto acsch(T z) noexcept; //2
                  }
                  kyosu::acsch
                  constexpr tags::callable_acsch acsch
                  Computes the inverse hyperbolic cosecant of the argument.
                  Definition: acsch.hpp:80
                  @@ -160,7 +160,7 @@

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

                  • Example

                  @@ -191,7 +191,7 @@

                  Example

                  Callable Signatures

                  namespace kyosu
                  {
                  -
                  template<eve::ordered_value T> constexpr auto acsch(T z) noexcept; //1
                  +
                  template<eve::floating_ordered_value T> constexpr auto acsch(T z) noexcept; //1
                  template<kyosu::concepts::complex T> constexpr auto acsch(T z) noexcept; //2
                  }

                  Parameters

                  @@ -200,7 +200,7 @@

                  Example

                Return value

                  -
                1. a real input z is treated as if complex(z) was entered.
                  2. +
                2. a real input z is treated as if kyosu::complex(z) was entered.
                3. Returns elementwise asinh(1/z).

                Example

                diff --git a/group__functions_ga6ead34ff89aeb18c2380188af5f83dcd.html b/group__functions_ga6ead34ff89aeb18c2380188af5f83dcd.html index 0e37e64f..a6629153 100644 --- a/group__functions_ga6ead34ff89aeb18c2380188af5f83dcd.html +++ b/group__functions_ga6ead34ff89aeb18c2380188af5f83dcd.html @@ -149,7 +149,7 @@

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexpr T sqr(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr T sqr(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr T sqr(T z) noexcept;
                }
                kyosu::sqr
                constexpr tags::callable_sqr sqr
                Computes the square value.
                Definition: sqr.hpp:72
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                diff --git a/group__functions_ga6f78a4312ac7bd38e25d0b09b18fe3e6.html b/group__functions_ga6f78a4312ac7bd38e25d0b09b18fe3e6.html index e0051341..de3e31a8 100644 --- a/group__functions_ga6f78a4312ac7bd38e25d0b09b18fe3e6.html +++ b/group__functions_ga6f78a4312ac7bd38e25d0b09b18fe3e6.html @@ -148,17 +148,37 @@

                Callable Signatures

                namespace kyosu
                {
                -
                template<kyosu::concepts::cayley_dickson T> constexpr T sqrt(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr T sqrt(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr T sqrt(T z) noexcept; //1
                +
                template<kyosu::concepts::complex T> constexpr T sqrt(T z) noexcept; //2
                +
                template<kyosu::concepts::cayley_dickson T> constexpr T sqrt(T z) noexcept; //3
                }
                -
                kyosu::sqrt
                constexpr tags::callable_sqrt sqrt
                Computes a square root value.
                Definition: sqrt.hpp:78
                +
                kyosu::sqrt
                constexpr tags::callable_sqrt sqrt
                Computes a square root value.
                Definition: sqrt.hpp:98
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                • z : Value to for which square root is computed.

                Return value

                -

                Returns a square root of its argument.

                +
                  +
                1. a real typed input z is treated as if kyosu::complex(z) was entered.
                  2. +
                2. Returns the elementwise the square root of z, in the range of the right half-plane, including the imaginary axis ( \([0, +\infty]\) along the real axis and \([-\infty, +\infty]\) along the imaginary axis.)
                    +
                  • The function is continuous onto the branch cut taking into account the sign of imaginary part
                    • +
                  • eve::sqrt(kyosu::conj(z)) == kyosu::conj(kyosu::sqrt(z))
                    • +
                  • If z is \(\pm0\), the result is \(+0\)
                    • +
                  • If z is \(x+i \infty\), the result is \(\infty+i \infty\) even if x is \(NaN\)
                    • +
                  • If z is \(x,NaN\), the result is \(NaN,NaN\) (unless x is \(\pm\infty\))
                    • +
                  • If z is \(-\infty+i y\), the result is \(+0+i \infty\) for finite positive y
                    • +
                  • If z is \(+\infty+i y\), the result is \(+\infty+i 0\) for finite positive y
                    • +
                  • If z is \(-\infty+i NaN\), the result is \(NaN \pm i \infty\) (sign of imaginary part unspecified)
                    • +
                  • If z is \(+\infty+i NaN\), the result is \(+\infty+i NaN\)
                    • +
                  • If z is \(NaN+i y\), the result is \(NaN+i NaN\)
                    • +
                  • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)
                    • +
                  +
                  3. +
                +
                  +
                1. Returns a square root of z.
                  2. +

                Example

                #include <kyosu/kyosu.hpp>
                #include <eve/wide.hpp>
                diff --git a/group__functions_ga72bd8b3dcf975e0e9bb4e5e83df4f4a0.html b/group__functions_ga72bd8b3dcf975e0e9bb4e5e83df4f4a0.html index 69d927d4..892415f7 100644 --- a/group__functions_ga72bd8b3dcf975e0e9bb4e5e83df4f4a0.html +++ b/group__functions_ga72bd8b3dcf975e0e9bb4e5e83df4f4a0.html @@ -148,7 +148,7 @@

                Callable Signatures

                namespace kyosu
                {
                -
                template<eve::ordered_value T> constexpr auto acoth(T z) noexcept; //1
                +
                template<eve::floating_ordered_value T> constexpr auto acoth(T z) noexcept; //1
                template<kyosu::concepts::complex T> constexpr auto acoth(T z) noexcept; //2
                template<kyosu::concepts::cayley_dickson T> constexpr auto acoth(T z) noexcept; //3
                }
                @@ -160,7 +160,7 @@

                -
              • a real input z is treated as if complex(z) was entered.
                • +
              • a real input z is treated as if kyosu::complex(z) was entered.
              • Returns the complex inverse hyperbolic cotangent of z, computed as \(\mathop{\mathrm{atanh}}(1/z)\).
              • Returns \((\log(z+1)-\log(z-1))/2 \).
                • diff --git a/group__functions_ga738d6a61ebf48d0bacd80f958d1b590b.html b/group__functions_ga738d6a61ebf48d0bacd80f958d1b590b.html index 54891632..471ac235 100644 --- a/group__functions_ga738d6a61ebf48d0bacd80f958d1b590b.html +++ b/group__functions_ga738d6a61ebf48d0bacd80f958d1b590b.html @@ -159,7 +159,7 @@

                -
              • a real input z is treated as if complex(z) was entered.
                • +
              • a real input z return eve::erfcx(z).
              • The value of the normalized complementary error function is returned.

                • Example

                diff --git a/group__functions_ga7586f69da3dd2de8eb36e571d0cda51a.html b/group__functions_ga7586f69da3dd2de8eb36e571d0cda51a.html index 07f0c34e..855e3701 100644 --- a/group__functions_ga7586f69da3dd2de8eb36e571d0cda51a.html +++ b/group__functions_ga7586f69da3dd2de8eb36e571d0cda51a.html @@ -148,11 +148,11 @@

                Callable Signatures

                namespace kyosu
                {
                -
                template<eve::ordered_value T> constexpr auto asin(T z) noexcept; //1
                +
                template<eve::floating_ordered_value T> constexpr auto asin(T z) noexcept; //1
                template<kyosu::concepts::complex T> constexpr auto asin(T z) noexcept; //2
                template<kyosu::concepts::cayley_dickson T> constexpr auto acos(T z) noexcept; //3
                }
                -
                kyosu::acos
                constexpr tags::callable_acos acos
                Computes the acosine of the argument.
                Definition: acos.hpp:100
                +
                kyosu::acos
                constexpr tags::callable_acos acos
                Computes the acosine of the argument.
                Definition: acos.hpp:101
                kyosu::asin
                constexpr tags::callable_asin asin
                Computes the arcsine of the argument.
                Definition: asin.hpp:87
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                @@ -161,11 +161,11 @@

                -
              • a real input z is treated as if complex(z) was entered.
                • +
              • a real input z is treated as if kyosu::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 \(-i\; \mathrm{asinh}(z\; i)\)

                • -
              • Returns \(-I_z \mathrm{asinh}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).
                • +
              • Returns \(-I_z \mathrm{asinh}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).

                • Example

                #include <kyosu/kyosu.hpp>
                diff --git a/group__functions_ga761c2a207a0417867f0eb4b3dc30ee2b.html b/group__functions_ga761c2a207a0417867f0eb4b3dc30ee2b.html index 98c30f9c..8fe79a03 100644 --- a/group__functions_ga761c2a207a0417867f0eb4b3dc30ee2b.html +++ b/group__functions_ga761c2a207a0417867f0eb4b3dc30ee2b.html @@ -142,23 +142,23 @@

                -

                Computes the exponential of the argument times i.

                +

                Computes the exponential of \(i\pi\) times the argument.

                Defined in Header

                #include <kyosu/functions.hpp>

                Callable Signatures

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexp_ipir T exp_ipi(T z) noexcept;
                -
                template<eve::ordered_value T> constexp_ipir T exp_ipi(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexp_ipir T exp_ipi(T z) noexcept;
                }
                -
                kyosu::exp_ipi
                constexpr tags::callable_exp_ipi exp_ipi
                Computes the exponential of the argument times i.
                Definition: exp_ipi.hpp:78
                +
                kyosu::exp_ipi
                constexpr tags::callable_exp_ipi exp_ipi
                Computes the exponential of times the argument.
                Definition: exp_ipi.hpp:78
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                • z : Value to process.

                Return value

                -

                Returns the exp(i*z).

                +

                Returns exp(i*pi(as(z))*z).

                Example

                #include <kyosu/kyosu.hpp>
                #include <eve/wide.hpp>
                diff --git a/group__functions_ga764d5554dc7ce3cac3302591c4d75947.html b/group__functions_ga764d5554dc7ce3cac3302591c4d75947.html index 9183f012..ffadd2c6 100644 --- a/group__functions_ga764d5554dc7ce3cac3302591c4d75947.html +++ b/group__functions_ga764d5554dc7ce3cac3302591c4d75947.html @@ -146,21 +146,18 @@

                #include <kyosu/functions.hpp>

                Callable Signatures

                -
                namespace kyosu
                -
                {
                -
                template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto pow_abs(T0 z0, T1, z1) noexcept;
                -
                template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto pow_abs(T0 z0, T1, z1) noexcept;
                -
                template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto pow_abs(T0 z0, T1, z1) noexcept;
                -
                template<eve::ordered_value T0, ordered_value T1> > constexpr auto pow_abs(T0 z0, T1, z1) noexcept;
                -
                ! }
                -
                kyosu::pow_abs
                constexpr tags::callable_pow_abs pow_abs
                Computes the computing the pow_abs operation .
                Definition: pow_abs.hpp:77
                +
                namespace kyosu
                +
                {
                +
                constexpr auto pow_abs(auto z0, auto, z1) noexcept;
                +
                }
                +
                kyosu::pow_abs
                constexpr tags::callable_pow_abs pow_abs
                Computes the computing the pow_abs operation .
                Definition: pow_abs.hpp:75
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                • z0, z1 : Values to process.

                Return value

                -

                the call is semantically equivalent to eve::exp(abs(z1)*log(z0))

                +

                the call is semantically equivalent to kyosu::exp(log_abs(z0)*z1) In particular if z1 is floating typed the result is floating_typed, which is not the case of kyosu::pow(abs(z0), z1);

                Example

                #include <kyosu/kyosu.hpp>
                #include <eve/wide.hpp>
                diff --git a/group__functions_ga783725b137881f9e6e60e1f9b3bae9fc.html b/group__functions_ga783725b137881f9e6e60e1f9b3bae9fc.html index 6a08cc86..d31a4689 100644 --- a/group__functions_ga783725b137881f9e6e60e1f9b3bae9fc.html +++ b/group__functions_ga783725b137881f9e6e60e1f9b3bae9fc.html @@ -149,7 +149,7 @@

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexpr T cot(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr T cot(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr T cot(T z) noexcept;
                }
                kyosu::cot
                constexpr tags::callable_cot cot
                Computes the cotangent of the argument.
                Definition: cot.hpp:73
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                diff --git a/group__functions_ga7859bd9f30d2ef73a22fc8d114faea47.html b/group__functions_ga7859bd9f30d2ef73a22fc8d114faea47.html index 6ce1ae61..4eed37f7 100644 --- a/group__functions_ga7859bd9f30d2ef73a22fc8d114faea47.html +++ b/group__functions_ga7859bd9f30d2ef73a22fc8d114faea47.html @@ -142,17 +142,17 @@

                -

                Computes the inverse hyperbolic tangent of the argument.

                +

                Computes the arctangent of the argument.

                Defined in Header

                #include <kyosu/functions.hpp>

                Callable Signatures

                namespace kyosu
                {
                -
                template<eve::ordered_value T> constexpr auto atan(T z) noexcept; //1
                +
                template<eve::floating_ordered_value T> constexpr auto atan(T z) noexcept; //1
                template<kyosu::concepts::complex T> constexpr auto atan(T z) noexcept; //2
                template<kyosu::concepts::cayley_dickson T> constexpr auto atan(T z) noexcept; //3
                }
                -
                kyosu::atan
                constexpr tags::callable_atan atan
                Computes the inverse hyperbolic tangent of the argument.
                Definition: atan.hpp:86
                +
                kyosu::atan
                constexpr tags::callable_atan atan
                Computes the arctangent of the argument.
                Definition: atan.hpp:86
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                  @@ -160,9 +160,9 @@

                  -
                • a real input z is treated as if complex(z) was entered.
                  • +
                • a real input z is treated as if kyosu::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 \(-i\; \mathrm{atanh}(z\; i)\).
                  • -
                • Returns \( -I_z \mathrm{atanh}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).
                  • +
                • Returns \( -I_z \mathrm{atanh}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).

                  • Example

                  #include <kyosu/kyosu.hpp>
                  diff --git a/group__functions_ga788b51ca9d3366567828c74d46f12168.html b/group__functions_ga788b51ca9d3366567828c74d46f12168.html index 28464be2..71c5f01d 100644 --- a/group__functions_ga788b51ca9d3366567828c74d46f12168.html +++ b/group__functions_ga788b51ca9d3366567828c74d46f12168.html @@ -148,17 +148,22 @@

                  Callable Signatures

                  namespace kyosu
                  {
                  -
                  template<kyosu::concepts::cayley_dickson T> constexpr T cos(T z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T cos(T z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T cos(T z) noexcept; //1
                  +
                  template<kyosu::concepts::complex T> constexpr T cos(T z) noexcept; //2
                  +
                  template<kyosu::concepts::cayley_dickson T> constexpr T cos(T z) noexcept; //3
                  }
                  -
                  kyosu::cos
                  constexpr tags::callable_cos cos
                  Computes the cosine of the argument.
                  Definition: cos.hpp:73
                  +
                  kyosu::cos
                  constexpr tags::callable_cos cos
                  Computes the cosine of the argument.
                  Definition: cos.hpp:79
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

                  • z : Value to process.

                  Return value

                  -

                  Returns the cosine of the argument.

                  +
                    +
                  1. Returns the cosine of the argument.
                    2. +
                  2. The behavior of this function is equivalent to eve::cosh(i*z).
                    3. +
                  +

                  3 Returns \(\cosh(I_z\; z)\) if \(z\) is not zero else \(\cos(z_0)\), where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  diff --git a/group__functions_ga7ab67d971ae8c2c4d99fe414d6085116.html b/group__functions_ga7ab67d971ae8c2c4d99fe414d6085116.html index 1416ff8d..3f015181 100644 --- a/group__functions_ga7ab67d971ae8c2c4d99fe414d6085116.html +++ b/group__functions_ga7ab67d971ae8c2c4d99fe414d6085116.html @@ -149,7 +149,7 @@

                  namespace kyosu
                  {
                  template<kyosu::concepts::cayley_dickson T> constexpr auto is_nez(T z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr auto is_nez(T z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr auto is_nez(T z) noexcept;
                  }
                  kyosu::is_nez
                  constexpr tags::callable_is_nez is_nez
                  test the parameter for non zero equality.
                  Definition: is_nez.hpp:72
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13
                  @@ -158,7 +158,7 @@

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  diff --git a/group__functions_ga7ad40bb479ce858eed855c2819c4ab22.html b/group__functions_ga7ad40bb479ce858eed855c2819c4ab22.html index 050c96bc..c7b3dc05 100644 --- a/group__functions_ga7ad40bb479ce858eed855c2819c4ab22.html +++ b/group__functions_ga7ad40bb479ce858eed855c2819c4ab22.html @@ -155,10 +155,10 @@

                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

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

                  Return value

                  -

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

                  +

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

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  diff --git a/group__functions_ga7bde9020d5e1ce1e69cdb7b011ef0a7d.html b/group__functions_ga7bde9020d5e1ce1e69cdb7b011ef0a7d.html index 20c6ee74..20a410e0 100644 --- a/group__functions_ga7bde9020d5e1ce1e69cdb7b011ef0a7d.html +++ b/group__functions_ga7bde9020d5e1ce1e69cdb7b011ef0a7d.html @@ -142,22 +142,19 @@

                  -

                  retuen true if and only if the two parameters are equal.

                  +

                  return true if and only if the two parameters are not equal.

                  Defined in Header

                  #include <kyosu/functions.hpp>

                  Callable Signatures

                  -
                  namespace kyosu
                  -
                  {
                  -
                  template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto is_not_equal(T0 z0, T1, z1) noexcept;
                  -
                  template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto is_not_equal(T0 z0, T1, z1) noexcept;
                  -
                  template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto is_not_equal(T0 z0, T1, z1) noexcept;
                  -
                  template<eve::ordered_value T0, ordered_value T1> > constexpr auto is_not_equal(T0 z0, T1, z1) noexcept;
                  -
                  ! }
                  -
                  kyosu::is_not_equal
                  constexpr tags::callable_is_not_equal is_not_equal
                  retuen true if and only if the two parameters are equal.
                  Definition: is_not_equal.hpp:79
                  +
                  namespace kyosu
                  +
                  {
                  +
                  constexpr auto is_equal(auto z0, auto z1) noexcept;
                  +
                  }
                  +
                  kyosu::is_equal
                  constexpr tags::callable_is_equal is_equal
                  retuen true if and only if the two parameters are equal.
                  Definition: is_equal.hpp:76
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

                    -
                  • z0, z1 : Value to process.
                    • +
                  • z0, z1 : Values to process.

                  Return value

                  Returns elemtwise true or false according the inequality of the parameters

                  @@ -207,6 +204,7 @@

                  Example

                  return 0;
                  }
                  +
                  kyosu::is_not_equal
                  constexpr tags::callable_is_not_equal is_not_equal
                  return true if and only if the two parameters are not equal.
                  Definition: is_not_equal.hpp:76
                  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_ga80b0877803d92aafcb11e1c641f7f0fd.html b/group__functions_ga80b0877803d92aafcb11e1c641f7f0fd.html index b74df86b..8ce9447d 100644 --- a/group__functions_ga80b0877803d92aafcb11e1c641f7f0fd.html +++ b/group__functions_ga80b0877803d92aafcb11e1c641f7f0fd.html @@ -142,24 +142,24 @@

                  -

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

                  +

                  Computes the Dirichlet sums \( \displaystyle \sum_{n = 0}^\infty \frac{(-1)^n}{(kn+1)^z}\).

                  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
                  +
                  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: beta.hpp:13

                  Parameters

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

                  Return value

                  -

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

                  +

                  Returns the Dirichlet sum \( \displaystyle \sum_{n = 0}^\infty \frac{(-1)^n}{(kn+1)^z}\)

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  diff --git a/group__functions_ga842342e7ca73ffdcaa7ca9141e45d56f.html b/group__functions_ga842342e7ca73ffdcaa7ca9141e45d56f.html index 0e297f38..21b50989 100644 --- a/group__functions_ga842342e7ca73ffdcaa7ca9141e45d56f.html +++ b/group__functions_ga842342e7ca73ffdcaa7ca9141e45d56f.html @@ -150,16 +150,16 @@

                  {

                  template<kyosu::concepts::cayley_dickson T> constexpr auto& jpart(T& z) noexcept;
                  template<kyosu::concepts::cayley_dickson T> constexpr auto jpart(T const& z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T jpart(T const& z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T jpart(T const& z) noexcept;
                  }
                  -
                  kyosu::jpart
                  constexpr tags::callable_jpart jpart
                  Extracts the part of a value.
                  Definition: jpart.hpp:72
                  +
                  kyosu::jpart
                  constexpr tags::callable_jpart jpart
                  Extracts the part of a value.
                  Definition: jpart.hpp:73
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

                  • z : Original value.

                  Return value

                  -

                  Returns the \(j\) part of its argument. For real and complex inputs, the call returns 0.

                  +

                  Returns the \(j\) part of its argument. For real and complex inputs, the call returns 0. Its the third coefficient in the z representation and so is 0 for complex and floating.

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  diff --git a/group__functions_ga87e87a2d786aa520b7a6f37208f369bc.html b/group__functions_ga87e87a2d786aa520b7a6f37208f369bc.html index a55556e2..0fb54c37 100644 --- a/group__functions_ga87e87a2d786aa520b7a6f37208f369bc.html +++ b/group__functions_ga87e87a2d786aa520b7a6f37208f369bc.html @@ -156,7 +156,7 @@

                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

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

                  Return value

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

                  diff --git a/group__functions_ga8be5621ef70c215de54eb8683578fa60.html b/group__functions_ga8be5621ef70c215de54eb8683578fa60.html index 4fbc8f6d..ed6786fd 100644 --- a/group__functions_ga8be5621ef70c215de54eb8683578fa60.html +++ b/group__functions_ga8be5621ef70c215de54eb8683578fa60.html @@ -148,8 +148,8 @@

                  Callable Signatures

                  namespace kyosu
                  {
                  -
                  template<kyosu::concepts::cayley_dickson T> constlog_absr T log_abs(T z) noexcept;
                  -
                  template<eve::ordered_value T> constlog_absr T log_abs(T z) noexcept;
                  +
                  template<kyosu::concepts::cayley_dickson T> constlog_absr auto log_abs(T z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constlog_absr auto log_abs(T z) noexcept;
                  }
                  kyosu::log_abs
                  constexpr tags::callable_log_abs log_abs
                  Computes the natural logarithm of the absolute value of the argument.
                  Definition: log_abs.hpp:78
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13
                  diff --git a/group__functions_ga8d6f64b6ed68055ef05917557d2e60b6.html b/group__functions_ga8d6f64b6ed68055ef05917557d2e60b6.html index 0abd656c..4c5cc2e5 100644 --- a/group__functions_ga8d6f64b6ed68055ef05917557d2e60b6.html +++ b/group__functions_ga8d6f64b6ed68055ef05917557d2e60b6.html @@ -149,13 +149,13 @@

                  namespace kyosu
                  {
                  template<kyosu::concepts::cayley_dickson T> constexpr T ceil(T z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T ceil(T z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T ceil(T z) noexcept;
                  }
                  kyosu::ceil
                  constexpr tags::callable_ceil ceil
                  Computes the ceil value.
                  Definition: ceil.hpp:72
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

                    -
                  • z : Value to for which ceil is computed.
                    • +
                  • z : Value for which ceil is computed.

                  Return value

                  Returns the ceil of its argument. i.e. the value with parts are the ceil of the original ones.

                  diff --git a/group__functions_ga8e242553caca873ace58560327d8bd4e.html b/group__functions_ga8e242553caca873ace58560327d8bd4e.html new file mode 100644 index 00000000..f2486a48 --- /dev/null +++ b/group__functions_ga8e242553caca873ace58560327d8bd4e.html @@ -0,0 +1,215 @@ + + + + + + + + +kyosu: kyosu::ljpart + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  + +
                  + + + + + + + + +
                  +
                  kyosu v0.1.0 +
                  +
                  Complex Without Complexes
                  +
                  + +   + + + + +
                  +
                  +
                  + + + + +
                  +
                  + +
                  +
                  +
                  + +
                  + +
                  +
                  + + +
                  +
                  +
                  +
                  +
                  +
                  Loading...
                  +
                  Searching...
                  +
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                  +
                  +
                  +
                  +
                  + +
                  + +

                  ◆ ljpart

                  + +
                  +
                  + + + + + +
                  + + + + +
                  kyosu::ljpart = {}
                  +                   		+inlineconstexpr
                  +
                  + +

                  Extracts the lj (seventh) part of a value.

                  +

                  Defined in Header

                  +
                  #include <kyosu/functions.hpp>
                  +

                  Callable Signatures

                  +
                  namespace kyosu
                  +
                  {
                  +
                  template<kyosu::concepts::cayley_dickson T> constexpr auto& ljpart(T& z) noexcept;
                  +
                  template<kyosu::concepts::cayley_dickson T> constexpr auto ljpart(T const& z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T ljpart(T const& z) noexcept;
                  +
                  }
                  +
                  kyosu::ljpart
                  constexpr tags::callable_ljpart ljpart
                  Extracts the lj (seventh) part of a value.
                  Definition: ljpart.hpp:80
                  +
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13
                  +

                  Parameters

                  +
                    +
                  • z : Original value.
                    • +
                  +

                  Return value

                  +

                  Returns the seventh part of its argument.

                  +

                  For up to quaterion inputs, the call always returns 0.

                  +

                  Example

                  +
                  #include <kyosu/kyosu.hpp>
                  +
                  #include <eve/wide.hpp>
                  +
                  #include <iostream>
                  +
                  +
                  int main()
                  +
                  {
                  +
                  using kyosu::ljpart;
                  +
                  using kyosu::complex_t;
                  +
                  using kyosu::quaternion_t;
                  +
                  +
                  std::cout << "Real: ";
                  +
                  float f = 72.9f;
                  +
                  std::cout << f << " -> " << ljpart(f) << "\n";
                  +
                  +
                  std::cout << "Complex: ";
                  +
                  auto z = kyosu::complex_t<float>(3.5f,-2.9f);
                  +
                  std::cout << z << " -> " << ljpart(z) << "\n";
                  +
                  +
                  std::cout << "Quaternion: ";
                  +
                  auto q = kyosu::quaternion_t<double>(1.,2.,3.,4.);
                  +
                  std::cout << q << " -> " << ljpart(q) << " => ";
                  +
                  +
                  std::cout << "octonion: ";
                  +
                  auto o = kyosu::octonion_t<double>(1.,2.,3.,4.,11.,12.,13.,14.);
                  +
                  std::cout << o << " -> " << ljpart(o) << " => ";
                  +
                  +
                  +
                  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
                  +
                  kyosu::octonion_t
                  as_cayley_dickson_n_t< 8, T > octonion_t
                  Type alias for quaternion numbers.
                  Definition: octonion.hpp:26
                  +
                  +
                  +
                  +
                  +
                  + + + +

                +
                +

                +

                +
                + + diff --git a/group__functions_ga8e2d2c2ba91d22a96ff3603b42e4760d.html b/group__functions_ga8e2d2c2ba91d22a96ff3603b42e4760d.html index ad0de8a3..f09654fe 100644 --- a/group__functions_ga8e2d2c2ba91d22a96ff3603b42e4760d.html +++ b/group__functions_ga8e2d2c2ba91d22a96ff3603b42e4760d.html @@ -149,7 +149,7 @@

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexpr auto is_not_denormal(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr auto is_not_denormal(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr auto is_not_denormal(T z) noexcept;
                }
                kyosu::is_not_denormal
                constexpr tags::callable_is_not_denormal is_not_denormal
                test if the parameter is not denormal.
                Definition: is_not_denormal.hpp:72
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                diff --git a/group__functions_ga8f4895e6ad347a36555c231f430684eb.html b/group__functions_ga8f4895e6ad347a36555c231f430684eb.html new file mode 100644 index 00000000..3077c242 --- /dev/null +++ b/group__functions_ga8f4895e6ad347a36555c231f430684eb.html @@ -0,0 +1,228 @@ + + + + + + + + +kyosu: kyosu::associator + + + + + + + + + + + + + + + + + + + + + + + + + + +
                + +
                + + + + + + + + +
                +
                kyosu v0.1.0 +
                +
                Complex Without Complexes
                +
                + +   + + + + +
                +
                +
                + + + + +
                +
                + +
                +
                +
                + +
                + +
                +
                + + +
                +
                +
                +
                +
                +
                Loading...
                +
                Searching...
                +
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                +
                +
                +
                +
                + +
                + +

                ◆ associator

                + +
                +
                + + + + + +
                + + + + +
                kyosu::associator = {}
                +                 		+inlineconstexpr
                +
                + +

                Computes the associator of the three parameters.

                +

                Defined in Header

                +
                #include <kyosu/functions.hpp>
                +

                Callable Signatures

                +
                namespace kyosu
                +
                {
                +
                constexpr auto associator(auto z0, auto, z1, auto, z2) noexcept;
                +
                }
                +
                kyosu::associator
                constexpr tags::callable_associator associator
                Computes the associator of the three parameters.
                Definition: associator.hpp:75
                +
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                +

                Parameters

                +
                  +
                • z0, z1, z2`: Values to process. Can be a mix of complex and real floating values and complex values.
                  • +
                +

                Return value

                +

                Returns the difference z0*(z1*z2)-(z0*z1)*z2.

                +

                Example

                +
                #include <kyosu/kyosu.hpp>
                +
                #include <eve/wide.hpp>
                +
                #include <iostream>
                +
                +
                int main()
                +
                {
                +
                using kyosu::associator;
                +
                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 o_t = kyosu::octonion_t<float>;
                +
                +
                std::cout << "Real: "<< "\n";
                +
                e_t e0(1);
                +
                e_t e1(2);
                +
                e_t e2(3);
                +
                std::cout << e0 << ", " << e1 << ", " << e2<< " -> " << associator(e0, e1, e2) << "\n";
                +
                +
                std::cout << "Complex: "<< "\n";
                +
                c_t c0(1, 5);
                +
                c_t c1(5, 9);
                +
                c_t c2(-1, 4);
                +
                std::cout << c0 << ", " << c1 << ", " << c2 << " -> " << associator(c0, c1, c2) << "\n";
                +
                +
                std::cout << "Quaternion: "<< "\n";
                +
                q_t q0(1, 5, -2, 3);
                +
                q_t q1(5, 9, 6, 7);
                +
                q_t q2(-3, 6, -1, 0);
                +
                std::cout << q0 << ", " << q1 << ", " << q2 << " -> " << associator(q0, q1, q2) << "\n";
                +
                +
                std::cout << "Octonion: "<< "\n";
                +
                o_t o0(1, 5, -2, 3, 4, 8, 13, 1);
                +
                o_t o1(5, 9, 6, 7, 6, -4, -1, 2);
                +
                o_t o2(-3, 6, -1, 0, 4, 5, -8, 2);
                +
                +
                std::cout << o0 << ", " << o1 << ", " << o2 << " -> " << associator(o0, o1, o2) << "\n";
                +
                std::cout << "Mixed: "<< "\n";
                +
                std::cout << kyosu::associator(c0, o1, o2) << std::endl;
                +
                std::cout << kyosu::associator(o0, o1, e0) << 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
                +
                kyosu::octonion_t
                as_cayley_dickson_n_t< 8, T > octonion_t
                Type alias for quaternion numbers.
                Definition: octonion.hpp:26
                +
                +
                +
                +
                +
                + + + +

                +

                +

                +
              +

              + + diff --git a/group__functions_ga8febd271f0bc94c5fb1d12cd5644778b.html b/group__functions_ga8febd271f0bc94c5fb1d12cd5644778b.html index 54f950f5..651dbf79 100644 --- a/group__functions_ga8febd271f0bc94c5fb1d12cd5644778b.html +++ b/group__functions_ga8febd271f0bc94c5fb1d12cd5644778b.html @@ -149,7 +149,7 @@

              namespace kyosu
              {
              template<kyosu::concepts::cayley_dickson T> constexpr T nearest(T z) noexcept;
              -
              template<eve::ordered_value T> constexpr T nearest(T z) noexcept;
              +
              template<eve::floating_ordered_value T> constexpr T nearest(T z) noexcept;
              }
              kyosu::nearest
              constexpr tags::callable_nearest nearest
              Computes the nearest value.
              Definition: nearest.hpp:73
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13
              diff --git a/group__functions_ga9187d90d21bff228986d00b254bcb818.html b/group__functions_ga9187d90d21bff228986d00b254bcb818.html index b9d4745c..a4cf7850 100644 --- a/group__functions_ga9187d90d21bff228986d00b254bcb818.html +++ b/group__functions_ga9187d90d21bff228986d00b254bcb818.html @@ -148,7 +148,7 @@

              Callable Signatures

              namespace kyosu
              {
              -
              template<eve::ordered_value T> constexpr auto asec(T z) noexcept; //1
              +
              template<eve::floating_ordered_value T> constexpr auto asec(T z) noexcept; //1
              template<kyosu::concepts::cayley_dickson T> constexpr auto asec(T z) noexcept; //2
              }
              kyosu::asec
              constexpr tags::callable_asec asec
              Computes the arcsecant of the argument.
              Definition: asec.hpp:79
              @@ -159,7 +159,7 @@

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

              • Example

              diff --git a/group__functions_ga926e8d9f232cf45c07fe4f2a23353bb9.html b/group__functions_ga926e8d9f232cf45c07fe4f2a23353bb9.html index 9d6fc8ce..6cf63975 100644 --- a/group__functions_ga926e8d9f232cf45c07fe4f2a23353bb9.html +++ b/group__functions_ga926e8d9f232cf45c07fe4f2a23353bb9.html @@ -167,7 +167,7 @@

              Example

              #include <kyosu/kyosu.hpp>
              #include <eve/wide.hpp>
              diff --git a/group__functions_ga92c4c9260b24c8171caca5c014ad4298.html b/group__functions_ga92c4c9260b24c8171caca5c014ad4298.html index aa4fd122..65fea465 100644 --- a/group__functions_ga92c4c9260b24c8171caca5c014ad4298.html +++ b/group__functions_ga92c4c9260b24c8171caca5c014ad4298.html @@ -142,16 +142,16 @@

              -

              Computes the arc sine of the argument times \(\pi\).

              +

              Computes the arc sine of the argument in \(\pi\) multiples.

              Defined in Header

              #include <kyosu/functions.hpp>

              Callable Signatures

              namespace kyosu
              {
              -
              template<eve::ordered_value T> constexpr auto asinpi(T z) noexcept; //1
              +
              template<eve::floating_ordered_value T> constexpr auto asinpi(T z) noexcept; //1
              template<kyosu::concepts::cayley_dickson T> constexpr auto asinpi(T z) noexcept; //2
              }
              -
              kyosu::asinpi
              constexpr tags::callable_asinpi asinpi
              Computes the arc sine of the argument times .
              Definition: asinpi.hpp:79
              +
              kyosu::asinpi
              constexpr tags::callable_asinpi asinpi
              Computes the arc sine of the argument in multiples.
              Definition: asinpi.hpp:79
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

                @@ -159,8 +159,8 @@

                -
              • a real input z is treated as if complex(z) was entered.
                • -
              • Returns invpi(as(z))*asin(z)
                • +
              • a real input z is treated as if kyosu::complex(z) was entered.
                • +
              • Returns kyosu::radinpi(kyosu::asin(z))

                • Example

                #include <kyosu/kyosu.hpp>
                diff --git a/group__functions_ga961299cde75efe464ea2e3f9944d1f33.html b/group__functions_ga961299cde75efe464ea2e3f9944d1f33.html index 1ac4e425..b85e1488 100644 --- a/group__functions_ga961299cde75efe464ea2e3f9944d1f33.html +++ b/group__functions_ga961299cde75efe464ea2e3f9944d1f33.html @@ -149,13 +149,13 @@

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexpr T sign(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr T sign(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr T sign(T z) noexcept;
                }
                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
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                  -
                • z : Value to for which square root is computed.
                  • +
                • z : Value to process.

                Return value

                Returns the "sign" of the argument i.e. its normalized value.

                diff --git a/group__functions_ga97d21d58bdd2678e7dacea216758a5a8.html b/group__functions_ga97d21d58bdd2678e7dacea216758a5a8.html index 6255b4d0..3dc0213d 100644 --- a/group__functions_ga97d21d58bdd2678e7dacea216758a5a8.html +++ b/group__functions_ga97d21d58bdd2678e7dacea216758a5a8.html @@ -149,7 +149,7 @@

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexpr auto is_real(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr auto is_real(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr auto is_real(T z) noexcept;
                }
                kyosu::is_real
                constexpr tags::callable_is_real is_real
                test if the parameter is real.
                Definition: is_real.hpp:72
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                @@ -158,7 +158,7 @@

                pure part is zero.

                Example

                #include <kyosu/kyosu.hpp>
                #include <eve/wide.hpp>
                diff --git a/group__functions_ga9b2e4c2e043be340f42910dbf5ec54ed.html b/group__functions_ga9b2e4c2e043be340f42910dbf5ec54ed.html index 3a9a7821..0858da4d 100644 --- a/group__functions_ga9b2e4c2e043be340f42910dbf5ec54ed.html +++ b/group__functions_ga9b2e4c2e043be340f42910dbf5ec54ed.html @@ -148,8 +148,8 @@

                Callable Signatures

                namespace kyosu
                {
                -
                template<kyosu::concepts::cayley_dickson T> constexpr T sech(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr T sech(T z) noexcept;
                +
                template<kyosu::concepts::cayley_dickson T> constexpr auto sech(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr auto sech(T z) noexcept;
                }
                kyosu::sech
                constexpr tags::callable_sech sech
                Computes the hyperbolic secant of the argument.
                Definition: sech.hpp:73
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                diff --git a/group__functions_ga9c043e0de4393e03663a8b017f3776d1.html b/group__functions_ga9c043e0de4393e03663a8b017f3776d1.html index 9ae5fba0..d295338c 100644 --- a/group__functions_ga9c043e0de4393e03663a8b017f3776d1.html +++ b/group__functions_ga9c043e0de4393e03663a8b017f3776d1.html @@ -149,7 +149,7 @@

                namespace kyosu
                {
                template<kyosu::concepts::cayley_dickson T> constexpr auto is_infinite(T z) noexcept;
                -
                template<eve::ordered_value T> constexpr auto is_infinite(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr auto is_infinite(T z) noexcept;
                }
                kyosu::is_infinite
                constexpr tags::callable_is_infinite is_infinite
                test if the parameter is infinite.
                Definition: is_infinite.hpp:72
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                @@ -158,7 +158,7 @@

                Example

                #include <kyosu/kyosu.hpp>
                #include <eve/wide.hpp>
                diff --git a/group__functions_ga9c08281f95af17445823ff698486d24b.html b/group__functions_ga9c08281f95af17445823ff698486d24b.html index 8ee5c36d..9af0fa03 100644 --- a/group__functions_ga9c08281f95af17445823ff698486d24b.html +++ b/group__functions_ga9c08281f95af17445823ff698486d24b.html @@ -148,8 +148,8 @@

                Callable Signatures

                namespace kyosu
                {
                -
                template<kyosu::concepts::cayley_dickson T> constexp10r T exp10(T z) noexcept;
                -
                template<eve::ordered_value T> constexp10r T exp10(T z) noexcept;
                +
                template<kyosu::concepts::cayley_dickson T> constexpr T exp10(T z) noexcept;
                +
                template<eve::floating_ordered_value T> constexpr T exp10(T z) noexcept;
                }
                kyosu::exp10
                constexpr tags::callable_exp10 exp10
                Computes the base 10 exponential of the argument.
                Definition: exp10.hpp:73
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                diff --git a/group__functions_gaa1c85fe49012f1d7bdabbfe0fe1abaf4.html b/group__functions_gaa1c85fe49012f1d7bdabbfe0fe1abaf4.html new file mode 100644 index 00000000..e2cf0c5c --- /dev/null +++ b/group__functions_gaa1c85fe49012f1d7bdabbfe0fe1abaf4.html @@ -0,0 +1,233 @@ + + + + + + + + +kyosu: kyosu::commutator + + + + + + + + + + + + + + + + + + + + + + + + + + +
                + +
                + + + + + + + + +
                +
                kyosu v0.1.0 +
                +
                Complex Without Complexes
                +
                + +   + + + + +
                +
                +
                + + + + +
                +
                + +
                +
                +
                + +
                + +
                +
                + + +
                +
                +
                +
                +
                +
                Loading...
                +
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                +
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                +
                +
                +
                +
                + +
                + +

                ◆ commutator

                + +
                +
                + + + + + +
                + + + + +
                kyosu::commutator = {}
                +                 		+inlineconstexpr
                +
                + +

                Computes the commutator of the two parameters.

                +

                Defined in Header

                +
                #include <kyosu/functions.hpp>
                +

                Callable Signatures

                +
                namespace kyosu
                +
                {
                +
                constexpr auto commutator(auto z0, auto, z1) noexcept;
                +
                }
                +
                kyosu::commutator
                constexpr tags::callable_commutator commutator
                Computes the commutator of the two parameters.
                Definition: commutator.hpp:74
                +
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13
                +

                Parameters

                +
                  +
                • z0, z1 : Values to process. Can be a mix of complex and real floating values and complex values.
                  • +
                +

                Return value

                +

                Returns the difference z0*z1-z1*z0.

                +

                Example

                +
                #include <kyosu/kyosu.hpp>
                +
                #include <eve/wide.hpp>
                +
                #include <iostream>
                +
                +
                int main()
                +
                {
                +
                using kyosu::commutator;
                +
                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<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);
                +
                e_t e1(2);
                +
                std::cout << e0 << ", " << e1 << " -> " << commutator(e0, e1) << "\n";
                +
                std::cout << e0 << ", " << e0 << " -> " << commutator(e0, e0) << "\n";
                +
                we_t we0(e0);
                +
                we_t we1(e1);
                +
                std::cout << we0 << ", " << we1 << " -> " << commutator(we0, we1) << "\n";
                +
                +
                std::cout << "Complex: "<< "\n";
                +
                c_t c0(1, 5);
                +
                c_t c1(5, 9);
                +
                std::cout << c0 << ", " << c1 << " -> " << commutator(c0, c1) << "\n";
                +
                std::cout << c0 << ", " << c0 << " -> " << commutator(c0, c0) << "\n";
                +
                wc_t wc0(c0, c1);
                +
                wc_t wc1(c1, c1);
                +
                std::cout << wc0 << ", " << wc1 << " -> " << commutator(wc0, wc1) << "\n";
                +
                +
                std::cout << "Quaternion: "<< "\n";
                +
                q_t q0(1, 5, 2, 3);
                +
                q_t q1(5, 9, 6, 7);
                +
                std::cout << q0 << ", " << q1 << " -> " << commutator(q0, q1) << "\n";
                +
                std::cout << q0 << ", " << q0 << " -> " << commutator(q0, q0) << "\n";
                +
                wq_t wq0(q0, q1);
                +
                wq_t wq1(q1, q1);
                +
                std::cout << wq0 << ", " << wq1 << " -> " << commutator(wq0, wq1) << "\n";
                +
                +
                std::cout << "Mixed: "<< "\n";
                +
                std::cout << kyosu::commutator(c0, q1) << std::endl;
                +
                std::cout << kyosu::commutator(e0, q1) << std::endl;
                +
                std::cout << kyosu::commutator(c0, wq1) << std::endl;
                +
                std::cout << kyosu::commutator(we0, q1) << 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_gaa2dcdb1644aa5086e764ee6de919ad93.html b/group__functions_gaa2dcdb1644aa5086e764ee6de919ad93.html index 2535910d..39d16d0c 100644 --- a/group__functions_gaa2dcdb1644aa5086e764ee6de919ad93.html +++ b/group__functions_gaa2dcdb1644aa5086e764ee6de919ad93.html @@ -146,21 +146,18 @@

              #include <kyosu/functions.hpp>

              Callable Signatures

              -
              namespace kyosu
              -
              {
              -
              template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto dot(T0 z0, T1, z1) noexcept;
              -
              template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto dot(T0 z0, T1, z1) noexcept;
              -
              template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto dot(T0 z0, T1, z1) noexcept;
              -
              template<eve::ordered_value T0, ordered_value T1> > constexpr auto dot(T0 z0, T1, z1) noexcept;
              -
              ! }
              -
              kyosu::dot
              constexpr tags::callable_dot dot
              Computes elementwise the dot product of the coordinates of the corresponding element.
              Definition: dot.hpp:80
              +
              namespace kyosu
              +
              {
              +
              constexpr auto dot(auto z0, auto z1) noexcept;
              +
              }
              +
              kyosu::dot
              constexpr tags::callable_dot dot
              Computes elementwise the dot product of the coordinates of the corresponding element.
              Definition: dot.hpp:78
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

                -
              • z0, z1 : Value to process.
                • +
              • z0, z1 : Values to process.

              Return value

              -

              Returns the dot product of z0 and z1. If z0 and z1 are floating point this is equivalent to z0*z1.

              +

              Returns the dot product of z0 and z1. If z0 and z1 are floating point this is equivalent to z0*z1. Arguments can be a mix of floting or Cayley-Dicson values.

              dot(z0, z0) is always semantically equivalent to sqr_abs(z0).

              Example

              #include <kyosu/kyosu.hpp>
              diff --git a/group__functions_gaa370bac6943c4ab923e63d86dcea41ea.html b/group__functions_gaa370bac6943c4ab923e63d86dcea41ea.html index 211d9ebb..6660fbb3 100644 --- a/group__functions_gaa370bac6943c4ab923e63d86dcea41ea.html +++ b/group__functions_gaa370bac6943c4ab923e63d86dcea41ea.html @@ -142,16 +142,17 @@

              -

              test if the parameter real part is zero.

              +

              alias of is_pure

              +

              test if the parameter real part is zero.

              Defined in Header

              #include <kyosu/functions.hpp>

              Callable Signatures

              namespace kyosu
              {
              template<kyosu::concepts::cayley_dicson T> constexpr auto is_imag(T z) noexcept;
              -
              template<eve::ordered_value T> constexpr auto is_imag(T z) noexcept;
              +
              template<eve::floating_ordered_value T> constexpr auto is_imag(T z) noexcept;
              }
              -
              kyosu::is_imag
              constexpr tags::callable_is_pure is_imag
              test if the parameter real part is zero.
              Definition: is_pure.hpp:73
              +
              kyosu::is_imag
              constexpr tags::callable_is_pure is_imag
              alias of is_pure
              Definition: is_pure.hpp:75
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

                diff --git a/group__functions_gaa3f0aecf42f2a0c04ae456b4c604551f.html b/group__functions_gaa3f0aecf42f2a0c04ae456b4c604551f.html index 778c8127..6ce171ef 100644 --- a/group__functions_gaa3f0aecf42f2a0c04ae456b4c604551f.html +++ b/group__functions_gaa3f0aecf42f2a0c04ae456b4c604551f.html @@ -142,16 +142,16 @@

                -

                Computes the arc cotangent of the argument times \(\pi\).

                +

                Computes the arc cotangent of the argument in \(\pi\) multiples.

                Defined in Header

                #include <kyosu/functions.hpp>

                Callable Signatures

                namespace kyosu
                {
                -
                template<eve::ordered_value T> constexpr auto acotpi(T z) noexcept; //1
                +
                template<eve::floating_ordered_value T> constexpr auto acotpi(T z) noexcept; //1
                template<kyosu::concepts::cayley_dickson T> constexpr auto acotpi(T z) noexcept; //2
                }
                -
                kyosu::acotpi
                constexpr tags::callable_acotpi acotpi
                Computes the arc cotangent of the argument times .
                Definition: acotpi.hpp:79
                +
                kyosu::acotpi
                constexpr tags::callable_acotpi acotpi
                Computes the arc cotangent of the argument in multiples.
                Definition: acotpi.hpp:79
                kyosu
                Main KYOSU namespace.
                Definition: beta.hpp:13

                Parameters

                  @@ -159,8 +159,8 @@

                  -
                • a real input z is treated as if complex(z) was entered.
                  • -
                • Returns invpi(as(z))*acot(z)
                  • +
                • a real input z is treated as if kyosu::complex(z) was entered.
                  • +
                • Returns kyosu::radinpi(kyosu::acot(z))

                  • Example

                  #include <kyosu/kyosu.hpp>
                  diff --git a/group__functions_gaa608876852fffef8d90a4f7280ff4549.html b/group__functions_gaa608876852fffef8d90a4f7280ff4549.html index b79d4cf1..8edfc1b7 100644 --- a/group__functions_gaa608876852fffef8d90a4f7280ff4549.html +++ b/group__functions_gaa608876852fffef8d90a4f7280ff4549.html @@ -143,22 +143,6 @@

                  Computes the hyperbolic cosine of the argument.

                  -

                  Defined in Header

                  -
                  #include <kyosu/functions.hpp>
                  -

                  Callable Signatures

                  -
                  namespace kyosu
                  -
                  {
                  -
                  template<kyosu::concepts::cayley_dickson T> constexpr T cosh(T z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T cosh(T z) noexcept;
                  -
                  }
                  -
                  kyosu::cosh
                  constexpr tags::callable_cosh cosh
                  Computes the hyperbolic cosine of the argument.
                  Definition: cosh.hpp:73
                  -
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13
                  -

                  Parameters

                  -
                    -
                  • z : Value to process.
                    • -
                  -

                  Return value

                  -

                  Returns the hyperbolic cosine of the argument.

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  @@ -202,10 +186,47 @@

                  Example

                  return 0;
                  }
                  -
                  kyosu::cos
                  constexpr tags::callable_cos cos
                  Computes the cosine of the argument.
                  Definition: cos.hpp:73
                  +
                  kyosu::cos
                  constexpr tags::callable_cos cos
                  Computes the cosine of the argument.
                  Definition: cos.hpp:79
                  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
                  -
                  +

                  Defined in Header

                  +
                  #include <kyosu/functions.hpp>
                  +

                  Callable Signatures

                  +
                  namespace kyosu
                  +
                  {
                  +
                  template<eve::floating_ordered_value T> constexpr T cosh(T z) noexcept; //1
                  +
                  template<kyosu::concepts::complex T> constexpr T cosh(T z) noexcept; //2
                  +
                  template<kyosu::concepts::cayley_dickson T> constexpr T cosh(T z) noexcept; //3
                  +
                  }
                  +
                  }
                  +
                  kyosu::cosh
                  constexpr tags::callable_cosh cosh
                  Computes the hyperbolic cosine of the argument.
                  Definition: cosh.hpp:94
                  +
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13
                  +

                  Parameters

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

                  Return value

                  +
                    +
                  1. Returns elementwise the complex value of the hyperbolic cosine of the input.
                      +
                    • for every z: kyosu::cosh(kyosu::conj(z)) == kyosu::conj(std::cosh(z))
                      • +
                    • for every z: kyosu::cosh(-z) == kyosu::cosh(z)
                      • +
                    • If z is \(0\), the result is \(1\)
                      • +
                    • If z is \(i \infty\), the result is \(NaN\)
                      • +
                    • If z is \(i NaN\), the result is \(NaN\)
                      • +
                    • If z is \(x+i \infty\) (for any finite non-zero x), the result is \(NaN+i NaN\)
                      • +
                    • If z is \(x+i NaN\) (for any finite non-zero x), the result is \(NaN+i NaN\)
                      • +
                    • If z is \(\infty+i 0\), the result is \(\infty+i 0\)
                      • +
                    • If z is \(\infty,y\) (for any finite non-zero y), the result is \(\infty e^{iy}\)
                      • +
                    • If z is \(\infty+i \infty\), the result is \(\pm \infty+i NaN\) (the sign of the real part is unspecified)
                      • +
                    • If z is \(\infty+i NaN\), the result is \(\infty+i NaN\)
                      • +
                    • If z is \(NaN\), the result is \(NaN\)
                      • +
                    • If z is \(NaN+i y\) (for any finite non-zero y), the result is \(NaN+i NaN\)
                      • +
                    • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)
                      • +
                    +
                    2. +
                  2. Is semantically equivalent to (exp(z)+exp(-z))/2.
                    3. +
                  +

              diff --git a/group__functions_gaa651f9b616ad1022127142bf9cdc68e8.html b/group__functions_gaa651f9b616ad1022127142bf9cdc68e8.html index 742d7ab8..938784f7 100644 --- a/group__functions_gaa651f9b616ad1022127142bf9cdc68e8.html +++ b/group__functions_gaa651f9b616ad1022127142bf9cdc68e8.html @@ -149,7 +149,7 @@

              namespace kyosu
              {
              template<kyosu::concepts::cayley_dickson T> constexpr T coth(T z) noexcept;
              -
              template<eve::ordered_value T> constexpr T coth(T z) noexcept;
              +
              template<eve::floating_ordered_value T> constexpr T coth(T z) noexcept;
              }
              kyosu::coth
              constexpr tags::callable_coth coth
              Computes the hyperbolic cotangent of the argument.
              Definition: coth.hpp:73
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13
              diff --git a/group__functions_gaa67951f7f8d8489a34dd23928f747757.html b/group__functions_gaa67951f7f8d8489a34dd23928f747757.html index 8be69f0e..9b2d9168 100644 --- a/group__functions_gaa67951f7f8d8489a34dd23928f747757.html +++ b/group__functions_gaa67951f7f8d8489a34dd23928f747757.html @@ -148,11 +148,11 @@

              Callable Signatures

              namespace kyosu
              {
              -
              template<eve::ordered_value T> constexpr auto acosh(T z) noexcept; //1
              +
              template<eve::floating_ordered_value T> constexpr auto acosh(T z) noexcept; //1
              template<kyosu::concepts::complex T> constexpr auto acosh(T z) noexcept; //2
              template<kyosu::concepts::cayley_dickson T> constexpr auto acosh(T z) noexcept; //3
              }
              -
              kyosu::acosh
              constexpr tags::callable_acosh acosh
              Computes the inverse hyperbolic cosine of the argument.
              Definition: acosh.hpp:99
              +
              kyosu::acosh
              constexpr tags::callable_acosh acosh
              Computes the inverse hyperbolic cosine of the argument.
              Definition: acosh.hpp:98
              kyosu
              Main KYOSU namespace.
              Definition: beta.hpp:13

              Parameters

                @@ -160,20 +160,19 @@

                -
              • 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)
                  • -
                • If z is \(+0\), the result is \(+0\)
                  • -
                • If z is \(NaN\), the result is \(NaN\)
                  • -
                • If z is \(+1\), the result is \(+\infty\)
                  • -
                • If z is \(x+i \infty\) (for any finite positive x), the result is \(+0,\pi/2\)
                  • -
                • If z is \(x+i NaN\) (for any finite nonzero x), the result is \(NaN+i NaN\)
                  • -
                • If z is \(+\infty+i y\) (for any finite positive y), the result is \(i \pi/2\)
                  • -
                • If z is \(+\infty+i \infty\), the result is \(i \pi/2\)
                  • -
                • If z is \(+\infty+i NaN\), the result is \(i NaN\)
                  • -
                • If z is \(NaN+i y\) (for any finite y), the result is \(NaN+i NaN\)
                  • -
                • If z is \(NaN+i \infty\), the result is \(i \pi/2\) (the sign of the real part is unspecified)
                  • +
                • a real input z is treated as if kyosu::complex(z) was entered.
                  • +
                • Returns the complex inverse hyperbolic cosine of z, in the range of a strip unbounded along the imaginary axis and in the interval \([0,\pi]\) along the real axis.
                    +
                  • for every z: kyosu::acosh( kyosu::conj(z)) == kyosu::conj(kyosu::acosh(z)
                    • +
                  • If z is \(\pm0\), the result is \(+0,\pi/2\)
                    • +
                  • If z is \(x+i\infty\) (for any finite x), the result is \(\infty+i\pi/2\)
                    • +
                  • If z is \(x+i NaN\) (for any finite non zero x), the result is \(NaN+i NaN\).
                    • +
                  • If z is \(i NaN\) the result is \(NaN+i\pi/2\).
                    • +
                  • If z is \(-\infty,y\) (for any positive finite y), the result is \(+\infty,\pi\)
                    • +
                  • If z is \(+\infty,y\) (for any positive finite y), the result is \(+\infty+i 0\)
                    • +
                  • If z is \(-\infty+i \infty\), the result is \(+\infty,3\pi/4\)
                    • +
                  • If z is \(\pm\infty+i NaN\), the result is \(+\infty+i NaN\)
                    • +
                  • If z is \(NaN,y\) (for any finite y), the result is \(NaN+i NaN\).
                    • +
                  • If z is \(NaN+i \infty\), the result is \(+\infty+i NaN\)
                  • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)
                  • diff --git a/group__functions_gaa683fad544774c6d87efc39b424f78e0.html b/group__functions_gaa683fad544774c6d87efc39b424f78e0.html index c7653435..fa943b72 100644 --- a/group__functions_gaa683fad544774c6d87efc39b424f78e0.html +++ b/group__functions_gaa683fad544774c6d87efc39b424f78e0.html @@ -142,23 +142,23 @@

                  -

                  Computes the cosine of the argument in \(\pi\) mutiples.

                  +

                  Computes the cosine from the argument in \(\pi\) multiples.

                  Defined in Header

                  #include <kyosu/functions.hpp>

                  Callable Signatures

                  namespace kyosu
                  {
                  template<kyosu::concepts::cayley_dickson T> constexpr T cospi(T z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T cospi(T z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T cospi(T z) noexcept;
                  }
                  -
                  kyosu::cospi
                  constexpr tags::callable_cospi cospi
                  Computes the cosine of the argument in mutiples.
                  Definition: cospi.hpp:73
                  +
                  kyosu::cospi
                  constexpr tags::callable_cospi cospi
                  Computes the cosine from the argument in multiples.
                  Definition: cospi.hpp:73
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

                  • z : Value to process.

                  Return value

                  -

                  Returns the cosine of the argument in \(\pi\) mutiples.

                  +

                  Returns the cosine from the argument in \(\pi\) multiples.

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  diff --git a/group__functions_gaa9d12dd4e1420039046c737ddd3240be.html b/group__functions_gaa9d12dd4e1420039046c737ddd3240be.html index cb336096..3087dd7a 100644 --- a/group__functions_gaa9d12dd4e1420039046c737ddd3240be.html +++ b/group__functions_gaa9d12dd4e1420039046c737ddd3240be.html @@ -150,8 +150,8 @@

                  {

                  template<kyosu::concepts::cayley_dickson T> constexpr auto& real(T& z) noexcept;
                  template<kyosu::concepts::cayley_dickson T> constexpr auto real(T const& z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T& real(T& z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T real(T const& z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T& real(T& z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T real(T const& z) noexcept;
                  }
                  kyosu::real
                  constexpr tags::callable_real real
                  Extracts the real part of a value.
                  Definition: real.hpp:83
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13
                  diff --git a/group__functions_gaae7085c537556dd281121a349ffb2b93.html b/group__functions_gaae7085c537556dd281121a349ffb2b93.html index 6c995e7f..37d12dd6 100644 --- a/group__functions_gaae7085c537556dd281121a349ffb2b93.html +++ b/group__functions_gaae7085c537556dd281121a349ffb2b93.html @@ -142,23 +142,23 @@

                  -

                  Computes the cosecant of the argument in \(\pi\) mutiples.

                  +

                  Computes the cosecant from the argument in \(\pi\) multiples.

                  Defined in Header

                  #include <kyosu/functions.hpp>

                  Callable Signatures

                  namespace kyosu
                  {
                  template<kyosu::concepts::cayley_dickson T> constexpr T cscpi(T z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T cscpi(T z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T cscpi(T z) noexcept;
                  }
                  -
                  kyosu::cscpi
                  constexpr tags::callable_cscpi cscpi
                  Computes the cosecant of the argument in mutiples.
                  Definition: cscpi.hpp:73
                  +
                  kyosu::cscpi
                  constexpr tags::callable_cscpi cscpi
                  Computes the cosecant from the argument in multiples.
                  Definition: cscpi.hpp:73
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

                  • z : Value to process.

                  Return value

                  -

                  Returns the cosecant of the argument in \(\pi\) mutiples.

                  +

                  Returns the cosecant from the argument in \(\pi\) multiples.

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  diff --git a/group__functions_gaae9065f698fe37841a85e340a16af948.html b/group__functions_gaae9065f698fe37841a85e340a16af948.html index f20b4632..37879240 100644 --- a/group__functions_gaae9065f698fe37841a85e340a16af948.html +++ b/group__functions_gaae9065f698fe37841a85e340a16af948.html @@ -146,21 +146,18 @@

                  #include <kyosu/functions.hpp>

                  Callable Signatures

                  -
                  namespace kyosu
                  -
                  {
                  -
                  template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto pow1p(T0 z0, T1, z1) noexcept;
                  -
                  template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto pow1p(T0 z0, T1, z1) noexcept;
                  -
                  template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto pow1p(T0 z0, T1, z1) noexcept;
                  -
                  template<eve::ordered_value T0, ordered_value T1> > constexpr auto pow1p(T0 z0, T1, z1) noexcept;
                  -
                  ! }
                  -
                  kyosu::pow1p
                  constexpr tags::callable_pow1p pow1p
                  Computes the computing the pow1p operation .
                  Definition: pow1p.hpp:77
                  +
                  namespace kyosu
                  +
                  {
                  +
                  constexpr auto average(auto z0, auto, z1) noexcept;
                  +
                  }
                  +
                  kyosu::average
                  constexpr tags::callable_average average
                  Computes the average of the two parameters.
                  Definition: average.hpp:74
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

                  • z0, z1 : Values to process.

                  Return value

                  -

                  the call is semantically equivalent to eve::exp(z1*eve::log1p(z0))

                  +

                  the call is semantically equivalent to pow(inc(z))

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  @@ -213,6 +210,7 @@

                  Example

                  return 0;
                  }
                  +
                  kyosu::pow1p
                  constexpr tags::callable_pow1p pow1p
                  Computes the computing the pow1p operation .
                  Definition: pow1p.hpp:74
                  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 2a2fadb8..6319d8c4 100644 --- a/group__functions_gaafed3076d5ce6fbfa0bfa53301927ae3.html +++ b/group__functions_gaafed3076d5ce6fbfa0bfa53301927ae3.html @@ -142,16 +142,16 @@

                  -

                  Computes the hyperbolic arcsecant of the argument.

                  +

                  Computes the inverse hyperbolic secant of the argument.

                  Defined in Header

                  #include <kyosu/functions.hpp>

                  Callable Signatures

                  namespace kyosu
                  {
                  -
                  template<eve::ordered_value T> constexpr auto asech(T z) noexcept; //1
                  -
                  template<kyosu::concepts::complex T> constexpr auto asech(T z) noexcept; //2
                  +
                  template<eve::floating_ordered_value T> constexpr auto asech(T z) noexcept; //1
                  +
                  template<kyosu::concepts::cayley_dickson T> constexpr auto asech(T z) noexcept; //2
                  }
                  -
                  kyosu::asech
                  constexpr tags::callable_asech asech
                  Computes the hyperbolic arcsecant of the argument.
                  Definition: asech.hpp:79
                  +
                  kyosu::asech
                  constexpr tags::callable_asech asech
                  Computes the inverse hyperbolic secant of the argument.
                  Definition: asech.hpp:79
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13

                  Parameters

                    @@ -159,7 +159,7 @@

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

                    • Example

                    diff --git a/group__functions_gab07fa9f73fd002dccfcb769a87bee81c.html b/group__functions_gab07fa9f73fd002dccfcb769a87bee81c.html index 0510b16e..5c4bfa2a 100644 --- a/group__functions_gab07fa9f73fd002dccfcb769a87bee81c.html +++ b/group__functions_gab07fa9f73fd002dccfcb769a87bee81c.html @@ -142,16 +142,16 @@

                    -

                    Computes the arc tangent of the argument times \(\pi\).

                    +

                    Computes the arc tangent of the argument in \(\pi\) multiples.

                    Defined in Header

                    #include <kyosu/functions.hpp>

                    Callable Signatures

                    namespace kyosu
                    {
                    -
                    template<eve::ordered_value T> constexpr auto atanpi(T z) noexcept; //1
                    +
                    template<eve::floating_ordered_value T> constexpr auto atanpi(T z) noexcept; //1
                    template<kyosu::concepts::cayley_dickson T> constexpr auto atanpi(T z) noexcept; //2
                    }
                    -
                    kyosu::atanpi
                    constexpr tags::callable_atanpi atanpi
                    Computes the arc tangent of the argument times .
                    Definition: atanpi.hpp:79
                    +
                    kyosu::atanpi
                    constexpr tags::callable_atanpi atanpi
                    Computes the arc tangent of the argument in multiples.
                    Definition: atanpi.hpp:79
                    kyosu
                    Main KYOSU namespace.
                    Definition: beta.hpp:13

                    Parameters

                      @@ -159,8 +159,8 @@

                      -
                    • a real input z is treated as if complex(z) was entered.
                      • -
                    • Returns invpi(as(z))*atan(z)
                      • +
                    • a real input z is treated as if kyosu::complex(z) was entered.
                      • +
                    • Returns kyosu::radinpi(kyosu::atan(z))

                      • Example

                      #include <kyosu/kyosu.hpp>
                      diff --git a/group__functions_gab0f1c35d5251d1f6db39bec53d8960b6.html b/group__functions_gab0f1c35d5251d1f6db39bec53d8960b6.html index b61012b5..b05c11ab 100644 --- a/group__functions_gab0f1c35d5251d1f6db39bec53d8960b6.html +++ b/group__functions_gab0f1c35d5251d1f6db39bec53d8960b6.html @@ -142,23 +142,23 @@

                      -

                      Computes the expm1onential of the argument minus 1.

                      +

                      Computes the exponential of the argument minus 1.

                      Defined in Header

                      #include <kyosu/functions.hpp>

                      Callable Signatures

                      namespace kyosu
                      {
                      template<kyosu::concepts::cayley_dickson T> constexpm1r T expm1(T z) noexcept;
                      -
                      template<eve::ordered_value T> constexpm1r T expm1(T z) noexcept;
                      +
                      template<eve::floating_ordered_value T> constexpm1r T expm1(T z) noexcept;
                      }
                      -
                      kyosu::expm1
                      constexpr tags::callable_expm1 expm1
                      Computes the expm1onential of the argument minus 1.
                      Definition: expm1.hpp:74
                      +
                      kyosu::expm1
                      constexpr tags::callable_expm1 expm1
                      Computes the exponential of the argument minus 1.
                      Definition: expm1.hpp:74
                      kyosu
                      Main KYOSU namespace.
                      Definition: beta.hpp:13

                      Parameters

                      • z : Value to process.

                      Return value

                      -

                      Returns the expm1onential of the argument minus &. for real and complex typed inputs, provisions are made to ensure good precision near zero.

                      +

                      Returns the expm1onential of the argument minus 1. for real and complex typed inputs, provisions are made to ensure good precision near zero.

                      Example

                      #include <kyosu/kyosu.hpp>
                      #include <eve/wide.hpp>
                      diff --git a/group__functions_gab1054201f9cf583c8723b683ac50abce.html b/group__functions_gab1054201f9cf583c8723b683ac50abce.html index cb8658a1..8f2231f0 100644 --- a/group__functions_gab1054201f9cf583c8723b683ac50abce.html +++ b/group__functions_gab1054201f9cf583c8723b683ac50abce.html @@ -146,21 +146,18 @@

                      #include <kyosu/functions.hpp>

                      Callable Signatures

                      -
                      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
                      +
                      namespace kyosu
                      +
                      {
                      +
                      constexpr auto ldiv(auto z0, auto, z1) noexcept;
                      +
                      }
                      +
                      kyosu::ldiv
                      constexpr tags::callable_ldiv ldiv
                      Computes the left division of the two parameters.
                      Definition: ldiv.hpp:75
                      kyosu
                      Main KYOSU namespace.
                      Definition: beta.hpp:13

                      Parameters

                      • z0, z1 : Values to process.

                      Return value

                      -

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

                      +

                      Returns the left division of the two arguments. This function not equivalent to z1/z0 as soon as multiplication is not commutative (i.e. for general Cayley-Dickson values with dimensionality strictly above 2).

                      Example

                      #include <kyosu/kyosu.hpp>
                      #include <eve/wide.hpp>
                      diff --git a/group__functions_gab4f4ec4acf88c38ee4101b3c6b69058f.html b/group__functions_gab4f4ec4acf88c38ee4101b3c6b69058f.html index 792377a3..edd5bd43 100644 --- a/group__functions_gab4f4ec4acf88c38ee4101b3c6b69058f.html +++ b/group__functions_gab4f4ec4acf88c38ee4101b3c6b69058f.html @@ -142,16 +142,16 @@

                      -

                      Computes the arc cosecant of the argument times \(\pi\).

                      +

                      Computes the arc cosecant of the argume!nt in \(\pi\) multiples.

                      Defined in Header

                      #include <kyosu/functions.hpp>

                      Callable Signatures

                      namespace kyosu
                      {
                      -
                      template<eve::ordered_value T> constexpr auto acscpi(T z) noexcept; //1
                      +
                      template<eve::floating_ordered_value T> constexpr auto acscpi(T z) noexcept; //1
                      template<kyosu::concepts::cayley_dickson T> constexpr auto acscpi(T z) noexcept; //2
                      }
                      -
                      kyosu::acscpi
                      constexpr tags::callable_acscpi acscpi
                      Computes the arc cosecant of the argument times .
                      Definition: acscpi.hpp:79
                      +
                      kyosu::acscpi
                      constexpr tags::callable_acscpi acscpi
                      Computes the arc cosecant of the argume!nt in multiples.
                      Definition: acscpi.hpp:79
                      kyosu
                      Main KYOSU namespace.
                      Definition: beta.hpp:13

                      Parameters

                        @@ -159,8 +159,8 @@

                        -
                      • a real input z is treated as if complex(z) was entered.
                        • -
                      • Returns invpi(as(z))*acsc(z)
                        • +
                      • a real input z is treated as if kyosu::complex(z) was entered.
                        • +
                      • Returns Returns kyosu::radinpi(kyosu::csc(z))

                        • Example

                        #include <kyosu/kyosu.hpp>
                        diff --git a/group__functions_gab64d320c3bacdf74f8a860ca960df8c2.html b/group__functions_gab64d320c3bacdf74f8a860ca960df8c2.html new file mode 100644 index 00000000..54675a85 --- /dev/null +++ b/group__functions_gab64d320c3bacdf74f8a860ca960df8c2.html @@ -0,0 +1,215 @@ + + + + + + + + +kyosu: kyosu::lipart + + + + + + + + + + + + + + + + + + + + + + + + + + +
                        + +
                        + + + + + + + + +
                        +
                        kyosu v0.1.0 +
                        +
                        Complex Without Complexes
                        +
                        + +   + + + + +
                        +
                        +
                        + + + + +
                        +
                        + +
                        +
                        +
                        + +
                        + +
                        +
                        + + +
                        +
                        +
                        +
                        +
                        +
                        Loading...
                        +
                        Searching...
                        +
                        No Matches
                        +
                        +
                        +
                        +
                        + +
                        + +

                        ◆ lipart

                        + +
                        +
                        + + + + + +
                        + + + + +
                        kyosu::lipart = {}
                        +                         		+inlineconstexpr
                        +
                        + +

                        Extracts the li (sixth) part of a value.

                        +

                        Defined in Header

                        +
                        #include <kyosu/functions.hpp>
                        +

                        Callable Signatures

                        +
                        namespace kyosu
                        +
                        {
                        +
                        template<kyosu::concepts::cayley_dickson T> constexpr auto& lipart(T& z) noexcept;
                        +
                        template<kyosu::concepts::cayley_dickson T> constexpr auto lipart(T const& z) noexcept;
                        +
                        template<eve::floating_ordered_value T> constexpr T lipart(T const& z) noexcept;
                        +
                        }
                        +
                        kyosu::lipart
                        constexpr tags::callable_lipart lipart
                        Extracts the li (sixth) part of a value.
                        Definition: lipart.hpp:80
                        +
                        kyosu
                        Main KYOSU namespace.
                        Definition: beta.hpp:13
                        +

                        Parameters

                        +
                          +
                        • z : Original value.
                          • +
                        +

                        Return value

                        +

                        Returns the sixth part of its argument.

                        +

                        For up to quaternion inputs, the call always returns 0.

                        +

                        Example

                        +
                        #include <kyosu/kyosu.hpp>
                        +
                        #include <eve/wide.hpp>
                        +
                        #include <iostream>
                        +
                        +
                        int main()
                        +
                        {
                        +
                        using kyosu::lipart;
                        +
                        using kyosu::complex_t;
                        +
                        using kyosu::quaternion_t;
                        +
                        +
                        std::cout << "Real: ";
                        +
                        float f = 72.9f;
                        +
                        std::cout << f << " -> " << lipart(f) << "\n";
                        +
                        +
                        std::cout << "Complex: ";
                        +
                        auto z = kyosu::complex_t<float>(3.5f,-2.9f);
                        +
                        std::cout << z << " -> " << lipart(z) << "\n";
                        +
                        +
                        std::cout << "Quaternion: ";
                        +
                        auto q = kyosu::quaternion_t<double>(1.,2.,3.,4.);
                        +
                        std::cout << q << " -> " << lipart(q) << " => ";
                        +
                        +
                        std::cout << "octonion: ";
                        +
                        auto o = kyosu::octonion_t<double>(1.,2.,3.,4.,11.,12.,13.,14.);
                        +
                        std::cout << o << " -> " << lipart(q) << " => ";
                        +
                        +
                        +
                        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
                        +
                        kyosu::octonion_t
                        as_cayley_dickson_n_t< 8, T > octonion_t
                        Type alias for quaternion numbers.
                        Definition: octonion.hpp:26
                        +
                        +
                        +
                        +
                        +
                        + + + +
                        +

                      +
                      +

                      +

                  + + diff --git a/group__functions_gabd703393200a757087fb7f2054546dcf.html b/group__functions_gabd703393200a757087fb7f2054546dcf.html index bb703080..76eeccfe 100644 --- a/group__functions_gabd703393200a757087fb7f2054546dcf.html +++ b/group__functions_gabd703393200a757087fb7f2054546dcf.html @@ -149,7 +149,7 @@

                  namespace kyosu
                  {
                  template<kyosu::concepts::cayley_dickson T> constexpr as_real_t<T> radinpi(T z) noexcept;
                  -
                  template<eve::ordered_value T> constexpr T radinpi(T z) noexcept;
                  +
                  template<eve::floating_ordered_value T> constexpr T radinpi(T z) noexcept;
                  }
                  kyosu::radinpi
                  constexpr tags::callable_radinpi radinpi
                  Computes the parameter divided by .
                  Definition: radinpi.hpp:72
                  kyosu::as_real_t
                  typename as_real< T >::type as_real_t
                  Compute the real type associated to a Cayley-Dickson-like type.
                  Definition: traits.hpp:79
                  diff --git a/group__functions_gabe0cc0a4ddad9387b7e6bc13e6b3bcfd.html b/group__functions_gabe0cc0a4ddad9387b7e6bc13e6b3bcfd.html index 608d12e9..2fbc06fb 100644 --- a/group__functions_gabe0cc0a4ddad9387b7e6bc13e6b3bcfd.html +++ b/group__functions_gabe0cc0a4ddad9387b7e6bc13e6b3bcfd.html @@ -142,7 +142,28 @@

                  -

                  complex number argument.

                  +

                  argument.

                  +

                  Defined in Header

                  +
                  #include <kyosu/functions.hpp>
                  +

                  Callable Signatures

                  +
                  namespace kyosu
                  +
                  {
                  +
                  template<eve::floating_ordered_value T> constexpr auto arg(T z) noexcept; //1
                  +
                  template<kyosu::concepts::complex T> constexpr auto arg(T z) noexcept; //2
                  +
                  template<kyosu::concepts::cayley_dickson T> constexpr auto arg(T z) noexcept; //3
                  +
                  }
                  +
                  kyosu::arg
                  constexpr tags::callable_arg arg
                  argument.
                  Definition: arg.hpp:78
                  +
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13
                  +

                  Parameters

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

                  Return value

                  +
                    +
                  1. Returns 0 or pi acording to the non negativity of z.
                    2. +
                  2. Returns elementwise the argument of the complex number i.e. eve::atan2(kyosu::imag(z)(z), kyosu::real(z)(z)).
                    3. +
                  3. Returns \(\mathrm{atan2}(\mathrm{sign}(z_1)|\underline{z}|, z_0)\) where \(z_0\) is the real part of \(z\), \(z_1\) is the ipart of \(z\) and \(\underline{z}\) the pure part of \(z\).
                    4. +

                  Example

                  #include <kyosu/kyosu.hpp>
                  #include <eve/wide.hpp>
                  @@ -165,29 +186,8 @@

                  Example

                  return 0;
                  }
                  -
                  kyosu::arg
                  constexpr tags::callable_arg arg
                  complex number argument.
                  Definition: arg.hpp:79
                  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
                  -
                  {
                  -
                  template<eve::ordered_value T> constexpr auto arg(T z) noexcept; //1
                  -
                  template<kyosu::concepts::complex T> constexpr auto arg(T z) noexcept; //2
                  -
                  template<kyosu::concepts::cayley_dickson T> constexpr auto arg(T z) noexcept; //3
                  -
                  }
                  -
                  kyosu
                  Main KYOSU namespace.
                  Definition: beta.hpp:13
                  -

                  Parameters

                  -
                    -
                  • z : Value to process.
                    • -
                  -

                  Return value

                  -
                    -
                  1. Returns 0 or pi acording to the non negativity of z.
                    2. -
                  2. Returns elementwise the argument of the complex number i.e. atan2(imag(z), real(z)).
                    3. -
                  3. Returns \(\mathrm{atan2}(|\underline{z}|, z_0)\) where \(z_0\) is the real part of \(z\) and \(\underline{z}\) is the pure part of \(z\).
                    4. -
                  - +

        • diff --git a/group__functions_gabe8cd1a34e2b6559105a1c6c101d52f7.html b/group__functions_gabe8cd1a34e2b6559105a1c6c101d52f7.html index 9073866d..189d5170 100644 --- a/group__functions_gabe8cd1a34e2b6559105a1c6c101d52f7.html +++ b/group__functions_gabe8cd1a34e2b6559105a1c6c101d52f7.html @@ -148,18 +148,20 @@

        Callable Signatures

        namespace kyosu
        {
        -
        template<kyosu::concepts::cayley_dickson T> constexpr T log10(T z) noexcept;
        -
        template<eve::ordered_value T> constexpr complex_t<T> log10(T z) noexcept;
        +
        template<eve::floating_ordered_value T> constexpr auto log10(T z) noexcept; //1
        +
        template<kyosu::concepts::cayley_dickson T> constexpr auto log10(T z) noexcept; //2
        }
        -
        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::log10
        constexpr tags::callable_log10 log10
        Computes the base 10 logarithm of the argument.
        Definition: log10.hpp:80
        kyosu
        Main KYOSU namespace.
        Definition: beta.hpp:13

        Parameters

        • z : Value to process.

        Return value

        -

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

        +
          +
        1. a real typed input z is treated as if kyosu::complex(z) was entered.
          2. +
        2. returns log(z)/log_10(as(z)).
          3. +

        Example

        #include <kyosu/kyosu.hpp>
        #include <eve/wide.hpp>
        @@ -204,6 +206,7 @@

        Example

        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_gabfab93a2a2b4f527d3c69eeb13856d2c.html b/group__functions_gabfab93a2a2b4f527d3c69eeb13856d2c.html index 7b3c684f..f4267701 100644 --- a/group__functions_gabfab93a2a2b4f527d3c69eeb13856d2c.html +++ b/group__functions_gabfab93a2a2b4f527d3c69eeb13856d2c.html @@ -146,18 +146,15 @@

    #include <kyosu/functions.hpp>

    Callable Signatures

    -
    namespace kyosu
    -
    {
    -
    template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto is_equal(T0 z0, T1, z1) noexcept;
    -
    template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto is_equal(T0 z0, T1, z1) noexcept;
    -
    template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto is_equal(T0 z0, T1, z1) noexcept;
    -
    template<eve::ordered_value T0, ordered_value T1> > constexpr auto is_equal(T0 z0, T1, z1) noexcept;
    -
    ! }
    -
    kyosu::is_equal
    constexpr tags::callable_is_equal is_equal
    retuen true if and only if the two parameters are equal.
    Definition: is_equal.hpp:79
    +
    namespace kyosu
    +
    {
    +
    constexpr auto is_equal(auto z0, auto z1) noexcept;
    +
    }
    +
    kyosu::is_equal
    constexpr tags::callable_is_equal is_equal
    retuen true if and only if the two parameters are equal.
    Definition: is_equal.hpp:76
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      -
    • z0, z1 : Value to process.
      • +
    • z0, z1 : Values to process.

    Return value

    Returns elemtwise true or false according the equality of the parameters

    diff --git a/group__functions_gabfd2527bde97bcd86c6d1933fce660a1.html b/group__functions_gabfd2527bde97bcd86c6d1933fce660a1.html index ade7b4b6..ba47ce82 100644 --- a/group__functions_gabfd2527bde97bcd86c6d1933fce660a1.html +++ b/group__functions_gabfd2527bde97bcd86c6d1933fce660a1.html @@ -142,23 +142,23 @@

    -

    Computes simultaneously the sine and cosine of the argument in \(\pi\) mutiples.

    +

    Computes simultaneously the sine and cosine of the argument in \(\pi\) multiples.

    Defined in Header

    #include <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr auto sinpicospi(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto sinpicospi(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto sinpicospi(T z) noexcept;
    }
    -
    kyosu::sinpicospi
    constexpr tags::callable_sinpicospi sinpicospi
    Computes simultaneously the sine and cosine of the argument in mutiples.
    Definition: sinpicospi.hpp:73
    +
    kyosu::sinpicospi
    constexpr tags::callable_sinpicospi sinpicospi
    Computes simultaneously the sine and cosine of the argument in multiples.
    Definition: sinpicospi.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns simultaneously the sine and cosine of the argument in \(\pi\) mutiples.

    +

    Returns simultaneously the sine and cosine of the argument in \(\pi\) multiples.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_gac01bdb4384827ce21ddddedd19f8b032.html b/group__functions_gac01bdb4384827ce21ddddedd19f8b032.html index 6d83ead1..40c117db 100644 --- a/group__functions_gac01bdb4384827ce21ddddedd19f8b032.html +++ b/group__functions_gac01bdb4384827ce21ddddedd19f8b032.html @@ -155,7 +155,7 @@

    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

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

    Return value

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

    diff --git a/group__functions_gac24fb66ef0ba0fd8adb3c596264f24e8.html b/group__functions_gac24fb66ef0ba0fd8adb3c596264f24e8.html new file mode 100644 index 00000000..de804e8e --- /dev/null +++ b/group__functions_gac24fb66ef0ba0fd8adb3c596264f24e8.html @@ -0,0 +1,215 @@ + + + + + + + + +kyosu: kyosu::lkpart + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
    Loading...
    +
    Searching...
    +
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    +
    +
    +
    +
    + +
    + +

    ◆ lkpart

    + +
    +
    + + + + + +
    + + + + +
    kyosu::lkpart = {}
    +     		+inlineconstexpr
    +
    + +

    Extracts the lk (eighth) part of a value.

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto& lkpart(T& z) noexcept;
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto lkpart(T const& z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T lkpart(T const& z) noexcept;
    +
    }
    +
    kyosu::lkpart
    constexpr tags::callable_lkpart lkpart
    Extracts the lk (eighth) part of a value.
    Definition: lkpart.hpp:80
    +
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    +

    Parameters

    +
      +
    • z : Original value.
      • +
    +

    Return value

    +

    Returns the eighth part of its argument.

    +

    For up to quaterion inputs, the call always returns 0.

    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::lkpart;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    +
    std::cout << "Real: ";
    +
    float f = 72.9f;
    +
    std::cout << f << " -> " << lkpart(f) << "\n";
    +
    +
    std::cout << "Complex: ";
    +
    auto z = kyosu::complex_t<float>(3.5f,-2.9f);
    +
    std::cout << z << " -> " << lkpart(z) << "\n";
    +
    +
    std::cout << "Quaternion: ";
    +
    auto q = kyosu::quaternion_t<double>(1.,2.,3.,4.);
    +
    std::cout << q << " -> " << lkpart(q) << " => ";
    +
    +
    std::cout << "octonion: ";
    +
    auto o = kyosu::octonion_t<double>(1.,2.,3.,4.,11.,12.,13.,14.);
    +
    std::cout << o << " -> " << lkpart(o) << " => ";
    +
    +
    +
    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
    +
    kyosu::octonion_t
    as_cayley_dickson_n_t< 8, T > octonion_t
    Type alias for quaternion numbers.
    Definition: octonion.hpp:26
    +
    +
    +
    +
    +
    + + + +

    +

    +
    +

    +
    + + diff --git a/group__functions_gac6ffcc3696c865798531628577792946.html b/group__functions_gac6ffcc3696c865798531628577792946.html index 528ecfa0..ca57c011 100644 --- a/group__functions_gac6ffcc3696c865798531628577792946.html +++ b/group__functions_gac6ffcc3696c865798531628577792946.html @@ -148,8 +148,8 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpr T sinc(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T sinc(T z) noexcept;
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto sinc(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto sinc(T z) noexcept;
    }
    kyosu::sinc
    constexpr tags::callable_sinc sinc
    Computes the sine cardinal of the argument.
    Definition: sinc.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    diff --git a/group__functions_gac828b36348f592f5f2d891bd546ee733.html b/group__functions_gac828b36348f592f5f2d891bd546ee733.html new file mode 100644 index 00000000..eb36a8e7 --- /dev/null +++ b/group__functions_gac828b36348f592f5f2d891bd546ee733.html @@ -0,0 +1,215 @@ + + + + + + + + +kyosu: kyosu::lpart + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
    Loading...
    +
    Searching...
    +
    No Matches
    +
    +
    +
    +
    + +
    + +

    ◆ lpart

    + +
    +
    + + + + + +
    + + + + +
    kyosu::lpart = {}
    +     		+inlineconstexpr
    +
    + +

    Extracts the l (fifth) part of a value.

    +

    Defined in Header

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto& lpart(T& z) noexcept;
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto lpart(T const& z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T lpart(T const& z) noexcept;
    +
    }
    +
    kyosu::lpart
    constexpr tags::callable_lpart lpart
    Extracts the l (fifth) part of a value.
    Definition: lpart.hpp:80
    +
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    +

    Parameters

    +
      +
    • z : Original value.
      • +
    +

    Return value

    +

    Returns the fifth part of its argument.

    +

    For up to quaterion inputs, the call always returns 0.

    +

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::lpart;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    +
    std::cout << "Real: ";
    +
    float f = 72.9f;
    +
    std::cout << f << " -> " << lpart(f) << "\n";
    +
    +
    std::cout << "Complex: ";
    +
    auto z = kyosu::complex_t<float>(3.5f,-2.9f);
    +
    std::cout << z << " -> " << lpart(z) << "\n";
    +
    +
    std::cout << "Quaternion: ";
    +
    auto q = kyosu::quaternion_t<double>(1.,2.,3.,4.);
    +
    std::cout << q << " -> " << lpart(q) << " => ";
    +
    +
    std::cout << "octonion: ";
    +
    auto o = kyosu::octonion_t<double>(1.,2.,3.,4.,11.,12.,13.,14.);
    +
    std::cout << o << " -> " << lpart(o) << " => ";
    +
    +
    +
    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
    +
    kyosu::octonion_t
    as_cayley_dickson_n_t< 8, T > octonion_t
    Type alias for quaternion numbers.
    Definition: octonion.hpp:26
    +
    +
    +
    +
    +
    + + + +
    +
    +
    +

    +
    + + diff --git a/group__functions_gac91bff00b4c1a3c8e0b249a07bd6c080.html b/group__functions_gac91bff00b4c1a3c8e0b249a07bd6c080.html index 8c5eb19f..e003b587 100644 --- a/group__functions_gac91bff00b4c1a3c8e0b249a07bd6c080.html +++ b/group__functions_gac91bff00b4c1a3c8e0b249a07bd6c080.html @@ -142,23 +142,23 @@

    -

    test if the parameter is not_nan.

    +

    test if the parameter is not a Nan.

    Defined in Header

    #include <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr auto is_not_nan(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto is_not_nan(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto is_not_nan(T z) noexcept;
    }
    -
    kyosu::is_not_nan
    constexpr tags::callable_is_not_nan is_not_nan
    test if the parameter is not_nan.
    Definition: is_not_nan.hpp:72
    +
    kyosu::is_not_nan
    constexpr tags::callable_is_not_nan is_not_nan
    test if the parameter is not a Nan.
    Definition: is_not_nan.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns elementwise true is a component of the element is not_nan .

    +

    Returns elementwise false is any component of the element is a Nan.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_gaca9f3f8f0c75ddbff90aab0785d7a23f.html b/group__functions_gaca9f3f8f0c75ddbff90aab0785d7a23f.html index 466c6582..d93da638 100644 --- a/group__functions_gaca9f3f8f0c75ddbff90aab0785d7a23f.html +++ b/group__functions_gaca9f3f8f0c75ddbff90aab0785d7a23f.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr auto is_finite(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto is_finite(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto is_finite(T z) noexcept;
    }
    kyosu::is_finite
    constexpr tags::callable_is_finite is_finite
    test if the parameter is finite.
    Definition: is_finite.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    diff --git a/group__functions_gacb0340f73510f30b99ad37fa82c22e8f.html b/group__functions_gacb0340f73510f30b99ad37fa82c22e8f.html index 239c1531..c73ddc16 100644 --- a/group__functions_gacb0340f73510f30b99ad37fa82c22e8f.html +++ b/group__functions_gacb0340f73510f30b99ad37fa82c22e8f.html @@ -160,7 +160,7 @@

    -
  • a real input z is treated as if complex(z) was entered.
    • +
  • a real input z returns eve::erf(z).
  • The value of the error function in the complex plane is returned

    • Example

    diff --git a/group__functions_gacb9f75de7a67c7d512f135c26b10cdf1.html b/group__functions_gacb9f75de7a67c7d512f135c26b10cdf1.html index fced622f..b9ee34eb 100644 --- a/group__functions_gacb9f75de7a67c7d512f135c26b10cdf1.html +++ b/group__functions_gacb9f75de7a67c7d512f135c26b10cdf1.html @@ -142,23 +142,23 @@

    -

    Computes the sine of the argument in \(\pi\) mutiples.

    +

    Computes the sine of the argument in \(\pi\) multiples.

    Defined in Header

    #include <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T sinpi(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T sinpi(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T sinpi(T z) noexcept;
    }
    -
    kyosu::sinpi
    constexpr tags::callable_sinpi sinpi
    Computes the sine of the argument in mutiples.
    Definition: sinpi.hpp:73
    +
    kyosu::sinpi
    constexpr tags::callable_sinpi sinpi
    Computes the sine of the argument in multiples.
    Definition: sinpi.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns the sine of the argument in \(\pi\) mutiples.

    +

    Returns the sine of the argument in \(\pi\) multiples.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_gad00c7ec9930289364786f5004c212c9b.html b/group__functions_gad00c7ec9930289364786f5004c212c9b.html index 4ef48798..d3fd1dad 100644 --- a/group__functions_gad00c7ec9930289364786f5004c212c9b.html +++ b/group__functions_gad00c7ec9930289364786f5004c212c9b.html @@ -149,7 +149,7 @@

    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;
    +
    template<eve::floating_ordered_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: beta.hpp:13
    diff --git a/group__functions_gad4e960a6cb254cdd741323efc8efa3a0.html b/group__functions_gad4e960a6cb254cdd741323efc8efa3a0.html index 254621bb..995b821a 100644 --- a/group__functions_gad4e960a6cb254cdd741323efc8efa3a0.html +++ b/group__functions_gad4e960a6cb254cdd741323efc8efa3a0.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T conj(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T conj(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T conj(T z) noexcept;
    }
    kyosu::conj
    constexpr tags::callable_conj conj
    Computes the conjugate value.
    Definition: conj.hpp:75
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    @@ -158,7 +158,7 @@

    pure part.

    For real inputs the call reduces to identity.

    Example

    #include <kyosu/kyosu.hpp>
    diff --git a/group__functions_gad5a796471bcfd81c38de6db0658fa23a.html b/group__functions_gad5a796471bcfd81c38de6db0658fa23a.html index 8b339155..302002ab 100644 --- a/group__functions_gad5a796471bcfd81c38de6db0658fa23a.html +++ b/group__functions_gad5a796471bcfd81c38de6db0658fa23a.html @@ -142,23 +142,23 @@

    -

    Computes the exponential of the argument times i.

    +

    Computes the exponential of i times the argument.

    Defined in Header

    #include <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexp_ir T exp_i(T z) noexcept;
    -
    template<eve::ordered_value T> constexp_ir T exp_i(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexp_ir T exp_i(T z) noexcept;
    }
    -
    kyosu::exp_i
    constexpr tags::callable_exp_i exp_i
    Computes the exponential of the argument times i.
    Definition: exp_i.hpp:78
    +
    kyosu::exp_i
    constexpr tags::callable_exp_i exp_i
    Computes the exponential of i times the argument.
    Definition: exp_i.hpp:78
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns the exp(i*z).

    +

    Returns exp(i*z).

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_gad65d1920bd1721b78982441aeb5b4036.html b/group__functions_gad65d1920bd1721b78982441aeb5b4036.html index 7bc76dc9..c1dde947 100644 --- a/group__functions_gad65d1920bd1721b78982441aeb5b4036.html +++ b/group__functions_gad65d1920bd1721b78982441aeb5b4036.html @@ -149,16 +149,35 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T tanh(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T tanh(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T tanh(T z) noexcept;
    }
    -
    kyosu::tanh
    constexpr tags::callable_tanh tanh
    Computes the hyperbolic tangent of the argument.
    Definition: tanh.hpp:73
    +
    kyosu::tanh
    constexpr tags::callable_tanh tanh
    Computes the hyperbolic tangent of the argument.
    Definition: tanh.hpp:92
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : Value to process.

    Return value

    -

    Returns the hyperbolic tangent of the argument.

    +
      +
    1. Returns eve::tanh(z).
      2. +
    2. Returns elementwise the complex value of the hyperbolic tangent of the input.
        +
      • for every z: kyosu::tanh(kyosu::conj(z)) == kyosu::conj(std::tanh(z))
        • +
      • for every z: kyosu::tanh(-z) == -kyosu::tanh(z)
        • +
      • If z is \(+0\), the result is \(+0\)
        • +
      • If z is \(x+i \infty\) (for any non zero finite x), the result is \(NaN+i NaN\)
        • +
      • If z is \(i \infty\) the result is \(i NaN\)
        • +
      • If z is \(x,NaN\) (for any non zero finite x), the result is \(NaN+i NaN\)
        • +
      • If z is \(i NaN\) the result is \(i NaN\)
        • +
      • If z is \(+\infty,y\) (for any finite positive y), the result is \(1\)
        • +
      • If z is \(+\infty+i \infty\), the result is \(1,\pm 0\) (the sign of the imaginary part is unspecified)
        • +
      • If z is \(+\infty+i NaN\), the result is \(1\) (the sign of the imaginary part is unspecified)
        • +
      • If z is \(NaN\), the result is \(NaN\)
        • +
      • If z is \(NaN+i y\) (for any non-zero y), the result is \(NaN+i NaN\)
        • +
      • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)
        • +
      +
      3. +
    3. The call is semantically equivalent to sinh(z)/cosh(z);
      4. +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_gad726f439fb9920c055c094631185d449.html b/group__functions_gad726f439fb9920c055c094631185d449.html index 84a2ba60..b3547c55 100644 --- a/group__functions_gad726f439fb9920c055c094631185d449.html +++ b/group__functions_gad726f439fb9920c055c094631185d449.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T exp(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T exp(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T exp(T z) noexcept;
    }
    kyosu::exp
    constexpr tags::callable_exp exp
    Computes the exponential of the argument.
    Definition: exp.hpp:73
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    diff --git a/group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html b/group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html index d0bf57e3..f86597c3 100644 --- a/group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html +++ b/group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html @@ -148,15 +148,15 @@

    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;
    +
    template<eve::floating_ordered_value T> constexpr auto complex(T r, T i = 0) noexcept;
    +
    template<kyosu::concepts::complex 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: beta.hpp:13

    Parameters

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

    Return value

    Returns a kyosu::complex constructed from its arguments.

    diff --git a/group__functions_gae33f5cc837b57f9adb2d203e36d09712.html b/group__functions_gae33f5cc837b57f9adb2d203e36d09712.html index c2c0098d..26ac968e 100644 --- a/group__functions_gae33f5cc837b57f9adb2d203e36d09712.html +++ b/group__functions_gae33f5cc837b57f9adb2d203e36d09712.html @@ -148,8 +148,8 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<kyosu::concepts::complex T> constexpr auto is_pure(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr auto is_pure(T z) noexcept;
    +
    template<kyosu::concepts::complex T> constexpr auto is_pure(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto is_pure(T z) noexcept;
    }
    kyosu::is_pure
    constexpr tags::callable_is_pure is_pure
    test if the parameter is pure.
    Definition: is_pure.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13
    @@ -158,7 +158,7 @@

    real part of the argument is zero.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    @@ -181,7 +181,7 @@

    Example

    return 0;
    }
    -
    kyosu::is_imag
    constexpr tags::callable_is_pure is_imag
    test if the parameter real part is zero.
    Definition: is_pure.hpp:73
    +
    kyosu::is_imag
    constexpr tags::callable_is_pure is_imag
    alias of is_pure
    Definition: is_pure.hpp:75
    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_gae6df724ac822c7361d9ea9252e62d0a4.html b/group__functions_gae6df724ac822c7361d9ea9252e62d0a4.html index 8371c97b..baa1a8a6 100644 --- a/group__functions_gae6df724ac822c7361d9ea9252e62d0a4.html +++ b/group__functions_gae6df724ac822c7361d9ea9252e62d0a4.html @@ -148,8 +148,8 @@

    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<eve::floating_ordered_value T> constexpr auto quaternion(T r, T i = 0, T j = 0, T k = 0) noexcept;
    +
    template<eve::floating_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
    diff --git a/group__functions_gae8a89a63722b9cdec2f2d4daf58bf025.html b/group__functions_gae8a89a63722b9cdec2f2d4daf58bf025.html index 8c0f9d75..a8019809 100644 --- a/group__functions_gae8a89a63722b9cdec2f2d4daf58bf025.html +++ b/group__functions_gae8a89a63722b9cdec2f2d4daf58bf025.html @@ -142,23 +142,23 @@

    -

    Computes the value 1 minus the argument.

    +

    Computes the value one minus the argument.

    Defined in Header

    #oneminuslude <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr T oneminus(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T oneminus(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T oneminus(T z) noexcept;
    }
    -
    kyosu::oneminus
    constexpr tags::callable_oneminus oneminus
    Computes the value 1 minus the argument.
    Definition: oneminus.hpp:72
    +
    kyosu::oneminus
    constexpr tags::callable_oneminus oneminus
    Computes the value one minus the argument.
    Definition: oneminus.hpp:72
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

    • z : argument.

    Return value

    -

    Returns 1 minus the argument.

    +

    Returns one minus the argument.

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_gae8e08be7b28ad1cf9159ae564115867f.html b/group__functions_gae8e08be7b28ad1cf9159ae564115867f.html index 174291bc..bcc3be4e 100644 --- a/group__functions_gae8e08be7b28ad1cf9159ae564115867f.html +++ b/group__functions_gae8e08be7b28ad1cf9159ae564115867f.html @@ -148,19 +148,44 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template<eve::value T, eve::value U, eve::value U>
    -
    constexpr auto convert(T x, eve::as<U> ) noexcept;
    +
    template<eve::floating_scalar_ordered_value U> constexpr auto convert(auto x, eve::as<U> ) noexcept;
    }
    kyosu::convert
    constexpr tags::callable_convert convert
    convert to a target typek
    Definition: convert.hpp:76
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      -
    • x : Value to process.
      • -
    • U`: target scalar type to convert to.
      • +
    • x: floating or Cayley Dickinson value to process.
      • +
    • U: target type to convert to.
    -

    Return value

    -

    Example

    -
    +

    Return value 

     a value resulting of the conversion of each of its elements to type U.
+

    Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    #include <iomanip>
    +
    +
    int main()
    +
    {
    +
    using kyosu::convert;
    +
    using kyosu::complex_t;
    +
    using kyosu::quaternion_t;
    +
    +
    double f = 72.987654321;
    +
    std::cout << "Real to complex of floats: ";
    +
    std::cout << std::setprecision(10) << f << " -> " << convert(f, eve::as<complex_t<float>>()) << "\n";
    +
    std::cout << "Real to quaternion of double: " ;
    +
    std::cout << f << " -> " << convert(f, eve::as<quaternion_t<double>>()) << "\n";
    +
    +
    std::cout << "Complex to quaternion ofdouble: ";
    +
    auto c = kyosu::complex(3.5f,-2.9f);
    +
    std::cout << c << " -> " << convert(c, eve::as<quaternion_t<double>>()) << "\n";
    +
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    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 index 101e22b3..cbbadcd0 100644 --- a/group__functions_gae97bce0027166d1321885e92abb15836.html +++ b/group__functions_gae97bce0027166d1321885e92abb15836.html @@ -149,17 +149,21 @@

    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;
    +
    template<eve::floating_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: beta.hpp:13

    Parameters

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

    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

    +
      +
    • For most z, 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 are the signs of the components of pure(z).
      • +
    +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    #include <iostream>
    diff --git a/group__quaternion_gaeb24f578562330d825ff8f68da4b9252.html b/group__functions_gaeb24f578562330d825ff8f68da4b9252.html similarity index 89% rename from group__quaternion_gaeb24f578562330d825ff8f68da4b9252.html rename to group__functions_gaeb24f578562330d825ff8f68da4b9252.html index 6d60d2ce..17c27091 100644 --- a/group__quaternion_gaeb24f578562330d825ff8f68da4b9252.html +++ b/group__functions_gaeb24f578562330d825ff8f68da4b9252.html @@ -96,7 +96,7 @@
    @@ -149,9 +149,9 @@

    Callable Signatures

    namespace kyosu
    {
    -
    auto from_angle_axis(auto angle, auto axis, auto norming = normalize) const noexcept;
    +
    auto from_angle_axis(auto angle, auto axis, auto norming = normalize) const noexcept;
    }
    -
    kyosu::from_angle_axis
    constexpr tags::callable_from_angle_axis from_angle_axis
    Callable object computing a quaternion from its angle_axis representation.
    Definition: from_angle_axis.hpp:90
    +
    kyosu::from_angle_axis
    constexpr tags::callable_from_angle_axis from_angle_axis
    Callable object computing a quaternion from its angle_axis representation.
    Definition: from_angle_axis.hpp:90
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      @@ -169,7 +169,7 @@

      Example

      int main()
      {
      -
      using kyosu::from_angle_axis;
      +
      using kyosu::from_angle_axis;
      using kyosu::complex_t;
      using kyosu::quaternion_t;
      @@ -179,8 +179,8 @@

      Example

      std::cout << " <- theta = " << theta << std::endl;
      std::cout << " <- axis = (" << ax[0] << ", " << ax[1] << ", " << ax[2] << ")" << std::endl;
      -
      auto q = kyosu::from_angle_axis(theta, ax);
      -
      std::cout << " -> " << kyosu::from_angle_axis(theta, ax) << "\n";
      +
      auto q = kyosu::from_angle_axis(theta, ax);
      +
      std::cout << " -> " << kyosu::from_angle_axis(theta, ax) << "\n";
      auto [aa, axx] = kyosu::to_angle_axis(q);
      std::cout << " ->theta = " << aa << std::endl;
      std::cout << " -> axis = (" << axx[0] << ", " << axx[1] << ", " << axx[2] << ")" << std::endl;
      diff --git a/group__functions_gaecbb072c068e6effd78aa84c6e65b329.html b/group__functions_gaecbb072c068e6effd78aa84c6e65b329.html index 7c877d0e..9f9370d1 100644 --- a/group__functions_gaecbb072c068e6effd78aa84c6e65b329.html +++ b/group__functions_gaecbb072c068e6effd78aa84c6e65b329.html @@ -149,7 +149,7 @@

      namespace kyosu
      {
      template<kyosu::concepts::cayley_dickson T> constexpr T csc(T z) noexcept;
      -
      template<eve::ordered_value T> constexpr T csc(T z) noexcept;
      +
      template<eve::floating_ordered_value T> constexpr T csc(T z) noexcept;
      }
      kyosu::csc
      constexpr tags::callable_csc csc
      Computes the cosecant of the argument.
      Definition: csc.hpp:73
      kyosu
      Main KYOSU namespace.
      Definition: beta.hpp:13
      diff --git a/group__functions_gaee536feee7876ba344199903c2852962.html b/group__functions_gaee536feee7876ba344199903c2852962.html index 4082288d..279f3c4c 100644 --- a/group__functions_gaee536feee7876ba344199903c2852962.html +++ b/group__functions_gaee536feee7876ba344199903c2852962.html @@ -142,16 +142,16 @@

      -

      Computes the arc secant of the argument times \(\pi\).

      +

      Computes the arc secant of the argument in \(\pi\) multiples.

      Defined in Header

      #include <kyosu/functions.hpp>

      Callable Signatures

      namespace kyosu
      {
      -
      template<eve::ordered_value T> constexpr auto asecpi(T z) noexcept; //1
      +
      template<eve::floating_ordered_value T> constexpr auto asecpi(T z) noexcept; //1
      template<kyosu::concepts::cayley_dickson T> constexpr auto asecpi(T z) noexcept; //2
      }
      -
      kyosu::asecpi
      constexpr tags::callable_asecpi asecpi
      Computes the arc secant of the argument times .
      Definition: asecpi.hpp:79
      +
      kyosu::asecpi
      constexpr tags::callable_asecpi asecpi
      Computes the arc secant of the argument in multiples.
      Definition: asecpi.hpp:79
      kyosu
      Main KYOSU namespace.
      Definition: beta.hpp:13

      Parameters

        @@ -159,8 +159,8 @@

        -
      • a real input z is treated as if complex(z) was entered.
        • -
      • Returns invpi(as(z))*asec(z)
        • +
      • a real input z is treated as if kyosu::complex(z) was entered.
        • +
      • Returns kyosu::radinpi(kyosu::asec(z))

        • Example

        #include <kyosu/kyosu.hpp>
        @@ -184,7 +184,7 @@

        Example

        return 0;
        }
        -
        kyosu::asech
        constexpr tags::callable_asech asech
        Computes the hyperbolic arcsecant of the argument.
        Definition: asech.hpp:79
        +
        kyosu::asech
        constexpr tags::callable_asech asech
        Computes the inverse hyperbolic secant 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 45ed0eb2..85dd97b5 100644 --- a/group__functions_gaee913dc7298d2917743440e9d056d971.html +++ b/group__functions_gaee913dc7298d2917743440e9d056d971.html @@ -149,7 +149,7 @@

    namespace kyosu
    {
    template<kyosu::concepts::cayley_dickson T> constexpr as_real_t<T> abs(T z) noexcept;
    -
    template<eve::ordered_value T> constexpr T abs(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T abs(T z) noexcept;
    }
    kyosu::abs
    constexpr tags::callable_abs abs
    Computes the absolute value of the parameter.
    Definition: abs.hpp:73
    kyosu::as_real_t
    typename as_real< T >::type as_real_t
    Compute the real type associated to a Cayley-Dickson-like type.
    Definition: traits.hpp:79
    @@ -160,7 +160,7 @@

    Example

    #include <kyosu/kyosu.hpp>
    diff --git a/group__functions_gaf0240aea3dcf4428abd35906e94323e7.html b/group__functions_gaf0240aea3dcf4428abd35906e94323e7.html index 85e17a68..db6e124d 100644 --- a/group__functions_gaf0240aea3dcf4428abd35906e94323e7.html +++ b/group__functions_gaf0240aea3dcf4428abd35906e94323e7.html @@ -148,16 +148,18 @@

    Callable Signatures

    namespace kyosu
    {
    -
    template< floating_value P, typename ... Ts>
    -
    auto operator()(Ts ... zi ) const noexcept
    +
    template< f typename ... Ts> auto hypot(Ts ... zi ) const noexcept
    ! }
    +
    kyosu::hypot
    constexpr tags::callable_hypot hypot
    Callable object computing the hypot operation.
    Definition: hypot.hpp:74
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      -
    • zi... : Values to process.
      • +
    • zi... : Values to process: mix of floating and Cayley-Dickson.

    Return value

    -

    Returns \( \sqrt\sum_{i = 0}^n//! |z_i|^2} \).

    +
      +
    • Returns \( \sqrt{\sum_{i = 0}^{n-1} |z_i|^2} \) where \(n\) is the number of arguments.
      • +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    @@ -201,7 +203,6 @@

    Example

    return 0;
    }
    -
    kyosu::hypot
    constexpr tags::callable_hypot hypot
    Callable object computing the hypot operation.
    Definition: hypot.hpp:75
    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 index 62981b98..35c1e717 100644 --- a/group__functions_gaf0517a14ea9458fd0698d804b465d366.html +++ b/group__functions_gaf0517a14ea9458fd0698d804b465d366.html @@ -142,24 +142,23 @@

    -

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

    +

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

    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
    +
    template<eve::floating_ordered_value T> constexpr auto zeta(T z) noexcept;
    +
    template<kyosu::concepts::complex T> constexpr auto zeta(T z) noexcept;
    }
    -
    kyosu::zeta
    constexpr tags::callable_zeta zeta
    Computes the Riemann .
    Definition: zeta.hpp:78
    +
    kyosu::zeta
    constexpr tags::callable_zeta zeta
    Computes the Riemann .
    Definition: zeta.hpp:77
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

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

    Return value

    -

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

    +

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

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__functions_gaf0f1fa52661fc9f3b89a02a76d001794.html b/group__functions_gaf0f1fa52661fc9f3b89a02a76d001794.html index 8a58a63f..e3b1c75b 100644 --- a/group__functions_gaf0f1fa52661fc9f3b89a02a76d001794.html +++ b/group__functions_gaf0f1fa52661fc9f3b89a02a76d001794.html @@ -142,16 +142,16 @@

    -

    Computes the arc cosine of the argument times \(\pi\).

    +

    Computes the arc cosine of the argument in \(\pi\) multiples.

    Defined in Header

    #include <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    -
    template<eve::ordered_value T> constexpr auto acospi(T z) noexcept; //1
    +
    template<eve::floating_ordered_value T> constexpr auto acospi(T z) noexcept; //1
    template<kyosu::concepts::cayley_dickson T> constexpr auto acospi(T z) noexcept; //2
    }
    -
    kyosu::acospi
    constexpr tags::callable_acospi acospi
    Computes the arc cosine of the argument times .
    Definition: acospi.hpp:79
    +
    kyosu::acospi
    constexpr tags::callable_acospi acospi
    Computes the arc cosine of the argument in multiples.
    Definition: acospi.hpp:79
    kyosu
    Main KYOSU namespace.
    Definition: beta.hpp:13

    Parameters

      @@ -159,8 +159,8 @@

      -
    • a real input z is treated as if complex(z) was entered.
      • -
    • Returns invpi(as(z))*acos(z)
      • +
    • a real input z is treated as if kyosu::complex(z) was entered.
      • +
    • Returns kyosu::radinpi(kyosu::acos(z))

      • Example

      #include <kyosu/kyosu.hpp>
      diff --git a/group__functions_gaf190a649d5907b9f6c177bb100a73c8d.html b/group__functions_gaf190a649d5907b9f6c177bb100a73c8d.html index 00a93a60..a0f22e9b 100644 --- a/group__functions_gaf190a649d5907b9f6c177bb100a73c8d.html +++ b/group__functions_gaf190a649d5907b9f6c177bb100a73c8d.html @@ -146,14 +146,11 @@

      #include <kyosu/functions.hpp>

      Callable Signatures

      -
      namespace kyosu
      -
      {
      -
      template<kyosu::concepts::cayley_dickson T0, kyosu::concepts::cayley_dickson T1 > constexpr auto lerp(T0 z0, T1, z1, auto eve::ordered_value t) noexcept;
      -
      template<eve::ordered_value T0, kyosu::concepts::cayley_dickson T1> > constexpr auto lerp(T0 z0, T1, z1, auto eve::ordered_value t) noexcept;
      -
      template<kyosu::concepts::cayley_dickson T0, eve::ordered_value T1 > constexpr auto lerp(T0 z0, T1, z1, auto eve::ordered_value t) noexcept;
      -
      template<eve::ordered_value T0, ordered_value T1> > constexpr auto lerp(T0 z0, T1, z1, auto eve::ordered_value t) noexcept;
      -
      ! }
      -
      kyosu::lerp
      constexpr tags::callable_lerp lerp
      Computes the linear interpolation.
      Definition: lerp.hpp:81
      +
      namespace kyosu
      +
      {
      +
      constexpr auto lerp(auto z0, auto, z1, floating_ordered_value t) noexcept;
      +
      }
      +
      kyosu::lerp
      constexpr tags::callable_lerp lerp
      Computes the linear interpolation.
      Definition: lerp.hpp:80
      kyosu
      Main KYOSU namespace.
      Definition: beta.hpp:13

      Parameters

        @@ -162,6 +159,7 @@

        See also
        slerp for better unitary quaternion (spheroidal) interpolation.

        Example

        #include <kyosu/kyosu.hpp>
        #include <eve/wide.hpp>
        diff --git a/group__functions_gaf34684f4a02ca7468c2f7cb440779a6d.html b/group__functions_gaf34684f4a02ca7468c2f7cb440779a6d.html index 2505aba7..9eb5c104 100644 --- a/group__functions_gaf34684f4a02ca7468c2f7cb440779a6d.html +++ b/group__functions_gaf34684f4a02ca7468c2f7cb440779a6d.html @@ -149,7 +149,7 @@

        namespace kyosu
        {
        template<kyosu::concepts::cayley_dickson T> constexpr auto sincos(T z) noexcept;
        -
        template<eve::ordered_value T> constexpr auto sincos(T z) noexcept;
        +
        template<eve::floating_ordered_value T> constexpr auto sincos(T z) noexcept;
        }
        kyosu::sincos
        constexpr tags::callable_sincos sincos
        Computes simultaneously the sine and cosine of the argument.
        Definition: sincos.hpp:73
        kyosu
        Main KYOSU namespace.
        Definition: beta.hpp:13
        diff --git a/group__functions_gaf57c0dd30eab1c6bf0a4c81c849307d5.html b/group__functions_gaf57c0dd30eab1c6bf0a4c81c849307d5.html index dd408aec..73715470 100644 --- a/group__functions_gaf57c0dd30eab1c6bf0a4c81c849307d5.html +++ b/group__functions_gaf57c0dd30eab1c6bf0a4c81c849307d5.html @@ -149,7 +149,7 @@

        namespace kyosu
        {
        template<kyosu::concepts::complex T> constexpr T tgamma(T z) noexcept;
        -
        template<eve::floatingordered_value T> constexpr T tgamma(T z) noexcept;
        +
        template<eve::floating_ordered_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: beta.hpp:13
        @@ -158,7 +158,7 @@

        complex(z) was used in the call.

        +

        Returns \(\Gamma(z)\).

        Example

        #include <kyosu/kyosu.hpp>
        #include <eve/wide.hpp>
        diff --git a/group__functions_gafb007a0b170f27331d8aa088e9f8f0b0.html b/group__functions_gafb007a0b170f27331d8aa088e9f8f0b0.html index a7e83ac9..8cd2d572 100644 --- a/group__functions_gafb007a0b170f27331d8aa088e9f8f0b0.html +++ b/group__functions_gafb007a0b170f27331d8aa088e9f8f0b0.html @@ -148,10 +148,10 @@

        Callable Signatures

        namespace kyosu
        {
        +
        template<eve::floating_ordered_value T> constexpr complex_t<T> log2(T z) noexcept;
        template<kyosu::concepts::cayley_dickson T> constexpr 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::log2
        constexpr tags::callable_log2 log2
        Computes the base 2 logarithm of the argument.
        Definition: log2.hpp:79
        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: beta.hpp:13

        Parameters

        @@ -159,7 +159,10 @@

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

        +
          +
        1. a real typed input z is treated as if kyosu::complex(z) was entered.
          2. +
        2. returns log(z)/log_2(as(z)).
          3. +

        Example

        #include <kyosu/kyosu.hpp>
        #include <eve/wide.hpp>
        diff --git a/group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html b/group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html index fb0754fc..ab5a0056 100644 --- a/group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html +++ b/group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html @@ -142,7 +142,7 @@

        -

        Computes the asinhine of the argument.

        +

        Computes the inverse hyperbolic sine of the argument.

        Defined in Header

        #include <kyosu/functions.hpp>

        Callable Signatures

        @@ -152,7 +152,7 @@

        template<kyosu::concepts::complex T> constexpr auto asinh(T z) noexcept; //2

        template<kyosu::concepts::cayley_dickson T> constexpr auto asinh(T z) noexcept; //3
        }
        -
        kyosu::asinh
        constexpr tags::callable_asinh asinh
        Computes the asinhine of the argument.
        Definition: asinh.hpp:95
        +
        kyosu::asinh
        constexpr tags::callable_asinh asinh
        Computes the inverse hyperbolic sine of the argument.
        Definition: asinh.hpp:95
        kyosu
        Main KYOSU namespace.
        Definition: beta.hpp:13

        Parameters

        Parameters

        -

        q : quaternion

        +

        q : quaternion, complex or floating

        Return value

        -

        the rotation angle in radian

        +

        the rotation angle in radian. This is two times the arg of the quaternion.

        Example

        diff --git a/group__quaternion_ga6b47fd35280cf1ec86c8596e0cd1b73c.html b/group__quaternion_ga6b47fd35280cf1ec86c8596e0cd1b73c.html index 94924e66..30d7021a 100644 --- a/group__quaternion_ga6b47fd35280cf1ec86c8596e0cd1b73c.html +++ b/group__quaternion_ga6b47fd35280cf1ec86c8596e0cd1b73c.html @@ -163,7 +163,33 @@

        Example

        -
        +
        #include <kyosu/kyosu.hpp>
        +
        #include <eve/wide.hpp>
        +
        #include <iostream>
        +
        +
        int main()
        +
        {
        +
        using kyosu::align;
        +
        auto norm = [](auto &v){
        +
        auto n = eve::hypot(v[0], v[1], v[2]);
        +
        for(int i=0; i <= 2; ++i) v[i]/= n;
        +
        };
        +
        +
        std::array<double, 3> v0{-1.0, 5.0, 4.0};
        +
        std::array<double, 3> v1{ 1.5, 2.0, -3.0};
        +
        norm(v0);
        +
        norm(v1);
        +
        auto q = kyosu::align(v0, v1);
        +
        std::cout << " v0 " << v0[0] << ", " << v0[1] << ", " << v0[2] << "\n";
        +
        std::cout << " v1 " << v1[0] << ", " << v1[1] << ", " << v1[2] << "\n";
        +
        std::cout << " q " << q << std::endl;
        +
        auto rv = kyosu::rotate_vec(q, v0);
        +
        std::cout << " rotate_vec(q, v0) " << rv[0] << ", " << rv[1] << ", " << rv[2] << "\n";
        +
        +
        return 0;
        +
        }
        +
        kyosu::rotate_vec
        constexpr tags::callable_rotate_vec rotate_vec
        Callable object rotating an vector using a quaternion.
        Definition: rotate_vec.hpp:105
        +

    diff --git a/group__quaternion_ga8d6d4d74663080af513e4428dcc01612.html b/group__quaternion_ga8d6d4d74663080af513e4428dcc01612.html index 600b4bca..5275f46a 100644 --- a/group__quaternion_ga8d6d4d74663080af513e4428dcc01612.html +++ b/group__quaternion_ga8d6d4d74663080af513e4428dcc01612.html @@ -222,7 +222,7 @@

    Example

    return 0;
    }
    -
    kyosu::average
    constexpr tags::callable_average average
    Computes the average of the two parameters.
    Definition: average.hpp:77
    +
    kyosu::average
    constexpr tags::callable_average average
    Computes the average of the two parameters.
    Definition: average.hpp:74
    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__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html b/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html index 1dc26963..49efe559 100644 --- a/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html +++ b/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html @@ -153,7 +153,7 @@

    }

    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

    +

    q : quaternion, complex or floating.

    Return value

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

    diff --git a/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html b/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html index 0f30edd5..54ae63cc 100644 --- a/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html +++ b/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html @@ -157,7 +157,7 @@

    +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__quaternion_gadc8b483ae153b0e6d1eb4d7ece78660d.html b/group__quaternion_gadc8b483ae153b0e6d1eb4d7ece78660d.html new file mode 100644 index 00000000..ea513897 --- /dev/null +++ b/group__quaternion_gadc8b483ae153b0e6d1eb4d7ece78660d.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::to_cylindrospherical + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
    Loading...
    +
    Searching...
    +
    No Matches
    +
    +
    +
    +
    + +
    + +

    ◆ to_cylindrospherical

    + +
    +
    + + + + + +
    + + + + +
    kyosu::to_cylindrospherical = {}
    +     		+inlineconstexpr
    +
    + +

    Callable object computing the cylindrospherical coordinates from a quaternion.

    +

    This function is the reciprocal of from_cylindrospherical.

    +

    Defined in header

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

    Callable Signatures

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

    Parameters

    +

    q : quaternion

    +

    Return value

    +

    a tuple containing in this order t, 'radius', longitude 'latitude': the components of the cylindrospherical parametrisation of \(\mathbb{R}^4\) coordinates

    +
    +

    +Example

    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::to_cylindrospherical;
    +
    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<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);
    +
    std::cout << e0 << " -> " << to_cylindrospherical(e0) << "\n";
    +
    we_t we0(e0);
    +
    std::cout << we0 << " -> " << to_cylindrospherical(we0) << "\n";
    +
    +
    std::cout << "Complex: "<< "\n";
    +
    c_t c0(1, 5);
    +
    std::cout << c0 << " -> " << to_cylindrospherical(c0) << "\n";
    +
    wc_t wc0(c0);
    +
    std::cout << wc0 << " -> " << to_cylindrospherical(wc0) << "\n";
    +
    +
    std::cout << "Quaternion: "<< "\n";
    +
    q_t q0(1, 5, 2, 3);
    +
    std::cout << q0 << " -> " << to_cylindrospherical(q0) << "\n";
    +
    wq_t wq0(q0);
    +
    std::cout << wq0 << " -> " << to_cylindrospherical(wq0) << "\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__quaternion_gae984161c55fda44efe7d7f9b274334c6.html b/group__quaternion_gae984161c55fda44efe7d7f9b274334c6.html index 352e0b07..05b20fca 100644 --- a/group__quaternion_gae984161c55fda44efe7d7f9b274334c6.html +++ b/group__quaternion_gae984161c55fda44efe7d7f9b274334c6.html @@ -157,7 +157,7 @@

    +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    @@ -210,7 +210,7 @@

    return 0;
    }
    -
    kyosu::average
    constexpr tags::callable_average average
    Computes the average of the two parameters.
    Definition: average.hpp:77
    +
    kyosu::average
    constexpr tags::callable_average average
    Computes the average of the two parameters.
    Definition: average.hpp:74
    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__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html b/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html index 1dc3075c..45c0b396 100644 --- a/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html +++ b/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html @@ -148,11 +148,12 @@

    Callable Signatures

    namespace eve
    {
    -
    auto rotate_vec( auto q) const noexcept;
    +
    auto rotate_vec( auto q, auto v) const noexcept;
    }
    -
    kyosu::rotate_vec
    constexpr tags::callable_rotate_vec rotate_vec
    Callable object rotating an vector using a quaternion.
    Definition: rotate_vec.hpp:104
    +
    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 value defining the rotation. x: span of 3 elements to rotate

    +

    q: quaternion value defining the rotation.

    +

    v: span of 3 elements to rotate.

    Return value

    the span rotated by q

    @@ -169,7 +170,7 @@

    auto theta = eve::pio_3(eve::as<double>());
    std::array<double, 3> ax{1., 2., 3.};
    std::array<double, 3> v{ 1.5, 2.0, -3.0};
    -
    auto q = kyosu::from_angle_axis(theta, ax);
    +
    auto q = kyosu::from_angle_axis(theta, ax);
    std::cout << " v " << v[0] << ", " << v[1] << ", " << v[2] << ")\n";
    std::cout << " q " << q << std::endl;
    auto rv = kyosu::rotate_vec(q, std::span<double, 3>(v));
    @@ -177,7 +178,7 @@

    return 0;
    }
    -
    kyosu::from_angle_axis
    constexpr tags::callable_from_angle_axis from_angle_axis
    Callable object computing a quaternion from its angle_axis representation.
    Definition: from_angle_axis.hpp:90
    +
    kyosu::from_angle_axis
    constexpr tags::callable_from_angle_axis from_angle_axis
    Callable object computing a quaternion from its angle_axis representation.
    Definition: from_angle_axis.hpp:90

    diff --git a/index.html b/index.html index 1349e005..30a7fe0b 100644 --- a/index.html +++ b/index.html @@ -130,7 +130,7 @@

    The Cayley-Dickson construction scheme defines a new algebra as a Cartesian product of an algebra with itself, with multiplication defined in a specific way (different from the componentwise multiplication) and an involution known as conjugation.

    We currently only implement the Cayley-Dickson algebras based on the IEEE float and double representations of real numbers.

    Kyosu proper usable objects are all in the namespace kyosu.

    -

    +

    Cayley-Dickson algebras

    These are algebras over the real numbers with an involution named conjugation. The product of an element by its conjugate is 'real' and its positive square root is a norm on the vector space defined by the algebra.

    Starting from the real numbers (supported by type T float or double) we define:

    @@ -159,27 +159,48 @@

  • quaternion is a non-commutative field
  • octonion is a non associative (but alternative) division algebra
    • +

    The functions commutator (resp. associator) can be used to see if two (resp. three) Cayley-Dickson value commute (resp. associate).

    Greater dimensions are not even alternative but keep power-associativity which allows to define most elementary functions.

    -

    +
    Note
    Let us recall that alternative means that every subalgrebra generated by two elements is associative.
    +

    What does this implementation provide

    All operators and functions implemented can receive a mix of scalar or simd of cayley-dickson and reals of various dimensionnality and are defined in the namespace kyosu.

    -

    Of course the algebra operation +, -, * and / are provided, but as \ is not an usable C++ character as an operator, the left division ais provided as the call ldiv(a,b).

    -

    +

    Of course the algebra operation +, -, * and / are provided, but as \ is not an usable C++ character as an operator, the left division a \ b is provided as the call ldiv(a,b).

    +

    Constructors

    complex and quaternion can be constructed using callables facilities complex and quaternion.

    -

    complex can also be constructed from their polar representation quaternion from various parametrizations of \(\mathbb{R}^4\) or from \(\mathbb{R}^3\) rotations:

    -
      -
    • angle and axis
      • -
    • cylindrical
      • -
    • cylindricospherical
      • -
    • euler
      • -
    • multipolar
      • -
    • rotation_matrix
      • -
    • semipolar
      • -
    • spherical
      • -
    -

    TODO cayley_dickson<N>

    -

    +

    complex can also be constructed from their polar representation
    +quaternion from various parametrizations of \(\mathbb{R}^4\) or from \(\mathbb{R}^3\) rotations:

    + + + + + + + + + + + + + + + + + + + + + +
    angle and axis from_angle_axis to_angle_axis
    cylindrical from_cylindrical to_cylindrical
    cylindrospherical from_cylindrospherical to_cylindrospherical
    euler from_euler to_euler
    multipolar from_multipolar to_multipolar
    rotation matrix from_rotation_matrix to_rotation_matrix
    semipolar from_semipolar to_semipolar
    spherical from_spherical to_spherical
    two vectors align
    +

    The third column references to the corresponding to_xxx version that gives back the chosen representation from a quaternion input.

    +

    TODO cayley_dickson<N> construction by a function.

    +

    +Operators

    +

    Operators (as said before) +, -, * and / can be used in infix form and can mix cayley-dickson values of different dimensinalities. Of course the biggest dimensionlity is recovered in the output.

    +

    Prefix forms are also provided as add, sub, multiply and div. Also plus and minus for unary versions.

    +

    The left division sometimes necessary if the dimensionality is greater than 2 is given as ldiv.

    +

    Functions

    Most KYOSU callables are usable with all cayley_dickson types. The exception being mainly special complex functions and rotation related quaternion usage.

    Warning
    : EVE callables that correspond to mathematical functions that are only defined on a proper part of the real axis as, for example, acos DOES NOT ever provide the same result if called in EVE or KYOSU context.
    @@ -187,12 +208,87 @@

    All these kinds of functions called with a floating value in the kyosu namespace will return a complex value.

    • callables usable with all cayley_dickson types

      -

      Most EVE arithmetic functions are provided.

      +

      Most EVE arithmetic and math functions are provided.

      • -
    • callables usable with complex only
      • -
    • callables usable with quaternion (and complex) only
    -

    Most EVE arithmetic functions are provided.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    abs acos acosh acospi acot
    acotpi atanpi acoth arg acsc
    acscpi acsch asec asecpi asech
    asin asinpi asinh atan atanh
    average ceil conj cos cosh
    cospi cot cotpi coth convert
    csc cscpi csch dec dist
    dot exp exp10 exp2 exp_i
    exp_ipi expm1 expmx2 expx2 floor
    frac from_polar hypot if_else inc
    ipart is_denormal is_equal is_eqz is_finite
    is_infinite is_imag is_nan is_nez is_not_denormal
    is_not_equal is_not_finite is_not_infinite is_not_nan is_not_real
    is_pure is_real is_unitary jpart kpart
    ldiv lerp log log10 log1p
    log_abs log2 lpnorm manhattan minus
    lpart lipart ljpart lkpart
    nearest oneminus pow pow1p pow_abs
    powm1 proj pure radinpi real
    rec reldist sec secpi sech
    sign sin sinc sincos sinpi
    sinpicospi sinh sinhcosh slerp sqr
    sqr_abs sqrt tan tanpi tanh
    to_polar trunc
    +
      +
    • callables usable with complex or real only. These are mainly implementation of some classical meromorphic functions.
      • +
    + + + + + + + + + + + +
    beta deta digamma erf erfcx
    erfi eta faddeeva lambda lbeta
    log_abs_gamma log_gamma lrising_factorial rising_factorial tgamma
    zeta
    +
      +

    • callables usable with quaternion complex and real only

      +

      These functions are related to \(\mathbb{R}^3\) rotations

      +
      • +
    + + + + + +
    rot_angle rot_axis rotate_vec
    diff --git a/namespacekyosu.html b/namespacekyosu.html index 7339595f..62844452 100644 --- a/namespacekyosu.html +++ b/namespacekyosu.html @@ -275,7 +275,7 @@  Computes the inverse hyperbolic cosine of the argument.
      constexpr tags::callable_acospi acospi = {} - Computes the arc cosine of the argument times \(\pi\).
    + Computes the arc cosine of the argument in \(\pi\) multiples.
      constexpr tags::callable_acot acot = {}  Computes the arc cotangent of the argument.
    @@ -284,7 +284,7 @@  Computes the inverse hyperbolic cotangent of the argument.
      constexpr tags::callable_acotpi acotpi = {} - Computes the arc cotangent of the argument times \(\pi\).
    + Computes the arc cotangent of the argument in \(\pi\) multiples.
      constexpr tags::callable_acsc acsc = {}  Computes the arccosecant of the argument.
    @@ -293,50 +293,56 @@  Computes the inverse hyperbolic cosecant of the argument.
      constexpr tags::callable_acscpi acscpi = {} - Computes the arc cosecant of the argument times \(\pi\).
    + Computes the arc cosecant of the argume!nt in \(\pi\) multiples.
      constexpr tags::callable_align align = {}  Callable object computing a quaternion from its angle_axis representation.
      constexpr tags::callable_arg arg = {} - complex number argument.
    + argument.
      constexpr tags::callable_asec asec = {}  Computes the arcsecant of the argument.
      constexpr tags::callable_asech asech = {} - Computes the hyperbolic arcsecant of the argument.
    + Computes the inverse hyperbolic secant of the argument.
      constexpr tags::callable_asecpi asecpi = {} - Computes the arc secant of the argument times \(\pi\).
    + Computes the arc secant of the argument in \(\pi\) multiples.
      constexpr tags::callable_asin asin = {}  Computes the arcsine of the argument.
      constexpr tags::callable_asinh asinh = {} - Computes the asinhine of the argument.
    + Computes the inverse hyperbolic sine of the argument.
      constexpr tags::callable_asinpi asinpi = {} - Computes the arc sine of the argument times \(\pi\).
    + Computes the arc sine of the argument in \(\pi\) multiples.
      +constexpr tags::callable_associator associator = {} + Computes the associator of the three parameters.
    +  constexpr tags::callable_atan atan = {} - Computes the inverse hyperbolic tangent of the argument.
    + Computes the arctangent of the argument.
      constexpr tags::callable_atanh atanh = {}  Computes the inverse hyperbolic tangent of the argument.
      constexpr tags::callable_atanpi atanpi = {} - Computes the arc tangent of the argument times \(\pi\).
    + Computes the arc tangent of the argument in \(\pi\) multiples.
      constexpr tags::callable_average average = {}  Computes the average of the two parameters.
      constexpr tags::callable_beta beta = {} - Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\).
    + Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) for real or complex entries.
      constexpr tags::callable_ceil ceil = {}  Computes the ceil value.
      +constexpr tags::callable_commutator commutator = {} + Computes the commutator of the two parameters.
    +  constexpr tags::callable_complex complex = {}  Constructs a kyosu::complex.
      @@ -353,7 +359,7 @@  Computes the hyperbolic cosine of the argument.
      constexpr tags::callable_cospi cospi = {} - Computes the cosine of the argument in \(\pi\) mutiples.
    + Computes the cosine from the argument in \(\pi\) multiples.
      constexpr tags::callable_cot cot = {}  Computes the cotangent of the argument.
    @@ -362,25 +368,25 @@  Computes the hyperbolic cotangent of the argument.
      constexpr tags::callable_cotpi cotpi = {} - Computes the cotangent of the argument in \(\pi\) mutiples.
    + Computes the cotangent from the argument in \(\pi\) multiples.
      constexpr tags::callable_csc csc = {}  Computes the cosecant of the argument.
      constexpr tags::callable_csch csch = {} - Computes the hyperbolic cscant of the argument.
    + Computes the hyperbolic cosecant of the argument.
      constexpr tags::callable_cscpi cscpi = {} - Computes the cosecant of the argument in \(\pi\) mutiples.
    + Computes the cosecant from the argument in \(\pi\) multiples.
      constexpr tags::callable_dec dec = {}  decrements the argument by 1.
      constexpr tags::callable_deta deta = {} - Computes the Dirichlet sums \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(kn+1)^z}\).
    + Computes the Dirichlet sums \( \displaystyle \sum_{n = 0}^\infty \frac{(-1)^n}{(kn+1)^z}\).
      constexpr tags::callable_digamma digamma = {} - Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\).
    + Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\) function.
      template<typename T > constexpr unsigned int dimension_v = *implementation-defined* @@ -415,13 +421,13 @@  Computes the base 2 exponential of the argument.
      constexpr tags::callable_exp_i exp_i = {} - Computes the exponential of the argument times i.
    + Computes the exponential of i times the argument.
      constexpr tags::callable_exp_ipi exp_ipi = {} - Computes the exponential of the argument times i.
    + Computes the exponential of \(i\pi\) times the argument.
      constexpr tags::callable_expm1 expm1 = {} - Computes the expm1onential of the argument minus 1.
    + Computes the exponential of the argument minus 1.
      constexpr tags::callable_expmx2 expmx2 = {}  Computes the exponential of the opposite of the squared argument.
    @@ -438,7 +444,7 @@ constexpr tags::callable_frac frac = {}  Computes the frac value.
      -constexpr tags::callable_from_angle_axis from_angle_axis = {} +constexpr tags::callable_from_angle_axis from_angle_axis = {}  Callable object computing a quaternion from its angle_axis representation.
      constexpr tags::callable_from_cylindrical from_cylindrical = {} @@ -454,7 +460,7 @@  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.
    + Callable object computing a complex or a general Cayley-Dickson from a polar representation.
      constexpr tags::callable_from_rotation_matrix from_rotation_matrix = {}  Callable object computing a quaternion from its rotation_matrix representation.
    @@ -471,12 +477,16 @@ constexpr tags::callable_if_else if_else = {}  Select a value between two arguments based on a logical mask.
      -constexpr tags::callable_ipart imag = {} - Alias for ipart.
    -  + +constexpr tags::callable_ipart imag = {} + Alias for ipart.
    +  constexpr tags::callable_inc inc = {}  Increments the argument.
      +constexpr tags::callable_ipart ipart = {} + Extracts the imaginary part of a value.
    +  constexpr tags::callable_is_denormal is_denormal = {}  test if the parameter is denormal.
      @@ -484,13 +494,13 @@  retuen true if and only if the two parameters are equal.
      constexpr tags::callable_is_eqz is_eqz = {} - test the parameter for zero equality.
    + test the parameter for equality to zero.
      constexpr tags::callable_is_finite is_finite = {}  test if the parameter is finite.
      constexpr tags::callable_is_pure is_imag = {} - test if the parameter real part is zero.
    + alias of is_pure
      constexpr tags::callable_is_infinite is_infinite = {}  test if the parameter is infinite.
    @@ -505,7 +515,7 @@  test if the parameter is not denormal.
      constexpr tags::callable_is_not_equal is_not_equal = {} - retuen true if and only if the two parameters are equal.
    + return true if and only if the two parameters are not equal.
      constexpr tags::callable_is_not_finite is_not_finite = {}  test if the parameter is not finite.
    @@ -514,7 +524,7 @@  test if the parameter is not infinite.
      constexpr tags::callable_is_not_nan is_not_nan = {} - test if the parameter is not_nan.
    + test if the parameter is not a Nan.
      constexpr tags::callable_is_not_real is_not_real = {}  test if the parameter is not_real.
    @@ -546,6 +556,15 @@ constexpr tags::callable_lerp lerp = {}  Computes the linear interpolation.
      +constexpr tags::callable_lipart lipart = {} + Extracts the li (sixth) part of a value.
    +  +constexpr tags::callable_ljpart ljpart = {} + Extracts the lj (seventh) part of a value.
    +  +constexpr tags::callable_lkpart lkpart = {} + Extracts the lk (eighth) part of a value.
    +  constexpr tags::callable_log log = {}  Computes the natural logarithm of the argument.
      @@ -567,6 +586,9 @@ constexpr tags::callable_log_gamma log_gamma = {}  Computes the log of the \(\Gamma\) function of the parameter.
      +constexpr tags::callable_lpart lpart = {} + Extracts the l (fifth) part of a value.
    +  constexpr tags::callable_lpnorm lpnorm = {}  Callable object computing the lpnorm operation \( \left(\sum_{i = 0}^n |x_i|^p\right)^{\frac1p} \).
    @@ -584,7 +606,7 @@  Computes the nearest value.
      constexpr tags::callable_oneminus oneminus = {} - Computes the value 1 minus the argument.
    + Computes the value one minus the argument.
      constexpr tags::callable_pow pow = {}  Computes the computing the pow operation \(x^y\).
    @@ -601,6 +623,9 @@ 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_pure pure = {} + Extracts the imaginary part of a value.
    +  constexpr tags::callable_quaternion quaternion = {}  Constructs a kyosu::quaternion.
      @@ -635,7 +660,7 @@  Computes the hyperbolic secant of the argument.
      constexpr tags::callable_secpi secpi = {} - Computes the secant of the argument in \(\pi\) mutiples.
    + Computes the secant of the argument in \(\pi\) multiples.
      constexpr tags::callable_sign sign = {}  Computes tne normalized value z/abs(z) if z is not zero else 0.
    @@ -656,10 +681,10 @@  Computes simultaneously the hyperbolic sine and cosine of the argument.
      constexpr tags::callable_sinpi sinpi = {} - Computes the sine of the argument in \(\pi\) mutiples.
    + Computes the sine of the argument in \(\pi\) multiples.
      constexpr tags::callable_sinpicospi sinpicospi = {} - Computes simultaneously the sine and cosine of the argument in \(\pi\) mutiples.
    + Computes simultaneously the sine and cosine of the argument in \(\pi\) multiples.
      constexpr tags::callable_slerp slerp = {}  Computes the spherical interpolation between unitary quaternions.
    @@ -680,7 +705,7 @@  Computes the hyperbolic tangent of the argument.
      constexpr tags::callable_tanpi tanpi = {} - Computes the tangent of the argument in \(\pi\) mutiples.
    + Computes the tangent of the argument in \(\pi\) multiples.
      constexpr tags::callable_tgamma tgamma = {}  Computes the tgammaolute value of the parameter.
    @@ -691,6 +716,9 @@ constexpr tags::callable_to_cylindrical to_cylindrical = {}  Callable object computing the cylindrical coordinates from a quaternion.
      +constexpr tags::callable_to_cylindrospherical to_cylindrospherical = {} + Callable object computing the cylindrospherical coordinates from a quaternion.
    +  constexpr tags::callable_to_euler to_euler = {}  Callable object computing euler angles from a quaternion.
      @@ -713,7 +741,7 @@  Computes the trunc value.
      constexpr tags::callable_zeta zeta = {} - Computes the Riemann \(\zeta\) \( \displaystyle \sum_0^\infty \frac{1}{(n+1)^z}\).
    + Computes the Riemann \( \displaystyle\zeta(z)=\sum_0^\infty \frac{1}{(n+1)^z}\).
      diff --git a/navtreedata.js b/navtreedata.js index a9830497..e61e4e9b 100644 --- a/navtreedata.js +++ b/navtreedata.js @@ -25,10 +25,11 @@ var NAVTREE = [ [ "kyosu", "index.html", [ - [ "Cayley-Dickson algebras", "index.html#autotoc_md27", null ], - [ "What does this implementation provide", "index.html#autotoc_md28", [ - [ "Constructors", "index.html#autotoc_md29", null ], - [ "Functions", "index.html#autotoc_md30", null ] + [ "Cayley-Dickson algebras", "index.html#autotoc_md29", null ], + [ "What does this implementation provide", "index.html#autotoc_md30", [ + [ "Constructors", "index.html#autotoc_md31", null ], + [ "Operators", "index.html#autotoc_md32", null ], + [ "Functions", "index.html#autotoc_md33", null ] ] ], [ "How-Tos", "usergroup0.html", null ], [ "Reference Documentation", "usergroup1.html", [ diff --git a/navtreeindex0.js b/navtreeindex0.js index c607cc85..a27ecba0 100644 --- a/navtreeindex0.js +++ b/navtreeindex0.js @@ -9,10 +9,11 @@ var NAVTREEINDEX0 = "group__traits.html":[3,2], "group__types.html":[3,0], "index.html":[], -"index.html#autotoc_md27":[0], -"index.html#autotoc_md28":[1], -"index.html#autotoc_md29":[1,0], -"index.html#autotoc_md30":[1,1], +"index.html#autotoc_md29":[0], +"index.html#autotoc_md30":[1], +"index.html#autotoc_md31":[1,0], +"index.html#autotoc_md32":[1,1], +"index.html#autotoc_md33":[1,2], "licence.html":[4,0], "pages.html":[], "usergroup0.html":[2], diff --git a/search/all_0.js b/search/all_0.js index 6c55887f..0c22f4ae 100644 --- a/search/all_0.js +++ b/search/all_0.js @@ -21,8 +21,9 @@ var searchData= ['asin_18',['asin',['../group__functions_ga7586f69da3dd2de8eb36e571d0cda51a.html#ga7586f69da3dd2de8eb36e571d0cda51a',1,'kyosu']]], ['asinh_19',['asinh',['../group__functions_gafb2c650b3e7a1251e5ace712ad2fad44.html#gafb2c650b3e7a1251e5ace712ad2fad44',1,'kyosu']]], ['asinpi_20',['asinpi',['../group__functions_ga92c4c9260b24c8171caca5c014ad4298.html#ga92c4c9260b24c8171caca5c014ad4298',1,'kyosu']]], - 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