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Cayley/extend complex #34

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Cayley/extend complex #34

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4490122
trigo et invtrigo use cayley_extend
jtlap Oct 8, 2023
f539592
math use cayley_extend
jtlap Oct 8, 2023
912f094
no more specific complex functions
jtlap Oct 9, 2023
5adf110
no more complex specific
jtlap Oct 9, 2023
045f30f
joel's remarks
jtlap Oct 9, 2023
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54 changes: 24 additions & 30 deletions doc/index.md
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Expand Up @@ -129,46 +129,40 @@ complex functions and rotation related quaternion usage.

* callables usable with all cayley_dickson types

Most **EVE** arithmetic and math functions are provided.
Most **EVE** arithmetic and math functions are provided. In particular, real analytic functions of one variable
can be quite naturally extended using the polar form described above from a mere complex implementation.

| | | | | |
|--------------|---------------|-----------------|------------|-----------------|
| [abs](@ref kyosu::abs ) | [acos](@ref kyosu::acos ) | [acosh](@ref kyosu::acosh ) | [acospi](@ref kyosu::acospi ) | [acot](@ref kyosu::acot ) |
| [acotpi](@ref kyosu::acotpi ) | [atanpi](@ref kyosu::atanpi ) | [acoth](@ref kyosu::acoth ) | [arg](@ref kyosu::arg ) | [acsc](@ref kyosu::acsc ) |
| [acscpi](@ref kyosu::acscpi ) | [acsch](@ref kyosu::acsch ) | [asec](@ref kyosu::asec ) | [asecpi](@ref kyosu::asecpi ) | [asech](@ref kyosu::asech ) |
| [asin](@ref kyosu::asin ) | [asinpi](@ref kyosu::asinpi ) | [asinh](@ref kyosu::asinh ) | [atan](@ref kyosu::atan ) | [atanh](@ref kyosu::atanh ) |
| [average](@ref kyosu::average ) | [ceil](@ref kyosu::ceil ) | [conj](@ref kyosu::conj ) | [cos](@ref kyosu::cos ) | [cosh](@ref kyosu::cosh ) |
| [cospi](@ref kyosu::cospi ) | [cot](@ref kyosu::cot ) | [cotpi](@ref kyosu::cotpi ) | [coth](@ref kyosu::coth ) | [convert](@ref kyosu::convert ) |
| [csc](@ref kyosu::csc ) | [cscpi](@ref kyosu::cscpi ) | [csch](@ref kyosu::csch ) | [dec](@ref kyosu::dec ) | [dist](@ref kyosu::dist ) |
| [dot](@ref kyosu::dot ) | [exp](@ref kyosu::exp ) | [exp10](@ref kyosu::exp10 ) | [exp2](@ref kyosu::exp2 ) | [exp_i](@ref kyosu::exp_i ) |
| [exp_ipi](@ref kyosu::exp_ipi ) | [expm1](@ref kyosu::expm1 ) | [expmx2](@ref kyosu::expmx2 ) | [expx2](@ref kyosu::expx2 ) | [fam](@ref kyosu::fam ) |
| [floor](@ref kyosu::floor ) | [fma](@ref kyosu::fma ) | [fms](@ref kyosu::fms ) | [fnma](@ref kyosu::fnma ) | [fnms](@ref kyosu::fnms ) |
| [frac](@ref kyosu::frac ) | [fsm](@ref kyosu::fsm ) | [from_polar](@ref kyosu::from_polar ) | [horner](@ref kyosu::horner ) | [hypot](@ref kyosu::hypot ) |
| [if_else](@ref kyosu::if_else ) | [inc](@ref kyosu::inc ) ||||
| [average](@ref kyosu::average ) | [beta](@ref kyosu::beta ) | [ceil](@ref kyosu::ceil ) | [conj](@ref kyosu::conj ) | [cos](@ref kyosu::cos ) |
| [cosh](@ref kyosu::cosh ) | [cospi](@ref kyosu::cospi ) | [cot](@ref kyosu::cot ) | [cotpi](@ref kyosu::cotpi ) | [coth](@ref kyosu::coth ) |
| [convert](@ref kyosu::convert ) | [csc](@ref kyosu::csc ) | [cscpi](@ref kyosu::cscpi ) | [csch](@ref kyosu::csch ) | [dec](@ref kyosu::dec ) |
| [deta](@ref kyosu::deta ) | [digamma](@ref kyosu::digamma ) | [dist](@ref kyosu::dist ) | [dot](@ref kyosu::dot ) | [erf](@ref kyosu::erf ) |
| [erfcx](@ref kyosu::erfcx ) | [erfi](@ref kyosu::erfi ) | [eta](@ref kyosu::eta ) | [exp](@ref kyosu::exp ) | [exp10](@ref kyosu::exp10 ) |
| [exp2](@ref kyosu::exp2 ) | [exp_i](@ref kyosu::exp_i ) | [exp_ipi](@ref kyosu::exp_ipi ) | [expm1](@ref kyosu::expm1 ) | [expmx2](@ref kyosu::expmx2 ) |
| [expx2](@ref kyosu::expx2 ) | [faddeeva](@ref kyosu::faddeeva ) | [fam](@ref kyosu::fam ) | [floor](@ref kyosu::floor ) | [fma](@ref kyosu::fma ) |
| [fms](@ref kyosu::fms ) | [fnma](@ref kyosu::fnma ) | [fnms](@ref kyosu::fnms ) | [frac](@ref kyosu::frac ) | [fsm](@ref kyosu::fsm ) |
| [from_polar](@ref kyosu::from_polar ) | [horner](@ref kyosu::horner ) | [hypot](@ref kyosu::hypot ) | [if_else](@ref kyosu::if_else )| [inc](@ref kyosu::inc ) |
| [ipart](@ref kyosu::ipart ) | [is_denormal](@ref kyosu::is_denormal ) | [is_equal](@ref kyosu::is_equal ) | [is_eqz](@ref kyosu::is_eqz ) | [is_finite](@ref kyosu::is_finite ) |
| [is_infinite](@ref kyosu::is_infinite ) | [is_imag](@ref kyosu::is_imag ) | [is_nan](@ref kyosu::is_nan ) | [is_nez](@ref kyosu::is_nez ) | [is_not_denormal](@ref kyosu::is_not_denormal ) |
| [is_not_equal](@ref kyosu::is_not_equal ) | [is_not_finite](@ref kyosu::is_not_finite ) | [is_not_infinite](@ref kyosu::is_not_finite ) | [is_not_nan](@ref kyosu::is_not_nan ) | [is_not_real](@ref kyosu::is_not_real ) |
| [is_not_equal](@ref kyosu::is_not_equal ) | [is_not_finite](@ref kyosu::is_not_finite ) | [is_not_infinite](@ref kyosu::is_not_finite ) | [is_not_nan](@ref kyosu::is_not_nan ) | [is_not_real](@ref kyosu::is_not_real ) |
| [is_pure](@ref kyosu::is_pure ) | [is_real](@ref kyosu::is_real ) | [is_unitary](@ref kyosu::is_unitary ) | [jpart](@ref kyosu::jpart ) | [kpart](@ref kyosu::kpart ) |
| [ldiv](@ref kyosu::ldiv ) | [lerp](@ref kyosu::lerp ) | [log](@ref kyosu::log ) | [log10](@ref kyosu::log10 ) | [log1p](@ref kyosu::log1p ) |
| [log_abs](@ref kyosu::log_abs ) | [log2](@ref kyosu::log2 ) | [lpnorm](@ref kyosu::lpnorm ) | [manhattan](@ref kyosu::manhattan ) | [minus](@ref kyosu::minus ) |
| [lpart](@ref kyosu::lpart ) | [lipart](@ref kyosu::lipart ) | [ljpart](@ref kyosu::ljpart ) | [lkpart](@ref kyosu::lkpart ) | |
| [nearest](@ref kyosu::nearest ) | [oneminus](@ref kyosu::oneminus ) | [pow](@ref kyosu::pow ) | [pow1p](@ref kyosu::pow1p ) | [pow_abs](@ref kyosu::pow_abs ) |
| [powm1](@ref kyosu::powm1 ) | [proj](@ref kyosu::proj ) | [pure](@ref kyosu::imag ) | [radinpi](@ref kyosu::radinpi )| [real](@ref kyosu::real ) |
| [rec](@ref kyosu::rec ) | [reldist](@ref kyosu::reldist ) | [reverse_horner](@ref kyosu::reverse_horner ) | [right_horner](@ref kyosu::right_horner ) | [right_reverse_horner](@ref kyosu::right_reverse_horner ) |
| [sec](@ref kyosu::sec ) | [secpi](@ref kyosu::secpi ) | [sech](@ref kyosu::sech ) | | |
| [sign](@ref kyosu::sign ) | [sin](@ref kyosu::sin ) | [sinc](@ref kyosu::sinc ) | [sincos](@ref kyosu::sincos ) | [sinpi](@ref kyosu::sinpi ) |
| [sinpicospi](@ref kyosu::sinpicospi ) | [sinh](@ref kyosu::sinh ) | [sinhcosh](@ref kyosu::sinhcosh ) | [slerp](@ref kyosu::slerp ) | [sqr](@ref kyosu::sqr ) |
| [sqr_abs](@ref kyosu::sqr_abs ) | [sqrt](@ref kyosu::sqrt ) | [tan](@ref kyosu::tan ) | [tanpi](@ref kyosu::tanpi ) | [tanh](@ref kyosu::tanh ) |
| [to_polar](@ref kyosu::to_polar ) | [trunc](@ref kyosu::trunc ) | | | |

* callables usable with complex or real only. These are mainly implementation of some classical meromorphic functions.

| | | | | |
|------------------|------------------|--------------------|------------------|---------------|
| [beta](@ref kyosu::beta ) | [deta](@ref kyosu::deta ) | [digamma](@ref kyosu::digamma ) | [erf](@ref kyosu::erf ) | [erfcx](@ref kyosu::erfcx ) |
| [erfi](@ref kyosu::erfi ) | [eta](@ref kyosu::eta ) | [faddeeva](@ref kyosu::faddeeva ) | [lambda](@ref kyosu::lambda ) | [lbeta](@ref kyosu::lbeta ) |
| [log_abs_gamma](@ref kyosu::log_abs_gamma ) | [log_gamma](@ref kyosu::log_gamma ) | [lrising_factorial](@ref kyosu::lrising_factorial ) | [rising_factorial](@ref kyosu::rising_factorial ) | [tgamma](@ref kyosu::tgamma ) |
| [zeta](@ref kyosu::zeta ) | | | | |
| [ldiv](@ref kyosu::ldiv ) | [lambda](@ref kyosu::lambda ) | [lbeta](@ref kyosu::lbeta ) | [lerp](@ref kyosu::lerp ) | [lipart](@ref kyosu::lipart ) |
| [ljpart](@ref kyosu::ljpart ) | [lkpart](@ref kyosu::lkpart ) | [log](@ref kyosu::log ) | [log2](@ref kyosu::log2 ) | [lpart](@ref kyosu::lpart ) |
| [lipart](@ref kyosu::lipart ) | [ljpart](@ref kyosu::ljpart ) | [lkpart](@ref kyosu::lkpart ) | [lpnorm](@ref kyosu::lpnorm ) | [lrising_factorial](@ref kyosu::lrising_factorial ) |
| [manhattan](@ref kyosu::manhattan ) | [minus](@ref kyosu::minus ) | [nearest](@ref kyosu::nearest ) | [oneminus](@ref kyosu::oneminus )| [pow](@ref kyosu::pow ) |
| [pow1p](@ref kyosu::pow1p ) | [pow_abs](@ref kyosu::pow_abs ) | [powm1](@ref kyosu::powm1 ) | [proj](@ref kyosu::proj ) | [pure](@ref kyosu::imag ) |
| [radinpi](@ref kyosu::radinpi ) | [real](@ref kyosu::real ) | [rec](@ref kyosu::rec ) | [reldist](@ref kyosu::reldist )| [reverse_horner](@ref kyosu::reverse_horner ) |
| [right_horner](@ref kyosu::right_horner ) | [right_reverse_horner](@ref kyosu::right_reverse_horner ) | [rising_factorial](@ref kyosu::rising_factorial ) | [sec](@ref kyosu::sec )| [secpi](@ref kyosu::secpi ) |
| [sech](@ref kyosu::sech ) | [sign](@ref kyosu::sign ) | [sin](@ref kyosu::sin ) | [sinc](@ref kyosu::sinc ) | [sincos](@ref kyosu::sincos ) |
| [sinpi](@ref kyosu::sinpi ) | [sinpicospi](@ref kyosu::sinpicospi ) | [sinh](@ref kyosu::sinh ) | [sinhcosh](@ref kyosu::sinhcosh ) | [slerp](@ref kyosu::slerp ) |
| [sqr](@ref kyosu::sqr ) | [sqr_abs](@ref kyosu::sqr_abs ) | [sqrt](@ref kyosu::sqrt ) | [tan](@ref kyosu::tan ) | [tanpi](@ref kyosu::tanpi ) |
| [tanh](@ref kyosu::tanh ) | [to_polar](@ref kyosu::to_polar ) | [tgamma](@ref kyosu::tgamma ) | [trunc](@ref kyosu::trunc ) | [zeta](@ref kyosu::zeta ) |


* callables usable with quaternion complex and real only

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34 changes: 34 additions & 0 deletions include/kyosu/details/cayleyify.hpp
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@@ -0,0 +1,34 @@
//======================================================================================================================
/*
Kyosu - Complex Without Complexes
Copyright : KYOSU Contributors & Maintainers
SPDX-License-Identifier: BSL-1.0
*/
//======================================================================================================================
#pragma once

auto cayley_extend(auto f, auto z, auto... rs)
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care to explain what if of them do ?

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pb with sincos etc.-> cayley_extend2
pb with deta(k,z) etc. -> cayley_extend_rev
cayley_extend works for all other

{
auto p = kyosu::pure(z);
auto az = kyosu::abs(p);
auto c = f(kyosu::complex(kyosu::real(z), az), rs...);
return kyosu::real(c) + kyosu::ipart(c)*kyosu::sign(p);
}

auto cayley_extend_rev(auto f, auto z1, auto z2)
{
auto p = kyosu::pure(z2);
auto az2 = kyosu::abs(p);
auto c = f(z1, kyosu::complex(kyosu::real(z2), az2));
return kyosu::real(c) + kyosu::ipart(c)*kyosu::sign(p);
}

auto cayley_extend2(auto f, auto z, auto... rs)
{
auto p = kyosu::pure(z);
auto az = kyosu::abs(p);
auto [c1, c2] = f(kyosu::complex(kyosu::real(z), az), rs...);
auto s = kyosu::sign(p);
return kumi::tuple{ kyosu::real(c1) + kyosu::ipart(c1)*s
, kyosu::real(c2) + kyosu::ipart(c2)*s};
}
39 changes: 17 additions & 22 deletions include/kyosu/functions.hpp
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Expand Up @@ -33,6 +33,7 @@
#include <kyosu/functions/atan.hpp>
#include <kyosu/functions/atanh.hpp>
#include <kyosu/functions/average.hpp>
#include <kyosu/functions/beta.hpp>
#include <kyosu/functions/ceil.hpp>
#include <kyosu/functions/commutator.hpp>
#include <kyosu/functions/conj.hpp>
Expand All @@ -47,8 +48,14 @@
#include <kyosu/functions/cscpi.hpp>
#include <kyosu/functions/csch.hpp>
#include <kyosu/functions/dec.hpp>
#include <kyosu/functions/deta.hpp>
#include <kyosu/functions/digamma.hpp>
#include <kyosu/functions/dist.hpp>
#include <kyosu/functions/dot.hpp>
#include <kyosu/functions/erf.hpp>
#include <kyosu/functions/erfcx.hpp>
#include <kyosu/functions/erfi.hpp>
#include <kyosu/functions/eta.hpp>
#include <kyosu/functions/exp.hpp>
#include <kyosu/functions/exp10.hpp>
#include <kyosu/functions/exp2.hpp>
Expand All @@ -57,6 +64,8 @@
#include <kyosu/functions/expm1.hpp>
#include <kyosu/functions/expmx2.hpp>
#include <kyosu/functions/expx2.hpp>
#include <kyosu/functions/faddeeva.hpp>

#include <kyosu/functions/fam.hpp>
#include <kyosu/functions/floor.hpp>
#include <kyosu/functions/fma.hpp>
Expand Down Expand Up @@ -90,18 +99,24 @@
#include <kyosu/functions/is_unitary.hpp>
#include <kyosu/functions/jpart.hpp>
#include <kyosu/functions/kpart.hpp>
#include <kyosu/functions/lambda.hpp>
#include <kyosu/functions/lbeta.hpp>
#include <kyosu/functions/ldiv.hpp>
#include <kyosu/functions/lerp.hpp>
#include <kyosu/functions/log.hpp>
#include <kyosu/functions/log10.hpp>
#include <kyosu/functions/log1p.hpp>
#include <kyosu/functions/log_abs.hpp>
#include <kyosu/functions/log_abs_gamma.hpp>
#include <kyosu/functions/log_gamma.hpp>
#include <kyosu/functions/log2.hpp>
#include <kyosu/functions/lpart.hpp>
#include <kyosu/functions/lipart.hpp>
#include <kyosu/functions/ljpart.hpp>
#include <kyosu/functions/lkpart.hpp>
#include <kyosu/functions/lpnorm.hpp>
#include <kyosu/functions/lrising_factorial.hpp>
#include <kyosu/functions/rising_factorial.hpp>
#include <kyosu/functions/manhattan.hpp>
#include <kyosu/functions/maxabs.hpp>
#include <kyosu/functions/maxmag.hpp>
Expand Down Expand Up @@ -143,35 +158,15 @@
#include <kyosu/functions/tan.hpp>
#include <kyosu/functions/tanpi.hpp>
#include <kyosu/functions/tanh.hpp>
#include <kyosu/functions/tgamma.hpp>
#include <kyosu/functions/to_polar.hpp>
#include <kyosu/functions/trunc.hpp>

//======================================================================================================================
//! @brief Functions performing computations over complex or real elements only.
//======================================================================================================================

#include <kyosu/complex/beta.hpp>
#include <kyosu/complex/deta.hpp>
#include <kyosu/complex/digamma.hpp>
#include <kyosu/complex/erf.hpp>
#include <kyosu/complex/erfcx.hpp>
#include <kyosu/complex/erfi.hpp>
#include <kyosu/complex/eta.hpp>
#include <kyosu/complex/faddeeva.hpp>
#include <kyosu/complex/lambda.hpp>
#include <kyosu/complex/lbeta.hpp>
#include <kyosu/complex/log_abs_gamma.hpp>
#include <kyosu/complex/log_gamma.hpp>
#include <kyosu/complex/lrising_factorial.hpp>
#include <kyosu/complex/rising_factorial.hpp>
#include <kyosu/complex/tgamma.hpp>
#include <kyosu/complex/zeta.hpp>
#include <kyosu/functions/zeta.hpp>

//======================================================================================================================
//! @brief Functions performing computations over quaternion complex or real elements only.
//======================================================================================================================


#include <kyosu/functions/align.hpp>
#include <kyosu/functions/from_angle_axis.hpp>
#include <kyosu/functions/from_cylindrical.hpp>
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4 changes: 2 additions & 2 deletions include/kyosu/complex/beta.hpp → include/kyosu/functions/beta.hpp
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Expand Up @@ -61,12 +61,12 @@ namespace kyosu
//!
//! **Parameters**
//!
//! * `x`,`y` : Values to process. Can be a mix of complex and real floating values and complex values.
//! * `x`,`y` : Values to process. Can be a mix of cayley_dickson and real floating values.
//!
//! **Return value**
//!
//! 1. If x and y are real typed values returns \f$\displaystyle \mathbf{B}(x,y) = \int_0^1 t^{x-1}(1-t)^{y-1}\mbox{d}t\f$
//! 2. if x or y is complex the value \f$\displaystyle \mathbf{B}(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\f$ is returned.
//! 2. \f$\displaystyle \mathbf{B}(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\f$ is returned.
//!
//! @groupheader{Example}
//!
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3 changes: 1 addition & 2 deletions include/kyosu/complex/deta.hpp → include/kyosu/functions/deta.hpp
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Expand Up @@ -56,8 +56,7 @@ namespace kyosu
//! @code
//! 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
//! constexpr auto deta(unsigned_scalar_value auto k, auto z) noexcept;
//! }
//! @endcode
//!
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5 changes: 2 additions & 3 deletions include/kyosu/complex/digamma.hpp → include/kyosu/functions/digamma.hpp
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Expand Up @@ -52,14 +52,13 @@ namespace kyosu
//! @code
//! namespace kyosu
//! {
//! template<kyosu::concepts::complex T> constexpr T digamma(T z) noexcept;
//! template<eve::floating_ordered_value T> constexpr T digamma(T z) noexcept;
//! constexpr auto digamma(auto z) noexcept;
//! }
//! @endcode
//!
//! **Parameters**
//!
//! * `z` : real or complex value to process.
//! * `z` : value to process.
//!
//! **Return value**
//!
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10 changes: 4 additions & 6 deletions include/kyosu/complex/erf.hpp → include/kyosu/functions/erf.hpp
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Expand Up @@ -44,7 +44,7 @@ namespace kyosu
//! @var erf
//! @brief Computes the error function: \f$ \displaystyle
//! \mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\f$ or
//! its analytic continuation in the complex plane
//! its extension to complex and general cayley-dickson values
//!
//! **Defined in Header**
//!
Expand All @@ -57,8 +57,8 @@ namespace kyosu
//! @code
//! namespace kyosu
//! {
//! template<eve::ordered_value T> constexpr auto erf(T z) noexcept; //1
//! template<kyosu::concepts::complex T> constexpr auto erf(T z) noexcept; //2
//! { template<eve::floating_ordered_value T> constexpr T erf(T z) noexcept;
//! template<kyosu::concepts::cayley_dickson T> constexpr T erf(T z) noexcept;
//! }
//! @endcode
//!
Expand All @@ -68,9 +68,7 @@ namespace kyosu
//!
//! **Return value**
//!
//! 1. a real input z returns eve::erf(z).
//!
//! 2. The value of the error function in the complex plane is returned
//! * The value of the error function is returned.
//!
//! @groupheader{Example}
//!
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4 changes: 2 additions & 2 deletions include/kyosu/complex/erfcx.hpp → include/kyosu/functions/erfcx.hpp
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Expand Up @@ -56,8 +56,8 @@ namespace kyosu
//! @code
//! namespace kyosu
//! {
//! template<eve::ordered_value T> constexpr auto erfcx(T z) noexcept; //1
//! template<kyosu::concepts::complex T> constexpr auto erfcx(T z) noexcept; //2
//! template<eve::ordered_value T> constexpr auto erfcx(T z) noexcept; //1
//! template<kyosu::concepts::cayley_dickson T> constexpr auto erfcx(T z) noexcept; //2
//! }
//! @endcode
//!
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6 changes: 3 additions & 3 deletions include/kyosu/complex/erfi.hpp → include/kyosu/functions/erfi.hpp
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Expand Up @@ -23,7 +23,7 @@ namespace kyosu::tags
{
auto over = eve::sqr(v) > 720;
auto r = eve::inf(eve::as(v))*eve::sign(v);
r = eve::if_else(over, r, -kyosu::imag(kyosu::erf(complex(eve::zero(eve::as(v)), -v))));
r = eve::if_else(over, r, -get<1>(kyosu::erf(complex(eve::zero(eve::as(v)), -v))));
return complex(r);
}

Expand Down Expand Up @@ -58,8 +58,8 @@ namespace kyosu
//! @code
//! namespace kyosu
//! {
//! template<eve::ordered_value T> constexpr auto erfi(T z) noexcept; //1
//! template<kyosu::concepts::complex T> constexpr auto erfi(T z) noexcept; //2
//! template<eve::ordered_value T> constexpr auto erfi(T z) noexcept; //1
//! template<kyosu::concepts::cayley_dickson T> constexpr auto erfi(T z) noexcept; //2
//! }
//! @endcode
//!
Expand Down
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