math/test/octonion_test_simple.cpp
2024-02-13 10:04:28 +01:00

617 lines
18 KiB
C++

// Copyright Hubert Holin 2001.
// Copyright Christopher Kormanyos 2024
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
#include <boost/mpl/list.hpp>
#include <boost/math/octonion.hpp>
#include <boost/core/lightweight_test.hpp>
#include <cstdint>
#include <random>
// test file for octonion.hpp
namespace local
{
std::mt19937 eng(static_cast<typename std::mt19937::result_type>(UINT8_C(42)));
std::uniform_int_distribution<int> dst_one(1, 1);
template<typename NumericType>
auto is_close_fraction(const NumericType& a,
const NumericType& b,
const NumericType& tol) noexcept -> bool
{
using std::fabs;
auto result_is_ok = bool { };
if(b == static_cast<NumericType>(0))
{
result_is_ok = (fabs(a - b) < tol);
}
else
{
const auto delta = fabs(1 - (a / b));
result_is_ok = (delta < tol);
}
return result_is_ok;
}
template<typename T>
auto is_close_fraction(const ::boost::math::octonion<T>& a,
const ::boost::math::octonion<T>& b,
const T& tol) noexcept -> bool
{
using std::fabs;
bool result_is_ok { true };
result_is_ok = (is_close_fraction(a.R_component_1(), b.R_component_1(), tol) && result_is_ok);
result_is_ok = (is_close_fraction(a.R_component_2(), b.R_component_2(), tol) && result_is_ok);
result_is_ok = (is_close_fraction(a.R_component_3(), b.R_component_3(), tol) && result_is_ok);
result_is_ok = (is_close_fraction(a.R_component_4(), b.R_component_4(), tol) && result_is_ok);
result_is_ok = (is_close_fraction(a.R_component_5(), b.R_component_5(), tol) && result_is_ok);
result_is_ok = (is_close_fraction(a.R_component_6(), b.R_component_6(), tol) && result_is_ok);
result_is_ok = (is_close_fraction(a.R_component_7(), b.R_component_7(), tol) && result_is_ok);
result_is_ok = (is_close_fraction(a.R_component_8(), b.R_component_8(), tol) && result_is_ok);
return result_is_ok;
}
template<typename T>
::boost::math::octonion<T> index_i_element(int idx)
{
return(
::boost::math::octonion<T>(
(idx == 0) ?
static_cast<T>(1) :
static_cast<T>(0),
(idx == 1) ?
static_cast<T>(1) :
static_cast<T>(0),
(idx == 2) ?
static_cast<T>(1) :
static_cast<T>(0),
(idx == 3) ?
static_cast<T>(1) :
static_cast<T>(0),
(idx == 4) ?
static_cast<T>(1) :
static_cast<T>(0),
(idx == 5) ?
static_cast<T>(1) :
static_cast<T>(0),
(idx == 6) ?
static_cast<T>(1) :
static_cast<T>(0),
(idx == 7) ?
static_cast<T>(1) :
static_cast<T>(0)
));
}
}
template<class T>
void multiplication_test()
{
using ::std::numeric_limits;
using ::boost::math::abs;
// Testing multiplication.
const auto one_by_one = ::boost::math::octonion<T>(1,0,0,0,0,0,0,0) * ::boost::math::octonion<T>(1,0,0,0,0,0,0,0);
const T delta { abs(one_by_one - static_cast<T>(1)) };
const auto result_mul_one_is_ok = (delta < numeric_limits<T>::epsilon());
BOOST_TEST(result_mul_one_is_ok);
for (int idx = 1; idx < 8; ++idx)
{
::boost::math::octonion<T> toto = local::index_i_element<T>(idx);
const T tabs { abs(toto*toto+static_cast<T>(1)) };
const auto result_mul_toto_is_ok = (tabs < numeric_limits<T>::epsilon());
BOOST_TEST(result_mul_toto_is_ok);
}
{
const boost::math::octonion<T> lhs(T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8));
const boost::math::octonion<T> rhs(T(8),T(7),T(6),T(5),T(4),T(3),T(2),T(1));
const boost::math::octonion<T> prod = lhs * rhs;
const boost::math::octonion<T> ctrl(T(-104), T(14), T(12), T(10), T(152), T(42), T(4), T(74));
BOOST_TEST(prod == ctrl);
}
for(auto i = static_cast<unsigned>(UINT8_C(0)); i < static_cast<unsigned>(UINT8_C(16)); ++i)
{
const boost::math::octonion<T> lhs(T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8));
const boost::math::octonion<T> rhs =
boost::math::octonion<T> { T(1),T(1),T(1),T(1),T(1),T(1),T(1),T(1) }
* static_cast<T>(local::dst_one(local::eng));
const boost::math::octonion<T> quot = lhs / rhs;
const boost::math::octonion<T> ctrl(T(4.5), T(0.25), T(0.5), T(0.75), T(-1), T(0.75), T(1.5), T(0.75));
BOOST_TEST(quot == ctrl);
}
}
template<class T>
void division_test()
{
{
const boost::math::octonion<T> lhs(T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8));
const boost::math::octonion<T> rhs(T(1),T(1),T(1),T(1),T(1),T(1),T(1),T(1));
const boost::math::octonion<T> quot = lhs / rhs;
const boost::math::octonion<T> ctrl(T(4.5), T(0.25), T(0.5), T(0.75), T(-1), T(0.75), T(1.5), T(0.75));
BOOST_TEST(quot == ctrl);
}
{
const std::complex<T> one_one(T(1), T(1));
const boost::math::octonion<T> lhs(T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8));
const boost::math::octonion<T> rhs(one_one, one_one, one_one, one_one);
const boost::math::octonion<T> quot = lhs / rhs;
const boost::math::octonion<T> ctrl(T(4.5), T(0.25), T(0.5), T(0.75), T(-1), T(0.75), T(1.5), T(0.75));
BOOST_TEST(quot == ctrl);
}
}
void octonion_original_manual_test()
{
// tests for evaluation by humans
// using default constructor
::boost::math::octonion<float> o0;
::boost::math::octonion<float> oa[2];
// using constructor "O seen as R^8"
::boost::math::octonion<float> o1(1,2,3,4,5,6,7,8);
::std::complex<double> c0(9,10);
// using constructor "O seen as C^4"
::boost::math::octonion<double> o2(c0);
::boost::math::quaternion<long double> q0(11,12,13,14);
// using constructor "O seen as H^2"
::boost::math::octonion<long double> o3(q0);
// using UNtemplated copy constructor
::boost::math::octonion<float> o4(o1);
// using templated copy constructor
::boost::math::octonion<long double> o5(o2);
// using UNtemplated assignment operator
o5 = o3;
oa[0] = o0;
// using templated assignment operator
o5 = o2;
oa[1] = o5;
float f0(15);
// using converting assignment operator
o0 = f0;
// using converting assignment operator
o2 = c0;
// using converting assignment operator
o5 = q0;
// using += (const T &)
o4 += f0;
// using == (const octonion<T> &,const octonion<T> &)
BOOST_TEST(o0 != o4);
// using += (const ::std::complex<T> &)
o2 += c0;
// using == (const ::boost::math::quaternion<T> &, const octonion<T> &)
BOOST_TEST(q0 == o3);
// using += (const ::boost::math::quaternion<T> &)
o3 += q0;
BOOST_TEST(2 * q0 == o3);
// using += (const quaternion<X> &)
o5 += o4;
// using -= (const T &)
o1 -= f0;
// using -= (const ::std::complex<T> &)
o2 -= c0;
// using -= (const ::boost::math::quaternion<T> &)
o5 -= q0;
// using -= (const octonion<X> &)
o3 -= o4;
// using == (const ::std::complex<T> &, const octonion<T> &)
BOOST_TEST(c0 == o2);
// using == (const octonion<T> &, const ::std::complex<T> &)
BOOST_TEST(o2 == c0);
double d0(16);
::std::complex<double> c1(17,18);
::boost::math::quaternion<double> q1(19,20,21,22);
// using *= (const T &)
o2 *= d0;
// using *= (const ::std::complex<T> &)
o2 *= c1;
// using *= (const ::boost::math::quaternion<T> &)
o2 *= q1;
// using *= (const octonion<X> &)
o2 *= o4;
long double l0(23);
::std::complex<long double> c2(24,25);
// using /= (const T &)
o5 /= l0;
// using /= (const ::std::complex<T> &)
o5 /= c2;
// using /= (const quaternion<X> &)
o5 /= q0;
// using /= (const octonion<X> &)
o5 /= o5;
// using + (const T &, const octonion<T> &)
::boost::math::octonion<float> o6 = f0+o0;
// using + (const octonion<T> &, const T &)
::boost::math::octonion<float> o7 = o0+f0;
// using + (const ::std::complex<T> &, const quaternion<T> &)
::boost::math::octonion<double> o8 = c0+o2;
// using + (const octonion<T> &, const ::std::complex<T> &)
::boost::math::octonion<double> o9 = o2+c0;
// using + (const ::boost::math::quaternion<T>, const octonion<T> &)
::boost::math::octonion<long double> o10 = q0+o3;
// using + (const octonion<T> &, const ::boost::math::quaternion<T> &)
::boost::math::octonion<long double> o11 = o3+q0;
// using + (const quaternion<T> &,const quaternion<T> &)
::boost::math::octonion<float> o12 = o0+o4;
// using - (const T &, const octonion<T> &)
o6 = f0-o0;
// using - (const octonion<T> &, const T &)
o7 = o0-f0;
// using - (const ::std::complex<T> &, const octonion<T> &)
o8 = c0-o2;
// using - (const octonion<T> &, const ::std::complex<T> &)
o9 = o2-c0;
// using - (const quaternion<T> &,const octonion<T> &)
o10 = q0-o3;
// using - (const octonion<T> &,const quaternion<T> &)
o11 = o3-q0;
// using - (const octonion<T> &,const octonion<T> &)
o12 = o0-o4;
// using * (const T &, const octonion<T> &)
o6 = f0*o0;
// using * (const octonion<T> &, const T &)
o7 = o0*f0;
// using * (const ::std::complex<T> &, const octonion<T> &)
o8 = c0*o2;
// using * (const octonion<T> &, const ::std::complex<T> &)
o9 = o2*c0;
// using * (const quaternion<T> &,const octonion<T> &)
o10 = q0*o3;
// using * (const octonion<T> &,const quaternion<T> &)
o11 = o3*q0;
// using * (const octonion<T> &,const octonion<T> &)
o12 = o0*o4;
// using / (const T &, const octonion<T> &)
o6 = f0/o0;
// using / (const octonion<T> &, const T &)
o7 = o0/f0;
// using / (const ::std::complex<T> &, const octonion<T> &)
o8 = c0/o2;
// using / (const octonion<T> &, const ::std::complex<T> &)
o9 = o2/c0;
// using / (const ::boost::math::quaternion<T> &, const octonion<T> &)
o10 = q0/o3;
// using / (const octonion<T> &, const ::boost::math::quaternion<T> &)
o11 = o3/q0;
// using / (const octonion<T> &,const octonion<T> &)
o12 = o0/o4;
// using + (const octonion<T> &)
o4 = +o0;
// using == (const T &, const octonion<T> &)
BOOST_TEST(f0 == o0);
// using == (const octonion<T> &, const T &)
BOOST_TEST(o0 == f0);
// using - (const octonion<T> &)
o0 = -o4;
// using != (const T &, const octonion<T> &)
BOOST_TEST(f0 != o0);
// using != (const octonion<T> &, const T &)
BOOST_TEST(o0 != f0);
// using != (const ::std::complex<T> &, const octonion<T> &)
BOOST_TEST(c0 != o2);
// using != (const octonion<T> &, const ::std::complex<T> &)
BOOST_TEST(o2 != c0);
// using != (const ::boost::math::quaternion<T> &, const octonion<T> &)
BOOST_TEST(q0 != o3);
// using != (const octonion<T> &, const ::boost::math::quaternion<T> &)
BOOST_TEST(o3 != q0);
// using != (const octonion<T> &,const octonion<T> &)
BOOST_TEST(o0 != o4);
}
template <class T>
void elem_func_test()
{
using ::std::numeric_limits;
using ::std::atan;
using ::boost::math::abs;
// Testing exp.
for(int idx = 1; idx < 8; ++idx)
{
::boost::math::octonion<T> toto =
static_cast<T>(4)*atan(static_cast<T>(1)) * local::index_i_element<T>(idx);
const T tabs { abs(exp(toto)+static_cast<T>(1)) };
const auto result_exp_toto_is_ok = (tabs < 2*numeric_limits<T>::epsilon());
BOOST_TEST(result_exp_toto_is_ok);
}
{
const std::complex<T> one_sixteenth_one_over_32 { T { 1 } / 16, T { 1 } / 32 };
const ::boost::math::octonion<T>
octo_small
{
one_sixteenth_one_over_32,
T { 2 } * one_sixteenth_one_over_32,
T { 3 } * one_sixteenth_one_over_32,
T { 4 } * one_sixteenth_one_over_32
};
const auto octo_small_exp = exp(octo_small);
const auto r0 = octo_small_exp.real();
using std::exp;
BOOST_TEST(r0 < exp(one_sixteenth_one_over_32.real()));
{
auto octo_small_exp_inv = ::boost::math::octonion<T>(1);
octo_small_exp_inv /= octo_small_exp;
const auto value_cosh = cosh(octo_small);
const auto value_cosh_ctrl = (octo_small_exp + octo_small_exp_inv) / T(2);
const auto result_cosh_is_ok = local::is_close_fraction(value_cosh, value_cosh_ctrl, std::numeric_limits<T>::epsilon() * 64);
BOOST_TEST(result_cosh_is_ok);
}
{
auto octo_small_exp_inv = ::boost::math::octonion<T>(1);
octo_small_exp_inv /= octo_small_exp;
const auto value_sinh = sinh(octo_small);
const auto value_sinh_ctrl = (octo_small_exp - octo_small_exp_inv) / T(2);
const auto result_sinh_is_ok = local::is_close_fraction(value_sinh, value_sinh_ctrl, std::numeric_limits<T>::epsilon() * 64);
BOOST_TEST(result_sinh_is_ok);
}
{
const auto value_sinh = sinh(octo_small);
const auto value_cosh = cosh(octo_small);
const auto value_tanh = tanh(octo_small);
const auto value_tanh_ctrl = value_sinh / value_cosh;
const auto result_tanh_is_ok = local::is_close_fraction(value_tanh, value_tanh_ctrl, std::numeric_limits<T>::epsilon() * 64);
BOOST_TEST(result_tanh_is_ok);
}
}
{
const std::complex<T> one_sixteenth_one_over_32 { T { 1 } / 16, T { 1 } / 32 };
const ::boost::math::octonion<T>
octo_small
{
one_sixteenth_one_over_32,
T { 2 } * one_sixteenth_one_over_32,
T { 3 } * one_sixteenth_one_over_32,
T { 4 } * one_sixteenth_one_over_32
};
const auto octo_small_sin = sin(octo_small);
const auto r0 = octo_small_sin.real();
using std::sin;
BOOST_TEST(r0 > sin(one_sixteenth_one_over_32.real()));
}
{
const std::complex<T> one_sixteenth_one_over_32 { T { 1 } / 16, T { 1 } / 32 };
const ::boost::math::octonion<T>
octo_small
{
one_sixteenth_one_over_32,
T { 2 } * one_sixteenth_one_over_32,
T { 3 } * one_sixteenth_one_over_32,
T { 4 } * one_sixteenth_one_over_32
};
const auto octo_small_cos = cos(octo_small);
const auto r0 = octo_small_cos.real();
using std::cos;
BOOST_TEST(r0 > cos(one_sixteenth_one_over_32.real()));
}
{
const std::complex<T> one_sixteenth_one_over_32 { T { 1 } / 16, T { 1 } / 32 };
const ::boost::math::octonion<T>
octo_small
{
one_sixteenth_one_over_32,
T { 2 } * one_sixteenth_one_over_32,
T { 3 } * one_sixteenth_one_over_32,
T { 4 } * one_sixteenth_one_over_32
};
const auto octo_small_sin = sin(octo_small);
const auto octo_small_cos = cos(octo_small);
const auto octo_small_tan = tan(octo_small);
const auto octo_small_tan_ctrl = octo_small_sin / octo_small_cos;
const auto result_tan_is_ok = local::is_close_fraction(octo_small_tan, octo_small_tan_ctrl, std::numeric_limits<T>::epsilon() * 64);
BOOST_TEST(result_tan_is_ok);
}
for(auto i = static_cast<unsigned>(UINT8_C(0)); i < static_cast<unsigned>(UINT8_C(8)); ++i)
{
static_cast<void>(i);
::boost::math::octonion<T> b { T {1}, T {2}, T {3}, T {4}, T {5}, T {6}, T {7}, T {8} };
b *= static_cast<T>(local::dst_one(local::eng));
{
::boost::math::octonion<T> bp0 = pow(b, 0);
::boost::math::octonion<T> bp0_ctrl { T { 1 } };
const auto result_b0_is_ok = local::is_close_fraction(bp0, bp0_ctrl, std::numeric_limits<T>::epsilon() * 64);
}
{
::boost::math::octonion<T> bp1 = pow(b, 1);
::boost::math::octonion<T> bp1_ctrl = b;
const auto result_b1_is_ok = local::is_close_fraction(bp1, bp1_ctrl, std::numeric_limits<T>::epsilon() * 64);
}
{
::boost::math::octonion<T> bp2 = pow(b, 2);
::boost::math::octonion<T> bp2_ctrl = b * b;
const auto result_b2_is_ok = local::is_close_fraction(bp2, bp2_ctrl, std::numeric_limits<T>::epsilon() * 64);
}
{
::boost::math::octonion<T> bp3 = pow(b, 3);
::boost::math::octonion<T> bp3_ctrl = (b * b) * b;
const auto result_b3_is_ok = local::is_close_fraction(bp3, bp3_ctrl, std::numeric_limits<T>::epsilon() * 64);
}
{
::boost::math::octonion<T> bp4 = pow(b, 4);
::boost::math::octonion<T> bp2_ctrl = b * b;
::boost::math::octonion<T> bp4_ctrl = bp2_ctrl * bp2_ctrl;
const auto result_b3_is_ok = local::is_close_fraction(bp4, bp4_ctrl, std::numeric_limits<T>::epsilon() * 64);
}
}
}
auto main() -> int
{
multiplication_test<float>();
multiplication_test<double>();
division_test<float>();
elem_func_test<float>();
elem_func_test<double>();
octonion_original_manual_test();
const auto result_is_ok = (boost::report_errors() == 0);
return (result_is_ok ? 0 : -1);
}