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Merge pull request #1090 from boostorg/more_octonion_cover
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Fix #1091 more octonion coverage
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@ckormanyos
ckormanyos authored Feb 13, 2024
2 parents 8d47ee0 + 77da185 commit f767420
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6 changes: 5 additions & 1 deletion include/boost/math/octonion.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -174,6 +174,10 @@ namespace boost
type g; \
type h; \

// LCOV_EXCL_START
// No code coverage for the generic case, like std::complex,
// the The behavior of octonion is unspecified if T is not
// one of float, double or long double.

template<typename T>
class octonion
Expand Down Expand Up @@ -658,7 +662,7 @@ namespace boost
private:

};

// LCOV_EXCL_STOP

// declaration of octonion specialization

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296 changes: 255 additions & 41 deletions test/octonion_test_simple.cpp
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Original file line number Diff line number Diff line change
@@ -1,50 +1,98 @@
// 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 <iomanip>
// 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
namespace local
{
template<typename T>
::boost::math::octonion<T> index_i_element(int idx)
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))
{
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)
));
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>
Expand All @@ -66,7 +114,7 @@ void multiplication_test()

for (int idx = 1; idx < 8; ++idx)
{
::boost::math::octonion<T> toto = index_i_element<T>(idx);
::boost::math::octonion<T> toto = local::index_i_element<T>(idx);

const T tabs { abs(toto*toto+static_cast<T>(1)) };

Expand All @@ -86,9 +134,13 @@ void multiplication_test()
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(T(1),T(1),T(1),T(1),T(1),T(1),T(1),T(1));

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;

Expand Down Expand Up @@ -361,7 +413,7 @@ void octonion_original_manual_test()
}

template <class T>
void exp_test()
void elem_func_test()
{
using ::std::numeric_limits;

Expand All @@ -374,14 +426,176 @@ void exp_test()
for(int idx = 1; idx < 8; ++idx)
{
::boost::math::octonion<T> toto =
static_cast<T>(4)*atan(static_cast<T>(1))*index_i_element<T>(idx);
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
Expand All @@ -391,8 +605,8 @@ auto main() -> int

division_test<float>();

exp_test<float>();
exp_test<double>();
elem_func_test<float>();
elem_func_test<double>();

octonion_original_manual_test();

Expand Down

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