mirror of
https://github.com/boostorg/math.git
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403 lines
11 KiB
C++
403 lines
11 KiB
C++
// Copyright Hubert Holin 2001.
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// Copyright Christopher Kormanyos 2024
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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#include <iomanip>
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#include <boost/mpl/list.hpp>
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#include <boost/math/octonion.hpp>
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#include <boost/core/lightweight_test.hpp>
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// test file for octonion.hpp
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namespace
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{
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template<typename T>
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::boost::math::octonion<T> index_i_element(int idx)
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{
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return(
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::boost::math::octonion<T>(
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(idx == 0) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 1) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 2) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 3) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 4) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 5) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 6) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 7) ?
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static_cast<T>(1) :
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static_cast<T>(0)
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));
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}
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}
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template<class T>
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void multiplication_test()
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{
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using ::std::numeric_limits;
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using ::boost::math::abs;
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// Testing multiplication.
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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);
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const T delta { abs(one_by_one - static_cast<T>(1)) };
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const auto result_mul_one_is_ok = (delta < numeric_limits<T>::epsilon());
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BOOST_TEST(result_mul_one_is_ok);
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for (int idx = 1; idx < 8; ++idx)
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{
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::boost::math::octonion<T> toto = index_i_element<T>(idx);
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const T tabs { abs(toto*toto+static_cast<T>(1)) };
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const auto result_mul_toto_is_ok = (tabs < numeric_limits<T>::epsilon());
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BOOST_TEST(result_mul_toto_is_ok);
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}
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{
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const boost::math::octonion<T> lhs(T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8));
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const boost::math::octonion<T> rhs(T(8),T(7),T(6),T(5),T(4),T(3),T(2),T(1));
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const boost::math::octonion<T> prod = lhs * rhs;
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const boost::math::octonion<T> ctrl(T(-104), T(14), T(12), T(10), T(152), T(42), T(4), T(74));
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BOOST_TEST(prod == ctrl);
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}
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{
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const boost::math::octonion<T> lhs(T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8));
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const boost::math::octonion<T> rhs(T(1),T(1),T(1),T(1),T(1),T(1),T(1),T(1));
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const boost::math::octonion<T> quot = lhs / rhs;
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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));
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BOOST_TEST(quot == ctrl);
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}
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}
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template<class T>
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void division_test()
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{
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{
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const boost::math::octonion<T> lhs(T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8));
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const boost::math::octonion<T> rhs(T(1),T(1),T(1),T(1),T(1),T(1),T(1),T(1));
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const boost::math::octonion<T> quot = lhs / rhs;
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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));
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BOOST_TEST(quot == ctrl);
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}
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{
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const std::complex<T> one_one(T(1), T(1));
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const boost::math::octonion<T> lhs(T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8));
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const boost::math::octonion<T> rhs(one_one, one_one, one_one, one_one);
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const boost::math::octonion<T> quot = lhs / rhs;
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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));
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BOOST_TEST(quot == ctrl);
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}
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}
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void octonion_original_manual_test()
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{
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// tests for evaluation by humans
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// using default constructor
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::boost::math::octonion<float> o0;
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::boost::math::octonion<float> oa[2];
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// using constructor "O seen as R^8"
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::boost::math::octonion<float> o1(1,2,3,4,5,6,7,8);
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::std::complex<double> c0(9,10);
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// using constructor "O seen as C^4"
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::boost::math::octonion<double> o2(c0);
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::boost::math::quaternion<long double> q0(11,12,13,14);
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// using constructor "O seen as H^2"
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::boost::math::octonion<long double> o3(q0);
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// using UNtemplated copy constructor
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::boost::math::octonion<float> o4(o1);
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// using templated copy constructor
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::boost::math::octonion<long double> o5(o2);
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// using UNtemplated assignment operator
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o5 = o3;
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oa[0] = o0;
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// using templated assignment operator
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o5 = o2;
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oa[1] = o5;
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float f0(15);
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// using converting assignment operator
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o0 = f0;
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// using converting assignment operator
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o2 = c0;
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// using converting assignment operator
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o5 = q0;
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// using += (const T &)
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o4 += f0;
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// using == (const octonion<T> &,const octonion<T> &)
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BOOST_TEST(o0 != o4);
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// using += (const ::std::complex<T> &)
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o2 += c0;
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// using == (const ::boost::math::quaternion<T> &, const octonion<T> &)
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BOOST_TEST(q0 == o3);
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// using += (const ::boost::math::quaternion<T> &)
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o3 += q0;
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BOOST_TEST(2 * q0 == o3);
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// using += (const quaternion<X> &)
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o5 += o4;
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// using -= (const T &)
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o1 -= f0;
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// using -= (const ::std::complex<T> &)
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o2 -= c0;
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// using -= (const ::boost::math::quaternion<T> &)
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o5 -= q0;
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// using -= (const octonion<X> &)
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o3 -= o4;
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// using == (const ::std::complex<T> &, const octonion<T> &)
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BOOST_TEST(c0 == o2);
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// using == (const octonion<T> &, const ::std::complex<T> &)
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BOOST_TEST(o2 == c0);
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double d0(16);
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::std::complex<double> c1(17,18);
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::boost::math::quaternion<double> q1(19,20,21,22);
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// using *= (const T &)
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o2 *= d0;
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// using *= (const ::std::complex<T> &)
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o2 *= c1;
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// using *= (const ::boost::math::quaternion<T> &)
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o2 *= q1;
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// using *= (const octonion<X> &)
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o2 *= o4;
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long double l0(23);
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::std::complex<long double> c2(24,25);
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// using /= (const T &)
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o5 /= l0;
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// using /= (const ::std::complex<T> &)
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o5 /= c2;
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// using /= (const quaternion<X> &)
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o5 /= q0;
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// using /= (const octonion<X> &)
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o5 /= o5;
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// using + (const T &, const octonion<T> &)
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::boost::math::octonion<float> o6 = f0+o0;
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// using + (const octonion<T> &, const T &)
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::boost::math::octonion<float> o7 = o0+f0;
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// using + (const ::std::complex<T> &, const quaternion<T> &)
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::boost::math::octonion<double> o8 = c0+o2;
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// using + (const octonion<T> &, const ::std::complex<T> &)
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::boost::math::octonion<double> o9 = o2+c0;
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// using + (const ::boost::math::quaternion<T>, const octonion<T> &)
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::boost::math::octonion<long double> o10 = q0+o3;
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// using + (const octonion<T> &, const ::boost::math::quaternion<T> &)
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::boost::math::octonion<long double> o11 = o3+q0;
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// using + (const quaternion<T> &,const quaternion<T> &)
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::boost::math::octonion<float> o12 = o0+o4;
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// using - (const T &, const octonion<T> &)
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o6 = f0-o0;
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// using - (const octonion<T> &, const T &)
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o7 = o0-f0;
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// using - (const ::std::complex<T> &, const octonion<T> &)
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o8 = c0-o2;
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// using - (const octonion<T> &, const ::std::complex<T> &)
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o9 = o2-c0;
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// using - (const quaternion<T> &,const octonion<T> &)
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o10 = q0-o3;
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// using - (const octonion<T> &,const quaternion<T> &)
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o11 = o3-q0;
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// using - (const octonion<T> &,const octonion<T> &)
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o12 = o0-o4;
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// using * (const T &, const octonion<T> &)
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o6 = f0*o0;
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// using * (const octonion<T> &, const T &)
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o7 = o0*f0;
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// using * (const ::std::complex<T> &, const octonion<T> &)
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o8 = c0*o2;
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// using * (const octonion<T> &, const ::std::complex<T> &)
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o9 = o2*c0;
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// using * (const quaternion<T> &,const octonion<T> &)
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o10 = q0*o3;
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// using * (const octonion<T> &,const quaternion<T> &)
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o11 = o3*q0;
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// using * (const octonion<T> &,const octonion<T> &)
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o12 = o0*o4;
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// using / (const T &, const octonion<T> &)
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o6 = f0/o0;
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// using / (const octonion<T> &, const T &)
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o7 = o0/f0;
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// using / (const ::std::complex<T> &, const octonion<T> &)
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o8 = c0/o2;
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// using / (const octonion<T> &, const ::std::complex<T> &)
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o9 = o2/c0;
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// using / (const ::boost::math::quaternion<T> &, const octonion<T> &)
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o10 = q0/o3;
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// using / (const octonion<T> &, const ::boost::math::quaternion<T> &)
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o11 = o3/q0;
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// using / (const octonion<T> &,const octonion<T> &)
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o12 = o0/o4;
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// using + (const octonion<T> &)
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o4 = +o0;
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// using == (const T &, const octonion<T> &)
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BOOST_TEST(f0 == o0);
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// using == (const octonion<T> &, const T &)
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BOOST_TEST(o0 == f0);
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// using - (const octonion<T> &)
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o0 = -o4;
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// using != (const T &, const octonion<T> &)
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BOOST_TEST(f0 != o0);
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// using != (const octonion<T> &, const T &)
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BOOST_TEST(o0 != f0);
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// using != (const ::std::complex<T> &, const octonion<T> &)
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BOOST_TEST(c0 != o2);
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// using != (const octonion<T> &, const ::std::complex<T> &)
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BOOST_TEST(o2 != c0);
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// using != (const ::boost::math::quaternion<T> &, const octonion<T> &)
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BOOST_TEST(q0 != o3);
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// using != (const octonion<T> &, const ::boost::math::quaternion<T> &)
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BOOST_TEST(o3 != q0);
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// using != (const octonion<T> &,const octonion<T> &)
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BOOST_TEST(o0 != o4);
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}
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template <class T>
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void exp_test()
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{
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using ::std::numeric_limits;
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using ::std::atan;
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using ::boost::math::abs;
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// Testing exp.
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for(int idx = 1; idx < 8; ++idx)
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{
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::boost::math::octonion<T> toto =
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static_cast<T>(4)*atan(static_cast<T>(1))*index_i_element<T>(idx);
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const T tabs { abs(exp(toto)+static_cast<T>(1)) };
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const auto result_exp_toto_is_ok = (tabs < 2*numeric_limits<T>::epsilon());
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BOOST_TEST(result_exp_toto_is_ok);
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}
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}
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auto main() -> int
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{
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multiplication_test<float>();
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multiplication_test<double>();
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division_test<float>();
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exp_test<float>();
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exp_test<double>();
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octonion_original_manual_test();
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const auto result_is_ok = (boost::report_errors() == 0);
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return (result_is_ok ? 0 : -1);
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}
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