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- // (C) Copyright John Maddock 2019.
- // Use, modification and distribution are subject to 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/multiprecision/cpp_int.hpp"
- #include "test.hpp"
- template <class T, unsigned Order>
- struct const_polynomial
- {
- public:
- T data[Order + 1];
- public:
- constexpr const_polynomial(T val = 0) : data{val} {}
- constexpr const_polynomial(const const_polynomial&) = default;
- constexpr const_polynomial(const std::initializer_list<T>& init) : data{}
- {
- if (init.size() > Order + 1)
- throw std::range_error("Too many initializers in list");
- for (unsigned i = 0; i < init.size(); ++i)
- data[i] = init.begin()[i];
- }
- constexpr T& operator[](std::size_t N)
- {
- return data[N];
- }
- constexpr const T& operator[](std::size_t N) const
- {
- return data[N];
- }
- template <class U>
- constexpr T operator()(U val) const
- {
- T result = data[Order];
- for (unsigned i = Order; i > 0; --i)
- {
- result *= val;
- result += data[i - 1];
- }
- return result;
- }
- constexpr const_polynomial<T, Order - 1> derivative() const
- {
- const_polynomial<T, Order - 1> result;
- for (unsigned i = 1; i <= Order; ++i)
- {
- result[i - 1] = (*this)[i] * i;
- }
- return result;
- }
- constexpr const_polynomial operator-()
- {
- const_polynomial t(*this);
- for (unsigned i = 0; i <= Order; ++i)
- t[i] = -t[i];
- return t;
- }
- template <class U>
- constexpr const_polynomial& operator*=(U val)
- {
- for (unsigned i = 0; i <= Order; ++i)
- data[i] = data[i] * val;
- return *this;
- }
- template <class U>
- constexpr const_polynomial& operator/=(U val)
- {
- for (unsigned i = 0; i <= Order; ++i)
- data[i] = data[i] / val;
- return *this;
- }
- template <class U>
- constexpr const_polynomial& operator+=(U val)
- {
- data[0] += val;
- return *this;
- }
- template <class U>
- constexpr const_polynomial& operator-=(U val)
- {
- data[0] -= val;
- return *this;
- }
- };
- template <class T, unsigned Order1, unsigned Order2>
- inline constexpr const_polynomial<T, (Order1 > Order2 ? Order1 : Order2)> operator+(const const_polynomial<T, Order1>& a, const const_polynomial<T, Order2>& b)
- {
- if
- constexpr(Order1 > Order2)
- {
- const_polynomial<T, Order1> result(a);
- for (unsigned i = 0; i <= Order2; ++i)
- result[i] += b[i];
- return result;
- }
- else
- {
- const_polynomial<T, Order2> result(b);
- for (unsigned i = 0; i <= Order1; ++i)
- result[i] += a[i];
- return result;
- }
- }
- template <class T, unsigned Order1, unsigned Order2>
- inline constexpr const_polynomial<T, (Order1 > Order2 ? Order1 : Order2)> operator-(const const_polynomial<T, Order1>& a, const const_polynomial<T, Order2>& b)
- {
- if
- constexpr(Order1 > Order2)
- {
- const_polynomial<T, Order1> result(a);
- for (unsigned i = 0; i <= Order2; ++i)
- result[i] -= b[i];
- return result;
- }
- else
- {
- const_polynomial<T, Order2> result(b);
- for (unsigned i = 0; i <= Order1; ++i)
- result[i] = a[i] - b[i];
- return result;
- }
- }
- template <class T, unsigned Order1, unsigned Order2>
- inline constexpr const_polynomial<T, Order1 + Order2> operator*(const const_polynomial<T, Order1>& a, const const_polynomial<T, Order2>& b)
- {
- const_polynomial<T, Order1 + Order2> result;
- for (unsigned i = 0; i <= Order1; ++i)
- {
- for (unsigned j = 0; j <= Order2; ++j)
- {
- result[i + j] += a[i] * b[j];
- }
- }
- return result;
- }
- template <class T, unsigned Order, class U>
- inline constexpr const_polynomial<T, Order> operator*(const const_polynomial<T, Order>& a, const U& b)
- {
- const_polynomial<T, Order> result(a);
- for (unsigned i = 0; i <= Order; ++i)
- {
- result[i] *= b;
- }
- return result;
- }
- template <class U, class T, unsigned Order>
- inline constexpr const_polynomial<T, Order> operator*(const U& b, const const_polynomial<T, Order>& a)
- {
- const_polynomial<T, Order> result(a);
- for (unsigned i = 0; i <= Order; ++i)
- {
- result[i] *= b;
- }
- return result;
- }
- template <class T, unsigned Order, class U>
- inline constexpr const_polynomial<T, Order> operator/(const const_polynomial<T, Order>& a, const U& b)
- {
- const_polynomial<T, Order> result;
- for (unsigned i = 0; i <= Order; ++i)
- {
- result[i] /= b;
- }
- return result;
- }
- template <class T, unsigned Order>
- class hermite_polynomial
- {
- const_polynomial<T, Order> m_data;
- public:
- constexpr hermite_polynomial() : m_data(hermite_polynomial<T, Order - 1>().data() * const_polynomial<T, 1>{0, 2} - hermite_polynomial<T, Order - 1>().data().derivative())
- {
- }
- constexpr const const_polynomial<T, Order>& data() const
- {
- return m_data;
- }
- constexpr const T& operator[](std::size_t N) const
- {
- return m_data[N];
- }
- template <class U>
- constexpr T operator()(U val) const
- {
- return m_data(val);
- }
- };
- template <class T>
- class hermite_polynomial<T, 0>
- {
- const_polynomial<T, 0> m_data;
- public:
- constexpr hermite_polynomial() : m_data{1} {}
- constexpr const const_polynomial<T, 0>& data() const
- {
- return m_data;
- }
- constexpr const T& operator[](std::size_t N) const
- {
- return m_data[N];
- }
- template <class U>
- constexpr T operator()(U val)
- {
- return m_data(val);
- }
- };
- template <class T>
- class hermite_polynomial<T, 1>
- {
- const_polynomial<T, 1> m_data;
- public:
- constexpr hermite_polynomial() : m_data{0, 2} {}
- constexpr const const_polynomial<T, 1>& data() const
- {
- return m_data;
- }
- constexpr const T& operator[](std::size_t N) const
- {
- return m_data[N];
- }
- template <class U>
- constexpr T operator()(U val)
- {
- return m_data(val);
- }
- };
- int main()
- {
- using namespace boost::multiprecision::literals;
- typedef boost::multiprecision::checked_int1024_t int_backend;
- // 8192 x^13 - 319488 x^11 + 4392960 x^9 - 26357760 x^7 + 69189120 x^5 - 69189120 x^3 + 17297280 x
- constexpr hermite_polynomial<int_backend, 13> h;
- static_assert(h[0] == 0);
- static_assert(h[1] == 17297280);
- static_assert(h[2] == 0);
- static_assert(h[3] == -69189120);
- static_assert(h[4] == 0);
- static_assert(h[5] == 69189120);
- static_assert(h[6] == 0);
- static_assert(h[7] == -26357760);
- static_assert(h[8] == 0);
- static_assert(h[9] == 4392960);
- static_assert(h[10] == 0);
- static_assert(h[11] == -319488);
- static_assert(h[12] == 0);
- static_assert(h[13] == 8192);
- return boost::report_errors();
- }
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