1 // (C) Copyright John Maddock 2019.
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0. (See accompanying file
4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
6 #include "boost/multiprecision/cpp_int.hpp"
9 template <class T, unsigned Order>
10 struct const_polynomial
16 constexpr const_polynomial(T val = 0) : data{val} {}
17 constexpr const_polynomial(const const_polynomial&) = default;
18 constexpr const_polynomial(const std::initializer_list<T>& init) : data{}
20 if (init.size() > Order + 1)
21 throw std::range_error("Too many initializers in list");
22 for (unsigned i = 0; i < init.size(); ++i)
23 data[i] = init.begin()[i];
25 constexpr T& operator[](std::size_t N)
29 constexpr const T& operator[](std::size_t N) const
34 constexpr T operator()(U val) const
36 T result = data[Order];
37 for (unsigned i = Order; i > 0; --i)
40 result += data[i - 1];
44 constexpr const_polynomial<T, Order - 1> derivative() const
46 const_polynomial<T, Order - 1> result;
47 for (unsigned i = 1; i <= Order; ++i)
49 result[i - 1] = (*this)[i] * i;
53 constexpr const_polynomial operator-()
55 const_polynomial t(*this);
56 for (unsigned i = 0; i <= Order; ++i)
61 constexpr const_polynomial& operator*=(U val)
63 for (unsigned i = 0; i <= Order; ++i)
64 data[i] = data[i] * val;
68 constexpr const_polynomial& operator/=(U val)
70 for (unsigned i = 0; i <= Order; ++i)
71 data[i] = data[i] / val;
75 constexpr const_polynomial& operator+=(U val)
81 constexpr const_polynomial& operator-=(U val)
88 template <class T, unsigned Order1, unsigned Order2>
89 inline constexpr const_polynomial<T, (Order1 > Order2 ? Order1 : Order2)> operator+(const const_polynomial<T, Order1>& a, const const_polynomial<T, Order2>& b)
92 constexpr(Order1 > Order2)
94 const_polynomial<T, Order1> result(a);
95 for (unsigned i = 0; i <= Order2; ++i)
101 const_polynomial<T, Order2> result(b);
102 for (unsigned i = 0; i <= Order1; ++i)
107 template <class T, unsigned Order1, unsigned Order2>
108 inline constexpr const_polynomial<T, (Order1 > Order2 ? Order1 : Order2)> operator-(const const_polynomial<T, Order1>& a, const const_polynomial<T, Order2>& b)
111 constexpr(Order1 > Order2)
113 const_polynomial<T, Order1> result(a);
114 for (unsigned i = 0; i <= Order2; ++i)
120 const_polynomial<T, Order2> result(b);
121 for (unsigned i = 0; i <= Order1; ++i)
122 result[i] = a[i] - b[i];
126 template <class T, unsigned Order1, unsigned Order2>
127 inline constexpr const_polynomial<T, Order1 + Order2> operator*(const const_polynomial<T, Order1>& a, const const_polynomial<T, Order2>& b)
129 const_polynomial<T, Order1 + Order2> result;
130 for (unsigned i = 0; i <= Order1; ++i)
132 for (unsigned j = 0; j <= Order2; ++j)
134 result[i + j] += a[i] * b[j];
139 template <class T, unsigned Order, class U>
140 inline constexpr const_polynomial<T, Order> operator*(const const_polynomial<T, Order>& a, const U& b)
142 const_polynomial<T, Order> result(a);
143 for (unsigned i = 0; i <= Order; ++i)
149 template <class U, class T, unsigned Order>
150 inline constexpr const_polynomial<T, Order> operator*(const U& b, const const_polynomial<T, Order>& a)
152 const_polynomial<T, Order> result(a);
153 for (unsigned i = 0; i <= Order; ++i)
159 template <class T, unsigned Order, class U>
160 inline constexpr const_polynomial<T, Order> operator/(const const_polynomial<T, Order>& a, const U& b)
162 const_polynomial<T, Order> result;
163 for (unsigned i = 0; i <= Order; ++i)
170 template <class T, unsigned Order>
171 class hermite_polynomial
173 const_polynomial<T, Order> m_data;
176 constexpr hermite_polynomial() : m_data(hermite_polynomial<T, Order - 1>().data() * const_polynomial<T, 1>{0, 2} - hermite_polynomial<T, Order - 1>().data().derivative())
179 constexpr const const_polynomial<T, Order>& data() const
183 constexpr const T& operator[](std::size_t N) const
188 constexpr T operator()(U val) const
195 class hermite_polynomial<T, 0>
197 const_polynomial<T, 0> m_data;
200 constexpr hermite_polynomial() : m_data{1} {}
201 constexpr const const_polynomial<T, 0>& data() const
205 constexpr const T& operator[](std::size_t N) const
210 constexpr T operator()(U val)
217 class hermite_polynomial<T, 1>
219 const_polynomial<T, 1> m_data;
222 constexpr hermite_polynomial() : m_data{0, 2} {}
223 constexpr const const_polynomial<T, 1>& data() const
227 constexpr const T& operator[](std::size_t N) const
232 constexpr T operator()(U val)
242 using namespace boost::multiprecision::literals;
244 typedef boost::multiprecision::checked_int1024_t int_backend;
246 // 8192 x^13 - 319488 x^11 + 4392960 x^9 - 26357760 x^7 + 69189120 x^5 - 69189120 x^3 + 17297280 x
247 constexpr hermite_polynomial<int_backend, 13> h;
249 static_assert(h[0] == 0);
250 static_assert(h[1] == 17297280);
251 static_assert(h[2] == 0);
252 static_assert(h[3] == -69189120);
253 static_assert(h[4] == 0);
254 static_assert(h[5] == 69189120);
255 static_assert(h[6] == 0);
256 static_assert(h[7] == -26357760);
257 static_assert(h[8] == 0);
258 static_assert(h[9] == 4392960);
259 static_assert(h[10] == 0);
260 static_assert(h[11] == -319488);
261 static_assert(h[12] == 0);
262 static_assert(h[13] == 8192);
264 return boost::report_errors();