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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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