93 lines
3.0 KiB
C++
93 lines
3.0 KiB
C++
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// Copyright 2020, Madhur Chauhan
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_SPECIAL_FIBO_HPP
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#define BOOST_MATH_SPECIAL_FIBO_HPP
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/policies/error_handling.hpp>
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#include <cmath>
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#include <limits>
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#ifdef _MSC_VER
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#pragma once
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#endif
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namespace boost {
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namespace math {
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namespace detail {
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constexpr double fib_bits_phi = 0.69424191363061730173879026;
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constexpr double fib_bits_deno = 1.1609640474436811739351597;
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} // namespace detail
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template <typename T>
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inline BOOST_CXX14_CONSTEXPR T unchecked_fibonacci(unsigned long long n) noexcept(std::is_fundamental<T>::value) {
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// This function is called by the rest and computes the actual nth fibonacci number
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// First few fibonacci numbers: 0 (0th), 1 (1st), 1 (2nd), 2 (3rd), ...
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if (n <= 2) return n == 0 ? 0 : 1;
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/*
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* This is based on the following identities by Dijkstra:
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* F(2*n) = F(n)^2 + F(n+1)^2
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* F(2*n+1) = (2 * F(n) + F(n+1)) * F(n+1)
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* The implementation is iterative and is unrolled version of trivial recursive implementation.
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*/
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unsigned long long mask = 1;
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for (int ct = 1; ct != std::numeric_limits<unsigned long long>::digits && (mask << 1) <= n; ++ct, mask <<= 1)
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;
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T a{1}, b{1};
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for (mask >>= 1; mask; mask >>= 1) {
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T t1 = a * a;
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a = 2 * a * b - t1, b = b * b + t1;
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if (mask & n)
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t1 = b, b = b + a, a = t1; // equivalent to: swap(a,b), b += a;
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}
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return a;
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}
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template <typename T, class Policy>
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T inline BOOST_CXX14_CONSTEXPR fibonacci(unsigned long long n, const Policy &pol) {
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// check for overflow using approximation to binet's formula: F_n ~ phi^n / sqrt(5)
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if (n > 20 && n * detail::fib_bits_phi - detail::fib_bits_deno > std::numeric_limits<T>::digits)
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return policies::raise_overflow_error<T>("boost::math::fibonacci<%1%>(unsigned long long)", "Possible overflow detected.", pol);
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return unchecked_fibonacci<T>(n);
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}
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template <typename T>
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T inline BOOST_CXX14_CONSTEXPR fibonacci(unsigned long long n) {
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return fibonacci<T>(n, policies::policy<>());
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}
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// generator for next fibonacci number (see examples/reciprocal_fibonacci_constant.hpp)
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template <typename T>
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class fibonacci_generator {
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public:
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// return next fibonacci number
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T operator()() noexcept(std::is_fundamental<T>::value) {
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T ret = a;
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a = b, b = b + ret; // could've simply: swap(a, b), b += a;
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return ret;
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}
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// after set(nth), subsequent calls to the generator returns consecutive
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// fibonacci numbers starting with the nth fibonacci number
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void set(unsigned long long nth) noexcept(std::is_fundamental<T>::value) {
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n = nth;
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a = unchecked_fibonacci<T>(n);
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b = unchecked_fibonacci<T>(n + 1);
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}
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private:
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unsigned long long n = 0;
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T a = 0, b = 1;
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};
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} // namespace math
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} // namespace boost
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#endif
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