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// Copyright 2020, Madhur Chauhan // 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) #ifndef BOOST_MATH_SPECIAL_FIBO_HPP #define BOOST_MATH_SPECIAL_FIBO_HPP #include #include #include #include #ifdef _MSC_VER #pragma once #endif namespace boost { namespace math { namespace detail { constexpr double fib_bits_phi = 0.69424191363061730173879026; constexpr double fib_bits_deno = 1.1609640474436811739351597; } // namespace detail template inline BOOST_MATH_CXX14_CONSTEXPR T unchecked_fibonacci(unsigned long long n) noexcept(std::is_fundamental::value) { // This function is called by the rest and computes the actual nth fibonacci number // First few fibonacci numbers: 0 (0th), 1 (1st), 1 (2nd), 2 (3rd), ... if (n <= 2) return n == 0 ? 0 : 1; /* * This is based on the following identities by Dijkstra: * F(2*n-1) = F(n-1)^2 + F(n)^2 * F(2*n) = (2*F(n-1) + F(n)) * F(n) * The implementation is iterative and is unrolled version of trivial recursive implementation. */ unsigned long long mask = 1; for (int ct = 1; ct != std::numeric_limits::digits && (mask << 1) <= n; ++ct, mask <<= 1) ; T a{1}, b{1}; for (mask >>= 1; mask; mask >>= 1) { T t1 = a * a; a = 2 * a * b - t1, b = b * b + t1; if (mask & n) t1 = b, b = b + a, a = t1; // equivalent to: swap(a,b), b += a; } return a; } template T inline BOOST_MATH_CXX14_CONSTEXPR fibonacci(unsigned long long n, const Policy &pol) { // check for overflow using approximation to binet's formula: F_n ~ phi^n / sqrt(5) if (n > 20 && n * detail::fib_bits_phi - detail::fib_bits_deno > std::numeric_limits::digits) return policies::raise_overflow_error("boost::math::fibonacci<%1%>(unsigned long long)", "Possible overflow detected.", pol); return unchecked_fibonacci(n); } template T inline BOOST_MATH_CXX14_CONSTEXPR fibonacci(unsigned long long n) { return fibonacci(n, policies::policy<>()); } // generator for next fibonacci number (see examples/reciprocal_fibonacci_constant.hpp) template class fibonacci_generator { public: // return next fibonacci number T operator()() noexcept(std::is_fundamental::value) { T ret = a; a = b, b = b + ret; // could've simply: swap(a, b), b += a; return ret; } // after set(nth), subsequent calls to the generator returns consecutive // fibonacci numbers starting with the nth fibonacci number void set(unsigned long long nth) noexcept(std::is_fundamental::value) { n = nth; a = unchecked_fibonacci(n); b = unchecked_fibonacci(n + 1); } private: unsigned long long n = 0; T a = 0, b = 1; }; } // namespace math } // namespace boost #endif