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510 lines
14 KiB
C++
510 lines
14 KiB
C++
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// Copyright Jeremy Murphy 2016.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifdef _MSC_VER
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# pragma warning (disable : 4224)
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#endif
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#include <boost/math/common_factor_rt.hpp>
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#include <boost/math/special_functions/prime.hpp>
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#include <boost/multiprecision/cpp_int.hpp>
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#include <boost/multiprecision/integer.hpp>
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#include <boost/random.hpp>
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#include <boost/array.hpp>
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#include <iostream>
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#include <algorithm>
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#include <numeric>
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#include <string>
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#include <tuple>
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#include <type_traits>
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#include <vector>
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#include <functional>
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#include "fibonacci.hpp"
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#include "../../test/table_type.hpp"
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#include "table_helper.hpp"
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#include "performance.hpp"
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using namespace std;
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boost::multiprecision::cpp_int total_sum(0);
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template <typename Func, class Table>
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double exec_timed_test_foo(Func f, const Table& data, double min_elapsed = 0.5)
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{
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double t = 0;
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unsigned repeats = 1;
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typename Table::value_type::first_type sum{0};
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stopwatch<boost::chrono::high_resolution_clock> w;
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do
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{
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for(unsigned count = 0; count < repeats; ++count)
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{
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for(typename Table::size_type n = 0; n < data.size(); ++n)
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sum += f(data[n].first, data[n].second);
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}
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t = boost::chrono::duration_cast<boost::chrono::duration<double>>(w.elapsed()).count();
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if(t < min_elapsed)
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repeats *= 2;
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}
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while(t < min_elapsed);
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total_sum += sum;
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return t / repeats;
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}
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template <typename T>
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struct test_function_template
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{
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vector<pair<T, T> > const & data;
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const char* data_name;
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test_function_template(vector<pair<T, T> > const &data, const char* name) : data(data), data_name(name) {}
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template <typename Function>
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void operator()(pair<Function, string> const &f) const
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{
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auto result = exec_timed_test_foo(f.first, data);
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auto table_name = string("gcd method comparison with ") + compiler_name() + string(" on ") + platform_name();
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report_execution_time(result,
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table_name,
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string(data_name),
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string(f.second) + "\n" + boost_name());
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}
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};
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boost::random::mt19937 rng;
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boost::random::uniform_int_distribution<> d_0_6(0, 6);
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boost::random::uniform_int_distribution<> d_1_20(1, 20);
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template <class T>
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T get_prime_products()
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{
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int n_primes = d_0_6(rng);
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switch(n_primes)
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{
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case 0:
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// Generate a power of 2:
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return static_cast<T>(1u) << d_1_20(rng);
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case 1:
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// prime number:
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return boost::math::prime(d_1_20(rng) + 3);
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}
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T result = 1;
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for(int i = 0; i < n_primes; ++i)
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result *= boost::math::prime(d_1_20(rng) + 3) * boost::math::prime(d_1_20(rng) + 3) * boost::math::prime(d_1_20(rng) + 3) * boost::math::prime(d_1_20(rng) + 3) * boost::math::prime(d_1_20(rng) + 3);
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return result;
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}
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template <class T>
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T get_uniform_random()
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{
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static boost::random::uniform_int_distribution<T> minmax(std::numeric_limits<T>::min(), std::numeric_limits<T>::max());
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return minmax(rng);
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}
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template <class T>
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inline bool even(T const& val)
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{
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return !(val & 1u);
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}
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template <class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
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inline bool even(boost::multiprecision::number<Backend, ExpressionTemplates> const& val)
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{
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return !bit_test(val, 0);
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}
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template <class T>
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T euclid_textbook(T a, T b)
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{
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using std::swap;
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if(a < b)
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swap(a, b);
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while(b)
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{
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T t = b;
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b = a % b;
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a = t;
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}
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return a;
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}
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template <class T>
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T binary_textbook(T u, T v)
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{
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if(u && v)
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{
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unsigned shifts = std::min(boost::multiprecision::lsb(u), boost::multiprecision::lsb(v));
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if(shifts)
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{
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u >>= shifts;
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v >>= shifts;
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}
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while(u)
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{
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unsigned bit_index = boost::multiprecision::lsb(u);
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if(bit_index)
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{
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u >>= bit_index;
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}
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else if(bit_index = boost::multiprecision::lsb(v))
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{
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v >>= bit_index;
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}
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else
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{
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if(u < v)
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v = (v - u) >> 1u;
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else
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u = (u - v) >> 1u;
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}
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}
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return v << shifts;
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}
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return u + v;
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}
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//
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// The Mixed Binary Euclid Algorithm
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// Sidi Mohamed Sedjelmaci
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// Electronic Notes in Discrete Mathematics 35 (2009) 169<36>176
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//
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template <class T>
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T mixed_binary_gcd(T u, T v)
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{
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using std::swap;
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if(u < v)
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swap(u, v);
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unsigned shifts = 0;
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if(!u)
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return v;
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if(!v)
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return u;
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while(even(u) && even(v))
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{
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u >>= 1u;
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v >>= 1u;
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++shifts;
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}
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while(v > 1)
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{
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u %= v;
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v -= u;
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if(!u)
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return v << shifts;
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if(!v)
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return u << shifts;
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while(even(u)) u >>= 1u;
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while(even(v)) v >>= 1u;
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if(u < v)
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swap(u, v);
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}
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return (v == 1 ? v : u) << shifts;
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}
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template <class T>
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void test_type(const char* name)
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{
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using namespace boost::math::detail;
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typedef T int_type;
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std::vector<pair<int_type, int_type> > data;
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for(unsigned i = 0; i < 1000; ++i)
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{
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data.push_back(std::make_pair(get_prime_products<T>(), get_prime_products<T>()));
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}
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std::string row_name("gcd<");
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row_name += name;
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row_name += "> (random prime number products)";
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typedef pair< function<int_type(int_type, int_type)>, string> f_test;
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array<f_test, 5> test_functions{ {
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{ Stein_gcd<int_type>, "Stein_gcd" } ,
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{ Euclid_gcd<int_type>, "Euclid_gcd" },
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{ binary_textbook<int_type>, "Stein_gcd_textbook" },
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{ euclid_textbook<int_type>, "gcd_euclid_textbook" },
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{ mixed_binary_gcd<int_type>, "mixed_binary_gcd" }
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} };
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for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(data, row_name.c_str()));
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data.clear();
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for(unsigned i = 0; i < 1000; ++i)
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{
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data.push_back(std::make_pair(get_uniform_random<T>(), get_uniform_random<T>()));
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}
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row_name.erase();
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row_name += "gcd<";
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row_name += name;
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row_name += "> (uniform random numbers)";
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for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(data, row_name.c_str()));
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// Fibonacci number tests:
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row_name.erase();
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row_name += "gcd<";
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row_name += name;
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row_name += "> (adjacent Fibonacci numbers)";
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for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(fibonacci_numbers_permution_1<T>(), row_name.c_str()));
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row_name.erase();
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row_name += "gcd<";
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row_name += name;
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row_name += "> (permutations of Fibonacci numbers)";
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for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(fibonacci_numbers_permution_2<T>(), row_name.c_str()));
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row_name.erase();
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row_name += "gcd<";
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row_name += name;
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row_name += "> (Trivial cases)";
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for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(trivial_gcd_test_cases<T>(), row_name.c_str()));
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}
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/*******************************************************************************************************************/
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template <class T>
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T generate_random(unsigned bits_wanted)
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{
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static boost::random::mt19937 gen;
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typedef boost::random::mt19937::result_type random_type;
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T max_val;
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unsigned digits;
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if(std::numeric_limits<T>::is_bounded && (bits_wanted == (unsigned)std::numeric_limits<T>::digits))
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{
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max_val = (std::numeric_limits<T>::max)();
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digits = std::numeric_limits<T>::digits;
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}
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else
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{
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max_val = T(1) << bits_wanted;
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digits = bits_wanted;
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}
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unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1;
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while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val;
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unsigned terms_needed = digits / bits_per_r_val + 1;
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T val = 0;
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for(unsigned i = 0; i < terms_needed; ++i)
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{
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val *= (gen.max)();
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val += gen();
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}
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val %= max_val;
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return val;
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}
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template <typename N>
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N gcd_stein(N m, N n)
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{
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BOOST_ASSERT(m >= static_cast<N>(0));
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BOOST_ASSERT(n >= static_cast<N>(0));
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if(m == N(0)) return n;
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if(n == N(0)) return m;
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// m > 0 && n > 0
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unsigned d_m = 0;
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while(even(m)) { m >>= 1; d_m++; }
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unsigned d_n = 0;
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while(even(n)) { n >>= 1; d_n++; }
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// odd(m) && odd(n)
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while(m != n) {
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if(n > m) swap(n, m);
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m -= n;
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do m >>= 1; while(even(m));
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// m == n
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}
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return m << std::min(d_m, d_n);
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}
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boost::multiprecision::cpp_int big_gcd(const boost::multiprecision::cpp_int& a, const boost::multiprecision::cpp_int& b)
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{
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return boost::multiprecision::gcd(a, b);
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}
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namespace boost { namespace multiprecision { namespace backends {
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_gcd_new(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
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const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b)
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{
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using default_ops::eval_lsb;
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using default_ops::eval_is_zero;
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using default_ops::eval_get_sign;
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if(a.size() == 1)
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{
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eval_gcd(result, b, *a.limbs());
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return;
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}
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if(b.size() == 1)
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{
|
|||
|
|
eval_gcd(result, a, *b.limbs());
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
int shift;
|
|||
|
|
|
|||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> u(a), v(b), mod;
|
|||
|
|
|
|||
|
|
int s = eval_get_sign(u);
|
|||
|
|
|
|||
|
|
/* GCD(0,x) := x */
|
|||
|
|
if(s < 0)
|
|||
|
|
{
|
|||
|
|
u.negate();
|
|||
|
|
}
|
|||
|
|
else if(s == 0)
|
|||
|
|
{
|
|||
|
|
result = v;
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
s = eval_get_sign(v);
|
|||
|
|
if(s < 0)
|
|||
|
|
{
|
|||
|
|
v.negate();
|
|||
|
|
}
|
|||
|
|
else if(s == 0)
|
|||
|
|
{
|
|||
|
|
result = u;
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/* Let shift := lg K, where K is the greatest power of 2
|
|||
|
|
dividing both u and v. */
|
|||
|
|
|
|||
|
|
unsigned us = eval_lsb(u);
|
|||
|
|
unsigned vs = eval_lsb(v);
|
|||
|
|
shift = (std::min)(us, vs);
|
|||
|
|
eval_right_shift(u, us);
|
|||
|
|
eval_right_shift(v, vs);
|
|||
|
|
|
|||
|
|
// From now on access u and v via pointers, that way we have a trivial swap:
|
|||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>* up(&u), *vp(&v), *mp(&mod);
|
|||
|
|
|
|||
|
|
do
|
|||
|
|
{
|
|||
|
|
/* Now u and v are both odd, so diff(u, v) is even.
|
|||
|
|
Let u = min(u, v), v = diff(u, v)/2. */
|
|||
|
|
s = up->compare(*vp);
|
|||
|
|
if(s > 0)
|
|||
|
|
std::swap(up, vp);
|
|||
|
|
if(s == 0)
|
|||
|
|
break;
|
|||
|
|
if(vp->size() <= 2)
|
|||
|
|
{
|
|||
|
|
if(vp->size() == 1)
|
|||
|
|
*up = mixed_binary_gcd(*vp->limbs(), *up->limbs());
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
double_limb_type i, j;
|
|||
|
|
i = vp->limbs()[0] | (static_cast<double_limb_type>(vp->limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
|
|||
|
|
j = (up->size() == 1) ? *up->limbs() : up->limbs()[0] | (static_cast<double_limb_type>(up->limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
|
|||
|
|
u = mixed_binary_gcd(i, j);
|
|||
|
|
}
|
|||
|
|
break;
|
|||
|
|
}
|
|||
|
|
if(vp->size() > up->size() /*eval_msb(*vp) > eval_msb(*up) + 32*/)
|
|||
|
|
{
|
|||
|
|
eval_modulus(*mp, *vp, *up);
|
|||
|
|
std::swap(vp, mp);
|
|||
|
|
eval_subtract(*up, *vp);
|
|||
|
|
if(eval_is_zero(*vp) == 0)
|
|||
|
|
{
|
|||
|
|
vs = eval_lsb(*vp);
|
|||
|
|
eval_right_shift(*vp, vs);
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
break;
|
|||
|
|
if(eval_is_zero(*up) == 0)
|
|||
|
|
{
|
|||
|
|
vs = eval_lsb(*up);
|
|||
|
|
eval_right_shift(*up, vs);
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
std::swap(up, vp);
|
|||
|
|
break;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
eval_subtract(*vp, *up);
|
|||
|
|
vs = eval_lsb(*vp);
|
|||
|
|
eval_right_shift(*vp, vs);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
while(true);
|
|||
|
|
|
|||
|
|
result = *up;
|
|||
|
|
eval_left_shift(result, shift);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
}}}
|
|||
|
|
|
|||
|
|
|
|||
|
|
boost::multiprecision::cpp_int big_gcd_new(const boost::multiprecision::cpp_int& a, const boost::multiprecision::cpp_int& b)
|
|||
|
|
{
|
|||
|
|
boost::multiprecision::cpp_int result;
|
|||
|
|
boost::multiprecision::backends::eval_gcd_new(result.backend(), a.backend(), b.backend());
|
|||
|
|
return result;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
#if 0
|
|||
|
|
void test_n_bits(unsigned n, std::string data_name, const std::vector<pair<boost::multiprecision::cpp_int, boost::multiprecision::cpp_int> >* p_data = 0)
|
|||
|
|
{
|
|||
|
|
using namespace boost::math::detail;
|
|||
|
|
typedef boost::multiprecision::cpp_int int_type;
|
|||
|
|
std::vector<pair<int_type, int_type> > data, data2;
|
|||
|
|
|
|||
|
|
for(unsigned i = 0; i < 1000; ++i)
|
|||
|
|
{
|
|||
|
|
data.push_back(std::make_pair(generate_random<int_type>(n), generate_random<int_type>(n)));
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
typedef pair< function<int_type(int_type, int_type)>, string> f_test;
|
|||
|
|
array<f_test, 2> test_functions{ { /*{ Stein_gcd<int_type>, "Stein_gcd" } ,{ Euclid_gcd<int_type>, "Euclid_gcd" },{ binary_textbook<int_type>, "Stein_gcd_textbook" },{ euclid_textbook<int_type>, "gcd_euclid_textbook" },{ mixed_binary_gcd<int_type>, "mixed_binary_gcd" },{ gcd_stein<int_type>, "gcd_stein" },*/{ big_gcd, "boost::multiprecision::gcd" },{ big_gcd_new, "big_gcd_new" } } };
|
|||
|
|
for_each(begin(test_functions), end(test_functions), test_function_template<int_type>(p_data ? *p_data : data, data_name.c_str(), true));
|
|||
|
|
}
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
int main()
|
|||
|
|
{
|
|||
|
|
test_type<unsigned short>("unsigned short");
|
|||
|
|
test_type<unsigned>("unsigned");
|
|||
|
|
test_type<unsigned long>("unsigned long");
|
|||
|
|
test_type<unsigned long long>("unsigned long long");
|
|||
|
|
|
|||
|
|
test_type<boost::multiprecision::uint256_t>("boost::multiprecision::uint256_t");
|
|||
|
|
test_type<boost::multiprecision::uint512_t>("boost::multiprecision::uint512_t");
|
|||
|
|
test_type<boost::multiprecision::uint1024_t>("boost::multiprecision::uint1024_t");
|
|||
|
|
|
|||
|
|
/*
|
|||
|
|
test_n_bits(16, " 16 bit random values");
|
|||
|
|
test_n_bits(32, " 32 bit random values");
|
|||
|
|
test_n_bits(64, " 64 bit random values");
|
|||
|
|
test_n_bits(125, " 125 bit random values");
|
|||
|
|
test_n_bits(250, " 250 bit random values");
|
|||
|
|
test_n_bits(500, " 500 bit random values");
|
|||
|
|
test_n_bits(1000, " 1000 bit random values");
|
|||
|
|
test_n_bits(5000, " 5000 bit random values");
|
|||
|
|
test_n_bits(10000, "10000 bit random values");
|
|||
|
|
//test_n_bits(100000);
|
|||
|
|
//test_n_bits(1000000);
|
|||
|
|
|
|||
|
|
test_n_bits(0, "consecutive first 1000 fibonacci numbers", &fibonacci_numbers_cpp_int_permution_1());
|
|||
|
|
test_n_bits(0, "permutations of first 1000 fibonacci numbers", &fibonacci_numbers_cpp_int_permution_2());
|
|||
|
|
*/
|
|||
|
|
}
|