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// Copyright 2020 John Maddock. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
#include <iostream>
#include <benchmark/benchmark.h>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/gmp.hpp>
#include <boost/multiprecision/integer.hpp>
#include <boost/random.hpp>
#include <cmath>
#include <immintrin.h>
using namespace boost::multiprecision;
using namespace boost::random;
template <class Integer>
BOOST_MP_CXX14_CONSTEXPR Integer sqrt_old(const Integer& x, Integer& r)
{
//
// This is slow bit-by-bit integer square root, see for example
// http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29
// There are better methods such as http://hal.inria.fr/docs/00/07/28/54/PDF/RR-3805.pdf
// and http://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf which should be implemented
// at some point.
//
Integer s = 0;
if (x == 0)
{
r = 0;
return s;
}
int g = msb(x);
if (g == 0)
{
r = 1;
return s;
}
Integer t = 0;
r = x;
g /= 2;
bit_set(s, g);
bit_set(t, 2 * g);
r = x - t;
--g;
do
{
t = s;
t <<= g + 1;
bit_set(t, 2 * g);
if (t <= r)
{
bit_set(s, g);
r -= t;
}
--g;
} while (g >= 0);
return s;
}
template <class Integer>
BOOST_MP_CXX14_CONSTEXPR Integer sqrt_old(const Integer& x)
{
Integer r(0);
return sqrt_old(x, r);
}
template <class T>
std::tuple<std::vector<T>, std::vector<T> >& get_test_vector(unsigned bits)
{
static std::map<unsigned, std::tuple<std::vector<T>, std::vector<T> > > data;
std::tuple<std::vector<T>, std::vector<T> >& result = data[bits];
if (std::get<0>(result).size() == 0)
{
mt19937 mt;
uniform_int_distribution<T> ui(T(1) << (bits - 1), T(1) << bits);
std::vector<T>& a = std::get<0>(result);
std::vector<T>& b = std::get<1>(result);
for (unsigned i = 0; i < 1000; ++i)
{
a.push_back(ui(mt));
b.push_back(0);
}
}
return result;
}
template <class T>
std::vector<T>& get_test_vector_a(unsigned bits)
{
return std::get<0>(get_test_vector<T>(bits));
}
template <class T>
std::vector<T>& get_test_vector_b(unsigned bits)
{
return std::get<1>(get_test_vector<T>(bits));
}
template <typename T>
static void BM_sqrt_old(benchmark::State& state)
{
int bits = state.range(0);
std::vector<T>& a = get_test_vector_a<T>(bits);
std::vector<T>& b = get_test_vector_b<T>(bits);
for (auto _ : state)
{
for (unsigned i = 0; i < a.size(); ++i)
b[i] = sqrt_old(a[i]);
}
state.SetComplexityN(bits);
}
template <typename T>
static void BM_sqrt_current(benchmark::State& state)
{
int bits = state.range(0);
std::vector<T>& a = get_test_vector_a<T>(bits);
std::vector<T>& b = get_test_vector_b<T>(bits);
for (auto _ : state)
{
for (unsigned i = 0; i < a.size(); ++i)
b[i] = sqrt(a[i]);
}
state.SetComplexityN(bits);
}
constexpr unsigned lower_range = 512;
constexpr unsigned upper_range = 1 << 15;
BENCHMARK_TEMPLATE(BM_sqrt_old, cpp_int)->RangeMultiplier(2)->Range(lower_range, upper_range)->Unit(benchmark::kMillisecond)->Complexity();
BENCHMARK_TEMPLATE(BM_sqrt_current, cpp_int)->RangeMultiplier(2)->Range(lower_range, upper_range)->Unit(benchmark::kMillisecond)->Complexity();
BENCHMARK_TEMPLATE(BM_sqrt_current, mpz_int)->RangeMultiplier(2)->Range(lower_range, upper_range)->Unit(benchmark::kMillisecond)->Complexity();
BENCHMARK_MAIN();
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