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- ///////////////////////////////////////////////////////////////////////////////
- // Copyright 2012 John Maddock.
- // Copyright 2012 Phil Endecott
- // Distributed under 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 "arithmetic_backend.hpp"
- #include <boost/chrono.hpp>
- #include <boost/random/mersenne_twister.hpp>
- #include <boost/random/uniform_int_distribution.hpp>
- #include <fstream>
- #include <iomanip>
- template <class Clock>
- struct stopwatch
- {
- typedef typename Clock::duration duration;
- stopwatch()
- {
- m_start = Clock::now();
- }
- duration elapsed()
- {
- return Clock::now() - m_start;
- }
- void reset()
- {
- m_start = Clock::now();
- }
- private:
- typename Clock::time_point m_start;
- };
- // Custom 128-bit maths used for exact calculation of the Delaunay test.
- // Only the few operators actually needed here are implemented.
- struct int128_t
- {
- int64_t high;
- uint64_t low;
- int128_t() {}
- int128_t(int32_t i) : high(i >> 31), low(static_cast<int64_t>(i)) {}
- int128_t(uint32_t i) : high(0), low(i) {}
- int128_t(int64_t i) : high(i >> 63), low(i) {}
- int128_t(uint64_t i) : high(0), low(i) {}
- };
- inline int128_t operator<<(int128_t val, int amt)
- {
- int128_t r;
- r.low = val.low << amt;
- r.high = val.low >> (64 - amt);
- r.high |= val.high << amt;
- return r;
- }
- inline int128_t& operator+=(int128_t& l, int128_t r)
- {
- l.low += r.low;
- bool carry = l.low < r.low;
- l.high += r.high;
- if (carry)
- ++l.high;
- return l;
- }
- inline int128_t operator-(int128_t val)
- {
- val.low = ~val.low;
- val.high = ~val.high;
- val.low += 1;
- if (val.low == 0)
- val.high += 1;
- return val;
- }
- inline int128_t operator+(int128_t l, int128_t r)
- {
- l += r;
- return l;
- }
- inline bool operator<(int128_t l, int128_t r)
- {
- if (l.high != r.high)
- return l.high < r.high;
- return l.low < r.low;
- }
- inline int128_t mult_64x64_to_128(int64_t a, int64_t b)
- {
- // Make life simple by dealing only with positive numbers:
- bool neg = false;
- if (a < 0)
- {
- neg = !neg;
- a = -a;
- }
- if (b < 0)
- {
- neg = !neg;
- b = -b;
- }
- // Divide input into 32-bit halves:
- uint32_t ah = a >> 32;
- uint32_t al = a & 0xffffffff;
- uint32_t bh = b >> 32;
- uint32_t bl = b & 0xffffffff;
- // Long multiplication, with 64-bit temporaries:
- // ah al
- // * bh bl
- // ----------------
- // al*bl (t1)
- // + ah*bl (t2)
- // + al*bh (t3)
- // + ah*bh (t4)
- // ----------------
- uint64_t t1 = static_cast<uint64_t>(al) * bl;
- uint64_t t2 = static_cast<uint64_t>(ah) * bl;
- uint64_t t3 = static_cast<uint64_t>(al) * bh;
- uint64_t t4 = static_cast<uint64_t>(ah) * bh;
- int128_t r(t1);
- r.high = t4;
- r += int128_t(t2) << 32;
- r += int128_t(t3) << 32;
- if (neg)
- r = -r;
- return r;
- }
- template <class R, class T>
- BOOST_FORCEINLINE void mul_2n(R& r, const T& a, const T& b)
- {
- r = a;
- r *= b;
- }
- template <class B, boost::multiprecision::expression_template_option ET, class T>
- BOOST_FORCEINLINE void mul_2n(boost::multiprecision::number<B, ET>& r, const T& a, const T& b)
- {
- multiply(r, a, b);
- }
- BOOST_FORCEINLINE void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b)
- {
- r = mult_64x64_to_128(a, b);
- }
- template <class Traits>
- inline bool delaunay_test(int32_t ax, int32_t ay, int32_t bx, int32_t by,
- int32_t cx, int32_t cy, int32_t dx, int32_t dy)
- {
- // Test whether the quadrilateral ABCD's diagonal AC should be flipped to BD.
- // This is the Cline & Renka method.
- // Flip if the sum of the angles ABC and CDA is greater than 180 degrees.
- // Equivalently, flip if sin(ABC + CDA) < 0.
- // Trig identity: cos(ABC) * sin(CDA) + sin(ABC) * cos(CDA) < 0
- // We can use scalar and vector products to find sin and cos, and simplify
- // to the following code.
- // Numerical robustness is important. This code addresses it by performing
- // exact calculations with large integer types.
- //
- // NOTE: This routine is limited to inputs with up to 30 BIT PRECISION, which
- // is to say all inputs must be in the range [INT_MIN/2, INT_MAX/2].
- typedef typename Traits::i64_t i64;
- typedef typename Traits::i128_t i128;
- i64 cos_abc, t;
- mul_2n(cos_abc, (ax - bx), (cx - bx)); // subtraction yields 31-bit values, multiplied to give 62-bit values
- mul_2n(t, (ay - by), (cy - by));
- cos_abc += t; // addition yields 63 bit value, leaving one left for the sign
- i64 cos_cda;
- mul_2n(cos_cda, (cx - dx), (ax - dx));
- mul_2n(t, (cy - dy), (ay - dy));
- cos_cda += t;
- if (cos_abc >= 0 && cos_cda >= 0)
- return false;
- if (cos_abc < 0 && cos_cda < 0)
- return true;
- i64 sin_abc;
- mul_2n(sin_abc, (ax - bx), (cy - by));
- mul_2n(t, (cx - bx), (ay - by));
- sin_abc -= t;
- i64 sin_cda;
- mul_2n(sin_cda, (cx - dx), (ay - dy));
- mul_2n(t, (ax - dx), (cy - dy));
- sin_cda -= t;
- i128 sin_sum, t128;
- mul_2n(sin_sum, sin_abc, cos_cda); // 63-bit inputs multiplied to 126-bit output
- mul_2n(t128, cos_abc, sin_cda);
- sin_sum += t128; // Addition yields 127 bit result, leaving one bit for the sign
- return sin_sum < 0;
- }
- struct dt_dat
- {
- int32_t ax, ay, bx, by, cx, cy, dx, dy;
- };
- typedef std::vector<dt_dat> data_t;
- data_t data;
- template <class Traits>
- void do_calc(const char* name)
- {
- std::cout << "Running calculations for: " << name << std::endl;
- stopwatch<boost::chrono::high_resolution_clock> w;
- boost::uint64_t flips = 0;
- boost::uint64_t calcs = 0;
- for (int j = 0; j < 1000; ++j)
- {
- for (data_t::const_iterator i = data.begin(); i != data.end(); ++i)
- {
- const dt_dat& d = *i;
- bool flip = delaunay_test<Traits>(d.ax, d.ay, d.bx, d.by, d.cx, d.cy, d.dx, d.dy);
- if (flip)
- ++flips;
- ++calcs;
- }
- }
- double t = boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count();
- std::cout << "Number of calculations = " << calcs << std::endl;
- std::cout << "Number of flips = " << flips << std::endl;
- std::cout << "Total execution time = " << t << std::endl;
- std::cout << "Time per calculation = " << t / calcs << std::endl
- << std::endl;
- }
- template <class I64, class I128>
- struct test_traits
- {
- typedef I64 i64_t;
- typedef I128 i128_t;
- };
- dt_dat generate_quadrilateral()
- {
- static boost::random::mt19937 gen;
- static boost::random::uniform_int_distribution<> dist(INT_MIN / 2, INT_MAX / 2);
- dt_dat result;
- result.ax = dist(gen);
- result.ay = dist(gen);
- result.bx = boost::random::uniform_int_distribution<>(result.ax, INT_MAX / 2)(gen); // bx is to the right of ax.
- result.by = dist(gen);
- result.cx = dist(gen);
- result.cy = boost::random::uniform_int_distribution<>(result.cx > result.bx ? result.by : result.ay, INT_MAX / 2)(gen); // cy is below at least one of ay and by.
- result.dx = boost::random::uniform_int_distribution<>(result.cx, INT_MAX / 2)(gen); // dx is to the right of cx.
- result.dy = boost::random::uniform_int_distribution<>(result.cx > result.bx ? result.by : result.ay, INT_MAX / 2)(gen); // cy is below at least one of ay and by.
- return result;
- }
- static void load_data()
- {
- for (unsigned i = 0; i < 100000; ++i)
- data.push_back(generate_quadrilateral());
- }
- int main()
- {
- using namespace boost::multiprecision;
- std::cout << "loading data...\n";
- load_data();
- std::cout << "calculating...\n";
- do_calc<test_traits<boost::int64_t, boost::int64_t> >("int64_t, int64_t");
- do_calc<test_traits<number<arithmetic_backend<boost::int64_t>, et_off>, number<arithmetic_backend<boost::int64_t>, et_off> > >("arithmetic_backend<int64_t>, arithmetic_backend<int64_t>");
- do_calc<test_traits<boost::int64_t, number<arithmetic_backend<boost::int64_t>, et_off> > >("int64_t, arithmetic_backend<int64_t>");
- do_calc<test_traits<number<cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, et_off>, number<cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, et_off> > >("multiprecision::int64_t, multiprecision::int64_t");
- do_calc<test_traits<boost::int64_t, ::int128_t> >("int64_t, int128_t");
- do_calc<test_traits<boost::int64_t, boost::multiprecision::int128_t> >("int64_t, boost::multiprecision::int128_t");
- do_calc<test_traits<boost::int64_t, number<cpp_int_backend<128, 128, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, et_on> > >("int64_t, int128_t (ET)");
- do_calc<test_traits<number<cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, et_off>, boost::multiprecision::int128_t> >("multiprecision::int64_t, multiprecision::int128_t");
- do_calc<test_traits<boost::int64_t, cpp_int> >("int64_t, cpp_int");
- do_calc<test_traits<boost::int64_t, number<cpp_int_backend<>, et_off> > >("int64_t, cpp_int (no ET's)");
- do_calc<test_traits<boost::int64_t, number<cpp_int_backend<128> > > >("int64_t, cpp_int(128-bit cache)");
- do_calc<test_traits<boost::int64_t, number<cpp_int_backend<128>, et_off> > >("int64_t, cpp_int (128-bit Cache no ET's)");
- return 0;
- }
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