multiprecision/performance/delaunay_test.cpp

///////////////////////////////////////////////////////////////////////////////
//  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;
}