EQ2EMu/EQ2/source/depends/boost_1_72_0/libs/multiprecision/test/test_cpp_int.cpp

///////////////////////////////////////////////////////////////
//  Copyright 2012 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

//
// Compare arithmetic results using fixed_int to GMP results.
//

#ifdef _MSC_VER
#define _SCL_SECURE_NO_WARNINGS
#endif

//
// This ensures all our code gets tested, even though it may
// not be the fastest configuration in normal use:
//
#define BOOST_MP_USE_LIMB_SHIFT

#include <boost/multiprecision/gmp.hpp>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/random/mersenne_twister.hpp>
#include <boost/random/uniform_int.hpp>
#include <boost/timer.hpp>
#include "test.hpp"

#ifdef _MSC_VER
#pragma warning(disable : 4127) //  Conditional expression is constant
#endif

#if !defined(TEST1) && !defined(TEST2) && !defined(TEST3)
#define TEST1
#define TEST2
#define TEST3
#endif

template <class T>
T generate_random(unsigned bits_wanted)
{
   static boost::random::mt19937               gen;
   typedef boost::random::mt19937::result_type random_type;

   T        max_val;
   unsigned digits;
   if (std::numeric_limits<T>::is_bounded && (bits_wanted == (unsigned)std::numeric_limits<T>::digits))
   {
      max_val = (std::numeric_limits<T>::max)();
      digits  = std::numeric_limits<T>::digits;
   }
   else
   {
      max_val = T(1) << bits_wanted;
      digits  = bits_wanted;
   }

   unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1;
   while ((random_type(1) << bits_per_r_val) > (gen.max)())
      --bits_per_r_val;

   unsigned terms_needed = digits / bits_per_r_val + 1;

   T val = 0;
   for (unsigned i = 0; i < terms_needed; ++i)
   {
      val *= (gen.max)();
      val += gen();
   }
   val %= max_val;
   return val;
}

template <class T>
struct is_checked_cpp_int : public boost::mpl::false_
{};
template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ET>
struct is_checked_cpp_int<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ET> > : public boost::mpl::true_
{};

template <class Number>
struct tester
{
   typedef Number                                         test_type;
   typedef typename test_type::backend_type::checked_type checked;

   unsigned     last_error_count;
   boost::timer tim;

   boost::multiprecision::mpz_int a, b, c, d;
   int                            si;
   unsigned                       ui;
   test_type                      a1, b1, c1, d1;

   void t1()
   {
      using namespace boost::multiprecision;
      BOOST_CHECK_EQUAL(a.str(), a1.str());
      BOOST_CHECK_EQUAL(b.str(), b1.str());
      BOOST_CHECK_EQUAL(c.str(), c1.str());
      BOOST_CHECK_EQUAL(d.str(), d1.str());
      BOOST_CHECK_EQUAL(mpz_int(a + b).str(), test_type(a1 + b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) += b).str(), (test_type(a1) += b1).str());
      BOOST_CHECK_EQUAL((mpz_int(b) += a).str(), (test_type(b1) += a1).str());
      BOOST_CHECK_EQUAL(mpz_int(a - b).str(), test_type(a1 - b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) -= b).str(), (test_type(a1) -= b1).str());
      BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a) + b).str(), test_type(test_type(-a1) + b1).str());
      BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a) - b).str(), test_type(test_type(-a1) - b1).str());
      BOOST_CHECK_EQUAL(mpz_int(c * d).str(), test_type(c1 * d1).str());
      BOOST_CHECK_EQUAL((mpz_int(c) *= d).str(), (test_type(c1) *= d1).str());
      BOOST_CHECK_EQUAL((mpz_int(d) *= c).str(), (test_type(d1) *= c1).str());
      BOOST_CHECK_EQUAL(mpz_int(c * -d).str(), test_type(c1 * -d1).str());
      BOOST_CHECK_EQUAL(mpz_int(-c * d).str(), test_type(-c1 * d1).str());
      BOOST_CHECK_EQUAL((mpz_int(c) *= -d).str(), (test_type(c1) *= -d1).str());
      BOOST_CHECK_EQUAL((mpz_int(-d) *= c).str(), (test_type(-d1) *= c1).str());
      BOOST_CHECK_EQUAL(mpz_int(b * c).str(), test_type(b1 * c1).str());
      BOOST_CHECK_EQUAL(mpz_int(a / b).str(), test_type(a1 / b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) /= b).str(), (test_type(a1) /= b1).str());
      BOOST_CHECK_EQUAL(mpz_int(a / -b).str(), test_type(a1 / -b1).str());
      BOOST_CHECK_EQUAL(mpz_int(-a / b).str(), test_type(-a1 / b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) /= -b).str(), (test_type(a1) /= -b1).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) /= b).str(), (test_type(-a1) /= b1).str());
      BOOST_CHECK_EQUAL(mpz_int(a / d).str(), test_type(a1 / d1).str());
      BOOST_CHECK_EQUAL(mpz_int(a % b).str(), test_type(a1 % b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) %= b).str(), (test_type(a1) %= b1).str());
      BOOST_CHECK_EQUAL(mpz_int(a % -b).str(), test_type(a1 % -b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) %= -b).str(), (test_type(a1) %= -b1).str());
      BOOST_CHECK_EQUAL(mpz_int(-a % b).str(), test_type(-a1 % b1).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) %= b).str(), (test_type(-a1) %= b1).str());
      BOOST_CHECK_EQUAL(mpz_int(a % d).str(), test_type(a1 % d1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) %= d).str(), (test_type(a1) %= d1).str());

      if (!std::numeric_limits<test_type>::is_bounded)
      {
         test_type p = a1 * b1;
         test_type r;
         divide_qr(p, b1, p, r);
         BOOST_CHECK_EQUAL(p, a1);
         BOOST_CHECK_EQUAL(r, test_type(0));

         p = a1 * d1;
         divide_qr(p, d1, p, r);
         BOOST_CHECK_EQUAL(p, a1);
         BOOST_CHECK_EQUAL(r, test_type(0));

         divide_qr(p, test_type(1), p, r);
         BOOST_CHECK_EQUAL(p, a1);
         BOOST_CHECK_EQUAL(r, test_type(0));
      }
   }

   void t2()
   {
      using namespace boost::multiprecision;
      // bitwise ops:
      BOOST_CHECK_EQUAL(mpz_int(a | b).str(), test_type(a1 | b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) |= b).str(), (test_type(a1) |= b1).str());
      if (!is_checked_cpp_int<test_type>::value)
      {
         BOOST_CHECK_EQUAL(mpz_int(-a | b).str(), test_type(-a1 | b1).str());
         BOOST_CHECK_EQUAL((mpz_int(-a) |= b).str(), (test_type(-a1) |= b1).str());
         BOOST_CHECK_EQUAL(mpz_int(a | -b).str(), test_type(a1 | -b1).str());
         BOOST_CHECK_EQUAL((mpz_int(a) |= -b).str(), (test_type(a1) |= -b1).str());
         BOOST_CHECK_EQUAL(mpz_int(-a | -b).str(), test_type(-a1 | -b1).str());
         BOOST_CHECK_EQUAL((mpz_int(-a) |= -b).str(), (test_type(-a1) |= -b1).str());
      }
      BOOST_CHECK_EQUAL(mpz_int(a & b).str(), test_type(a1 & b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) &= b).str(), (test_type(a1) &= b1).str());
      if (!is_checked_cpp_int<test_type>::value)
      {
         BOOST_CHECK_EQUAL(mpz_int(-a & b).str(), test_type(-a1 & b1).str());
         BOOST_CHECK_EQUAL((mpz_int(-a) &= b).str(), (test_type(-a1) &= b1).str());
         BOOST_CHECK_EQUAL(mpz_int(a & -b).str(), test_type(a1 & -b1).str());
         BOOST_CHECK_EQUAL((mpz_int(a) &= -b).str(), (test_type(a1) &= -b1).str());
         BOOST_CHECK_EQUAL(mpz_int(-a & -b).str(), test_type(-a1 & -b1).str());
         BOOST_CHECK_EQUAL((mpz_int(-a) &= -b).str(), (test_type(-a1) &= -b1).str());
      }
      BOOST_CHECK_EQUAL(mpz_int(a ^ b).str(), test_type(a1 ^ b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) ^= b).str(), (test_type(a1) ^= b1).str());
      if (!is_checked_cpp_int<test_type>::value)
      {
         BOOST_CHECK_EQUAL(mpz_int(-a ^ b).str(), test_type(-a1 ^ b1).str());
         BOOST_CHECK_EQUAL((mpz_int(-a) ^= b).str(), (test_type(-a1) ^= b1).str());
         BOOST_CHECK_EQUAL(mpz_int(a ^ -b).str(), test_type(a1 ^ -b1).str());
         BOOST_CHECK_EQUAL((mpz_int(a) ^= -b).str(), (test_type(a1) ^= -b1).str());
         BOOST_CHECK_EQUAL(mpz_int(-a ^ -b).str(), test_type(-a1 ^ -b1).str());
         BOOST_CHECK_EQUAL((mpz_int(-a) ^= -b).str(), (test_type(-a1) ^= -b1).str());
      }
      // Shift ops:
      for (unsigned i = 0; i < 128; ++i)
      {
         if (!std::numeric_limits<test_type>::is_bounded)
         {
            BOOST_CHECK_EQUAL(mpz_int(a << i).str(), test_type(a1 << i).str());
            BOOST_CHECK_EQUAL(mpz_int(-a << i).str(), test_type(-a1 << i).str());
         }
         else if (!is_checked_cpp_int<test_type>::value)
         {
            test_type t1(mpz_int(a << i).str());
            test_type t2 = a1 << i;
            BOOST_CHECK_EQUAL(t1, t2);
            t1 = test_type(mpz_int(-a << i).str());
            t2 = -a1 << i;
            BOOST_CHECK_EQUAL(t1, t2);
         }
         BOOST_CHECK_EQUAL(mpz_int(a >> i).str(), test_type(a1 >> i).str());
         if (!is_checked_cpp_int<test_type>::value)
         {
            BOOST_CHECK_EQUAL(mpz_int(-a >> i).str(), test_type(-a1 >> i).str());
         }
      }
      // gcd/lcm
      BOOST_CHECK_EQUAL(mpz_int(gcd(a, b)).str(), test_type(gcd(a1, b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(c, d)).str(), test_type(lcm(c1, d1)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(-a, b)).str(), test_type(gcd(-a1, b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(-c, d)).str(), test_type(lcm(-c1, d1)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(-a, -b)).str(), test_type(gcd(-a1, -b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -d)).str(), test_type(lcm(-c1, -d1)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), test_type(gcd(a1, -b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), test_type(lcm(c1, -d1)).str());
      // Integer sqrt:
      mpz_int   r;
      test_type r1;
      BOOST_CHECK_EQUAL(sqrt(a, r).str(), sqrt(a1, r1).str());
      BOOST_CHECK_EQUAL(r.str(), r1.str());
   }

   void t3()
   {
      using namespace boost::multiprecision;
      // Now check operations involving signed integers:
      BOOST_CHECK_EQUAL(mpz_int(a + si).str(), test_type(a1 + si).str());
      BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), test_type(a1 + -si).str());
      BOOST_CHECK_EQUAL(mpz_int(-a + si).str(), test_type(-a1 + si).str());
      BOOST_CHECK_EQUAL(mpz_int(si + a).str(), test_type(si + a1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) += si).str(), (test_type(a1) += si).str());
      BOOST_CHECK_EQUAL((mpz_int(a) += -si).str(), (test_type(a1) += -si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) += si).str(), (test_type(-a1) += si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) += -si).str(), (test_type(-a1) += -si).str());
      BOOST_CHECK_EQUAL(mpz_int(a - si).str(), test_type(a1 - si).str());
      BOOST_CHECK_EQUAL(mpz_int(a - -si).str(), test_type(a1 - -si).str());
      BOOST_CHECK_EQUAL(mpz_int(-a - si).str(), test_type(-a1 - si).str());
      BOOST_CHECK_EQUAL(mpz_int(si - a).str(), test_type(si - a1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) -= si).str(), (test_type(a1) -= si).str());
      BOOST_CHECK_EQUAL((mpz_int(a) -= -si).str(), (test_type(a1) -= -si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) -= si).str(), (test_type(-a1) -= si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) -= -si).str(), (test_type(-a1) -= -si).str());
      BOOST_CHECK_EQUAL(mpz_int(b * si).str(), test_type(b1 * si).str());
      BOOST_CHECK_EQUAL(mpz_int(b * -si).str(), test_type(b1 * -si).str());
      BOOST_CHECK_EQUAL(mpz_int(-b * si).str(), test_type(-b1 * si).str());
      BOOST_CHECK_EQUAL(mpz_int(si * b).str(), test_type(si * b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) *= si).str(), (test_type(a1) *= si).str());
      BOOST_CHECK_EQUAL((mpz_int(a) *= -si).str(), (test_type(a1) *= -si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) *= si).str(), (test_type(-a1) *= si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) *= -si).str(), (test_type(-a1) *= -si).str());
      BOOST_CHECK_EQUAL(mpz_int(a / si).str(), test_type(a1 / si).str());
      BOOST_CHECK_EQUAL(mpz_int(a / -si).str(), test_type(a1 / -si).str());
      BOOST_CHECK_EQUAL(mpz_int(-a / si).str(), test_type(-a1 / si).str());
      BOOST_CHECK_EQUAL((mpz_int(a) /= si).str(), (test_type(a1) /= si).str());
      BOOST_CHECK_EQUAL((mpz_int(a) /= -si).str(), (test_type(a1) /= -si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) /= si).str(), (test_type(-a1) /= si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) /= -si).str(), (test_type(-a1) /= -si).str());
      BOOST_CHECK_EQUAL(mpz_int(a % si).str(), test_type(a1 % si).str());
      BOOST_CHECK_EQUAL(mpz_int(a % -si).str(), test_type(a1 % -si).str());
      BOOST_CHECK_EQUAL(mpz_int(-a % si).str(), test_type(-a1 % si).str());
      BOOST_CHECK_EQUAL((mpz_int(a) %= si).str(), (test_type(a1) %= si).str());
      BOOST_CHECK_EQUAL((mpz_int(a) %= -si).str(), (test_type(a1) %= -si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) %= si).str(), (test_type(-a1) %= si).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) %= -si).str(), (test_type(-a1) %= -si).str());
      if ((si > 0) || !is_checked_cpp_int<test_type>::value)
      {
         BOOST_CHECK_EQUAL(mpz_int(a | si).str(), test_type(a1 | si).str());
         BOOST_CHECK_EQUAL((mpz_int(a) |= si).str(), (test_type(a1) |= si).str());
         BOOST_CHECK_EQUAL(mpz_int(a & si).str(), test_type(a1 & si).str());
         BOOST_CHECK_EQUAL((mpz_int(a) &= si).str(), (test_type(a1) &= si).str());
         BOOST_CHECK_EQUAL(mpz_int(a ^ si).str(), test_type(a1 ^ si).str());
         BOOST_CHECK_EQUAL((mpz_int(a) ^= si).str(), (test_type(a1) ^= si).str());
         BOOST_CHECK_EQUAL(mpz_int(si | a).str(), test_type(si | a1).str());
         BOOST_CHECK_EQUAL(mpz_int(si & a).str(), test_type(si & a1).str());
         BOOST_CHECK_EQUAL(mpz_int(si ^ a).str(), test_type(si ^ a1).str());
      }
      BOOST_CHECK_EQUAL(mpz_int(gcd(a, si)).str(), test_type(gcd(a1, si)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(si, b)).str(), test_type(gcd(si, b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(c, si)).str(), test_type(lcm(c1, si)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(si, d)).str(), test_type(lcm(si, d1)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(-a, si)).str(), test_type(gcd(-a1, si)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(-si, b)).str(), test_type(gcd(-si, b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(-c, si)).str(), test_type(lcm(-c1, si)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(-si, d)).str(), test_type(lcm(-si, d1)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(-a, -si)).str(), test_type(gcd(-a1, -si)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(-si, -b)).str(), test_type(gcd(-si, -b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -si)).str(), test_type(lcm(-c1, -si)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(-si, -d)).str(), test_type(lcm(-si, -d1)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(a, -si)).str(), test_type(gcd(a1, -si)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(si, -b)).str(), test_type(gcd(si, -b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(c, -si)).str(), test_type(lcm(c1, -si)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(si, -d)).str(), test_type(lcm(si, -d1)).str());
   }

   void t4()
   {
      using namespace boost::multiprecision;
      // Now check operations involving unsigned integers:
      BOOST_CHECK_EQUAL(mpz_int(a + ui).str(), test_type(a1 + ui).str());
      BOOST_CHECK_EQUAL(mpz_int(-a + ui).str(), test_type(-a1 + ui).str());
      BOOST_CHECK_EQUAL(mpz_int(ui + a).str(), test_type(ui + a1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) += ui).str(), (test_type(a1) += ui).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) += ui).str(), (test_type(-a1) += ui).str());
      BOOST_CHECK_EQUAL(mpz_int(a - ui).str(), test_type(a1 - ui).str());
      BOOST_CHECK_EQUAL(mpz_int(-a - ui).str(), test_type(-a1 - ui).str());
      BOOST_CHECK_EQUAL(mpz_int(ui - a).str(), test_type(ui - a1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) -= ui).str(), (test_type(a1) -= ui).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) -= ui).str(), (test_type(-a1) -= ui).str());
      BOOST_CHECK_EQUAL(mpz_int(b * ui).str(), test_type(b1 * ui).str());
      BOOST_CHECK_EQUAL(mpz_int(-b * ui).str(), test_type(-b1 * ui).str());
      BOOST_CHECK_EQUAL(mpz_int(ui * b).str(), test_type(ui * b1).str());
      BOOST_CHECK_EQUAL((mpz_int(a) *= ui).str(), (test_type(a1) *= ui).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) *= ui).str(), (test_type(-a1) *= ui).str());
      BOOST_CHECK_EQUAL(mpz_int(a / ui).str(), test_type(a1 / ui).str());
      BOOST_CHECK_EQUAL(mpz_int(-a / ui).str(), test_type(-a1 / ui).str());
      BOOST_CHECK_EQUAL((mpz_int(a) /= ui).str(), (test_type(a1) /= ui).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) /= ui).str(), (test_type(-a1) /= ui).str());
      BOOST_CHECK_EQUAL(mpz_int(a % ui).str(), test_type(a1 % ui).str());
      BOOST_CHECK_EQUAL(mpz_int(-a % ui).str(), test_type(-a1 % ui).str());
      BOOST_CHECK_EQUAL((mpz_int(a) %= ui).str(), (test_type(a1) %= ui).str());
      BOOST_CHECK_EQUAL((mpz_int(-a) %= ui).str(), (test_type(-a1) %= ui).str());
      BOOST_CHECK_EQUAL(mpz_int(a | ui).str(), test_type(a1 | ui).str());
      BOOST_CHECK_EQUAL((mpz_int(a) |= ui).str(), (test_type(a1) |= ui).str());
      BOOST_CHECK_EQUAL(mpz_int(a & ui).str(), test_type(a1 & ui).str());
      BOOST_CHECK_EQUAL((mpz_int(a) &= ui).str(), (test_type(a1) &= ui).str());
      BOOST_CHECK_EQUAL(mpz_int(a ^ ui).str(), test_type(a1 ^ ui).str());
      BOOST_CHECK_EQUAL((mpz_int(a) ^= ui).str(), (test_type(a1) ^= ui).str());
      BOOST_CHECK_EQUAL(mpz_int(ui | a).str(), test_type(ui | a1).str());
      BOOST_CHECK_EQUAL(mpz_int(ui & a).str(), test_type(ui & a1).str());
      BOOST_CHECK_EQUAL(mpz_int(ui ^ a).str(), test_type(ui ^ a1).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(a, ui)).str(), test_type(gcd(a1, ui)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(ui, b)).str(), test_type(gcd(ui, b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(c, ui)).str(), test_type(lcm(c1, ui)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(ui, d)).str(), test_type(lcm(ui, d1)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(-a, ui)).str(), test_type(gcd(-a1, ui)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(-c, ui)).str(), test_type(lcm(-c1, ui)).str());
      BOOST_CHECK_EQUAL(mpz_int(gcd(ui, -b)).str(), test_type(gcd(ui, -b1)).str());
      BOOST_CHECK_EQUAL(mpz_int(lcm(ui, -d)).str(), test_type(lcm(ui, -d1)).str());

      if (std::numeric_limits<test_type>::is_modulo && checked::value)
      {
         static mpz_int m = mpz_int(1) << std::numeric_limits<test_type>::digits;
         mpz_int        t(a);
         test_type      t1(a1);
         for (unsigned i = 0; i < 10; ++i)
         {
            t *= a;
            t %= m;
            t += a;
            t %= m;
            t1 *= a1;
            t1 += a1;
         }
         BOOST_CHECK_EQUAL(t.str(), t1.str());
      }
   }

   void t5()
   {
      using namespace boost::multiprecision;
      //
      // Now integer functions:
      //
      mpz_int   z1, z2;
      test_type t1, t2;
      divide_qr(a, b, z1, z2);
      divide_qr(a1, b1, t1, t2);
      BOOST_CHECK_EQUAL(z1.str(), t1.str());
      BOOST_CHECK_EQUAL(z2.str(), t2.str());
      BOOST_CHECK_EQUAL(integer_modulus(a, si), integer_modulus(a1, si));
      BOOST_CHECK_EQUAL(lsb(a), lsb(a1));
      BOOST_CHECK_EQUAL(msb(a), msb(a1));

      for (unsigned i = 0; i < 1000; i += 13)
      {
         BOOST_CHECK_EQUAL(bit_test(a, i), bit_test(a1, i));
      }
      if (!std::numeric_limits<test_type>::is_modulo)
      {
         // We have to take care that our powers don't grow too large, otherwise this takes "forever",
         // also don't test for modulo types, as these may give a different result from arbitrary
         // precision types:
         BOOST_CHECK_EQUAL(mpz_int(pow(d, ui % 19)).str(), test_type(pow(d1, ui % 19)).str());
         BOOST_CHECK_EQUAL(mpz_int(powm(a, b, c)).str(), test_type(powm(a1, b1, c1)).str());
         BOOST_CHECK_EQUAL(mpz_int(powm(a, b, ui)).str(), test_type(powm(a1, b1, ui)).str());
         BOOST_CHECK_EQUAL(mpz_int(powm(a, ui, c)).str(), test_type(powm(a1, ui, c1)).str());
      }
      BOOST_CHECK_EQUAL(lsb(a), lsb(a1));
      BOOST_CHECK_EQUAL(msb(a), msb(a1));
   }

   static void test_bug_cases()
   {
      if (!std::numeric_limits<test_type>::is_bounded)
      {
         // https://svn.boost.org/trac/boost/ticket/7878
         test_type a("0x1000000000000000000000000000000000000000000000000000000000000000");
         test_type b = 0xFFFFFFFF;
         test_type c = a * b + b; // quotient has 1 in the final place
         test_type q, r;
         divide_qr(c, b, q, r);
         BOOST_CHECK_EQUAL(a + 1, q);
         BOOST_CHECK_EQUAL(r, 0);

         b = static_cast<test_type>("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
         c = a * b + b; // quotient has 1 in the final place
         divide_qr(c, b, q, r);
         BOOST_CHECK_EQUAL(a + 1, q);
         BOOST_CHECK_EQUAL(r, 0);
         //
         // Not a bug, but test some other special cases that don't otherwise occur through
         // random testing:
         //
         c = a * b; // quotient has zero in the final place
         divide_qr(c, b, q, r);
         BOOST_CHECK_EQUAL(q, a);
         BOOST_CHECK_EQUAL(r, 0);
         divide_qr(c, a, q, r);
         BOOST_CHECK_EQUAL(q, b);
         BOOST_CHECK_EQUAL(r, 0);
         ++c;
         divide_qr(c, b, q, r);
         BOOST_CHECK_EQUAL(q, a);
         BOOST_CHECK_EQUAL(r, 1);
      }
      // Bug https://svn.boost.org/trac/boost/ticket/8126:
      test_type a("-4294967296");
      test_type b("4294967296");
      test_type c("-1");
      a = (a / b);
      BOOST_CHECK_EQUAL(a, -1);
      a = -4294967296;
      a = (a / b) * c;
      BOOST_CHECK_EQUAL(a, 1);
      a = -23;
      b = 23;
      a = (a / b) * c;
      BOOST_CHECK_EQUAL(a, 1);
      a = -23;
      a = (a / b) / c;
      BOOST_CHECK_EQUAL(a, 1);
      a = test_type("-26607734784073568386365259775");
      b = test_type("8589934592");
      a = a / b;
      BOOST_CHECK_EQUAL(a, test_type("-3097548007973652377"));
      // Bug https://svn.boost.org/trac/boost/ticket/8133:
      a           = test_type("0x12345600012434ffffffffffffffffffffffff");
      unsigned ui = 0xffffffff;
      a           = a - ui;
      BOOST_CHECK_EQUAL(a, test_type("0x12345600012434ffffffffffffffff00000000"));
      a = test_type("0x12345600012434ffffffffffffffffffffffff");
#ifndef BOOST_NO_LONG_LONG
      unsigned long long ull = 0xffffffffffffffffuLL;
      a                      = a - ull;
      BOOST_CHECK_EQUAL(a, test_type("0x12345600012434ffffffff0000000000000000"));
#endif
      //
      // Now check that things which should be zero really are
      // https://svn.boost.org/trac/boost/ticket/8145:
      //
      a = -1;
      a += 1;
      BOOST_CHECK_EQUAL(a, 0);
      a = 1;
      a += -1;
      BOOST_CHECK_EQUAL(a, 0);
      a = -1;
      a += test_type(1);
      BOOST_CHECK_EQUAL(a, 0);
      a = 1;
      a += test_type(-1);
      BOOST_CHECK_EQUAL(a, 0);
      a = test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
      a -= test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
      BOOST_CHECK_EQUAL(a, 0);
      a = -test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
      a += test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
      BOOST_CHECK_EQUAL(a, 0);
      a = 2;
      a *= 0;
      BOOST_CHECK_EQUAL(a, 0);
      a = -2;
      a *= 0;
      BOOST_CHECK_EQUAL(a, 0);
      a = 2;
      a *= test_type(0);
      BOOST_CHECK_EQUAL(a, 0);
      a = -2;
      a *= test_type(0);
      BOOST_CHECK_EQUAL(a, 0);
      a = -2;
      a /= 50;
      BOOST_CHECK_EQUAL(a, 0);
      a = -test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
      a /= (1 + test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"));
      BOOST_CHECK_EQUAL(a, 0);
      // https://svn.boost.org/trac/boost/ticket/8160
      a = 1;
      a = 0 / test_type(1);
      BOOST_CHECK_EQUAL(a, 0);
      a = 1;
      a = 0 % test_type(25);
      BOOST_CHECK_EQUAL(a, 0);
#ifndef TEST2
      // https://svn.boost.org/trac/boost/ticket/11364
      a           = 0xfffffffeu;
      b           = -2;
      c           = a ^ b;
      test_type d = ~(a ^ ~b);
      BOOST_CHECK_EQUAL(c, d);
#endif
#if defined(TEST2) || defined(TEST3)
      // https://svn.boost.org/trac/boost/ticket/11648
      a = (std::numeric_limits<test_type>::max)() - 69;
      b = a / 139;
      ++b;
      c           = a / b;
      test_type r = a % b;
      BOOST_CHECK(r < b);
      BOOST_CHECK_EQUAL(a - c * b, r);
#endif
      for (ui = 0; ui < 1000; ++ui)
      {
         boost::multiprecision::mpz_int t;
         boost::multiprecision::mpz_int s1 = sqrt(boost::multiprecision::mpz_int(ui), t);
         a                                 = sqrt(test_type(ui), b);
         BOOST_CHECK_EQUAL(a.str(), s1.str());
         BOOST_CHECK_EQUAL(b.str(), t.str());
      }
      a = -1;
      ++a;
      BOOST_CHECK_EQUAL(a, 0);
      ++--a;
      BOOST_CHECK_EQUAL(a, 0);
      --++a;
      BOOST_CHECK_EQUAL(a, 0);

      {
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<> >                                                                                            bigint;
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<64, 64, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked, void> >   u64;
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<128, 128, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked, void> > u128;
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<256, 256, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked, void> > u256;
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<256, 256, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void> >   s256;
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<160, 160, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked, void> > u160;
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<160, 160, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void> >   s160;
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<512, 512, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked, void> > u512;
         typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<512, 512, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void> >   s512;

         {
            u256   a = 14;
            bigint b = bigint("115792089237316195423570985008687907853269984665640564039457584007913129639948");
            // to fix cast `a` to dev::bigint
            BOOST_CHECK(a < b);
         }
         {
            u256            a      = 1;
            boost::uint64_t amount = 1;
            u256            b      = a << amount;
            BOOST_CHECK_EQUAL(b, 2);

            u256 high_bit = u256(0);
            bit_set(high_bit, 255);
            BOOST_CHECK_EQUAL(a << 255, high_bit);
            BOOST_CHECK_EQUAL(a << boost::uint64_t(256), 0);
            BOOST_CHECK_EQUAL(a << 0, a);

            u256 c = 3;
            BOOST_CHECK_EQUAL(c, 3);
            BOOST_CHECK_EQUAL(c << boost::uint64_t(256), 0);
            BOOST_CHECK_EQUAL(c << 0, c);

            // Bug workaround:
            BOOST_CHECK_EQUAL(static_cast<u256>(bigint(u256(3)) << 255), u256(1) << 255);
         }
         {
            BOOST_CHECK_EQUAL(u256(3) << 255, u256(1) << 255);

            u256            a      = 1;
            boost::uint64_t amount = 1;
            u256            b      = a >> amount;
            BOOST_CHECK_EQUAL(b, 0);
            BOOST_CHECK_EQUAL(a >> 255, 0);
            BOOST_CHECK_EQUAL(a >> boost::uint64_t(256), 0);
            BOOST_CHECK_EQUAL(a >> boost::uint64_t(-1), 0);

            u256 h;
            bit_set(h, 255);
            BOOST_CHECK_EQUAL(h >> 0, u256(1) << 255);
            BOOST_CHECK_EQUAL(h >> 1, u256(1) << 254);
            BOOST_CHECK_EQUAL(h >> 2, u256(1) << 253);
            BOOST_CHECK_EQUAL(h >> 254, u256(1) << 1);
            BOOST_CHECK_EQUAL(h >> 255, u256(1) << 0);
            BOOST_CHECK_EQUAL(h >> 256, 0);
            BOOST_CHECK_EQUAL(h >> boost::uint64_t(-1), 0);

            u256 g;
            bit_set(g, 255);
            bit_set(g, 254);
            BOOST_CHECK_EQUAL(g >> 255, 1);
            BOOST_CHECK_EQUAL(g >> 254, 3);
            BOOST_CHECK_EQUAL(g >> 253, 3 << 1);
            BOOST_CHECK_EQUAL(g >> 252, 3 << 2);
            BOOST_CHECK_EQUAL(g >> 251, 3 << 3);
            BOOST_CHECK_EQUAL(g >> 0, u256(3) << 254);
            BOOST_CHECK_EQUAL(g >> 1, u256(3) << 253);
            BOOST_CHECK_EQUAL(g >> 2, u256(3) << 252);
            BOOST_CHECK_EQUAL(g >> 3, u256(3) << 251);
            BOOST_CHECK_EQUAL(g >> 100, u256(3) << 154);
            BOOST_CHECK_EQUAL(g >> 256, 0);
            BOOST_CHECK_EQUAL(g >> 257, 0);
            BOOST_CHECK_EQUAL(g >> boost::uint32_t(-1), 0);
            BOOST_CHECK_EQUAL(g >> boost::uint64_t(-1), 0);
            BOOST_CHECK_EQUAL(g >> boost::uint16_t(-1), 0);
            BOOST_CHECK_EQUAL(g >> (boost::uint16_t(-1) - 1), 0);
         }
         {
            s256     a      = 1;
            uint64_t amount = 1;
            s256     b      = a >> amount;
            BOOST_CHECK_EQUAL(b, 0);
            BOOST_CHECK_EQUAL(a >> 255, 0);
            BOOST_CHECK_EQUAL(a >> boost::uint64_t(256), 0);
            BOOST_CHECK_EQUAL(a >> boost::uint64_t(-1), 0);

            s256 n = -1;
            BOOST_CHECK_EQUAL(n >> 0, n);
            BOOST_CHECK_EQUAL(n >> 1, n);
            BOOST_CHECK_EQUAL(n >> 2, n);
            BOOST_CHECK_EQUAL(n >> 254, n);
            BOOST_CHECK_EQUAL(n >> 255, n);
            BOOST_CHECK_EQUAL(n >> 256, n);
            BOOST_CHECK_EQUAL(n >> 257, n);
            BOOST_CHECK_EQUAL(n >> ~boost::uint64_t(0), n);

            // Test min value. This actually -(2^256-1), not -(2^255) as in C.
            s256 h = (std::numeric_limits<s256>::min)();
            BOOST_CHECK_LT(h, 0);
            BOOST_CHECK_EQUAL(h >> 0, h);
            BOOST_CHECK_EQUAL(h >> 256, -1);

            // Test EVM min value.
            s256 g = s256(-1) << 255;
            BOOST_CHECK_LT(g, 0);
            BOOST_CHECK_EQUAL(static_cast<u256>(g), u256(1) << 255);
            BOOST_CHECK_EQUAL(g >> 0, g);
            BOOST_CHECK_EQUAL(static_cast<u256>(g >> 1), u256(0b11) << 254);
            BOOST_CHECK_EQUAL(static_cast<u256>(g >> 2), u256(0b111) << 253);
            BOOST_CHECK_EQUAL(static_cast<u256>(g >> 3), u256(0b1111) << 252);

            BOOST_CHECK_EQUAL(static_cast<u256>(g >> 255), ~u256(0));
            BOOST_CHECK_EQUAL(static_cast<u256>(g >> 254), ~u256(0b1));
            BOOST_CHECK_EQUAL(static_cast<u256>(g >> 253), ~u256(0b11));

            // Test shifting more that one bit.
            s256 k = s256(0b111) << 252;
            BOOST_CHECK_EQUAL(k, u256(0b111) << 252);
            BOOST_CHECK_EQUAL(k >> 1, u256(0b111) << 251);
            BOOST_CHECK_EQUAL(k >> 2, u256(0b111) << 250);
            BOOST_CHECK_EQUAL(k >> 252, 0b111);
            BOOST_CHECK_EQUAL(k >> 253, 0b11);
            BOOST_CHECK_EQUAL(k >> 254, 0b1);
            BOOST_CHECK_EQUAL(k >> 255, 0);
            BOOST_CHECK_EQUAL(k >> 256, 0);
            BOOST_CHECK_EQUAL(k >> ~boost::uint32_t(0), 0);

            // Division equivalence.

            // Built-in type:
            if (std::numeric_limits<boost::int64_t>::is_specialized)
            {
               boost::int64_t d = (std::numeric_limits<boost::int64_t>::min)();
               BOOST_CHECK_EQUAL(d >> 1, d / 2);
               int64_t e = d + 1;
               BOOST_CHECK_EQUAL(e >> 1, e / 2 - 1);

               // Boost type:
               BOOST_CHECK_EQUAL(h >> 1, h / 2 - 1);
            }
         }
      }
   }

   void test()
   {
      using namespace boost::multiprecision;

      test_bug_cases();

      last_error_count = 0;

      BOOST_CHECK_EQUAL(Number(), 0);

      for (int i = 0; i < 10000; ++i)
      {
         a = generate_random<mpz_int>(1000);
         b = generate_random<mpz_int>(512);
         c = generate_random<mpz_int>(256);
         d = generate_random<mpz_int>(32);

         si = d.convert_to<int>();
         ui = si;

         a1 = static_cast<test_type>(a.str());
         b1 = static_cast<test_type>(b.str());
         c1 = static_cast<test_type>(c.str());
         d1 = static_cast<test_type>(d.str());

         t1();
         t2();
#ifndef SLOW_COMPILER
         t3();
         t4();
         t5();
#endif

         if (last_error_count != (unsigned)boost::detail::test_errors())
         {
            last_error_count = boost::detail::test_errors();
            std::cout << std::hex << std::showbase;

            std::cout << "a    = " << a << std::endl;
            std::cout << "a1   = " << a1 << std::endl;
            std::cout << "b    = " << b << std::endl;
            std::cout << "b1   = " << b1 << std::endl;
            std::cout << "c    = " << c << std::endl;
            std::cout << "c1   = " << c1 << std::endl;
            std::cout << "d    = " << d << std::endl;
            std::cout << "d1   = " << d1 << std::endl;
            std::cout << "a + b   = " << a + b << std::endl;
            std::cout << "a1 + b1 = " << a1 + b1 << std::endl;
            std::cout << std::dec;
            std::cout << "a - b   = " << a - b << std::endl;
            std::cout << "a1 - b1 = " << a1 - b1 << std::endl;
            std::cout << "-a + b   = " << mpz_int(-a) + b << std::endl;
            std::cout << "-a1 + b1 = " << test_type(-a1) + b1 << std::endl;
            std::cout << "-a - b   = " << mpz_int(-a) - b << std::endl;
            std::cout << "-a1 - b1 = " << test_type(-a1) - b1 << std::endl;
            std::cout << "c*d    = " << c * d << std::endl;
            std::cout << "c1*d1  = " << c1 * d1 << std::endl;
            std::cout << "b*c    = " << b * c << std::endl;
            std::cout << "b1*c1  = " << b1 * c1 << std::endl;
            std::cout << "a/b    = " << a / b << std::endl;
            std::cout << "a1/b1  = " << a1 / b1 << std::endl;
            std::cout << "a/d    = " << a / d << std::endl;
            std::cout << "a1/d1  = " << a1 / d1 << std::endl;
            std::cout << "a%b    = " << a % b << std::endl;
            std::cout << "a1%b1  = " << a1 % b1 << std::endl;
            std::cout << "a%d    = " << a % d << std::endl;
            std::cout << "a1%d1  = " << a1 % d1 << std::endl;
         }

         //
         // Check to see if test is taking too long.
         // Tests run on the compiler farm time out after 300 seconds,
         // so don't get too close to that:
         //
#ifndef CI_SUPPRESS_KNOWN_ISSUES
         if (tim.elapsed() > 200)
#else
         if (tim.elapsed() > 25)
#endif
         {
            std::cout << "Timeout reached, aborting tests now....\n";
            break;
         }
      }
   }
};

int main()
{
   using namespace boost::multiprecision;

#ifdef TEST1
   tester<cpp_int> t1;
   t1.test();
#endif
#ifdef TEST2
   tester<number<cpp_int_backend<2048, 2048, signed_magnitude, checked, void> > > t2;
   t2.test();
#endif
#ifdef TEST3
   // Unchecked test verifies modulo arithmetic:
   tester<number<cpp_int_backend<2048, 2048, signed_magnitude, unchecked, void> > > t3;
   t3.test();
#endif
#ifdef TEST4
   tester<number<cpp_int_backend<0, 2048, signed_magnitude, unchecked, std::allocator<char> > > > t4;
   t4.test();
#endif
#ifdef TEST5
   tester<number<cpp_int_backend<0, 2048, signed_magnitude, unchecked> > > t5;
   t5.test();
#endif
   return boost::report_errors();
}