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include/boost/random/detail/const_mod.hpp  view on Meta::CPAN

      return x;
    else if(c <= traits::const_max - m)    // i.e. m+c < max
      return add_small(x, c);
    else
      return detail::do_add<traits::is_signed>::add(m, x, c);
  }

  static IntType mult(IntType a, IntType x)
  {
    if(a == 1)
      return x;
    else if(m <= traits::const_max/a)      // i.e. a*m <= max
      return mult_small(a, x);
    else if(traits::is_signed && (m%a < m/a))
      return mult_schrage(a, x);
    else {
      // difficult
      assert(!"const_mod::mult with a too large");
      return 0;
    }
  }

  static IntType mult_add(IntType a, IntType x, IntType c)
  {
    if(m <= (traits::const_max-c)/a)   // i.e. a*m+c <= max
      return (a*x+c) % m;
    else
      return add(mult(a, x), c);
  }

  static IntType invert(IntType x)
  { return x == 0 ? 0 : invert_euclidian(x); }

private:
  typedef integer_traits<IntType> traits;

  const_mod();      // don't instantiate

  static IntType add_small(IntType x, IntType c)
  {
    x += c;
    if(x >= m)
      x -= m;
    return x;
  }

  static IntType mult_small(IntType a, IntType x)
  {
    return a*x % m;
  }

  static IntType mult_schrage(IntType a, IntType value)
  {
    const IntType q = m / a;
    const IntType r = m % a;

    assert(r < q);        // check that overflow cannot happen

    value = a*(value%q) - r*(value/q);
    // An optimizer bug in the SGI MIPSpro 7.3.1.x compiler requires this
    // convoluted formulation of the loop (Synge Todo)
    for(;;) {
      if (value > 0)
        break;
      value += m;
    }
    return value;
  }

  // invert c in the finite field (mod m) (m must be prime)
  static IntType invert_euclidian(IntType c)
  {
    // we are interested in the gcd factor for c, because this is our inverse
    BOOST_STATIC_ASSERT(m > 0);
#if BOOST_WORKAROUND(__MWERKS__, BOOST_TESTED_AT(0x3003))
    assert(boost::integer_traits<IntType>::is_signed);
#elif !defined(BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS)
    BOOST_STATIC_ASSERT(boost::integer_traits<IntType>::is_signed);
#endif
    assert(c > 0);
    IntType l1 = 0;
    IntType l2 = 1;
    IntType n = c;
    IntType p = m;
    for(;;) {
      IntType q = p / n;
      l1 -= q * l2;           // this requires a signed IntType!
      p -= q * n;
      if(p == 0)
        return (l2 < 1 ? l2 + m : l2);
      IntType q2 = n / p;
      l2 -= q2 * l1;
      n -= q2 * p;
      if(n == 0)
        return (l1 < 1 ? l1 + m : l1);
    }
  }
};

// The modulus is exactly the word size: rely on machine overflow handling.
// Due to a GCC bug, we cannot partially specialize in the presence of
// template value parameters.
template<>
class const_mod<unsigned int, 0>
{
  typedef unsigned int IntType;
public:
  static IntType add(IntType x, IntType c) { return x+c; }
  static IntType mult(IntType a, IntType x) { return a*x; }
  static IntType mult_add(IntType a, IntType x, IntType c) { return a*x+c; }

  // m is not prime, thus invert is not useful
private:                      // don't instantiate
  const_mod();
};

template<>
class const_mod<unsigned long, 0>
{
  typedef unsigned long IntType;
public: