Chris@16: ///////////////////////////////////////////////////////////////
Chris@16: //  Copyright 2012 John Maddock. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
Chris@16: //
Chris@16: // Comparison operators for cpp_int_backend:
Chris@16: //
Chris@16: #ifndef BOOST_MP_CPP_INT_MISC_HPP
Chris@16: #define BOOST_MP_CPP_INT_MISC_HPP
Chris@16: 
Chris@16: #include <boost/multiprecision/detail/bitscan.hpp> // lsb etc
Chris@101: #include <boost/integer/common_factor_rt.hpp> // gcd/lcm
Chris@16: 
Chris@16: #ifdef BOOST_MSVC
Chris@16: #pragma warning(push)
Chris@16: #pragma warning(disable:4702)
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost{ namespace multiprecision{ namespace backends{
Chris@16: 
Chris@16: template <class R, class CppInt>
Chris@16: void check_in_range(const CppInt& val, const mpl::int_<checked>&)
Chris@16: {
Chris@16:    typedef typename boost::multiprecision::detail::canonical<R, CppInt>::type cast_type;
Chris@16:    if(val.sign())
Chris@16:    {
Chris@16:       if(val.compare(static_cast<cast_type>((std::numeric_limits<R>::min)())) < 0)
Chris@16:          BOOST_THROW_EXCEPTION(std::overflow_error("Could not convert to the target type - -value is out of range."));
Chris@16:    }
Chris@16:    else
Chris@16:    {
Chris@16:       if(val.compare(static_cast<cast_type>((std::numeric_limits<R>::max)())) > 0)
Chris@16:          BOOST_THROW_EXCEPTION(std::overflow_error("Could not convert to the target type - -value is out of range."));
Chris@16:    }
Chris@16: }
Chris@16: template <class R, class CppInt>
Chris@16: inline void check_in_range(const CppInt& /*val*/, const mpl::int_<unchecked>&) BOOST_NOEXCEPT {}
Chris@16: 
Chris@16: inline void check_is_negative(const mpl::true_&) BOOST_NOEXCEPT {}
Chris@16: inline void check_is_negative(const mpl::false_&)
Chris@16: {
Chris@16:    BOOST_THROW_EXCEPTION(std::range_error("Attempt to assign a negative value to an unsigned type."));
Chris@16: }
Chris@16: 
Chris@16: template <class Integer>
Chris@16: inline Integer negate_integer(Integer i, const mpl::true_&) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return -i;
Chris@16: }
Chris@16: template <class Integer>
Chris@16: inline Integer negate_integer(Integer i, const mpl::false_&) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return ~(i-1);
Chris@16: }
Chris@16: 
Chris@16: template <class R, unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<is_integral<R>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, void>::type
Chris@16:    eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& backend) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@16: {
Chris@16:    typedef mpl::int_<Checked1> checked_type;
Chris@16:    check_in_range<R>(backend, checked_type());
Chris@16: 
Chris@16:    *result = static_cast<R>(backend.limbs()[0]);
Chris@16:    unsigned shift = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    for(unsigned i = 1; (i < backend.size()) && (shift < static_cast<unsigned>(std::numeric_limits<R>::digits)); ++i)
Chris@16:    {
Chris@16:       *result += static_cast<R>(backend.limbs()[i]) << shift;
Chris@16:       shift += cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    }
Chris@16:    if(backend.sign())
Chris@16:    {
Chris@16:       check_is_negative(boost::is_signed<R>());
Chris@16:       *result = negate_integer(*result, boost::is_signed<R>());
Chris@16:    }
Chris@16: }
Chris@16: 
Chris@16: template <class R, unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<is_floating_point<R>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, void>::type
Chris@16:    eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& backend) BOOST_NOEXCEPT_IF(is_arithmetic<R>::value)
Chris@16: {
Chris@16:    typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::const_limb_pointer p = backend.limbs();
Chris@16:    unsigned shift = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    *result = static_cast<R>(*p);
Chris@16:    for(unsigned i = 1; i < backend.size(); ++i)
Chris@16:    {
Chris@16:       *result += static_cast<R>(std::ldexp(static_cast<long double>(p[i]), shift));
Chris@16:       shift += cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    }
Chris@16:    if(backend.sign())
Chris@16:       *result = -*result;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, bool>::type
Chris@16:    eval_is_zero(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return (val.size() == 1) && (val.limbs()[0] == 0);
Chris@16: }
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, int>::type
Chris@16:    eval_get_sign(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1;
Chris@16: }
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_abs(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@16: {
Chris@16:    result = val;
Chris@16:    result.sign(false);
Chris@16: }
Chris@16: 
Chris@16: //
Chris@16: // Get the location of the least-significant-bit:
Chris@16: //
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
Chris@16:    eval_lsb(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
Chris@16: {
Chris@16:    using default_ops::eval_get_sign;
Chris@16:    if(eval_get_sign(a) == 0)
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
Chris@16:    }
Chris@16:    if(a.sign())
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
Chris@16:    }
Chris@16: 
Chris@16:    //
Chris@16:    // Find the index of the least significant limb that is non-zero:
Chris@16:    //
Chris@16:    unsigned index = 0;
Chris@16:    while(!a.limbs()[index] && (index < a.size()))
Chris@16:       ++index;
Chris@16:    //
Chris@16:    // Find the index of the least significant bit within that limb:
Chris@16:    //
Chris@16:    unsigned result = boost::multiprecision::detail::find_lsb(a.limbs()[index]);
Chris@16: 
Chris@16:    return result + index * cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16: }
Chris@16: 
Chris@16: //
Chris@16: // Get the location of the most-significant-bit:
Chris@16: //
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
Chris@16:    eval_msb(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
Chris@16: {
Chris@16:    using default_ops::eval_get_sign;
Chris@16:    if(eval_get_sign(a) == 0)
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
Chris@16:    }
Chris@16:    if(a.sign())
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
Chris@16:    }
Chris@16: 
Chris@16:    //
Chris@16:    // Find the index of the most significant bit that is non-zero:
Chris@16:    //
Chris@16:    return (a.size() - 1) * cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits + boost::multiprecision::detail::find_msb(a.limbs()[a.size() - 1]);
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, bool>::type
Chris@16:    eval_bit_test(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, unsigned index) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    unsigned offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    unsigned shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
Chris@16:    if(offset >= val.size())
Chris@16:       return false;
Chris@16:    return val.limbs()[offset] & mask ? true : false;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_bit_set(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, unsigned index)
Chris@16: {
Chris@16:    unsigned offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    unsigned shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
Chris@16:    if(offset >= val.size())
Chris@16:    {
Chris@16:       unsigned os = val.size();
Chris@16:       val.resize(offset + 1, offset + 1);
Chris@16:       if(offset >= val.size())
Chris@16:          return;  // fixed precision overflow
Chris@16:       for(unsigned i = os; i <= offset; ++i)
Chris@16:          val.limbs()[i] = 0;
Chris@16:    }
Chris@16:    val.limbs()[offset] |= mask;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_bit_unset(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, unsigned index) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    unsigned offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    unsigned shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
Chris@16:    if(offset >= val.size())
Chris@16:       return;
Chris@16:    val.limbs()[offset] &= ~mask;
Chris@16:    val.normalize();
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_bit_flip(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, unsigned index)
Chris@16: {
Chris@16:    unsigned offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    unsigned shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:    limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
Chris@16:    if(offset >= val.size())
Chris@16:    {
Chris@16:       unsigned os = val.size();
Chris@16:       val.resize(offset + 1, offset + 1);
Chris@16:       if(offset >= val.size())
Chris@16:          return;  // fixed precision overflow
Chris@16:       for(unsigned i = os; i <= offset; ++i)
Chris@16:          val.limbs()[i] = 0;
Chris@16:    }
Chris@16:    val.limbs()[offset] ^= mask;
Chris@16:    val.normalize();
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_qr(
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x,
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& y,
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& q,
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& r) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@16: {
Chris@16:    divide_unsigned_helper(&q, x, y, r);
Chris@16:    q.sign(x.sign() != y.sign());
Chris@16:    r.sign(x.sign());
Chris@16: }
Chris@16: 
Chris@101: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@101: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@101:    eval_qr(
Chris@101:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x,
Chris@101:       limb_type y,
Chris@101:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& q,
Chris@101:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& r) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@101: {
Chris@101:    divide_unsigned_helper(&q, x, y, r);
Chris@101:    q.sign(x.sign());
Chris@101:    r.sign(x.sign());
Chris@101: }
Chris@101: 
Chris@101: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class U>
Chris@101: inline typename enable_if_c<is_integral<U>::value>::type eval_qr(
Chris@101:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x,
Chris@101:       U y,
Chris@101:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& q,
Chris@101:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& r) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@101: {
Chris@101:    using default_ops::eval_qr;
Chris@101:    cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(y);
Chris@101:    eval_qr(x, t, q, r);
Chris@101: }
Chris@101: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
Chris@16: inline typename enable_if_c<is_unsigned<Integer>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, Integer>::type
Chris@16:    eval_integer_modulus(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x, Integer val)
Chris@16: {
Chris@16:    if((sizeof(Integer) <= sizeof(limb_type)) || (val <= (std::numeric_limits<limb_type>::max)()))
Chris@16:    {
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> d;
Chris@16:       divide_unsigned_helper(static_cast<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>*>(0), x, static_cast<limb_type>(val), d);
Chris@16:       return d.limbs()[0];
Chris@16:    }
Chris@16:    else
Chris@16:    {
Chris@16:       return default_ops::eval_integer_modulus(x, val);
Chris@16:    }
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<is_signed<Integer>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, Integer>::type
Chris@16:    eval_integer_modulus(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x, Integer val)
Chris@16: {
Chris@101:    return eval_integer_modulus(x, boost::multiprecision::detail::unsigned_abs(val));
Chris@16: }
Chris@16: 
Chris@16: inline limb_type integer_gcd_reduce(limb_type u, limb_type v)
Chris@16: {
Chris@16:    do
Chris@16:    {
Chris@16:       if(u > v)
Chris@16:          std::swap(u, v);
Chris@16:       if(u == v)
Chris@16:          break;
Chris@16:       v -= u;
Chris@16:       v >>= boost::multiprecision::detail::find_lsb(v);
Chris@16:    } while(true);
Chris@16:    return u;
Chris@16: }
Chris@16: 
Chris@16: inline double_limb_type integer_gcd_reduce(double_limb_type u, double_limb_type v)
Chris@16: {
Chris@16:    do
Chris@16:    {
Chris@16:       if(u > v)
Chris@16:          std::swap(u, v);
Chris@16:       if(u == v)
Chris@16:          break;
Chris@16:       if(v <= ~static_cast<limb_type>(0))
Chris@16:       {
Chris@16:          u = integer_gcd_reduce(static_cast<limb_type>(v), static_cast<limb_type>(u));
Chris@16:          break;
Chris@16:       }
Chris@16:       v -= u;
Chris@16:       while((static_cast<unsigned>(v) & 1u) == 0)
Chris@16:          v >>= 1;
Chris@16:    } while(true);
Chris@16:    return u;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_gcd(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a, 
Chris@16:       limb_type v)
Chris@16: {
Chris@16:    using default_ops::eval_lsb;
Chris@16:    using default_ops::eval_is_zero;
Chris@16:    using default_ops::eval_get_sign;
Chris@16: 
Chris@16:    int shift;
Chris@16: 
Chris@16:    cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> u(a);
Chris@16: 
Chris@16:    int s = eval_get_sign(u);
Chris@16: 
Chris@16:    /* GCD(0,x) := x */
Chris@16:    if(s < 0)
Chris@16:    {
Chris@16:       u.negate();
Chris@16:    }
Chris@16:    else if(s == 0)
Chris@16:    {
Chris@16:       result = v;
Chris@16:       return;
Chris@16:    }
Chris@16:    if(v == 0)
Chris@16:    {
Chris@16:       result = u;
Chris@16:       return;
Chris@16:    }
Chris@16: 
Chris@16:    /* Let shift := lg K, where K is the greatest power of 2
Chris@16:    dividing both u and v. */
Chris@16: 
Chris@16:    unsigned us = eval_lsb(u);
Chris@16:    unsigned vs = boost::multiprecision::detail::find_lsb(v);
Chris@16:    shift = (std::min)(us, vs);
Chris@16:    eval_right_shift(u, us);
Chris@16:    if(vs)
Chris@16:       v >>= vs;
Chris@16: 
Chris@16:    do 
Chris@16:    {
Chris@16:       /* Now u and v are both odd, so diff(u, v) is even.
Chris@16:       Let u = min(u, v), v = diff(u, v)/2. */
Chris@16:       if(u.size() <= 2)
Chris@16:       {
Chris@16:          if(u.size() == 1)
Chris@16:             v = integer_gcd_reduce(*u.limbs(), v);
Chris@16:          else
Chris@16:          {
Chris@16:             double_limb_type i;
Chris@16:             i = u.limbs()[0] | (static_cast<double_limb_type>(u.limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
Chris@16:             v = static_cast<limb_type>(integer_gcd_reduce(i, static_cast<double_limb_type>(v)));
Chris@16:          }
Chris@16:          break;
Chris@16:       }
Chris@16:       eval_subtract(u, v);
Chris@16:       us = eval_lsb(u);
Chris@16:       eval_right_shift(u, us);
Chris@16:    } 
Chris@16:    while(true);
Chris@16: 
Chris@16:    result = v;
Chris@16:    eval_left_shift(result, shift);
Chris@16: }
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
Chris@16: inline typename enable_if_c<is_unsigned<Integer>::value && (sizeof(Integer) <= sizeof(limb_type)) && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_gcd(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a, 
Chris@16:       const Integer& v)
Chris@16: {
Chris@16:    eval_gcd(result, a, static_cast<limb_type>(v));
Chris@16: }
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
Chris@16: inline typename enable_if_c<is_signed<Integer>::value && (sizeof(Integer) <= sizeof(limb_type)) && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_gcd(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a, 
Chris@16:       const Integer& v)
Chris@16: {
Chris@16:    eval_gcd(result, a, static_cast<limb_type>(v < 0 ? -v : v));
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_gcd(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a, 
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b)
Chris@16: {
Chris@16:    using default_ops::eval_lsb;
Chris@16:    using default_ops::eval_is_zero;
Chris@16:    using default_ops::eval_get_sign;
Chris@16: 
Chris@16:    if(a.size() == 1)
Chris@16:    {
Chris@16:       eval_gcd(result, b, *a.limbs());
Chris@16:       return;
Chris@16:    }
Chris@16:    if(b.size() == 1)
Chris@16:    {
Chris@16:       eval_gcd(result, a, *b.limbs());
Chris@16:       return;
Chris@16:    }
Chris@16: 
Chris@16:    int shift;
Chris@16: 
Chris@16:    cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> u(a), v(b);
Chris@16: 
Chris@16:    int s = eval_get_sign(u);
Chris@16: 
Chris@16:    /* GCD(0,x) := x */
Chris@16:    if(s < 0)
Chris@16:    {
Chris@16:       u.negate();
Chris@16:    }
Chris@16:    else if(s == 0)
Chris@16:    {
Chris@16:       result = v;
Chris@16:       return;
Chris@16:    }
Chris@16:    s = eval_get_sign(v);
Chris@16:    if(s < 0)
Chris@16:    {
Chris@16:       v.negate();
Chris@16:    }
Chris@16:    else if(s == 0)
Chris@16:    {
Chris@16:       result = u;
Chris@16:       return;
Chris@16:    }
Chris@16: 
Chris@16:    /* Let shift := lg K, where K is the greatest power of 2
Chris@16:    dividing both u and v. */
Chris@16: 
Chris@16:    unsigned us = eval_lsb(u);
Chris@16:    unsigned vs = eval_lsb(v);
Chris@16:    shift = (std::min)(us, vs);
Chris@16:    eval_right_shift(u, us);
Chris@16:    eval_right_shift(v, vs);
Chris@16: 
Chris@16:    do 
Chris@16:    {
Chris@16:       /* Now u and v are both odd, so diff(u, v) is even.
Chris@16:       Let u = min(u, v), v = diff(u, v)/2. */
Chris@16:       s = u.compare(v);
Chris@16:       if(s > 0)
Chris@16:          u.swap(v);
Chris@16:       if(s == 0)
Chris@16:          break;
Chris@16:       if(v.size() <= 2)
Chris@16:       {
Chris@16:          if(v.size() == 1)
Chris@16:             u = integer_gcd_reduce(*v.limbs(), *u.limbs());
Chris@16:          else
Chris@16:          {
Chris@16:             double_limb_type i, j;
Chris@16:             i = v.limbs()[0] | (static_cast<double_limb_type>(v.limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
Chris@16:             j = (u.size() == 1) ? *u.limbs() : u.limbs()[0] | (static_cast<double_limb_type>(u.limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
Chris@16:             u = integer_gcd_reduce(i, j);
Chris@16:          }
Chris@16:          break;
Chris@16:       }
Chris@16:       eval_subtract(v, u);
Chris@16:       vs = eval_lsb(v);
Chris@16:       eval_right_shift(v, vs);
Chris@16:    } 
Chris@16:    while(true);
Chris@16: 
Chris@16:    result = u;
Chris@16:    eval_left_shift(result, shift);
Chris@16: }
Chris@16: //
Chris@16: // Now again for trivial backends:
Chris@16: //
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
Chris@16:    eval_gcd(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b) BOOST_NOEXCEPT
Chris@16: {
Chris@101:    *result.limbs() = boost::integer::gcd(*a.limbs(), *b.limbs());
Chris@16: }
Chris@16: // This one is only enabled for unchecked cpp_int's, for checked int's we need the checking in the default version:
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && (Checked1 == unchecked)>::type
Chris@16:    eval_lcm(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@16: {
Chris@101:    *result.limbs() = boost::integer::lcm(*a.limbs(), *b.limbs());
Chris@16:    result.normalize(); // result may overflow the specified number of bits
Chris@16: }
Chris@16: 
Chris@16: inline void conversion_overflow(const mpl::int_<checked>&)
Chris@16: {
Chris@16:    BOOST_THROW_EXCEPTION(std::overflow_error("Overflow in conversion to narrower type"));
Chris@16: }
Chris@16: inline void conversion_overflow(const mpl::int_<unchecked>&){}
Chris@16: 
Chris@16: template <class R, unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<
Chris@16:             is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
Chris@16:             && is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
Chris@16:          >::type
Chris@16:    eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val)
Chris@16: {
Chris@16:    typedef typename common_type<R, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type>::type common_type;
Chris@16:    if(std::numeric_limits<R>::is_specialized && (static_cast<common_type>(*val.limbs()) > static_cast<common_type>((std::numeric_limits<R>::max)())))
Chris@16:    {
Chris@16:       conversion_overflow(typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
Chris@16:       *result = (std::numeric_limits<R>::max)();
Chris@16:    }
Chris@16:    else
Chris@16:       *result = static_cast<R>(*val.limbs());
Chris@16:    if(val.isneg())
Chris@16:    {
Chris@16:       check_is_negative(mpl::bool_<boost::is_signed<R>::value || boost::is_floating_point<R>::value>());
Chris@16:       *result = negate_integer(*result, mpl::bool_<boost::is_signed<R>::value || boost::is_floating_point<R>::value>());
Chris@16:    }
Chris@16: }
Chris@16: 
Chris@16: template <class R, unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<
Chris@16:             is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
Chris@16:             && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
Chris@16:          >::type
Chris@16:    eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val)
Chris@16: {
Chris@16:    typedef typename common_type<R, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type>::type common_type;
Chris@16:    if(std::numeric_limits<R>::is_specialized && (static_cast<common_type>(*val.limbs()) > static_cast<common_type>((std::numeric_limits<R>::max)())))
Chris@16:    {
Chris@16:       conversion_overflow(typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
Chris@16:       *result = (std::numeric_limits<R>::max)();
Chris@16:    }
Chris@16:    else
Chris@16:       *result = static_cast<R>(*val.limbs());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
Chris@16:    eval_lsb(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
Chris@16: {
Chris@16:    using default_ops::eval_get_sign;
Chris@16:    if(eval_get_sign(a) == 0)
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
Chris@16:    }
Chris@16:    if(a.sign())
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
Chris@16:    }
Chris@16:    //
Chris@16:    // Find the index of the least significant bit within that limb:
Chris@16:    //
Chris@16:    return boost::multiprecision::detail::find_lsb(*a.limbs());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline typename enable_if_c<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
Chris@16:    eval_msb(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
Chris@16: {
Chris@16:    using default_ops::eval_get_sign;
Chris@16:    if(eval_get_sign(a) == 0)
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
Chris@16:    }
Chris@16:    if(a.sign())
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
Chris@16:    }
Chris@16:    //
Chris@16:    // Find the index of the least significant bit within that limb:
Chris@16:    //
Chris@16:    return boost::multiprecision::detail::find_msb(*a.limbs());
Chris@16: }
Chris@16: 
Chris@16: #ifdef BOOST_MSVC
Chris@16: #pragma warning(pop)
Chris@16: #endif
Chris@16: 
Chris@16: }}} // namespaces
Chris@16: 
Chris@16: #endif