R safe_convert_to_float(const LargeInteger& i)
{
using std::ldexp;
if(!i)
return R(0);
if(std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::max_exponent)
{
LargeInteger val(i);
if(val.sign() < 0)
val = -val;
unsigned mb = msb(val);
if(mb >= std::numeric_limits<R>::max_exponent)
{
int scale_factor = (int)mb + 1 - std::numeric_limits<R>::max_exponent;
BOOST_ASSERT(scale_factor >= 1);
val >>= scale_factor;
R result = val.template convert_to<R>();
if(std::numeric_limits<R>::digits == 0 || std::numeric_limits<R>::digits >= std::numeric_limits<R>::max_exponent)
{
//
// Calculate and add on the remainder, only if there are more
// digits in the mantissa that the size of the exponent, in
// other words if we are dropping digits in the conversion
// otherwise:
//
LargeInteger remainder(i);
remainder &= (LargeInteger(1) << scale_factor) - 1;
result += ldexp(safe_convert_to_float<R>(remainder), -scale_factor);
}
return i.sign() < 0 ? static_cast<R>(-result) : result;
}
void test_spots(T)
{
using std::ldexp;
T tolerance = boost::math::tools::epsilon<T>() * 40000;
BOOST_CHECK_CLOSE(
::boost::math::ibeta_derivative(
static_cast<T>(2),
static_cast<T>(4),
ldexp(static_cast<T>(1), -557)),
static_cast<T>(4.23957586190238472641508753637420672781472122471791800210e-167L), tolerance * 4);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_derivative(
static_cast<T>(2),
static_cast<T>(4.5),
ldexp(static_cast<T>(1), -557)),
static_cast<T>(5.24647512910420109893867082626308082567071751558842352760e-167L), tolerance * 4);
}
inline
quantity<Unit, Y>
ldexp(const quantity<Unit, Y>& q,const Int& ex)
{
using std::ldexp;
typedef quantity<Unit,Y> quantity_type;
return quantity_type::from_value(ldexp(q.value(), ex));
}
/**
* The latitude resolution of a geohash.
*
* @param[in] len the length of the geohash.
* @return the latitude resolution (degrees).
*
* Internally, \e len is first put in the range [0, 18].
**********************************************************************/
static Math::real LatitudeResolution(int len) {
using std::ldexp;
len = (std::max)(0, (std::min)(int(maxlen_), len));
return ldexp(real(180), -(5 * len / 2));
}