inline BigFloat SafeMin( const BigFloat& alpha )
{
// TODO: Decide how to only recompute this when the precision changes
const BigFloat one = BigFloat(1,alpha.Precision());
const BigFloat eps = Epsilon(alpha);
const BigFloat minVal = Min(alpha);
const BigFloat invMax = one/Max(alpha);
return ( invMax>minVal ? invMax*(one+eps) : minVal );
}
inline BigFloat Epsilon<BigFloat>( const BigFloat& alpha )
{
// NOTE: This 'precision' is the number of bits in the mantissa
auto p = alpha.Precision();
// epsilon = b^{-(p-1)} / 2 = 2^{-p}
BigFloat one(1,p);
return one >> p;
}
inline Int NumMantissaBits<BigFloat>( const BigFloat& alpha )
{ return alpha.Precision(); }
inline BigFloat Infinity<BigFloat>( const BigFloat& alpha )
{
BigFloat inf(0,alpha.Precision());
mpfr_set_inf( inf.Pointer(), 1 );
return inf;
}
inline BigFloat Min<BigFloat>( const BigFloat& alpha )
{
BigFloat one(1,alpha.Precision());
return one << (MinExponent<BigFloat>()-1);
}
inline BigFloat Max<BigFloat>( const BigFloat& alpha )
{
BigFloat one(1,alpha.Precision());
return (one-Epsilon(one)) << MaxExponent<BigFloat>();
}
