public static MultiPrecision <N> Pow2(MultiPrecision <N> x)
{
if (x.IsNaN)
{
return(NaN);
}
MultiPrecision <N> x_int = Floor(x);
if (x_int.Exponent >= UIntUtil.UInt32Bits)
{
if (x.Sign == Sign.Plus)
{
return(PositiveInfinity);
}
else
{
return(Zero);
}
}
Int64 exponent = x_int.mantissa.Value.Last() >> (UIntUtil.UInt32Bits - (int)x_int.Exponent - 1);
if (x_int.Sign == Sign.Minus)
{
exponent = -exponent;
}
MultiPrecision <N> x_frac = x - x_int;
MultiPrecision <N> v = Ln2 * x_frac;
if (v.IsZero || v.Exponent < int.MinValue)
{
return(new MultiPrecision <N>(Sign.Plus, exponent, Mantissa <N> .One, round: false));
}
Accumulator <N> a = Accumulator <N> .One, m = new(v.mantissa, (int)v.Exponent), w = m;
foreach (var t in Accumulator <N> .TaylorTable)
{
Accumulator <N> d = w * t;
if (d.Digits < Length)
{
break;
}
a += d;
w = Accumulator <N> .RightRoundShift(w *m, Mantissa <N> .Bits - 1);
}
(Mantissa <N> n, int sft) = a.Mantissa;
MultiPrecision <N> y = new(Sign.Plus, exponent - sft + 1, n, round : false);
return(y);
}
public static MultiPrecision <N> Log2(MultiPrecision <N> x)
{
if (!(x >= Zero))
{
return(NaN);
}
if (x.IsZero)
{
return(NegativeInfinity);
}
if (x == PositiveInfinity)
{
return(PositiveInfinity);
}
if (x.mantissa == Mantissa <N> .One)
{
return(x.Exponent);
}
Accumulator <N> v = new(x.mantissa);
int sft;
for (sft = 0; sft < Accumulator <N> .Bits; sft++)
{
v *= v;
if (v.Value[Accumulator <N> .Length - 1] > UIntUtil.UInt32Round)
{
v = Accumulator <N> .RightRoundBlockShift(v, Mantissa <N> .Length);
break;
}
else
{
v = Accumulator <N> .RightRoundShift(v, Mantissa <N> .Bits - 1);
}
}
if (sft == Accumulator <N> .Bits)
{
return(x.Exponent);
}
UInt32[] mantissa = new UInt32[Mantissa <N> .Length];
UInt32 m = 1;
for (int i = mantissa.Length - 1; i >= 0; i--)
{
for (int j = (i < mantissa.Length - 1) ? 0 : 1; j < UIntUtil.UInt32Bits; j++)
{
v *= v;
m <<= 1;
if (v.Value[Accumulator <N> .Length - 1] > UIntUtil.UInt32Round)
{
v = Accumulator <N> .RightRoundBlockShift(v, Mantissa <N> .Length);
m |= 1u;
}
else
{
v = Accumulator <N> .RightRoundShift(v, Mantissa <N> .Bits - 1);
}
}
mantissa[i] = m;
m = 0;
}
v *= v;
bool round = v.Value[Accumulator <N> .Length - 1] > UIntUtil.UInt32Round;
long intpart = x.Exponent;
MultiPrecision <N> decpart = new(Sign.Plus, -(Int64)sft - 1, new Mantissa <N>(mantissa, enable_clone: false), round);
MultiPrecision <N> y = intpart + decpart;
return(y);
}