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);
}
private static MultiPrecision <N> SinCurveTaylorApprox(MultiPrecision <N> x)
{
MultiPrecision <N> x_abs = Abs(x);
MultiPrecision <N> x_int = Round(x_abs), x_frac = x_abs - x_int, xpi = x_frac * PI / 2, squa_xpi = xpi * xpi;
Int64 cycle = x_int.Exponent < UIntUtil.UInt32Bits / 2 ? ((Int64)x_int) % 4 : (Int64)(x_int % 4);
if ((cycle == 0 || cycle == 2) && x_frac.IsZero)
{
return(Zero);
}
Accumulator <N> a = Accumulator <N> .One, m = new(squa_xpi.mantissa, squa_xpi.Exponent), w = m;
Sign s = Sign.Minus;
for (int i = (cycle == 0 || cycle == 2) ? 2 : 1; i + 1 < Accumulator <N> .TaylorTable.Count; i += 2)
{
Accumulator <N> t = Accumulator <N> .TaylorTable[i];
Accumulator <N> d = w * t;
if (s == Sign.Plus)
{
a += d;
s = Sign.Minus;
}
else
{
a -= d;
s = Sign.Plus;
}
if (d.Digits < Length)
{
break;
}
w = Accumulator <N> .MulShift(w, m);
}
(Mantissa <N> n, int sft) = a.Mantissa;
MultiPrecision <N> y;
if (cycle == 0 || cycle == 2)
{
y = new MultiPrecision <N>((cycle == 0 ^ x.Sign == Sign.Plus) ? Sign.Minus : Sign.Plus, -sft + 1, n, round: false);
y *= xpi;
}
else
{
y = new MultiPrecision <N>((cycle == 1 ^ x.Sign == Sign.Plus) ? Sign.Minus : Sign.Plus, -sft + 1, n, round: false);
}
return(y);
}
public static bool TryParse(string s, out Accumulator <N> result)
{
try {
result = Parse(s);
return(true);
}
catch (Exception e) when(e is FormatException || e is OverflowException)
{
result = null;
return(false);
}
}
private static ReadOnlyCollection <Accumulator <N> > GenerateTaylorTable()
{
List <Accumulator <N> > table = new();
Accumulator <N> v = One, d = 1;
while (table.Count < 1 || !(table.Last().IsZero))
{
table.Add(RightRoundShift(v, TaylorTableShift));
d += 1;
v /= d;
}
table = table.Take(table.Count - 1).ToList();
return(table.AsReadOnly());
}
public int CompareTo([AllowNull] Accumulator <N> other)
{
if (other is null)
{
return(1);
}
if (this < other)
{
return(-1);
}
if (this == other)
{
return(0);
}
return(1);
}
private static MultiPrecision <N> CreateInteger(Sign sign, Accumulator <N> acc)
{
(Mantissa <N> n, int sft) = acc.Mantissa;
return(new MultiPrecision <N>(sign, (Int64)Accumulator <N> .Bits - sft - 1, n, round: false));
}
public static Accumulator <N> RoundDiv(Accumulator <N> v1, Accumulator <N> v2)
{
return(new Accumulator <N>(BigUInt <Double <N> > .RoundDiv(v1.value, v2.value)));
}
public static Accumulator <N> MulShift(Accumulator <N> v1, Accumulator <N> v2)
{
Accumulator <N> v = new(BigUInt <Double <N> > .Mul(v1.value, v2.value));
return(RightRoundShift(v, Mantissa <N> .Bits - 1));
}
public static (Accumulator <N> div, Accumulator <N> rem) Div(Accumulator <N> v1, Accumulator <N> v2)
{
(BigUInt <Double <N> > div, BigUInt <Double <N> > rem) = BigUInt <Double <N> > .Div(v1.value, v2.value);
return(new Accumulator <N>(div), new Accumulator <N>(rem));
}
public static Accumulator <N> Mul(Accumulator <N> v1, Accumulator <N> v2)
{
return(new Accumulator <N>(BigUInt <Double <N> > .Mul(v1.value, v2.value)));
}
public static Accumulator <N> Sub(Accumulator <N> v1, UInt32 v2)
{
return(new Accumulator <N>(BigUInt <Double <N> > .Sub(v1.value, v2)));
}
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);
}