public static MultiPrecision <N> ReadMultiPrecision <N>(this BinaryReader reader) where N : struct, IConstant
{
Sign sign = (Sign)reader.ReadByte();
if (!Enum.IsDefined(typeof(Sign), sign))
{
throw new FormatException(nameof(sign));
}
UInt32 exponent = (UInt32)reader.ReadUInt32();
UInt32[] mantissa = new UInt32[MultiPrecision <N> .Length];
for (int i = 0; i < MultiPrecision <N> .Length; i++)
{
mantissa[i] = reader.ReadUInt32();
}
if (UIntUtil.IsZero(mantissa))
{
if (exponent != MultiPrecision <N> .ExponentMin && exponent != MultiPrecision <N> .ExponentMax)
{
throw new FormatException(nameof(exponent));
}
}
else
{
if (UIntUtil.LeadingZeroCount(mantissa) != 0u)
{
throw new FormatException(nameof(mantissa));
}
}
return(new MultiPrecision <N>(sign, exponent, new Mantissa <N>(mantissa, enable_clone: false)));
}
public static MultiPrecision <N> Truncate(MultiPrecision <N> x)
{
if (!x.IsFinite)
{
return(NaN);
}
if (x.Exponent >= Mantissa <N> .Bits)
{
throw new ArgumentException(
"The Truncate function was given an input value with no decimal precision.",
nameof(x)
);
}
if (x.Exponent < 0)
{
return(Zero);
}
UInt32[] vs = x.mantissa.Value.ToArray();
UIntUtil.FlushLSB(vs, (int)x.Exponent);
MultiPrecision <N> y = new(x.Sign, x.exponent, new Mantissa <N>(vs, enable_clone: false));
return(y);
}
public static MultiPrecision <N> Add(MultiPrecision <N> a, long b)
{
if (b == 0)
{
return(a);
}
if (a.IsNaN)
{
return(NaN);
}
if (a.IsZero)
{
return(b);
}
if (!a.IsFinite)
{
return(a);
}
UInt64 b_abs = UIntUtil.Abs(b);
if (a.Sign == UIntUtil.Sign(b))
{
(Mantissa <N> n, Int64 exponent, bool round) = Add(a.mantissa, b_abs, -a.Exponent);
return(new MultiPrecision <N>(a.Sign, exponent + a.Exponent, n, round));
}
else
{
(Mantissa <N> n, Int64 exponent, bool round, Sign sign) = Diff(a.mantissa, b_abs, -a.Exponent);
return(new MultiPrecision <N>(sign == Sign.Plus ? a.Sign : UIntUtil.Sign(b), exponent + a.Exponent, n, round));
}
}
public static MultiPrecision <N> Random(Random random)
{
Accumulator <N> acc = new(new Mantissa <N>(UIntUtil.Random(random, Length, Bits), enable_clone: false));
(Mantissa <N> n, int sft) = acc.Mantissa;
return(new MultiPrecision <N>(Sign.Plus, Mantissa <N> .Bits - sft - 1, n, round: false));
}
public static MultiPrecision <N> Div(MultiPrecision <N> a, long b)
{
if (a.IsNaN)
{
return(NaN);
}
if (a.IsZero)
{
if (b == 0)
{
return(NaN);
}
return((a.Sign == UIntUtil.Sign(b)) ? Zero : MinusZero);
}
if (!a.IsFinite)
{
return((a.Sign == UIntUtil.Sign(b)) ? PositiveInfinity : NegativeInfinity);
}
if (b == 0)
{
return((a.Sign == Sign.Plus) ? PositiveInfinity : NegativeInfinity);
}
if (b == 1)
{
return(a);
}
if (b == -1)
{
return(Neg(a));
}
UInt64 b_abs = UIntUtil.Abs(b);
if (UIntUtil.IsPower2(b_abs))
{
MultiPrecision <N> a_power2 = Ldexp(a, -UIntUtil.Power2(b_abs));
return(b >= 0 ? a_power2 : Neg(a_power2));
}
int expands = BigUInt <Plus4 <N> > .Length - BigUInt <N> .Length;
BigUInt <Plus4 <N> > acc = new(a.mantissa.Value.ToArray(), expands);
acc /= b_abs;
int lzc = acc.LeadingZeroCount;
acc <<= lzc;
Int64 exponent = a.Exponent - lzc;
Sign sign = (a.Sign == UIntUtil.Sign(b)) ? Sign.Plus : Sign.Minus;
bool round = acc[expands - 1] > UIntUtil.UInt32Round;
Mantissa <N> mantissa = new(acc.Value.Skip(expands).ToArray(), enable_clone : false);
return(new MultiPrecision <N>(sign, exponent, mantissa, round));
}
public static BigUInt <N> RightRoundShift(BigUInt <N> n, int sft)
{
BigUInt <N> ret = n.Copy();
ret.RightShift(sft);
if (sft >= 1 && sft <= Bits && UIntUtil.GetLSB(n.value, sft - 1) != 0)
{
ret.CarryAdd(0, 1);
}
return(ret);
}
public override string ToString()
{
int bin_digits = (int)Digits, dec_digits = 0;
// dec_digits <= bin_digits * digits(2^32 - 1) / digits(10^9 - 1) + 2
UInt32[] dec = new UInt32[checked (bin_digits * 10 / 9 + 2)];
for (int j = bin_digits - 1; j >= 0; j--)
{
UInt32 carry = value[j];
for (int i = 0; i < dec_digits; i++)
{
UInt64 res = UIntUtil.Pack(dec[i], carry);
(carry, dec[i]) = UIntUtil.DecimalUnpack(res);
public static int MatchBits(BigUInt <N> a, BigUInt <N> b)
{
return(UIntUtil.MatchBits(Length, a.value, b.value));
}
public static bool operator ==(BigUInt <N> a, BigUInt <N> b)
{
return(UIntUtil.Equal(Length, a.value, b.value));
}
public static bool operator >=(BigUInt <N> a, BigUInt <N> b)
{
return(UIntUtil.GreaterThanOrEqual(Length, a.value, b.value));
}
public BigUInt(UInt64 v) : this()
{
(this.value[1], this.value[0]) = UIntUtil.Unpack(v);
}
/// <summary>Shift uint32 array v >>= sft</summary>
private unsafe void RightShift(int sft)
{
UIntUtil.RightShift(value, sft);
}
/// <summary>Shift uint32 array v <<= sft</summary>
private unsafe void LeftShift(int sft)
{
UIntUtil.LeftShift(value, sft);
}
/// <summary>Shift uint32 array v >>= sft * UInt32Bits</summary>
private void RightBlockShift(int sft)
{
UIntUtil.RightBlockShift(value, sft);
}
