/// <summary>
/// Returns a base-10 string representing the number.
///
/// Note: This is inefficient and possibly inaccurate. Please use with enough
/// rounding digits (set using the RoundingDigits property) to ensure accuracy
/// </summary>
public override string ToString()
{
if (IsSpecialValue)
{
SpecialValueType s = SpecialValue;
if (s == SpecialValueType.ZERO)
{
return String.Format("0{0}0", System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator);
}
else if (s == SpecialValueType.INF_PLUS)
{
return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.PositiveInfinitySymbol;
}
else if (s == SpecialValueType.INF_MINUS)
{
return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NegativeInfinitySymbol;
}
else if (s == SpecialValueType.NAN)
{
return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NaNSymbol;
}
else
{
return "Unrecognised special type";
}
}
if (scratch.Precision.NumBits != mantissa.Precision.NumBits)
{
scratch = new BigInt(mantissa.Precision);
}
//The mantissa expresses 1.xxxxxxxxxxx
//The highest possible value for the mantissa without the implicit 1. is 0.9999999...
scratch.Assign(mantissa);
//scratch.Round(3);
scratch.Sign = false;
BigInt denom = new BigInt("0", mantissa.Precision);
denom.SetBit(mantissa.Precision.NumBits - 1);
bool useExponentialNotation = false;
int halfBits = mantissa.Precision.NumBits / 2;
if (halfBits > 60) halfBits = 60;
int precDec = 10;
if (exponent > 0)
{
if (exponent < halfBits)
{
denom.RSH(exponent);
}
else
{
useExponentialNotation = true;
}
}
else if (exponent < 0)
{
int shift = -(exponent);
if (shift < precDec)
{
scratch.RSH(shift);
}
else
{
useExponentialNotation = true;
}
}
string output;
if (useExponentialNotation)
{
int absExponent = exponent;
if (absExponent < 0) absExponent = -absExponent;
int powerOf10 = (int)((double)absExponent * Math.Log10(2.0));
//Use 1 extra digit of precision (this is actually 32 bits more, nb)
BigFloat thisFloat = new BigFloat(this, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
thisFloat.mantissa.Sign = false;
//Multiplicative correction factor to bring number into range.
BigFloat one = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
BigFloat ten = new BigFloat(10, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
BigFloat tenRCP = ten.Reciprocal();
//Accumulator for the power of 10 calculation.
BigFloat acc = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
BigFloat tenToUse;
if (exponent > 0)
{
tenToUse = new BigFloat(tenRCP, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
}
else
{
tenToUse = new BigFloat(ten, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
}
BigFloat tenToPower = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
int powerTemp = powerOf10;
//Fast power function
while (powerTemp != 0)
{
tenToPower.Mul(tenToUse);
tenToUse.Assign(tenToPower);
if ((powerTemp & 1) != 0)
{
acc.Mul(tenToPower);
}
powerTemp >>= 1;
}
thisFloat.Mul(acc);
//If we are out of range, correct.
if (thisFloat.GreaterThan(ten))
{
thisFloat.Mul(tenRCP);
if (exponent > 0)
{
powerOf10++;
}
else
{
powerOf10--;
}
}
else if (thisFloat.LessThan(one))
{
thisFloat.Mul(ten);
if (exponent > 0)
{
powerOf10--;
}
else
{
powerOf10++;
}
}
//Restore the precision and the sign.
BigFloat printable = new BigFloat(thisFloat, mantissa.Precision);
printable.mantissa.Sign = mantissa.Sign;
output = printable.ToString();
if (exponent < 0) powerOf10 = -powerOf10;
output = String.Format("{0}E{1}", output, powerOf10);
}
else
{
BigInt bigDigit = BigInt.Div(scratch, denom);
bigDigit.Sign = false;
scratch.Sub(BigInt.Mul(denom, bigDigit));
if (mantissa.Sign)
{
output = String.Format("-{0}.", bigDigit);
}
else
{
output = String.Format("{0}.", bigDigit);
}
denom = BigInt.Div(denom, 10u);
while (!denom.IsZero())
{
uint digit = (uint)BigInt.Div(scratch, denom);
if (digit == 10) digit--;
scratch.Sub(BigInt.Mul(denom, digit));
output = String.Format("{0}{1}", output, digit);
denom = BigInt.Div(denom, 10u);
}
output = RoundString(output, RoundingDigits);
}
return output;
}
/// <summary>
/// Calculates 'this' mod n2 (using the schoolbook division algorithm as above)
/// </summary>
/// <param name="n2"></param>
public void Mod(BigInt n2)
{
if (n2.digitArray.Length != digitArray.Length) MakeSafe(ref n2);
int OldLength = digitArray.Length;
//First, we need to prepare the operands for division using Div_32, which requires
//That the most significant digit of n2 be set. To do this, we need to shift n2 (and therefore n1) up.
//This operation can potentially increase the precision of the operands.
int shift = MakeSafeDiv(this, n2);
BigInt Q = new BigInt(this.pres);
BigInt R = new BigInt(this.pres);
Q.digitArray = new UInt32[this.digitArray.Length];
R.digitArray = new UInt32[this.digitArray.Length];
Div_32(this, n2, Q, R);
//Restore n2 to its pre-shift value
n2.RSH(shift);
R.RSH(shift);
R.sign = (sign != n2.sign);
AssignInt(R);
//Reset the lengths of the operands
SetNumDigits(OldLength);
n2.SetNumDigits(OldLength);
}
/// <summary>
/// Calculates 'this'^power
/// </summary>
/// <param name="power"></param>
public void Power(BigInt power)
{
if (power.IsZero() || power.sign)
{
Zero();
digitArray[0] = 1;
return;
}
BigInt pow = new BigInt(power);
BigInt temp = new BigInt(this);
BigInt powTerm = new BigInt(this);
pow.Decrement();
for (; !pow.IsZero(); pow.RSH(1))
{
if ((pow.digitArray[0] & 1) == 1)
{
temp.Mul(powTerm);
}
powTerm.Square();
}
Assign(temp);
}
/// <summary>
/// The right-shift operator
/// </summary>
public static BigInt operator >>(BigInt n1, int n2)
{
BigInt res = new BigInt(n1);
res.RSH(n2);
return res;
}