private T ReturnQuietNaN(T thisValue, EContext ctx)
{
EInteger mant = this.GetHelper().GetMantissa(thisValue).Abs();
var mantChanged = false;
if (!mant.IsZero && ctx != null && ctx.HasMaxPrecision)
{
EInteger limit = this.GetHelper().MultiplyByRadixPower(
EInteger.One,
FastInteger.FromBig(ctx.Precision));
if (mant.CompareTo(limit) >= 0)
{
mant %= (EInteger)limit;
mantChanged = true;
}
}
int flags = this.GetHelper().GetFlags(thisValue);
if (!mantChanged && (flags & BigNumberFlags.FlagQuietNaN) != 0)
{
return(thisValue);
}
flags &= BigNumberFlags.FlagNegative;
flags |= BigNumberFlags.FlagQuietNaN;
return(this.GetHelper().CreateNewWithFlags(mant, EInteger.Zero, flags));
}
private FastInteger CalcKnownBitLength()
{
if (this.isSmall)
{
int kb = SmallBitLength;
for (int i = SmallBitLength - 1; i >= 0; --i)
{
if ((this.shiftedSmall & (1 << i)) != 0)
{
break;
}
--kb;
}
// Make sure bit length is 1 if value is 0
if (kb == 0)
{
++kb;
}
return(new FastInteger(kb));
}
if (this.shiftedBigInt.IsZero)
{
{ return(new FastInteger(1)); }
}
long sbe = this.shiftedBigInt.GetSignedBitLengthAsInt64();
return((sbe < Int32.MaxValue) ? new FastInteger((int)sbe) :
FastInteger.FromBig(this.shiftedBigInt.GetSignedBitLengthAsEInteger()));
}
public static FastIntegerFixed[] DigitLengthBoundsFixed <THelper>(
IRadixMathHelper <THelper> helper,
FastIntegerFixed fei)
{
int radix = helper.GetRadix();
FastIntegerFixed fastpath = FastPathDigitLength(fei, radix);
if (fastpath != null)
{
return(new FastIntegerFixed[] { fastpath, fastpath });
}
if (radix == 10)
{
EInteger[] fi = DecimalDigitLengthBoundsAsEI(fei.ToEInteger());
return(new FastIntegerFixed[] {
FastIntegerFixed.FromBig(fi[0]),
FastIntegerFixed.FromBig(fi[1]),
});
}
else
{
FastInteger fi = helper.GetDigitLength(fei.ToEInteger());
FastIntegerFixed fif = FastIntegerFixed.FromFastInteger(fi);
return(new FastIntegerFixed[] { fif, fif });
}
}
public void ShiftRight(FastInteger fastint)
{
if (fastint.Sign <= 0)
{
return;
}
if (fastint.CanFitInInt32())
{
this.ShiftRightInt(fastint.ToInt32());
}
else
{
EInteger bi = fastint.ToEInteger();
while (bi.Sign > 0)
{
var count = 1000000;
if (bi.CompareTo((EInteger)1000000) < 0)
{
count = (int)bi;
}
this.ShiftRightInt(count);
bi -= (EInteger)count;
if (this.isSmall ? this.shiftedSmall == 0 :
this.shiftedBigInt.IsZero)
{
break;
}
}
}
}
private void ShiftToDigitsSmall(int digits)
{
var kb = 0;
int v2 = this.shiftedSmall;
kb = (v2 >= 1000000000) ? 10 : ((v2 >= 100000000) ? 9 : ((v2 >=
10000000) ? 8 : ((v2 >= 1000000) ? 7 : ((v2 >= 100000) ? 6 : ((v2 >=
10000) ? 5 : ((v2 >= 1000) ? 4 : ((v2 >= 100) ? 3 : ((v2 >= 10) ? 2 :
1))))))));
this.knownDigitLength = new FastInteger(kb);
if (kb > digits)
{
var digitShift = (int)(kb - digits);
this.UpdateKnownLengthInt(digitShift);
this.discardedBitCount = this.discardedBitCount != null?
this.discardedBitCount.AddInt(digitShift) :
(new FastInteger(digitShift));
for (var i = 0; i < digitShift; ++i)
{
var digit = (int)(this.shiftedSmall % 10);
this.shiftedSmall /= 10;
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = digit;
}
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
}
}
public void TruncateRight(FastInteger fastint)
{
if (fastint == null)
{
throw new ArgumentNullException("fastint");
}
if (fastint.CanFitInInt32())
{
int fi = fastint.AsInt32();
if (fi < 0)
{
return;
}
if (!this.isSmall)
{
if (this.shiftedBigInt.CanFitInInt64())
{
this.TruncateRightLong(this.shiftedBigInt.ToInt64Checked(), fi);
}
else
{
this.ShiftRightBig(fi, true);
}
}
else
{
this.TruncateRightSmall(fi);
}
}
else
{
this.ShiftRight(fastint);
}
}
public static FastIntegerFixed FromFastInteger(FastInteger fi)
{
if (fi.CanFitInInt32())
{
return(new FastIntegerFixed(fi.AsInt32()));
}
else
{
return(FastIntegerFixed.FromBig(fi.AsEInteger()));
}
}
public static FastIntegerFixed FromFastInteger(FastInteger fi)
{
if (fi.CanFitInInt32())
{
return(FromInt32(fi.ToInt32()));
}
else
{
return(FastIntegerFixed.FromBig(fi.ToEInteger()));
}
}
public FastInteger ToFastInteger()
{
if (this.integerMode == IntegerMode.SmallValue)
{
return(new FastInteger(this.smallValue));
}
else
{
return(FastInteger.FromBig(this.largeValue));
}
}
private void UpdateKnownLength(FastInteger digitsFast)
{
if (this.knownDigitLength != null)
{
this.knownDigitLength.Subtract(digitsFast);
if (this.knownDigitLength.CompareToInt(1) < 0)
{
this.knownDigitLength.SetInt(1);
}
this.VerifyKnownLength();
}
}
/// <summary>This is an internal API.</summary>
/// <returns>A text string.</returns>
public override string ToString()
{
switch (this.integerMode)
{
case IntegerMode.SmallValue:
return(FastInteger.IntToString(this.smallValue));
case IntegerMode.LargeValue:
return(this.largeValue.ToString());
default: return(String.Empty);
}
}
public int CompareTo(FastInteger fint)
{
switch (this.integerMode)
{
case IntegerMode.SmallValue:
return(-fint.CompareToInt(this.smallValue));
case IntegerMode.LargeValue:
return(-fint.CompareTo(this.largeValue));
default: throw new InvalidOperationException();
}
}
public static FastIntegerFixed DigitLengthFixed <THelper>(
IRadixMathHelper <THelper> helper,
FastIntegerFixed fei)
{
FastIntegerFixed fastpath = FastPathDigitLength(fei, helper.GetRadix());
if (fastpath != null)
{
return(fastpath);
}
FastInteger fi = helper.GetDigitLength(fei.ToEInteger());
FastIntegerFixed fif = FastIntegerFixed.FromFastInteger(fi);
return(fif);
}
internal static EInteger FindPowerOfTenFromBig(EInteger
bigintExponent)
{
int sign = bigintExponent.Sign;
if (sign < 0)
{
return(EInteger.Zero);
}
if (sign == 0)
{
return(EInteger.One);
}
if (bigintExponent.CompareTo(ValueBigInt36) <= 0)
{
return(FindPowerOfTen((int)bigintExponent));
}
FastInteger intcurexp = FastInteger.FromBig(bigintExponent);
EInteger mantissa = EInteger.One;
EInteger bigpow = EInteger.Zero;
// DebugUtility.Log("Getting power of ten from big "+bigintExponent);
while (intcurexp.Sign > 0)
{
if (intcurexp.CompareToInt(18) <= 0)
{
bigpow = FindPowerOfTen(intcurexp.AsInt32());
mantissa *= (EInteger)bigpow;
break;
}
if (intcurexp.CompareToInt(9999999) <= 0)
{
int val = intcurexp.AsInt32();
bigpow = FindPowerOfFive(val);
bigpow <<= val;
mantissa *= (EInteger)bigpow;
break;
}
if (bigpow.IsZero)
{
bigpow = FindPowerOfFive(9999999);
bigpow <<= 9999999;
}
mantissa *= bigpow;
intcurexp.AddInt(-9999999);
}
return(mantissa);
}
public BitShiftAccumulator(
int smallint,
int lastDiscarded,
int olderDiscarded)
{
this.shiftedSmall = smallint;
if (this.shiftedSmall < 0)
{
throw new ArgumentException("shiftedSmall(" + this.shiftedSmall +
") is less than 0");
}
this.isSmall = true;
this.discardedBitCount = new FastInteger(0);
this.bitsAfterLeftmost = (olderDiscarded != 0) ? 1 : 0;
this.bitLeftmost = (lastDiscarded != 0) ? 1 : 0;
}
private void ShiftRightSmall(int bits)
{
if (bits <= 0)
{
return;
}
if (this.shiftedSmall == 0)
{
this.discardedBitCount.AddInt(bits);
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
this.knownBitLength = new FastInteger(1);
return;
}
int kb = SmallBitLength;
for (int i = SmallBitLength - 1; i >= 0; --i)
{
if ((this.shiftedSmall & (1 << i)) != 0)
{
break;
}
--kb;
}
var shift = (int)Math.Min(kb, bits);
bool shiftingMoreBits = bits > kb;
kb -= shift;
this.knownBitLength = new FastInteger(kb);
this.discardedBitCount.AddInt(bits);
this.bitsAfterLeftmost |= this.bitLeftmost;
// Get the bottommost shift minus 1 bits
this.bitsAfterLeftmost |= (shift > 1 && (this.shiftedSmall <<
(SmallBitLength - shift + 1)) != 0) ? 1 : 0;
// Get the bit just above that bit
this.bitLeftmost = (int)((this.shiftedSmall >> (shift - 1)) & 0x01);
this.shiftedSmall >>= shift;
if (shiftingMoreBits)
{
// Shifted more bits than the bit length
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
}
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
}
#pragma warning disable CS0618 // certain ERounding values are obsolete
private T SignalOverflow2(EContext pc, bool neg)
{
if (pc != null)
{
ERounding roundingOnOverflow = pc.Rounding;
if (pc.HasFlags)
{
pc.Flags |= EContext.FlagOverflow |
EContext.FlagInexact | EContext.FlagRounded;
}
if (pc.HasMaxPrecision && pc.HasExponentRange &&
(roundingOnOverflow == ERounding.Down ||
roundingOnOverflow == ERounding.ZeroFiveUp ||
roundingOnOverflow == ERounding.OddOrZeroFiveUp ||
roundingOnOverflow == ERounding.Odd ||
(roundingOnOverflow == ERounding.Ceiling && neg) ||
(roundingOnOverflow == ERounding.Floor && !neg)))
{
// Set to the highest possible value for
// the given precision
EInteger overflowMant = EInteger.Zero;
FastInteger fastPrecision = FastInteger.FromBig(pc.Precision);
overflowMant = this.GetHelper().MultiplyByRadixPower(
EInteger.One,
fastPrecision);
overflowMant -= EInteger.One;
FastInteger clamp =
FastInteger.FromBig(pc.EMax).Increment().Subtract(fastPrecision);
return(this.GetHelper().CreateNewWithFlags(
overflowMant,
clamp.AsEInteger(),
neg ? BigNumberFlags.FlagNegative : 0));
}
}
int flagneg = neg ? BigNumberFlags.FlagNegative : 0;
return(this.GetHelper().GetArithmeticSupport() ==
BigNumberFlags.FiniteOnly ?
default(T) : this.GetHelper().CreateNewWithFlags(
EInteger.Zero,
EInteger.Zero,
flagneg | BigNumberFlags.FlagInfinity));
}
public void ShiftRight(FastInteger fastint)
{
if (fastint == null)
{
throw new ArgumentNullException("fastint");
}
if (fastint.CanFitInInt32())
{
int fi = fastint.AsInt32();
if (fi < 0)
{
return;
}
this.ShiftRightInt(fi);
}
else
{
if (fastint.Sign <= 0)
{
return;
}
EInteger bi = fastint.AsEInteger();
while (bi.Sign > 0)
{
var count = 1000000;
if (bi.CompareTo((EInteger)1000000) < 0)
{
count = (int)bi;
}
this.ShiftRightInt(count);
bi -= (EInteger)count;
if (this.isSmall ? this.shiftedSmall == 0 :
this.shiftedBigInt.IsZero)
{
break;
}
}
}
}
public static FastInteger[] DigitLengthBounds <THelper>(
IRadixMathHelper <THelper> helper,
EInteger ei)
{
int radix = helper.GetRadix();
if (radix == 2)
{
FastInteger fi =
FastInteger.FromBig(ei.GetUnsignedBitLengthAsEInteger());
return(new FastInteger[] { fi, fi });
}
else if (radix == 10)
{
return(DecimalDigitLengthBounds(ei));
}
else
{
FastInteger fi = helper.GetDigitLength(ei);
return(new FastInteger[] { fi, fi });
}
}
public BitShiftAccumulator(
EInteger bigint,
int lastDiscarded,
int olderDiscarded)
{
if (bigint.Sign < 0)
{
throw new ArgumentException("bigint's sign(" + bigint.Sign +
") is less than 0");
}
if (bigint.CanFitInInt32())
{
this.isSmall = true;
this.shiftedSmall = (int)bigint;
}
else
{
this.shiftedBigInt = bigint;
}
this.discardedBitCount = new FastInteger(0);
this.bitsAfterLeftmost = (olderDiscarded != 0) ? 1 : 0;
this.bitLeftmost = (lastDiscarded != 0) ? 1 : 0;
}
private void ShiftSmallToBits(int bits)
{
if (this.knownBitLength != null)
{
if (this.knownBitLength.CompareToInt(bits) <= 0)
{
return;
}
}
this.knownBitLength = this.knownBitLength ?? this.CalcKnownBitLength();
if (this.knownBitLength.CompareToInt(bits) <= 0)
{
return;
}
int kbl = this.knownBitLength.ToInt32();
// Shift by the difference in bit length
if (kbl > bits)
{
int bitShift = kbl - (int)bits;
var shift = (int)bitShift;
this.knownBitLength = new FastInteger(bits);
this.discardedBitCount.AddInt(bitShift);
this.bitsAfterLeftmost |= this.bitLeftmost;
// Get the bottommost shift minus 1 bits
this.bitsAfterLeftmost |= (shift > 1 && (this.shiftedSmall <<
(SmallBitLength - shift + 1)) != 0) ? 1 : 0;
// Get the bit just above that bit
this.bitLeftmost = (int)((this.shiftedSmall >> (shift - 1)) & 0x01);
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
this.shiftedSmall >>= shift;
}
else
{
this.knownBitLength = new FastInteger(kbl);
}
}
private FastInteger CalcKnownBitLength()
{
if (this.isSmall)
{
int kb = SmallBitLength;
for (int i = SmallBitLength - 1; i >= 0; --i)
{
if ((this.shiftedSmall & (1 << i)) != 0)
{
break;
}
--kb;
}
// Make sure bit length is 1 if value is 0
if (kb == 0)
{
++kb;
}
// Console.WriteLine("{0:X8} kbl=" + kb);
return(new FastInteger(kb));
}
return(this.shiftedBigInt.IsZero ? new FastInteger(1) :
FastInteger.FromBig(this.shiftedBigInt.GetSignedBitLengthAsEInteger()));
}
public static EInteger ReduceTrailingZeros(
EInteger bigmant,
FastInteger exponentMutable,
int radix,
FastInteger digits,
FastInteger precision,
FastInteger idealExp)
{
#if DEBUG
if (precision != null && digits == null)
{
throw new ArgumentException("doesn't satisfy precision==null || digits!=null");
}
#endif
if (bigmant.IsZero)
{
exponentMutable.SetInt(0);
return(bigmant);
}
var bigradix = (EInteger)radix;
var bitToTest = 0;
var bitsToShift = new FastInteger(0);
while (!bigmant.IsZero)
{
if (precision != null && digits.CompareTo(precision) == 0)
{
break;
}
if (idealExp != null && exponentMutable.CompareTo(idealExp) == 0)
{
break;
}
if (radix == 2)
{
if (bitToTest < Int32.MaxValue)
{
if (bigmant.GetSignedBit(bitToTest))
{
break;
}
++bitToTest;
bitsToShift.Increment();
}
else
{
if (!bigmant.IsEven)
{
break;
}
bigmant >>= 1;
}
}
else
{
EInteger bigrem;
EInteger bigquo;
{
EInteger[] divrem = bigmant.DivRem(bigradix);
bigquo = divrem[0];
bigrem = divrem[1];
}
if (!bigrem.IsZero)
{
break;
}
bigmant = bigquo;
}
exponentMutable.Increment();
if (digits != null)
{
digits.Decrement();
}
}
if (radix == 2 && !bitsToShift.IsValueZero)
{
while (bitsToShift.CompareToInt(1000000) > 0)
{
bigmant >>= 1000000;
bitsToShift.SubtractInt(1000000);
}
int tmpshift = bitsToShift.AsInt32();
bigmant >>= tmpshift;
}
return(bigmant);
}
private T PostProcessEx(
T thisValue,
EContext ctxDest,
EContext ctxSrc,
bool afterDivision,
bool afterQuantize)
{
int thisFlags = this.GetHelper().GetFlags(thisValue);
if (ctxDest != null && ctxSrc != null)
{
if (ctxDest.HasFlags)
{
if (!ctxSrc.ClampNormalExponents)
{
ctxSrc.Flags &= ~EContext.FlagClamped;
}
ctxDest.Flags |= ctxSrc.Flags;
if ((ctxSrc.Flags & EContext.FlagSubnormal) != 0)
{
// Treat subnormal numbers as underflows
ctxDest.Flags |= BigNumberFlags.UnderflowFlags;
}
}
}
if ((thisFlags & BigNumberFlags.FlagSpecial) != 0)
{
return((ctxDest.Flags == 0) ? this.SignalInvalid(ctxDest) : thisValue);
}
EInteger mant = this.GetHelper().GetMantissa(thisValue).Abs();
if (mant.IsZero)
{
return(afterQuantize ? this.GetHelper().CreateNewWithFlags(
mant,
this.GetHelper().GetExponent(thisValue),
0) : this.wrapper.RoundToPrecision(
this.GetHelper().ValueOf(0),
ctxDest));
}
if (afterQuantize)
{
return(thisValue);
}
EInteger exp = this.GetHelper().GetExponent(thisValue);
if (exp.Sign > 0)
{
FastInteger fastExp = FastInteger.FromBig(exp);
if (ctxDest == null || !ctxDest.HasMaxPrecision)
{
mant = this.GetHelper().MultiplyByRadixPower(mant, fastExp);
return(this.GetHelper().CreateNewWithFlags(
mant,
EInteger.Zero,
thisFlags));
}
if (!ctxDest.ExponentWithinRange(exp))
{
return(thisValue);
}
FastInteger prec = FastInteger.FromBig(ctxDest.Precision);
FastInteger digits =
this.GetHelper().CreateShiftAccumulator(mant).GetDigitLength();
prec.Subtract(digits);
if (prec.Sign > 0 && prec.CompareTo(fastExp) >= 0)
{
mant = this.GetHelper().MultiplyByRadixPower(mant, fastExp);
return(this.GetHelper().CreateNewWithFlags(
mant,
EInteger.Zero,
thisFlags));
}
if (afterDivision)
{
int radix = this.GetHelper().GetRadix();
mant = NumberUtility.ReduceTrailingZeros(
mant,
fastExp,
radix,
null,
null,
null);
thisValue = this.GetHelper().CreateNewWithFlags(
mant,
fastExp.AsEInteger(),
thisFlags);
}
}
else if (afterDivision && exp.Sign < 0)
{
FastInteger fastExp = FastInteger.FromBig(exp);
int radix = this.GetHelper().GetRadix();
mant = NumberUtility.ReduceTrailingZeros(
mant, fastExp, radix, null, null, new FastInteger(0));
thisValue = this.GetHelper().CreateNewWithFlags(
mant,
fastExp.AsEInteger(),
thisFlags);
}
return(thisValue);
}
internal static EInteger FindPowerOfFiveFromBig(EInteger diff)
{
int sign = diff.Sign;
if (sign < 0)
{
return(EInteger.Zero);
}
if (sign == 0)
{
return(EInteger.One);
}
FastInteger intcurexp = FastInteger.FromBig(diff);
if (intcurexp.CompareToInt(54) <= 0)
{
return(FindPowerOfFive(intcurexp.AsInt32()));
}
EInteger mantissa = EInteger.One;
EInteger bigpow;
EInteger origdiff = diff;
bigpow = ValuePowerOfFiveCache.GetCachedPower(origdiff);
if (bigpow != null)
{
return(bigpow);
}
EInteger[] otherPower =
ValuePowerOfFiveCache.FindCachedPowerOrSmaller(origdiff);
if (otherPower != null)
{
intcurexp.SubtractBig(otherPower[0]);
bigpow = otherPower[1];
mantissa = bigpow;
}
else
{
bigpow = EInteger.Zero;
}
while (intcurexp.Sign > 0)
{
if (intcurexp.CompareToInt(27) <= 0)
{
bigpow = FindPowerOfFive(intcurexp.AsInt32());
mantissa *= (EInteger)bigpow;
break;
}
if (intcurexp.CompareToInt(9999999) <= 0)
{
bigpow = FindPowerOfFive(1).Pow(intcurexp.AsInt32());
mantissa *= (EInteger)bigpow;
break;
}
if (bigpow.IsZero)
{
bigpow = FindPowerOfFive(1).Pow(9999999);
}
mantissa *= bigpow;
intcurexp.AddInt(-9999999);
}
ValuePowerOfFiveCache.AddPower(origdiff, mantissa);
return(mantissa);
}
private T RoundBeforeOp(T val, EContext ctx)
{
if (ctx == null || !ctx.HasMaxPrecision)
{
return(val);
}
int thisFlags = this.GetHelper().GetFlags(val);
if ((thisFlags & BigNumberFlags.FlagSpecial) != 0)
{
return(val);
}
FastInteger fastPrecision = FastInteger.FromBig(ctx.Precision);
EInteger mant = this.GetHelper().GetMantissa(val).Abs();
FastInteger digits =
this.GetHelper().CreateShiftAccumulator(mant).GetDigitLength();
EContext ctx2 = ctx.WithBlankFlags().WithTraps(0);
if (digits.CompareTo(fastPrecision) <= 0)
{
// Rounding is only to be done if the digit count is
// too big (distinguishing this case is material
// if the value also has an exponent that's out of range)
return(val);
}
val = this.wrapper.RoundToPrecision(val, ctx2);
// the only time rounding can signal an invalid
// operation is if an operand is signaling NaN, but
// this was already checked beforehand
#if DEBUG
if ((ctx2.Flags & EContext.FlagInvalid) != 0)
{
throw new
ArgumentException("doesn't satisfy (ctx2.Flags&FlagInvalid)==0");
}
#endif
if ((ctx2.Flags & EContext.FlagInexact) != 0)
{
if (ctx.HasFlags)
{
ctx.Flags |= BigNumberFlags.LostDigitsFlags;
}
}
if ((ctx2.Flags & EContext.FlagRounded) != 0)
{
if (ctx.HasFlags)
{
ctx.Flags |= EContext.FlagRounded;
}
}
if ((ctx2.Flags & EContext.FlagSubnormal) != 0)
{
// Console.WriteLine("Subnormal input: " + val);
}
if ((ctx2.Flags & EContext.FlagUnderflow) != 0)
{
// Console.WriteLine("Underflow");
}
if ((ctx2.Flags & EContext.FlagOverflow) != 0)
{
bool neg = (thisFlags & BigNumberFlags.FlagNegative) != 0;
ctx.Flags |= EContext.FlagLostDigits;
return(this.SignalOverflow2(ctx, neg));
}
return(val);
}
private void ShiftRightBig(int digits, bool truncate)
{
if (digits <= 0)
{
return;
}
if (this.shiftedBigInt.IsZero)
{
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.AddInt(digits);
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
this.knownDigitLength = new FastInteger(1);
return;
}
if (truncate)
{
EInteger bigquo;
if (digits > 50)
{
// To avoid having to calculate a very big power of 10,
// check the digit count to see if doing so can be avoided
int bitLength = this.shiftedBigInt.GetUnsignedBitLength();
var bigPower = false;
// 10^48 has 160 bits; 10^98 has 326; bit length is cheaper
// to calculate than base-10 digit length
if (bitLength < 160 || (digits > 100 && bitLength < 326))
{
bigPower = true;
}
else
{
FastInteger knownDigits = this.GetDigitLength();
bigPower = knownDigits.Copy().SubtractInt(digits)
.CompareToInt(-2) < 0;
if (!bigPower)
{
// DebugUtility.Log("digitlength {0} [todiscard: {1}]"
// , knownDigits, digits);
}
}
if (bigPower)
{
// Power of 10 to be divided would be much bigger
this.discardedBitCount = this.discardedBitCount ?? (new
FastInteger(0));
this.discardedBitCount.AddInt(digits);
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitsAfterLeftmost |= this.shiftedBigInt.IsZero ? 0 : 1;
this.bitLeftmost = 0;
this.knownDigitLength = new FastInteger(1);
this.isSmall = true;
this.shiftedSmall = 0;
return;
}
}
if (this.shiftedBigInt.IsEven && this.bitLeftmost == 0)
{
EInteger[] quorem = this.shiftedBigInt.DivRem(
NumberUtility.FindPowerOfTen(digits));
bigquo = quorem[0];
this.bitLeftmost |= quorem[1].IsZero ? 0 : 1;
}
else
{
this.bitLeftmost = 1;
bigquo = this.shiftedBigInt.Divide(
NumberUtility.FindPowerOfTen(digits));
}
this.bitsAfterLeftmost |= this.bitLeftmost;
this.discardedBitCount = this.discardedBitCount == null ?
new FastInteger(digits) : this.discardedBitCount.AddInt(digits);
if (bigquo.IsZero)
{
// Shifted all the way to 0
this.isSmall = true;
this.shiftedBigInt = null;
this.shiftedSmall = 0;
this.knownDigitLength = new FastInteger(1);
}
else if (bigquo.CanFitInInt32())
{
this.isSmall = true;
this.shiftedSmall = bigquo.ToInt32Unchecked();
this.shiftedBigInt = null;
this.UpdateKnownLengthInt(digits);
}
else
{
this.isSmall = false;
this.shiftedBigInt = bigquo;
this.UpdateKnownLengthInt(digits);
}
return;
}
if (digits == 1)
{
EInteger bigrem;
EInteger bigquo;
EInteger[] divrem = this.shiftedBigInt.DivRem((EInteger)10);
bigquo = divrem[0];
bigrem = divrem[1];
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = (int)bigrem;
this.shiftedBigInt = bigquo;
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.AddInt(digits);
this.UpdateKnownLengthInt(digits);
return;
}
if (digits >= 2 && digits <= 8)
{
EInteger bigrem;
EInteger bigquo;
EInteger[] divrem =
this.shiftedBigInt.DivRem(NumberUtility.FindPowerOfTen(digits));
bigquo = divrem[0];
bigrem = divrem[1];
var intRem = (int)bigrem;
int smallPower = ValueTenPowers[digits - 1];
int leftBit = intRem / smallPower;
int otherBits = intRem - (leftBit * smallPower);
this.bitsAfterLeftmost |= otherBits | this.bitLeftmost;
this.bitLeftmost = leftBit;
this.shiftedBigInt = bigquo;
this.discardedBitCount = (this.discardedBitCount != null) ?
this.discardedBitCount.AddInt(digits) : (new FastInteger(digits));
this.UpdateKnownLengthInt(digits);
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
if (this.shiftedBigInt.CanFitInInt32())
{
this.isSmall = true;
this.shiftedSmall = this.shiftedBigInt.ToInt32Unchecked();
this.shiftedBigInt = null;
}
return;
}
this.knownDigitLength = this.knownDigitLength ??
this.CalcKnownDigitLength();
if (new FastInteger(digits).Decrement().CompareTo(this.knownDigitLength)
>= 0)
{
// Shifting more bits than available
this.bitsAfterLeftmost |= this.shiftedBigInt.IsZero ? 0 : 1;
this.isSmall = true;
this.shiftedSmall = 0;
this.knownDigitLength = new FastInteger(1);
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.AddInt(digits);
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
return;
}
if (this.shiftedBigInt.CanFitInInt32())
{
this.isSmall = true;
this.shiftedSmall = (int)this.shiftedBigInt;
this.ShiftRightSmall(digits);
return;
}
if (this.shiftedBigInt.CanFitInInt64())
{
this.ShiftRightLong(this.shiftedBigInt.ToInt64Unchecked(), digits);
return;
}
string str = this.shiftedBigInt.ToString();
// NOTE: Will be 1 if the value is 0
int digitLength = str.Length;
var bitDiff = 0;
if (digits > digitLength)
{
bitDiff = digits - digitLength;
}
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.AddInt(digits);
this.bitsAfterLeftmost |= this.bitLeftmost;
int digitShift = Math.Min(digitLength, digits);
if (digits >= digitLength)
{
this.isSmall = true;
this.shiftedSmall = 0;
this.knownDigitLength = new FastInteger(1);
}
else
{
var newLength = (int)(digitLength - digitShift);
if (newLength <= 9)
{
// Fits in a small number
this.isSmall = true;
this.shiftedSmall = FastParseLong(str, 0, newLength);
}
else
{
this.shiftedBigInt = EInteger.FromSubstring(str, 0, newLength);
}
this.UpdateKnownLengthInt(digitShift);
}
for (int i = str.Length - 1; i >= 0; --i)
{
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = (int)(str[i] - '0');
--digitShift;
if (digitShift <= 0)
{
break;
}
}
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
if (bitDiff > 0)
{
// Shifted more digits than the digit length
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
}
}
private void ShiftToDigitsBig(int digits, bool truncate)
{
// Shifts a number until it reaches the given number of digits,
// gathering information on whether the last digit discarded is set
// and whether the discarded digits to the right of that digit are set.
// Assumes that the big integer being shifted is positive.
if (this.knownDigitLength != null)
{
if (this.knownDigitLength.CompareToInt(digits) <= 0)
{
return;
}
}
string str;
this.knownDigitLength = this.knownDigitLength ??
this.CalcKnownDigitLength();
if (this.knownDigitLength.CompareToInt(digits) <= 0)
{
return;
}
FastInteger digitDiff = this.knownDigitLength.Copy().SubtractInt(digits);
if (truncate && digitDiff.CanFitInInt32())
{
this.TruncateRight(digitDiff);
return;
}
if (digitDiff.CompareToInt(1) == 0)
{
EInteger bigrem;
EInteger bigquo;
EInteger[] divrem = this.shiftedBigInt.DivRem(ValueTen);
bigquo = divrem[0];
bigrem = divrem[1];
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = (int)bigrem;
this.shiftedBigInt = bigquo;
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.Add(digitDiff);
this.UpdateKnownLength(digitDiff);
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
return;
}
if (digitDiff.CompareToInt(9) <= 0)
{
EInteger bigrem;
int diffInt = digitDiff.AsInt32();
EInteger radixPower = NumberUtility.FindPowerOfTen(diffInt);
EInteger bigquo;
EInteger[] divrem = this.shiftedBigInt.DivRem(radixPower);
bigquo = divrem[0];
bigrem = divrem[1];
var rem = (int)bigrem;
this.bitsAfterLeftmost |= this.bitLeftmost;
for (var i = 0; i < diffInt; ++i)
{
if (i == diffInt - 1)
{
this.bitLeftmost = rem % 10;
}
else
{
int intQuot = (rem < 43698) ? ((rem * 26215) >> 18) : (rem / 10);
this.bitsAfterLeftmost |= rem - (intQuot * 10);
rem = intQuot;
}
}
this.shiftedBigInt = bigquo;
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.Add(digitDiff);
this.UpdateKnownLength(digitDiff);
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
return;
}
if (digitDiff.CanFitInInt32())
{
#if DEBUG
if (!(digitDiff.CompareToInt(2) > 0))
{
throw new ArgumentException(
"doesn't satisfy digitDiff.CompareToInt(2)>0");
}
#endif
EInteger bigrem = null;
EInteger bigquo;
EInteger[] divrem;
if (!this.shiftedBigInt.IsEven || this.bitsAfterLeftmost != 0)
{
EInteger radixPower =
NumberUtility.FindPowerOfTen(digitDiff.AsInt32() - 1);
this.bitsAfterLeftmost |= 1;
bigquo = this.shiftedBigInt.Divide(radixPower);
}
else
{
EInteger radixPower =
NumberUtility.FindPowerOfTen(digitDiff.AsInt32() - 1);
divrem = this.shiftedBigInt.DivRem(radixPower);
bigquo = divrem[0];
bigrem = divrem[1];
this.bitsAfterLeftmost |= this.bitLeftmost;
if (!bigrem.IsZero)
{
this.bitsAfterLeftmost |= 1;
}
}
EInteger bigquo2;
divrem = bigquo.DivRem(ValueTen);
bigquo2 = divrem[0];
bigrem = divrem[1];
this.bitLeftmost = (int)bigrem;
this.shiftedBigInt = bigquo2;
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.Add(digitDiff);
this.UpdateKnownLength(digitDiff);
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
return;
}
str = this.shiftedBigInt.ToString();
// NOTE: Will be 1 if the value is 0
int digitLength = str.Length;
this.knownDigitLength = new FastInteger(digitLength);
// Shift by the difference in digit length
if (digitLength > digits)
{
int digitShift = digitLength - digits;
this.UpdateKnownLengthInt(digitShift);
var newLength = (int)(digitLength - digitShift);
// Console.WriteLine("dlen= " + digitLength + " dshift=" +
// digitShift + " newlen= " + newLength);
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
if (digitShift <= Int32.MaxValue)
{
this.discardedBitCount.AddInt((int)digitShift);
}
else
{
this.discardedBitCount.AddBig((EInteger)digitShift);
}
for (int i = str.Length - 1; i >= 0; --i)
{
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = (int)(str[i] - '0');
--digitShift;
if (digitShift <= 0)
{
break;
}
}
if (newLength <= 9)
{
this.isSmall = true;
this.shiftedSmall = FastParseLong(str, 0, newLength);
}
else
{
this.shiftedBigInt = EInteger.FromSubstring(str, 0, newLength);
}
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
}
}
private void ShiftRightSmall(int digits)
{
if (digits <= 0)
{
return;
}
if (this.shiftedSmall == 0)
{
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.AddInt(digits);
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
this.knownDigitLength = new FastInteger(1);
return;
}
if (digits >= 2 && digits <= 8)
{
if (this.shiftedSmall >= ValueTenPowers[digits])
{
int bigPower = ValueTenPowers[digits];
int smallPower = ValueTenPowers[digits - 1];
this.discardedBitCount = this.discardedBitCount ?? (new
FastInteger(0));
this.discardedBitCount.AddInt(digits);
int div = this.shiftedSmall / bigPower;
int rem = this.shiftedSmall - (div * bigPower);
int rem2 = rem / smallPower;
this.bitLeftmost = rem2;
this.bitsAfterLeftmost |= rem - (rem2 * smallPower);
this.shiftedSmall = div;
this.knownDigitLength = (div < 10) ? (new FastInteger(1)) :
this.CalcKnownDigitLength();
return;
}
else if (this.shiftedSmall >= ValueTenPowers[digits - 1])
{
int smallPower = ValueTenPowers[digits - 1];
if (this.discardedBitCount != null)
{
this.discardedBitCount.AddInt(digits);
}
else
{
this.discardedBitCount = new FastInteger(digits);
}
int rem = this.shiftedSmall;
int rem2 = rem / smallPower;
this.bitLeftmost = rem2;
this.bitsAfterLeftmost |= rem - (rem2 * smallPower);
this.shiftedSmall = 0;
this.knownDigitLength = new FastInteger(1);
return;
}
else
{
if (this.discardedBitCount != null)
{
this.discardedBitCount.AddInt(digits);
}
else
{
this.discardedBitCount = new FastInteger(digits);
}
int rem = this.shiftedSmall;
this.bitLeftmost = 0;
this.bitsAfterLeftmost |= rem;
this.shiftedSmall = 0;
this.knownDigitLength = new FastInteger(1);
return;
}
}
int v2 = this.shiftedSmall;
int kb = (v2 >= 1000000000) ? 10 : ((v2 >= 100000000) ? 9 : ((v2 >=
10000000) ? 8 : ((v2 >= 1000000) ? 7 : ((v2 >= 100000) ? 6 : ((v2 >=
10000) ? 5 : ((v2 >= 1000) ? 4 : ((v2 >= 100) ? 3 : ((v2 >= 10) ? 2 :
1))))))));
this.knownDigitLength = new FastInteger(kb);
if (this.discardedBitCount != null)
{
this.discardedBitCount.AddInt(digits);
}
else
{
this.discardedBitCount = new FastInteger(digits);
}
var digitsShifted = 0;
while (digits > 0)
{
if (this.shiftedSmall == 0)
{
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
this.knownDigitLength = new FastInteger(1);
break;
}
else
{
var digit = (int)(this.shiftedSmall % 10);
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = digit;
--digits;
++digitsShifted;
this.shiftedSmall /= 10;
}
}
this.UpdateKnownLengthInt(digitsShifted);
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
}
private void ShiftRightLong(long shiftedLong, int digits)
{
if (digits <= 0)
{
return;
}
if (shiftedLong == 0)
{
this.shiftedSmall = 0;
this.isSmall = true;
this.discardedBitCount = this.discardedBitCount ?? (new FastInteger(0));
this.discardedBitCount.AddInt(digits);
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
this.knownDigitLength = new FastInteger(1);
return;
}
if (digits >= 2 && digits <= 8)
{
if (shiftedLong >= ValueTenPowers[digits])
{
long bigPower = ValueTenPowers[digits];
long smallPower = ValueTenPowers[digits - 1];
this.discardedBitCount = this.discardedBitCount ?? (new
FastInteger(0));
this.discardedBitCount.AddInt(digits);
long div = shiftedLong / bigPower;
long rem = shiftedLong - (div * bigPower);
long rem2 = rem / smallPower;
this.bitLeftmost = (int)rem2;
this.bitsAfterLeftmost |= ((rem - (rem2 * smallPower)) == 0) ? 0 : 1;
this.isSmall = div <= Int32.MaxValue;
if (this.isSmall)
{
this.shiftedSmall = (int)div;
this.knownDigitLength = (div < 10) ? (new FastInteger(1)) :
new FastInteger(LongDigitLength(div));
}
else
{
this.shiftedBigInt = EInteger.FromInt64(div);
this.knownDigitLength = (div < 10) ? (new FastInteger(1)) :
this.CalcKnownDigitLength();
}
return;
}
else if (this.shiftedSmall >= ValueTenPowers[digits - 1])
{
int smallPower = ValueTenPowers[digits - 1];
if (this.discardedBitCount != null)
{
this.discardedBitCount.AddInt(digits);
}
else
{
this.discardedBitCount = new FastInteger(digits);
}
long rem = shiftedLong;
long rem2 = rem / smallPower;
this.bitLeftmost = (int)rem2;
this.bitsAfterLeftmost |= ((rem - (rem2 * smallPower)) == 0) ? 0 : 1;
this.isSmall = true;
this.shiftedSmall = 0;
this.knownDigitLength = new FastInteger(1);
return;
}
else
{
if (this.discardedBitCount != null)
{
this.discardedBitCount.AddInt(digits);
}
else
{
this.discardedBitCount = new FastInteger(digits);
}
this.bitLeftmost = 0;
this.bitsAfterLeftmost |= (shiftedLong == 0) ? 0 : 1;
this.isSmall = true;
this.shiftedSmall = 0;
this.knownDigitLength = new FastInteger(1);
return;
}
}
this.knownDigitLength = new FastInteger(
LongDigitLength(shiftedLong));
if (this.discardedBitCount != null)
{
this.discardedBitCount.AddInt(digits);
}
else
{
this.discardedBitCount = new FastInteger(digits);
}
var digitsShifted = 0;
while (digits > 0)
{
if (shiftedLong == 0)
{
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = 0;
break;
}
else
{
long newShift = (shiftedLong < 43698) ? ((shiftedLong * 26215) >>
18) : (shiftedLong / 10);
var digit = (int)(shiftedLong - (newShift * 10));
this.bitsAfterLeftmost |= this.bitLeftmost;
this.bitLeftmost = digit;
--digits;
++digitsShifted;
shiftedLong = newShift;
}
}
this.isSmall = shiftedLong <= Int32.MaxValue;
if (this.isSmall)
{
this.shiftedSmall = (int)shiftedLong;
}
else
{
this.shiftedBigInt = EInteger.FromInt64(shiftedLong);
}
this.UpdateKnownLengthInt(digitsShifted);
this.bitsAfterLeftmost = (this.bitsAfterLeftmost != 0) ? 1 : 0;
}