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 FastInteger ToFastInteger()
{
if (this.integerMode == IntegerMode.SmallValue)
{
return(new FastInteger(this.smallValue));
}
else
{
return(FastInteger.FromBig(this.largeValue));
}
}
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 void ShiftToDigits(
FastInteger bits,
FastInteger preShift,
bool truncate)
{
if (bits.Sign < 0)
{
throw new ArgumentException("bits's sign(" + bits.Sign +
") is less than 0");
}
if (preShift != null && preShift.Sign > 0)
{
this.knownBitLength = this.knownBitLength ?? this.CalcKnownBitLength();
// DebugUtility.Log("bits=" + bits + " pre=" + preShift + " known=" +
// (//kbl) + " [" + this.shiftedBigInt + "]");
if (this.knownBitLength.CompareTo(bits) <= 0)
{
// Known digit length is already small enough
// NOTE: For BitShiftAccumulator, truncating and shifting
// are the same, unlike in DigitShiftAccumulator
this.ShiftRight(preShift);
VerifyKnownLength();
return;
}
else
{
FastInteger bitDiff = this.knownBitLength.Copy()
.Subtract(bits);
// DebugUtility.Log("bitDiff=" + bitDiff);
int cmp = bitDiff.CompareTo(preShift);
if (cmp <= 0)
{
// NOTE: For BitShiftAccumulator, truncating and shifting
// are the same, unlike in DigitShiftAccumulator
this.ShiftRight(preShift);
VerifyKnownLength();
return;
}
else
{
// NOTE: For BitShiftAccumulator, truncating and shifting
// are the same, unlike in DigitShiftAccumulator
this.ShiftRight(bitDiff);
VerifyKnownLength();
return;
}
}
}
if (bits.CanFitInInt32())
{
this.ShiftToDigitsInt(bits.ToInt32());
VerifyKnownLength();
}
else
{
this.knownBitLength = this.knownBitLength ?? this.CalcKnownBitLength();
EInteger bigintDiff = this.knownBitLength.ToEInteger();
EInteger bitsBig = bits.ToEInteger();
bigintDiff -= (EInteger)bitsBig;
if (bigintDiff.Sign > 0)
{
// current length is greater than the
// desired bit length
this.ShiftRight(FastInteger.FromBig(bigintDiff));
}
VerifyKnownLength();
}
}
public static FastInteger[] DecimalDigitLengthBounds(EInteger ei)
{
long longBitLength = ei.GetUnsignedBitLengthAsInt64();
if (longBitLength < 33)
{
// Can easily be calculated without estimation
var fi = new FastInteger((int)ei.GetDigitCountAsInt64());
return(new FastInteger[] { fi, fi });
}
else if (longBitLength <= 2135)
{
var bitlen = (int)longBitLength;
int minDigits = 1 + (((bitlen - 1) * 631305) >> 21);
int maxDigits = 1 + ((bitlen * 631305) >> 21);
if (minDigits == maxDigits)
{
var fi = new FastInteger(minDigits);
return(new FastInteger[] { fi, fi });
}
else
{
return(new FastInteger[] {
new FastInteger(minDigits), // lower bound
new FastInteger(maxDigits), // upper bound
});
}
}
else if (longBitLength <= 6432162)
{
var bitlen = (int)longBitLength;
// Approximation of ln(2)/ln(10)
int minDigits = 1 + (int)(((long)(bitlen - 1) * 661971961083L) >> 41);
int maxDigits = 1 + (int)(((long)bitlen * 661971961083L) >> 41);
if (minDigits == maxDigits)
{
var fi = new FastInteger(minDigits);
return(new FastInteger[] { fi, fi });
}
else
{
return(new FastInteger[] {
new FastInteger(minDigits), // lower bound
new FastInteger(maxDigits), // upper bound
});
}
}
else
{
// Bit length is big enough that these bounds will
// overestimate or underestimate the true base-10 digit length
// as appropriate.
EInteger bigBitLength = ei.GetUnsignedBitLengthAsEInteger();
EInteger lowerBound = bigBitLength.Multiply(100).Divide(335);
EInteger upperBound = bigBitLength.Divide(3);
return(new FastInteger[] {
FastInteger.FromBig(lowerBound), // lower bound
FastInteger.FromBig(upperBound), // upper bound
});
}
}
public static THelper PreRound <THelper>(
THelper val,
EContext ctx,
IRadixMath <THelper> wrapper)
{
if (ctx == null || !ctx.HasMaxPrecision)
{
return(val);
}
IRadixMathHelper <THelper> helper = wrapper.GetHelper();
int thisFlags = helper.GetFlags(val);
if ((thisFlags & BigNumberFlags.FlagSpecial) != 0)
{
// Infinity or NaN
return(val);
}
FastInteger fastPrecision = FastInteger.FromBig(ctx.Precision);
EInteger mant = helper.GetMantissa(val).Abs();
// 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)
FastInteger[] digitBounds = NumberUtility.DigitLengthBounds(
helper,
mant);
if (digitBounds[1].CompareTo(fastPrecision) <= 0)
{
// Upper bound is less than or equal to precision
return(val);
}
EContext ctx2 = ctx;
if (digitBounds[0].CompareTo(fastPrecision) <= 0)
{
// Lower bound is less than or equal to precision, so
// calculate digit length more precisely
FastInteger digits = helper.GetDigitLength(mant);
ctx2 = ctx.WithBlankFlags().WithTraps(0);
if (digits.CompareTo(fastPrecision) <= 0)
{
return(val);
}
}
val = wrapper.RoundToPrecision(val, ctx2);
// the only time rounding can signal an invalid
// operation is if an operand is a signaling NaN, but
// this was already checked beforehand
#if DEBUG
if ((ctx2.Flags & EContext.FlagInvalid) != 0)
{
throw new ArgumentException("doesn't" +
"\u0020satisfy(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.FlagOverflow) != 0)
{
bool neg = (thisFlags & BigNumberFlags.FlagNegative) != 0;
if (ctx.HasFlags)
{
ctx.Flags |= EContext.FlagLostDigits;
ctx.Flags |= EContext.FlagOverflow |
EContext.FlagInexact | EContext.FlagRounded;
}
}
return(val);
}
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 |= EContext.FlagUnderflow |
EContext.FlagSubnormal | EContext.FlagInexact | EContext.FlagRounded;
}
}
}
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().GetDigitLength(mant);
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.ToEInteger(),
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.ToEInteger(),
thisFlags);
}
return(thisValue);
}
