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;
}
}
internal static EFloat DoubleEFloatFromString(
string chars,
int offset,
int length,
EContext ctx,
bool throwException)
{
int tmpoffset = offset;
if (chars == null)
{
if (!throwException)
{
return(null);
}
else
{
throw new ArgumentNullException(nameof(chars));
}
}
if (length == 0)
{
if (!throwException)
{
return(null);
}
else
{
throw new FormatException();
}
}
int endStr = tmpoffset + length;
var negative = false;
var haveDecimalPoint = false;
var haveDigits = false;
var haveExponent = false;
var newScaleInt = 0;
var digitStart = 0;
int i = tmpoffset;
long mantissaLong = 0L;
// Ordinary number
if (chars[i] == '+' || chars[i] == '-')
{
if (chars[i] == '-')
{
negative = true;
}
++i;
}
digitStart = i;
int digitEnd = i;
int decimalDigitStart = i;
var haveNonzeroDigit = false;
var decimalPrec = 0;
int decimalDigitEnd = i;
var nonzeroBeyondMax = false;
var lastdigit = -1;
// 768 is maximum precision of a decimal
// half-ULP in double format
var maxDecimalPrec = 768;
if (length > 21)
{
int eminInt = ctx.EMin.ToInt32Checked();
int emaxInt = ctx.EMax.ToInt32Checked();
int precInt = ctx.Precision.ToInt32Checked();
if (eminInt >= -14 && emaxInt <= 15)
{
maxDecimalPrec = (precInt <= 11) ? 21 : 63;
}
else if (eminInt >= -126 && emaxInt <= 127)
{
maxDecimalPrec = (precInt <= 24) ? 113 : 142;
}
}
for (; i < endStr; ++i)
{
char ch = chars[i];
if (ch >= '0' && ch <= '9')
{
var thisdigit = (int)(ch - '0');
haveDigits = true;
haveNonzeroDigit |= thisdigit != 0;
if (decimalPrec > maxDecimalPrec)
{
if (thisdigit != 0)
{
nonzeroBeyondMax = true;
}
if (!haveDecimalPoint)
{
// NOTE: Absolute value will not be more than
// the string portion's length, so will fit comfortably
// in an 'int'.
newScaleInt = checked (newScaleInt + 1);
}
continue;
}
lastdigit = thisdigit;
if (haveNonzeroDigit)
{
++decimalPrec;
}
if (haveDecimalPoint)
{
decimalDigitEnd = i + 1;
}
else
{
digitEnd = i + 1;
}
if (mantissaLong <= 922337203685477580L)
{
mantissaLong *= 10;
mantissaLong += thisdigit;
}
else
{
mantissaLong = Int64.MaxValue;
}
if (haveDecimalPoint)
{
// NOTE: Absolute value will not be more than
// the portion's length, so will fit comfortably
// in an 'int'.
newScaleInt = checked (newScaleInt - 1);
}
}
else if (ch == '.')
{
if (haveDecimalPoint)
{
if (!throwException)
{
return(null);
}
else
{
throw new FormatException();
}
}
haveDecimalPoint = true;
decimalDigitStart = i + 1;
decimalDigitEnd = i + 1;
}
else if (ch == 'E' || ch == 'e')
{
haveExponent = true;
++i;
break;
}
else
{
if (!throwException)
{
return(null);
}
else
{
throw new FormatException();
}
}
}
if (!haveDigits)
{
if (!throwException)
{
return(null);
}
else
{
throw new FormatException();
}
}
var expInt = 0;
var expoffset = 1;
var expDigitStart = -1;
var expPrec = 0;
bool zeroMantissa = !haveNonzeroDigit;
haveNonzeroDigit = false;
EFloat ef1, ef2;
if (haveExponent)
{
haveDigits = false;
if (i == endStr)
{
if (!throwException)
{
return(null);
}
else
{
throw new FormatException();
}
}
char ch = chars[i];
if (ch == '+' || ch == '-')
{
if (ch == '-')
{
expoffset = -1;
}
++i;
}
expDigitStart = i;
for (; i < endStr; ++i)
{
ch = chars[i];
if (ch >= '0' && ch <= '9')
{
haveDigits = true;
var thisdigit = (int)(ch - '0');
haveNonzeroDigit |= thisdigit != 0;
if (haveNonzeroDigit)
{
++expPrec;
}
if (expInt <= 214748364)
{
expInt *= 10;
expInt += thisdigit;
}
else
{
expInt = Int32.MaxValue;
}
}
else
{
if (!throwException)
{
return(null);
}
else
{
throw new FormatException();
}
}
}
if (!haveDigits)
{
if (!throwException)
{
return(null);
}
else
{
throw new FormatException();
}
}
expInt *= expoffset;
if (expPrec > 12)
{
// Exponent that can't be compensated by digit
// length without remaining beyond Int32 range
if (expoffset < 0)
{
return(EFloat.SignalUnderflow(ctx, negative, zeroMantissa));
}
else
{
return(EFloat.SignalOverflow(ctx, negative, zeroMantissa));
}
}
}
if (i != endStr)
{
if (!throwException)
{
return(null);
}
else
{
throw new FormatException();
}
}
if (expInt != Int32.MaxValue && expInt > -Int32.MaxValue &&
mantissaLong != Int64.MaxValue && (ctx == null ||
!ctx.HasFlagsOrTraps))
{
if (mantissaLong == 0)
{
EFloat ef = EFloat.Create(
EInteger.Zero,
EInteger.FromInt32(expInt));
if (negative)
{
ef = ef.Negate();
}
return(ef.RoundToPrecision(ctx));
}
var finalexp = (long)expInt + (long)newScaleInt;
long ml = mantissaLong;
if (finalexp >= -22 && finalexp <= 44)
{
var iexp = (int)finalexp;
while (ml <= 900719925474099L && iexp > 22)
{
ml *= 10;
--iexp;
}
int iabsexp = Math.Abs(iexp);
if (ml < 9007199254740992L && iabsexp == 0)
{
return(EFloat.FromInt64(negative ?
-mantissaLong : mantissaLong).RoundToPrecision(ctx));
}
else if (ml < 9007199254740992L && iabsexp <= 22)
{
EFloat efn =
EFloat.FromEInteger(NumberUtility.FindPowerOfTen(iabsexp));
if (negative)
{
ml = -ml;
}
EFloat efml = EFloat.FromInt64(ml);
if (iexp < 0)
{
return(efml.Divide(efn, ctx));
}
else
{
return(efml.Multiply(efn, ctx));
}
}
}
long adjexpUpperBound = finalexp + (decimalPrec - 1);
long adjexpLowerBound = finalexp;
if (adjexpUpperBound < -326)
{
return(EFloat.SignalUnderflow(ctx, negative, zeroMantissa));
}
else if (adjexpLowerBound > 309)
{
return(EFloat.SignalOverflow(ctx, negative, zeroMantissa));
}
if (negative)
{
mantissaLong = -mantissaLong;
}
long absfinalexp = Math.Abs(finalexp);
ef1 = EFloat.Create(mantissaLong, (int)0);
ef2 = EFloat.FromEInteger(NumberUtility.FindPowerOfTen(absfinalexp));
if (finalexp < 0)
{
EFloat efret = ef1.Divide(ef2, ctx);
/* Console.WriteLine("div " + ef1 + "/" + ef2 + " -> " + (efret));
*/return(efret);
}
else
{
return(ef1.Multiply(ef2, ctx));
}
}
EInteger mant = null;
EInteger exp = (!haveExponent) ? EInteger.Zero :
EInteger.FromSubstring(chars, expDigitStart, endStr);
if (expoffset < 0)
{
exp = exp.Negate();
}
exp = exp.Add(newScaleInt);
if (nonzeroBeyondMax)
{
exp = exp.Subtract(1);
++decimalPrec;
}
EInteger adjExpUpperBound = exp.Add(decimalPrec).Subtract(1);
EInteger adjExpLowerBound = exp;
// DebugUtility.Log("exp=" + adjExpLowerBound + "~" + (adjExpUpperBound));
if (adjExpUpperBound.CompareTo(-326) < 0)
{
return(EFloat.SignalUnderflow(ctx, negative, zeroMantissa));
}
else if (adjExpLowerBound.CompareTo(309) > 0)
{
return(EFloat.SignalOverflow(ctx, negative, zeroMantissa));
}
if (zeroMantissa)
{
EFloat ef = EFloat.Create(
EInteger.Zero,
exp);
if (negative)
{
ef = ef.Negate();
}
return(ef.RoundToPrecision(ctx));
}
else if (decimalDigitStart != decimalDigitEnd)
{
if (digitEnd - digitStart == 1 && chars[digitStart] == '0')
{
mant = EInteger.FromSubstring(
chars,
decimalDigitStart,
decimalDigitEnd);
}
else
{
string ctmpstr = Extras.CharsConcat(
chars,
digitStart,
digitEnd - digitStart,
chars,
decimalDigitStart,
decimalDigitEnd - decimalDigitStart);
mant = EInteger.FromString(ctmpstr);
}
}
else
{
mant = EInteger.FromSubstring(chars, digitStart, digitEnd);
}
if (nonzeroBeyondMax)
{
mant = mant.Multiply(10).Add(1);
}
if (negative)
{
mant = mant.Negate();
}
return(EDecimal.Create(mant, exp).ToEFloat(ctx));
}
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;
}
}