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 static EInteger FromRadixSubstringGeneral(
byte[] cs,
int radix,
int index,
int endIndex,
bool negative,
bool throwException)
{
if (endIndex - index > 72)
{
int midIndex = index + ((endIndex - index) / 2);
EInteger eia = FromRadixSubstringGeneral(
cs,
radix,
index,
midIndex,
false,
throwException);
// DebugUtility.Log("eia="+eia);
EInteger eib = FromRadixSubstringGeneral(
cs,
radix,
midIndex,
endIndex,
false,
throwException);
// DebugUtility.Log("eib="+eib);
EInteger mult = null;
int intpow = endIndex - midIndex;
if (radix == 10)
{
eia = NumberUtility.MultiplyByPowerOfFive(eia,
intpow).ShiftLeft(intpow);
}
else if (radix == 5)
{
eia = NumberUtility.MultiplyByPowerOfFive(eia, intpow);
}
else
{
mult = EInteger.FromInt32(radix).Pow(endIndex - midIndex);
eia = eia.Multiply(mult);
}
eia = eia.Add(eib);
// DebugUtility.Log("index={0} {1} {2} [pow={3}] [pow={4} ms, muladd={5} ms]",
// index, midIndex, endIndex, endIndex-midIndex, swPow.ElapsedMilliseconds,
// swMulAdd.ElapsedMilliseconds);
if (negative)
{
eia = eia.Negate();
}
// DebugUtility.Log("eia now="+eia);
return(eia);
}
else
{
return(FromRadixSubstringInner(
cs,
radix,
index,
endIndex,
negative,
throwException));
}
}
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);
}
internal static EFloat DoubleEFloatFromString(
char[] 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 char[] 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
{
char[] 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 T PreRound(T val, EContext ctx)
{
return(NumberUtility.PreRound(val, ctx, this.wrapper));
}