public static FastIntegerFixed Add(FastIntegerFixed a, FastIntegerFixed b) { if (a.integerMode == 0 && b.integerMode == 0) { if (a.smallValue == 0) { return(b); } if (b.smallValue == 0) { return(a); } if ((a.smallValue < 0 && b.smallValue >= Int32.MinValue - a.smallValue) || (a.smallValue > 0 && b.smallValue <= Int32.MaxValue - a.smallValue)) { return(new FastIntegerFixed(a.smallValue + b.smallValue)); } } EInteger bigA = a.ToEInteger(); EInteger bigB = b.ToEInteger(); return(FastIntegerFixed.FromBig(bigA.Add(bigB))); }
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 static EInteger FromRadixSubstringGeneral( char[] 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)); } }