Ejemplo n.º 1
0
        // This leaves the GCD in reg1 and trash in reg2.
        // This uses Lehmer's method, with test due to Jebelean / Belnkiy and Vidunas.
        // See Knuth, vol 2, page 345; Jebelean (1993) "Improving the Multiprecision Euclidean Algorithm";
        // and Belenkiy & Vidunas (1998) "A Greatest Common Divisor Algorithm".
        private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2)
        {
            // This value has no real significance. Occ----ionally we want to subtract
            // the two registers and keep the absolute value of the difference. To do
            // so we need to pass a ref sign to Sub.
            int signTmp = +1;

            for (;;)
            {
                int cuMax = reg1._iuLast + 1;
                int cuMin = reg2._iuLast + 1;
                if (cuMax < cuMin)
                {
                    NumericsHelpers.Swap(ref reg1, ref reg2);
                    NumericsHelpers.Swap(ref cuMax, ref cuMin);
                }

                if (cuMin == 1)
                {
                    if (cuMax == 1)
                    {
                        reg1._uSmall = NumericsHelpers.GCD(reg1._uSmall, reg2._uSmall);
                    }
                    else if (reg2._uSmall != 0)
                    {
                        reg1.Set(NumericsHelpers.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall));
                    }
                    return;
                }

                if (cuMax == 2)
                {
                    reg1.Set(NumericsHelpers.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2)));
                    return;
                }

                if (cuMin <= cuMax - 2)
                {
                    // reg1 is much larger than reg2, so just mod.
                    reg1.Mod(ref reg2);
                    continue;
                }

                ulong uu1 = reg1.GetHigh2(cuMax);
                ulong uu2 = reg2.GetHigh2(cuMax);

                int cbit = NumericsHelpers.CbitHighZero(uu1 | uu2);
                if (cbit > 0)
                {
                    uu1 = (uu1 << cbit) | (reg1._rgu[cuMax - 3] >> (kcbitUint - cbit));
                    // Note that [cuMax - 3] is correct, NOT [cuMin - 3].
                    uu2 = (uu2 << cbit) | (reg2._rgu[cuMax - 3] >> (kcbitUint - cbit));
                }
                if (uu1 < uu2)
                {
                    NumericsHelpers.Swap(ref uu1, ref uu2);
                    NumericsHelpers.Swap(ref reg1, ref reg2);
                }

                // Make sure we don't overflow.
                if (uu1 == ulong.MaxValue || uu2 == ulong.MaxValue)
                {
                    uu1 >>= 1;
                    uu2 >>= 1;
                }
                if (uu1 == uu2)
                {
                    // The high bits are the same, so we don't know which
                    // is larger. No matter, just subtract one from the other
                    // and keep the absolute value of the result.
                    reg1.Sub(ref signTmp, ref reg2);
                    continue;
                }
                if (NumericsHelpers.GetHi(uu2) == 0)
                {
                    // reg1 is much larger than reg2, so just mod.
                    reg1.Mod(ref reg2);
                    continue;
                }

                // These are the coefficients to apply to reg1 and reg2 to get
                // the new values, using: a * reg1 - b * reg2 and -c * reg1 + d * reg2.
                uint a = 1, b = 0;
                uint c = 0, d = 1;

                for (;;)
                {
                    uint  uQuo  = 1;
                    ulong uuNew = uu1 - uu2;
                    while (uuNew >= uu2 && uQuo < 32)
                    {
                        uuNew -= uu2;
                        uQuo++;
                    }
                    if (uuNew >= uu2)
                    {
                        ulong uuQuo = uu1 / uu2;
                        if (uuQuo > uint.MaxValue)
                        {
                            break;
                        }
                        uQuo  = (uint)uuQuo;
                        uuNew = uu1 - uQuo * uu2;
                    }
                    ulong uuAdNew = a + (ulong)uQuo * c;
                    ulong uuBcNew = b + (ulong)uQuo * d;
                    if (uuAdNew > int.MaxValue || uuBcNew > int.MaxValue)
                    {
                        break;
                    }
                    // Jebelean / Belenkiy-Vidunas conditions
                    if (uuNew < uuBcNew || uuNew + uuAdNew > uu2 - c)
                    {
                        break;
                    }


                    a   = (uint)uuAdNew;
                    b   = (uint)uuBcNew;
                    uu1 = uuNew;

                    if (uu1 <= b)
                    {
                        break;
                    }

                    uQuo  = 1;
                    uuNew = uu2 - uu1;
                    while (uuNew >= uu1 && uQuo < 32)
                    {
                        uuNew -= uu1;
                        uQuo++;
                    }
                    if (uuNew >= uu1)
                    {
                        ulong uuQuo = uu2 / uu1;
                        if (uuQuo > uint.MaxValue)
                        {
                            break;
                        }
                        uQuo  = (uint)uuQuo;
                        uuNew = uu2 - uQuo * uu1;
                    }
                    uuAdNew = d + (ulong)uQuo * b;
                    uuBcNew = c + (ulong)uQuo * a;
                    if (uuAdNew > int.MaxValue || uuBcNew > int.MaxValue)
                    {
                        break;
                    }
                    // Jebelean / Belenkiy-Vidunas conditions
                    if (uuNew < uuBcNew || uuNew + uuAdNew > uu1 - b)
                    {
                        break;
                    }


                    d   = (uint)uuAdNew;
                    c   = (uint)uuBcNew;
                    uu2 = uuNew;

                    if (uu2 <= c)
                    {
                        break;
                    }
                }

                if (b == 0)
                {
                    if (uu1 / 2 >= uu2)
                    {
                        reg1.Mod(ref reg2);
                    }
                    else
                    {
                        reg1.Sub(ref signTmp, ref reg2);
                    }
                }
                else
                {
                    // Replace reg1 with  a * reg1 - b * reg2.
                    // Replace reg2 with -c * reg1 + d * reg2.
                    // Do everything mod cuMin uint's.
                    reg1.SetSizeKeep(cuMin, 0);
                    reg2.SetSizeKeep(cuMin, 0);
                    int nCarry1 = 0;
                    int nCarry2 = 0;
                    for (int iu = 0; iu < cuMin; iu++)
                    {
                        uint u1  = reg1._rgu[iu];
                        uint u2  = reg2._rgu[iu];
                        long nn1 = (long)u1 * a - (long)u2 * b + nCarry1;
                        long nn2 = (long)u2 * d - (long)u1 * c + nCarry2;
                        nCarry1       = (int)(nn1 >> kcbitUint);
                        nCarry2       = (int)(nn2 >> kcbitUint);
                        reg1._rgu[iu] = (uint)nn1;
                        reg2._rgu[iu] = (uint)nn2;
                    }
                    reg1.Trim();
                    reg2.Trim();
                }
            }
        }
Ejemplo n.º 2
0
        private static void ModDivCore(ref BigIntegerBuilder regNum, ref BigIntegerBuilder regDen, bool fQuo, ref BigIntegerBuilder regQuo)
        {
            regQuo.Set(0);
            if (regNum._iuLast < regDen._iuLast)
            {
                return;
            }

            int cuDen  = regDen._iuLast + 1;
            int cuDiff = regNum._iuLast - regDen._iuLast;

            // Determine whether the result will have cuDiff "digits" or cuDiff+1 "digits".
            int cuQuo = cuDiff;

            for (int iu = regNum._iuLast; ; iu--)
            {
                if (iu < cuDiff)
                {
                    cuQuo++;
                    break;
                }
                if (regDen._rgu[iu - cuDiff] != regNum._rgu[iu])
                {
                    if (regDen._rgu[iu - cuDiff] < regNum._rgu[iu])
                    {
                        cuQuo++;
                    }
                    break;
                }
            }

            if (cuQuo == 0)
            {
                return;
            }

            if (fQuo)
            {
                regQuo.SetSizeLazy(cuQuo);
            }

            // Get the uint to use for the trial divisions. We normalize so the high bit is set.
            uint uDen           = regDen._rgu[cuDen - 1];
            uint uDenNext       = regDen._rgu[cuDen - 2];
            int  cbitShiftLeft  = NumericsHelpers.CbitHighZero(uDen);
            int  cbitShiftRight = kcbitUint - cbitShiftLeft;

            if (cbitShiftLeft > 0)
            {
                uDen       = (uDen << cbitShiftLeft) | (uDenNext >> cbitShiftRight);
                uDenNext <<= cbitShiftLeft;
                if (cuDen > 2)
                {
                    uDenNext |= regDen._rgu[cuDen - 3] >> cbitShiftRight;
                }
            }

            // Allocate and initialize working space.
            regNum.EnsureWritable();

            for (int iu = cuQuo; --iu >= 0;)
            {
                // Get the high (normalized) bits of regNum.
                uint uNumHi = (iu + cuDen <= regNum._iuLast) ? regNum._rgu[iu + cuDen] : 0;

                ulong uuNum    = NumericsHelpers.MakeUlong(uNumHi, regNum._rgu[iu + cuDen - 1]);
                uint  uNumNext = regNum._rgu[iu + cuDen - 2];
                if (cbitShiftLeft > 0)
                {
                    uuNum      = (uuNum << cbitShiftLeft) | (uNumNext >> cbitShiftRight);
                    uNumNext <<= cbitShiftLeft;
                    if (iu + cuDen >= 3)
                    {
                        uNumNext |= regNum._rgu[iu + cuDen - 3] >> cbitShiftRight;
                    }
                }

                // Divide to get the quotient digit.
                ulong uuQuo = uuNum / uDen;
                ulong uuRem = (uint)(uuNum % uDen);
                if (uuQuo > uint.MaxValue)
                {
                    uuRem += uDen * (uuQuo - uint.MaxValue);
                    uuQuo  = uint.MaxValue;
                }
                while (uuRem <= uint.MaxValue && uuQuo * uDenNext > NumericsHelpers.MakeUlong((uint)uuRem, uNumNext))
                {
                    uuQuo--;
                    uuRem += uDen;
                }

                // Multiply and subtract. Note that uuQuo may be 1 too large. If we have a borrow
                // at the end, we'll add the denominator back on and decrement uuQuo.
                if (uuQuo > 0)
                {
                    ulong uuBorrow = 0;
                    for (int iu2 = 0; iu2 < cuDen; iu2++)
                    {
                        uuBorrow += regDen._rgu[iu2] * uuQuo;
                        uint uSub = (uint)uuBorrow;
                        uuBorrow >>= kcbitUint;
                        if (regNum._rgu[iu + iu2] < uSub)
                        {
                            uuBorrow++;
                        }
                        regNum._rgu[iu + iu2] -= uSub;
                    }

                    if (uNumHi < uuBorrow)
                    {
                        // Add, tracking carry.
                        uint uCarry = 0;
                        for (int iu2 = 0; iu2 < cuDen; iu2++)
                        {
                            uCarry = AddCarry(ref regNum._rgu[iu + iu2], regDen._rgu[iu2], uCarry);
                        }
                        uuQuo--;
                    }
                    regNum._iuLast = iu + cuDen - 1;
                }

                if (fQuo)
                {
                    if (cuQuo == 1)
                    {
                        regQuo._uSmall = (uint)uuQuo;
                    }
                    else
                    {
                        regQuo._rgu[iu] = (uint)uuQuo;
                    }
                }
            }

            regNum._iuLast = cuDen - 1;
            regNum.Trim();
        }
Ejemplo n.º 3
0
        static String FormatBigInteger(BigInteger value, String format, NumberFormatInfo info)
        {
            int  digits = 0;
            char fmt    = ParseFormatSpecifier(format, out digits);

            if (fmt == 'x' || fmt == 'X')
            {
                return(FormatBigIntegerToHexString(value, fmt, digits, info));
            }

            bool decimalFmt = (fmt == 'g' || fmt == 'G' || fmt == 'd' || fmt == 'D' || fmt == 'r' || fmt == 'R');


            if (value._bits == null)
            {
                if (fmt == 'g' || fmt == 'G' || fmt == 'r' || fmt == 'R')
                {
                    if (digits > 0)
                    {
                        format = String.Format(CultureInfo.InvariantCulture, "D{0}", digits.ToString(CultureInfo.InvariantCulture));
                    }
                    else
                    {
                        format = "D";
                    }
                }
                return(value._sign.ToString(format, info));
            }


            // First convert to base 10^9.
            const uint kuBase   = 1000000000;           // 10^9
            const int  kcchBase = 9;

            int cuSrc = BigInteger.Length(value._bits);
            int cuMax;

            try
            {
                cuMax = checked (cuSrc * 10 / 9 + 2);
            }
            catch (OverflowException e) { throw new FormatException("SR.Format_TooLarge", e); }
            uint[] rguDst = new uint[cuMax];
            int    cuDst  = 0;

            for (int iuSrc = cuSrc; --iuSrc >= 0;)
            {
                uint uCarry = value._bits[iuSrc];
                for (int iuDst = 0; iuDst < cuDst; iuDst++)
                {
                    ulong uuRes = NumericsHelpers.MakeUlong(rguDst[iuDst], uCarry);
                    rguDst[iuDst] = (uint)(uuRes % kuBase);
                    uCarry        = (uint)(uuRes / kuBase);
                }
                if (uCarry != 0)
                {
                    rguDst[cuDst++] = uCarry % kuBase;
                    uCarry         /= kuBase;
                    if (uCarry != 0)
                    {
                        rguDst[cuDst++] = uCarry;
                    }
                }
            }

            int cchMax;

            try
            {
                // Each uint contributes at most 9 digits to the decimal representation.
                cchMax = checked (cuDst * kcchBase);
            }
            catch (OverflowException e) { throw new FormatException("SR.Format_TooLarge", e); }

            if (decimalFmt)
            {
                if (digits > 0 && digits > cchMax)
                {
                    cchMax = digits;
                }
                if (value._sign < 0)
                {
                    try
                    {
                        // Leave an extra slot for a minus sign.
                        cchMax = checked (cchMax + info.NegativeSign.Length);
                    }
                    catch (OverflowException e) { throw new FormatException("SR.Format_TooLarge", e); }
                }
            }

            int rgchBufSize;

            try
            {
                // We'll pass the rgch buffer to native code, which is going to treat it like a string of digits, so it needs
                // to be null terminated.  Let's ensure that we can allocate a buffer of that size.
                rgchBufSize = checked (cchMax + 1);
            }
            catch (OverflowException e) { throw new FormatException("SR.Format_TooLarge", e); }

            char[] rgch = new char[rgchBufSize];

            int ichDst = cchMax;

            for (int iuDst = 0; iuDst < cuDst - 1; iuDst++)
            {
                uint uDig = rguDst[iuDst];
                for (int cch = kcchBase; --cch >= 0;)
                {
                    rgch[--ichDst] = (char)('0' + uDig % 10);
                    uDig          /= 10;
                }
            }
            for (uint uDig = rguDst[cuDst - 1]; uDig != 0;)
            {
                rgch[--ichDst] = (char)('0' + uDig % 10);
                uDig          /= 10;
            }

#if !SILVERLIGHT || FEATURE_NETCORE
            if (!decimalFmt)
            {
                //
                // Go to the VM for GlobLoc aware formatting
                //
                Byte *numberBufferBytes        = stackalloc Byte[NumberPort.NumberBuffer.NumberBufferBytes];
                NumberPort.NumberBuffer number = new NumberPort.NumberBuffer(numberBufferBytes);
                // sign = true for negative and false for 0 and positive values
                number.sign = (value._sign < 0);
                // the cut-off point to switch (G)eneral from (F)ixed-point to (E)xponential form
                number.precision = 29;
                number.digits[0] = '\0';
                number.scale     = cchMax - ichDst;

                int maxDigits = Math.Min(ichDst + 50, cchMax);
                for (int i = ichDst; i < maxDigits; i++)
                {
                    number.digits[i - ichDst] = rgch[i];
                }

                fixed(char *pinnedExtraDigits = rgch)
                {
                    throw new NotImplementedException($"Could not implement NumberPort.FormatNumberBuffer. Therefore, some {nameof(BigInteger)} functionality is unimplemented.");
                }
            }
#endif //!SILVERLIGHT ||FEATURE_NETCORE

            // Format Round-trip decimal
            // This format is supported for integral types only. The number is converted to a string of
            // decimal digits (0-9), prefixed by a minus sign if the number is negative. The precision
            // specifier indicates the minimum number of digits desired in the resulting string. If required,
            // the number is padded with zeros to its left to produce the number of digits given by the
            // precision specifier.
            int numDigitsPrinted = cchMax - ichDst;
            while (digits > 0 && digits > numDigitsPrinted)
            {
                // pad leading zeros
                rgch[--ichDst] = '0';
                digits--;
            }
            if (value._sign < 0)
            {
                String negativeSign = info.NegativeSign;
                for (int i = info.NegativeSign.Length - 1; i > -1; i--)
                {
                    rgch[--ichDst] = info.NegativeSign[i];
                }
            }
            return(new String(rgch, ichDst, cchMax - ichDst));
        }