Exemplo n.º 1
0
        // Divide regNum by regDen, leaving the remainder in regNum and the quotient in regQuo (if fQuo is true).
        public void ModDiv(ref BigIntegerBuilder regDen, ref BigIntegerBuilder regQuo)
        {
            if (regDen._iuLast == 0)
            {
                regQuo.Set(DivMod(regDen._uSmall));
                NumericsHelpers.Swap(ref this, ref regQuo);
                return;
            }
            if (_iuLast == 0)
            {
                return;
            }

            ModDivCore(ref this, ref regDen, true, ref regQuo);
        }
Exemplo n.º 2
0
        // Divide 'this' by regDen, leaving the quotient in 'this' and tossing the remainder.
        public void Div(ref BigIntegerBuilder regDen)
        {
            if (regDen._iuLast == 0)
            {
                DivMod(regDen._uSmall);
                return;
            }
            if (_iuLast == 0)
            {
                _uSmall = 0;
                return;
            }

            BigIntegerBuilder regTmp = new BigIntegerBuilder();

            ModDivCore(ref this, ref regDen, true, ref regTmp);
            NumericsHelpers.Swap(ref this, ref regTmp);
        }
Exemplo n.º 3
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();
                }
            }
        }