// 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); }
// 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); }
// 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(); } } }