// Multiply reg1 times reg2, putting the result in 'this'. This version never shares memory // with either of the operands. This is useful when performing a series of arithmetic operations // and large working buffers are allocated up front. public void Mul(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2) { if (reg1._iuLast == 0) { if (reg2._iuLast == 0) { Set((ulong)reg1._uSmall * reg2._uSmall); } else { Load(ref reg2, 1); Mul(reg1._uSmall); } } else if (reg2._iuLast == 0) { Load(ref reg1, 1); Mul(reg2._uSmall); } else { SetSizeClear(reg1._iuLast + reg2._iuLast + 2); uint[] rgu1, rgu2; int cu1, cu2; // We prefer more iterations on the inner loop and fewer on the outer. if (reg1.CuNonZero <= reg2.CuNonZero) { rgu1 = reg1._rgu; cu1 = reg1._iuLast + 1; rgu2 = reg2._rgu; cu2 = reg2._iuLast + 1; } else { rgu1 = reg2._rgu; cu1 = reg2._iuLast + 1; rgu2 = reg1._rgu; cu2 = reg1._iuLast + 1; } for (int iu1 = 0; iu1 < cu1; iu1++) { uint uCur = rgu1[iu1]; if (uCur == 0) { continue; } uint uCarry = 0; int iuRes = iu1; for (int iu2 = 0; iu2 < cu2; iu2++, iuRes++) { uCarry = AddMulCarry(ref _rgu[iuRes], uCur, rgu2[iu2], uCarry); } while (uCarry != 0) { uCarry = AddCarry(ref _rgu[iuRes++], 0, uCarry); } } Trim(); } }
// 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); }
// This version may share memory with regMul. public void Mul(ref BigIntegerBuilder regMul) { if (regMul._iuLast == 0) { Mul(regMul._uSmall); } else if (_iuLast == 0) { uint u = _uSmall; if (u == 1) { this = new BigIntegerBuilder(ref regMul); } else if (u != 0) { Load(ref regMul, 1); Mul(u); } } else { int cuBase = _iuLast + 1; SetSizeKeep(cuBase + regMul._iuLast, 1); for (int iu = cuBase; --iu >= 0;) { uint uMul = _rgu[iu]; _rgu[iu] = 0; uint uCarry = 0; for (int iuSrc = 0; iuSrc <= regMul._iuLast; iuSrc++) { uCarry = AddMulCarry(ref _rgu[iu + iuSrc], regMul._rgu[iuSrc], uMul, uCarry); } if (uCarry != 0) { for (int iuDst = iu + regMul._iuLast + 1; uCarry != 0 && iuDst <= _iuLast; iuDst++) { uCarry = AddCarry(ref _rgu[iuDst], 0, uCarry); } if (uCarry != 0) { SetSizeKeep(_iuLast + 2, 0); _rgu[_iuLast] = uCarry; } } } } }
// Divide 'this' by regDen, leaving the remainder in 'this' and tossing the quotient. public void Mod(ref BigIntegerBuilder regDen) { if (regDen._iuLast == 0) { Set(Mod(ref this, regDen._uSmall)); return; } if (_iuLast == 0) { return; } BigIntegerBuilder regTmp = new BigIntegerBuilder(); ModDivCore(ref this, ref regDen, false, ref regTmp); }
public BigIntegerBuilder(ref BigIntegerBuilder reg) { this = reg; if (_fWritable) { _fWritable = false; if (_iuLast == 0) { _rgu = null; } else { reg._fWritable = false; } } }
public void Add(ref BigIntegerBuilder reg) { if (reg._iuLast == 0) { Add(reg._uSmall); return; } if (_iuLast == 0) { uint u = _uSmall; if (u == 0) { this = new BigIntegerBuilder(ref reg); } else { Load(ref reg, 1); Add(u); } return; } EnsureWritable(Math.Max(_iuLast, reg._iuLast) + 1, 1); int cuAdd = reg._iuLast + 1; if (_iuLast < reg._iuLast) { cuAdd = _iuLast + 1; Array.Copy(reg._rgu, _iuLast + 1, _rgu, _iuLast + 1, reg._iuLast - _iuLast); _iuLast = reg._iuLast; } // Add, tracking carry. uint uCarry = 0; for (int iu = 0; iu < cuAdd; iu++) { uCarry = AddCarry(ref _rgu[iu], reg._rgu[iu], uCarry); } // Deal with extra carry. if (uCarry != 0) { ApplyCarry(cuAdd); } }
// 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); }
// Loads the value of reg into this register. If we need to allocate memory // to perform the load, allocate cuExtra elements. public void Load(ref BigIntegerBuilder reg, int cuExtra) { if (reg._iuLast == 0) { _uSmall = reg._uSmall; _iuLast = 0; } else { if (!_fWritable || _rgu.Length <= reg._iuLast) { _rgu = new uint[reg._iuLast + 1 + cuExtra]; _fWritable = true; } _iuLast = reg._iuLast; Array.Copy(reg._rgu, _rgu, _iuLast + 1); } }
public static void GCD(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2) { // Use Lehmer's GCD, with improvements, after eliminating common powers of 2. if (reg1._iuLast > 0 && reg1._rgu[0] == 0 || reg2._iuLast > 0 && reg2._rgu[0] == 0) { int cbit1 = reg1.MakeOdd(); int cbit2 = reg2.MakeOdd(); LehmerGcd(ref reg1, ref reg2); int cbitMin = Math.Min(cbit1, cbit2); if (cbitMin > 0) { reg1.ShiftLeft(cbitMin); } } else { LehmerGcd(ref reg1, ref reg2); } }
// Divide regNum by uDen, returning the remainder and tossing the quotient. public static uint Mod(ref BigIntegerBuilder regNum, uint uDen) { if (uDen == 1) { return(0); } if (regNum._iuLast == 0) { return(regNum._uSmall % uDen); } ulong uu = 0; for (int iv = regNum._iuLast; iv >= 0; iv--) { uu = NumericsHelpers.MakeUlong((uint)uu, regNum._rgu[iv]); uu %= uDen; } return((uint)uu); }
// Subtract this register from the given one and put the result in this one. // Asserts that reg is larger in the most significant uint. private void SubRev(ref BigIntegerBuilder reg) { EnsureWritable(reg._iuLast + 1, 0); int cuSub = _iuLast + 1; if (_iuLast < reg._iuLast) { Array.Copy(reg._rgu, _iuLast + 1, _rgu, _iuLast + 1, reg._iuLast - _iuLast); _iuLast = reg._iuLast; } uint uBorrow = 0; for (int iu = 0; iu < cuSub; iu++) { uBorrow = SubRevBorrow(ref _rgu[iu], reg._rgu[iu], uBorrow); } if (uBorrow != 0) { ApplyBorrow(cuSub); } Trim(); }
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(); }
public void Sub(ref int sign, ref BigIntegerBuilder reg) { if (reg._iuLast == 0) { Sub(ref sign, reg._uSmall); return; } if (_iuLast == 0) { uint u = _uSmall; if (u == 0) { this = new BigIntegerBuilder(ref reg); } else { Load(ref reg); Sub(ref sign, u); } sign = -sign; return; } if (_iuLast < reg._iuLast) { SubRev(ref reg); sign = -sign; return; } int cuSub = reg._iuLast + 1; if (_iuLast == reg._iuLast) { // Determine which is larger. _iuLast = BigInteger.GetDiffLength(_rgu, reg._rgu, _iuLast + 1) - 1; if (_iuLast < 0) { _iuLast = 0; _uSmall = 0; return; } uint u1 = _rgu[_iuLast]; uint u2 = reg._rgu[_iuLast]; if (_iuLast == 0) { if (u1 < u2) { _uSmall = u2 - u1; sign = -sign; } else { _uSmall = u1 - u2; } return; } if (u1 < u2) { reg._iuLast = _iuLast; SubRev(ref reg); reg._iuLast = cuSub - 1; sign = -sign; return; } cuSub = _iuLast + 1; } EnsureWritable(); // Subtract, tracking borrow. uint uBorrow = 0; for (int iu = 0; iu < cuSub; iu++) { uBorrow = SubBorrow(ref _rgu[iu], reg._rgu[iu], uBorrow); } if (uBorrow != 0) { ApplyBorrow(cuSub); } Trim(); }
// Loads the value of reg into this register. public void Load(ref BigIntegerBuilder reg) { Load(ref reg, 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(); } } }