public void ModDiv(ref BigIntegerBuilder regDen, ref BigIntegerBuilder regQuo) { if (regDen._iuLast == 0) { regQuo.Set(DivMod(regDen._uSmall)); NumericsHelpers.Swap <BigIntegerBuilder>(ref this, ref regQuo); } else if (_iuLast != 0) { ModDivCore(ref this, ref regDen, true, ref regQuo); } }
public void ModDiv(ref BigIntegerBuilder regDen, ref BigIntegerBuilder regQuo) { if (regDen._iuLast == 0) { regQuo.Set(DivMod(regDen._uSmall)); NumericHelper.Swap(ref this, ref regQuo); return; } if (_iuLast == 0) { return; } ModDivCore(ref this, ref regDen, true, ref regQuo); }
public void ModDiv(ref BigIntegerBuilder regDen, ref BigIntegerBuilder regQuo) { if (regDen._iuLast == 0) { regQuo.Set(this.DivMod(regDen._uSmall)); #if !(dotNET10 || dotNET11 || dotNETCF10) NumericsHelpers.Swap <BigIntegerBuilder>(ref this, ref regQuo); #else NumericsHelpers.Swap(ref this, ref regQuo); #endif } else if (this._iuLast != 0) { ModDivCore(ref this, ref regDen, true, ref regQuo); } }
private static void ModDivCore(ref BigIntegerBuilder regNum, ref BigIntegerBuilder regDen, bool fQuo, ref BigIntegerBuilder regQuo) { regQuo.Set((uint)0); if (regNum._iuLast >= regDen._iuLast) { int num = regDen._iuLast + 1; int num2 = regNum._iuLast - regDen._iuLast; int cu = num2; int index = regNum._iuLast; while (true) { if (index < num2) { cu++; break; } if (regDen._rgu[index - num2] != regNum._rgu[index]) { if (regDen._rgu[index - num2] < regNum._rgu[index]) { cu++; } break; } index--; } if (cu != 0) { if (fQuo) { regQuo.SetSizeLazy(cu); } uint u = regDen._rgu[num - 1]; uint num6 = regDen._rgu[num - 2]; int num7 = NumericsHelpers.CbitHighZero(u); int num8 = 0x20 - num7; if (num7 > 0) { u = (u << num7) | (num6 >> num8); num6 = num6 << num7; if (num > 2) { num6 |= regDen._rgu[num - 3] >> num8; } } regNum.EnsureWritable(); int num9 = cu; while (--num9 >= 0) { uint uHi = ((num9 + num) <= regNum._iuLast) ? regNum._rgu[num9 + num] : 0; ulong num11 = NumericsHelpers.MakeUlong(uHi, regNum._rgu[(num9 + num) - 1]); uint uLo = regNum._rgu[(num9 + num) - 2]; if (num7 > 0) { num11 = (num11 << num7) | (uLo >> num8); uLo = uLo << num7; if ((num9 + num) >= 3) { uLo |= regNum._rgu[(num9 + num) - 3] >> num8; } } ulong num13 = num11 / ((ulong)u); ulong num14 = (uint)(num11 % ((ulong)u)); if (num13 > 0xffffffffL) { num14 += (ulong)u * (num13 - 0xffffffffL); num13 = 0xffffffffL; } while ((num14 <= 0xffffffffL) && ((num13 * num6) > NumericsHelpers.MakeUlong((uint)num14, uLo))) { num13 -= (ulong)1L; num14 += (ulong)u; } if (num13 > 0L) { ulong num15 = 0L; for (int i = 0; i < num; i++) { num15 += regDen._rgu[i] * num13; uint num17 = (uint)num15; num15 = num15 >> 0x20; if (regNum._rgu[num9 + i] < num17) { num15 += (ulong)1L; } regNum._rgu[num9 + i] -= num17; } if (uHi < num15) { uint uCarry = 0; for (int j = 0; j < num; j++) { uCarry = AddCarry(ref regNum._rgu[num9 + j], regDen._rgu[j], uCarry); } num13 -= (ulong)1L; } regNum._iuLast = (num9 + num) - 1; } if (fQuo) { if (cu == 1) { regQuo._uSmall = (uint)num13; } else { regQuo._rgu[num9] = (uint)num13; } } } regNum._iuLast = num - 1; regNum.Trim(); } } }
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2) { int num2; uint num11; int sign = 1; Label_0002: num2 = reg1._iuLast + 1; int b = reg2._iuLast + 1; if (num2 < b) { #if !(dotNET10 || dotNET11 || dotNETCF10) NumericsHelpers.Swap <BigIntegerBuilder>(ref reg1, ref reg2); NumericsHelpers.Swap <int>(ref num2, ref b); #else NumericsHelpers.Swap(ref reg1, ref reg2); NumericsHelpers.Swap(ref num2, ref b); #endif } if (b == 1) { if (num2 == 1) { reg1._uSmall = NumericsHelpers.GCD(reg1._uSmall, reg2._uSmall); return; } if (reg2._uSmall != 0) { reg1.Set(NumericsHelpers.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall)); } return; } if (num2 == 2) { reg1.Set(NumericsHelpers.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2))); return; } if (b <= (num2 - 2)) { reg1.Mod(ref reg2); goto Label_0002; } ulong a = reg1.GetHigh2(num2); ulong num5 = reg2.GetHigh2(num2); int num6 = NumericsHelpers.CbitHighZero((ulong)(a | num5)); if (num6 > 0) { a = (a << num6) | (reg1._rgu[num2 - 3] >> (0x20 - num6)); num5 = (num5 << num6) | (reg2._rgu[num2 - 3] >> (0x20 - num6)); } if (a < num5) { #if !(dotNET10 || dotNET11 || dotNETCF10) NumericsHelpers.Swap <ulong>(ref a, ref num5); NumericsHelpers.Swap <BigIntegerBuilder>(ref reg1, ref reg2); #else NumericsHelpers.Swap(ref a, ref num5); NumericsHelpers.Swap(ref reg1, ref reg2); #endif } if ((a == ulong.MaxValue) || (num5 == ulong.MaxValue)) { a = a >> 1; num5 = num5 >> 1; } if (a == num5) { reg1.Sub(ref sign, ref reg2); goto Label_0002; } if (NumericsHelpers.GetHi(num5) == 0) { reg1.Mod(ref reg2); goto Label_0002; } uint num7 = 1; uint num8 = 0; uint num9 = 0; uint num10 = 1; Label_0159: num11 = 1; ulong num12 = a - num5; while ((num12 >= num5) && (num11 < 0x20)) { num12 -= num5; num11++; } if (num12 >= num5) { ulong num13 = a / num5; if (num13 > 0xffffffffL) { goto Label_029E; } num11 = (uint)num13; num12 = a - (num11 * num5); } ulong num14 = (ulong)num7 + (ulong)num11 * (ulong)num9; ulong num15 = (ulong)num8 + (ulong)num11 * (ulong)num10; if (((num14 <= 0x7fffffffL) && (num15 <= 0x7fffffffL)) && ((num12 >= num15) && ((num12 + num14) <= (num5 - num9)))) { num7 = (uint)num14; num8 = (uint)num15; a = num12; if (a > num8) { num11 = 1; num12 = num5 - a; while ((num12 >= a) && (num11 < 0x20)) { num12 -= a; num11++; } if (num12 >= a) { ulong num16 = num5 / a; if (num16 > 0xffffffffL) { goto Label_029E; } num11 = (uint)num16; num12 = num5 - (num11 * a); } num14 = (ulong)num10 + (ulong)num11 * (ulong)num8; num15 = (ulong)num9 + (ulong)num11 * (ulong)num7; if (((num14 <= 0x7fffffffL) && (num15 <= 0x7fffffffL)) && ((num12 >= num15) && ((num12 + num14) <= (a - num8)))) { num10 = (uint)num14; num9 = (uint)num15; num5 = num12; if (num5 > num9) { goto Label_0159; } } } } Label_029E: if (num8 == 0) { if ((a / ((ulong)2L)) >= num5) { reg1.Mod(ref reg2); } else { reg1.Sub(ref sign, ref reg2); } } else { reg1.SetSizeKeep(b, 0); reg2.SetSizeKeep(b, 0); int num17 = 0; int num18 = 0; for (int i = 0; i < b; i++) { uint num20 = reg1._rgu[i]; uint num21 = reg2._rgu[i]; long num22 = (long)num20 * (long)num7 - (long)num21 * (long)num8 + (long)num17; long num23 = (long)num21 * (long)num10 - (long)num20 * (long)num9 + (long)num18; num17 = (int)(num22 >> 0x20); num18 = (int)(num23 >> 0x20); reg1._rgu[i] = (uint)num22; reg2._rgu[i] = (uint)num23; } reg1.Trim(); reg2.Trim(); } goto Label_0002; }
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(); }
// 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(); } } }
private static void ModDivCore(ref BigIntegerBuilder regNum, ref BigIntegerBuilder regDen, bool fQuo, ref BigIntegerBuilder regQuo) { regQuo.Set(0); if (regNum._iuLast < regDen._iuLast) { return; } var num1 = regDen._iuLast + 1; var num2 = regNum._iuLast - regDen._iuLast; var num3 = num2; var num4 = regNum._iuLast; while (true) { if (num4 < num2) { num3++; break; } if (regDen._bits[num4 - num2] == regNum._bits[num4]) { num4--; } else { if (regDen._bits[num4 - num2] < regNum._bits[num4]) { num3++; } break; } } if (num3 == 0) { return; } if (fQuo) { regQuo.SetSizeLazy(num3); } var num5 = regDen._bits[num1 - 1]; var num6 = regDen._bits[num1 - 2]; var num7 = NumericHelper.CbitHighZero(num5); var num8 = 32 - num7; if (num7 > 0) { num5 = (num5 << (num7 & 31)) | (num6 >> (num8 & 31)); num6 <<= num7 & 31; if (num1 > 2) { num6 |= regDen._bits[num1 - 3] >> (num8 & 31); } } regNum.EnsureWritable(); var num9 = num3; while (true) { var num10 = num9 - 1; num9 = num10; if (num10 < 0) { break; } var num = num9 + num1 > regNum._iuLast ? 0 : regNum._bits[num9 + num1]; var num11 = num; var num12 = NumericHelper.BuildUInt64(num11, regNum._bits[num9 + num1 - 1]); var num13 = regNum._bits[num9 + num1 - 2]; if (num7 > 0) { num12 = (num12 << (num7 & 63)) | (num13 >> (num8 & 31)); num13 <<= num7 & 31; if (num9 + num1 >= 3) { num13 |= regNum._bits[num9 + num1 - 3] >> (num8 & 31); } } var num14 = num12 / num5; var num15 = (ulong)(uint)(num12 % num5); if (num14 > uint.MaxValue) { num15 += num5 * (num14 - uint.MaxValue); num14 = uint.MaxValue; } while (num15 <= uint.MaxValue && num14 * num6 > NumericHelper.BuildUInt64((uint)num15, num13)) { num14--; num15 += num5; } if (num14 > 0) { var num16 = (ulong)0; for (var i = 0; i < num1; i++) { num16 += regDen._bits[i] * num14; var num17 = (uint)num16; num16 >>= 32; if (regNum._bits[num9 + i] < num17) { num16++; } regNum._bits[num9 + i] -= num17; } if (num11 < num16) { uint num18 = 0; for (var j = 0; j < num1; j++) { num18 = AddCarry(ref regNum._bits[num9 + j], regDen._bits[j], num18); } num14--; } regNum._iuLast = num9 + num1 - 1; } if (!fQuo) { continue; } if (num3 != 1) { regQuo._bits[num9] = (uint)num14; } else { regQuo._uSmall = (uint)num14; } } regNum._iuLast = num1 - 1; regNum.Trim(); }
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2) { var num = 1; while (true) { var num1 = reg1._iuLast + 1; var num2 = reg2._iuLast + 1; if (num1 < num2) { NumericHelper.Swap(ref reg1, ref reg2); NumericHelper.Swap(ref num1, ref num2); } if (num2 == 1) { if (num1 == 1) { reg1._uSmall = NumericHelper.GCD(reg1._uSmall, reg2._uSmall); } else if (reg2._uSmall != 0) { reg1.Set(NumericHelper.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall)); } return; } if (num1 == 2) { break; } if (num2 > num1 - 2) { var high2 = reg1.GetHigh2(num1); var high21 = reg2.GetHigh2(num1); var num3 = NumericHelper.CbitHighZero(high2 | high21); if (num3 > 0) { high2 = (high2 << (num3 & 63)) | (reg1._bits[num1 - 3] >> ((32 - num3) & 31)); high21 = (high21 << (num3 & 63)) | (reg2._bits[num1 - 3] >> ((32 - num3) & 31)); } if (high2 < high21) { NumericHelper.Swap(ref high2, ref high21); NumericHelper.Swap(ref reg1, ref reg2); } if (high2 == ulong.MaxValue || high21 == ulong.MaxValue) { high2 >>= 1; high21 >>= 1; } if (high2 == high21) { reg1.Sub(ref num, ref reg2); } else if (NumericHelper.GetHi(high21) != 0) { uint num4 = 1; uint num5 = 0; uint num6 = 0; uint num7 = 1; while (true) { uint num8 = 1; var num9 = high2 - high21; while (num9 >= high21 && num8 < 32) { num9 -= high21; num8++; } if (num9 >= high21) { var num10 = high2 / high21; if (num10 <= uint.MaxValue) { num8 = (uint)num10; num9 = high2 - (num8 * high21); } else { break; } } var num11 = num4 + (num8 * (ulong)num6); var num12 = num5 + (num8 * (ulong)num7); if (num11 > 2147483647 || num12 > 2147483647) { break; } if (num9 < num12 || num9 + num11 > high21 - num6) { break; } num4 = (uint)num11; num5 = (uint)num12; high2 = num9; if (high2 > num5) { num8 = 1; num9 = high21 - high2; while (num9 >= high2 && num8 < 32) { num9 -= high2; num8++; } if (num9 >= high2) { var num13 = high21 / high2; if (num13 <= uint.MaxValue) { num8 = (uint)num13; num9 = high21 - (num8 * high2); } else { break; } } num11 = num7 + (num8 * (ulong)num5); num12 = num6 + (num8 * (ulong)num4); if (num11 > 2147483647 || num12 > 2147483647) { break; } if (num9 < num12 || num9 + num11 > high2 - num5) { break; } num7 = (uint)num11; num6 = (uint)num12; high21 = num9; if (high21 <= num6) { break; } } else { break; } } if (num5 != 0) { reg1.SetSizeKeep(num2, 0); reg2.SetSizeKeep(num2, 0); var num14 = 0; var num15 = 0; for (var i = 0; i < num2; i++) { var num16 = reg1._bits[i]; var num17 = reg2._bits[i]; var num18 = ((long)num16 * num4) - ((long)num17 * num5) + num14; var num19 = ((long)num17 * num7) - ((long)num16 * num6) + num15; num14 = (int)(num18 >> 32); num15 = (int)(num19 >> 32); reg1._bits[i] = (uint)num18; reg2._bits[i] = (uint)num19; } reg1.Trim(); reg2.Trim(); } else if (high2 / 2 < high21) { reg1.Sub(ref num, ref reg2); } else { reg1.Mod(ref reg2); } } else { reg1.Mod(ref reg2); } } else { reg1.Mod(ref reg2); } } reg1.Set(NumericHelper.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2))); }
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2) { int num2; uint num11; int sign = 1; Label_0002: num2 = reg1._iuLast + 1; int b = reg2._iuLast + 1; if (num2 < b) { #if !(dotNET10 || dotNET11 || dotNETCF10) NumericsHelpers.Swap<BigIntegerBuilder>(ref reg1, ref reg2); NumericsHelpers.Swap<int>(ref num2, ref b); #else NumericsHelpers.Swap(ref reg1, ref reg2); NumericsHelpers.Swap(ref num2, ref b); #endif } if (b == 1) { if (num2 == 1) { reg1._uSmall = NumericsHelpers.GCD(reg1._uSmall, reg2._uSmall); return; } if (reg2._uSmall != 0) { reg1.Set(NumericsHelpers.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall)); } return; } if (num2 == 2) { reg1.Set(NumericsHelpers.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2))); return; } if (b <= (num2 - 2)) { reg1.Mod(ref reg2); goto Label_0002; } ulong a = reg1.GetHigh2(num2); ulong num5 = reg2.GetHigh2(num2); int num6 = NumericsHelpers.CbitHighZero((ulong)(a | num5)); if (num6 > 0) { a = (a << num6) | (reg1._rgu[num2 - 3] >> (0x20 - num6)); num5 = (num5 << num6) | (reg2._rgu[num2 - 3] >> (0x20 - num6)); } if (a < num5) { #if !(dotNET10 || dotNET11 || dotNETCF10) NumericsHelpers.Swap<ulong>(ref a, ref num5); NumericsHelpers.Swap<BigIntegerBuilder>(ref reg1, ref reg2); #else NumericsHelpers.Swap(ref a, ref num5); NumericsHelpers.Swap(ref reg1, ref reg2); #endif } if ((a == ulong.MaxValue) || (num5 == ulong.MaxValue)) { a = a >> 1; num5 = num5 >> 1; } if (a == num5) { reg1.Sub(ref sign, ref reg2); goto Label_0002; } if (NumericsHelpers.GetHi(num5) == 0) { reg1.Mod(ref reg2); goto Label_0002; } uint num7 = 1; uint num8 = 0; uint num9 = 0; uint num10 = 1; Label_0159: num11 = 1; ulong num12 = a - num5; while ((num12 >= num5) && (num11 < 0x20)) { num12 -= num5; num11++; } if (num12 >= num5) { ulong num13 = a / num5; if (num13 > 0xffffffffL) { goto Label_029E; } num11 = (uint)num13; num12 = a - (num11 * num5); } ulong num14 = (ulong)num7 + (ulong)num11 * (ulong)num9; ulong num15 = (ulong)num8 + (ulong)num11 * (ulong)num10; if (((num14 <= 0x7fffffffL) && (num15 <= 0x7fffffffL)) && ((num12 >= num15) && ((num12 + num14) <= (num5 - num9)))) { num7 = (uint)num14; num8 = (uint)num15; a = num12; if (a > num8) { num11 = 1; num12 = num5 - a; while ((num12 >= a) && (num11 < 0x20)) { num12 -= a; num11++; } if (num12 >= a) { ulong num16 = num5 / a; if (num16 > 0xffffffffL) { goto Label_029E; } num11 = (uint)num16; num12 = num5 - (num11 * a); } num14 = (ulong)num10 + (ulong)num11 * (ulong)num8; num15 = (ulong)num9 + (ulong)num11 * (ulong)num7; if (((num14 <= 0x7fffffffL) && (num15 <= 0x7fffffffL)) && ((num12 >= num15) && ((num12 + num14) <= (a - num8)))) { num10 = (uint)num14; num9 = (uint)num15; num5 = num12; if (num5 > num9) { goto Label_0159; } } } } Label_029E: if (num8 == 0) { if ((a / ((ulong)2L)) >= num5) { reg1.Mod(ref reg2); } else { reg1.Sub(ref sign, ref reg2); } } else { reg1.SetSizeKeep(b, 0); reg2.SetSizeKeep(b, 0); int num17 = 0; int num18 = 0; for (int i = 0; i < b; i++) { uint num20 = reg1._rgu[i]; uint num21 = reg2._rgu[i]; long num22 = (long)num20 * (long)num7 - (long)num21 * (long)num8 + (long)num17; long num23 = (long)num21 * (long)num10 - (long)num20 * (long)num9 + (long)num18; num17 = (int)(num22 >> 0x20); num18 = (int)(num23 >> 0x20); reg1._rgu[i] = (uint)num22; reg2._rgu[i] = (uint)num23; } reg1.Trim(); reg2.Trim(); } goto Label_0002; }
public void ModDiv(ref BigIntegerBuilder regDen, ref BigIntegerBuilder regQuo) { if (regDen._iuLast == 0) { regQuo.Set(this.DivMod(regDen._uSmall)); #if !(dotNET10 || dotNET11 || dotNETCF10) NumericsHelpers.Swap<BigIntegerBuilder>(ref this, ref regQuo); #else NumericsHelpers.Swap(ref this, ref regQuo); #endif } else if (this._iuLast != 0) { ModDivCore(ref this, ref regDen, true, ref regQuo); } }
private static void ModDivCore(ref BigIntegerBuilder regNum, ref BigIntegerBuilder regDen, bool fQuo, ref BigIntegerBuilder regQuo) { Contract.Assert(regNum._iuLast > 0 && regDen._iuLast > 0); regQuo.Set(0); if (regNum._iuLast < regDen._iuLast) return; Contract.Assert(0 < regDen._iuLast && regDen._iuLast <= regNum._iuLast); 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; } Contract.Assert((uDen & 0x80000000) != 0); // Allocate and initialize working space. Contract.Assert(cuQuo + cuDen == regNum._iuLast + 1 || cuQuo + cuDen == regNum._iuLast + 2); 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; Contract.Assert(uNumHi <= regDen._rgu[cuDen - 1]); 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); Contract.Assert(uuQuo <= (ulong)uint.MaxValue + 2); 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; } Contract.Assert(uNumHi == uuBorrow || uNumHi == uuBorrow - 1); 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); Contract.Assert(uCarry <= 1); } Contract.Assert(uCarry == 1); uuQuo--; } regNum._iuLast = iu + cuDen - 1; } if (fQuo) { if (cuQuo == 1) regQuo._uSmall = (uint)uuQuo; else regQuo._rgu[iu] = (uint)uuQuo; } } Contract.Assert(cuDen > 1 && regNum._iuLast > 0); regNum._iuLast = cuDen - 1; regNum.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 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 (; ; ) { reg1.AssertValid(true); reg2.AssertValid(true); 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); } Contract.Assert(cuMax == reg1._iuLast + 1); Contract.Assert(cuMin == reg2._iuLast + 1); 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); Contract.Assert(uu1 != 0 && uu2 != 0); 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; } Contract.Assert(uu1 >= uu2); // We ensured this above. 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. Contract.Assert(cuMax == cuMin); reg1.Sub(ref signTmp, ref reg2); Contract.Assert(reg1._iuLast < cuMin - 1); 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 (; ; ) { Contract.Assert(uu1 + a > a); // no overflow Contract.Assert(uu2 + d > d); Contract.Assert(uu1 > b); Contract.Assert(uu2 > c); Contract.Assert(uu2 + d <= uu1 - b); 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; Contract.Assert(uQuo == (uu1 + a - 1) / (uu2 - c)); Contract.Assert(uQuo == (uu1 - b) / (uu2 + d)); a = (uint)uuAdNew; b = (uint)uuBcNew; uu1 = uuNew; if (uu1 <= b) { Contract.Assert(uu1 == b); break; } Contract.Assert(uu1 + a > a); // no overflow Contract.Assert(uu2 + d > d); Contract.Assert(uu2 > c); Contract.Assert(uu1 > b); Contract.Assert(uu1 + a <= uu2 - c); 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; Contract.Assert(uQuo == (uu2 + d - 1) / (uu1 - b)); Contract.Assert(uQuo == (uu2 - c) / (uu1 + a)); d = (uint)uuAdNew; c = (uint)uuBcNew; uu2 = uuNew; if (uu2 <= c) { Contract.Assert(uu2 == c); break; } } if (b == 0) { Contract.Assert(a == 1 && c == 0 && d == 1); Contract.Assert(uu1 > uu2); // We ensured this above. 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(); } } }
public void ModDiv(ref BigIntegerBuilder regDen, ref BigIntegerBuilder regQuo) { if (regDen._iuLast == 0) { regQuo.Set(this.DivMod(regDen._uSmall)); NumericsHelpers.Swap<BigIntegerBuilder>(ref this, ref regQuo); } else if (this._iuLast != 0) { ModDivCore(ref this, ref regDen, true, ref regQuo); } }