Rescope loop variables for divisor workflows
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Marek Lemańczyk committed
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@@ -75,8 +75,7 @@ public static class ULongExtensions
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uint mod5Value = PerfectNumbersMath.FastRemainder5(byteSum);
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uint mod3Value = PerfectNumbersMath.FastRemainder3(byteSum);
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ulong parity = mod8 & 1UL;
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mod10 = parity == 0UL
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mod10 = (mod8 & 1UL) == 0UL
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? mod5Value switch
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{
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0U => 0UL,
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@@ -137,10 +136,9 @@ public static class ULongExtensions
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod10(this ulong value)
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{
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ulong parity = value & 1UL;
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ulong mod5 = value.Mod5();
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if (parity == 0UL)
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if ((value & 1UL) == 0UL)
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{
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return mod5 switch
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{
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@@ -265,253 +263,282 @@ public static class ULongExtensions
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public static ulong MulMod64(this ulong a, ulong b, ulong modulus) => (ulong)(UInt128)(((a % modulus) * (b % modulus)) % modulus);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 PowMod(this ulong exponent, UInt128 modulus)
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{
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// Return 1 because 2^0 = 1
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if (exponent == 0UL)
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return UInt128.One;
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public static UInt128 PowMod(this ulong exponent, UInt128 modulus)
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{
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UInt128 result = UInt128.One;
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ulong exponentLoopIndex = 0UL;
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// Any number mod 1 is 0
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if (modulus == UInt128.One)
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return UInt128.Zero;
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// Return 1 because 2^0 = 1
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if (exponent == 0UL)
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return result;
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UInt128 result;
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// For small exponents, do classic method
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if (exponent < 64 || modulus < 4)
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{
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result = UInt128.One;
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for (ulong i = 0; i < exponent; i++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// Any number mod 1 is 0
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if (modulus == UInt128.One)
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return UInt128.Zero;
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return result;
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}
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// For small exponents, do classic method
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if (exponent < 64 || modulus < 4)
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{
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for (; exponentLoopIndex < exponent; exponentLoopIndex++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// Special case: if modulus is a power of two, use bitmasking for efficiency and correctness
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if ((modulus & (modulus - 1)) == 0)
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{
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result = UInt128.One << (int)(exponent & 127);
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return result & (modulus - 1);
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}
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return result;
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}
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// For general modulus, use classic left-to-right binary method for 2^exponent mod modulus
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UInt128 resultBin = UInt128.One;
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for (ulong i = 0; i < exponent; i++)
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{
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resultBin <<= 1;
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if (resultBin >= modulus)
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resultBin -= modulus;
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}
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// Special case: if modulus is a power of two, use bitmasking for efficiency and correctness
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if ((modulus & (modulus - 1)) == 0)
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{
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result = UInt128.One << (int)(exponent & 127);
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return result & (modulus - 1);
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}
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return resultBin;
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}
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// Reusing exponentLoopIndex to iterate again over the exponent range for the general-case accumulation.
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exponentLoopIndex = 0UL;
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// Reusing result after resetting it for the general modulus accumulation phase.
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result = UInt128.One;
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for (; exponentLoopIndex < exponent; exponentLoopIndex++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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return result;
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}
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/// <summary>
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/// Computes 2^exponent mod modulus using a known cycle length.
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/// </summary>
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public static UInt128 PowModWithCycle(this ulong exponent, UInt128 modulus, ulong cycleLength)
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{
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// Return 1 because 2^0 = 1
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if (exponent == 0UL)
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return UInt128.One;
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public static UInt128 PowModWithCycle(this ulong exponent, UInt128 modulus, ulong cycleLength)
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{
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UInt128 result = UInt128.One;
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ulong exponentLoopIndex = 0UL;
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ulong rotationCount = 0UL;
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// Any number mod 1 is 0
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if (modulus == UInt128.One)
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return UInt128.Zero;
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// Return 1 because 2^0 = 1
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if (exponent == 0UL)
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return result;
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// For small exponents, do classic method
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UInt128 result;
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if (exponent < 64 || modulus < 4)
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{
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result = UInt128.One;
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for (ulong i = 0; i < exponent; i++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// Any number mod 1 is 0
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if (modulus == UInt128.One)
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return UInt128.Zero;
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return result;
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}
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// For small exponents, do classic method
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if (exponent < 64 || modulus < 4)
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{
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for (; exponentLoopIndex < exponent; exponentLoopIndex++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// Special case: if modulus is a power of two, use bitmasking for efficiency and correctness
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if ((modulus & (modulus - 1)) == 0)
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{
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result = UInt128.One << (int)(exponent & 127);
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return result & (modulus - 1);
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}
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return result;
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}
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// For general modulus, use classic left-to-right binary method for 2^exponent mod modulus
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result = UInt128.One;
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UInt128 rotations = exponent % cycleLength;
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for (ulong i = 0; i < rotations; i++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// Special case: if modulus is a power of two, use bitmasking for efficiency and correctness
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if ((modulus & (modulus - 1)) == 0)
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{
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result = UInt128.One << (int)(exponent & 127);
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return result & (modulus - 1);
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}
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return result;
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}
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// Reusing exponentLoopIndex to iterate over the rotation count for the cycle-aware path.
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exponentLoopIndex = 0UL;
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// Reusing result after resetting it for the rotation-accumulation pass.
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result = UInt128.One;
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rotationCount = exponent % cycleLength;
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for (; exponentLoopIndex < rotationCount; exponentLoopIndex++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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return result;
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}
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/// <summary>
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/// Computes 2^exponent mod modulus using a known cycle length.
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/// </summary>
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public static UInt128 PowModWithCycle(this ulong exponent, UInt128 modulus, UInt128 cycleLength)
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{
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// Return 1 because 2^0 = 1
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if (exponent == UInt128.Zero)
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return UInt128.One;
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// Any number mod 1 is 0
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if (modulus == UInt128.One)
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return UInt128.Zero;
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public static UInt128 PowModWithCycle(this ulong exponent, UInt128 modulus, UInt128 cycleLength)
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{
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UInt128 result = UInt128.One;
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ulong exponentLoopIndex = 0UL;
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UInt128 rotationIndex = UInt128.Zero;
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UInt128 rotationCount = UInt128.Zero;
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// For small exponents, do classic method
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UInt128 result;
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if (exponent < UInt128Numbers.SixtyFour || modulus < UInt128Numbers.Four)
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{
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result = UInt128.One;
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for (ulong i = 0; i < exponent; i++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// Return 1 because 2^0 = 1
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if (exponent == UInt128.Zero)
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return result;
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return result;
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}
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// Any number mod 1 is 0
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if (modulus == UInt128.One)
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return UInt128.Zero;
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// Special case: if modulus is a power of two, use bitmasking for efficiency and correctness
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if ((modulus & (modulus - UInt128.One)) == UInt128.Zero)
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{
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result = UInt128.One << (int)(exponent & UInt128Numbers.OneHundredTwentySeven);
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return result & (modulus - 1);
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}
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// For small exponents, do classic method
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if (exponent < UInt128Numbers.SixtyFour || modulus < UInt128Numbers.Four)
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{
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for (; exponentLoopIndex < exponent; exponentLoopIndex++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// For general modulus, use classic left-to-right binary method for 2^exponent mod modulus
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result = UInt128.One;
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UInt128 rotations = exponent % cycleLength;
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for (UInt128 i = 0; i < rotations; i++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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return result;
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}
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return result;
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}
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// Special case: if modulus is a power of two, use bitmasking for efficiency and correctness
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if ((modulus & (modulus - UInt128.One)) == UInt128.Zero)
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{
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result = UInt128.One << (int)(exponent & UInt128Numbers.OneHundredTwentySeven);
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return result & (modulus - 1);
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}
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// Reusing result after resetting it for the rotation-driven accumulation phase.
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result = UInt128.One;
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rotationCount = exponent % cycleLength;
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rotationIndex = UInt128.Zero;
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while (rotationIndex < rotationCount)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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rotationIndex += UInt128.One;
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}
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return result;
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}
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/// <summary>
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/// Computes 2^exponent mod modulus using a known cycle length.
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/// </summary>
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public static UInt128 PowModWithCycle(this UInt128 exponent, UInt128 modulus, UInt128 cycleLength)
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{
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// Return 1 because 2^0 = 1
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if (exponent == UInt128.Zero)
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return UInt128.One;
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public static UInt128 PowModWithCycle(this UInt128 exponent, UInt128 modulus, UInt128 cycleLength)
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{
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UInt128 result = UInt128.One;
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ulong exponentLoopIndex = 0UL;
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UInt128 rotationIndex = UInt128.Zero;
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UInt128 rotationCount = UInt128.Zero;
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// Any number mod 1 is 0
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if (modulus == UInt128.One)
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return UInt128.Zero;
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// Return 1 because 2^0 = 1
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if (exponent == UInt128.Zero)
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return result;
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UInt128 result;
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// Any number mod 1 is 0
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if (modulus == UInt128.One)
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return UInt128.Zero;
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// For small exponents, do classic method
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if (exponent < UInt128Numbers.SixtyFour || modulus < UInt128Numbers.Four)
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{
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result = UInt128.One;
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for (ulong i = 0; i < exponent; i++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// For small exponents, do classic method
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if (exponent < UInt128Numbers.SixtyFour || modulus < UInt128Numbers.Four)
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{
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for (; exponentLoopIndex < exponent; exponentLoopIndex++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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return result;
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}
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return result;
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}
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// Special case: if modulus is a power of two, use bitmasking for efficiency and correctness
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if ((modulus & (modulus - UInt128.One)) == UInt128.Zero)
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{
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result = UInt128.One << (int)(exponent & UInt128Numbers.OneHundredTwentySeven);
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return result & (modulus - 1);
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}
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// Special case: if modulus is a power of two, use bitmasking for efficiency and correctness
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if ((modulus & (modulus - UInt128.One)) == UInt128.Zero)
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{
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result = UInt128.One << (int)(exponent & UInt128Numbers.OneHundredTwentySeven);
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return result & (modulus - 1);
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}
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// For general modulus, use classic left-to-right binary method for 2^exponent mod modulus
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result = UInt128.One;
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UInt128 rotations = exponent % cycleLength;
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for (UInt128 i = 0; i < rotations; i++)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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}
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// Reusing result after resetting it for the rotation-driven accumulation phase.
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result = UInt128.One;
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rotationCount = exponent % cycleLength;
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rotationIndex = UInt128.Zero;
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while (rotationIndex < rotationCount)
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{
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result <<= 1;
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if (result >= modulus)
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result -= modulus;
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return result;
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}
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rotationIndex += UInt128.One;
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}
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return result;
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}
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/// <summary>
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/// Computes 2^exponent mod modulus using iterative CRT composition from mod 10 up to modulus.
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/// Only for modulus >= 10 and reasonable size.
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/// </summary>
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public static UInt128 PowModCrt(this ulong exponent, UInt128 modulus, MersenneDivisorCycles cycles)
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{
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if (modulus < 10)
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return PowMod(exponent, modulus); // fallback to classic
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public static UInt128 PowModCrt(this ulong exponent, UInt128 modulus, MersenneDivisorCycles cycles)
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{
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if (modulus < 10)
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return PowMod(exponent, modulus); // fallback to classic
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// Use cycle length 4 for mod 10
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UInt128 result = PowModWithCycle(exponent, 10, 4);
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// Use cycle length 4 for mod 10
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UInt128 result = PowModWithCycle(exponent, 10, 4);
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UInt128 currentModulus = 10;
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UInt128 modulusCandidate = 11;
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UInt128 cycle = UInt128.Zero;
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UInt128 remainderForCandidate = UInt128.Zero;
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UInt128 currentModulus = 10;
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for (UInt128 m = 11; m <= modulus; m++)
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{
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UInt128 cycle = MersenneDivisorCycles.GetCycle(m);
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UInt128 remM = cycle > 0
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? PowModWithCycle(exponent, m, cycle)
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: PowMod(exponent, m);
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for (; modulusCandidate <= modulus; modulusCandidate++)
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{
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cycle = MersenneDivisorCycles.GetCycle(modulusCandidate);
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remainderForCandidate = cycle > UInt128.Zero
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? PowModWithCycle(exponent, modulusCandidate, cycle)
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: PowMod(exponent, modulusCandidate);
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// Solve x ≡ result mod currentModulus
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// x ≡ remM mod m
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// Find x mod (currentModulus * m)
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// Since currentModulus and m are coprime, use CRT:
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// x = result + currentModulus * t, where t ≡ (remM - result) * inv(currentModulus, m) mod m
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// Solve x ≡ result mod currentModulus
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// x ≡ remM mod m
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// Find x mod (currentModulus * m)
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// Since currentModulus and m are coprime, use CRT:
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// x = result + currentModulus * t, where t ≡ (remM - result) * inv(currentModulus, m) mod m
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UInt128 inv = ModInverse(currentModulus, m);
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UInt128 t = ((remM + m - (result % m)) * inv) % m;
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result += currentModulus * t;
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currentModulus *= m;
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result += currentModulus * ((remainderForCandidate + modulusCandidate - (result % modulusCandidate)) * ModInverse(currentModulus, modulusCandidate) % modulusCandidate);
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currentModulus *= modulusCandidate;
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if (currentModulus >= modulus)
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break;
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}
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if (currentModulus >= modulus)
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break;
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}
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return result % modulus;
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}
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return result % modulus;
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}
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// Helper: modular inverse (extended Euclidean algorithm)
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private static UInt128 ModInverse(UInt128 a, UInt128 m)
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{
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UInt128 m0 = m, t, q;
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UInt128 x0 = 0, x1 = 1;
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if (m == 1) return 0;
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while (a > 1)
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{
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q = a / m;
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t = m;
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m = a % m; a = t;
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t = x0;
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x0 = x1 - q * x0;
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x1 = t;
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}
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// Helper: modular inverse (extended Euclidean algorithm)
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private static UInt128 ModInverse(UInt128 a, UInt128 m)
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{
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UInt128 m0 = m, temp;
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UInt128 x0 = 0, x1 = 1;
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UInt128 originalA = UInt128.Zero;
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UInt128 originalM = UInt128.Zero;
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if (m == 1)
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{
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return 0;
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}
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if (x1 < 0) x1 += m0;
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while (a > 1)
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{
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originalA = a;
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originalM = m;
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m = originalA % originalM;
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a = originalM;
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temp = x0;
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x0 = x1 - (originalA / originalM) * x0;
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x1 = temp;
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}
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return x1;
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}
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if (x1 < 0)
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{
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x1 += m0;
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}
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return x1;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
public static bool SharesFactorWithExponentMinusOne(this ulong exponent)
|
||||
|
||||
Reference in new issue
Block a user