mlemanczyk/even-perfect-numbers-scanner
1
0 Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Reapply modulo helpers and inline fast remainders

Browse Source
This commit is contained in:
Marek Lemańczyk committed 2025-09-22 19:26:07 +02:00
1 parent 5db0c4fa95
commit ca866ffc5b
43 files changed
+982 -134
Download Patch File Download Diff File Expand all files Collapse all files

No files matched your search

PerfectNumbers.Core/Cpu/MersenneNumberLucasLehmerCpuTester.cs
+10 -6
View File
@@ -8,12 +8,16 @@ public class MersenneNumberLucasLehmerCpuTester
// - If 3 | p and p != 3, then 7 | M_p -> composite.
// - If p ≡ 1 (mod 4) and p shares a factor with (p-1), reject fast.
// - If p is divisible by divisors specific to numbers ending with 1 or 7, reject fast.
if (
((exponent % 3UL) == 0UL && exponent != 3UL) ||
((exponent % 5UL) == 0UL && exponent != 5UL) ||
((exponent % 7UL) == 0UL && exponent != 7UL) ||
((exponent % 11UL) == 0UL && exponent != 11UL)
)
ulong mod3 = exponent.Mod3();
ulong mod5 = exponent.Mod5();
ulong mod7 = exponent.Mod7();
ulong mod11 = exponent.Mod11();
if (
(mod3 == 0UL && exponent != 3UL) ||
(mod5 == 0UL && exponent != 5UL) ||
(mod7 == 0UL && exponent != 7UL) ||
(mod11 == 0UL && exponent != 11UL)
)
{
return false;
}
PerfectNumbers.Core/Cpu/MersenneNumberResidueCpuTester.cs
+1 -1
View File
@@ -21,7 +21,7 @@ public class MersenneNumberResidueCpuTester
q.Mod10_8_5_3(out ulong r10, out ulong r8, out ulong r5, out ulong r3);
// Step residues for q += 2*p
twoP.Mod10_8_5_3(out ulong step10, out ulong step8, out ulong step5, out ulong step3);
step10 = step10.Mod10();
step10 %= 10UL;
// Allowed last-digit sets for q depending on last digit of M_p
// lastIsSeven == true => allow {7,9}
PerfectNumbers.Core/Gpu/MersenneNumberLucasLehmerGpuTester.cs
+4 -4
View File
@@ -51,7 +51,7 @@ public class MersenneNumberLucasLehmerGpuTester
// Early rejections aligned with incremental/order sieves, but safe for small p:
// - If 3 | p and p != 3, then 7 | M_p -> composite.
// - If p ≡ 1 (mod 4) and p shares a factor with (p-1), reject fast.
if ((exponent % 3UL) == 0UL && exponent != 3UL)
if (exponent % 3UL == 0UL && exponent != 3UL)
{
return false;
}
@@ -548,7 +548,7 @@ public class MersenneNumberLucasLehmerGpuTester
}
}
int topBits = (int)(exponent % 128UL);
int topBits = (int)exponent.Mod128();
if (topBits == 0)
{
topBits = 128;
@@ -672,7 +672,7 @@ public class MersenneNumberLucasLehmerGpuTester
}
}
int topBits = (int)(exponent % 128UL);
int topBits = (int)exponent.Mod128();
if (topBits == 0)
{
topBits = 128;
@@ -803,7 +803,7 @@ public class MersenneNumberLucasLehmerGpuTester
vLow.Add(vHigh);
// Mask to keep only p low bits and fold the carry bits (v >> p)
int topBits = (int)(p % 128UL);
int topBits = (int)p.Mod128();
if (topBits == 0)
{
topBits = 128;
PerfectNumbers.Core/Gpu/MersenneNumberOrderGpuTester.cs
+3 -3
View File
@@ -27,10 +27,10 @@ public class MersenneNumberOrderGpuTester(GpuKernelType kernelType, bool useGpuO
var foundBuffer = accelerator.Allocate1D<int>(1);
UInt128 exponent128 = exponent;
exponent128.Mod10_8_5_3(out ulong exponentMod10, out ulong exponentMod8, out ulong exponentMod5, out ulong exponentMod3);
ulong step10 = (exponentMod10 << 1).Mod10();
ulong step10 = (exponentMod10 << 1) % 10UL;
ulong step8 = (exponentMod8 << 1) & 7UL;
ulong step3 = (exponentMod3 << 1) % 3UL;
ulong step5 = (exponentMod5 << 1) % 5UL;
ulong step3 = (exponentMod3 << 1) % 3UL;
ulong step5 = (exponentMod5 << 1) % 5UL;
try
{
UInt128 remaining;
PerfectNumbers.Core/MersenneNumberTester.cs
+7 -7
View File
@@ -67,7 +67,7 @@ public sealed class MersenneNumberTester(
for (; k <= limit; k++)
{
q = twoP * k + UInt128.One;
remainder = q.Mod10();
remainder = (ulong)(q % 10UL);
bool shouldCheck = lastIsSeven
? remainder == 7UL || remainder == 9UL || remainder == 3UL
: remainder == 1UL || remainder == 3UL || remainder == 9UL;
@@ -75,12 +75,12 @@ public sealed class MersenneNumberTester(
// Early modular filters for odd order and small-prime rejections
if (shouldCheck)
{
ulong mod8 = q.Mod8();
ulong mod8 = (ulong)(q % 8UL);
if (mod8 != 1UL && mod8 != 7UL)
{
continue;
}
else if (q.Mod3() == 0UL || q.Mod5() == 0UL)
else if ((ulong)(q % 3UL) == 0UL || (ulong)(q % 5UL) == 0UL)
{
continue;
}
@@ -106,7 +106,7 @@ public sealed class MersenneNumberTester(
for (; k2 <= limit; k2++)
{
q2 = twoP * k2 + 1UL;
remainder2 = q2.Mod10();
remainder2 = (ulong)(q2 % 10UL);
bool shouldCheck2 = lastIsSeven
? remainder2 == 7UL || remainder2 == 9UL || remainder2 == 3UL
: remainder2 == 1UL || remainder2 == 3UL || remainder2 == 9UL;
@@ -114,12 +114,12 @@ public sealed class MersenneNumberTester(
// Early modular filters for odd order and small-prime rejections
if (shouldCheck2)
{
ulong mod8 = q2.Mod8();
ulong mod8 = (ulong)(q2 % 8UL);
if (mod8 != 1UL && mod8 != 7UL)
{
shouldCheck2 = false;
}
else if (q2.Mod3() == 0UL || q2.Mod5() == 0UL)
else if ((ulong)(q2 % 3UL) == 0UL || (ulong)(q2 % 5UL) == 0UL)
{
shouldCheck2 = false;
}
@@ -203,7 +203,7 @@ public sealed class MersenneNumberTester(
{
// Safe early rejections using known orders for tiny primes:
// 7 | M_p iff 3 | p. Avoid rejecting p == 3 where M_3 == 7 is prime.
if ((exponent % 3UL) == 0UL && exponent != 3UL)
if (exponent % 3UL == 0UL && exponent != 3UL)
{
return false;
}
PerfectNumbers.Core/PerfectNumbersMath.cs
-21
View File
@@ -1,21 +0,0 @@
using System.Runtime.CompilerServices;
namespace PerfectNumbers.Core;
public static class PerfectNumbersMath
{
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint FastRemainder3(uint value)
{
uint quotient = (uint)(((ulong)value * 0xAAAAAAABUL) >> 33);
return value - quotient * 3U;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint FastRemainder5(uint value)
{
uint quotient = (uint)(((ulong)value * 0xCCCCCCCDUL) >> 34);
return value - quotient * 5U;
}
}
PerfectNumbers.Core/PrimeTester.cs
+4 -4
View File
@@ -53,13 +53,13 @@ public sealed class PrimeTester(bool useInternal = false)
{
result = false;
}
else if (n > 5UL && (n % 5UL) == 0UL)
else if (n > 5UL && n % 5UL == 0UL)
{
result = false;
}
else
{
if (n.Mod10() == 1UL && SharesFactorWithMaxExponent(n))
if (n % 10UL == 1UL && SharesFactorWithMaxExponent(n))
{
result = false;
}
@@ -260,13 +260,13 @@ public sealed class PrimeTester(bool useInternal = false)
return;
}
if ((n & 1UL) == 0UL || (n > 5UL && (n % 5UL) == 0UL))
if ((n & 1UL) == 0UL || (n > 5UL && n % 5UL == 0UL))
{
results[index] = 0;
return;
}
if (n.Mod10() == 1UL)
if (n % 10UL == 1UL)
{
// Early reject special GCD heuristic with floor(log2 n)
ulong m = 63UL - (ulong)ILGPU.Algorithms.XMath.LeadingZeroCount(n);
PerfectNumbers.Core/PrimesGenerator.cs
+2 -2
View File
@@ -100,14 +100,14 @@ public static class PrimesGenerator
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool IsAllowedForLastOne(uint prime)
{
uint mod10 = prime % 10U;
uint mod10 = prime % 10U;
return mod10 == 1U || mod10 == 3U || mod10 == 9U || prime == 7U || prime == 11U;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool IsAllowedForLastSeven(uint prime)
{
uint mod10 = prime % 10U;
uint mod10 = prime % 10U;
return mod10 == 3U || mod10 == 7U || mod10 == 9U || prime == 11U;
}
}
PerfectNumbers.Core/UInt128Extensions.cs
+18 -2
View File
@@ -135,8 +135,8 @@ public static class UInt128Extensions
mod8 = (ulong)value & 7UL;
uint mod5Value = PerfectNumbersMath.FastRemainder5(byteSum);
uint mod3Value = PerfectNumbersMath.FastRemainder3(byteSum);
uint mod5Value = byteSum.Mod5();
uint mod3Value = byteSum.Mod3();
mod10 = (mod8 & 1UL) == 0UL
? mod5Value switch
@@ -238,6 +238,22 @@ public static class UInt128Extensions
return remainder >= 5UL ? remainder - 5UL : remainder;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static ulong Mod6(this UInt128 value)
{
ulong mod3 = value.Mod3();
ulong key = (mod3 << 1) | ((ulong)value & 1UL);
return key switch
{
0UL => 0UL,
1UL => 3UL,
2UL => 4UL,
3UL => 1UL,
4UL => 2UL,
_ => 5UL,
};
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static ulong Mod7(this UInt128 value)
{
PerfectNumbers.Core/UIntExtensions.cs
+59 -42
View File
@@ -4,57 +4,74 @@ namespace PerfectNumbers.Core;
public static class UIntExtensions
{
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod3(this uint value) => PerfectNumbersMath.FastRemainder3(value);
private static readonly byte[] Mod6Lookup = { 0, 3, 4, 1, 2, 5 };
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod5(this uint value) => PerfectNumbersMath.FastRemainder5(value);
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod3(this uint value)
{
uint quotient = (uint)(((ulong)value * 0xAAAAAAABUL) >> 33);
return value - quotient * 3U;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod7(this uint value)
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod5(this uint value)
{
uint quotient = (uint)(((ulong)value * 0xCCCCCCCDUL) >> 34);
return value - quotient * 5U;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod6(this uint value)
{
uint key = (value.Mod3() << 1) | (value & 1U);
return Mod6Lookup[(int)key];
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod7(this uint value)
{
uint remainder = 0U;
uint temp = value;
while (temp != 0U)
{
uint remainder = 0U;
uint temp = value;
while (temp != 0U)
{
remainder += temp & 7U;
temp >>= 3;
if (remainder >= 7U)
{
remainder -= 7U;
}
}
return remainder >= 7U ? remainder - 7U : remainder;
remainder += temp & 7U;
temp >>= 3;
if (remainder >= 7U)
{
remainder -= 7U;
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod8(this uint value) => value & 7U;
return remainder >= 7U ? remainder - 7U : remainder;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod10(this uint value)
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod8(this uint value) => value & 7U;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod10(this uint value)
{
return value - (uint)(((ulong)value * 0xCCCCCCCDUL) >> 35) * 10U;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod11(this uint value)
{
uint remainder = 0U;
uint temp = value;
while (temp != 0U)
{
return value - (uint)(((ulong)value * 0xCCCCCCCDUL) >> 35) * 10U;
remainder += temp & 1023U;
temp >>= 10;
remainder -= 11U * (remainder / 11U);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod11(this uint value)
{
uint remainder = 0U;
uint temp = value;
return remainder;
}
while (temp != 0U)
{
remainder += temp & 1023U;
temp >>= 10;
remainder -= 11U * (remainder / 11U);
}
return remainder;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod128(this uint value) => value & 127U;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint Mod128(this uint value) => value & 127U;
}
PerfectNumbers.Core/ULongExtensions.cs
+75 -5
View File
@@ -57,7 +57,11 @@ public static class ULongExtensions
return q;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static readonly byte[] Mod6Lookup = { 0, 3, 4, 1, 2, 5 };
private static readonly byte[] Mod7ByteCoefficients = { 1, 4, 2, 1, 4, 2, 1, 4 };
private static readonly byte[] Mod11ByteCoefficients = { 1, 3, 9, 5, 4, 1, 3, 9 };
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Mod10_8_5_3(this ulong value, out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3)
{
ulong temp = value;
@@ -72,8 +76,8 @@ public static class ULongExtensions
mod8 = value & 7UL;
uint mod5Value = PerfectNumbersMath.FastRemainder5(byteSum);
uint mod3Value = PerfectNumbersMath.FastRemainder3(byteSum);
uint mod5Value = byteSum.Mod5();
uint mod3Value = byteSum.Mod3();
mod10 = (mod8 & 1UL) == 0UL
? mod5Value switch
@@ -97,6 +101,35 @@ public static class ULongExtensions
mod3 = mod3Value;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Mod11_7_5_3(this ulong value, out ulong mod11, out ulong mod7, out ulong mod5, out ulong mod3)
{
uint mod3Accumulator = 0U;
uint mod5Accumulator = 0U;
uint mod7Accumulator = 0U;
uint mod11Accumulator = 0U;
ulong temp = value;
int index = 0;
do
{
byte current = (byte)temp;
mod3Accumulator += current;
mod5Accumulator += current;
mod7Accumulator += (uint)(current * Mod7ByteCoefficients[index]);
mod11Accumulator += (uint)(current * Mod11ByteCoefficients[index]);
temp >>= 8;
index++;
}
while (temp != 0UL);
mod3 = mod3Accumulator.Mod3();
mod5 = mod5Accumulator.Mod5();
mod7 = ReduceMod7(mod7Accumulator);
mod11 = ReduceMod11(mod11Accumulator);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Mod10_8_5_3Steps(this ulong value, out ulong step10, out ulong step8, out ulong step5, out ulong step3)
{
@@ -171,7 +204,7 @@ public static class ULongExtensions
sum += (uint)((value >> 32) & 0xFFFFUL);
sum += (uint)((value >> 48) & 0xFFFFUL);
return PerfectNumbersMath.FastRemainder3(sum);
return sum.Mod3();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -182,7 +215,14 @@ public static class ULongExtensions
sum += (uint)((value >> 32) & 0xFFFFUL);
sum += (uint)((value >> 48) & 0xFFFFUL);
return PerfectNumbersMath.FastRemainder5(sum);
return sum.Mod5();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static ulong Mod6(this ulong value)
{
ulong key = (value.Mod3() << 1) | (value & 1UL);
return Mod6Lookup[(int)key];
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -218,6 +258,36 @@ public static class ULongExtensions
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static ulong Mod128(this ulong value) => value & 127UL;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong ReduceMod7(uint value)
{
while (value >= 7U)
{
value = (value >> 3) + (value & 7U);
if (value >= 7U && value < 14U)
{
value -= 7U;
}
}
return value;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong ReduceMod11(uint value)
{
while (value >= 11U)
{
value = (value & 15U) + ((value >> 4) * 5U);
if (value >= 11U && value < 22U)
{
value -= 11U;
}
}
return value;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static UInt128 Mul64(this ulong a, ulong b) => ((UInt128)a.MulHigh(b) << 64) | (UInt128)(a * b);