Ensure GPU residue copies are synchronized and cover high divisor sets

PerfectNumbers.Core.Tests/Gpu/GpuUInt128Pow2Minus1ModTests.cs

@@ -1,3 +1,5 @@
+using System.Numerics;
+using System.Runtime.CompilerServices;
 using FluentAssertions;
 using PerfectNumbers.Core.Gpu;
 using Xunit;
@@ -41,4 +43,69 @@ public class GpuUInt128Pow2Minus1ModTests
             results[i].Should().Be(single);
         }
     }
+
+    [Fact]
+    public void Pow2Minus1Mod_matches_bigint_for_large_mersenne_residue_candidates()
+    {
+        const ulong exponent = 107UL;
+        const int limit = 500_000;
+        UInt128 twoP = (UInt128)(2UL * exponent);
+
+        for (int k = 1; k <= limit; k++)
+        {
+            UInt128 q = checked(twoP * (UInt128)(ulong)k + UInt128.One);
+            GpuUInt128 gpuRemainder = GpuUInt128.Pow2Minus1Mod(exponent, (GpuUInt128)q);
+
+            BigInteger bigQ = ToBigInteger(q);
+            BigInteger bigPow = BigInteger.ModPow(new BigInteger(2), checked((int)exponent), bigQ);
+            BigInteger bigRemainder = (bigPow - BigInteger.One) % bigQ;
+            if (bigRemainder.Sign < 0)
+            {
+                bigRemainder += bigQ;
+            }
+
+            gpuRemainder.Should().Be(ToGpuUInt128(bigRemainder));
+        }
+
+        UInt128[] largeKs =
+        {
+            UInt128.Parse("1000000000000000"),
+            UInt128.Parse("1000000000000000000"),
+            UInt128.Parse("1000000000000000000000"),
+            UInt128.Parse("99999999998192000000000")
+        };
+
+        foreach (UInt128 kValue in largeKs)
+        {
+            UInt128 q = checked(twoP * kValue + UInt128.One);
+            GpuUInt128 gpuRemainder = GpuUInt128.Pow2Minus1Mod(exponent, (GpuUInt128)q);
+
+            BigInteger bigQ = ToBigInteger(q);
+            BigInteger bigPow = BigInteger.ModPow(new BigInteger(2), checked((int)exponent), bigQ);
+            BigInteger bigRemainder = (bigPow - BigInteger.One) % bigQ;
+            if (bigRemainder.Sign < 0)
+            {
+                bigRemainder += bigQ;
+            }
+
+            gpuRemainder.Should().Be(ToGpuUInt128(bigRemainder));
+        }
+    }
+
+    private static BigInteger ToBigInteger(UInt128 value)
+    {
+        Span<byte> buffer = stackalloc byte[16];
+        buffer.Clear();
+        Unsafe.WriteUnaligned(ref buffer[0], value);
+        return new BigInteger(buffer, isUnsigned: true, isBigEndian: false);
+    }
+
+    private static GpuUInt128 ToGpuUInt128(BigInteger value)
+    {
+        Span<byte> buffer = stackalloc byte[16];
+        buffer.Clear();
+        value.TryWriteBytes(buffer, out _, isUnsigned: true, isBigEndian: false);
+        UInt128 converted = Unsafe.ReadUnaligned<UInt128>(ref buffer[0]);
+        return (GpuUInt128)converted;
+    }
 }