Document GPU kernel audit progress

PerfectNumbers.Core/Gpu/Kernels/OrderKernels.cs

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+using ILGPU;
+using ILGPU.Runtime;
+
+namespace PerfectNumbers.Core.Gpu;
+
+internal static class OrderKernels
+{
+    public static void OrderKernelScan(
+        Index1D index,
+        ulong exponent,
+        ulong divMul,
+        ArrayView<GpuUInt128> qs,
+        ArrayView<ulong> orders)
+    {
+        GpuUInt128 q = qs[index];
+        ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
+        GpuUInt128 phi = q - GpuUInt128.One;
+        if (phi.High != 0UL)
+        {
+            orders[index] = 0UL;
+            return;
+        }
+
+        ulong phi64 = phi.Low;
+        // TODO: Once the ProcessEightBitWindows helper is available, switch this order kernel to that faster
+        // Pow2Mod variant so cycle checks inherit the same gains observed in GpuPow2ModBenchmarks.
+        GpuUInt128 pow = GpuUInt128.Pow2Mod(phi64, in readOnlyQ);
+        if (pow != GpuUInt128.One)
+        {
+            orders[index] = 0UL;
+            return;
+        }
+
+        GpuUInt128 halfPow = GpuUInt128.Pow2Mod(phi64 >> 1, in readOnlyQ) - GpuUInt128.One;
+        if (GpuUInt128.BinaryGcd(halfPow, q) != GpuUInt128.One)
+        {
+            orders[index] = 0UL;
+            return;
+        }
+
+        ulong div = KernelMathHelpers.FastDiv64Gpu(phi64, exponent, divMul);
+        GpuUInt128 divPow = GpuUInt128.Pow2Mod(div, in readOnlyQ) - GpuUInt128.One;
+        if (GpuUInt128.BinaryGcd(divPow, q) != GpuUInt128.One)
+        {
+            orders[index] = 0UL;
+            return;
+        }
+
+        orders[index] = exponent;
+    }
+}