Document GPU kernel audit progress

PerfectNumbers.Core/Gpu/Kernels/KernelMathHelpers.cs

@@ -0,0 +1,69 @@
+using System.Runtime.CompilerServices;
+
+namespace PerfectNumbers.Core.Gpu;
+
+internal static class KernelMathHelpers
+{
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public static ulong FastDiv64Gpu(ulong value, ulong divisor, ulong mul)
+    {
+        ulong quotient = GpuUInt128.MulHigh(value, mul);
+        GpuUInt128 remainder = new(0UL, value);
+        GpuUInt128 product = new(GpuUInt128.MulHigh(quotient, divisor), quotient * divisor);
+        remainder.Sub(product);
+
+        if (remainder.High != 0UL || remainder.Low >= divisor)
+        {
+            quotient++;
+        }
+
+        return quotient;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public static ulong Mod128By64(GpuUInt128 value, ulong modulus)
+    {
+        ulong rem = 0UL;
+        ulong part = value.High;
+        for (int i = 0; i < 64; i++)
+        {
+            rem = (rem << 1) | (part >> 63);
+            if (rem >= modulus)
+            {
+                rem -= modulus;
+            }
+            part <<= 1;
+        }
+
+        part = value.Low;
+        for (int i = 0; i < 64; i++)
+        {
+            rem = (rem << 1) | (part >> 63);
+            if (rem >= modulus)
+            {
+                rem -= modulus;
+            }
+            part <<= 1;
+        }
+
+        return rem;
+    }
+
+    public static ulong CalculateCycleLengthSmall(ulong divisor)
+    {
+        if ((divisor & (divisor - 1UL)) == 0UL)
+            return 1UL;
+
+        ulong order = 1UL, pow = 2UL;
+        while (pow != 1UL)
+        {
+            pow <<= 1;
+            if (pow > divisor)
+                pow -= divisor;
+
+            order++;
+        }
+
+        return order;
+    }
+}