Document GPU kernel audit progress
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Marek Lemańczyk committed
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using System;
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using System.Runtime.CompilerServices;
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using ILGPU;
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using ILGPU.Runtime;
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using UInt128 = System.UInt128;
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namespace PerfectNumbers.Core.Gpu;
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internal static class LucasLehmerKernels
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{
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public static void AddSmallKernel(Index1D index, ulong add, ArrayView<GpuUInt128> value)
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{
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ulong carry = add;
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for (int i = 0; i < value.Length && carry != 0UL; i++)
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{
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var limb = value[i];
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ulong low = limb.Low + carry;
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ulong carryOut = low < carry ? 1UL : 0UL;
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ulong high = limb.High + carryOut;
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carry = high < limb.High ? 1UL : 0UL;
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value[i] = new GpuUInt128(high, low);
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}
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}
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public static void SubtractSmallKernel(Index1D index, ulong subtract, ArrayView<GpuUInt128> value)
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{
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ulong borrow = subtract;
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for (int i = 0; i < value.Length && borrow != 0UL; i++)
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{
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var limb = value[i];
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ulong low = limb.Low;
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ulong high = limb.High;
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if (low >= borrow)
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{
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low -= borrow;
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borrow = 0UL;
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}
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else
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{
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low = unchecked(low - borrow);
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borrow = 1UL;
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if (high != 0UL)
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{
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high--;
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borrow = 0UL;
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}
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else
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{
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high = ulong.MaxValue;
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}
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}
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value[i] = new GpuUInt128(high, low);
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}
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}
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public static void ReduceModMersenneKernel(Index1D index, ulong exponent, ArrayView<GpuUInt128> value)
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{
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int limbCount = (int)((exponent + 127UL) / 128UL);
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for (int i = limbCount; i < value.Length; i++)
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{
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var limb = value[i];
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if (limb.IsZero)
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{
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continue;
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}
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int target = i - limbCount;
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var sum = value[target];
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var original = sum;
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sum.Add(limb);
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value[target] = sum;
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value[i] = new GpuUInt128(0UL, 0UL);
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if (sum.CompareTo(original) < 0)
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{
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int j = target + 1;
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while (j < limbCount)
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{
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var next = value[j];
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var nextOriginal = next;
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next.Add(1UL);
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value[j] = next;
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if (next.CompareTo(nextOriginal) >= 0)
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{
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break;
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}
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j++;
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}
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}
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}
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int topBits = (int)exponent.Mod128();
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if (topBits == 0)
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{
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topBits = 128;
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}
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int topIndex = limbCount - 1;
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ulong topLowMask = topBits >= 64 ? ulong.MaxValue : (1UL << topBits) - 1UL;
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ulong topHighMask = topBits > 64 ? (1UL << (topBits - 64)) - 1UL : 0UL;
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var top = value[topIndex];
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var carryBits = top >> topBits;
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top = new(top.High & topHighMask, top.Low & topLowMask);
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value[topIndex] = top;
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if (!carryBits.IsZero)
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{
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int j = 0;
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while (j < limbCount && !carryBits.IsZero)
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{
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var cur = value[j];
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var curOriginal = cur;
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cur.Add(carryBits);
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value[j] = cur;
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carryBits = cur.CompareTo(curOriginal) < 0 ? new GpuUInt128(0UL, 1UL) : new GpuUInt128(0UL, 0UL);
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j++;
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}
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}
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bool geq = true;
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for (int i = topIndex; i >= 0; i--)
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{
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var limb = value[i];
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ulong modHigh = i == topIndex ? topHighMask : ulong.MaxValue;
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ulong modLow = i == topIndex ? topLowMask : ulong.MaxValue;
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if (limb.High > modHigh || (limb.High == modHigh && limb.Low > modLow))
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{
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geq = true;
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break;
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}
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if (limb.High < modHigh || (limb.High == modHigh && limb.Low < modLow))
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{
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geq = false;
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break;
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}
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}
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if (geq)
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{
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ulong borrow = 0UL;
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for (int i = 0; i < limbCount - 1; i++)
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{
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var limb = value[i];
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ulong newLow = limb.Low - ulong.MaxValue - borrow;
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borrow = limb.Low < ulong.MaxValue + borrow ? 1UL : 0UL;
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ulong newHigh = limb.High - ulong.MaxValue - borrow;
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borrow = limb.High < ulong.MaxValue + borrow ? 1UL : 0UL;
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value[i] = new GpuUInt128(newHigh, newLow);
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}
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var topLimb = value[topIndex];
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ulong newTopLow = topLimb.Low - topLowMask - borrow;
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borrow = topLimb.Low < topLowMask + borrow ? 1UL : 0UL;
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ulong newTopHigh = topLimb.High - topHighMask - borrow;
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value[topIndex] = new GpuUInt128(newTopHigh, newTopLow);
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}
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for (int i = limbCount; i < value.Length; i++)
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{
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value[i] = new GpuUInt128(0UL, 0UL);
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}
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}
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public static void IsZeroKernel(Index1D index, ArrayView<GpuUInt128> value, ArrayView<byte> result)
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{
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byte isZero = 1;
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for (int i = 0; i < value.Length; i++)
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{
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var limb = value[i];
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if (limb.High != 0UL || limb.Low != 0UL)
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{
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isZero = 0;
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break;
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}
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}
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result[0] = isZero;
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}
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private static void ReduceModMersenne(Span<GpuUInt128> value, ulong exponent)
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{
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int limbCount = (int)((exponent + 127UL) / 128UL);
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for (int i = limbCount; i < value.Length; i++)
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{
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var limb = value[i];
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if (limb.IsZero)
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{
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continue;
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}
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int target = i - limbCount;
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UInt128 original = value[target];
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UInt128 sum = original + (UInt128)limb;
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bool carry = sum < original;
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value[target] = new GpuUInt128(sum);
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value[i] = new GpuUInt128(0UL, 0UL);
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if (carry)
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{
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int j = target + 1;
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while (j < limbCount)
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{
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UInt128 next = value[j];
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UInt128 nextSum = next + 1UL;
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value[j] = new GpuUInt128(nextSum);
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if (nextSum != 0UL)
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{
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break;
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}
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j++;
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}
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}
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}
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int topBits = (int)exponent.Mod128();
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if (topBits == 0)
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{
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topBits = 128;
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}
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int topIndex = limbCount - 1;
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ulong topLowMask = topBits >= 64 ? ulong.MaxValue : (1UL << topBits) - 1UL;
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ulong topHighMask = topBits > 64 ? (1UL << (topBits - 64)) - 1UL : 0UL;
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UInt128 mask = ((UInt128)topHighMask << 64) | topLowMask;
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UInt128 top = value[topIndex];
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UInt128 carryBits = top >> topBits;
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top &= mask;
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value[topIndex] = new GpuUInt128(top);
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if (carryBits != 0UL)
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{
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int j = 0;
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UInt128 carry = carryBits;
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while (j < limbCount && carry != 0UL)
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{
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UInt128 cur = value[j];
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UInt128 sum = cur + carry;
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bool overflow = sum < cur;
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value[j] = new GpuUInt128(sum);
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carry = overflow ? 1UL : 0UL;
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j++;
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}
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}
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bool geq = true;
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for (int i = topIndex; i >= 0; i--)
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{
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UInt128 limb = value[i];
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UInt128 modLimb = i == topIndex ? mask : UInt128.MaxValue;
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if (limb > modLimb)
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{
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geq = true;
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break;
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}
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if (limb < modLimb)
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{
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geq = false;
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break;
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}
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}
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if (geq)
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{
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ulong borrow = 0UL;
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for (int i = 0; i < limbCount - 1; i++)
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{
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ulong low = value[i].Low;
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ulong high = value[i].High;
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ulong newLow = low - ulong.MaxValue - borrow;
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borrow = low < ulong.MaxValue + borrow ? 1UL : 0UL;
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ulong newHigh = high - ulong.MaxValue - borrow;
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borrow = high < ulong.MaxValue + borrow ? 1UL : 0UL;
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value[i] = new GpuUInt128(newHigh, newLow);
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}
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ulong topLow = value[topIndex].Low;
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ulong topHigh = value[topIndex].High;
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ulong newTopLow = topLow - topLowMask - borrow;
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borrow = topLow < topLowMask + borrow ? 1UL : 0UL;
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ulong newTopHigh = topHigh - topHighMask - borrow;
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value[topIndex] = new GpuUInt128(newTopHigh, newTopLow);
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}
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for (int i = limbCount; i < value.Length; i++)
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{
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value[i] = new GpuUInt128(0UL, 0UL);
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}
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}
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public static void KernelBatch(Index1D index, ArrayView<ulong> exponents, ArrayView<GpuUInt128> moduli, ArrayView<GpuUInt128> states)
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{
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int idx = index.X;
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ulong exponent = exponents[idx];
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GpuUInt128 modulus = moduli[idx];
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var s = new GpuUInt128(0UL, 4UL);
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ulong limit = exponent - 2UL;
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for (ulong i = 0UL; i < limit; i++)
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{
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s = SquareModMersenne128(s, exponent);
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s.SubMod(2UL, modulus);
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}
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states[idx] = s;
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}
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public static void Kernel(Index1D index, ulong exponent, GpuUInt128 modulus, ArrayView<GpuUInt128> state)
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{
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// Lucas–Lehmer iteration in the field GF(2^p-1).
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// For p < 128, use a Mersenne-specific squaring + reduction to avoid
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// the generic 128-bit long-division-like reduction.
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var s = new GpuUInt128(0UL, 4UL);
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ulong i = 0UL, limit = exponent - 2UL;
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if (exponent < 128UL)
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{
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for (; i < limit; i++)
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{
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s = SquareModMersenne128(s, exponent);
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s.SubMod(2UL, modulus);
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}
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}
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else
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{
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for (; i < limit; i++)
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{
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s.SquareMod(modulus);
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s.SubMod(2UL, modulus);
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}
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}
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state[0] = s;
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}
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// Squares a 128-bit value and reduces modulo M_p = 2^p - 1 using
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// Mersenne folding. Valid for 0 < p < 128 and input s in [0, M_p].
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private static GpuUInt128 SquareModMersenne128(GpuUInt128 s, ulong p)
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{
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// Full square: (H*2^64 + L)^2 = H^2*2^128 + 2HL*2^64 + L^2
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SquareFull128(s, out var q3, out var q2, out var q1, out var q0);
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// v = low128 + high128 (fold by 128 bits once)
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var vHigh = new GpuUInt128(q3, q2);
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var vLow = new GpuUInt128(q1, q0);
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vLow.Add(vHigh);
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// Mask to keep only p low bits and fold the carry bits (v >> p)
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int topBits = (int)p.Mod128();
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if (topBits == 0)
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{
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topBits = 128;
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}
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ulong maskLow = topBits >= 64 ? ulong.MaxValue : (1UL << topBits) - 1UL;
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ulong maskHigh = topBits > 64 ? (1UL << (topBits - 64)) - 1UL : 0UL;
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var carryBits = vLow >> topBits;
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vLow = new(vLow.High & maskHigh, vLow.Low & maskLow);
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// Propagate carryBits back into the masked value (single-limb fold)
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GpuUInt128 before;
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while (!carryBits.IsZero)
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{
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before = vLow;
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vLow.Add(carryBits);
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carryBits = vLow.CompareTo(before) < 0 ? GpuUInt128.One : GpuUInt128.Zero;
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}
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// Final correction if v >= modulus (mask)
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if (vLow.High > maskHigh || (vLow.High == maskHigh && vLow.Low >= maskLow))
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{
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ulong borrow = 0UL;
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ulong newLow = vLow.Low - maskLow;
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borrow = vLow.Low < maskLow ? 1UL : 0UL;
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ulong newHigh = vLow.High - maskHigh - borrow;
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vLow = new GpuUInt128(newHigh, newLow);
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}
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return vLow;
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}
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// Helper: 128-bit square -> 256-bit product as four 64-bit limbs (q3..q0)
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private static void SquareFull128(GpuUInt128 value, out ulong q3, out ulong q2, out ulong q1, out ulong q0)
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{
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ulong L = value.Low;
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ulong H = value.High;
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Mul64Parts(L, L, out var hLL, out var lLL); // L^2
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Mul64Parts(H, H, out var hHH, out var lHH); // H^2
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Mul64Parts(L, H, out var hLH, out var lLH); // L*H
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// double LH
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ulong dLH_low = lLH << 1;
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ulong carry = (lLH >> 63) & 1UL;
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ulong dLH_high = (hLH << 1) | carry;
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q0 = lLL;
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ulong sum1 = hLL + dLH_low;
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ulong c1 = sum1 < hLL ? 1UL : 0UL;
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q1 = sum1;
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ulong sum2 = lHH + dLH_high;
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ulong c2 = sum2 < lHH ? 1UL : 0UL;
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sum2 += c1;
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if (sum2 < c1)
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{
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c2++;
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}
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q2 = sum2;
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q3 = hHH + c2;
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}
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// 64x64 -> 128 multiply (high,low)
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[MethodImpl(System.Runtime.CompilerServices.MethodImplOptions.AggressiveInlining)]
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private static void Mul64Parts(ulong a, ulong b, out ulong high, out ulong low)
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{
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ulong a0 = (uint)a;
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ulong a1 = a >> 32;
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ulong b0 = (uint)b;
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ulong b1 = b >> 32;
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ulong lo = a0 * b0;
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ulong mid1 = a1 * b0;
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ulong mid2 = a0 * b1;
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ulong hi = a1 * b1;
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ulong carry = (lo >> 32) + (uint)mid1 + (uint)mid2;
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low = (lo & 0xFFFFFFFFUL) | (carry << 32);
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hi += (mid1 >> 32) + (mid2 >> 32) + (carry >> 32);
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high = hi;
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}
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[MethodImpl(System.Runtime.CompilerServices.MethodImplOptions.AggressiveInlining)]
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private static ulong ModPow64(ulong value, ulong exponent, ulong modulus)
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{
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ulong result = 1UL;
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ulong baseValue = value % modulus;
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ulong exp = exponent;
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while (exp != 0UL)
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{
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if ((exp & 1UL) != 0UL)
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{
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result = (ulong)(((UInt128)result * baseValue) % modulus);
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}
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baseValue = (ulong)(((UInt128)baseValue * baseValue) % modulus);
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exp >>= 1;
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}
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return result;
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}
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}
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