1481 lines
44 KiB
C#
1481 lines
44 KiB
C#
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using ILGPU;
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using ILGPU.Algorithms;
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using ILGPU.Runtime;
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using PerfectNumbers.Core;
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namespace PerfectNumbers.Core.Gpu.Kernels;
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internal static class BitContradictionKernels
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{
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public const int BatchCount = PerfectNumberConstants.BitContradictionGpuBatchCount;
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public const int ForcedALowBits = 1024;
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public const int ForcedALowWords = 16;
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public const int MaxQBitLength = 4096;
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public const int MaxQWordCount = MaxQBitLength / 64;
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public const int MaxQOffsets = 4096;
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public const int MaxAWordCount = MaxQBitLength / 64;
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private const int InverseIterations = 10;
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private const int HighBitCarryPrefilterColumns = 16;
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private const int TopDownBorrowColumns = 4096;
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private const int TopDownBorrowMinUnknown = 12;
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private const int TailCarryBatchColumns = 16384;
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private const int DeltaColumnsAtOnce = 8;
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private const int DeltaLength = 1 << DeltaColumnsAtOnce;
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private const int IntervalBufferLength = 64;
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private struct CarryRange
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{
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public long Min;
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public long Max;
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public CarryRange(long min, long max)
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{
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Min = min;
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Max = max;
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}
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public static CarryRange Zero => new(0, 0);
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}
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public static void BitContradictionKernelScan(
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Index1D index,
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ulong exponent,
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ArrayView1D<ulong, Stride1D.Dense> batchIndexWords,
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int countQ,
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ArrayView1D<int, Stride1D.Dense> foundOut)
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{
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int slot = index;
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foundOut[slot] = -1;
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if (countQ <= 0)
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{
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return;
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}
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int localCountQ = countQ;
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ulong twoP = exponent << 1;
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int startOffset = slot * MaxQWordCount;
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var baseKWords = LocalMemory.Allocate<ulong>(MaxQWordCount);
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var kWords = LocalMemory.Allocate<ulong>(MaxQWordCount);
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var qWords = LocalMemory.Allocate<ulong>(MaxQWordCount);
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var qOffsets = LocalMemory.Allocate<int>(MaxQOffsets);
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var qPrefix = LocalMemory.Allocate<ulong>(ForcedALowWords);
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var reversePrefix = LocalMemory.Allocate<ulong>(ForcedALowWords);
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var prefixMask = LocalMemory.Allocate<ulong>(ForcedALowWords);
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var invWords = LocalMemory.Allocate<ulong>(ForcedALowWords);
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var tmpWords = LocalMemory.Allocate<ulong>(ForcedALowWords);
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var tmpWords2 = LocalMemory.Allocate<ulong>(ForcedALowWords);
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var aLowWords = LocalMemory.Allocate<ulong>(ForcedALowWords);
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var delta8 = LocalMemory.Allocate<int>(DeltaLength);
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var knownOne0 = LocalMemory.Allocate<ulong>(MaxAWordCount);
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var knownOne1 = LocalMemory.Allocate<ulong>(MaxAWordCount);
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var knownZero0 = LocalMemory.Allocate<ulong>(MaxAWordCount);
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var knownZero1 = LocalMemory.Allocate<ulong>(MaxAWordCount);
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var qMaskWords = LocalMemory.Allocate<ulong>(MaxQWordCount);
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var aOneWin = LocalMemory.Allocate<ulong>(MaxQWordCount);
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var aZeroWin = LocalMemory.Allocate<ulong>(MaxQWordCount);
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var lo0 = LocalMemory.Allocate<long>(IntervalBufferLength);
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var hi0 = LocalMemory.Allocate<long>(IntervalBufferLength);
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var lo1 = LocalMemory.Allocate<long>(IntervalBufferLength);
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var hi1 = LocalMemory.Allocate<long>(IntervalBufferLength);
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for (int i = 0; i < MaxQWordCount; i++)
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{
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baseKWords[i] = batchIndexWords[startOffset + i];
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}
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if (MultiplyWordsByUInt64(baseKWords, kWords, MaxQWordCount, (ulong)BatchCount) != 0UL)
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{
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return;
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}
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if (AddUInt64ToWords(kWords, MaxQWordCount, 1UL) != 0UL)
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{
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return;
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}
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CopyWords(kWords, baseKWords, MaxQWordCount);
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for (int batch = 0; batch < localCountQ; batch++)
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{
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CopyWords(baseKWords, kWords, MaxQWordCount);
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if (batch != 0)
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{
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if (AddUInt64ToWords(kWords, MaxQWordCount, (ulong)batch) != 0UL)
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{
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break;
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}
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}
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if (MultiplyWordsByUInt64(kWords, qWords, MaxQWordCount, twoP) != 0UL)
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{
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continue;
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}
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if (AddUInt64ToWords(qWords, MaxQWordCount, 1UL) != 0UL)
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{
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continue;
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}
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int qBitLen = GetBitLength(qWords, MaxQWordCount);
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if (qBitLen <= 0 || qBitLen > MaxQBitLength)
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{
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continue;
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}
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if ((ulong)qBitLen >= exponent)
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{
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continue;
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}
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int pLong = (int)exponent;
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int maxAllowedA = pLong - qBitLen;
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if (maxAllowedA < 0)
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{
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continue;
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}
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int qWordCount = (qBitLen + 63) >> 6;
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int offsetCount;
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if (!BuildQOneOffsetsWords(qWords, qWordCount, qOffsets, out offsetCount))
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{
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continue;
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}
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if (offsetCount <= 0)
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{
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continue;
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}
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int windowSize = qBitLen < ForcedALowBits ? ForcedALowBits : qBitLen;
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windowSize = (windowSize + 63) & ~63;
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int aWordCount = (windowSize + 63) >> 6;
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ClearWords(knownOne0, aWordCount);
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ClearWords(knownOne1, aWordCount);
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ClearWords(knownZero0, aWordCount);
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ClearWords(knownZero1, aWordCount);
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ClearWords(qMaskWords, qWordCount);
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ClearWords(aOneWin, qWordCount);
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ClearWords(aZeroWin, qWordCount);
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ClearWords(qPrefix, ForcedALowWords);
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CopyWords(qWords, qPrefix, ForcedALowWords);
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CopyWords(qPrefix, invWords, ForcedALowWords);
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ComputeInverseMod2k(qPrefix, invWords, tmpWords, tmpWords2, ForcedALowWords);
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NegateMod2k(invWords, aLowWords, ForcedALowWords);
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for (int i = 0; i < qWordCount; i++)
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{
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qMaskWords[i] = qWords[i];
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}
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ulong lastWordMask = (qBitLen & 63) == 0 ? ulong.MaxValue : ((1UL << (qBitLen & 63)) - 1UL);
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if (qWordCount > 0)
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{
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qMaskWords[qWordCount - 1] &= lastWordMask;
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}
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int maxFixed = maxAllowedA < (ForcedALowBits - 1) ? maxAllowedA : (ForcedALowBits - 1);
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if (maxFixed >= 0)
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{
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int fullWords = maxFixed >> 6;
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int lastBit = maxFixed & 63;
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for (int w = 0; w < fullWords; w++)
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{
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ulong wordValue = aLowWords[w];
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knownOne0[w] = wordValue;
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knownZero0[w] = ~wordValue;
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}
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if (fullWords < aWordCount)
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{
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ulong wordValue = aLowWords[fullWords];
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ulong mask = lastBit == 63 ? ulong.MaxValue : ((1UL << (lastBit + 1)) - 1UL);
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knownOne0[fullWords] = wordValue & mask;
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knownZero0[fullWords] = (~wordValue) & mask;
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}
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}
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int maxKnownA = maxFixed >= 0 ? maxFixed : -1;
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int maxFixedPrefilter = 512 - 1;
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if (maxFixedPrefilter > maxKnownA)
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{
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maxFixedPrefilter = maxKnownA;
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}
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if (maxFixedPrefilter > maxAllowedA)
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{
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maxFixedPrefilter = maxAllowedA;
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}
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if (maxFixedPrefilter >= 8)
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{
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ReverseBits1024(qPrefix, reversePrefix);
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bool prefixOk = true;
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CarryRange carryLow = CarryRange.Zero;
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for (int column = 0; column <= maxFixedPrefilter; column++)
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{
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int forced = 0;
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if (column <= 1023)
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{
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int shift = 1023 - column;
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int wordShift = shift >> 6;
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int bitShift = shift & 63;
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for (int word = 0; word < ForcedALowWords; word++)
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{
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int src = word + wordShift;
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ulong value = 0UL;
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if (src < ForcedALowWords)
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{
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value = reversePrefix[src] >> bitShift;
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if (bitShift != 0 && src + 1 < ForcedALowWords)
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{
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value |= reversePrefix[src + 1] << (64 - bitShift);
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}
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}
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prefixMask[word] = value;
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}
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for (int word = 0; word < ForcedALowWords; word++)
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{
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forced += XMath.PopCount(knownOne0[word] & prefixMask[word]);
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}
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}
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else
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{
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for (int i = 0; i < offsetCount; i++)
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{
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int t = qOffsets[i];
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if (t > column)
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{
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break;
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}
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int aIndex = column - t;
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int word = aIndex >> 6;
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ulong mask = 1UL << (aIndex & 63);
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if ((knownOne0[word] & mask) != 0UL)
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{
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forced++;
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}
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}
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}
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if (!TryPropagateCarry(ref carryLow, forced, forced, 1))
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{
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prefixOk = false;
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break;
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}
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}
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if (!prefixOk)
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{
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continue;
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}
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}
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int segmentBase = 0;
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int windowColumn = 0;
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int initialState = GetAKnownStateRowAware(0, segmentBase, windowSize, knownOne0, knownZero0, knownOne1, knownZero1);
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if (initialState == 1)
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{
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aOneWin[0] |= 1UL;
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}
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else if (initialState == 2)
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{
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aZeroWin[0] |= 1UL;
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}
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if (!TryRunHighBitAndBorrowPrefiltersCombinedGpu(qOffsets, offsetCount, pLong, maxAllowedA, lo0, hi0, lo1, hi1))
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{
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continue;
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}
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BuildStableUnknownDelta8(offsetCount, delta8);
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CarryRange carry = CarryRange.Zero;
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bool ok = TryProcessBottomUpBlockRowAwareGpu(
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qOffsets,
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offsetCount,
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qMaskWords,
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qWordCount,
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lastWordMask,
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maxAllowedA,
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0,
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pLong,
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ref carry,
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ref maxKnownA,
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ref segmentBase,
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knownOne0,
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knownOne1,
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knownZero0,
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knownZero1,
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windowSize,
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aWordCount,
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aOneWin,
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aZeroWin,
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ref windowColumn,
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delta8,
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offsetCount);
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if (ok)
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{
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foundOut[slot] = batch;
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return;
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}
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}
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}
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internal static bool TryBuildQWordsFromBatchIndex(
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ulong exponent,
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ReadOnlySpan<ulong> batchIndexWords,
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int wordCount,
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int batchOffset,
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Span<ulong> qWords,
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out int qBitLen)
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{
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Span<ulong> baseKWords = stackalloc ulong[wordCount];
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Span<ulong> kWords = stackalloc ulong[wordCount];
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for (int i = 0; i < wordCount; i++)
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{
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baseKWords[i] = batchIndexWords[i];
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}
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if (MultiplyWordsByUInt64(baseKWords, kWords, wordCount, (ulong)BatchCount) != 0UL)
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{
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qBitLen = 0;
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return false;
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}
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if (AddUInt64ToWords(kWords, wordCount, 1UL) != 0UL)
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{
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qBitLen = 0;
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return false;
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}
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if (batchOffset != 0)
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{
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if (AddUInt64ToWords(kWords, wordCount, (ulong)batchOffset) != 0UL)
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{
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qBitLen = 0;
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return false;
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}
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}
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if (MultiplyWordsByUInt64(kWords, qWords, wordCount, exponent << 1) != 0UL)
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{
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qBitLen = 0;
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return false;
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}
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if (AddUInt64ToWords(qWords, wordCount, 1UL) != 0UL)
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{
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qBitLen = 0;
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return false;
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}
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qBitLen = GetBitLength(qWords, wordCount);
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return true;
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}
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private static ulong AddUInt64ToWords(Span<ulong> words, int wordCount, ulong value)
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{
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ulong carry = value;
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for (int i = 0; i < wordCount; i++)
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{
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if (carry == 0UL)
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{
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return 0UL;
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}
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ulong sum = words[i] + carry;
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words[i] = sum;
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carry = sum < carry ? 1UL : 0UL;
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}
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return carry;
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}
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private static ulong MultiplyWordsByUInt64(ReadOnlySpan<ulong> source, Span<ulong> destination, int wordCount, ulong factor)
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{
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ulong carry = 0UL;
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ulong carryExtra = 0UL;
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for (int i = 0; i < wordCount; i++)
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{
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ulong high;
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ulong low;
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MultiplyPartsGpu(source[i], factor, out high, out low);
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ulong sum = low + carry;
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ulong carryOut = sum < low ? 1UL : 0UL;
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if (carryExtra != 0UL)
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{
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sum += 1UL;
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if (sum == 0UL)
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{
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carryOut++;
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}
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}
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destination[i] = sum;
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ulong nextCarry = high + carryOut;
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carryExtra = nextCarry < high ? 1UL : 0UL;
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carry = nextCarry;
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}
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return carry + carryExtra;
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}
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private static int GetBitLength(ReadOnlySpan<ulong> words, int wordCount)
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{
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for (int i = wordCount - 1; i >= 0; i--)
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{
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ulong word = words[i];
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if (word != 0UL)
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{
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int leading = XMath.LeadingZeroCount(word);
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return (i << 6) + (64 - leading);
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}
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}
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return 0;
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}
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private static ulong AddUInt64ToWords(ArrayView<ulong> words, int wordCount, ulong value)
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{
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ulong carry = value;
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for (int i = 0; i < wordCount; i++)
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{
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if (carry == 0UL)
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{
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return 0UL;
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}
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ulong sum = words[i] + carry;
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words[i] = sum;
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carry = sum < carry ? 1UL : 0UL;
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}
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return carry;
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}
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private static ulong MultiplyWordsByUInt64(ArrayView<ulong> source, ArrayView<ulong> destination, int wordCount, ulong factor)
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{
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ulong carry = 0UL;
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ulong carryExtra = 0UL;
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for (int i = 0; i < wordCount; i++)
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{
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ulong high;
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ulong low;
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MultiplyPartsGpu(source[i], factor, out high, out low);
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ulong sum = low + carry;
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ulong carryOut = sum < low ? 1UL : 0UL;
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if (carryExtra != 0UL)
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{
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sum += 1UL;
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if (sum == 0UL)
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{
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carryOut++;
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}
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}
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destination[i] = sum;
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ulong nextCarry = high + carryOut;
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carryExtra = nextCarry < high ? 1UL : 0UL;
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carry = nextCarry;
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}
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return carry + carryExtra;
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}
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private static ulong ReverseBits64(ulong value)
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{
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value = ((value >> 1) & 0x5555555555555555UL) | ((value & 0x5555555555555555UL) << 1);
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value = ((value >> 2) & 0x3333333333333333UL) | ((value & 0x3333333333333333UL) << 2);
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value = ((value >> 4) & 0x0F0F0F0F0F0F0F0FUL) | ((value & 0x0F0F0F0F0F0F0F0FUL) << 4);
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value = ((value >> 8) & 0x00FF00FF00FF00FFUL) | ((value & 0x00FF00FF00FF00FFUL) << 8);
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value = ((value >> 16) & 0x0000FFFF0000FFFFUL) | ((value & 0x0000FFFF0000FFFFUL) << 16);
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value = (value >> 32) | (value << 32);
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return value;
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}
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private static void ReverseBits1024(ArrayView<ulong> prefix, ArrayView<ulong> reversed)
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{
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reversed[0] = ReverseBits64(prefix[15]);
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reversed[1] = ReverseBits64(prefix[14]);
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reversed[2] = ReverseBits64(prefix[13]);
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reversed[3] = ReverseBits64(prefix[12]);
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reversed[4] = ReverseBits64(prefix[11]);
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reversed[5] = ReverseBits64(prefix[10]);
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reversed[6] = ReverseBits64(prefix[9]);
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reversed[7] = ReverseBits64(prefix[8]);
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reversed[8] = ReverseBits64(prefix[7]);
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reversed[9] = ReverseBits64(prefix[6]);
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reversed[10] = ReverseBits64(prefix[5]);
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reversed[11] = ReverseBits64(prefix[4]);
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reversed[12] = ReverseBits64(prefix[3]);
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reversed[13] = ReverseBits64(prefix[2]);
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reversed[14] = ReverseBits64(prefix[1]);
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reversed[15] = ReverseBits64(prefix[0]);
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}
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private static void MultiplyPartsGpu(ulong left, ulong right, out ulong high, out ulong low)
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{
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ulong leftLow = (uint)left;
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ulong leftHigh = left >> 32;
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ulong rightLow = (uint)right;
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ulong rightHigh = right >> 32;
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ulong lowProduct = unchecked(leftLow * rightLow);
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ulong cross1 = unchecked(leftHigh * rightLow);
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ulong cross2 = unchecked(leftLow * rightHigh);
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|
ulong highProduct = unchecked(leftHigh * rightHigh);
|
|
|
|
ulong carry = unchecked((lowProduct >> 32) + (uint)cross1 + (uint)cross2);
|
|
low = unchecked((lowProduct & 0xFFFFFFFFUL) | (carry << 32));
|
|
high = unchecked(highProduct + (cross1 >> 32) + (cross2 >> 32) + (carry >> 32));
|
|
}
|
|
|
|
private static int GetBitLength(ArrayView<ulong> words, int wordCount)
|
|
{
|
|
for (int i = wordCount - 1; i >= 0; i--)
|
|
{
|
|
ulong word = words[i];
|
|
if (word != 0UL)
|
|
{
|
|
int leading = XMath.LeadingZeroCount(word);
|
|
return (i << 6) + (64 - leading);
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
private static bool BuildQOneOffsetsWords(
|
|
ArrayView<ulong> words,
|
|
int wordCount,
|
|
ArrayView<int> offsets,
|
|
out int offsetCount)
|
|
{
|
|
offsetCount = 0;
|
|
for (int wordIndex = 0; wordIndex < wordCount; wordIndex++)
|
|
{
|
|
ulong word = words[wordIndex];
|
|
while (word != 0UL)
|
|
{
|
|
int bit = XMath.TrailingZeroCount(word);
|
|
if (offsetCount >= MaxQOffsets)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
offsets[offsetCount] = (wordIndex << 6) + bit;
|
|
offsetCount++;
|
|
word &= word - 1UL;
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
private static void FindBounds(ArrayView<int> values, int valueCount, int lowerTarget, int upperTarget, out int lower, out int upper)
|
|
{
|
|
int lo = 0;
|
|
int hi = valueCount;
|
|
int mid;
|
|
while (lo < hi)
|
|
{
|
|
mid = lo + ((hi - lo) >> 1);
|
|
if (values[mid] < lowerTarget)
|
|
{
|
|
lo = mid + 1;
|
|
}
|
|
else
|
|
{
|
|
hi = mid;
|
|
}
|
|
}
|
|
|
|
lower = lo;
|
|
hi = valueCount;
|
|
while (lo < hi)
|
|
{
|
|
mid = lo + ((hi - lo) >> 1);
|
|
if (values[mid] <= upperTarget)
|
|
{
|
|
lo = mid + 1;
|
|
}
|
|
else
|
|
{
|
|
hi = mid;
|
|
}
|
|
}
|
|
|
|
upper = lo;
|
|
}
|
|
private static bool TryRunHighBitAndBorrowPrefiltersCombinedGpu(
|
|
ArrayView<int> qOffsets,
|
|
int qOffsetCount,
|
|
int pLong,
|
|
int maxAllowedA,
|
|
ArrayView<long> lo0,
|
|
ArrayView<long> hi0,
|
|
ArrayView<long> lo1,
|
|
ArrayView<long> hi1)
|
|
{
|
|
int column = pLong - 1;
|
|
int columnPlusOne = column + 1;
|
|
|
|
int highBitColumns = HighBitCarryPrefilterColumns;
|
|
if (highBitColumns > columnPlusOne)
|
|
{
|
|
highBitColumns = columnPlusOne;
|
|
}
|
|
|
|
int borrowColumns = 0;
|
|
bool runBorrowPrefilter = qOffsetCount >= TopDownBorrowMinUnknown;
|
|
if (runBorrowPrefilter)
|
|
{
|
|
borrowColumns = TopDownBorrowColumns;
|
|
if (borrowColumns > columnPlusOne)
|
|
{
|
|
borrowColumns = columnPlusOne;
|
|
}
|
|
}
|
|
|
|
int sequentialColumns = highBitColumns > borrowColumns ? highBitColumns : borrowColumns;
|
|
|
|
var outLo = lo0;
|
|
var outHi = hi0;
|
|
var inLo = lo1;
|
|
var inHi = hi1;
|
|
|
|
int outCount = 1;
|
|
outLo[0] = 0;
|
|
outHi[0] = 0;
|
|
|
|
int inCount = 0;
|
|
bool flip = false;
|
|
CarryRange borrow = CarryRange.Zero;
|
|
|
|
int step = 0;
|
|
int upperT;
|
|
int lowerT = column - maxAllowedA;
|
|
if (lowerT < 0)
|
|
{
|
|
lowerT = 0;
|
|
}
|
|
|
|
FindBounds(qOffsets, qOffsetCount, lowerT, column, out lowerT, out upperT);
|
|
int n = upperT - lowerT;
|
|
if (n < 0)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
if (runBorrowPrefilter && n < TopDownBorrowMinUnknown)
|
|
{
|
|
runBorrowPrefilter = false;
|
|
if (highBitColumns < sequentialColumns)
|
|
{
|
|
sequentialColumns = highBitColumns;
|
|
}
|
|
}
|
|
|
|
while (true)
|
|
{
|
|
if (step < highBitColumns)
|
|
{
|
|
inCount = 0;
|
|
for (int i = 0; i < outCount; i++)
|
|
{
|
|
long rMin = outLo[i];
|
|
long rMax = outHi[i];
|
|
|
|
if (rMax < 0) continue;
|
|
if (rMin < 0) rMin = 0;
|
|
if (rMax < rMin) continue;
|
|
|
|
const long TwicePlusOneOverflowLimit = (long.MaxValue - 1) >> 1;
|
|
if (rMin > TwicePlusOneOverflowLimit || rMax > TwicePlusOneOverflowLimit)
|
|
{
|
|
return true;
|
|
}
|
|
|
|
rMin = (rMin << 1) + 1;
|
|
rMax = (rMax << 1) + 1;
|
|
|
|
if (n <= 0)
|
|
{
|
|
AddInterval(ref inCount, inLo, inHi, rMin, rMax);
|
|
if (inCount == 0) return true;
|
|
continue;
|
|
}
|
|
|
|
if (n == 1)
|
|
{
|
|
AddInterval(ref inCount, inLo, inHi, rMin - 1, rMax);
|
|
if (inCount == 0) return true;
|
|
continue;
|
|
}
|
|
|
|
if (rMax <= n)
|
|
{
|
|
AddInterval(ref inCount, inLo, inHi, 0, rMax);
|
|
if (inCount == 0) return true;
|
|
}
|
|
else if (rMin > n)
|
|
{
|
|
AddInterval(ref inCount, inLo, inHi, rMin - n, rMax);
|
|
if (inCount == 0) return true;
|
|
}
|
|
else
|
|
{
|
|
AddInterval(ref inCount, inLo, inHi, 0, rMax);
|
|
if (inCount == 0) return true;
|
|
}
|
|
}
|
|
|
|
if (inCount <= 0)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
outCount = inCount;
|
|
flip = !flip;
|
|
if (!flip)
|
|
{
|
|
outLo = lo0; outHi = hi0;
|
|
inLo = lo1; inHi = hi1;
|
|
}
|
|
else
|
|
{
|
|
outLo = lo1; outHi = hi1;
|
|
inLo = lo0; inHi = hi0;
|
|
}
|
|
}
|
|
|
|
if (runBorrowPrefilter && step < borrowColumns)
|
|
{
|
|
if (!TryPropagateCarry(ref borrow, 0, n, 1))
|
|
{
|
|
return false;
|
|
}
|
|
}
|
|
|
|
step++;
|
|
column--;
|
|
if (step >= sequentialColumns || column < 0)
|
|
{
|
|
break;
|
|
}
|
|
|
|
lowerT = column - maxAllowedA;
|
|
if (lowerT < 0)
|
|
{
|
|
lowerT = 0;
|
|
}
|
|
|
|
FindBounds(qOffsets, qOffsetCount, lowerT, column, out lowerT, out upperT);
|
|
n = upperT - lowerT;
|
|
if (n < 0)
|
|
{
|
|
return false;
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
private static void AddInterval(ref int count, ArrayView<long> loArr, ArrayView<long> hiArr, long lo, long hi)
|
|
{
|
|
if (hi < lo)
|
|
{
|
|
return;
|
|
}
|
|
|
|
if (lo < 0) lo = 0;
|
|
if (hi < 0) return;
|
|
|
|
if (count == 0)
|
|
{
|
|
loArr[0] = lo;
|
|
hiArr[0] = hi;
|
|
count = 1;
|
|
return;
|
|
}
|
|
|
|
long lastHi = hiArr[count - 1];
|
|
if (lo <= lastHi + 1)
|
|
{
|
|
if (hi > lastHi)
|
|
{
|
|
hiArr[count - 1] = hi;
|
|
}
|
|
|
|
return;
|
|
}
|
|
|
|
if (count >= IntervalBufferLength)
|
|
{
|
|
count = 0;
|
|
return;
|
|
}
|
|
|
|
loArr[count] = lo;
|
|
hiArr[count] = hi;
|
|
count++;
|
|
}
|
|
private static void CopyWords(ArrayView<ulong> source, ArrayView<ulong> destination, int wordCount)
|
|
{
|
|
for (int i = 0; i < wordCount; i++)
|
|
{
|
|
destination[i] = source[i];
|
|
}
|
|
}
|
|
|
|
private static void ClearWords(ArrayView<ulong> words, int wordCount)
|
|
{
|
|
for (int i = 0; i < wordCount; i++)
|
|
{
|
|
words[i] = 0UL;
|
|
}
|
|
}
|
|
|
|
private static void MulMod2k(ArrayView<ulong> left, ArrayView<ulong> right, ArrayView<ulong> result, int wordCount)
|
|
{
|
|
ClearWords(result, wordCount);
|
|
|
|
for (int i = 0; i < wordCount; i++)
|
|
{
|
|
ulong carry = 0UL;
|
|
ulong carryExtra = 0UL;
|
|
ulong leftValue = left[i];
|
|
int maxJ = wordCount - i;
|
|
for (int j = 0; j < maxJ; j++)
|
|
{
|
|
int target = i + j;
|
|
ulong high;
|
|
ulong low;
|
|
MultiplyPartsGpu(leftValue, right[j], out high, out low);
|
|
|
|
ulong sum = result[target] + low;
|
|
ulong carryOut = sum < low ? 1UL : 0UL;
|
|
sum += carry;
|
|
if (sum < carry)
|
|
{
|
|
carryOut++;
|
|
}
|
|
if (carryExtra != 0UL)
|
|
{
|
|
sum += 1UL;
|
|
if (sum == 0UL)
|
|
{
|
|
carryOut++;
|
|
}
|
|
}
|
|
|
|
result[target] = sum;
|
|
ulong nextCarry = high + carryOut;
|
|
carryExtra = nextCarry < high ? 1UL : 0UL;
|
|
carry = nextCarry;
|
|
}
|
|
}
|
|
}
|
|
|
|
private static void ComputeInverseMod2k(
|
|
ArrayView<ulong> modulus,
|
|
ArrayView<ulong> inverse,
|
|
ArrayView<ulong> tmp,
|
|
ArrayView<ulong> tmp2,
|
|
int wordCount)
|
|
{
|
|
CopyWords(modulus, inverse, wordCount);
|
|
|
|
for (int i = 0; i < InverseIterations; i++)
|
|
{
|
|
MulMod2k(modulus, inverse, tmp, wordCount);
|
|
SubtractFromTwo(tmp, tmp2, wordCount);
|
|
MulMod2k(inverse, tmp2, tmp, wordCount);
|
|
CopyWords(tmp, inverse, wordCount);
|
|
}
|
|
}
|
|
|
|
private static void SubtractFromTwo(ArrayView<ulong> value, ArrayView<ulong> result, int wordCount)
|
|
{
|
|
ulong borrow = 0UL;
|
|
for (int i = 0; i < wordCount; i++)
|
|
{
|
|
ulong minuend = i == 0 ? 2UL : 0UL;
|
|
ulong sub = value[i];
|
|
ulong res;
|
|
if (borrow == 0UL)
|
|
{
|
|
res = minuend - sub;
|
|
borrow = minuend < sub ? 1UL : 0UL;
|
|
}
|
|
else
|
|
{
|
|
res = minuend - sub - 1UL;
|
|
borrow = minuend <= sub ? 1UL : 0UL;
|
|
}
|
|
|
|
result[i] = res;
|
|
}
|
|
}
|
|
|
|
private static void NegateMod2k(ArrayView<ulong> value, ArrayView<ulong> result, int wordCount)
|
|
{
|
|
ulong carry = 1UL;
|
|
for (int i = 0; i < wordCount; i++)
|
|
{
|
|
ulong inverted = ~value[i];
|
|
ulong sum = inverted + carry;
|
|
result[i] = sum;
|
|
carry = sum < inverted ? 1UL : 0UL;
|
|
}
|
|
}
|
|
private static void BuildStableUnknownDelta8(int unknown, ArrayView<int> delta)
|
|
{
|
|
for (int low = 0; low < DeltaLength; low++)
|
|
{
|
|
long value = low;
|
|
for (int i = 0; i < DeltaColumnsAtOnce; i++)
|
|
{
|
|
int sMax = (((unknown ^ (int)value) & 1) != 0) ? unknown : (unknown - 1);
|
|
value = (value + sMax - 1) >> 1;
|
|
}
|
|
|
|
delta[low] = (int)((value << DeltaColumnsAtOnce) - low);
|
|
}
|
|
}
|
|
|
|
private static bool TryAdvanceZeroColumns(ref CarryRange carry, int columnCount)
|
|
{
|
|
const int Step = 30;
|
|
long carryMin = carry.Min;
|
|
long carryMax = carry.Max;
|
|
int add;
|
|
while (columnCount >= Step)
|
|
{
|
|
add = (1 << Step) - 1;
|
|
carryMin = (carryMin + add) >> Step;
|
|
carryMax >>= Step;
|
|
if (carryMin > carryMax)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
columnCount -= Step;
|
|
}
|
|
|
|
if (columnCount > 0)
|
|
{
|
|
add = (1 << columnCount) - 1;
|
|
carryMin = (carryMin + add) >> columnCount;
|
|
carryMax >>= columnCount;
|
|
if (carryMin > carryMax)
|
|
{
|
|
return false;
|
|
}
|
|
}
|
|
|
|
carry = new CarryRange(carryMin, carryMax);
|
|
return true;
|
|
}
|
|
|
|
private static bool TryAdvanceStableUnknownGpu(ref CarryRange carry, int unknown, int columnCount, ArrayView<int> delta)
|
|
{
|
|
if (columnCount <= 0)
|
|
{
|
|
return true;
|
|
}
|
|
|
|
if (unknown <= 0)
|
|
{
|
|
return TryAdvanceZeroColumns(ref carry, columnCount);
|
|
}
|
|
|
|
long carryMin = columnCount >= 63 ? 0 : (carry.Min >> columnCount);
|
|
long carryMax = carry.Max;
|
|
int remaining = columnCount;
|
|
|
|
while (remaining > 0)
|
|
{
|
|
int sMax = (((unknown ^ (int)carryMax) & 1) != 0) ? unknown : unknown - 1;
|
|
carryMax = (carryMax + sMax - 1) >> 1;
|
|
remaining--;
|
|
}
|
|
|
|
if (carryMax < carryMin)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
carry = new CarryRange(carryMin, carryMax);
|
|
return true;
|
|
}
|
|
|
|
private static bool TryPropagateCarry(ref CarryRange carry, int min, int max, int requiredParity)
|
|
{
|
|
long minSum = carry.Min + min;
|
|
long maxSum = carry.Max + max;
|
|
|
|
long alignedMin = AlignUpToParity(minSum, requiredParity);
|
|
long alignedMax = AlignDownToParity(maxSum, requiredParity);
|
|
if (alignedMin > alignedMax)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
carry.Min = (alignedMin - requiredParity) >> 1;
|
|
carry.Max = (alignedMax - requiredParity) >> 1;
|
|
return true;
|
|
}
|
|
|
|
private static long AlignUpToParity(long value, int parity) => (value & 1L) == parity ? value : value + 1L;
|
|
|
|
private static long AlignDownToParity(long value, int parity) => (value & 1L) == parity ? value : value - 1L;
|
|
private static void GetQPrefixMask(int startColumn, int qBitLen, int qWordCount, out int words, out ulong lastMask)
|
|
{
|
|
if (startColumn >= qBitLen - 1)
|
|
{
|
|
words = qWordCount;
|
|
lastMask = ulong.MaxValue;
|
|
return;
|
|
}
|
|
|
|
if (startColumn < 0)
|
|
{
|
|
words = 0;
|
|
lastMask = 0;
|
|
return;
|
|
}
|
|
|
|
int wordIndex = startColumn >> 6;
|
|
words = wordIndex + 1;
|
|
|
|
int bit = startColumn & 63;
|
|
lastMask = bit == 63 ? ulong.MaxValue : ((1UL << (bit + 1)) - 1UL);
|
|
}
|
|
|
|
private static int GetAKnownStateRowAware(
|
|
int aIndex,
|
|
int segmentBase,
|
|
int windowSize,
|
|
ArrayView<ulong> knownOne0,
|
|
ArrayView<ulong> knownZero0,
|
|
ArrayView<ulong> knownOne1,
|
|
ArrayView<ulong> knownZero1)
|
|
{
|
|
if (aIndex < 0)
|
|
{
|
|
return 2;
|
|
}
|
|
|
|
int rel;
|
|
int word;
|
|
ulong mask;
|
|
if (aIndex >= segmentBase && aIndex < segmentBase + windowSize)
|
|
{
|
|
rel = aIndex - segmentBase;
|
|
word = rel >> 6;
|
|
mask = 1UL << (rel & 63);
|
|
if ((knownOne0[word] & mask) != 0UL) return 1;
|
|
if ((knownZero0[word] & mask) != 0UL) return 2;
|
|
return 0;
|
|
}
|
|
|
|
int segment1Start = segmentBase - windowSize;
|
|
if (aIndex >= segment1Start && aIndex < segmentBase)
|
|
{
|
|
rel = aIndex - segment1Start;
|
|
word = rel >> 6;
|
|
mask = 1UL << (rel & 63);
|
|
if ((knownOne1[word] & mask) != 0UL) return 1;
|
|
if ((knownZero1[word] & mask) != 0UL) return 2;
|
|
return 0;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
private static void SetAKnownRowAware(
|
|
int aIndex,
|
|
bool isOne,
|
|
int segmentBase,
|
|
int windowSize,
|
|
ArrayView<ulong> knownOne0,
|
|
ArrayView<ulong> knownZero0,
|
|
ArrayView<ulong> knownOne1,
|
|
ArrayView<ulong> knownZero1)
|
|
{
|
|
if (aIndex < 0)
|
|
{
|
|
return;
|
|
}
|
|
|
|
int rel;
|
|
int word;
|
|
ulong mask;
|
|
if (aIndex >= segmentBase && aIndex < segmentBase + windowSize)
|
|
{
|
|
rel = aIndex - segmentBase;
|
|
word = rel >> 6;
|
|
mask = 1UL << (rel & 63);
|
|
if (isOne)
|
|
{
|
|
knownOne0[word] |= mask;
|
|
knownZero0[word] &= ~mask;
|
|
}
|
|
else
|
|
{
|
|
knownZero0[word] |= mask;
|
|
knownOne0[word] &= ~mask;
|
|
}
|
|
|
|
return;
|
|
}
|
|
|
|
int segment1Start = segmentBase - windowSize;
|
|
if (aIndex >= segment1Start && aIndex < segmentBase)
|
|
{
|
|
rel = aIndex - segment1Start;
|
|
word = rel >> 6;
|
|
mask = 1UL << (rel & 63);
|
|
if (isOne)
|
|
{
|
|
knownOne1[word] |= mask;
|
|
knownZero1[word] &= ~mask;
|
|
}
|
|
else
|
|
{
|
|
knownZero1[word] |= mask;
|
|
knownOne1[word] &= ~mask;
|
|
}
|
|
}
|
|
}
|
|
|
|
private static void ShiftLeft1InPlace(ArrayView<ulong> wordsOne, ArrayView<ulong> wordsZero, int wordCount, ulong lastWordMask)
|
|
{
|
|
ulong carryOne = 0UL;
|
|
ulong carryZero = 0UL;
|
|
|
|
for (int i = 0; i < wordCount; i++)
|
|
{
|
|
ulong word = wordsOne[i];
|
|
ulong newCarry = word >> 63;
|
|
wordsOne[i] = (word << 1) | carryOne;
|
|
carryOne = newCarry;
|
|
|
|
word = wordsZero[i];
|
|
newCarry = word >> 63;
|
|
wordsZero[i] = (word << 1) | carryZero;
|
|
carryZero = newCarry;
|
|
}
|
|
|
|
if (wordCount > 0)
|
|
{
|
|
int last = wordCount - 1;
|
|
wordsOne[last] &= lastWordMask;
|
|
wordsZero[last] &= lastWordMask;
|
|
}
|
|
}
|
|
|
|
private static void ComputeForcedRemainingAndCleanPrefix(
|
|
ArrayView<ulong> qMask,
|
|
ArrayView<ulong> oneWin,
|
|
ArrayView<ulong> zeroWin,
|
|
int wordCount,
|
|
ulong lastMask,
|
|
out int forced,
|
|
out int remaining)
|
|
{
|
|
forced = 0;
|
|
remaining = 0;
|
|
|
|
int lastIndex = wordCount - 1;
|
|
for (int i = 0; i < wordCount; i++)
|
|
{
|
|
ulong q = qMask[i];
|
|
if (i == lastIndex)
|
|
{
|
|
q &= lastMask;
|
|
}
|
|
|
|
ulong one = oneWin[i] & q;
|
|
ulong known = (oneWin[i] | zeroWin[i]);
|
|
ulong unknown = q & ~known;
|
|
|
|
forced += XMath.PopCount(one);
|
|
remaining += XMath.PopCount(unknown);
|
|
}
|
|
}
|
|
|
|
private static bool TryFindSingleUnknownInQPrefix(
|
|
ArrayView<ulong> qMask,
|
|
ArrayView<ulong> oneWin,
|
|
ArrayView<ulong> zeroWin,
|
|
int wordCount,
|
|
ulong lastMask,
|
|
out int offset)
|
|
{
|
|
offset = -1;
|
|
int found = 0;
|
|
int lastIndex = wordCount - 1;
|
|
for (int w = 0; w < wordCount; w++)
|
|
{
|
|
ulong q = qMask[w];
|
|
if (w == lastIndex)
|
|
{
|
|
q &= lastMask;
|
|
}
|
|
|
|
ulong known = oneWin[w] | zeroWin[w];
|
|
ulong unknown = q & ~known;
|
|
if (unknown == 0UL)
|
|
{
|
|
continue;
|
|
}
|
|
|
|
found += XMath.PopCount(unknown);
|
|
if (found > 1)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
int bit = XMath.TrailingZeroCount(unknown);
|
|
offset = (w << 6) + bit;
|
|
}
|
|
|
|
return found == 1;
|
|
}
|
|
private static bool TryProcessBottomUpBlockRowAwareGpu(
|
|
ArrayView<int> qOffsets,
|
|
int qOffsetCount,
|
|
ArrayView<ulong> qMaskWords,
|
|
int qWordCount,
|
|
ulong lastWordMask,
|
|
int maxAllowedA,
|
|
int startColumn,
|
|
int columnCount,
|
|
ref CarryRange carry,
|
|
ref int maxKnownA,
|
|
ref int segmentBase,
|
|
ArrayView<ulong> knownOne0,
|
|
ArrayView<ulong> knownOne1,
|
|
ArrayView<ulong> knownZero0,
|
|
ArrayView<ulong> knownZero1,
|
|
int windowSize,
|
|
int wordCount,
|
|
ArrayView<ulong> aOneWin,
|
|
ArrayView<ulong> aZeroWin,
|
|
ref int windowColumn,
|
|
ArrayView<int> stableUnknownDelta,
|
|
int stableUnknown)
|
|
{
|
|
bool needRebuildWindow = false;
|
|
int endColumn = startColumn + columnCount;
|
|
int endColumnMinusOne = endColumn - 1;
|
|
int maxOffset = qOffsets[qOffsetCount - 1];
|
|
int maxOffsetPlusOne = maxOffset + 1;
|
|
|
|
if (windowColumn != startColumn)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
int qWordCountMinusOne = qWordCount - 1;
|
|
|
|
while (startColumn < endColumn)
|
|
{
|
|
int bound = (startColumn / windowSize) * windowSize;
|
|
if (bound != segmentBase)
|
|
{
|
|
if (bound == segmentBase + windowSize)
|
|
{
|
|
var temp = knownOne0;
|
|
knownOne0 = knownOne1;
|
|
knownOne1 = temp;
|
|
temp = knownZero0;
|
|
knownZero0 = knownZero1;
|
|
knownZero1 = temp;
|
|
ClearWords(knownOne0, wordCount);
|
|
ClearWords(knownZero0, wordCount);
|
|
}
|
|
else
|
|
{
|
|
ClearWords(knownOne0, wordCount);
|
|
ClearWords(knownOne1, wordCount);
|
|
ClearWords(knownZero0, wordCount);
|
|
ClearWords(knownZero1, wordCount);
|
|
needRebuildWindow = true;
|
|
}
|
|
|
|
segmentBase = bound;
|
|
if (needRebuildWindow)
|
|
{
|
|
ClearWords(aOneWin, qWordCount);
|
|
ClearWords(aZeroWin, qWordCount);
|
|
|
|
for (int step = 0; step <= maxOffset; step++)
|
|
{
|
|
int aIndex = startColumn - step;
|
|
int state = aIndex < 0 || aIndex > maxAllowedA
|
|
? 2
|
|
: GetAKnownStateRowAware(aIndex, segmentBase, windowSize, knownOne0, knownZero0, knownOne1, knownZero1);
|
|
|
|
if (state == 1)
|
|
{
|
|
aOneWin[step >> 6] |= 1UL << (step & 63);
|
|
}
|
|
else if (state == 2)
|
|
{
|
|
aZeroWin[step >> 6] |= 1UL << (step & 63);
|
|
}
|
|
}
|
|
|
|
if (qWordCount > 0)
|
|
{
|
|
aOneWin[qWordCountMinusOne] &= lastWordMask;
|
|
aZeroWin[qWordCountMinusOne] &= lastWordMask;
|
|
}
|
|
|
|
needRebuildWindow = false;
|
|
}
|
|
}
|
|
|
|
int qWordsEff = qWordCount;
|
|
ulong qLastEff = lastWordMask;
|
|
if (startColumn < maxOffset)
|
|
{
|
|
GetQPrefixMask(startColumn, maxOffsetPlusOne, qWordCount, out qWordsEff, out qLastEff);
|
|
}
|
|
|
|
if (startColumn >= maxOffset && startColumn <= maxAllowedA)
|
|
{
|
|
int remaining = endColumnMinusOne;
|
|
if (remaining > maxAllowedA)
|
|
{
|
|
remaining = maxAllowedA;
|
|
}
|
|
|
|
remaining = remaining - startColumn + 1;
|
|
if (remaining > 0)
|
|
{
|
|
while (remaining >= TailCarryBatchColumns)
|
|
{
|
|
if (!TryAdvanceStableUnknownGpu(ref carry, stableUnknown, TailCarryBatchColumns, stableUnknownDelta))
|
|
{
|
|
return false;
|
|
}
|
|
|
|
startColumn += TailCarryBatchColumns;
|
|
windowColumn = startColumn;
|
|
remaining -= TailCarryBatchColumns;
|
|
}
|
|
|
|
if (remaining > 0)
|
|
{
|
|
if (!TryAdvanceStableUnknownGpu(ref carry, stableUnknown, remaining, stableUnknownDelta))
|
|
{
|
|
return false;
|
|
}
|
|
|
|
startColumn += remaining;
|
|
windowColumn = startColumn;
|
|
}
|
|
|
|
ClearWords(aOneWin, qWordCount);
|
|
ClearWords(aZeroWin, qWordCount);
|
|
continue;
|
|
}
|
|
}
|
|
|
|
ComputeForcedRemainingAndCleanPrefix(qMaskWords, aOneWin, aZeroWin, qWordsEff, qLastEff, out int forced, out int remainingCols);
|
|
|
|
if (remainingCols == 1 && ((carry.Min ^ carry.Max) & 1L) == 0)
|
|
{
|
|
int step;
|
|
if (TryFindSingleUnknownInQPrefix(qMaskWords, aOneWin, aZeroWin, qWordsEff, qLastEff, out step))
|
|
{
|
|
int aIndex = startColumn - step;
|
|
const int requiredBit = 1;
|
|
int parity = (int)(carry.Min & 1L);
|
|
int needOne = (requiredBit ^ parity ^ (forced & 1)) & 1;
|
|
|
|
int state = GetAKnownStateRowAware(aIndex, segmentBase, windowSize, knownOne0, knownZero0, knownOne1, knownZero1);
|
|
if (needOne != 0)
|
|
{
|
|
if (state == 2)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
SetAKnownRowAware(aIndex, true, segmentBase, windowSize, knownOne0, knownZero0, knownOne1, knownZero1);
|
|
int w = step >> 6;
|
|
int b = step & 63;
|
|
aOneWin[w] |= 1UL << b;
|
|
forced++;
|
|
}
|
|
else
|
|
{
|
|
if (state == 1)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
SetAKnownRowAware(aIndex, false, segmentBase, windowSize, knownOne0, knownZero0, knownOne1, knownZero1);
|
|
int w = step >> 6;
|
|
int b = step & 63;
|
|
aZeroWin[w] |= 1UL << b;
|
|
}
|
|
|
|
remainingCols = 0;
|
|
if (aIndex > maxKnownA)
|
|
{
|
|
maxKnownA = aIndex;
|
|
}
|
|
}
|
|
}
|
|
|
|
int max = forced + remainingCols;
|
|
if (!TryPropagateCarry(ref carry, forced, max, 1))
|
|
{
|
|
return false;
|
|
}
|
|
|
|
int nextA = startColumn + 1;
|
|
ShiftLeft1InPlace(aOneWin, aZeroWin, qWordCount, lastWordMask);
|
|
|
|
int nextState = nextA > maxAllowedA
|
|
? 2
|
|
: GetAKnownStateRowAware(nextA, segmentBase, windowSize, knownOne0, knownZero0, knownOne1, knownZero1);
|
|
|
|
if (nextState == 1)
|
|
{
|
|
aOneWin[0] |= 1UL;
|
|
}
|
|
else if (nextState == 2)
|
|
{
|
|
aZeroWin[0] |= 1UL;
|
|
}
|
|
|
|
startColumn++;
|
|
windowColumn = startColumn;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
}
|