private PermutationNetwork CreateBorderSorter(int borderBitLength, int intraBlockSortQuality)
{
PermutationNetwork pn = new PermutationNetwork(1 << (borderBitLength + 1));
int borderSize = 1 << borderBitLength;
int listCount = (1 << (intraBlockSortQuality + 1));
int listSize = borderSize / listCount;
pn.AppendGate(PermutationGateFactory.CreateUnshuffleGate(borderSize, listCount), 0);
pn.AppendGate(PermutationGateFactory.CreateUnshuffleGate(borderSize, listCount), borderSize);
// merge the corresponding lists
for (int i = 0; i < listCount; i++)
{
int[] wires = new int[listSize * 2];
for (int j = 0; i < listSize; i++)
{
wires[j] = i * listSize + j;
wires[j + listSize] = wires[j] + borderSize;
}
pn.AppendNetwork(SortingNetworkFactory.CreateBitonicMerge(listSize * 2, false), wires);
}
// shuffle the lists back into the blocks
pn.AppendGate(PermutationGateFactory.CreateShuffleGate(borderSize, listCount), 0);
pn.AppendGate(PermutationGateFactory.CreateShuffleGate(borderSize, listCount), borderSize);
return(pn);
}
// Lemma 4.1
private PermutationNetwork CreateBlockCorrectionNetwork(int blockBitLength, int unsortedness)
{
PermutationNetwork pn = new PermutationNetwork(1 << blockBitLength);
SortedSet <int> ySet = new SortedSet <int>(CalculationCache.generateY(blockBitLength));
Debug.Assert(ySet.Count <= 1 << unsortedness);
// augment Y with arbitrary elements
int ySize = 1 << (unsortedness + 1);
int blockSize = 1 << blockBitLength;
Random rand = new Random(0);
while (ySet.Count < ySize)
{
ySet.Add(rand.Next(blockSize));
}
// here our implementation differs from the paper. The paper first to extract Y then order the X by the permutation pi.
// Instead, we will order all of the inputs by the permutation pi, then map Y using the permutation pi and move X to the top of the block
// and Y to the bottom so that we can unshuffle X and add Y.
int[] pi = CalculationCache.generatePi(blockBitLength);
pn.AppendGate(new PermutationGate(pi), 0);
int[] mappedY = new int[ySize];
int i = 0;
foreach (var yElem in ySet)
{
mappedY[i++] = pi[yElem];
}
pn.AppendGate(PermutationGateFactory.CreateSplitGate(blockSize, mappedY, false), 0);
// we now want to unshuffle X into 2^(l+1) groups and add one element of Y to each group
pn.AppendGate(PermutationGateFactory.CreateUnshuffleGate(blockSize - ySize, ySize), 0);
pn.AppendGate(PermutationGateFactory.CreateMultiGroupInserterGate(blockSize, (blockSize / ySize) - 1, ySize), 0);
var treeInsertion = SortingNetworkFactory.CreateBinaryTreeInsertion(blockSize / ySize);
// use binary tree insertion to insert the elemnt we just added to each group
for (int j = 0; j < ySize; j++)
{
pn.AppendNetwork(treeInsertion.Clone() as PermutationNetwork, j * blockSize / ySize);
}
// now shuffle all of the lists back together
pn.AppendGate(PermutationGateFactory.CreateShuffleGate(blockSize, ySize), 0);
return(pn);
}
// Lemma 4.2
private PermutationNetwork CreateTournament(int sortInaccuracy)
{
PermutationNetwork pn = new PermutationNetwork(1 << K);
int blockSize = 1 << sortInaccuracy;
// for the permutation rho
PermutationGate permuteGate = new PermutationGate(GenerateArbitraryPermutation(blockSize));
pn.AppendGate(permuteGate.Copy() as Gate, 0);
pn.AppendNetwork(SortingNetworkFactory.CreateButterflyTournament(blockSize), 0);
return(pn);
}
// Lemma 4.3
private PermutationNetwork CreateFinalSorter(int blockBitLength)
{
PermutationNetwork pn = new PermutationNetwork(1 << K);
int blockSize = 1 << blockBitLength;
int blockCount = 1 << (K - blockBitLength);
// sort each block, alternate orders for bitonic merge coming up
var bitonicSort = SortingNetworkFactory.CreateBitonicSort(blockSize, false);
for (int i = 0; i < blockCount; i++)
{
pn.AppendNetwork(bitonicSort, i * blockSize);
if (i % 2 == 1)
{
pn.AppendGate(PermutationGateFactory.CreateInvertGate(blockSize), i * blockSize);
}
}
PermutationNetwork twoBlockMerge = SortingNetworkFactory.CreateBitonicMerge(blockSize * 2, false);
// merge each block with the one next to it. alternate ordern for bitonic merge coming up
var bitonicMerge = SortingNetworkFactory.CreateBitonicMerge(blockSize * 2, false);
for (int i = 0; i < blockCount; i += 2)
{
pn.AppendNetwork(bitonicMerge.Clone() as PermutationNetwork, i * blockSize);
if ((i / 2) % 2 == 1)
{
pn.AppendGate(PermutationGateFactory.CreateInvertGate(2 * blockSize), i * blockSize);
}
}
// do another round of merges, this time offset by 1
for (int i = 1; i < blockCount; i += 2)
{
pn.AppendNetwork(bitonicMerge.Clone() as PermutationNetwork, i * blockSize);
}
// the last block will be inverted, so uninvert it
pn.AppendGate(PermutationGateFactory.CreateInvertGate(blockSize), (blockCount - 1) * blockSize);
return(pn);
}
// the subsequent rounds
private LPSortingNetwork(int k, int l, LPSortingCalculationCache calculationCache)
: base(1 << k)
{
Console.WriteLine(k + " " + l);
CalculationCache = calculationCache;
K = k;
if (l <= (int)Math.Floor(gamma * (l + 2)) + c + 5)
{
// if we would get worse by doing the procedure, then finish
if (k <= l)
{
AppendNetwork(SortingNetworkFactory.CreateBitonicSort(1 << K, false), 0);
}
else
{
// Apply Lemma 4.3
AppendNetwork(CreateFinalSorter(l), 0);
}
}
else
{
// Apply Lemma 4.2
PermutationNetwork tournament = CreateTournament(l + 2);
// Apply Lemma 4.1
PermutationNetwork tournamentCorrecter = CreateBlockCorrectionNetwork(l + 2, (int)Math.Floor(gamma * (l + 2)) + c);
for (int i = 0; i < 1 << (k - (l + 2)); i++)
{
AppendNetwork(tournament.Clone() as PermutationNetwork, i * (1 << (l + 2)));
AppendNetwork(tournamentCorrecter.Clone() as PermutationNetwork, i * (1 << (l + 2)));
}
// Apply Lemma 4.4
PermutationNetwork neighborCorrecter = CreateBlockNeighborSorter(l + 2, l + 1, (int)Math.Floor(gamma * (l + 2)) + c + 2);
AppendNetwork(neighborCorrecter, 0);
AppendNetwork(new LPSortingNetwork(k, (int)Math.Floor(gamma * (l + 2)) + c + 5, CalculationCache), 0);
}
}
// the initial round
private LPSortingNetwork(int k, LPSortingCalculationCache calculationCache)
: base(1 << k)
{
CalculationCache = calculationCache;
K = k;
if (k <= (int)Math.Floor(gamma * (k)) + c + 2)
{
// network too small to be sorted by this method
AppendNetwork(SortingNetworkFactory.CreateBitonicSort(1 << K, false), 0);
}
else
{
// Apply Lemma 4.2
AppendNetwork(CreateTournament(k), 0);
// Apply Lemma 4.1
AppendNetwork(CreateBlockCorrectionNetwork(k, (int)Math.Floor(gamma * (k)) + c), 0);
AppendNetwork(new LPSortingNetwork(K, (int)Math.Floor(gamma * (k)) + c + 2, CalculationCache), 0);
}
}
