package mil.nga.giat.geowave.index.sfc.hilbert;
import java.math.BigInteger;
import java.nio.ByteBuffer;
import java.util.ArrayList;
import java.util.List;
import mil.nga.giat.geowave.index.ByteArrayId;
import mil.nga.giat.geowave.index.ByteArrayRange;
import mil.nga.giat.geowave.index.sfc.RangeDecomposition;
import mil.nga.giat.geowave.index.sfc.SFCDimensionDefinition;
import mil.nga.giat.geowave.index.sfc.data.BasicNumericDataset;
import mil.nga.giat.geowave.index.sfc.data.MultiDimensionalNumericData;
import mil.nga.giat.geowave.index.sfc.data.NumericData;
import mil.nga.giat.geowave.index.sfc.data.NumericRange;
import com.google.common.base.Functions;
import com.google.common.collect.ImmutableList;
import com.google.uzaygezen.core.BacktrackingQueryBuilder;
import com.google.uzaygezen.core.BitVector;
import com.google.uzaygezen.core.BitVectorFactories;
import com.google.uzaygezen.core.CompactHilbertCurve;
import com.google.uzaygezen.core.FilteredIndexRange;
import com.google.uzaygezen.core.LongContent;
import com.google.uzaygezen.core.PlainFilterCombiner;
import com.google.uzaygezen.core.QueryBuilder;
import com.google.uzaygezen.core.RegionInspector;
import com.google.uzaygezen.core.SimpleRegionInspector;
import com.google.uzaygezen.core.ZoomingSpaceVisitorAdapter;
import com.google.uzaygezen.core.ranges.LongRange;
import com.google.uzaygezen.core.ranges.LongRangeHome;
/**
* This supports Compact Hilbert SFC operations using a primitive long
* internally to represent intermediate results. This can be significantly
* faster than using unbounded representations such as BigInteger, but can only
* support up to certain levels of precision. For getID() operations it is
* currently used if no single dimension is more than 48 bits of precision, and
* for query decomposition it is currently used if the total precision is <= 62
* bits.
*
*
*/
public class PrimitiveHilbertSFCOperations implements
HilbertSFCOperations
{
protected final static long UNIT_CELL_SIZE = (long) Math.pow(
2,
20);
protected long[] binsPerDimension;
protected long minHilbertValue;
protected long maxHilbertValue;
@Override
public void init(
final SFCDimensionDefinition[] dimensionDefs ) {
binsPerDimension = new long[dimensionDefs.length];
int totalPrecision = 0;
for (int d = 0; d < dimensionDefs.length; d++) {
final SFCDimensionDefinition dimension = dimensionDefs[d];
binsPerDimension[d] = (long) Math.pow(
2,
dimension.getBitsOfPrecision());
totalPrecision += dimension.getBitsOfPrecision();
}
minHilbertValue = 0;
maxHilbertValue = (long) (Math.pow(
2,
totalPrecision) - 1);
}
@Override
public byte[] convertToHilbert(
final double[] values,
final CompactHilbertCurve compactHilbertCurve,
final SFCDimensionDefinition[] dimensionDefinitions ) {
final List<Long> dimensionValues = new ArrayList<Long>();
// Compare the number of dimensions to the number of values sent in
if (dimensionDefinitions.length != values.length) {
throw new ArrayIndexOutOfBoundsException(
"Number of dimensions supplied (" + values.length + ") is different than initialized (" + dimensionDefinitions.length + ").");
}
// Loop through each value, then normalize the value based on the
// dimension definition
for (int i = 0; i < dimensionDefinitions.length; i++) {
dimensionValues.add(normalizeDimension(
dimensionDefinitions[i],
values[i],
binsPerDimension[i]));
}
// Convert the normalized values to a BitVector
final BitVector hilbertBitVector = convertToHilbert(
dimensionValues,
compactHilbertCurve,
dimensionDefinitions);
return hilbertBitVector.toBigEndianByteArray();
}
/***
* Converts the incoming values (one per dimension) into a BitVector using
* the Compact Hilbert instance. BitVector is a wrapper to allow values
* longer than 64 bits.
*
* @param values
* n-dimensional point to transoform to a point on the hilbert
* SFC
* @return point on hilbert SFC
*/
private BitVector convertToHilbert(
final List<Long> values,
final CompactHilbertCurve compactHilbertCurve,
final SFCDimensionDefinition[] dimensionDefinitions ) {
final BitVector[] bitVectors = new BitVector[values.size()];
final BitVector hilbertBitVector = BitVectorFactories.OPTIMAL.apply(compactHilbertCurve.getSpec().sumBitsPerDimension());
for (int i = 0; i < values.size(); i++) {
bitVectors[i] = BitVectorFactories.OPTIMAL.apply(dimensionDefinitions[i].getBitsOfPrecision());
bitVectors[i].copyFrom(values.get(i));
}
compactHilbertCurve.index(
bitVectors,
0,
hilbertBitVector);
return hilbertBitVector;
}
@Override
public long[] indicesFromHilbert(
final byte[] hilbertValue,
final CompactHilbertCurve compactHilbertCurve,
final SFCDimensionDefinition[] dimensionDefinitions ) {
// because it returns an array of longs right now, just use a static
// method that the unbounded operations can use as well
return internalIndicesFromHilbert(
hilbertValue,
compactHilbertCurve,
dimensionDefinitions);
}
protected static long[] internalIndicesFromHilbert(
final byte[] hilbertValue,
final CompactHilbertCurve compactHilbertCurve,
final SFCDimensionDefinition[] dimensionDefinitions ) {
final BitVector[] perDimensionBitVectors = indexInverse(
hilbertValue,
compactHilbertCurve,
dimensionDefinitions);
final long[] retVal = new long[dimensionDefinitions.length];
for (int i = 0; i < retVal.length; i++) {
retVal[i] = perDimensionBitVectors[i].toExactLong();
}
return retVal;
}
@Override
public MultiDimensionalNumericData convertFromHilbert(
final byte[] hilbertValue,
final CompactHilbertCurve compactHilbertCurve,
final SFCDimensionDefinition[] dimensionDefinitions ) {
final BitVector[] perDimensionBitVectors = indexInverse(
hilbertValue,
compactHilbertCurve,
dimensionDefinitions);
final NumericRange[] retVal = new NumericRange[dimensionDefinitions.length];
for (int i = 0; i < retVal.length; i++) {
retVal[i] = denormalizeDimension(
dimensionDefinitions[i],
perDimensionBitVectors[i].toExactLong(),
binsPerDimension[i]);
}
return new BasicNumericDataset(
retVal);
}
protected static BitVector[] indexInverse(
final byte[] hilbertValue,
final CompactHilbertCurve compactHilbertCurve,
final SFCDimensionDefinition[] dimensionDefinitions ) {
final BitVector[] perDimensionBitVectors = new BitVector[dimensionDefinitions.length];
final BitVector hilbertBitVector = BitVectorFactories.OPTIMAL.apply(compactHilbertCurve.getSpec().sumBitsPerDimension());
hilbertBitVector.copyFromBigEndian(hilbertValue);
for (int i = 0; i < dimensionDefinitions.length; i++) {
perDimensionBitVectors[i] = BitVectorFactories.OPTIMAL.apply(dimensionDefinitions[i].getBitsOfPrecision());
}
compactHilbertCurve.indexInverse(
hilbertBitVector,
perDimensionBitVectors);
return perDimensionBitVectors;
}
/***
* Used to normalize the value based on the dimension definition, which
* includes the dimensional bounds and the bits of precision. This ensures
* the maximum amount of fidelity for represented values.
*
* @param boundedDimensionDefinition
* describes the min, max, and cardinality of a dimension
* @param value
* value to be normalized
* @param bins
* precomputed number of bins in this dimension the number of
* bins expected based on the cardinality of the definition
* @return value after normalization
* @throws IllegalArgumentException
* thrown when the value passed doesn't fit with in the
* dimension definition provided
*/
private long normalizeDimension(
final SFCDimensionDefinition boundedDimensionDefinition,
final double value,
final long bins )
throws IllegalArgumentException {
final double normalizedValue = boundedDimensionDefinition.normalize(value);
if ((normalizedValue < 0) || (normalizedValue > 1)) {
throw new IllegalArgumentException(
"Value (" + value + ") is not within dimension bounds. The normalized value (" + normalizedValue + ") must be within (0,1)");
}
// scale it to a value within the bits of precision, and round up
return (long) Math.max(
Math.ceil(normalizedValue * bins) - 1L,
0);
}
/***
* Used to normalize the value based on the dimension definition, which
* includes the dimensional bounds and the bits of precision. This ensures
* the maximum amount of fidelity for represented values.
*
* @param boundedDimensionDefinition
* describes the min, max, and cardinality of a dimension
* @param value
* hilbert value to be denormalized
* @param bins
* precomputed number of bins in this dimension the number of
* bins expected based on the cardinality of the definition
* @return range of values reprenenting this hilbert value (exlusive on the
* end)
* @throws IllegalArgumentException
* thrown when the value passed doesn't fit with in the hilbert
* SFC for the dimension definition provided
*/
private NumericRange denormalizeDimension(
final SFCDimensionDefinition boundedDimensionDefinition,
final long value,
final long bins )
throws IllegalArgumentException {
final double min = (double) (value) / (double) bins;
final double max = (double) (value + 1) / (double) bins;
if ((min < 0) || (min > 1)) {
throw new IllegalArgumentException(
"Value (" + value + ") is not within bounds. The normalized value (" + min + ") must be within (0,1)");
}
if ((max < 0) || (max > 1)) {
throw new IllegalArgumentException(
"Value (" + value + ") is not within bounds. The normalized value (" + max + ") must be within (0,1)");
}
// scale it to a value within the dimension definition range
return new NumericRange(
boundedDimensionDefinition.denormalize(min),
boundedDimensionDefinition.denormalize(max));
}
@Override
public RangeDecomposition decomposeRange(
final NumericData[] rangePerDimension,
final CompactHilbertCurve compactHilbertCurve,
final SFCDimensionDefinition[] dimensionDefinitions,
final int totalPrecision,
final int maxFilteredIndexedRanges,
final boolean removeVacuum ) {// List of query range minimum and
// maximum
// values
final List<Long> minRangeList = new ArrayList<Long>();
final List<Long> maxRangeList = new ArrayList<Long>();
final LongContent zero = new LongContent(
0L);
final List<LongRange> region = new ArrayList<LongRange>(
dimensionDefinitions.length);
for (int d = 0; d < dimensionDefinitions.length; d++) {
final long normalizedMin = normalizeDimension(
dimensionDefinitions[d],
rangePerDimension[d].getMin(),
binsPerDimension[d]);
final long normalizedMax = normalizeDimension(
dimensionDefinitions[d],
rangePerDimension[d].getMax(),
binsPerDimension[d]);
minRangeList.add(normalizedMin);
maxRangeList.add(normalizedMax);
region.add(LongRange.of(
normalizedMin,
normalizedMax + 1L));
}
final long minQuadSize = getMinimumQuadSize(
minRangeList,
maxRangeList);
final RegionInspector<LongRange, LongContent> regionInspector = SimpleRegionInspector.create(
ImmutableList.of(region),
new LongContent(
minQuadSize),
Functions.<LongRange> identity(),
LongRangeHome.INSTANCE,
zero);
final PlainFilterCombiner<LongRange, Long, LongContent, LongRange> intervalCombiner = new PlainFilterCombiner<LongRange, Long, LongContent, LongRange>(
LongRange.of(
0,
1));
final QueryBuilder<LongRange, LongRange> queryBuilder = BacktrackingQueryBuilder.create(
regionInspector,
intervalCombiner,
maxFilteredIndexedRanges,
removeVacuum,
LongRangeHome.INSTANCE,
zero);
compactHilbertCurve.accept(new ZoomingSpaceVisitorAdapter(
compactHilbertCurve,
queryBuilder));
final List<FilteredIndexRange<LongRange, LongRange>> hilbertRanges = queryBuilder.get().getFilteredIndexRanges();
final ByteArrayRange[] sfcRanges = new ByteArrayRange[hilbertRanges.size()];
final int expectedByteCount = (int) Math.ceil(totalPrecision / 8.0);
if (expectedByteCount <= 0) {
// special case for no precision
return new RangeDecomposition(
new ByteArrayRange[] {
new ByteArrayRange(
new ByteArrayId(
new byte[] {}),
new ByteArrayId(
new byte[] {}))
});
}
for (int i = 0; i < hilbertRanges.size(); i++) {
final FilteredIndexRange<LongRange, LongRange> range = hilbertRanges.get(i);
// sanity check that values fit within the expected range
// it seems that uzaygezen can produce a value at 2^totalPrecision
// rather than 2^totalPrecision - 1
final long startValue = clamp(
minHilbertValue,
maxHilbertValue,
range.getIndexRange().getStart());
final long endValue = clamp(
minHilbertValue,
maxHilbertValue,
range.getIndexRange().getEnd() - 1);
// make sure its padded if necessary
final byte[] start = HilbertSFC.fitExpectedByteCount(
expectedByteCount,
ByteBuffer.allocate(
8).putLong(
startValue).array());
// make sure its padded if necessary
final byte[] end = HilbertSFC.fitExpectedByteCount(
expectedByteCount,
ByteBuffer.allocate(
8).putLong(
endValue).array());
sfcRanges[i] = new ByteArrayRange(
new ByteArrayId(
start),
new ByteArrayId(
end));
}
final RangeDecomposition rangeDecomposition = new RangeDecomposition(
sfcRanges);
return rangeDecomposition;
}
private static long clamp(
final long min,
final long max,
final long value ) {
return Math.max(
Math.min(
value,
max),
0);
}
/***
* Returns the smallest range that will be fully decomposed (i.e.
* decomposition stops when the range is equal or smaller than this value).
* Values is based on the _maximumRangeDecompsed and _minRangeDecompsed
* instance members.
*
* @param minRangeList
* minimum values for each dimension (ordered)
* @param maxRangeList
* maximum values for each dimension (ordered)
* @return largest range that will be fully decomposed
*/
private long getMinimumQuadSize(
final List<Long> minRangeList,
final List<Long> maxRangeList ) {
long maxRange = 1;
final int dimensionality = Math.min(
minRangeList.size(),
maxRangeList.size());
for (int d = 0; d < dimensionality; d++) {
maxRange = Math.max(
maxRange,
(Math.abs(maxRangeList.get(d) - minRangeList.get(d)) + 1));
}
final long maxRangeDecomposed = (long) Math.pow(
maxRange,
dimensionality);
if (maxRangeDecomposed <= UNIT_CELL_SIZE) {
return 1L;
}
return maxRangeDecomposed / UNIT_CELL_SIZE;
}
/**
* The estimated ID count is the cross product of normalized range
* of all dimensions per the bits of precision provided by the dimension definitions.
*/
@Override
public BigInteger getEstimatedIdCount(
final MultiDimensionalNumericData data,
final SFCDimensionDefinition[] dimensionDefinitions ) {
final double[] mins = data.getMinValuesPerDimension();
final double[] maxes = data.getMaxValuesPerDimension();
long estimatedIdCount = 1L;
for (int d = 0; d < data.getDimensionCount(); d++) {
final long binMin = normalizeDimension(
dimensionDefinitions[d],
mins[d],
binsPerDimension[d]);
final long binMax = normalizeDimension(
dimensionDefinitions[d],
maxes[d],
binsPerDimension[d]);
estimatedIdCount *= (Math.abs(binMax - binMin) + 1);
}
return BigInteger.valueOf(estimatedIdCount);
}
@Override
public double[] getInsertionIdRangePerDimension(
final SFCDimensionDefinition[] dimensionDefinitions ) {
final double[] retVal = new double[dimensionDefinitions.length];
for (int i = 0; i < dimensionDefinitions.length; i++) {
retVal[i] = dimensionDefinitions[i].getRange() / binsPerDimension[i];
}
return retVal;
}
}