org.apache.datasketches.quantiles.DoublesAuxiliary Maven / Gradle / Ivy
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package org.apache.datasketches.quantiles;
import static java.lang.System.arraycopy;
import static org.apache.datasketches.quantiles.DoublesSketchAccessor.BB_LVL_IDX;
import static org.apache.datasketches.quantiles.Util.checkFractionalRankBounds;
import java.util.Arrays;
import org.apache.datasketches.QuantilesHelper;
/**
* Auxiliary data structure for answering quantile queries
*
* @author Kevin Lang
* @author Lee Rhodes
*/
final class DoublesAuxiliary {
long auxN_;
double[] auxSamplesArr_; //array of size samples
long[] auxCumWtsArr_;
/**
* Constructs the Auxiliary structure from the DoublesSketch
* @param qs a DoublesSketch
*/
DoublesAuxiliary(final DoublesSketch qs ) {
final int k = qs.getK();
final long n = qs.getN();
final long bitPattern = qs.getBitPattern();
final int numSamples = qs.getRetainedItems();
final DoublesSketchAccessor sketchAccessor = DoublesSketchAccessor.wrap(qs);
final double[] itemsArr = new double[numSamples];
final long[] cumWtsArr = new long[numSamples + 1]; // the extra slot is very important
// Populate from DoublesSketch:
// copy over the "levels" and then the base buffer, all with appropriate weights
populateFromDoublesSketch(k, n, bitPattern, sketchAccessor, itemsArr, cumWtsArr);
// Sort the first "numSamples" slots of the two arrays in tandem,
// taking advantage of the already sorted blocks of length k
blockyTandemMergeSort(itemsArr, cumWtsArr, numSamples, k);
final long total = QuantilesHelper.convertToPrecedingCummulative(cumWtsArr);
assert total == n;
auxN_ = n;
auxSamplesArr_ = itemsArr;
auxCumWtsArr_ = cumWtsArr;
}
/**
* Get the estimated quantile given a fractional rank.
* @param fRank the fractional rank where: 0 ≤ fRank ≤ 1.0.
* @return the estimated quantile
*/
double getQuantile(final double fRank) {
checkFractionalRankBounds(fRank);
final long pos = QuantilesHelper.posOfPhi(fRank, auxN_);
return approximatelyAnswerPositionalQuery(pos);
}
/**
* Assuming that there are n items in the true stream, this asks what
* item would appear in position 0 ≤ pos < n of a hypothetical sorted
* version of that stream.
*
* Note that since that since the true stream is unavailable,
* we don't actually answer the question for that stream, but rather for
* a different stream of the same length, that could hypothetically
* be reconstructed from the weighted samples in our sketch.
* @param pos position
* @return approximate answer
*/
private double approximatelyAnswerPositionalQuery(final long pos) {
assert 0 <= pos;
assert pos < auxN_;
final int index = QuantilesHelper.chunkContainingPos(auxCumWtsArr_, pos);
return auxSamplesArr_[index];
}
/**
* Populate the arrays and registers from a DoublesSketch
* @param k K value of sketch
* @param n The current size of the stream
* @param bitPattern the bit pattern for valid log levels
* @param sketchAccessor A DoublesSketchAccessor around the sketch
* @param itemsArr the consolidated array of all items from the sketch populated here
* @param cumWtsArr the cumulative weights for each item from the sketch populated here
*/
private final static void populateFromDoublesSketch(
final int k, final long n, final long bitPattern,
final DoublesSketchAccessor sketchAccessor,
final double[] itemsArr, final long[] cumWtsArr) {
long weight = 1;
int nxt = 0;
long bits = bitPattern;
assert bits == (n / (2L * k)); // internal consistency check
for (int lvl = 0; bits != 0L; lvl++, bits >>>= 1) {
weight *= 2;
if ((bits & 1L) > 0L) {
sketchAccessor.setLevel(lvl);
for (int i = 0; i < sketchAccessor.numItems(); i++) {
itemsArr[nxt] = sketchAccessor.get(i);
cumWtsArr[nxt] = weight;
nxt++;
}
}
}
weight = 1; //NOT a mistake! We just copied the highest level; now we need to copy the base buffer
final int startOfBaseBufferBlock = nxt;
// Copy BaseBuffer over, along with weight = 1
sketchAccessor.setLevel(BB_LVL_IDX);
for (int i = 0; i < sketchAccessor.numItems(); i++) {
itemsArr[nxt] = sketchAccessor.get(i);
cumWtsArr[nxt] = weight;
nxt++;
}
assert nxt == itemsArr.length;
// Must sort the items that came from the base buffer.
// Don't need to sort the corresponding weights because they are all the same.
final int numSamples = nxt;
Arrays.sort(itemsArr, startOfBaseBufferBlock, numSamples);
cumWtsArr[numSamples] = 0;
}
/**
* blockyTandemMergeSort() is an implementation of top-down merge sort specialized
* for the case where the input contains successive equal-length blocks
* that have already been sorted, so that only the top part of the
* merge tree remains to be executed. Also, two arrays are sorted in tandem,
* as discussed below.
* @param keyArr array of keys
* @param valArr array of values
* @param arrLen length of keyArr and valArr
* @param blkSize size of internal sorted blocks
*/
//used by DoublesAuxiliary and UtilTest
static void blockyTandemMergeSort(final double[] keyArr, final long[] valArr, final int arrLen,
final int blkSize) {
assert blkSize >= 1;
if (arrLen <= blkSize) { return; }
int numblks = arrLen / blkSize;
if ((numblks * blkSize) < arrLen) { numblks += 1; }
assert ((numblks * blkSize) >= arrLen);
// duplicate the input is preparation for the "ping-pong" copy reduction strategy.
final double[] keyTmp = Arrays.copyOf(keyArr, arrLen);
final long[] valTmp = Arrays.copyOf(valArr, arrLen);
blockyTandemMergeSortRecursion(keyTmp, valTmp,
keyArr, valArr,
0, numblks,
blkSize, arrLen);
}
/**
* blockyTandemMergeSortRecursion() is called by blockyTandemMergeSort().
* In addition to performing the algorithm's top down recursion,
* it manages the buffer swapping that eliminates most copying.
* It also maps the input's pre-sorted blocks into the subarrays
* that are processed by tandemMerge().
* @param keySrc key source
* @param valSrc value source
* @param keyDst key destination
* @param valDst value destination
* @param grpStart group start, refers to pre-sorted blocks such as block 0, block 1, etc.
* @param grpLen group length, refers to pre-sorted blocks such as block 0, block 1, etc.
* @param blkSize block size
* @param arrLim array limit
*/
private static void blockyTandemMergeSortRecursion(final double[] keySrc, final long[] valSrc,
final double[] keyDst, final long[] valDst, final int grpStart, final int grpLen,
/* indices of blocks */ final int blkSize, final int arrLim) {
// Important note: grpStart and grpLen do NOT refer to positions in the underlying array.
// Instead, they refer to the pre-sorted blocks, such as block 0, block 1, etc.
assert (grpLen > 0);
if (grpLen == 1) { return; }
final int grpLen1 = grpLen / 2;
final int grpLen2 = grpLen - grpLen1;
assert (grpLen1 >= 1);
assert (grpLen2 >= grpLen1);
final int grpStart1 = grpStart;
final int grpStart2 = grpStart + grpLen1;
//swap roles of src and dst
blockyTandemMergeSortRecursion(keyDst, valDst,
keySrc, valSrc,
grpStart1, grpLen1, blkSize, arrLim);
//swap roles of src and dst
blockyTandemMergeSortRecursion(keyDst, valDst,
keySrc, valSrc,
grpStart2, grpLen2, blkSize, arrLim);
// here we convert indices of blocks into positions in the underlying array.
final int arrStart1 = grpStart1 * blkSize;
final int arrStart2 = grpStart2 * blkSize;
final int arrLen1 = grpLen1 * blkSize;
int arrLen2 = grpLen2 * blkSize;
// special case for the final block which might be shorter than blkSize.
if ((arrStart2 + arrLen2) > arrLim) { arrLen2 = arrLim - arrStart2; }
tandemMerge(keySrc, valSrc,
arrStart1, arrLen1,
arrStart2, arrLen2,
keyDst, valDst,
arrStart1); // which will be arrStart3
}
/**
* Performs two merges in tandem. One of them provides the sort keys
* while the other one passively undergoes the same data motion.
* @param keySrc key source
* @param valSrc value source
* @param arrStart1 Array 1 start offset
* @param arrLen1 Array 1 length
* @param arrStart2 Array 2 start offset
* @param arrLen2 Array 2 length
* @param keyDst key destination
* @param valDst value destination
* @param arrStart3 Array 3 start offset
*/
private static void tandemMerge(final double[] keySrc, final long[] valSrc,
final int arrStart1, final int arrLen1,
final int arrStart2, final int arrLen2,
final double[] keyDst, final long[] valDst,
final int arrStart3) {
final int arrStop1 = arrStart1 + arrLen1;
final int arrStop2 = arrStart2 + arrLen2;
int i1 = arrStart1;
int i2 = arrStart2;
int i3 = arrStart3;
while ((i1 < arrStop1) && (i2 < arrStop2)) {
if (keySrc[i2] < keySrc[i1]) {
keyDst[i3] = keySrc[i2];
valDst[i3] = valSrc[i2];
i2++;
} else {
keyDst[i3] = keySrc[i1];
valDst[i3] = valSrc[i1];
i1++;
}
i3++;
}
if (i1 < arrStop1) {
arraycopy(keySrc, i1, keyDst, i3, arrStop1 - i1);
arraycopy(valSrc, i1, valDst, i3, arrStop1 - i1);
} else {
assert i2 < arrStop2;
arraycopy(keySrc, i2, keyDst, i3, arrStop2 - i2);
arraycopy(valSrc, i2, valDst, i3, arrStop2 - i2);
}
}
} // end of class Auxiliary