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Core sketch algorithms used alone and by other Java repositories in the DataSketches library.
/*
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
package org.apache.datasketches.kll;
import static java.lang.Math.abs;
import static java.lang.Math.ceil;
import static java.lang.Math.exp;
import static java.lang.Math.log;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.pow;
import static java.lang.Math.round;
import static org.apache.datasketches.common.Family.KLL;
import static org.apache.datasketches.common.Util.floorPowerOf2;
import static org.apache.datasketches.kll.KllPreambleUtil.DATA_START_ADR;
import static org.apache.datasketches.kll.KllPreambleUtil.EMPTY_BIT_MASK;
import static org.apache.datasketches.kll.KllPreambleUtil.LEVEL_ZERO_SORTED_BIT_MASK;
import static org.apache.datasketches.kll.KllPreambleUtil.SINGLE_ITEM_BIT_MASK;
import static org.apache.datasketches.kll.KllSketch.SketchStructure.COMPACT_EMPTY;
import static org.apache.datasketches.kll.KllSketch.SketchStructure.COMPACT_FULL;
import static org.apache.datasketches.kll.KllSketch.SketchStructure.COMPACT_SINGLE;
import static org.apache.datasketches.kll.KllSketch.SketchStructure.UPDATABLE;
import static org.apache.datasketches.kll.KllSketch.SketchType.DOUBLES_SKETCH;
import static org.apache.datasketches.kll.KllSketch.SketchType.FLOATS_SKETCH;
import static org.apache.datasketches.kll.KllSketch.SketchType.ITEMS_SKETCH;
import static org.apache.datasketches.quantilescommon.QuantilesAPI.UNSUPPORTED_MSG;
import java.nio.ByteOrder;
import java.util.Arrays;
import org.apache.datasketches.common.ArrayOfItemsSerDe;
import org.apache.datasketches.common.SketchesArgumentException;
import org.apache.datasketches.kll.KllSketch.SketchStructure;
import org.apache.datasketches.kll.KllSketch.SketchType;
import org.apache.datasketches.memory.WritableBuffer;
import org.apache.datasketches.memory.WritableMemory;
/**
* This class provides some useful sketch analysis tools that are used internally.
*
* @author Lee Rhodes
*/
final class KllHelper {
public static final String LS = System.getProperty("line.separator");
static final double EPS_DELTA_THRESHOLD = 1E-6;
static final double MIN_EPS = 4.7634E-5;
static final double PMF_COEF = 2.446;
static final double PMF_EXP = 0.9433;
static final double CDF_COEF = 2.296;
static final double CDF_EXP = 0.9723;
static class GrowthStats {
SketchType sketchType;
int k;
int m;
long givenN;
long maxN;
int numLevels;
int maxItems;
int compactBytes;
int updatableBytes;
}
static class LevelStats {
long n;
public int numLevels;
int numItems;
LevelStats(final long n, final int numLevels, final int numItems) {
this.n = n;
this.numLevels = numLevels;
this.numItems = numItems;
}
}
/**
* This is the exact powers of 3 from 3^0 to 3^30 where the exponent is the index
*/
private static long[] powersOfThree =
new long[] {1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441,
1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467,
3486784401L, 10460353203L, 31381059609L, 94143178827L, 282429536481L,
847288609443L, 2541865828329L, 7625597484987L, 22876792454961L, 68630377364883L,
205891132094649L};
/**
* Checks the validity of the given k
* @param k must be greater than 7 and less than 65536.
*/
static void checkK(final int k, final int m) {
if (k < m || k > KllSketch.MAX_K) {
throw new SketchesArgumentException(
"K must be >= " + m + " and <= " + KllSketch.MAX_K + ": " + k);
}
}
static void checkM(final int m) {
if (m < KllSketch.MIN_M || m > KllSketch.MAX_M || ((m & 1) == 1)) {
throw new SketchesArgumentException(
"M must be >= 2, <= 8 and even: " + m);
}
}
/**
* Returns the approximate maximum number of items that this sketch can handle
* @param k The sizing / accuracy parameter of the sketch in items.
* Note: this method actually works for k items up to k = 2^29 and 61 levels,
* however only k items up to (2^16 - 1) are currently used by the sketch.
* @param m the size of the smallest level in items. Default is 8.
* @param numLevels the upper bound number of levels based on n items.
* @return the total item capacity of the sketch.
*/
static int computeTotalItemCapacity(final int k, final int m, final int numLevels) {
long total = 0;
for (int level = 0; level < numLevels; level++) {
total += levelCapacity(k, numLevels, level, m);
}
return (int) total;
}
/**
* Convert the individual weights into cumulative weights.
* An array of {1,1,1,1} becomes {1,2,3,4}
* @param array of actual weights from the sketch, where first element is not zero.
* @return total weight
*/
public static long convertToCumulative(final long[] array) {
long subtotal = 0;
for (int i = 0; i < array.length; i++) {
final long newSubtotal = subtotal + array[i];
subtotal = array[i] = newSubtotal;
}
return subtotal;
}
static int currentLevelSizeItems(final int level, final int numLevels, final int[] levels) {
if (level >= numLevels) { return 0; }
return levels[level + 1] - levels[level];
}
/**
* Given k, m, and numLevels, this computes and optionally prints the structure of the sketch when the given
* number of levels are completely filled.
* @param k the given user configured sketch parameter
* @param m the given user configured sketch parameter
* @param numLevels the given number of levels of the sketch
* @param printSketchStructure if true will print the details of the sketch structure at the given numLevels.
* @return LevelStats with the final summary of the sketch's cumulative N,
* and cumulative items at the given numLevels.
*/
static LevelStats getFinalSketchStatsAtNumLevels(
final int k,
final int m,
final int numLevels,
final boolean printSketchStructure) {
int cumItems = 0;
long cumN = 0;
if (printSketchStructure) {
println("SKETCH STRUCTURE:");
println("Given K : " + k);
println("Given M : " + m);
println("Given NumLevels: " + numLevels);
printf("%6s %8s %12s %18s %18s\n", "Level", "Items", "CumItems", "N at Level", "CumN");
}
for (int level = 0; level < numLevels; level++) {
final LevelStats lvlStats = getLevelCapacityItems(k, m, numLevels, level);
cumItems += lvlStats.numItems;
cumN += lvlStats.n;
if (printSketchStructure) {
printf("%6d %,8d %,12d %,18d %,18d\n", level, lvlStats.numItems, cumItems, lvlStats.n, cumN);
}
}
return new LevelStats(cumN, numLevels, cumItems);
}
/**
* This method is for direct Double and Float sketches only.
* Given k, m, n, and the sketch type, this computes (and optionally prints) the growth scheme for a sketch as it
* grows large enough to accommodate a stream length of n items.
* @param k the given user configured sketch parameter
* @param m the given user configured sketch parameter
* @param n the desired stream length
* @param sketchType the given sketch type: either DOUBLES_SKETCH or FLOATS_SKETCH.
* @param printGrowthScheme if true the entire growth scheme of the sketch will be printed.
* @return GrowthStats with the final numItems of the growth scheme
*/
static GrowthStats getGrowthSchemeForGivenN(
final int k,
final int m,
final long n,
final SketchType sketchType,
final boolean printGrowthScheme) {
if (sketchType == ITEMS_SKETCH) { throw new SketchesArgumentException(UNSUPPORTED_MSG); }
LevelStats lvlStats;
final GrowthStats gStats = new GrowthStats();
gStats.numLevels = 0;
gStats.k = k;
gStats.m = m;
gStats.givenN = n;
gStats.sketchType = sketchType;
if (printGrowthScheme) {
println("GROWTH SCHEME:");
println("Given SketchType: " + gStats.sketchType.toString());
println("Given K : " + gStats.k);
println("Given M : " + gStats.m);
println("Given N : " + gStats.givenN);
printf("%10s %10s %20s %13s %15s\n", "NumLevels", "MaxItems", "MaxN", "CompactBytes", "UpdatableBytes");
}
final int typeBytes = sketchType.getBytes();
do {
gStats.numLevels++; //
lvlStats = getFinalSketchStatsAtNumLevels(gStats.k, gStats.m, gStats.numLevels, false);
gStats.maxItems = lvlStats.numItems;
gStats.maxN = lvlStats.n; //
gStats.compactBytes =
gStats.maxItems * typeBytes + gStats.numLevels * Integer.BYTES + 2 * typeBytes + DATA_START_ADR;
gStats.updatableBytes = gStats.compactBytes + Integer.BYTES;
if (printGrowthScheme) {
printf("%10d %,10d %,20d %,13d %,15d\n",
gStats.numLevels, gStats.maxItems, gStats.maxN, gStats.compactBytes, gStats.updatableBytes);
}
} while (lvlStats.n < n);
//gStats.numLevels = lvlStats.numLevels; //
//gStats.maxItems = lvlStats.numItems; //
return gStats;
}
// constants were derived as the best fit to 99 percentile empirically measured max error in
// thousands of trials
static int getKFromEpsilon(final double epsilon, final boolean pmf) {
//Ensure that eps is >= than the lowest possible eps given MAX_K and pmf=false.
final double eps = max(epsilon, MIN_EPS);
final double kdbl = pmf
? exp(log(PMF_COEF / eps) / PMF_EXP)
: exp(log(CDF_COEF / eps) / CDF_EXP);
final double krnd = round(kdbl);
final double del = abs(krnd - kdbl);
final int k = (int) (del < EPS_DELTA_THRESHOLD ? krnd : ceil(kdbl));
return max(KllSketch.MIN_M, min(KllSketch.MAX_K, k));
}
/**
* Given k, m, numLevels, this computes the item capacity of a single level.
* @param k the given user sketch configuration parameter
* @param m the given user sketch configuration parameter
* @param numLevels the given number of levels of the sketch
* @param level the specific level to compute its item capacity
* @return LevelStats with the computed N and items for the given level.
*/
static LevelStats getLevelCapacityItems(
final int k,
final int m,
final int numLevels,
final int level) {
final int items = KllHelper.levelCapacity(k, numLevels, level, m);
final long n = (long)items << level;
return new LevelStats(n, numLevels, items);
}
/**
* Gets the normalized rank error given k and pmf.
* Static method version of the getNormalizedRankError(boolean).
* @param k the configuration parameter
* @param pmf if true, returns the "double-sided" normalized rank error for the getPMF() function.
* Otherwise, it is the "single-sided" normalized rank error for all the other queries.
* @return if pmf is true, the normalized rank error for the getPMF() function.
* Otherwise, it is the "single-sided" normalized rank error for all the other queries.
* @see KllHeapDoublesSketch
*/
// constants were derived as the best fit to 99 percentile empirically measured max error in
// thousands of trials
static double getNormalizedRankError(final int k, final boolean pmf) {
return pmf
? PMF_COEF / pow(k, PMF_EXP)
: CDF_COEF / pow(k, CDF_EXP);
}
static int getNumRetainedAboveLevelZero(final int numLevels, final int[] levels) {
return levels[numLevels] - levels[1];
}
/**
* Returns the item capacity of a specific level.
* @param k the accuracy parameter of the sketch. Because of the Java limits on array sizes,
* the theoretical maximum k is 2^29. However, this implementation of the KLL sketch
* limits k to 2^16 -1.
* @param numLevels the number of current levels in the sketch. Maximum is 61.
* @param level the zero-based index of a level. This varies from 0 to 60.
* @param m the minimum level width. Default is 8.
* @return the capacity of a specific level
*/
static int levelCapacity(final int k, final int numLevels, final int level, final int m) {
assert (k <= (1 << 29));
assert (numLevels >= 1) && (numLevels <= 61);
assert (level >= 0) && (level < numLevels);
final int depth = numLevels - level - 1; //depth is # levels from the top level (= 0)
return (int) Math.max(m, intCapAux(k, depth));
}
/**
* This method is for direct Double and Float sketches only and does the following:
*
* - Determines if the required sketch bytes will fit in the current Memory.
* If so, it will stretch the positioning of the arrays to fit. Otherwise:
*
- Allocates a new WritableMemory of the required size
* - Copies over the preamble as is (20 bytes)
* - The caller is responsible for filling the remainder and updating the preamble.
*
*
* @param sketch The current sketch that needs to be expanded.
* @param newLevelsArrLen the element length of the new Levels array.
* @param newItemsArrLen the element length of the new Items array.
* @return the new expanded memory with preamble.
*/
static WritableMemory memorySpaceMgmt(
final KllSketch sketch,
final int newLevelsArrLen,
final int newItemsArrLen) {
final KllSketch.SketchType sketchType = sketch.sketchType;
if (sketchType == ITEMS_SKETCH) { throw new SketchesArgumentException(UNSUPPORTED_MSG); }
final WritableMemory wmem = sketch.getWritableMemory();
if (wmem == null) { return null; }
final WritableMemory oldWmem = wmem;
final int typeBytes = sketchType.getBytes();
final int requiredSketchBytes = DATA_START_ADR
+ newLevelsArrLen * Integer.BYTES
+ 2 * typeBytes
+ newItemsArrLen * typeBytes;
final WritableMemory newWmem;
if (requiredSketchBytes > oldWmem.getCapacity()) { //Acquire new WritableMemory
newWmem = sketch.getMemoryRequestServer().request(oldWmem, requiredSketchBytes);
oldWmem.copyTo(0, newWmem, 0, DATA_START_ADR); //copy preamble (first 20 bytes)
}
else { //Expand or contract in current memory
newWmem = oldWmem;
}
assert requiredSketchBytes <= newWmem.getCapacity();
return newWmem;
}
private static String outputData(final KllSketch sketch) {
final int[] levelsArr = sketch.getLevelsArray(SketchStructure.UPDATABLE);
final int numLevels = sketch.getNumLevels();
final int k = sketch.getK();
final int m = sketch.getM();
final StringBuilder sb = new StringBuilder();
sb.append("### KllSketch itemsArray & levelsArray data:").append(LS);
sb.append("Index, Value").append(LS);
if (levelsArr[0] > 0) {
final String gbg = " Empty or Garbage, size = " + levelsArr[0];
for (int i = 0; i < levelsArr[0]; i++) {
sb.append(" ").append(i + ", ").append(sketch.getItemAsString(i));
if (i == 0) { sb.append(gbg); }
sb.append(LS);
}
}
int level = 0;
while (level < numLevels) {
final int fromIndex = levelsArr[level];
final int toIndex = levelsArr[level + 1]; // exclusive
String lvlData = "";
if (fromIndex < toIndex) {
lvlData = " level[" + level + "]=" + levelsArr[level]
+ ", cap=" + KllHelper.levelCapacity(k, numLevels, level, m)
+ ", size=" + KllHelper.currentLevelSizeItems(level, numLevels, levelsArr)
+ ", wt=" + (1 << level) + LS;
}
for (int i = fromIndex; i < toIndex; i++) {
sb.append(" ").append(i + ", ").append(sketch.getItemAsString(i));
if (i == fromIndex) { sb.append(lvlData); } else { sb.append(LS); }
}
level++;
}
sb.append(" ----------level[" + level + "]=" + levelsArr[level] + ": itemsArray[].length");
sb.append(LS);
sb.append("### End data").append(LS);
return sb.toString();
}
static long sumTheSampleWeights(final int num_levels, final int[] levels) {
long total = 0;
long weight = 1;
for (int i = 0; i < num_levels; i++) {
total += weight * (levels[i + 1] - levels[i]);
weight *= 2;
}
return total;
}
static byte[] toByteArray(final KllSketch srcSk, final boolean updatable) {
//ITEMS_SKETCH byte array is never updatable
final boolean myUpdatable = srcSk.sketchType == ITEMS_SKETCH ? false : updatable;
final long srcN = srcSk.getN();
final SketchStructure tgtStructure;
if (myUpdatable) { tgtStructure = UPDATABLE; }
else if (srcN == 0) { tgtStructure = COMPACT_EMPTY; }
else if (srcN == 1) { tgtStructure = COMPACT_SINGLE; }
else { tgtStructure = COMPACT_FULL; }
final int totalBytes = srcSk.currentSerializedSizeBytes(myUpdatable);
final byte[] bytesOut = new byte[totalBytes];
final WritableBuffer wbuf = WritableMemory.writableWrap(bytesOut).asWritableBuffer(ByteOrder.LITTLE_ENDIAN);
//ints 0,1
final byte preInts = (byte)tgtStructure.getPreInts();
final byte serVer = (byte)tgtStructure.getSerVer();
final byte famId = (byte)(KLL.getID());
final byte flags = (byte) ((srcSk.isEmpty() ? EMPTY_BIT_MASK : 0)
| (srcSk.isLevelZeroSorted() ? LEVEL_ZERO_SORTED_BIT_MASK : 0)
| (srcSk.getN() == 1 ? SINGLE_ITEM_BIT_MASK : 0));
final short k = (short) srcSk.getK();
final byte m = (byte) srcSk.getM();
//load first 8 bytes
wbuf.putByte(preInts); //byte 0
wbuf.putByte(serVer);
wbuf.putByte(famId);
wbuf.putByte(flags);
wbuf.putShort(k);
wbuf.putByte(m);
wbuf.incrementPosition(1); //byte 7 is unused
if (tgtStructure == COMPACT_EMPTY) {
return bytesOut;
}
if (tgtStructure == COMPACT_SINGLE) {
final byte[] siByteArr = srcSk.getSingleItemByteArr();
final int len = siByteArr.length;
wbuf.putByteArray(siByteArr, 0, len);
wbuf.incrementPosition(-len);
return bytesOut;
}
// Tgt is either COMPACT_FULL or UPDATABLE
//ints 2,3
final long n = srcSk.getN();
//ints 4
final short minK = (short) srcSk.getMinK();
final byte numLevels = (byte) srcSk.getNumLevels();
//end of full preamble
final int[] lvlsArr = srcSk.getLevelsArray(tgtStructure);
final byte[] minMaxByteArr = srcSk.getMinMaxByteArr();
final byte[] itemsByteArr = tgtStructure == COMPACT_FULL
? srcSk.getRetainedItemsByteArr()
: srcSk.getTotalItemsByteArr();
wbuf.putLong(n);
wbuf.putShort(minK);
wbuf.putByte(numLevels);
wbuf.incrementPosition(1);
wbuf.putIntArray(lvlsArr, 0, lvlsArr.length);
wbuf.putByteArray(minMaxByteArr, 0, minMaxByteArr.length);
wbuf.putByteArray(itemsByteArr, 0, itemsByteArr.length);
return bytesOut;
}
static String toStringImpl(final KllSketch sketch, final boolean withSummary, final boolean withData,
final ArrayOfItemsSerDe serDe) {
final SketchType sketchType = sketch.sketchType;
final boolean hasMemory = sketch.hasMemory();
final int k = sketch.getK();
final int m = sketch.getM();
final long n = sketch.getN();
final int numLevels = sketch.getNumLevels();
final int[] fullLevelsArr = sketch.getLevelsArray(UPDATABLE);
//final int[] levelsArr = sketch.getLevelsArray(sketch.sketchStructure);
final String epsPct = String.format("%.3f%%", sketch.getNormalizedRankError(false) * 100);
final String epsPMFPct = String.format("%.3f%%", sketch.getNormalizedRankError(true) * 100);
final boolean compact = sketch.isCompactMemoryFormat();
final StringBuilder sb = new StringBuilder();
final String directStr = hasMemory ? "Direct" : "";
final String compactStr = compact ? "Compact" : "";
final String readOnlyStr = sketch.isReadOnly() ? "true" + ("(" + (compact ? "Format" : "Memory") + ")") : "false";
final String skTypeStr = sketchType.getName();
final String className = "Kll" + directStr + compactStr + skTypeStr;
sb.append(LS).append("### ").append(className).append(" Summary:").append(LS);
sb.append(" K : ").append(k).append(LS);
sb.append(" Dynamic min K : ").append(sketch.getMinK()).append(LS);
sb.append(" M : ").append(m).append(LS);
sb.append(" N : ").append(n).append(LS);
sb.append(" Epsilon : ").append(epsPct).append(LS);
sb.append(" Epsilon PMF : ").append(epsPMFPct).append(LS);
sb.append(" Empty : ").append(sketch.isEmpty()).append(LS);
sb.append(" Estimation Mode : ").append(sketch.isEstimationMode()).append(LS);
sb.append(" Levels : ").append(numLevels).append(LS);
sb.append(" Level 0 Sorted : ").append(sketch.isLevelZeroSorted()).append(LS);
sb.append(" Capacity Items : ").append(fullLevelsArr[numLevels]).append(LS);
sb.append(" Retained Items : ").append(sketch.getNumRetained()).append(LS);
sb.append(" Empty/Garbage Items : ").append(sketch.levelsArr[0]).append(LS);
sb.append(" ReadOnly : ").append(readOnlyStr).append(LS);
if (sketchType != ITEMS_SKETCH) {
sb.append(" Updatable Storage Bytes: ").append(sketch.currentSerializedSizeBytes(true)).append(LS);
}
sb.append(" Compact Storage Bytes : ").append(sketch.currentSerializedSizeBytes(false)).append(LS);
final String emptyStr = (sketchType == ITEMS_SKETCH) ? "Null" : "NaN";
sb.append(" Min Item : ").append(sketch.isEmpty() ? emptyStr : sketch.getMinItemAsString())
.append(LS);
sb.append(" Max Item : ").append(sketch.isEmpty() ? emptyStr : sketch.getMaxItemAsString())
.append(LS);
sb.append("### End sketch summary").append(LS);
if (! withSummary) { sb.setLength(0); }
if (withData) { sb.append(outputData(sketch)); }
return sb.toString();
}
/**
* Returns very conservative upper bound of the number of levels based on n.
* @param n the length of the stream
* @return floor( log_2(n) )
*/
static int ubOnNumLevels(final long n) {
return 1 + Long.numberOfTrailingZeros(floorPowerOf2(n));
}
/**
* This grows the levels arr by 1 (if needed) and increases the capacity of the items array
* at the bottom. Only numLevels, the levels array and the items array are affected.
* This assumes sketch is writable and UPDATABLE.
* @param sketch the current sketch
*/
static void addEmptyTopLevelToCompletelyFullSketch(final KllSketch sketch) {
final SketchType sketchType = sketch.sketchType;
final int[] myCurLevelsArr = sketch.getLevelsArray(sketch.sketchStructure);
final int myCurNumLevels = sketch.getNumLevels();
final int myCurTotalItemsCapacity = myCurLevelsArr[myCurNumLevels];
final int myNewNumLevels;
final int[] myNewLevelsArr;
final int myNewTotalItemsCapacity;
double[] myCurDoubleItemsArr = null;
double[] myNewDoubleItemsArr = null;
double minDouble = Double.NaN;
double maxDouble = Double.NaN;
float[] myCurFloatItemsArr = null;
float[] myNewFloatItemsArr = null;
float minFloat = Float.NaN;
float maxFloat = Float.NaN;
Object[] myCurItemsArr = null;
Object[] myNewItemsArr = null;
Object minItem = null;
Object maxItem = null;
if (sketchType == DOUBLES_SKETCH) {
final KllDoublesSketch dblSk = (KllDoublesSketch) sketch;
myCurDoubleItemsArr = dblSk.getDoubleItemsArray();
minDouble = dblSk.getMinItem();
maxDouble = dblSk.getMaxItem();
//assert we are following a certain growth scheme
assert myCurDoubleItemsArr.length == myCurTotalItemsCapacity;
}
else if (sketchType == FLOATS_SKETCH) {
final KllFloatsSketch fltSk = (KllFloatsSketch) sketch;
myCurFloatItemsArr = fltSk.getFloatItemsArray();
minFloat = fltSk.getMinItem();
maxFloat = fltSk.getMaxItem();
//assert we are following a certain growth scheme
assert myCurFloatItemsArr.length == myCurTotalItemsCapacity;
}
else { //sketchType == ITEMS_SKETCH
final KllItemsSketch itmSk = (KllItemsSketch) sketch;
myCurItemsArr = itmSk.getTotalItemsArray();
minItem = itmSk.getMinItem();
maxItem = itmSk.getMaxItem();
}
assert myCurLevelsArr[0] == 0; //definition of full is part of the growth scheme
final int deltaItemsCap = levelCapacity(sketch.getK(), myCurNumLevels + 1, 0, sketch.getM());
myNewTotalItemsCapacity = myCurTotalItemsCapacity + deltaItemsCap;
// Check if growing the levels arr if required.
// Note that merging MIGHT over-grow levels_, in which case we might not have to grow it
final boolean growLevelsArr = myCurLevelsArr.length < myCurNumLevels + 2;
// GROW LEVELS ARRAY
if (growLevelsArr) {
//grow levels arr by one and copy the old data to the new array, extra space at the top.
myNewLevelsArr = Arrays.copyOf(myCurLevelsArr, myCurNumLevels + 2);
assert myNewLevelsArr.length == myCurLevelsArr.length + 1;
myNewNumLevels = myCurNumLevels + 1;
sketch.incNumLevels(); //increment for off-heap
} else {
myNewLevelsArr = myCurLevelsArr;
myNewNumLevels = myCurNumLevels;
}
// This loop updates all level indices EXCLUDING the "extra" index at the top
for (int level = 0; level <= myNewNumLevels - 1; level++) {
myNewLevelsArr[level] += deltaItemsCap;
}
myNewLevelsArr[myNewNumLevels] = myNewTotalItemsCapacity; // initialize the new "extra" index at the top
// GROW items ARRAY
if (sketchType == DOUBLES_SKETCH) {
myNewDoubleItemsArr = new double[myNewTotalItemsCapacity];
// copy and shift the current data into the new array
System.arraycopy(myCurDoubleItemsArr, 0, myNewDoubleItemsArr, deltaItemsCap, myCurTotalItemsCapacity);
}
else if (sketchType == FLOATS_SKETCH) {
myNewFloatItemsArr = new float[myNewTotalItemsCapacity];
// copy and shift the current items data into the new array
System.arraycopy(myCurFloatItemsArr, 0, myNewFloatItemsArr, deltaItemsCap, myCurTotalItemsCapacity);
}
else { //sketchType == ITEMS_SKETCH
myNewItemsArr = new Object[myNewTotalItemsCapacity];
// copy and shift the current items data into the new array
System.arraycopy(myCurItemsArr, 0, myNewItemsArr, deltaItemsCap, myCurTotalItemsCapacity);
}
//MEMORY SPACE MANAGEMENT
if (sketch.getWritableMemory() != null) {
final WritableMemory wmem = memorySpaceMgmt(sketch, myNewLevelsArr.length, myNewTotalItemsCapacity);
sketch.setWritableMemory(wmem);
}
//update our sketch with new expanded spaces
sketch.setNumLevels(myNewNumLevels); //for off-heap only
sketch.setLevelsArray(myNewLevelsArr); //the KllSketch copy
if (sketchType == DOUBLES_SKETCH) {
final KllDoublesSketch dblSk = (KllDoublesSketch) sketch;
dblSk.setMinItem(minDouble);
dblSk.setMaxItem(maxDouble);
dblSk.setDoubleItemsArray(myNewDoubleItemsArr);
}
else if (sketchType == FLOATS_SKETCH) {
final KllFloatsSketch fltSk = (KllFloatsSketch) sketch;
fltSk.setMinItem(minFloat);
fltSk.setMaxItem(maxFloat);
fltSk.setFloatItemsArray(myNewFloatItemsArr);
}
else { //sketchType == ITEMS_SKETCH
final KllItemsSketch itmSk = (KllItemsSketch) sketch;
itmSk.setMinItem(minItem);
itmSk.setMaxItem(maxItem);
itmSk.setItemsArray(myNewItemsArr);
}
}
/**
* Finds the first level starting with level 0 that exceeds its nominal capacity
* @param k configured size of sketch. Range [m, 2^16]
* @param m minimum level size. Default is 8.
* @param numLevels one-based number of current levels
* @return level to compact
*/
static int findLevelToCompact(final int k, final int m, final int numLevels, final int[] levels) {
int level = 0;
while (true) {
assert level < numLevels;
final int pop = levels[level + 1] - levels[level];
final int cap = KllHelper.levelCapacity(k, numLevels, level, m);
if (pop >= cap) {
return level;
}
level++;
}
}
/**
* Computes the actual item capacity of a given level given its depth index.
* If the depth of levels exceeds 30, this uses a folding technique to accurately compute the
* actual level capacity up to a depth of 60 (or 61 levels).
* Without folding, the internal calculations would exceed the capacity of a long.
* This method just decides whether folding is required or not.
* @param k the configured k of the sketch
* @param depth the zero-based index of the level being computed.
* @return the actual capacity of a given level given its depth index.
*/
private static long intCapAux(final int k, final int depth) {
if (depth <= 30) { return intCapAuxAux(k, depth); }
final int half = depth / 2;
final int rest = depth - half;
final long tmp = intCapAuxAux(k, half);
return intCapAuxAux(tmp, rest);
}
/**
* Performs the integer based calculation of an individual level (or folded level).
* @param k the configured k of the sketch
* @param depth the zero-based index of the level being computed. The max depth is 30!
* @return the actual capacity of a given level given its depth index.
*/
private static long intCapAuxAux(final long k, final int depth) {
final long twok = k << 1; // for rounding at the end, pre-multiply by 2 here, divide by 2 during rounding.
final long tmp = ((twok << depth) / powersOfThree[depth]); //2k* (2/3)^depth. 2k also keeps the fraction larger.
final long result = ((tmp + 1L) >>> 1); // (tmp + 1)/2. If odd, round up. This guarantees an integer.
assert (result <= k);
return result;
}
private final static boolean enablePrinting = false;
/**
* @param format the format
* @param args the args
*/
private static final void printf(final String format, final Object ... args) {
if (enablePrinting) { System.out.printf(format, args); }
}
/**
* @param o the Object to println
*/
private static final void println(final Object o) {
if (enablePrinting) { System.out.println(o.toString()); }
}
}
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