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lifengchao
2024-08-15 14:44:06 +08:00
commit 808c6b8e1e
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.gitignore vendored Normal file
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.idea
target
*.iml

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pom.xml Normal file
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<?xml version="1.0" encoding="UTF-8"?>
<project xmlns="http://maven.apache.org/POM/4.0.0"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
<modelVersion>4.0.0</modelVersion>
<groupId>com.geedgenetworks</groupId>
<artifactId>sketches</artifactId>
<version>1.0.0</version>
<properties>
<maven.compiler.source>11</maven.compiler.source>
<maven.compiler.target>11</maven.compiler.target>
<project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
</properties>
<dependencies>
<dependency>
<groupId>it.unimi.dsi</groupId>
<artifactId>fastutil</artifactId>
<version>8.5.12</version>
</dependency>
<dependency>
<groupId>org.hdrhistogram</groupId>
<artifactId>HdrHistogram</artifactId>
<version>2.1.12</version>
</dependency>
<dependency>
<groupId>junit</groupId>
<artifactId>junit</artifactId>
<version>4.13.2</version>
<scope>test</scope>
</dependency>
</dependencies>
<build>
<finalName>sketches</finalName>
<plugins>
<!-- Java Compiler -->
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-compiler-plugin</artifactId>
<version>3.1</version>
<configuration>
<source>${maven.compiler.source}</source>
<target>${maven.compiler.target}</target>
</configuration>
</plugin>
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-surefire-plugin</artifactId>
</plugin>
<plugin>
<groupId>org.codehaus.mojo</groupId>
<artifactId>build-helper-maven-plugin</artifactId>
<version>1.7</version>
<executions>
<!-- Add src/main/scala to eclipse build path -->
<execution>
<id>add-source</id>
<phase>generate-sources</phase>
<goals>
<goal>add-source</goal>
</goals>
<configuration>
<sources>
<source>src/main/scala</source>
</sources>
</configuration>
</execution>
<!-- Add src/test/scala to eclipse build path -->
<execution>
<id>add-test-source</id>
<phase>generate-test-sources</phase>
<goals>
<goal>add-test-source</goal>
</goals>
<configuration>
<sources>
<source>src/test/scala</source>
</sources>
</configuration>
</execution>
</executions>
</plugin>
</plugins>
</build>
</project>

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src/main/java/com/geedgenetworks/sketch/hlld/DirectHllIntArray.java Normal file
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package com.geedgenetworks.sketch.hlld;
import java.nio.ByteBuffer;
import java.nio.ByteOrder;
/**
* 基于ByteBuffer操作Hll，主要用于druid中聚合使用堆外内存的情况
*/
public class DirectHllIntArray extends HllImpl {
/**
* byte offset:
* Byte 0: version
* Byte 1: precision
* Byte 2: regs
*/
public static final int PRECISION_BYTE = 1;
public static final int REGS_BYTE = 2;
private ByteBuffer byteBuffer;
private int initPosition;
DirectHllIntArray(int precision, ByteBuffer byteBuffer) {
this.byteBuffer = byteBuffer;
this.initPosition = byteBuffer.position();
int reg = 1 << precision;
assert byteBuffer.limit() - byteBuffer.position() >= (reg + REG_PER_WORD - 1) / REG_PER_WORD * 4;
if(!byteBuffer.isReadOnly()){
this.byteBuffer.put(this.initPosition, (byte)1);
this.byteBuffer.put(this.initPosition + PRECISION_BYTE, (byte)precision);
}
}
// druid内部使用
void resetByteBuffer(ByteBuffer byteBuffer){
this.byteBuffer = byteBuffer;
this.initPosition = byteBuffer.position();
}
@Override
int getRegister(int idx) {
int word = byteBuffer.getInt(initPosition + REGS_BYTE + ((idx / REG_PER_WORD) << 2) );
word = word >>> (REG_WIDTH * (idx % REG_PER_WORD));
return word & ((1 << REG_WIDTH) - 1);
}
@Override
void setRegister(int idx, int val) {
int i = idx / REG_PER_WORD;
int pos = initPosition + REGS_BYTE + (i << 2);
int word = byteBuffer.getInt(pos);
// Shift the val into place
int shift = REG_WIDTH * (idx % REG_PER_WORD);
val = val << shift;
int val_mask = ((1 << REG_WIDTH) - 1) << shift;
// Store the word
byteBuffer.putInt(pos, (word & ~val_mask) | val);
}
@Override
int getWord(int idx) {
return byteBuffer.getInt(initPosition + REGS_BYTE + ((idx / REG_PER_WORD) << 2) );
}
@Override
void setWord(int idx, int word) {
int i = idx / REG_PER_WORD;
int pos = initPosition + REGS_BYTE + (i << 2);
byteBuffer.putInt(pos, word);
}
@Override
boolean isMemory() {
return true;
}
@Override
void reset() {
resetCacheZero();
int p = getPrecision();
int reg = 1 << p;
int words = (reg + REG_PER_WORD - 1) / REG_PER_WORD;
final long endBytes = initPosition + REGS_BYTE + (words << 2);
for (int i = initPosition + REGS_BYTE; i < endBytes; i++) {
byteBuffer.put(i, (byte)0);
}
}
@Override
int getPrecision() {
return byteBuffer.get(initPosition + PRECISION_BYTE);
}
@Override
void setPrecision(int precision) {
this.byteBuffer.put(initPosition + PRECISION_BYTE, (byte)precision);
}
@Override
HllImpl copy() {
int p = getPrecision();
HllIntArray hll = new HllIntArray(p);
for (int i = 0; i < hll.regs.length; i++) {
int pos = initPosition + REGS_BYTE + (i << 2);
int word = byteBuffer.getInt(pos);
hll.regs[i] = word;
}
return hll;
}
private int sparseWordCount(){
int p = getPrecision();
if(p > 17){
return -1;
}
int reg = 1 << p;
int words = (reg + REG_PER_WORD - 1) / REG_PER_WORD;
int halfWord = words >>> 1;
int count = 0;
for (int i = 0; i < words; i++) {
int pos = initPosition + REGS_BYTE + (i << 2);
int word = byteBuffer.getInt(pos);
if(word != 0){
count++;
if(count > halfWord){
return -1;
}
}
}
return count;
}
private byte[] toSparseBytes(int sparseLen) {
int size = getSparseSerializationBytes(sparseLen);
int p = getPrecision();
int reg = 1 << p;
ByteBuffer byteBuf = ByteBuffer.allocate(size);
byteBuf.put((byte)0); // flag
byteBuf.put((byte)1); // version
byteBuf.put((byte)p); // p
byteBuf.putShort((short)sparseLen); // len
int words = (reg + REG_PER_WORD - 1) / REG_PER_WORD;
for (int i = 0; i < words; i++) {
int pos = initPosition + REGS_BYTE + (i << 2);
int word = byteBuffer.getInt(pos);
if(word != 0){
byteBuf.putShort((short)i);
byteBuf.putInt(word);
}
}
return byteBuf.array();
}
private byte[] toDenseBytes() {
int size = getSerializationBytes();
byte[] bytes = new byte[size];
assert byteBuffer.order() == ByteOrder.BIG_ENDIAN;
int oldPosition = byteBuffer.position();
byteBuffer.position(initPosition);
byteBuffer.get(bytes, 0, size);
byteBuffer.position(oldPosition);
return bytes;
}
@Override
byte[] toBytes() {
int sparseLen = sparseWordCount();
if(sparseLen == -1){
return toDenseBytes();
}else{
return toSparseBytes(sparseLen);
}
}
public static DirectHllIntArray wrapBytes(byte[] bytes) {
ByteBuffer byteBuffer = ByteBuffer.wrap(bytes);
return wrapByteBuffer(byteBuffer);
}
public static DirectHllIntArray wrapByteBuffer(ByteBuffer byteBuffer) {
int initPosition = byteBuffer.position();
int version = byteBuffer.get(initPosition);
if(version != 1){
throw new IllegalArgumentException("Unsupported version:" + version);
}
int p = byteBuffer.get(initPosition + PRECISION_BYTE);
DirectHllIntArray hll = new DirectHllIntArray(p, byteBuffer);
return hll;
}
public static final int getUpdatableSerializationBytes(final int precision){
int reg = 1 << precision;
int words = (reg + REG_PER_WORD - 1) / REG_PER_WORD;
// version + p + regs
return 1 + 1 + words * 4;
}
}

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src/main/java/com/geedgenetworks/sketch/hlld/DirectHllIntSparseArray.java Normal file
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package com.geedgenetworks.sketch.hlld;
import java.nio.ByteBuffer;
import java.nio.ByteOrder;
/**
* 只支持读的DirectHllIntArray，主要用于druid中反序列使用稀疏数组压缩储存的Hll
*/
public class DirectHllIntSparseArray extends HllImpl {
/**
* byte offset:
* Byte 0: flag
* Byte 1: version
* Byte 2: precision
* Byte 3: len
* Byte 5: regs
*/
public static final int VERSION_BYTE = 1;
public static final int PRECISION_BYTE = 2;
public static final int LEN_BYTE = 3;
public static final int REGS_BYTE = 5;
final ByteBuffer byteBuffer;
final int initPosition;
final int p;
final int len;
private DirectHllIntSparseArray(ByteBuffer byteBuffer) {
int initPosition = byteBuffer.position();
int version = byteBuffer.get(initPosition + VERSION_BYTE);
int p = byteBuffer.get(initPosition + PRECISION_BYTE);
int len = byteBuffer.getShort(initPosition + LEN_BYTE);
if(version != 1){
throw new IllegalArgumentException("Unsupported version:" + version);
}
assert byteBuffer.limit() - initPosition - REGS_BYTE >= len * 6;
this.byteBuffer = byteBuffer;
this.initPosition = initPosition;
this.p = p;
this.len = len;
}
public static DirectHllIntSparseArray wrapBytes(byte[] bytes) {
ByteBuffer byteBuffer = ByteBuffer.wrap(bytes);
return wrapByteBuffer(byteBuffer);
}
public static DirectHllIntSparseArray wrapByteBuffer(ByteBuffer byteBuffer) {
DirectHllIntSparseArray hll = new DirectHllIntSparseArray(byteBuffer);
return hll;
}
/*int getRegsPosition() {
return initPosition + REGS_BYTE;
}*/
int getWordIdx(int i) {
return byteBuffer.getShort(initPosition + REGS_BYTE + i * 6);
}
int getWordValue(int i) {
return byteBuffer.getInt(initPosition + REGS_BYTE + i * 6 + 2);
}
@Override
int getRegister(int idx) {
throw new UnsupportedOperationException("unsupported method");
}
@Override
void setRegister(int idx, int val) {
throw new UnsupportedOperationException("unsupported method");
}
@Override
int getWord(int idx) {
throw new UnsupportedOperationException("unsupported method");
}
@Override
void setWord(int idx, int word) {
throw new UnsupportedOperationException("unsupported method");
}
@Override
void reset() {
throw new UnsupportedOperationException("unsupported method");
}
@Override
boolean isMemory() {
return true;
}
@Override
int getPrecision() {
return p;
}
@Override
void setPrecision(int precision) {
throw new UnsupportedOperationException("unsupported method");
}
@Override
HllImpl copy() {
throw new UnsupportedOperationException("unsupported method");
}
@Override
byte[] toBytes() {
int size = getSparseSerializationBytes(len);
byte[] bytes = new byte[size];
assert byteBuffer.order() == ByteOrder.BIG_ENDIAN;
int oldPosition = byteBuffer.position();
byteBuffer.position(initPosition);
byteBuffer.get(bytes, 0, size);
byteBuffer.position(oldPosition);
return bytes;
}
@Override
public double size() {
if(cached){
return cachedCount;
}
int p = getPrecision();
int reg = 1 << p;
int notZeros = 0;
int regVal;
for (int k = 0; k < len; k++) {
int word = getWordValue(k);
for (int j = 0; j < 5; j++) {
regVal = getRegisterFromWord(word, j);
if (regVal != 0) {
notZeros++;
}
}
}
int numZeros = reg - notZeros;
assert numZeros > 0;
cachedCount = linearCount(reg, numZeros);
cached = true;
return cachedCount;
}
}

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src/main/java/com/geedgenetworks/sketch/hlld/Hll.java Normal file
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package com.geedgenetworks.sketch.hlld;
import java.io.Serializable;
import java.nio.ByteBuffer;
public class Hll implements Serializable {
static final int DEFAULT_PRECISION = 12;
static final int HLL_MIN_PRECISION = 4; // 16 registers
static final int HLL_MAX_PRECISION = 18; // 262,144 registers
static final long DEFAULT_HASH_SEED = 0L; // 9001L
public HllImpl hllImpl = null;
public Hll() {
this(DEFAULT_PRECISION);
}
public Hll(int precision) {
if (precision > HLL_MAX_PRECISION || precision < HLL_MIN_PRECISION) {
throw new RuntimeException("precision");
}
hllImpl = new HllIntArray(precision);
}
public Hll(int precision, ByteBuffer byteBuffer) {
hllImpl = new DirectHllIntArray(precision, byteBuffer);
}
Hll(final HllImpl that) {
hllImpl = that;
}
/**
* Copy constructor used by copy().
*/
Hll(final Hll that) {
hllImpl = that.hllImpl.copy();
}
/**
* 复制Hll到堆内存实例HllIntArray
*/
public Hll copy() {
return new Hll(this);
}
// druid内部使用
public void resetByteBuffer(ByteBuffer byteBuffer){
((DirectHllIntArray)hllImpl).resetByteBuffer(byteBuffer);
}
public void add(long val) {
hllImpl.add(val);
}
public void add(double val) {
hllImpl.add(val);
}
public void add(String val) {
hllImpl.add(val);
}
public void add(byte[] val) {
hllImpl.add(val);
}
public void reset() {
hllImpl.reset();
}
public double getEstimate() {
return hllImpl.getEstimate();
}
public double size() {
return hllImpl.size();
}
public int getPrecision() {
return hllImpl.getPrecision();
}
public int getP() {
return hllImpl.getPrecision();
}
public static final int getUpdatableSerializationBytes(final int precision){
return DirectHllIntArray.getUpdatableSerializationBytes(precision);
}
public byte[] toBytes() {
return hllImpl.toBytes();
}
public static Hll fromBytes(byte[] bytes) {
return new Hll(HllIntArray.fromBytes(bytes));
}
public static Hll fromByteBuffer(ByteBuffer byteBuffer) {
return new Hll(HllIntArray.fromByteBuffer(byteBuffer));
}
public static Hll wrapBytes(byte[] bytes) {
if(bytes[0] == 0){
return new Hll(DirectHllIntSparseArray.wrapBytes(bytes));
}else{
return new Hll(DirectHllIntArray.wrapBytes(bytes));
}
}
public static Hll wrapByteBuffer(ByteBuffer byteBuffer) {
if(byteBuffer.get(byteBuffer.position()) == 0){
return new Hll(DirectHllIntSparseArray.wrapByteBuffer(byteBuffer));
}else{
return new Hll(DirectHllIntArray.wrapByteBuffer(byteBuffer));
}
}
}

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src/main/java/com/geedgenetworks/sketch/hlld/HllConstants.java Normal file
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package com.geedgenetworks.sketch.hlld;
import java.util.stream.IntStream;
public class HllConstants {
public static double[] inversePow2Data = IntStream.rangeClosed(0, Byte.MAX_VALUE).mapToDouble(v -> Math.pow(2, -v)).toArray();
public static final int K_NEAREST_NEIGHBOR = 6;
public static final double[] thresholdData = { 10, 20, 40, 80, 220, 400, 900, 1800, 3100, 6500,
15500, 20000, 50000, 120000, 350000 };
public static final double[][] rawEstimateData = {
// precision 4
{ 11, 11.717, 12.207, 12.7896, 13.2882, 13.8204, 14.3772, 14.9342, 15.5202, 16.161, 16.7722,
17.4636, 18.0396, 18.6766, 19.3566, 20.0454, 20.7936, 21.4856, 22.2666, 22.9946, 23.766,
24.4692, 25.3638, 26.0764, 26.7864, 27.7602, 28.4814, 29.433, 30.2926, 31.0664, 31.9996,
32.7956, 33.5366, 34.5894, 35.5738, 36.2698, 37.3682, 38.0544, 39.2342, 40.0108, 40.7966,
41.9298, 42.8704, 43.6358, 44.5194, 45.773, 46.6772, 47.6174, 48.4888, 49.3304, 50.2506,
51.4996, 52.3824, 53.3078, 54.3984, 55.5838, 56.6618, 57.2174, 58.3514, 59.0802, 60.1482,
61.0376, 62.3598, 62.8078, 63.9744, 64.914, 65.781, 67.1806, 68.0594, 68.8446, 69.7928,
70.8248, 71.8324, 72.8598, 73.6246, 74.7014, 75.393, 76.6708, 77.2394, },
// precision 5
{ 23, 23.1194, 23.8208, 24.2318, 24.77, 25.2436, 25.7774, 26.2848, 26.8224, 27.3742, 27.9336,
28.503, 29.0494, 29.6292, 30.2124, 30.798, 31.367, 31.9728, 32.5944, 33.217, 33.8438,
34.3696, 35.0956, 35.7044, 36.324, 37.0668, 37.6698, 38.3644, 39.049, 39.6918, 40.4146,
41.082, 41.687, 42.5398, 43.2462, 43.857, 44.6606, 45.4168, 46.1248, 46.9222, 47.6804,
48.447, 49.3454, 49.9594, 50.7636, 51.5776, 52.331, 53.19, 53.9676, 54.7564, 55.5314,
56.4442, 57.3708, 57.9774, 58.9624, 59.8796, 60.755, 61.472, 62.2076, 63.1024, 63.8908,
64.7338, 65.7728, 66.629, 67.413, 68.3266, 69.1524, 70.2642, 71.1806, 72.0566, 72.9192,
73.7598, 74.3516, 75.5802, 76.4386, 77.4916, 78.1524, 79.1892, 79.8414, 80.8798, 81.8376,
82.4698, 83.7656, 84.331, 85.5914, 86.6012, 87.7016, 88.5582, 89.3394, 90.3544, 91.4912,
92.308, 93.3552, 93.9746, 95.2052, 95.727, 97.1322, 98.3944, 98.7588, 100.242, 101.1914,
102.2538, 102.8776, 103.6292, 105.1932, 105.9152, 107.0868, 107.6728, 108.7144, 110.3114,
110.8716, 111.245, 112.7908, 113.7064, 114.636, 115.7464, 116.1788, 117.7464, 118.4896,
119.6166, 120.5082, 121.7798, 122.9028, 123.4426, 124.8854, 125.705, 126.4652, 128.3464,
128.3462, 130.0398, 131.0342, 131.0042, 132.4766, 133.511, 134.7252, 135.425, 136.5172,
138.0572, 138.6694, 139.3712, 140.8598, 141.4594, 142.554, 143.4006, 144.7374, 146.1634,
146.8994, 147.605, 147.9304, 149.1636, 150.2468, 151.5876, 152.2096, 153.7032, 154.7146,
155.807, 156.9228, 157.0372, 158.5852, },
// precision 6
{ 46, 46.1902, 47.271, 47.8358, 48.8142, 49.2854, 50.317, 51.354, 51.8924, 52.9436, 53.4596,
54.5262, 55.6248, 56.1574, 57.2822, 57.837, 58.9636, 60.074, 60.7042, 61.7976, 62.4772,
63.6564, 64.7942, 65.5004, 66.686, 67.291, 68.5672, 69.8556, 70.4982, 71.8204, 72.4252,
73.7744, 75.0786, 75.8344, 77.0294, 77.8098, 79.0794, 80.5732, 81.1878, 82.5648, 83.2902,
84.6784, 85.3352, 86.8946, 88.3712, 89.0852, 90.499, 91.2686, 92.6844, 94.2234, 94.9732,
96.3356, 97.2286, 98.7262, 100.3284, 101.1048, 102.5962, 103.3562, 105.1272, 106.4184,
107.4974, 109.0822, 109.856, 111.48, 113.2834, 114.0208, 115.637, 116.5174, 118.0576,
119.7476, 120.427, 122.1326, 123.2372, 125.2788, 126.6776, 127.7926, 129.1952, 129.9564,
131.6454, 133.87, 134.5428, 136.2, 137.0294, 138.6278, 139.6782, 141.792, 143.3516,
144.2832, 146.0394, 147.0748, 148.4912, 150.849, 151.696, 153.5404, 154.073, 156.3714,
157.7216, 158.7328, 160.4208, 161.4184, 163.9424, 165.2772, 166.411, 168.1308, 168.769,
170.9258, 172.6828, 173.7502, 175.706, 176.3886, 179.0186, 180.4518, 181.927, 183.4172,
184.4114, 186.033, 188.5124, 189.5564, 191.6008, 192.4172, 193.8044, 194.997, 197.4548,
198.8948, 200.2346, 202.3086, 203.1548, 204.8842, 206.6508, 206.6772, 209.7254, 210.4752,
212.7228, 214.6614, 215.1676, 217.793, 218.0006, 219.9052, 221.66, 223.5588, 225.1636,
225.6882, 227.7126, 229.4502, 231.1978, 232.9756, 233.1654, 236.727, 238.1974, 237.7474,
241.1346, 242.3048, 244.1948, 245.3134, 246.879, 249.1204, 249.853, 252.6792, 253.857,
254.4486, 257.2362, 257.9534, 260.0286, 260.5632, 262.663, 264.723, 265.7566, 267.2566,
267.1624, 270.62, 272.8216, 273.2166, 275.2056, 276.2202, 278.3726, 280.3344, 281.9284,
283.9728, 284.1924, 286.4872, 287.587, 289.807, 291.1206, 292.769, 294.8708, 296.665,
297.1182, 299.4012, 300.6352, 302.1354, 304.1756, 306.1606, 307.3462, 308.5214, 309.4134,
310.8352, 313.9684, 315.837, 316.7796, 318.9858, },
// precision 7
{ 92, 93.4934, 94.9758, 96.4574, 97.9718, 99.4954, 101.5302, 103.0756, 104.6374, 106.1782,
107.7888, 109.9522, 111.592, 113.2532, 114.9086, 116.5938, 118.9474, 120.6796, 122.4394,
124.2176, 125.9768, 128.4214, 130.2528, 132.0102, 133.8658, 135.7278, 138.3044, 140.1316,
142.093, 144.0032, 145.9092, 148.6306, 150.5294, 152.5756, 154.6508, 156.662, 159.552,
161.3724, 163.617, 165.5754, 167.7872, 169.8444, 172.7988, 174.8606, 177.2118, 179.3566,
181.4476, 184.5882, 186.6816, 189.0824, 191.0258, 193.6048, 196.4436, 198.7274, 200.957,
203.147, 205.4364, 208.7592, 211.3386, 213.781, 215.8028, 218.656, 221.6544, 223.996,
226.4718, 229.1544, 231.6098, 234.5956, 237.0616, 239.5758, 242.4878, 244.5244, 248.2146,
250.724, 252.8722, 255.5198, 258.0414, 261.941, 264.9048, 266.87, 269.4304, 272.028,
274.4708, 278.37, 281.0624, 283.4668, 286.5532, 289.4352, 293.2564, 295.2744, 298.2118,
300.7472, 304.1456, 307.2928, 309.7504, 312.5528, 315.979, 318.2102, 322.1834, 324.3494,
327.325, 330.6614, 332.903, 337.2544, 339.9042, 343.215, 345.2864, 348.0814, 352.6764,
355.301, 357.139, 360.658, 363.1732, 366.5902, 369.9538, 373.0828, 375.922, 378.9902,
382.7328, 386.4538, 388.1136, 391.2234, 394.0878, 396.708, 401.1556, 404.1852, 406.6372,
409.6822, 412.7796, 416.6078, 418.4916, 422.131, 424.5376, 428.1988, 432.211, 434.4502,
438.5282, 440.912, 444.0448, 447.7432, 450.8524, 453.7988, 456.7858, 458.8868, 463.9886,
466.5064, 468.9124, 472.6616, 475.4682, 478.582, 481.304, 485.2738, 488.6894, 490.329,
496.106, 497.6908, 501.1374, 504.5322, 506.8848, 510.3324, 513.4512, 516.179, 520.4412,
522.6066, 526.167, 528.7794, 533.379, 536.067, 538.46, 542.9116, 545.692, 547.9546,
552.493, 555.2722, 557.335, 562.449, 564.2014, 569.0738, 571.0974, 574.8564, 578.2996,
581.409, 583.9704, 585.8098, 589.6528, 594.5998, 595.958, 600.068, 603.3278, 608.2016,
609.9632, 612.864, 615.43, 620.7794, 621.272, 625.8644, 629.206, 633.219, 634.5154,
638.6102, },
// precision 8
{ 184.2152, 187.2454, 190.2096, 193.6652, 196.6312, 199.6822, 203.249, 206.3296, 210.0038,
213.2074, 216.4612, 220.27, 223.5178, 227.4412, 230.8032, 234.1634, 238.1688, 241.6074,
245.6946, 249.2664, 252.8228, 257.0432, 260.6824, 264.9464, 268.6268, 272.2626, 276.8376,
280.4034, 284.8956, 288.8522, 292.7638, 297.3552, 301.3556, 305.7526, 309.9292, 313.8954,
318.8198, 322.7668, 327.298, 331.6688, 335.9466, 340.9746, 345.1672, 349.3474, 354.3028,
358.8912, 364.114, 368.4646, 372.9744, 378.4092, 382.6022, 387.843, 392.5684, 397.1652,
402.5426, 407.4152, 412.5388, 417.3592, 422.1366, 427.486, 432.3918, 437.5076, 442.509,
447.3834, 453.3498, 458.0668, 463.7346, 469.1228, 473.4528, 479.7, 484.644, 491.0518,
495.5774, 500.9068, 506.432, 512.1666, 517.434, 522.6644, 527.4894, 533.6312, 538.3804,
544.292, 550.5496, 556.0234, 562.8206, 566.6146, 572.4188, 579.117, 583.6762, 590.6576,
595.7864, 601.509, 607.5334, 612.9204, 619.772, 624.2924, 630.8654, 636.1836, 642.745,
649.1316, 655.0386, 660.0136, 666.6342, 671.6196, 678.1866, 684.4282, 689.3324, 695.4794,
702.5038, 708.129, 713.528, 720.3204, 726.463, 732.7928, 739.123, 744.7418, 751.2192,
756.5102, 762.6066, 769.0184, 775.2224, 781.4014, 787.7618, 794.1436, 798.6506, 805.6378,
811.766, 819.7514, 824.5776, 828.7322, 837.8048, 843.6302, 849.9336, 854.4798, 861.3388,
867.9894, 873.8196, 880.3136, 886.2308, 892.4588, 899.0816, 905.4076, 912.0064, 917.3878,
923.619, 929.998, 937.3482, 943.9506, 947.991, 955.1144, 962.203, 968.8222, 975.7324,
981.7826, 988.7666, 994.2648, 1000.3128, 1007.4082, 1013.7536, 1020.3376, 1026.7156,
1031.7478, 1037.4292, 1045.393, 1051.2278, 1058.3434, 1062.8726, 1071.884, 1076.806,
1082.9176, 1089.1678, 1095.5032, 1102.525, 1107.2264, 1115.315, 1120.93, 1127.252,
1134.1496, 1139.0408, 1147.5448, 1153.3296, 1158.1974, 1166.5262, 1174.3328, 1175.657,
1184.4222, 1190.9172, 1197.1292, 1204.4606, 1210.4578, 1218.8728, 1225.3336, 1226.6592,
1236.5768, 1241.363, 1249.4074, 1254.6566, 1260.8014, 1266.5454, 1274.5192, },
// precision 9
{ 369, 374.8294, 381.2452, 387.6698, 394.1464, 400.2024, 406.8782, 413.6598, 420.462,
427.2826, 433.7102, 440.7416, 447.9366, 455.1046, 462.285, 469.0668, 476.306, 483.8448,
491.301, 498.9886, 506.2422, 513.8138, 521.7074, 529.7428, 537.8402, 545.1664, 553.3534,
561.594, 569.6886, 577.7876, 585.65, 594.228, 602.8036, 611.1666, 620.0818, 628.0824,
637.2574, 646.302, 655.1644, 664.0056, 672.3802, 681.7192, 690.5234, 700.2084, 708.831,
718.485, 728.1112, 737.4764, 746.76, 756.3368, 766.5538, 775.5058, 785.2646, 795.5902,
804.3818, 814.8998, 824.9532, 835.2062, 845.2798, 854.4728, 864.9582, 875.3292, 886.171,
896.781, 906.5716, 916.7048, 927.5322, 937.875, 949.3972, 958.3464, 969.7274, 980.2834,
992.1444, 1003.4264, 1013.0166, 1024.018, 1035.0438, 1046.34, 1057.6856, 1068.9836,
1079.0312, 1091.677, 1102.3188, 1113.4846, 1124.4424, 1135.739, 1147.1488, 1158.9202,
1169.406, 1181.5342, 1193.2834, 1203.8954, 1216.3286, 1226.2146, 1239.6684, 1251.9946,
1262.123, 1275.4338, 1285.7378, 1296.076, 1308.9692, 1320.4964, 1333.0998, 1343.9864,
1357.7754, 1368.3208, 1380.4838, 1392.7388, 1406.0758, 1416.9098, 1428.9728, 1440.9228,
1453.9292, 1462.617, 1476.05, 1490.2996, 1500.6128, 1513.7392, 1524.5174, 1536.6322,
1548.2584, 1562.3766, 1572.423, 1587.1232, 1596.5164, 1610.5938, 1622.5972, 1633.1222,
1647.7674, 1658.5044, 1671.57, 1683.7044, 1695.4142, 1708.7102, 1720.6094, 1732.6522,
1747.841, 1756.4072, 1769.9786, 1782.3276, 1797.5216, 1808.3186, 1819.0694, 1834.354,
1844.575, 1856.2808, 1871.1288, 1880.7852, 1893.9622, 1906.3418, 1920.6548, 1932.9302,
1945.8584, 1955.473, 1968.8248, 1980.6446, 1995.9598, 2008.349, 2019.8556, 2033.0334,
2044.0206, 2059.3956, 2069.9174, 2082.6084, 2093.7036, 2106.6108, 2118.9124, 2132.301,
2144.7628, 2159.8422, 2171.0212, 2183.101, 2193.5112, 2208.052, 2221.3194, 2233.3282,
2247.295, 2257.7222, 2273.342, 2286.5638, 2299.6786, 2310.8114, 2322.3312, 2335.516,
2349.874, 2363.5968, 2373.865, 2387.1918, 2401.8328, 2414.8496, 2424.544, 2436.7592,
2447.1682, 2464.1958, 2474.3438, 2489.0006, 2497.4526, 2513.6586, 2527.19, 2540.7028,
2553.768, },
// precision 10
{ 738.1256, 750.4234, 763.1064, 775.4732, 788.4636, 801.0644, 814.488, 827.9654, 841.0832,
854.7864, 868.1992, 882.2176, 896.5228, 910.1716, 924.7752, 938.899, 953.6126, 968.6492,
982.9474, 998.5214, 1013.1064, 1028.6364, 1044.2468, 1059.4588, 1075.3832, 1091.0584,
1106.8606, 1123.3868, 1139.5062, 1156.1862, 1172.463, 1189.339, 1206.1936, 1223.1292,
1240.1854, 1257.2908, 1275.3324, 1292.8518, 1310.5204, 1328.4854, 1345.9318, 1364.552,
1381.4658, 1400.4256, 1419.849, 1438.152, 1456.8956, 1474.8792, 1494.118, 1513.62,
1532.5132, 1551.9322, 1570.7726, 1590.6086, 1610.5332, 1630.5918, 1650.4294, 1669.7662,
1690.4106, 1710.7338, 1730.9012, 1750.4486, 1770.1556, 1791.6338, 1812.7312, 1833.6264,
1853.9526, 1874.8742, 1896.8326, 1918.1966, 1939.5594, 1961.07, 1983.037, 2003.1804,
2026.071, 2047.4884, 2070.0848, 2091.2944, 2114.333, 2135.9626, 2158.2902, 2181.0814,
2202.0334, 2224.4832, 2246.39, 2269.7202, 2292.1714, 2314.2358, 2338.9346, 2360.891,
2384.0264, 2408.3834, 2430.1544, 2454.8684, 2476.9896, 2501.4368, 2522.8702, 2548.0408,
2570.6738, 2593.5208, 2617.0158, 2640.2302, 2664.0962, 2687.4986, 2714.2588, 2735.3914,
2759.6244, 2781.8378, 2808.0072, 2830.6516, 2856.2454, 2877.2136, 2903.4546, 2926.785,
2951.2294, 2976.468, 3000.867, 3023.6508, 3049.91, 3073.5984, 3098.162, 3121.5564,
3146.2328, 3170.9484, 3195.5902, 3221.3346, 3242.7032, 3271.6112, 3296.5546, 3317.7376,
3345.072, 3369.9518, 3394.326, 3418.1818, 3444.6926, 3469.086, 3494.2754, 3517.8698,
3544.248, 3565.3768, 3588.7234, 3616.979, 3643.7504, 3668.6812, 3695.72, 3719.7392,
3742.6224, 3770.4456, 3795.6602, 3819.9058, 3844.002, 3869.517, 3895.6824, 3920.8622,
3947.1364, 3973.985, 3995.4772, 4021.62, 4046.628, 4074.65, 4096.2256, 4121.831,
4146.6406, 4173.276, 4195.0744, 4223.9696, 4251.3708, 4272.9966, 4300.8046, 4326.302,
4353.1248, 4374.312, 4403.0322, 4426.819, 4450.0598, 4478.5206, 4504.8116, 4528.8928,
4553.9584, 4578.8712, 4603.8384, 4632.3872, 4655.5128, 4675.821, 4704.6222, 4731.9862,
4755.4174, 4781.2628, 4804.332, 4832.3048, 4862.8752, 4883.4148, 4906.9544, 4935.3516,
4954.3532, 4984.0248, 5011.217, 5035.3258, 5057.3672, 5084.1828, },
// precision 11
{ 1477, 1501.6014, 1526.5802, 1551.7942, 1577.3042, 1603.2062, 1629.8402, 1656.2292,
1682.9462, 1709.9926, 1737.3026, 1765.4252, 1793.0578, 1821.6092, 1849.626, 1878.5568,
1908.527, 1937.5154, 1967.1874, 1997.3878, 2027.37, 2058.1972, 2089.5728, 2120.1012,
2151.9668, 2183.292, 2216.0772, 2247.8578, 2280.6562, 2313.041, 2345.714, 2380.3112,
2414.1806, 2447.9854, 2481.656, 2516.346, 2551.5154, 2586.8378, 2621.7448, 2656.6722,
2693.5722, 2729.1462, 2765.4124, 2802.8728, 2838.898, 2876.408, 2913.4926, 2951.4938,
2989.6776, 3026.282, 3065.7704, 3104.1012, 3143.7388, 3181.6876, 3221.1872, 3261.5048,
3300.0214, 3339.806, 3381.409, 3421.4144, 3461.4294, 3502.2286, 3544.651, 3586.6156,
3627.337, 3670.083, 3711.1538, 3753.5094, 3797.01, 3838.6686, 3882.1678, 3922.8116,
3967.9978, 4009.9204, 4054.3286, 4097.5706, 4140.6014, 4185.544, 4229.5976, 4274.583,
4316.9438, 4361.672, 4406.2786, 4451.8628, 4496.1834, 4543.505, 4589.1816, 4632.5188,
4678.2294, 4724.8908, 4769.0194, 4817.052, 4861.4588, 4910.1596, 4956.4344, 5002.5238,
5048.13, 5093.6374, 5142.8162, 5187.7894, 5237.3984, 5285.6078, 5331.0858, 5379.1036,
5428.6258, 5474.6018, 5522.7618, 5571.5822, 5618.59, 5667.9992, 5714.88, 5763.454,
5808.6982, 5860.3644, 5910.2914, 5953.571, 6005.9232, 6055.1914, 6104.5882, 6154.5702,
6199.7036, 6251.1764, 6298.7596, 6350.0302, 6398.061, 6448.4694, 6495.933, 6548.0474,
6597.7166, 6646.9416, 6695.9208, 6742.6328, 6793.5276, 6842.1934, 6894.2372, 6945.3864,
6996.9228, 7044.2372, 7094.1374, 7142.2272, 7192.2942, 7238.8338, 7288.9006, 7344.0908,
7394.8544, 7443.5176, 7490.4148, 7542.9314, 7595.6738, 7641.9878, 7694.3688, 7743.0448,
7797.522, 7845.53, 7899.594, 7950.3132, 7996.455, 8050.9442, 8092.9114, 8153.1374,
8197.4472, 8252.8278, 8301.8728, 8348.6776, 8401.4698, 8453.551, 8504.6598, 8553.8944,
8604.1276, 8657.6514, 8710.3062, 8758.908, 8807.8706, 8862.1702, 8910.4668, 8960.77,
9007.2766, 9063.164, 9121.0534, 9164.1354, 9218.1594, 9267.767, 9319.0594, 9372.155,
9419.7126, 9474.3722, 9520.1338, 9572.368, 9622.7702, 9675.8448, 9726.5396, 9778.7378,
9827.6554, 9878.1922, 9928.7782, 9978.3984, 10026.578, 10076.5626, 10137.1618,
10177.5244, 10229.9176, },
// precision 12
{ 2954, 3003.4782, 3053.3568, 3104.3666, 3155.324, 3206.9598, 3259.648, 3312.539, 3366.1474,
3420.2576, 3474.8376, 3530.6076, 3586.451, 3643.38, 3700.4104, 3757.5638, 3815.9676,
3875.193, 3934.838, 3994.8548, 4055.018, 4117.1742, 4178.4482, 4241.1294, 4304.4776,
4367.4044, 4431.8724, 4496.3732, 4561.4304, 4627.5326, 4693.949, 4761.5532, 4828.7256,
4897.6182, 4965.5186, 5034.4528, 5104.865, 5174.7164, 5244.6828, 5316.6708, 5387.8312,
5459.9036, 5532.476, 5604.8652, 5679.6718, 5753.757, 5830.2072, 5905.2828, 5980.0434,
6056.6264, 6134.3192, 6211.5746, 6290.0816, 6367.1176, 6447.9796, 6526.5576, 6606.1858,
6686.9144, 6766.1142, 6847.0818, 6927.9664, 7010.9096, 7091.0816, 7175.3962, 7260.3454,
7344.018, 7426.4214, 7511.3106, 7596.0686, 7679.8094, 7765.818, 7852.4248, 7936.834,
8022.363, 8109.5066, 8200.4554, 8288.5832, 8373.366, 8463.4808, 8549.7682, 8642.0522,
8728.3288, 8820.9528, 8907.727, 9001.0794, 9091.2522, 9179.988, 9269.852, 9362.6394,
9453.642, 9546.9024, 9640.6616, 9732.6622, 9824.3254, 9917.7484, 10007.9392, 10106.7508,
10196.2152, 10289.8114, 10383.5494, 10482.3064, 10576.8734, 10668.7872, 10764.7156,
10862.0196, 10952.793, 11049.9748, 11146.0702, 11241.4492, 11339.2772, 11434.2336,
11530.741, 11627.6136, 11726.311, 11821.5964, 11918.837, 12015.3724, 12113.0162,
12213.0424, 12306.9804, 12408.4518, 12504.8968, 12604.586, 12700.9332, 12798.705,
12898.5142, 12997.0488, 13094.788, 13198.475, 13292.7764, 13392.9698, 13486.8574,
13590.1616, 13686.5838, 13783.6264, 13887.2638, 13992.0978, 14081.0844, 14189.9956,
14280.0912, 14382.4956, 14486.4384, 14588.1082, 14686.2392, 14782.276, 14888.0284,
14985.1864, 15088.8596, 15187.0998, 15285.027, 15383.6694, 15495.8266, 15591.3736,
15694.2008, 15790.3246, 15898.4116, 15997.4522, 16095.5014, 16198.8514, 16291.7492,
16402.6424, 16499.1266, 16606.2436, 16697.7186, 16796.3946, 16902.3376, 17005.7672,
17100.814, 17206.8282, 17305.8262, 17416.0744, 17508.4092, 17617.0178, 17715.4554,
17816.758, 17920.1748, 18012.9236, 18119.7984, 18223.2248, 18324.2482, 18426.6276,
18525.0932, 18629.8976, 18733.2588, 18831.0466, 18940.1366, 19032.2696, 19131.729,
19243.4864, 19349.6932, 19442.866, 19547.9448, 19653.2798, 19754.4034, 19854.0692,
19965.1224, 20065.1774, 20158.2212, 20253.353, 20366.3264, 20463.22, },
// precision 13
{ 5908.5052, 6007.2672, 6107.347, 6208.5794, 6311.2622, 6414.5514, 6519.3376, 6625.6952,
6732.5988, 6841.3552, 6950.5972, 7061.3082, 7173.5646, 7287.109, 7401.8216, 7516.4344,
7633.3802, 7751.2962, 7870.3784, 7990.292, 8110.79, 8233.4574, 8356.6036, 8482.2712,
8607.7708, 8735.099, 8863.1858, 8993.4746, 9123.8496, 9255.6794, 9388.5448, 9522.7516,
9657.3106, 9792.6094, 9930.5642, 10068.794, 10206.7256, 10347.81, 10490.3196, 10632.0778,
10775.9916, 10920.4662, 11066.124, 11213.073, 11358.0362, 11508.1006, 11659.1716,
11808.7514, 11959.4884, 12112.1314, 12265.037, 12420.3756, 12578.933, 12734.311,
12890.0006, 13047.2144, 13207.3096, 13368.5144, 13528.024, 13689.847, 13852.7528,
14018.3168, 14180.5372, 14346.9668, 14513.5074, 14677.867, 14846.2186, 15017.4186,
15184.9716, 15356.339, 15529.2972, 15697.3578, 15871.8686, 16042.187, 16216.4094,
16389.4188, 16565.9126, 16742.3272, 16919.0042, 17094.7592, 17273.965, 17451.8342,
17634.4254, 17810.5984, 17988.9242, 18171.051, 18354.7938, 18539.466, 18721.0408,
18904.9972, 19081.867, 19271.9118, 19451.8694, 19637.9816, 19821.2922, 20013.1292,
20199.3858, 20387.8726, 20572.9514, 20770.7764, 20955.1714, 21144.751, 21329.9952,
21520.709, 21712.7016, 21906.3868, 22096.2626, 22286.0524, 22475.051, 22665.5098,
22862.8492, 23055.5294, 23249.6138, 23437.848, 23636.273, 23826.093, 24020.3296,
24213.3896, 24411.7392, 24602.9614, 24805.7952, 24998.1552, 25193.9588, 25389.0166,
25585.8392, 25780.6976, 25981.2728, 26175.977, 26376.5252, 26570.1964, 26773.387,
26962.9812, 27163.0586, 27368.164, 27565.0534, 27758.7428, 27961.1276, 28163.2324,
28362.3816, 28565.7668, 28758.644, 28956.9768, 29163.4722, 29354.7026, 29561.1186,
29767.9948, 29959.9986, 30164.0492, 30366.9818, 30562.5338, 30762.9928, 30976.1592,
31166.274, 31376.722, 31570.3734, 31770.809, 31974.8934, 32179.5286, 32387.5442,
32582.3504, 32794.076, 32989.9528, 33191.842, 33392.4684, 33595.659, 33801.8672,
34000.3414, 34200.0922, 34402.6792, 34610.0638, 34804.0084, 35011.13, 35218.669,
35418.6634, 35619.0792, 35830.6534, 36028.4966, 36229.7902, 36438.6422, 36630.7764,
36833.3102, 37048.6728, 37247.3916, 37453.5904, 37669.3614, 37854.5526, 38059.305,
38268.0936, 38470.2516, 38674.7064, 38876.167, 39068.3794, 39281.9144, 39492.8566,
39684.8628, 39898.4108, 40093.1836, 40297.6858, 40489.7086, 40717.2424, },
// precision 14
{ 11817.475, 12015.0046, 12215.3792, 12417.7504, 12623.1814, 12830.0086, 13040.0072,
13252.503, 13466.178, 13683.2738, 13902.0344, 14123.9798, 14347.394, 14573.7784,
14802.6894, 15033.6824, 15266.9134, 15502.8624, 15741.4944, 15980.7956, 16223.8916,
16468.6316, 16715.733, 16965.5726, 17217.204, 17470.666, 17727.8516, 17986.7886,
18247.6902, 18510.9632, 18775.304, 19044.7486, 19314.4408, 19587.202, 19862.2576,
20135.924, 20417.0324, 20697.9788, 20979.6112, 21265.0274, 21550.723, 21841.6906,
22132.162, 22428.1406, 22722.127, 23020.5606, 23319.7394, 23620.4014, 23925.2728,
24226.9224, 24535.581, 24845.505, 25155.9618, 25470.3828, 25785.9702, 26103.7764,
26420.4132, 26742.0186, 27062.8852, 27388.415, 27714.6024, 28042.296, 28365.4494,
28701.1526, 29031.8008, 29364.2156, 29704.497, 30037.1458, 30380.111, 30723.8168,
31059.5114, 31404.9498, 31751.6752, 32095.2686, 32444.7792, 32794.767, 33145.204,
33498.4226, 33847.6502, 34209.006, 34560.849, 34919.4838, 35274.9778, 35635.1322,
35996.3266, 36359.1394, 36722.8266, 37082.8516, 37447.7354, 37815.9606, 38191.0692,
38559.4106, 38924.8112, 39294.6726, 39663.973, 40042.261, 40416.2036, 40779.2036,
41161.6436, 41540.9014, 41921.1998, 42294.7698, 42678.5264, 43061.3464, 43432.375,
43818.432, 44198.6598, 44583.0138, 44970.4794, 45353.924, 45729.858, 46118.2224,
46511.5724, 46900.7386, 47280.6964, 47668.1472, 48055.6796, 48446.9436, 48838.7146,
49217.7296, 49613.7796, 50010.7508, 50410.0208, 50793.7886, 51190.2456, 51583.1882,
51971.0796, 52376.5338, 52763.319, 53165.5534, 53556.5594, 53948.2702, 54346.352,
54748.7914, 55138.577, 55543.4824, 55941.1748, 56333.7746, 56745.1552, 57142.7944,
57545.2236, 57935.9956, 58348.5268, 58737.5474, 59158.5962, 59542.6896, 59958.8004,
60349.3788, 60755.0212, 61147.6144, 61548.194, 61946.0696, 62348.6042, 62763.603,
63162.781, 63560.635, 63974.3482, 64366.4908, 64771.5876, 65176.7346, 65597.3916,
65995.915, 66394.0384, 66822.9396, 67203.6336, 67612.2032, 68019.0078, 68420.0388,
68821.22, 69235.8388, 69640.0724, 70055.155, 70466.357, 70863.4266, 71276.2482,
71677.0306, 72080.2006, 72493.0214, 72893.5952, 73314.5856, 73714.9852, 74125.3022,
74521.2122, 74933.6814, 75341.5904, 75743.0244, 76166.0278, 76572.1322, 76973.1028,
77381.6284, 77800.6092, 78189.328, 78607.0962, 79012.2508, 79407.8358, 79825.725,
80238.701, 80646.891, 81035.6436, 81460.0448, 81876.3884, },
// precision 15
{ 23635.0036, 24030.8034, 24431.4744, 24837.1524, 25246.7928, 25661.326, 26081.3532,
26505.2806, 26933.9892, 27367.7098, 27805.318, 28248.799, 28696.4382, 29148.8244,
29605.5138, 30066.8668, 30534.2344, 31006.32, 31480.778, 31962.2418, 32447.3324,
32938.0232, 33432.731, 33930.728, 34433.9896, 34944.1402, 35457.5588, 35974.5958,
36497.3296, 37021.9096, 37554.326, 38088.0826, 38628.8816, 39171.3192, 39723.2326,
40274.5554, 40832.3142, 41390.613, 41959.5908, 42532.5466, 43102.0344, 43683.5072,
44266.694, 44851.2822, 45440.7862, 46038.0586, 46640.3164, 47241.064, 47846.155,
48454.7396, 49076.9168, 49692.542, 50317.4778, 50939.65, 51572.5596, 52210.2906,
52843.7396, 53481.3996, 54127.236, 54770.406, 55422.6598, 56078.7958, 56736.7174,
57397.6784, 58064.5784, 58730.308, 59404.9784, 60077.0864, 60751.9158, 61444.1386,
62115.817, 62808.7742, 63501.4774, 64187.5454, 64883.6622, 65582.7468, 66274.5318,
66976.9276, 67688.7764, 68402.138, 69109.6274, 69822.9706, 70543.6108, 71265.5202,
71983.3848, 72708.4656, 73433.384, 74158.4664, 74896.4868, 75620.9564, 76362.1434,
77098.3204, 77835.7662, 78582.6114, 79323.9902, 80067.8658, 80814.9246, 81567.0136,
82310.8536, 83061.9952, 83821.4096, 84580.8608, 85335.547, 86092.5802, 86851.6506,
87612.311, 88381.2016, 89146.3296, 89907.8974, 90676.846, 91451.4152, 92224.5518,
92995.8686, 93763.5066, 94551.2796, 95315.1944, 96096.1806, 96881.0918, 97665.679,
98442.68, 99229.3002, 100011.0994, 100790.6386, 101580.1564, 102377.7484, 103152.1392,
103944.2712, 104730.216, 105528.6336, 106324.9398, 107117.6706, 107890.3988, 108695.2266,
109485.238, 110294.7876, 111075.0958, 111878.0496, 112695.2864, 113464.5486, 114270.0474,
115068.608, 115884.3626, 116673.2588, 117483.3716, 118275.097, 119085.4092, 119879.2808,
120687.5868, 121499.9944, 122284.916, 123095.9254, 123912.5038, 124709.0454, 125503.7182,
126323.259, 127138.9412, 127943.8294, 128755.646, 129556.5354, 130375.3298, 131161.4734,
131971.1962, 132787.5458, 133588.1056, 134431.351, 135220.2906, 136023.398, 136846.6558,
137667.0004, 138463.663, 139283.7154, 140074.6146, 140901.3072, 141721.8548, 142543.2322,
143356.1096, 144173.7412, 144973.0948, 145794.3162, 146609.5714, 147420.003, 148237.9784,
149050.5696, 149854.761, 150663.1966, 151494.0754, 152313.1416, 153112.6902, 153935.7206,
154746.9262, 155559.547, 156401.9746, 157228.7036, 158008.7254, 158820.75, 159646.9184,
160470.4458, 161279.5348, 162093.3114, 162918.542, 163729.2842, },
// precision 16
{ 47271, 48062.3584, 48862.7074, 49673.152, 50492.8416, 51322.9514, 52161.03, 53009.407,
53867.6348, 54734.206, 55610.5144, 56496.2096, 57390.795, 58297.268, 59210.6448,
60134.665, 61068.0248, 62010.4472, 62962.5204, 63923.5742, 64895.0194, 65876.4182,
66862.6136, 67862.6968, 68868.8908, 69882.8544, 70911.271, 71944.0924, 72990.0326,
74040.692, 75100.6336, 76174.7826, 77252.5998, 78340.2974, 79438.2572, 80545.4976,
81657.2796, 82784.6336, 83915.515, 85059.7362, 86205.9368, 87364.4424, 88530.3358,
89707.3744, 90885.9638, 92080.197, 93275.5738, 94479.391, 95695.918, 96919.2236,
98148.4602, 99382.3474, 100625.6974, 101878.0284, 103141.6278, 104409.4588, 105686.2882,
106967.5402, 108261.6032, 109548.1578, 110852.0728, 112162.231, 113479.0072, 114806.2626,
116137.9072, 117469.5048, 118813.5186, 120165.4876, 121516.2556, 122875.766, 124250.5444,
125621.2222, 127003.2352, 128387.848, 129775.2644, 131181.7776, 132577.3086, 133979.9458,
135394.1132, 136800.9078, 138233.217, 139668.5308, 141085.212, 142535.2122, 143969.0684,
145420.2872, 146878.1542, 148332.7572, 149800.3202, 151269.66, 152743.6104, 154213.0948,
155690.288, 157169.4246, 158672.1756, 160160.059, 161650.6854, 163145.7772, 164645.6726,
166159.1952, 167682.1578, 169177.3328, 170700.0118, 172228.8964, 173732.6664,
175265.5556, 176787.799, 178317.111, 179856.6914, 181400.865, 182943.4612, 184486.742,
186033.4698, 187583.7886, 189148.1868, 190688.4526, 192250.1926, 193810.9042,
195354.2972, 196938.7682, 198493.5898, 200079.2824, 201618.912, 203205.5492, 204765.5798,
206356.1124, 207929.3064, 209498.7196, 211086.229, 212675.1324, 214256.7892, 215826.2392,
217412.8474, 218995.6724, 220618.6038, 222207.1166, 223781.0364, 225387.4332,
227005.7928, 228590.4336, 230217.8738, 231805.1054, 233408.9, 234995.3432, 236601.4956,
238190.7904, 239817.2548, 241411.2832, 243002.4066, 244640.1884, 246255.3128,
247849.3508, 249479.9734, 251106.8822, 252705.027, 254332.9242, 255935.129, 257526.9014,
259154.772, 260777.625, 262390.253, 264004.4906, 265643.59, 267255.4076, 268873.426,
270470.7252, 272106.4804, 273722.4456, 275337.794, 276945.7038, 278592.9154, 280204.3726,
281841.1606, 283489.171, 285130.1716, 286735.3362, 288364.7164, 289961.1814, 291595.5524,
293285.683, 294899.6668, 296499.3434, 298128.0462, 299761.8946, 301394.2424, 302997.6748,
304615.1478, 306269.7724, 307886.114, 309543.1028, 311153.2862, 312782.8546, 314421.2008,
316033.2438, 317692.9636, 319305.2648, 320948.7406, 322566.3364, 324228.4224,
325847.1542, },
// precision 17
{ 94542, 96125.811, 97728.019, 99348.558, 100987.9705, 102646.7565, 104324.5125, 106021.7435,
107736.7865, 109469.272, 111223.9465, 112995.219, 114787.432, 116593.152, 118422.71,
120267.2345, 122134.6765, 124020.937, 125927.2705, 127851.255, 129788.9485, 131751.016,
133726.8225, 135722.592, 137736.789, 139770.568, 141821.518, 143891.343, 145982.1415,
148095.387, 150207.526, 152355.649, 154515.6415, 156696.05, 158887.7575, 161098.159,
163329.852, 165569.053, 167837.4005, 170121.6165, 172420.4595, 174732.6265, 177062.77,
179412.502, 181774.035, 184151.939, 186551.6895, 188965.691, 191402.8095, 193857.949,
196305.0775, 198774.6715, 201271.2585, 203764.78, 206299.3695, 208818.1365, 211373.115,
213946.7465, 216532.076, 219105.541, 221714.5375, 224337.5135, 226977.5125, 229613.0655,
232270.2685, 234952.2065, 237645.3555, 240331.1925, 243034.517, 245756.0725, 248517.6865,
251232.737, 254011.3955, 256785.995, 259556.44, 262368.335, 265156.911, 267965.266,
270785.583, 273616.0495, 276487.4835, 279346.639, 282202.509, 285074.3885, 287942.2855,
290856.018, 293774.0345, 296678.5145, 299603.6355, 302552.6575, 305492.9785, 308466.8605,
311392.581, 314347.538, 317319.4295, 320285.9785, 323301.7325, 326298.3235, 329301.3105,
332301.987, 335309.791, 338370.762, 341382.923, 344431.1265, 347464.1545, 350507.28,
353619.2345, 356631.2005, 359685.203, 362776.7845, 365886.488, 368958.2255, 372060.6825,
375165.4335, 378237.935, 381328.311, 384430.5225, 387576.425, 390683.242, 393839.648,
396977.8425, 400101.9805, 403271.296, 406409.8425, 409529.5485, 412678.7, 415847.423,
419020.8035, 422157.081, 425337.749, 428479.6165, 431700.902, 434893.1915, 438049.582,
441210.5415, 444379.2545, 447577.356, 450741.931, 453959.548, 457137.0935, 460329.846,
463537.4815, 466732.3345, 469960.5615, 473164.681, 476347.6345, 479496.173, 482813.1645,
486025.6995, 489249.4885, 492460.1945, 495675.8805, 498908.0075, 502131.802, 505374.3855,
508550.9915, 511806.7305, 515026.776, 518217.0005, 521523.9855, 524705.9855, 527950.997,
531210.0265, 534472.497, 537750.7315, 540926.922, 544207.094, 547429.4345, 550666.3745,
553975.3475, 557150.7185, 560399.6165, 563662.697, 566916.7395, 570146.1215, 573447.425,
576689.6245, 579874.5745, 583202.337, 586503.0255, 589715.635, 592910.161, 596214.3885,
599488.035, 602740.92, 605983.0685, 609248.67, 612491.3605, 615787.912, 619107.5245,
622307.9555, 625577.333, 628840.4385, 632085.2155, 635317.6135, 638691.7195, 641887.467,
645139.9405, 648441.546, 651666.252, 654941.845, },
// precision 18
{ 189084, 192250.913, 195456.774, 198696.946, 201977.762, 205294.444, 208651.754, 212042.099,
215472.269, 218941.91, 222443.912, 225996.845, 229568.199, 233193.568, 236844.457,
240543.233, 244279.475, 248044.27, 251854.588, 255693.2, 259583.619, 263494.621,
267445.385, 271454.061, 275468.769, 279549.456, 283646.446, 287788.198, 291966.099,
296181.164, 300431.469, 304718.618, 309024.004, 313393.508, 317760.803, 322209.731,
326675.061, 331160.627, 335654.47, 340241.442, 344841.833, 349467.132, 354130.629,
358819.432, 363574.626, 368296.587, 373118.482, 377914.93, 382782.301, 387680.669,
392601.981, 397544.323, 402529.115, 407546.018, 412593.658, 417638.657, 422762.865,
427886.169, 433017.167, 438213.273, 443441.254, 448692.421, 453937.533, 459239.049,
464529.569, 469910.083, 475274.03, 480684.473, 486070.26, 491515.237, 496995.651,
502476.617, 507973.609, 513497.19, 519083.233, 524726.509, 530305.505, 535945.728,
541584.404, 547274.055, 552967.236, 558667.862, 564360.216, 570128.148, 575965.08,
581701.952, 587532.523, 593361.144, 599246.128, 605033.418, 610958.779, 616837.117,
622772.818, 628672.04, 634675.369, 640574.831, 646585.739, 652574.547, 658611.217,
664642.684, 670713.914, 676737.681, 682797.313, 688837.897, 694917.874, 701009.882,
707173.648, 713257.254, 719415.392, 725636.761, 731710.697, 737906.209, 744103.074,
750313.39, 756504.185, 762712.579, 768876.985, 775167.859, 781359, 787615.959,
793863.597, 800245.477, 806464.582, 812785.294, 819005.925, 825403.057, 831676.197,
837936.284, 844266.968, 850642.711, 856959.756, 863322.774, 869699.931, 876102.478,
882355.787, 888694.463, 895159.952, 901536.143, 907872.631, 914293.672, 920615.14,
927130.974, 933409.404, 939922.178, 946331.47, 952745.93, 959209.264, 965590.224,
972077.284, 978501.961, 984953.19, 991413.271, 997817.479, 1004222.658, 1010725.676,
1017177.138, 1023612.529, 1030098.236, 1036493.719, 1043112.207, 1049537.036,
1056008.096, 1062476.184, 1068942.337, 1075524.95, 1081932.864, 1088426.025, 1094776.005,
1101327.448, 1107901.673, 1114423.639, 1120884.602, 1127324.923, 1133794.24, 1140328.886,
1146849.376, 1153346.682, 1159836.502, 1166478.703, 1172953.304, 1179391.502,
1185950.982, 1192544.052, 1198913.41, 1205430.994, 1212015.525, 1218674.042, 1225121.683,
1231551.101, 1238126.379, 1244673.795, 1251260.649, 1257697.86, 1264320.983, 1270736.319,
1277274.694, 1283804.95, 1290211.514, 1296858.568, 1303455.691, } };
public static final double[][] biasData = {
// precision 4
{ 10, 9.717, 9.207, 8.7896, 8.2882, 7.8204, 7.3772, 6.9342, 6.5202, 6.161, 5.7722, 5.4636,
5.0396, 4.6766, 4.3566, 4.0454, 3.7936, 3.4856, 3.2666, 2.9946, 2.766, 2.4692, 2.3638,
2.0764, 1.7864, 1.7602, 1.4814, 1.433, 1.2926, 1.0664, 0.999600000000001, 0.7956, 0.5366,
0.589399999999998, 0.573799999999999, 0.269799999999996, 0.368200000000002,
0.0544000000000011, 0.234200000000001, 0.0108000000000033, -0.203400000000002,
-0.0701999999999998, -0.129600000000003, -0.364199999999997, -0.480600000000003,
-0.226999999999997, -0.322800000000001, -0.382599999999996, -0.511200000000002,
-0.669600000000003, -0.749400000000001, -0.500399999999999, -0.617600000000003, -0.6922,
-0.601599999999998, -0.416200000000003, -0.338200000000001, -0.782600000000002,
-0.648600000000002, -0.919800000000002, -0.851799999999997, -0.962400000000002, -0.6402,
-1.1922, -1.0256, -1.086, -1.21899999999999, -0.819400000000002, -0.940600000000003,
-1.1554, -1.2072, -1.1752, -1.16759999999999, -1.14019999999999, -1.3754,
-1.29859999999999, -1.607, -1.3292, -1.7606, },
// precision 5
{ 22, 21.1194, 20.8208, 20.2318, 19.77, 19.2436, 18.7774, 18.2848, 17.8224, 17.3742, 16.9336,
16.503, 16.0494, 15.6292, 15.2124, 14.798, 14.367, 13.9728, 13.5944, 13.217, 12.8438,
12.3696, 12.0956, 11.7044, 11.324, 11.0668, 10.6698, 10.3644, 10.049, 9.6918, 9.4146,
9.082, 8.687, 8.5398, 8.2462, 7.857, 7.6606, 7.4168, 7.1248, 6.9222, 6.6804, 6.447,
6.3454, 5.9594, 5.7636, 5.5776, 5.331, 5.19, 4.9676, 4.7564, 4.5314, 4.4442, 4.3708,
3.9774, 3.9624, 3.8796, 3.755, 3.472, 3.2076, 3.1024, 2.8908, 2.7338, 2.7728, 2.629,
2.413, 2.3266, 2.1524, 2.2642, 2.1806, 2.0566, 1.9192, 1.7598, 1.3516, 1.5802,
1.43859999999999, 1.49160000000001, 1.1524, 1.1892, 0.841399999999993, 0.879800000000003,
0.837599999999995, 0.469800000000006, 0.765600000000006, 0.331000000000003,
0.591399999999993, 0.601200000000006, 0.701599999999999, 0.558199999999999,
0.339399999999998, 0.354399999999998, 0.491200000000006, 0.308000000000007,
0.355199999999996, -0.0254000000000048, 0.205200000000005, -0.272999999999996,
0.132199999999997, 0.394400000000005, -0.241200000000006, 0.242000000000004,
0.191400000000002, 0.253799999999998, -0.122399999999999, -0.370800000000003,
0.193200000000004, -0.0848000000000013, 0.0867999999999967, -0.327200000000005,
-0.285600000000002, 0.311400000000006, -0.128399999999999, -0.754999999999995,
-0.209199999999996, -0.293599999999998, -0.364000000000004, -0.253600000000006,
-0.821200000000005, -0.253600000000006, -0.510400000000004, -0.383399999999995,
-0.491799999999998, -0.220200000000006, -0.0972000000000008, -0.557400000000001,
-0.114599999999996, -0.295000000000002, -0.534800000000004, 0.346399999999988,
-0.65379999999999, 0.0398000000000138, 0.0341999999999985, -0.995800000000003,
-0.523400000000009, -0.489000000000004, -0.274799999999999, -0.574999999999989,
-0.482799999999997, 0.0571999999999946, -0.330600000000004, -0.628800000000012,
-0.140199999999993, -0.540600000000012, -0.445999999999998, -0.599400000000003,
-0.262599999999992, 0.163399999999996, -0.100599999999986, -0.39500000000001,
-1.06960000000001, -0.836399999999998, -0.753199999999993, -0.412399999999991,
-0.790400000000005, -0.29679999999999, -0.28540000000001, -0.193000000000012,
-0.0772000000000048, -0.962799999999987, -0.414800000000014, },
// precision 6
{ 45, 44.1902, 43.271, 42.8358, 41.8142, 41.2854, 40.317, 39.354, 38.8924, 37.9436, 37.4596,
36.5262, 35.6248, 35.1574, 34.2822, 33.837, 32.9636, 32.074, 31.7042, 30.7976, 30.4772,
29.6564, 28.7942, 28.5004, 27.686, 27.291, 26.5672, 25.8556, 25.4982, 24.8204, 24.4252,
23.7744, 23.0786, 22.8344, 22.0294, 21.8098, 21.0794, 20.5732, 20.1878, 19.5648, 19.2902,
18.6784, 18.3352, 17.8946, 17.3712, 17.0852, 16.499, 16.2686, 15.6844, 15.2234, 14.9732,
14.3356, 14.2286, 13.7262, 13.3284, 13.1048, 12.5962, 12.3562, 12.1272, 11.4184, 11.4974,
11.0822, 10.856, 10.48, 10.2834, 10.0208, 9.637, 9.51739999999999, 9.05759999999999,
8.74760000000001, 8.42700000000001, 8.1326, 8.2372, 8.2788, 7.6776, 7.79259999999999,
7.1952, 6.9564, 6.6454, 6.87, 6.5428, 6.19999999999999, 6.02940000000001,
5.62780000000001, 5.6782, 5.792, 5.35159999999999, 5.28319999999999, 5.0394,
5.07480000000001, 4.49119999999999, 4.84899999999999, 4.696, 4.54040000000001,
4.07300000000001, 4.37139999999999, 3.7216, 3.7328, 3.42080000000001, 3.41839999999999,
3.94239999999999, 3.27719999999999, 3.411, 3.13079999999999, 2.76900000000001,
2.92580000000001, 2.68279999999999, 2.75020000000001, 2.70599999999999, 2.3886,
3.01859999999999, 2.45179999999999, 2.92699999999999, 2.41720000000001, 2.41139999999999,
2.03299999999999, 2.51240000000001, 2.5564, 2.60079999999999, 2.41720000000001,
1.80439999999999, 1.99700000000001, 2.45480000000001, 1.8948, 2.2346, 2.30860000000001,
2.15479999999999, 1.88419999999999, 1.6508, 0.677199999999999, 1.72540000000001, 1.4752,
1.72280000000001, 1.66139999999999, 1.16759999999999, 1.79300000000001, 1.00059999999999,
0.905200000000008, 0.659999999999997, 1.55879999999999, 1.1636, 0.688199999999995,
0.712600000000009, 0.450199999999995, 1.1978, 0.975599999999986, 0.165400000000005,
1.727, 1.19739999999999, -0.252600000000001, 1.13460000000001, 1.3048, 1.19479999999999,
0.313400000000001, 0.878999999999991, 1.12039999999999, 0.853000000000009,
1.67920000000001, 0.856999999999999, 0.448599999999999, 1.2362, 0.953399999999988,
1.02859999999998, 0.563199999999995, 0.663000000000011, 0.723000000000013,
0.756599999999992, 0.256599999999992, -0.837600000000009, 0.620000000000005,
0.821599999999989, 0.216600000000028, 0.205600000000004, 0.220199999999977,
0.372599999999977, 0.334400000000016, 0.928400000000011, 0.972800000000007,
0.192400000000021, 0.487199999999973, -0.413000000000011, 0.807000000000016,
0.120600000000024, 0.769000000000005, 0.870799999999974, 0.66500000000002,
0.118200000000002, 0.401200000000017, 0.635199999999998, 0.135400000000004,
0.175599999999974, 1.16059999999999, 0.34620000000001, 0.521400000000028,
-0.586599999999976, -1.16480000000001, 0.968399999999974, 0.836999999999989,
0.779600000000016, 0.985799999999983, },
// precision 7
{ 91, 89.4934, 87.9758, 86.4574, 84.9718, 83.4954, 81.5302, 80.0756, 78.6374, 77.1782,
75.7888, 73.9522, 72.592, 71.2532, 69.9086, 68.5938, 66.9474, 65.6796, 64.4394, 63.2176,
61.9768, 60.4214, 59.2528, 58.0102, 56.8658, 55.7278, 54.3044, 53.1316, 52.093, 51.0032,
49.9092, 48.6306, 47.5294, 46.5756, 45.6508, 44.662, 43.552, 42.3724, 41.617, 40.5754,
39.7872, 38.8444, 37.7988, 36.8606, 36.2118, 35.3566, 34.4476, 33.5882, 32.6816, 32.0824,
31.0258, 30.6048, 29.4436, 28.7274, 27.957, 27.147, 26.4364, 25.7592, 25.3386, 24.781,
23.8028, 23.656, 22.6544, 21.996, 21.4718, 21.1544, 20.6098, 19.5956, 19.0616, 18.5758,
18.4878, 17.5244, 17.2146, 16.724, 15.8722, 15.5198, 15.0414, 14.941, 14.9048, 13.87,
13.4304, 13.028, 12.4708, 12.37, 12.0624, 11.4668, 11.5532, 11.4352, 11.2564, 10.2744,
10.2118, 9.74720000000002, 10.1456, 9.2928, 8.75040000000001, 8.55279999999999,
8.97899999999998, 8.21019999999999, 8.18340000000001, 7.3494, 7.32499999999999,
7.66140000000001, 6.90300000000002, 7.25439999999998, 6.9042, 7.21499999999997,
6.28640000000001, 6.08139999999997, 6.6764, 6.30099999999999, 5.13900000000001,
5.65800000000002, 5.17320000000001, 4.59019999999998, 4.9538, 5.08280000000002,
4.92200000000003, 4.99020000000002, 4.7328, 5.4538, 4.11360000000002, 4.22340000000003,
4.08780000000002, 3.70800000000003, 4.15559999999999, 4.18520000000001, 3.63720000000001,
3.68220000000002, 3.77960000000002, 3.6078, 2.49160000000001, 3.13099999999997, 2.5376,
3.19880000000001, 3.21100000000001, 2.4502, 3.52820000000003, 2.91199999999998,
3.04480000000001, 2.7432, 2.85239999999999, 2.79880000000003, 2.78579999999999,
1.88679999999999, 2.98860000000002, 2.50639999999999, 1.91239999999999, 2.66160000000002,
2.46820000000002, 1.58199999999999, 1.30399999999997, 2.27379999999999, 2.68939999999998,
1.32900000000001, 3.10599999999999, 1.69080000000002, 2.13740000000001, 2.53219999999999,
1.88479999999998, 1.33240000000001, 1.45119999999997, 1.17899999999997, 2.44119999999998,
1.60659999999996, 2.16700000000003, 0.77940000000001, 2.37900000000002, 2.06700000000001,
1.46000000000004, 2.91160000000002, 1.69200000000001, 0.954600000000028,
2.49300000000005, 2.2722, 1.33500000000004, 2.44899999999996, 1.20140000000004,
3.07380000000001, 2.09739999999999, 2.85640000000001, 2.29960000000005, 2.40899999999999,
1.97040000000004, 0.809799999999996, 1.65279999999996, 2.59979999999996,
0.95799999999997, 2.06799999999998, 2.32780000000002, 4.20159999999998, 1.96320000000003,
1.86400000000003, 1.42999999999995, 3.77940000000001, 1.27200000000005, 1.86440000000005,
2.20600000000002, 3.21900000000005, 1.5154, 2.61019999999996, },
// precision 8
{ 183.2152, 180.2454, 177.2096, 173.6652, 170.6312, 167.6822, 164.249, 161.3296, 158.0038,
155.2074, 152.4612, 149.27, 146.5178, 143.4412, 140.8032, 138.1634, 135.1688, 132.6074,
129.6946, 127.2664, 124.8228, 122.0432, 119.6824, 116.9464, 114.6268, 112.2626, 109.8376,
107.4034, 104.8956, 102.8522, 100.7638, 98.3552, 96.3556, 93.7526, 91.9292, 89.8954,
87.8198, 85.7668, 83.298, 81.6688, 79.9466, 77.9746, 76.1672, 74.3474, 72.3028, 70.8912,
69.114, 67.4646, 65.9744, 64.4092, 62.6022, 60.843, 59.5684, 58.1652, 56.5426, 55.4152,
53.5388, 52.3592, 51.1366, 49.486, 48.3918, 46.5076, 45.509, 44.3834, 43.3498, 42.0668,
40.7346, 40.1228, 38.4528, 37.7, 36.644, 36.0518, 34.5774, 33.9068, 32.432, 32.1666,
30.434, 29.6644, 28.4894, 27.6312, 26.3804, 26.292, 25.5496000000001, 25.0234, 24.8206,
22.6146, 22.4188, 22.117, 20.6762, 20.6576, 19.7864, 19.509, 18.5334, 17.9204, 17.772,
16.2924, 16.8654, 15.1836, 15.745, 15.1316, 15.0386, 14.0136, 13.6342, 12.6196, 12.1866,
12.4281999999999, 11.3324, 10.4794000000001, 11.5038, 10.129, 9.52800000000002,
10.3203999999999, 9.46299999999997, 9.79280000000006, 9.12300000000005, 8.74180000000001,
9.2192, 7.51020000000005, 7.60659999999996, 7.01840000000004, 7.22239999999999,
7.40139999999997, 6.76179999999999, 7.14359999999999, 5.65060000000005, 5.63779999999997,
5.76599999999996, 6.75139999999999, 5.57759999999996, 3.73220000000003, 5.8048,
5.63019999999995, 4.93359999999996, 3.47979999999995, 4.33879999999999, 3.98940000000005,
3.81960000000004, 3.31359999999995, 3.23080000000004, 3.4588, 3.08159999999998, 3.4076,
3.00639999999999, 2.38779999999997, 2.61900000000003, 1.99800000000005, 3.34820000000002,
2.95060000000001, 0.990999999999985, 2.11440000000005, 2.20299999999997,
2.82219999999995, 2.73239999999998, 2.7826, 3.76660000000004, 2.26480000000004,
2.31280000000004, 2.40819999999997, 2.75360000000001, 3.33759999999995, 2.71559999999999,
1.7478000000001, 1.42920000000004, 2.39300000000003, 2.22779999999989, 2.34339999999997,
0.87259999999992, 3.88400000000001, 1.80600000000004, 1.91759999999999, 1.16779999999994,
1.50320000000011, 2.52500000000009, 0.226400000000012, 2.31500000000005,
0.930000000000064, 1.25199999999995, 2.14959999999996, 0.0407999999999902,
2.5447999999999, 1.32960000000003, 0.197400000000016, 2.52620000000002, 3.33279999999991,
-1.34300000000007, 0.422199999999975, 0.917200000000093, 1.12920000000008,
1.46060000000011, 1.45779999999991, 2.8728000000001, 3.33359999999993, -1.34079999999994,
1.57680000000005, 0.363000000000056, 1.40740000000005, 0.656600000000026,
0.801400000000058, -0.454600000000028, 1.51919999999996, },
// precision 9
{ 368, 361.8294, 355.2452, 348.6698, 342.1464, 336.2024, 329.8782, 323.6598, 317.462,
311.2826, 305.7102, 299.7416, 293.9366, 288.1046, 282.285, 277.0668, 271.306, 265.8448,
260.301, 254.9886, 250.2422, 244.8138, 239.7074, 234.7428, 229.8402, 225.1664, 220.3534,
215.594, 210.6886, 205.7876, 201.65, 197.228, 192.8036, 188.1666, 184.0818, 180.0824,
176.2574, 172.302, 168.1644, 164.0056, 160.3802, 156.7192, 152.5234, 149.2084, 145.831,
142.485, 139.1112, 135.4764, 131.76, 129.3368, 126.5538, 122.5058, 119.2646, 116.5902,
113.3818, 110.8998, 107.9532, 105.2062, 102.2798, 99.4728, 96.9582, 94.3292, 92.171,
89.7809999999999, 87.5716, 84.7048, 82.5322, 79.875, 78.3972, 75.3464, 73.7274, 71.2834,
70.1444, 68.4263999999999, 66.0166, 64.018, 62.0437999999999, 60.3399999999999, 58.6856,
57.9836, 55.0311999999999, 54.6769999999999, 52.3188, 51.4846, 49.4423999999999, 47.739,
46.1487999999999, 44.9202, 43.4059999999999, 42.5342000000001, 41.2834, 38.8954000000001,
38.3286000000001, 36.2146, 36.6684, 35.9946, 33.123, 33.4338, 31.7378000000001, 29.076,
28.9692, 27.4964, 27.0998, 25.9864, 26.7754, 24.3208, 23.4838, 22.7388000000001,
24.0758000000001, 21.9097999999999, 20.9728, 19.9228000000001, 19.9292, 16.617, 17.05,
18.2996000000001, 15.6128000000001, 15.7392, 14.5174, 13.6322, 12.2583999999999,
13.3766000000001, 11.423, 13.1232, 9.51639999999998, 10.5938000000001, 9.59719999999993,
8.12220000000002, 9.76739999999995, 7.50440000000003, 7.56999999999994, 6.70440000000008,
6.41419999999994, 6.71019999999999, 5.60940000000005, 4.65219999999999, 6.84099999999989,
3.4072000000001, 3.97859999999991, 3.32760000000007, 5.52160000000003, 3.31860000000006,
2.06940000000009, 4.35400000000004, 1.57500000000005, 0.280799999999999,
2.12879999999996, -0.214799999999968, -0.0378000000000611, -0.658200000000079,
0.654800000000023, -0.0697999999999865, 0.858400000000074, -2.52700000000004,
-2.1751999999999, -3.35539999999992, -1.04019999999991, -0.651000000000067,
-2.14439999999991, -1.96659999999997, -3.97939999999994, -0.604400000000169,
-3.08260000000018, -3.39159999999993, -5.29640000000018, -5.38920000000007,
-5.08759999999984, -4.69900000000007, -5.23720000000003, -3.15779999999995,
-4.97879999999986, -4.89899999999989, -7.48880000000008, -5.94799999999987,
-5.68060000000014, -6.67180000000008, -4.70499999999993, -7.27779999999984,
-4.6579999999999, -4.4362000000001, -4.32139999999981, -5.18859999999995,
-6.66879999999992, -6.48399999999992, -5.1260000000002, -4.4032000000002,
-6.13500000000022, -5.80819999999994, -4.16719999999987, -4.15039999999999,
-7.45600000000013, -7.24080000000004, -9.83179999999993, -5.80420000000004,
-8.6561999999999, -6.99940000000015, -10.5473999999999, -7.34139999999979,
-6.80999999999995, -6.29719999999998, -6.23199999999997, },
// precision 10
{ 737.1256, 724.4234, 711.1064, 698.4732, 685.4636, 673.0644, 660.488, 647.9654, 636.0832,
623.7864, 612.1992, 600.2176, 588.5228, 577.1716, 565.7752, 554.899, 543.6126, 532.6492,
521.9474, 511.5214, 501.1064, 490.6364, 480.2468, 470.4588, 460.3832, 451.0584, 440.8606,
431.3868, 422.5062, 413.1862, 404.463, 395.339, 386.1936, 378.1292, 369.1854, 361.2908,
353.3324, 344.8518, 337.5204, 329.4854, 321.9318, 314.552, 306.4658, 299.4256, 292.849,
286.152, 278.8956, 271.8792, 265.118, 258.62, 252.5132, 245.9322, 239.7726, 233.6086,
227.5332, 222.5918, 216.4294, 210.7662, 205.4106, 199.7338, 194.9012, 188.4486, 183.1556,
178.6338, 173.7312, 169.6264, 163.9526, 159.8742, 155.8326, 151.1966, 147.5594, 143.07,
140.037, 134.1804, 131.071, 127.4884, 124.0848, 120.2944, 117.333, 112.9626, 110.2902,
107.0814, 103.0334, 99.4832000000001, 96.3899999999999, 93.7202000000002,
90.1714000000002, 87.2357999999999, 85.9346, 82.8910000000001, 80.0264000000002,
78.3834000000002, 75.1543999999999, 73.8683999999998, 70.9895999999999, 69.4367999999999,
64.8701999999998, 65.0408000000002, 61.6738, 59.5207999999998, 57.0158000000001, 54.2302,
53.0962, 50.4985999999999, 52.2588000000001, 47.3914, 45.6244000000002, 42.8377999999998,
43.0072, 40.6516000000001, 40.2453999999998, 35.2136, 36.4546, 33.7849999999999,
33.2294000000002, 32.4679999999998, 30.8670000000002, 28.6507999999999, 28.9099999999999,
27.5983999999999, 26.1619999999998, 24.5563999999999, 23.2328000000002, 21.9484000000002,
21.5902000000001, 21.3346000000001, 17.7031999999999, 20.6111999999998, 19.5545999999999,
15.7375999999999, 17.0720000000001, 16.9517999999998, 15.326, 13.1817999999998,
14.6925999999999, 13.0859999999998, 13.2754, 10.8697999999999, 11.248, 7.3768,
4.72339999999986, 7.97899999999981, 8.7503999999999, 7.68119999999999, 9.7199999999998,
7.73919999999998, 5.6224000000002, 7.44560000000001, 6.6601999999998, 5.9058,
4.00199999999995, 4.51699999999983, 4.68240000000014, 3.86220000000003, 5.13639999999987,
5.98500000000013, 2.47719999999981, 2.61999999999989, 1.62800000000016, 4.65000000000009,
0.225599999999758, 0.831000000000131, -0.359400000000278, 1.27599999999984,
-2.92559999999958, -0.0303999999996449, 2.37079999999969, -2.0033999999996,
0.804600000000391, 0.30199999999968, 1.1247999999996, -2.6880000000001,
0.0321999999996478, -1.18099999999959, -3.9402, -1.47940000000017, -0.188400000000001,
-2.10720000000038, -2.04159999999956, -3.12880000000041, -4.16160000000036,
-0.612799999999879, -3.48719999999958, -8.17900000000009, -5.37780000000021,
-4.01379999999972, -5.58259999999973, -5.73719999999958, -7.66799999999967,
-5.69520000000011, -1.1247999999996, -5.58520000000044, -8.04560000000038,
-4.64840000000004, -11.6468000000004, -7.97519999999986, -5.78300000000036,
-7.67420000000038, -10.6328000000003, -9.81720000000041, },
// precision 11
{ 1476, 1449.6014, 1423.5802, 1397.7942, 1372.3042, 1347.2062, 1321.8402, 1297.2292,
1272.9462, 1248.9926, 1225.3026, 1201.4252, 1178.0578, 1155.6092, 1132.626, 1110.5568,
1088.527, 1066.5154, 1045.1874, 1024.3878, 1003.37, 982.1972, 962.5728, 942.1012,
922.9668, 903.292, 884.0772, 864.8578, 846.6562, 828.041, 809.714, 792.3112, 775.1806,
757.9854, 740.656, 724.346, 707.5154, 691.8378, 675.7448, 659.6722, 645.5722, 630.1462,
614.4124, 600.8728, 585.898, 572.408, 558.4926, 544.4938, 531.6776, 517.282, 505.7704,
493.1012, 480.7388, 467.6876, 456.1872, 445.5048, 433.0214, 420.806, 411.409, 400.4144,
389.4294, 379.2286, 369.651, 360.6156, 350.337, 342.083, 332.1538, 322.5094, 315.01,
305.6686, 298.1678, 287.8116, 280.9978, 271.9204, 265.3286, 257.5706, 249.6014, 242.544,
235.5976, 229.583, 220.9438, 214.672, 208.2786, 201.8628, 195.1834, 191.505, 186.1816,
178.5188, 172.2294, 167.8908, 161.0194, 158.052, 151.4588, 148.1596, 143.4344, 138.5238,
133.13, 127.6374, 124.8162, 118.7894, 117.3984, 114.6078, 109.0858, 105.1036, 103.6258,
98.6018000000004, 95.7618000000002, 93.5821999999998, 88.5900000000001, 86.9992000000002,
82.8800000000001, 80.4539999999997, 74.6981999999998, 74.3644000000004, 73.2914000000001,
65.5709999999999, 66.9232000000002, 65.1913999999997, 62.5882000000001, 61.5702000000001,
55.7035999999998, 56.1764000000003, 52.7596000000003, 53.0302000000001, 49.0609999999997,
48.4694, 44.933, 46.0474000000004, 44.7165999999997, 41.9416000000001, 39.9207999999999,
35.6328000000003, 35.5276000000003, 33.1934000000001, 33.2371999999996, 33.3864000000003,
33.9228000000003, 30.2371999999996, 29.1373999999996, 25.2272000000003, 24.2942000000003,
19.8338000000003, 18.9005999999999, 23.0907999999999, 21.8544000000002, 19.5176000000001,
15.4147999999996, 16.9314000000004, 18.6737999999996, 12.9877999999999, 14.3688000000002,
12.0447999999997, 15.5219999999999, 12.5299999999997, 14.5940000000001, 14.3131999999996,
9.45499999999993, 12.9441999999999, 3.91139999999996, 13.1373999999996, 5.44720000000052,
9.82779999999912, 7.87279999999919, 3.67760000000089, 5.46980000000076, 5.55099999999948,
5.65979999999945, 3.89439999999922, 3.1275999999998, 5.65140000000065, 6.3062000000009,
3.90799999999945, 1.87060000000019, 5.17020000000048, 2.46680000000015,
0.770000000000437, -3.72340000000077, 1.16400000000067, 8.05340000000069,
0.135399999999208, 2.15940000000046, 0.766999999999825, 1.0594000000001,
3.15500000000065, -0.287399999999252, 2.37219999999979, -2.86620000000039,
-1.63199999999961, -2.22979999999916, -0.15519999999924, -1.46039999999994,
-0.262199999999211, -2.34460000000036, -2.8078000000005, -3.22179999999935,
-5.60159999999996, -8.42200000000048, -9.43740000000071, 0.161799999999857,
-10.4755999999998, -10.0823999999993, },
// precision 12
{ 2953, 2900.4782, 2848.3568, 2796.3666, 2745.324, 2694.9598, 2644.648, 2595.539, 2546.1474,
2498.2576, 2450.8376, 2403.6076, 2357.451, 2311.38, 2266.4104, 2221.5638, 2176.9676,
2134.193, 2090.838, 2048.8548, 2007.018, 1966.1742, 1925.4482, 1885.1294, 1846.4776,
1807.4044, 1768.8724, 1731.3732, 1693.4304, 1657.5326, 1621.949, 1586.5532, 1551.7256,
1517.6182, 1483.5186, 1450.4528, 1417.865, 1385.7164, 1352.6828, 1322.6708, 1291.8312,
1260.9036, 1231.476, 1201.8652, 1173.6718, 1145.757, 1119.2072, 1092.2828, 1065.0434,
1038.6264, 1014.3192, 988.5746, 965.0816, 940.1176, 917.9796, 894.5576, 871.1858,
849.9144, 827.1142, 805.0818, 783.9664, 763.9096, 742.0816, 724.3962, 706.3454, 688.018,
667.4214, 650.3106, 633.0686, 613.8094, 597.818, 581.4248, 563.834, 547.363, 531.5066,
520.455400000001, 505.583199999999, 488.366, 476.480799999999, 459.7682, 450.0522,
434.328799999999, 423.952799999999, 408.727000000001, 399.079400000001, 387.252200000001,
373.987999999999, 360.852000000001, 351.6394, 339.642, 330.902400000001,
322.661599999999, 311.662200000001, 301.3254, 291.7484, 279.939200000001, 276.7508,
263.215200000001, 254.811400000001, 245.5494, 242.306399999999, 234.8734,
223.787200000001, 217.7156, 212.0196, 200.793, 195.9748, 189.0702, 182.449199999999,
177.2772, 170.2336, 164.741, 158.613600000001, 155.311, 147.5964, 142.837, 137.3724,
132.0162, 130.0424, 121.9804, 120.451800000001, 114.8968, 111.585999999999,
105.933199999999, 101.705, 98.5141999999996, 95.0488000000005, 89.7880000000005,
91.4750000000004, 83.7764000000006, 80.9698000000008, 72.8574000000008, 73.1615999999995,
67.5838000000003, 62.6263999999992, 63.2638000000006, 66.0977999999996, 52.0843999999997,
58.9956000000002, 47.0912000000008, 46.4956000000002, 48.4383999999991, 47.1082000000006,
43.2392, 37.2759999999998, 40.0283999999992, 35.1864000000005, 35.8595999999998, 32.0998,
28.027, 23.6694000000007, 33.8266000000003, 26.3736000000008, 27.2008000000005,
21.3245999999999, 26.4115999999995, 23.4521999999997, 19.5013999999992, 19.8513999999996,
10.7492000000002, 18.6424000000006, 13.1265999999996, 18.2436000000016, 6.71860000000015,
3.39459999999963, 6.33759999999893, 7.76719999999841, 0.813999999998487,
3.82819999999992, 0.826199999999517, 8.07440000000133, -1.59080000000176,
5.01780000000144, 0.455399999998917, -0.24199999999837, 0.174800000000687,
-9.07640000000174, -4.20160000000033, -3.77520000000004, -4.75179999999818,
-5.3724000000002, -8.90680000000066, -6.10239999999976, -5.74120000000039,
-9.95339999999851, -3.86339999999836, -13.7304000000004, -16.2710000000006,
-7.51359999999841, -3.30679999999847, -13.1339999999982, -10.0551999999989,
-6.72019999999975, -8.59660000000076, -10.9307999999983, -1.8775999999998,
-4.82259999999951, -13.7788, -21.6470000000008, -10.6735999999983, -15.7799999999988, },
// precision 13
{ 5907.5052, 5802.2672, 5697.347, 5593.5794, 5491.2622, 5390.5514, 5290.3376, 5191.6952,
5093.5988, 4997.3552, 4902.5972, 4808.3082, 4715.5646, 4624.109, 4533.8216, 4444.4344,
4356.3802, 4269.2962, 4183.3784, 4098.292, 4014.79, 3932.4574, 3850.6036, 3771.2712,
3691.7708, 3615.099, 3538.1858, 3463.4746, 3388.8496, 3315.6794, 3244.5448, 3173.7516,
3103.3106, 3033.6094, 2966.5642, 2900.794, 2833.7256, 2769.81, 2707.3196, 2644.0778,
2583.9916, 2523.4662, 2464.124, 2406.073, 2347.0362, 2292.1006, 2238.1716, 2182.7514,
2128.4884, 2077.1314, 2025.037, 1975.3756, 1928.933, 1879.311, 1831.0006, 1783.2144,
1738.3096, 1694.5144, 1649.024, 1606.847, 1564.7528, 1525.3168, 1482.5372, 1443.9668,
1406.5074, 1365.867, 1329.2186, 1295.4186, 1257.9716, 1225.339, 1193.2972, 1156.3578,
1125.8686, 1091.187, 1061.4094, 1029.4188, 1000.9126, 972.3272, 944.004199999999,
915.7592, 889.965, 862.834200000001, 840.4254, 812.598399999999, 785.924200000001,
763.050999999999, 741.793799999999, 721.466, 699.040799999999, 677.997200000002,
649.866999999998, 634.911800000002, 609.8694, 591.981599999999, 570.2922,
557.129199999999, 538.3858, 521.872599999999, 502.951400000002, 495.776399999999,
475.171399999999, 459.751, 439.995200000001, 426.708999999999, 413.7016, 402.3868,
387.262599999998, 372.0524, 357.050999999999, 342.5098, 334.849200000001,
322.529399999999, 311.613799999999, 295.848000000002, 289.273000000001, 274.093000000001,
263.329600000001, 251.389599999999, 245.7392, 231.9614, 229.7952, 217.155200000001,
208.9588, 199.016599999999, 190.839199999999, 180.6976, 176.272799999999,
166.976999999999, 162.5252, 151.196400000001, 149.386999999999, 133.981199999998,
130.0586, 130.164000000001, 122.053400000001, 110.7428, 108.1276, 106.232400000001,
100.381600000001, 98.7668000000012, 86.6440000000002, 79.9768000000004, 82.4722000000002,
68.7026000000005, 70.1186000000016, 71.9948000000004, 58.998599999999, 59.0492000000013,
56.9818000000014, 47.5338000000011, 42.9928, 51.1591999999982, 37.2740000000013,
42.7220000000016, 31.3734000000004, 26.8090000000011, 25.8934000000008, 26.5286000000015,
29.5442000000003, 19.3503999999994, 26.0760000000009, 17.9527999999991, 14.8419999999969,
10.4683999999979, 8.65899999999965, 9.86720000000059, 4.34139999999752,
-0.907800000000861, -3.32080000000133, -0.936199999996461, -11.9916000000012,
-8.87000000000262, -6.33099999999831, -11.3366000000024, -15.9207999999999,
-9.34659999999712, -15.5034000000014, -19.2097999999969, -15.357799999998,
-28.2235999999975, -30.6898000000001, -19.3271999999997, -25.6083999999973,
-24.409599999999, -13.6385999999984, -33.4473999999973, -32.6949999999997,
-28.9063999999998, -31.7483999999968, -32.2935999999972, -35.8329999999987,
-47.620600000002, -39.0855999999985, -33.1434000000008, -46.1371999999974,
-37.5892000000022, -46.8164000000033, -47.3142000000007, -60.2914000000019,
-37.7575999999972, },
// precision 14
{ 11816.475, 11605.0046, 11395.3792, 11188.7504, 10984.1814, 10782.0086, 10582.0072,
10384.503, 10189.178, 9996.2738, 9806.0344, 9617.9798, 9431.394, 9248.7784, 9067.6894,
8889.6824, 8712.9134, 8538.8624, 8368.4944, 8197.7956, 8031.8916, 7866.6316, 7703.733,
7544.5726, 7386.204, 7230.666, 7077.8516, 6926.7886, 6778.6902, 6631.9632, 6487.304,
6346.7486, 6206.4408, 6070.202, 5935.2576, 5799.924, 5671.0324, 5541.9788, 5414.6112,
5290.0274, 5166.723, 5047.6906, 4929.162, 4815.1406, 4699.127, 4588.5606, 4477.7394,
4369.4014, 4264.2728, 4155.9224, 4055.581, 3955.505, 3856.9618, 3761.3828, 3666.9702,
3575.7764, 3482.4132, 3395.0186, 3305.8852, 3221.415, 3138.6024, 3056.296, 2970.4494,
2896.1526, 2816.8008, 2740.2156, 2670.497, 2594.1458, 2527.111, 2460.8168, 2387.5114,
2322.9498, 2260.6752, 2194.2686, 2133.7792, 2074.767, 2015.204, 1959.4226, 1898.6502,
1850.006, 1792.849, 1741.4838, 1687.9778, 1638.1322, 1589.3266, 1543.1394, 1496.8266,
1447.8516, 1402.7354, 1361.9606, 1327.0692, 1285.4106, 1241.8112, 1201.6726, 1161.973,
1130.261, 1094.2036, 1048.2036, 1020.6436, 990.901400000002, 961.199800000002,
924.769800000002, 899.526400000002, 872.346400000002, 834.375, 810.432000000001,
780.659800000001, 756.013800000001, 733.479399999997, 707.923999999999, 673.858,
652.222399999999, 636.572399999997, 615.738599999997, 586.696400000001, 564.147199999999,
541.679600000003, 523.943599999999, 505.714599999999, 475.729599999999, 461.779600000002,
449.750800000002, 439.020799999998, 412.7886, 400.245600000002, 383.188199999997,
362.079599999997, 357.533799999997, 334.319000000003, 327.553399999997, 308.559399999998,
291.270199999999, 279.351999999999, 271.791400000002, 252.576999999997, 247.482400000001,
236.174800000001, 218.774599999997, 220.155200000001, 208.794399999999, 201.223599999998,
182.995600000002, 185.5268, 164.547400000003, 176.5962, 150.689599999998, 157.8004,
138.378799999999, 134.021200000003, 117.614399999999, 108.194000000003, 97.0696000000025,
89.6042000000016, 95.6030000000028, 84.7810000000027, 72.635000000002, 77.3482000000004,
59.4907999999996, 55.5875999999989, 50.7346000000034, 61.3916000000027, 50.9149999999936,
39.0384000000049, 58.9395999999979, 29.633600000001, 28.2032000000036, 26.0078000000067,
17.0387999999948, 9.22000000000116, 13.8387999999977, 8.07240000000456, 14.1549999999988,
15.3570000000036, 3.42660000000615, 6.24820000000182, -2.96940000000177,
-8.79940000000352, -5.97860000000219, -14.4048000000039, -3.4143999999942,
-13.0148000000045, -11.6977999999945, -25.7878000000055, -22.3185999999987,
-24.409599999999, -31.9756000000052, -18.9722000000038, -22.8678000000073,
-30.8972000000067, -32.3715999999986, -22.3907999999938, -43.6720000000059, -35.9038,
-39.7492000000057, -54.1641999999993, -45.2749999999942, -42.2989999999991,
-44.1089999999967, -64.3564000000042, -49.9551999999967, -42.6116000000038, },
// precision 15
{ 23634.0036, 23210.8034, 22792.4744, 22379.1524, 21969.7928, 21565.326, 21165.3532,
20770.2806, 20379.9892, 19994.7098, 19613.318, 19236.799, 18865.4382, 18498.8244,
18136.5138, 17778.8668, 17426.2344, 17079.32, 16734.778, 16397.2418, 16063.3324,
15734.0232, 15409.731, 15088.728, 14772.9896, 14464.1402, 14157.5588, 13855.5958,
13559.3296, 13264.9096, 12978.326, 12692.0826, 12413.8816, 12137.3192, 11870.2326,
11602.5554, 11340.3142, 11079.613, 10829.5908, 10583.5466, 10334.0344, 10095.5072,
9859.694, 9625.2822, 9395.7862, 9174.0586, 8957.3164, 8738.064, 8524.155, 8313.7396,
8116.9168, 7913.542, 7718.4778, 7521.65, 7335.5596, 7154.2906, 6968.7396, 6786.3996,
6613.236, 6437.406, 6270.6598, 6107.7958, 5945.7174, 5787.6784, 5635.5784, 5482.308,
5337.9784, 5190.0864, 5045.9158, 4919.1386, 4771.817, 4645.7742, 4518.4774, 4385.5454,
4262.6622, 4142.74679999999, 4015.5318, 3897.9276, 3790.7764, 3685.13800000001,
3573.6274, 3467.9706, 3368.61079999999, 3271.5202, 3170.3848, 3076.4656,
2982.38400000001, 2888.4664, 2806.4868, 2711.9564, 2634.1434, 2551.3204, 2469.7662,
2396.61139999999, 2318.9902, 2243.8658, 2171.9246, 2105.01360000001, 2028.8536,
1960.9952, 1901.4096, 1841.86079999999, 1777.54700000001, 1714.5802, 1654.65059999999,
1596.311, 1546.2016, 1492.3296, 1433.8974, 1383.84600000001, 1339.4152, 1293.5518,
1245.8686, 1193.50659999999, 1162.27959999999, 1107.19439999999, 1069.18060000001,
1035.09179999999, 999.679000000004, 957.679999999993, 925.300199999998, 888.099400000006,
848.638600000006, 818.156400000007, 796.748399999997, 752.139200000005, 725.271200000003,
692.216, 671.633600000001, 647.939799999993, 621.670599999998, 575.398799999995,
561.226599999995, 532.237999999998, 521.787599999996, 483.095799999996, 467.049599999998,
465.286399999997, 415.548599999995, 401.047399999996, 380.607999999993, 377.362599999993,
347.258799999996, 338.371599999999, 310.096999999994, 301.409199999995, 276.280799999993,
265.586800000005, 258.994399999996, 223.915999999997, 215.925399999993, 213.503800000006,
191.045400000003, 166.718200000003, 166.259000000005, 162.941200000001, 148.829400000002,
141.645999999993, 123.535399999993, 122.329800000007, 89.473399999988, 80.1962000000058,
77.5457999999926, 59.1056000000099, 83.3509999999951, 52.2906000000075, 36.3979999999865,
40.6558000000077, 42.0003999999899, 19.6630000000005, 19.7153999999864,
-8.38539999999921, -0.692799999989802, 0.854800000000978, 3.23219999999856,
-3.89040000000386, -5.25880000001052, -24.9052000000083, -22.6837999999989,
-26.4286000000138, -34.997000000003, -37.0216000000073, -43.430400000012,
-58.2390000000014, -68.8034000000043, -56.9245999999985, -57.8583999999973,
-77.3097999999882, -73.2793999999994, -81.0738000000129, -87.4530000000086,
-65.0254000000132, -57.296399999992, -96.2746000000043, -103.25, -96.081600000005,
-91.5542000000132, -102.465200000006, -107.688599999994, -101.458000000013,
-109.715800000005, },
// precision 16
{ 47270, 46423.3584, 45585.7074, 44757.152, 43938.8416, 43130.9514, 42330.03, 41540.407,
40759.6348, 39988.206, 39226.5144, 38473.2096, 37729.795, 36997.268, 36272.6448,
35558.665, 34853.0248, 34157.4472, 33470.5204, 32793.5742, 32127.0194, 31469.4182,
30817.6136, 30178.6968, 29546.8908, 28922.8544, 28312.271, 27707.0924, 27114.0326,
26526.692, 25948.6336, 25383.7826, 24823.5998, 24272.2974, 23732.2572, 23201.4976,
22674.2796, 22163.6336, 21656.515, 21161.7362, 20669.9368, 20189.4424, 19717.3358,
19256.3744, 18795.9638, 18352.197, 17908.5738, 17474.391, 17052.918, 16637.2236,
16228.4602, 15823.3474, 15428.6974, 15043.0284, 14667.6278, 14297.4588, 13935.2882,
13578.5402, 13234.6032, 12882.1578, 12548.0728, 12219.231, 11898.0072, 11587.2626,
11279.9072, 10973.5048, 10678.5186, 10392.4876, 10105.2556, 9825.766, 9562.5444,
9294.2222, 9038.2352, 8784.848, 8533.2644, 8301.7776, 8058.30859999999, 7822.94579999999,
7599.11319999999, 7366.90779999999, 7161.217, 6957.53080000001, 6736.212,
6548.21220000001, 6343.06839999999, 6156.28719999999, 5975.15419999999, 5791.75719999999,
5621.32019999999, 5451.66, 5287.61040000001, 5118.09479999999, 4957.288, 4798.4246,
4662.17559999999, 4512.05900000001, 4364.68539999999, 4220.77720000001, 4082.67259999999,
3957.19519999999, 3842.15779999999, 3699.3328, 3583.01180000001, 3473.8964,
3338.66639999999, 3233.55559999999, 3117.799, 3008.111, 2909.69140000001,
2814.86499999999, 2719.46119999999, 2624.742, 2532.46979999999, 2444.7886, 2370.1868,
2272.45259999999, 2196.19260000001, 2117.90419999999, 2023.2972, 1969.76819999999,
1885.58979999999, 1833.2824, 1733.91200000001, 1682.54920000001, 1604.57980000001,
1556.11240000001, 1491.3064, 1421.71960000001, 1371.22899999999, 1322.1324, 1264.7892,
1196.23920000001, 1143.8474, 1088.67240000001, 1073.60380000001, 1023.11660000001,
959.036400000012, 927.433199999999, 906.792799999996, 853.433599999989, 841.873800000001,
791.1054, 756.899999999994, 704.343200000003, 672.495599999995, 622.790399999998,
611.254799999995, 567.283200000005, 519.406599999988, 519.188400000014, 495.312800000014,
451.350799999986, 443.973399999988, 431.882199999993, 392.027000000002, 380.924200000009,
345.128999999986, 298.901400000002, 287.771999999997, 272.625, 247.253000000026,
222.490600000019, 223.590000000026, 196.407599999977, 176.425999999978, 134.725199999986,
132.4804, 110.445599999977, 86.7939999999944, 56.7038000000175, 64.915399999998,
38.3726000000024, 37.1606000000029, 46.170999999973, 49.1716000000015, 15.3362000000197,
6.71639999997569, -34.8185999999987, -39.4476000000141, 12.6830000000191,
-12.3331999999937, -50.6565999999875, -59.9538000000175, -65.1054000000004,
-70.7576000000117, -106.325200000021, -126.852200000023, -110.227599999984,
-132.885999999999, -113.897200000007, -142.713800000027, -151.145399999979,
-150.799200000009, -177.756200000003, -156.036399999983, -182.735199999996,
-177.259399999981, -198.663600000029, -174.577600000019, -193.84580000001, },
// precision 17
{ 94541, 92848.811, 91174.019, 89517.558, 87879.9705, 86262.7565, 84663.5125, 83083.7435,
81521.7865, 79977.272, 78455.9465, 76950.219, 75465.432, 73994.152, 72546.71, 71115.2345,
69705.6765, 68314.937, 66944.2705, 65591.255, 64252.9485, 62938.016, 61636.8225,
60355.592, 59092.789, 57850.568, 56624.518, 55417.343, 54231.1415, 53067.387, 51903.526,
50774.649, 49657.6415, 48561.05, 47475.7575, 46410.159, 45364.852, 44327.053, 43318.4005,
42325.6165, 41348.4595, 40383.6265, 39436.77, 38509.502, 37594.035, 36695.939,
35818.6895, 34955.691, 34115.8095, 33293.949, 32465.0775, 31657.6715, 30877.2585,
30093.78, 29351.3695, 28594.1365, 27872.115, 27168.7465, 26477.076, 25774.541,
25106.5375, 24452.5135, 23815.5125, 23174.0655, 22555.2685, 21960.2065, 21376.3555,
20785.1925, 20211.517, 19657.0725, 19141.6865, 18579.737, 18081.3955, 17578.995,
17073.44, 16608.335, 16119.911, 15651.266, 15194.583, 14749.0495, 14343.4835, 13925.639,
13504.509, 13099.3885, 12691.2855, 12328.018, 11969.0345, 11596.5145, 11245.6355,
10917.6575, 10580.9785, 10277.8605, 9926.58100000001, 9605.538, 9300.42950000003,
8989.97850000003, 8728.73249999998, 8448.3235, 8175.31050000002, 7898.98700000002,
7629.79100000003, 7413.76199999999, 7149.92300000001, 6921.12650000001, 6677.1545,
6443.28000000003, 6278.23450000002, 6014.20049999998, 5791.20299999998, 5605.78450000001,
5438.48800000001, 5234.2255, 5059.6825, 4887.43349999998, 4682.935, 4496.31099999999,
4322.52250000002, 4191.42499999999, 4021.24200000003, 3900.64799999999, 3762.84250000003,
3609.98050000001, 3502.29599999997, 3363.84250000003, 3206.54849999998, 3079.70000000001,
2971.42300000001, 2867.80349999998, 2727.08100000001, 2630.74900000001, 2496.6165,
2440.902, 2356.19150000002, 2235.58199999999, 2120.54149999999, 2012.25449999998,
1933.35600000003, 1820.93099999998, 1761.54800000001, 1663.09350000002, 1578.84600000002,
1509.48149999999, 1427.3345, 1379.56150000001, 1306.68099999998, 1212.63449999999,
1084.17300000001, 1124.16450000001, 1060.69949999999, 1007.48849999998, 941.194499999983,
879.880500000028, 836.007500000007, 782.802000000025, 748.385499999975, 647.991500000004,
626.730500000005, 570.776000000013, 484.000500000024, 513.98550000001, 418.985499999952,
386.996999999974, 370.026500000036, 355.496999999974, 356.731499999994, 255.92200000002,
259.094000000041, 205.434499999974, 165.374500000034, 197.347500000033, 95.718499999959,
67.6165000000037, 54.6970000000438, 31.7395000000251, -15.8784999999916,
8.42500000004657, -26.3754999999655, -118.425500000012, -66.6629999999423,
-42.9745000000112, -107.364999999991, -189.839000000036, -162.611499999999,
-164.964999999967, -189.079999999958, -223.931499999948, -235.329999999958,
-269.639500000048, -249.087999999989, -206.475499999942, -283.04449999996,
-290.667000000016, -304.561499999953, -336.784499999951, -380.386500000022,
-283.280499999993, -364.533000000054, -389.059499999974, -364.454000000027,
-415.748000000021, -417.155000000028, },
// precision 18
{ 189083, 185696.913, 182348.774, 179035.946, 175762.762, 172526.444, 169329.754, 166166.099,
163043.269, 159958.91, 156907.912, 153906.845, 150924.199, 147996.568, 145093.457,
142239.233, 139421.475, 136632.27, 133889.588, 131174.2, 128511.619, 125868.621,
123265.385, 120721.061, 118181.769, 115709.456, 113252.446, 110840.198, 108465.099,
106126.164, 103823.469, 101556.618, 99308.004, 97124.508, 94937.803, 92833.731,
90745.061, 88677.627, 86617.47, 84650.442, 82697.833, 80769.132, 78879.629, 77014.432,
75215.626, 73384.587, 71652.482, 69895.93, 68209.301, 66553.669, 64921.981, 63310.323,
61742.115, 60205.018, 58698.658, 57190.657, 55760.865, 54331.169, 52908.167, 51550.273,
50225.254, 48922.421, 47614.533, 46362.049, 45098.569, 43926.083, 42736.03, 41593.473,
40425.26, 39316.237, 38243.651, 37170.617, 36114.609, 35084.19, 34117.233, 33206.509,
32231.505, 31318.728, 30403.404, 29540.0550000001, 28679.236, 27825.862, 26965.216,
26179.148, 25462.08, 24645.952, 23922.523, 23198.144, 22529.128, 21762.4179999999,
21134.779, 20459.117, 19840.818, 19187.04, 18636.3689999999, 17982.831, 17439.7389999999,
16874.547, 16358.2169999999, 15835.684, 15352.914, 14823.681, 14329.313, 13816.897,
13342.874, 12880.882, 12491.648, 12021.254, 11625.392, 11293.7610000001, 10813.697,
10456.209, 10099.074, 9755.39000000001, 9393.18500000006, 9047.57900000003,
8657.98499999999, 8395.85900000005, 8033, 7736.95900000003, 7430.59699999995,
7258.47699999996, 6924.58200000005, 6691.29399999999, 6357.92500000005, 6202.05700000003,
5921.19700000004, 5628.28399999999, 5404.96799999999, 5226.71100000001, 4990.75600000005,
4799.77399999998, 4622.93099999998, 4472.478, 4171.78700000001, 3957.46299999999,
3868.95200000005, 3691.14300000004, 3474.63100000005, 3341.67200000002, 3109.14000000001,
3071.97400000005, 2796.40399999998, 2756.17799999996, 2611.46999999997, 2471.93000000005,
2382.26399999997, 2209.22400000005, 2142.28399999999, 2013.96100000001, 1911.18999999994,
1818.27099999995, 1668.47900000005, 1519.65800000005, 1469.67599999998, 1367.13800000004,
1248.52899999998, 1181.23600000003, 1022.71900000004, 1088.20700000005, 959.03600000008,
876.095999999903, 791.183999999892, 703.337000000058, 731.949999999953, 586.86400000006,
526.024999999907, 323.004999999888, 320.448000000091, 340.672999999952, 309.638999999966,
216.601999999955, 102.922999999952, 19.2399999999907, -0.114000000059605,
-32.6240000000689, -89.3179999999702, -153.497999999905, -64.2970000000205,
-143.695999999996, -259.497999999905, -253.017999999924, -213.948000000091,
-397.590000000084, -434.006000000052, -403.475000000093, -297.958000000101,
-404.317000000039, -528.898999999976, -506.621000000043, -513.205000000075,
-479.351000000024, -596.139999999898, -527.016999999993, -664.681000000099,
-680.306000000099, -704.050000000047, -850.486000000034, -757.43200000003,
-713.308999999892, } };
}

225
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package com.geedgenetworks.sketch.hlld;
import com.geedgenetworks.sketch.util.XxHash64;
import it.unimi.dsi.fastutil.doubles.Double2IntAVLTreeMap;
import it.unimi.dsi.fastutil.doubles.Double2IntSortedMap;
import java.io.Serializable;
import java.util.Map;
import static com.geedgenetworks.sketch.hlld.Hll.DEFAULT_HASH_SEED;
import static com.geedgenetworks.sketch.hlld.HllConstants.*;
abstract class HllImpl implements Serializable {
static final int REG_WIDTH = 6; // Bits per register
static final int REG_PER_WORD = 5; // floor(INT_WIDTH / REG_WIDTH)
public boolean cached = false;
public double cachedCount = 0D;
public void add(long val) {
final long[] data = { val };
long h = XxHash64.hashLongs(data, 0, data.length, DEFAULT_HASH_SEED);
addHash(h);
}
public void add(double val) {
final double[] data = { val };
long h = XxHash64.hashDoubles(data, 0, data.length, DEFAULT_HASH_SEED);
addHash(h);
}
public void add(String val) {
if(val == null || val.isEmpty()){
return;
}
long h = XxHash64.hashString(val, 0, val.length(), DEFAULT_HASH_SEED);
addHash(h);
}
public void add(byte[] val) {
long h = XxHash64.hashBytes(val, 0, val.length, DEFAULT_HASH_SEED);
addHash(h);
}
public void addHash(long hashcode){
int p = getPrecision();
// Determine the index using the first p bits
final int idx = (int) (hashcode >>> (64 - p));
// Shift out the index bits
final long w = hashcode << p | 1 << (p - 1);
// Determine the count of leading zeros
final int leading = Long.numberOfLeadingZeros(w) + 1;
// Update the register if the new value is larger
if (leading > getRegister(idx)) {
setRegister(idx, leading);
cached = false;
}
}
void resetCacheZero(){
cached = true;
cachedCount = 0D;
}
abstract int getRegister(int idx);
abstract void setRegister(int idx, int val);
abstract int getWord(int idx);
abstract void setWord(int idx, int word);
static int getRegisterFromWord(int word, int idx){
word = word >>> (REG_WIDTH * idx);
return word & ((1 << REG_WIDTH) - 1);
}
static int wordSetRegister(int word, int idx, int val){
int shift = REG_WIDTH * idx;
val = val << shift;
int val_mask = ((1 << REG_WIDTH) - 1) << shift;
return (word & ~val_mask) | val;
}
abstract void reset();
public double getEstimate() {
return size();
}
public double size() {
if(cached){
return cachedCount;
}
//System.out.println("size");
int p = getPrecision();
int reg = 1 << p;
RawEstAndNumZeros estAndNumZeros = rawEstimate(p, reg);
double rawEst = estAndNumZeros.rawEst;
int numZeros = estAndNumZeros.numZeros;
// Check if we need to apply bias correction
if (rawEst <= 5 * reg) {
//rawEst -= biasEstimate(rawEst);
rawEst -= estimateBias(rawEst, p);
}
// Check if linear counting should be used
double altEst;
if (numZeros != 0) {
altEst = linearCount(reg, numZeros);
} else {
altEst = rawEst;
}
// Determine which estimate to use
if (altEst <= thresholdData[p-4]) {
cachedCount = altEst;
} else {
cachedCount = rawEst;
}
cached = true;
return cachedCount;
}
private double alpha(int p, int reg) {
switch (p) {
case 4:
return 0.673;
case 5:
return 0.697;
case 6:
return 0.709;
default:
return 0.7213 / (1 + 1.079 / reg);
}
}
private RawEstAndNumZeros rawEstimate(int p, int reg) {
double multi = alpha(p, reg) * reg * reg;
int numZeros = 0;
double sum = 0;
int regVal;
for (int i = 0; i < reg; i++) {
regVal = getRegister(i);
sum += inversePow2Data[regVal];
if (regVal == 0) {
numZeros++;
}
}
return new RawEstAndNumZeros(multi / sum, numZeros);
}
private long estimateBias(double rawEst, int p) {
double[] rawEstForP = rawEstimateData[p - 4];
// compute distance and store it in sorted map
Double2IntSortedMap estIndexMap = new Double2IntAVLTreeMap();
double distance = 0;
for (int i = 0; i < rawEstForP.length; i++) {
distance = Math.pow(rawEst - rawEstForP[i], 2);
estIndexMap.put(distance, i);
}
// take top-k closest neighbors and compute the bias corrected cardinality
long result = 0;
double[] biasForP = biasData[p - 4];
double biasSum = 0;
int kNeighbors = K_NEAREST_NEIGHBOR;
for (Map.Entry<Double, Integer> entry : estIndexMap.entrySet()) {
biasSum += biasForP[entry.getValue()];
kNeighbors--;
if (kNeighbors <= 0) {
break;
}
}
// 0.5 added for rounding off
result = (long) ((biasSum / K_NEAREST_NEIGHBOR) + 0.5);
return result;
}
long linearCount(int reg, long numZeros) {
return Math.round(reg * Math.log(reg / ((double) numZeros)));
}
abstract boolean isMemory();
abstract int getPrecision();
abstract void setPrecision(int precision);
// 复制Hll到堆内存实例HllIntArray
abstract HllImpl copy();
int getSerializationBytes(){
int precision = getPrecision();
int reg = 1 << precision;
int words = (reg + REG_PER_WORD - 1) / REG_PER_WORD;
// version + p + regs
return 1 + 1 + words * 4;
}
int getSparseSerializationBytes(int sparseLen){
int precision = getPrecision();
int reg = 1 << precision;
// flag + version + p + len + regs
return 1 + 1 + 1 + 2 + sparseLen * 6;
}
abstract byte[] toBytes();
static class RawEstAndNumZeros {
double rawEst;
int numZeros;
public RawEstAndNumZeros(double rawEst, int numZeros) {
this.rawEst = rawEst;
this.numZeros = numZeros;
}
}
}

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package com.geedgenetworks.sketch.hlld;
import java.nio.ByteBuffer;
public class HllIntArray extends HllImpl {
public int p; // precision, number of register bits
public int reg; // reg = 2^p
public int[] regs;
HllIntArray(int precision) {
this.p = precision;
// Determine how many registers are needed
this.reg = 1 << p;
// Get the full words required
int words = (reg + REG_PER_WORD - 1) / REG_PER_WORD;
this.regs = new int[words];
}
@Override
int getRegister(int idx) {
int word = regs[idx / REG_PER_WORD];
word = word >>> (REG_WIDTH * (idx % REG_PER_WORD));
return word & ((1 << REG_WIDTH) - 1);
}
@Override
void setRegister(int idx, int val) {
int i = idx / REG_PER_WORD;
int word = regs[i];
// Shift the val into place
int shift = REG_WIDTH * (idx % REG_PER_WORD);
val = val << shift;
int val_mask = ((1 << REG_WIDTH) - 1) << shift;
// Store the word
regs[i] = (word & ~val_mask) | val;
}
@Override
int getWord(int idx) {
return regs[idx / REG_PER_WORD];
}
@Override
void setWord(int idx, int word) {
int i = idx / REG_PER_WORD;
regs[i] = word;
}
@Override
void reset() {
resetCacheZero();
for (int i = 0; i < regs.length; i++) {
regs[i] = 0;
}
}
@Override
boolean isMemory() {
return false;
}
@Override
int getPrecision() {
return p;
}
@Override
void setPrecision(int precision) {
this.p = precision;
this.reg = 1 << p;
}
@Override
HllImpl copy() {
HllIntArray hll = new HllIntArray(p);
System.arraycopy(regs, 0, hll.regs, 0, regs.length);
return hll;
}
private int sparseWordCount(){
if(p > 17){
return -1;
}
int words = (reg + REG_PER_WORD - 1) / REG_PER_WORD;
int halfWord = words >>> 1;
int count = 0;
for (int i = 0; i < words; i++) {
int word = regs[i];
if(word != 0){
count++;
if(count > halfWord){
return -1;
}
}
}
return count;
}
private byte[] toSparseBytes(int sparseLen) {
int size = getSparseSerializationBytes(sparseLen);
ByteBuffer byteBuffer = ByteBuffer.allocate(size);
byteBuffer.put((byte)0); // flag
byteBuffer.put((byte)1); // version
byteBuffer.put((byte)p); // p
byteBuffer.putShort((short)sparseLen); // len
int words = (reg + REG_PER_WORD - 1) / REG_PER_WORD;
for (int i = 0; i < words; i++) {
int word = regs[i];
if(word != 0){
byteBuffer.putShort((short)i);
byteBuffer.putInt(word);
}
}
return byteBuffer.array();
}
private byte[] toDenseBytes() {
int size = getSerializationBytes();
ByteBuffer byteBuffer = ByteBuffer.allocate(size);
byteBuffer.put((byte)1); // version
byteBuffer.put((byte)p); // p
for (int i = 0; i < regs.length; i++) {
byteBuffer.putInt(regs[i]);
}
return byteBuffer.array();
}
@Override
byte[] toBytes() {
int sparseLen = sparseWordCount();
if(sparseLen == -1){
return toDenseBytes();
}else{
return toSparseBytes(sparseLen);
}
}
public static HllIntArray fromBytes(byte[] bytes) {
ByteBuffer byteBuffer = ByteBuffer.wrap(bytes);
return fromByteBuffer(byteBuffer);
}
public static HllIntArray fromByteBuffer(ByteBuffer byteBuffer) {
int version = byteBuffer.get();
if(version == 0){
return fromByteBufferSparse(byteBuffer);
}
if(version != 1){
throw new IllegalArgumentException("Unsupported version:" + version);
}
int p = byteBuffer.get();
HllIntArray hll = new HllIntArray(p);
int len = hll.regs.length;
for (int i = 0; i < len; i++) {
hll.regs[i] = byteBuffer.getInt();
}
return hll;
}
private static HllIntArray fromByteBufferSparse(ByteBuffer byteBuffer) {
int version = byteBuffer.get();
if(version != 1){
throw new IllegalArgumentException("Unsupported version:" + version);
}
int p = byteBuffer.get();
HllIntArray hll = new HllIntArray(p);
int len = byteBuffer.getShort();
for (int j = 0; j < len; j++) {
int i = byteBuffer.getShort();
hll.regs[i] = byteBuffer.getInt();
}
return hll;
}
public int getP() {
return p;
}
public void setP(int p) {
this.p = p;
}
public int getReg() {
return reg;
}
public void setReg(int reg) {
this.reg = reg;
}
public int[] getRegs() {
return regs;
}
public void setRegs(int[] regs) {
this.regs = regs;
}
}

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package com.geedgenetworks.sketch.hlld;
import java.io.Serializable;
import java.nio.ByteBuffer;
import static com.geedgenetworks.sketch.hlld.HllImpl.REG_PER_WORD;
public class HllUnion implements Serializable {
private int maxP;
private Hll impl;
public HllUnion() {
this(Hll.DEFAULT_PRECISION);
}
public HllUnion(int maxP) {
this.maxP = maxP;
impl = new Hll(this.maxP);
}
public HllUnion(int maxP, ByteBuffer byteBuffer) {
this.maxP = maxP;
impl = new Hll(this.maxP, byteBuffer);
}
private HllUnion(Hll hll) {
this.maxP = hll.getPrecision();
impl = hll;
}
// druid内部使用
public void resetByteBuffer(ByteBuffer byteBuffer){
((DirectHllIntArray)impl.hllImpl).resetByteBuffer(byteBuffer);
}
public void reset() {
impl.reset();
}
public Hll getResult() {
return impl;
}
public void update(final Hll hll) {
impl.hllImpl = unionImpl(hll, impl);
impl.hllImpl.cached = false;
}
private static HllImpl unionImpl(Hll source, Hll dest) {
if (source == null) {
return dest.hllImpl;
}
HllImpl descHllImpl = dest.hllImpl;
HllImpl sourceHllImpl = source.hllImpl;
int destP = descHllImpl.getPrecision();
int sourceP = sourceHllImpl.getPrecision();
HllImpl hllImpl = null;
if (destP < sourceP) {
if(sourceHllImpl instanceof DirectHllIntSparseArray){
squashSourceAndMerge((DirectHllIntSparseArray)sourceHllImpl, descHllImpl);
}else{
sourceHllImpl = squash(sourceHllImpl, destP);
merge(sourceHllImpl, descHllImpl);
}
hllImpl = descHllImpl;
} else if (destP > sourceP) {
descHllImpl = squash(descHllImpl, sourceP);
merge(sourceHllImpl, descHllImpl);
if (!dest.hllImpl.isMemory()) {
hllImpl = descHllImpl;
} else {
// 使用ByteBuffer, 可能是堆外内存
hllImpl = dest.hllImpl;
hllImpl.setPrecision(descHllImpl.getPrecision());
hllImpl.reset();
updateRegisters(descHllImpl, hllImpl);
}
} else {
merge(sourceHllImpl, descHllImpl);
hllImpl = descHllImpl;
}
return hllImpl;
}
private static void squashSourceAndMerge(DirectHllIntSparseArray sourceHllImpl, HllImpl descHllImpl){
int p = sourceHllImpl.getPrecision();
int len = sourceHllImpl.len;
for (int k = 0; k < len; k++) {
int i = sourceHllImpl.getWordIdx(k);
int idx = i * REG_PER_WORD;
int word = sourceHllImpl.getWordValue(k);
for (int j = 0; j < 5; j++) {
int regVal = HllImpl.getRegisterFromWord(word, j);
if (regVal != 0) {
descHllImpl.addHash(((long) (idx + j) << (64 - p)) | (1L << (64 - p - regVal)));
}
}
}
}
// 比merge2快，普通int数组快1/5，字节数组模式快3倍左右
private static void merge(HllImpl sourceHllImpl, HllImpl descHllImpl) {
int srcV, tgtV, reg = 1 << sourceHllImpl.getPrecision();
if(sourceHllImpl instanceof DirectHllIntSparseArray){
DirectHllIntSparseArray sourceSparseHll = (DirectHllIntSparseArray) sourceHllImpl;
int srcLen = sourceSparseHll.len;
for (int k = 0; k < srcLen; k++) {
int i = sourceSparseHll.getWordIdx(k);
int idx = i * REG_PER_WORD;
int srcWord = sourceSparseHll.getWordValue(k);
int tgtWord = descHllImpl.getWord(idx);
int word = tgtWord;
for (int j = 0; j < 5; j++) {
srcV = HllImpl.getRegisterFromWord(srcWord, j);
tgtV = HllImpl.getRegisterFromWord(word, j);
if (srcV > tgtV) {
word = HllImpl.wordSetRegister(word, j, srcV);
}
}
if (word != tgtWord) {
descHllImpl.setWord(idx, word);
}
}
}else{
for (int i = 0; i < reg; i += 5) {
int srcWord = sourceHllImpl.getWord(i);
int tgtWord = descHllImpl.getWord(i);
int word = tgtWord;
for (int j = 0; j < 5; j++) {
srcV = HllImpl.getRegisterFromWord(srcWord, j);
tgtV = HllImpl.getRegisterFromWord(word, j);
if (srcV > tgtV) {
word = HllImpl.wordSetRegister(word, j, srcV);
}
}
if (word != tgtWord) {
descHllImpl.setWord(i, word);
}
}
}
}
private static void merge2(HllImpl sourceHllImpl, HllImpl descHllImpl) {
int srcV, tgtV, reg = 1 << sourceHllImpl.getPrecision();
for (int i = 0; i < reg; i++) {
srcV = sourceHllImpl.getRegister(i);
tgtV = descHllImpl.getRegister(i);
if (srcV > tgtV) {
descHllImpl.setRegister(i, srcV);
}
}
}
private static void updateRegisters(HllImpl sourceHllImpl, HllImpl descHllImpl) {
int srcV, tgtV, reg = 1 << sourceHllImpl.getPrecision();
for (int i = 0; i < reg; i++) {
srcV = sourceHllImpl.getRegister(i);
descHllImpl.setRegister(i, srcV);
}
}
// p, 64 - p
// +-------------|-------------+
// |1000000000000|000000001xxxx| (lr=9 + idx=1024)
// +-------------|-------------+
// \
// +---------------|-----------+
// |00000000000|01000000001xxxx| (lr=2 + idx=0)
// +---------------|-----------+
private static HllImpl squash(HllImpl hll, final int p0) {
int p = hll.getPrecision();
int reg = 1 << p;
if (p0 > p) {
throw new IllegalArgumentException(
"HyperLogLog cannot be be squashed to be bigger. Current: "
+ p + " Provided: " + p0);
}
if (p0 == p) {
return hll;
}
final HllImpl dest = new HllIntArray(p0);
for (int idx = 0; idx < reg; idx++) {
int regVal = hll.getRegister(idx); // this can be a max of 65, never > 127
if (regVal != 0) {
dest.addHash(((long) idx << (64 - p)) | (1L << (64 - p - regVal)));
}
}
return dest;
}
public static final int getUpdatableSerializationBytes(final int precision){
return Hll.getUpdatableSerializationBytes(precision);
}
public byte[] toBytes() {
return impl.toBytes();
}
public static HllUnion fromBytes(byte[] bytes) {
return new HllUnion(Hll.fromBytes(bytes));
}
public static HllUnion fromByteBuffer(ByteBuffer byteBuffer) {
return new HllUnion(Hll.fromByteBuffer(byteBuffer));
}
public static HllUnion wrapBytes(byte[] bytes) {
return new HllUnion(Hll.wrapBytes(bytes));
}
public static HllUnion wrapByteBuffer(ByteBuffer byteBuffer) {
return new HllUnion(Hll.wrapByteBuffer(byteBuffer));
}
}

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package com.geedgenetworks.sketch.hlld;
import com.geedgenetworks.sketch.util.StringUtils;
import java.nio.ByteBuffer;
import java.nio.charset.StandardCharsets;
public class HllUtils {
public static Hll deserializeHll(final Object object) {
if (object instanceof String) {
byte[] bytes = StringUtils.decodeBase64(((String) object).getBytes(StandardCharsets.UTF_8));
return Hll.wrapBytes(bytes);
} else if (object instanceof byte[]) {
return Hll.wrapBytes((byte[]) object);
} else if (object instanceof ByteBuffer) {
return Hll.wrapByteBuffer((ByteBuffer) object);
} else if (object instanceof Hll) {
return (Hll) object;
}
throw new IllegalArgumentException("Object is not of a type that can be deserialized to an Hll:" + object.getClass().getName());
}
public static byte[] toBytes(Hll hll) {
return hll.toBytes();
}
}

32
src/main/java/com/geedgenetworks/sketch/util/StringUtils.java Normal file
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package com.geedgenetworks.sketch.util;
import java.util.Base64;
public class StringUtils {
private static final Base64.Encoder BASE64_ENCODER = Base64.getEncoder();
private static final Base64.Decoder BASE64_DECODER = Base64.getDecoder();
/**
* Convert an input byte array into a string using the {@link Base64} encoding scheme
*
* @param input The byte array to convert to base64
*
* @return the base64 of the input in string form
*/
public static String encodeBase64String(byte[] input)
{
return BASE64_ENCODER.encodeToString(input);
}
/**
* Decode an input byte array using the {@link Base64} encoding scheme and return a newly-allocated byte array
*
* @param input The byte array to decode from base64
*
* @return a newly-allocated byte array
*/
public static byte[] decodeBase64(byte[] input)
{
return BASE64_DECODER.decode(input);
}
}

204
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package com.geedgenetworks.sketch.util;
import sun.misc.Unsafe;
import java.lang.reflect.Constructor;
import java.lang.reflect.InvocationTargetException;
/**
* Provides access to the sun.misc.Unsafe class and its key static fields.
*
* @author Lee Rhodes
*/
@SuppressWarnings({"restriction"})
public final class UnsafeUtil {
public static final Unsafe unsafe;
public static final String JDK; //must be at least "1.8"
public static final int JDK_MAJOR; //8, 9, 10, 11, 12, etc
//not an indicator of whether compressed references are used.
public static final int ADDRESS_SIZE;
//For 64-bit JVMs: these offsets vary depending on coop: 16 for JVM <= 32GB; 24 for JVM > 32GB.
// Making this constant long-typed, rather than int, to exclude possibility of accidental overflow
// in expressions like arrayLength * ARRAY_BYTE_BASE_OFFSET, where arrayLength is int-typed.
// The same consideration for constants below: ARRAY_*_INDEX_SCALE, ARRAY_*_INDEX_SHIFT.
public static final long ARRAY_BOOLEAN_BASE_OFFSET;
public static final long ARRAY_BYTE_BASE_OFFSET;
public static final long ARRAY_SHORT_BASE_OFFSET;
public static final long ARRAY_CHAR_BASE_OFFSET;
public static final long ARRAY_INT_BASE_OFFSET;
public static final long ARRAY_LONG_BASE_OFFSET;
public static final long ARRAY_FLOAT_BASE_OFFSET;
public static final long ARRAY_DOUBLE_BASE_OFFSET;
public static final long ARRAY_OBJECT_BASE_OFFSET;
//@formatter:off
// Setting those values directly instead of using unsafe.arrayIndexScale(), because it may be
// beneficial for runtime execution, those values are backed into generated machine code as
// constants. E. g. see https://shipilev.net/jvm-anatomy-park/14-constant-variables/
public static final int ARRAY_BOOLEAN_INDEX_SCALE = 1;
public static final int ARRAY_BYTE_INDEX_SCALE = 1;
public static final long ARRAY_SHORT_INDEX_SCALE = 2;
public static final long ARRAY_CHAR_INDEX_SCALE = 2;
public static final long ARRAY_INT_INDEX_SCALE = 4;
public static final long ARRAY_LONG_INDEX_SCALE = 8;
public static final long ARRAY_FLOAT_INDEX_SCALE = 4;
public static final long ARRAY_DOUBLE_INDEX_SCALE = 8;
public static final long ARRAY_OBJECT_INDEX_SCALE; // varies, 4 or 8 depending on coop
//Used to convert "type" to bytes: bytes = longs << LONG_SHIFT
public static final int BOOLEAN_SHIFT = 0;
public static final int BYTE_SHIFT = 0;
public static final long SHORT_SHIFT = 1;
public static final long CHAR_SHIFT = 1;
public static final long INT_SHIFT = 2;
public static final long LONG_SHIFT = 3;
public static final long FLOAT_SHIFT = 2;
public static final long DOUBLE_SHIFT = 3;
public static final long OBJECT_SHIFT; // varies, 2 or 3 depending on coop
public static final String LS = System.getProperty("line.separator");
//@formatter:on
static {
try {
final Constructor<Unsafe> unsafeConstructor = Unsafe.class.getDeclaredConstructor();
unsafeConstructor.setAccessible(true);
unsafe = unsafeConstructor.newInstance();
// Alternative, but may not work across different JVMs.
// Field field = Unsafe.class.getDeclaredField("theUnsafe");
// field.setAccessible(true);
// unsafe = (Unsafe) field.get(null);
} catch (final InstantiationException | IllegalAccessException | IllegalArgumentException
| InvocationTargetException | NoSuchMethodException e) {
e.printStackTrace();
throw new RuntimeException("Unable to acquire Unsafe. " + e);
}
//4 on 32-bit systems. 4 on 64-bit systems < 32GB, otherwise 8.
//This alone is not an indicator of compressed ref (coop)
ADDRESS_SIZE = unsafe.addressSize();
ARRAY_BOOLEAN_BASE_OFFSET = unsafe.arrayBaseOffset(boolean[].class);
ARRAY_BYTE_BASE_OFFSET = unsafe.arrayBaseOffset(byte[].class);
ARRAY_SHORT_BASE_OFFSET = unsafe.arrayBaseOffset(short[].class);
ARRAY_CHAR_BASE_OFFSET = unsafe.arrayBaseOffset(char[].class);
ARRAY_INT_BASE_OFFSET = unsafe.arrayBaseOffset(int[].class);
ARRAY_LONG_BASE_OFFSET = unsafe.arrayBaseOffset(long[].class);
ARRAY_FLOAT_BASE_OFFSET = unsafe.arrayBaseOffset(float[].class);
ARRAY_DOUBLE_BASE_OFFSET = unsafe.arrayBaseOffset(double[].class);
ARRAY_OBJECT_BASE_OFFSET = unsafe.arrayBaseOffset(Object[].class);
ARRAY_OBJECT_INDEX_SCALE = unsafe.arrayIndexScale(Object[].class);
OBJECT_SHIFT = ARRAY_OBJECT_INDEX_SCALE == 4 ? 2 : 3;
final String jdkVer = System.getProperty("java.version");
final int[] p = parseJavaVersion(jdkVer);
JDK = p[0] + "." + p[1];
JDK_MAJOR = (p[0] == 1) ? p[1] : p[0];
}
private UnsafeUtil() {}
/**
* Returns first two number groups of the java version string.
* @param jdkVer the java version string from System.getProperty("java.version").
* @return first two number groups of the java version string.
*/
public static int[] parseJavaVersion(final String jdkVer) {
final int p0, p1;
try {
String[] parts = jdkVer.trim().split("[^0-9\\.]");//grab only number groups and "."
parts = parts[0].split("\\."); //split out the number groups
p0 = Integer.parseInt(parts[0]); //the first number group
p1 = (parts.length > 1) ? Integer.parseInt(parts[1]) : 0; //2nd number group, or 0
} catch (final NumberFormatException | ArrayIndexOutOfBoundsException e) {
throw new IllegalArgumentException("Improper Java -version string: " + jdkVer + "\n" + e);
}
//checkJavaVersion(jdkVer, p0, p1); //TODO Optional to omit this.
return new int[] {p0, p1};
}
public static void checkJavaVersion(final String jdkVer, final int p0, final int p1) {
if ( (p0 < 1) || ((p0 == 1) && (p1 < 8)) || (p0 > 13) ) {
throw new IllegalArgumentException(
"Unsupported JDK Major Version, must be one of 1.8, 8, 9, 10, 11, 12, 13: " + jdkVer);
}
}
public static long getFieldOffset(final Class<?> c, final String fieldName) {
try {
return unsafe.objectFieldOffset(c.getDeclaredField(fieldName));
} catch (final NoSuchFieldException e) {
throw new IllegalStateException(e);
}
}
/**
* Like {@link Unsafe#arrayBaseOffset(Class)}, but caches return values for common array types.
* Useful because calling {@link Unsafe#arrayBaseOffset(Class)} directly incurs more overhead.
* @param c The given Class&lt;?&gt;.
* @return the base-offset
*/
public static long getArrayBaseOffset(final Class<?> c) {
// Ordering here is roughly in order of what we expect to be most popular.
if (c == byte[].class) {
return ARRAY_BYTE_BASE_OFFSET;
} else if (c == int[].class) {
return ARRAY_INT_BASE_OFFSET;
} else if (c == long[].class) {
return ARRAY_LONG_BASE_OFFSET;
} else if (c == float[].class) {
return ARRAY_FLOAT_BASE_OFFSET;
} else if (c == double[].class) {
return ARRAY_DOUBLE_BASE_OFFSET;
} else if (c == boolean[].class) {
return ARRAY_BOOLEAN_BASE_OFFSET;
} else if (c == short[].class) {
return ARRAY_SHORT_BASE_OFFSET;
} else if (c == char[].class) {
return ARRAY_CHAR_BASE_OFFSET;
} else if (c == Object[].class) {
return ARRAY_OBJECT_BASE_OFFSET;
} else {
return unsafe.arrayBaseOffset(c);
}
}
/**
* Assert the requested offset and length against the allocated size.
* The invariants equation is: {@code 0 <= reqOff <= reqLen <= reqOff + reqLen <= allocSize}.
* If this equation is violated and assertions are enabled, an {@link AssertionError} will
* be thrown.
* @param reqOff the requested offset
* @param reqLen the requested length
* @param allocSize the allocated size.
*/
public static void assertBounds(final long reqOff, final long reqLen, final long allocSize) {
assert ((reqOff | reqLen | (reqOff + reqLen) | (allocSize - (reqOff + reqLen))) >= 0) :
"reqOffset: " + reqOff + ", reqLength: " + reqLen
+ ", (reqOff + reqLen): " + (reqOff + reqLen) + ", allocSize: " + allocSize;
}
/**
* Check the requested offset and length against the allocated size.
* The invariants equation is: {@code 0 <= reqOff <= reqLen <= reqOff + reqLen <= allocSize}.
* If this equation is violated an {@link IllegalArgumentException} will be thrown.
* @param reqOff the requested offset
* @param reqLen the requested length
* @param allocSize the allocated size.
*/
public static void checkBounds(final long reqOff, final long reqLen, final long allocSize) {
if ((reqOff | reqLen | (reqOff + reqLen) | (allocSize - (reqOff + reqLen))) < 0) {
throw new IllegalArgumentException(
"reqOffset: " + reqOff + ", reqLength: " + reqLen
+ ", (reqOff + reqLen): " + (reqOff + reqLen) + ", allocSize: " + allocSize);
}
}
}

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src/main/java/com/geedgenetworks/sketch/util/XxHash64.java Normal file
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package com.geedgenetworks.sketch.util;
import static com.geedgenetworks.sketch.util.UnsafeUtil.*;
/**
* The XxHash is a fast, non-cryptographic, 64-bit hash function that has
* excellent avalanche and 2-way bit independence properties.
* This java version adapted the C++ version and the OpenHFT/Zero-Allocation-Hashing implementation
* referenced below as inspiration.
*
* <p>The C++ source repository:
* <a href="https://github.com/Cyan4973/xxHash">
* https://github.com/Cyan4973/xxHash</a>. It has a BSD 2-Clause License:
* <a href="http://www.opensource.org/licenses/bsd-license.php">
* http://www.opensource.org/licenses/bsd-license.php</a>. See LICENSE.
*
* <p>Portions of this code were adapted from
* <a href="https://github.com/OpenHFT/Zero-Allocation-Hashing/blob/master/src/main/java/net/openhft/hashing/XxHash.java">
* OpenHFT/Zero-Allocation-Hashing</a>, which has an Apache 2 license as does this site. See LICENSE.
*
* @author Lee Rhodes
*/
@SuppressWarnings("restriction")
public class XxHash64 {
// Unsigned, 64-bit primes
private static final long P1 = -7046029288634856825L;
private static final long P2 = -4417276706812531889L;
private static final long P3 = 1609587929392839161L;
private static final long P4 = -8796714831421723037L;
private static final long P5 = 2870177450012600261L;
/**
* Returns the 64-bit hash of the sequence of bytes in the unsafeObject specified by
* <i>cumOffsetBytes</i>, <i>lengthBytes</i> and a <i>seed</i>.
*
* @param unsafeObj A reference to the object parameter required by unsafe. It may be null.
* @param cumOffsetBytes cumulative offset in bytes of this object from the backing resource
* including any user given offsetBytes. This offset may also include other offset components
* such as the native off-heap memory address, DirectByteBuffer split offsets, region offsets,
* and unsafe arrayBaseOffsets.
* @param lengthBytes the length in bytes of the sequence to be hashed
* @param seed a given seed
* @return the 64-bit hash of the sequence of bytes in the unsafeObject specified by
* <i>cumOffsetBytes</i>, <i>lengthBytes</i> and a <i>seed</i>.
*/
static long hash(final Object unsafeObj, long cumOffsetBytes, final long lengthBytes,
final long seed) {
long hash;
long remaining = lengthBytes;
if (remaining >= 32) {
long v1 = seed + P1 + P2;
long v2 = seed + P2;
long v3 = seed;
long v4 = seed - P1;
do {
v1 += unsafe.getLong(unsafeObj, cumOffsetBytes) * P2;
v1 = Long.rotateLeft(v1, 31);
v1 *= P1;
v2 += unsafe.getLong(unsafeObj, cumOffsetBytes + 8L) * P2;
v2 = Long.rotateLeft(v2, 31);
v2 *= P1;
v3 += unsafe.getLong(unsafeObj, cumOffsetBytes + 16L) * P2;
v3 = Long.rotateLeft(v3, 31);
v3 *= P1;
v4 += unsafe.getLong(unsafeObj, cumOffsetBytes + 24L) * P2;
v4 = Long.rotateLeft(v4, 31);
v4 *= P1;
cumOffsetBytes += 32;
remaining -= 32;
} while (remaining >= 32);
hash = Long.rotateLeft(v1, 1)
+ Long.rotateLeft(v2, 7)
+ Long.rotateLeft(v3, 12)
+ Long.rotateLeft(v4, 18);
v1 *= P2;
v1 = Long.rotateLeft(v1, 31);
v1 *= P1;
hash ^= v1;
hash = (hash * P1) + P4;
v2 *= P2;
v2 = Long.rotateLeft(v2, 31);
v2 *= P1;
hash ^= v2;
hash = (hash * P1) + P4;
v3 *= P2;
v3 = Long.rotateLeft(v3, 31);
v3 *= P1;
hash ^= v3;
hash = (hash * P1) + P4;
v4 *= P2;
v4 = Long.rotateLeft(v4, 31);
v4 *= P1;
hash ^= v4;
hash = (hash * P1) + P4;
} //end remaining >= 32
else {
hash = seed + P5;
}
hash += lengthBytes;
while (remaining >= 8) {
long k1 = unsafe.getLong(unsafeObj, cumOffsetBytes);
k1 *= P2;
k1 = Long.rotateLeft(k1, 31);
k1 *= P1;
hash ^= k1;
hash = (Long.rotateLeft(hash, 27) * P1) + P4;
cumOffsetBytes += 8;
remaining -= 8;
}
if (remaining >= 4) { //treat as unsigned ints
hash ^= (unsafe.getInt(unsafeObj, cumOffsetBytes) & 0XFFFF_FFFFL) * P1;
hash = (Long.rotateLeft(hash, 23) * P2) + P3;
cumOffsetBytes += 4;
remaining -= 4;
}
while (remaining != 0) { //treat as unsigned bytes
hash ^= (unsafe.getByte(unsafeObj, cumOffsetBytes) & 0XFFL) * P5;
hash = Long.rotateLeft(hash, 11) * P1;
--remaining;
++cumOffsetBytes;
}
return finalize(hash);
}
/**
* Returns a 64-bit hash from a single long. This method has been optimized for speed when only
* a single hash of a long is required.
* @param in A long.
* @param seed A long valued seed.
* @return the hash.
*/
public static long hash(final long in, final long seed) {
long hash = seed + P5;
hash += 8;
long k1 = in;
k1 *= P2;
k1 = Long.rotateLeft(k1, 31);
k1 *= P1;
hash ^= k1;
hash = (Long.rotateLeft(hash, 27) * P1) + P4;
return finalize(hash);
}
private static long finalize(long hash) {
hash ^= hash >>> 33;
hash *= P2;
hash ^= hash >>> 29;
hash *= P3;
hash ^= hash >>> 32;
return hash;
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param arr the given array
* @param offsetBooleans starting at this offset
* @param lengthBooleans continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashBooleans(final boolean[] arr, final long offsetBooleans,
final long lengthBooleans, final long seed) {
return hash(arr, ARRAY_BOOLEAN_BASE_OFFSET + offsetBooleans, lengthBooleans, seed);
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param arr the given array
* @param offsetBytes starting at this offset
* @param lengthBytes continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashBytes(final byte[] arr, final long offsetBytes,
final long lengthBytes, final long seed) {
return hash(arr, ARRAY_BYTE_BASE_OFFSET + offsetBytes, lengthBytes, seed);
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param arr the given array
* @param offsetShorts starting at this offset
* @param lengthShorts continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashShorts(final short[] arr, final long offsetShorts,
final long lengthShorts, final long seed) {
return hash(arr, ARRAY_SHORT_BASE_OFFSET + (offsetShorts << SHORT_SHIFT),
lengthShorts << SHORT_SHIFT, seed);
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param arr the given array
* @param offsetChars starting at this offset
* @param lengthChars continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashChars(final char[] arr, final long offsetChars,
final long lengthChars, final long seed) {
return hash(arr, ARRAY_CHAR_BASE_OFFSET + (offsetChars << CHAR_SHIFT),
lengthChars << CHAR_SHIFT, seed);
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param arr the given array
* @param offsetInts starting at this offset
* @param lengthInts continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashInts(final int[] arr, final long offsetInts,
final long lengthInts, final long seed) {
return hash(arr, ARRAY_INT_BASE_OFFSET + (offsetInts << INT_SHIFT),
lengthInts << INT_SHIFT, seed);
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param arr the given array
* @param offsetLongs starting at this offset
* @param lengthLongs continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashLongs(final long[] arr, final long offsetLongs,
final long lengthLongs, final long seed) {
return hash(arr, ARRAY_LONG_BASE_OFFSET + (offsetLongs << LONG_SHIFT),
lengthLongs << LONG_SHIFT, seed);
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param arr the given array
* @param offsetFloats starting at this offset
* @param lengthFloats continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashFloats(final float[] arr, final long offsetFloats,
final long lengthFloats, final long seed) {
return hash(arr, ARRAY_FLOAT_BASE_OFFSET + (offsetFloats << FLOAT_SHIFT),
lengthFloats << FLOAT_SHIFT, seed);
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param arr the given array
* @param offsetDoubles starting at this offset
* @param lengthDoubles continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashDoubles(final double[] arr, final long offsetDoubles,
final long lengthDoubles, final long seed) {
return hash(arr, ARRAY_DOUBLE_BASE_OFFSET + (offsetDoubles << DOUBLE_SHIFT),
lengthDoubles << DOUBLE_SHIFT, seed);
}
/**
* Hash the given arr starting at the given offset and continuing for the given length using the
* given seed.
* @param str the given string
* @param offsetChars starting at this offset
* @param lengthChars continuing for this length
* @param seed the given seed
* @return the hash
*/
public static long hashString(final String str, final long offsetChars,
final long lengthChars, final long seed) {
return hashChars(str.toCharArray(), offsetChars, lengthChars, seed);
}
}

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package org.HdrHistogram; /**
* Written by Gil Tene of Azul Systems, and released to the public domain,
* as explained at http://creativecommons.org/publicdomain/zero/1.0/
*
* @author Gil Tene
*/
import java.io.IOException;
import java.io.ObjectInputStream;
import java.nio.ByteBuffer;
import java.util.*;
import java.util.zip.DataFormatException;
/**
* <h3>A High Dynamic Range (HDR) Histogram</h3>
* <p>
* {@link ArrayHistogram} supports the recording and analyzing sampled data value counts across a configurable integer value
* range with configurable value precision within the range. Value precision is expressed as the number of significant
* digits in the value recording, and provides control over value quantization behavior across the value range and the
* subsequent value resolution at any given level.
* <p>
* For example, a Histogram could be configured to track the counts of observed integer values between 0 and
* 3,600,000,000 while maintaining a value precision of 3 significant digits across that range. Value quantization
* within the range will thus be no larger than 1/1,000th (or 0.1%) of any value. This example Histogram could
* be used to track and analyze the counts of observed response times ranging between 1 microsecond and 1 hour
* in magnitude, while maintaining a value resolution of 1 microsecond up to 1 millisecond, a resolution of
* 1 millisecond (or better) up to one second, and a resolution of 1 second (or better) up to 1,000 seconds. At its
* maximum tracked value (1 hour), it would still maintain a resolution of 3.6 seconds (or better).
* <p>
* Histogram tracks value counts in <b><code>long</code></b> fields. Smaller field types are available in the
* {@link IntCountsHistogram} and {@link ShortCountsHistogram} implementations of
* {@link AbstractHistogram}.
* <p>
* Auto-resizing: When constructed with no specified value range range (or when auto-resize is turned on with {@link
* ArrayHistogram#setAutoResize}) a {@link ArrayHistogram} will auto-resize its dynamic range to include recorded values as
* they are encountered. Note that recording calls that cause auto-resizing may take longer to execute, as resizing
* incurs allocation and copying of internal data structures.
* <p>
* See package description for {@link org.HdrHistogram} for details.
*/
public class ArrayHistogram extends AbstractHistogram implements Histogramer{
long totalCount;
long[] counts;
int normalizingIndexOffset;
@Override
long getCountAtIndex(final int index) {
return counts[normalizeIndex(index, normalizingIndexOffset, countsArrayLength)];
}
@Override
long getCountAtNormalizedIndex(final int index) {
return counts[index];
}
@Override
void incrementCountAtIndex(final int index) {
counts[normalizeIndex(index, normalizingIndexOffset, countsArrayLength)]++;
}
@Override
void addToCountAtIndex(final int index, final long value) {
// 正常情况下normalizingIndexOffset = 0, index不用偏移
counts[normalizeIndex(index, normalizingIndexOffset, countsArrayLength)] += value;
}
@Override
void setCountAtIndex(int index, long value) {
counts[normalizeIndex(index, normalizingIndexOffset, countsArrayLength)] = value;
}
@Override
void setCountAtNormalizedIndex(int index, long value) {
counts[index] = value;
}
@Override
int getNormalizingIndexOffset() {
return normalizingIndexOffset;
}
@Override
void setNormalizingIndexOffset(int normalizingIndexOffset) {
this.normalizingIndexOffset = normalizingIndexOffset;
}
@Override
void setIntegerToDoubleValueConversionRatio(double integerToDoubleValueConversionRatio) {
nonConcurrentSetIntegerToDoubleValueConversionRatio(integerToDoubleValueConversionRatio);
}
@Override
void shiftNormalizingIndexByOffset(int offsetToAdd,
boolean lowestHalfBucketPopulated,
double newIntegerToDoubleValueConversionRatio) {
nonConcurrentNormalizingIndexShift(offsetToAdd, lowestHalfBucketPopulated);
}
@Override
void clearCounts() {
Arrays.fill(counts, 0);
totalCount = 0;
}
@Override
public Histogramer makeCopy() {
return miniCopy();
}
@Override
public ArrayHistogram copy() {
ArrayHistogram copy = new ArrayHistogram(this);
copy.add(this);
return copy;
}
public ArrayHistogram miniCopy() {
ArrayHistogram copy = new ArrayHistogram(lowestDiscernibleValue, maxValue < highestTrackableValue ? Math.max(maxValue, lowestDiscernibleValue * 2) : highestTrackableValue, numberOfSignificantValueDigits);
copy.add(this);
return copy;
}
@Override
public ArrayHistogram copyCorrectedForCoordinatedOmission(final long expectedIntervalBetweenValueSamples) {
ArrayHistogram copy = new ArrayHistogram(this);
copy.addWhileCorrectingForCoordinatedOmission(this, expectedIntervalBetweenValueSamples);
return copy;
}
@Override
public long getTotalCount() {
return totalCount;
}
@Override
void setTotalCount(final long totalCount) {
this.totalCount = totalCount;
}
@Override
void incrementTotalCount() {
totalCount++;
}
@Override
void addToTotalCount(final long value) {
totalCount += value;
}
@Override
int _getEstimatedFootprintInBytes() {
return (512 + (8 * counts.length));
}
@Override
void resize(long newHighestTrackableValue) {
int oldNormalizedZeroIndex = normalizeIndex(0, normalizingIndexOffset, countsArrayLength);
establishSize(newHighestTrackableValue);
int countsDelta = countsArrayLength - counts.length;
counts = Arrays.copyOf(counts, countsArrayLength);
if (oldNormalizedZeroIndex != 0) {
// We need to shift the stuff from the zero index and up to the end of the array:
int newNormalizedZeroIndex = oldNormalizedZeroIndex + countsDelta;
int lengthToCopy = (countsArrayLength - countsDelta) - oldNormalizedZeroIndex;
System.arraycopy(counts, oldNormalizedZeroIndex, counts, newNormalizedZeroIndex, lengthToCopy);
Arrays.fill(counts, oldNormalizedZeroIndex, newNormalizedZeroIndex, 0);
}
}
/**
* Construct an auto-resizing histogram with a lowest discernible value of 1 and an auto-adjusting
* highestTrackableValue. Can auto-resize up to track values up to (Long.MAX_VALUE / 2).
*
* @param numberOfSignificantValueDigits Specifies the precision to use. This is the number of significant
* decimal digits to which the histogram will maintain value resolution
* and separation. Must be a non-negative integer between 0 and 5.
*/
public ArrayHistogram(final int numberOfSignificantValueDigits) {
this(1, 2, numberOfSignificantValueDigits);
setAutoResize(true);
}
/**
* Construct a Histogram given the Highest value to be tracked and a number of significant decimal digits. The
* histogram will be constructed to implicitly track (distinguish from 0) values as low as 1.
*
* @param highestTrackableValue The highest value to be tracked by the histogram. Must be a positive
* integer that is {@literal >=} 2.
* @param numberOfSignificantValueDigits Specifies the precision to use. This is the number of significant
* decimal digits to which the histogram will maintain value resolution
* and separation. Must be a non-negative integer between 0 and 5.
*/
public ArrayHistogram(final long highestTrackableValue, final int numberOfSignificantValueDigits) {
this(1, highestTrackableValue, numberOfSignificantValueDigits);
}
/**
* Construct a Histogram given the Lowest and Highest values to be tracked and a number of significant
* decimal digits. Providing a lowestDiscernibleValue is useful is situations where the units used
* for the histogram's values are much smaller that the minimal accuracy required. E.g. when tracking
* time values stated in nanosecond units, where the minimal accuracy required is a microsecond, the
* proper value for lowestDiscernibleValue would be 1000.
*
* @param lowestDiscernibleValue The lowest value that can be discerned (distinguished from 0) by the
* histogram. Must be a positive integer that is {@literal >=} 1. May be
* internally rounded down to nearest power of 2.
* @param highestTrackableValue The highest value to be tracked by the histogram. Must be a positive
* integer that is {@literal >=} (2 * lowestDiscernibleValue).
* @param numberOfSignificantValueDigits Specifies the precision to use. This is the number of significant
* decimal digits to which the histogram will maintain value resolution
* and separation. Must be a non-negative integer between 0 and 5.
*/
public ArrayHistogram(final long lowestDiscernibleValue, final long highestTrackableValue,
final int numberOfSignificantValueDigits) {
this(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits, true);
}
/**
* Construct a histogram with the same range settings as a given source histogram,
* duplicating the source's start/end timestamps (but NOT its contents)
* @param source The source histogram to duplicate
*/
public ArrayHistogram(final AbstractHistogram source) {
this(source, true);
}
ArrayHistogram(final AbstractHistogram source, boolean allocateCountsArray) {
super(source);
if (allocateCountsArray) {
counts = new long[countsArrayLength];
}
wordSizeInBytes = 8;
}
ArrayHistogram(final long lowestDiscernibleValue, final long highestTrackableValue,
final int numberOfSignificantValueDigits, boolean allocateCountsArray) {
super(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits);
if (allocateCountsArray) {
counts = new long[countsArrayLength];
}
// 写死 = 8
wordSizeInBytes = 8;
}
/**
* Construct a new histogram by decoding it from a ByteBuffer.
* @param buffer The buffer to decode from
* @param minBarForHighestTrackableValue Force highestTrackableValue to be set at least this high
* @return The newly constructed histogram
*/
public static ArrayHistogram decodeFromByteBuffer(final ByteBuffer buffer,
final long minBarForHighestTrackableValue) {
return decodeFromByteBuffer(buffer, ArrayHistogram.class, minBarForHighestTrackableValue);
}
/**
* Construct a new histogram by decoding it from a compressed form in a ByteBuffer.
* @param buffer The buffer to decode from
* @param minBarForHighestTrackableValue Force highestTrackableValue to be set at least this high
* @return The newly constructed histogram
* @throws DataFormatException on error parsing/decompressing the buffer
*/
public static ArrayHistogram decodeFromCompressedByteBuffer(final ByteBuffer buffer,
final long minBarForHighestTrackableValue)
throws DataFormatException {
return decodeFromCompressedByteBuffer(buffer, ArrayHistogram.class, minBarForHighestTrackableValue);
}
private void readObject(final ObjectInputStream o)
throws IOException, ClassNotFoundException {
o.defaultReadObject();
}
/**
* Construct a new Histogram by decoding it from a String containing a base64 encoded
* compressed histogram representation.
*
* @param base64CompressedHistogramString A string containing a base64 encoding of a compressed histogram
* @return A Histogream decoded from the string
* @throws DataFormatException on error parsing/decompressing the input
*/
public static ArrayHistogram fromString(final String base64CompressedHistogramString)
throws DataFormatException {
// 这还有个base64字符串的解析
return decodeFromCompressedByteBuffer(
ByteBuffer.wrap(Base64Helper.parseBase64Binary(base64CompressedHistogramString)),
0);
}
@Override
public List<Percentile> percentileList(int percentileTicksPerHalfDistance) {
List<Percentile> percentiles = new ArrayList<>();
for (HistogramIterationValue percentile : this.percentiles(percentileTicksPerHalfDistance)) {
if(percentile.getCountAddedInThisIterationStep() > 0){
percentiles.add(new Percentile(percentile.getValueIteratedTo(), percentile.getCountAddedInThisIterationStep(), percentile.getPercentile()));
}
}
return percentiles;
}
@Override
public Map<String, Object> describe() {
long min = getMinValue();
long max = getMaxValue(); // max = this.maxValue;
long count = getTotalCount();
double mean = getMean();
long sum = (long) (mean * count);
mean = Math.round(mean * 100.0) / 100.0;
long p25 = getValueAtPercentile(25);
long p50 = getValueAtPercentile(50);
long p75 = getValueAtPercentile(75);
long p90 = getValueAtPercentile(90);
long p95 = getValueAtPercentile(95);
long p99 = getValueAtPercentile(99);
Map<String, Object> rst = new LinkedHashMap<>();
rst.put("count", count);
rst.put("mean", mean);
rst.put("sum", sum);
rst.put("min", min);
rst.put("p25", p25);
rst.put("p50", p50);
rst.put("p75", p75);
rst.put("p90", p90);
rst.put("p95", p95);
rst.put("p99", p99);
rst.put("max", max);
return rst;
}
@Override
public Histogramer resetHistogram() {
if(isAutoResize()){
return new ArrayHistogram(this.numberOfSignificantValueDigits);
}else{
this.reset();
return this;
}
}
@Override
public Histogramer merge(Histogramer histogram) {
if(histogram instanceof AbstractHistogram){
this.add((AbstractHistogram)histogram);
return this;
}else if(histogram instanceof DirectMapHistogram){
try {
((DirectMapHistogram)histogram).mergeInto(this);
return this;
} catch (Exception e) {
throw new RuntimeException(e);
}
}else{
throw new UnsupportedOperationException("unsupported method");
}
}
@Override
public byte[] toBytes() {
ByteBuffer byteBuffer = ByteBuffer.allocate(this.getNeededByteBufferCapacity());
this.encodeIntoByteBuffer(byteBuffer);
return byteBuffer2Bytes(byteBuffer);
}
public static ArrayHistogram fromBytes(byte[] bytes) {
ByteBuffer byteBuffer = ByteBuffer.wrap(bytes);
return fromByteBuffer(byteBuffer);
}
public static ArrayHistogram fromByteBuffer(ByteBuffer byteBuffer) {
int initPosition = byteBuffer.position();
int cookie = byteBuffer.getInt(initPosition);
if(DirectMapHistogram.getCookieBase(cookie) == DirectMapHistogram.V2CompressedEncodingCookieBase){
try {
return ArrayHistogram.decodeFromCompressedByteBuffer(byteBuffer, 2);
} catch (DataFormatException e) {
throw new RuntimeException(e);
}
}else if(DirectMapHistogram.getCookieBase(cookie) == DirectMapHistogram.V2EncodingCookieBase){
return ArrayHistogram.decodeFromByteBuffer(byteBuffer, 2);
}
throw new UnsupportedOperationException("unsupported method");
}
}

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src/main/java/org/HdrHistogram/DirectArrayHistogram.java Normal file
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package org.HdrHistogram;
import java.nio.ByteBuffer;
import java.util.ArrayList;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;
public class DirectArrayHistogram extends AbstractHistogram implements Histogramer{
long totalCount;
int normalizingIndexOffset;
private ByteBuffer byteBuffer;
private int initPosition;
public DirectArrayHistogram(final long lowestDiscernibleValue, final long highestTrackableValue,
final int numberOfSignificantValueDigits, ByteBuffer byteBuffer) {
super(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits);
this.byteBuffer = byteBuffer;
this.initPosition = byteBuffer.position();
wordSizeInBytes = 8;
}
// druid内部使用
public void resetByteBuffer(ByteBuffer byteBuffer){
this.byteBuffer = byteBuffer;
this.initPosition = byteBuffer.position();
}
@Override
long getCountAtIndex(int index) {
int i = normalizeIndex(index, normalizingIndexOffset, countsArrayLength);
return byteBuffer.getLong(initPosition + i * 8);
}
@Override
long getCountAtNormalizedIndex(int index) {
return byteBuffer.getLong(initPosition + index * 8);
}
@Override
void incrementCountAtIndex(int index) {
int i = normalizeIndex(index, normalizingIndexOffset, countsArrayLength);
int pos = initPosition + i * 8;
long val = byteBuffer.getLong(pos);
byteBuffer.putLong(pos, val + 1);
}
@Override
void addToCountAtIndex(int index, long value) {
int i = normalizeIndex(index, normalizingIndexOffset, countsArrayLength);
int pos = initPosition + i * 8;
long val = byteBuffer.getLong(pos);
byteBuffer.putLong(pos, val + value);
}
@Override
void setCountAtIndex(int index, long value) {
int i = normalizeIndex(index, normalizingIndexOffset, countsArrayLength);
int pos = initPosition + i * 8;
byteBuffer.putLong(pos, value);
}
@Override
void setCountAtNormalizedIndex(int index, long value) {
int pos = initPosition + index * 8;
byteBuffer.putLong(pos, value);
}
@Override
int getNormalizingIndexOffset() {
return normalizingIndexOffset;
}
@Override
void setNormalizingIndexOffset(int normalizingIndexOffset) {
if(normalizingIndexOffset == 0){
this.normalizingIndexOffset = normalizingIndexOffset;
}else{
throw new RuntimeException("cant not setNormalizingIndexOffset");
}
}
@Override
void setIntegerToDoubleValueConversionRatio(double integerToDoubleValueConversionRatio) {
nonConcurrentSetIntegerToDoubleValueConversionRatio(integerToDoubleValueConversionRatio);
}
@Override
void shiftNormalizingIndexByOffset(int offsetToAdd, boolean lowestHalfBucketPopulated, double newIntegerToDoubleValueConversionRatio) {
nonConcurrentNormalizingIndexShift(offsetToAdd, lowestHalfBucketPopulated);
}
@Override
void clearCounts() {
for (int i = 0; i < countsArrayLength; i++) {
byteBuffer.putLong(initPosition + i * 8, 0L);
}
totalCount = 0;
}
@Override
public Histogramer makeCopy() {
return miniCopy();
}
@Override
public ArrayHistogram copy() {
ArrayHistogram copy = new ArrayHistogram(this);
copy.add(this);
return copy;
}
public ArrayHistogram miniCopy() {
ArrayHistogram copy = new ArrayHistogram(lowestDiscernibleValue, maxValue < highestTrackableValue ? Math.max(maxValue, lowestDiscernibleValue * 2) : highestTrackableValue, numberOfSignificantValueDigits);
copy.add(this);
return copy;
}
@Override
public AbstractHistogram copyCorrectedForCoordinatedOmission(long expectedIntervalBetweenValueSamples) {
Histogram copy = new Histogram(this);
copy.addWhileCorrectingForCoordinatedOmission(this, expectedIntervalBetweenValueSamples);
return copy;
}
@Override
public long getTotalCount() {
return totalCount;
}
@Override
void setTotalCount(final long totalCount) {
this.totalCount = totalCount;
}
@Override
void incrementTotalCount() {
totalCount++;
}
@Override
void addToTotalCount(long value) {
totalCount += value;
}
@Override
int _getEstimatedFootprintInBytes() {
return (512 + (8 * countsArrayLength));
}
@Override
void resize(long newHighestTrackableValue) {
throw new RuntimeException("cant not resize");
}
public static int getCountsArrayLength(long lowestDiscernibleValue, long highestTrackableValue, int numberOfSignificantValueDigits){
Histogram his = new Histogram(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits, false);
return his.countsArrayLength;
}
public static final int getUpdatableSerializationBytes(long lowestDiscernibleValue, long highestTrackableValue, int numberOfSignificantValueDigits){
return getCountsArrayLength(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits) * 8;
}
@Override
public List<Percentile> percentileList(int percentileTicksPerHalfDistance) {
List<Percentile> percentiles = new ArrayList<>();
for (HistogramIterationValue percentile : this.percentiles(percentileTicksPerHalfDistance)) {
if(percentile.getCountAddedInThisIterationStep() > 0){
percentiles.add(new Percentile(percentile.getValueIteratedTo(), percentile.getCountAddedInThisIterationStep(), percentile.getPercentile()));
}
}
return percentiles;
}
@Override
public Map<String, Object> describe() {
long min = getMinValue();
long max = getMaxValue(); // max = this.maxValue;
long count = getTotalCount();
double mean = getMean();
long sum = (long) (mean * count);
mean = Math.round(mean * 100.0) / 100.0;
long p25 = getValueAtPercentile(25);
long p50 = getValueAtPercentile(50);
long p75 = getValueAtPercentile(75);
long p90 = getValueAtPercentile(90);
long p95 = getValueAtPercentile(95);
long p99 = getValueAtPercentile(99);
Map<String, Object> rst = new LinkedHashMap<>();
rst.put("count", count);
rst.put("mean", mean);
rst.put("sum", sum);
rst.put("min", min);
rst.put("p25", p25);
rst.put("p50", p50);
rst.put("p75", p75);
rst.put("p90", p90);
rst.put("p95", p95);
rst.put("p99", p99);
rst.put("max", max);
return rst;
}
@Override
public Histogramer resetHistogram() {
throw new UnsupportedOperationException("unsupported method");
}
@Override
public Histogramer merge(Histogramer histogram) {
if(histogram instanceof AbstractHistogram){
this.add((AbstractHistogram)histogram);
return this;
}else if(histogram instanceof DirectMapHistogram){
try {
((DirectMapHistogram)histogram).mergeInto(this);
return this;
} catch (Exception e) {
throw new RuntimeException(e);
}
}else{
throw new UnsupportedOperationException("unsupported method");
}
}
@Override
public byte[] toBytes() {
ByteBuffer byteBuffer = ByteBuffer.allocate(this.getNeededByteBufferCapacity());
this.encodeIntoByteBuffer(byteBuffer);
return byteBuffer2Bytes(byteBuffer);
}
}

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src/main/java/org/HdrHistogram/DirectMapHistogram.java Normal file
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package org.HdrHistogram;
import java.nio.ByteBuffer;
import java.nio.ByteOrder;
import java.util.List;
import java.util.Map;
import java.util.zip.DataFormatException;
import java.util.zip.Inflater;
import static java.nio.ByteOrder.BIG_ENDIAN;
/**
* 直接映射字节数组到Histogram，只读的Histogram，用于druid查询，减少gc减少计算，序列化后的是稀疏数组的形式
*/
public class DirectMapHistogram implements Histogramer{
static final int V2maxWordSizeInBytes = 9; // LEB128-64b9B + ZigZag require up to 9 bytes per word
static final int V2EncodingCookieBase = 0x1c849303;
static final int V2CompressedEncodingCookieBase = 0x1c849304;
final ByteBuffer byteBuffer;
final int initPosition;
long totalCount;
private DirectMapHistogram(ByteBuffer byteBuffer) {
int initPosition = byteBuffer.position();
this.byteBuffer = byteBuffer;
this.initPosition = initPosition;
this.totalCount = -1;
}
public static boolean byteBufferCanToDirectMapHistogram(ByteBuffer byteBuffer) {
int initPosition = byteBuffer.position();
int cookie = byteBuffer.getInt(initPosition);
return getCookieBase(cookie) == V2EncodingCookieBase || getCookieBase(cookie) == V2CompressedEncodingCookieBase;
}
public static DirectMapHistogram wrapBytes(byte[] bytes) {
ByteBuffer byteBuffer = ByteBuffer.wrap(bytes);
return wrapByteBuffer(byteBuffer);
}
public static DirectMapHistogram wrapByteBuffer(ByteBuffer byteBuffer) {
if(byteBufferCanToDirectMapHistogram(byteBuffer)){
DirectMapHistogram hll = new DirectMapHistogram(byteBuffer);
return hll;
}
throw new RuntimeException("can not wrapByteBuffer");
}
public void mergeInto(AbstractHistogram histogram) throws Exception{
int cookie = byteBuffer.getInt(initPosition);
if(getCookieBase(cookie) == V2CompressedEncodingCookieBase){
final int lengthOfCompressedContents = byteBuffer.getInt(initPosition + 4);
final Inflater decompressor = new Inflater();
if (byteBuffer.hasArray()) {
decompressor.setInput(byteBuffer.array(), initPosition + 8, lengthOfCompressedContents);
} else {
byte[] compressedContents = new byte[lengthOfCompressedContents];
byteBuffer.position(initPosition + 8);
try {
byteBuffer.get(compressedContents);
decompressor.setInput(compressedContents);
}finally {
byteBuffer.position(initPosition);
}
}
final int headerSize = 40;
final ByteBuffer headerBuffer = ByteBuffer.allocate(headerSize).order(BIG_ENDIAN);
decompressor.inflate(headerBuffer.array());
cookie = headerBuffer.getInt();
final int payloadLengthInBytes;
final int normalizingIndexOffset;
final int numberOfSignificantValueDigits;
final long lowestTrackableUnitValue;
long highestTrackableValue;
final double integerToDoubleValueConversionRatio;
assert getCookieBase(cookie) == V2EncodingCookieBase;
payloadLengthInBytes = headerBuffer.getInt(4);
normalizingIndexOffset = headerBuffer.getInt(8);
numberOfSignificantValueDigits = headerBuffer.getInt( 12);
lowestTrackableUnitValue = headerBuffer.getLong(16);
highestTrackableValue = headerBuffer.getLong(24);
integerToDoubleValueConversionRatio = headerBuffer.getDouble(32);
highestTrackableValue = Math.max(highestTrackableValue, 2);
final long largestValueWithSingleUnitResolution = 2 * (long) Math.pow(10, numberOfSignificantValueDigits);
final int unitMagnitude = (int) (Math.log(lowestTrackableUnitValue)/Math.log(2));
final long unitMagnitudeMask = (1 << unitMagnitude) - 1;
int subBucketCountMagnitude = (int) Math.ceil(Math.log(largestValueWithSingleUnitResolution)/Math.log(2));
final int subBucketHalfCountMagnitude = subBucketCountMagnitude - 1;
final int subBucketCount = 1 << subBucketCountMagnitude;
final int subBucketHalfCount = subBucketCount / 2;
final long subBucketMask = ((long)subBucketCount - 1) << unitMagnitude;
if (subBucketCountMagnitude + unitMagnitude > 62) {
// subBucketCount entries can't be represented, with unitMagnitude applied, in a positive long.
// Technically it still sort of works if their sum is 63: you can represent all but the last number
// in the shifted subBucketCount. However, the utility of such a histogram vs ones whose magnitude here
// fits in 62 bits is debatable, and it makes it harder to work through the logic.
// Sums larger than 64 are totally broken as leadingZeroCountBase would go negative.
throw new IllegalArgumentException("Cannot represent numberOfSignificantValueDigits worth of values " +
"beyond lowestDiscernibleValue");
}
final int expectedCapacity = payloadLengthInBytes;
ByteBuffer sourceBuffer = ByteBuffer.allocate(expectedCapacity).order(BIG_ENDIAN);
int decompressedByteCount = decompressor.inflate(sourceBuffer.array());
decompressor.end(); // 必须手动调用，否则快速调用可能内存溢出(堆外内存)
if ((payloadLengthInBytes != Integer.MAX_VALUE) && (decompressedByteCount < payloadLengthInBytes)) {
throw new IllegalArgumentException("The buffer does not contain the indicated payload amount");
}
assert decompressedByteCount == expectedCapacity;
int dstIndex = 0;
int endPosition = sourceBuffer.position() + expectedCapacity; //期望的结束读取的索引
while (sourceBuffer.position() < endPosition) {
long count;
int zerosCount = 0;
// V2 encoding format uses a long encoded in a ZigZag LEB128 format (up to V2maxWordSizeInBytes):
count = ZigZagEncoding.getLong(sourceBuffer);
if (count < 0) {
long zc = -count; // 0值的连续个数
if (zc > Integer.MAX_VALUE) {
throw new IllegalArgumentException(
"An encoded zero count of > Integer.MAX_VALUE was encountered in the source");
}
zerosCount = (int) zc;
}
if (zerosCount > 0) {
dstIndex += zerosCount; // No need to set zeros in array. Just skip them.
} else {
// 单个非连续的0也会被输出
if(count > 0){
long value = valueFromIndex(dstIndex, subBucketHalfCountMagnitude, subBucketHalfCount, unitMagnitude);
histogram.recordValueWithCount(value, count);
}
dstIndex++;
}
}
}else if(getCookieBase(cookie) == V2EncodingCookieBase){
final int payloadLengthInBytes;
final int normalizingIndexOffset;
final int numberOfSignificantValueDigits;
final long lowestTrackableUnitValue;
long highestTrackableValue;
final double integerToDoubleValueConversionRatio;
payloadLengthInBytes = byteBuffer.getInt(initPosition + 4);
normalizingIndexOffset = byteBuffer.getInt(initPosition + 8);
numberOfSignificantValueDigits = byteBuffer.getInt(initPosition + 12);
lowestTrackableUnitValue = byteBuffer.getLong(initPosition + 16);
highestTrackableValue = byteBuffer.getLong(initPosition + 24);
integerToDoubleValueConversionRatio = byteBuffer.getDouble(initPosition + 32);
highestTrackableValue = Math.max(highestTrackableValue, 2);
final long largestValueWithSingleUnitResolution = 2 * (long) Math.pow(10, numberOfSignificantValueDigits);
final int unitMagnitude = (int) (Math.log(lowestTrackableUnitValue)/Math.log(2));
final long unitMagnitudeMask = (1 << unitMagnitude) - 1;
int subBucketCountMagnitude = (int) Math.ceil(Math.log(largestValueWithSingleUnitResolution)/Math.log(2));
final int subBucketHalfCountMagnitude = subBucketCountMagnitude - 1;
final int subBucketCount = 1 << subBucketCountMagnitude;
final int subBucketHalfCount = subBucketCount / 2;
final long subBucketMask = ((long)subBucketCount - 1) << unitMagnitude;
if (subBucketCountMagnitude + unitMagnitude > 62) {
// subBucketCount entries can't be represented, with unitMagnitude applied, in a positive long.
// Technically it still sort of works if their sum is 63: you can represent all but the last number
// in the shifted subBucketCount. However, the utility of such a histogram vs ones whose magnitude here
// fits in 62 bits is debatable, and it makes it harder to work through the logic.
// Sums larger than 64 are totally broken as leadingZeroCountBase would go negative.
throw new IllegalArgumentException("Cannot represent numberOfSignificantValueDigits worth of values " +
"beyond lowestDiscernibleValue");
}
final int expectedCapacity =payloadLengthInBytes;
assert expectedCapacity == payloadLengthInBytes;
if(expectedCapacity > byteBuffer.limit() - 40){
throw new IllegalArgumentException("The buffer does not contain the full Histogram payload");
}
final int position = initPosition + 40;
final int lengthInBytes = expectedCapacity;
final int wordSizeInBytes = V2maxWordSizeInBytes;
// fillCountsArrayFromSourceBuffer
ByteBuffer sourceBuffer = byteBuffer.duplicate();
sourceBuffer.position(position);
final long maxAllowableCountInHistigram = Long.MAX_VALUE;
int dstIndex = 0;
int endPosition = sourceBuffer.position() + lengthInBytes; //期望的结束读取的索引
while (sourceBuffer.position() < endPosition) {
long count;
int zerosCount = 0;
// V2 encoding format uses a long encoded in a ZigZag LEB128 format (up to V2maxWordSizeInBytes):
count = ZigZagEncoding.getLong(sourceBuffer);
if (count < 0) {
long zc = -count; // 0值的连续个数
if (zc > Integer.MAX_VALUE) {
throw new IllegalArgumentException(
"An encoded zero count of > Integer.MAX_VALUE was encountered in the source");
}
zerosCount = (int) zc;
}
if (zerosCount > 0) {
dstIndex += zerosCount; // No need to set zeros in array. Just skip them.
} else {
// 单个非连续的0也会被输出
if(count > 0){
long value = valueFromIndex(dstIndex, subBucketHalfCountMagnitude, subBucketHalfCount, unitMagnitude);
histogram.recordValueWithCount(value, count);
}
dstIndex++;
}
}
}else{
throw new RuntimeException("can not wrapByteBuffer");
}
}
final long valueFromIndex(final int index, int subBucketHalfCountMagnitude, int subBucketHalfCount, int unitMagnitude) {
int bucketIndex = (index >> subBucketHalfCountMagnitude) - 1;
int subBucketIndex = (index & (subBucketHalfCount - 1)) + subBucketHalfCount;
if (bucketIndex < 0) {
subBucketIndex -= subBucketHalfCount;
bucketIndex = 0;
}
return valueFromIndex(bucketIndex, subBucketIndex, unitMagnitude);
}
private long valueFromIndex(final int bucketIndex, final int subBucketIndex, int unitMagnitude) {
return ((long) subBucketIndex) << (bucketIndex + unitMagnitude);
}
static int getCookieBase(final int cookie) {
return (cookie & ~0xf0);
}
@Override
public long getTotalCount() {
if(totalCount >= 0){
return totalCount;
}
try {
totalCount = 0;
int cookie = byteBuffer.getInt(initPosition);
if(getCookieBase(cookie) == V2CompressedEncodingCookieBase){
final int lengthOfCompressedContents = byteBuffer.getInt(initPosition + 4);
final Inflater decompressor = new Inflater();
if (byteBuffer.hasArray()) {
decompressor.setInput(byteBuffer.array(), initPosition + 8, lengthOfCompressedContents);
} else {
byte[] compressedContents = new byte[lengthOfCompressedContents];
byteBuffer.position(initPosition + 8);
try {
byteBuffer.get(compressedContents);
decompressor.setInput(compressedContents);
}finally {
byteBuffer.position(initPosition);
}
}
final int headerSize = 40;
final ByteBuffer headerBuffer = ByteBuffer.allocate(headerSize).order(BIG_ENDIAN);
decompressor.inflate(headerBuffer.array());
cookie = headerBuffer.getInt();
final int payloadLengthInBytes;
final int normalizingIndexOffset;
final int numberOfSignificantValueDigits;
final long lowestTrackableUnitValue;
long highestTrackableValue;
final double integerToDoubleValueConversionRatio;
assert getCookieBase(cookie) == V2EncodingCookieBase;
payloadLengthInBytes = headerBuffer.getInt(4);
normalizingIndexOffset = headerBuffer.getInt(8);
numberOfSignificantValueDigits = headerBuffer.getInt( 12);
lowestTrackableUnitValue = headerBuffer.getLong(16);
highestTrackableValue = headerBuffer.getLong(24);
integerToDoubleValueConversionRatio = headerBuffer.getDouble(32);
highestTrackableValue = Math.max(highestTrackableValue, 2);
final long largestValueWithSingleUnitResolution = 2 * (long) Math.pow(10, numberOfSignificantValueDigits);
final int unitMagnitude = (int) (Math.log(lowestTrackableUnitValue)/Math.log(2));
final long unitMagnitudeMask = (1 << unitMagnitude) - 1;
int subBucketCountMagnitude = (int) Math.ceil(Math.log(largestValueWithSingleUnitResolution)/Math.log(2));
final int subBucketHalfCountMagnitude = subBucketCountMagnitude - 1;
final int subBucketCount = 1 << subBucketCountMagnitude;
final int subBucketHalfCount = subBucketCount / 2;
final long subBucketMask = ((long)subBucketCount - 1) << unitMagnitude;
if (subBucketCountMagnitude + unitMagnitude > 62) {
// subBucketCount entries can't be represented, with unitMagnitude applied, in a positive long.
// Technically it still sort of works if their sum is 63: you can represent all but the last number
// in the shifted subBucketCount. However, the utility of such a histogram vs ones whose magnitude here
// fits in 62 bits is debatable, and it makes it harder to work through the logic.
// Sums larger than 64 are totally broken as leadingZeroCountBase would go negative.
throw new IllegalArgumentException("Cannot represent numberOfSignificantValueDigits worth of values " +
"beyond lowestDiscernibleValue");
}
final int expectedCapacity = payloadLengthInBytes;
ByteBuffer sourceBuffer = ByteBuffer.allocate(expectedCapacity).order(BIG_ENDIAN);
int decompressedByteCount = decompressor.inflate(sourceBuffer.array());
decompressor.end(); // 必须手动调用，否则快速调用可能内存溢出(堆外内存)
if ((payloadLengthInBytes != Integer.MAX_VALUE) && (decompressedByteCount < payloadLengthInBytes)) {
throw new IllegalArgumentException("The buffer does not contain the indicated payload amount");
}
assert decompressedByteCount == expectedCapacity;
int dstIndex = 0;
int endPosition = sourceBuffer.position() + expectedCapacity; //期望的结束读取的索引
while (sourceBuffer.position() < endPosition) {
long count;
int zerosCount = 0;
// V2 encoding format uses a long encoded in a ZigZag LEB128 format (up to V2maxWordSizeInBytes):
count = ZigZagEncoding.getLong(sourceBuffer);
if (count < 0) {
long zc = -count; // 0值的连续个数
if (zc > Integer.MAX_VALUE) {
throw new IllegalArgumentException(
"An encoded zero count of > Integer.MAX_VALUE was encountered in the source");
}
zerosCount = (int) zc;
}
if (zerosCount > 0) {
dstIndex += zerosCount; // No need to set zeros in array. Just skip them.
} else {
// 单个非连续的0也会被输出
if(count > 0){
//long value = valueFromIndex(dstIndex, subBucketHalfCountMagnitude, subBucketHalfCount, unitMagnitude);
//histogram.recordValueWithCount(value, count);
totalCount += count;
}
dstIndex++;
}
}
return totalCount;
}else if(getCookieBase(cookie) == V2EncodingCookieBase){
final int payloadLengthInBytes;
final int normalizingIndexOffset;
final int numberOfSignificantValueDigits;
final long lowestTrackableUnitValue;
long highestTrackableValue;
final double integerToDoubleValueConversionRatio;
payloadLengthInBytes = byteBuffer.getInt(initPosition + 4);
normalizingIndexOffset = byteBuffer.getInt(initPosition + 8);
numberOfSignificantValueDigits = byteBuffer.getInt(initPosition + 12);
lowestTrackableUnitValue = byteBuffer.getLong(initPosition + 16);
highestTrackableValue = byteBuffer.getLong(initPosition + 24);
integerToDoubleValueConversionRatio = byteBuffer.getDouble(initPosition + 32);
highestTrackableValue = Math.max(highestTrackableValue, 2);
final long largestValueWithSingleUnitResolution = 2 * (long) Math.pow(10, numberOfSignificantValueDigits);
final int unitMagnitude = (int) (Math.log(lowestTrackableUnitValue)/Math.log(2));
final long unitMagnitudeMask = (1 << unitMagnitude) - 1;
int subBucketCountMagnitude = (int) Math.ceil(Math.log(largestValueWithSingleUnitResolution)/Math.log(2));
final int subBucketHalfCountMagnitude = subBucketCountMagnitude - 1;
final int subBucketCount = 1 << subBucketCountMagnitude;
final int subBucketHalfCount = subBucketCount / 2;
final long subBucketMask = ((long)subBucketCount - 1) << unitMagnitude;
if (subBucketCountMagnitude + unitMagnitude > 62) {
// subBucketCount entries can't be represented, with unitMagnitude applied, in a positive long.
// Technically it still sort of works if their sum is 63: you can represent all but the last number
// in the shifted subBucketCount. However, the utility of such a histogram vs ones whose magnitude here
// fits in 62 bits is debatable, and it makes it harder to work through the logic.
// Sums larger than 64 are totally broken as leadingZeroCountBase would go negative.
throw new IllegalArgumentException("Cannot represent numberOfSignificantValueDigits worth of values " +
"beyond lowestDiscernibleValue");
}
final int expectedCapacity =payloadLengthInBytes;
assert expectedCapacity == payloadLengthInBytes;
if(expectedCapacity > byteBuffer.limit() - 40){
throw new IllegalArgumentException("The buffer does not contain the full Histogram payload");
}
final int position = initPosition + 40;
final int lengthInBytes = expectedCapacity;
final int wordSizeInBytes = V2maxWordSizeInBytes;
// fillCountsArrayFromSourceBuffer
ByteBuffer sourceBuffer = byteBuffer.duplicate();
sourceBuffer.position(position);
final long maxAllowableCountInHistigram = Long.MAX_VALUE;
int dstIndex = 0;
int endPosition = sourceBuffer.position() + lengthInBytes; //期望的结束读取的索引
while (sourceBuffer.position() < endPosition) {
long count;
int zerosCount = 0;
// V2 encoding format uses a long encoded in a ZigZag LEB128 format (up to V2maxWordSizeInBytes):
count = ZigZagEncoding.getLong(sourceBuffer);
if (count < 0) {
long zc = -count; // 0值的连续个数
if (zc > Integer.MAX_VALUE) {
throw new IllegalArgumentException(
"An encoded zero count of > Integer.MAX_VALUE was encountered in the source");
}
zerosCount = (int) zc;
}
if (zerosCount > 0) {
dstIndex += zerosCount; // No need to set zeros in array. Just skip them.
} else {
// 单个非连续的0也会被输出
if(count > 0){
//long value = valueFromIndex(dstIndex, subBucketHalfCountMagnitude, subBucketHalfCount, unitMagnitude);
//histogram.recordValueWithCount(value, count);
totalCount += count;
}
dstIndex++;
}
}
return totalCount;
}else{
throw new UnsupportedOperationException("unsupported method");
}
} catch (DataFormatException e) {
throw new RuntimeException(e);
}
}
@Override
public void recordValue(long value) throws RuntimeException {
throw new UnsupportedOperationException("unsupported method");
}
@Override
public void recordValueWithCount(long value, long count) throws RuntimeException {
throw new UnsupportedOperationException("unsupported method");
}
@Override
public long getValueAtPercentile(double percentile) {
throw new UnsupportedOperationException("unsupported method");
}
@Override
public List<Percentile> percentileList(int percentileTicksPerHalfDistance) {
throw new UnsupportedOperationException("unsupported method");
}
@Override
public Map<String, Object> describe() {
throw new UnsupportedOperationException("unsupported method");
}
@Override
public Histogramer resetHistogram() {
throw new UnsupportedOperationException("unsupported method");
}
@Override
public Histogramer merge(Histogramer histogram) {
throw new UnsupportedOperationException("unsupported method");
}
@Override
public Histogramer makeCopy() throws RuntimeException{
int cookie = byteBuffer.getInt(initPosition);
if(getCookieBase(cookie) == V2CompressedEncodingCookieBase){
try {
return ArrayHistogram.decodeFromCompressedByteBuffer(byteBuffer, 2);
} catch (DataFormatException e) {
throw new RuntimeException(e);
}
}else if(getCookieBase(cookie) == V2EncodingCookieBase){
return ArrayHistogram.decodeFromByteBuffer(byteBuffer, 2);
}
throw new UnsupportedOperationException("unsupported method");
}
@Override
public byte[] toBytes() {
int size = byteBuffer.limit() - initPosition;
byte[] bytes = new byte[size];
assert byteBuffer.order() == ByteOrder.BIG_ENDIAN;
int oldPosition = byteBuffer.position();
byteBuffer.position(initPosition);
byteBuffer.get(bytes, 0, size);
byteBuffer.position(oldPosition);
return bytes;
}
}

90
src/main/java/org/HdrHistogram/HistogramSketch.java Normal file
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package org.HdrHistogram;
import java.nio.ByteBuffer;
import java.util.List;
import java.util.Map;
public class HistogramSketch {
public Histogramer hisImpl = null;
public HistogramSketch(final int numberOfSignificantValueDigits){
hisImpl = new ArrayHistogram(numberOfSignificantValueDigits);
}
public HistogramSketch(final long lowestDiscernibleValue, final long highestTrackableValue,
final int numberOfSignificantValueDigits, final boolean autoResize){
ArrayHistogram histogram = new ArrayHistogram(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits);
histogram.setAutoResize(autoResize);
hisImpl = histogram;
}
public HistogramSketch(final Histogramer that) {
hisImpl = that;
}
/**
* Copy constructor used by copy().
*/
HistogramSketch(final HistogramSketch that) {
hisImpl = that.hisImpl.makeCopy();
}
/**
* 复制hisImpl到堆内存实例hisImpl
*/
public HistogramSketch copy() {
return new HistogramSketch(this);
}
public void reset() {
hisImpl = hisImpl.resetHistogram();
}
public long getTotalCount(){
return hisImpl.getTotalCount();
}
public void recordValue(long value){
hisImpl.recordValue(value);
}
public void recordValueWithCount(long value, long count){
hisImpl.recordValueWithCount(value, count);
}
public long getValueAtPercentile(double percentile){
return hisImpl.getValueAtPercentile(percentile);
}
public List<Percentile> percentileList(int percentileTicksPerHalfDistance){
return hisImpl.percentileList(percentileTicksPerHalfDistance);
}
public Map<String, Object> describe(){
return hisImpl.describe();
}
public static final int getUpdatableSerializationBytes(long lowestDiscernibleValue, long highestTrackableValue, int numberOfSignificantValueDigits){
return DirectArrayHistogram.getUpdatableSerializationBytes(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits);
}
public byte[] toBytes() {
return hisImpl.toBytes();
}
public static HistogramSketch fromBytes(byte[] bytes) {
return new HistogramSketch(ArrayHistogram.fromBytes(bytes));
}
public static HistogramSketch fromByteBuffer(ByteBuffer byteBuffer) {
return new HistogramSketch(ArrayHistogram.fromByteBuffer(byteBuffer));
}
public static HistogramSketch wrapBytes(byte[] bytes) {
return new HistogramSketch(DirectMapHistogram.wrapBytes(bytes));
}
public static HistogramSketch wrapByteBuffer(ByteBuffer byteBuffer) {
return new HistogramSketch(DirectMapHistogram.wrapByteBuffer(byteBuffer));
}
}

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src/main/java/org/HdrHistogram/HistogramUnion.java Normal file
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package org.HdrHistogram;
import java.nio.ByteBuffer;
public class HistogramUnion {
public HistogramSketch impl;
public HistogramUnion(final int numberOfSignificantValueDigits){
impl = new HistogramSketch(numberOfSignificantValueDigits);
}
public HistogramUnion(final long lowestDiscernibleValue, final long highestTrackableValue,
final int numberOfSignificantValueDigits, final boolean autoResize){
impl = new HistogramSketch(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits, autoResize);
}
public HistogramUnion(final long lowestDiscernibleValue, final long highestTrackableValue,
final int numberOfSignificantValueDigits, ByteBuffer byteBuffer) {
impl = new HistogramSketch(new DirectArrayHistogram(lowestDiscernibleValue, highestTrackableValue, numberOfSignificantValueDigits, byteBuffer));
}
public HistogramUnion(HistogramSketch his) {
impl = his;
}
// druid内部使用
public void resetByteBuffer(ByteBuffer byteBuffer){
((DirectArrayHistogram)impl.hisImpl).resetByteBuffer(byteBuffer);
}
public void reset() {
impl.reset();
}
public HistogramSketch getResult() {
return impl;
}
public void update(final HistogramSketch his) {
if(his != null){
impl.hisImpl = unionImpl(his, impl);
}
}
private static Histogramer unionImpl(HistogramSketch source, HistogramSketch dest) {
return dest.hisImpl.merge(source.hisImpl);
}
}

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src/main/java/org/HdrHistogram/Histogramer.java Normal file
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package org.HdrHistogram;
import java.nio.ByteBuffer;
import java.util.List;
import java.util.Map;
public interface Histogramer {
long getTotalCount();
void recordValue(long value) throws RuntimeException;
void recordValueWithCount(long value, long count) throws RuntimeException;
long getValueAtPercentile(double percentile);
List<Percentile> percentileList(int percentileTicksPerHalfDistance);
Map<String, Object> describe();
Histogramer resetHistogram();
Histogramer merge(Histogramer histogram);
// 复制到堆内存实例ArrayHistogram
Histogramer makeCopy();
byte[] toBytes();
default byte[] byteBuffer2Bytes(ByteBuffer byteBuffer){
//必须调用完后flip()才可以调用此方法
byteBuffer.flip();
int len = byteBuffer.limit() - byteBuffer.position();
byte[] bytes = new byte[len];
byteBuffer.get(bytes);
return bytes;
}
}

50
src/main/java/org/HdrHistogram/Percentile.java Normal file
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package org.HdrHistogram;
public class Percentile {
public long value;
public long count;
public double percentile;
public Percentile() {
}
public Percentile(long value, long count, double percentile) {
this.value = value;
this.count = count;
this.percentile = percentile;
}
public long getValue() {
return value;
}
public void setValue(long value) {
this.value = value;
}
public long getCount() {
return count;
}
public void setCount(long count) {
this.count = count;
}
public double getPercentile() {
return percentile;
}
public void setPercentile(double percentile) {
this.percentile = percentile;
}
@Override
public String toString() {
return "Percentile{" +
"value=" + value +
", count=" + count +
", percentile=" + percentile +
'}';
}
}

266
src/test/java/com/geedgenetworks/sketch/hlld/HllTest.java Normal file
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package com.geedgenetworks.sketch.hlld;
import org.junit.Test;
import java.nio.ByteBuffer;
public class HllTest {
@Test
public void testSize() {
long[] ns = new long[]{100, 1000, 10000, 100000, 10000000, 50000000, 100000000};
for (long n : ns) {
Hll hll = new Hll(14);
for (int i = 0; i < n; i++) {
String key = i + "";
hll.add(key);
}
long estimate = Math.round(hll.size()) ;
double percentErr = Math.abs(estimate - n) * 100D / n;
System.out.println("n:" + n + ",estimate:" + estimate+ ",percentErr:" + percentErr);
}
}
@Test
public void testSizeByteBuffer() {
long[] ns = new long[]{100, 1000, 10000, 100000, 10000000, 100000000};
for (long n : ns) {
int p = 14;
int bytes = DirectHllIntArray.getUpdatableSerializationBytes(p);
Hll hll = new Hll(p, ByteBuffer.allocate(bytes));
for (int i = 0; i < n; i++) {
String key = i + "";
hll.add(key);
}
long estimate = Math.round(hll.size()) ;
double percentErr = Math.abs(estimate - n) * 100D / n;
System.out.println("n:" + n + ",estimate:" + estimate+ ",percentErr:" + percentErr);
}
}
@Test
public void testCopy() {
Hll hll1 = new Hll(14);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll1.add(key);
}
Hll hll2 = new Hll(12, ByteBuffer.allocate(DirectHllIntArray.getUpdatableSerializationBytes(12)));
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll2.add(key);
}
Hll copy1 = hll1.copy();
Hll copy2 = hll2.copy();
System.out.println((long)hll1.size());
System.out.println((long)hll2.size());
System.out.println("#####################");
System.out.println(copy1.hllImpl.getPrecision());
System.out.println(copy2.hllImpl.getPrecision());
System.out.println((long)copy1.size());
System.out.println((long)copy2.size());
}
@Test
public void testMerge0() {
// 两个普通Hll, 普通HllUnion
Hll hll1 = new Hll(14);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll1.add(key);
}
Hll hll2 = new Hll(12);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
//String key = i + "a";
hll2.add(key);
}
System.out.println((long)hll1.size());
System.out.println((long)hll2.size());
HllUnion union = new HllUnion(14);
union.update(hll1);
union.update(hll2);
System.out.println((long) union.getResult().size());
}
@Test
public void testMerge1() {
// 两个普通Hll, 字节数组HllUnion
Hll hll1 = new Hll(14);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll1.add(key);
}
Hll hll2 = new Hll(12);
for (int i = 0; i < 1000000; i++) {
//String key = i + "";
String key = i + "a";
hll2.add(key);
}
System.out.println((long)hll1.size());
System.out.println((long)hll2.size());
int p = 14;
int bytes = DirectHllIntArray.getUpdatableSerializationBytes(p);
HllUnion union = new HllUnion(p, ByteBuffer.allocate(bytes));
union.update(hll1);
union.update(hll2);
System.out.println((long) union.getResult().size());
System.out.println(union.getResult().hllImpl.isMemory());
}
@Test
public void testMerge2() {
// 一个普通Hll一个字节数组Hll, 普通HllUnion
Hll hll1 = new Hll(14);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll1.add(key);
}
Hll hll2 = new Hll(12, ByteBuffer.allocate(DirectHllIntArray.getUpdatableSerializationBytes(12)));
for (int i = 0; i < 1000000; i++) {
//String key = i + "";
String key = i + "a";
hll2.add(key);
}
System.out.println((long)hll1.size());
System.out.println((long)hll2.size());
HllUnion union = new HllUnion(14);
union.update(hll1);
union.update(hll2);
System.out.println((long) union.getResult().size());
}
@Test
public void testMerge3() {
// 一个普通Hll一个字节数组Hll, 字节数组HllUnion
Hll hll1 = new Hll(14);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll1.add(key);
}
Hll hll2 = new Hll(12, ByteBuffer.allocate(DirectHllIntArray.getUpdatableSerializationBytes(12)));
for (int i = 0; i < 1000000; i++) {
//String key = i + "";
String key = i + "a";
hll2.add(key);
}
System.out.println((long)hll1.size());
System.out.println((long)hll2.size());
int p = 14;
int bytes = DirectHllIntArray.getUpdatableSerializationBytes(p);
HllUnion union = new HllUnion(p, ByteBuffer.allocate(bytes));
union.update(hll1);
union.update(hll2);
System.out.println((long) union.getResult().size());
System.out.println(union.getResult().hllImpl.isMemory());
}
@Test
public void testMerge4() {
// 两个字节数组Hll, 字节数组HllUnion
Hll hll1 = new Hll(14, ByteBuffer.allocate(DirectHllIntArray.getUpdatableSerializationBytes(14)));
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll1.add(key);
}
Hll hll2 = new Hll(12, ByteBuffer.allocate(DirectHllIntArray.getUpdatableSerializationBytes(12)));
for (int i = 0; i < 1000000; i++) {
//String key = i + "";
String key = i + "a";
hll2.add(key);
}
System.out.println((long)hll1.size());
System.out.println((long)hll2.size());
int p = 14;
int bytes = DirectHllIntArray.getUpdatableSerializationBytes(p);
HllUnion union = new HllUnion(p, ByteBuffer.allocate(bytes));
union.update(hll1);
union.update(hll2);
System.out.println((long) union.getResult().size());
System.out.println(union.getResult().hllImpl.isMemory());
}
@Test
public void testSer() {
Hll hll1 = new Hll(14);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll1.add(key);
}
int position = 8;
ByteBuffer byteBuffer = ByteBuffer.allocate(position + DirectHllIntArray.getUpdatableSerializationBytes(12));
byteBuffer.position(position);
Hll hll2 = new Hll(12, byteBuffer);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll2.add(key);
}
System.out.println(hll1.size());
System.out.println(hll2.size());
byte[] bytes1 = hll1.toBytes();
byte[] bytes2 = hll2.toBytes();
Hll hllDer1 = Hll.fromBytes(bytes1);
Hll hllDer2 = Hll.fromBytes(bytes2);
System.out.println(hllDer1.size());
System.out.println(hllDer2.size());
assert !hllDer1.hllImpl.isMemory();
assert !hllDer2.hllImpl.isMemory();
}
@Test
public void testWrapBytes() {
Hll hll1 = new Hll(14);
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll1.add(key);
}
Hll hll2 = new Hll(12, ByteBuffer.allocate(DirectHllIntArray.getUpdatableSerializationBytes(12)));
for (int i = 0; i < 1000000; i++) {
String key = i + "";
hll2.add(key);
}
System.out.println(hll1.size());
System.out.println(hll2.size());
byte[] bytes1 = hll1.toBytes();
byte[] bytes2 = hll2.toBytes();
Hll hllDer1 = Hll.wrapBytes(bytes1);
Hll hllDer2 = Hll.wrapBytes(bytes2);
System.out.println(hllDer1.size());
System.out.println(hllDer2.size());
assert hllDer1.hllImpl.isMemory();
assert hllDer2.hllImpl.isMemory();
}
}

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src/test/java/org/HdrHistogram/HistogramSketchTest.java Normal file
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package org.HdrHistogram;
import org.junit.Test;
import java.nio.ByteBuffer;
import java.util.concurrent.ThreadLocalRandom;
public class HistogramSketchTest {
String line = "###################";
@Test
public void testArrayHistogram() {
ArrayHistogram histogram = new ArrayHistogram(1);
System.out.println(histogram.describe());
for (int i = 0; i < 10000; i++) {
histogram.recordValue(i);
}
System.out.println(histogram.describe());
for (Percentile percentile : histogram.percentileList(5)) {
System.out.println(percentile);
}
System.out.println(line);
histogram = new ArrayHistogram(1);
for (int i = 0; i < 10000; i++) {
histogram.recordValue(ThreadLocalRandom.current().nextLong(100000));
}
System.out.println(histogram.describe());
for (Percentile percentile : histogram.percentileList(5)) {
System.out.println(percentile);
}
}
@Test
public void testDirectArrayHistogram() {
ByteBuffer byteBuffer = ByteBuffer.allocate(DirectArrayHistogram.getUpdatableSerializationBytes(1, 100000, 1));
DirectArrayHistogram histogram = new DirectArrayHistogram(1, 100000, 1,
byteBuffer);
System.out.println(histogram.describe());
for (int i = 0; i < 10000; i++) {
histogram.recordValue(i);
}
System.out.println(histogram.describe());
for (Percentile percentile : histogram.percentileList(5)) {
System.out.println(percentile);
}
System.out.println(line);
histogram.resetByteBuffer(ByteBuffer.allocate(DirectArrayHistogram.getUpdatableSerializationBytes(1, 100000, 1)));
histogram.reset();
for (int i = 0; i < 10000; i++) {
histogram.recordValue(ThreadLocalRandom.current().nextLong(100000));
}
System.out.println(histogram.describe());
for (Percentile percentile : histogram.percentileList(5)) {
System.out.println(percentile);
}
}
@Test
public void testCopy() {
ArrayHistogram histogram1 = new ArrayHistogram(1);
ByteBuffer byteBuffer = ByteBuffer.allocate(DirectArrayHistogram.getUpdatableSerializationBytes(1, 100000, 1));
DirectArrayHistogram histogram2 = new DirectArrayHistogram(1, 100000, 1,
byteBuffer);
for (int i = 0; i < 10000; i++) {
histogram1.recordValue(i);
histogram2.recordValue(i);
}
ArrayHistogram copy1 = histogram1.copy();
ArrayHistogram copy2 = histogram2.copy();
System.out.println(histogram1.describe());
System.out.println(histogram2.describe());
System.out.println(line);
System.out.println(copy1.describe());
System.out.println(copy2.describe());
}
@Test
public void testArrayHistogramMerge() {
ArrayHistogram histogram1 = new ArrayHistogram(1);
for (int i = 0; i < 1000; i++) {
histogram1.recordValue(i);
}
byte[] bytes1 = histogram1.toBytes();
DirectMapHistogram directHistogram = DirectMapHistogram.wrapBytes(bytes1);
ArrayHistogram histogram2 = new ArrayHistogram(1);
histogram2.merge(directHistogram);
System.out.println(histogram2.describe());
}
@Test
public void testDirectArrayHistogramMerge() {
ArrayHistogram histogram1 = new ArrayHistogram(1);
int updatableSerializationBytes = DirectArrayHistogram.getUpdatableSerializationBytes(1, 100000, 1);
DirectArrayHistogram histogram2 = new DirectArrayHistogram(1, 100000, 1, ByteBuffer.allocate(updatableSerializationBytes));
for (int i = 0; i < 10000; i++) {
histogram1.recordValue(i);
histogram2.recordValue(i);
}
byte[] bytes1 = histogram1.toBytes();
byte[] bytes2 = histogram2.toBytes();
DirectArrayHistogram histogram = new DirectArrayHistogram(1, 100000, 1, ByteBuffer.allocate(updatableSerializationBytes));
histogram.merge(DirectMapHistogram.wrapBytes(bytes1));
histogram.merge(DirectMapHistogram.wrapBytes(bytes2));
System.out.println(histogram.describe());
for (Percentile percentile : histogram.percentileList(5)) {
System.out.println(percentile);
}
}
}