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/*
* Copyright 2004-2019 H2 Group. Multiple-Licensed under the MPL 2.0,
* and the EPL 1.0 (https://h2database.com/html/license.html).
* Initial Developer: H2 Group
*/
package org.h2.tools;
import java.sql.PreparedStatement;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import org.h2.util.StringUtils;
/**
* A tool to help an application execute multi-dimensional range queries.
* The algorithm used is database independent, the only requirement
* is that the engine supports a range index (for example b-tree).
*/
public class MultiDimension implements Comparator {
private static final MultiDimension INSTANCE = new MultiDimension();
protected MultiDimension() {
// don't allow construction by normal code
// but allow tests
}
/**
* Get the singleton.
*
* @return the singleton
*/
public static MultiDimension getInstance() {
return INSTANCE;
}
/**
* Normalize a value so that it is between the minimum and maximum for the
* given number of dimensions.
*
* @param dimensions the number of dimensions
* @param value the value (must be in the range min..max)
* @param min the minimum value
* @param max the maximum value (must be larger than min)
* @return the normalized value in the range 0..getMaxValue(dimensions)
*/
public int normalize(int dimensions, double value, double min, double max) {
if (value < min || value > max) {
throw new IllegalArgumentException(min + "<" + value + "<" + max);
}
double x = (value - min) / (max - min);
return (int) (x * getMaxValue(dimensions));
}
/**
* Get the maximum value for the given dimension count. For two dimensions,
* each value must contain at most 32 bit, for 3: 21 bit, 4: 16 bit, 5: 12
* bit, 6: 10 bit, 7: 9 bit, 8: 8 bit.
*
* @param dimensions the number of dimensions
* @return the maximum value
*/
public int getMaxValue(int dimensions) {
if (dimensions < 2 || dimensions > 32) {
throw new IllegalArgumentException(Integer.toString(dimensions));
}
int bitsPerValue = getBitsPerValue(dimensions);
return (int) ((1L << bitsPerValue) - 1);
}
private static int getBitsPerValue(int dimensions) {
return Math.min(31, 64 / dimensions);
}
/**
* Convert the multi-dimensional value into a one-dimensional (scalar)
* value. This is done by interleaving the bits of the values. Each values
* must be between 0 (including) and the maximum value for the given number
* of dimensions (getMaxValue, excluding). To normalize values to this
* range, use the normalize function.
*
* @param values the multi-dimensional value
* @return the scalar value
*/
public long interleave(int... values) {
int dimensions = values.length;
long max = getMaxValue(dimensions);
int bitsPerValue = getBitsPerValue(dimensions);
long x = 0;
for (int i = 0; i < dimensions; i++) {
long k = values[i];
if (k < 0 || k > max) {
throw new IllegalArgumentException(0 + "<" + k + "<" + max);
}
for (int b = 0; b < bitsPerValue; b++) {
x |= (k & (1L << b)) << (i + (dimensions - 1) * b);
}
}
return x;
}
/**
* Convert the two-dimensional value into a one-dimensional (scalar) value.
* This is done by interleaving the bits of the values.
* Each values must be between 0 (including) and the maximum value
* for the given number of dimensions (getMaxValue, excluding).
* To normalize values to this range, use the normalize function.
*
* @param x the value of the first dimension, normalized
* @param y the value of the second dimension, normalized
* @return the scalar value
*/
public long interleave(int x, int y) {
if (x < 0) {
throw new IllegalArgumentException(0 + "<" + x);
}
if (y < 0) {
throw new IllegalArgumentException(0 + "<" + y);
}
long z = 0;
for (int i = 0; i < 32; i++) {
z |= (x & (1L << i)) << i;
z |= (y & (1L << i)) << (i + 1);
}
return z;
}
/**
* Gets one of the original multi-dimensional values from a scalar value.
*
* @param dimensions the number of dimensions
* @param scalar the scalar value
* @param dim the dimension of the returned value (starting from 0)
* @return the value
*/
public int deinterleave(int dimensions, long scalar, int dim) {
int bitsPerValue = getBitsPerValue(dimensions);
int value = 0;
for (int i = 0; i < bitsPerValue; i++) {
value |= (scalar >> (dim + (dimensions - 1) * i)) & (1L << i);
}
return value;
}
/**
* Generates an optimized multi-dimensional range query. The query contains
* parameters. It can only be used with the H2 database.
*
* @param table the table name
* @param columns the list of columns
* @param scalarColumn the column name of the computed scalar column
* @return the query
*/
public String generatePreparedQuery(String table, String scalarColumn,
String[] columns) {
StringBuilder buff = new StringBuilder("SELECT D.* FROM ");
StringUtils.quoteIdentifier(buff, table).
append(" D, TABLE(_FROM_ BIGINT=?, _TO_ BIGINT=?) WHERE ");
StringUtils.quoteIdentifier(buff, scalarColumn).
append(" BETWEEN _FROM_ AND _TO_");
for (String col : columns) {
buff.append(" AND ");
StringUtils.quoteIdentifier(buff, col).
append("+1 BETWEEN ?+1 AND ?+1");
}
return buff.toString();
}
/**
* Executes a prepared query that was generated using generatePreparedQuery.
*
* @param prep the prepared statement
* @param min the lower values
* @param max the upper values
* @return the result set
*/
public ResultSet getResult(PreparedStatement prep, int[] min, int[] max)
throws SQLException {
long[][] ranges = getMortonRanges(min, max);
int len = ranges.length;
Long[] from = new Long[len];
Long[] to = new Long[len];
for (int i = 0; i < len; i++) {
from[i] = ranges[i][0];
to[i] = ranges[i][1];
}
prep.setObject(1, from);
prep.setObject(2, to);
len = min.length;
for (int i = 0, idx = 3; i < len; i++) {
prep.setInt(idx++, min[i]);
prep.setInt(idx++, max[i]);
}
return prep.executeQuery();
}
/**
* Gets a list of ranges to be searched for a multi-dimensional range query
* where min <= value <= max. In most cases, the ranges will be larger
* than required in order to combine smaller ranges into one. Usually, about
* double as many points will be included in the resulting range.
*
* @param min the minimum value
* @param max the maximum value
* @return the list of ranges (low, high pairs)
*/
private long[][] getMortonRanges(int[] min, int[] max) {
int len = min.length;
if (max.length != len) {
throw new IllegalArgumentException(len + "=" + max.length);
}
for (int i = 0; i < len; i++) {
if (min[i] > max[i]) {
int temp = min[i];
min[i] = max[i];
max[i] = temp;
}
}
int total = getSize(min, max, len);
ArrayList list = new ArrayList<>();
addMortonRanges(list, min, max, len, 0);
combineEntries(list, total);
return list.toArray(new long[0][]);
}
private static int getSize(int[] min, int[] max, int len) {
int size = 1;
for (int i = 0; i < len; i++) {
int diff = max[i] - min[i];
size *= diff + 1;
}
return size;
}
/**
* Combine entries if the size of the list is too large.
*
* @param list list of pairs(low, high)
* @param total product of the gap lengths
*/
private void combineEntries(ArrayList list, int total) {
Collections.sort(list, this);
for (int minGap = 10; minGap < total; minGap += minGap / 2) {
for (int i = 0; i < list.size() - 1; i++) {
long[] current = list.get(i);
long[] next = list.get(i + 1);
if (current[1] + minGap >= next[0]) {
current[1] = next[1];
list.remove(i + 1);
i--;
}
}
int searched = 0;
for (long[] range : list) {
searched += range[1] - range[0] + 1;
}
if (searched > 2 * total || list.size() < 100) {
break;
}
}
}
@Override
public int compare(long[] a, long[] b) {
return a[0] > b[0] ? 1 : -1;
}
private void addMortonRanges(ArrayList list, int[] min, int[] max,
int len, int level) {
if (level > 100) {
throw new IllegalArgumentException(Integer.toString(level));
}
int largest = 0, largestDiff = 0;
long size = 1;
for (int i = 0; i < len; i++) {
int diff = max[i] - min[i];
if (diff < 0) {
throw new IllegalArgumentException(Integer.toString(diff));
}
size *= diff + 1;
if (size < 0) {
throw new IllegalArgumentException(Long.toString(size));
}
if (diff > largestDiff) {
largestDiff = diff;
largest = i;
}
}
long low = interleave(min), high = interleave(max);
if (high < low) {
throw new IllegalArgumentException(high + "<" + low);
}
long range = high - low + 1;
if (range == size) {
long[] item = { low, high };
list.add(item);
} else {
int middle = findMiddle(min[largest], max[largest]);
int temp = max[largest];
max[largest] = middle;
addMortonRanges(list, min, max, len, level + 1);
max[largest] = temp;
temp = min[largest];
min[largest] = middle + 1;
addMortonRanges(list, min, max, len, level + 1);
min[largest] = temp;
}
}
private static int roundUp(int x, int blockSizePowerOf2) {
return (x + blockSizePowerOf2 - 1) & (-blockSizePowerOf2);
}
private static int findMiddle(int a, int b) {
int diff = b - a - 1;
if (diff == 0) {
return a;
}
if (diff == 1) {
return a + 1;
}
int scale = 0;
while ((1 << scale) < diff) {
scale++;
}
scale--;
int m = roundUp(a + 2, 1 << scale) - 1;
if (m <= a || m >= b) {
throw new IllegalArgumentException(a + "<" + m + "<" + b);
}
return m;
}
}
