/**
    * Licensed to the Apache Software Foundation (ASF) under one
    * or more contributor license agreements.  See the NOTICE file
    * distributed with this work for additional information
    * regarding copyright ownership.  The ASF licenses this file
    * to you under the Apache License, Version 2.0 (the
    * "License"); you may not use this file except in compliance
    * with the License.  You may obtain a copy of the License at
    *
   *     http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  
  package org.apache.hadoop.metrics2.util;
  
  import java.io.IOException;
  import java.util.Arrays;
  import java.util.HashMap;
  import java.util.LinkedList;
  import java.util.ListIterator;
  import java.util.Map;
  
  import org.apache.hadoop.hbase.classification.InterfaceAudience;
  
  /**
   * Implementation of the Cormode, Korn, Muthukrishnan, and Srivastava algorithm
   * for streaming calculation of targeted high-percentile epsilon-approximate
   * quantiles.
   * 
   * This is a generalization of the earlier work by Greenwald and Khanna (GK),
   * which essentially allows different error bounds on the targeted quantiles,
   * which allows for far more efficient calculation of high-percentiles.
   * 
   * See: Cormode, Korn, Muthukrishnan, and Srivastava
   * "Effective Computation of Biased Quantiles over Data Streams" in ICDE 2005
   * 
   * Greenwald and Khanna,
   * "Space-efficient online computation of quantile summaries" in SIGMOD 2001
   * 
   */
  @InterfaceAudience.Private
  public class MetricSampleQuantiles {
  
    /**
     * Total number of items in stream
     */
    private long count = 0;
  
    /**
     * Current list of sampled items, maintained in sorted order with error bounds
     */
    private LinkedList<SampleItem> samples;
  
    /**
     * Buffers incoming items to be inserted in batch. Items are inserted into 
     * the buffer linearly. When the buffer fills, it is flushed into the samples
     * array in its entirety.
     */
    private long[] buffer = new long[500];
    private int bufferCount = 0;
  
    /**
     * Array of Quantiles that we care about, along with desired error.
     */
    private final MetricQuantile quantiles[];
  
    public MetricSampleQuantiles(MetricQuantile[] quantiles) {
      this.quantiles = Arrays.copyOf(quantiles, quantiles.length);
      this.samples = new LinkedList<SampleItem>();
    }
  
    /**
     * Specifies the allowable error for this rank, depending on which quantiles
     * are being targeted.
     * 
     * This is the f(r_i, n) function from the CKMS paper. It's basically how wide
     * the range of this rank can be.
     * 
     * @param rank
     *          the index in the list of samples
     */
    private double allowableError(int rank) {
      int size = samples.size();
      double minError = size + 1;
      for (MetricQuantile q : quantiles) {
        double error;
        if (rank <= q.quantile * size) {
          error = (2.0 * q.error * (size - rank)) / (1.0 - q.quantile);
        } else {
          error = (2.0 * q.error * rank) / q.quantile;
        }
        if (error < minError) {
          minError = error;
        }
     }
 
     return minError;
   }
 
   /**
    * Add a new value from the stream.
    * 
    * @param v
    */
   synchronized public void insert(long v) {
     buffer[bufferCount] = v;
     bufferCount++;
 
     count++;
 
     if (bufferCount == buffer.length) {
       insertBatch();
       compress();
     }
   }
 
   /**
    * Merges items from buffer into the samples array in one pass.
    * This is more efficient than doing an insert on every item.
    */
   private void insertBatch() {
     if (bufferCount == 0) {
       return;
     }
 
     Arrays.sort(buffer, 0, bufferCount);
 
     // Base case: no samples
     int start = 0;
     if (samples.size() == 0) {
       SampleItem newItem = new SampleItem(buffer[0], 1, 0);
       samples.add(newItem);
       start++;
     }
 
     ListIterator<SampleItem> it = samples.listIterator();
     SampleItem item = it.next();
     for (int i = start; i < bufferCount; i++) {
       long v = buffer[i];
       while (it.nextIndex() < samples.size() && item.value < v) {
         item = it.next();
       }
       // If we found that bigger item, back up so we insert ourselves before it
       if (item.value > v) {
         it.previous();
       }
       // We use different indexes for the edge comparisons, because of the above
       // if statement that adjusts the iterator
       int delta;
       if (it.previousIndex() == 0 || it.nextIndex() == samples.size()) {
         delta = 0;
       } else {
         delta = ((int) Math.floor(allowableError(it.nextIndex()))) - 1;
       }
       SampleItem newItem = new SampleItem(v, 1, delta);
       it.add(newItem);
       item = newItem;
     }
 
     bufferCount = 0;
   }
 
   /**
    * Try to remove extraneous items from the set of sampled items. This checks
    * if an item is unnecessary based on the desired error bounds, and merges it
    * with the adjacent item if it is.
    */
   private void compress() {
     if (samples.size() < 2) {
       return;
     }
 
     ListIterator<SampleItem> it = samples.listIterator();
     SampleItem prev = null;
     SampleItem next = it.next();
 
     while (it.hasNext()) {
       prev = next;
       next = it.next();
       if (prev.g + next.g + next.delta <= allowableError(it.previousIndex())) {
         next.g += prev.g;
         // Remove prev. it.remove() kills the last thing returned.
         it.previous();
         it.previous();
         it.remove();
         // it.next() is now equal to next, skip it back forward again
         it.next();
       }
     }
   }
 
   /**
    * Get the estimated value at the specified quantile.
    * 
    * @param quantile Queried quantile, e.g. 0.50 or 0.99.
    * @return Estimated value at that quantile.
    */
   private long query(double quantile) throws IOException {
     if (samples.size() == 0) {
       throw new IOException("No samples present");
     }
 
     int rankMin = 0;
     int desired = (int) (quantile * count);
 
     for (int i = 1; i < samples.size(); i++) {
       SampleItem prev = samples.get(i - 1);
       SampleItem cur = samples.get(i);
 
       rankMin += prev.g;
 
       if (rankMin + cur.g + cur.delta > desired + (allowableError(i) / 2)) {
         return prev.value;
       }
     }
 
     // edge case of wanting max value
     return samples.get(samples.size() - 1).value;
   }
 
   /**
    * Get a snapshot of the current values of all the tracked quantiles.
    * 
    * @return snapshot of the tracked quantiles
    * @throws IOException
    *           if no items have been added to the estimator
    */
   synchronized public Map<MetricQuantile, Long> snapshot() throws IOException {
     // flush the buffer first for best results
     insertBatch();
     Map<MetricQuantile, Long> values = new HashMap<MetricQuantile, Long>(quantiles.length);
     for (int i = 0; i < quantiles.length; i++) {
       values.put(quantiles[i], query(quantiles[i].quantile));
     }
 
     return values;
   }
 
   /**
    * Returns the number of items that the estimator has processed
    * 
    * @return count total number of items processed
    */
   synchronized public long getCount() {
     return count;
   }
 
   /**
    * Returns the number of samples kept by the estimator
    * 
    * @return count current number of samples
    */
   synchronized public int getSampleCount() {
     return samples.size();
   }
 
   /**
    * Resets the estimator, clearing out all previously inserted items
    */
   synchronized public void clear() {
     count = 0;
     bufferCount = 0;
     samples.clear();
   }
 
   /**
    * Describes a measured value passed to the estimator, tracking additional
    * metadata required by the CKMS algorithm.
    */
   private static class SampleItem {
     
     /**
      * Value of the sampled item (e.g. a measured latency value)
      */
     public final long value;
     
     /**
      * Difference between the lowest possible rank of the previous item, and 
      * the lowest possible rank of this item.
      * 
      * The sum of the g of all previous items yields this item's lower bound. 
      */
     public int g;
     
     /**
      * Difference between the item's greatest possible rank and lowest possible
      * rank.
      */
     public final int delta;
 
     public SampleItem(long value, int lowerDelta, int delta) {
       this.value = value;
       this.g = lowerDelta;
       this.delta = delta;
     }
 
     @Override
     public String toString() {
       return String.format("%d, %d, %d", value, g, delta);
     }
   }
 }