/*
    * 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.commons.rng.sampling.distribution;
  
  import org.apache.commons.rng.UniformRandomProvider;
  
  /**
   * Sampler for the <a href="http://mathworld.wolfram.com/PoissonDistribution.html">Poisson
   * distribution</a>.
   *
   * <ul>
   *   <li>
   *     Kemp, A, W, (1981) Efficient Generation of Logarithmically Distributed
   *     Pseudo-Random Variables. Journal of the Royal Statistical Society. Vol. 30, No. 3, pp.
   *     249-253.
   *   </li>
   * </ul>
   *
   * <p>This sampler is suitable for {@code mean < 40}. For large means,
   * {@link LargeMeanPoissonSampler} should be used instead.</p>
   *
   * <p>Note: The algorithm uses a recurrence relation to compute the Poisson probability
   * and a rolling summation for the cumulative probability. When the mean is large the
   * initial probability (Math.exp(-mean)) is zero and an exception is raised by the
   * constructor.</p>
   *
   * <p>Sampling uses 1 call to {@link UniformRandomProvider#nextDouble()}. This method provides
   * an alternative to the {@link SmallMeanPoissonSampler} for slow generators of {@code double}.</p>
   *
   * @see <a href="https://www.jstor.org/stable/2346348">Kemp, A.W. (1981) JRSS Vol. 30, pp.
   * 249-253</a>
   * @since 1.3
   */
  public final class KempSmallMeanPoissonSampler
      implements SharedStateDiscreteSampler {
      /** Underlying source of randomness. */
      private final UniformRandomProvider rng;
      /**
       * Pre-compute {@code Math.exp(-mean)}.
       * Note: This is the probability of the Poisson sample {@code p(x=0)}.
       */
      private final double p0;
      /**
       * The mean of the Poisson sample.
       */
      private final double mean;
  
      /**
       * @param rng Generator of uniformly distributed random numbers.
       * @param p0 Probability of the Poisson sample {@code p(x=0)}.
       * @param mean Mean.
       */
      private KempSmallMeanPoissonSampler(UniformRandomProvider rng,
                                          double p0,
                                          double mean) {
          this.rng = rng;
          this.p0 = p0;
          this.mean = mean;
      }
  
      /** {@inheritDoc} */
      @Override
      public int sample() {
          // Note on the algorithm:
          // - X is the unknown sample deviate (the output of the algorithm)
          // - x is the current value from the distribution
          // - p is the probability of the current value x, p(X=x)
          // - u is effectively the cumulative probability that the sample X
          //   is equal or above the current value x, p(X>=x)
          // So if p(X>=x) > p(X=x) the sample must be above x, otherwise it is x
          double u = rng.nextDouble();
          int x = 0;
          double p = p0;
          while (u > p) {
              u -= p;
              // Compute the next probability using a recurrence relation.
              // p(x+1) = p(x) * mean / (x+1)
              p *= mean / ++x;
              // The algorithm listed in Kemp (1981) does not check that the rolling probability
              // is positive. This check is added to ensure no errors when the limit of the summation
              // 1 - sum(p(x)) is above 0 due to cumulative error in floating point arithmetic.
              if (p == 0) {
                  return x;
              }
          }
         return x;
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString() {
         return "Kemp Small Mean Poisson deviate [" + rng.toString() + "]";
     }
 
     /** {@inheritDoc} */
     @Override
     public SharedStateDiscreteSampler withUniformRandomProvider(UniformRandomProvider rng) {
         return new KempSmallMeanPoissonSampler(rng, p0, mean);
     }
 
     /**
      * Creates a new sampler for the Poisson distribution.
      *
      * @param rng Generator of uniformly distributed random numbers.
      * @param mean Mean of the distribution.
      * @return the sampler
      * @throws IllegalArgumentException if {@code mean <= 0} or
      * {@code Math.exp(-mean) == 0}.
      */
     public static SharedStateDiscreteSampler of(UniformRandomProvider rng,
                                                 double mean) {
         if (mean <= 0) {
             throw new IllegalArgumentException("Mean is not strictly positive: " + mean);
         }
 
         final double p0 = Math.exp(-mean);
 
         // Probability must be positive. As mean increases then p(0) decreases.
         if (p0 > 0) {
             return new KempSmallMeanPoissonSampler(rng, p0, mean);
         }
 
         // This catches the edge case of a NaN mean
         throw new IllegalArgumentException("No probability for mean: " + mean);
     }
 }