/*
    * 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.math4.legacy.distribution;
  
  import org.apache.commons.statistics.distribution.DiscreteDistribution;
  import org.apache.commons.math4.legacy.exception.MathInternalError;
  import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
  import org.apache.commons.math4.legacy.exception.OutOfRangeException;
  import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
  import org.apache.commons.rng.UniformRandomProvider;
  import org.apache.commons.rng.sampling.distribution.InverseTransformDiscreteSampler;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  
  /**
   * Base class for integer-valued discrete distributions.  Default
   * implementations are provided for some of the methods that do not vary
   * from distribution to distribution.
   *
   */
  public abstract class AbstractIntegerDistribution
      implements DiscreteDistribution {
      /**
       * {@inheritDoc}
       *
       * The default implementation uses the identity
       * <p>{@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)}</p>
       *
       * @since 4.0, was previously named cumulativeProbability
       */
      @Override
      public double probability(int x0, int x1) throws NumberIsTooLargeException {
          if (x1 < x0) {
              throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
                      x0, x1, true);
          }
          return cumulativeProbability(x1) - cumulativeProbability(x0);
      }
  
      /**
       * {@inheritDoc}
       *
       * The default implementation returns
       * <ul>
       * <li>{@link #getSupportLowerBound()} for {@code p = 0},</li>
       * <li>{@link #getSupportUpperBound()} for {@code p = 1}, and</li>
       * <li>{@link #solveInverseCumulativeProbability(double, int, int)} for
       *     {@code 0 < p < 1}.</li>
       * </ul>
       */
      @Override
      public int inverseCumulativeProbability(final double p) throws OutOfRangeException {
          if (p < 0.0 || p > 1.0) {
              throw new OutOfRangeException(p, 0, 1);
          }
  
          int lower = getSupportLowerBound();
          if (p == 0.0) {
              return lower;
          }
          if (lower == Integer.MIN_VALUE) {
              if (checkedCumulativeProbability(lower) >= p) {
                  return lower;
              }
          } else {
              lower -= 1; // this ensures cumulativeProbability(lower) < p, which
                          // is important for the solving step
          }
  
          int upper = getSupportUpperBound();
          if (p == 1.0) {
              return upper;
          }
  
          // use the one-sided Chebyshev inequality to narrow the bracket
          // cf. AbstractRealDistribution.inverseCumulativeProbability(double)
          final double mu = getMean();
          final double sigma = JdkMath.sqrt(getVariance());
          final boolean chebyshevApplies = !(Double.isInfinite(mu) || Double.isNaN(mu) ||
                  Double.isInfinite(sigma) || Double.isNaN(sigma) || sigma == 0.0);
          if (chebyshevApplies) {
              double k = JdkMath.sqrt((1.0 - p) / p);
              double tmp = mu - k * sigma;
              if (tmp > lower) {
                  lower = ((int) JdkMath.ceil(tmp)) - 1;
              }
             k = 1.0 / k;
             tmp = mu + k * sigma;
             if (tmp < upper) {
                 upper = ((int) JdkMath.ceil(tmp)) - 1;
             }
         }
 
         return solveInverseCumulativeProbability(p, lower, upper);
     }
 
     /**
      * This is a utility function used by {@link
      * #inverseCumulativeProbability(double)}. It assumes {@code 0 < p < 1} and
      * that the inverse cumulative probability lies in the bracket {@code
      * (lower, upper]}. The implementation does simple bisection to find the
      * smallest {@code p}-quantile {@code inf{x in Z | P(X<=x) >= p}}.
      *
      * @param p the cumulative probability
      * @param lower a value satisfying {@code cumulativeProbability(lower) < p}
      * @param upper a value satisfying {@code p <= cumulativeProbability(upper)}
      * @return the smallest {@code p}-quantile of this distribution
      */
     protected int solveInverseCumulativeProbability(final double p, int lower, int upper) {
         while (lower + 1 < upper) {
             int xm = (lower + upper) / 2;
             if (xm < lower || xm > upper) {
                 /*
                  * Overflow.
                  * There will never be an overflow in both calculation methods
                  * for xm at the same time
                  */
                 xm = lower + (upper - lower) / 2;
             }
 
             double pm = checkedCumulativeProbability(xm);
             if (pm >= p) {
                 upper = xm;
             } else {
                 lower = xm;
             }
         }
         return upper;
     }
 
     /**
      * Computes the cumulative probability function and checks for {@code NaN}
      * values returned. Throws {@code MathInternalError} if the value is
      * {@code NaN}. Rethrows any exception encountered evaluating the cumulative
      * probability function. Throws {@code MathInternalError} if the cumulative
      * probability function returns {@code NaN}.
      *
      * @param argument input value
      * @return the cumulative probability
      * @throws MathInternalError if the cumulative probability is {@code NaN}
      */
     private double checkedCumulativeProbability(int argument)
         throws MathInternalError {
         final double result = cumulativeProbability(argument);
         if (Double.isNaN(result)) {
             throw new MathInternalError(LocalizedFormats
                     .DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN, argument);
         }
         return result;
     }
 
     /**
      * {@inheritDoc}
      * <p>
      * The default implementation simply computes the logarithm of {@code probability(x)}.
      */
     @Override
     public double logProbability(int x) {
         return JdkMath.log(probability(x));
     }
 
     /**
      * Utility function for allocating an array and filling it with {@code n}
      * samples generated by the given {@code sampler}.
      *
      * @param n Number of samples.
      * @param sampler Sampler.
      * @return an array of size {@code n}.
      */
     public static int[] sample(int n,
                                DiscreteDistribution.Sampler sampler) {
         final int[] samples = new int[n];
         for (int i = 0; i < n; i++) {
             samples[i] = sampler.sample();
         }
         return samples;
     }
 
     /**{@inheritDoc} */
     @Override
     public DiscreteDistribution.Sampler createSampler(final UniformRandomProvider rng) {
         // Inversion method distribution sampler.
         return InverseTransformDiscreteSampler.of(rng, this::inverseCumulativeProbability)::sample;
     }
 }