/*
    * 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  package org.hipparchus.distribution.discrete;
  
  import java.io.Serializable;
  
  import org.hipparchus.distribution.IntegerDistribution;
  import org.hipparchus.exception.LocalizedCoreFormats;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.exception.MathRuntimeException;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathUtils;
  
  /**
   * Base class for integer-valued discrete distributions.
   * <p>
   * Default implementations are provided for some of the methods that
   * do not vary from distribution to distribution.
   */
  public abstract class AbstractIntegerDistribution implements IntegerDistribution, Serializable {
  
      /** Serializable version identifier */
      private static final long serialVersionUID = 20160320L;
  
      /** Empty constructor.
       * <p>
       * This constructor is not strictly necessary, but it prevents spurious
       * javadoc warnings with JDK 18 and later.
       * </p>
       * @since 3.0
       */
      public AbstractIntegerDistribution() { // NOPMD - unnecessary constructor added intentionally to make javadoc happy
          // nothing to do
      }
  
      /**
       * {@inheritDoc}
       *
       * The default implementation uses the identity
       * <p>
       * {@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)}
       */
      @Override
      public double probability(int x0, int x1) throws MathIllegalArgumentException {
          if (x1 < x0) {
              throw new MathIllegalArgumentException(LocalizedCoreFormats.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 MathIllegalArgumentException {
          MathUtils.checkRangeInclusive(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 = getNumericalMean();
         final double sigma = FastMath.sqrt(getNumericalVariance());
         final boolean chebyshevApplies =
                 !(Double.isInfinite(mu)    || Double.isNaN(mu)    ||
                   Double.isInfinite(sigma) || Double.isNaN(sigma) ||
                   sigma == 0.0);
         if (chebyshevApplies) {
             double k = FastMath.sqrt((1.0 - p) / p);
             double tmp = mu - k * sigma;
             if (tmp > lower) {
                 lower = ((int) FastMath.ceil(tmp)) - 1;
             }
             k = 1.0 / k;
             tmp = mu + k * sigma;
             if (tmp < upper) {
                 upper = ((int) FastMath.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.
      * <p>
      * Throws {@code MathRuntimeException} if the value is {@code NaN}.
      * Rethrows any exception encountered evaluating the cumulative
      * probability function.
      * Throws {@code MathRuntimeException} if the cumulative
      * probability function returns {@code NaN}.
      *
      * @param argument input value
      * @return the cumulative probability
      * @throws MathRuntimeException if the cumulative probability is {@code NaN}
      */
     private double checkedCumulativeProbability(int argument)
         throws MathRuntimeException {
         double result = cumulativeProbability(argument);
         if (Double.isNaN(result)) {
             throw new MathRuntimeException(LocalizedCoreFormats.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 FastMath.log(probability(x));
     }
 }