/*
    * Licensed to the Hipparchus project under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The Hipparchus project 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.
   */
  package org.hipparchus.distribution.discrete;
  
  import org.junit.Assert;
  import org.junit.Test;
  
  public class SaddlePointExpansionTest {
  
      @Test
      public void testSmallInteger() {
          for (int n = 4; n < 16; ++n) {
               Assert.assertEquals(alternateStirlingErrorImplementation(n, 8),
                                  SaddlePointExpansion.getStirlingError(n),
                                  1.0e-10);
          }
      }
  
      @Test
      public void testSmallNonInteger() {
          for (double z = 3.75; z < 14.8; z += 1.0) {
              Assert.assertEquals(alternateStirlingErrorImplementation(z, 12),
                                  SaddlePointExpansion.getStirlingError(z),
                                  1.0e-10);
          }
      }
  
      @Test
      public void testLargeValues() {
          for (double z = 15.25; z < 25.5; z += 1.0) {
              Assert.assertEquals(alternateStirlingErrorImplementation(z, 21),
                                  SaddlePointExpansion.getStirlingError(z),
                                  1.0e-15);
          }
      }
  
      @Test
      public void testSpecialValues() {
          Assert.assertEquals(0.0, SaddlePointExpansion.logBinomialProbability(0, 0, 0.6, 0.4), 1.0e-15);
          Assert.assertEquals(Double.NEGATIVE_INFINITY, SaddlePointExpansion.logBinomialProbability(1, 0, 0.6, 0.4), 1.0e-15);
      }
  
      private double alternateStirlingErrorImplementation(final double z, final int kMax) {
          // numerators of coefficients in Stirling's expansion for log(Γ(z)) from https://oeis.org/A046968
          final double[] A046968 = {
              1.0, -1.0, 1.0, -1.0, 1.0, -691.0, 1.0,
              -3617.0, 43867.0, -174611.0, 77683.0, -236364091.0, 657931.0, -3392780147.0,
              1723168255201.0, -7709321041217.0, 151628697551.0, -26315271553053477373.0,
              154210205991661.0, -261082718496449122051.0, 1520097643918070802691.0
          };
          // denominators of coefficients in Stirling's expansion for log(Γ(z)) from https://oeis.org/A046969
          final double[] A046969 = {
              12.0, 360.0, 1260.0, 1680.0, 1188.0, 360360.0, 156.0,
              122400.0, 244188.0, 125400.0, 5796.0, 1506960.0, 300.0, 93960.0,
              2492028.0, 505920.0, 396.0, 2418179400.0, 444.0, 21106800.0, 3109932.0
          };
          double zk   = z;
          double expansion = 0.0;
          for (int i = 0; i < kMax; ++i) {
              expansion += A046968[i] / (zk * A046969[i]);
              zk *= z * z;
          }
          return expansion;
      }
  }