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1   /*
2    * Licensed to the Hipparchus project under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The Hipparchus project licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      https://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.hipparchus.special.elliptic.jacobi;
18  
19  import org.hipparchus.util.FastMath;
20  import org.hipparchus.util.SinCos;
21  
22  /** Algorithm for computing the principal Jacobi functions for parameters slightly above zero.
23   * <p>
24   * The algorithm for evaluating the functions is based on approximation
25   * in terms of circular functions. It is given in Abramowitz and Stegun,
26   * sections 16.13.
27   * </p>
28   * @since 2.0
29   */
30  class NearZeroParameter extends JacobiElliptic {
31  
32      /** Simple constructor.
33       * @param m parameter of the Jacobi elliptic function (must be zero or slightly positive here)
34       */
35      NearZeroParameter(final double m) {
36          super(m);
37      }
38  
39      /** {@inheritDoc} */
40      @Override
41      public CopolarN valuesN(final double u) {
42          final SinCos sc     = FastMath.sinCos(u);
43          final double factor = 0.25 * getM() * (u - sc.sin() * sc.cos());
44          return new CopolarN(sc.sin() - factor * sc.cos(),            // equation 16.13.1
45                              sc.cos() + factor * sc.sin(),            // equation 16.13.2
46                              1 - 0.5 * getM() * sc.sin() * sc.sin()); // equation 16.13.3
47      }
48  
49  }