/*
    * 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.transform;
  
  import java.io.Serializable;
  
  import org.hipparchus.analysis.FunctionUtils;
  import org.hipparchus.analysis.UnivariateFunction;
  import org.hipparchus.complex.Complex;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.exception.MathRuntimeException;
  import org.hipparchus.util.ArithmeticUtils;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathArrays;
  import org.hipparchus.util.MathUtils;
  
  /**
   * Implements the Fast Fourier Transform for transformation of one-dimensional
   * real or complex data sets. For reference, see <em>Applied Numerical Linear
   * Algebra</em>, ISBN 0898713897, chapter 6.
   * <p>
   * There are several variants of the discrete Fourier transform, with various
   * normalization conventions, which are specified by the parameter
   * {@link DftNormalization}.
   * <p>
   * The current implementation of the discrete Fourier transform as a fast
   * Fourier transform requires the length of the data set to be a power of 2.
   * This greatly simplifies and speeds up the code. Users can pad the data with
   * zeros to meet this requirement. There are other flavors of FFT, for
   * reference, see S. Winograd,
   * <i>On computing the discrete Fourier transform</i>, Mathematics of
   * Computation, 32 (1978), 175 - 199.
   *
   * @see DftNormalization
   */
  public class FastFourierTransformer implements Serializable {
  
      /** Serializable version identifier. */
      private static final long serialVersionUID = 20120210L;
  
      /**
       * {@code W_SUB_N_R[i]} is the real part of
       * {@code exp(- 2 * i * pi / n)}:
       * {@code W_SUB_N_R[i] = cos(2 * pi/ n)}, where {@code n = 2^i}.
       */
      private static final double[] W_SUB_N_R =
              {  0x1.0p0, -0x1.0p0, 0x1.1a62633145c07p-54, 0x1.6a09e667f3bcdp-1
              , 0x1.d906bcf328d46p-1, 0x1.f6297cff75cbp-1, 0x1.fd88da3d12526p-1, 0x1.ff621e3796d7ep-1
              , 0x1.ffd886084cd0dp-1, 0x1.fff62169b92dbp-1, 0x1.fffd8858e8a92p-1, 0x1.ffff621621d02p-1
              , 0x1.ffffd88586ee6p-1, 0x1.fffff62161a34p-1, 0x1.fffffd8858675p-1, 0x1.ffffff621619cp-1
              , 0x1.ffffffd885867p-1, 0x1.fffffff62161ap-1, 0x1.fffffffd88586p-1, 0x1.ffffffff62162p-1
              , 0x1.ffffffffd8858p-1, 0x1.fffffffff6216p-1, 0x1.fffffffffd886p-1, 0x1.ffffffffff621p-1
              , 0x1.ffffffffffd88p-1, 0x1.fffffffffff62p-1, 0x1.fffffffffffd9p-1, 0x1.ffffffffffff6p-1
              , 0x1.ffffffffffffep-1, 0x1.fffffffffffffp-1, 0x1.0p0, 0x1.0p0
              , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0
              , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0
              , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0
              , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0
              , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0
              , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0
              , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0
              , 0x1.0p0, 0x1.0p0, 0x1.0p0 };
  
      /**
       * {@code W_SUB_N_I[i]} is the imaginary part of
       * {@code exp(- 2 * i * pi / n)}:
       * {@code W_SUB_N_I[i] = -sin(2 * pi/ n)}, where {@code n = 2^i}.
       */
      private static final double[] W_SUB_N_I =
              {  0x1.1a62633145c07p-52, -0x1.1a62633145c07p-53, -0x1.0p0, -0x1.6a09e667f3bccp-1
              , -0x1.87de2a6aea963p-2, -0x1.8f8b83c69a60ap-3, -0x1.917a6bc29b42cp-4, -0x1.91f65f10dd814p-5
              , -0x1.92155f7a3667ep-6, -0x1.921d1fcdec784p-7, -0x1.921f0fe670071p-8, -0x1.921f8becca4bap-9
              , -0x1.921faaee6472dp-10, -0x1.921fb2aecb36p-11, -0x1.921fb49ee4ea6p-12, -0x1.921fb51aeb57bp-13
              , -0x1.921fb539ecf31p-14, -0x1.921fb541ad59ep-15, -0x1.921fb5439d73ap-16, -0x1.921fb544197ap-17
              , -0x1.921fb544387bap-18, -0x1.921fb544403c1p-19, -0x1.921fb544422c2p-20, -0x1.921fb54442a83p-21
              , -0x1.921fb54442c73p-22, -0x1.921fb54442cefp-23, -0x1.921fb54442d0ep-24, -0x1.921fb54442d15p-25
              , -0x1.921fb54442d17p-26, -0x1.921fb54442d18p-27, -0x1.921fb54442d18p-28, -0x1.921fb54442d18p-29
              , -0x1.921fb54442d18p-30, -0x1.921fb54442d18p-31, -0x1.921fb54442d18p-32, -0x1.921fb54442d18p-33
              , -0x1.921fb54442d18p-34, -0x1.921fb54442d18p-35, -0x1.921fb54442d18p-36, -0x1.921fb54442d18p-37
              , -0x1.921fb54442d18p-38, -0x1.921fb54442d18p-39, -0x1.921fb54442d18p-40, -0x1.921fb54442d18p-41
             , -0x1.921fb54442d18p-42, -0x1.921fb54442d18p-43, -0x1.921fb54442d18p-44, -0x1.921fb54442d18p-45
             , -0x1.921fb54442d18p-46, -0x1.921fb54442d18p-47, -0x1.921fb54442d18p-48, -0x1.921fb54442d18p-49
             , -0x1.921fb54442d18p-50, -0x1.921fb54442d18p-51, -0x1.921fb54442d18p-52, -0x1.921fb54442d18p-53
             , -0x1.921fb54442d18p-54, -0x1.921fb54442d18p-55, -0x1.921fb54442d18p-56, -0x1.921fb54442d18p-57
             , -0x1.921fb54442d18p-58, -0x1.921fb54442d18p-59, -0x1.921fb54442d18p-60 };
 
     /** The type of DFT to be performed. */
     private final DftNormalization normalization;
 
     /**
      * Creates a new instance of this class, with various normalization
      * conventions.
      *
      * @param normalization the type of normalization to be applied to the
      * transformed data
      */
     public FastFourierTransformer(final DftNormalization normalization) {
         this.normalization = normalization;
     }
 
     /**
      * Performs identical index bit reversal shuffles on two arrays of identical
      * size. Each element in the array is swapped with another element based on
      * the bit-reversal of the index. For example, in an array with length 16,
      * item at binary index 0011 (decimal 3) would be swapped with the item at
      * binary index 1100 (decimal 12).
      *
      * @param a the first array to be shuffled
      * @param b the second array to be shuffled
      */
     private static void bitReversalShuffle2(double[] a, double[] b) {
         final int n = a.length;
         assert b.length == n;
         final int halfOfN = n >> 1;
 
         int j = 0;
         for (int i = 0; i < n; i++) {
             if (i < j) {
                 // swap indices i & j
                 double temp = a[i];
                 a[i] = a[j];
                 a[j] = temp;
 
                 temp = b[i];
                 b[i] = b[j];
                 b[j] = temp;
             }
 
             int k = halfOfN;
             while (k <= j && k > 0) {
                 j -= k;
                 k >>= 1;
             }
             j += k;
         }
     }
 
     /**
      * Applies the proper normalization to the specified transformed data.
      *
      * @param dataRI the unscaled transformed data
      * @param normalization the normalization to be applied
      * @param type the type of transform (forward, inverse) which resulted in the specified data
      */
     private static void normalizeTransformedData(final double[][] dataRI,
         final DftNormalization normalization, final TransformType type) {
 
         final double[] dataR = dataRI[0];
         final double[] dataI = dataRI[1];
         final int n = dataR.length;
         assert dataI.length == n;
 
         switch (normalization) {
             case STANDARD:
                 if (type == TransformType.INVERSE) {
                     final double scaleFactor = 1.0 / n;
                     for (int i = 0; i < n; i++) {
                         dataR[i] *= scaleFactor;
                         dataI[i] *= scaleFactor;
                     }
                 }
                 break;
             case UNITARY:
                 final double scaleFactor = 1.0 / FastMath.sqrt(n);
                 for (int i = 0; i < n; i++) {
                     dataR[i] *= scaleFactor;
                     dataI[i] *= scaleFactor;
                 }
                 break;
             default:
                 // This should never occur in normal conditions. However this
                 // clause has been added as a safeguard if other types of
                 // normalizations are ever implemented, and the corresponding
                 // test is forgotten in the present switch.
                 throw MathRuntimeException.createInternalError();
         }
     }
 
     /**
      * Computes the standard transform of the specified complex data. The
      * computation is done in place. The input data is laid out as follows
      * <ul>
      *   <li>{@code dataRI[0][i]} is the real part of the {@code i}-th data point,</li>
      *   <li>{@code dataRI[1][i]} is the imaginary part of the {@code i}-th data point.</li>
      * </ul>
      *
      * @param dataRI the two dimensional array of real and imaginary parts of the data
      * @param normalization the normalization to be applied to the transformed data
      * @param type the type of transform (forward, inverse) to be performed
      * @throws MathIllegalArgumentException if the number of rows of the specified
      *   array is not two, or the array is not rectangular
      * @throws MathIllegalArgumentException if the number of data points is not
      *   a power of two
      */
     public static void transformInPlace(final double[][] dataRI,
         final DftNormalization normalization, final TransformType type) {
 
         MathUtils.checkDimension(dataRI.length, 2);
         final double[] dataR = dataRI[0];
         final double[] dataI = dataRI[1];
         MathArrays.checkEqualLength(dataR, dataI);
 
         final int n = dataR.length;
         if (!ArithmeticUtils.isPowerOfTwo(n)) {
             throw new MathIllegalArgumentException(LocalizedFFTFormats.NOT_POWER_OF_TWO_CONSIDER_PADDING,
                                                    Integer.valueOf(n));
         }
 
         if (n == 1) {
             return;
         } else if (n == 2) {
             final double srcR0 = dataR[0];
             final double srcI0 = dataI[0];
             final double srcR1 = dataR[1];
             final double srcI1 = dataI[1];
 
             // X_0 = x_0 + x_1
             dataR[0] = srcR0 + srcR1;
             dataI[0] = srcI0 + srcI1;
             // X_1 = x_0 - x_1
             dataR[1] = srcR0 - srcR1;
             dataI[1] = srcI0 - srcI1;
 
             normalizeTransformedData(dataRI, normalization, type);
             return;
         }
 
         bitReversalShuffle2(dataR, dataI);
 
         // Do 4-term DFT.
         if (type == TransformType.INVERSE) {
             for (int i0 = 0; i0 < n; i0 += 4) {
                 final int i1 = i0 + 1;
                 final int i2 = i0 + 2;
                 final int i3 = i0 + 3;
 
                 final double srcR0 = dataR[i0];
                 final double srcI0 = dataI[i0];
                 final double srcR1 = dataR[i2];
                 final double srcI1 = dataI[i2];
                 final double srcR2 = dataR[i1];
                 final double srcI2 = dataI[i1];
                 final double srcR3 = dataR[i3];
                 final double srcI3 = dataI[i3];
 
                 // 4-term DFT
                 // X_0 = x_0 + x_1 + x_2 + x_3
                 dataR[i0] = srcR0 + srcR1 + srcR2 + srcR3;
                 dataI[i0] = srcI0 + srcI1 + srcI2 + srcI3;
                 // X_1 = x_0 - x_2 + j * (x_3 - x_1)
                 dataR[i1] = srcR0 - srcR2 + (srcI3 - srcI1);
                 dataI[i1] = srcI0 - srcI2 + (srcR1 - srcR3);
                 // X_2 = x_0 - x_1 + x_2 - x_3
                 dataR[i2] = srcR0 - srcR1 + srcR2 - srcR3;
                 dataI[i2] = srcI0 - srcI1 + srcI2 - srcI3;
                 // X_3 = x_0 - x_2 + j * (x_1 - x_3)
                 dataR[i3] = srcR0 - srcR2 + (srcI1 - srcI3);
                 dataI[i3] = srcI0 - srcI2 + (srcR3 - srcR1);
             }
         } else {
             for (int i0 = 0; i0 < n; i0 += 4) {
                 final int i1 = i0 + 1;
                 final int i2 = i0 + 2;
                 final int i3 = i0 + 3;
 
                 final double srcR0 = dataR[i0];
                 final double srcI0 = dataI[i0];
                 final double srcR1 = dataR[i2];
                 final double srcI1 = dataI[i2];
                 final double srcR2 = dataR[i1];
                 final double srcI2 = dataI[i1];
                 final double srcR3 = dataR[i3];
                 final double srcI3 = dataI[i3];
 
                 // 4-term DFT
                 // X_0 = x_0 + x_1 + x_2 + x_3
                 dataR[i0] = srcR0 + srcR1 + srcR2 + srcR3;
                 dataI[i0] = srcI0 + srcI1 + srcI2 + srcI3;
                 // X_1 = x_0 - x_2 + j * (x_3 - x_1)
                 dataR[i1] = srcR0 - srcR2 + (srcI1 - srcI3);
                 dataI[i1] = srcI0 - srcI2 + (srcR3 - srcR1);
                 // X_2 = x_0 - x_1 + x_2 - x_3
                 dataR[i2] = srcR0 - srcR1 + srcR2 - srcR3;
                 dataI[i2] = srcI0 - srcI1 + srcI2 - srcI3;
                 // X_3 = x_0 - x_2 + j * (x_1 - x_3)
                 dataR[i3] = srcR0 - srcR2 + (srcI3 - srcI1);
                 dataI[i3] = srcI0 - srcI2 + (srcR1 - srcR3);
             }
         }
 
         int lastN0 = 4;
         int lastLogN0 = 2;
         while (lastN0 < n) {
             int n0 = lastN0 << 1;
             int logN0 = lastLogN0 + 1;
             double wSubN0R = W_SUB_N_R[logN0];
             double wSubN0I = W_SUB_N_I[logN0];
             if (type == TransformType.INVERSE) {
                 wSubN0I = -wSubN0I;
             }
 
             // Combine even/odd transforms of size lastN0 into a transform of size N0 (lastN0 * 2).
             for (int destEvenStartIndex = 0; destEvenStartIndex < n; destEvenStartIndex += n0) {
                 int destOddStartIndex = destEvenStartIndex + lastN0;
 
                 double wSubN0ToRR = 1;
                 double wSubN0ToRI = 0;
 
                 for (int r = 0; r < lastN0; r++) {
                     double grR = dataR[destEvenStartIndex + r];
                     double grI = dataI[destEvenStartIndex + r];
                     double hrR = dataR[destOddStartIndex + r];
                     double hrI = dataI[destOddStartIndex + r];
 
                     // dest[destEvenStartIndex + r] = Gr + WsubN0ToR * Hr
                     dataR[destEvenStartIndex + r] = grR + wSubN0ToRR * hrR - wSubN0ToRI * hrI;
                     dataI[destEvenStartIndex + r] = grI + wSubN0ToRR * hrI + wSubN0ToRI * hrR;
                     // dest[destOddStartIndex + r] = Gr - WsubN0ToR * Hr
                     dataR[destOddStartIndex + r] = grR - (wSubN0ToRR * hrR - wSubN0ToRI * hrI);
                     dataI[destOddStartIndex + r] = grI - (wSubN0ToRR * hrI + wSubN0ToRI * hrR);
 
                     // WsubN0ToR *= WsubN0R
                     double nextWsubN0ToRR = wSubN0ToRR * wSubN0R - wSubN0ToRI * wSubN0I;
                     double nextWsubN0ToRI = wSubN0ToRR * wSubN0I + wSubN0ToRI * wSubN0R;
                     wSubN0ToRR = nextWsubN0ToRR;
                     wSubN0ToRI = nextWsubN0ToRI;
                 }
             }
 
             lastN0 = n0;
             lastLogN0 = logN0;
         }
 
         normalizeTransformedData(dataRI, normalization, type);
     }
 
     /**
      * Returns the (forward, inverse) transform of the specified real data set.
      *
      * @param f the real data array to be transformed
      * @param type the type of transform (forward, inverse) to be performed
      * @return the complex transformed array
      * @throws MathIllegalArgumentException if the length of the data array is not a power of two
      */
     public Complex[] transform(final double[] f, final TransformType type) {
         final double[][] dataRI = { f.clone(), new double[f.length] };
         transformInPlace(dataRI, normalization, type);
         return TransformUtils.createComplexArray(dataRI);
     }
 
     /**
      * Returns the (forward, inverse) transform of the specified real function,
      * sampled on the specified interval.
      *
      * @param f the function to be sampled and transformed
      * @param min the (inclusive) lower bound for the interval
      * @param max the (exclusive) upper bound for the interval
      * @param n the number of sample points
      * @param type the type of transform (forward, inverse) to be performed
      * @return the complex transformed array
      * @throws org.hipparchus.exception.MathIllegalArgumentException
      *   if the lower bound is greater than, or equal to the upper bound
      * @throws org.hipparchus.exception.MathIllegalArgumentException
      *   if the number of sample points {@code n} is negative
      * @throws MathIllegalArgumentException if the number of sample points
      *   {@code n} is not a power of two
      */
     public Complex[] transform(final UnivariateFunction f,
                                final double min, final double max, final int n,
                                final TransformType type) {
 
         final double[] data = FunctionUtils.sample(f, min, max, n);
         return transform(data, type);
     }
 
     /**
      * Returns the (forward, inverse) transform of the specified complex data set.
      *
      * @param f the complex data array to be transformed
      * @param type the type of transform (forward, inverse) to be performed
      * @return the complex transformed array
      * @throws MathIllegalArgumentException if the length of the data array is not a power of two
      */
     public Complex[] transform(final Complex[] f, final TransformType type) {
         final double[][] dataRI = TransformUtils.createRealImaginaryArray(f);
 
         transformInPlace(dataRI, normalization, type);
 
         return TransformUtils.createComplexArray(dataRI);
     }
 
 }