text: // FFT.c
  // Runs on any processor
  // Jonathan Valvano
  // July 13, 2020
  
  /* This example accompanies the book
     "Embedded Systems: Introduction to Robotics,
     Jonathan W. Valvano, ISBN: 9781074544300, copyright (c) 2020
   For more information about my classes, my research, and my books, see
   http://users.ece.utexas.edu/~valvano/
  
  Simplified BSD License (FreeBSD License)
  Copyright (c) 2020, Jonathan Valvano, All rights reserved.
  
  Redistribution and use in source and binary forms, with or without modification,
  are permitted provided that the following conditions are met:
  
  1. Redistributions of source code must retain the above copyright notice,
     this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice,
     this list of conditions and the following disclaimer in the documentation
     and/or other materials provided with the distribution.
  
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
  AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
  OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
  USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  
  The views and conclusions contained in the software and documentation are
  those of the authors and should not be interpreted as representing official
  policies, either expressed or implied, of the FreeBSD Project.
  */
  /* Factored discrete Fourier transform, or FFT, and its inverse iFFT */
  // Derived from 
  // http://www.math.wustl.edu/~victor/mfmm/index.html#mfmm-software
  // Mathematics for Multimedia, ISBN 978-0-8176-4879-4, was formerly managed by Elsevier/Academic Press.
  
  #include <math.h>
  #include <stdlib.h>
  #include "../inc/FFT.h"
  
  const float cosTab[1024][11]={
    {1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546, 0.99969882, 0.99992470, 0.99998118, 0.99999529},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546, 0.99969882, 0.99992470, 0.99998118},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651, 0.99729046, 0.99932238, 0.99983058, 0.99995764},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546, 0.99969882, 0.99992470},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, 0.97003125, 0.99247953, 0.99811811, 0.99952942, 0.99988235},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651, 0.99729046, 0.99932238, 0.99983058},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, 0.77301045, 0.94154407, 0.98527764, 0.99631261, 0.99907773, 0.99976941},
    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546, 0.99969882},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, 0.63439328, 0.90398929, 0.97570213, 0.99390697, 0.99847558, 0.99961882},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, 0.97003125, 0.99247953, 0.99811811, 0.99952942},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, 0.47139674, 0.85772861, 0.96377607, 0.99090264, 0.99772307, 0.99943060},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651, 0.99729046, 0.99932238},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, 0.29028468, 0.80320753, 0.94952818, 0.98730142, 0.99682030, 0.99920476},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, 0.77301045, 0.94154407, 0.98527764, 0.99631261, 0.99907773},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, 0.09801714, 0.74095113, 0.93299280, 0.98310549, 0.99576741, 0.99894129},
    {1.00000000, 1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, -0.09801714, 0.67155895, 0.91420976, 0.97831737, 0.99456457, 0.99864022},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, 0.63439328, 0.90398929, 0.97570213, 0.99390697, 0.99847558},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, -0.29028468, 0.59569930, 0.89322430, 0.97293995, 0.99321195, 0.99830154},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, 0.97003125, 0.99247953, 0.99811811},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, -0.47139674, 0.51410274, 0.87008699, 0.96697647, 0.99170975, 0.99792529},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, 0.47139674, 0.85772861, 0.96377607, 0.99090264, 0.99772307},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, -0.63439328, 0.42755509, 0.84485357, 0.96043052, 0.99005821, 0.99751146},
    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651, 0.99729046},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, -0.77301045, 0.33688985, 0.81758481, 0.95330604, 0.98825757, 0.99706007},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, 0.29028468, 0.80320753, 0.94952818, 0.98730142, 0.99682030},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, -0.88192126, 0.24298018, 0.78834643, 0.94560733, 0.98630810, 0.99657115},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, 0.77301045, 0.94154407, 0.98527764, 0.99631261},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, -0.95694034, 0.14673047, 0.75720885, 0.93733901, 0.98421009, 0.99604470},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, 0.09801714, 0.74095113, 0.93299280, 0.98310549, 0.99576741},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, -0.99518473, 0.04906767, 0.72424708, 0.92850608, 0.98196387, 0.99548076},
    {1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, -0.99518473, -0.04906767, 0.68954054, 0.91911385, 0.97956977, 0.99487933},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, -0.09801714, 0.67155895, 0.91420976, 0.97831737, 0.99456457},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, -0.95694034, -0.14673047, 0.65317284, 0.90916798, 0.97702814, 0.99424045},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, 0.63439328, 0.90398929, 0.97570213, 0.99390697},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, -0.88192126, -0.24298018, 0.61523159, 0.89867447, 0.97433938, 0.99356414},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, -0.29028468, 0.59569930, 0.89322430, 0.97293995, 0.99321195},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, -0.77301045, -0.33688985, 0.57580819, 0.88763962, 0.97150389, 0.99285041},
    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, 0.97003125, 0.99247953},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, -0.63439328, -0.42755509, 0.53499762, 0.87607009, 0.96852209, 0.99209931},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, -0.47139674, 0.51410274, 0.87008699, 0.96697647, 0.99170975},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, -0.47139674, -0.51410274, 0.49289819, 0.86397286, 0.96539444, 0.99131086},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, 0.47139674, 0.85772861, 0.96377607, 0.99090264},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, -0.29028468, -0.59569930, 0.44961133, 0.85135519, 0.96212140, 0.99048508},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, -0.63439328, 0.42755509, 0.84485357, 0.96043052, 0.99005821},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, -0.09801714, -0.67155895, 0.40524131, 0.83822471, 0.95870347, 0.98962202},
    {1.00000000, 1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, 0.09801714, -0.74095113, 0.35989504, 0.82458930, 0.95514117, 0.98872169},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, -0.77301045, 0.33688985, 0.81758481, 0.95330604, 0.98825757},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, 0.29028468, -0.80320753, 0.31368174, 0.81045720, 0.95143502, 0.98778414},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, 0.29028468, 0.80320753, 0.94952818, 0.98730142},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, 0.47139674, -0.85772861, 0.26671276, 0.79583690, 0.94758559, 0.98680940},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, -0.88192126, 0.24298018, 0.78834643, 0.94560733, 0.98630810},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, 0.63439328, -0.90398929, 0.21910124, 0.78073723, 0.94359346, 0.98579751},
    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, 0.77301045, 0.94154407, 0.98527764},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, 0.77301045, -0.94154407, 0.17096189, 0.76516727, 0.93945922, 0.98474850},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, -0.95694034, 0.14673047, 0.75720885, 0.93733901, 0.98421009},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, -0.97003125, 0.12241068, 0.74913639, 0.93518351, 0.98366242},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, 0.09801714, 0.74095113, 0.93299280, 0.98310549},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, -0.98917651, 0.07356456, 0.73265427, 0.93076696, 0.98253930},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, -0.99518473, 0.04906767, 0.72424708, 0.92850608, 0.98196387},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, -0.99879546, 0.02454123, 0.71573083, 0.92621024, 0.98137919},
    {1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, -0.99879546, -0.02454123, 0.69837625, 0.92151404, 0.98018214},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, -0.99518473, -0.04906767, 0.68954054, 0.91911385, 0.97956977},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, -0.98917651, -0.07356456, 0.68060100, 0.91667906, 0.97894818},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, -0.09801714, 0.67155895, 0.91420976, 0.97831737},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, -0.97003125, -0.12241068, 0.66241578, 0.91170603, 0.97767736},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, -0.95694034, -0.14673047, 0.65317284, 0.90916798, 0.97702814},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, 0.77301045, -0.94154407, -0.17096189, 0.64383154, 0.90659570, 0.97636973},
    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, 0.63439328, 0.90398929, 0.97570213},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, 0.63439328, -0.90398929, -0.21910124, 0.62485949, 0.90134885, 0.97502535},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, -0.88192126, -0.24298018, 0.61523159, 0.89867447, 0.97433938},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, 0.47139674, -0.85772861, -0.26671276, 0.60551104, 0.89596625, 0.97364425},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, -0.29028468, 0.59569930, 0.89322430, 0.97293995},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, 0.29028468, -0.80320753, -0.31368174, 0.58579786, 0.89044872, 0.97222650},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, -0.77301045, -0.33688985, 0.57580819, 0.88763962, 0.97150389},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, 0.09801714, -0.74095113, -0.35989504, 0.56573181, 0.88479710, 0.97077214},
    {1.00000000, 1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, 0.97003125},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, -0.09801714, -0.67155895, -0.40524131, 0.54532499, 0.87901223, 0.96928124},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, -0.63439328, -0.42755509, 0.53499762, 0.87607009, 0.96852209},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, -0.29028468, -0.59569930, -0.44961133, 0.52458968, 0.87309498, 0.96775384},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, -0.47139674, 0.51410274, 0.87008699, 0.96697647},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, -0.47139674, -0.51410274, -0.49289819, 0.50353838, 0.86704625, 0.96619000},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, -0.47139674, -0.51410274, 0.49289819, 0.86397286, 0.96539444},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, -0.63439328, -0.42755509, -0.53499762, 0.48218377, 0.86086694, 0.96458979},
    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, 0.47139674, 0.85772861, 0.96377607},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, -0.77301045, -0.33688985, -0.57580819, 0.46053871, 0.85455799, 0.96295327},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, -0.29028468, -0.59569930, 0.44961133, 0.85135519, 0.96212140},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, -0.88192126, -0.24298018, -0.61523159, 0.43861624, 0.84812034, 0.96128049},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, -0.63439328, 0.42755509, 0.84485357, 0.96043052},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, -0.95694034, -0.14673047, -0.65317284, 0.41642956, 0.84155498, 0.95957151},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, -0.09801714, -0.67155895, 0.40524131, 0.83822471, 0.95870347},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, -0.99518473, -0.04906767, -0.68954054, 0.39399204, 0.83486287, 0.95782641},
    {1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, -0.99518473, 0.04906767, -0.72424708, 0.37131719, 0.82804505, 0.95604525},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, 0.09801714, -0.74095113, 0.35989504, 0.82458930, 0.95514117},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, -0.95694034, 0.14673047, -0.75720885, 0.34841868, 0.82110251, 0.95422810},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, -0.77301045, 0.33688985, 0.81758481, 0.95330604},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, -0.88192126, 0.24298018, -0.78834643, 0.32531029, 0.81403633, 0.95237501},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, 0.29028468, -0.80320753, 0.31368174, 0.81045720, 0.95143502},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, -0.77301045, 0.33688985, -0.81758481, 0.30200595, 0.80684755, 0.95048607},
    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, 0.29028468, 0.80320753, 0.94952818},
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    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651, -0.99729046},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, -0.63439328, 0.42755509, 0.84485357, 0.96043052, 0.99005821, -0.99751146},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, 0.47139674, 0.85772861, 0.96377607, 0.99090264, -0.99772307},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, -0.47139674, 0.51410274, 0.87008699, 0.96697647, 0.99170975, -0.99792529},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, 0.97003125, 0.99247953, -0.99811811},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, -0.29028468, 0.59569930, 0.89322430, 0.97293995, 0.99321195, -0.99830154},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, 0.63439328, 0.90398929, 0.97570213, 0.99390697, -0.99847558},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, -0.09801714, 0.67155895, 0.91420976, 0.97831737, 0.99456457, -0.99864022},
    {1.00000000, 1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, -0.99879546},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, -0.98078528, 0.09801714, 0.74095113, 0.93299280, 0.98310549, 0.99576741, -0.99894129},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, 0.77301045, 0.94154407, 0.98527764, 0.99631261, -0.99907773},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, -0.83146961, 0.29028468, 0.80320753, 0.94952818, 0.98730142, 0.99682030, -0.99920476},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651, 0.99729046, -0.99932238},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, -0.55557023, 0.47139674, 0.85772861, 0.96377607, 0.99090264, 0.99772307, -0.99943060},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, 0.97003125, 0.99247953, 0.99811811, -0.99952942},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, -0.19509032, 0.63439328, 0.90398929, 0.97570213, 0.99390697, 0.99847558, -0.99961882},
    {1.00000000, 1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546, -0.99969882},
    {-1.00000000, 0.00000000, 0.70710678, -0.92387953, 0.19509032, 0.77301045, 0.94154407, 0.98527764, 0.99631261, 0.99907773, -0.99976941},
    {1.00000000, -1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651, 0.99729046, 0.99932238, -0.99983058},
    {-1.00000000, 0.00000000, -0.70710678, -0.38268343, 0.55557023, 0.88192126, 0.97003125, 0.99247953, 0.99811811, 0.99952942, -0.99988235},
    {1.00000000, 1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546, 0.99969882, -0.99992470},
    {-1.00000000, 0.00000000, -0.70710678, 0.38268343, 0.83146961, 0.95694034, 0.98917651, 0.99729046, 0.99932238, 0.99983058, -0.99995764},
    {1.00000000, -1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546, 0.99969882, 0.99992470, -0.99998118},
    {-1.00000000, 0.00000000, 0.70710678, 0.92387953, 0.98078528, 0.99518473, 0.99879546, 0.99969882, 0.99992470, 0.99998118, -0.99999529}
  };
  
  const float sinTab[1024][11]={
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
    {0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, 0.09801714, 0.04906767, 0.02454123, 0.01227154, 0.00613588, 0.00306796},
    {0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, 0.09801714, 0.04906767, 0.02454123, 0.01227154, 0.00613588},
    {0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, 0.29028468, 0.14673047, 0.07356456, 0.03680722, 0.01840673, 0.00920375},
    {0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, 0.09801714, 0.04906767, 0.02454123, 0.01227154},
    {0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, 0.47139674, 0.24298018, 0.12241068, 0.06132074, 0.03067480, 0.01533921},
    {0.00000000, 0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, 0.29028468, 0.14673047, 0.07356456, 0.03680722, 0.01840673},
    {0.00000000, -1.00000000, -0.70710678, 0.38268343, 0.98078528, 0.63439328, 0.33688985, 0.17096189, 0.08579731, 0.04293826, 0.02147408},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, 0.09801714, 0.04906767, 0.02454123},
    {0.00000000, 1.00000000, 0.70710678, -0.38268343, 0.98078528, 0.77301045, 0.42755509, 0.21910124, 0.11022221, 0.05519524, 0.02760815},
    {0.00000000, 0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, 0.47139674, 0.24298018, 0.12241068, 0.06132074, 0.03067480},
    {0.00000000, -1.00000000, 0.70710678, -0.92387953, 0.83146961, 0.88192126, 0.51410274, 0.26671276, 0.13458071, 0.06744392, 0.03374117},
    {0.00000000, 0.00000000, 0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, 0.29028468, 0.14673047, 0.07356456, 0.03680722},
    {0.00000000, 1.00000000, -0.70710678, -0.92387953, 0.55557023, 0.95694034, 0.59569930, 0.31368174, 0.15885814, 0.07968244, 0.03987293},
    {0.00000000, 0.00000000, -1.00000000, -0.70710678, 0.38268343, 0.98078528, 0.63439328, 0.33688985, 0.17096189, 0.08579731, 0.04293826},
    {0.00000000, -1.00000000, -0.70710678, -0.38268343, 0.19509032, 0.99518473, 0.67155895, 0.35989504, 0.18303989, 0.09190896, 0.04600318},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, 0.09801714, 0.04906767},
    {0.00000000, 1.00000000, 0.70710678, 0.38268343, -0.19509032, 0.99518473, 0.74095113, 0.40524131, 0.20711138, 0.10412163, 0.05213170},
    {0.00000000, 0.00000000, 1.00000000, 0.70710678, -0.38268343, 0.98078528, 0.77301045, 0.42755509, 0.21910124, 0.11022221, 0.05519524},
    {0.00000000, -1.00000000, 0.70710678, 0.92387953, -0.55557023, 0.95694034, 0.80320753, 0.44961133, 0.23105811, 0.11631863, 0.05825826},
    {0.00000000, 0.00000000, 0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, 0.47139674, 0.24298018, 0.12241068, 0.06132074},
    {0.00000000, 1.00000000, -0.70710678, 0.92387953, -0.83146961, 0.88192126, 0.85772861, 0.49289819, 0.25486566, 0.12849811, 0.06438263},
    {0.00000000, 0.00000000, -1.00000000, 0.70710678, -0.92387953, 0.83146961, 0.88192126, 0.51410274, 0.26671276, 0.13458071, 0.06744392},
    {0.00000000, -1.00000000, -0.70710678, 0.38268343, -0.98078528, 0.77301045, 0.90398929, 0.53499762, 0.27851969, 0.14065824, 0.07050457},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, 0.29028468, 0.14673047, 0.07356456},
    {0.00000000, 1.00000000, 0.70710678, -0.38268343, -0.98078528, 0.63439328, 0.94154407, 0.57580819, 0.30200595, 0.15279719, 0.07662386},
    {0.00000000, 0.00000000, 1.00000000, -0.70710678, -0.92387953, 0.55557023, 0.95694034, 0.59569930, 0.31368174, 0.15885814, 0.07968244},
    {0.00000000, -1.00000000, 0.70710678, -0.92387953, -0.83146961, 0.47139674, 0.97003125, 0.61523159, 0.32531029, 0.16491312, 0.08274026},
    {0.00000000, 0.00000000, 0.00000000, -1.00000000, -0.70710678, 0.38268343, 0.98078528, 0.63439328, 0.33688985, 0.17096189, 0.08579731},
    {0.00000000, 1.00000000, -0.70710678, -0.92387953, -0.55557023, 0.29028468, 0.98917651, 0.65317284, 0.34841868, 0.17700422, 0.08885355},
    {0.00000000, 0.00000000, -1.00000000, -0.70710678, -0.38268343, 0.19509032, 0.99518473, 0.67155895, 0.35989504, 0.18303989, 0.09190896},
    {0.00000000, -1.00000000, -0.70710678, -0.38268343, -0.19509032, 0.09801714, 0.99879546, 0.68954054, 0.37131719, 0.18906866, 0.09496350},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, 0.09801714},
    {0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, -0.09801714, 0.99879546, 0.72424708, 0.39399204, 0.20110463, 0.10106986},
    {0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, -0.19509032, 0.99518473, 0.74095113, 0.40524131, 0.20711138, 0.10412163},
    {0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, -0.29028468, 0.98917651, 0.75720885, 0.41642956, 0.21311032, 0.10717242},
    {0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, -0.38268343, 0.98078528, 0.77301045, 0.42755509, 0.21910124, 0.11022221},
    {0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, -0.47139674, 0.97003125, 0.78834643, 0.43861624, 0.22508391, 0.11327095},
    {0.00000000, 0.00000000, -1.00000000, 0.70710678, 0.92387953, -0.55557023, 0.95694034, 0.80320753, 0.44961133, 0.23105811, 0.11631863},
    {0.00000000, -1.00000000, -0.70710678, 0.38268343, 0.98078528, -0.63439328, 0.94154407, 0.81758481, 0.46053871, 0.23702361, 0.11936521},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, 0.47139674, 0.24298018, 0.12241068},
    {0.00000000, 1.00000000, 0.70710678, -0.38268343, 0.98078528, -0.77301045, 0.90398929, 0.84485357, 0.48218377, 0.24892761, 0.12545498},
    {0.00000000, 0.00000000, 1.00000000, -0.70710678, 0.92387953, -0.83146961, 0.88192126, 0.85772861, 0.49289819, 0.25486566, 0.12849811},
    {0.00000000, -1.00000000, 0.70710678, -0.92387953, 0.83146961, -0.88192126, 0.85772861, 0.87008699, 0.50353838, 0.26079412, 0.13154003},
    {0.00000000, 0.00000000, 0.00000000, -1.00000000, 0.70710678, -0.92387953, 0.83146961, 0.88192126, 0.51410274, 0.26671276, 0.13458071},
    {0.00000000, 1.00000000, -0.70710678, -0.92387953, 0.55557023, -0.95694034, 0.80320753, 0.89322430, 0.52458968, 0.27262136, 0.13762012},
    {0.00000000, 0.00000000, -1.00000000, -0.70710678, 0.38268343, -0.98078528, 0.77301045, 0.90398929, 0.53499762, 0.27851969, 0.14065824},
    {0.00000000, -1.00000000, -0.70710678, -0.38268343, 0.19509032, -0.99518473, 0.74095113, 0.91420976, 0.54532499, 0.28440754, 0.14369503},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, 0.29028468, 0.14673047},
    {0.00000000, 1.00000000, 0.70710678, 0.38268343, -0.19509032, -0.99518473, 0.67155895, 0.93299280, 0.56573181, 0.29615089, 0.14976453},
    {0.00000000, 0.00000000, 1.00000000, 0.70710678, -0.38268343, -0.98078528, 0.63439328, 0.94154407, 0.57580819, 0.30200595, 0.15279719},
    {0.00000000, -1.00000000, 0.70710678, 0.92387953, -0.55557023, -0.95694034, 0.59569930, 0.94952818, 0.58579786, 0.30784964, 0.15582840},
    {0.00000000, 0.00000000, 0.00000000, 1.00000000, -0.70710678, -0.92387953, 0.55557023, 0.95694034, 0.59569930, 0.31368174, 0.15885814},
    {0.00000000, 1.00000000, -0.70710678, 0.92387953, -0.83146961, -0.88192126, 0.51410274, 0.96377607, 0.60551104, 0.31950203, 0.16188639},
    {0.00000000, 0.00000000, -1.00000000, 0.70710678, -0.92387953, -0.83146961, 0.47139674, 0.97003125, 0.61523159, 0.32531029, 0.16491312},
    {0.00000000, -1.00000000, -0.70710678, 0.38268343, -0.98078528, -0.77301045, 0.42755509, 0.97570213, 0.62485949, 0.33110631, 0.16793829},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, -1.00000000, -0.70710678, 0.38268343, 0.98078528, 0.63439328, 0.33688985, 0.17096189},
    {0.00000000, 1.00000000, 0.70710678, -0.38268343, -0.98078528, -0.63439328, 0.33688985, 0.98527764, 0.64383154, 0.34266072, 0.17398387},
    {0.00000000, 0.00000000, 1.00000000, -0.70710678, -0.92387953, -0.55557023, 0.29028468, 0.98917651, 0.65317284, 0.34841868, 0.17700422},
    {0.00000000, -1.00000000, 0.70710678, -0.92387953, -0.83146961, -0.47139674, 0.24298018, 0.99247953, 0.66241578, 0.35416353, 0.18002290},
    {0.00000000, 0.00000000, 0.00000000, -1.00000000, -0.70710678, -0.38268343, 0.19509032, 0.99518473, 0.67155895, 0.35989504, 0.18303989},
    {0.00000000, 1.00000000, -0.70710678, -0.92387953, -0.55557023, -0.29028468, 0.14673047, 0.99729046, 0.68060100, 0.36561300, 0.18605515},
    {0.00000000, 0.00000000, -1.00000000, -0.70710678, -0.38268343, -0.19509032, 0.09801714, 0.99879546, 0.68954054, 0.37131719, 0.18906866},
    {0.00000000, -1.00000000, -0.70710678, -0.38268343, -0.19509032, -0.09801714, 0.04906767, 0.99969882, 0.69837625, 0.37700741, 0.19208040},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032},
    {0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, 0.09801714, -0.04906767, 0.99969882, 0.71573083, 0.38834505, 0.19809841},
    {0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, -0.09801714, 0.99879546, 0.72424708, 0.39399204, 0.20110463},
    {0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, 0.29028468, -0.14673047, 0.99729046, 0.73265427, 0.39962420, 0.20410897},
    {0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, -0.19509032, 0.99518473, 0.74095113, 0.40524131, 0.20711138},
    {0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, 0.47139674, -0.24298018, 0.99247953, 0.74913639, 0.41084317, 0.21011184},
    {0.00000000, 0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, -0.29028468, 0.98917651, 0.75720885, 0.41642956, 0.21311032},
    {0.00000000, -1.00000000, -0.70710678, 0.38268343, 0.98078528, 0.63439328, -0.33688985, 0.98527764, 0.76516727, 0.42200027, 0.21610680},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, -0.38268343, 0.98078528, 0.77301045, 0.42755509, 0.21910124},
    {0.00000000, 1.00000000, 0.70710678, -0.38268343, 0.98078528, 0.77301045, -0.42755509, 0.97570213, 0.78073723, 0.43309382, 0.22209362},
    {0.00000000, 0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, -0.47139674, 0.97003125, 0.78834643, 0.43861624, 0.22508391},
    {0.00000000, -1.00000000, 0.70710678, -0.92387953, 0.83146961, 0.88192126, -0.51410274, 0.96377607, 0.79583690, 0.44412214, 0.22807208},
    {0.00000000, 0.00000000, 0.00000000, -1.00000000, 0.70710678, 0.92387953, -0.55557023, 0.95694034, 0.80320753, 0.44961133, 0.23105811},
    {0.00000000, 1.00000000, -0.70710678, -0.92387953, 0.55557023, 0.95694034, -0.59569930, 0.94952818, 0.81045720, 0.45508359, 0.23404196},
    {0.00000000, 0.00000000, -1.00000000, -0.70710678, 0.38268343, 0.98078528, -0.63439328, 0.94154407, 0.81758481, 0.46053871, 0.23702361},
    {0.00000000, -1.00000000, -0.70710678, -0.38268343, 0.19509032, 0.99518473, -0.67155895, 0.93299280, 0.82458930, 0.46597650, 0.24000302},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, 0.47139674, 0.24298018},
    {0.00000000, 1.00000000, 0.70710678, 0.38268343, -0.19509032, 0.99518473, -0.74095113, 0.91420976, 0.83822471, 0.47679923, 0.24595505},
    {0.00000000, 0.00000000, 1.00000000, 0.70710678, -0.38268343, 0.98078528, -0.77301045, 0.90398929, 0.84485357, 0.48218377, 0.24892761},
    {0.00000000, -1.00000000, 0.70710678, 0.92387953, -0.55557023, 0.95694034, -0.80320753, 0.89322430, 0.85135519, 0.48755016, 0.25189782},
    {0.00000000, 0.00000000, 0.00000000, 1.00000000, -0.70710678, 0.92387953, -0.83146961, 0.88192126, 0.85772861, 0.49289819, 0.25486566},
    {0.00000000, 1.00000000, -0.70710678, 0.92387953, -0.83146961, 0.88192126, -0.85772861, 0.87008699, 0.86397286, 0.49822767, 0.25783110},
    {0.00000000, 0.00000000, -1.00000000, 0.70710678, -0.92387953, 0.83146961, -0.88192126, 0.85772861, 0.87008699, 0.50353838, 0.26079412},
    {0.00000000, -1.00000000, -0.70710678, 0.38268343, -0.98078528, 0.77301045, -0.90398929, 0.84485357, 0.87607009, 0.50883014, 0.26375468},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, -1.00000000, 0.70710678, -0.92387953, 0.83146961, 0.88192126, 0.51410274, 0.26671276},
    {0.00000000, 1.00000000, 0.70710678, -0.38268343, -0.98078528, 0.63439328, -0.94154407, 0.81758481, 0.88763962, 0.51935599, 0.26966833},
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    {0.00000000, 1.00000000, 0.70710678, 0.38268343, 0.19509032, -0.09801714, -0.99879546, -0.68954054, -0.37131719, -0.18906866, 0.09496350},
    {0.00000000, 0.00000000, 1.00000000, 0.70710678, 0.38268343, -0.19509032, -0.99518473, -0.67155895, -0.35989504, -0.18303989, 0.09190896},
    {0.00000000, -1.00000000, 0.70710678, 0.92387953, 0.55557023, -0.29028468, -0.98917651, -0.65317284, -0.34841868, -0.17700422, 0.08885355},
    {0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.70710678, -0.38268343, -0.98078528, -0.63439328, -0.33688985, -0.17096189, 0.08579731},
    {0.00000000, 1.00000000, -0.70710678, 0.92387953, 0.83146961, -0.47139674, -0.97003125, -0.61523159, -0.32531029, -0.16491312, 0.08274026},
    {0.00000000, 0.00000000, -1.00000000, 0.70710678, 0.92387953, -0.55557023, -0.95694034, -0.59569930, -0.31368174, -0.15885814, 0.07968244},
    {0.00000000, -1.00000000, -0.70710678, 0.38268343, 0.98078528, -0.63439328, -0.94154407, -0.57580819, -0.30200595, -0.15279719, 0.07662386},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, -0.70710678, -0.92387953, -0.55557023, -0.29028468, -0.14673047, 0.07356456},
    {0.00000000, 1.00000000, 0.70710678, -0.38268343, 0.98078528, -0.77301045, -0.90398929, -0.53499762, -0.27851969, -0.14065824, 0.07050457},
    {0.00000000, 0.00000000, 1.00000000, -0.70710678, 0.92387953, -0.83146961, -0.88192126, -0.51410274, -0.26671276, -0.13458071, 0.06744392},
    {0.00000000, -1.00000000, 0.70710678, -0.92387953, 0.83146961, -0.88192126, -0.85772861, -0.49289819, -0.25486566, -0.12849811, 0.06438263},
    {0.00000000, 0.00000000, 0.00000000, -1.00000000, 0.70710678, -0.92387953, -0.83146961, -0.47139674, -0.24298018, -0.12241068, 0.06132074},
    {0.00000000, 1.00000000, -0.70710678, -0.92387953, 0.55557023, -0.95694034, -0.80320753, -0.44961133, -0.23105811, -0.11631863, 0.05825826},
    {0.00000000, 0.00000000, -1.00000000, -0.70710678, 0.38268343, -0.98078528, -0.77301045, -0.42755509, -0.21910124, -0.11022221, 0.05519524},
    {0.00000000, -1.00000000, -0.70710678, -0.38268343, 0.19509032, -0.99518473, -0.74095113, -0.40524131, -0.20711138, -0.10412163, 0.05213170},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, -1.00000000, -0.70710678, -0.38268343, -0.19509032, -0.09801714, 0.04906767},
    {0.00000000, 1.00000000, 0.70710678, 0.38268343, -0.19509032, -0.99518473, -0.67155895, -0.35989504, -0.18303989, -0.09190896, 0.04600318},
    {0.00000000, 0.00000000, 1.00000000, 0.70710678, -0.38268343, -0.98078528, -0.63439328, -0.33688985, -0.17096189, -0.08579731, 0.04293826},
    {0.00000000, -1.00000000, 0.70710678, 0.92387953, -0.55557023, -0.95694034, -0.59569930, -0.31368174, -0.15885814, -0.07968244, 0.03987293},
    {0.00000000, 0.00000000, 0.00000000, 1.00000000, -0.70710678, -0.92387953, -0.55557023, -0.29028468, -0.14673047, -0.07356456, 0.03680722},
    {0.00000000, 1.00000000, -0.70710678, 0.92387953, -0.83146961, -0.88192126, -0.51410274, -0.26671276, -0.13458071, -0.06744392, 0.03374117},
    {0.00000000, 0.00000000, -1.00000000, 0.70710678, -0.92387953, -0.83146961, -0.47139674, -0.24298018, -0.12241068, -0.06132074, 0.03067480},
    {0.00000000, -1.00000000, -0.70710678, 0.38268343, -0.98078528, -0.77301045, -0.42755509, -0.21910124, -0.11022221, -0.05519524, 0.02760815},
    {0.00000000, 0.00000000, 0.00000000, 0.00000000, -1.00000000, -0.70710678, -0.38268343, -0.19509032, -0.09801714, -0.04906767, 0.02454123},
    {0.00000000, 1.00000000, 0.70710678, -0.38268343, -0.98078528, -0.63439328, -0.33688985, -0.17096189, -0.08579731, -0.04293826, 0.02147408},
    {0.00000000, 0.00000000, 1.00000000, -0.70710678, -0.92387953, -0.55557023, -0.29028468, -0.14673047, -0.07356456, -0.03680722, 0.01840673},
    {0.00000000, -1.00000000, 0.70710678, -0.92387953, -0.83146961, -0.47139674, -0.24298018, -0.12241068, -0.06132074, -0.03067480, 0.01533921},
    {0.00000000, 0.00000000, 0.00000000, -1.00000000, -0.70710678, -0.38268343, -0.19509032, -0.09801714, -0.04906767, -0.02454123, 0.01227154},
    {0.00000000, 1.00000000, -0.70710678, -0.92387953, -0.55557023, -0.29028468, -0.14673047, -0.07356456, -0.03680722, -0.01840673, 0.00920375},
    {0.00000000, 0.00000000, -1.00000000, -0.70710678, -0.38268343, -0.19509032, -0.09801714, -0.04906767, -0.02454123, -0.01227154, 0.00613588},
    {0.00000000, -1.00000000, -0.70710678, -0.38268343, -0.19509032, -0.09801714, -0.04906767, -0.02454123, -0.01227154, -0.00613588, 0.00306796}
  
  };
  
  
  
  /* 
     fft(v,N):
     [0] If N==1 then return.
     [1] For k = 0 to N/2-1, let ve[k] = v[2*k]
     [2] Compute fft(ve, N/2);
     [3] For k = 0 to N/2-1, let vo[k] = v[2*k+1]
     [4] Compute fft(vo, N/2);
     [5] For m = 0 to N/2-1, do [6] through [9]
     [6]   Let w.Real = cos(2*PI*m/N)
     [7]   Let w.Imag = -sin(2*PI*m/N)
     [8]   Let v[m] = ve[m] + w*vo[m]
     [9]   Let v[m+N/2] = ve[m] - w*vo[m]
  Time to convert
     n    Time(us)
       64   1659
      128   3892
      256   8979
      512  20440
     1024  46035
     2048 102760
   */
  void fft( complex_t *v, int n, complex_t *tmp ){
    if(n>1) {			/* otherwise, do nothing and return */
      int k,m,j,n1;
  	complex_t z, w, *vo, *ve;
      ve = tmp; 
  	vo = tmp+n/2;
      for(k=0; k<n/2; k++) {
        ve[k] = v[2*k];
        vo[k] = v[2*k+1];
      }
      fft( ve, n/2, v );		/* FFT on even-indexed elements of v[] */
      fft( vo, n/2, v );		/* FFT on odd-indexed elements of v[] */
      for(m=0; m<n/2; m++){
        j = 0; n1 = 2;
        while(n1<n){
          j++; n1 = n1*2;
        }
        // j goes 0,1,2, 3, 4, 5,  6,  7,  8,   9, 10,  11
        // n goes 2,4,8,16,32,64,128,256,512,1024,2048,4096
        w.Real = cosTab[m][j];
        w.Imag = -sinTab[m][j];;
      //  w.Real = cos(2*PI*m/(float)n);
      //  w.Imag = -sin(2*PI*m/(float)n);
        z.Real = w.Real*vo[m].Real - w.Imag*vo[m].Imag;	/* Re(w*vo[m]) */
        z.Imag = w.Real*vo[m].Imag + w.Imag*vo[m].Real;	/* Im(w*vo[m]) */
        v[  m  ].Real = ve[m].Real + z.Real;
        v[  m  ].Imag = ve[m].Imag + z.Imag;
        v[m+n/2].Real = ve[m].Real - z.Real;
        v[m+n/2].Imag = ve[m].Imag - z.Imag;
      }
    }
    return;
  }
  
  
  /* 
     ifft(v,N):
     [0] If N==1 then return.
     [1] For k = 0 to N/2-1, let ve[k] = v[2*k]
     [2] Compute ifft(ve, N/2);
     [3] For k = 0 to N/2-1, let vo[k] = v[2*k+1]
     [4] Compute ifft(vo, N/2);
     [5] For m = 0 to N/2-1, do [6] through [9]
     [6]   Let w.Real = cos(2*PI*m/N)
     [7]   Let w.Imag = sin(2*PI*m/N)
     [8]   Let v[m] = ve[m] + w*vo[m]
     [9]   Let v[m+N/2] = ve[m] - w*vo[m]
   */
  void ifft( complex_t *v, int n, complex_t *tmp ){
    if(n>1) {			/* otherwise, do nothing and return */
      int k,m,j,n1;
  	complex_t z, w, *vo, *ve;
      ve = tmp; vo = tmp+n/2;
      for(k=0; k<n/2; k++){
        ve[k] = v[2*k];
        vo[k] = v[2*k+1];
      }
      ifft( ve, n/2, v );		/* FFT on even-indexed elements of v[] */
      ifft( vo, n/2, v );		/* FFT on odd-indexed elements of v[] */
      for(m=0; m<n/2; m++) {
        j = 0; n1 = 2;
        while(n1<n){
          j++; n1 = n1*2;
        }
        // j goes 0,1,2, 3, 4, 5,  6,  7,  8,   9, 10,  11
        // n goes 2,4,8,16,32,64,128,256,512,1024,2048,4096
        w.Real = cosTab[m][j];
        w.Imag = sinTab[m][j];;
       // w.Real = cos(2*PI*m/(float)n);
       // w.Imag = sin(2*PI*m/(float)n);
        z.Real = w.Real*vo[m].Real - w.Imag*vo[m].Imag;	/* Re(w*vo[m]) */
        z.Imag = w.Real*vo[m].Imag + w.Imag*vo[m].Real;	/* Im(w*vo[m]) */
        v[  m  ].Real = ve[m].Real + z.Real;
        v[  m  ].Imag = ve[m].Imag + z.Imag;
        v[m+n/2].Real = ve[m].Real - z.Real;
        v[m+n/2].Imag = ve[m].Imag - z.Imag;
      }
    }
    return;
  }
  
  