/* fft4096.c  complex data stored  re, im, re, im, re, ... im */

void fft4096(float Z[8192]) /* input data points and output  [0] to [8191] */
{
  static float W[8192];    /* scratch vector, used many times, */
  static float E[4098] =   /* constants for FFT algorithm */
  {1.0, 0.0, 0.999999, 0.00153398,
   0.999995, 0.00306796, 0.999989, 0.00460193,
   0.999981, 0.00613589, 0.999971, 0.00766983,
   0.999958, 0.00920376, 0.999942, 0.0107377,
   0.999925, 0.0122715, 0.999905, 0.0138054,
   0.999882, 0.0153392, 0.999858, 0.016873,
   0.999831, 0.0184067, 0.999801, 0.0199404,
   0.999769, 0.0214741, 0.999735, 0.0230077,
   0.999699, 0.0245412, 0.99966, 0.0260747,
   0.999619, 0.0276081, 0.999575, 0.0291415,
   0.999529, 0.0306748, 0.999481, 0.032208,
   0.999431, 0.0337412, 0.999378, 0.0352742,
   0.999322, 0.0368072, 0.999265, 0.0383401,
   0.999205, 0.0398729, 0.999142, 0.0414056,
   0.999078, 0.0429383, 0.999011, 0.0444708,
   0.998941, 0.0460032, 0.99887, 0.0475355,
   0.998796, 0.0490677, 0.998719, 0.0505997,
   0.99864, 0.0521317, 0.998559, 0.0536635,
   0.998476, 0.0551952, 0.99839, 0.0567268,
   0.998302, 0.0582583, 0.998211, 0.0597896,
   0.998118, 0.0613207, 0.998023, 0.0628518,
   0.997925, 0.0643826, 0.997825, 0.0659134,
   0.997723, 0.0674439, 0.997619, 0.0689743,
   0.997512, 0.0705046, 0.997402, 0.0720346,
   0.99729, 0.0735646, 0.997176, 0.0750943,
   0.99706, 0.0766239, 0.996941, 0.0781532,
   0.99682, 0.0796824, 0.996697, 0.0812114,
   0.996571, 0.0827403, 0.996443, 0.0842689,
   0.996313, 0.0857973, 0.99618, 0.0873255,
   0.996045, 0.0888535, 0.995907, 0.0903814,
   0.995768, 0.091909, 0.995625, 0.0934363,
   0.995481, 0.0949635, 0.995334, 0.0964904,
   0.995185, 0.0980171, 0.995033, 0.0995436,
   0.994879, 0.10107, 0.994723, 0.102596,
   0.994565, 0.104122, 0.994404, 0.105647,
   0.994241, 0.107172, 0.994075, 0.108697,
   0.993907, 0.110222, 0.993737, 0.111747,
   0.993564, 0.113271, 0.993389, 0.114795,
   0.993212, 0.116319, 0.993032, 0.117842,
   0.99285, 0.119365, 0.992666, 0.120888,
   0.99248, 0.122411, 0.992291, 0.123933,
   0.992099, 0.125455, 0.991906, 0.126977,
   0.99171, 0.128498, 0.991511, 0.130019,
   0.991311, 0.13154, 0.991108, 0.133061,
   0.990903, 0.134581, 0.990695, 0.136101,
   0.990485, 0.13762, 0.990273, 0.139139,
   0.990058, 0.140658, 0.989841, 0.142177,
   0.989622, 0.143695, 0.989401, 0.145213,
   0.989177, 0.14673, 0.98895, 0.148248,
   0.988722, 0.149765, 0.988491, 0.151281,
   0.988258, 0.152797, 0.988022, 0.154313,
   0.987784, 0.155828, 0.987544, 0.157343,
   0.987302, 0.158858, 0.987057, 0.160372,
   0.986809, 0.161886, 0.98656, 0.1634,
   0.986308, 0.164913, 0.986054, 0.166426,
   0.985798, 0.167938, 0.985539, 0.16945,
   0.985278, 0.170962, 0.985014, 0.172473,
   0.984749, 0.173984, 0.984481, 0.175494,
   0.98421, 0.177004, 0.983938, 0.178514,
   0.983662, 0.180023, 0.983385, 0.181532,
   0.983106, 0.18304, 0.982824, 0.184548,
   0.982539, 0.186055, 0.982253, 0.187562,
   0.981964, 0.189069, 0.981673, 0.190575,
   0.981379, 0.19208, 0.981084, 0.193586,
   0.980785, 0.19509, 0.980485, 0.196595,
   0.980182, 0.198098, 0.979877, 0.199602,
   0.97957, 0.201105, 0.97926, 0.202607,
   0.978948, 0.204109, 0.978634, 0.20561,
   0.978318, 0.207111, 0.977999, 0.208612,
   0.977677, 0.210112, 0.977354, 0.211611,
   0.977028, 0.21311, 0.9767, 0.214609,
   0.97637, 0.216107, 0.976037, 0.217604,
   0.975702, 0.219101, 0.975365, 0.220598,
   0.975025, 0.222094, 0.974684, 0.223589,
   0.974339, 0.225084, 0.973993, 0.226578,
   0.973644, 0.228072, 0.973293, 0.229565,
   0.97294, 0.231058, 0.972584, 0.23255,
   0.972227, 0.234042, 0.971866, 0.235533,
   0.971504, 0.237024, 0.971139, 0.238514,
   0.970772, 0.240003, 0.970403, 0.241492,
   0.970031, 0.24298, 0.969657, 0.244468,
   0.969281, 0.245955, 0.968903, 0.247442,
   0.968522, 0.248928, 0.968139, 0.250413,
   0.967754, 0.251898, 0.967366, 0.253382,
   0.966977, 0.254866, 0.966584, 0.256349,
   0.96619, 0.257831, 0.965793, 0.259313,
   0.965395, 0.260794, 0.964993, 0.262275,
   0.96459, 0.263755, 0.964184, 0.265234,
   0.963776, 0.266713, 0.963366, 0.268191,
   0.962953, 0.269668, 0.962539, 0.271145,
   0.962121, 0.272621, 0.961702, 0.274097,
   0.961281, 0.275572, 0.960857, 0.277046,
   0.960431, 0.27852, 0.960002, 0.279993,
   0.959572, 0.281465, 0.959139, 0.282937,
   0.958704, 0.284408, 0.958266, 0.285878,
   0.957826, 0.287347, 0.957385, 0.288816,
   0.95694, 0.290285, 0.956494, 0.291752,
   0.956045, 0.293219, 0.955594, 0.294685,
   0.955141, 0.296151, 0.954686, 0.297616,
   0.954228, 0.29908, 0.953768, 0.300543,
   0.953306, 0.302006, 0.952842, 0.303468,
   0.952375, 0.304929, 0.951906, 0.30639,
   0.951435, 0.30785, 0.950962, 0.309309,
   0.950486, 0.310767, 0.950008, 0.312225,
   0.949528, 0.313682, 0.949046, 0.315138,
   0.948561, 0.316593, 0.948075, 0.318048,
   0.947586, 0.319502, 0.947094, 0.320955,
   0.946601, 0.322408, 0.946105, 0.323859,
   0.945607, 0.32531, 0.945107, 0.326761,
   0.944605, 0.32821, 0.9441, 0.329658,
   0.943594, 0.331106, 0.943085, 0.332553,
   0.942573, 0.334, 0.94206, 0.335445,
   0.941544, 0.33689, 0.941026, 0.338334,
   0.940506, 0.339777, 0.939984, 0.341219,
   0.939459, 0.342661, 0.938933, 0.344101,
   0.938404, 0.345541, 0.937872, 0.34698,
   0.937339, 0.348419, 0.936804, 0.349856,
   0.936266, 0.351293, 0.935726, 0.352729,
   0.935184, 0.354164, 0.934639, 0.355598,
   0.934093, 0.357031, 0.933544, 0.358463,
   0.932993, 0.359895, 0.93244, 0.361326,
   0.931884, 0.362756, 0.931327, 0.364185,
   0.930767, 0.365613, 0.930205, 0.36704,
   0.929641, 0.368467, 0.929075, 0.369892,
   0.928506, 0.371317, 0.927935, 0.372741,
   0.927363, 0.374164, 0.926788, 0.375586,
   0.92621, 0.377007, 0.925631, 0.378428,
   0.925049, 0.379847, 0.924465, 0.381266,
   0.92388, 0.382683, 0.923291, 0.3841,
   0.922701, 0.385516, 0.922109, 0.386931,
   0.921514, 0.388345, 0.920917, 0.389758,
   0.920318, 0.39117, 0.919717, 0.392582,
   0.919114, 0.393992, 0.918508, 0.395402,
   0.917901, 0.39681, 0.917291, 0.398218,
   0.916679, 0.399624, 0.916065, 0.40103,
   0.915449, 0.402435, 0.91483, 0.403838,
   0.91421, 0.405241, 0.913587, 0.406643,
   0.912962, 0.408044, 0.912335, 0.409444,
   0.911706, 0.410843, 0.911075, 0.412241,
   0.910441, 0.413638, 0.909806, 0.415034,
   0.909168, 0.41643, 0.908528, 0.417824,
   0.907886, 0.419217, 0.907242, 0.420609,
   0.906596, 0.422, 0.905947, 0.423391,
   0.905297, 0.42478, 0.904644, 0.426168,
   0.903989, 0.427555, 0.903332, 0.428941,
   0.902673, 0.430326, 0.902012, 0.431711,
   0.901349, 0.433094, 0.900684, 0.434476,
   0.900016, 0.435857, 0.899346, 0.437237,
   0.898675, 0.438616, 0.898001, 0.439994,
   0.897325, 0.441371, 0.896646, 0.442747,
   0.895966, 0.444122, 0.895284, 0.445496,
   0.894599, 0.446869, 0.893913, 0.448241,
   0.893224, 0.449611, 0.892534, 0.450981,
   0.891841, 0.45235, 0.891146, 0.453717,
   0.890449, 0.455084, 0.88975, 0.456449,
   0.889048, 0.457813, 0.888345, 0.459177,
   0.88764, 0.460539, 0.886932, 0.4619,
   0.886223, 0.46326, 0.885511, 0.464619,
   0.884797, 0.465977, 0.884081, 0.467333,
   0.883363, 0.468689, 0.882643, 0.470043,
   0.881921, 0.471397, 0.881197, 0.472749,
   0.880471, 0.4741, 0.879743, 0.47545,
   0.879012, 0.476799, 0.87828, 0.478147,
   0.877545, 0.479494, 0.876809, 0.480839,
   0.87607, 0.482184, 0.875329, 0.483527,
   0.874587, 0.484869, 0.873842, 0.48621,
   0.873095, 0.48755, 0.872346, 0.488889,
   0.871595, 0.490226, 0.870842, 0.491563,
   0.870087, 0.492898, 0.86933, 0.494232,
   0.868571, 0.495565, 0.867809, 0.496897,
   0.867046, 0.498228, 0.866281, 0.499557,
   0.865514, 0.500885, 0.864744, 0.502213,
   0.863973, 0.503538, 0.863199, 0.504863,
   0.862424, 0.506187, 0.861646, 0.507509,
   0.860867, 0.50883, 0.860085, 0.51015,
   0.859302, 0.511469, 0.858516, 0.512786,
   0.857729, 0.514103, 0.856939, 0.515418,
   0.856147, 0.516732, 0.855354, 0.518044,
   0.854558, 0.519356, 0.85376, 0.520666,
   0.852961, 0.521975, 0.852159, 0.523283,
   0.851355, 0.52459, 0.85055, 0.525895,
   0.849742, 0.527199, 0.848932, 0.528502,
   0.84812, 0.529804, 0.847307, 0.531104,
   0.846491, 0.532403, 0.845673, 0.533701,
   0.844854, 0.534998, 0.844032, 0.536293,
   0.843208, 0.537587, 0.842383, 0.53888,
   0.841555, 0.540172, 0.840725, 0.541462,
   0.839894, 0.542751, 0.83906, 0.544038,
   0.838225, 0.545325, 0.837387, 0.54661,
   0.836548, 0.547894, 0.835706, 0.549177,
   0.834863, 0.550458, 0.834018, 0.551738,
   0.83317, 0.553017, 0.832321, 0.554294,
   0.83147, 0.55557, 0.830616, 0.556845,
   0.829761, 0.558119, 0.828904, 0.559391,
   0.828045, 0.560662, 0.827184, 0.561931,
   0.826321, 0.563199, 0.825456, 0.564466,
   0.824589, 0.565732, 0.823721, 0.566996,
   0.82285, 0.568259, 0.821977, 0.56952,
   0.821103, 0.570781, 0.820226, 0.57204,
   0.819348, 0.573297, 0.818467, 0.574553,
   0.817585, 0.575808, 0.816701, 0.577062,
   0.815814, 0.578314, 0.814926, 0.579565,
   0.814036, 0.580814, 0.813144, 0.582062,
   0.812251, 0.583309, 0.811355, 0.584554,
   0.810457, 0.585798, 0.809558, 0.58704,
   0.808656, 0.588282, 0.807753, 0.589521,
   0.806848, 0.59076, 0.80594, 0.591997,
   0.805031, 0.593232, 0.80412, 0.594467,
   0.803208, 0.595699, 0.802293, 0.596931,
   0.801376, 0.598161, 0.800458, 0.599389,
   0.799537, 0.600617, 0.798615, 0.601842,
   0.797691, 0.603067, 0.796765, 0.60429,
   0.795837, 0.605511, 0.794907, 0.606731,
   0.793975, 0.60795, 0.793042, 0.609167,
   0.792107, 0.610383, 0.791169, 0.611597,
   0.79023, 0.61281, 0.789289, 0.614022,
   0.788346, 0.615232, 0.787402, 0.61644,
   0.786455, 0.617647, 0.785507, 0.618853,
   0.784557, 0.620057, 0.783605, 0.62126,
   0.782651, 0.622461, 0.781695, 0.623661,
   0.780737, 0.62486, 0.779778, 0.626056,
   0.778816, 0.627252, 0.777853, 0.628446,
   0.776888, 0.629638, 0.775922, 0.630829,
   0.774953, 0.632019, 0.773983, 0.633207,
   0.77301, 0.634393, 0.772036, 0.635578,
   0.77106, 0.636762, 0.770083, 0.637944,
   0.769103, 0.639125, 0.768122, 0.640304,
   0.767139, 0.641481, 0.766154, 0.642657,
   0.765167, 0.643832, 0.764179, 0.645005,
   0.763188, 0.646176, 0.762196, 0.647346,
   0.761202, 0.648514, 0.760207, 0.649681,
   0.759209, 0.650847, 0.75821, 0.652011,
   0.757209, 0.653173, 0.756206, 0.654334,
   0.755201, 0.655493, 0.754195, 0.656651,
   0.753187, 0.657807, 0.752177, 0.658961,
   0.751165, 0.660114, 0.750152, 0.661266,
   0.749136, 0.662416, 0.748119, 0.663564,
   0.747101, 0.664711, 0.74608, 0.665856,
   0.745058, 0.667, 0.744034, 0.668142,
   0.743008, 0.669283, 0.74198, 0.670422,
   0.740951, 0.671559, 0.73992, 0.672695,
   0.738887, 0.673829, 0.737853, 0.674962,
   0.736817, 0.676093, 0.735779, 0.677222,
   0.734739, 0.67835, 0.733697, 0.679476,
   0.732654, 0.680601, 0.731609, 0.681724,
   0.730563, 0.682845, 0.729514, 0.683965,
   0.728464, 0.685084, 0.727413, 0.6862,
   0.726359, 0.687315, 0.725304, 0.688429,
   0.724247, 0.689541, 0.723188, 0.690651,
   0.722128, 0.691759, 0.721066, 0.692866,
   0.720003, 0.693971, 0.718937, 0.695075,
   0.71787, 0.696177, 0.716801, 0.697277,
   0.715731, 0.698376, 0.714659, 0.699473,
   0.713585, 0.700569, 0.712509, 0.701663,
   0.711432, 0.702755, 0.710353, 0.703845,
   0.709273, 0.704934, 0.708191, 0.706021,
   0.707107, 0.707107, 0.706021, 0.708191,
   0.704934, 0.709273, 0.703845, 0.710353,
   0.702755, 0.711432, 0.701663, 0.712509,
   0.700569, 0.713585, 0.699473, 0.714659,
   0.698376, 0.715731, 0.697277, 0.716801,
   0.696177, 0.71787, 0.695075, 0.718937,
   0.693971, 0.720003, 0.692866, 0.721066,
   0.691759, 0.722128, 0.690651, 0.723188,
   0.689541, 0.724247, 0.688429, 0.725304,
   0.687315, 0.726359, 0.6862, 0.727413,
   0.685084, 0.728464, 0.683965, 0.729514,
   0.682845, 0.730563, 0.681724, 0.731609,
   0.680601, 0.732654, 0.679476, 0.733697,
   0.67835, 0.734739, 0.677222, 0.735779,
   0.676093, 0.736817, 0.674962, 0.737853,
   0.673829, 0.738887, 0.672695, 0.73992,
   0.671559, 0.740951, 0.670422, 0.74198,
   0.669283, 0.743008, 0.668142, 0.744034,
   0.667, 0.745058, 0.665856, 0.74608,
   0.664711, 0.747101, 0.663564, 0.748119,
   0.662416, 0.749136, 0.661266, 0.750152,
   0.660114, 0.751165, 0.658961, 0.752177,
   0.657807, 0.753187, 0.656651, 0.754195,
   0.655493, 0.755201, 0.654334, 0.756206,
   0.653173, 0.757209, 0.652011, 0.75821,
   0.650847, 0.759209, 0.649681, 0.760207,
   0.648514, 0.761202, 0.647346, 0.762196,
   0.646176, 0.763188, 0.645005, 0.764179,
   0.643832, 0.765167, 0.642657, 0.766154,
   0.641481, 0.767139, 0.640304, 0.768122,
   0.639125, 0.769103, 0.637944, 0.770083,
   0.636762, 0.77106, 0.635578, 0.772036,
   0.634393, 0.77301, 0.633207, 0.773983,
   0.632019, 0.774953, 0.630829, 0.775922,
   0.629638, 0.776888, 0.628446, 0.777853,
   0.627252, 0.778816, 0.626056, 0.779778,
   0.62486, 0.780737, 0.623661, 0.781695,
   0.622461, 0.782651, 0.62126, 0.783605,
   0.620057, 0.784557, 0.618853, 0.785507,
   0.617647, 0.786455, 0.61644, 0.787402,
   0.615232, 0.788346, 0.614022, 0.789289,
   0.61281, 0.79023, 0.611597, 0.791169,
   0.610383, 0.792107, 0.609167, 0.793042,
   0.60795, 0.793975, 0.606731, 0.794907,
   0.605511, 0.795837, 0.60429, 0.796765,
   0.603067, 0.797691, 0.601842, 0.798615,
   0.600617, 0.799537, 0.599389, 0.800458,
   0.598161, 0.801376, 0.596931, 0.802293,
   0.595699, 0.803208, 0.594467, 0.80412,
   0.593232, 0.805031, 0.591997, 0.80594,
   0.59076, 0.806848, 0.589521, 0.807753,
   0.588282, 0.808656, 0.58704, 0.809558,
   0.585798, 0.810457, 0.584554, 0.811355,
   0.583309, 0.812251, 0.582062, 0.813144,
   0.580814, 0.814036, 0.579565, 0.814926,
   0.578314, 0.815814, 0.577062, 0.816701,
   0.575808, 0.817585, 0.574553, 0.818467,
   0.573297, 0.819348, 0.57204, 0.820226,
   0.570781, 0.821103, 0.56952, 0.821977,
   0.568259, 0.82285, 0.566996, 0.823721,
   0.565732, 0.824589, 0.564466, 0.825456,
   0.563199, 0.826321, 0.561931, 0.827184,
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   -0.953306, 0.302006, -0.953768, 0.300543,
   -0.954228, 0.29908, -0.954686, 0.297616,
   -0.955141, 0.296151, -0.955594, 0.294685,
   -0.956045, 0.293219, -0.956494, 0.291752,
   -0.95694, 0.290285, -0.957385, 0.288816,
   -0.957826, 0.287347, -0.958266, 0.285878,
   -0.958704, 0.284408, -0.959139, 0.282937,
   -0.959572, 0.281465, -0.960002, 0.279993,
   -0.960431, 0.27852, -0.960857, 0.277046,
   -0.961281, 0.275572, -0.961702, 0.274097,
   -0.962121, 0.272621, -0.962539, 0.271145,
   -0.962953, 0.269668, -0.963366, 0.268191,
   -0.963776, 0.266713, -0.964184, 0.265234,
   -0.96459, 0.263755, -0.964993, 0.262275,
   -0.965395, 0.260794, -0.965793, 0.259313,
   -0.96619, 0.257831, -0.966584, 0.256349,
   -0.966977, 0.254866, -0.967366, 0.253382,
   -0.967754, 0.251898, -0.968139, 0.250413,
   -0.968522, 0.248928, -0.968903, 0.247442,
   -0.969281, 0.245955, -0.969657, 0.244468,
   -0.970031, 0.24298, -0.970403, 0.241492,
   -0.970772, 0.240003, -0.971139, 0.238514,
   -0.971504, 0.237024, -0.971866, 0.235533,
   -0.972227, 0.234042, -0.972584, 0.23255,
   -0.97294, 0.231058, -0.973293, 0.229565,
   -0.973644, 0.228072, -0.973993, 0.226578,
   -0.974339, 0.225084, -0.974684, 0.223589,
   -0.975025, 0.222094, -0.975365, 0.220598,
   -0.975702, 0.219101, -0.976037, 0.217604,
   -0.97637, 0.216107, -0.9767, 0.214609,
   -0.977028, 0.21311, -0.977354, 0.211611,
   -0.977677, 0.210112, -0.977999, 0.208612,
   -0.978318, 0.207111, -0.978634, 0.20561,
   -0.978948, 0.204109, -0.97926, 0.202607,
   -0.97957, 0.201105, -0.979877, 0.199602,
   -0.980182, 0.198098, -0.980485, 0.196595,
   -0.980785, 0.19509, -0.981084, 0.193586,
   -0.981379, 0.19208, -0.981673, 0.190575,
   -0.981964, 0.189069, -0.982253, 0.187562,
   -0.982539, 0.186055, -0.982824, 0.184548,
   -0.983106, 0.18304, -0.983385, 0.181532,
   -0.983662, 0.180023, -0.983938, 0.178514,
   -0.98421, 0.177004, -0.984481, 0.175494,
   -0.984749, 0.173984, -0.985014, 0.172473,
   -0.985278, 0.170962, -0.985539, 0.16945,
   -0.985798, 0.167938, -0.986054, 0.166426,
   -0.986308, 0.164913, -0.98656, 0.1634,
   -0.986809, 0.161886, -0.987057, 0.160372,
   -0.987302, 0.158858, -0.987544, 0.157343,
   -0.987784, 0.155828, -0.988022, 0.154313,
   -0.988258, 0.152797, -0.988491, 0.151281,
   -0.988722, 0.149765, -0.98895, 0.148248,
   -0.989177, 0.14673, -0.989401, 0.145213,
   -0.989622, 0.143695, -0.989841, 0.142177,
   -0.990058, 0.140658, -0.990273, 0.139139,
   -0.990485, 0.13762, -0.990695, 0.136101,
   -0.990903, 0.134581, -0.991108, 0.133061,
   -0.991311, 0.13154, -0.991511, 0.130019,
   -0.99171, 0.128498, -0.991906, 0.126977,
   -0.992099, 0.125455, -0.992291, 0.123933,
   -0.99248, 0.122411, -0.992666, 0.120888,
   -0.99285, 0.119365, -0.993032, 0.117842,
   -0.993212, 0.116319, -0.993389, 0.114795,
   -0.993564, 0.113271, -0.993737, 0.111747,
   -0.993907, 0.110222, -0.994075, 0.108697,
   -0.994241, 0.107172, -0.994404, 0.105647,
   -0.994565, 0.104122, -0.994723, 0.102596,
   -0.994879, 0.10107, -0.995033, 0.0995436,
   -0.995185, 0.0980171, -0.995334, 0.0964904,
   -0.995481, 0.0949635, -0.995625, 0.0934363,
   -0.995768, 0.091909, -0.995907, 0.0903814,
   -0.996045, 0.0888535, -0.99618, 0.0873255,
   -0.996313, 0.0857973, -0.996443, 0.0842689,
   -0.996571, 0.0827403, -0.996697, 0.0812114,
   -0.99682, 0.0796824, -0.996941, 0.0781532,
   -0.99706, 0.0766239, -0.997176, 0.0750943,
   -0.99729, 0.0735646, -0.997402, 0.0720346,
   -0.997512, 0.0705046, -0.997619, 0.0689743,
   -0.997723, 0.0674439, -0.997825, 0.0659134,
   -0.997925, 0.0643826, -0.998023, 0.0628518,
   -0.998118, 0.0613207, -0.998211, 0.0597896,
   -0.998302, 0.0582583, -0.99839, 0.0567268,
   -0.998476, 0.0551952, -0.998559, 0.0536635,
   -0.99864, 0.0521317, -0.998719, 0.0505997,
   -0.998796, 0.0490677, -0.99887, 0.0475355,
   -0.998941, 0.0460032, -0.999011, 0.0444708,
   -0.999078, 0.0429383, -0.999142, 0.0414056,
   -0.999205, 0.0398729, -0.999265, 0.0383401,
   -0.999322, 0.0368072, -0.999378, 0.0352742,
   -0.999431, 0.0337412, -0.999481, 0.032208,
   -0.999529, 0.0306748, -0.999575, 0.0291415,
   -0.999619, 0.0276081, -0.99966, 0.0260747,
   -0.999699, 0.0245412, -0.999735, 0.0230077,
   -0.999769, 0.0214741, -0.999801, 0.0199404,
   -0.999831, 0.0184067, -0.999858, 0.016873,
   -0.999882, 0.0153392, -0.999905, 0.0138054,
   -0.999925, 0.0122715, -0.999942, 0.0107377,
   -0.999958, 0.00920376, -0.999971, 0.00766983,
   -0.999981, 0.00613589, -0.999989, 0.00460193,
   -0.999995, 0.00306796, -0.999999, 0.00153398,
   -1.0, 0.0};
  float Tre, Tim;
  int i, j, k, l, m;

   m = 2048;
   l = 1;
   while(1)
   { 
      k = 0;
      j = l;
      i = 0;
      while(1)
      { 
         while(1)
	 {
	   /* W[i+k] = Z[i] + Z[m+i]; complex */
           W[2*(i+k)]   = Z[2*i]   + Z[2*(m+i)];
           W[2*(i+k)+1] = Z[2*i+1] + Z[2*(m+i)+1];

           /* W[i+j] = E[k] * (Z[i] - Z[m+i]); complex */
           Tre = Z[2*i]   - Z[2*(m+i)];
           Tim = Z[2*i+1] - Z[2*(m+i)+1];
           W[2*(i+j)]   = E[2*k] * Tre - E[2*k+1] * Tim;
           W[2*(i+j)+1] = E[2*k] * Tim + E[2*k+1] * Tre; 
           i++;
           if(i >= j) break;
	 }
         k = j;
         j = k+l;
         if(j > m) break;
      }
      l = l+l;
                  /* work back other way without copying */
      k = 0;
      j = l;
      i = 0;
      while(1)
      {
        while(1)
	{
          /* Z[i+k] = W[i] + W[m+i]; complex */
          Z[2*(i+k)]   = W[2*i]   + W[2*(m+i)];
          Z[2*(i+k)+1] = W[2*i+1] + W[2*(m+i)+1];

          /* Z[i+j] = E[k] * (W[i] - W[m+i]); complex */
          Tre = W[2*i]   - W[2*(m+i)];
          Tim = W[2*i+1] - W[2*(m+i)+1];
          Z[2*(i+j)]   = E[2*k] * Tre - E[2*k+1] * Tim;
          Z[2*(i+j)+1] = E[2*k] * Tim + E[2*k+1] * Tre;
          i++;
          if(i >= j) break;
	}
        k = j;
        j = k+l;
        if(j > m) break;
      }
      l = l+l;
      if(l > m) break; // result is in Z
   }
} /* end fft4096 */