/* fft2048.c  complex data stored  re, im, re, im, re, ... im */

void fft2048(float Z[4096]) /* input data points and output  [0] to [4095] */
{
  static float W[4096];    /* scratch vector, used many times, */
  static float E[2050] =   /* constants for FFT algorithm */
  {1.0, 0.0, 0.999995, 0.00306796,
   0.999981, 0.00613589, 0.999958, 0.00920376,
   0.999925, 0.0122715, 0.999882, 0.0153392,
   0.999831, 0.0184067, 0.999769, 0.0214741,
   0.999699, 0.0245412, 0.999619, 0.0276081,
   0.999529, 0.0306748, 0.999431, 0.0337412,
   0.999322, 0.0368072, 0.999205, 0.0398729,
   0.999078, 0.0429383, 0.998941, 0.0460032,
   0.998796, 0.0490677, 0.99864, 0.0521317,
   0.998476, 0.0551952, 0.998302, 0.0582583,
   0.998118, 0.0613207, 0.997925, 0.0643826,
   0.997723, 0.0674439, 0.997512, 0.0705046,
   0.99729, 0.0735646, 0.99706, 0.0766239,
   0.99682, 0.0796824, 0.996571, 0.0827403,
   0.996313, 0.0857973, 0.996045, 0.0888535,
   0.995768, 0.091909, 0.995481, 0.0949635,
   0.995185, 0.0980171, 0.994879, 0.10107,
   0.994565, 0.104122, 0.994241, 0.107172,
   0.993907, 0.110222, 0.993564, 0.113271,
   0.993212, 0.116319, 0.99285, 0.119365,
   0.99248, 0.122411, 0.992099, 0.125455,
   0.99171, 0.128498, 0.991311, 0.13154,
   0.990903, 0.134581, 0.990485, 0.13762,
   0.990058, 0.140658, 0.989622, 0.143695,
   0.989177, 0.14673, 0.988722, 0.149765,
   0.988258, 0.152797, 0.987784, 0.155828,
   0.987302, 0.158858, 0.986809, 0.161886,
   0.986308, 0.164913, 0.985798, 0.167938,
   0.985278, 0.170962, 0.984749, 0.173984,
   0.98421, 0.177004, 0.983662, 0.180023,
   0.983106, 0.18304, 0.982539, 0.186055,
   0.981964, 0.189069, 0.981379, 0.19208,
   0.980785, 0.19509, 0.980182, 0.198098,
   0.97957, 0.201105, 0.978948, 0.204109,
   0.978318, 0.207111, 0.977677, 0.210112,
   0.977028, 0.21311, 0.97637, 0.216107,
   0.975702, 0.219101, 0.975025, 0.222094,
   0.974339, 0.225084, 0.973644, 0.228072,
   0.97294, 0.231058, 0.972227, 0.234042,
   0.971504, 0.237024, 0.970772, 0.240003,
   0.970031, 0.24298, 0.969281, 0.245955,
   0.968522, 0.248928, 0.967754, 0.251898,
   0.966977, 0.254866, 0.96619, 0.257831,
   0.965395, 0.260794, 0.96459, 0.263755,
   0.963776, 0.266713, 0.962953, 0.269668,
   0.962121, 0.272621, 0.961281, 0.275572,
   0.960431, 0.27852, 0.959572, 0.281465,
   0.958704, 0.284408, 0.957826, 0.287347,
   0.95694, 0.290285, 0.956045, 0.293219,
   0.955141, 0.296151, 0.954228, 0.29908,
   0.953306, 0.302006, 0.952375, 0.304929,
   0.951435, 0.30785, 0.950486, 0.310767,
   0.949528, 0.313682, 0.948561, 0.316593,
   0.947586, 0.319502, 0.946601, 0.322408,
   0.945607, 0.32531, 0.944605, 0.32821,
   0.943594, 0.331106, 0.942573, 0.334,
   0.941544, 0.33689, 0.940506, 0.339777,
   0.939459, 0.342661, 0.938404, 0.345541,
   0.937339, 0.348419, 0.936266, 0.351293,
   0.935184, 0.354164, 0.934093, 0.357031,
   0.932993, 0.359895, 0.931884, 0.362756,
   0.930767, 0.365613, 0.929641, 0.368467,
   0.928506, 0.371317, 0.927363, 0.374164,
   0.92621, 0.377007, 0.925049, 0.379847,
   0.92388, 0.382683, 0.922701, 0.385516,
   0.921514, 0.388345, 0.920318, 0.39117,
   0.919114, 0.393992, 0.917901, 0.39681,
   0.916679, 0.399624, 0.915449, 0.402435,
   0.91421, 0.405241, 0.912962, 0.408044,
   0.911706, 0.410843, 0.910441, 0.413638,
   0.909168, 0.41643, 0.907886, 0.419217,
   0.906596, 0.422, 0.905297, 0.42478,
   0.903989, 0.427555, 0.902673, 0.430326,
   0.901349, 0.433094, 0.900016, 0.435857,
   0.898675, 0.438616, 0.897325, 0.441371,
   0.895966, 0.444122, 0.894599, 0.446869,
   0.893224, 0.449611, 0.891841, 0.45235,
   0.890449, 0.455084, 0.889048, 0.457813,
   0.88764, 0.460539, 0.886223, 0.46326,
   0.884797, 0.465977, 0.883363, 0.468689,
   0.881921, 0.471397, 0.880471, 0.4741,
   0.879012, 0.476799, 0.877545, 0.479494,
   0.87607, 0.482184, 0.874587, 0.484869,
   0.873095, 0.48755, 0.871595, 0.490226,
   0.870087, 0.492898, 0.868571, 0.495565,
   0.867046, 0.498228, 0.865514, 0.500885,
   0.863973, 0.503538, 0.862424, 0.506187,
   0.860867, 0.50883, 0.859302, 0.511469,
   0.857729, 0.514103, 0.856147, 0.516732,
   0.854558, 0.519356, 0.852961, 0.521975,
   0.851355, 0.52459, 0.849742, 0.527199,
   0.84812, 0.529804, 0.846491, 0.532403,
   0.844854, 0.534998, 0.843208, 0.537587,
   0.841555, 0.540172, 0.839894, 0.542751,
   0.838225, 0.545325, 0.836548, 0.547894,
   0.834863, 0.550458, 0.83317, 0.553017,
   0.83147, 0.55557, 0.829761, 0.558119,
   0.828045, 0.560662, 0.826321, 0.563199,
   0.824589, 0.565732, 0.82285, 0.568259,
   0.821103, 0.570781, 0.819348, 0.573297,
   0.817585, 0.575808, 0.815814, 0.578314,
   0.814036, 0.580814, 0.812251, 0.583309,
   0.810457, 0.585798, 0.808656, 0.588282,
   0.806848, 0.59076, 0.805031, 0.593232,
   0.803208, 0.595699, 0.801376, 0.598161,
   0.799537, 0.600617, 0.797691, 0.603067,
   0.795837, 0.605511, 0.793975, 0.60795,
   0.792107, 0.610383, 0.79023, 0.61281,
   0.788346, 0.615232, 0.786455, 0.617647,
   0.784557, 0.620057, 0.782651, 0.622461,
   0.780737, 0.62486, 0.778816, 0.627252,
   0.776888, 0.629638, 0.774953, 0.632019,
   0.77301, 0.634393, 0.77106, 0.636762,
   0.769103, 0.639125, 0.767139, 0.641481,
   0.765167, 0.643832, 0.763188, 0.646176,
   0.761202, 0.648514, 0.759209, 0.650847,
   0.757209, 0.653173, 0.755201, 0.655493,
   0.753187, 0.657807, 0.751165, 0.660114,
   0.749136, 0.662416, 0.747101, 0.664711,
   0.745058, 0.667, 0.743008, 0.669283,
   0.740951, 0.671559, 0.738887, 0.673829,
   0.736817, 0.676093, 0.734739, 0.67835,
   0.732654, 0.680601, 0.730563, 0.682845,
   0.728464, 0.685084, 0.726359, 0.687315,
   0.724247, 0.689541, 0.722128, 0.691759,
   0.720003, 0.693971, 0.71787, 0.696177,
   0.715731, 0.698376, 0.713585, 0.700569,
   0.711432, 0.702755, 0.709273, 0.704934,
   0.707107, 0.707107, 0.704934, 0.709273,
   0.702755, 0.711432, 0.700569, 0.713585,
   0.698376, 0.715731, 0.696177, 0.71787,
   0.693971, 0.720003, 0.691759, 0.722128,
   0.689541, 0.724247, 0.687315, 0.726359,
   0.685084, 0.728464, 0.682845, 0.730563,
   0.680601, 0.732654, 0.67835, 0.734739,
   0.676093, 0.736817, 0.673829, 0.738887,
   0.671559, 0.740951, 0.669283, 0.743008,
   0.667, 0.745058, 0.664711, 0.747101,
   0.662416, 0.749136, 0.660114, 0.751165,
   0.657807, 0.753187, 0.655493, 0.755201,
   0.653173, 0.757209, 0.650847, 0.759209,
   0.648514, 0.761202, 0.646176, 0.763188,
   0.643832, 0.765167, 0.641481, 0.767139,
   0.639125, 0.769103, 0.636762, 0.77106,
   0.634393, 0.77301, 0.632019, 0.774953,
   0.629638, 0.776888, 0.627252, 0.778816,
   0.62486, 0.780737, 0.622461, 0.782651,
   0.620057, 0.784557, 0.617647, 0.786455,
   0.615232, 0.788346, 0.61281, 0.79023,
   0.610383, 0.792107, 0.60795, 0.793975,
   0.605511, 0.795837, 0.603067, 0.797691,
   0.600617, 0.799537, 0.598161, 0.801376,
   0.595699, 0.803208, 0.593232, 0.805031,
   0.59076, 0.806848, 0.588282, 0.808656,
   0.585798, 0.810457, 0.583309, 0.812251,
   0.580814, 0.814036, 0.578314, 0.815814,
   0.575808, 0.817585, 0.573297, 0.819348,
   0.570781, 0.821103, 0.568259, 0.82285,
   0.565732, 0.824589, 0.563199, 0.826321,
   0.560662, 0.828045, 0.558119, 0.829761,
   0.55557, 0.83147, 0.553017, 0.83317,
   0.550458, 0.834863, 0.547894, 0.836548,
   0.545325, 0.838225, 0.542751, 0.839894,
   0.540172, 0.841555, 0.537587, 0.843208,
   0.534998, 0.844854, 0.532403, 0.846491,
   0.529804, 0.84812, 0.527199, 0.849742,
   0.52459, 0.851355, 0.521975, 0.852961,
   0.519356, 0.854558, 0.516732, 0.856147,
   0.514103, 0.857729, 0.511469, 0.859302,
   0.50883, 0.860867, 0.506187, 0.862424,
   0.503538, 0.863973, 0.500885, 0.865514,
   0.498228, 0.867046, 0.495565, 0.868571,
   0.492898, 0.870087, 0.490226, 0.871595,
   0.48755, 0.873095, 0.484869, 0.874587,
   0.482184, 0.87607, 0.479494, 0.877545,
   0.476799, 0.879012, 0.4741, 0.880471,
   0.471397, 0.881921, 0.468689, 0.883363,
   0.465977, 0.884797, 0.46326, 0.886223,
   0.460539, 0.88764, 0.457813, 0.889048,
   0.455084, 0.890449, 0.45235, 0.891841,
   0.449611, 0.893224, 0.446869, 0.894599,
   0.444122, 0.895966, 0.441371, 0.897325,
   0.438616, 0.898675, 0.435857, 0.900016,
   0.433094, 0.901349, 0.430326, 0.902673,
   0.427555, 0.903989, 0.42478, 0.905297,
   0.422, 0.906596, 0.419217, 0.907886,
   0.41643, 0.909168, 0.413638, 0.910441,
   0.410843, 0.911706, 0.408044, 0.912962,
   0.405241, 0.91421, 0.402435, 0.915449,
   0.399624, 0.916679, 0.39681, 0.917901,
   0.393992, 0.919114, 0.39117, 0.920318,
   0.388345, 0.921514, 0.385516, 0.922701,
   0.382683, 0.92388, 0.379847, 0.925049,
   0.377007, 0.92621, 0.374164, 0.927363,
   0.371317, 0.928506, 0.368467, 0.929641,
   0.365613, 0.930767, 0.362756, 0.931884,
   0.359895, 0.932993, 0.357031, 0.934093,
   0.354164, 0.935184, 0.351293, 0.936266,
   0.348419, 0.937339, 0.345541, 0.938404,
   0.342661, 0.939459, 0.339777, 0.940506,
   0.33689, 0.941544, 0.334, 0.942573,
   0.331106, 0.943594, 0.32821, 0.944605,
   0.32531, 0.945607, 0.322408, 0.946601,
   0.319502, 0.947586, 0.316593, 0.948561,
   0.313682, 0.949528, 0.310767, 0.950486,
   0.30785, 0.951435, 0.304929, 0.952375,
   0.302006, 0.953306, 0.29908, 0.954228,
   0.296151, 0.955141, 0.293219, 0.956045,
   0.290285, 0.95694, 0.287347, 0.957826,
   0.284408, 0.958704, 0.281465, 0.959572,
   0.27852, 0.960431, 0.275572, 0.961281,
   0.272621, 0.962121, 0.269668, 0.962953,
   0.266713, 0.963776, 0.263755, 0.96459,
   0.260794, 0.965395, 0.257831, 0.96619,
   0.254866, 0.966977, 0.251898, 0.967754,
   0.248928, 0.968522, 0.245955, 0.969281,
   0.24298, 0.970031, 0.240003, 0.970772,
   0.237024, 0.971504, 0.234042, 0.972227,
   0.231058, 0.97294, 0.228072, 0.973644,
   0.225084, 0.974339, 0.222094, 0.975025,
   0.219101, 0.975702, 0.216107, 0.97637,
   0.21311, 0.977028, 0.210112, 0.977677,
   0.207111, 0.978318, 0.204109, 0.978948,
   0.201105, 0.97957, 0.198098, 0.980182,
   0.19509, 0.980785, 0.19208, 0.981379,
   0.189069, 0.981964, 0.186055, 0.982539,
   0.18304, 0.983106, 0.180023, 0.983662,
   0.177004, 0.98421, 0.173984, 0.984749,
   0.170962, 0.985278, 0.167938, 0.985798,
   0.164913, 0.986308, 0.161886, 0.986809,
   0.158858, 0.987302, 0.155828, 0.987784,
   0.152797, 0.988258, 0.149765, 0.988722,
   0.14673, 0.989177, 0.143695, 0.989622,
   0.140658, 0.990058, 0.13762, 0.990485,
   0.134581, 0.990903, 0.13154, 0.991311,
   0.128498, 0.99171, 0.125455, 0.992099,
   0.122411, 0.99248, 0.119365, 0.99285,
   0.116319, 0.993212, 0.113271, 0.993564,
   0.110222, 0.993907, 0.107172, 0.994241,
   0.104122, 0.994565, 0.10107, 0.994879,
   0.0980171, 0.995185, 0.0949635, 0.995481,
   0.091909, 0.995768, 0.0888535, 0.996045,
   0.0857973, 0.996313, 0.0827403, 0.996571,
   0.0796824, 0.99682, 0.0766239, 0.99706,
   0.0735646, 0.99729, 0.0705046, 0.997512,
   0.0674439, 0.997723, 0.0643826, 0.997925,
   0.0613207, 0.998118, 0.0582583, 0.998302,
   0.0551952, 0.998476, 0.0521317, 0.99864,
   0.0490677, 0.998796, 0.0460032, 0.998941,
   0.0429383, 0.999078, 0.0398729, 0.999205,
   0.0368072, 0.999322, 0.0337412, 0.999431,
   0.0306748, 0.999529, 0.0276081, 0.999619,
   0.0245412, 0.999699, 0.0214741, 0.999769,
   0.0184067, 0.999831, 0.0153392, 0.999882,
   0.0122715, 0.999925, 0.00920376, 0.999958,
   0.00613589, 0.999981, 0.00306796, 0.999995,
   0.0, 1.0, -0.00306796, 0.999995,
   -0.00613589, 0.999981, -0.00920376, 0.999958,
   -0.0122715, 0.999925, -0.0153392, 0.999882,
   -0.0184067, 0.999831, -0.0214741, 0.999769,
   -0.0245412, 0.999699, -0.0276081, 0.999619,
   -0.0306748, 0.999529, -0.0337412, 0.999431,
   -0.0368072, 0.999322, -0.0398729, 0.999205,
   -0.0429383, 0.999078, -0.0460032, 0.998941,
   -0.0490677, 0.998796, -0.0521317, 0.99864,
   -0.0551952, 0.998476, -0.0582583, 0.998302,
   -0.0613207, 0.998118, -0.0643826, 0.997925,
   -0.0674439, 0.997723, -0.0705046, 0.997512,
   -0.0735646, 0.99729, -0.0766239, 0.99706,
   -0.0796824, 0.99682, -0.0827403, 0.996571,
   -0.0857973, 0.996313, -0.0888535, 0.996045,
   -0.091909, 0.995768, -0.0949635, 0.995481,
   -0.0980171, 0.995185, -0.10107, 0.994879,
   -0.104122, 0.994565, -0.107172, 0.994241,
   -0.110222, 0.993907, -0.113271, 0.993564,
   -0.116319, 0.993212, -0.119365, 0.99285,
   -0.122411, 0.99248, -0.125455, 0.992099,
   -0.128498, 0.99171, -0.13154, 0.991311,
   -0.134581, 0.990903, -0.13762, 0.990485,
   -0.140658, 0.990058, -0.143695, 0.989622,
   -0.14673, 0.989177, -0.149765, 0.988722,
   -0.152797, 0.988258, -0.155828, 0.987784,
   -0.158858, 0.987302, -0.161886, 0.986809,
   -0.164913, 0.986308, -0.167938, 0.985798,
   -0.170962, 0.985278, -0.173984, 0.984749,
   -0.177004, 0.98421, -0.180023, 0.983662,
   -0.18304, 0.983106, -0.186055, 0.982539,
   -0.189069, 0.981964, -0.19208, 0.981379,
   -0.19509, 0.980785, -0.198098, 0.980182,
   -0.201105, 0.97957, -0.204109, 0.978948,
   -0.207111, 0.978318, -0.210112, 0.977677,
   -0.21311, 0.977028, -0.216107, 0.97637,
   -0.219101, 0.975702, -0.222094, 0.975025,
   -0.225084, 0.974339, -0.228072, 0.973644,
   -0.231058, 0.97294, -0.234042, 0.972227,
   -0.237024, 0.971504, -0.240003, 0.970772,
   -0.24298, 0.970031, -0.245955, 0.969281,
   -0.248928, 0.968522, -0.251898, 0.967754,
   -0.254866, 0.966977, -0.257831, 0.96619,
   -0.260794, 0.965395, -0.263755, 0.96459,
   -0.266713, 0.963776, -0.269668, 0.962953,
   -0.272621, 0.962121, -0.275572, 0.961281,
   -0.27852, 0.960431, -0.281465, 0.959572,
   -0.284408, 0.958704, -0.287347, 0.957826,
   -0.290285, 0.95694, -0.293219, 0.956045,
   -0.296151, 0.955141, -0.29908, 0.954228,
   -0.302006, 0.953306, -0.304929, 0.952375,
   -0.30785, 0.951435, -0.310767, 0.950486,
   -0.313682, 0.949528, -0.316593, 0.948561,
   -0.319502, 0.947586, -0.322408, 0.946601,
   -0.32531, 0.945607, -0.32821, 0.944605,
   -0.331106, 0.943594, -0.334, 0.942573,
   -0.33689, 0.941544, -0.339777, 0.940506,
   -0.342661, 0.939459, -0.345541, 0.938404,
   -0.348419, 0.937339, -0.351293, 0.936266,
   -0.354164, 0.935184, -0.357031, 0.934093,
   -0.359895, 0.932993, -0.362756, 0.931884,
   -0.365613, 0.930767, -0.368467, 0.929641,
   -0.371317, 0.928506, -0.374164, 0.927363,
   -0.377007, 0.92621, -0.379847, 0.925049,
   -0.382683, 0.92388, -0.385516, 0.922701,
   -0.388345, 0.921514, -0.39117, 0.920318,
   -0.393992, 0.919114, -0.39681, 0.917901,
   -0.399624, 0.916679, -0.402435, 0.915449,
   -0.405241, 0.91421, -0.408044, 0.912962,
   -0.410843, 0.911706, -0.413638, 0.910441,
   -0.41643, 0.909168, -0.419217, 0.907886,
   -0.422, 0.906596, -0.42478, 0.905297,
   -0.427555, 0.903989, -0.430326, 0.902673,
   -0.433094, 0.901349, -0.435857, 0.900016,
   -0.438616, 0.898675, -0.441371, 0.897325,
   -0.444122, 0.895966, -0.446869, 0.894599,
   -0.449611, 0.893224, -0.45235, 0.891841,
   -0.455084, 0.890449, -0.457813, 0.889048,
   -0.460539, 0.88764, -0.46326, 0.886223,
   -0.465977, 0.884797, -0.468689, 0.883363,
   -0.471397, 0.881921, -0.4741, 0.880471,
   -0.476799, 0.879012, -0.479494, 0.877545,
   -0.482184, 0.87607, -0.484869, 0.874587,
   -0.48755, 0.873095, -0.490226, 0.871595,
   -0.492898, 0.870087, -0.495565, 0.868571,
   -0.498228, 0.867046, -0.500885, 0.865514,
   -0.503538, 0.863973, -0.506187, 0.862424,
   -0.50883, 0.860867, -0.511469, 0.859302,
   -0.514103, 0.857729, -0.516732, 0.856147,
   -0.519356, 0.854558, -0.521975, 0.852961,
   -0.52459, 0.851355, -0.527199, 0.849742,
   -0.529804, 0.84812, -0.532403, 0.846491,
   -0.534998, 0.844854, -0.537587, 0.843208,
   -0.540172, 0.841555, -0.542751, 0.839894,
   -0.545325, 0.838225, -0.547894, 0.836548,
   -0.550458, 0.834863, -0.553017, 0.83317,
   -0.55557, 0.83147, -0.558119, 0.829761,
   -0.560662, 0.828045, -0.563199, 0.826321,
   -0.565732, 0.824589, -0.568259, 0.82285,
   -0.570781, 0.821103, -0.573297, 0.819348,
   -0.575808, 0.817585, -0.578314, 0.815814,
   -0.580814, 0.814036, -0.583309, 0.812251,
   -0.585798, 0.810457, -0.588282, 0.808656,
   -0.59076, 0.806848, -0.593232, 0.805031,
   -0.595699, 0.803208, -0.598161, 0.801376,
   -0.600617, 0.799537, -0.603067, 0.797691,
   -0.605511, 0.795837, -0.60795, 0.793975,
   -0.610383, 0.792107, -0.61281, 0.79023,
   -0.615232, 0.788346, -0.617647, 0.786455,
   -0.620057, 0.784557, -0.622461, 0.782651,
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   -0.685084, 0.728464, -0.687315, 0.726359,
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   -0.693971, 0.720003, -0.696177, 0.71787,
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   -0.740951, 0.671559, -0.743008, 0.669283,
   -0.745058, 0.667, -0.747101, 0.664711,
   -0.749136, 0.662416, -0.751165, 0.660114,
   -0.753187, 0.657807, -0.755201, 0.655493,
   -0.757209, 0.653173, -0.759209, 0.650847,
   -0.761202, 0.648514, -0.763188, 0.646176,
   -0.765167, 0.643832, -0.767139, 0.641481,
   -0.769103, 0.639125, -0.77106, 0.636762,
   -0.77301, 0.634393, -0.774953, 0.632019,
   -0.776888, 0.629638, -0.778816, 0.627252,
   -0.780737, 0.62486, -0.782651, 0.622461,
   -0.784557, 0.620057, -0.786455, 0.617647,
   -0.788346, 0.615232, -0.79023, 0.61281,
   -0.792107, 0.610383, -0.793975, 0.60795,
   -0.795837, 0.605511, -0.797691, 0.603067,
   -0.799537, 0.600617, -0.801376, 0.598161,
   -0.803208, 0.595699, -0.805031, 0.593232,
   -0.806848, 0.59076, -0.808656, 0.588282,
   -0.810457, 0.585798, -0.812251, 0.583309,
   -0.814036, 0.580814, -0.815814, 0.578314,
   -0.817585, 0.575808, -0.819348, 0.573297,
   -0.821103, 0.570781, -0.82285, 0.568259,
   -0.824589, 0.565732, -0.826321, 0.563199,
   -0.828045, 0.560662, -0.829761, 0.558119,
   -0.83147, 0.55557, -0.83317, 0.553017,
   -0.834863, 0.550458, -0.836548, 0.547894,
   -0.838225, 0.545325, -0.839894, 0.542751,
   -0.841555, 0.540172, -0.843208, 0.537587,
   -0.844854, 0.534998, -0.846491, 0.532403,
   -0.84812, 0.529804, -0.849742, 0.527199,
   -0.851355, 0.52459, -0.852961, 0.521975,
   -0.854558, 0.519356, -0.856147, 0.516732,
   -0.857729, 0.514103, -0.859302, 0.511469,
   -0.860867, 0.50883, -0.862424, 0.506187,
   -0.863973, 0.503538, -0.865514, 0.500885,
   -0.867046, 0.498228, -0.868571, 0.495565,
   -0.870087, 0.492898, -0.871595, 0.490226,
   -0.873095, 0.48755, -0.874587, 0.484869,
   -0.87607, 0.482184, -0.877545, 0.479494,
   -0.879012, 0.476799, -0.880471, 0.4741,
   -0.881921, 0.471397, -0.883363, 0.468689,
   -0.884797, 0.465977, -0.886223, 0.46326,
   -0.88764, 0.460539, -0.889048, 0.457813,
   -0.890449, 0.455084, -0.891841, 0.45235,
   -0.893224, 0.449611, -0.894599, 0.446869,
   -0.895966, 0.444122, -0.897325, 0.441371,
   -0.898675, 0.438616, -0.900016, 0.435857,
   -0.901349, 0.433094, -0.902673, 0.430326,
   -0.903989, 0.427555, -0.905297, 0.42478,
   -0.906596, 0.422, -0.907886, 0.419217,
   -0.909168, 0.41643, -0.910441, 0.413638,
   -0.911706, 0.410843, -0.912962, 0.408044,
   -0.91421, 0.405241, -0.915449, 0.402435,
   -0.916679, 0.399624, -0.917901, 0.39681,
   -0.919114, 0.393992, -0.920318, 0.39117,
   -0.921514, 0.388345, -0.922701, 0.385516,
   -0.92388, 0.382683, -0.925049, 0.379847,
   -0.92621, 0.377007, -0.927363, 0.374164,
   -0.928506, 0.371317, -0.929641, 0.368467,
   -0.930767, 0.365613, -0.931884, 0.362756,
   -0.932993, 0.359895, -0.934093, 0.357031,
   -0.935184, 0.354164, -0.936266, 0.351293,
   -0.937339, 0.348419, -0.938404, 0.345541,
   -0.939459, 0.342661, -0.940506, 0.339777,
   -0.941544, 0.33689, -0.942573, 0.334,
   -0.943594, 0.331106, -0.944605, 0.32821,
   -0.945607, 0.32531, -0.946601, 0.322408,
   -0.947586, 0.319502, -0.948561, 0.316593,
   -0.949528, 0.313682, -0.950486, 0.310767,
   -0.951435, 0.30785, -0.952375, 0.304929,
   -0.953306, 0.302006, -0.954228, 0.29908,
   -0.955141, 0.296151, -0.956045, 0.293219,
   -0.95694, 0.290285, -0.957826, 0.287347,
   -0.958704, 0.284408, -0.959572, 0.281465,
   -0.960431, 0.27852, -0.961281, 0.275572,
   -0.962121, 0.272621, -0.962953, 0.269668,
   -0.963776, 0.266713, -0.96459, 0.263755,
   -0.965395, 0.260794, -0.96619, 0.257831,
   -0.966977, 0.254866, -0.967754, 0.251898,
   -0.968522, 0.248928, -0.969281, 0.245955,
   -0.970031, 0.24298, -0.970772, 0.240003,
   -0.971504, 0.237024, -0.972227, 0.234042,
   -0.97294, 0.231058, -0.973644, 0.228072,
   -0.974339, 0.225084, -0.975025, 0.222094,
   -0.975702, 0.219101, -0.97637, 0.216107,
   -0.977028, 0.21311, -0.977677, 0.210112,
   -0.978318, 0.207111, -0.978948, 0.204109,
   -0.97957, 0.201105, -0.980182, 0.198098,
   -0.980785, 0.19509, -0.981379, 0.19208,
   -0.981964, 0.189069, -0.982539, 0.186055,
   -0.983106, 0.18304, -0.983662, 0.180023,
   -0.98421, 0.177004, -0.984749, 0.173984,
   -0.985278, 0.170962, -0.985798, 0.167938,
   -0.986308, 0.164913, -0.986809, 0.161886,
   -0.987302, 0.158858, -0.987784, 0.155828,
   -0.988258, 0.152797, -0.988722, 0.149765,
   -0.989177, 0.14673, -0.989622, 0.143695,
   -0.990058, 0.140658, -0.990485, 0.13762,
   -0.990903, 0.134581, -0.991311, 0.13154,
   -0.99171, 0.128498, -0.992099, 0.125455,
   -0.99248, 0.122411, -0.99285, 0.119365,
   -0.993212, 0.116319, -0.993564, 0.113271,
   -0.993907, 0.110222, -0.994241, 0.107172,
   -0.994565, 0.104122, -0.994879, 0.10107,
   -0.995185, 0.0980171, -0.995481, 0.0949635,
   -0.995768, 0.091909, -0.996045, 0.0888535,
   -0.996313, 0.0857973, -0.996571, 0.0827403,
   -0.99682, 0.0796824, -0.99706, 0.0766239,
   -0.99729, 0.0735646, -0.997512, 0.0705046,
   -0.997723, 0.0674439, -0.997925, 0.0643826,
   -0.998118, 0.0613207, -0.998302, 0.0582583,
   -0.998476, 0.0551952, -0.99864, 0.0521317,
   -0.998796, 0.0490677, -0.998941, 0.0460032,
   -0.999078, 0.0429383, -0.999205, 0.0398729,
   -0.999322, 0.0368072, -0.999431, 0.0337412,
   -0.999529, 0.0306748, -0.999619, 0.0276081,
   -0.999699, 0.0245412, -0.999769, 0.0214741,
   -0.999831, 0.0184067, -0.999882, 0.0153392,
   -0.999925, 0.0122715, -0.999958, 0.00920376,
   -0.999981, 0.00613589, -0.999995, 0.00306796,
   -1.0, 0.0};
  float Tre, Tim;
  int i, j, k, l, m;

   m = 1024;
   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;
      if(l > m)
      {
        for(i=0; i<4*m; i++) Z[i] = W[i]; // odd power finish
        return;
      }
                  /* 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 fft2048 */