-- fft4096.adb
with Ada.Numerics.Complex_Types; use Ada.Numerics.Complex_Types;
with Complex_Arrays; use Complex_Arrays;

procedure fft4096(Z : in out Complex_Vector) is --  (0..4095)
  pragma Suppress(All_Checks);
  W: Complex_Vector(0..4095);  -- scratch vector, used many times
  E: Complex_Vector(0..2048) :=   -- 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),
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   (-0.910441, 0.413638), (-0.911075, 0.412241),
   (-0.911706, 0.410843), (-0.912335, 0.409444),
   (-0.912962, 0.408044), (-0.913587, 0.406643),
   (-0.91421, 0.405241), (-0.91483, 0.403838),
   (-0.915449, 0.402435), (-0.916065, 0.40103),
   (-0.916679, 0.399624), (-0.917291, 0.398218),
   (-0.917901, 0.39681), (-0.918508, 0.395402),
   (-0.919114, 0.393992), (-0.919717, 0.392582),
   (-0.920318, 0.39117), (-0.920917, 0.389758),
   (-0.921514, 0.388345), (-0.922109, 0.386931),
   (-0.922701, 0.385516), (-0.923291, 0.3841),
   (-0.92388, 0.382683), (-0.924465, 0.381266),
   (-0.925049, 0.379847), (-0.925631, 0.378428),
   (-0.92621, 0.377007), (-0.926788, 0.375586),
   (-0.927363, 0.374164), (-0.927935, 0.372741),
   (-0.928506, 0.371317), (-0.929075, 0.369892),
   (-0.929641, 0.368467), (-0.930205, 0.36704),
   (-0.930767, 0.365613), (-0.931327, 0.364185),
   (-0.931884, 0.362756), (-0.93244, 0.361326),
   (-0.932993, 0.359895), (-0.933544, 0.358463),
   (-0.934093, 0.357031), (-0.934639, 0.355598),
   (-0.935184, 0.354164), (-0.935726, 0.352729),
   (-0.936266, 0.351293), (-0.936804, 0.349856),
   (-0.937339, 0.348419), (-0.937872, 0.34698),
   (-0.938404, 0.345541), (-0.938933, 0.344101),
   (-0.939459, 0.342661), (-0.939984, 0.341219),
   (-0.940506, 0.339777), (-0.941026, 0.338334),
   (-0.941544, 0.33689), (-0.94206, 0.335445),
   (-0.942573, 0.334), (-0.943085, 0.332553),
   (-0.943594, 0.331106), (-0.9441, 0.329658),
   (-0.944605, 0.32821), (-0.945107, 0.326761),
   (-0.945607, 0.32531), (-0.946105, 0.323859),
   (-0.946601, 0.322408), (-0.947094, 0.320955),
   (-0.947586, 0.319502), (-0.948075, 0.318048),
   (-0.948561, 0.316593), (-0.949046, 0.315138),
   (-0.949528, 0.313682), (-0.950008, 0.312225),
   (-0.950486, 0.310767), (-0.950962, 0.309309),
   (-0.951435, 0.30785), (-0.951906, 0.30639),
   (-0.952375, 0.304929), (-0.952842, 0.303468),
   (-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));
  I, J, K, L, M : Integer;
begin

   M := 2048;
   L := 1;
   loop
      K := 0;
      J := L;
      I := 0;
      loop
         loop
            W(I+K) := Z(I) + Z(M+I);
            W(I+J) := E(K) * (Z(I) - Z(M+I));
            I := I+1;
            if I >= J then exit; end if;
         end loop;
         K := J;
         J := K+L;
         if J > M then exit; end if;
      end loop;
      L := L+L;
                -- work back other way without copying
      K := 0;
      J := L;
      I := 0;
      loop
        loop
          Z(I+K) := W(I) + W(M+I);
          Z(I+J) := E(K) * (W(I) - W(M+I));
          I := I+1;
          if I >= J then exit; end if;
        end loop;
        K := J;
        J := K+L;
        if J > M then exit; end if;
      end loop;
      L := L+L;
      if L > M then return; end if;  -- result is in Z
   end loop;
end fft4096;