src/fftw.c

//
// Copyright © 2025 Agora
// This file is part of TEN Framework, an open source project.
// Licensed under the Apache License, Version 2.0, with certain conditions.
// Refer to the "LICENSE" file in the root directory for more information.
//
#include <math.h>
#include <string.h>
#include <stdlib.h>
#include <stdio.h>

#include "fftw.h"

static const int AUP_FFTW_g_ip256[] = {64, 64, 0, 16, 0, 64, 32, 96};
static const float AUP_FFTW_g_w256[] = {
    1.000000e+00f, 7.071068e-01f, 5.006030e-01f,  5.054710e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    1.000000e+00f, 7.071068e-01f, 5.024193e-01f,  5.224986e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    1.000000e+00f, 7.071068e-01f, 5.097956e-01f,  6.013449e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    1.000000e+00f, 7.071068e-01f, 9.238795e-01f,  3.826834e-01f,
    1.000000e+00f, 7.071068e-01f, 0.000000e+00f,  0.000000e+00f,
    7.071068e-01f, 4.998494e-01f, 4.993977e-01f,  4.986452e-01f,
    4.975924e-01f, 4.962398e-01f, 4.945883e-01f,  4.926388e-01f,
    4.903926e-01f, 4.878511e-01f, 4.850156e-01f,  4.818880e-01f,
    4.784702e-01f, 4.747641e-01f, 4.707720e-01f,  4.664964e-01f,
    4.619398e-01f, 4.571049e-01f, 4.519946e-01f,  4.466122e-01f,
    4.409606e-01f, 4.350435e-01f, 4.288643e-01f,  4.224268e-01f,
    4.157348e-01f, 4.087924e-01f, 4.016038e-01f,  3.941732e-01f,
    3.865052e-01f, 3.786044e-01f, 3.704756e-01f,  3.621235e-01f,
    3.535534e-01f, 3.447703e-01f, 3.357795e-01f,  3.265864e-01f,
    3.171966e-01f, 3.076158e-01f, 2.978497e-01f,  2.879041e-01f,
    2.777851e-01f, 2.674988e-01f, 2.570514e-01f,  2.464491e-01f,
    2.356984e-01f, 2.248057e-01f, 2.137775e-01f,  2.026207e-01f,
    1.913417e-01f, 1.799475e-01f, 1.684449e-01f,  1.568409e-01f,
    1.451423e-01f, 1.333564e-01f, 1.214901e-01f,  1.095506e-01f,
    9.754516e-02f, 8.548094e-02f, 7.336524e-02f,  6.120534e-02f,
    4.900857e-02f, 3.678228e-02f, 2.453384e-02f,  1.227061e-02f};
static const int AUP_FFTW_g_ip512[] = {128, 128, 0, 16, 0, 64, 32, 96};
static const float AUP_FFTW_g_w512[] = {
    1.000000e+00f, 7.071068e-01f, 5.001506e-01f,  5.013585e-01f,
    9.987955e-01f, 4.906767e-02f, 9.891765e-01f,  -1.467305e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.891765e-01f, 1.467305e-01f, 9.039893e-01f,  -4.275551e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.700313e-01f, 2.429802e-01f, 7.409511e-01f,  -6.715590e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.415441e-01f, 3.368899e-01f, 5.141027e-01f,  -8.577286e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    9.039893e-01f, 4.275551e-01f, 2.429802e-01f,  -9.700313e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.577286e-01f, 5.141027e-01f, -4.906767e-02f, -9.987955e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    8.032075e-01f, 5.956993e-01f, -3.368899e-01f, -9.415441e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    7.409511e-01f, 6.715590e-01f, -5.956993e-01f, -8.032075e-01f,
    1.000000e+00f, 7.071068e-01f, 5.006030e-01f,  5.054710e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    1.000000e+00f, 7.071068e-01f, 5.024193e-01f,  5.224986e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    1.000000e+00f, 7.071068e-01f, 5.097956e-01f,  6.013449e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    1.000000e+00f, 7.071068e-01f, 9.238795e-01f,  3.826834e-01f,
    1.000000e+00f, 7.071068e-01f, 0.000000e+00f,  0.000000e+00f,
    7.071068e-01f, 4.999624e-01f, 4.998494e-01f,  4.996612e-01f,
    4.993977e-01f, 4.990591e-01f, 4.986452e-01f,  4.981563e-01f,
    4.975924e-01f, 4.969535e-01f, 4.962398e-01f,  4.954513e-01f,
    4.945883e-01f, 4.936507e-01f, 4.926388e-01f,  4.915527e-01f,
    4.903926e-01f, 4.891587e-01f, 4.878511e-01f,  4.864700e-01f,
    4.850156e-01f, 4.834882e-01f, 4.818880e-01f,  4.802153e-01f,
    4.784702e-01f, 4.766530e-01f, 4.747641e-01f,  4.728037e-01f,
    4.707720e-01f, 4.686695e-01f, 4.664964e-01f,  4.642530e-01f,
    4.619398e-01f, 4.595569e-01f, 4.571049e-01f,  4.545840e-01f,
    4.519946e-01f, 4.493372e-01f, 4.466122e-01f,  4.438198e-01f,
    4.409606e-01f, 4.380350e-01f, 4.350435e-01f,  4.319864e-01f,
    4.288643e-01f, 4.256776e-01f, 4.224268e-01f,  4.191124e-01f,
    4.157348e-01f, 4.122947e-01f, 4.087924e-01f,  4.052286e-01f,
    4.016038e-01f, 3.979185e-01f, 3.941732e-01f,  3.903686e-01f,
    3.865052e-01f, 3.825836e-01f, 3.786044e-01f,  3.745682e-01f,
    3.704756e-01f, 3.663271e-01f, 3.621235e-01f,  3.578654e-01f,
    3.535534e-01f, 3.491881e-01f, 3.447703e-01f,  3.403005e-01f,
    3.357795e-01f, 3.312079e-01f, 3.265864e-01f,  3.219158e-01f,
    3.171966e-01f, 3.124297e-01f, 3.076158e-01f,  3.027555e-01f,
    2.978497e-01f, 2.928989e-01f, 2.879041e-01f,  2.828659e-01f,
    2.777851e-01f, 2.726625e-01f, 2.674988e-01f,  2.622948e-01f,
    2.570514e-01f, 2.517692e-01f, 2.464491e-01f,  2.410919e-01f,
    2.356984e-01f, 2.302694e-01f, 2.248057e-01f,  2.193081e-01f,
    2.137775e-01f, 2.082148e-01f, 2.026207e-01f,  1.969960e-01f,
    1.913417e-01f, 1.856586e-01f, 1.799475e-01f,  1.742093e-01f,
    1.684449e-01f, 1.626551e-01f, 1.568409e-01f,  1.510030e-01f,
    1.451423e-01f, 1.392598e-01f, 1.333564e-01f,  1.274328e-01f,
    1.214901e-01f, 1.155291e-01f, 1.095506e-01f,  1.035557e-01f,
    9.754516e-02f, 9.151994e-02f, 8.548094e-02f,  7.942907e-02f,
    7.336524e-02f, 6.729035e-02f, 6.120534e-02f,  5.511110e-02f,
    4.900857e-02f, 4.289866e-02f, 3.678228e-02f,  3.066037e-02f,
    2.453384e-02f, 1.840361e-02f, 1.227061e-02f,  6.135769e-03f};
static const int AUP_FFTW_g_ip1024[] = {256, 256, 0,   16,  0,  64,  32,  96,
                                        0,   256, 128, 384, 64, 320, 192, 448};
static const float AUP_FFTW_g_w1024[] = {
    1.000000e+00f, 7.071068e-01f, 5.000377e-01f,  5.003390e-01f,
    9.996988e-01f, 2.454123e-02f, 9.972905e-01f,  -7.356456e-02f,
    9.987955e-01f, 4.906767e-02f, 9.891765e-01f,  -1.467305e-01f,
    9.972905e-01f, 7.356456e-02f, 9.757021e-01f,  -2.191012e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.924795e-01f, 1.224107e-01f, 9.329928e-01f,  -3.598950e-01f,
    9.891765e-01f, 1.467305e-01f, 9.039893e-01f,  -4.275551e-01f,
    9.852776e-01f, 1.709619e-01f, 8.700870e-01f,  -4.928982e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.757021e-01f, 2.191012e-01f, 7.883464e-01f,  -6.152316e-01f,
    9.700313e-01f, 2.429802e-01f, 7.409511e-01f,  -6.715590e-01f,
    9.637761e-01f, 2.667128e-01f, 6.895405e-01f,  -7.242471e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.495282e-01f, 3.136817e-01f, 5.758082e-01f,  -8.175848e-01f,
    9.415441e-01f, 3.368899e-01f, 5.141027e-01f,  -8.577286e-01f,
    9.329928e-01f, 3.598950e-01f, 4.496113e-01f,  -8.932243e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    9.142098e-01f, 4.052413e-01f, 3.136817e-01f,  -9.495282e-01f,
    9.039893e-01f, 4.275551e-01f, 2.429802e-01f,  -9.700313e-01f,
    8.932243e-01f, 4.496113e-01f, 1.709619e-01f,  -9.852776e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.700870e-01f, 4.928982e-01f, 2.454123e-02f,  -9.996988e-01f,
    8.577286e-01f, 5.141027e-01f, -4.906767e-02f, -9.987955e-01f,
    8.448536e-01f, 5.349976e-01f, -1.224107e-01f, -9.924795e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    8.175848e-01f, 5.758082e-01f, -2.667128e-01f, -9.637761e-01f,
    8.032075e-01f, 5.956993e-01f, -3.368899e-01f, -9.415441e-01f,
    7.883464e-01f, 6.152316e-01f, -4.052413e-01f, -9.142098e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    7.572088e-01f, 6.531728e-01f, -5.349976e-01f, -8.448536e-01f,
    7.409511e-01f, 6.715590e-01f, -5.956993e-01f, -8.032075e-01f,
    7.242471e-01f, 6.895405e-01f, -6.531728e-01f, -7.572088e-01f,
    1.000000e+00f, 7.071068e-01f, 5.001506e-01f,  5.013585e-01f,
    9.987955e-01f, 4.906767e-02f, 9.891765e-01f,  -1.467305e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.891765e-01f, 1.467305e-01f, 9.039893e-01f,  -4.275551e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.700313e-01f, 2.429802e-01f, 7.409511e-01f,  -6.715590e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.415441e-01f, 3.368899e-01f, 5.141027e-01f,  -8.577286e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    9.039893e-01f, 4.275551e-01f, 2.429802e-01f,  -9.700313e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.577286e-01f, 5.141027e-01f, -4.906767e-02f, -9.987955e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    8.032075e-01f, 5.956993e-01f, -3.368899e-01f, -9.415441e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    7.409511e-01f, 6.715590e-01f, -5.956993e-01f, -8.032075e-01f,
    1.000000e+00f, 7.071068e-01f, 5.006030e-01f,  5.054710e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    1.000000e+00f, 7.071068e-01f, 5.024193e-01f,  5.224986e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    1.000000e+00f, 7.071068e-01f, 5.097956e-01f,  6.013449e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    1.000000e+00f, 7.071068e-01f, 9.238795e-01f,  3.826834e-01f,
    1.000000e+00f, 7.071068e-01f, 0.000000e+00f,  0.000000e+00f,
    7.071068e-01f, 4.999906e-01f, 4.999624e-01f,  4.999153e-01f,
    4.998494e-01f, 4.997647e-01f, 4.996612e-01f,  4.995389e-01f,
    4.993977e-01f, 4.992378e-01f, 4.990591e-01f,  4.988615e-01f,
    4.986452e-01f, 4.984101e-01f, 4.981563e-01f,  4.978837e-01f,
    4.975924e-01f, 4.972823e-01f, 4.969535e-01f,  4.966060e-01f,
    4.962398e-01f, 4.958549e-01f, 4.954513e-01f,  4.950291e-01f,
    4.945883e-01f, 4.941288e-01f, 4.936507e-01f,  4.931540e-01f,
    4.926388e-01f, 4.921050e-01f, 4.915527e-01f,  4.909819e-01f,
    4.903926e-01f, 4.897849e-01f, 4.891587e-01f,  4.885141e-01f,
    4.878511e-01f, 4.871697e-01f, 4.864700e-01f,  4.857519e-01f,
    4.850156e-01f, 4.842610e-01f, 4.834882e-01f,  4.826972e-01f,
    4.818880e-01f, 4.810607e-01f, 4.802153e-01f,  4.793517e-01f,
    4.784702e-01f, 4.775706e-01f, 4.766530e-01f,  4.757175e-01f,
    4.747641e-01f, 4.737928e-01f, 4.728037e-01f,  4.717967e-01f,
    4.707720e-01f, 4.697296e-01f, 4.686695e-01f,  4.675918e-01f,
    4.664964e-01f, 4.653835e-01f, 4.642530e-01f,  4.631051e-01f,
    4.619398e-01f, 4.607570e-01f, 4.595569e-01f,  4.583395e-01f,
    4.571049e-01f, 4.558530e-01f, 4.545840e-01f,  4.532979e-01f,
    4.519946e-01f, 4.506744e-01f, 4.493372e-01f,  4.479831e-01f,
    4.466122e-01f, 4.452244e-01f, 4.438198e-01f,  4.423985e-01f,
    4.409606e-01f, 4.395061e-01f, 4.380350e-01f,  4.365475e-01f,
    4.350435e-01f, 4.335231e-01f, 4.319864e-01f,  4.304335e-01f,
    4.288643e-01f, 4.272790e-01f, 4.256776e-01f,  4.240602e-01f,
    4.224268e-01f, 4.207775e-01f, 4.191124e-01f,  4.174314e-01f,
    4.157348e-01f, 4.140225e-01f, 4.122947e-01f,  4.105513e-01f,
    4.087924e-01f, 4.070182e-01f, 4.052286e-01f,  4.034238e-01f,
    4.016038e-01f, 3.997686e-01f, 3.979185e-01f,  3.960533e-01f,
    3.941732e-01f, 3.922783e-01f, 3.903686e-01f,  3.884442e-01f,
    3.865052e-01f, 3.845517e-01f, 3.825836e-01f,  3.806012e-01f,
    3.786044e-01f, 3.765934e-01f, 3.745682e-01f,  3.725289e-01f,
    3.704756e-01f, 3.684083e-01f, 3.663271e-01f,  3.642322e-01f,
    3.621235e-01f, 3.600013e-01f, 3.578654e-01f,  3.557161e-01f,
    3.535534e-01f, 3.513774e-01f, 3.491881e-01f,  3.469857e-01f,
    3.447703e-01f, 3.425418e-01f, 3.403005e-01f,  3.380464e-01f,
    3.357795e-01f, 3.335000e-01f, 3.312079e-01f,  3.289033e-01f,
    3.265864e-01f, 3.242572e-01f, 3.219158e-01f,  3.195622e-01f,
    3.171966e-01f, 3.148191e-01f, 3.124297e-01f,  3.100286e-01f,
    3.076158e-01f, 3.051914e-01f, 3.027555e-01f,  3.003082e-01f,
    2.978497e-01f, 2.953799e-01f, 2.928989e-01f,  2.904070e-01f,
    2.879041e-01f, 2.853904e-01f, 2.828659e-01f,  2.803308e-01f,
    2.777851e-01f, 2.752290e-01f, 2.726625e-01f,  2.700857e-01f,
    2.674988e-01f, 2.649018e-01f, 2.622948e-01f,  2.596780e-01f,
    2.570514e-01f, 2.544151e-01f, 2.517692e-01f,  2.491138e-01f,
    2.464491e-01f, 2.437751e-01f, 2.410919e-01f,  2.383996e-01f,
    2.356984e-01f, 2.329882e-01f, 2.302694e-01f,  2.275418e-01f,
    2.248057e-01f, 2.220611e-01f, 2.193081e-01f,  2.165469e-01f,
    2.137775e-01f, 2.110001e-01f, 2.082148e-01f,  2.054216e-01f,
    2.026207e-01f, 1.998121e-01f, 1.969960e-01f,  1.941725e-01f,
    1.913417e-01f, 1.885037e-01f, 1.856586e-01f,  1.828065e-01f,
    1.799475e-01f, 1.770818e-01f, 1.742093e-01f,  1.713304e-01f,
    1.684449e-01f, 1.655532e-01f, 1.626551e-01f,  1.597510e-01f,
    1.568409e-01f, 1.539248e-01f, 1.510030e-01f,  1.480754e-01f,
    1.451423e-01f, 1.422038e-01f, 1.392598e-01f,  1.363107e-01f,
    1.333564e-01f, 1.303971e-01f, 1.274328e-01f,  1.244638e-01f,
    1.214901e-01f, 1.185118e-01f, 1.155291e-01f,  1.125420e-01f,
    1.095506e-01f, 1.065552e-01f, 1.035557e-01f,  1.005523e-01f,
    9.754516e-02f, 9.453433e-02f, 9.151994e-02f,  8.850211e-02f,
    8.548094e-02f, 8.245656e-02f, 7.942907e-02f,  7.639859e-02f,
    7.336524e-02f, 7.032912e-02f, 6.729035e-02f,  6.424906e-02f,
    6.120534e-02f, 5.815932e-02f, 5.511110e-02f,  5.206082e-02f,
    4.900857e-02f, 4.595448e-02f, 4.289866e-02f,  3.984122e-02f,
    3.678228e-02f, 3.372196e-02f, 3.066037e-02f,  2.759762e-02f,
    2.453384e-02f, 2.146913e-02f, 1.840361e-02f,  1.533740e-02f,
    1.227061e-02f, 9.203365e-03f, 6.135769e-03f,  3.067942e-03f};
static const int AUP_FFTW_g_ip2048[] = {512, 512, 0,   16,  0,  64,  32,  96,
                                        0,   256, 128, 384, 64, 320, 192, 448};
static const float AUP_FFTW_g_w2048[] = {
    1.000000e+00f, 7.071068e-01f, 5.000094e-01f,  5.000847e-01f,
    9.999247e-01f, 1.227154e-02f, 9.993224e-01f,  -3.680722e-02f,
    9.996988e-01f, 2.454123e-02f, 9.972905e-01f,  -7.356456e-02f,
    9.993224e-01f, 3.680722e-02f, 9.939070e-01f,  -1.102222e-01f,
    9.987955e-01f, 4.906767e-02f, 9.891765e-01f,  -1.467305e-01f,
    9.981181e-01f, 6.132074e-02f, 9.831055e-01f,  -1.830399e-01f,
    9.972905e-01f, 7.356456e-02f, 9.757021e-01f,  -2.191012e-01f,
    9.963126e-01f, 8.579731e-02f, 9.669765e-01f,  -2.548657e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.939070e-01f, 1.102222e-01f, 9.456073e-01f,  -3.253103e-01f,
    9.924795e-01f, 1.224107e-01f, 9.329928e-01f,  -3.598950e-01f,
    9.909026e-01f, 1.345807e-01f, 9.191139e-01f,  -3.939920e-01f,
    9.891765e-01f, 1.467305e-01f, 9.039893e-01f,  -4.275551e-01f,
    9.873014e-01f, 1.588581e-01f, 8.876396e-01f,  -4.605387e-01f,
    9.852776e-01f, 1.709619e-01f, 8.700870e-01f,  -4.928982e-01f,
    9.831055e-01f, 1.830399e-01f, 8.513552e-01f,  -5.245897e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.783174e-01f, 2.071114e-01f, 8.104572e-01f,  -5.857979e-01f,
    9.757021e-01f, 2.191012e-01f, 7.883464e-01f,  -6.152316e-01f,
    9.729400e-01f, 2.310581e-01f, 7.651673e-01f,  -6.438315e-01f,
    9.700313e-01f, 2.429802e-01f, 7.409511e-01f,  -6.715590e-01f,
    9.669765e-01f, 2.548657e-01f, 7.157308e-01f,  -6.983762e-01f,
    9.637761e-01f, 2.667128e-01f, 6.895405e-01f,  -7.242471e-01f,
    9.604305e-01f, 2.785197e-01f, 6.624158e-01f,  -7.491364e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.533060e-01f, 3.020059e-01f, 6.055110e-01f,  -7.958369e-01f,
    9.495282e-01f, 3.136817e-01f, 5.758082e-01f,  -8.175848e-01f,
    9.456073e-01f, 3.253103e-01f, 5.453250e-01f,  -8.382247e-01f,
    9.415441e-01f, 3.368899e-01f, 5.141027e-01f,  -8.577286e-01f,
    9.373390e-01f, 3.484187e-01f, 4.821838e-01f,  -8.760701e-01f,
    9.329928e-01f, 3.598950e-01f, 4.496113e-01f,  -8.932243e-01f,
    9.285061e-01f, 3.713172e-01f, 4.164296e-01f,  -9.091680e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    9.191139e-01f, 3.939920e-01f, 3.484187e-01f,  -9.373390e-01f,
    9.142098e-01f, 4.052413e-01f, 3.136817e-01f,  -9.495282e-01f,
    9.091680e-01f, 4.164296e-01f, 2.785197e-01f,  -9.604305e-01f,
    9.039893e-01f, 4.275551e-01f, 2.429802e-01f,  -9.700313e-01f,
    8.986745e-01f, 4.386162e-01f, 2.071114e-01f,  -9.783174e-01f,
    8.932243e-01f, 4.496113e-01f, 1.709619e-01f,  -9.852776e-01f,
    8.876396e-01f, 4.605387e-01f, 1.345807e-01f,  -9.909026e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.760701e-01f, 4.821838e-01f, 6.132074e-02f,  -9.981181e-01f,
    8.700870e-01f, 4.928982e-01f, 2.454123e-02f,  -9.996988e-01f,
    8.639729e-01f, 5.035384e-01f, -1.227154e-02f, -9.999247e-01f,
    8.577286e-01f, 5.141027e-01f, -4.906767e-02f, -9.987955e-01f,
    8.513552e-01f, 5.245897e-01f, -8.579731e-02f, -9.963126e-01f,
    8.448536e-01f, 5.349976e-01f, -1.224107e-01f, -9.924795e-01f,
    8.382247e-01f, 5.453250e-01f, -1.588581e-01f, -9.873014e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    8.245893e-01f, 5.657318e-01f, -2.310581e-01f, -9.729400e-01f,
    8.175848e-01f, 5.758082e-01f, -2.667128e-01f, -9.637761e-01f,
    8.104572e-01f, 5.857979e-01f, -3.020059e-01f, -9.533060e-01f,
    8.032075e-01f, 5.956993e-01f, -3.368899e-01f, -9.415441e-01f,
    7.958369e-01f, 6.055110e-01f, -3.713172e-01f, -9.285061e-01f,
    7.883464e-01f, 6.152316e-01f, -4.052413e-01f, -9.142098e-01f,
    7.807372e-01f, 6.248595e-01f, -4.386162e-01f, -8.986745e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    7.651673e-01f, 6.438315e-01f, -5.035384e-01f, -8.639729e-01f,
    7.572088e-01f, 6.531728e-01f, -5.349976e-01f, -8.448536e-01f,
    7.491364e-01f, 6.624158e-01f, -5.657318e-01f, -8.245893e-01f,
    7.409511e-01f, 6.715590e-01f, -5.956993e-01f, -8.032075e-01f,
    7.326543e-01f, 6.806010e-01f, -6.248595e-01f, -7.807372e-01f,
    7.242471e-01f, 6.895405e-01f, -6.531728e-01f, -7.572088e-01f,
    7.157308e-01f, 6.983762e-01f, -6.806010e-01f, -7.326543e-01f,
    1.000000e+00f, 7.071068e-01f, 5.000377e-01f,  5.003390e-01f,
    9.996988e-01f, 2.454123e-02f, 9.972905e-01f,  -7.356456e-02f,
    9.987955e-01f, 4.906767e-02f, 9.891765e-01f,  -1.467305e-01f,
    9.972905e-01f, 7.356456e-02f, 9.757021e-01f,  -2.191012e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.924795e-01f, 1.224107e-01f, 9.329928e-01f,  -3.598950e-01f,
    9.891765e-01f, 1.467305e-01f, 9.039893e-01f,  -4.275551e-01f,
    9.852776e-01f, 1.709619e-01f, 8.700870e-01f,  -4.928982e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.757021e-01f, 2.191012e-01f, 7.883464e-01f,  -6.152316e-01f,
    9.700313e-01f, 2.429802e-01f, 7.409511e-01f,  -6.715590e-01f,
    9.637761e-01f, 2.667128e-01f, 6.895405e-01f,  -7.242471e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.495282e-01f, 3.136817e-01f, 5.758082e-01f,  -8.175848e-01f,
    9.415441e-01f, 3.368899e-01f, 5.141027e-01f,  -8.577286e-01f,
    9.329928e-01f, 3.598950e-01f, 4.496113e-01f,  -8.932243e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    9.142098e-01f, 4.052413e-01f, 3.136817e-01f,  -9.495282e-01f,
    9.039893e-01f, 4.275551e-01f, 2.429802e-01f,  -9.700313e-01f,
    8.932243e-01f, 4.496113e-01f, 1.709619e-01f,  -9.852776e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.700870e-01f, 4.928982e-01f, 2.454123e-02f,  -9.996988e-01f,
    8.577286e-01f, 5.141027e-01f, -4.906767e-02f, -9.987955e-01f,
    8.448536e-01f, 5.349976e-01f, -1.224107e-01f, -9.924795e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    8.175848e-01f, 5.758082e-01f, -2.667128e-01f, -9.637761e-01f,
    8.032075e-01f, 5.956993e-01f, -3.368899e-01f, -9.415441e-01f,
    7.883464e-01f, 6.152316e-01f, -4.052413e-01f, -9.142098e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    7.572088e-01f, 6.531728e-01f, -5.349976e-01f, -8.448536e-01f,
    7.409511e-01f, 6.715590e-01f, -5.956993e-01f, -8.032075e-01f,
    7.242471e-01f, 6.895405e-01f, -6.531728e-01f, -7.572088e-01f,
    1.000000e+00f, 7.071068e-01f, 5.001506e-01f,  5.013585e-01f,
    9.987955e-01f, 4.906767e-02f, 9.891765e-01f,  -1.467305e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.891765e-01f, 1.467305e-01f, 9.039893e-01f,  -4.275551e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.700313e-01f, 2.429802e-01f, 7.409511e-01f,  -6.715590e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.415441e-01f, 3.368899e-01f, 5.141027e-01f,  -8.577286e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    9.039893e-01f, 4.275551e-01f, 2.429802e-01f,  -9.700313e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.577286e-01f, 5.141027e-01f, -4.906767e-02f, -9.987955e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    8.032075e-01f, 5.956993e-01f, -3.368899e-01f, -9.415441e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    7.409511e-01f, 6.715590e-01f, -5.956993e-01f, -8.032075e-01f,
    1.000000e+00f, 7.071068e-01f, 5.006030e-01f,  5.054710e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    8.819213e-01f, 4.713967e-01f, 9.801714e-02f,  -9.951847e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    7.730105e-01f, 6.343933e-01f, -4.713967e-01f, -8.819213e-01f,
    1.000000e+00f, 7.071068e-01f, 5.024193e-01f,  5.224986e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    8.314696e-01f, 5.555702e-01f, -1.950903e-01f, -9.807853e-01f,
    1.000000e+00f, 7.071068e-01f, 5.097956e-01f,  6.013449e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    1.000000e+00f, 7.071068e-01f, 9.238795e-01f,  3.826834e-01f,
    1.000000e+00f, 7.071068e-01f, 0.000000e+00f,  0.000000e+00f,
    7.071068e-01f, 4.999976e-01f, 4.999906e-01f,  4.999788e-01f,
    4.999624e-01f, 4.999412e-01f, 4.999153e-01f,  4.998847e-01f,
    4.998494e-01f, 4.998094e-01f, 4.997647e-01f,  4.997153e-01f,
    4.996612e-01f, 4.996024e-01f, 4.995389e-01f,  4.994706e-01f,
    4.993977e-01f, 4.993201e-01f, 4.992378e-01f,  4.991508e-01f,
    4.990591e-01f, 4.989626e-01f, 4.988615e-01f,  4.987557e-01f,
    4.986452e-01f, 4.985300e-01f, 4.984101e-01f,  4.982856e-01f,
    4.981563e-01f, 4.980224e-01f, 4.978837e-01f,  4.977404e-01f,
    4.975924e-01f, 4.974397e-01f, 4.972823e-01f,  4.971202e-01f,
    4.969535e-01f, 4.967821e-01f, 4.966060e-01f,  4.964252e-01f,
    4.962398e-01f, 4.960497e-01f, 4.958549e-01f,  4.956554e-01f,
    4.954513e-01f, 4.952425e-01f, 4.950291e-01f,  4.948110e-01f,
    4.945883e-01f, 4.943608e-01f, 4.941288e-01f,  4.938921e-01f,
    4.936507e-01f, 4.934047e-01f, 4.931540e-01f,  4.928988e-01f,
    4.926388e-01f, 4.923743e-01f, 4.921050e-01f,  4.918312e-01f,
    4.915527e-01f, 4.912697e-01f, 4.909819e-01f,  4.906896e-01f,
    4.903926e-01f, 4.900911e-01f, 4.897849e-01f,  4.894741e-01f,
    4.891587e-01f, 4.888387e-01f, 4.885141e-01f,  4.881849e-01f,
    4.878511e-01f, 4.875127e-01f, 4.871697e-01f,  4.868221e-01f,
    4.864700e-01f, 4.861132e-01f, 4.857519e-01f,  4.853861e-01f,
    4.850156e-01f, 4.846406e-01f, 4.842610e-01f,  4.838769e-01f,
    4.834882e-01f, 4.830950e-01f, 4.826972e-01f,  4.822949e-01f,
    4.818880e-01f, 4.814766e-01f, 4.810607e-01f,  4.806402e-01f,
    4.802153e-01f, 4.797858e-01f, 4.793517e-01f,  4.789132e-01f,
    4.784702e-01f, 4.780226e-01f, 4.775706e-01f,  4.771140e-01f,
    4.766530e-01f, 4.761875e-01f, 4.757175e-01f,  4.752430e-01f,
    4.747641e-01f, 4.742807e-01f, 4.737928e-01f,  4.733005e-01f,
    4.728037e-01f, 4.723024e-01f, 4.717967e-01f,  4.712866e-01f,
    4.707720e-01f, 4.702530e-01f, 4.697296e-01f,  4.692018e-01f,
    4.686695e-01f, 4.681328e-01f, 4.675918e-01f,  4.670463e-01f,
    4.664964e-01f, 4.659421e-01f, 4.653835e-01f,  4.648204e-01f,
    4.642530e-01f, 4.636813e-01f, 4.631051e-01f,  4.625246e-01f,
    4.619398e-01f, 4.613506e-01f, 4.607570e-01f,  4.601591e-01f,
    4.595569e-01f, 4.589504e-01f, 4.583395e-01f,  4.577244e-01f,
    4.571049e-01f, 4.564811e-01f, 4.558530e-01f,  4.552206e-01f,
    4.545840e-01f, 4.539431e-01f, 4.532979e-01f,  4.526484e-01f,
    4.519946e-01f, 4.513367e-01f, 4.506744e-01f,  4.500079e-01f,
    4.493372e-01f, 4.486623e-01f, 4.479831e-01f,  4.472997e-01f,
    4.466122e-01f, 4.459204e-01f, 4.452244e-01f,  4.445242e-01f,
    4.438198e-01f, 4.431113e-01f, 4.423985e-01f,  4.416817e-01f,
    4.409606e-01f, 4.402354e-01f, 4.395061e-01f,  4.387726e-01f,
    4.380350e-01f, 4.372933e-01f, 4.365475e-01f,  4.357975e-01f,
    4.350435e-01f, 4.342854e-01f, 4.335231e-01f,  4.327568e-01f,
    4.319864e-01f, 4.312120e-01f, 4.304335e-01f,  4.296509e-01f,
    4.288643e-01f, 4.280737e-01f, 4.272790e-01f,  4.264803e-01f,
    4.256776e-01f, 4.248709e-01f, 4.240602e-01f,  4.232455e-01f,
    4.224268e-01f, 4.216041e-01f, 4.207775e-01f,  4.199469e-01f,
    4.191124e-01f, 4.182739e-01f, 4.174314e-01f,  4.165851e-01f,
    4.157348e-01f, 4.148806e-01f, 4.140225e-01f,  4.131605e-01f,
    4.122947e-01f, 4.114249e-01f, 4.105513e-01f,  4.096738e-01f,
    4.087924e-01f, 4.079072e-01f, 4.070182e-01f,  4.061253e-01f,
    4.052286e-01f, 4.043281e-01f, 4.034238e-01f,  4.025157e-01f,
    4.016038e-01f, 4.006881e-01f, 3.997686e-01f,  3.988454e-01f,
    3.979185e-01f, 3.969877e-01f, 3.960533e-01f,  3.951151e-01f,
    3.941732e-01f, 3.932276e-01f, 3.922783e-01f,  3.913253e-01f,
    3.903686e-01f, 3.894083e-01f, 3.884442e-01f,  3.874766e-01f,
    3.865052e-01f, 3.855303e-01f, 3.845517e-01f,  3.835695e-01f,
    3.825836e-01f, 3.815942e-01f, 3.806012e-01f,  3.796046e-01f,
    3.786044e-01f, 3.776007e-01f, 3.765934e-01f,  3.755826e-01f,
    3.745682e-01f, 3.735503e-01f, 3.725289e-01f,  3.715040e-01f,
    3.704756e-01f, 3.694437e-01f, 3.684083e-01f,  3.673694e-01f,
    3.663271e-01f, 3.652814e-01f, 3.642322e-01f,  3.631796e-01f,
    3.621235e-01f, 3.610641e-01f, 3.600013e-01f,  3.589350e-01f,
    3.578654e-01f, 3.567924e-01f, 3.557161e-01f,  3.546364e-01f,
    3.535534e-01f, 3.524670e-01f, 3.513774e-01f,  3.502844e-01f,
    3.491881e-01f, 3.480886e-01f, 3.469857e-01f,  3.458796e-01f,
    3.447703e-01f, 3.436577e-01f, 3.425418e-01f,  3.414228e-01f,
    3.403005e-01f, 3.391750e-01f, 3.380464e-01f,  3.369145e-01f,
    3.357795e-01f, 3.346413e-01f, 3.335000e-01f,  3.323555e-01f,
    3.312079e-01f, 3.300572e-01f, 3.289033e-01f,  3.277464e-01f,
    3.265864e-01f, 3.254233e-01f, 3.242572e-01f,  3.230880e-01f,
    3.219158e-01f, 3.207405e-01f, 3.195622e-01f,  3.183809e-01f,
    3.171966e-01f, 3.160094e-01f, 3.148191e-01f,  3.136259e-01f,
    3.124297e-01f, 3.112306e-01f, 3.100286e-01f,  3.088237e-01f,
    3.076158e-01f, 3.064050e-01f, 3.051914e-01f,  3.039749e-01f,
    3.027555e-01f, 3.015333e-01f, 3.003082e-01f,  2.990804e-01f,
    2.978497e-01f, 2.966161e-01f, 2.953799e-01f,  2.941408e-01f,
    2.928989e-01f, 2.916543e-01f, 2.904070e-01f,  2.891569e-01f,
    2.879041e-01f, 2.866486e-01f, 2.853904e-01f,  2.841295e-01f,
    2.828659e-01f, 2.815997e-01f, 2.803308e-01f,  2.790593e-01f,
    2.777851e-01f, 2.765084e-01f, 2.752290e-01f,  2.739470e-01f,
    2.726625e-01f, 2.713754e-01f, 2.700857e-01f,  2.687935e-01f,
    2.674988e-01f, 2.662016e-01f, 2.649018e-01f,  2.635996e-01f,
    2.622948e-01f, 2.609876e-01f, 2.596780e-01f,  2.583659e-01f,
    2.570514e-01f, 2.557344e-01f, 2.544151e-01f,  2.530933e-01f,
    2.517692e-01f, 2.504427e-01f, 2.491138e-01f,  2.477826e-01f,
    2.464491e-01f, 2.451132e-01f, 2.437751e-01f,  2.424346e-01f,
    2.410919e-01f, 2.397469e-01f, 2.383996e-01f,  2.370501e-01f,
    2.356984e-01f, 2.343444e-01f, 2.329882e-01f,  2.316299e-01f,
    2.302694e-01f, 2.289067e-01f, 2.275418e-01f,  2.261748e-01f,
    2.248057e-01f, 2.234344e-01f, 2.220611e-01f,  2.206856e-01f,
    2.193081e-01f, 2.179285e-01f, 2.165469e-01f,  2.151632e-01f,
    2.137775e-01f, 2.123898e-01f, 2.110001e-01f,  2.096084e-01f,
    2.082148e-01f, 2.068192e-01f, 2.054216e-01f,  2.040221e-01f,
    2.026207e-01f, 2.012173e-01f, 1.998121e-01f,  1.984050e-01f,
    1.969960e-01f, 1.955852e-01f, 1.941725e-01f,  1.927580e-01f,
    1.913417e-01f, 1.899236e-01f, 1.885037e-01f,  1.870820e-01f,
    1.856586e-01f, 1.842334e-01f, 1.828065e-01f,  1.813779e-01f,
    1.799475e-01f, 1.785155e-01f, 1.770818e-01f,  1.756464e-01f,
    1.742093e-01f, 1.727707e-01f, 1.713304e-01f,  1.698884e-01f,
    1.684449e-01f, 1.669998e-01f, 1.655532e-01f,  1.641049e-01f,
    1.626551e-01f, 1.612038e-01f, 1.597510e-01f,  1.582967e-01f,
    1.568409e-01f, 1.553836e-01f, 1.539248e-01f,  1.524646e-01f,
    1.510030e-01f, 1.495399e-01f, 1.480754e-01f,  1.466096e-01f,
    1.451423e-01f, 1.436737e-01f, 1.422038e-01f,  1.407325e-01f,
    1.392598e-01f, 1.377859e-01f, 1.363107e-01f,  1.348342e-01f,
    1.333564e-01f, 1.318773e-01f, 1.303971e-01f,  1.289156e-01f,
    1.274328e-01f, 1.259489e-01f, 1.244638e-01f,  1.229775e-01f,
    1.214901e-01f, 1.200015e-01f, 1.185118e-01f,  1.170210e-01f,
    1.155291e-01f, 1.140360e-01f, 1.125420e-01f,  1.110468e-01f,
    1.095506e-01f, 1.080534e-01f, 1.065552e-01f,  1.050559e-01f,
    1.035557e-01f, 1.020545e-01f, 1.005523e-01f,  9.904921e-02f,
    9.754516e-02f, 9.604020e-02f, 9.453433e-02f,  9.302758e-02f,
    9.151994e-02f, 9.001145e-02f, 8.850211e-02f,  8.699194e-02f,
    8.548094e-02f, 8.396915e-02f, 8.245656e-02f,  8.094320e-02f,
    7.942907e-02f, 7.791420e-02f, 7.639859e-02f,  7.488227e-02f,
    7.336524e-02f, 7.184752e-02f, 7.032912e-02f,  6.881006e-02f,
    6.729035e-02f, 6.577001e-02f, 6.424906e-02f,  6.272749e-02f,
    6.120534e-02f, 5.968261e-02f, 5.815932e-02f,  5.663548e-02f,
    5.511110e-02f, 5.358621e-02f, 5.206082e-02f,  5.053493e-02f,
    4.900857e-02f, 4.748175e-02f, 4.595448e-02f,  4.442678e-02f,
    4.289866e-02f, 4.137013e-02f, 3.984122e-02f,  3.831193e-02f,
    3.678228e-02f, 3.525229e-02f, 3.372196e-02f,  3.219132e-02f,
    3.066037e-02f, 2.912913e-02f, 2.759762e-02f,  2.606585e-02f,
    2.453384e-02f, 2.300159e-02f, 2.146913e-02f,  1.993646e-02f,
    1.840361e-02f, 1.687059e-02f, 1.533740e-02f,  1.380407e-02f,
    1.227061e-02f, 1.073704e-02f, 9.203365e-03f,  7.669603e-03f,
    6.135769e-03f, 4.601877e-03f, 3.067942e-03f,  1.533978e-03f};
static const int AUP_FFTW_g_ip4096[] = {
    1024, 1024, 0,   16,   0,   64,   32,   96,   0,    256, 128,
    384,  64,   320, 192,  448, 0,    1024, 512,  1536, 256, 1280,
    768,  1792, 128, 1152, 640, 1664, 384,  1408, 896,  1920};
static const float AUP_FFTW_g_w4096[] = {
    1.000000e+00f, 7.071068e-01f, 5.000024e-01f,  5.000212e-01f,
    9.999812e-01f, 6.135885e-03f, 9.998306e-01f,  -1.840673e-02f,
    9.999247e-01f, 1.227154e-02f, 9.993224e-01f,  -3.680722e-02f,
    9.998306e-01f, 1.840673e-02f, 9.984756e-01f,  -5.519524e-02f,
    9.996988e-01f, 2.454123e-02f, 9.972905e-01f,  -7.356456e-02f,
    9.995294e-01f, 3.067480e-02f, 9.957674e-01f,  -9.190896e-02f,
    9.993224e-01f, 3.680722e-02f, 9.939070e-01f,  -1.102222e-01f,
    9.990777e-01f, 4.293826e-02f, 9.917098e-01f,  -1.284981e-01f,
    9.987955e-01f, 4.906767e-02f, 9.891765e-01f,  -1.467305e-01f,
    9.984756e-01f, 5.519524e-02f, 9.863081e-01f,  -1.649131e-01f,
    9.981181e-01f, 6.132074e-02f, 9.831055e-01f,  -1.830399e-01f,
    9.977231e-01f, 6.744392e-02f, 9.795698e-01f,  -2.011046e-01f,
    9.972905e-01f, 7.356456e-02f, 9.757021e-01f,  -2.191012e-01f,
    9.968203e-01f, 7.968244e-02f, 9.715039e-01f,  -2.370236e-01f,
    9.963126e-01f, 8.579731e-02f, 9.669765e-01f,  -2.548657e-01f,
    9.957674e-01f, 9.190896e-02f, 9.621214e-01f,  -2.726214e-01f,
    9.951847e-01f, 9.801714e-02f, 9.569403e-01f,  -2.902847e-01f,
    9.945646e-01f, 1.041216e-01f, 9.514350e-01f,  -3.078496e-01f,
    9.939070e-01f, 1.102222e-01f, 9.456073e-01f,  -3.253103e-01f,
    9.932119e-01f, 1.163186e-01f, 9.394592e-01f,  -3.426607e-01f,
    9.924795e-01f, 1.224107e-01f, 9.329928e-01f,  -3.598950e-01f,
    9.917098e-01f, 1.284981e-01f, 9.262102e-01f,  -3.770074e-01f,
    9.909026e-01f, 1.345807e-01f, 9.191139e-01f,  -3.939920e-01f,
    9.900582e-01f, 1.406582e-01f, 9.117060e-01f,  -4.108432e-01f,
    9.891765e-01f, 1.467305e-01f, 9.039893e-01f,  -4.275551e-01f,
    9.882576e-01f, 1.527972e-01f, 8.959662e-01f,  -4.441221e-01f,
    9.873014e-01f, 1.588581e-01f, 8.876396e-01f,  -4.605387e-01f,
    9.863081e-01f, 1.649131e-01f, 8.790122e-01f,  -4.767992e-01f,
    9.852776e-01f, 1.709619e-01f, 8.700870e-01f,  -4.928982e-01f,
    9.842101e-01f, 1.770042e-01f, 8.608669e-01f,  -5.088301e-01f,
    9.831055e-01f, 1.830399e-01f, 8.513552e-01f,  -5.245897e-01f,
    9.819639e-01f, 1.890687e-01f, 8.415550e-01f,  -5.401715e-01f,
    9.807853e-01f, 1.950903e-01f, 8.314696e-01f,  -5.555702e-01f,
    9.795698e-01f, 2.011046e-01f, 8.211025e-01f,  -5.707807e-01f,
    9.783174e-01f, 2.071114e-01f, 8.104572e-01f,  -5.857979e-01f,
    9.770281e-01f, 2.131103e-01f, 7.995373e-01f,  -6.006165e-01f,
    9.757021e-01f, 2.191012e-01f, 7.883464e-01f,  -6.152316e-01f,
    9.743394e-01f, 2.250839e-01f, 7.768885e-01f,  -6.296382e-01f,
    9.729400e-01f, 2.310581e-01f, 7.651673e-01f,  -6.438315e-01f,
    9.715039e-01f, 2.370236e-01f, 7.531868e-01f,  -6.578067e-01f,
    9.700313e-01f, 2.429802e-01f, 7.409511e-01f,  -6.715590e-01f,
    9.685221e-01f, 2.489276e-01f, 7.284644e-01f,  -6.850837e-01f,
    9.669765e-01f, 2.548657e-01f, 7.157308e-01f,  -6.983762e-01f,
    9.653944e-01f, 2.607941e-01f, 7.027547e-01f,  -7.114322e-01f,
    9.637761e-01f, 2.667128e-01f, 6.895405e-01f,  -7.242471e-01f,
    9.621214e-01f, 2.726214e-01f, 6.760927e-01f,  -7.368166e-01f,
    9.604305e-01f, 2.785197e-01f, 6.624158e-01f,  -7.491364e-01f,
    9.587035e-01f, 2.844075e-01f, 6.485144e-01f,  -7.612024e-01f,
    9.569403e-01f, 2.902847e-01f, 6.343933e-01f,  -7.730105e-01f,
    9.551412e-01f, 2.961509e-01f, 6.200572e-01f,  -7.845566e-01f,
    9.533060e-01f, 3.020059e-01f, 6.055110e-01f,  -7.958369e-01f,
    9.514350e-01f, 3.078496e-01f, 5.907597e-01f,  -8.068476e-01f,
    9.495282e-01f, 3.136817e-01f, 5.758082e-01f,  -8.175848e-01f,
    9.475856e-01f, 3.195020e-01f, 5.606616e-01f,  -8.280450e-01f,
    9.456073e-01f, 3.253103e-01f, 5.453250e-01f,  -8.382247e-01f,
    9.435935e-01f, 3.311063e-01f, 5.298036e-01f,  -8.481203e-01f,
    9.415441e-01f, 3.368899e-01f, 5.141027e-01f,  -8.577286e-01f,
    9.394592e-01f, 3.426607e-01f, 4.982277e-01f,  -8.670462e-01f,
    9.373390e-01f, 3.484187e-01f, 4.821838e-01f,  -8.760701e-01f,
    9.351835e-01f, 3.541635e-01f, 4.659765e-01f,  -8.847971e-01f,
    9.329928e-01f, 3.598950e-01f, 4.496113e-01f,  -8.932243e-01f,
    9.307670e-01f, 3.656130e-01f, 4.330938e-01f,  -9.013488e-01f,
    9.285061e-01f, 3.713172e-01f, 4.164296e-01f,  -9.091680e-01f,
    9.262102e-01f, 3.770074e-01f, 3.996242e-01f,  -9.166791e-01f,
    9.238795e-01f, 3.826834e-01f, 3.826834e-01f,  -9.238795e-01f,
    9.215140e-01f, 3.883450e-01f, 3.656130e-01f,  -9.307670e-01f,
    9.191139e-01f, 3.939920e-01f, 3.484187e-01f,  -9.373390e-01f,
    9.166791e-01f, 3.996242e-01f, 3.311063e-01f,  -9.435935e-01f,
    9.142098e-01f, 4.052413e-01f, 3.136817e-01f,  -9.495282e-01f,
    9.117060e-01f, 4.108432e-01f, 2.961509e-01f,  -9.551412e-01f,
    9.091680e-01f, 4.164296e-01f, 2.785197e-01f,  -9.604305e-01f,
    9.065957e-01f, 4.220003e-01f, 2.607941e-01f,  -9.653944e-01f,
    9.039893e-01f, 4.275551e-01f, 2.429802e-01f,  -9.700313e-01f,
    9.013488e-01f, 4.330938e-01f, 2.250839e-01f,  -9.743394e-01f,
    8.986745e-01f, 4.386162e-01f, 2.071114e-01f,  -9.783174e-01f,
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    1.799475e-01f, 1.792317e-01f, 1.785155e-01f,  1.777988e-01f,
    1.770818e-01f, 1.763643e-01f, 1.756464e-01f,  1.749281e-01f,
    1.742093e-01f, 1.734902e-01f, 1.727707e-01f,  1.720507e-01f,
    1.713304e-01f, 1.706096e-01f, 1.698884e-01f,  1.691669e-01f,
    1.684449e-01f, 1.677226e-01f, 1.669998e-01f,  1.662767e-01f,
    1.655532e-01f, 1.648292e-01f, 1.641049e-01f,  1.633802e-01f,
    1.626551e-01f, 1.619297e-01f, 1.612038e-01f,  1.604776e-01f,
    1.597510e-01f, 1.590240e-01f, 1.582967e-01f,  1.575690e-01f,
    1.568409e-01f, 1.561124e-01f, 1.553836e-01f,  1.546544e-01f,
    1.539248e-01f, 1.531949e-01f, 1.524646e-01f,  1.517340e-01f,
    1.510030e-01f, 1.502716e-01f, 1.495399e-01f,  1.488079e-01f,
    1.480754e-01f, 1.473427e-01f, 1.466096e-01f,  1.458761e-01f,
    1.451423e-01f, 1.444082e-01f, 1.436737e-01f,  1.429389e-01f,
    1.422038e-01f, 1.414683e-01f, 1.407325e-01f,  1.399963e-01f,
    1.392598e-01f, 1.385230e-01f, 1.377859e-01f,  1.370485e-01f,
    1.363107e-01f, 1.355726e-01f, 1.348342e-01f,  1.340954e-01f,
    1.333564e-01f, 1.326170e-01f, 1.318773e-01f,  1.311374e-01f,
    1.303971e-01f, 1.296565e-01f, 1.289156e-01f,  1.281743e-01f,
    1.274328e-01f, 1.266910e-01f, 1.259489e-01f,  1.252065e-01f,
    1.244638e-01f, 1.237208e-01f, 1.229775e-01f,  1.222340e-01f,
    1.214901e-01f, 1.207459e-01f, 1.200015e-01f,  1.192568e-01f,
    1.185118e-01f, 1.177665e-01f, 1.170210e-01f,  1.162752e-01f,
    1.155291e-01f, 1.147827e-01f, 1.140360e-01f,  1.132891e-01f,
    1.125420e-01f, 1.117945e-01f, 1.110468e-01f,  1.102988e-01f,
    1.095506e-01f, 1.088021e-01f, 1.080534e-01f,  1.073044e-01f,
    1.065552e-01f, 1.058057e-01f, 1.050559e-01f,  1.043059e-01f,
    1.035557e-01f, 1.028052e-01f, 1.020545e-01f,  1.013035e-01f,
    1.005523e-01f, 9.980088e-02f, 9.904921e-02f,  9.829730e-02f,
    9.754516e-02f, 9.679279e-02f, 9.604020e-02f,  9.528738e-02f,
    9.453433e-02f, 9.378106e-02f, 9.302758e-02f,  9.227387e-02f,
    9.151994e-02f, 9.076580e-02f, 9.001145e-02f,  8.925689e-02f,
    8.850211e-02f, 8.774713e-02f, 8.699194e-02f,  8.623654e-02f,
    8.548094e-02f, 8.472515e-02f, 8.396915e-02f,  8.321295e-02f,
    8.245656e-02f, 8.169997e-02f, 8.094320e-02f,  8.018623e-02f,
    7.942907e-02f, 7.867173e-02f, 7.791420e-02f,  7.715649e-02f,
    7.639859e-02f, 7.564052e-02f, 7.488227e-02f,  7.412384e-02f,
    7.336524e-02f, 7.260646e-02f, 7.184752e-02f,  7.108840e-02f,
    7.032912e-02f, 6.956967e-02f, 6.881006e-02f,  6.805029e-02f,
    6.729035e-02f, 6.653026e-02f, 6.577001e-02f,  6.500961e-02f,
    6.424906e-02f, 6.348835e-02f, 6.272749e-02f,  6.196649e-02f,
    6.120534e-02f, 6.044404e-02f, 5.968261e-02f,  5.892103e-02f,
    5.815932e-02f, 5.739746e-02f, 5.663548e-02f,  5.587336e-02f,
    5.511110e-02f, 5.434872e-02f, 5.358621e-02f,  5.282358e-02f,
    5.206082e-02f, 5.129793e-02f, 5.053493e-02f,  4.977181e-02f,
    4.900857e-02f, 4.824522e-02f, 4.748175e-02f,  4.671817e-02f,
    4.595448e-02f, 4.519068e-02f, 4.442678e-02f,  4.366277e-02f,
    4.289866e-02f, 4.213444e-02f, 4.137013e-02f,  4.060572e-02f,
    3.984122e-02f, 3.907662e-02f, 3.831193e-02f,  3.754715e-02f,
    3.678228e-02f, 3.601733e-02f, 3.525229e-02f,  3.448716e-02f,
    3.372196e-02f, 3.295668e-02f, 3.219132e-02f,  3.142588e-02f,
    3.066037e-02f, 2.989479e-02f, 2.912913e-02f,  2.836341e-02f,
    2.759762e-02f, 2.683177e-02f, 2.606585e-02f,  2.529987e-02f,
    2.453384e-02f, 2.376774e-02f, 2.300159e-02f,  2.223539e-02f,
    2.146913e-02f, 2.070282e-02f, 1.993646e-02f,  1.917006e-02f,
    1.840361e-02f, 1.763712e-02f, 1.687059e-02f,  1.610401e-02f,
    1.533740e-02f, 1.457075e-02f, 1.380407e-02f,  1.303736e-02f,
    1.227061e-02f, 1.150384e-02f, 1.073704e-02f,  9.970214e-03f,
    9.203365e-03f, 8.436494e-03f, 7.669603e-03f,  6.902694e-03f,
    6.135769e-03f, 5.368830e-03f, 4.601877e-03f,  3.834914e-03f,
    3.067942e-03f, 2.300963e-03f, 1.533978e-03f,  7.669901e-04f};

// ==========================================================================================
// internal tools
// ==========================================================================================
static void AUP_FFTW_cftleaf(int n, int isplt, float* a, int nw, float* w);
static void AUP_FFTW_cftf1st(int n, float* a, float* w);
static void AUP_FFTW_cftrec4(int n, float* a, int nw, float* w);
static void AUP_FFTW_cftfsub(int n, float* a, int* ip, int nw, float* w);
static void AUP_FFTW_cftbsub(int n, float* a, int* ip, int nw, float* w);
static void AUP_FFTW_bitrv2(int n, int* ip, float* a);
static void AUP_FFTW_bitrv2conj(int n, int* ip, float* a);
static void AUP_FFTW_bitrv216(float* a);
static void AUP_FFTW_bitrv216neg(float* a);
static void AUP_FFTW_bitrv208(float* a);
static void AUP_FFTW_bitrv208neg(float* a);
static void AUP_FFTW_cftb1st(int n, float* a, float* w);
static int AUP_FFTW_cfttree(int n, int j, int k, float* a, int nw, float* w);
static void AUP_FFTW_cftmdl1(int n, float* a, float* w);
static void AUP_FFTW_cftmdl2(int n, float* a, float* w);
static void AUP_FFTW_cftfx41(int n, float* a, int nw, float* w);
static void AUP_FFTW_cftf161(float* a, float* w);
static void AUP_FFTW_cftf162(float* a, float* w);
static void AUP_FFTW_cftf081(float* a, float* w);
static void AUP_FFTW_cftf082(float* a, float* w);
static void AUP_FFTW_cftf040(float* a);
static void AUP_FFTW_cftb040(float* a);
static void AUP_FFTW_cftx020(float* a);
static void AUP_FFTW_rftfsub(int n, float* a, int nc, float* c);
static void AUP_FFTW_rftbsub(int n, float* a, int nc, float* c);
static void AUP_FFTW_dctsub(int n, float* a, int nc, float* c);
static void AUP_FFTW_dstsub(int n, float* a, int nc, float* c);
static void AUP_FFTW_rdft(int n, int isgn, float* a, int* ip, float* w);

static void AUP_FFTW_cftleaf(int n, int isplt, float* a, int nw, float* w) {
  if (n == 512) {
    AUP_FFTW_cftmdl1(128, a, &w[nw - 64]);
    AUP_FFTW_cftf161(a, &w[nw - 8]);
    AUP_FFTW_cftf162(&a[32], &w[nw - 32]);
    AUP_FFTW_cftf161(&a[64], &w[nw - 8]);
    AUP_FFTW_cftf161(&a[96], &w[nw - 8]);
    AUP_FFTW_cftmdl2(128, &a[128], &w[nw - 128]);
    AUP_FFTW_cftf161(&a[128], &w[nw - 8]);
    AUP_FFTW_cftf162(&a[160], &w[nw - 32]);
    AUP_FFTW_cftf161(&a[192], &w[nw - 8]);
    AUP_FFTW_cftf162(&a[224], &w[nw - 32]);
    AUP_FFTW_cftmdl1(128, &a[256], &w[nw - 64]);
    AUP_FFTW_cftf161(&a[256], &w[nw - 8]);
    AUP_FFTW_cftf162(&a[288], &w[nw - 32]);
    AUP_FFTW_cftf161(&a[320], &w[nw - 8]);
    AUP_FFTW_cftf161(&a[352], &w[nw - 8]);
    if (isplt != 0) {
      AUP_FFTW_cftmdl1(128, &a[384], &w[nw - 64]);
      AUP_FFTW_cftf161(&a[480], &w[nw - 8]);
    } else {
      AUP_FFTW_cftmdl2(128, &a[384], &w[nw - 128]);
      AUP_FFTW_cftf162(&a[480], &w[nw - 32]);
    }
    AUP_FFTW_cftf161(&a[384], &w[nw - 8]);
    AUP_FFTW_cftf162(&a[416], &w[nw - 32]);
    AUP_FFTW_cftf161(&a[448], &w[nw - 8]);
  } else {
    AUP_FFTW_cftmdl1(64, a, &w[nw - 32]);
    AUP_FFTW_cftf081(a, &w[nw - 8]);
    AUP_FFTW_cftf082(&a[16], &w[nw - 8]);
    AUP_FFTW_cftf081(&a[32], &w[nw - 8]);
    AUP_FFTW_cftf081(&a[48], &w[nw - 8]);
    AUP_FFTW_cftmdl2(64, &a[64], &w[nw - 64]);
    AUP_FFTW_cftf081(&a[64], &w[nw - 8]);
    AUP_FFTW_cftf082(&a[80], &w[nw - 8]);
    AUP_FFTW_cftf081(&a[96], &w[nw - 8]);
    AUP_FFTW_cftf082(&a[112], &w[nw - 8]);
    AUP_FFTW_cftmdl1(64, &a[128], &w[nw - 32]);
    AUP_FFTW_cftf081(&a[128], &w[nw - 8]);
    AUP_FFTW_cftf082(&a[144], &w[nw - 8]);
    AUP_FFTW_cftf081(&a[160], &w[nw - 8]);
    AUP_FFTW_cftf081(&a[176], &w[nw - 8]);
    if (isplt != 0) {
      AUP_FFTW_cftmdl1(64, &a[192], &w[nw - 32]);
      AUP_FFTW_cftf081(&a[240], &w[nw - 8]);
    } else {
      AUP_FFTW_cftmdl2(64, &a[192], &w[nw - 64]);
      AUP_FFTW_cftf082(&a[240], &w[nw - 8]);
    }
    AUP_FFTW_cftf081(&a[192], &w[nw - 8]);
    AUP_FFTW_cftf082(&a[208], &w[nw - 8]);
    AUP_FFTW_cftf081(&a[224], &w[nw - 8]);
  }
}

static void AUP_FFTW_cftf1st(int n, float* a, float* w) {
  int j, j0, j1, j2, j3, k, m, mh;
  float wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i,
      y3r, y3i;

  mh = n >> 3;
  m = 2 * mh;
  j1 = m;
  j2 = j1 + m;
  j3 = j2 + m;
  x0r = a[0] + a[j2];
  x0i = a[1] + a[j2 + 1];
  x1r = a[0] - a[j2];
  x1i = a[1] - a[j2 + 1];
  x2r = a[j1] + a[j3];
  x2i = a[j1 + 1] + a[j3 + 1];
  x3r = a[j1] - a[j3];
  x3i = a[j1 + 1] - a[j3 + 1];
  a[0] = x0r + x2r;
  a[1] = x0i + x2i;
  a[j1] = x0r - x2r;
  a[j1 + 1] = x0i - x2i;
  a[j2] = x1r - x3i;
  a[j2 + 1] = x1i + x3r;
  a[j3] = x1r + x3i;
  a[j3 + 1] = x1i - x3r;
  wn4r = w[1];
  csc1 = w[2];
  csc3 = w[3];
  wd1r = 1;
  wd1i = 0;
  wd3r = 1;
  wd3i = 0;
  k = 0;
  for (j = 2; j < mh - 2; j += 4) {
    k += 4;
    wk1r = csc1 * (wd1r + w[k]);
    wk1i = csc1 * (wd1i + w[k + 1]);
    wk3r = csc3 * (wd3r + w[k + 2]);
    wk3i = csc3 * (wd3i + w[k + 3]);
    wd1r = w[k];
    wd1i = w[k + 1];
    wd3r = w[k + 2];
    wd3i = w[k + 3];
    j1 = j + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j] + a[j2];
    x0i = a[j + 1] + a[j2 + 1];
    x1r = a[j] - a[j2];
    x1i = a[j + 1] - a[j2 + 1];
    y0r = a[j + 2] + a[j2 + 2];
    y0i = a[j + 3] + a[j2 + 3];
    y1r = a[j + 2] - a[j2 + 2];
    y1i = a[j + 3] - a[j2 + 3];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    y2r = a[j1 + 2] + a[j3 + 2];
    y2i = a[j1 + 3] + a[j3 + 3];
    y3r = a[j1 + 2] - a[j3 + 2];
    y3i = a[j1 + 3] - a[j3 + 3];
    a[j] = x0r + x2r;
    a[j + 1] = x0i + x2i;
    a[j + 2] = y0r + y2r;
    a[j + 3] = y0i + y2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    a[j1 + 2] = y0r - y2r;
    a[j1 + 3] = y0i - y2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2] = wk1r * x0r - wk1i * x0i;
    a[j2 + 1] = wk1r * x0i + wk1i * x0r;
    x0r = y1r - y3i;
    x0i = y1i + y3r;
    a[j2 + 2] = wd1r * x0r - wd1i * x0i;
    a[j2 + 3] = wd1r * x0i + wd1i * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3] = wk3r * x0r + wk3i * x0i;
    a[j3 + 1] = wk3r * x0i - wk3i * x0r;
    x0r = y1r + y3i;
    x0i = y1i - y3r;
    a[j3 + 2] = wd3r * x0r + wd3i * x0i;
    a[j3 + 3] = wd3r * x0i - wd3i * x0r;
    j0 = m - j;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0] + a[j2];
    x0i = a[j0 + 1] + a[j2 + 1];
    x1r = a[j0] - a[j2];
    x1i = a[j0 + 1] - a[j2 + 1];
    y0r = a[j0 - 2] + a[j2 - 2];
    y0i = a[j0 - 1] + a[j2 - 1];
    y1r = a[j0 - 2] - a[j2 - 2];
    y1i = a[j0 - 1] - a[j2 - 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    y2r = a[j1 - 2] + a[j3 - 2];
    y2i = a[j1 - 1] + a[j3 - 1];
    y3r = a[j1 - 2] - a[j3 - 2];
    y3i = a[j1 - 1] - a[j3 - 1];
    a[j0] = x0r + x2r;
    a[j0 + 1] = x0i + x2i;
    a[j0 - 2] = y0r + y2r;
    a[j0 - 1] = y0i + y2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    a[j1 - 2] = y0r - y2r;
    a[j1 - 1] = y0i - y2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2] = wk1i * x0r - wk1r * x0i;
    a[j2 + 1] = wk1i * x0i + wk1r * x0r;
    x0r = y1r - y3i;
    x0i = y1i + y3r;
    a[j2 - 2] = wd1i * x0r - wd1r * x0i;
    a[j2 - 1] = wd1i * x0i + wd1r * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3] = wk3i * x0r + wk3r * x0i;
    a[j3 + 1] = wk3i * x0i - wk3r * x0r;
    x0r = y1r + y3i;
    x0i = y1i - y3r;
    a[j3 - 2] = wd3i * x0r + wd3r * x0i;
    a[j3 - 1] = wd3i * x0i - wd3r * x0r;
  }
  wk1r = csc1 * (wd1r + wn4r);
  wk1i = csc1 * (wd1i + wn4r);
  wk3r = csc3 * (wd3r - wn4r);
  wk3i = csc3 * (wd3i - wn4r);
  j0 = mh;
  j1 = j0 + m;
  j2 = j1 + m;
  j3 = j2 + m;
  x0r = a[j0 - 2] + a[j2 - 2];
  x0i = a[j0 - 1] + a[j2 - 1];
  x1r = a[j0 - 2] - a[j2 - 2];
  x1i = a[j0 - 1] - a[j2 - 1];
  x2r = a[j1 - 2] + a[j3 - 2];
  x2i = a[j1 - 1] + a[j3 - 1];
  x3r = a[j1 - 2] - a[j3 - 2];
  x3i = a[j1 - 1] - a[j3 - 1];
  a[j0 - 2] = x0r + x2r;
  a[j0 - 1] = x0i + x2i;
  a[j1 - 2] = x0r - x2r;
  a[j1 - 1] = x0i - x2i;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  a[j2 - 2] = wk1r * x0r - wk1i * x0i;
  a[j2 - 1] = wk1r * x0i + wk1i * x0r;
  x0r = x1r + x3i;
  x0i = x1i - x3r;
  a[j3 - 2] = wk3r * x0r + wk3i * x0i;
  a[j3 - 1] = wk3r * x0i - wk3i * x0r;
  x0r = a[j0] + a[j2];
  x0i = a[j0 + 1] + a[j2 + 1];
  x1r = a[j0] - a[j2];
  x1i = a[j0 + 1] - a[j2 + 1];
  x2r = a[j1] + a[j3];
  x2i = a[j1 + 1] + a[j3 + 1];
  x3r = a[j1] - a[j3];
  x3i = a[j1 + 1] - a[j3 + 1];
  a[j0] = x0r + x2r;
  a[j0 + 1] = x0i + x2i;
  a[j1] = x0r - x2r;
  a[j1 + 1] = x0i - x2i;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  a[j2] = wn4r * (x0r - x0i);
  a[j2 + 1] = wn4r * (x0i + x0r);
  x0r = x1r + x3i;
  x0i = x1i - x3r;
  a[j3] = -wn4r * (x0r + x0i);
  a[j3 + 1] = -wn4r * (x0i - x0r);
  x0r = a[j0 + 2] + a[j2 + 2];
  x0i = a[j0 + 3] + a[j2 + 3];
  x1r = a[j0 + 2] - a[j2 + 2];
  x1i = a[j0 + 3] - a[j2 + 3];
  x2r = a[j1 + 2] + a[j3 + 2];
  x2i = a[j1 + 3] + a[j3 + 3];
  x3r = a[j1 + 2] - a[j3 + 2];
  x3i = a[j1 + 3] - a[j3 + 3];
  a[j0 + 2] = x0r + x2r;
  a[j0 + 3] = x0i + x2i;
  a[j1 + 2] = x0r - x2r;
  a[j1 + 3] = x0i - x2i;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  a[j2 + 2] = wk1i * x0r - wk1r * x0i;
  a[j2 + 3] = wk1i * x0i + wk1r * x0r;
  x0r = x1r + x3i;
  x0i = x1i - x3r;
  a[j3 + 2] = wk3i * x0r + wk3r * x0i;
  a[j3 + 3] = wk3i * x0i - wk3r * x0r;
}

static void AUP_FFTW_cftrec4(int n, float* a, int nw, float* w) {
  int isplt, j, k, m;

  m = n;
  while (m > 512) {
    m >>= 2;
    AUP_FFTW_cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
  }
  AUP_FFTW_cftleaf(m, 1, &a[n - m], nw, w);
  k = 0;
  for (j = n - m; j > 0; j -= m) {
    k++;
    isplt = AUP_FFTW_cfttree(m, j, k, a, nw, w);
    AUP_FFTW_cftleaf(m, isplt, &a[j - m], nw, w);
  }
}

static void AUP_FFTW_cftfsub(int n, float* a, int* ip, int nw, float* w) {
  if (n > 8) {
    if (n > 32) {
      AUP_FFTW_cftf1st(n, a, &w[nw - (n >> 2)]);
      if (n > 512) {
        AUP_FFTW_cftrec4(n, a, nw, w);
      } else if (n > 128) {
        AUP_FFTW_cftleaf(n, 1, a, nw, w);
      } else {
        AUP_FFTW_cftfx41(n, a, nw, w);
      }
      AUP_FFTW_bitrv2(n, ip, a);
    } else if (n == 32) {
      AUP_FFTW_cftf161(a, &w[nw - 8]);
      AUP_FFTW_bitrv216(a);
    } else {
      AUP_FFTW_cftf081(a, w);
      AUP_FFTW_bitrv208(a);
    }
  } else if (n == 8) {
    AUP_FFTW_cftf040(a);
  } else if (n == 4) {
    AUP_FFTW_cftx020(a);
  }
}

static void AUP_FFTW_cftbsub(int n, float* a, int* ip, int nw, float* w) {
  if (n > 8) {
    if (n > 32) {
      AUP_FFTW_cftb1st(n, a, &w[nw - (n >> 2)]);
      if (n > 512) {
        AUP_FFTW_cftrec4(n, a, nw, w);
      } else if (n > 128) {
        AUP_FFTW_cftleaf(n, 1, a, nw, w);
      } else {
        AUP_FFTW_cftfx41(n, a, nw, w);
      }
      AUP_FFTW_bitrv2conj(n, ip, a);
    } else if (n == 32) {
      AUP_FFTW_cftf161(a, &w[nw - 8]);
      AUP_FFTW_bitrv216neg(a);
    } else {
      AUP_FFTW_cftf081(a, w);
      AUP_FFTW_bitrv208neg(a);
    }
  } else if (n == 8) {
    AUP_FFTW_cftb040(a);
  } else if (n == 4) {
    AUP_FFTW_cftx020(a);
  }
}

static void AUP_FFTW_bitrv2(int n, int* ip, float* a) {
  int j, j1, k, k1, l, m, nh, nm;
  float xr, xi, yr, yi;

  m = 1;
  for (l = n >> 2; l > 8; l >>= 2) {
    m <<= 1;
  }
  nh = n >> 1;
  nm = 4 * m;
  if (l == 8) {
    for (k = 0; k < m; k++) {
      for (j = 0; j < k; j++) {
        j1 = 4 * j + 2 * ip[m + k];
        k1 = 4 * k + 2 * ip[m + j];
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += 2 * nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 -= nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += 2 * nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nh;
        k1 += 2;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= 2 * nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 += nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= 2 * nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += 2;
        k1 += nh;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += 2 * nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 -= nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += 2 * nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nh;
        k1 -= 2;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= 2 * nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 += nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= 2 * nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
      }
      k1 = 4 * k + 2 * ip[m + k];
      j1 = k1 + 2;
      k1 += nh;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 += nm;
      k1 += 2 * nm;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 += nm;
      k1 -= nm;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 -= 2;
      k1 -= nh;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 += nh + 2;
      k1 += nh + 2;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 -= nh - nm;
      k1 += 2 * nm - 2;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
    }
  } else {
    for (k = 0; k < m; k++) {
      for (j = 0; j < k; j++) {
        j1 = 4 * j + ip[m + k];
        k1 = 4 * k + ip[m + j];
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nh;
        k1 += 2;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += 2;
        k1 += nh;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nh;
        k1 -= 2;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= nm;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
      }
      k1 = 4 * k + ip[m + k];
      j1 = k1 + 2;
      k1 += nh;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 += nm;
      k1 += nm;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
    }
  }
}

static void AUP_FFTW_bitrv2conj(int n, int* ip, float* a) {
  int j, j1, k, k1, l, m, nh, nm;
  float xr, xi, yr, yi;

  m = 1;
  for (l = n >> 2; l > 8; l >>= 2) {
    m <<= 1;
  }
  nh = n >> 1;
  nm = 4 * m;
  if (l == 8) {
    for (k = 0; k < m; k++) {
      for (j = 0; j < k; j++) {
        j1 = 4 * j + 2 * ip[m + k];
        k1 = 4 * k + 2 * ip[m + j];
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += 2 * nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 -= nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += 2 * nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nh;
        k1 += 2;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= 2 * nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 += nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= 2 * nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += 2;
        k1 += nh;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += 2 * nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 -= nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += 2 * nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nh;
        k1 -= 2;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= 2 * nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 += nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= 2 * nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
      }
      k1 = 4 * k + 2 * ip[m + k];
      j1 = k1 + 2;
      k1 += nh;
      a[j1 - 1] = -a[j1 - 1];
      xr = a[j1];
      xi = -a[j1 + 1];
      yr = a[k1];
      yi = -a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      a[k1 + 3] = -a[k1 + 3];
      j1 += nm;
      k1 += 2 * nm;
      xr = a[j1];
      xi = -a[j1 + 1];
      yr = a[k1];
      yi = -a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 += nm;
      k1 -= nm;
      xr = a[j1];
      xi = -a[j1 + 1];
      yr = a[k1];
      yi = -a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 -= 2;
      k1 -= nh;
      xr = a[j1];
      xi = -a[j1 + 1];
      yr = a[k1];
      yi = -a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 += nh + 2;
      k1 += nh + 2;
      xr = a[j1];
      xi = -a[j1 + 1];
      yr = a[k1];
      yi = -a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      j1 -= nh - nm;
      k1 += 2 * nm - 2;
      a[j1 - 1] = -a[j1 - 1];
      xr = a[j1];
      xi = -a[j1 + 1];
      yr = a[k1];
      yi = -a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      a[k1 + 3] = -a[k1 + 3];
    }
  } else {
    for (k = 0; k < m; k++) {
      for (j = 0; j < k; j++) {
        j1 = 4 * j + ip[m + k];
        k1 = 4 * k + ip[m + j];
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nh;
        k1 += 2;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += 2;
        k1 += nh;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 += nm;
        k1 += nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nh;
        k1 -= 2;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        j1 -= nm;
        k1 -= nm;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
      }
      k1 = 4 * k + ip[m + k];
      j1 = k1 + 2;
      k1 += nh;
      a[j1 - 1] = -a[j1 - 1];
      xr = a[j1];
      xi = -a[j1 + 1];
      yr = a[k1];
      yi = -a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      a[k1 + 3] = -a[k1 + 3];
      j1 += nm;
      k1 += nm;
      a[j1 - 1] = -a[j1 - 1];
      xr = a[j1];
      xi = -a[j1 + 1];
      yr = a[k1];
      yi = -a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
      a[k1 + 3] = -a[k1 + 3];
    }
  }
}

static void AUP_FFTW_bitrv216(float* a) {
  float x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x7r, x7i, x8r, x8i,
      x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i;

  x1r = a[2];
  x1i = a[3];
  x2r = a[4];
  x2i = a[5];
  x3r = a[6];
  x3i = a[7];
  x4r = a[8];
  x4i = a[9];
  x5r = a[10];
  x5i = a[11];
  x7r = a[14];
  x7i = a[15];
  x8r = a[16];
  x8i = a[17];
  x10r = a[20];
  x10i = a[21];
  x11r = a[22];
  x11i = a[23];
  x12r = a[24];
  x12i = a[25];
  x13r = a[26];
  x13i = a[27];
  x14r = a[28];
  x14i = a[29];
  a[2] = x8r;
  a[3] = x8i;
  a[4] = x4r;
  a[5] = x4i;
  a[6] = x12r;
  a[7] = x12i;
  a[8] = x2r;
  a[9] = x2i;
  a[10] = x10r;
  a[11] = x10i;
  a[14] = x14r;
  a[15] = x14i;
  a[16] = x1r;
  a[17] = x1i;
  a[20] = x5r;
  a[21] = x5i;
  a[22] = x13r;
  a[23] = x13i;
  a[24] = x3r;
  a[25] = x3i;
  a[26] = x11r;
  a[27] = x11i;
  a[28] = x7r;
  a[29] = x7i;
}

static void AUP_FFTW_bitrv216neg(float* a) {
  float x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i,
      x8r, x8i, x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r,
      x14i, x15r, x15i;

  x1r = a[2];
  x1i = a[3];
  x2r = a[4];
  x2i = a[5];
  x3r = a[6];
  x3i = a[7];
  x4r = a[8];
  x4i = a[9];
  x5r = a[10];
  x5i = a[11];
  x6r = a[12];
  x6i = a[13];
  x7r = a[14];
  x7i = a[15];
  x8r = a[16];
  x8i = a[17];
  x9r = a[18];
  x9i = a[19];
  x10r = a[20];
  x10i = a[21];
  x11r = a[22];
  x11i = a[23];
  x12r = a[24];
  x12i = a[25];
  x13r = a[26];
  x13i = a[27];
  x14r = a[28];
  x14i = a[29];
  x15r = a[30];
  x15i = a[31];
  a[2] = x15r;
  a[3] = x15i;
  a[4] = x7r;
  a[5] = x7i;
  a[6] = x11r;
  a[7] = x11i;
  a[8] = x3r;
  a[9] = x3i;
  a[10] = x13r;
  a[11] = x13i;
  a[12] = x5r;
  a[13] = x5i;
  a[14] = x9r;
  a[15] = x9i;
  a[16] = x1r;
  a[17] = x1i;
  a[18] = x14r;
  a[19] = x14i;
  a[20] = x6r;
  a[21] = x6i;
  a[22] = x10r;
  a[23] = x10i;
  a[24] = x2r;
  a[25] = x2i;
  a[26] = x12r;
  a[27] = x12i;
  a[28] = x4r;
  a[29] = x4i;
  a[30] = x8r;
  a[31] = x8i;
}

static void AUP_FFTW_bitrv208(float* a) {
  float x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;

  x1r = a[2];
  x1i = a[3];
  x3r = a[6];
  x3i = a[7];
  x4r = a[8];
  x4i = a[9];
  x6r = a[12];
  x6i = a[13];
  a[2] = x4r;
  a[3] = x4i;
  a[6] = x6r;
  a[7] = x6i;
  a[8] = x1r;
  a[9] = x1i;
  a[12] = x3r;
  a[13] = x3i;
}

static void AUP_FFTW_bitrv208neg(float* a) {
  float x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i;

  x1r = a[2];
  x1i = a[3];
  x2r = a[4];
  x2i = a[5];
  x3r = a[6];
  x3i = a[7];
  x4r = a[8];
  x4i = a[9];
  x5r = a[10];
  x5i = a[11];
  x6r = a[12];
  x6i = a[13];
  x7r = a[14];
  x7i = a[15];
  a[2] = x7r;
  a[3] = x7i;
  a[4] = x3r;
  a[5] = x3i;
  a[6] = x5r;
  a[7] = x5i;
  a[8] = x1r;
  a[9] = x1i;
  a[10] = x6r;
  a[11] = x6i;
  a[12] = x2r;
  a[13] = x2i;
  a[14] = x4r;
  a[15] = x4i;
}

static void AUP_FFTW_cftb1st(int n, float* a, float* w) {
  int j, j0, j1, j2, j3, k, m, mh;
  float wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i,
      y3r, y3i;

  mh = n >> 3;
  m = 2 * mh;
  j1 = m;
  j2 = j1 + m;
  j3 = j2 + m;
  x0r = a[0] + a[j2];
  x0i = -a[1] - a[j2 + 1];
  x1r = a[0] - a[j2];
  x1i = -a[1] + a[j2 + 1];
  x2r = a[j1] + a[j3];
  x2i = a[j1 + 1] + a[j3 + 1];
  x3r = a[j1] - a[j3];
  x3i = a[j1 + 1] - a[j3 + 1];
  a[0] = x0r + x2r;
  a[1] = x0i - x2i;
  a[j1] = x0r - x2r;
  a[j1 + 1] = x0i + x2i;
  a[j2] = x1r + x3i;
  a[j2 + 1] = x1i + x3r;
  a[j3] = x1r - x3i;
  a[j3 + 1] = x1i - x3r;
  wn4r = w[1];
  csc1 = w[2];
  csc3 = w[3];
  wd1r = 1;
  wd1i = 0;
  wd3r = 1;
  wd3i = 0;
  k = 0;
  for (j = 2; j < mh - 2; j += 4) {
    k += 4;
    wk1r = csc1 * (wd1r + w[k]);
    wk1i = csc1 * (wd1i + w[k + 1]);
    wk3r = csc3 * (wd3r + w[k + 2]);
    wk3i = csc3 * (wd3i + w[k + 3]);
    wd1r = w[k];
    wd1i = w[k + 1];
    wd3r = w[k + 2];
    wd3i = w[k + 3];
    j1 = j + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j] + a[j2];
    x0i = -a[j + 1] - a[j2 + 1];
    x1r = a[j] - a[j2];
    x1i = -a[j + 1] + a[j2 + 1];
    y0r = a[j + 2] + a[j2 + 2];
    y0i = -a[j + 3] - a[j2 + 3];
    y1r = a[j + 2] - a[j2 + 2];
    y1i = -a[j + 3] + a[j2 + 3];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    y2r = a[j1 + 2] + a[j3 + 2];
    y2i = a[j1 + 3] + a[j3 + 3];
    y3r = a[j1 + 2] - a[j3 + 2];
    y3i = a[j1 + 3] - a[j3 + 3];
    a[j] = x0r + x2r;
    a[j + 1] = x0i - x2i;
    a[j + 2] = y0r + y2r;
    a[j + 3] = y0i - y2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i + x2i;
    a[j1 + 2] = y0r - y2r;
    a[j1 + 3] = y0i + y2i;
    x0r = x1r + x3i;
    x0i = x1i + x3r;
    a[j2] = wk1r * x0r - wk1i * x0i;
    a[j2 + 1] = wk1r * x0i + wk1i * x0r;
    x0r = y1r + y3i;
    x0i = y1i + y3r;
    a[j2 + 2] = wd1r * x0r - wd1i * x0i;
    a[j2 + 3] = wd1r * x0i + wd1i * x0r;
    x0r = x1r - x3i;
    x0i = x1i - x3r;
    a[j3] = wk3r * x0r + wk3i * x0i;
    a[j3 + 1] = wk3r * x0i - wk3i * x0r;
    x0r = y1r - y3i;
    x0i = y1i - y3r;
    a[j3 + 2] = wd3r * x0r + wd3i * x0i;
    a[j3 + 3] = wd3r * x0i - wd3i * x0r;
    j0 = m - j;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0] + a[j2];
    x0i = -a[j0 + 1] - a[j2 + 1];
    x1r = a[j0] - a[j2];
    x1i = -a[j0 + 1] + a[j2 + 1];
    y0r = a[j0 - 2] + a[j2 - 2];
    y0i = -a[j0 - 1] - a[j2 - 1];
    y1r = a[j0 - 2] - a[j2 - 2];
    y1i = -a[j0 - 1] + a[j2 - 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    y2r = a[j1 - 2] + a[j3 - 2];
    y2i = a[j1 - 1] + a[j3 - 1];
    y3r = a[j1 - 2] - a[j3 - 2];
    y3i = a[j1 - 1] - a[j3 - 1];
    a[j0] = x0r + x2r;
    a[j0 + 1] = x0i - x2i;
    a[j0 - 2] = y0r + y2r;
    a[j0 - 1] = y0i - y2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i + x2i;
    a[j1 - 2] = y0r - y2r;
    a[j1 - 1] = y0i + y2i;
    x0r = x1r + x3i;
    x0i = x1i + x3r;
    a[j2] = wk1i * x0r - wk1r * x0i;
    a[j2 + 1] = wk1i * x0i + wk1r * x0r;
    x0r = y1r + y3i;
    x0i = y1i + y3r;
    a[j2 - 2] = wd1i * x0r - wd1r * x0i;
    a[j2 - 1] = wd1i * x0i + wd1r * x0r;
    x0r = x1r - x3i;
    x0i = x1i - x3r;
    a[j3] = wk3i * x0r + wk3r * x0i;
    a[j3 + 1] = wk3i * x0i - wk3r * x0r;
    x0r = y1r - y3i;
    x0i = y1i - y3r;
    a[j3 - 2] = wd3i * x0r + wd3r * x0i;
    a[j3 - 1] = wd3i * x0i - wd3r * x0r;
  }
  wk1r = csc1 * (wd1r + wn4r);
  wk1i = csc1 * (wd1i + wn4r);
  wk3r = csc3 * (wd3r - wn4r);
  wk3i = csc3 * (wd3i - wn4r);
  j0 = mh;
  j1 = j0 + m;
  j2 = j1 + m;
  j3 = j2 + m;
  x0r = a[j0 - 2] + a[j2 - 2];
  x0i = -a[j0 - 1] - a[j2 - 1];
  x1r = a[j0 - 2] - a[j2 - 2];
  x1i = -a[j0 - 1] + a[j2 - 1];
  x2r = a[j1 - 2] + a[j3 - 2];
  x2i = a[j1 - 1] + a[j3 - 1];
  x3r = a[j1 - 2] - a[j3 - 2];
  x3i = a[j1 - 1] - a[j3 - 1];
  a[j0 - 2] = x0r + x2r;
  a[j0 - 1] = x0i - x2i;
  a[j1 - 2] = x0r - x2r;
  a[j1 - 1] = x0i + x2i;
  x0r = x1r + x3i;
  x0i = x1i + x3r;
  a[j2 - 2] = wk1r * x0r - wk1i * x0i;
  a[j2 - 1] = wk1r * x0i + wk1i * x0r;
  x0r = x1r - x3i;
  x0i = x1i - x3r;
  a[j3 - 2] = wk3r * x0r + wk3i * x0i;
  a[j3 - 1] = wk3r * x0i - wk3i * x0r;
  x0r = a[j0] + a[j2];
  x0i = -a[j0 + 1] - a[j2 + 1];
  x1r = a[j0] - a[j2];
  x1i = -a[j0 + 1] + a[j2 + 1];
  x2r = a[j1] + a[j3];
  x2i = a[j1 + 1] + a[j3 + 1];
  x3r = a[j1] - a[j3];
  x3i = a[j1 + 1] - a[j3 + 1];
  a[j0] = x0r + x2r;
  a[j0 + 1] = x0i - x2i;
  a[j1] = x0r - x2r;
  a[j1 + 1] = x0i + x2i;
  x0r = x1r + x3i;
  x0i = x1i + x3r;
  a[j2] = wn4r * (x0r - x0i);
  a[j2 + 1] = wn4r * (x0i + x0r);
  x0r = x1r - x3i;
  x0i = x1i - x3r;
  a[j3] = -wn4r * (x0r + x0i);
  a[j3 + 1] = -wn4r * (x0i - x0r);
  x0r = a[j0 + 2] + a[j2 + 2];
  x0i = -a[j0 + 3] - a[j2 + 3];
  x1r = a[j0 + 2] - a[j2 + 2];
  x1i = -a[j0 + 3] + a[j2 + 3];
  x2r = a[j1 + 2] + a[j3 + 2];
  x2i = a[j1 + 3] + a[j3 + 3];
  x3r = a[j1 + 2] - a[j3 + 2];
  x3i = a[j1 + 3] - a[j3 + 3];
  a[j0 + 2] = x0r + x2r;
  a[j0 + 3] = x0i - x2i;
  a[j1 + 2] = x0r - x2r;
  a[j1 + 3] = x0i + x2i;
  x0r = x1r + x3i;
  x0i = x1i + x3r;
  a[j2 + 2] = wk1i * x0r - wk1r * x0i;
  a[j2 + 3] = wk1i * x0i + wk1r * x0r;
  x0r = x1r - x3i;
  x0i = x1i - x3r;
  a[j3 + 2] = wk3i * x0r + wk3r * x0i;
  a[j3 + 3] = wk3i * x0i - wk3r * x0r;
}

static int AUP_FFTW_cfttree(int n, int j, int k, float* a, int nw, float* w) {
  int i, isplt, m;

  if ((k & 3) != 0) {
    isplt = k & 1;
    if (isplt != 0) {
      AUP_FFTW_cftmdl1(n, &a[j - n], &w[nw - (n >> 1)]);
    } else {
      AUP_FFTW_cftmdl2(n, &a[j - n], &w[nw - n]);
    }
  } else {
    m = n;
    for (i = k; (i & 3) == 0; i >>= 2) {
      m <<= 2;
    }
    isplt = i & 1;
    if (isplt != 0) {
      while (m > 128) {
        AUP_FFTW_cftmdl1(m, &a[j - m], &w[nw - (m >> 1)]);
        m >>= 2;
      }
    } else {
      while (m > 128) {
        AUP_FFTW_cftmdl2(m, &a[j - m], &w[nw - m]);
        m >>= 2;
      }
    }
  }
  return isplt;
}

static void AUP_FFTW_cftmdl1(int n, float* a, float* w) {
  int j, j0, j1, j2, j3, k, m, mh;
  float wn4r, wk1r, wk1i, wk3r, wk3i;
  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

  mh = n >> 3;
  m = 2 * mh;
  j1 = m;
  j2 = j1 + m;
  j3 = j2 + m;
  x0r = a[0] + a[j2];
  x0i = a[1] + a[j2 + 1];
  x1r = a[0] - a[j2];
  x1i = a[1] - a[j2 + 1];
  x2r = a[j1] + a[j3];
  x2i = a[j1 + 1] + a[j3 + 1];
  x3r = a[j1] - a[j3];
  x3i = a[j1 + 1] - a[j3 + 1];
  a[0] = x0r + x2r;
  a[1] = x0i + x2i;
  a[j1] = x0r - x2r;
  a[j1 + 1] = x0i - x2i;
  a[j2] = x1r - x3i;
  a[j2 + 1] = x1i + x3r;
  a[j3] = x1r + x3i;
  a[j3 + 1] = x1i - x3r;
  wn4r = w[1];
  k = 0;
  for (j = 2; j < mh; j += 2) {
    k += 4;
    wk1r = w[k];
    wk1i = w[k + 1];
    wk3r = w[k + 2];
    wk3i = w[k + 3];
    j1 = j + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j] + a[j2];
    x0i = a[j + 1] + a[j2 + 1];
    x1r = a[j] - a[j2];
    x1i = a[j + 1] - a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[j] = x0r + x2r;
    a[j + 1] = x0i + x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2] = wk1r * x0r - wk1i * x0i;
    a[j2 + 1] = wk1r * x0i + wk1i * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3] = wk3r * x0r + wk3i * x0i;
    a[j3 + 1] = wk3r * x0i - wk3i * x0r;
    j0 = m - j;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0] + a[j2];
    x0i = a[j0 + 1] + a[j2 + 1];
    x1r = a[j0] - a[j2];
    x1i = a[j0 + 1] - a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[j0] = x0r + x2r;
    a[j0 + 1] = x0i + x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2] = wk1i * x0r - wk1r * x0i;
    a[j2 + 1] = wk1i * x0i + wk1r * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3] = wk3i * x0r + wk3r * x0i;
    a[j3 + 1] = wk3i * x0i - wk3r * x0r;
  }
  j0 = mh;
  j1 = j0 + m;
  j2 = j1 + m;
  j3 = j2 + m;
  x0r = a[j0] + a[j2];
  x0i = a[j0 + 1] + a[j2 + 1];
  x1r = a[j0] - a[j2];
  x1i = a[j0 + 1] - a[j2 + 1];
  x2r = a[j1] + a[j3];
  x2i = a[j1 + 1] + a[j3 + 1];
  x3r = a[j1] - a[j3];
  x3i = a[j1 + 1] - a[j3 + 1];
  a[j0] = x0r + x2r;
  a[j0 + 1] = x0i + x2i;
  a[j1] = x0r - x2r;
  a[j1 + 1] = x0i - x2i;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  a[j2] = wn4r * (x0r - x0i);
  a[j2 + 1] = wn4r * (x0i + x0r);
  x0r = x1r + x3i;
  x0i = x1i - x3r;
  a[j3] = -wn4r * (x0r + x0i);
  a[j3 + 1] = -wn4r * (x0i - x0r);
}

static void AUP_FFTW_cftmdl2(int n, float* a, float* w) {
  int j, j0, j1, j2, j3, k, kr, m, mh;
  float wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;

  mh = n >> 3;
  m = 2 * mh;
  wn4r = w[1];
  j1 = m;
  j2 = j1 + m;
  j3 = j2 + m;
  x0r = a[0] - a[j2 + 1];
  x0i = a[1] + a[j2];
  x1r = a[0] + a[j2 + 1];
  x1i = a[1] - a[j2];
  x2r = a[j1] - a[j3 + 1];
  x2i = a[j1 + 1] + a[j3];
  x3r = a[j1] + a[j3 + 1];
  x3i = a[j1 + 1] - a[j3];
  y0r = wn4r * (x2r - x2i);
  y0i = wn4r * (x2i + x2r);
  a[0] = x0r + y0r;
  a[1] = x0i + y0i;
  a[j1] = x0r - y0r;
  a[j1 + 1] = x0i - y0i;
  y0r = wn4r * (x3r - x3i);
  y0i = wn4r * (x3i + x3r);
  a[j2] = x1r - y0i;
  a[j2 + 1] = x1i + y0r;
  a[j3] = x1r + y0i;
  a[j3 + 1] = x1i - y0r;
  k = 0;
  kr = 2 * m;
  for (j = 2; j < mh; j += 2) {
    k += 4;
    wk1r = w[k];
    wk1i = w[k + 1];
    wk3r = w[k + 2];
    wk3i = w[k + 3];
    kr -= 4;
    wd1i = w[kr];
    wd1r = w[kr + 1];
    wd3i = w[kr + 2];
    wd3r = w[kr + 3];
    j1 = j + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j] - a[j2 + 1];
    x0i = a[j + 1] + a[j2];
    x1r = a[j] + a[j2 + 1];
    x1i = a[j + 1] - a[j2];
    x2r = a[j1] - a[j3 + 1];
    x2i = a[j1 + 1] + a[j3];
    x3r = a[j1] + a[j3 + 1];
    x3i = a[j1 + 1] - a[j3];
    y0r = wk1r * x0r - wk1i * x0i;
    y0i = wk1r * x0i + wk1i * x0r;
    y2r = wd1r * x2r - wd1i * x2i;
    y2i = wd1r * x2i + wd1i * x2r;
    a[j] = y0r + y2r;
    a[j + 1] = y0i + y2i;
    a[j1] = y0r - y2r;
    a[j1 + 1] = y0i - y2i;
    y0r = wk3r * x1r + wk3i * x1i;
    y0i = wk3r * x1i - wk3i * x1r;
    y2r = wd3r * x3r + wd3i * x3i;
    y2i = wd3r * x3i - wd3i * x3r;
    a[j2] = y0r + y2r;
    a[j2 + 1] = y0i + y2i;
    a[j3] = y0r - y2r;
    a[j3 + 1] = y0i - y2i;
    j0 = m - j;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0] - a[j2 + 1];
    x0i = a[j0 + 1] + a[j2];
    x1r = a[j0] + a[j2 + 1];
    x1i = a[j0 + 1] - a[j2];
    x2r = a[j1] - a[j3 + 1];
    x2i = a[j1 + 1] + a[j3];
    x3r = a[j1] + a[j3 + 1];
    x3i = a[j1 + 1] - a[j3];
    y0r = wd1i * x0r - wd1r * x0i;
    y0i = wd1i * x0i + wd1r * x0r;
    y2r = wk1i * x2r - wk1r * x2i;
    y2i = wk1i * x2i + wk1r * x2r;
    a[j0] = y0r + y2r;
    a[j0 + 1] = y0i + y2i;
    a[j1] = y0r - y2r;
    a[j1 + 1] = y0i - y2i;
    y0r = wd3i * x1r + wd3r * x1i;
    y0i = wd3i * x1i - wd3r * x1r;
    y2r = wk3i * x3r + wk3r * x3i;
    y2i = wk3i * x3i - wk3r * x3r;
    a[j2] = y0r + y2r;
    a[j2 + 1] = y0i + y2i;
    a[j3] = y0r - y2r;
    a[j3 + 1] = y0i - y2i;
  }
  wk1r = w[m];
  wk1i = w[m + 1];
  j0 = mh;
  j1 = j0 + m;
  j2 = j1 + m;
  j3 = j2 + m;
  x0r = a[j0] - a[j2 + 1];
  x0i = a[j0 + 1] + a[j2];
  x1r = a[j0] + a[j2 + 1];
  x1i = a[j0 + 1] - a[j2];
  x2r = a[j1] - a[j3 + 1];
  x2i = a[j1 + 1] + a[j3];
  x3r = a[j1] + a[j3 + 1];
  x3i = a[j1 + 1] - a[j3];
  y0r = wk1r * x0r - wk1i * x0i;
  y0i = wk1r * x0i + wk1i * x0r;
  y2r = wk1i * x2r - wk1r * x2i;
  y2i = wk1i * x2i + wk1r * x2r;
  a[j0] = y0r + y2r;
  a[j0 + 1] = y0i + y2i;
  a[j1] = y0r - y2r;
  a[j1 + 1] = y0i - y2i;
  y0r = wk1i * x1r - wk1r * x1i;
  y0i = wk1i * x1i + wk1r * x1r;
  y2r = wk1r * x3r - wk1i * x3i;
  y2i = wk1r * x3i + wk1i * x3r;
  a[j2] = y0r - y2r;
  a[j2 + 1] = y0i - y2i;
  a[j3] = y0r + y2r;
  a[j3 + 1] = y0i + y2i;
}

static void AUP_FFTW_cftfx41(int n, float* a, int nw, float* w) {
  if (n == 128) {
    AUP_FFTW_cftf161(a, &w[nw - 8]);
    AUP_FFTW_cftf162(&a[32], &w[nw - 32]);
    AUP_FFTW_cftf161(&a[64], &w[nw - 8]);
    AUP_FFTW_cftf161(&a[96], &w[nw - 8]);
  } else {
    AUP_FFTW_cftf081(a, &w[nw - 8]);
    AUP_FFTW_cftf082(&a[16], &w[nw - 8]);
    AUP_FFTW_cftf081(&a[32], &w[nw - 8]);
    AUP_FFTW_cftf081(&a[48], &w[nw - 8]);
  }
}

static void AUP_FFTW_cftf161(float* a, float* w) {
  float wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r,
      y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i,
      y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i,
      y15r, y15i;

  wn4r = w[1];
  wk1r = w[2];
  wk1i = w[3];
  x0r = a[0] + a[16];
  x0i = a[1] + a[17];
  x1r = a[0] - a[16];
  x1i = a[1] - a[17];
  x2r = a[8] + a[24];
  x2i = a[9] + a[25];
  x3r = a[8] - a[24];
  x3i = a[9] - a[25];
  y0r = x0r + x2r;
  y0i = x0i + x2i;
  y4r = x0r - x2r;
  y4i = x0i - x2i;
  y8r = x1r - x3i;
  y8i = x1i + x3r;
  y12r = x1r + x3i;
  y12i = x1i - x3r;
  x0r = a[2] + a[18];
  x0i = a[3] + a[19];
  x1r = a[2] - a[18];
  x1i = a[3] - a[19];
  x2r = a[10] + a[26];
  x2i = a[11] + a[27];
  x3r = a[10] - a[26];
  x3i = a[11] - a[27];
  y1r = x0r + x2r;
  y1i = x0i + x2i;
  y5r = x0r - x2r;
  y5i = x0i - x2i;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  y9r = wk1r * x0r - wk1i * x0i;
  y9i = wk1r * x0i + wk1i * x0r;
  x0r = x1r + x3i;
  x0i = x1i - x3r;
  y13r = wk1i * x0r - wk1r * x0i;
  y13i = wk1i * x0i + wk1r * x0r;
  x0r = a[4] + a[20];
  x0i = a[5] + a[21];
  x1r = a[4] - a[20];
  x1i = a[5] - a[21];
  x2r = a[12] + a[28];
  x2i = a[13] + a[29];
  x3r = a[12] - a[28];
  x3i = a[13] - a[29];
  y2r = x0r + x2r;
  y2i = x0i + x2i;
  y6r = x0r - x2r;
  y6i = x0i - x2i;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  y10r = wn4r * (x0r - x0i);
  y10i = wn4r * (x0i + x0r);
  x0r = x1r + x3i;
  x0i = x1i - x3r;
  y14r = wn4r * (x0r + x0i);
  y14i = wn4r * (x0i - x0r);
  x0r = a[6] + a[22];
  x0i = a[7] + a[23];
  x1r = a[6] - a[22];
  x1i = a[7] - a[23];
  x2r = a[14] + a[30];
  x2i = a[15] + a[31];
  x3r = a[14] - a[30];
  x3i = a[15] - a[31];
  y3r = x0r + x2r;
  y3i = x0i + x2i;
  y7r = x0r - x2r;
  y7i = x0i - x2i;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  y11r = wk1i * x0r - wk1r * x0i;
  y11i = wk1i * x0i + wk1r * x0r;
  x0r = x1r + x3i;
  x0i = x1i - x3r;
  y15r = wk1r * x0r - wk1i * x0i;
  y15i = wk1r * x0i + wk1i * x0r;
  x0r = y12r - y14r;
  x0i = y12i - y14i;
  x1r = y12r + y14r;
  x1i = y12i + y14i;
  x2r = y13r - y15r;
  x2i = y13i - y15i;
  x3r = y13r + y15r;
  x3i = y13i + y15i;
  a[24] = x0r + x2r;
  a[25] = x0i + x2i;
  a[26] = x0r - x2r;
  a[27] = x0i - x2i;
  a[28] = x1r - x3i;
  a[29] = x1i + x3r;
  a[30] = x1r + x3i;
  a[31] = x1i - x3r;
  x0r = y8r + y10r;
  x0i = y8i + y10i;
  x1r = y8r - y10r;
  x1i = y8i - y10i;
  x2r = y9r + y11r;
  x2i = y9i + y11i;
  x3r = y9r - y11r;
  x3i = y9i - y11i;
  a[16] = x0r + x2r;
  a[17] = x0i + x2i;
  a[18] = x0r - x2r;
  a[19] = x0i - x2i;
  a[20] = x1r - x3i;
  a[21] = x1i + x3r;
  a[22] = x1r + x3i;
  a[23] = x1i - x3r;
  x0r = y5r - y7i;
  x0i = y5i + y7r;
  x2r = wn4r * (x0r - x0i);
  x2i = wn4r * (x0i + x0r);
  x0r = y5r + y7i;
  x0i = y5i - y7r;
  x3r = wn4r * (x0r - x0i);
  x3i = wn4r * (x0i + x0r);
  x0r = y4r - y6i;
  x0i = y4i + y6r;
  x1r = y4r + y6i;
  x1i = y4i - y6r;
  a[8] = x0r + x2r;
  a[9] = x0i + x2i;
  a[10] = x0r - x2r;
  a[11] = x0i - x2i;
  a[12] = x1r - x3i;
  a[13] = x1i + x3r;
  a[14] = x1r + x3i;
  a[15] = x1i - x3r;
  x0r = y0r + y2r;
  x0i = y0i + y2i;
  x1r = y0r - y2r;
  x1i = y0i - y2i;
  x2r = y1r + y3r;
  x2i = y1i + y3i;
  x3r = y1r - y3r;
  x3i = y1i - y3i;
  a[0] = x0r + x2r;
  a[1] = x0i + x2i;
  a[2] = x0r - x2r;
  a[3] = x0i - x2i;
  a[4] = x1r - x3i;
  a[5] = x1i + x3r;
  a[6] = x1r + x3i;
  a[7] = x1i - x3r;
}

static void AUP_FFTW_cftf162(float* a, float* w) {
  float wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, x0r, x0i, x1r, x1i, x2r, x2i,
      y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r,
      y7i, y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i,
      y14r, y14i, y15r, y15i;

  wn4r = w[1];
  wk1r = w[4];
  wk1i = w[5];
  wk3r = w[6];
  wk3i = -w[7];
  wk2r = w[8];
  wk2i = w[9];
  x1r = a[0] - a[17];
  x1i = a[1] + a[16];
  x0r = a[8] - a[25];
  x0i = a[9] + a[24];
  x2r = wn4r * (x0r - x0i);
  x2i = wn4r * (x0i + x0r);
  y0r = x1r + x2r;
  y0i = x1i + x2i;
  y4r = x1r - x2r;
  y4i = x1i - x2i;
  x1r = a[0] + a[17];
  x1i = a[1] - a[16];
  x0r = a[8] + a[25];
  x0i = a[9] - a[24];
  x2r = wn4r * (x0r - x0i);
  x2i = wn4r * (x0i + x0r);
  y8r = x1r - x2i;
  y8i = x1i + x2r;
  y12r = x1r + x2i;
  y12i = x1i - x2r;
  x0r = a[2] - a[19];
  x0i = a[3] + a[18];
  x1r = wk1r * x0r - wk1i * x0i;
  x1i = wk1r * x0i + wk1i * x0r;
  x0r = a[10] - a[27];
  x0i = a[11] + a[26];
  x2r = wk3i * x0r - wk3r * x0i;
  x2i = wk3i * x0i + wk3r * x0r;
  y1r = x1r + x2r;
  y1i = x1i + x2i;
  y5r = x1r - x2r;
  y5i = x1i - x2i;
  x0r = a[2] + a[19];
  x0i = a[3] - a[18];
  x1r = wk3r * x0r - wk3i * x0i;
  x1i = wk3r * x0i + wk3i * x0r;
  x0r = a[10] + a[27];
  x0i = a[11] - a[26];
  x2r = wk1r * x0r + wk1i * x0i;
  x2i = wk1r * x0i - wk1i * x0r;
  y9r = x1r - x2r;
  y9i = x1i - x2i;
  y13r = x1r + x2r;
  y13i = x1i + x2i;
  x0r = a[4] - a[21];
  x0i = a[5] + a[20];
  x1r = wk2r * x0r - wk2i * x0i;
  x1i = wk2r * x0i + wk2i * x0r;
  x0r = a[12] - a[29];
  x0i = a[13] + a[28];
  x2r = wk2i * x0r - wk2r * x0i;
  x2i = wk2i * x0i + wk2r * x0r;
  y2r = x1r + x2r;
  y2i = x1i + x2i;
  y6r = x1r - x2r;
  y6i = x1i - x2i;
  x0r = a[4] + a[21];
  x0i = a[5] - a[20];
  x1r = wk2i * x0r - wk2r * x0i;
  x1i = wk2i * x0i + wk2r * x0r;
  x0r = a[12] + a[29];
  x0i = a[13] - a[28];
  x2r = wk2r * x0r - wk2i * x0i;
  x2i = wk2r * x0i + wk2i * x0r;
  y10r = x1r - x2r;
  y10i = x1i - x2i;
  y14r = x1r + x2r;
  y14i = x1i + x2i;
  x0r = a[6] - a[23];
  x0i = a[7] + a[22];
  x1r = wk3r * x0r - wk3i * x0i;
  x1i = wk3r * x0i + wk3i * x0r;
  x0r = a[14] - a[31];
  x0i = a[15] + a[30];
  x2r = wk1i * x0r - wk1r * x0i;
  x2i = wk1i * x0i + wk1r * x0r;
  y3r = x1r + x2r;
  y3i = x1i + x2i;
  y7r = x1r - x2r;
  y7i = x1i - x2i;
  x0r = a[6] + a[23];
  x0i = a[7] - a[22];
  x1r = wk1i * x0r + wk1r * x0i;
  x1i = wk1i * x0i - wk1r * x0r;
  x0r = a[14] + a[31];
  x0i = a[15] - a[30];
  x2r = wk3i * x0r - wk3r * x0i;
  x2i = wk3i * x0i + wk3r * x0r;
  y11r = x1r + x2r;
  y11i = x1i + x2i;
  y15r = x1r - x2r;
  y15i = x1i - x2i;
  x1r = y0r + y2r;
  x1i = y0i + y2i;
  x2r = y1r + y3r;
  x2i = y1i + y3i;
  a[0] = x1r + x2r;
  a[1] = x1i + x2i;
  a[2] = x1r - x2r;
  a[3] = x1i - x2i;
  x1r = y0r - y2r;
  x1i = y0i - y2i;
  x2r = y1r - y3r;
  x2i = y1i - y3i;
  a[4] = x1r - x2i;
  a[5] = x1i + x2r;
  a[6] = x1r + x2i;
  a[7] = x1i - x2r;
  x1r = y4r - y6i;
  x1i = y4i + y6r;
  x0r = y5r - y7i;
  x0i = y5i + y7r;
  x2r = wn4r * (x0r - x0i);
  x2i = wn4r * (x0i + x0r);
  a[8] = x1r + x2r;
  a[9] = x1i + x2i;
  a[10] = x1r - x2r;
  a[11] = x1i - x2i;
  x1r = y4r + y6i;
  x1i = y4i - y6r;
  x0r = y5r + y7i;
  x0i = y5i - y7r;
  x2r = wn4r * (x0r - x0i);
  x2i = wn4r * (x0i + x0r);
  a[12] = x1r - x2i;
  a[13] = x1i + x2r;
  a[14] = x1r + x2i;
  a[15] = x1i - x2r;
  x1r = y8r + y10r;
  x1i = y8i + y10i;
  x2r = y9r - y11r;
  x2i = y9i - y11i;
  a[16] = x1r + x2r;
  a[17] = x1i + x2i;
  a[18] = x1r - x2r;
  a[19] = x1i - x2i;
  x1r = y8r - y10r;
  x1i = y8i - y10i;
  x2r = y9r + y11r;
  x2i = y9i + y11i;
  a[20] = x1r - x2i;
  a[21] = x1i + x2r;
  a[22] = x1r + x2i;
  a[23] = x1i - x2r;
  x1r = y12r - y14i;
  x1i = y12i + y14r;
  x0r = y13r + y15i;
  x0i = y13i - y15r;
  x2r = wn4r * (x0r - x0i);
  x2i = wn4r * (x0i + x0r);
  a[24] = x1r + x2r;
  a[25] = x1i + x2i;
  a[26] = x1r - x2r;
  a[27] = x1i - x2i;
  x1r = y12r + y14i;
  x1i = y12i - y14r;
  x0r = y13r - y15i;
  x0i = y13i + y15r;
  x2r = wn4r * (x0r - x0i);
  x2i = wn4r * (x0i + x0r);
  a[28] = x1r - x2i;
  a[29] = x1i + x2r;
  a[30] = x1r + x2i;
  a[31] = x1i - x2r;
}

static void AUP_FFTW_cftf081(float* a, float* w) {
  float wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r,
      y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;

  wn4r = w[1];
  x0r = a[0] + a[8];
  x0i = a[1] + a[9];
  x1r = a[0] - a[8];
  x1i = a[1] - a[9];
  x2r = a[4] + a[12];
  x2i = a[5] + a[13];
  x3r = a[4] - a[12];
  x3i = a[5] - a[13];
  y0r = x0r + x2r;
  y0i = x0i + x2i;
  y2r = x0r - x2r;
  y2i = x0i - x2i;
  y1r = x1r - x3i;
  y1i = x1i + x3r;
  y3r = x1r + x3i;
  y3i = x1i - x3r;
  x0r = a[2] + a[10];
  x0i = a[3] + a[11];
  x1r = a[2] - a[10];
  x1i = a[3] - a[11];
  x2r = a[6] + a[14];
  x2i = a[7] + a[15];
  x3r = a[6] - a[14];
  x3i = a[7] - a[15];
  y4r = x0r + x2r;
  y4i = x0i + x2i;
  y6r = x0r - x2r;
  y6i = x0i - x2i;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  x2r = x1r + x3i;
  x2i = x1i - x3r;
  y5r = wn4r * (x0r - x0i);
  y5i = wn4r * (x0r + x0i);
  y7r = wn4r * (x2r - x2i);
  y7i = wn4r * (x2r + x2i);
  a[8] = y1r + y5r;
  a[9] = y1i + y5i;
  a[10] = y1r - y5r;
  a[11] = y1i - y5i;
  a[12] = y3r - y7i;
  a[13] = y3i + y7r;
  a[14] = y3r + y7i;
  a[15] = y3i - y7r;
  a[0] = y0r + y4r;
  a[1] = y0i + y4i;
  a[2] = y0r - y4r;
  a[3] = y0i - y4i;
  a[4] = y2r - y6i;
  a[5] = y2i + y6r;
  a[6] = y2r + y6i;
  a[7] = y2i - y6r;
}

static void AUP_FFTW_cftf082(float* a, float* w) {
  float wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, y0r, y0i, y1r, y1i, y2r, y2i, y3r,
      y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;

  wn4r = w[1];
  wk1r = w[2];
  wk1i = w[3];
  y0r = a[0] - a[9];
  y0i = a[1] + a[8];
  y1r = a[0] + a[9];
  y1i = a[1] - a[8];
  x0r = a[4] - a[13];
  x0i = a[5] + a[12];
  y2r = wn4r * (x0r - x0i);
  y2i = wn4r * (x0i + x0r);
  x0r = a[4] + a[13];
  x0i = a[5] - a[12];
  y3r = wn4r * (x0r - x0i);
  y3i = wn4r * (x0i + x0r);
  x0r = a[2] - a[11];
  x0i = a[3] + a[10];
  y4r = wk1r * x0r - wk1i * x0i;
  y4i = wk1r * x0i + wk1i * x0r;
  x0r = a[2] + a[11];
  x0i = a[3] - a[10];
  y5r = wk1i * x0r - wk1r * x0i;
  y5i = wk1i * x0i + wk1r * x0r;
  x0r = a[6] - a[15];
  x0i = a[7] + a[14];
  y6r = wk1i * x0r - wk1r * x0i;
  y6i = wk1i * x0i + wk1r * x0r;
  x0r = a[6] + a[15];
  x0i = a[7] - a[14];
  y7r = wk1r * x0r - wk1i * x0i;
  y7i = wk1r * x0i + wk1i * x0r;
  x0r = y0r + y2r;
  x0i = y0i + y2i;
  x1r = y4r + y6r;
  x1i = y4i + y6i;
  a[0] = x0r + x1r;
  a[1] = x0i + x1i;
  a[2] = x0r - x1r;
  a[3] = x0i - x1i;
  x0r = y0r - y2r;
  x0i = y0i - y2i;
  x1r = y4r - y6r;
  x1i = y4i - y6i;
  a[4] = x0r - x1i;
  a[5] = x0i + x1r;
  a[6] = x0r + x1i;
  a[7] = x0i - x1r;
  x0r = y1r - y3i;
  x0i = y1i + y3r;
  x1r = y5r - y7r;
  x1i = y5i - y7i;
  a[8] = x0r + x1r;
  a[9] = x0i + x1i;
  a[10] = x0r - x1r;
  a[11] = x0i - x1i;
  x0r = y1r + y3i;
  x0i = y1i - y3r;
  x1r = y5r + y7r;
  x1i = y5i + y7i;
  a[12] = x0r - x1i;
  a[13] = x0i + x1r;
  a[14] = x0r + x1i;
  a[15] = x0i - x1r;
}

static void AUP_FFTW_cftf040(float* a) {
  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

  x0r = a[0] + a[4];
  x0i = a[1] + a[5];
  x1r = a[0] - a[4];
  x1i = a[1] - a[5];
  x2r = a[2] + a[6];
  x2i = a[3] + a[7];
  x3r = a[2] - a[6];
  x3i = a[3] - a[7];
  a[0] = x0r + x2r;
  a[1] = x0i + x2i;
  a[2] = x1r - x3i;
  a[3] = x1i + x3r;
  a[4] = x0r - x2r;
  a[5] = x0i - x2i;
  a[6] = x1r + x3i;
  a[7] = x1i - x3r;
}

static void AUP_FFTW_cftb040(float* a) {
  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

  x0r = a[0] + a[4];
  x0i = a[1] + a[5];
  x1r = a[0] - a[4];
  x1i = a[1] - a[5];
  x2r = a[2] + a[6];
  x2i = a[3] + a[7];
  x3r = a[2] - a[6];
  x3i = a[3] - a[7];
  a[0] = x0r + x2r;
  a[1] = x0i + x2i;
  a[2] = x1r + x3i;
  a[3] = x1i - x3r;
  a[4] = x0r - x2r;
  a[5] = x0i - x2i;
  a[6] = x1r - x3i;
  a[7] = x1i + x3r;
}

static void AUP_FFTW_cftx020(float* a) {
  float x0r, x0i;

  x0r = a[0] - a[2];
  x0i = a[1] - a[3];
  a[0] += a[2];
  a[1] += a[3];
  a[2] = x0r;
  a[3] = x0i;
}

static void AUP_FFTW_rftfsub(int n, float* a, int nc, float* c) {
  int j, k, kk, ks, m;
  float wkr, wki, xr, xi, yr, yi;

  m = n >> 1;
  ks = 2 * nc / m;
  kk = 0;
  for (j = 2; j < m; j += 2) {
    k = n - j;
    kk += ks;
    wkr = 0.5f - c[nc - kk];
    wki = c[kk];
    xr = a[j] - a[k];
    xi = a[j + 1] + a[k + 1];
    yr = wkr * xr - wki * xi;
    yi = wkr * xi + wki * xr;
    a[j] -= yr;
    a[j + 1] -= yi;
    a[k] += yr;
    a[k + 1] -= yi;
  }
}

static void AUP_FFTW_rftbsub(int n, float* a, int nc, float* c) {
  int j, k, kk, ks, m;
  float wkr, wki, xr, xi, yr, yi;

  m = n >> 1;
  ks = 2 * nc / m;
  kk = 0;
  for (j = 2; j < m; j += 2) {
    k = n - j;
    kk += ks;
    wkr = 0.5f - c[nc - kk];
    wki = c[kk];
    xr = a[j] - a[k];
    xi = a[j + 1] + a[k + 1];
    yr = wkr * xr + wki * xi;
    yi = wkr * xi - wki * xr;
    a[j] -= yr;
    a[j + 1] -= yi;
    a[k] += yr;
    a[k + 1] -= yi;
  }
}

static void AUP_FFTW_dctsub(int n, float* a, int nc, float* c) {
  int j, k, kk, ks, m;
  float wkr, wki, xr;

  m = n >> 1;
  ks = nc / n;
  kk = 0;
  for (j = 1; j < m; j++) {
    k = n - j;
    kk += ks;
    wkr = c[kk] - c[nc - kk];
    wki = c[kk] + c[nc - kk];
    xr = wki * a[j] - wkr * a[k];
    a[j] = wkr * a[j] + wki * a[k];
    a[k] = xr;
  }
  a[m] *= c[0];
}

static void AUP_FFTW_dstsub(int n, float* a, int nc, float* c) {
  int j, k, kk, ks, m;
  float wkr, wki, xr;

  m = n >> 1;
  ks = nc / n;
  kk = 0;
  for (j = 1; j < m; j++) {
    k = n - j;
    kk += ks;
    wkr = c[kk] - c[nc - kk];
    wki = c[kk] + c[nc - kk];
    xr = wki * a[k] - wkr * a[j];
    a[k] = wkr * a[k] + wki * a[j];
    a[j] = xr;
  }
  a[m] *= c[0];
}

static void AUP_FFTW_rdft(int n, int isgn, float* a, int* ip, float* w) {
  float xi;

  int nw = ip[0];
  int nc = ip[1];

  if (isgn >= 0) {
    if (n > 4) {
      AUP_FFTW_cftfsub(n, a, ip, nw, w);
      AUP_FFTW_rftfsub(n, a, nc, w + nw);
    } else if (n == 4) {
      AUP_FFTW_cftfsub(n, a, ip, nw, w);
    }
    xi = a[0] - a[1];
    a[0] += a[1];
    a[1] = xi;
  } else {
    a[1] = 0.5f * (a[0] - a[1]);
    a[0] -= a[1];
    if (n > 4) {
      AUP_FFTW_rftbsub(n, a, nc, w + nw);
      AUP_FFTW_cftbsub(n, a, ip, nw, w);
    } else if (n == 4) {
      AUP_FFTW_cftbsub(n, a, ip, nw, w);
    }
  }
}

// ==========================================================================================
// public APIs
// ==========================================================================================

void AUP_FFTW_r2c_256(float* in, float* out) {
  int i;

  float tmp[258] = {0};

  // scale
  for (i = 0; i < 256; ++i) {
    tmp[i] = in[i] * 0.00390625f;
  }

  AUP_FFTW_rdft(256, 1, tmp, (int*)AUP_FFTW_g_ip256, (float*)AUP_FFTW_g_w256);

  out[0] = tmp[0];
  out[255] = tmp[1];
  for (i = 1; i < 255; i += 2) {
    out[i] = tmp[i + 1];
    out[i + 1] = -tmp[i + 2];
  }
}

void AUP_FFTW_c2r_256(float* in, float* out) {
  int i;

  out[0] = in[0];
  out[1] = in[255];
  for (i = 2; i < 256; i += 2) {
    out[i] = in[i - 1];
    out[i + 1] = -in[i];
  }

  AUP_FFTW_rdft(256, -1, out, (int*)AUP_FFTW_g_ip256, (float*)AUP_FFTW_g_w256);
  /* 1/N */
  for (i = 0; i < 256; i++) {
    out[i] *= 2;
  }
}

void AUP_FFTW_c2r_512(float* in, float* out) {
  int i;

  out[0] = in[0];
  out[1] = in[511];
  for (i = 2; i < 512; i += 2) {
    out[i] = in[i - 1];
    out[i + 1] = -in[i];
  }
  AUP_FFTW_rdft(512, -1, out, (int*)AUP_FFTW_g_ip512, (float*)AUP_FFTW_g_w512);
  /* 1/N */
  for (i = 0; i < 512; i++) {
    out[i] *= 2;
  }
}

void AUP_FFTW_r2c_512(float* in, float* out) {
  int i;

  float tmp[514] = {0};

  // scale
  for (i = 0; i < 512; ++i) {
    tmp[i] = in[i] * 0.001953125f;
  }

  AUP_FFTW_rdft(512, 1, tmp, (int*)AUP_FFTW_g_ip512, (float*)AUP_FFTW_g_w512);

  out[0] = tmp[0];
  out[511] = tmp[1];
  for (i = 1; i < 511; i += 2) {
    out[i] = tmp[i + 1];
    out[i + 1] = -tmp[i + 2];
  }
}

void AUP_FFTW_r2c_1024(float* in, float* out) {
  int i;

  float tmp[1026] = {0};
  // scale
  for (i = 0; i < 1024; ++i) {
    tmp[i] = in[i] * 0.0009765625f;
  }

  AUP_FFTW_rdft(1024, 1, tmp, (int*)AUP_FFTW_g_ip1024,
                (float*)AUP_FFTW_g_w1024);

  out[0] = tmp[0];
  out[1023] = tmp[1];
  for (i = 1; i < 1023; i += 2) {
    out[i] = tmp[i + 1];
    out[i + 1] = -tmp[i + 2];
  }
}

void AUP_FFTW_c2r_1024(float* in, float* out) {
  int i;
  // memcpy(out,in,sizeof(float)*1024);
  out[0] = in[0];
  out[1] = in[1023];
  for (i = 2; i < 1024; i += 2) {
    out[i] = in[i - 1];
    out[i + 1] = -in[i];
  }
  AUP_FFTW_rdft(1024, -1, out, (int*)AUP_FFTW_g_ip1024,
                (float*)AUP_FFTW_g_w1024);
  /* 1/N */
  for (i = 0; i < 1024; i++) {
    out[i] *= 2;
  }
}

void AUP_FFTW_r2c_2048(float* in, float* out) {
  int i;

  float tmp[2050] = {0};

  // scale
  for (i = 0; i < 2048; ++i) {
    tmp[i] = in[i] * 0.00048828125f;
  }

  AUP_FFTW_rdft(2048, 1, tmp, (int*)AUP_FFTW_g_ip2048,
                (float*)AUP_FFTW_g_w2048);

  out[0] = tmp[0];
  out[2047] = tmp[1];
  for (i = 1; i < 2047; i += 2) {
    out[i] = tmp[i + 1];
    out[i + 1] = -tmp[i + 2];
  }
}

void AUP_FFTW_c2r_2048(float* in, float* out) {
  int i;

  out[0] = in[0];
  out[1] = in[2047];
  for (i = 2; i < 2048; i += 2) {
    out[i] = in[i - 1];
    out[i + 1] = -in[i];
  }
  AUP_FFTW_rdft(2048, -1, out, (int*)AUP_FFTW_g_ip2048,
                (float*)AUP_FFTW_g_w2048);
  /* 1/N */
  for (i = 0; i < 2048; i++) {
    out[i] *= 2;
  }
}

void AUP_FFTW_r2c_4096(float* in, float* out) {
  int i;

  float tmp[4098] = {0};

  // scale
  for (i = 0; i < 4096; ++i) {
    tmp[i] = in[i] * 0.000244140625f;
  }

  AUP_FFTW_rdft(4096, 1, tmp, (int*)AUP_FFTW_g_ip4096,
                (float*)AUP_FFTW_g_w4096);

  out[0] = tmp[0];
  out[4095] = tmp[1];
  for (i = 1; i < 4095; i += 2) {
    out[i] = tmp[i + 1];
    out[i + 1] = -tmp[i + 2];
  }
}

void AUP_FFTW_c2r_4096(float* in, float* out) {
  int i;

  out[0] = in[0];
  out[1] = in[4095];
  for (i = 2; i < 4096; i += 2) {
    out[i] = in[i - 1];
    out[i + 1] = -in[i];
  }
  AUP_FFTW_rdft(4096, -1, out, (int*)AUP_FFTW_g_ip4096,
                (float*)AUP_FFTW_g_w4096);
  for (i = 0; i < 4096; i++) {
    out[i] *= 2;
  }
}

// if direction == 0: format1->format2
// if direction == 1: format2->format1
void AUP_FFTW_InplaceTransf(int direction, int fftSz, float* inplaceTranfBuf) {
  float nyqReal;
  int idx;

  if (direction == 0) {
    // [Real-0, Real-Nyq, Real-1, Imag-1, Real-2, Imag-2, ...] ->
    // [Real-0, Real-1, (-1)*Imag-1, Real-2, (-1)*Imag-2, ..., Real-Nyq]
    nyqReal = inplaceTranfBuf[1];
    for (idx = 1; idx < (fftSz - 1); idx += 2) {
      inplaceTranfBuf[idx] = inplaceTranfBuf[idx + 1];
      inplaceTranfBuf[idx + 1] = -(inplaceTranfBuf[idx + 2]);
    }
    inplaceTranfBuf[fftSz - 1] = nyqReal;
  } else {
    // [Real-0, Real-1, (-1)*Imag-1, Real-2, (-1)*Imag-2, ..., Real-Nyq] ->
    // [Real-0, Real-Nyq, Real-1, Imag-1, Real-2, Imag-2, ...]
    nyqReal = inplaceTranfBuf[fftSz - 1];
    for (idx = fftSz - 1; idx > 2; idx -= 2) {
      inplaceTranfBuf[idx] = -(inplaceTranfBuf[idx - 1]);
      inplaceTranfBuf[idx - 1] = inplaceTranfBuf[idx - 2];
    }
    inplaceTranfBuf[1] = nyqReal;
  }
  return;
}

void AUP_FFTW_RescaleFFTOut(int fftSz, float* inplaceBuf) {
  int idx;
  for (idx = 0; idx < fftSz; idx++) {
    inplaceBuf[idx] *= (float)fftSz;
  }
  return;
}

void AUP_FFTW_RescaleIFFTOut(int fftSz, float* inplaceBuf) {
  int idx;
  for (idx = 0; idx < fftSz; idx++) {
    inplaceBuf[idx] *= 0.5f;
  }
  return;
}