/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_rfft_init_f32.c
 * Description:  RFFT & RIFFT Floating point initialisation function
 *
 * $Date:        27. January 2017
 * $Revision:    V.1.5.1
 *
 * Target Processor: Cortex-M cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
 *
 * SPDX-License-Identifier: Apache-2.0
 *
 * Licensed under the Apache License, Version 2.0 (the License); you may
 * not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include "arm_math.h"

/**
 * @ingroup RealFFT
 */

/**
 * @addtogroup RealFFT_Table Real FFT Tables
 * @{
 */

/**
* \par
* Generation of realCoefA array:
* \par
* 	n = 4096
* <pre>for (i = 0; i < n; i++)
*  {
*    pATable[2 * i] = 0.5 * (1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
*    pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
*  } </pre>
*/
static const float32_t realCoefA[8192] = {
  0.500000000000000f, -0.500000000000000f, 0.499616503715515f, -0.499999850988388f,
  0.499233007431030f, -0.499999403953552f, 0.498849511146545f, -0.499998688697815f,
  0.498466014862061f, -0.499997645616531f, 0.498082518577576f, -0.499996334314346f,
  0.497699022293091f, -0.499994695186615f, 0.497315555810928f, -0.499992787837982f,
  0.496932059526443f, -0.499990582466125f, 0.496548563241959f, -0.499988079071045f,
  0.496165096759796f, -0.499985307455063f, 0.495781600475311f, -0.499982208013535f,
  0.495398133993149f, -0.499978810548782f, 0.495014637708664f, -0.499975144863129f,
  0.494631171226501f, -0.499971181154251f, 0.494247704744339f, -0.499966919422150f,
  0.493864238262177f, -0.499962359666824f, 0.493480771780014f, -0.499957501888275f,
  0.493097305297852f, -0.499952346086502f, 0.492713838815689f, -0.499946922063828f,
  0.492330402135849f, -0.499941170215607f, 0.491946935653687f, -0.499935150146484f,
  0.491563498973846f, -0.499928832054138f, 0.491180062294006f, -0.499922215938568f,
  0.490796625614166f, -0.499915301799774f, 0.490413218736649f, -0.499908089637756f,
  0.490029782056808f, -0.499900579452515f, 0.489646375179291f, -0.499892801046371f,
  0.489262968301773f, -0.499884694814682f, 0.488879561424255f, -0.499876320362091f,
  0.488496154546738f, -0.499867647886276f, 0.488112777471542f, -0.499858677387238f,
  0.487729400396347f, -0.499849408864975f, 0.487346023321152f, -0.499839842319489f,
  0.486962646245956f, -0.499830007553101f, 0.486579269170761f, -0.499819844961166f,
  0.486195921897888f, -0.499809414148331f, 0.485812574625015f, -0.499798685312271f,
  0.485429257154465f, -0.499787658452988f, 0.485045909881592f, -0.499776333570480f,
  0.484662592411041f, -0.499764710664749f, 0.484279274940491f, -0.499752789735794f,
  0.483895987272263f, -0.499740600585938f, 0.483512699604034f, -0.499728083610535f,
  0.483129411935806f, -0.499715298414230f, 0.482746154069901f, -0.499702215194702f,
  0.482362866401672f, -0.499688833951950f, 0.481979638338089f, -0.499675154685974f,
  0.481596380472183f, -0.499661177396774f, 0.481213152408600f, -0.499646931886673f,
  0.480829954147339f, -0.499632388353348f, 0.480446726083755f, -0.499617516994476f,
  0.480063527822495f, -0.499602377414703f, 0.479680359363556f, -0.499586939811707f,
  0.479297190904617f, -0.499571204185486f, 0.478914022445679f, -0.499555170536041f,
  0.478530883789063f, -0.499538868665695f, 0.478147745132446f, -0.499522238969803f,
  0.477764606475830f, -0.499505341053009f, 0.477381497621536f, -0.499488145112991f,
  0.476998418569565f, -0.499470651149750f, 0.476615339517593f, -0.499452859163284f,
  0.476232260465622f, -0.499434769153595f, 0.475849211215973f, -0.499416410923004f,
  0.475466161966324f, -0.499397724866867f, 0.475083142518997f, -0.499378770589828f,
  0.474700123071671f, -0.499359518289566f, 0.474317133426666f, -0.499339967966080f,
  0.473934143781662f, -0.499320119619370f, 0.473551183938980f, -0.499299973249435f,
  0.473168224096298f, -0.499279528856277f, 0.472785294055939f, -0.499258816242218f,
  0.472402364015579f, -0.499237775802612f, 0.472019463777542f, -0.499216467142105f,
  0.471636593341827f, -0.499194860458374f, 0.471253722906113f, -0.499172955751419f,
  0.470870882272720f, -0.499150782823563f, 0.470488041639328f, -0.499128282070160f,
  0.470105201005936f, -0.499105513095856f, 0.469722419977188f, -0.499082416296005f,
  0.469339638948441f, -0.499059051275253f, 0.468956857919693f, -0.499035388231277f,
  0.468574106693268f, -0.499011427164078f, 0.468191385269165f, -0.498987197875977f,
  0.467808693647385f, -0.498962640762329f, 0.467426002025604f, -0.498937815427780f,
  0.467043310403824f, -0.498912662267685f, 0.466660678386688f, -0.498887240886688f,
  0.466278046369553f, -0.498861521482468f, 0.465895414352417f, -0.498835533857346f,
  0.465512841939926f, -0.498809218406677f, 0.465130269527435f, -0.498782604932785f,
  0.464747726917267f, -0.498755723237991f, 0.464365184307098f, -0.498728543519974f,
  0.463982671499252f, -0.498701065778732f, 0.463600188493729f, -0.498673290014267f,
  0.463217705488205f, -0.498645216226578f, 0.462835282087326f, -0.498616874217987f,
  0.462452858686447f, -0.498588204383850f, 0.462070435285568f, -0.498559266328812f,
  0.461688071489334f, -0.498530030250549f, 0.461305707693100f, -0.498500496149063f,
  0.460923373699188f, -0.498470664024353f, 0.460541069507599f, -0.498440563678741f,
  0.460158795118332f, -0.498410135507584f, 0.459776520729065f, -0.498379439115524f,
  0.459394276142120f, -0.498348444700241f, 0.459012061357498f, -0.498317152261734f,
  0.458629876375198f, -0.498285561800003f, 0.458247691392899f, -0.498253703117371f,
  0.457865566015244f, -0.498221516609192f, 0.457483440637589f, -0.498189061880112f,
  0.457101345062256f, -0.498156309127808f, 0.456719279289246f, -0.498123258352280f,
  0.456337243318558f, -0.498089909553528f, 0.455955207347870f, -0.498056292533875f,
  0.455573230981827f, -0.498022347688675f, 0.455191254615784f, -0.497988134622574f,
  0.454809308052063f, -0.497953623533249f, 0.454427421092987f, -0.497918814420700f,
  0.454045534133911f, -0.497883707284927f, 0.453663676977158f, -0.497848302125931f,
  0.453281819820404f, -0.497812628746033f, 0.452900022268295f, -0.497776657342911f,
  0.452518254518509f, -0.497740387916565f, 0.452136516571045f, -0.497703820466995f,
  0.451754778623581f, -0.497666954994202f, 0.451373100280762f, -0.497629791498184f,
  0.450991421937943f, -0.497592359781265f, 0.450609803199768f, -0.497554630041122f,
  0.450228184461594f, -0.497516602277756f, 0.449846625328064f, -0.497478276491165f,
  0.449465066194534f, -0.497439652681351f, 0.449083566665649f, -0.497400760650635f,
  0.448702067136765f, -0.497361570596695f, 0.448320597410202f, -0.497322082519531f,
  0.447939187288284f, -0.497282296419144f, 0.447557777166367f, -0.497242212295532f,
  0.447176426649094f, -0.497201830148697f, 0.446795076131821f, -0.497161179780960f,
  0.446413785219193f, -0.497120231389999f, 0.446032524108887f, -0.497078984975815f,
  0.445651292800903f, -0.497037440538406f, 0.445270061492920f, -0.496995598077774f,
  0.444888889789581f, -0.496953487396240f, 0.444507747888565f, -0.496911078691483f,
  0.444126635789871f, -0.496868371963501f, 0.443745553493500f, -0.496825367212296f,
  0.443364530801773f, -0.496782064437866f, 0.442983508110046f, -0.496738493442535f,
  0.442602545022964f, -0.496694594621658f, 0.442221581935883f, -0.496650427579880f,
  0.441840678453445f, -0.496605962514877f, 0.441459804773331f, -0.496561229228973f,
  0.441078960895538f, -0.496516168117523f, 0.440698176622391f, -0.496470838785172f,
  0.440317392349243f, -0.496425211429596f, 0.439936667680740f, -0.496379286050797f,
  0.439555943012238f, -0.496333062648773f, 0.439175277948380f, -0.496286571025848f,
  0.438794672489166f, -0.496239781379700f, 0.438414067029953f, -0.496192663908005f,
  0.438033521175385f, -0.496145308017731f, 0.437653005123138f, -0.496097624301910f,
  0.437272518873215f, -0.496049642562866f, 0.436892062425613f, -0.496001392602921f,
  0.436511665582657f, -0.495952844619751f, 0.436131268739700f, -0.495903998613358f,
  0.435750931501389f, -0.495854884386063f, 0.435370653867722f, -0.495805442333221f,
  0.434990376234055f, -0.495755732059479f, 0.434610158205032f, -0.495705723762512f,
  0.434229999780655f, -0.495655417442322f, 0.433849841356277f, -0.495604842901230f,
  0.433469742536545f, -0.495553970336914f, 0.433089673519135f, -0.495502769947052f,
  0.432709634304047f, -0.495451331138611f, 0.432329654693604f, -0.495399564504623f,
  0.431949704885483f, -0.495347499847412f, 0.431569814682007f, -0.495295166969299f,
  0.431189924478531f, -0.495242536067963f, 0.430810123682022f, -0.495189607143402f,
  0.430430322885513f, -0.495136409997940f, 0.430050581693649f, -0.495082914829254f,
  0.429670870304108f, -0.495029091835022f, 0.429291218519211f, -0.494975030422211f,
  0.428911596536636f, -0.494920641183853f, 0.428532034158707f, -0.494865983724594f,
  0.428152471780777f, -0.494810998439789f, 0.427772998809814f, -0.494755744934082f,
  0.427393525838852f, -0.494700223207474f, 0.427014142274857f, -0.494644373655319f,
  0.426634758710861f, -0.494588255882263f, 0.426255434751511f, -0.494531840085983f,
  0.425876170396805f, -0.494475126266479f, 0.425496935844421f, -0.494418144226074f,
  0.425117731094360f, -0.494360834360123f, 0.424738585948944f, -0.494303256273270f,
  0.424359470605850f, -0.494245409965515f, 0.423980414867401f, -0.494187235832214f,
  0.423601418733597f, -0.494128793478012f, 0.423222452402115f, -0.494070053100586f,
  0.422843515872955f, -0.494011014699936f, 0.422464638948441f, -0.493951678276062f,
  0.422085791826248f, -0.493892073631287f, 0.421707004308701f, -0.493832170963287f,
  0.421328276395798f, -0.493771970272064f, 0.420949578285217f, -0.493711471557617f,
  0.420570939779282f, -0.493650704622269f, 0.420192331075668f, -0.493589639663696f,
  0.419813781976700f, -0.493528276681900f, 0.419435262680054f, -0.493466645479202f,
  0.419056802988052f, -0.493404686450958f, 0.418678402900696f, -0.493342459201813f,
  0.418300032615662f, -0.493279963731766f, 0.417921721935272f, -0.493217140436172f,
  0.417543441057205f, -0.493154048919678f, 0.417165219783783f, -0.493090659379959f,
  0.416787058115005f, -0.493026971817017f, 0.416408926248550f, -0.492963016033173f,
  0.416030853986740f, -0.492898762226105f, 0.415652841329575f, -0.492834210395813f,
  0.415274858474731f, -0.492769360542297f, 0.414896935224533f, -0.492704242467880f,
  0.414519041776657f, -0.492638826370239f, 0.414141237735748f, -0.492573112249374f,
  0.413763463497162f, -0.492507129907608f, 0.413385748863220f, -0.492440819740295f,
  0.413008064031601f, -0.492374241352081f, 0.412630438804626f, -0.492307394742966f,
  0.412252873182297f, -0.492240220308304f, 0.411875367164612f, -0.492172777652740f,
  0.411497890949249f, -0.492105036973953f, 0.411120474338531f, -0.492037028074265f,
  0.410743117332459f, -0.491968721151352f, 0.410365819931030f, -0.491900116205215f,
  0.409988552331924f, -0.491831213235855f, 0.409611344337463f, -0.491762012243271f,
  0.409234195947647f, -0.491692543029785f, 0.408857107162476f, -0.491622805595398f,
  0.408480048179626f, -0.491552740335464f, 0.408103078603745f, -0.491482406854630f,
  0.407726138830185f, -0.491411775350571f, 0.407349258661270f, -0.491340845823288f,
  0.406972438097000f, -0.491269648075104f, 0.406595647335052f, -0.491198152303696f,
  0.406218945980072f, -0.491126358509064f, 0.405842274427414f, -0.491054296493530f,
  0.405465662479401f, -0.490981936454773f, 0.405089110136032f, -0.490909278392792f,
  0.404712617397308f, -0.490836352109909f, 0.404336184263229f, -0.490763127803802f,
  0.403959810733795f, -0.490689605474472f, 0.403583467006683f, -0.490615785121918f,
  0.403207212686539f, -0.490541696548462f, 0.402830988168716f, -0.490467309951782f,
  0.402454853057861f, -0.490392625331879f, 0.402078747749329f, -0.490317672491074f,
  0.401702702045441f, -0.490242421627045f, 0.401326715946198f, -0.490166902542114f,
  0.400950789451599f, -0.490091055631638f, 0.400574922561646f, -0.490014940500259f,
  0.400199115276337f, -0.489938557147980f, 0.399823367595673f, -0.489861875772476f,
  0.399447679519653f, -0.489784896373749f, 0.399072051048279f, -0.489707618951797f,
  0.398696482181549f, -0.489630073308945f, 0.398320972919464f, -0.489552229642868f,
  0.397945523262024f, -0.489474087953568f, 0.397570133209229f, -0.489395678043365f,
  0.397194802761078f, -0.489316970109940f, 0.396819531917572f, -0.489237964153290f,
  0.396444320678711f, -0.489158689975739f, 0.396069169044495f, -0.489079117774963f,
  0.395694077014923f, -0.488999247550964f, 0.395319044589996f, -0.488919109106064f,
  0.394944071769714f, -0.488838672637939f, 0.394569188356400f, -0.488757967948914f,
  0.394194334745407f, -0.488676935434341f, 0.393819570541382f, -0.488595664501190f,
  0.393444836139679f, -0.488514065742493f, 0.393070191144943f, -0.488432198762894f,
  0.392695605754852f, -0.488350033760071f, 0.392321079969406f, -0.488267600536346f,
  0.391946613788605f, -0.488184869289398f, 0.391572207212448f, -0.488101840019226f,
  0.391197860240936f, -0.488018542528152f, 0.390823602676392f, -0.487934947013855f,
  0.390449374914169f, -0.487851053476334f, 0.390075236558914f, -0.487766891717911f,
  0.389701157808304f, -0.487682431936264f, 0.389327138662338f, -0.487597703933716f,
  0.388953179121017f, -0.487512677907944f, 0.388579308986664f, -0.487427353858948f,
  0.388205498456955f, -0.487341761589050f, 0.387831717729568f, -0.487255871295929f,
  0.387458056211472f, -0.487169682979584f, 0.387084424495697f, -0.487083226442337f,
  0.386710882186890f, -0.486996471881866f, 0.386337369680405f, -0.486909449100494f,
  0.385963946580887f, -0.486822128295898f, 0.385590612888336f, -0.486734509468079f,
  0.385217308998108f, -0.486646622419357f, 0.384844094514847f, -0.486558437347412f,
  0.384470939636230f, -0.486469984054565f, 0.384097874164581f, -0.486381232738495f,
  0.383724838495255f, -0.486292183399200f, 0.383351892232895f, -0.486202865839005f,
  0.382979035377502f, -0.486113250255585f, 0.382606208324432f, -0.486023366451263f,
  0.382233470678329f, -0.485933154821396f, 0.381860792636871f, -0.485842704772949f,
  0.381488204002380f, -0.485751956701279f, 0.381115674972534f, -0.485660910606384f,
  0.380743205547333f, -0.485569566488266f, 0.380370795726776f, -0.485477954149246f,
  0.379998475313187f, -0.485386073589325f, 0.379626244306564f, -0.485293895006180f,
  0.379254043102264f, -0.485201418399811f, 0.378881961107254f, -0.485108673572540f,
  0.378509908914566f, -0.485015630722046f, 0.378137946128845f, -0.484922289848328f,
  0.377766042947769f, -0.484828680753708f, 0.377394229173660f, -0.484734803438187f,
  0.377022475004196f, -0.484640628099442f, 0.376650810241699f, -0.484546154737473f,
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  0.422085791826248f, 0.493892073631287f, 0.422464638948441f, 0.493951678276062f,
  0.422843515872955f, 0.494011014699936f, 0.423222452402115f, 0.494070053100586f,
  0.423601418733597f, 0.494128793478012f, 0.423980414867401f, 0.494187235832214f,
  0.424359470605850f, 0.494245409965515f, 0.424738585948944f, 0.494303256273270f,
  0.425117731094360f, 0.494360834360123f, 0.425496935844421f, 0.494418144226074f,
  0.425876170396805f, 0.494475126266479f, 0.426255434751511f, 0.494531840085983f,
  0.426634758710861f, 0.494588255882263f, 0.427014142274857f, 0.494644373655319f,
  0.427393525838852f, 0.494700223207474f, 0.427772998809814f, 0.494755744934082f,
  0.428152471780777f, 0.494810998439789f, 0.428532034158707f, 0.494865983724594f,
  0.428911596536636f, 0.494920641183853f, 0.429291218519211f, 0.494975030422211f,
  0.429670870304108f, 0.495029091835022f, 0.430050581693649f, 0.495082914829254f,
  0.430430322885513f, 0.495136409997940f, 0.430810123682022f, 0.495189607143402f,
  0.431189924478531f, 0.495242536067963f, 0.431569814682007f, 0.495295166969299f,
  0.431949704885483f, 0.495347499847412f, 0.432329654693604f, 0.495399564504623f,
  0.432709634304047f, 0.495451331138611f, 0.433089673519135f, 0.495502769947052f,
  0.433469742536545f, 0.495553970336914f, 0.433849841356277f, 0.495604842901230f,
  0.434229999780655f, 0.495655417442322f, 0.434610158205032f, 0.495705723762512f,
  0.434990376234055f, 0.495755732059479f, 0.435370653867722f, 0.495805442333221f,
  0.435750931501389f, 0.495854884386063f, 0.436131268739700f, 0.495903998613358f,
  0.436511665582657f, 0.495952844619751f, 0.436892062425613f, 0.496001392602921f,
  0.437272518873215f, 0.496049642562866f, 0.437653005123138f, 0.496097624301910f,
  0.438033521175385f, 0.496145308017731f, 0.438414067029953f, 0.496192663908005f,
  0.438794672489166f, 0.496239781379700f, 0.439175277948380f, 0.496286571025848f,
  0.439555943012238f, 0.496333062648773f, 0.439936667680740f, 0.496379286050797f,
  0.440317392349243f, 0.496425211429596f, 0.440698176622391f, 0.496470838785172f,
  0.441078960895538f, 0.496516168117523f, 0.441459804773331f, 0.496561229228973f,
  0.441840678453445f, 0.496605962514877f, 0.442221581935883f, 0.496650427579880f,
  0.442602545022964f, 0.496694594621658f, 0.442983508110046f, 0.496738493442535f,
  0.443364530801773f, 0.496782064437866f, 0.443745553493500f, 0.496825367212296f,
  0.444126635789871f, 0.496868371963501f, 0.444507747888565f, 0.496911078691483f,
  0.444888889789581f, 0.496953487396240f, 0.445270061492920f, 0.496995598077774f,
  0.445651292800903f, 0.497037440538406f, 0.446032524108887f, 0.497078984975815f,
  0.446413785219193f, 0.497120231389999f, 0.446795076131821f, 0.497161179780960f,
  0.447176426649094f, 0.497201830148697f, 0.447557777166367f, 0.497242212295532f,
  0.447939187288284f, 0.497282296419144f, 0.448320597410202f, 0.497322082519531f,
  0.448702067136765f, 0.497361570596695f, 0.449083566665649f, 0.497400760650635f,
  0.449465066194534f, 0.497439652681351f, 0.449846625328064f, 0.497478276491165f,
  0.450228184461594f, 0.497516602277756f, 0.450609803199768f, 0.497554630041122f,
  0.450991421937943f, 0.497592359781265f, 0.451373100280762f, 0.497629791498184f,
  0.451754778623581f, 0.497666954994202f, 0.452136516571045f, 0.497703820466995f,
  0.452518254518509f, 0.497740387916565f, 0.452900022268295f, 0.497776657342911f,
  0.453281819820404f, 0.497812628746033f, 0.453663676977158f, 0.497848302125931f,
  0.454045534133911f, 0.497883707284927f, 0.454427421092987f, 0.497918814420700f,
  0.454809308052063f, 0.497953623533249f, 0.455191254615784f, 0.497988134622574f,
  0.455573230981827f, 0.498022347688675f, 0.455955207347870f, 0.498056292533875f,
  0.456337243318558f, 0.498089909553528f, 0.456719279289246f, 0.498123258352280f,
  0.457101345062256f, 0.498156309127808f, 0.457483440637589f, 0.498189061880112f,
  0.457865566015244f, 0.498221516609192f, 0.458247691392899f, 0.498253703117371f,
  0.458629876375198f, 0.498285561800003f, 0.459012061357498f, 0.498317152261734f,
  0.459394276142120f, 0.498348444700241f, 0.459776520729065f, 0.498379439115524f,
  0.460158795118332f, 0.498410135507584f, 0.460541069507599f, 0.498440563678741f,
  0.460923373699188f, 0.498470664024353f, 0.461305707693100f, 0.498500496149063f,
  0.461688071489334f, 0.498530030250549f, 0.462070435285568f, 0.498559266328812f,
  0.462452858686447f, 0.498588204383850f, 0.462835282087326f, 0.498616874217987f,
  0.463217705488205f, 0.498645216226578f, 0.463600188493729f, 0.498673290014267f,
  0.463982671499252f, 0.498701065778732f, 0.464365184307098f, 0.498728543519974f,
  0.464747726917267f, 0.498755723237991f, 0.465130269527435f, 0.498782604932785f,
  0.465512841939926f, 0.498809218406677f, 0.465895414352417f, 0.498835533857346f,
  0.466278046369553f, 0.498861521482468f, 0.466660678386688f, 0.498887240886688f,
  0.467043310403824f, 0.498912662267685f, 0.467426002025604f, 0.498937815427780f,
  0.467808693647385f, 0.498962640762329f, 0.468191385269165f, 0.498987197875977f,
  0.468574106693268f, 0.499011427164078f, 0.468956857919693f, 0.499035388231277f,
  0.469339638948441f, 0.499059051275253f, 0.469722419977188f, 0.499082416296005f,
  0.470105201005936f, 0.499105513095856f, 0.470488041639328f, 0.499128282070160f,
  0.470870882272720f, 0.499150782823563f, 0.471253722906113f, 0.499172955751419f,
  0.471636593341827f, 0.499194860458374f, 0.472019463777542f, 0.499216467142105f,
  0.472402364015579f, 0.499237775802612f, 0.472785294055939f, 0.499258816242218f,
  0.473168224096298f, 0.499279528856277f, 0.473551183938980f, 0.499299973249435f,
  0.473934143781662f, 0.499320119619370f, 0.474317133426666f, 0.499339967966080f,
  0.474700123071671f, 0.499359518289566f, 0.475083142518997f, 0.499378770589828f,
  0.475466161966324f, 0.499397724866867f, 0.475849211215973f, 0.499416410923004f,
  0.476232260465622f, 0.499434769153595f, 0.476615339517593f, 0.499452859163284f,
  0.476998418569565f, 0.499470651149750f, 0.477381497621536f, 0.499488145112991f,
  0.477764606475830f, 0.499505341053009f, 0.478147745132446f, 0.499522238969803f,
  0.478530883789063f, 0.499538868665695f, 0.478914022445679f, 0.499555170536041f,
  0.479297190904617f, 0.499571204185486f, 0.479680359363556f, 0.499586939811707f,
  0.480063527822495f, 0.499602377414703f, 0.480446726083755f, 0.499617516994476f,
  0.480829954147339f, 0.499632388353348f, 0.481213152408600f, 0.499646931886673f,
  0.481596380472183f, 0.499661177396774f, 0.481979638338089f, 0.499675154685974f,
  0.482362866401672f, 0.499688833951950f, 0.482746154069901f, 0.499702215194702f,
  0.483129411935806f, 0.499715298414230f, 0.483512699604034f, 0.499728083610535f,
  0.483895987272263f, 0.499740600585938f, 0.484279274940491f, 0.499752789735794f,
  0.484662592411041f, 0.499764710664749f, 0.485045909881592f, 0.499776333570480f,
  0.485429257154465f, 0.499787658452988f, 0.485812574625015f, 0.499798685312271f,
  0.486195921897888f, 0.499809414148331f, 0.486579269170761f, 0.499819844961166f,
  0.486962646245956f, 0.499830007553101f, 0.487346023321152f, 0.499839842319489f,
  0.487729400396347f, 0.499849408864975f, 0.488112777471542f, 0.499858677387238f,
  0.488496154546738f, 0.499867647886276f, 0.488879561424255f, 0.499876320362091f,
  0.489262968301773f, 0.499884694814682f, 0.489646375179291f, 0.499892801046371f,
  0.490029782056808f, 0.499900579452515f, 0.490413218736649f, 0.499908089637756f,
  0.490796625614166f, 0.499915301799774f, 0.491180062294006f, 0.499922215938568f,
  0.491563498973846f, 0.499928832054138f, 0.491946935653687f, 0.499935150146484f,
  0.492330402135849f, 0.499941170215607f, 0.492713838815689f, 0.499946922063828f,
  0.493097305297852f, 0.499952346086502f, 0.493480771780014f, 0.499957501888275f,
  0.493864238262177f, 0.499962359666824f, 0.494247704744339f, 0.499966919422150f,
  0.494631171226501f, 0.499971181154251f, 0.495014637708664f, 0.499975144863129f,
  0.495398133993149f, 0.499978810548782f, 0.495781600475311f, 0.499982208013535f,
  0.496165096759796f, 0.499985307455063f, 0.496548563241959f, 0.499988079071045f,
  0.496932059526443f, 0.499990582466125f, 0.497315555810928f, 0.499992787837982f,
  0.497699022293091f, 0.499994695186615f, 0.498082518577576f, 0.499996334314346f,
  0.498466014862061f, 0.499997645616531f, 0.498849511146545f, 0.499998688697815f,
  0.499233007431030f, 0.499999403953552f, 0.499616503715515f, 0.499999850988388f,
};


/**
* \par
* Generation of realCoefB array:
* \par
* n = 4096
* <pre>for (i = 0; i < n; i++)
* {
*    pBTable[2 * i] = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
*    pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
*  } </pre>
*
*/
static const float32_t realCoefB[8192] = {
  0.500000000000000f, 0.500000000000000f, 0.500383496284485f, 0.499999850988388f,
  0.500766992568970f, 0.499999403953552f, 0.501150488853455f, 0.499998688697815f,
  0.501533985137939f, 0.499997645616531f, 0.501917481422424f, 0.499996334314346f,
  0.502300977706909f, 0.499994695186615f, 0.502684473991394f, 0.499992787837982f,
  0.503067970275879f, 0.499990582466125f, 0.503451406955719f, 0.499988079071045f,
  0.503834903240204f, 0.499985307455063f, 0.504218399524689f, 0.499982208013535f,
  0.504601895809174f, 0.499978810548782f, 0.504985332489014f, 0.499975144863129f,
  0.505368828773499f, 0.499971181154251f, 0.505752325057983f, 0.499966919422150f,
  0.506135761737823f, 0.499962359666824f, 0.506519258022308f, 0.499957501888275f,
  0.506902694702148f, 0.499952346086502f, 0.507286131381989f, 0.499946922063828f,
  0.507669627666473f, 0.499941170215607f, 0.508053064346313f, 0.499935150146484f,
  0.508436501026154f, 0.499928832054138f, 0.508819937705994f, 0.499922215938568f,
  0.509203374385834f, 0.499915301799774f, 0.509586811065674f, 0.499908089637756f,
  0.509970188140869f, 0.499900579452515f, 0.510353624820709f, 0.499892801046371f,
  0.510737061500549f, 0.499884694814682f, 0.511120438575745f, 0.499876320362091f,
  0.511503815650940f, 0.499867647886276f, 0.511887252330780f, 0.499858677387238f,
  0.512270629405975f, 0.499849408864975f, 0.512654006481171f, 0.499839842319489f,
  0.513037383556366f, 0.499830007553101f, 0.513420701026917f, 0.499819844961166f,
  0.513804078102112f, 0.499809414148331f, 0.514187395572662f, 0.499798685312271f,
  0.514570772647858f, 0.499787658452988f, 0.514954090118408f, 0.499776333570480f,
  0.515337407588959f, 0.499764710664749f, 0.515720725059509f, 0.499752789735794f,
  0.516103982925415f, 0.499740600585938f, 0.516487300395966f, 0.499728083610535f,
  0.516870558261871f, 0.499715298414230f, 0.517253875732422f, 0.499702215194702f,
  0.517637133598328f, 0.499688833951950f, 0.518020391464233f, 0.499675154685974f,
  0.518403589725494f, 0.499661177396774f, 0.518786847591400f, 0.499646931886673f,
  0.519170045852661f, 0.499632388353348f, 0.519553244113922f, 0.499617516994476f,
  0.519936442375183f, 0.499602377414703f, 0.520319640636444f, 0.499586939811707f,
  0.520702838897705f, 0.499571204185486f, 0.521085977554321f, 0.499555170536041f,
  0.521469116210938f, 0.499538868665695f, 0.521852254867554f, 0.499522238969803f,
  0.522235393524170f, 0.499505341053009f, 0.522618472576141f, 0.499488145112991f,
  0.523001611232758f, 0.499470651149750f, 0.523384690284729f, 0.499452859163284f,
  0.523767769336700f, 0.499434769153595f, 0.524150788784027f, 0.499416410923004f,
  0.524533808231354f, 0.499397724866867f, 0.524916887283325f, 0.499378770589828f,
  0.525299847126007f, 0.499359518289566f, 0.525682866573334f, 0.499339967966080f,
  0.526065826416016f, 0.499320119619370f, 0.526448845863342f, 0.499299973249435f,
  0.526831746101379f, 0.499279528856277f, 0.527214705944061f, 0.499258816242218f,
  0.527597606182098f, 0.499237775802612f, 0.527980506420136f, 0.499216467142105f,
  0.528363406658173f, 0.499194860458374f, 0.528746306896210f, 0.499172955751419f,
  0.529129147529602f, 0.499150782823563f, 0.529511988162994f, 0.499128282070160f,
  0.529894769191742f, 0.499105513095856f, 0.530277609825134f, 0.499082416296005f,
  0.530660390853882f, 0.499059051275253f, 0.531043112277985f, 0.499035388231277f,
  0.531425893306732f, 0.499011427164078f, 0.531808614730835f, 0.498987197875977f,
  0.532191336154938f, 0.498962640762329f, 0.532573997974396f, 0.498937815427780f,
  0.532956659793854f, 0.498912662267685f, 0.533339321613312f, 0.498887240886688f,
  0.533721983432770f, 0.498861521482468f, 0.534104585647583f, 0.498835533857346f,
  0.534487187862396f, 0.498809218406677f, 0.534869730472565f, 0.498782604932785f,
  0.535252273082733f, 0.498755723237991f, 0.535634815692902f, 0.498728543519974f,
  0.536017298698425f, 0.498701065778732f, 0.536399841308594f, 0.498673290014267f,
  0.536782264709473f, 0.498645216226578f, 0.537164747714996f, 0.498616874217987f,
  0.537547171115875f, 0.498588204383850f, 0.537929534912109f, 0.498559266328812f,
  0.538311958312988f, 0.498530030250549f, 0.538694262504578f, 0.498500496149063f,
  0.539076626300812f, 0.498470664024353f, 0.539458930492401f, 0.498440563678741f,
  0.539841234683990f, 0.498410135507584f, 0.540223479270935f, 0.498379439115524f,
  0.540605723857880f, 0.498348444700241f, 0.540987968444824f, 0.498317152261734f,
  0.541370153427124f, 0.498285561800003f, 0.541752278804779f, 0.498253703117371f,
  0.542134463787079f, 0.498221516609192f, 0.542516589164734f, 0.498189061880112f,
  0.542898654937744f, 0.498156309127808f, 0.543280720710754f, 0.498123258352280f,
  0.543662786483765f, 0.498089909553528f, 0.544044792652130f, 0.498056292533875f,
  0.544426798820496f, 0.498022347688675f, 0.544808745384216f, 0.497988134622574f,
  0.545190691947937f, 0.497953623533249f, 0.545572578907013f, 0.497918814420700f,
  0.545954465866089f, 0.497883707284927f, 0.546336352825165f, 0.497848302125931f,
  0.546718180179596f, 0.497812628746033f, 0.547099947929382f, 0.497776657342911f,
  0.547481775283813f, 0.497740387916565f, 0.547863483428955f, 0.497703820466995f,
  0.548245191574097f, 0.497666954994202f, 0.548626899719238f, 0.497629791498184f,
  0.549008548259735f, 0.497592359781265f, 0.549390196800232f, 0.497554630041122f,
  0.549771785736084f, 0.497516602277756f, 0.550153374671936f, 0.497478276491165f,
  0.550534904003143f, 0.497439652681351f, 0.550916433334351f, 0.497400760650635f,
  0.551297962665558f, 0.497361570596695f, 0.551679372787476f, 0.497322082519531f,
  0.552060842514038f, 0.497282296419144f, 0.552442193031311f, 0.497242212295532f,
  0.552823603153229f, 0.497201830148697f, 0.553204894065857f, 0.497161179780960f,
  0.553586184978485f, 0.497120231389999f, 0.553967475891113f, 0.497078984975815f,
  0.554348707199097f, 0.497037440538406f, 0.554729938507080f, 0.496995598077774f,
  0.555111110210419f, 0.496953487396240f, 0.555492222309113f, 0.496911078691483f,
  0.555873334407806f, 0.496868371963501f, 0.556254446506500f, 0.496825367212296f,
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  0.523767769336700f, -0.499434769153595f, 0.523384690284729f, -0.499452859163284f,
  0.523001611232758f, -0.499470651149750f, 0.522618472576141f, -0.499488145112991f,
  0.522235393524170f, -0.499505341053009f, 0.521852254867554f, -0.499522238969803f,
  0.521469116210938f, -0.499538868665695f, 0.521085977554321f, -0.499555170536041f,
  0.520702838897705f, -0.499571204185486f, 0.520319640636444f, -0.499586939811707f,
  0.519936442375183f, -0.499602377414703f, 0.519553244113922f, -0.499617516994476f,
  0.519170045852661f, -0.499632388353348f, 0.518786847591400f, -0.499646931886673f,
  0.518403589725494f, -0.499661177396774f, 0.518020391464233f, -0.499675154685974f,
  0.517637133598328f, -0.499688833951950f, 0.517253875732422f, -0.499702215194702f,
  0.516870558261871f, -0.499715298414230f, 0.516487300395966f, -0.499728083610535f,
  0.516103982925415f, -0.499740600585938f, 0.515720725059509f, -0.499752789735794f,
  0.515337407588959f, -0.499764710664749f, 0.514954090118408f, -0.499776333570480f,
  0.514570772647858f, -0.499787658452988f, 0.514187395572662f, -0.499798685312271f,
  0.513804078102112f, -0.499809414148331f, 0.513420701026917f, -0.499819844961166f,
  0.513037383556366f, -0.499830007553101f, 0.512654006481171f, -0.499839842319489f,
  0.512270629405975f, -0.499849408864975f, 0.511887252330780f, -0.499858677387238f,
  0.511503815650940f, -0.499867647886276f, 0.511120438575745f, -0.499876320362091f,
  0.510737061500549f, -0.499884694814682f, 0.510353624820709f, -0.499892801046371f,
  0.509970188140869f, -0.499900579452515f, 0.509586811065674f, -0.499908089637756f,
  0.509203374385834f, -0.499915301799774f, 0.508819937705994f, -0.499922215938568f,
  0.508436501026154f, -0.499928832054138f, 0.508053064346313f, -0.499935150146484f,
  0.507669627666473f, -0.499941170215607f, 0.507286131381989f, -0.499946922063828f,
  0.506902694702148f, -0.499952346086502f, 0.506519258022308f, -0.499957501888275f,
  0.506135761737823f, -0.499962359666824f, 0.505752325057983f, -0.499966919422150f,
  0.505368828773499f, -0.499971181154251f, 0.504985332489014f, -0.499975144863129f,
  0.504601895809174f, -0.499978810548782f, 0.504218399524689f, -0.499982208013535f,
  0.503834903240204f, -0.499985307455063f, 0.503451406955719f, -0.499988079071045f,
  0.503067970275879f, -0.499990582466125f, 0.502684473991394f, -0.499992787837982f,
  0.502300977706909f, -0.499994695186615f, 0.501917481422424f, -0.499996334314346f,
  0.501533985137939f, -0.499997645616531f, 0.501150488853455f, -0.499998688697815f,
  0.500766992568970f, -0.499999403953552f, 0.500383496284485f, -0.499999850988388f,
};


/**
* @brief  Initialization function for the floating-point RFFT/RIFFT.
* @deprecated Do not use this function.  It has been superceded by \ref arm_rfft_fast_init_f32 and will be removed
* in the future.
* @param[in,out] *S             points to an instance of the floating-point RFFT/RIFFT structure.
* @param[in,out] *S_CFFT        points to an instance of the floating-point CFFT/CIFFT structure.
* @param[in]     fftLenReal     length of the FFT.
* @param[in]     ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
* @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
*
* \par Description:
* \par
* The parameter <code>fftLenReal</code>	Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 128, 512, 2048.
* \par
* The parameter <code>ifftFlagR</code> controls whether a forward or inverse transform is computed.
* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated.
* \par
* The parameter <code>bitReverseFlag</code> controls whether output is in normal order or bit reversed order.
* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
* \par
* This function also initializes Twiddle factor table.
*/

/**
* @} end of RealFFT_Table group
*/

/**
* @addtogroup RealFFT
* @{
*/

arm_status arm_rfft_init_f32(
  arm_rfft_instance_f32 * S,
  arm_cfft_radix4_instance_f32 * S_CFFT,
  uint32_t fftLenReal,
  uint32_t ifftFlagR,
  uint32_t bitReverseFlag)
{

  /*  Initialise the default arm status */
  arm_status status = ARM_MATH_SUCCESS;

  /*  Initialize the Real FFT length */
  S->fftLenReal = (uint16_t) fftLenReal;

  /*  Initialize the Complex FFT length */
  S->fftLenBy2 = (uint16_t) fftLenReal / 2U;

  /*  Initialize the Twiddle coefficientA pointer */
  S->pTwiddleAReal = (float32_t *) realCoefA;

  /*  Initialize the Twiddle coefficientB pointer */
  S->pTwiddleBReal = (float32_t *) realCoefB;

  /*  Initialize the Flag for selection of RFFT or RIFFT */
  S->ifftFlagR = (uint8_t) ifftFlagR;

  /*  Initialize the Flag for calculation Bit reversal or not */
  S->bitReverseFlagR = (uint8_t) bitReverseFlag;

  /*  Initializations of structure parameters depending on the FFT length */
  switch (S->fftLenReal)
  {
    /* Init table modifier value */
  case 8192U:
    S->twidCoefRModifier = 1U;
    break;
  case 2048U:
    S->twidCoefRModifier = 4U;
    break;
  case 512U:
    S->twidCoefRModifier = 16U;
    break;
  case 128U:
    S->twidCoefRModifier = 64U;
    break;
  default:
    /*  Reporting argument error if rfftSize is not valid value */
    status = ARM_MATH_ARGUMENT_ERROR;
    break;
  }

  /* Init Complex FFT Instance */
  S->pCfft = S_CFFT;

  if (S->ifftFlagR)
  {
    /* Initializes the CIFFT Module for fftLenreal/2 length */
    arm_cfft_radix4_init_f32(S->pCfft, S->fftLenBy2, 1U, 0U);
  }
  else
  {
    /* Initializes the CFFT Module for fftLenreal/2 length */
    arm_cfft_radix4_init_f32(S->pCfft, S->fftLenBy2, 0U, 0U);
  }

  /* return the status of RFFT Init function */
  return (status);

}

  /**
   * @} end of RealFFT group
   */