% The multiplicative constants for the 113 point FFT

I = sqrt(-1);
u = [
       -1.008928571428571
       -0.094912016185131
        0.251298392703462
        0.094421630759423
       -0.172860011731442
       -0.234027796076585
        0.379278832546667
        0.124972404071575
       -0.584779593031541
       -0.189583748418309
        0.080528356413299
        0.409403694554063
       -0.094847542064179
       -0.102750380242437
        0.548714808618475*I
       -0.379178198609425*I
        0.378338982874398*I
       -0.080947905487851*I
        0.228357206756189*I
        0.081787121222879*I
        0.322752240834198*I
        0.323591456569226*I
       -0.511713743078065*I
       -0.360237056213365*I
       -1.530495714911666*I
        0.670381384192432*I
        0.753034328585655*I
       -1.034133793626451*I
        0.107080002133579*I
        0.118432720867018*I
        0.978547051586252*I
       -0.240454762337246*I
       -0.094238876202555*I
        0.954836956760546*I
       -0.524360183533415*I
       -0.336043211548902*I
        0.402888293435131*I
       -0.094433561678229*I
       -0.220592480850608*I
       -0.651069254077739*I
        0.376084252707655*I
        1.095221438073834
       -0.487045368286899
       -0.374387149068895
        0.031345246766741
        0.122338034180957
       -0.120689082427221
        0.250162553025456
       -0.174187477636614
       -0.093389747877545
        1.153126723167094
       -0.358013516761479
        0.241848554717308
        0.151419326467362
       -0.027611231248954
        0.321289119457616
       -0.069418737426282
       -0.108393624083055
       -0.298524902595726
        0.049282221078445
       -0.177463789694256
       -0.269072115473168
       -0.419695652249467
       -0.002268330067525
        0.106647050649932
       -0.857333785055297
       -0.241883290740130
        0.279287869070545
        0.202280287692694
       -0.060244537499281
        0.234729728722474
        1.481350625014844
       -1.280223612487484
        0.258186582723042
        0.137170477123164
       -0.983081542815654
        1.843285050841020
       -0.829168888221382
       -0.595233131873234
        0.022163347478806
        0.473304388060150
       -1.030295900748742
        0.624765148734061
        0.093347487197412
       -0.057507792589815
        0.428805060472054
        0.031373147824323
       -0.515054454323903
        0.467251974341132
        0.056560422036572
       -1.094584273268024
        1.675330661506362
       -0.369082015714105
       -0.719784401073115
       -0.056641192346680
        1.954994404455970
        0.114599290785475
       -0.335228280981669
        0.101937473597692
        0.121185327193332
       -1.663049527236375
       -0.756361886419584
        0.897639033405694
       -0.362719278532087
       -0.096865449579868
        1.038832908041839
       -1.759307856173691
        0.599125451967743
        0.657508766473174
        0.017238922433937
       -1.214149396258061
        0.457848304981634
       -0.144768433876196
       -0.097642480397552
       -0.031838767301758
        0.617122233382160
        0.136811515231779
       -0.825037756854747
        0.613105714624635
        0.203938729706664
       -3.348570034662107
       -1.788853084493913
        1.328936241299198
        0.521518264585058
       -0.254967787564271
        2.100211892435744
        2.017162482922166
       -0.388545394814032
       -0.926307655963837
       -0.004117027882777
        2.207736103872147
        2.433666023909673
        0.217234579440685
        0.422131040123184
       -0.144990298329532
        0.370882047039733
        0.081199103658241
        1.759119106876196
       -0.167158908741360
       -0.308340454474322
        0.413445728310314
       -0.891781496474162
        0.086488695248128
       -0.384466820263497
       -0.042270898526057
        2.670323326560707
       -1.612392109795558
        0.576911869291499
       -0.465198005575046
        0.056580229550756
       -1.421344875194334
       -0.846668439188164
       -0.352425867606772
       -0.449362671742623
        0.153705267264963
       -0.213397720361663
        0.683054372897286
       -0.474908928715416
        0.612169961475213
        0.058948940653588
       -1.645277753434880
        0.444514962232435
       -2.465767176625512
       -1.067052653223395
        0.358650200430704
        0.217507961011972
       -0.277438935015353
       -2.141474755429206
        0.726156601142403
        0.222270009258641
        0.588652673334323
       -0.120222541036129
        1.414436290108761
        0.116399289174445
       -0.193987291818679
        0.059932169058290
       -0.209791718217228
       -1.919746615456576
       -0.962211909625668
        0.530759090909349
       -5.602869776999069
       -3.678429794227354
        0.241728857532644
        0.181790613500855
       -0.033627698250027
        2.675514853357056
        2.371267191206448
        0.162561733112024
        0.029964735897536
       -0.122477336920337
        1.647436092621384
       -1.265788876346550
        1.671620727893328
        1.110119618675258
       -0.270240131651929
        0.832954867142629
        1.042908270545277
        0.734781516159782
       -0.109635020658421
       -0.067634822049281
       -0.788700681282974
        0.328949664613004
       -1.026016056641472
       -0.344102430386161
        0.177309249691149
       -1.084977742184117
       -0.290663238732107
        1.645402466740130
        0.226973469299380
       -0.281294465068684
        1.565531036825068
        1.033146009754633
        0.406269257065004
       -0.623837432863731
        0.016348889152815
       -1.344432282885033
       -0.948469970943019
       -0.512945447647364
        0.404954183394696
        0.099052159850728
       -1.133834136465219
       -1.111937152846222
        0.851256018007946
        0.270040434751242
       -0.192884396289908
        2.615993864979668
        1.798615345284557
       -1.000423982204420
       -0.007315852379748
        0.170984076362175
       -1.544480290833685
       -0.739742847366143
       -0.124525214180076
        0.177251042182980
        0.082374117723197
       -2.158879709591046
        1.439090493071054
       -1.124266298592414
       -0.322460806550106
        0.106829951050586
        0.294195004025852
       -0.098119915678556
       -0.191177824276505
        0.279498846200522
       -0.043035222607841
        0.501049200822319
       -0.506002018755145
        0.750462492678444
       -0.134033765544526
       -0.118129095172368
        1.365127747809499
        0.058928565724265*I
       -0.603863504212382*I
       -0.376924964350468*I
        0.404058798722799*I
       -8.450044168509129*I
       -1.655931047636108*I
        0.954449924780294*I
       -2.206514462285410*I
       -0.097536264779255*I
        3.330445878088978*I
        1.499384863268411*I
       -0.926121803484961*I
        1.032000808485826*I
        0.079693518617083*I
       -0.213819020103626*I
       -6.368708123195354*I
        8.181512598080902*I
        1.550114127515311*I
       -1.505803198836413*I
       11.649786693868037*I
       -1.624372821685646*I
        6.324082381709196*I
        1.681093246665056*I
       -0.965775686562891*I
        5.590119953067557*I
        4.511277906823648*I
       -5.698494284345543*I
       -1.306031984361566*I
        1.044891579746604*I
       -9.304980385810971*I
        2.790235810960610*I
       -3.419952506975571*I
       -0.489957664292244*I
        0.495534349805970*I
       -0.966072149367044*I
        0.215395146351109*I
       -2.800829636652217*I
        1.118015569560598*I
        0.433138964976080*I
       -4.623269362024428*I
       -2.171112940637256*I
        3.135267721452371*I
       -0.417216097688069*I
       -0.577117870253975*I
        5.861515102671135*I
        5.364570666997302*I
       -3.083047981302073*I
       -1.799433210894260*I
        0.727341115658669*I
       -9.504281937032864*I
       -0.868274162124843*I
       -0.810554842360562*I
       -3.090810140601107*I
        0.234524990224973*I
       -1.060465451097540*I
       -3.092077528055791*I
        2.241849375146547*I
        2.066372819257432*I
       -0.499206577771781*I
        5.605451728980564*I
        0.964912486570258*I
        1.748144213282708*I
        0.533465774135071*I
       -0.349662352035352*I
        2.333041477256403*I
       -1.121930954922241*I
        2.167563684752689*I
        0.753864270490233*I
       -0.216876623185502*I
       -2.348262106227575*I
       -0.545493015100276*I
       -0.180696717593180*I
       -0.713568267557649*I
       -0.055715596154342*I
        3.187101049167539*I
       -1.786098354762558*I
       -1.678512109803259*I
        0.739276747671192*I
        0.282927733371774*I
       -1.179432607468128*I
        2.277251837459382*I
       -2.712697902696417*I
        0.291701324375454*I
        0.298111731361838*I
        0.093614860054410*I
        0.751912561869399*I
        0.321377187746626*I
       -0.343124737207797*I
        0.031432868279152*I
       -2.161986445840727*I
       -0.113305260488433*I
        1.950037853680531*I
       -0.597553565506479*I
       -0.807311479379697*I
       13.690354947041335*I
        1.196589181469498*I
        0.775132191380820*I
        2.259781947507183*I
       -0.320602904506932*I
        1.662864784916988*I
       -1.061600401811278*I
       -0.241603871995055*I
       -0.635296580617067*I
        0.225529550400737*I
       -4.012676109516410*I
        3.465167051746312*I
       -2.811522237424801*I
       -1.657710028729546*I
        0.202957369650746*I
        3.006640402540341*I
        2.605566856804035*I
       -2.748120553676157*I
       -0.539326868718470*I
        0.212033817079879*I
        0.696014193873859*I
       -3.401765367997669*I
        2.321622690898117*I
        1.087951501432568*I
       -0.242244159091892*I
       -0.569210826376572*I
       -1.401684251440124*I
        0.872825847924388*I
        0.454986504505396*I
        0.044603902587722*I
       -2.874935032415781*I
       -1.881469026604570*I
        0.972636227295701*I
        0.135833486363152*I
       -0.001671251175050*I
       -1.052461698435441*I
        1.501494630811437*I
       -0.713975634926901*I
       -0.312045058662826*I
        0.014676278480717*I
        1.252082457178066*I
       -3.377969396822870*I
        1.513340883217051*I
        2.930749687202856*I
       -0.295325349856960*I
        1.368040471311870*I
        3.479026142717776*I
       -0.412699877966358*I
        0.700532080744732*I
        0.013153257345338*I
       -1.269080144043861*I
        1.451928635639461*I
       -1.497592366737872*I
       -1.494634090443226*I
        0.320381722513500*I
       -2.583001378322956*I
       -5.133255325500776*I
        4.513725375341600*I
        2.597437857458276*I
       -0.546302956505066*I
       -2.470186235138615*I
        2.569702293864101*I
        2.551664177496957*I
       -2.294222267776848*I
       -0.373008069427006*I
        4.279082250317952*I
        3.171194127656133*I
       -4.640166774061432*I
        0.175402404800060*I
        0.853733581630494*I
       -8.203204646007238*I
        2.556783528630570*I
       -1.443708779737603*I
       -1.658007165396594*I
        0.228590731193383*I
       -0.214431601523597*I
       -2.323705260180635*I
       -0.132434339977370*I
        0.345033514120955*I
        0.068081850830997*I
       -0.985567102129302*I
       -1.245509088870338*I
        1.638272836891318*I
        0.437941085677781*I
       -0.344664450388690*I
        3.608115981649768*I
        1.818919314921833*I
        1.726505105063658*I
       -0.440715619054829*I
       -0.778548394234887*I
       10.794424259852546*I
        3.347999295895820*I
        1.281459587215015*I
       -0.077228627127419*I
       -0.491063826222808*I
        4.326629852781552*I
       -2.263964832770474*I
       -0.665072539066398*I
        0.333146376065898*I
        0.351927764160276*I
       -5.216720888478838*I
       -3.606716858633250*I
        8.820337711855608*I
        1.365597701649565*I
       -1.995853768075339*I
       17.525922741066505*I
        5.034532230864284*I
        5.547069136606524*I
       -0.937918488058500*I
       -1.131592745015641*I
        8.912968484905647*I
        0.333448283384167*I
       -5.876112394203921*I
        0.331705155745981*I
        1.358421247038971*I
      -15.459505635403815*I
        0.757552481948374*I
       -4.796521700667655*I
       -0.498715073006853*I
        1.096260619546570*I
       -8.109806423190333*I
       -3.593996329579285*I
       -3.700689424734602*I
        2.026417380783312*I
        0.795990044818816*I
       -7.620145000970200*I
        0.338279793984679*I
        3.666966476236512*I
       -0.946489866543738*I
       -0.860996895402079*I
        9.811809552836307*I
       -1.873296009685999*I
       -0.380330755595508*I
       -0.533762910802118*I
        0.375295713577989*I
       -5.554113481320339*I
       -3.807341162062430*I
        0.448122528946099*I
        0.130496112349192*I
        0.072924656936621*I
        0.666680810224414*I
        2.701749294227607*I
       -0.502653136413619*I
        0.063557851802861*I
       -0.046704695142455*I
        0.990225758858801*I
        0.703175787184207*I
       -3.450347351199507*I
       -1.473193602863801*I
        0.693007938889672*I
       -2.869495644658128*I
       -4.053338195745895*I
       -1.971107308573488*I
        2.079684866005085*I
        0.377850875532629*I
       -2.626834337964233*I
        0.776064255441812*I
        2.499240800756496*I
       -0.549785638674979*I
       -0.555773826384259*I
        5.585314423216271*I
        0.630999077572112*I
        2.249395041616473*I
        0.463743913220005*I
       -0.556122367152879*I
        4.268799241407507*I
        1.927922449325823*I
        1.872496015378086*I
       -0.772568324859561*I
       -0.364522331017785*I
        1.944413940510331*I
       -1.007898103810499*I
       -1.245674389711042*I
        0.217228710192843*I
        0.298555303628821*I
       -2.698211992987107*I
        1.659520415549302*I
       -0.454738689502334*I
       -1.276912361426194*I
       -0.054366724432919*I
        3.541001848598630*I
       -0.911547547540834*I
       -0.270875023406968*I
        0.752991190770339*I
        0.042191503716958*I
       -1.030682867022558*I
       -1.475656749453936*I
        1.211857085111417*I
        0.231316640978700*I
       -0.200037620565292*I
        1.398410199213291*I
        5.750981724348065*I
       -6.347618986711251*I
       -2.073775992486794*I
        1.026053077670739*I
       -4.589800229364711*I
       -0.472664736089227*I
       -4.437873279603076*I
        0.306564510555896*I
        0.669391877994948*I
       -4.934601101692750*I
       -3.841236017239890*I
        5.169330529203488*I
        0.565314789780753*I
       -0.949312580688549*I
        8.754092515909104*I
       -2.673509669795590*I
        2.431830643356586*I
        1.073982414844419*I
       -0.362062540499676*I
        0.590251875445320*I
        1.054155056914764*I
        1.466631988314793*I
       -0.731524541840777*I
       -0.250610407903539*I
        2.804418232076865*I
        1.708311014753797*I
       -2.386770279171844*I
       -0.010362493994856*I
        0.460891160321333*I
       -4.734815542160451*I
       -3.591744990959568*I
        0.678271438119208*I
        1.120074414974544*I
        0.025603639288109*I
       -0.645071161409840*I
       -1.239862566885489*I
       -0.235452372427227*I
        1.584019383864263*I
        0.128269417998917*I
       -1.633082200842007*I
        2.678021180413133*I
       -0.788388418040075*I
       -1.199759597661665*I
        0.073639406805753*I
       -0.194365420250863*I
        1.320902186031496*I
       -5.284240962569157*I
       -0.949531737892318*I
        1.172758060055345*I
       -9.929482109161453*I
       -1.956300637971021*I
       -3.857316410679607*I
        0.092027108784133*I
        0.674234684100572*I
       -3.282353189339036*I
        0.106022365858054*I
        3.028404555898550*I
        0.190931555905834*I
       -0.651352825442315*I
        6.136202293118139*I
        0.514272936407092*I
        3.237516905235457*I
       -0.120280837332170*I
       -0.689594176459172*I
        4.644619515329230*I
        0.658372246059951*I
        3.206693663715509*I
       -1.159059352579383*I
       -0.547050888090327*I
        3.763265070457896*I
       -0.545096177927039*I
       -1.994171831991569*I
        0.644807301875767*I
        0.414782013561464*I
       -3.824911553497790*I
        0.993300635087216*I
       -0.784853549042511*I
        0.565658238154299*I
        0.216007882900854*I
       -4.068120732860499*I
        1.305375990296466*I
       -0.611627360163460*I
       -1.195139029928188*I
        0.123839123785156*I
       -1.164772797570702*I
       -0.820074446208165*I
        0.372128504204337*I
        0.285869364407103*I
       -0.089412427629141*I
        1.511225175328804*I
       -2.084171419465259*I
        3.130934794312154*I
        1.565451815796673*I
       -0.447982654270209*I
       -0.068572378941107*I
        0.723885669470929*I
        2.359613931124822*I
       -0.770178998643307*I
       -0.294942346306254*I
        0.965410072045188*I
        1.312850556277928*I
       -2.410431745827306*I
       -0.269082931378795*I
        0.399008992738076*I
       -2.508051798419850*I
        0.385342586934007*I
       -1.561110444770431*I
       -0.459365208862701*I
        0.255759232282579*I
       -0.696932104495863*I
       -0.023226711360627*I
       -1.422566121336893*I
        0.318367419248204*I
        0.183096791096418*I
       -0.445976121037446*I
       -0.246798263500469*I
        0.979825012318972*I
        0.047408174234992*I
       -0.156615791054769*I
        0.723064767904520*I
];


% The input permutation for the 113 point FFT

ip = [
   1
   2
   107
   50
   110
   29
   31
   17
   49
   4
   93
   35
   102
   85
   91
   45
   32
   10
   51
   103
   78
   27
   79
   20
   94
   28
   38
   81
   6
   16
   9
   58
   54
   82
   112
   15
   43
   46
   25
   59
   47
   18
   108
   96
   14
   23
   73
   62
   26
   52
   41
   60
   40
   67
   104
   71
   76
   113
   8
   65
   5
   86
   84
   98
   66
   111
   22
   80
   13
   30
   24
   70
   83
   105
   64
   12
   37
   88
   36
   95
   21
   87
   77
   34
   109
   99
   106
   57
   61
   33
   3
   100
   72
   69
   90
   56
   68
   97
   7
   19
   101
   92
   42
   53
   89
   63
   74
   55
   75
   48
   11
   44
   39
];


% The output permutation for the 113 point FFT

op = [
   1
   113
   83
   2
   53
   21
   91
   51
   23
   10
   103
   68
   61
   37
   28
   29
   112
   34
   99
   16
   73
   59
   38
   63
   31
   41
   14
   18
   110
   62
   111
   9
   82
   76
   4
   78
   69
   19
   105
   45
   50
   95
   36
   104
   15
   30
   33
   102
   8
   108
   11
   42
   96
   25
   100
   88
   80
   24
   32
   44
   81
   40
   98
   67
   52
   64
   46
   89
   86
   71
   48
   92
   39
   106
   101
   49
   75
   13
   22
   60
   20
   26
   65
   55
   6
   54
   74
   70
   97
   87
   7
   94
   3
   17
   72
   43
   90
   56
   85
   84
   93
   5
   12
   47
   66
   79
   107
   35
   77
   109
   58
   27
   57
];