Strange C program Latency behaviour

Question

A simple (vanila) DFT program was being written and an unusual behaviour was observed:

To recreate

Compile the following program:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <string.h>
#include <complex.h>

#define N   16384
#define PI2  (2 * M_PI)  //6.2832 

int main(void) {
    // time and frequency domain data arrays
    int n, k;             // indices for time and frequency domains
    float Xre[2000], Xim[2000]; // DFT of x (real and imaginary parts)
    float P[2000];           // power spectrum of x

    float x[N] = { 0 };

    // Generate 2*pi*50*t sine wave  in range (-1,+1)
    float y[] = {
        0.0, 0.0984079408900634, 0.195860568724094, 0.291411844321996, 0.384134186227703, 0.473127475375545, 0.557527793160445, 0.636515808085535, 0.709324729572274, 0.775247751720011, 0.833644914753334, 0.883949317548447, 0.925672620929349, 0.958409788309562, 0.981843017658750, 0.995744826623968,
        0.999980260856137, 0.994508204104035, 0.979381777357810, 0.954747823167273, 0.920845480141026, 0.878003861464755, 0.826638859974879, 0.767249110802900, 0.700411150783807, 0.626773821619470, 0.547051971129342, 0.462019513734716, 0.372501917543151, 0.279368190966096, 0.183522446661037, 0.0858951246927854,
        -0.0125660398833526, -0.110905217332694, -0.208167762132862, -0.303409480369524, -0.395705795671223, -0.484160724703344, -0.567915575089941, -0.646157281326779, -0.718126297763189, -0.783123972030169, -0.840519327335832, -0.889755187787833, -0.930353587280090, -0.961920409436037, -0.984149213565316, -0.996824209492737,
        -0.999822352380809, -0.993114537209969, -0.976765881320872, -0.950935092275919, -0.915872927176609, -0.871919758393194, -0.819502269337733, -0.759129312356960, -0.691386968955206, -0.616932860301177, -0.536489763250371, -0.450838593856768, -0.360810826487642, -0.267280422134304, -0.171155344276191, -0.0733687446595907,
        0.0251300954433374, 0.123384980555854, 0.220442083438833, 0.315359204542867, 0.407214918582441, 0.495117519440145, 0.578213676566644, 0.655696718842807, 0.726814465486903, 0.790876527986881, 0.847261012172933, 0.895420555368697, 0.934887640014398, 0.965279132178928, 0.986300000902440, 0.997746182263274,
        0.999506560365732, 0.991564046017929, 0.973995742628244, 0.946972197709905, 0.910755747259856, 0.865697969084168, 0.812236269792286, 0.750889638592492, 0.682253609109396, 0.606994478132532, 0.525842837418596, 0.439586481338564, 0.349062759219976, 0.255150446625443, 0.158761214478388, 0.0608307788510959,
        -0.0376901826699336, -0.135845259860259, -0.232681594384382, -0.327259129842054, -0.418659737537428, -0.505996129381040, -0.588420471400950, -0.665132614245854, -0.735387860781017, -0.798504195371694, -0.853868904674451, -0.900944525663825, -0.939274063152787, -0.968485426156976, -0.988295040035869, -0.998510599345391,
        -0.999032934678125, -0.989856975368447, -0.971071798716938, -0.942859765256222, -0.905494748452794, -0.859339476030335, -0.804842008724098, -0.742531390649502, -0.673012513509774, -0.596960244499286, -0.515112874907027, -0.428264953019107, -0.337259570896168, -0.242980179903264, -0.146342014444403, -0.0482832071574495,
        0.0502443181797695, 0.148284087623366, 0.244884362208849, 0.339107377130930, 0.430038445266602, 0.516794836667414, 0.598534347821637, 0.674463477498649, 0.743845129807025, 0.806005769687504, 0.860341961377560, 0.906326226374270, 0.943512164028194, 0.971538785059195, 0.990134015925798, 0.999117340028769,
        0.998401550108975, 0.987993594827769, 0.967994511311594, 0.938598444315629, 0.900090761528124, 0.852845283311457, 0.797320653772707, 0.734055888392230, 0.663665141432458, 0.586831743923250, 0.504301570101134, 0.416875796698963, 0.325403125376477, 0.230771543793960, 0.133899705309884, 0.0357280109856745,
        -0.0627905195293142, -0.160699499610071, -0.257048459953733, -0.350902075433899, -0.441349244940104, -0.527511936058200, -0.608553708730373, -0.683687835149718, -0.752184937064112, -0.813380066348762, -0.866679160111565, -0.911564807667102, -0.947601273395360, -0.974438726724819, -0.991816638176614, -0.999566308502021,
        -0.997612506361225, -0.985974198645282, -0.964764366351565, -0.934188907800099, -0.894544639838025, -0.846216416435848, -0.789673392647252, -0.725464470200735, -0.654212968935859, -0.576610575812079, -0.493410630231271, -0.405420810857945, -0.313495294931096, -0.218526466182705, -0.121436251859683, -0.0231671729467908,
        0.0753268055279309, 0.173089535282900, 0.269171966766988, 0.362641362231371, 0.452590350451546, 0.538145735199171, 0.618476971953920, 0.692804230566056, 0.760405965600031, 0.820625920868545, 0.872879500159325, 0.916659442309612, 0.951540745536515, 0.977184793219440, 0.993342641082758, 0.999857433867821,
        0.996665928034030, 0.983799105707054, 0.961381873914185, 0.929631852026567, 0.888857259179404, 0.839453922178432, 0.781901432938911, 0.716758492759546, 0.644657488627590, 0.566298354206707, 0.482441775103100, 0.393901804371106, 0.301537959944494, 0.206246880709201, 0.108953622217581, 0.0106026765427436,
        -0.0878511965507475, -0.185452238111593, -0.281252968206354, -0.374323383753877, -0.463759986700061, -0.548694554890174, -0.628302570493986, -0.701811224163148, -0.768506917219076, -0.827742189042424, -0.878942002415270, -0.921609325799925, -0.955329958363339, -0.979776550907327, -0.994711783670682, -0.999990670154097,
        -0.995561964603080, -0.981468659485473, -0.957847568134224, -0.924927996606965, -0.883029517655600, -0.832558868415444, -0.774006001930223, -0.707939330843420, -0.635000209428760, -0.555896707526464, -0.471396736825997, -0.382320596223098, -0.289533008618479, -0.193934726462339, -0.0964537875354998, 0.00196349414684702,
        0.100361714851215, 0.197785655882052, 0.293289556541649, 0.385946295274789, 0.474856389870597, 0.559156729350287, 0.638028952774654, 0.710707393632289, 0.776486512687080, 0.834727747129162, 0.884865709540016, 0.926413676494061, 0.958968313515203, 0.982213590519895, 0.995923849736900, 0.999965996321297,
        0.994300790396999, 0.978983227985015, 0.954162007119530, 0.920078084334595, 0.877062335534554, 0.825532343955807, 0.765988346401266, 0.699008377100263, 0.625242656335702, 0.545407278311946, 0.460277259539545, 0.370679015220949, 0.277482336674029, 0.181591947674010, 0.0839387216822394, -0.0145293547779467,
        -0.112856384873481, -0.210087841004649, -0.305279831056042, -0.397508261401654, -0.485877807712459, -0.569530606480889, -0.647654582887413, -0.719491334165196, -0.784343491933411, -0.841581492028159, -0.890649686111535, -0.931071735729352, -0.962455236453648, -0.984495527220340, -0.996978647882129, -0.999783416265704,
        -0.992882604569814, -0.976343203684123, -0.950325772862918, -0.915082881066822, -0.870956655103499, -0.818375458369187, -0.757849732432795, -0.689967041831200, -0.615386370179169, -0.534831722965621, -0.449085099138105, -0.358978899705249, -0.265387847051938, -0.169220493412062, -0.0714104009317734, 0.0270929210554974,
        0.125333233564306, 0.222356850821733, 0.317221898346202, 0.409007456365973, 0.496822499816019, 0.579814548126516, 0.657177940833683, 0.728161658675826, 0.792076614249970, 0.848302341453640, 0.896293018772879, 0.935582767944242, 0.965790176553122, 0.986622000664402, 0.997876011541515, 0.999442958818825,
        0.991307631069506, 0.973549003473241, 0.946339471150244, 0.909943175604153, 0.864713440520154, 0.811089341810776, 0.749591445206302, 0.680816752767877, 0.605432907381000, 0.524171711490274, 0.437822022993559, 0.347222097259867, 0.253251449612327, 0.156822317272532, 0.0588708036511916, -0.0396522090467458,
        -0.137790290684639, -0.234590747914437, -0.329113872621261, -0.420442064311573, -0.507688737887499, -0.590006930333573, -0.666597522764850, -0.736716998019437, -0.799684658487090, -0.854889234105571, -0.901794816376402, -0.939946060794457, -0.968972607187923, -0.988592675057273, -0.998615799010932, -0.998944677742839,
        -0.989576118602650, -0.970601068588971, -0.942203731464759, -0.904659779565662, -0.858333677660472, -0.803675144842848, -0.741214788801068, -0.671558954847019, -0.595383839708351, -0.513428927225288, -0.426489809676181, -0.335410464420208, -0.241075060833035, -0.144399377071172, -0.0463219099882471, 0.0522052354945227,
        0.150225589120753, 0.246787600408572, 0.340953876000616, 0.431810279581299, 0.518474806021958, 0.600106143606748, 0.675911841219724, 0.745156001208767, 0.807166423246402, 0.861341129837251, 0.907154210124478, 0.944160925265473, 0.972002025815363, 0.990407239206624, 0.999197893469363, 0.998288651722103,
        0.987688340595138, 0.967499864544408, 0.937919206887704, 0.899233527260826, 0.851818373962972, 0.796134038253055, 0.732721085988247, 0.662195109982227, 0.585240754025510, 0.502605066580843, 0.415090248673835, 0.323545866380009, 0.228860603507013, 0.131953634534243, 0.0337657015587562, -0.0647500181304328,
        -0.162637165194890, -0.258945482279751, -0.352740038810489, -0.443110307002175, -0.529179000974195, -0.610110593163201, -0.685119425359456, -0.753477335627384, -0.814520727070512, -0.867657009819546, -0.912370353706714, -0.948226695781328, -0.974877954055122, -0.992065406571739, -0.999622202997347, -0.997474984350731,
        -0.985644595148997, -0.964245881055618, -0.933486573995179, -0.893665275557789, -0.845168558269628, -0.788467212869540, -0.724111678021981, -0.652726696833165, -0.575005252043276, -0.491701838769995, -0.403625140109338, -0.311630176696852, -0.216610006438655, -0.119487054988758, -0.0212041611335505, 0.0772845759878599,
        0.175023058975285, 0.271062473657499, 0.364470499879154, 0.454340362168866, 0.539799632427741, 0.620018699184368, 0.694218821199767, 0.761679687240114, 0.821746408629595, 0.873835876701791, 0.917442423433567, 0.952142730309724, 0.977599937764792, 0.993566915308769, 0.999888660591489, 0.996503804116233,
        0.983445204995330, 0.960839631964316, 0.928906532751298, 0.887955903748049, 0.838385280663432, 0.780675879372910, 0.715387924427582, 0.643155210572020, 0.564678950066079, 0.480720965538817, 0.392096294456247, 0.299665276996257, 0.204325204139264, 0.107001607052153, 0.00863927232549537, -0.0898069297148414,
        -0.187381314585722, -0.283136661128381, -0.376143406830793, -0.465498671725509, -0.550335023261759, -0.629828897065438, -0.703208591840560, -0.769761760800563, -0.828842326904764, -0.879876754769274, -0.922369618366427, -0.955908410463418, -0.980167547111590, -0.994911528312078, -0.999997224175046, -0.995375264379227,
        -0.981090517443334, -0.957281655156723, -0.924179806397673, -0.882106313407595, -0.831469612302545, -0.772761268105050, -0.706551202786880, -0.633482162647440, -0.554263478736693, -0.469664180894493, -0.380505532252943, -0.287653056674601, -0.192008136521520, -0.0944992623213991, 0.00392698072380246, 0.102315101886539,
        0.199709980514407, 0.295166138038260, 0.387756916378113, 0.476583473645635, 0.560783509815936, 0.639539637662464, 0.712087317692860, 0.777722280055610, 0.835807361368273, 0.885778690097328, 0.927151160444101, 0.959523141597856, 0.982580376640236, 0.996099033251688, 0.999947876604571, 0.994089543349219,
        0.978580904325473, 0.953572512478617, 0.919307141339182, 0.876117428254551, 0.824422645251177, 0.764724628874819, 0.697602908520652, 0.623709080545813, 0.543760482778796, 0.458533230831479, 0.368854683815130, 0.275595412600709, 0.179660748593197, 0.0819819950616476, -0.0164926136573281, -0.114807117317581,
        -0.212007109922050, -0.307149004793269, -0.399309194613317, -0.487593017510555, -0.571143442153087, -0.649149387536929, -0.720853596702917, -0.785559987947003, -0.842640412160429, -0.891540750701937, -0.931786294605665, -0.962986352905092, -0.984838045336978, -0.997129242606799, -0.999740625672616, -0.992646844056464,
        -0.975916761938747, -0.949712789646630, -0.914289307026130, -0.869990194003309, -0.817245492307110, -0.756567230760720, -0.688544454668300, -0.613837507550104, -0.533171620737190, -0.447329873055838, -0.357145588946850, -0.263494248816364, -0.167284990149970, -0.0694517818945103, 0.0290556422159688, 0.127281003373913,
        0.224270760949379, 0.319083369159829, 0.410798417297745, 0.498525564785646, 0.581413184319829, 0.658656629197908, 0.729506044573661, 0.793273646809804, 0.849340400263315, 0.897162026686948, 0.936274288909695, 0.966297497503909, 0.986940196689757, 0.998001993695415, 0.999375504106507, 0.991047394319906,
        0.973098510982126, 0.945703096155735, 0.909127095832718, 0.863725578215192, 0.809939286825997, 0.748290361910482, 0.679377271664694, 0.603869002496122, 0.522498564715948, 0.436055876707622, 0.345380096649905, 0.251351476235615, 0.154882815467577, 0.0569106014859085, -0.0416140825518728, -0.139734790284324,
        -0.236498997023725, -0.330967346563474, -0.422222770149962, -0.509379389094972, -0.591591114604805, -0.668059861341758, -0.738043294983249, -0.800862038567848, -0.855906267671136, -0.902641630387714, -0.940614434649876, -0.969456052526198, -0.988886498744503, -0.998717148700020, -0.998852569563171, -0.989291446711198,
        -0.970126596490105, -0.941544065183020, -0.903821322931938, -0.857324570145646, -0.802505182542385, -0.739895329337642, -0.670102807114307, -0.593805139526380, -0.511743000114341, -0.424713022081554, -0.333560064831927, -0.239169012343003, -0.142456182993156, -0.0443604342336034, 0.0541659515417433, 0.152166511451484,
        0.248689887164858, 0.342799060386402, 0.433580449132212, 0.520152776493846, 0.601675625794849, 0.677357599089101, 0.746463999800899, 0.808323964926108, 0.862336977557309, 0.907978696511290, 0.944806046466880, 0.972461519199504, 0.990676644157565, 0.999274594689349, 0.998171904620035, 0.987379278514827,
        0.967001487762437, 0.937236353487686, 0.898372826166838, 0.850788180588052, 0.794944353387510, 0.731383458715156, 0.660722525562598, 0.583647507841499, 0.500906625360716, 0.413303100345869, 0.321687360012960, 0.226948780890808, 0.130007055036036, 0.0318032619544833, -0.0667092670999465, -0.164574203762531,
        -0.260841506289903, -0.354576642263842, -0.444869660735319, -0.530844025739510, -0.611665125428735, -0.686548374219374, -0.754766829299691, -0.815658247559921, -0.868631514438194, -0.913172382273058, -0.948848462456602, -0.975313422925793, -0.992310350244224, -0.999674243636218, -0.997333616761983, -0.985311191684313,
        -0.963723678290009, -0.932780641307352, -0.892782465918221, -0.844117441714098, -0.787257993303952, -0.722756094166077, -0.651237908264765, -0.573397711449273, -0.489991151644234, -0.401827913259485, -0.309763857030723, -0.214692711595228, -0.117537397457843, -0.0192410675716325, 0.0792420484915564, 0.176955907898970,
        0.272951935517313, 0.366298232379078, 0.456088622261896, 0.541451448559776, 0.621558036048674, 0.695630735402642, 0.762950472366612, 0.822863728301042, 0.874788884333453, 0.918221867529835, 0.952741044274703, 0.978011313356413, 0.993787359023354, 0.999916032431425, 0.996337838364386, 0.983087512794541,
        0.960293685676943, 0.928177632250618, 0.887051124968773, 0.837313406910770, 0.779447316057058, 0.714014598051266, 0.641650452951816, 0.563057368911361, 0.478998302644763, 0.390289272887461, 0.297791438744591, 0.202402739831719, 0.105049179362040, 0.00667583480114843, -0.0917623166451206, -0.189309668646243,
        -0.285019262469973, -0.377961979757159, -0.467235562107885, -0.551973369919598, -0.631352795449380, -0.704603248428773, -0.771013636709533, -0.829939269320517, -0.880808114923002, -0.923126354909364, -0.956483177237392, -0.980554764463184, -0.995107437258145, -0.999999922893717, -0.995184726672197, -0.980708592990188,
        -0.956712051558832, -0.923428053185976, -0.881179708363663, -0.830377150614053, -0.771513555043328, -0.705160350754312, -0.631961673594109, -0.552628113087742, -0.467929814260579, -0.378689001314870, -0.285771995738146, -0.190080806329236, -0.0925443727830621, 0.00589045216103947, 0.104268094465144, 0.201633535202275,
        0.297041581577028, 0.389566042557161, 0.478308720042225, 0.562408128285632, 0.641047856924812, 0.713464496433956, 0.778955049061354, 0.836883753308413, 0.886688255700559, 0.927885069936238, 0.960074270418487, 0.982943374605696, 0.996270376492941, 0.999925901775817, 0.993874463775118, 0.978174807930265,
        0.952979341517217, 0.918532654127013, 0.875169143267650, 0.823309768139218, 0.763457963095587, 0.696194750463496, 0.622173100162199, 0.542111590878786, 0.456787434334296, 0.367028930359057, 0.273707426020814, 0.177728856863960, 0.0800249523748130, -0.0184558089525184, -0.116757407144309, -0.213925561485702,
        -0.309016994374950, -0.401108588363064, -0.489306347484964, -0.572754075888567, -0.650641689512372, -0.722213080124420, -0.786773455380986, -0.843696083650190, -0.892428378123718, -0.932497261154178, -0.963513756742748, -0.985176766594716, -0.997275993086157, -0.999693980766518, -0.992407256578852, -0.975486557728811,
        -0.949096144990295, -0.913492208114000, -0.869020378818633, -0.816112375507883, -0.755281812285189, -0.687119212951036, -0.612286278385335, -0.531509462965285, -0.445572922376897, -0.355310901280419, -0.261599634727995, -0.165348841951888, -0.0674928950989053, 0.0310182513578315, 0.129228282475433, 0.226183806443067,
        0.320943609807221, 0.412587794473066, 0.500226707783204, 0.583009578983345, 0.660132778234681, 0.730847617997353, 0.794467621051437, 0.850375184599931, 0.898027575760620, 0.936962200244736, 0.966801093075418, 0.987254587751762, 0.998124128239275, 0.999304196488835, 0.990783336772423, 0.972644266891692,
        0.945063075179802, 0.908307511091783, 0.862734385977789, 0.808786109271773, 0.746986393721116, 0.677935171349503, 0.602302769507245, 0.520823403546116, 0.434288049289797, 0.343536764491561, 0.249450533820281, 0.152942716540872, 0.0549501799124448, -0.0435757956216944, -0.141678751162651, -0.238406334355361,
        -0.332819544522994, -0.424001848187439, -0.511068076485486, -0.593173018107150, -0.669519624338816, -0.739366746559169, -0.802036331074781, -0.856920001450147, -0.903484964433038, -0.941279182142260, -0.969935760307973, -0.989176509964781, -0.998814648021921, -0.998756610494226, -0.989002960791592, -0.969648384249581,
        -0.940880768954224, -0.902979381784135, -0.856312157376272, -0.801332126333271, -0.738573017346144, -0.668644075925549, -0.592224150039745, -0.510055100073975, -0.422934597085312, -0.331708379265198, -0.237262041781567, -0.140512439701961, -0.0423987874555876, 0.0561264587622677, 0.154106847132682, 0.250591215143780,
        0.344642923174507, 0.435348947094810, 0.521828741614001, 0.603242788335117, 0.678800745532949, 0.747769120540683, 0.809478390263939, 0.863329500698409, 0.908799682356035, 0.945447525145274, 0.972917263440128, 0.990942229739981, 0.999347443393019, 0.998051309252864, 0.987066409778365, 0.966499382887074,
        0.936549886748192, 0.897508661564435, 0.849754707158412, 0.793751603762675, 0.730043011729913, 0.659247393850829, 0.582052011513663, 0.499206252988763, 0.411514358605109, 0.319827613440464, 0.225036083316014, 0.128059974319935, 0.0298406997386746, -0.0686682588843781, -0.166510607845101, -0.262736524674396,
        -0.356411878713249, -0.446627299356684, -0.532507003934973, -0.613217299533782, -0.687974676220444, -0.756053413109658, -0.816792623431512, -0.869602670210485, -0.913970890274060, -0.949466571024084, -0.975745131657964, -0.992551468249736, -0.999722430218001, -0.997188404139995, -0.984973989536599, -0.963197760067995,
        -0.932071112458212, -0.891896214322823, -0.843063070821639, -0.786045738612394, -0.721397723859212, -0.649746608970392, -0.571787960227613, -0.488278575449232, -0.400029137237269, -0.307896343128008, -0.212774589044232, -0.115587286783459, -0.0172778998293627, 0.0811992154923688, 0.178888074602276, 0.274840345062014
    };
    float freq=0;
    float ind=0;
    float val = 0;
    float maxV = 0;

    int XN = sizeof(y) / sizeof(*y);

    for (k = 0; k < XN; k++) {
        x[k] = y[k];
    }

    struct timespec sT, eT;
    clock_gettime(CLOCK_MONOTONIC, &sT);

    printf("Starting DFT\n");
    // Calculate DFT of x using brute force
    for (k = 0; k < 2000; ++k) {
        // Real part of X[k]
        Xre[k] = 0;
        for (n = 0; n < XN; ++n)
            Xre[k] += x[n] * cos(n * k * PI2 / N);

        // Imaginary part of X[k]
        Xim[k] = 0;
        for (n = 0; n < XN; ++n)
            Xim[k] -= x[n] * sin(n * k * PI2 / N);

        // Power at kth frequency bin
        P[k] = Xre[k] * Xre[k] + Xim[k] * Xim[k];

        //  printf("\n%+f %+f %f",Xre[k],Xim[k],P[k]);
    }
    printf("DFT over\n");

    ind = 0;

    printf("Freq Compute start\n");
/*
    for (k = 0; k < 2000; k++) { 
        //val = (Xre[k] * Xre[k]) + (Xim[k] * Xim[k]);
        val = P[k];

        if (val > maxV) {
            //printf("%f\n", val);
            maxV = val;
            ind = k;
        }
    }
    printf("Freq Compute over\n");

    freq = ind * 0.195;

    printf("maxV=%f ind = %f Freq= %f\n", maxV, ind, freq);
*/
    clock_gettime(CLOCK_MONOTONIC, &eT);

    printf("%ld.%09ld  %ld uSec\n",
           eT.tv_sec, eT.tv_nsec,
           ((eT.tv_sec - sT.tv_sec) * 1000000 + (eT.tv_nsec - sT.tv_nsec) / 1000));

    return 0;
}

with following compiler flag:

gcc -O3 DFT.c -o DFT_try -lm -lrt

This program takes just 3-5 us (micro seconds) to run on BeagleBone Black and even lesser on PC. Where as now,

if you uncomment the "Freq compute" part show below:

for (k=0;k<2000;k++)
{ 
    val = (Xre[k]*Xre[k])+(Xim[k]*Xim[k]);

    if(val> maxV){
        printf("%f",val);
        maxV = val;
        ind = k;
        a=val;
    }
}

to make the code look like the following:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <string.h>
#include <complex.h>

#define N   16384
#define PI2  (2 * M_PI)  //6.2832 

int main(void) {
    // time and frequency domain data arrays
    int n, k;             // indices for time and frequency domains
    float Xre[2000], Xim[2000]; // DFT of x (real and imaginary parts)
    float P[2000];           // power spectrum of x

    float x[N] = { 0 };

    // Generate 2*pi*50*t sine wave  in range (-1,+1)
    float y[] = {
        //<Copy data HERE, from above program        };
    float freq=0;
    float ind=0;
    float val = 0;
    float maxV = 0;

    int XN = sizeof(y) / sizeof(*y);

    for (k = 0; k < XN; k++) {
        x[k] = y[k];
    }

    struct timespec sT, eT;
    clock_gettime(CLOCK_MONOTONIC, &sT);

    printf("Starting DFT\n");
    // Calculate DFT of x using brute force
    for (k = 0; k < 2000; ++k) {
        // Real part of X[k]
        Xre[k] = 0;
        for (n = 0; n < XN; ++n)
            Xre[k] += x[n] * cos(n * k * PI2 / N);

        // Imaginary part of X[k]
        Xim[k] = 0;
        for (n = 0; n < XN; ++n)
            Xim[k] -= x[n] * sin(n * k * PI2 / N);

        // Power at kth frequency bin
        P[k] = Xre[k] * Xre[k] + Xim[k] * Xim[k];

        //  printf("\n%+f %+f %f",Xre[k],Xim[k],P[k]);
    }
    printf("DFT over\n");

    ind = 0;

    printf("Freq Compute start\n");

    for (k = 0; k < 2000; k++) { 
        //val = (Xre[k] * Xre[k]) + (Xim[k] * Xim[k]);
        val = P[k];

        if (val > maxV) {
            //printf("%f\n", val);
            maxV = val;
            ind = k;
        }
    }
    printf("Freq Compute over\n");

    freq = ind * 0.195;

    printf("maxV=%f ind = %f Freq= %f\n", maxV, ind, freq);

    clock_gettime(CLOCK_MONOTONIC, &eT);

    printf("%ld.%09ld  %ld uSec\n",
           eT.tv_sec, eT.tv_nsec,
           ((eT.tv_sec - sT.tv_sec) * 1000000 + (eT.tv_nsec - sT.tv_nsec) / 1000));

    return 0;
}

and then recompile it, as above

This program will take humongous time of 16198709 uSec or even more to run on BeagleBone Black and approx 0.001 sec on 64bit modern system(s) as stated by chqrlie in comments

Can anyone tell Why such odd behaviour?

@stargateur: I am just trying out different DFT and DFT method implementation. So no it's not my assignment. — rathin2j, Jun 18 '17 at 22:20
@wilsplasser : they are. Please look at 14th line of code. :) — rathin2j, Jun 18 '17 at 22:22
I don't see any time-related functions in your code. Read [ask] and provide **all required information along with a [mcve]. After 4 years you really should know how it works! — too honest for this site, Jun 18 '17 at 22:26
@rodrigo - Did you try both the ways? Please uncomment the for loop shown above and try. There is huge difference in both scenario. — rathin2j, Jun 18 '17 at 22:27
@rathin2j: Yes 0.001s without the code, 1.9s with it, mine is a 64bit machine. I've tried compiling to 32 bits, just for fun and I got 3.1s, which is interesting but way off your measurements. Maybe you are using an old computer? — rodrigo, Jun 18 '17 at 22:30
@olaf: They are there! I have timed them using timespec and clock_gettime(). — rathin2j, Jun 18 '17 at 22:33
@rodrigo- yes, I wrote that code using a BeagleBone Black , so its bit low end compared to PC or Laptop. But don't you find it strange? I am not pro coder so I am not sure. — rathin2j, Jun 18 '17 at 22:36
@rathin2j: I'm pretty sure my browser does not swallow text that selectively! Ignoring the site rules is not really a good idea. — too honest for this site, Jun 18 '17 at 22:49
Dear @Olaf I respect your impeccable concern for rules but rest assured I am a "law abiding citizen", as well. And If you run the code you will see the code displaying 'time', which would be not possible without "any kind of timing function. — rathin2j, Jun 18 '17 at 22:57
@rathin2j: Which code? There is only a snippet **in the question itself**. How about actually reading the comments here and following the links?? You must have **all** information in the question, no external links, etc! — too honest for this site, Jun 18 '17 at 23:08

chqrlie · Accepted Answer · 2017-06-18T23:51:12.600

When you comment the block of code, the compiler can determine that you do not use any of the computation results in the first loop and removes all the code, leaving a simple output statement:

maxV = 0;
ind = 0;
freq = 0;
printf("maxV=%f ind = %f Freq= %f\n", maxV, ind, freq);

If you uncomment the loop, ind is computed from the complex values Xre[k] and Xim[k] computed in the first loop, so it must compute these too, hence a much longer computation time, although not as long as you mention (1s on my laptop).

Note that a more aggressive optimizer would determine that the computation can be performed at compile time and produce a trivial program that executes as fast in both cases. To avoid protentially infinite compile times, such a compiler would set a timeout and give up after a while, but it only takes 1 second on my laptop to run the full code.

There are more problems in your code:

you should use a more precise value for 2*PI: 2 * M_PI.
there are only 960 values in the y array. entries in the x array are zero all the way to 16383. The computation can be simplified: the inner loops can be stopped at the size of y.
you compute P[k] in the first loop but you do not use it in the second loop.

If you reduce the value of N to the size of y, the computation is much faster. It runs 20 times faster on my system:

maxV=228694.692537 ind = 257.000000 Freq= 50.115000
2115850.697709000  47955 uSec

Regarding the huge difference between the Beaglebone system and a 64-bit modern PC, the embedded processor does not seem to have a floating point unit, making the computation times much slower, even as float. Note that on the PC, computing as double is actually sightly faster than float due to fewer conversions.

Here is the updated code:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <string.h>
#include <complex.h>

#define N   16384
#define PI2  (2 * M_PI)  //6.2832 

int main(void) {
    // time and frequency domain data arrays
    int n, k;             // indices for time and frequency domains
    float a = 1.09;  // unused: b = 2.098;
    float Xre[2000], Xim[2000]; // DFT of x (real and imaginary parts)
    float P[2000];           // power spectrum of x

    float x[N] = { 0 };

    // Generate random discrete-time signal x in range (-1,+1)
    float y[] = {
        0.0, 0.0984079408900634, 0.195860568724094, 0.291411844321996, 0.384134186227703, 0.473127475375545, 0.557527793160445, 0.636515808085535, 0.709324729572274, 0.775247751720011, 0.833644914753334, 0.883949317548447, 0.925672620929349, 0.958409788309562, 0.981843017658750, 0.995744826623968,
        0.999980260856137, 0.994508204104035, 0.979381777357810, 0.954747823167273, 0.920845480141026, 0.878003861464755, 0.826638859974879, 0.767249110802900, 0.700411150783807, 0.626773821619470, 0.547051971129342, 0.462019513734716, 0.372501917543151, 0.279368190966096, 0.183522446661037, 0.0858951246927854,
        -0.0125660398833526, -0.110905217332694, -0.208167762132862, -0.303409480369524, -0.395705795671223, -0.484160724703344, -0.567915575089941, -0.646157281326779, -0.718126297763189, -0.783123972030169, -0.840519327335832, -0.889755187787833, -0.930353587280090, -0.961920409436037, -0.984149213565316, -0.996824209492737,
        -0.999822352380809, -0.993114537209969, -0.976765881320872, -0.950935092275919, -0.915872927176609, -0.871919758393194, -0.819502269337733, -0.759129312356960, -0.691386968955206, -0.616932860301177, -0.536489763250371, -0.450838593856768, -0.360810826487642, -0.267280422134304, -0.171155344276191, -0.0733687446595907,
        0.0251300954433374, 0.123384980555854, 0.220442083438833, 0.315359204542867, 0.407214918582441, 0.495117519440145, 0.578213676566644, 0.655696718842807, 0.726814465486903, 0.790876527986881, 0.847261012172933, 0.895420555368697, 0.934887640014398, 0.965279132178928, 0.986300000902440, 0.997746182263274,
        0.999506560365732, 0.991564046017929, 0.973995742628244, 0.946972197709905, 0.910755747259856, 0.865697969084168, 0.812236269792286, 0.750889638592492, 0.682253609109396, 0.606994478132532, 0.525842837418596, 0.439586481338564, 0.349062759219976, 0.255150446625443, 0.158761214478388, 0.0608307788510959,
        -0.0376901826699336, -0.135845259860259, -0.232681594384382, -0.327259129842054, -0.418659737537428, -0.505996129381040, -0.588420471400950, -0.665132614245854, -0.735387860781017, -0.798504195371694, -0.853868904674451, -0.900944525663825, -0.939274063152787, -0.968485426156976, -0.988295040035869, -0.998510599345391,
        -0.999032934678125, -0.989856975368447, -0.971071798716938, -0.942859765256222, -0.905494748452794, -0.859339476030335, -0.804842008724098, -0.742531390649502, -0.673012513509774, -0.596960244499286, -0.515112874907027, -0.428264953019107, -0.337259570896168, -0.242980179903264, -0.146342014444403, -0.0482832071574495,
        0.0502443181797695, 0.148284087623366, 0.244884362208849, 0.339107377130930, 0.430038445266602, 0.516794836667414, 0.598534347821637, 0.674463477498649, 0.743845129807025, 0.806005769687504, 0.860341961377560, 0.906326226374270, 0.943512164028194, 0.971538785059195, 0.990134015925798, 0.999117340028769,
        0.998401550108975, 0.987993594827769, 0.967994511311594, 0.938598444315629, 0.900090761528124, 0.852845283311457, 0.797320653772707, 0.734055888392230, 0.663665141432458, 0.586831743923250, 0.504301570101134, 0.416875796698963, 0.325403125376477, 0.230771543793960, 0.133899705309884, 0.0357280109856745,
        -0.0627905195293142, -0.160699499610071, -0.257048459953733, -0.350902075433899, -0.441349244940104, -0.527511936058200, -0.608553708730373, -0.683687835149718, -0.752184937064112, -0.813380066348762, -0.866679160111565, -0.911564807667102, -0.947601273395360, -0.974438726724819, -0.991816638176614, -0.999566308502021,
        -0.997612506361225, -0.985974198645282, -0.964764366351565, -0.934188907800099, -0.894544639838025, -0.846216416435848, -0.789673392647252, -0.725464470200735, -0.654212968935859, -0.576610575812079, -0.493410630231271, -0.405420810857945, -0.313495294931096, -0.218526466182705, -0.121436251859683, -0.0231671729467908,
        0.0753268055279309, 0.173089535282900, 0.269171966766988, 0.362641362231371, 0.452590350451546, 0.538145735199171, 0.618476971953920, 0.692804230566056, 0.760405965600031, 0.820625920868545, 0.872879500159325, 0.916659442309612, 0.951540745536515, 0.977184793219440, 0.993342641082758, 0.999857433867821,
        0.996665928034030, 0.983799105707054, 0.961381873914185, 0.929631852026567, 0.888857259179404, 0.839453922178432, 0.781901432938911, 0.716758492759546, 0.644657488627590, 0.566298354206707, 0.482441775103100, 0.393901804371106, 0.301537959944494, 0.206246880709201, 0.108953622217581, 0.0106026765427436,
        -0.0878511965507475, -0.185452238111593, -0.281252968206354, -0.374323383753877, -0.463759986700061, -0.548694554890174, -0.628302570493986, -0.701811224163148, -0.768506917219076, -0.827742189042424, -0.878942002415270, -0.921609325799925, -0.955329958363339, -0.979776550907327, -0.994711783670682, -0.999990670154097,
        -0.995561964603080, -0.981468659485473, -0.957847568134224, -0.924927996606965, -0.883029517655600, -0.832558868415444, -0.774006001930223, -0.707939330843420, -0.635000209428760, -0.555896707526464, -0.471396736825997, -0.382320596223098, -0.289533008618479, -0.193934726462339, -0.0964537875354998, 0.00196349414684702,
        0.100361714851215, 0.197785655882052, 0.293289556541649, 0.385946295274789, 0.474856389870597, 0.559156729350287, 0.638028952774654, 0.710707393632289, 0.776486512687080, 0.834727747129162, 0.884865709540016, 0.926413676494061, 0.958968313515203, 0.982213590519895, 0.995923849736900, 0.999965996321297,
        0.994300790396999, 0.978983227985015, 0.954162007119530, 0.920078084334595, 0.877062335534554, 0.825532343955807, 0.765988346401266, 0.699008377100263, 0.625242656335702, 0.545407278311946, 0.460277259539545, 0.370679015220949, 0.277482336674029, 0.181591947674010, 0.0839387216822394, -0.0145293547779467,
        -0.112856384873481, -0.210087841004649, -0.305279831056042, -0.397508261401654, -0.485877807712459, -0.569530606480889, -0.647654582887413, -0.719491334165196, -0.784343491933411, -0.841581492028159, -0.890649686111535, -0.931071735729352, -0.962455236453648, -0.984495527220340, -0.996978647882129, -0.999783416265704,
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    };
    float freq;
    float ind;
    float val = 0;
    float maxV = 0;

    int XN = sizeof(y) / sizeof(*y);

    for (k = 0; k < XN; k++) {
        x[k] = y[k];
    }

    struct timespec sT, eT;
    clock_gettime(CLOCK_MONOTONIC, &sT);

    printf("Starting DFT\n");
    // Calculate DFT of x using brute force
    for (k = 0; k < 2000; ++k) {
        // Real part of X[k]
        Xre[k] = 0;
        for (n = 0; n < XN; ++n)
            Xre[k] += x[n] * cos(n * k * PI2 / N);

        // Imaginary part of X[k]
        Xim[k] = 0;
        for (n = 0; n < XN; ++n)
            Xim[k] -= x[n] * sin(n * k * PI2 / N);

        // Power at kth frequency bin
        P[k] = Xre[k] * Xre[k] + Xim[k] * Xim[k];

        //  printf("\n%+f %+f %f",Xre[k],Xim[k],P[k]);
    }
    printf("DFT over\n");

    ind = 0;

#if 1
    printf("Freq Compute start\n");

    for (k = 0; k < 2000; k++) { 
        //val = (Xre[k] * Xre[k]) + (Xim[k] * Xim[k]);
        val = P[k];

        if (val > maxV) {
            //printf("%f\n", val);
            maxV = val;
            ind = k;
            a = val;
        }
    }
    printf("Freq Compute over\n");

#endif

    freq = ind * 0.195;

    printf("maxV=%f ind = %f Freq= %f\n", maxV, ind, freq);

    clock_gettime(CLOCK_MONOTONIC, &eT);

    printf("%ld.%09ld  %ld uSec\n",
           eT.tv_sec, eT.tv_nsec,
           ((eT.tv_sec - sT.tv_sec) * 1000000 + (eT.tv_nsec - sT.tv_nsec) / 1000));

    return 0;
}

Can there be anything more aggressive then -O3 optimization? And it means basically it leaves out computation and hence it slows down when the value is being used. — rathin2j, Jun 18 '17 at 22:49
`-O3` is the most aggressive setting. You could try some extra optimization settings, check the compiler documentation. Yet one cannot say the *it slows down when the value is used*: the compiler generates more code when the value is used because the code to compute the value must be run. The program behaves differently when the block is commented and is much faster because most of the code is not even generated as the results are computed trivially. — chqrlie, Jun 18 '17 at 22:53
@chqrlie- Ok sure. Thank you for such detailed explanation. *Grateful* — rathin2j, Jun 18 '17 at 23:02
@chqrlie- yes, 'y' is to simulate the discreet data samples from ADC. And 'x' is my DFT Window, so initialized just till 960 (equivalent to data sample length), and thrn intentionally to zero padding is created. The remaining part is set to zero by 'x[]={0}'. So I believe it's not having junk values. — rathin2j, Jun 18 '17 at 23:08
@rathin2j: OK, my bad, `x` is correctly initialized, yet you should use `k < sizeof(y) / sizeof(*y)` to avoid hard-coding the sizeof the `float` type. There is still a 20x improvement to get from reducing the computations. — chqrlie, Jun 18 '17 at 23:24
woah! 20x improvement is unfathomable for me but yes, I can think of only one other optimization 1) using look up tables for sin and cos. And I deeply honored for your time — rathin2j, Jun 19 '17 at 06:38
@rathin2j: although the question is on hold (which I disapprove of), you can still accept this answer. — chqrlie, Jun 19 '17 at 06:44
Well said, DONE! And I will also update the question within 2 hours, with more 'rule abiding' syntax and structure, so hoping for the best :) — rathin2j, Jun 19 '17 at 07:49

Strange C program Latency behaviour

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