[/ Copyright 2011 - 2020 John Maddock. Copyright 2013 - 2019 Paul A. Bristow. Copyright 2013 Christopher Kormanyos. Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt). ] [section:rational_real_world Rational Real World Tests] The first set of [@../../performance/rational_bernoulli_bench.cpp tests] measure the times taken to calculate the n'th Bernoulli number via mixed rational/integer arithmetic to give an exact rational result. [table Relative times taken to calculate Bm [[m][cpp_rational (time in seconds)][mpq_rational (time relative to cpp_rational)][mpq_class (time relative to cpp_rational)]] [[50][1.888453][1.7317576874][1.893438174]] [[54][2.250503][2.1519411438][2.4936252029]] [[58][2.734527][2.2056805437][1.9866752093]] [[62][3.318122][2.5182796172][2.2662876772]] [[66][3.887281][2.4263077457][2.588347485]] [[70][4.628535][1.9756346231][2.5367158291]] [[74][5.3541][1.7052929531][2.3345854579]] [[78][6.321172][1.6669601776][2.0390342171]] [[82][7.13052][1.7689101216][1.9837833706]] [[86][8.390095][1.6245518078][1.5785492298]] [[90][10.62176][1.6294440846][1.5779053566]] [[94][11.364409][1.5786845581][1.5614997665]] [[98][14.030636][1.2616490799][1.4799734666]] [[102][15.268211][1.6145657798][1.6128342738]] [[106][15.253028][1.8985381788][1.8206293859]] [[110][17.637756][1.8283953469][1.6559522084]] [[114][18.335007][1.8018346543][1.8343225612]] [[118][21.044146][2.0462015897][1.8106934346]] [[122][23.71295][2.0041556196][1.7127701108]] [[126][25.993901][1.9901613075][1.6974264848]] [[130][30.17278][1.8897211328][1.6405006433]] [[134][43.992333][1.2223514038][1.2232961594]] [[138][40.702777][1.3551305848][1.492072224]] [[142][47.01495][1.4361410785][1.4005683724]] [[146][51.468592][1.4279172043][1.4072223891]] [[150][70.736106][1.3628087048][1.2309294917]] [[154][74.638691][1.2509392749][1.2846060497]] [[158][76.642396][1.3383691449][1.2555573941]] [[162][104.906795][1.1722665057][1.0121124375]] [[166][108.175914][0.9272805682][1.2472813403]] [[170][125.363885][0.8114005082][1.1349673712]] [[174][119.813754][0.9747547014][1.5677900135]] [[178][130.672631][0.904429444][1.6089208382]] [[182][136.002124][0.8359445107][1.3173987636]] [[186][152.169271][0.7919228515][1.3523570012]] [[190][149.444035][0.8353259734][1.4571606823]] [[194][149.609183][0.8898088896][1.6132629038]] [[198][167.594528][0.8947434429][1.326461858]] ] In this use case, most the of the rational numbers are fairly small and so the times taken are dominated by the number of allocations performed. The following table illustrates how well each type performs on suppressing allocations: [table Total Allocation Counts for Bernoulli Number Calculation [[m][cpp_rational][mpq_rational][mpq_class]] [[2][0][77][101]] [[4][0][187][252]] [[6][0][345][471]] [[8][0][551][758]] [[10][0][805][1113]] [[12][0][1107][1536]] [[14][0][1457][2027]] [[16][0][1857][2587]] [[18][0][2336][3216]] [[20][0][2885][3913]] [[22][6][3511][4706]] [[24][22][4203][5600]] [[26][83][4963][6575]] [[28][377][5806][7632]] [[30][780][6738][8769]] [[32][1454][7771][9988]] [[34][2001][9357][11289]] [[36][2789][10598][12704]] [[38][3669][11948][14252]] [[40][4653][13403][15891]] [[42][5923][14976][17620]] [[44][7379][16622][19449]] [[46][8839][18367][21367]] [[48][10296][20227][23431]] [[50][12045][22857][25646]] [[52][13603][25044][27962]] [[54][15276][27331][30389]] [[56][17239][29749][32919]] [[58][19337][32257][35552]] [[60][21409][34958][38417]] [[62][23694][37800][41396]] [[64][27923][39556][44498]] [[66][30240][44706][47711]] [[68][32566][47934][51042]] [[70][35019][51417][54637]] [[72][37460][55047][58363]] [[74][40282][58777][62211]] [[76][42914][62691][66183]] [[78][45752][66694][70296]] [[80][48681][70905][74620]] [[82][51986][77633][79160]] [[84][54855][82364][83842]] [[86][59032][87239][88659]] [[88][63595][92256][93618]] [[90][68352][97486][98820]] [[92][72446][102974][104256]] [[94][76468][108620][109844]] [[96][80361][111109][115594]] [[98][84783][121460][121486]] [[100][89044][127730][127633]] [[102][93561][134241][134050]] [[104][98452][140919][140616]] [[106][103530][147763][147364]] [[108][108326][154804][154276]] [[110][113891][162184][161562]] [[112][119213][169736][169038]] [[114][124770][182417][176693]] [[116][130624][190589][184519]] [[118][137941][198975][192525]] [[120][144829][207759][200952]] [[122][152045][216736][209561]] [[124][158610][225905][218371]] [[126][165383][235283][227360]] [[128][173971][230678][236670]] [[130][181696][248593][246308]] [[132][189310][258615][256148]] [[134][197708][268800][266192]] [[136][205800][279215][276436]] [[138][212940][290112][287167]] [[140][217502][301235][298101]] [[142][223486][312564][309243]] [[144][229579][324133][320605]] [[146][237213][344671][332333]] [[148][248799][357200][344420]] [[150][261345][369947][356745]] [[152][272741][382909][369279]] [[154][283982][396162][382048]] [[156][293626][409993][395353]] [[158][304036][424022][408907]] [[160][313869][427747][422690]] [[162][323626][454723][436715]] [[164][333294][469863][451304]] [[166][343072][485238][466149]] [[168][352236][500922][481221]] [[170][362793][516840][496561]] [[172][372645][533169][512315]] [[174][382908][549962][528510]] [[176][392507][567018][544947]] [[178][404163][597694][561666]] [[180][417539][615615][578647]] [[182][432009][634079][596234]] [[184][444684][652902][614114]] [[186][457104][672042][632248]] [[188][469331][691451][650654]] [[190][481583][711512][669753]] [[192][477225][698188][689111]] [[194][488955][736905][708760]] [[196][499797][757502][728675]] [[198][511163][778591][749102]] ] The second [@../../performance/rational_determinant_bench.cpp example] measures the time taken to calculate the determinant of a 3x3 matrix of rational numbers. These numbers are randomly generated with /n/ bits in both numerator and denominator. In this case the rate limiting step is the cost of calculating the GCD's during the computation: [table Relative Time Taken to Calculate 100 Determinants of Random 3x3 Matrixes [[Bits][cpp_rational (ms)][mpq_rational (relative to cpp_rational)][mpq_class (relative to cpp_rational)]] [[512][45][0.3111111111][0.3177777778]] [[1024][103][0.3038834951][0.3038834951]] [[2048][251][0.3087649402][0.3011952191]] [[4096][667][0.2983508246][0.2893553223]] [[8192][2033][0.261682243][0.2956222332]] [[16384][6423][0.2358710883][0.3059318076]] [[32768][24223][0.1875903067][0.1955992239]] ] [table:platform Platform Details [[][Version]] [[Compiler][GNU C++ version 10.3.0]] [[GMP][6.2.0]] [[MPFR][262146]] [[Boost][107800]] [[Run date][Sep 30 2021]] ] [endsect]