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* Update Jamfile.v2 * Update introduction.qbk * Update tutorial.qbk * Update tutorial_cpp_int.qbk * Update tutorial_gmp_int.qbk * Update tutorial_tommath.qbk * Update integer_examples.cpp * Update tutorial_cpp_bin_float.qbk * Update tutorial_cpp_dec_float.qbk * Update tutorial_gmp_float.qbk * Update tutorial_mpfr_float.qbk * Update tutorial_float128.qbk * Update tutorial_float_builtin_ctor.qbk * Update big_seventh.cpp * Update tutorial_float_eg.qbk * Update floating_point_examples.cpp * Update mpfr_precision.cpp * Update gauss_laguerre_quadrature.cpp * Update tutorial_interval_mpfi.qbk * Update tutorial_cpp_complex.qbk * Update tutorial_mpc_complex.qbk * Update tutorial_float128_complex.qbk * Update tutorial_complex_adaptor.qbk * Update tutorial_rational.qbk * Update tutorial_tommath_rational.qbk * Update tutorial_logged_adaptor.qbk * Update tutorial_debug_adaptor.qbk * Update tutorial_visualizers.qbk * Update tutorial_fwd.qbk * Update tutorial_conversions.qbk * Update tutorial_random.qbk * Update random_snips.cpp * Update tutorial_constexpr.qbk * Update tutorial_import_export.qbk * Update cpp_int_import_export.cpp * Update tutorial_mixed_precision.qbk * Update tutorial_variable_precision.qbk * Update scoped_precision_example.cpp * Update tutorial_numeric_limits.qbk * Update tutorial_numeric_limits.qbk * Update numeric_limits_snips.cpp * Update numeric_limits_snips.cpp * Update tutorial_numeric_limits.qbk * Update numeric_limits_snips.cpp * Update numeric_limits_snips.cpp * Update tutorial_io.qbk * Update reference_number.qbk * Update reference_cpp_bin_float.qbk * Update reference_cpp_double_fp_backend.qbk * Update reference_internal_support.qbk * Update reference_backend_requirements.qbk * Update performance.qbk * Update performance_overhead.qbk * Update performance_real_world.qbk * Update performance_integer_real_world.qbk * Update performance_rational_real_world.qbk * Update reference_number.qbk * Update tutorial_numeric_limits.qbk * Update reference_backend_requirements.qbk
191 lines
6.5 KiB
Plaintext
191 lines
6.5 KiB
Plaintext
[/
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Copyright 2011 - 2020 John Maddock.
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Copyright 2013 - 2019 Paul A. Bristow.
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Copyright 2013 Christopher Kormanyos.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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[section:rational_real_world Rational Real World Tests]
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The first set of [@../../performance/rational_bernoulli_bench.cpp tests] measure the times taken to
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calculate the n'th Bernoulli number via mixed rational/integer arithmetic to give an exact rational result.
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[table Relative times taken to calculate Bm
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[[m][cpp_rational (time in seconds)][mpq_rational (time relative to cpp_rational)][mpq_class (time relative to cpp_rational)]]
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[[50][1.888453][1.7317576874][1.893438174]]
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[[54][2.250503][2.1519411438][2.4936252029]]
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[[58][2.734527][2.2056805437][1.9866752093]]
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[[62][3.318122][2.5182796172][2.2662876772]]
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[[66][3.887281][2.4263077457][2.588347485]]
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[[70][4.628535][1.9756346231][2.5367158291]]
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[[74][5.3541][1.7052929531][2.3345854579]]
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[[78][6.321172][1.6669601776][2.0390342171]]
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[[82][7.13052][1.7689101216][1.9837833706]]
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[[86][8.390095][1.6245518078][1.5785492298]]
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[[90][10.62176][1.6294440846][1.5779053566]]
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[[94][11.364409][1.5786845581][1.5614997665]]
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[[98][14.030636][1.2616490799][1.4799734666]]
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[[102][15.268211][1.6145657798][1.6128342738]]
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[[106][15.253028][1.8985381788][1.8206293859]]
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[[110][17.637756][1.8283953469][1.6559522084]]
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[[114][18.335007][1.8018346543][1.8343225612]]
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[[118][21.044146][2.0462015897][1.8106934346]]
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[[122][23.71295][2.0041556196][1.7127701108]]
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[[126][25.993901][1.9901613075][1.6974264848]]
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[[130][30.17278][1.8897211328][1.6405006433]]
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[[134][43.992333][1.2223514038][1.2232961594]]
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[[138][40.702777][1.3551305848][1.492072224]]
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[[142][47.01495][1.4361410785][1.4005683724]]
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[[146][51.468592][1.4279172043][1.4072223891]]
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[[150][70.736106][1.3628087048][1.2309294917]]
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[[154][74.638691][1.2509392749][1.2846060497]]
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[[158][76.642396][1.3383691449][1.2555573941]]
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[[162][104.906795][1.1722665057][1.0121124375]]
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[[166][108.175914][0.9272805682][1.2472813403]]
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[[170][125.363885][0.8114005082][1.1349673712]]
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[[174][119.813754][0.9747547014][1.5677900135]]
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[[178][130.672631][0.904429444][1.6089208382]]
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[[182][136.002124][0.8359445107][1.3173987636]]
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[[186][152.169271][0.7919228515][1.3523570012]]
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[[190][149.444035][0.8353259734][1.4571606823]]
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[[194][149.609183][0.8898088896][1.6132629038]]
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[[198][167.594528][0.8947434429][1.326461858]]
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]
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In this use case, most of the rational numbers are fairly small and so the times taken are dominated by
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the number of allocations performed. The following table illustrates how well each type performs on suppressing
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allocations:
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[table Total Allocation Counts for Bernoulli Number Calculation
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[[m][cpp_rational][mpq_rational][mpq_class]]
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[[2][0][77][101]]
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[[4][0][187][252]]
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[[6][0][345][471]]
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[[8][0][551][758]]
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[[10][0][805][1113]]
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[[12][0][1107][1536]]
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[[14][0][1457][2027]]
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[[16][0][1857][2587]]
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[[18][0][2336][3216]]
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[[20][0][2885][3913]]
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[[22][6][3511][4706]]
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[[24][22][4203][5600]]
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[[26][83][4963][6575]]
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[[28][377][5806][7632]]
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[[30][780][6738][8769]]
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[[32][1454][7771][9988]]
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[[34][2001][9357][11289]]
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[[36][2789][10598][12704]]
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[[38][3669][11948][14252]]
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[[40][4653][13403][15891]]
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[[42][5923][14976][17620]]
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[[44][7379][16622][19449]]
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[[46][8839][18367][21367]]
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[[48][10296][20227][23431]]
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[[50][12045][22857][25646]]
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[[52][13603][25044][27962]]
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[[54][15276][27331][30389]]
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[[56][17239][29749][32919]]
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[[58][19337][32257][35552]]
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[[60][21409][34958][38417]]
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[[62][23694][37800][41396]]
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[[64][27923][39556][44498]]
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[[66][30240][44706][47711]]
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[[68][32566][47934][51042]]
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[[70][35019][51417][54637]]
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[[72][37460][55047][58363]]
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[[74][40282][58777][62211]]
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[[76][42914][62691][66183]]
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[[78][45752][66694][70296]]
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[[80][48681][70905][74620]]
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[[82][51986][77633][79160]]
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[[84][54855][82364][83842]]
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[[86][59032][87239][88659]]
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[[88][63595][92256][93618]]
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[[90][68352][97486][98820]]
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[[92][72446][102974][104256]]
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[[94][76468][108620][109844]]
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[[96][80361][111109][115594]]
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[[98][84783][121460][121486]]
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[[100][89044][127730][127633]]
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[[102][93561][134241][134050]]
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[[104][98452][140919][140616]]
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[[106][103530][147763][147364]]
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[[108][108326][154804][154276]]
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[[110][113891][162184][161562]]
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[[112][119213][169736][169038]]
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[[114][124770][182417][176693]]
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[[116][130624][190589][184519]]
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[[118][137941][198975][192525]]
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[[120][144829][207759][200952]]
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[[122][152045][216736][209561]]
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[[124][158610][225905][218371]]
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[[126][165383][235283][227360]]
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[[128][173971][230678][236670]]
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[[130][181696][248593][246308]]
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[[132][189310][258615][256148]]
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[[134][197708][268800][266192]]
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[[136][205800][279215][276436]]
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[[138][212940][290112][287167]]
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[[140][217502][301235][298101]]
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[[142][223486][312564][309243]]
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[[144][229579][324133][320605]]
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[[146][237213][344671][332333]]
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[[148][248799][357200][344420]]
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[[150][261345][369947][356745]]
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[[152][272741][382909][369279]]
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[[154][283982][396162][382048]]
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[[156][293626][409993][395353]]
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[[158][304036][424022][408907]]
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[[160][313869][427747][422690]]
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[[162][323626][454723][436715]]
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[[164][333294][469863][451304]]
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[[166][343072][485238][466149]]
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[[168][352236][500922][481221]]
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[[170][362793][516840][496561]]
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[[172][372645][533169][512315]]
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[[174][382908][549962][528510]]
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[[176][392507][567018][544947]]
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[[178][404163][597694][561666]]
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[[180][417539][615615][578647]]
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[[182][432009][634079][596234]]
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[[184][444684][652902][614114]]
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[[186][457104][672042][632248]]
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[[188][469331][691451][650654]]
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[[190][481583][711512][669753]]
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[[192][477225][698188][689111]]
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[[194][488955][736905][708760]]
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[[196][499797][757502][728675]]
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[[198][511163][778591][749102]]
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]
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The second [@../../performance/rational_determinant_bench.cpp example] measures the time taken to calculate the determinant of a 3x3 matrix of rational
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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
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calculating the GCD's during the computation:
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[table Relative Time Taken to Calculate 100 Determinants of Random 3x3 Matrixes
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[[Bits][cpp_rational (ms)][mpq_rational (relative to cpp_rational)][mpq_class (relative to cpp_rational)]]
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[[512][45][0.3111111111][0.3177777778]]
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[[1024][103][0.3038834951][0.3038834951]]
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[[2048][251][0.3087649402][0.3011952191]]
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[[4096][667][0.2983508246][0.2893553223]]
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[[8192][2033][0.261682243][0.2956222332]]
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[[16384][6423][0.2358710883][0.3059318076]]
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[[32768][24223][0.1875903067][0.1955992239]]
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]
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[table:platform Platform Details
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[[][Version]]
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[[Compiler][GNU C++ version 10.3.0]]
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[[GMP][6.2.0]]
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[[MPFR][262146]]
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[[Boost][107800]]
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[[Run date][Sep 30 2021]]
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]
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[endsect]
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