std::mersenne_twister_engine に内部の処理方法をテンプレート引数に追加したものを作ってみました。

std::mt19937 と std::mt19937_64 に対応する型を namespace RngMTE に定義してあります。

std::mt19937	std::mt19937_64
RngMT19937SeqB32	RngMT19937SeqB64
RngMT19937SeqC32	RngMT19937SeqC64
RngMT19937SeqBP32	RngMT19937SeqBP64
RngMT19937SeqCP32	RngMT19937SeqCP64
RngMT19937SeqSB32	RngMT19937SeqSB64
RngMT19937SeqSC32	RngMT19937SeqSC64
RngMT19937BlkB32	RngMT19937BlkB64
RngMT19937BlkC32	RngMT19937BlkC64
RngMT19937BlkBV32	RngMT19937BlkBV64
RngMT19937BlkCV32	RngMT19937BlkCV64
RngMT19937BlkBT32	RngMT19937BlkBT64
RngMT19937BlkCT32	RngMT19937BlkCT64
RngMT19937BlkSB32	RngMT19937BlkSB64
RngMT19937BlkSC32	RngMT19937BlkSC64
RngMT19937BlkSBV32	RngMT19937BlkSBV64
RngMT19937BlkSCV32	RngMT19937BlkSCV64
RngMT19937BlkSBT32	RngMT19937BlkSBT64
RngMT19937BlkSCT32	RngMT19937BlkSCT64

実行速度測定

32ビット版乱数生成 100,000 回(※)を 1000 回テストして最速だったものを選択した。計測は処理(※)を Intel プロセッサでは RDTSC でサイクル数を、他 CPU では clock_gettime のナノ秒を 100,000 で割っています。

テストした実行環境は以下のとおり。

CPU	OS
Core i3-13100	Ubuntu 22.04
Core i7-8700B	Ubuntu 24.04, macOS 15.4, Windows 11
Apple M4	Ubuntu 24.04
Arm Cortex A76	Raspberry Pi OS (Debian 12)

コンパイラ	最適化オプション
Clang	`-O3 -march=native`
GNU C/C++	`-O3 -march=native` Intel プロセッサでは `-mtune=intel` を追加
Microsoft C/C++	`/O2 /Ob2 /Oi /Ot /Oy- /arch:AVX2`

表は std::mt19937 → std 、RngMT19937{Type}32 → {Type} と省略しています。

CPU: Core i3-13100

コンパイラ: Clang

Version	11.1	12.0	13.0	14.0	15.0
`std`	`5.331`	`5.350`	`5.313`	`5.304`	`5.323`
`SeqB`	`5.523`	`5.508`	`5.475`	`5.470`	`5.434`
`SeqC`	`5.743`	`5.743`	`5.728`	`5.728`	`5.716`
`SeqBP`	`5.915`	`5.915`	`5.572`	`5.575`	`5.572`
`SeqCP`	`6.102`	`6.102`	`5.720`	`5.721`	`5.720`
`SeqSB`	`5.500`	`5.236`	`5.185`	`5.411`	`5.549`
`SeqSC`	`5.462`	`5.595`	`5.373`	`5.377`	`5.484`
`BlkB`	`5.308`	`5.256`	`5.008`	`5.008`	`4.926`
`BlkC`	`5.255`	`5.382`	`5.010`	`5.010`	`4.928`
`BlkBV`	`6.087`	`6.099`	`5.544`	`5.561`	`4.305`
`BlkCV`	`6.086`	`6.102`	`5.552`	`5.544`	`4.258`
`BlkBT`	`5.133`	`5.110`	`5.130`	`5.050`	`4.546`
`BlkCT`	`5.115`	`5.155`	`5.112`	`5.103`	`4.531`
`BlkSB`	`5.446`	`5.581`	`5.125`	`5.144`	`4.768`
`BlkSC`	`5.436`	`5.548`	`5.129`	`5.125`	`4.779`
`BlkSBV`	`5.482`	`5.547`	`5.335`	`5.351`	`4.950`
`BlkSCV`	`5.450`	`5.570`	`5.375`	`5.333`	`4.964`
`BlkSBT`	`5.088`	`5.002`	`5.062`	`4.996`	`5.024`
`BlkSCT`	`5.051`	`5.000`	`5.079`	`5.055`	`4.993`

コンパイラ: GNU C/C++

Version	9.5	10.5	11.4	12.3
`std`	`5.077`	`5.203`	`5.191`	`5.053`
`SeqB`	`6.330`	`5.569`	`5.576`	`5.533`
`SeqC`	`6.125`	`5.744`	`6.122`	`6.118`
`SeqBP`	`6.915`	`6.361`	`6.592`	`6.565`
`SeqCP`	`6.880`	`6.522`	`6.883`	`6.879`
`SeqSB`	`7.863`	`6.033`	`6.026`	`7.451`
`SeqSC`	`8.010`	`5.626`	`5.495`	`7.564`
`BlkB`	`5.720`	`5.809`	`6.169`	`6.131`
`BlkC`	`5.792`	`5.792`	`6.165`	`6.140`
`BlkBV`	`3.262`	`3.260`	`3.504`	`3.536`
`BlkCV`	`3.258`	`3.314`	`3.553`	`3.543`
`BlkBT`	`2.906`	`2.941`	`3.200`	`3.416`
`BlkCT`	`2.943`	`2.893`	`3.200`	`3.311`
`BlkSB`	`5.187`	`5.411`	`5.421`	`5.854`
`BlkSC`	`5.167`	`5.400`	`5.425`	`5.852`
`BlkSBV`	`5.075`	`5.258`	`5.309`	`5.280`
`BlkSCV`	`5.059`	`5.295`	`5.201`	`5.356`
`BlkSBT`	`5.247`	`5.288`	`5.305`	`5.240`
`BlkSCT`	`5.282`	`5.303`	`5.291`	`5.307`

CPU: Core i7-8700B

コンパイラ: Clang

Version	17.0(※)	14.0	15.0	16.0	17.0	18.1	19.1
`std`	`14.714`	`9.301`	`9.604`	`8.593`	`9.124`	`8.795`	`8.107`
`SeqB`	`9.925`	`7.738`	`7.714`	`9.386`	`8.710`	`7.713`	`10.000`
`SeqC`	`8.934`	`8.458`	`8.462`	`8.455`	`8.394`	`8.394`	`8.397`
`SeqBP`	`10.333`	`10.197`	`10.196`	`9.454`	`8.455`	`10.159`	`10.736`
`SeqCP`	`9.680`	`8.951`	`8.969`	`8.951`	`8.951`	`8.951`	`8.950`
`SeqSB`	`8.866`	`8.934`	`8.026`	`8.691`	`8.658`	`10.562`	`10.898`
`SeqSC`	`7.461`	`8.215`	`8.961`	`8.697`	`8.962`	`11.237`	`11.259`
`BlkB`	`5.803`	`7.181`	`7.169`	`7.168`	`7.199`	`6.500`	`6.484`
`BlkC`	`5.807`	`7.161`	`7.190`	`7.307`	`7.161`	`6.454`	`6.458`
`BlkBV`	`5.496`	`7.601`	`7.455`	`6.703`	`7.447`	`6.039`	`6.043`
`BlkCV`	`5.501`	`7.588`	`8.177`	`6.714`	`5.923`	`5.355`	`6.694`
`BlkBT`	`5.845`	`8.374`	`7.371`	`7.180`	`6.685`	`6.496`	`6.504`
`BlkCT`	`5.852`	`8.293`	`7.744`	`7.202`	`6.721`	`7.225`	`5.828`
`BlkSB`	`6.134`	`7.546`	`7.624`	`7.211`	`7.612`	`7.629`	`7.328`
`BlkSC`	`6.124`	`7.651`	`7.212`	`7.215`	`7.614`	`7.632`	`7.020`
`BlkSBV`	`6.116`	`7.509`	`7.179`	`7.937`	`7.437`	`8.131`	`7.817`
`BlkSCV`	`6.121`	`7.553`	`8.682`	`7.926`	`8.610`	`7.452`	`6.849`
`BlkSBT`	`4.928`	`8.159`	`8.144`	`8.138`	`7.638`	`7.393`	`7.391`
`BlkSCT`	`4.950`	`7.752`	`8.194`	`8.141`	`7.765`	`8.126`	`8.127`

※は macOS Xcode の Apple clang version 17.0.0 (clang-1700.0.13.3)
他は Ubuntu 24.04 の apt でインストール

コンパイラ: GNU C/C++

Version	14.2(※)	9.5	10.5	11.4	12.3	13.3	14.2
`std`	`6.099`	`8.068`	`8.071`	`7.087`	`7.074`	`6.791`	`7.776`
`SeqB`	`9.662`	`9.100`	`10.468`	`10.199`	`8.210`	`10.195`	`10.202`
`SeqC`	`9.696`	`11.931`	`8.563`	`11.188`	`8.955`	`8.589`	`8.588`
`SeqBP`	`8.723`	`10.268`	`9.240`	`9.466`	`11.426`	`9.468`	`11.425`
`SeqCP`	`9.040`	`9.717`	`9.702`	`9.943`	`11.190`	`9.744`	`11.189`
`SeqSB`	`7.675`	`11.408`	`10.406`	`10.507`	`12.300`	`12.296`	`11.995`
`SeqSC`	`7.175`	`11.613`	`9.062`	`8.577`	`12.028`	`11.335`	`10.161`
`BlkB`	`8.530`	`8.198`	`8.596`	`9.298`	`8.842`	`8.894`	`8.538`
`BlkC`	`8.560`	`8.197`	`8.563`	`9.306`	`8.823`	`8.629`	`8.478`
`BlkBV`	`4.699`	`5.623`	`5.604`	`5.618`	`5.705`	`5.655`	`5.786`
`BlkCV`	`4.640`	`5.606`	`5.602`	`5.727`	`5.134`	`5.611`	`5.778`
`BlkBT`	`4.077`	`5.477`	`5.464`	`5.455`	`5.621`	`5.495`	`5.551`
`BlkCT`	`4.725`	`5.473`	`5.454`	`5.463`	`5.604`	`5.496`	`6.280`
`BlkSB`	`7.347`	`7.789`	`7.787`	`7.411`	`9.282`	`7.411`	`8.347`
`BlkSC`	`6.346`	`7.380`	`7.404`	`7.786`	`9.282`	`7.414`	`8.347`
`BlkSBV`	`5.672`	`8.051`	`7.821`	`7.761`	`7.058`	`7.184`	`8.330`
`BlkSCV`	`6.035`	`7.291`	`7.795`	`7.812`	`7.817`	`8.562`	`8.331`
`BlkSBT`	`5.554`	`6.897`	`8.288`	`8.285`	`7.558`	`7.638`	`7.344`
`BlkSCT`	`5.548`	`8.303`	`8.294`	`8.283`	`7.647`	`7.547`	`7.575`

※は macOS 上でレポジトリから clone してビルドしたもの
他は Ubuntu 24.04 の apt でインストール

コンパイラ: Microsoft C/C++

Version	19.43
`std`	`11.064`
`SeqB`	`9.424`
`SeqC`	`12.032`
`SeqBP`	`10.445`
`SeqCP`	`11.506`
`SeqSB`	`7.145`
`SeqSC`	`6.182`
`BlkB`	`10.726`
`BlkC`	`9.363`
`BlkBV`	`13.111`
`BlkCV`	`11.824`
`BlkBT`	`14.377`
`BlkCT`	`11.827`
`BlkSB`	`8.269`
`BlkSC`	`7.905`
`BlkSBV`	`8.669`
`BlkSCV`	`7.975`
`BlkSBT`	`7.851`
`BlkSCT`	`7.086`

CPU: Apple M4

コンパイラ: Clang

Version	14.0	15.0	16.0	17.0	18.1	19.1
`std`	`1.413`	`1.412`	`1.634`	`1.636`	`1.413`	`1.413`
`SeqB`	`1.126`	`1.151`	`1.231`	`1.178`	`1.160`	`1.222`
`SeqC`	`1.138`	`1.151`	`1.145`	`1.182`	`1.152`	`1.061`
`SeqBP`	`1.135`	`1.202`	`1.202`	`1.244`	`1.245`	`1.245`
`SeqCP`	`1.296`	`1.376`	`1.187`	`1.251`	`1.242`	`1.408`
`SeqSB`	`1.398`	`1.552`	`1.434`	`1.414`	`1.636`	`1.666`
`SeqSC`	`1.360`	`1.550`	`1.582`	`1.450`	`1.616`	`1.617`
`BlkB`	`1.222`	`1.192`	`1.198`	`1.216`	`1.241`	`1.290`
`BlkC`	`1.216`	`1.207`	`1.195`	`1.202`	`1.244`	`1.255`
`BlkBV`	`1.685`	`1.556`	`1.559`	`1.569`	`1.353`	`1.389`
`BlkCV`	`1.678`	`1.562`	`1.565`	`1.563`	`1.350`	`1.388`
`BlkBT`	`1.424`	`1.342`	`1.362`	`1.388`	`1.315`	`1.357`
`BlkCT`	`1.410`	`1.332`	`1.355`	`1.360`	`1.308`	`1.344`
`BlkSB`	`1.281`	`1.288`	`1.281`	`1.307`	`1.310`	`1.323`
`BlkSC`	`1.504`	`1.286`	`1.281`	`1.282`	`1.314`	`1.331`
`BlkSBV`	`1.425`	`1.432`	`1.425`	`1.425`	`1.427`	`1.467`
`BlkSCV`	`1.425`	`1.425`	`1.425`	`1.425`	`1.426`	`1.467`
`BlkSBT`	`1.440`	`1.442`	`1.434`	`1.441`	`1.442`	`1.425`
`BlkSCT`	`1.440`	`1.434`	`1.441`	`1.434`	`1.442`	`1.426`

コンパイラ: GNU C/C++

Version	9.5	10.5	11.4	12.3	13.3	14.2
`std`	`1.165`	`1.169`	`1.165`	`1.168`	`1.168`	`1.282`
`SeqB`	`1.338`	`1.183`	`1.182`	`1.182`	`1.182`	`1.182`
`SeqC`	`1.242`	`1.357`	`1.178`	`1.418`	`1.425`	`1.486`
`SeqBP`	`1.339`	`1.337`	`1.296`	`1.317`	`1.337`	`1.309`
`SeqCP`	`1.244`	`1.242`	`1.242`	`1.445`	`1.487`	`1.434`
`SeqSB`	`2.291`	`1.670`	`1.655`	`1.603`	`1.796`	`1.616`
`SeqSC`	`1.458`	`1.778`	`1.537`	`1.568`	`1.524`	`1.457`
`BlkB`	`1.262`	`1.260`	`1.214`	`1.255`	`1.312`	`1.214`
`BlkC`	`1.243`	`1.246`	`1.212`	`1.256`	`1.260`	`1.210`
`BlkBV`	`1.352`	`1.357`	`1.319`	`1.352`	`1.391`	`1.330`
`BlkCV`	`1.352`	`1.352`	`1.319`	`1.349`	`1.396`	`1.319`
`BlkBT`	`1.264`	`1.279`	`1.276`	`1.265`	`1.307`	`1.263`
`BlkCT`	`1.272`	`1.297`	`1.260`	`1.262`	`1.328`	`1.257`
`BlkSB`	`1.226`	`1.224`	`1.182`	`1.206`	`1.187`	`1.207`
`BlkSC`	`1.235`	`1.185`	`1.183`	`1.269`	`1.229`	`1.207`
`BlkSBV`	`1.378`	`1.347`	`1.317`	`1.453`	`1.390`	`1.345`
`BlkSCV`	`1.380`	`1.347`	`1.324`	`1.453`	`1.392`	`1.345`
`BlkSBT`	`1.420`	`1.405`	`1.371`	`1.415`	`1.419`	`1.423`
`BlkSCT`	`1.441`	`1.459`	`1.431`	`1.414`	`1.457`	`1.443`

CPU: Arm Cortex A76

コンパイラ: Clang

Version	13.0	14.0	15.0	16.0	19.1
`std`	`4.422`	`4.363`	`4.316`	`4.318`	`4.169`
`SeqB`	`4.992`	`5.350`	`5.104`	`4.946`	`4.608`
`SeqC`	`5.493`	`5.592`	`5.188`	`5.019`	`4.646`
`SeqBP`	`5.323`	`5.471`	`5.589`	`5.485`	`5.062`
`SeqCP`	`5.704`	`5.659`	`5.642`	`5.557`	`5.076`
`SeqSB`	`6.572`	`6.468`	`6.542`	`6.552`	`8.416`
`SeqSC`	`6.494`	`6.379`	`6.589`	`6.454`	`8.313`
`BlkB`	`4.672`	`4.636`	`4.473`	`4.473`	`4.229`
`BlkC`	`4.665`	`4.633`	`4.471`	`4.471`	`4.232`
`BlkBV`	`6.309`	`5.904`	`5.610`	`5.351`	`5.499`
`BlkCV`	`5.922`	`5.852`	`5.578`	`5.393`	`5.487`
`BlkBT`	`6.641`	`6.722`	`6.031`	`6.029`	`5.562`
`BlkCT`	`6.695`	`6.729`	`6.122`	`6.091`	`5.617`
`BlkSB`	`4.943`	`5.022`	`5.011`	`5.011`	`4.670`
`BlkSC`	`4.979`	`5.021`	`5.011`	`5.012`	`4.670`
`BlkSBV`	`6.102`	`6.109`	`6.147`	`6.146`	`6.093`
`BlkSCV`	`5.917`	`6.147`	`6.148`	`6.148`	`6.034`
`BlkSBT`	`6.147`	`6.148`	`6.084`	`6.148`	`5.860`
`BlkSCT`	`6.194`	`6.238`	`6.148`	`6.150`	`5.658`

コンパイラ: GNU C/C++

Version	11.3	12.2
`std`	`4.647`	`4.757`
`SeqB`	`4.328`	`4.328`
`SeqC`	`4.627`	`4.503`
`SeqBP`	`5.060`	`5.064`
`SeqCP`	`5.230`	`5.137`
`SeqSB`	`8.098`	`8.228`
`SeqSC`	`5.975`	`8.309`
`BlkB`	`4.227`	`4.218`
`BlkC`	`4.213`	`4.217`
`BlkBV`	`5.329`	`5.375`
`BlkCV`	`5.369`	`5.317`
`BlkBT`	`5.465`	`5.462`
`BlkCT`	`5.464`	`5.464`
`BlkSB`	`4.072`	`4.841`
`BlkSC`	`4.075`	`4.841`
`BlkSBV`	`5.313`	`6.319`
`BlkSCV`	`5.383`	`6.319`
`BlkSBT`	`6.421`	`6.500`
`BlkSCT`	`6.422`	`6.523`

メルセンヌツイスタ規模のプログラムだと、高速な生成が必要ならば目的に応じたターゲット専用コードを書いた方がいいでしょう。