R comes with built-in parallel random number generation facilities. It’s quite easy to do PRNG correctly with only a default installation of R. Without getting into the details, which are far outside the scope of this documentation, the goal is to use an appropriate random number generator and an appropriate seed such that you get a new stream that can be treated as independent of other streams.
The function prngInit does all the setup for you, so that you can generate draws from distributions on multiple processors simultaneously. All you need to do is pass it the number of the stream:
prngInit(1) // Generate from the first stream
prngInit(2) // Generate from the second stream
.
.
.After that call, you can generate draws using runif, rnorm, etc. as always. If you call prngInit with the same stream number, you’ll always generate the same random draws. Note that prngInit takes an optional second argument that sets the seed. There is typically no value in setting that to anything other than the default, but it doesn’t harm anything to do so, so it’s an option if you want it.
The above has described all you need to know. I’ll provide you here with a few details on R in case they’re of interest.
You can get the current seed from the variable .Random.seed. What that returns will depend on the generator in use. The function set.seed can be used to convert a single integer value into a seed appropriate for the generator in use. It’s easy to see this if we play with some code. Start R (which is important to replicate these results) and check the current RNG state.
.Random.seedThat returns
Error: object '.Random.seed' not foundOkay, the RNG state has not yet been set. You need to either generate random numbers or set the seed before it’s initialized. Let’s set the seed to whatever state corresponds with the integer 2745:
set.seed(2745)Now check the current value of the RNG state:
[1] 10403 624 -2010919067 -1516620574 -1509043461 2143531520
[7] -239105535 -630943794 -1918722569 1261767116 -188468131 740534138
[13] -813150541 1792613464 -1297864071 -1911085082 494379311 1294628260
[19] 1755154517 1315405074 -2025123477 946495920 -170513935 -426650882
[25] -579151001 1944906876 -919098547 -1600907862 827915043 69526024
[31] 319514729 1020850454 -1358091105 91213396 -698974907 -2065444542
[37] -850334757 1906441568 905299425 1992090158 -1897171753 -598574292
[43] 427417149 1964838874 1374536595 1910969272 96674393 -1470495162
[49] 1756271631 1163940612 -983716299 2081567090 2022072907 -1192917744
[55] 1016946129 -442974882 1514891847 -1928284708 -2055615187 -551447030
[61] -124934141 -486887064 791304265 1135437686 1737676671 1023869876
[67] 1031936805 -139092574 856847547 1248852160 1141633473 177759374
[73] -1649296457 160603276 -1192855523 1019521082 1312794739 -1929725160
[79] 1533020729 379983014 -1498351889 1865343076 1246938133 2085688786
[85] -1059314901 -1053009808 641761713 1777260478 -856331993 208700
[91] 1529798413 1156138602 1305134307 1547841736 1849899049 -304673322
[97] 1858073183 1633872148 -350312187 2133301762 1871343003 -955931616
[103] 1291455905 1687099118 -508726633 -112366100 -8257027 926052506
[109] 867564883 -1544809864 1400037913 -1970056442 -969487921 1273896388
[115] 49596917 -1774441934 -2038148085 -1001989168 -1581804143 1747722782
[121] -885991417 152852636 349102317 201533130 -297250365 -841785304
[127] -296876023 -756161482 -515080897 -908362124 1218717413 -1471035806
[133] -1225730437 -1875181696 2109217153 523827534 -560555657 2111500108
[139] -708543523 -1535219462 -1920417229 177412568 166963705 28950886
[145] -1846014801 -1997141212 918274005 485191314 -1950944021 551358256
[151] -1711629967 -1595368322 1186313959 -1867238916 953275085 -91801814
[157] -1287762269 25575304 1229113321 -695604586 -1208977377 -104283180
[163] -74804027 206316226 -646074533 988285664 -12708511 -1590817874
[169] 1948594263 361963692 -534387267 1354797402 49280787 -2134388424
[175] 383410649 -978231354 -1330856049 -6379388 1763681717 1870062322
[181] 783025611 567734928 -167670447 -1598273826 -1925446201 723696476
[187] 162509997 1653438346 -1847280765 758304488 -1793493047 675487990
[193] -949755137 -1602045644 -448138587 1345236770 1130952763 1206175296
[199] -159121087 486952462 -569297097 -355597812 2132688797 -1810830918
[205] 1461951475 845297816 -1910568519 1813130790 -1525882257 -1254099484
[211] 1503165333 -118061230 1771800235 -32733712 -1731956431 -1069604546
[217] 1216070823 415233212 -2048883059 573433834 -1686923165 -223277496
[223] 1674188713 1135707990 -1067532833 -1721672044 593117317 621898626
[229] -51728101 604582304 -2071864031 -1856389010 -1273844201 -740060308
[235] -819623555 1384608282 1767616723 -1220915208 -4611687 -697029498
[241] -841976497 -617483452 60703093 813849522 -759335029 -665466544
[247] 1631274257 604580766 2116875143 1172561436 1742489709 -1551857590
[253] -48044733 1608056232 -1018386551 -261284426 798558399 -339954700
[259] 255032933 1208768482 -1438983685 674057472 -969955071 -926915890
[265] -371092233 1395381452 -1464614051 -63165830 886060467 321394520
[271] 2007116153 846158566 1705998383 -825450332 -1633093803 -1724751854
[277] -1672882069 -1081426768 710805745 -1129159170 -1878551961 1256617852
[283] 639302221 -593667926 2794019 -293430008 1033447273 1108206614
[289] 2110440351 -890455724 1045277765 -2110294974 -1953402149 -1725360032
[295] -729455391 1506948398 -818549801 -1761688020 -1606357699 -1924721958
[301] -793171309 -1241280840 2110824793 -107235002 -2090734833 426245636
[307] -1640981195 -1038183310 -1804031669 -1367121904 -886784815 1188221022
[313] 1002676551 1814020316 -216753107 1335646474 163761923 -2071597976
[319] -660105399 -1741956490 -273944961 -1773572428 -2111780315 -1465204574
[325] 2099674043 -1479240768 -998567743 -1490602098 264745655 2041866124
[331] 105187101 -1916785862 1884196723 2074392088 373098809 -242137178
[337] 429903343 1885080420 -1314049259 1180629202 629271083 -1944603792
[343] 377970865 1258449598 -1692852185 -1712866756 -1119801843 177572202
[349] -1692177437 1941629896 376436521 -1637941034 -1510700705 -651504620
[355] -400238587 -1669448446 -147721061 1896333088 -1492603743 -547919378
[361] -1286674025 -2119911188 -415756035 297759642 1657300051 -1411150472
[367] -1059102439 736626182 -148823857 -1258239804 -996755211 -854880974
[373] 1436392203 723498704 -612502383 500774174 599789319 1888904092
[379] 790147053 -1482626614 1367636163 2046401320 -185972983 1279219510
[385] -1654877121 1256778100 -1177430555 1254746466 233561467 -40199552
[391] -1993983871 -50672562 495161463 -517490100 194120413 -1185092614
[397] 324970803 -90696488 2041555193 104330342 -962731089 -189909468
[403] -26923307 154947986 -956056597 1249077808 -452953999 -537972866
[409] -1485804057 948157692 -1357700659 1289124394 -434244189 -1055262072
[415] -301037847 -446374506 -1365504225 -824463660 2090845125 -1398422078
[421] 1905014363 1113925088 1942729825 -961978706 236824407 1989503916
[427] -137694019 -1330604966 155803155 -2019931080 -1197088551 706286278
[433] 248387215 1757172612 -1030712139 -1173797390 -1209250613 -1796551280
[439] -100209583 2111592926 1407335623 -435698084 1604879277 -1404159350
[445] 774365827 -554432024 -137054519 -110652426 -1905591809 1952130100
[451] -234446427 -953560542 1850408763 541024576 1810964545 -822402802
[457] -1596641737 -867840756 -329593187 -1345164102 -406813965 -557698152
[463] 1908017337 -1927061210 845789551 1988305124 -1332680043 -1433769390
[469] 42945963 -1587683088 -578203599 -1338461122 -1295156313 427458492
[475] 525391245 69217002 450510691 -715142840 -2076911959 1675590230
[481] -847162145 1992247700 394162053 -1418850686 -329238501 1677806752
[487] 1921940513 1955074926 1298277655 412147308 -440821635 -86346470
[493] 1845237715 -135804168 350494873 1894702982 1881721935 -1353015740
[499] -1545719691 -1311261006 488947339 -224091056 1316987921 -73646434
[505] -1444271481 523495708 -2004609171 509889354 -1184035773 305477800
[511] -2128157047 1281659062 -661184577 1029709556 645868901 1988786914
[517] 1879302395 -964499456 -2070165503 -504875570 -411268105 1036951500
[523] -1671474595 1642114426 1999903923 920851032 -1910757255 1662225894
[529] -490516689 -795161692 -1276090795 -1291238638 434413419 -141092944
[535] 132245489 -1331758850 2062567783 -276036996 -239449779 1362271146
[541] 857229603 1867274248 1487070825 646895382 -127640929 1536533588
[547] -1803494587 1368856386 426637787 -325307552 -1693383711 229869614
[553] -1629723945 -900263636 -2067530691 1090328026 -90140269 1804339640
[559] 1163534425 1026124870 -2131672561 -1013208828 876579893 -1657342094
[565] -1492717493 185416464 -1062724655 -338107554 -1013458873 786090972
[571] 1835756333 2124618762 -854329853 847062888 -257894839 -1309258378
[577] 1369507199 -1866999372 318470437 1907090338 -1529445701 1730490048
[583] -1427755071 -1165882738 -12998217 -125685108 -815819235 -2142785990
[589] 192509555 -776294120 513148985 617118374 493528303 -1649068444
[595] -1270636011 1803082706 247705899 1943998064 734674865 -1780351554
[601] 2107168551 762856764 -904954611 349031530 -392686877 228566728
[607] -1424443863 -97324074 -452648865 -937509100 -1889073403 400613378
[613] 1786084251 -1292510688 -1525462111 1995160814 -263429993 -1364720660
[619] 1755979773 -1814530406 -654914733 289867896 2043142169 -1953974010
[625] 1726445519 -1606454332Wow. The state of the default RNG is represented as 626 integers. If you wanted, you could save the current 626 integer state, generate some random draws, reset the state to those 626 integers, and then draw the same numbers.
To save the state:
rngstate <- .Random.seedGenerate some draws:
runif(5)That returns
[1] 0.39984780 0.04520027 0.40373013 0.02144889 0.02943068Now take some more draws:
runif(5)and you’ll get different values. Let’s reset the state:
.Random.seed <- rngstateAnd generating numbers as before:
runif(5)we get the same vector:
[1] 0.39984780 0.04520027 0.40373013 0.02144889 0.02943068However, we know that set.seed(2745) corresponds to that RNG state:
set.seed(2745)
runif(5)And we verify that we get the same draws:
[1] 0.39984780 0.04520027 0.40373013 0.02144889 0.02943068So that’s really all there is to it. The difficult thing when working on multiple processors is to set the RNG state appropriately to deliver independent streams. You could do set.seed(101) on the first processor, set.seed(102) on the second, and so on, but the draws would almost certainly be correlated, which would invalidate the simulation.
The magic of the function nextRNGStream is that given the current RNG state, it provides you with a new RNG state that is sufficiently far away that you can take random draws that are independent of the other streams. Thus, with appropriate calls to nextRNGStream, we can set the RNG state in ways that lets us take valid draws on multiple processors simultaneously. It is possibly surprising that the L’Ecuyer generator state is summarized with only six integers. If you want, you can save those six integers and restart the draws from that point in the current stream anywhere else in your program.