diff options
| author | Raimo Niskanen <[email protected]> | 2018-05-10 01:13:03 +0200 |
|---|---|---|
| committer | Raimo Niskanen <[email protected]> | 2018-09-13 13:35:14 +0200 |
| commit | c4408318c97be75915b3dff23a933bbc4b5c2046 (patch) | |
| tree | 2c7c0b603fc37e1354793ec3fc66cc370f7767de /lib/stdlib/test | |
| parent | f709eac3a0cb6ed3e9ee1126863c46a8c6c2b6b8 (diff) | |
| download | otp-c4408318c97be75915b3dff23a933bbc4b5c2046.tar.gz otp-c4408318c97be75915b3dff23a933bbc4b5c2046.tar.bz2 otp-c4408318c97be75915b3dff23a933bbc4b5c2046.zip | |
Implement Xoroshiro928**
Diffstat (limited to 'lib/stdlib/test')
| -rw-r--r-- | lib/stdlib/test/rand_SUITE.erl | 148 | ||||
| -rw-r--r-- | lib/stdlib/test/rand_Xoroshiro928ss_dev.txt | 343 |
2 files changed, 480 insertions, 11 deletions
diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl index a7094f1987..2a721dad0d 100644 --- a/lib/stdlib/test/rand_SUITE.erl +++ b/lib/stdlib/test/rand_SUITE.erl @@ -34,12 +34,15 @@ stats_standard_normal/1, uniform_real_conv/1, plugin/1, measure/1, - reference_jump_state/1, reference_jump_procdict/1]). + reference_jump_state/1, reference_jump_procdict/1, + short_jump/1]). -export([test/0, gen/1]). -export([uniform_real_gen/1, uniform_gen/2]). +-compile(export_all). + -include_lib("common_test/include/ct.hrl"). -define(LOOP, 1000000). @@ -56,7 +59,8 @@ all() -> {group, distr_stats}, uniform_real_conv, plugin, measure, - {group, reference_jump} + {group, reference_jump}, + short_jump ]. groups() -> @@ -95,7 +99,7 @@ test() -> end, Tests). algs() -> - [exrop, exsp, exs1024s, exs64, exsplus, exs1024]. + [exrop, exsp, exs1024s, exs64, exsplus, exs1024, exro928ss]. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -267,27 +271,38 @@ reference_1(Alg) -> Refval =:= not_implemented -> Refval; true -> case gen(Alg) of - Refval -> ok; + Refval -> + io:format("Ok: ~p~n",[Alg]), + ok; Testval -> io:format("Failed: ~p~n",[Alg]), io:format("Length ~p ~p~n",[length(Refval), length(Testval)]), io:format("Head ~p ~p~n",[hd(Refval), hd(Testval)]), + show_wrong(Refval, Testval), exit(wrong_value) end end. +show_wrong([], []) -> + ok; +show_wrong([H|T1], [H|T2]) -> + show_wrong(T1, T2); +show_wrong([H1|_], [H2|_]) -> + io:format("Wrong ~p ~p~n",[H1,H2]). + + gen(Algo) -> State = - case Algo of - exs64 -> %% Printed with orig 'C' code and this seed + if + Algo =:= exs64 -> %% Printed with orig 'C' code and this seed rand:seed_s({exs64, 12345678}); - _ when Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop -> + Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop -> %% Printed with orig 'C' code and this seed rand:seed_s({Algo, [12345678|12345678]}); - _ when Algo =:= exs1024; Algo =:= exs1024s -> + Algo =:= exs1024; Algo =:= exs1024s; Algo =:= exro928ss -> %% Printed with orig 'C' code and this seed rand:seed_s({Algo, {lists:duplicate(16, 12345678), []}}); - _ -> + true -> rand:seed(Algo, {100, 200, 300}) end, Max = range(State), @@ -1173,7 +1188,7 @@ gen_jump_1(Algo) -> %% Printed with orig 'C' code and this seed gen_jump_2( rand:seed_s({Algo, [12345678|12345678]})); - _ when Algo =:= exs1024; Algo =:= exs1024s -> + _ when Algo =:= exs1024; Algo =:= exs1024s; Algo =:= exro928ss -> %% Printed with orig 'C' code and this seed gen_jump_2( rand:seed_s({Algo, {lists:duplicate(16, 12345678), []}})) @@ -1227,7 +1242,7 @@ gen_jump_p1(Algo) -> %% Printed with orig 'C' code and this seed gen_jump_p2( rand:seed({Algo, [12345678|12345678]})); - _ when Algo =:= exs1024; Algo =:= exs1024s -> + _ when Algo =:= exs1024; Algo =:= exs1024s; Algo =:= exro928ss -> %% Printed with orig 'C' code and this seed gen_jump_p2( rand:seed({Algo, {lists:duplicate(16, 12345678), []}})) @@ -1248,6 +1263,37 @@ gen_jump_p3(N, Max, Acc) when N > 0 -> gen_jump_p3(_, _, Acc) -> lists:reverse(Acc). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +short_jump(Config) when is_list(Config) -> + State_0 = {#{bits := Bits},_} = rand:seed(exro928ss, {1,2,3}), + Range = 1 bsl Bits, + %% + State_1a = repeat(1 bsl 20, Range, State_0), + State_1b = exro928_jump_2pow20(State_0), + check(17, Range, State_1a, State_1b), + %% + {_,State_2a} = rand:uniform_s(Range, State_1a), + State_3a = exro928_jump_2pow20(State_2a), + State_3b = repeat((1 bsl 20) + 1, Range, State_1b), + check(17, Range, State_3a, State_3b). + +exro928_jump_2pow20({Alg, AlgState}) -> + {Alg,rand:exro928_jump_2pow20(AlgState)}. + +repeat(0, _Range, State) -> + State; +repeat(N, Range, State) -> + {_, NewState} = rand:uniform_s(Range, State), + repeat(N - 1, Range, NewState). + +check(0, _Range, _StateA, _StateB) -> + ok; +check(N, Range, StateA, StateB) -> + {V,NewStateA} = rand:uniform_s(Range, StateA), + {V,NewStateB} = rand:uniform_s(Range, StateB), + check(N - 1, Range, NewStateA, NewStateB). + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Data reference_val(exs64) -> [16#3737ad0c703ff6c3,16#3868a78fe71adbbd,16#1f01b62b4338b605,16#50876a917437965f, @@ -1397,6 +1443,46 @@ reference_val(exrop) -> 98223942961505519,191144652663779840, 102425686803727694,89058927716079076,80721467542933080, 8462479817391645,2774921106204163]; + +reference_val(exro928ss) -> +%% Same as for exrop, but this state init: +%% for (n = 0; n < 16; n++) { +%% s[n] = 12345678; + [16#000000108e8d5b01,16#03604028f2769dff,16#007f92f60bc7170c, + 16#035ea81a9898a5e2,16#0104c90c5a0c8178,16#0313514025cca717, + 16#03c5506b2a2e98cf,16#0098a5405961552e,16#004ad29eabb785a0, + 16#033ea8ec4efb8058,16#00b21545e62bef1c,16#0333fc5320703482, + 16#02c3c650e51a8d47,16#03a3b7fc848c9cda,16#03775adea6cddff5, + 16#01ae5499c9049973,16#03d3c90e5504e16b,16#0383cd6b6cb852e6, + 16#009c8d0996ef543a,16#0059cf671371af60,16#03dfd68ed980b719, + 16#0290f2a0acf2c5b0,16#029061df18d63b55,16#02e702ea4b45137b, + 16#029a0ccca604d848,16#01664c7cd31f0fa6,16#00dced83e60ccddc, + 16#008764d2c9a05f3e,16#02b9ca5f6a80c4ba,16#02daf93d2c566750, + 16#0147d326ead18ace,16#014b452efc19297f,16#0242d3f7a7237eca, + 16#0141bb68c2abce39,16#02d798e1230baf45,16#0216bf8f25c1ec2d, + 16#003a43ea733f1e1f,16#036c75390db736f3,16#028cca5f5f48c6f9, + 16#0186e4a17174d6cf,16#02152679dfa4c25c,16#01429b9f15e3b9d6, + 16#0134a61411d22bb0,16#01593f7d970d1c94,16#0205a7d8a305490f, + 16#01dd092272595a9c,16#0028c95208aad2d4,16#016347c25cc24162, + 16#025306acfb891309,16#0207a07e2bebef2f,16#024ee78d86ff5288, + 16#030b53192db97613,16#03f765cb9e98e611,16#025ec35a1e237377, + 16#03d81fd73102ef6f,16#0242dc8fea9a68b2,16#00abb876c1d4ea1b, + 16#00871ffd2b7e45fb,16#03593ff73c9be08d,16#00b96b2b8aca3688, + 16#0174aba957b7cf7b,16#012b7a5d4cf4a5b7,16#032a5260f2123db8, + 16#00f9374d88ee0080,16#030df39bec2ad657,16#00dce0cb81d006c4, + 16#038213b806303c76,16#03940aafdbfabf84,16#0398dbb26aeba037, + 16#01eb28d61951587f,16#00fed3d2aacfeef4,16#03499587547d6e40, + 16#01b192fe6e979e3c,16#00e974bf5f0a26d0,16#012ed94f76459c83, + 16#02d76859e7a82587,16#00d1d2c7b791f51b,16#03988058017a031b, + 16#00bbcf4b59d8e86d,16#015ed8b73a1b767c,16#0277283ea6a5ee74, + 16#002211460dd6d422,16#001ad62761ee9fbd,16#037311b44518b067, + 16#02b5ed61bf70904e,16#011862a05c1929fa,16#014be68683c3bab4, + 16#025c29aa5c508b07,16#00895c6106f97378,16#026ce91a3d671c7f, + 16#02591f4c74784293,16#02f0ed2a70bc1853,16#00a2762ff614bfbc, + 16#008f4e354f0c20d4,16#038b66fb587ed430,16#00636296e188de89, + 16#0278fadd143e74f5,16#029697ccf1b3a4c2,16#011eccb273404458, + 16#03f204064a9fe0c0]; + reference_val(_) -> not_implemented. @@ -1527,6 +1613,46 @@ reference_jump_val(exrop) -> 241227318715885854,77323084015890802, 1663590009695191,234064400749487599,222983191707424780, 254956809144783896,203898972156838252]; + +reference_jump_val(exro928ss) -> +%% Same as for exrop, but this state init: +%% for (n = 0; n < 16; n++) { +%% s[n] = 12345678; + [16#031ee449e53b6689,16#001afeee12813137,16#005e2172711df36b, + 16#02850aea3a595d36,16#0029705187e891c7,16#001794badd489667, + 16#00ab621be15be56c,16#024b663a6924786b,16#03cab70b8ab854bf, + 16#01daa37601285320,16#02db955a53c40e89,16#01fbef51d5c65891, + 16#02fecf4116ed5f77,16#0349c2057246ac5d,16#01217f257c4fa148, + 16#0367ee84d020697d,16#01d5cf647fe23335,16#020941838adfb750, + 16#02c2da26b1d7b3e5,16#00d1583d34cea6c0,16#038be9cb5b527f50, + 16#00bfa93c1d7f4864,16#03778912a4f56b14,16#037fcabc483fa5c5, + 16#00a3c9de6aaf5fc7,16#03600b883b2f2b42,16#03797a99ffddfdfb, + 16#0189fead429945b7,16#0103ac90cd912508,16#03e3d872fd950d64, + 16#0214fc3e77dc2f02,16#02a084f4f0e580ca,16#035d2fe72266a7f3, + 16#02887c49ae7e41a4,16#0011dc026af83c51,16#02d28bfd32c2c517, + 16#022e4165c33ad4f3,16#01f053cf0687b052,16#035315e6e53c8918, + 16#01255312da07b572,16#0237f1da11ec9221,16#02faf2e282fb1fb1, + 16#0227423ec1787ebc,16#011fa5eb1505571c,16#0275ff9eaaa1abdd, + 16#03e2d032c3981cb4,16#0181bb32d51d3072,16#01b1d3939b9f16ec, + 16#0259f09f55d1112f,16#0396464a2767e428,16#039777c0368bdb9e, + 16#0320925f35f36c5f,16#02a35289e0af1248,16#02e80bd4bc72254b, + 16#00a8b11af1674d68,16#027735036100a69e,16#03c8c268ded7f254, + 16#03de80aa57c65217,16#00f2247754d24000,16#005582a42b467f89, + 16#0031906569729477,16#00fd523f2ca4fefe,16#00ad223113d1e336, + 16#0238ddf026cbfca9,16#028b98211cfed876,16#0354353ebcc0de9a, + 16#009ee370c1e154f4,16#033131af3b8a7f88,16#032291baa45801e3, + 16#00941fc2b45eb217,16#035d6a61fa101647,16#03fdb51f736f1bbc, + 16#0232f7b98539faa0,16#0311b35319e3a61e,16#0048356b17860eb5, + 16#01a205b2554ce71e,16#03f873ea136e29d6,16#003c67d5c3df5ffd, + 16#00cd19e7a8641648,16#0149a8c54e4ba45e,16#0329498d134d2f6a, + 16#03b69421ae65ee2b,16#01a8d20b59447429,16#006b2292571032a2, + 16#00c193b17da22ba5,16#01faa7ab62181249,16#00acd401cd596a00, + 16#005b5086c3531402,16#0259113d5d3d058d,16#00bef3f3ce4a43b2, + 16#014837a4070b893c,16#00460a26ac2eeec1,16#026219a8b8c63d7e, + 16#03c7b8ed032cf5a6,16#004da912a1fff131,16#0297de3716215741, + 16#0079fb9b4c715466,16#00a73bad4ae5a356,16#0072e606c0d4ab86, + 16#02374382d5f9bd2e]; + reference_jump_val(_) -> not_implemented. diff --git a/lib/stdlib/test/rand_Xoroshiro928ss_dev.txt b/lib/stdlib/test/rand_Xoroshiro928ss_dev.txt new file mode 100644 index 0000000000..150f37fcfa --- /dev/null +++ b/lib/stdlib/test/rand_Xoroshiro928ss_dev.txt @@ -0,0 +1,343 @@ +%CopyrightBegin% + +Copyright Ericsson AB 2015-2017. All Rights Reserved. + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. + +%CopyrightEnd% + + +Memorable facts from designing the Xoroshiro928** generator +=========================================================== +AKA: exro928ss in the rand module + +Author: Raimo Niskanen, for the Erlang/OTP team @ Ericsson. + +Reference URL: http://vigna.di.unimi.it/ftp/papers/ScrambledLinear.pdf +i.e the Xoroshiro1024 generator with ** scrambler: + + int p; + uint64_t s[16]; + + const int q = p; + const uint64_t s0 = s[p = (p + 1) & 15]; + + uint64_t s15 = s[q]; + + const uint64_t result_starstar = rotl(s0 * S, R) * T; + + s15 ^= s0; + s[q] = rotl(s0, A) ^ s15 ^ (s15 << B); + s[p] = rotl(s15, C); + +Where {S, R, T} = {5, 7, 9} as recommended in the paper. + +We want to scale down to 58 bit words (16 of them) +so we get a generator with period 2^928 - 1. + +{A, B, C} were deduced as follows +--------------------------------- + +First, to find which triplets that give a full period generator +one have to factor 2^928 - 1. + +https://www.alpertron.com.ar/ECM.HTM actually could do that +and gave the result: + + Value + 2^928 - 1 + + 2269 007733 883335 972287 082669 296112 915239 349672 942191 252221 331572 + 442536 403137 824056 312817 862695 551072 066953 619064 625508 194663 + 368599 769448 406663 254670 871573 830845 597595 897613 333042 429214 + 224697 474472 410882 236254 024057 110212 260250 671521 235807 709272 + 244389 361641 091086 035023 229622 419455 (280 digits) = 3 × 5 × 17 × 59 × + 233 × 257 × 929 × 1103 × 2089 × 5569 × 8353 × 59393 × 65537 × 3 033169 × + 39 594977 × 107 367629 × 536 903681 × 748 264961 × 2245 984577 × 239 + 686663 718401 × 15 929619 591127 520827 829953 × 82280 195167 144119 + 832390 568177 × 6033 312171 721035 031651 315652 130497 (34 digits) × 18 + 774318 450142 955120 650303 957350 521748 903233 (44 digits) × 15 694604 + 006012 505869 851221 169365 594050 637743 819041 (50 digits) + +Sebastiano Vigna from that calculated all full period triplets, at the +end of this document, and the ones with the highest degree were: + + 23-25-12 411 + 36-2-35 411 + 55-5-54 411 + 14-19-11 415 + 34-37-5 415 + 37-3-56 415 + 55-11-54 417 + 30-3-41 419 + 11-45-50 423 + 50-19-47 423 + 52-27-13 427 + 54-9-25 433 + 56-43-35 433 + 44-9-45 441 + +All these candidates were tested with TestU01-1.2.3: + + http://simul.iro.umontreal.ca/testu01/tu01.html + +A plugin was created with parameters for {A, B, C} and, since +TestU01 is a 32-bit test tool, with parameters to reverse +the generated bits or not, and to take the 32 highest or lowest +bits from the reversed or non-reversed 58 bit output. + +The generators were seeded with a SplitMix64 generator like the +one used for seeding this generator in the rand module, +taking the 58 lowest bits and wasting all zero values. + +3 runs were made with all candidates and all four bit selection variants. +For these runs the seeder was initialized with 12345678, 876543212345678 +and 1234567890. + +After all these runs the candidate with the highest degree: 44-9-45 +had not gotten any suspicious p-value at all. All the other +got p-values around 5.0e-4 worst 9.8e-6 suggesting only random +failures, so they would probably have worked about as well. + +Finally 44-9-45 was run through PractRand-0.93: + + http://pracrand.sourceforge.net/ + +Again, all 4 bit selection variants of 32 bits were run. +Random failures with p-values around e-3..e-4 for the "smaller" +tests, but for 8, 16 and 32 TB tests no anomalies were found +(with the internal seeder masked to 58 bits): + + Xoroshiro928High seed: 0x3178ec5d + Xoroshiro928Low seed: 0xa9a04fb9 + Xoroshiro928ReverseHigh seed: 0xfa0bdbab + Xoroshiro928ReverseLow seed: 0xada51705 + + +Then, S. Vigna calculated the 2^512 jump coefficient as well +as a 2^20 jump coefficient (for testing purposes) for 44-9-45. + +2^512: + { 0x44085302f77130ca, 0xba05381fdfd14902, 0x10a1de1d7d6813d2, + 0xb83fe51a1eb3be19, 0xa81b0090567fd9f0, 0x5ac26d5d20f9b49f, + 0x4ddd98ee4be41e01, 0x0657e19f00d4b358, 0xf02f778573cf0f0a, + 0xb45a3a8a3cef3cc0, 0x6e62a33cc2323831, 0xbcb3b7c4cc049c53, + 0x83f240c6007e76ce, 0xe19f5fc1a1504acd, 0x00000000b10773cb } + +2^20: + { 0xbdb966a3daf905e6, 0x644807a56270cf78, 0xda90f4a806c17e9e, + 0x4a426866bfad3c77, 0xaf699c306d8e7566, 0x8ebc73c700b8b091, + 0xc081a7bf148531fb, 0xdc4d3af15f8a4dfd, 0x90627c014098f4b6, + 0x06df2eb1feaf0fb6, 0x5bdeb1a5a90f2e6b, 0xa480c5878c3549bd, + 0xff45ef33c82f3d48, 0xa30bebc15fefcc78, 0x00000000cb3d181c } + +Standard jump function pseudocode: + + Jump constant j = 0xb10773cb...44085302f77130ca + Generator state: s + New generator state: t = 0 + foreach bit in j, low to high: + if the bit is one: + t ^= s + next s + s = t + + +The complete list of full period constants +------------------------------------------ + +29-48-54 27 x^928 + x^874 + x^870 + x^840 + x^814 + x^784 + x^759 + x^750 + x^724 + x^720 + x^634 + x^630 + x^600 + x^574 + x^544 + x^519 + x^510 + x^484 + x^480 + x^390 + x^360 + x^270 + x^240 + x^150 + x^120 + x^30 + 1 + +29-18-56 65 x^928 + x^870 + x^850 + x^840 + x^832 + x^821 + x^802 + x^791 + x^761 + x^750 + x^734 + x^731 + x^720 + x^712 + x^701 + x^686 + x^674 + x^671 + x^663 + x^641 + x^630 + x^611 + x^610 + x^603 + x^600 + x^596 + x^577 + x^566 + x^547 + x^524 + x^517 + x^510 + x^487 + x^480 + x^476 + x^464 + x^457 + x^446 + x^427 + x^423 + x^397 + x^390 + x^367 + x^363 + x^360 + x^356 + x^352 + x^341 + x^326 + x^322 + x^311 + x^281 + x^270 + x^251 + x^240 + x^236 + x^232 + x^221 + x^191 + x^161 + x^150 + x^131 + x^120 + x^30 + 1 + +29-32-36 81 x^928 + x^874 + x^870 + x^840 + x^820 + x^819 + x^794 + x^790 + x^770 + x^765 + x^764 + x^760 + x^754 + x^750 + x^740 + x^739 + x^735 + x^734 + x^730 + x^709 + x^704 + x^674 + x^670 + x^665 + x^660 + x^650 + x^649 + x^635 + x^634 + x^619 + x^614 + x^605 + x^595 + x^585 + x^584 + x^579 + x^564 + x^555 + x^545 + x^540 + x^524 + x^515 + x^514 + x^495 + x^490 + x^485 + x^460 + x^455 + x^435 + x^425 + x^400 + x^395 + x^375 + x^370 + x^365 + x^340 + x^315 + x^310 + x^305 + x^300 + x^290 + x^285 + x^275 + x^260 + x^250 + x^245 + x^240 + x^215 + x^190 + x^180 + x^170 + x^150 + x^130 + x^120 + x^115 + x^105 + x^100 + x^75 + x^40 + x^30 + 1 + +39-10-20 105 x^928 + x^898 + x^870 + x^841 + x^840 + x^808 + x^783 + x^782 + x^781 + x^780 + x^778 + x^754 + x^752 + x^724 + x^721 + x^720 + x^696 + x^692 + x^688 + x^667 + x^666 + x^661 + x^660 + x^658 + x^638 + x^636 + x^632 + x^609 + x^607 + x^606 + x^605 + x^604 + x^601 + x^600 + x^580 + x^578 + x^576 + x^572 + x^568 + x^549 + x^548 + x^541 + x^540 + x^538 + x^516 + x^512 + x^489 + x^485 + x^484 + x^481 + x^480 + x^456 + x^452 + x^448 + x^429 + x^428 + x^421 + x^420 + x^418 + x^400 + x^398 + x^396 + x^392 + 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