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Diffstat (limited to 'lib/stdlib/src/rand.erl')
| -rw-r--r-- | lib/stdlib/src/rand.erl | 591 |
1 files changed, 591 insertions, 0 deletions
diff --git a/lib/stdlib/src/rand.erl b/lib/stdlib/src/rand.erl new file mode 100644 index 0000000000..6a805eb69e --- /dev/null +++ b/lib/stdlib/src/rand.erl @@ -0,0 +1,591 @@ +%% +%% %CopyrightBegin% +%% +%% Copyright Ericsson AB 2015. All Rights Reserved. +%% +%% The contents of this file are subject to the Erlang Public License, +%% Version 1.1, (the "License"); you may not use this file except in +%% compliance with the License. You should have received a copy of the +%% Erlang Public License along with this software. If not, it can be +%% retrieved online at http://www.erlang.org/. +%% +%% Software distributed under the License is distributed on an "AS IS" +%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See +%% the License for the specific language governing rights and limitations +%% under the License. +%% +%% %CopyrightEnd% +%% +%% ===================================================================== +%% Multiple PRNG module for Erlang/OTP +%% Copyright (c) 2015 Kenji Rikitake +%% ===================================================================== + +-module(rand). + +-export([seed_s/1, seed_s/2, seed/1, seed/2, + export_seed/0, export_seed_s/1, + uniform/0, uniform/1, uniform_s/1, uniform_s/2, + normal/0, normal_s/1 + ]). + +-compile({inline, [exs64_next/1, exsplus_next/1, + exs1024_next/1, exs1024_calc/2, + get_52/1, normal_kiwi/1]}). + +-define(DEFAULT_ALG_HANDLER, exsplus). +-define(SEED_DICT, rand_seed). + +%% ===================================================================== +%% Types +%% ===================================================================== + +%% This depends on the algorithm handler function +-type alg_seed() :: exs64_state() | exsplus_state() | exs1024_state(). +%% This is the algorithm handler function within this module +-type alg_handler() :: #{type => alg(), + max => integer(), + next => fun(), + uniform => fun(), + uniform_n => fun()}. + +%% Internal state +-opaque state() :: {alg_handler(), alg_seed()}. +-type alg() :: exs64 | exsplus | exs1024. +-opaque export_state() :: {alg(), alg_seed()}. +-export_type([alg/0, state/0, export_state/0]). + +%% ===================================================================== +%% API +%% ===================================================================== + +%% Return algorithm and seed so that RNG state can be recreated with seed/1 +-spec export_seed() -> undefined | export_state(). +export_seed() -> + case seed_get() of + {#{type:=Alg}, Seed} -> {Alg, Seed}; + _ -> undefined + end. + +-spec export_seed_s(state()) -> export_state(). +export_seed_s({#{type:=Alg}, Seed}) -> {Alg, Seed}. + +%% seed(Alg) seeds RNG with runtime dependent values +%% and return the NEW state + +%% seed({Alg,Seed}) setup RNG with a previously exported seed +%% and return the NEW state + +-spec seed(AlgOrExpState::alg() | export_state()) -> state(). +seed(Alg) -> + R = seed_s(Alg), + _ = seed_put(R), + R. + +-spec seed_s(AlgOrExpState::alg() | export_state()) -> state(). +seed_s(Alg) when is_atom(Alg) -> + seed_s(Alg, {erlang:phash2([{node(),self()}]), + erlang:system_time(), + erlang:unique_integer()}); +seed_s({Alg0, Seed}) -> + {Alg,_SeedFun} = mk_alg(Alg0), + {Alg, Seed}. + +%% seed/2: seeds RNG with the algorithm and given values +%% and returns the NEW state. + +-spec seed(Alg :: alg(), {integer(), integer(), integer()}) -> state(). +seed(Alg0, S0) -> + State = seed_s(Alg0, S0), + _ = seed_put(State), + State. + +-spec seed_s(Alg :: alg(), {integer(), integer(), integer()}) -> state(). +seed_s(Alg0, S0 = {_, _, _}) -> + {Alg, Seed} = mk_alg(Alg0), + AS = Seed(S0), + {Alg, AS}. + +%%% uniform/0, uniform/1, uniform_s/1, uniform_s/2 are all +%%% uniformly distributed random numbers. + +%% uniform/0: returns a random float X where 0.0 < X < 1.0, +%% updating the state in the process dictionary. + +-spec uniform() -> X::float(). +uniform() -> + {X, Seed} = uniform_s(seed_get()), + _ = seed_put(Seed), + X. + +%% uniform/1: given an integer N >= 1, +%% uniform/1 returns a random integer X where 1 =< X =< N, +%% updating the state in the process dictionary. + +-spec uniform(N :: pos_integer()) -> X::pos_integer(). +uniform(N) -> + {X, Seed} = uniform_s(N, seed_get()), + _ = seed_put(Seed), + X. + +%% uniform_s/1: given a state, uniform_s/1 +%% returns a random float X where 0.0 < X < 1.0, +%% and a new state. + +-spec uniform_s(state()) -> {X::float(), NewS :: state()}. +uniform_s(State = {#{uniform:=Uniform}, _}) -> + Uniform(State). + +%% uniform_s/2: given an integer N >= 1 and a state, uniform_s/2 +%% uniform_s/2 returns a random integer X where 1 =< X =< N, +%% and a new state. + +-spec uniform_s(N::pos_integer(), state()) -> {X::pos_integer(), NewS::state()}. +uniform_s(N, State = {#{uniform_n:=Uniform, max:=Max}, _}) + when 0 < N, N =< Max -> + Uniform(N, State); +uniform_s(N, State0 = {#{uniform:=Uniform}, _}) + when is_integer(N), 0 < N -> + {F, State} = Uniform(State0), + {trunc(F * N) + 1, State}. + +%% normal/0: returns a random float with standard normal distribution +%% updating the state in the process dictionary. + +-spec normal() -> float(). +normal() -> + {X, Seed} = normal_s(seed_get()), + _ = seed_put(Seed), + X. + +%% normal_s/1: returns a random float with standard normal distribution +%% The Ziggurat Method for generating random variables - Marsaglia and Tsang +%% Paper and reference code: http://www.jstatsoft.org/v05/i08/ + +-spec normal_s(state()) -> {float(), NewS :: state()}. +normal_s(State0) -> + {Sign, R, State} = get_52(State0), + Idx = R band 16#FF, + Idx1 = Idx+1, + {Ki, Wi} = normal_kiwi(Idx1), + X = R * Wi, + case R < Ki of + %% Fast path 95% of the time + true when Sign =:= 0 -> {X, State}; + true -> {-X, State}; + %% Slow path + false when Sign =:= 0 -> normal_s(Idx, Sign, X, State); + false -> normal_s(Idx, Sign, -X, State) + end. + +%% ===================================================================== +%% Internal functions + +-define(UINT21MASK, 16#00000000001fffff). +-define(UINT32MASK, 16#00000000ffffffff). +-define(UINT33MASK, 16#00000001ffffffff). +-define(UINT39MASK, 16#0000007fffffffff). +-define(UINT58MASK, 16#03ffffffffffffff). +-define(UINT64MASK, 16#ffffffffffffffff). + +-type uint64() :: 0..16#ffffffffffffffff. +-type uint58() :: 0..16#03ffffffffffffff. + +-spec seed_put(state()) -> undefined | state(). +seed_put(Seed) -> + put(?SEED_DICT, Seed). + +seed_get() -> + case get(?SEED_DICT) of + undefined -> seed(?DEFAULT_ALG_HANDLER); + Old -> Old % no type checking here + end. + +%% Setup alg record +mk_alg(exs64) -> + {#{type=>exs64, max=>?UINT64MASK, next=>fun exs64_next/1, + uniform=>fun exs64_uniform/1, uniform_n=>fun exs64_uniform/2}, + fun exs64_seed/1}; +mk_alg(exsplus) -> + {#{type=>exsplus, max=>?UINT58MASK, next=>fun exsplus_next/1, + uniform=>fun exsplus_uniform/1, uniform_n=>fun exsplus_uniform/2}, + fun exsplus_seed/1}; +mk_alg(exs1024) -> + {#{type=>exs1024, max=>?UINT64MASK, next=>fun exs1024_next/1, + uniform=>fun exs1024_uniform/1, uniform_n=>fun exs1024_uniform/2}, + fun exs1024_seed/1}. + +%% ===================================================================== +%% exs64 PRNG: Xorshift64* +%% Algorithm by Sebastiano Vigna +%% Reference URL: http://xorshift.di.unimi.it/ +%% ===================================================================== + +-type exs64_state() :: uint64(). + +exs64_seed({A1, A2, A3}) -> + {V1, _} = exs64_next(((A1 band ?UINT32MASK) * 4294967197 + 1)), + {V2, _} = exs64_next(((A2 band ?UINT32MASK) * 4294967231 + 1)), + {V3, _} = exs64_next(((A3 band ?UINT32MASK) * 4294967279 + 1)), + ((V1 * V2 * V3) rem (?UINT64MASK - 1)) + 1. + +%% Advance xorshift64* state for one step and generate 64bit unsigned integer +-spec exs64_next(exs64_state()) -> {uint64(), exs64_state()}. +exs64_next(R) -> + R1 = R bxor (R bsr 12), + R2 = R1 bxor ((R1 band ?UINT39MASK) bsl 25), + R3 = R2 bxor (R2 bsr 27), + {(R3 * 2685821657736338717) band ?UINT64MASK, R3}. + +exs64_uniform({Alg, R0}) -> + {V, R1} = exs64_next(R0), + {V / 18446744073709551616, {Alg, R1}}. + +exs64_uniform(Max, {Alg, R}) -> + {V, R1} = exs64_next(R), + {(V rem Max) + 1, {Alg, R1}}. + +%% ===================================================================== +%% exsplus PRNG: Xorshift116+ +%% Algorithm by Sebastiano Vigna +%% Reference URL: http://xorshift.di.unimi.it/ +%% 58 bits fits into an immediate on 64bits erlang and is thus much faster. +%% Modification of the original Xorshift128+ algorithm to 116 +%% by Sebastiano Vigna, a lot of thanks for his help and work. +%% ===================================================================== +-type exsplus_state() :: nonempty_improper_list(uint58(), uint58()). + +exsplus_seed({A1, A2, A3}) -> + {_, R1} = exsplus_next([(((A1 * 4294967197) + 1) band ?UINT58MASK)| + (((A2 * 4294967231) + 1) band ?UINT58MASK)]), + {_, R2} = exsplus_next([(((A3 * 4294967279) + 1) band ?UINT58MASK)| + tl(R1)]), + R2. + +%% Advance xorshift116+ state for one step and generate 58bit unsigned integer +-spec exsplus_next(exsplus_state()) -> {uint58(), exsplus_state()}. +exsplus_next([S1|S0]) -> + %% Note: members s0 and s1 are swapped here + S11 = (S1 bxor (S1 bsl 24)) band ?UINT58MASK, + S12 = S11 bxor S0 bxor (S11 bsr 11) bxor (S0 bsr 41), + {(S0 + S12) band ?UINT58MASK, [S0|S12]}. + +exsplus_uniform({Alg, R0}) -> + {I, R1} = exsplus_next(R0), + {I / (?UINT58MASK+1), {Alg, R1}}. + +exsplus_uniform(Max, {Alg, R}) -> + {V, R1} = exsplus_next(R), + {(V rem Max) + 1, {Alg, R1}}. + +%% ===================================================================== +%% exs1024 PRNG: Xorshift1024* +%% Algorithm by Sebastiano Vigna +%% Reference URL: http://xorshift.di.unimi.it/ +%% ===================================================================== + +-type exs1024_state() :: {list(uint64()), list(uint64())}. + +exs1024_seed({A1, A2, A3}) -> + B1 = (((A1 band ?UINT21MASK) + 1) * 2097131) band ?UINT21MASK, + B2 = (((A2 band ?UINT21MASK) + 1) * 2097133) band ?UINT21MASK, + B3 = (((A3 band ?UINT21MASK) + 1) * 2097143) band ?UINT21MASK, + {exs1024_gen1024((B1 bsl 43) bor (B2 bsl 22) bor (B3 bsl 1) bor 1), + []}. + +%% Generate a list of 16 64-bit element list +%% of the xorshift64* random sequence +%% from a given 64-bit seed. +%% Note: dependent on exs64_next/1 +-spec exs1024_gen1024(uint64()) -> list(uint64()). +exs1024_gen1024(R) -> + exs1024_gen1024(16, R, []). + +exs1024_gen1024(0, _, L) -> + L; +exs1024_gen1024(N, R, L) -> + {X, R2} = exs64_next(R), + exs1024_gen1024(N - 1, R2, [X|L]). + +%% Calculation of xorshift1024*. +%% exs1024_calc(S0, S1) -> {X, NS1}. +%% X: random number output +-spec exs1024_calc(uint64(), uint64()) -> {uint64(), uint64()}. +exs1024_calc(S0, S1) -> + S11 = S1 bxor ((S1 band ?UINT33MASK) bsl 31), + S12 = S11 bxor (S11 bsr 11), + S01 = S0 bxor (S0 bsr 30), + NS1 = S01 bxor S12, + {(NS1 * 1181783497276652981) band ?UINT64MASK, NS1}. + +%% Advance xorshift1024* state for one step and generate 64bit unsigned integer +-spec exs1024_next(exs1024_state()) -> {uint64(), exs1024_state()}. +exs1024_next({[S0,S1|L3], RL}) -> + {X, NS1} = exs1024_calc(S0, S1), + {X, {[NS1|L3], [S0|RL]}}; +exs1024_next({[H], RL}) -> + NL = [H|lists:reverse(RL)], + exs1024_next({NL, []}). + +exs1024_uniform({Alg, R0}) -> + {V, R1} = exs1024_next(R0), + {V / 18446744073709551616, {Alg, R1}}. + +exs1024_uniform(Max, {Alg, R}) -> + {V, R1} = exs1024_next(R), + {(V rem Max) + 1, {Alg, R1}}. + +%% ===================================================================== +%% Ziggurat cont +%% ===================================================================== +-define(NOR_R, 3.6541528853610087963519472518). +-define(NOR_INV_R, 1/?NOR_R). + +%% return a {sign, Random51bits, State} +get_52({Alg=#{next:=Next}, S0}) -> + {Int,S1} = Next(S0), + {((1 bsl 51) band Int), Int band ((1 bsl 51)-1), {Alg, S1}}. + +%% Slow path +normal_s(0, Sign, X0, State0) -> + {U0, S1} = uniform_s(State0), + X = -?NOR_INV_R*math:log(U0), + {U1, S2} = uniform_s(S1), + Y = -math:log(U1), + case Y+Y > X*X of + false -> + normal_s(0, Sign, X0, S2); + true when Sign =:= 0 -> + {?NOR_R + X, S2}; + true -> + {-?NOR_R - X, S2} + end; +normal_s(Idx, _Sign, X, State0) -> + Fi2 = normal_fi(Idx+1), + {U0, S1} = uniform_s(State0), + case ((normal_fi(Idx) - Fi2)*U0 + Fi2) < math:exp(-0.5*X*X) of + true -> {X, S1}; + false -> normal_s(S1) + end. + +%% Tables for generating normal_s +%% ki is zipped with wi (slightly faster) +normal_kiwi(Indx) -> + element(Indx, + {{2104047571236786,1.736725412160263e-15}, {0,9.558660351455634e-17}, + {1693657211986787,1.2708704834810623e-16},{1919380038271141,1.4909740962495474e-16}, + {2015384402196343,1.6658733631586268e-16},{2068365869448128,1.8136120810119029e-16}, + {2101878624052573,1.9429720153135588e-16},{2124958784102998,2.0589500628482093e-16}, + {2141808670795147,2.1646860576895422e-16},{2154644611568301,2.2622940392218116e-16}, + {2164744887587275,2.353271891404589e-16},{2172897953696594,2.438723455742877e-16}, + {2179616279372365,2.5194879829274225e-16},{2185247251868649,2.5962199772528103e-16}, + {2190034623107822,2.6694407473648285e-16},{2194154434521197,2.7395729685142446e-16}, + {2197736978774660,2.8069646002484804e-16},{2200880740891961,2.871905890411393e-16}, + {2203661538010620,2.9346417484728883e-16},{2206138681109102,2.9953809336782113e-16}, + {2208359231806599,3.054303000719244e-16},{2210361007258210,3.111563633892157e-16}, + {2212174742388539,3.1672988018581815e-16},{2213825672704646,3.2216280350549905e-16}, + {2215334711002614,3.274657040793975e-16},{2216719334487595,3.326479811684171e-16}, + {2217994262139172,3.377180341735323e-16},{2219171977965032,3.4268340353119356e-16}, + {2220263139538712,3.475508873172976e-16},{2221276900117330,3.523266384600203e-16}, + {2222221164932930,3.5701624633953494e-16},{2223102796829069,3.616248057159834e-16}, + {2223927782546658,3.661569752965354e-16},{2224701368170060,3.7061702777236077e-16}, + {2225428170204312,3.75008892787478e-16},{2226112267248242,3.7933619401549554e-16}, + {2226757276105256,3.836022812967728e-16},{2227366415328399,3.8781025861250247e-16}, + {2227942558554684,3.919630085325768e-16},{2228488279492521,3.9606321366256378e-16}, + {2229005890047222,4.001133755254669e-16},{2229497472775193,4.041158312414333e-16}, + {2229964908627060,4.080727683096045e-16},{2230409900758597,4.119862377480744e-16}, + {2230833995044585,4.1585816580828064e-16},{2231238597816133,4.1969036444740733e-16}, + {2231624991250191,4.234845407152071e-16},{2231994346765928,4.272423051889976e-16}, + {2232347736722750,4.309651795716294e-16},{2232686144665934,4.346546035512876e-16}, + {2233010474325959,4.383119410085457e-16},{2233321557544881,4.4193848564470665e-16}, + {2233620161276071,4.455354660957914e-16},{2233906993781271,4.491040505882875e-16}, + {2234182710130335,4.52645351185714e-16},{2234447917093496,4.561604276690038e-16}, + {2234703177503020,4.596502910884941e-16},{2234949014150181,4.631159070208165e-16}, + {2235185913274316,4.665581985600875e-16},{2235414327692884,4.699780490694195e-16}, + {2235634679614920,4.733763047158324e-16},{2235847363174595,4.767537768090853e-16}, + {2236052746716837,4.8011124396270155e-16},{2236251174862869,4.834494540935008e-16}, + {2236442970379967,4.867691262742209e-16},{2236628435876762,4.900709524522994e-16}, + {2236807855342765,4.933555990465414e-16},{2236981495548562,4.966237084322178e-16}, + {2237149607321147,4.998759003240909e-16},{2237312426707209,5.031127730659319e-16}, + {2237470176035652,5.0633490483427195e-16},{2237623064889403,5.095428547633892e-16}, + {2237771290995388,5.127371639978797e-16},{2237915041040597,5.159183566785736e-16}, + {2238054491421305,5.190869408670343e-16},{2238189808931712,5.222434094134042e-16}, + {2238321151397660,5.253882407719454e-16},{2238448668260432,5.285218997682382e-16}, + {2238572501115169,5.316448383216618e-16},{2238692784207942,5.34757496126473e-16}, + {2238809644895133,5.378603012945235e-16},{2238923204068402,5.409536709623993e-16}, + {2239033576548190,5.440380118655467e-16},{2239140871448443,5.471137208817361e-16}, + {2239245192514958,5.501811855460336e-16},{2239346638439541,5.532407845392784e-16}, + {2239445303151952,5.56292888151909e-16},{2239541276091442,5.593378587248462e-16}, + {2239634642459498,5.623760510690043e-16},{2239725483455293,5.65407812864896e-16}, + {2239813876495186,5.684334850436814e-16},{2239899895417494,5.714534021509204e-16}, + {2239983610673676,5.744678926941961e-16},{2240065089506935,5.774772794756965e-16}, + {2240144396119183,5.804818799107686e-16},{2240221591827230,5.834820063333892e-16}, + {2240296735208969,5.864779662894365e-16},{2240369882240293,5.894700628185872e-16}, + {2240441086423386,5.924585947256134e-16},{2240510398907004,5.95443856841806e-16}, + {2240577868599305,5.984261402772028e-16},{2240643542273726,6.014057326642664e-16}, + {2240707464668391,6.043829183936125e-16},{2240769678579486,6.073579788423606e-16}, + {2240830224948980,6.103311925956439e-16},{2240889142947082,6.133028356617911e-16}, + {2240946470049769,6.162731816816596e-16},{2241002242111691,6.192425021325847e-16}, + {2241056493434746,6.222110665273788e-16},{2241109256832602,6.251791426088e-16}, + {2241160563691400,6.281469965398895e-16},{2241210444026879,6.311148930905604e-16}, + {2241258926538122,6.34083095820806e-16},{2241306038658137,6.370518672608815e-16}, + 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