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diff --git a/lib/stdlib/src/rand.erl b/lib/stdlib/src/rand.erl
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+%%
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2015. 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%
+%%
+%% =====================================================================
+%% 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},
+ {2241351806601435,6.400214690888025e-16},{2241396255408788,6.429921623054896e-16},
+ {2241439408989313,6.459642074078832e-16},{2241481290160038,6.489378645603397e-16},
+ {2241521920683062,6.519133937646159e-16},{2241561321300462,6.548910550287415e-16},
+ {2241599511767028,6.578711085350741e-16},{2241636510880960,6.608538148078259e-16},
+ {2241672336512612,6.638394348803506e-16},{2241707005631362,6.668282304624746e-16},
+ {2241740534330713,6.698204641081558e-16},{2241772937851689,6.728163993837531e-16},
+ {2241804230604585,6.758163010371901e-16},{2241834426189161,6.78820435168298e-16},
+ {2241863537413311,6.818290694006254e-16},{2241891576310281,6.848424730550038e-16},
+ {2241918554154466,6.878609173251664e-16},{2241944481475843,6.908846754557169e-16},
+ {2241969368073071,6.939140229227569e-16},{2241993223025298,6.969492376174829e-16},
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generated by cgit v1.2.3 (git 2.25.1) at 2024-12-12 09:40:46 +0000