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authorDan Gudmundsson <[email protected]>2015-04-28 14:37:33 +0200
committerDan Gudmundsson <[email protected]>2015-04-30 13:06:58 +0200
commit401bf07f5908137cde206f2f755af83c9a7ff71e (patch)
tree2771a5b1bc341b13458209b66a16c51f5c0bdc04 /lib/stdlib
parent95aff702b5e4b21ec277b1e0125f639ce30f997a (diff)
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stdlib: Document and add normal distributed random value function
It is needed in various tests. It uses the Ziggurat algorithm, which is the fastest that I know.
Diffstat (limited to 'lib/stdlib')
-rw-r--r--lib/stdlib/doc/src/Makefile1
-rw-r--r--lib/stdlib/doc/src/rand.xml246
-rw-r--r--lib/stdlib/doc/src/random.xml3
-rw-r--r--lib/stdlib/doc/src/ref_man.xml1
-rw-r--r--lib/stdlib/doc/src/specs.xml1
-rw-r--r--lib/stdlib/src/rand.erl323
-rw-r--r--lib/stdlib/test/rand_SUITE.erl83
7 files changed, 615 insertions, 43 deletions
diff --git a/lib/stdlib/doc/src/Makefile b/lib/stdlib/doc/src/Makefile
index f5d8b2072a..031e60f64e 100644
--- a/lib/stdlib/doc/src/Makefile
+++ b/lib/stdlib/doc/src/Makefile
@@ -81,6 +81,7 @@ XML_REF3_FILES = \
proplists.xml \
qlc.xml \
queue.xml \
+ rand.xml \
random.xml \
re.xml \
sets.xml \
diff --git a/lib/stdlib/doc/src/rand.xml b/lib/stdlib/doc/src/rand.xml
new file mode 100644
index 0000000000..178afda5a0
--- /dev/null
+++ b/lib/stdlib/doc/src/rand.xml
@@ -0,0 +1,246 @@
+<?xml version="1.0" encoding="utf-8" ?>
+<!DOCTYPE erlref SYSTEM "erlref.dtd">
+
+<erlref>
+ <header>
+ <copyright>
+ <year>2015</year>
+ <holder>Ericsson AB. All Rights Reserved.</holder>
+ </copyright>
+ <legalnotice>
+ 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.
+
+ </legalnotice>
+
+ <title>rand</title>
+ <prepared></prepared>
+ <responsible></responsible>
+ <docno>1</docno>
+ <approved></approved>
+ <checked></checked>
+ <date></date>
+ <rev>A</rev>
+ <file>rand.xml</file>
+ </header>
+ <module>rand</module>
+ <modulesummary>Pseudo random number generation</modulesummary>
+ <description>
+ <p>Random number generator.</p>
+
+ <p>The module contains several different algorithms and can be
+ extended with more in the future. The current uniform
+ distribution algorithms uses the
+ <url href="http://xorshift.di.unimi.it">
+ scrambled Xorshift algorithms by Sebastiano Vigna</url> and the
+ normal distribution algorithm uses the
+ <url href="http://www.jstatsoft.org/v05/i08">
+ Ziggurat Method by Marsaglia and Tsang</url>.
+ </p>
+
+ <p>The implemented algorithms are:</p>
+ <taglist>
+ <tag><c>exsplus</c></tag> <item>Xorshift116+, 58 bits precision and period of 2^116-1.</item>
+ <tag><c>exs64</c></tag> <item>Xorshift64*, 64 bits precision and a period of 2^64-1.</item>
+ <tag><c>exs1024</c></tag> <item>Xorshift1024*, 64 bits precision and a period of 2^1024-1.</item>
+ </taglist>
+
+ <p>The current default algorithm is <c>exsplus</c>. The default
+ may change in future. If a specific algorithm is required make
+ sure to always use <seealso marker="#seed-1">seed/1</seealso>
+ to initialize the state.
+ </p>
+
+ <p>Every time a random number is requested, a state is used to
+ calculate it and a new state produced. The state can either be
+ implicit or it can be an explicit argument and return value.
+ </p>
+
+ <p>The functions with implicit state use the process dictionary
+ variable <c>rand_seed</c> to remember the current state.</p>
+
+ <p>If a process calls <seealso marker="#uniform-0">uniform/0</seealso> or
+ <seealso marker="#uniform-1">uniform/1</seealso> without
+ setting a seed first, <seealso marker="#seed-1">seed/1</seealso>
+ is called automatically with the default algorithm and creates a
+ non-constant seed.</p>
+
+ <p>The functions with explicit state never use the process
+ dictionary.</p>
+
+ <p>Examples:</p>
+ <pre>
+ %% Simple usage. Creates and seeds the default algorithm
+ %% with a non-constant seed if not already done.
+ R0 = rand:uniform(),
+ R1 = rand:uniform(),
+
+ %% Use a given algorithm.
+ _ = rand:seed(exs1024),
+ R2 = rand:uniform(),
+
+ %% Use a given algorithm with a constant seed.
+ _ = rand:seed(exs1024, {123, 123534, 345345}),
+ R3 = rand:uniform(),
+
+ %% Use the functional api with non-constant seed.
+ S0 = rand:seed_s(exsplus),
+ {R4, S1} = rand:uniform_s(S0),
+
+ %% Create a standard normal deviate.
+ {SND0, S2} = rand:normal_s(S1),
+ </pre>
+
+ <note><p>This random number generator is not cryptographically
+ strong. If a strong cryptographic random number generator is
+ needed, use one of functions in the
+ <seealso marker="crypto:crypto">crypto</seealso>
+ module, for example <c>crypto:rand_bytes/1</c>.</p></note>
+ </description>
+ <datatypes>
+ <datatype>
+ <name name="alg"/>
+ </datatype>
+
+ <datatype>
+ <name name="state"/>
+ <desc><p>Algorithm dependent state.</p></desc>
+ </datatype>
+
+ <datatype>
+ <name name="export_state"/>
+ <desc><p>Algorithm dependent state which can be printed or saved to file.</p></desc>
+ </datatype>
+ </datatypes>
+
+ <funcs>
+ <func>
+ <name name="seed" arity="1"/>
+ <fsummary>Seed random number generator</fsummary>
+ <desc>
+ <marker id="seed-1"/>
+ <p>Seeds random number generation with the given algorithm and time dependent
+ data if <anno>AlgOrExpState</anno> is an algorithm.</p>
+ <p>Otherwise recreates the exported seed in the process
+ dictionary, and returns the state.
+ <em>See also:</em> <seealso marker="#export_seed-0">export_seed/0</seealso>.</p>
+ </desc>
+ </func>
+ <func>
+ <name name="seed_s" arity="1"/>
+ <fsummary>Seed random number generator</fsummary>
+ <desc>
+ <p>Seeds random number generation with the given algorithm and time dependent
+ data if <anno>AlgOrExpState</anno> is an algorithm.</p>
+ <p>Otherwise recreates the exported seed and returns the state.
+ <em>See also:</em> <seealso marker="#export_seed-0">export_seed/0</seealso>.</p>
+ </desc>
+ </func>
+ <func>
+ <name name="seed" arity="2"/>
+ <fsummary>Seed the random number generation</fsummary>
+ <desc>
+ <p>Seeds random number generation with the given algorithm and
+ integers in the process dictionary and returns
+ the state.</p>
+ </desc>
+ </func>
+ <func>
+ <name name="seed_s" arity="2"/>
+ <fsummary>Seed the random number generation</fsummary>
+ <desc>
+ <p>Seeds random number generation with the given algorithm and
+ integers and returns the state.</p>
+ </desc>
+ </func>
+
+ <func>
+ <name name="export_seed" arity="0"/>
+ <fsummary>Export the random number generation state</fsummary>
+ <desc><marker id="export_seed-0"/>
+ <p>Returns the random number state in an external format.
+ To be used with <seealso marker="#seed-1">seed/1</seealso>.</p>
+ </desc>
+ </func>
+
+ <func>
+ <name name="export_seed_s" arity="1"/>
+ <fsummary>Export the random number generation state</fsummary>
+ <desc><marker id="export_seed_s-1"/>
+ <p>Returns the random number generator state in an external format.
+ To be used with <seealso marker="#seed-1">seed/1</seealso>.</p>
+ </desc>
+ </func>
+
+ <func>
+ <name name="uniform" arity="0"/>
+ <fsummary>Return a random float</fsummary>
+ <desc>
+ <marker id="uniform-0"/>
+ <p>Returns a random float uniformly distributed in the value
+ range <c>0.0 &lt; <anno>X</anno> &lt; 1.0 </c> and
+ updates the state in the process dictionary.</p>
+ </desc>
+ </func>
+ <func>
+ <name name="uniform_s" arity="1"/>
+ <fsummary>Return a random float</fsummary>
+ <desc>
+ <p>Given a state, <c>uniform_s/1</c> returns a random float
+ uniformly distributed in the value range <c>0.0 &lt;
+ <anno>X</anno> &lt; 1.0</c> and a new state.</p>
+ </desc>
+ </func>
+
+ <func>
+ <name name="uniform" arity="1"/>
+ <fsummary>Return a random integer</fsummary>
+ <desc>
+ <marker id="uniform-1"/>
+ <p>Given an integer <c><anno>N</anno> >= 1</c>,
+ <c>uniform/1</c> returns a random integer uniformly
+ distributed in the value range
+ <c>1 &lt;= <anno>X</anno> &lt;= <anno>N</anno></c> and
+ updates the state in the process dictionary.</p>
+ </desc>
+ </func>
+ <func>
+ <name name="uniform_s" arity="2"/>
+ <fsummary>Return a random integer</fsummary>
+ <desc>
+ <p>Given an integer <c><anno>N</anno> >= 1</c> and a state,
+ <c>uniform_s/2</c> returns a random integer uniformly
+ distributed in the value range <c>1 &lt;= <anno>X</anno> &lt;=
+ <anno>N</anno></c> and a new state.</p>
+ </desc>
+ </func>
+
+ <func>
+ <name name="normal" arity="0"/>
+ <fsummary>Return a standard normal distributed random float</fsummary>
+ <desc>
+ <p>Returns a standard normal deviate float (that is, the mean
+ is 0 and the standard deviation is 1) and updates the state in
+ the process dictionary.</p>
+ </desc>
+ </func>
+ <func>
+ <name name="normal_s" arity="1"/>
+ <fsummary>Return a standard normal distributed random float</fsummary>
+ <desc>
+ <p>Given a state, <c>normal_s/1</c> returns a standard normal
+ deviate float (that is, the mean is 0 and the standard
+ deviation is 1) and a new state.</p>
+ </desc>
+ </func>
+
+ </funcs>
+</erlref>
diff --git a/lib/stdlib/doc/src/random.xml b/lib/stdlib/doc/src/random.xml
index 2cc621ffc3..e475cda23d 100644
--- a/lib/stdlib/doc/src/random.xml
+++ b/lib/stdlib/doc/src/random.xml
@@ -48,6 +48,9 @@
<p>It should be noted that this random number generator is not cryptographically
strong. If a strong cryptographic random number generator is needed for
example <c>crypto:rand_bytes/1</c> could be used instead.</p>
+ <note><p>The new and improved <seealso
+ marker="stdlib:rand">rand</seealso> module should be used
+ instead of this module.</p></note>
</description>
<datatypes>
<datatype>
diff --git a/lib/stdlib/doc/src/ref_man.xml b/lib/stdlib/doc/src/ref_man.xml
index ea4009dc3e..459fc8c8ed 100644
--- a/lib/stdlib/doc/src/ref_man.xml
+++ b/lib/stdlib/doc/src/ref_man.xml
@@ -78,6 +78,7 @@
<xi:include href="proplists.xml"/>
<xi:include href="qlc.xml"/>
<xi:include href="queue.xml"/>
+ <xi:include href="rand.xml"/>
<xi:include href="random.xml"/>
<xi:include href="re.xml"/>
<xi:include href="sets.xml"/>
diff --git a/lib/stdlib/doc/src/specs.xml b/lib/stdlib/doc/src/specs.xml
index fd77b52da6..f12e00b263 100644
--- a/lib/stdlib/doc/src/specs.xml
+++ b/lib/stdlib/doc/src/specs.xml
@@ -44,6 +44,7 @@
<xi:include href="../specs/specs_proplists.xml"/>
<xi:include href="../specs/specs_qlc.xml"/>
<xi:include href="../specs/specs_queue.xml"/>
+ <xi:include href="../specs/specs_rand.xml"/>
<xi:include href="../specs/specs_random.xml"/>
<xi:include href="../specs/specs_re.xml"/>
<xi:include href="../specs/specs_sets.xml"/>
diff --git a/lib/stdlib/src/rand.erl b/lib/stdlib/src/rand.erl
index 0cafb35dd8..6a805eb69e 100644
--- a/lib/stdlib/src/rand.erl
+++ b/lib/stdlib/src/rand.erl
@@ -25,10 +25,13 @@
-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]).
+ 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]}).
+ exs1024_next/1, exs1024_calc/2,
+ get_52/1, normal_kiwi/1]}).
-define(DEFAULT_ALG_HANDLER, exsplus).
-define(SEED_DICT, rand_seed).
@@ -38,31 +41,33 @@
%% =====================================================================
%% This depends on the algorithm handler function
--opaque alg_seed() :: exs64_state() | exsplus_state() | exs1024_state().
+-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
--type state() :: {alg_handler(), alg_seed()}.
+-opaque state() :: {alg_handler(), alg_seed()}.
-type alg() :: exs64 | exsplus | exs1024.
--export_type([alg/0, alg_handler/0, state/0, alg_seed/0]).
+-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 | {alg(), alg_seed()}.
+-spec export_seed() -> undefined | export_state().
export_seed() ->
case seed_get() of
{#{type:=Alg}, Seed} -> {Alg, Seed};
_ -> undefined
end.
--spec export_seed_s(state()) -> {alg(), alg_seed()}.
+-spec export_seed_s(state()) -> export_state().
export_seed_s({#{type:=Alg}, Seed}) -> {Alg, Seed}.
%% seed(Alg) seeds RNG with runtime dependent values
@@ -71,13 +76,13 @@ export_seed_s({#{type:=Alg}, Seed}) -> {Alg, Seed}.
%% seed({Alg,Seed}) setup RNG with a previously exported seed
%% and return the NEW state
--spec seed(alg() | {alg(), alg_seed()}) -> state().
+-spec seed(AlgOrExpState::alg() | export_state()) -> state().
seed(Alg) ->
R = seed_s(Alg),
_ = seed_put(R),
R.
--spec seed_s(alg() | {alg(), alg_seed()}) -> state().
+-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(),
@@ -107,7 +112,7 @@ seed_s(Alg0, S0 = {_, _, _}) ->
%% uniform/0: returns a random float X where 0.0 < X < 1.0,
%% updating the state in the process dictionary.
--spec uniform() -> float().
+-spec uniform() -> X::float().
uniform() ->
{X, Seed} = uniform_s(seed_get()),
_ = seed_put(Seed),
@@ -117,7 +122,7 @@ uniform() ->
%% uniform/1 returns a random integer X where 1 =< X =< N,
%% updating the state in the process dictionary.
--spec uniform(N :: pos_integer()) -> pos_integer().
+-spec uniform(N :: pos_integer()) -> X::pos_integer().
uniform(N) ->
{X, Seed} = uniform_s(N, seed_get()),
_ = seed_put(Seed),
@@ -127,7 +132,7 @@ uniform(N) ->
%% returns a random float X where 0.0 < X < 1.0,
%% and a new state.
--spec uniform_s(state()) -> {float(), NewS :: state()}.
+-spec uniform_s(state()) -> {X::float(), NewS :: state()}.
uniform_s(State = {#{uniform:=Uniform}, _}) ->
Uniform(State).
@@ -135,7 +140,7 @@ uniform_s(State = {#{uniform:=Uniform}, _}) ->
%% uniform_s/2 returns a random integer X where 1 =< X =< N,
%% and a new state.
--spec uniform_s(N::pos_integer(), state()) -> {pos_integer(), NewS::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);
@@ -144,6 +149,35 @@ uniform_s(N, State0 = {#{uniform:=Uniform}, _})
{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
@@ -169,15 +203,15 @@ seed_get() ->
%% Setup alg record
mk_alg(exs64) ->
- {#{type=>exs64, max=>?UINT64MASK,
+ {#{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,
+ {#{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,
+ {#{type=>exs1024, max=>?UINT64MASK, next=>fun exs1024_next/1,
uniform=>fun exs1024_uniform/1, uniform_n=>fun exs1024_uniform/2},
fun exs1024_seed/1}.
@@ -219,7 +253,7 @@ exs64_uniform(Max, {Alg, R}) ->
%% Modification of the original Xorshift128+ algorithm to 116
%% by Sebastiano Vigna, a lot of thanks for his help and work.
%% =====================================================================
--type exsplus_state() :: [uint58()|uint58()].
+-type exsplus_state() :: nonempty_improper_list(uint58(), uint58()).
exsplus_seed({A1, A2, A3}) ->
{_, R1} = exsplus_next([(((A1 * 4294967197) + 1) band ?UINT58MASK)|
@@ -300,3 +334,258 @@ exs1024_uniform({Alg, R0}) ->
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},
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+ 3.6884215688567284e-02,3.4980941461716084e-02,3.3093219458578522e-02,
+ 3.1221417191920245e-02,2.9365939758133314e-02,2.7527235669603082e-02,
+ 2.5705804008548896e-02,2.3902203305795882e-02,2.2117062707308864e-02,
+ 2.0351096230044517e-02,1.8605121275724643e-02,1.6880083152543166e-02,
+ 1.5177088307935325e-02,1.3497450601739880e-02,1.1842757857907888e-02,
+ 1.0214971439701471e-02,8.6165827693987316e-03,7.0508754713732268e-03,
+ 5.5224032992509968e-03,4.0379725933630305e-03,2.6090727461021627e-03,
+ 1.2602859304985975e-03}).
diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl
index 70d219ddaf..9a1f37aa75 100644
--- a/lib/stdlib/test/rand_SUITE.erl
+++ b/lib/stdlib/test/rand_SUITE.erl
@@ -139,6 +139,7 @@ api_eq(_Config) ->
Algs = algs(),
Small = fun(Alg) ->
Seed = rand:seed(Alg),
+ io:format("Seed ~p~n",[rand:export_seed_s(Seed)]),
api_eq_1(Seed)
end,
_ = [Small(Alg) || Alg <- Algs],
@@ -150,28 +151,31 @@ api_eq_1(S00) ->
V0 = rand:uniform(),
{V1, S1} = rand:uniform_s(1000000, S0),
V1 = rand:uniform(1000000),
- S1
+ {V2, S2} = rand:normal_s(S1),
+ V2 = rand:normal(),
+ S2
end,
S1 = lists:foldl(Check, S00, lists:seq(1, 200)),
S1 = get(rand_seed),
- Exported = rand:export_seed(),
- Exported = rand:export_seed_s(S1),
{V0, S2} = rand:uniform_s(S1),
V0 = rand:uniform(),
+ S2 = get(rand_seed),
- S3 = lists:foldl(Check, S2, lists:seq(1, 200)),
- S1 = rand:seed(Exported),
- S1 = rand:seed_s(Exported),
+ Exported = rand:export_seed(),
+ Exported = rand:export_seed_s(S2),
- S4 = lists:foldl(Check, S1, lists:seq(1, 200)),
+ S3 = lists:foldl(Check, S2, lists:seq(1, 200)),
+ S3 = get(rand_seed),
+ S4 = lists:foldl(Check, S3, lists:seq(1, 200)),
+ S4 = get(rand_seed),
%% Verify that we do not have loops
false = S1 =:= S2,
false = S2 =:= S3,
false = S3 =:= S4,
- S1 = rand:seed(Exported),
- S4 = lists:foldl(Check, S1, lists:seq(1, 200)),
+ S2 = rand:seed(Exported),
+ S3 = lists:foldl(Check, S2, lists:seq(1, 200)),
ok.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -183,14 +187,16 @@ interval_int(suite) ->
interval_int(Config) when is_list(Config) ->
Algs = algs(),
Small = fun(Alg) ->
- _ = rand:seed(Alg),
+ Seed = rand:seed(Alg),
+ io:format("Seed ~p~n",[rand:export_seed_s(Seed)]),
Max = interval_int_1(100000, 7, 0),
Max =:= 7 orelse exit({7, Alg, Max})
end,
_ = [Small(Alg) || Alg <- Algs],
%% Test large integers
Large = fun(Alg) ->
- _ = rand:seed(Alg),
+ Seed = rand:seed(Alg),
+ io:format("Seed ~p~n",[rand:export_seed_s(Seed)]),
Max = interval_int_1(100000, 1 bsl 128, 0),
Max > 1 bsl 64 orelse exit({large, Alg, Max})
end,
@@ -287,18 +293,21 @@ gen(_, _, Acc) -> lists:reverse(Acc).
basic_stats(doc) -> ["Check that the algorithms generate sound values."];
basic_stats(suite) -> [];
basic_stats(Config) when is_list(Config) ->
- [basic_stats_1(?LOOP, rand:seed_s(Alg), 0.0, array:new([{default, 0}]))
+ io:format("Testing uniform~n",[]),
+ [basic_uniform_1(?LOOP, rand:seed_s(Alg), 0.0, array:new([{default, 0}]))
|| Alg <- algs()],
- [basic_stats_2(?LOOP, rand:seed_s(Alg), 0, array:new([{default, 0}]))
+ [basic_uniform_2(?LOOP, rand:seed_s(Alg), 0, array:new([{default, 0}]))
|| Alg <- algs()],
+ io:format("Testing normal~n",[]),
+ [basic_normal_1(?LOOP, rand:seed_s(Alg), 0, 0) || Alg <- algs()],
ok.
-basic_stats_1(N, S0, Sum, A0) when N > 0 ->
+basic_uniform_1(N, S0, Sum, A0) when N > 0 ->
{X,S} = rand:uniform_s(S0),
I = trunc(X*100),
A = array:set(I, 1+array:get(I,A0), A0),
- basic_stats_1(N-1, S, Sum+X, A);
-basic_stats_1(0, {#{type:=Alg}, _}, Sum, A) ->
+ basic_uniform_1(N-1, S, Sum+X, A);
+basic_uniform_1(0, {#{type:=Alg}, _}, Sum, A) ->
AverN = Sum / ?LOOP,
io:format("~.10w: Average: ~.4f~n", [Alg, AverN]),
Counters = array:to_list(A),
@@ -313,11 +322,11 @@ basic_stats_1(0, {#{type:=Alg}, _}, Sum, A) ->
abs(?LOOP div 100 - Max) < 1000 orelse test_server:fail({max, Alg, Max}),
ok.
-basic_stats_2(N, S0, Sum, A0) when N > 0 ->
+basic_uniform_2(N, S0, Sum, A0) when N > 0 ->
{X,S} = rand:uniform_s(100, S0),
A = array:set(X-1, 1+array:get(X-1,A0), A0),
- basic_stats_2(N-1, S, Sum+X, A);
-basic_stats_2(0, {#{type:=Alg}, _}, Sum, A) ->
+ basic_uniform_2(N-1, S, Sum+X, A);
+basic_uniform_2(0, {#{type:=Alg}, _}, Sum, A) ->
AverN = Sum / ?LOOP,
io:format("~.10w: Average: ~.4f~n", [Alg, AverN]),
Counters = tl(array:to_list(A)),
@@ -332,6 +341,19 @@ basic_stats_2(0, {#{type:=Alg}, _}, Sum, A) ->
abs(?LOOP div 100 - Max) < 1000 orelse test_server:fail({max, Alg, Max}),
ok.
+basic_normal_1(N, S0, Sum, Sq) when N > 0 ->
+ {X,S} = rand:normal_s(S0),
+ basic_normal_1(N-1, S, X+Sum, X*X+Sq);
+basic_normal_1(0, {#{type:=Alg}, _}, Sum, SumSq) ->
+ Mean = Sum / ?LOOP,
+ StdDev = math:sqrt((SumSq - (Sum*Sum/?LOOP))/(?LOOP - 1)),
+ io:format("~.10w: Average: ~7.4f StdDev ~6.4f~n", [Alg, Mean, StdDev]),
+ %% Verify that the basic statistics are ok
+ %% be gentle we don't want to see to many failing tests
+ abs(Mean) < 0.005 orelse test_server:fail({average, Alg, Mean}),
+ abs(StdDev - 1.0) < 0.005 orelse test_server:fail({stddev, Alg, StdDev}),
+ ok.
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
plugin(doc) -> ["Test that the user can write algorithms"];
@@ -349,11 +371,12 @@ plugin(Config) when is_list(Config) ->
%% Test implementation
crypto_seed() ->
{#{type=>crypto,
+ max=>(1 bsl 64)-1,
+ next=>fun crypto_next/1,
uniform=>fun crypto_uniform/1,
uniform_n=>fun crypto_uniform_n/2},
<<>>}.
-
%% Be fair and create bignums i.e. 64bits otherwise use 58bits
crypto_next(<<Num:64, Bin/binary>>) ->
{Num, Bin};
@@ -377,15 +400,21 @@ crypto_uniform_n(N, State0) ->
measure(Suite) when is_atom(Suite) -> [];
measure(_Config) ->
Algos = [crypto64|algs()],
- io:format("RNG integer performance~n",[]),
- _ = [measure_1(Algo, fun(State) -> rand:uniform_s(10000, State) end) || Algo <- Algos],
- io:format("RNG float performance~n",[]),
- _ = [measure_1(Algo, fun(State) -> rand:uniform_s(State) end) || Algo <- Algos],
+ io:format("RNG uniform integer performance~n",[]),
+ _ = measure_1(random, fun(State) -> {int, random:uniform_s(10000, State)} end),
+ _ = [measure_1(Algo, fun(State) -> {int, rand:uniform_s(10000, State)} end) || Algo <- Algos],
+ io:format("RNG uniform float performance~n",[]),
+ _ = measure_1(random, fun(State) -> {uniform, random:uniform_s(State)} end),
+ _ = [measure_1(Algo, fun(State) -> {uniform, rand:uniform_s(State)} end) || Algo <- Algos],
+ io:format("RNG normal float performance~n",[]),
+ io:format("~.10w: not implemented (too few bits)~n", [random]),
+ _ = [measure_1(Algo, fun(State) -> {normal, rand:normal_s(State)} end) || Algo <- Algos],
ok.
measure_1(Algo, Gen) ->
Parent = self(),
Seed = fun(crypto64) -> crypto_seed();
+ (random) -> random:seed(os:timestamp()), get(random_seed);
(Alg) -> rand:seed_s(Alg)
end,
@@ -402,10 +431,12 @@ measure_1(Algo, Gen) ->
measure_2(N, State0, Fun) when N > 0 ->
case Fun(State0) of
- {Random, State}
+ {int, {Random, State}}
when is_integer(Random), Random >= 1, Random =< 100000 ->
measure_2(N-1, State, Fun);
- {Random, State} when is_float(Random), Random > 0, Random < 1 ->
+ {uniform, {Random, State}} when is_float(Random), Random > 0, Random < 1 ->
+ measure_2(N-1, State, Fun);
+ {normal, {Random, State}} when is_float(Random) ->
measure_2(N-1, State, Fun);
Res ->
exit({error, Res, State0})