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.

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},
+	 {2229964908627060,4.080727683096045e-16},{2230409900758597,4.119862377480744e-16},
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+	 {2242197728218684,8.093412784821501e-16},{2242184577261310,8.128120042284501e-16},
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+	 {2240993584191742,9.341301313425265e-16},{2240919374095536,9.38665656618666e-16},
+	 {2240841848084890,9.432558359676707e-16},{2240760846432232,9.479027264651738e-16},
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+	 {2239842221996530,9.926785548807976e-16},{2239714417896699,9.980350026183645e-16},
+	 {2239580280957725,1.003480452143618e-15},{2239439398282193,1.0090190861637457e-15},
+	 {2239291317986196,1.0146553831467086e-15},{2239135544468203,1.0203941464683124e-15},
+	 {2238971532964979,1.0262405372613567e-15},{2238798683265269,1.0322001115486456e-15},
+	 {2238616332424351,1.03827886235154e-15},{2238423746288095,1.044483267600047e-15},
+	 {2238220109591890,1.0508203448355195e-15},{2238004514345216,1.057297713900989e-15},
+	 {2237775946143212,1.06392366906768e-15},{2237533267957822,1.0707072623632994e-15},
+	 {2237275200846753,1.0776584002668106e-15},{2237000300869952,1.0847879564403425e-15},
+	 {2236706931309099,1.0921079038149563e-15},{2236393229029147,1.0996314701785628e-15},
+	 {2236057063479501,1.1073733224935752e-15},{2235695986373246,1.1153497865853155e-15},
+	 {2235307169458859,1.1235791107110833e-15},{2234887326941578,1.1320817840164846e-15},
+	 {2234432617919447,1.140880924258278e-15},{2233938522519765,1.1500027537839792e-15},
+	 {2233399683022677,1.159477189144919e-15},{2232809697779198,1.169338578691096e-15},
+	 {2232160850599817,1.17962663529558e-15},{2231443750584641,1.190387629928289e-15},
+	 {2230646845562170,1.2016759392543819e-15},{2229755753817986,1.2135560818666897e-15},
+	 {2228752329126533,1.2261054417450561e-15},{2227613325162504,1.2394179789163251e-15},
+	 {2226308442121174,1.2536093926602567e-15},{2224797391720399,1.268824481425501e-15},
+	 {2223025347823832,1.2852479319096109e-15},{2220915633329809,1.3031206634689985e-15},
+	 {2218357446087030,1.3227655770195326e-15},{2215184158448668,1.3446300925011171e-15},
+	 {2211132412537369,1.3693606835128518e-15},{2205758503851065,1.397943667277524e-15},
+	 {2198248265654987,1.4319989869661328e-15},{2186916352102141,1.4744848603597596e-15},
+	 {2167562552481814,1.5317872741611144e-15},{2125549880839716,1.6227698675312968e-15}}).
+
+normal_fi(Indx) ->
+    element(Indx,
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+	     8.6645194450557961e-02,8.4428509570353374e-02,8.2223595813202863e-02,
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+	     6.7124653827788497e-02,6.5016577971242842e-02,6.2921024437758113e-02,
+	     6.0838108349539864e-02,5.8767952920933758e-02,5.6710690106202902e-02,
+	     5.4666461324888914e-02,5.2635418276792176e-02,5.0617723860947761e-02,
+	     4.8613553215868521e-02,4.6623094901930368e-02,4.4646552251294443e-02,
+	     4.2684144916474431e-02,4.0736110655940933e-02,3.8802707404526113e-02,
+	     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})