Implement Xoroshiro928**

4 files changed, 815 insertions, 29 deletions

diff --git a/lib/stdlib/doc/src/rand.xml b/lib/stdlib/doc/src/rand.xml
index 21f680a0ee..5f1ec84786 100644
--- a/lib/stdlib/doc/src/rand.xml
+++ b/lib/stdlib/doc/src/rand.xml
@@ -67,6 +67,26 @@
         <p>Xorshift1024*, 64 bits precision and a period of 2^1024-1</p>
         <p>Jump function: equivalent to 2^512 calls</p>
       </item>
+      <tag><c>exro928ss</c></tag>
+      <item>
+        <p>Xoroshiro928**, 58 bits precision and a period of 2^928-1</p>
+        <p>Jump function: equivalent to 2^512 calls</p>
+	<p>
+	  This is a 58 bit version of Xoroshiro1024**,
+	  from the 2018 paper by David Blackman and Sebastiano Vigna:
+	  <url href="http://vigna.di.unimi.it/ftp/papers/ScrambledLinear.pdf">
+	    Scrambled Linear Pseudorandom Number Generators
+	  </url>
+	  that on a 64 bit Erlang system executes only about 30% slower than
+	  the default <c>exrop</c> algorithm but with much longer period
+	  and better statistical properties, and on the flip side
+	  a larger state.
+	</p>
+	<p>
+	  Many thanks to Sebastiano Vigna for his help with
+	  the 58 bit adaption.
+	</p>
+      </item>
       <tag><c>exsp</c></tag>
       <item>
         <p>Xorshift116+, 58 bits precision and period of 2^116-1</p>
@@ -195,8 +215,8 @@ SND0 = math:sqrt(-2 * math:log(R5)) * math:cos(math:pi() * R6)</pre>
     </note>
 
     <p>
-      For all these generators the lowest bit(s) has got
-      a slightly less random behaviour than all other bits.
+      For all these generators except <c>exro928ss</c> the lowest bit(s)
+      has got a slightly less random behaviour than all other bits.
       1 bit for <c>exrop</c> (and <c>exsp</c>),
       and 3 bits for <c>exs1024s</c>.
       See for example the explanation in the
@@ -254,19 +274,23 @@ tests. We suggest to use a sign test to extract a random Boolean value.</pre>
       </desc>
     </datatype>
     <datatype>
-      <name name="exs64_state"/>
+      <name name="exrop_state"/>
       <desc><p>Algorithm specific internal state</p></desc>
     </datatype>
     <datatype>
-      <name name="exsplus_state"/>
+      <name name="exs1024_state"/>
       <desc><p>Algorithm specific internal state</p></desc>
     </datatype>
     <datatype>
-      <name name="exs1024_state"/>
+      <name name="exro928_state"/>
       <desc><p>Algorithm specific internal state</p></desc>
     </datatype>
     <datatype>
-      <name name="exrop_state"/>
+      <name name="exsplus_state"/>
+      <desc><p>Algorithm specific internal state</p></desc>
+    </datatype>
+    <datatype>
+      <name name="exs64_state"/>
       <desc><p>Algorithm specific internal state</p></desc>
     </datatype>
   </datatypes>
diff --git a/lib/stdlib/src/rand.erl b/lib/stdlib/src/rand.erl
index 4951dc727b..3a32f40fcd 100644
--- a/lib/stdlib/src/rand.erl
+++ b/lib/stdlib/src/rand.erl
@@ -32,14 +32,19 @@
          uniform/0, uniform/1, uniform_s/1, uniform_s/2,
          uniform_real/0, uniform_real_s/1,
          jump/0, jump/1,
-	     normal/0, normal/2, normal_s/1, normal_s/3
+         normal/0, normal/2, normal_s/1, normal_s/3
 	]).
 
+%% Test, dev and internal
+-export([exro928_jump_2pow512/1, exro928_jump_2pow20/1,
+	 format_jumpconst58/1, seed58/2]).
+
 %% Debug
 -export([make_float/3, float2str/1, bc64/1]).
 
 -compile({inline, [exs64_next/1, exsplus_next/1,
 		   exs1024_next/1, exs1024_calc/2,
+                   exro928_next_state/4,
                    exrop_next/1, exrop_next_s/2,
 		   get_52/1, normal_kiwi/1]}).
 
@@ -80,8 +85,8 @@
 
 %% This depends on the algorithm handler function
 -type alg_state() ::
-        exs64_state() | exsplus_state() | exs1024_state() |
-        exrop_state() | term().
+	exrop_state() | exs1024_state() |  exro928_state() |  exsplus_state() |
+	exs64_state() | term().
 
 %% This is the algorithm handling definition within this module,
 %% and the type to use for plugins.
@@ -124,14 +129,16 @@
 
 %% Algorithm state
 -type state() :: {alg_handler(), alg_state()}.
--type builtin_alg() :: exs64 | exsplus | exsp | exs1024 | exs1024s | exrop.
+-type builtin_alg() ::
+	exrop | exs1024s | exro928ss | exsp | exs64 | exsplus | exs1024.
 -type alg() :: builtin_alg() | atom().
 -type export_state() :: {alg(), alg_state()}.
 -export_type(
    [builtin_alg/0, alg/0, alg_handler/0, alg_state/0,
     state/0, export_state/0]).
 -export_type(
-   [exs64_state/0, exsplus_state/0, exs1024_state/0, exrop_state/0]).
+   [exrop_state/0, exs1024_state/0, exro928_state/0, exsplus_state/0,
+    exs64_state/0]).
 
 %% =====================================================================
 %% Range macro and helper
@@ -260,15 +267,17 @@ seed_s(Alg) ->
 %% and returns the NEW state.
 
 -spec seed(
-        Alg :: builtin_alg(), Seed :: {integer(), integer(), integer()}) ->
+        Alg :: builtin_alg(),
+	Seed :: {integer(), integer(), integer()}) ->
                   state().
 seed(Alg0, S0) ->
     seed_put(seed_s(Alg0, S0)).
 
 -spec seed_s(
-        Alg :: builtin_alg(), Seed :: {integer(), integer(), integer()}) ->
+        Alg :: builtin_alg(),
+	Seed :: {integer(), integer(), integer()}) ->
                     state().
-seed_s(Alg0, S0 = {_, _, _}) ->
+seed_s(Alg0, S0) ->
     {Alg, Seed} = mk_alg(Alg0),
     AS = Seed(S0),
     {Alg, AS}.
@@ -625,7 +634,13 @@ mk_alg(exrop) ->
     {#{type=>exrop, bits=>58, weak_low_bits=>1, next=>fun exrop_next/1,
        uniform=>fun exrop_uniform/1, uniform_n=>fun exrop_uniform/2,
        jump=>fun exrop_jump/1},
-     fun exrop_seed/1}.
+     fun exrop_seed/1};
+mk_alg(exro928ss) ->
+    {#{type=>exro928ss, bits=>58, next=>fun exro928ss_next/1,
+       uniform=>fun exro928ss_uniform/1,
+       uniform_n=>fun exro928ss_uniform/2,
+       jump=>fun exro928_jump/1},
+     fun exro928_seed/1}.
 
 %% =====================================================================
 %% exs64 PRNG: Xorshift64*
@@ -708,7 +723,8 @@ exsp_uniform(Range, {Alg, R}) ->
 -define(JUMPELEMLEN, 58).
 
 -dialyzer({no_improper_lists, exsplus_jump/1}).
--spec exsplus_jump(state()) -> state().
+-spec exsplus_jump({alg_handler(), exsplus_state()}) ->
+                          {alg_handler(), exsplus_state()}.
 exsplus_jump({Alg, S}) ->
     {S1, AS1} = exsplus_jump(S, [0|0], ?JUMPCONST1, ?JUMPELEMLEN),
     {_,  AS2} = exsplus_jump(S1, AS1,  ?JUMPCONST2, ?JUMPELEMLEN),
@@ -806,8 +822,8 @@ exs1024_next({[H], RL}) ->
 -define(JUMPTOTALLEN, 1024).
 -define(RINGLEN, 16).
 
--spec exs1024_jump(state()) -> state().
-
+-spec exs1024_jump({alg_handler(), exs1024_state()}) ->
+                          {alg_handler(), exs1024_state()}.
 exs1024_jump({Alg, {L, RL}}) ->
     P = length(RL),
     AS = exs1024_jump({L, RL},
@@ -832,6 +848,255 @@ exs1024_jump({L, RL}, AS, JL, J, N, TN) ->
     end.
 
 %% =====================================================================
+%% exro928ss PRNG: Xoroshiro928**
+%%
+%% Reference URL: http://vigna.di.unimi.it/ftp/papers/ScrambledLinear.pdf
+%% i.e the Xoroshiro1024 generator with ** scrambler
+%% with {S, R, T} = {5, 7, 9} as recommended in the paper.
+%%
+%% {A, B, C} were tried out and selected as {44, 9, 45}
+%% and the jump coefficients calculated.
+%%
+%% Standard jump function pseudocode:
+%% 
+%%     Jump constant j = 0xb10773cb...44085302f77130ca
+%%     Generator state: s
+%%     New generator state: t = 0
+%%     foreach bit in j, low to high:
+%%         if the bit is one:
+%%             t ^= s
+%%         next s
+%%     s = t
+%%
+%% Generator used for reference value calculation:
+%%
+%%     #include <stdint.h>
+%%     #include <stdio.h>
+%%     
+%%     int p = 0;
+%%     uint64_t s[16];
+%%     
+%%     #define MASK(x) ((x) & ((UINT64_C(1) << 58) - 1))
+%%     static __inline uint64_t rotl(uint64_t x, int n) {
+%%         return MASK(x << n) | (x >> (58 - n));
+%%     }
+%%     
+%%     uint64_t next() {
+%%         const int q = p;
+%%         const uint64_t s0 = s[p = (p + 1) & 15];
+%%         uint64_t s15 = s[q];
+%%     
+%%         const uint64_t result_starstar = MASK(rotl(MASK(s0 * 5), 7) * 9);
+%%     
+%%         s15 ^= s0;
+%%         s[q] = rotl(s0, 44) ^ s15 ^ MASK(s15 << 9);
+%%         s[p] = rotl(s15, 45);
+%%     
+%%         return result_starstar;
+%%     }
+%%
+%%     static const uint64_t jump_2pow512[15] =
+%%         { 0x44085302f77130ca, 0xba05381fdfd14902, 0x10a1de1d7d6813d2,
+%%           0xb83fe51a1eb3be19, 0xa81b0090567fd9f0, 0x5ac26d5d20f9b49f,
+%%           0x4ddd98ee4be41e01, 0x0657e19f00d4b358, 0xf02f778573cf0f0a,
+%%           0xb45a3a8a3cef3cc0, 0x6e62a33cc2323831, 0xbcb3b7c4cc049c53,
+%%           0x83f240c6007e76ce, 0xe19f5fc1a1504acd, 0x00000000b10773cb };
+%%
+%%     static const uint64_t jump_2pow20[15] =
+%%         { 0xbdb966a3daf905e6, 0x644807a56270cf78, 0xda90f4a806c17e9e,
+%%           0x4a426866bfad3c77, 0xaf699c306d8e7566, 0x8ebc73c700b8b091,
+%%           0xc081a7bf148531fb, 0xdc4d3af15f8a4dfd, 0x90627c014098f4b6,
+%%           0x06df2eb1feaf0fb6, 0x5bdeb1a5a90f2e6b, 0xa480c5878c3549bd,
+%%           0xff45ef33c82f3d48, 0xa30bebc15fefcc78, 0x00000000cb3d181c };
+%%
+%%     void jump(const uint64_t *jump) {
+%%         uint64_t j, t[16] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
+%%         int m, n, k;
+%%         for (m = 0;  m < 15;  m++, jump++) {
+%%             for (n = 0, j = *jump;  n < 64;  n++, j >>= 1) {
+%%                 if ((j & 1) != 0) {
+%%                     for (k = 0;  k < 16;  k++) {
+%%                         t[k] ^= s[(p + k) & 15];
+%%                     }
+%%                 }
+%%                 next();
+%%             }
+%%         }
+%%         for (k = 0;  k < 16;  k++) {
+%%             s[(p + k) & 15] = t[k];
+%%         }
+%%     }
+%%
+%% =====================================================================
+
+-opaque exro928_state() :: {list(uint58()), list(uint58())}.
+
+
+%%% %% Seed raw words
+%%% exro928_seed({S0,S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,S13,S14,S15})
+%%%   when S0 bor S1 bor S2 bor S3 bor S4 bor S5 bor S6 bor S7 bor
+%%%        S8 bor S9 bor S10 bor S11 bor S12 bor S13 bor S14 bor S15 > 0,
+%%%        S0 bor S1 bor S2 bor S3 bor S4 bor S5 bor S6 bor S7 bor
+%%%        S8 bor S9 bor S10 bor S11 bor S12 bor S13 bor S14 bor S15 < 1 bsl 58 ->
+%%%     {[S0,S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,S13,S14,S15], []};
+%%% %%
+%%% %% Seed from one 64-bit integer through splitmix
+%%% exro928_seed(X) when is_integer(X), 0 =< X, X =< 1 bsl 64 ->
+%%%     {exro928_seed(X, 16),[]};
+%%
+%% Seed from traditional triple - splitmix mixed with the 3 integers
+exro928_seed({A1, A2, A3}) ->
+    {S0, X0} = seed58(?MASK(64, A1)),
+    {S1, X1} = seed58(?MASK(64, A2 bxor X0)),
+    {S2, X2} = seed58(?MASK(64, A3 bxor X1)),
+    {[S0,S1,S2|exro928_seed(X2, 13)],[]}.
+%%
+%% Splitmix seed the rest of the state words
+exro928_seed(_X, 0) ->
+    [];
+exro928_seed(X, N) ->
+    {S, NewX} = seed58(X),
+    [S|exro928_seed(NewX, N-1)].
+
+
+%% Update the state and calculate output word
+-spec exro928ss_next(exro928_state()) -> {uint58(), exro928_state()}.
+exro928ss_next({[S15,S0|Ss], Rs}) ->
+    SR = exro928_next_state(Ss, Rs, S15, S0),
+    %%
+    %% {S, R, T} = {5, 7, 9}
+    %% const uint64_t result_starstar = rotl(s0 * S, R) * T;
+    %%
+    %% The multiply by add shifted trick avoids creating bignums
+    %% which improves performance significantly
+    %%
+    V0 = ?MASK(58, S0 + ?BSL(58, S0, 2)), % V0 = S0 * 5
+    V1 = ?ROTL(58, V0, 7),
+    V = ?MASK(58, V1 + ?BSL(58, V1, 3)), % V = V1 * 9
+    {V, SR};
+exro928ss_next({[S15], Rs}) ->
+    exro928ss_next({[S15|lists:reverse(Rs)], []}).
+
+%% Just update the state
+exro928_next_state({[S15,S0|Ss], Rs}) ->
+    exro928_next_state(Ss, Rs, S15, S0);
+exro928_next_state({[S15], Rs}) ->
+    [S0|Ss] = lists:reverse(Rs),
+    exro928_next_state(Ss, [], S15, S0).
+
+exro928_next_state(Ss, Rs, S15, S0) ->
+    %% {A, B, C} = {44, 9, 45},
+    %% s15 ^= s0;
+    %% NewS15: s[q] = rotl(s0, A) ^ s15 ^ (s15 << B);
+    %% NewS0: s[p] = rotl(s15, C);
+    %%
+    Q = S15 bxor S0,
+    NewS15 = ?ROTL(58, S0, 44) bxor Q bxor ?BSL(58, Q, 9),
+    NewS0 = ?ROTL(58, Q, 45),
+    {[NewS0|Ss], [NewS15|Rs]}.
+
+
+exro928ss_uniform({Alg, SR}) ->
+    {V, NewSR} = exro928ss_next(SR),
+    {(V bsr (58-53)) * ?TWO_POW_MINUS53, {Alg, NewSR}}.
+
+exro928ss_uniform(Range, {Alg, SR}) ->
+    {V, NewSR} = exro928ss_next(SR),
+    MaxMinusRange = ?BIT(58) - Range,
+    ?uniform_range(Range, Alg, NewSR, V, MaxMinusRange, I).
+
+
+-spec exro928_jump({alg_handler(), exro928_state()}) ->
+                          {alg_handler(), exro928_state()}.
+exro928_jump({Alg, SR}) ->
+    {Alg,exro928_jump_2pow512(SR)}.
+
+exro928_jump_2pow512(SR) ->
+    polyjump(
+      SR, fun exro928_next_state/1,
+      %% 2^512
+      [16#4085302F77130CA, 16#54E07F7F4524091,
+       16#5E1D7D6813D2BA0, 16#4687ACEF8644287,
+       16#4567FD9F0B83FE5, 16#43E6D27EA06C024,
+       16#641E015AC26D5D2, 16#6CD61377663B92F,
+       16#70A0657E19F00D4, 16#43C0BDDE15CF3C3,
+       16#745A3A8A3CEF3CC, 16#58A8CF308C8E0C6,
+       16#7B7C4CC049C536E, 16#431801F9DB3AF2C,
+       16#41A1504ACD83F24, 16#6C41DCF2F867D7F]).
+
+exro928_jump_2pow20(SR) ->
+    polyjump(
+      SR, fun exro928_next_state/1,
+      %% 2^20
+      [16#5B966A3DAF905E6, 16#601E9589C33DE2F,
+       16#74A806C17E9E644, 16#59AFEB4F1DF6A43,
+       16#46D8E75664A4268, 16#42E2C246BDA670C,
+       16#4531FB8EBC73C70, 16#537F702069EFC52,
+       16#4B6DC4D3AF15F8A, 16#5A4189F0050263D,
+       16#46DF2EB1FEAF0FB, 16#77AC696A43CB9AC,
+       16#4C5878C3549BD5B, 16#7CCF20BCF522920,
+       16#415FEFCC78FF45E, 16#72CF460728C2FAF]).
+
+%% =====================================================================
+%% Polynomial jump with a jump constant word list,
+%% high bit in each word marking top of word,
+%% SR is a {Forward, Reverse} queue tuple with Forward never empty
+%% =====================================================================
+
+polyjump({Ss, Rs} = SR, NextState, JumpConst) ->
+    %% Create new state accumulator T
+    Ts = lists:duplicate(length(Ss) + length(Rs), 0),
+    polyjump(SR, NextState, JumpConst, Ts).
+%%
+%% Foreach jump word
+polyjump(_SR, _NextState, [], Ts) ->
+    %% Return new calculated state
+    {Ts, []};
+polyjump(SR, NextState, [J|Js], Ts) ->
+    polyjump(SR, NextState, Js, Ts, J).
+%%
+%% Foreach bit in jump word until top bit
+polyjump(SR, NextState, Js, Ts, 1) ->
+
+    polyjump(SR, NextState, Js, Ts);
+polyjump({Ss, Rs} = SR, NextState, Js, Ts, J) when J =/= 0 ->
+    NewSR = NextState(SR),
+    NewJ = J bsr 1,
+    case ?MASK(1, J) of
+        0 ->
+            polyjump(NewSR, NextState, Js, Ts, NewJ);
+        1 ->
+            %% Xor this state onto T
+            polyjump(NewSR, NextState, Js, xorzip_sr(Ts, Ss, Rs), NewJ)
+    end.
+
+xorzip_sr([], [], undefined) ->
+    [];
+xorzip_sr(Ts, [], Rs) ->
+    xorzip_sr(Ts, lists:reverse(Rs), undefined);
+xorzip_sr([T|Ts], [S|Ss], Rs) ->
+    [T bxor S|xorzip_sr(Ts, Ss, Rs)].
+
+%% =====================================================================
+
+format_jumpconst58(String) ->
+    ReOpts = [{newline,any},{capture,all_but_first,binary},global],
+    {match,Matches} = re:run(String, "0x([a-zA-Z0-9]+)", ReOpts),
+    format_jumcons58_matches(lists:reverse(Matches), 0).
+
+format_jumcons58_matches([], J) ->
+    format_jumpconst58_value(J);
+format_jumcons58_matches([[Bin]|Matches], J) ->
+    NewJ = (J bsl 64) bor binary_to_integer(Bin, 16),
+    format_jumcons58_matches(Matches, NewJ).
+
+format_jumpconst58_value(0) ->
+    ok;
+format_jumpconst58_value(J) ->
+    io:format("16#~s,~n", [integer_to_list(?MASK(58, J) bor ?BIT(58), 16)]),
+    format_jumpconst58_value(J bsr 58).
+
+%% =====================================================================
 %% exrop PRNG: Xoroshiro116+
 %%
 %% Reference URL: http://xorshift.di.unimi.it/
@@ -962,6 +1227,34 @@ exrop_jump([S__0|S__1] = _S, S0, S1, J, Js) ->
     end.
 
 %% =====================================================================
+%% 58-bit seeder; lowest 58 bits of SplitMix64, zeros skipped
+%%
+%% uint64_t splitmix64_next() {
+%% 	uint64_t z = (x += 0x9e3779b97f4a7c15);
+%% 	z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
+%% 	z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
+%% 	return z ^ (z >> 31);
+%% }
+%% =====================================================================
+
+seed58(0, _X) ->
+    [];
+seed58(N, X) ->
+    {Z,NewX} = seed58(X),
+    [Z|seed58(N - 1, NewX)].
+%%
+seed58(X_0) ->
+    X = ?MASK(64, X_0 + 16#9e3779b97f4a7c15),
+    Z_0 = ?MASK(64, (X bxor (X bsr 30)) * 16#bf58476d1ce4e5b9),
+    Z_1 = ?MASK(64, (Z_0 bxor (Z_0 bsr 27)) * 16#94d049bb133111eb),
+    case ?MASK(58, Z_1 bxor (Z_1 bsr 31)) of
+	0 ->
+	    seed58(X);
+	Z ->
+	    {Z, X}
+    end.
+
+%% =====================================================================
 %% Ziggurat cont
 %% =====================================================================
 -define(NOR_R, 3.6541528853610087963519472518).
diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl
index a7094f1987..2a721dad0d 100644
--- a/lib/stdlib/test/rand_SUITE.erl
+++ b/lib/stdlib/test/rand_SUITE.erl
@@ -34,12 +34,15 @@
          stats_standard_normal/1,
          uniform_real_conv/1,
 	 plugin/1, measure/1,
-	 reference_jump_state/1, reference_jump_procdict/1]).
+	 reference_jump_state/1, reference_jump_procdict/1,
+	 short_jump/1]).
 
 -export([test/0, gen/1]).
 
 -export([uniform_real_gen/1, uniform_gen/2]).
 
+-compile(export_all).
+
 -include_lib("common_test/include/ct.hrl").
 
 -define(LOOP, 1000000).
@@ -56,7 +59,8 @@ all() ->
      {group, distr_stats},
      uniform_real_conv,
      plugin, measure,
-     {group, reference_jump}
+     {group, reference_jump},
+     short_jump
     ].
 
 groups() ->
@@ -95,7 +99,7 @@ test() ->
       end, Tests).
 
 algs() ->
-    [exrop, exsp, exs1024s, exs64, exsplus, exs1024].
+    [exrop, exsp, exs1024s, exs64, exsplus, exs1024, exro928ss].
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -267,27 +271,38 @@ reference_1(Alg) ->
 	Refval =:= not_implemented -> Refval;
 	true ->
 	    case gen(Alg) of
-		Refval -> ok;
+		Refval ->
+		    io:format("Ok: ~p~n",[Alg]),
+                    ok;
 		Testval ->
 		    io:format("Failed: ~p~n",[Alg]),
 		    io:format("Length ~p ~p~n",[length(Refval), length(Testval)]),
 		    io:format("Head ~p ~p~n",[hd(Refval), hd(Testval)]),
+                    show_wrong(Refval, Testval),
 		    exit(wrong_value)
 	    end
     end.
 
+show_wrong([], []) ->
+    ok;
+show_wrong([H|T1], [H|T2]) ->
+    show_wrong(T1, T2);
+show_wrong([H1|_], [H2|_]) ->
+    io:format("Wrong ~p ~p~n",[H1,H2]).
+
+
 gen(Algo) ->
     State =
-        case Algo of
-            exs64 -> %% Printed with orig 'C' code and this seed
+        if
+            Algo =:= exs64 -> %% Printed with orig 'C' code and this seed
                 rand:seed_s({exs64, 12345678});
-            _ when Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop ->
+            Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop ->
                 %% Printed with orig 'C' code and this seed
                 rand:seed_s({Algo, [12345678|12345678]});
-            _ when Algo =:= exs1024; Algo =:= exs1024s ->
+            Algo =:= exs1024; Algo =:= exs1024s; Algo =:= exro928ss ->
                 %% Printed with orig 'C' code and this seed
                 rand:seed_s({Algo, {lists:duplicate(16, 12345678), []}});
-            _ ->
+            true ->
                 rand:seed(Algo, {100, 200, 300})
         end,
     Max = range(State),
@@ -1173,7 +1188,7 @@ gen_jump_1(Algo) ->
 	    %% Printed with orig 'C' code and this seed
 	    gen_jump_2(
 	      rand:seed_s({Algo, [12345678|12345678]}));
-	_ when Algo =:= exs1024; Algo =:= exs1024s ->
+	_ when Algo =:= exs1024; Algo =:= exs1024s; Algo =:= exro928ss ->
 	    %% Printed with orig 'C' code and this seed
 	    gen_jump_2(
 	      rand:seed_s({Algo, {lists:duplicate(16, 12345678), []}}))
@@ -1227,7 +1242,7 @@ gen_jump_p1(Algo) ->
 	    %% Printed with orig 'C' code and this seed
 	    gen_jump_p2(
 	      rand:seed({Algo, [12345678|12345678]}));
-	_ when Algo =:= exs1024; Algo =:= exs1024s ->
+	_ when Algo =:= exs1024; Algo =:= exs1024s; Algo =:= exro928ss ->
 	    %% Printed with orig 'C' code and this seed
 	    gen_jump_p2(
 	      rand:seed({Algo, {lists:duplicate(16, 12345678), []}}))
@@ -1248,6 +1263,37 @@ gen_jump_p3(N, Max, Acc) when N > 0 ->
 gen_jump_p3(_, _, Acc) -> lists:reverse(Acc).
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+short_jump(Config) when is_list(Config) ->
+    State_0 = {#{bits := Bits},_} = rand:seed(exro928ss, {1,2,3}),
+    Range = 1 bsl Bits,
+    %%
+    State_1a = repeat(1 bsl 20, Range, State_0),
+    State_1b = exro928_jump_2pow20(State_0),
+    check(17, Range, State_1a, State_1b),
+    %%
+    {_,State_2a} = rand:uniform_s(Range, State_1a),
+    State_3a = exro928_jump_2pow20(State_2a),
+    State_3b = repeat((1 bsl 20) + 1, Range, State_1b),
+    check(17, Range, State_3a, State_3b).
+
+exro928_jump_2pow20({Alg, AlgState}) ->
+    {Alg,rand:exro928_jump_2pow20(AlgState)}.
+
+repeat(0, _Range, State) ->
+    State;
+repeat(N, Range, State) ->
+    {_, NewState} = rand:uniform_s(Range, State),
+    repeat(N - 1, Range, NewState).
+
+check(0, _Range, _StateA, _StateB) ->
+    ok;
+check(N, Range, StateA, StateB) ->
+    {V,NewStateA} = rand:uniform_s(Range, StateA),
+    {V,NewStateB} = rand:uniform_s(Range, StateB),
+    check(N - 1, Range, NewStateA, NewStateB).
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%% Data
 reference_val(exs64) ->
     [16#3737ad0c703ff6c3,16#3868a78fe71adbbd,16#1f01b62b4338b605,16#50876a917437965f,
@@ -1397,6 +1443,46 @@ reference_val(exrop) ->
      98223942961505519,191144652663779840,
      102425686803727694,89058927716079076,80721467542933080,
      8462479817391645,2774921106204163];
+
+reference_val(exro928ss) ->
+%% Same as for exrop, but this state init:
+%%     for (n = 0;  n < 16;  n++) {
+%%         s[n] = 12345678;
+    [16#000000108e8d5b01,16#03604028f2769dff,16#007f92f60bc7170c,
+     16#035ea81a9898a5e2,16#0104c90c5a0c8178,16#0313514025cca717,
+     16#03c5506b2a2e98cf,16#0098a5405961552e,16#004ad29eabb785a0,
+     16#033ea8ec4efb8058,16#00b21545e62bef1c,16#0333fc5320703482,
+     16#02c3c650e51a8d47,16#03a3b7fc848c9cda,16#03775adea6cddff5,
+     16#01ae5499c9049973,16#03d3c90e5504e16b,16#0383cd6b6cb852e6,
+     16#009c8d0996ef543a,16#0059cf671371af60,16#03dfd68ed980b719,
+     16#0290f2a0acf2c5b0,16#029061df18d63b55,16#02e702ea4b45137b,
+     16#029a0ccca604d848,16#01664c7cd31f0fa6,16#00dced83e60ccddc,
+     16#008764d2c9a05f3e,16#02b9ca5f6a80c4ba,16#02daf93d2c566750,
+     16#0147d326ead18ace,16#014b452efc19297f,16#0242d3f7a7237eca,
+     16#0141bb68c2abce39,16#02d798e1230baf45,16#0216bf8f25c1ec2d,
+     16#003a43ea733f1e1f,16#036c75390db736f3,16#028cca5f5f48c6f9,
+     16#0186e4a17174d6cf,16#02152679dfa4c25c,16#01429b9f15e3b9d6,
+     16#0134a61411d22bb0,16#01593f7d970d1c94,16#0205a7d8a305490f,
+     16#01dd092272595a9c,16#0028c95208aad2d4,16#016347c25cc24162,
+     16#025306acfb891309,16#0207a07e2bebef2f,16#024ee78d86ff5288,
+     16#030b53192db97613,16#03f765cb9e98e611,16#025ec35a1e237377,
+     16#03d81fd73102ef6f,16#0242dc8fea9a68b2,16#00abb876c1d4ea1b,
+     16#00871ffd2b7e45fb,16#03593ff73c9be08d,16#00b96b2b8aca3688,
+     16#0174aba957b7cf7b,16#012b7a5d4cf4a5b7,16#032a5260f2123db8,
+     16#00f9374d88ee0080,16#030df39bec2ad657,16#00dce0cb81d006c4,
+     16#038213b806303c76,16#03940aafdbfabf84,16#0398dbb26aeba037,
+     16#01eb28d61951587f,16#00fed3d2aacfeef4,16#03499587547d6e40,
+     16#01b192fe6e979e3c,16#00e974bf5f0a26d0,16#012ed94f76459c83,
+     16#02d76859e7a82587,16#00d1d2c7b791f51b,16#03988058017a031b,
+     16#00bbcf4b59d8e86d,16#015ed8b73a1b767c,16#0277283ea6a5ee74,
+     16#002211460dd6d422,16#001ad62761ee9fbd,16#037311b44518b067,
+     16#02b5ed61bf70904e,16#011862a05c1929fa,16#014be68683c3bab4,
+     16#025c29aa5c508b07,16#00895c6106f97378,16#026ce91a3d671c7f,
+     16#02591f4c74784293,16#02f0ed2a70bc1853,16#00a2762ff614bfbc,
+     16#008f4e354f0c20d4,16#038b66fb587ed430,16#00636296e188de89,
+     16#0278fadd143e74f5,16#029697ccf1b3a4c2,16#011eccb273404458,
+     16#03f204064a9fe0c0];
+
 reference_val(_) ->
     not_implemented.
 
@@ -1527,6 +1613,46 @@ reference_jump_val(exrop) ->
      241227318715885854,77323084015890802,
      1663590009695191,234064400749487599,222983191707424780,
      254956809144783896,203898972156838252];
+
+reference_jump_val(exro928ss) ->
+%% Same as for exrop, but this state init:
+%%     for (n = 0;  n < 16;  n++) {
+%%         s[n] = 12345678;
+    [16#031ee449e53b6689,16#001afeee12813137,16#005e2172711df36b,
+     16#02850aea3a595d36,16#0029705187e891c7,16#001794badd489667,
+     16#00ab621be15be56c,16#024b663a6924786b,16#03cab70b8ab854bf,
+     16#01daa37601285320,16#02db955a53c40e89,16#01fbef51d5c65891,
+     16#02fecf4116ed5f77,16#0349c2057246ac5d,16#01217f257c4fa148,
+     16#0367ee84d020697d,16#01d5cf647fe23335,16#020941838adfb750,
+     16#02c2da26b1d7b3e5,16#00d1583d34cea6c0,16#038be9cb5b527f50,
+     16#00bfa93c1d7f4864,16#03778912a4f56b14,16#037fcabc483fa5c5,
+     16#00a3c9de6aaf5fc7,16#03600b883b2f2b42,16#03797a99ffddfdfb,
+     16#0189fead429945b7,16#0103ac90cd912508,16#03e3d872fd950d64,
+     16#0214fc3e77dc2f02,16#02a084f4f0e580ca,16#035d2fe72266a7f3,
+     16#02887c49ae7e41a4,16#0011dc026af83c51,16#02d28bfd32c2c517,
+     16#022e4165c33ad4f3,16#01f053cf0687b052,16#035315e6e53c8918,
+     16#01255312da07b572,16#0237f1da11ec9221,16#02faf2e282fb1fb1,
+     16#0227423ec1787ebc,16#011fa5eb1505571c,16#0275ff9eaaa1abdd,
+     16#03e2d032c3981cb4,16#0181bb32d51d3072,16#01b1d3939b9f16ec,
+     16#0259f09f55d1112f,16#0396464a2767e428,16#039777c0368bdb9e,
+     16#0320925f35f36c5f,16#02a35289e0af1248,16#02e80bd4bc72254b,
+     16#00a8b11af1674d68,16#027735036100a69e,16#03c8c268ded7f254,
+     16#03de80aa57c65217,16#00f2247754d24000,16#005582a42b467f89,
+     16#0031906569729477,16#00fd523f2ca4fefe,16#00ad223113d1e336,
+     16#0238ddf026cbfca9,16#028b98211cfed876,16#0354353ebcc0de9a,
+     16#009ee370c1e154f4,16#033131af3b8a7f88,16#032291baa45801e3,
+     16#00941fc2b45eb217,16#035d6a61fa101647,16#03fdb51f736f1bbc,
+     16#0232f7b98539faa0,16#0311b35319e3a61e,16#0048356b17860eb5,
+     16#01a205b2554ce71e,16#03f873ea136e29d6,16#003c67d5c3df5ffd,
+     16#00cd19e7a8641648,16#0149a8c54e4ba45e,16#0329498d134d2f6a,
+     16#03b69421ae65ee2b,16#01a8d20b59447429,16#006b2292571032a2,
+     16#00c193b17da22ba5,16#01faa7ab62181249,16#00acd401cd596a00,
+     16#005b5086c3531402,16#0259113d5d3d058d,16#00bef3f3ce4a43b2,
+     16#014837a4070b893c,16#00460a26ac2eeec1,16#026219a8b8c63d7e,
+     16#03c7b8ed032cf5a6,16#004da912a1fff131,16#0297de3716215741,
+     16#0079fb9b4c715466,16#00a73bad4ae5a356,16#0072e606c0d4ab86,
+     16#02374382d5f9bd2e];
+
 reference_jump_val(_) ->
     not_implemented.
 
diff --git a/lib/stdlib/test/rand_Xoroshiro928ss_dev.txt b/lib/stdlib/test/rand_Xoroshiro928ss_dev.txt
new file mode 100644
index 0000000000..150f37fcfa
--- /dev/null
+++ b/lib/stdlib/test/rand_Xoroshiro928ss_dev.txt
@@ -0,0 +1,343 @@
+%CopyrightBegin%
+
+Copyright Ericsson AB 2015-2017. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+%CopyrightEnd%
+
+
+Memorable facts from designing the Xoroshiro928** generator
+===========================================================
+AKA: exro928ss in the rand module
+
+Author: Raimo Niskanen, for the Erlang/OTP team @ Ericsson.
+
+Reference URL: http://vigna.di.unimi.it/ftp/papers/ScrambledLinear.pdf
+i.e the Xoroshiro1024 generator with ** scrambler:
+
+    int p;
+    uint64_t s[16];
+    
+    const int q = p;
+    const uint64_t s0 = s[p = (p + 1) & 15];
+    
+    uint64_t s15 = s[q];
+    
+    const uint64_t result_starstar = rotl(s0 * S, R) * T;
+    
+    s15 ^= s0;
+    s[q] = rotl(s0, A) ^ s15 ^ (s15 << B);
+    s[p] = rotl(s15, C);
+
+Where {S, R, T} = {5, 7, 9} as recommended in the paper.
+
+We want to scale down to 58 bit words (16 of them)
+so we get a generator with period 2^928 - 1.
+
+{A, B, C} were deduced as follows
+---------------------------------
+
+First, to find which triplets that give a full period generator
+one have to factor 2^928 - 1.
+
+https://www.alpertron.com.ar/ECM.HTM actually could do that
+and gave the result:
+
+    Value
+    2^928 - 1
+    
+    2269 007733 883335 972287 082669 296112 915239 349672 942191 252221 331572
+    442536 403137 824056 312817 862695 551072 066953 619064 625508 194663
+    368599 769448 406663 254670 871573 830845 597595 897613 333042 429214
+    224697 474472 410882 236254 024057 110212 260250 671521 235807 709272
+    244389 361641 091086 035023 229622 419455 (280 digits) = 3 × 5 × 17 × 59 ×
+    233 × 257 × 929 × 1103 × 2089 × 5569 × 8353 × 59393 × 65537 × 3 033169 ×
+    39 594977 × 107 367629 × 536 903681 × 748 264961 × 2245 984577 × 239
+    686663 718401 × 15 929619 591127 520827 829953 × 82280 195167 144119
+    832390 568177 × 6033 312171 721035 031651 315652 130497 (34 digits) × 18
+    774318 450142 955120 650303 957350 521748 903233 (44 digits) × 15 694604
+    006012 505869 851221 169365 594050 637743 819041 (50 digits) 
+
+Sebastiano Vigna from that calculated all full period triplets, at the
+end of this document, and the ones with the highest degree were:
+
+    23-25-12  411
+    36-2-35   411
+    55-5-54   411
+    14-19-11  415
+    34-37-5   415
+    37-3-56   415
+    55-11-54  417
+    30-3-41   419
+    11-45-50  423
+    50-19-47  423
+    52-27-13  427
+    54-9-25   433
+    56-43-35  433
+    44-9-45   441
+
+All these candidates were tested with TestU01-1.2.3:
+
+    http://simul.iro.umontreal.ca/testu01/tu01.html
+
+A plugin was created with parameters for {A, B, C} and, since
+TestU01 is a 32-bit test tool, with parameters to reverse
+the generated bits or not, and to take the 32 highest or lowest
+bits from the reversed or non-reversed 58 bit output.
+
+The generators were seeded with a SplitMix64 generator like the
+one used for seeding this generator in the rand module,
+taking the 58 lowest bits and wasting all zero values.
+
+3 runs were made with all candidates and all four bit selection variants.
+For these runs the seeder was initialized with 12345678, 876543212345678
+and 1234567890.
+
+After all these runs the candidate with the highest degree: 44-9-45
+had not gotten any suspicious p-value at all.  All the other
+got p-values around 5.0e-4 worst 9.8e-6 suggesting only random
+failures, so they would probably have worked about as well.
+
+Finally 44-9-45 was run through PractRand-0.93:
+
+    http://pracrand.sourceforge.net/
+
+Again, all 4 bit selection variants of 32 bits were run.
+Random failures with p-values around e-3..e-4 for the "smaller"
+tests, but for 8, 16 and 32 TB tests no anomalies were found
+(with the internal seeder masked to 58 bits):
+
+    Xoroshiro928High seed:        0x3178ec5d
+    Xoroshiro928Low seed:         0xa9a04fb9
+    Xoroshiro928ReverseHigh seed: 0xfa0bdbab
+    Xoroshiro928ReverseLow seed:  0xada51705
+
+
+Then, S. Vigna calculated the 2^512 jump coefficient as well
+as a 2^20 jump coefficient (for testing purposes) for 44-9-45.
+
+2^512:
+  { 0x44085302f77130ca, 0xba05381fdfd14902, 0x10a1de1d7d6813d2,
+    0xb83fe51a1eb3be19, 0xa81b0090567fd9f0, 0x5ac26d5d20f9b49f,
+    0x4ddd98ee4be41e01, 0x0657e19f00d4b358, 0xf02f778573cf0f0a,
+    0xb45a3a8a3cef3cc0, 0x6e62a33cc2323831, 0xbcb3b7c4cc049c53,
+    0x83f240c6007e76ce, 0xe19f5fc1a1504acd, 0x00000000b10773cb }
+
+2^20:
+  { 0xbdb966a3daf905e6, 0x644807a56270cf78, 0xda90f4a806c17e9e,
+    0x4a426866bfad3c77, 0xaf699c306d8e7566, 0x8ebc73c700b8b091,
+    0xc081a7bf148531fb, 0xdc4d3af15f8a4dfd, 0x90627c014098f4b6,
+    0x06df2eb1feaf0fb6, 0x5bdeb1a5a90f2e6b, 0xa480c5878c3549bd,
+    0xff45ef33c82f3d48, 0xa30bebc15fefcc78, 0x00000000cb3d181c }
+
+Standard jump function pseudocode:
+
+    Jump constant j = 0xb10773cb...44085302f77130ca
+    Generator state: s
+    New generator state: t = 0
+    foreach bit in j, low to high:
+        if the bit is one:
+            t ^= s
+        next s
+    s = t
+
+
+The complete list of full period constants
+------------------------------------------
+
+29-48-54	27	x^928 + x^874 + x^870 + x^840 + x^814 + x^784 + x^759 + x^750 + x^724 + x^720 + x^634 + x^630 + x^600 + x^574 + x^544 + x^519 + x^510 + x^484 + x^480 + x^390 + x^360 + x^270 + x^240 + x^150 + x^120 + x^30 + 1
+
+29-18-56	65	x^928 + x^870 + x^850 + x^840 + x^832 + x^821 + x^802 + x^791 + x^761 + x^750 + x^734 + x^731 + x^720 + x^712 + x^701 + x^686 + x^674 + x^671 + x^663 + x^641 + x^630 + x^611 + x^610 + x^603 + x^600 + x^596 + x^577 + x^566 + x^547 + x^524 + x^517 + x^510 + x^487 + x^480 + x^476 + x^464 + x^457 + x^446 + x^427 + x^423 + x^397 + x^390 + x^367 + x^363 + x^360 + x^356 + x^352 + x^341 + x^326 + x^322 + x^311 + x^281 + x^270 + x^251 + x^240 + x^236 + x^232 + x^221 + x^191 + x^161 + x^150 + x^131 + x^120 + x^30 + 1
+
+29-32-36	81	x^928 + x^874 + x^870 + x^840 + x^820 + x^819 + x^794 + x^790 + x^770 + x^765 + x^764 + x^760 + x^754 + x^750 + x^740 + x^739 + x^735 + x^734 + x^730 + x^709 + x^704 + x^674 + x^670 + x^665 + x^660 + x^650 + x^649 + x^635 + x^634 + x^619 + x^614 + x^605 + x^595 + x^585 + x^584 + x^579 + x^564 + x^555 + x^545 + x^540 + x^524 + x^515 + x^514 + x^495 + x^490 + x^485 + x^460 + x^455 + x^435 + x^425 + x^400 + x^395 + x^375 + x^370 + x^365 + x^340 + x^315 + x^310 + x^305 + x^300 + x^290 + x^285 + x^275 + x^260 + x^250 + x^245 + x^240 + x^215 + x^190 + x^180 + x^170 + x^150 + x^130 + x^120 + x^115 + x^105 + x^100 + x^75 + x^40 + x^30 + 1
+
+39-10-20	105	x^928 + x^898 + x^870 + x^841 + x^840 + x^808 + x^783 + x^782 + x^781 + x^780 + x^778 + x^754 + x^752 + x^724 + x^721 + x^720 + x^696 + x^692 + x^688 + x^667 + x^666 + x^661 + x^660 + x^658 + x^638 + x^636 + x^632 + x^609 + x^607 + x^606 + x^605 + x^604 + x^601 + x^600 + x^580 + x^578 + x^576 + x^572 + x^568 + x^549 + x^548 + x^541 + x^540 + x^538 + x^516 + x^512 + x^489 + x^485 + x^484 + x^481 + x^480 + x^456 + x^452 + x^448 + x^429 + x^428 + x^421 + x^420 + x^418 + x^400 + x^398 + x^396 + x^392 + x^368 + x^365 + x^364 + x^336 + x^328 + x^319 + x^318 + x^315 + x^314 + x^298 + x^286 + x^278 + x^276 + x^274 + x^255 + x^254 + x^249 + x^245 + x^228 + x^226 + x^220 + x^208 + x^199 + x^198 + x^189 + x^188 + x^178 + x^168 + x^166 + x^160 + x^129 + x^128 + x^108 + x^100 + x^88 + x^79 + x^78 + x^69 + x^68 + x^58 + x^40 + 1
+
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