Merge pull request #1969 from RaimoNiskanen/raimo/stdlib/rand-xorshift116ss

OTP-14731 Implement 'exsss' (Xorshift116**) as new default 'rand' algorithm

The new algorithm is a combination of the Xorshift116 ('exsp') state update and a new scrambler  "StarStar" from the 2018 paper "Scrambled Linear Pseudorandom Number Generators" by David Blackman and Sebastiano Vigna. This combination should not have the caveat of weak low bits that the previous default algorithm(s) have had, with the cost of about 10% lower speed.

1 files changed, 63 insertions, 8 deletions

diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl
index 6c9fab51dc..7685c17967 100644
--- a/lib/stdlib/test/rand_SUITE.erl
+++ b/lib/stdlib/test/rand_SUITE.erl
@@ -79,7 +79,7 @@ test() ->
       end, Tests).
 
 algs() ->
-    [exrop, exsp, exs1024s, exs64, exsplus, exs1024, exro928ss].
+    [exsss, exrop, exsp, exs1024s, exs64, exsplus, exs1024, exro928ss].
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -276,7 +276,7 @@ gen(Algo) ->
         if
             Algo =:= exs64 -> %% Printed with orig 'C' code and this seed
                 rand:seed_s(exs64, [12345678]);
-            Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop ->
+            Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop; Algo =:= exsss ->
                 %% Printed with orig 'C' code and this seed
                 rand:seed_s(Algo, [12345678,12345678]);
             Algo =:= exs1024; Algo =:= exs1024s; Algo =:= exro928ss ->
@@ -438,7 +438,7 @@ stats_standard_normal_box_muller(Config) when is_list(Config) ->
                     ([S|Z]) ->
                         {Z, [S]}
                 end,
-            State = [rand:seed(exrop)],
+            State = [rand:seed(exsss)],
             stats_standard_normal(NormalS, State, 3)
     catch error:_ ->
             {skip, "math:erfc/1 not supported"}
@@ -463,7 +463,7 @@ stats_standard_normal_box_muller_2(Config) when is_list(Config) ->
                     ([S|Z]) ->
                         {Z, [S]}
                 end,
-            State = [rand:seed(exrop)],
+            State = [rand:seed(exsss)],
             stats_standard_normal(NormalS, State, 3)
     catch error:_ ->
             {skip, "math:erfc/1 not supported"}
@@ -475,7 +475,7 @@ stats_standard_normal(Config) when is_list(Config) ->
     try math:erfc(1.0) of
         _ ->
             stats_standard_normal(
-              fun rand:normal_s/1, rand:seed_s(exrop), Retries)
+              fun rand:normal_s/1, rand:seed_s(exsss), Retries)
     catch error:_ ->
             {skip, "math:erfc/1 not supported"}
     end.
@@ -1071,7 +1071,7 @@ do_measure(_Config) ->
                     end,
                     State)
           end,
-          exrop, TMarkNormalFloat),
+          exsss, TMarkNormalFloat),
     ok.
 
 -define(LOOP_MEASURE, (?LOOP div 5)).
@@ -1170,7 +1170,7 @@ gen_jump_1(Algo) ->
 	    catch
 		error:not_implemented -> [error_not_implemented]
 	    end;
-	_ when Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop ->
+	_ when Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop; Algo =:= exsss ->
 	    %% Printed with orig 'C' code and this seed
 	    gen_jump_2(
 	      rand:seed_s(Algo, [12345678,12345678]));
@@ -1224,7 +1224,7 @@ gen_jump_p1(Algo) ->
 	    catch
 		error:not_implemented -> [error_not_implemented]
 	    end;
-	_ when Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop ->
+	_ when Algo =:= exsplus; Algo =:= exsp; Algo =:= exrop; Algo =:= exsss ->
 	    %% Printed with orig 'C' code and this seed
 	    gen_jump_p2(
 	      rand:seed(Algo, [12345678,12345678]));
@@ -1377,6 +1377,34 @@ reference_val(exsplus) ->
      16#3dd493b8012970f,16#be13bed1e00e5c,16#ceef033b74ae10,16#3da38c6a50abe03,
      16#15cbd1a421c7a8c,16#22794e3ec6ef3b1,16#26154d26e7ea99f,16#3a66681359a6ab6];
 
+reference_val(exsss) ->
+    [16#108e8d5b01,16#33b72092117209a,16#224d4d2961a2d0a,16#2c4c81aac3da48d,
+     16#2f4bc39bfc36f3a,16#41826d4c4d243a,16#19871b8bb4e23ee,16#3e2112cdf9384b1,
+     16#69801943bf91ab,16#2de1a603c31ec45,16#a90ca1991b831e,16#51ca29571a69a7,
+     16#93ce3e511906cf,16#93ebc5768aef75,16#2412f284b902ae7,16#1ac10e758410c52,
+     16#3f32494560368f6,16#39a5e82dcf0de95,16#3f4b14d59cc6a21,16#3174668db0b36ae,
+     16#1449812fb8bd54e,16#eaca1f8ece51e1,16#2564b2545fd23c1,16#3cf3a2d2217e0d7,
+     16#226f4164ba1d054,16#10dac9ae207ceef,16#17f2c4b2d40fcb9,16#1c1b282d386fdcb,
+     16#a264f450ba2912,16#2a0a1dd67e52666,16#2be84eb835cb1e1,16#2a1cd9aa16ccc37,
+     16#7dd5e8c2b3f490,16#254a3db4976c05b,16#2a0a67971ec1e63,16#13a0cbf7c0eed8a,
+     16#3192d7edc0a20bc,16#2705ad756292e84,16#3ec429a18119c81,16#25944b38baa975b,
+     16#291dcc43e3256f4,16#30d10b759237db,16#c1522a652058a,16#8ef1e9378381e6,
+     16#1f442f33c2439f4,16#186087710a73818,16#12887f94b2b8387,16#3e42e8b1f3c9b4b,
+     16#e462859d55f9d8,16#2356ae85be908de,16#15e96a927b3bc52,16#35c6dc52511ce46,
+     16#7bc0624ce66e01,16#33ab7d95b738322,16#26f01effc182aa0,16#1b66ae7eaafea88,
+     16#278f3dc14943b90,16#22178bc8d8faf28,16#396c37d53c11985,16#5e0d79d0b10f18,
+     16#1be3de3b5675ec,16#d4db298f1f4b50,16#2da6cb99bb5c7b1,16#130b2dc17d03be8,
+     16#f1847e7e059e9f,16#2da6591788326e7,16#222e4a18c24211c,16#949213ca49baab,
+     16#b5129fec56f6a2,16#30f25f1e926f43e,16#1ddd8d04445fb4d,16#15995b542514150,
+     16#1595fe879296296,16#e2f237a488453b,16#23e5cd2d6047890,16#3a5dc88fc954666,
+     16#89bca9969b103,16#5e6893cd35dc63,16#1fed534feeeef5a,16#26f40e2147ee558,
+     16#30c131a00625837,16#2618a7e617422e9,16#23630b297e45e7,16#1143b17502f3219,
+     16#15607dac41168da,16#2886bdc314b3fb8,16#465d1cc1536546,16#30b09123e3a02e4,
+     16#245a375f810be52,16#6a1b0792376a03,16#221425f59f2470f,16#867ce16dfac81c,
+     16#9c62d95fae9b58,16#380381db1394426,16#34908dedc01c324,16#1f0ff517089b561,
+     16#1571366dd873d32,16#3ee353dc56e192,16#15a1dee8d889b11,16#41036ad76d9888
+    ];
+
 reference_val(exsp) ->
     reference_val(exsplus);
 reference_val(exs1024s) ->
@@ -1517,6 +1545,33 @@ reference_jump_val(exsplus) ->
      12504080415362731, 45083100453836317, 270968267812126657, 93505647407734103,
      252852934678537969, 258758309277167202, 74250882143432077, 141629095984552833];
 
+reference_jump_val(exsss) ->
+    [16#304ae783d40db2b,16#1dfb196b3a5600a,16#2a24116effc6a0d,16#1f138d68c56725,
+     16#9360a445e2f989,16#32ed8080390e242,16#294ca85a270cff6,16#1418e6296a88bf,
+     16#114fae3dc578ba7,16#479c42c760eb72,16#334a40655df22d6,16#e7a85dd4d37d72,
+     16#181db16c8925c77,16#1b8a5a8afd16cbd,16#329107bf9777a39,16#2fc915c08535e42,
+     16#16696d142c6078,16#2e2a2601c919448,16#2246150d1000568,16#26109007cb3dd44,
+     16#3761360723e3175,16#169abd352db74de,16#1c97d520983684f,16#12455f0adee8c66,
+     16#46719cff00622d,16#1fc92792ed4e437,16#18e2edae21affb5,16#3a67fa9e3e7d46e,
+     16#1313fdc2728aa74,16#1c1a2b577581db8,16#db49357ea196b1,16#10e219a21d93fc7,
+     16#3c43abede083666,16#3eef5055a58bbf9,16#1975056f95d90e3,16#3916c133ab16d87,
+     16#2bc0bea891c26f1,16#391e4b369fc6b36,16#183f83155a359f6,16#1d9f137e9d2e488,
+     16#ef084de5f4cd3c,16#36a9cf7e29e55d3,16#19eca704e0409a7,16#1bdb99902896c69,
+     16#21777e2ad128203,16#5d0369ec0563e4,16#36db40b863bd74a,16#33feb71b7515159,
+     16#208d923ce26f257,16#3841b32891c082d,16#2748f224c2ba226,16#2fcd93b2daf79bb,
+     16#2c8e6cacad58ec4,16#39850131a1a85f,16#134648d6eea624d,16#2e102e197d5725c,
+     16#12ac280fa744758,16#1c18266c7442d16,16#22b5f91b15fe17e,16#316740ca870f7c8,
+     16#720ed4836c426,16#1aac0f738d04f8c,16#34fcd2a647b462c,16#3d430ac755114a3,
+     16#3692e3670fdf2a,16#265279ab0fc0a15,16#10bd883dee80945,16#10e7843413175e4,
+     16#b291deba08cee2,16#3915a8234caf11,16#34b911b96707dbd,16#ae63fcda15fde6,
+     16#b13b9091e82e41,16#29de1b6d70dc04f,16#23fbcbc409617e8,16#1389a0738061066,
+     16#360f39af790f5d1,16#f436da2a7d12f5,16#2d06ba8da21e08,16#3601a6492b887d,
+     16#2b2590b8c6cc186,16#f8d613b6904464,16#e5456786e46b78,16#201b8b1f96ed80c,
+     16#1b75b86d9b843f2,16#2e8bfaa7243a630,16#125ff068a78c3b4,16#3875a28c48bd26e,
+     16#f09a06941fc9d7,16#107c4de8ca77744,16#357c34144bb9ed6,16#3ccc55d3ebb3378,
+     16#28db7cea7d3fdee,16#3197fd0b49f6370,16#11af6fedb708ea6,16#2bde0382e37469e,
+     16#10666171abddb3f,16#1a8876c1f4e78a8,16#169c0efd4422043,16#1501c49abf0440f];
+
 reference_jump_val(exs1024) ->
     [2655961906500790629, 17003395417078685063, 10466831598958356428, 7603399148503548021,
      1650550950190587188, 12294992315080723704, 15743995773860389219, 5492181000145247327,