File 2956-Tweak-mwc59-generator-constants.patch of Package erlang

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File 2956-Tweak-mwc59-generator-constants.patch of Package erlang (Revision 22913b88332bf024e9a94e5904b07e48)

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From f27eafccf2b372cf61f3a1fb4d607b6d69569a41 Mon Sep 17 00:00:00 2001
From: Raimo Niskanen <raimo@erlang.org>
Date: Mon, 9 May 2022 15:51:46 +0200
Subject: [PATCH 6/6] Tweak mwc59 generator constants

After thorough testing by Sebastiano Vigna we decided on the
scramblers Xorshift 8 as a fast scrambler with still some
small remaining problems in 2- and 3-dimensional collision
and birthday spacings tests, and Xorshift 4 followed by
Xorshift 27 as a thorough scrambler that passes extensive
PRNG tests.
---
 lib/stdlib/doc/src/rand.xml    | 69 ++++++++++++++++++++++------------
 lib/stdlib/src/rand.erl        | 31 +++++++--------
 lib/stdlib/test/rand_SUITE.erl | 48 +++++++++++------------
 3 files changed, 81 insertions(+), 67 deletions(-)

diff --git a/lib/stdlib/doc/src/rand.xml b/lib/stdlib/doc/src/rand.xml
index 0465ee21e1..25dec14a51 100644
--- a/lib/stdlib/doc/src/rand.xml
+++ b/lib/stdlib/doc/src/rand.xml
@@ -909,29 +909,49 @@ end.</pre>
 <c><anno>CX1</anno>&nbsp;=&nbsp;16#7fa6502&nbsp;*&nbsp;X&nbsp;+&nbsp;C</c>
 
 
- The quality of the generated bits is best in the low end;
- the low 16 bits of the generator state
- <c><anno>CX1</anno></c> can be used without any scrambling.
- <seemfa marker="#mwc59_value/1"><c>mwc59_value</c></seemfa>
- is a fast scrambler that gives 32 high quality bits.
- With the slightly slower
- <seemfa marker="#mwc59_full_value/1">
- <c>mwc59_full_value</c>
+ Because the generator uses a multiplier that is
+ a power of 2 it gets statistical flaws for collision tests
+ and birthday spacings tests in 2 and 3 dimensions,
+ so the state should be scrambled, to create
+ an output value.
+ 
+ The quality of the state bits <c><anno>CX1</anno></c>
+ as a random value is far from good, but if speed is
+ much more important than these imperfections, the lowest
+ say 16 bits of the generator state could be used
+ without scrambling.
+ 
+ 
+ Function
+ <seemfa marker="#mwc59_fast_value/1">
+ <c>mwc59_fast_value</c>
 </seemfa>
- all 58 returned bits are of good quality, and
+ is a fast scrambler that gives 32 decent bits, but still
+ some problems in 2- and 3-dimensional collision tests
+ show through.
+ The slightly slower
+ <seemfa marker="#mwc59_value/1">
+ <c>mwc59_value</c>
+ </seemfa>
+ scrambler returns 58 bits of very good quality, and
 <seemfa marker="#mwc59_float/1"><c>mwc59_float</c></seemfa>
- returns a good quality <c>float()</c>.
+ returns a <c>float()</c> of very good quality.
 
 
 On a typical 64 bit Erlang VM this generator executes
 in below 8% (1/13) of the time
- for the default algorithm in this module.
- Adding the
- <seemfa marker="#mwc59_value/1"><c>mwc59_value</c></seemfa>
+ for the default algorithm in the
+ <seeerl marker="#plug_in_api">
+ plug-in framework API
+ </seeerl>
+ of this module. With the
+ <seemfa marker="#mwc59_fast_value/1">
+ <c>mwc59_fast_value</c>
+ </seemfa>
 scrambler the total time becomes 16% (1/6),
 and with
- <seemfa marker="#mwc59_full_value/1">
- <c>mwc59_full_value</c>
+ <seemfa marker="#mwc59_value/1">
+ <c>mwc59_value</c>
 </seemfa>
 it becomes 20% (1/5) of the time for the default algorithm.
 With
@@ -945,9 +965,8 @@ end.</pre>
 applications. It has a much shorter period
 than the default generator, which in itself
 is a quality concern, although when used with the
- value scramblers it passes strict PRNG tests
- (most of TestU01 BigCrush and PractRand 2 TB).
- The generator is significantly faster than
+ value scramblers it passes strict PRNG tests.
+ The generator is much faster than
 <seemfa marker="#exsp_next/1"><c>exsp_next/1</c></seemfa>
 but with a bit lower quality.
 
@@ -955,34 +974,34 @@ end.</pre>
 </desc>
 </func>
 <func>
- <name name="mwc59_value" arity="1" since="OTP 25.0"/>
+ <name name="mwc59_fast_value" arity="1" since="OTP 25.0"/>
 <fsummary>Return the generator value.</fsummary>
 <desc>
 
 Returns a 58-bit value <c><anno>V</anno></c>
 from a generator state <c><anno>CX</anno></c>.
 The generator state is scrambled using
- a 10-bit xorshift which masks
+ an 8-bit xorshift which masks
 the statistical imperfecions of the base generator
 <seemfa marker="#mwc59/1"><c>mwc59</c></seemfa>
- enough that the 32 lowest bits are of good quality.
+ enough that the 32 lowest bits are of decent quality.
 It is not recommended to generate numbers
 in a range > 2^32 with this function.
 
 </desc>
 </func>
 <func>
- <name name="mwc59_full_value" arity="1" since="OTP 25.0"/>
+ <name name="mwc59_value" arity="1" since="OTP 25.0"/>
 <fsummary>Return the generator value.</fsummary>
 <desc>
 
 Returns a 58-bit value <c><anno>V</anno></c>
 from a generator state <c><anno>CX</anno></c>.
 The generator state is scrambled using
- an 8-bit followed by a 16-bit xorshift which masks
+ an 4-bit followed by a 27-bit xorshift, which masks
 the statistical imperfecions of the base generator
 <seemfa marker="#mwc59/1"><c>mwc59</c></seemfa>
- enough that all 58 bits are of good quality.
+ enough that all 58 bits are of very good quality.
 Beware of bias in the generated numbers if
 generating on a non power of 2 range too close to 2^58.
 
@@ -998,7 +1017,7 @@ end.</pre>
 as a <c>float()</c>.
 The generator state is scrambled as with
 <seemfa marker="#mwc59_value/1">
- <c>mwc59_full_value/1</c>
+ <c>mwc59_value/1</c>
 </seemfa>
 before converted to a <c>float()</c>.
 
diff --git a/lib/stdlib/src/rand.erl b/lib/stdlib/src/rand.erl
index 47766f2547..6c85a79323 100644
--- a/lib/stdlib/src/rand.erl
+++ b/lib/stdlib/src/rand.erl
@@ -38,7 +38,7 @@
 
 %% Utilities
 -export([exsp_next/1, exsp_jump/1, splitmix64_next/1,
- mwc59/1, mwc59_value/1, mwc59_full_value/1, mwc59_float/1,
+ mwc59/1, mwc59_fast_value/1, mwc59_value/1, mwc59_float/1,
 mwc59_seed/0, mwc59_seed/1]).
 
 %% Test, dev and internal
@@ -1478,8 +1478,8 @@ dummy_seed({A1, A2, A3}) ->
 %% The chosen parameters are:
 %% A = 16#7fa6502
 %% B = 32
-%% Single Xorshift: 16
-%% Double Xorshift: 8, 16
+%% Single Xorshift: 8
+%% Double Xorshift: 4, 27
 %%
 %% These parameters gives the MWC "digit" size 32 bits
 %% which gives them theoretical statistical guarantees,
@@ -1490,19 +1490,13 @@ dummy_seed({A1, A2, A3}) ->
 %% be masked or rem:ed out.
 %%
 %% =====================================================================
-%%% -define(MWC_A, (6)).
-%%% -define(MWC_B, (3)).
-
-%%% -define(MWC59_A, (16#20075dc0)). % 16#1ffb0729
-%%% -define(MWC59_B, (29)).
-
--define(MWC59_A, (16#7fa6502)). % 16#7f17555 16#3f35301
+-define(MWC59_A, (16#7fa6502)).
 -define(MWC59_B, (32)).
 -define(MWC59_P, ((?MWC59_A bsl ?MWC59_B) - 1)).
 
--define(MWC59_XS, 16).
--define(MWC59_XS1, 8).
--define(MWC59_XS2, 16).
+-define(MWC59_XS, 8).
+-define(MWC59_XS1, 4).
+-define(MWC59_XS2, 27).
 
 -type mwc59_state() :: 1..?MWC59_P-1.
 
@@ -1513,13 +1507,13 @@ mwc59(CX0) -> % when is_integer(CX0), 1 =< CX0, CX0 < ?MWC59_P ->
 X = ?MASK(?MWC59_B, CX),
 ?MWC59_A * X + C.
 
--spec mwc59_value(CX :: mwc59_state()) -> V :: 0..?MASK(58).
-mwc59_value(CX1) -> % when is_integer(CX0), 1 =< CX0, CX0 < ?MWC59_P ->
+-spec mwc59_fast_value(CX :: mwc59_state()) -> V :: 0..?MASK(58).
+mwc59_fast_value(CX1) -> % when is_integer(CX1), 1 =< CX1, CX1 < ?MWC59_P ->
 CX = ?MASK(58, CX1),
 CX bxor ?BSL(58, CX, ?MWC59_XS).
 
--spec mwc59_full_value(CX :: mwc59_state()) -> V :: 0..?MASK(58).
-mwc59_full_value(CX1) -> % when is_integer(CX0), 1 =< CX0, CX0 < ?MWC59_P ->
+-spec mwc59_value(CX :: mwc59_state()) -> V :: 0..?MASK(58).
+mwc59_value(CX1) -> % when is_integer(CX1), 1 =< CX1, CX1 < ?MWC59_P ->
 CX = ?MASK(58, CX1),
 CX2 = CX bxor ?BSL(58, CX, ?MWC59_XS1),
 CX2 bxor ?BSL(58, CX2, ?MWC59_XS2).
@@ -1528,7 +1522,8 @@ mwc59_full_value(CX1) -> % when is_integer(CX0), 1 =< CX0, CX0 < ?MWC59_P ->
 mwc59_float(CX1) ->
 CX = ?MASK(53, CX1),
 CX2 = CX bxor ?BSL(53, CX, ?MWC59_XS1),
- (CX2 bxor ?BSL(53, CX2, ?MWC59_XS2)) * ?TWO_POW_MINUS53.
+ CX3 = CX2 bxor ?BSL(53, CX2, ?MWC59_XS2),
+ CX3 * ?TWO_POW_MINUS53.
 
 -spec mwc59_seed() -> CX :: mwc59_state().
 mwc59_seed() ->
diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl
index eabb9396ad..c03a687b3a 100644
--- a/lib/stdlib/test/rand_SUITE.erl
+++ b/lib/stdlib/test/rand_SUITE.erl
@@ -216,11 +216,11 @@ mwc59_api(Config) when is_list(Config) ->
 mwc59_api(CX0, 0) ->
 CX = 216355295181821136,
 {CX, CX} = {CX0, CX},
- V0 = rand:mwc59_value(CX0),
- V = 215617979550160080,
+ V0 = rand:mwc59_fast_value(CX0),
+ V = 262716604851324112,
 {V, V} = {V0, V},
- W0 = rand:mwc59_full_value(CX0),
- W = 70209996550472912,
+ W0 = rand:mwc59_value(CX0),
+ W = 240206843777063376,
 {W, W} = {W0, W},
 F0 = rand:mwc59_float(CX0),
 F = (W band ((1 bsl 53) - 1)) * (1 / (1 bsl 53)),
@@ -228,8 +228,8 @@ mwc59_api(CX0, 0) ->
 ok;
 mwc59_api(CX, N)
 when is_integer(CX), 1 =< CX, CX < (16#7fa6502 bsl 32) - 1 ->
- V = rand:mwc59_value(CX),
- W = rand:mwc59_full_value(CX),
+ V = rand:mwc59_fast_value(CX),
+ W = rand:mwc59_value(CX),
 F = rand:mwc59_float(CX),
 true = 0 =< V,
 true = V < 1 bsl 58,
@@ -1129,13 +1129,13 @@ do_measure(Iterations) ->
 fun (St0) ->
 St1 = rand:mwc59(St0),
 %% Just a 'rem' with slightly skewed distribution
- case (rand:mwc59_value(St1) rem Range) + 1 of
+ case (rand:mwc59_fast_value(St1) rem Range) + 1 of
 R when is_integer(R), 0 < R, R =< Range ->
 St1
 end
 end
 end,
- {mwc59,value_mod}, Iterations,
+ {mwc59,fast_mod}, Iterations,
 TMarkUniformRange10000, OverheadUniformRange1000),
 _ =
 measure_1(
@@ -1144,13 +1144,13 @@ do_measure(Iterations) ->
 fun (St0) ->
 St1 = rand:mwc59(St0),
 %% Just a 'rem' with slightly skewed distribution
- case (rand:mwc59_full_value(St1) rem Range) + 1 of
+ case (rand:mwc59_value(St1) rem Range) + 1 of
 R when is_integer(R), 0 < R, R =< Range ->
 St1
 end
 end
 end,
- {mwc59,full_mod}, Iterations,
+ {mwc59,value_mod}, Iterations,
 TMarkUniformRange10000, OverheadUniformRange1000),
 _ =
 measure_1(
@@ -1231,13 +1231,13 @@ do_measure(Iterations) ->
 Range = 1 bsl 32,
 fun (St0) ->
 St1 = rand:mwc59(St0),
- case rand:mwc59_value(St1) band ((1 bsl 32)-1) of
+ case rand:mwc59_fast_value(St1) band ((1 bsl 32)-1) of
 R when is_integer(R), 0 =< R, R < Range ->
 St1
 end
 end
 end,
- {mwc59,value_mask}, Iterations,
+ {mwc59,fast_mask}, Iterations,
 TMarkUniform32Bit, OverheadUniform32Bit),
 _ =
 measure_1(
@@ -1246,7 +1246,7 @@ do_measure(Iterations) ->
 fun (St0) ->
 St1 = rand:mwc59(St0),
 case
- rand:mwc59_full_value(St1) band
+ rand:mwc59_value(St1) band
 ((1 bsl 32)-1)
 of
 R when is_integer(R), 0 =< R, R < Range ->
@@ -1254,7 +1254,7 @@ do_measure(Iterations) ->
 end
 end
 end,
- {mwc59,full_mask}, Iterations,
+ {mwc59,value_mask}, Iterations,
 TMarkUniform32Bit, OverheadUniform32Bit),
 _ =
 measure_1(
@@ -1372,14 +1372,14 @@ do_measure(Iterations) ->
 Range = 1 bsl 58,
 fun (St0) ->
 St1 = rand:mwc59(St0),
- V = rand:mwc59_value(St1),
+ V = rand:mwc59_fast_value(St1),
 if
 is_integer(V), 0 =< V, V < Range ->
 St1
 end
 end
 end,
- {mwc59,value}, Iterations,
+ {mwc59,fast}, Iterations,
 TMarkUniformFullRange, OverheadUniformFullRange),
 _ =
 measure_1(
@@ -1387,14 +1387,14 @@ do_measure(Iterations) ->
 Range = 1 bsl 58,
 fun (St0) ->
 St1 = rand:mwc59(St0),
- V = rand:mwc59_full_value(St1),
+ V = rand:mwc59_value(St1),
 if
 is_integer(V), 0 =< V, V < Range ->
 St1
 end
 end
 end,
- {mwc59,full_value}, Iterations,
+ {mwc59,value}, Iterations,
 TMarkUniformFullRange, OverheadUniformFullRange),
 _ =
 measure_1(
@@ -1791,19 +1791,19 @@ mwc59_bytes(N, R0, Bin) when is_integer(N), 7*4 =< N ->
 R2 = rand:mwc59(R1),
 R3 = rand:mwc59(R2),
 R4 = rand:mwc59(R3),
- V1 = rand:mwc59_value(R1),
- V2 = rand:mwc59_value(R2),
- V3 = rand:mwc59_value(R3),
- V4 = rand:mwc59_value(R4),
+ V1 = rand:mwc59_fast_value(R1),
+ V2 = rand:mwc59_fast_value(R2),
+ V3 = rand:mwc59_fast_value(R3),
+ V4 = rand:mwc59_fast_value(R4),
 mwc59_bytes(N-7*4, R4, <<Bin/binary, V1:56, V2:56, V3:56, V4:56>>);
 mwc59_bytes(N, R0, Bin) when is_integer(N), 7 =< N ->
 R1 = rand:mwc59(R0),
- V = rand:mwc59_value(R1),
+ V = rand:mwc59_fast_value(R1),
 mwc59_bytes(N-7, R1, <<Bin/binary, V:56>>);
 mwc59_bytes(N, R0, Bin) when is_integer(N), 0 < N ->
 R1 = rand:mwc59(R0),
 Bits = N bsl 3,
- V = rand:mwc59_value(R1),
+ V = rand:mwc59_fast_value(R1),
 {<<Bin/binary, V:Bits>>, R1};
 mwc59_bytes(0, R0, Bin) ->
 {Bin, R0}.
-- 
2.35.3

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File 2956-Tweak-mwc59-generator-constants.patch of Package erlang (Revision 22913b88332bf024e9a94e5904b07e48)

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