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-rw-r--r--lib/stdlib/test/rand_SUITE.erl776
1 files changed, 593 insertions, 183 deletions
diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl
index 432293b656..3d3241b33d 100644
--- a/lib/stdlib/test/rand_SUITE.erl
+++ b/lib/stdlib/test/rand_SUITE.erl
@@ -29,11 +29,17 @@
basic_stats_uniform_1/1, basic_stats_uniform_2/1,
basic_stats_standard_normal/1,
basic_stats_normal/1,
+ stats_standard_normal_box_muller/1,
+ stats_standard_normal_box_muller_2/1,
+ stats_standard_normal/1,
+ uniform_real_conv/1,
plugin/1, measure/1,
reference_jump_state/1, reference_jump_procdict/1]).
-export([test/0, gen/1]).
+-export([uniform_real_gen/1, uniform_gen/2]).
+
-include_lib("common_test/include/ct.hrl").
-define(LOOP, 1000000).
@@ -46,7 +52,7 @@ all() ->
[seed, interval_int, interval_float,
api_eq,
reference,
- {group, basic_stats},
+ {group, basic_stats}, uniform_real_conv,
plugin, measure,
{group, reference_jump}
].
@@ -54,7 +60,10 @@ all() ->
groups() ->
[{basic_stats, [parallel],
[basic_stats_uniform_1, basic_stats_uniform_2,
- basic_stats_standard_normal]},
+ basic_stats_standard_normal,
+ stats_standard_normal_box_muller,
+ stats_standard_normal_box_muller_2,
+ stats_standard_normal]},
{reference_jump, [parallel],
[reference_jump_state, reference_jump_procdict]}].
@@ -80,7 +89,7 @@ test() ->
end, Tests).
algs() ->
- [exs64, exsplus, exsp, exrop, exs1024, exs1024s].
+ [exrop, exsp, exs1024s, exs64, exsplus, exs1024].
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -101,7 +110,7 @@ seed_1(Alg) ->
_ = rand:uniform(),
S00 = get(rand_seed),
erase(),
- _ = rand:uniform(),
+ _ = rand:uniform_real(),
false = S00 =:= get(rand_seed), %% hopefully
%% Choosing algo and seed
@@ -228,11 +237,13 @@ interval_float(Config) when is_list(Config) ->
interval_float_1(0) -> ok;
interval_float_1(N) ->
X = rand:uniform(),
+ Y = rand:uniform_real(),
if
- 0.0 =< X, X < 1.0 ->
+ 0.0 =< X, X < 1.0, 0.0 < Y, Y < 1.0 ->
ok;
true ->
- io:format("X=~p 0=<~p<1.0~n", [X,X]),
+ io:format("X=~p 0.0=<~p<1.0~n", [X,X]),
+ io:format("Y=~p 0.0<~p<1.0~n", [Y,Y]),
exit({X, rand:export_seed()})
end,
interval_float_1(N-1).
@@ -334,7 +345,13 @@ basic_stats_normal(Config) when is_list(Config) ->
IntendedMeanVariancePairs).
basic_uniform_1(N, S0, Sum, A0) when N > 0 ->
- {X,S} = rand:uniform_s(S0),
+ {X,S} =
+ case N band 1 of
+ 0 ->
+ rand:uniform_s(S0);
+ 1 ->
+ rand:uniform_real_s(S0)
+ end,
I = trunc(X*100),
A = array:set(I, 1+array:get(I,A0), A0),
basic_uniform_1(N-1, S, Sum+X, A);
@@ -399,6 +416,337 @@ normal_s(Mean, Variance, State0) when Mean == 0, Variance == 1 ->
normal_s(Mean, Variance, State0) ->
rand:normal_s(Mean, Variance, State0).
+
+
+-dialyzer({no_improper_lists, stats_standard_normal_box_muller/1}).
+stats_standard_normal_box_muller(Config) when is_list(Config) ->
+ try math:erfc(1.0) of
+ _ ->
+ TwoPi = 2.0 * math:pi(),
+ NormalS =
+ fun
+ ([S0]) ->
+ {U1, S1} = rand:uniform_real_s(S0),
+ R = math:sqrt(-2.0 * math:log(U1)),
+ {U2, S2} = rand:uniform_s(S1),
+ T = TwoPi * U2,
+ Z0 = R * math:cos(T),
+ Z1 = R * math:sin(T),
+ {Z0, [S2|Z1]};
+ ([S|Z]) ->
+ {Z, [S]}
+ end,
+ State = [rand:seed(exrop)],
+ stats_standard_normal(NormalS, State)
+ catch error:_ ->
+ {skip, "math:erfc/1 not supported"}
+ end.
+
+-dialyzer({no_improper_lists, stats_standard_normal_box_muller_2/1}).
+stats_standard_normal_box_muller_2(Config) when is_list(Config) ->
+ try math:erfc(1.0) of
+ _ ->
+ TwoPi = 2.0 * math:pi(),
+ NormalS =
+ fun
+ ([S0]) ->
+ {U0, S1} = rand:uniform_s(S0),
+ U1 = 1.0 - U0,
+ R = math:sqrt(-2.0 * math:log(U1)),
+ {U2, S2} = rand:uniform_s(S1),
+ T = TwoPi * U2,
+ Z0 = R * math:cos(T),
+ Z1 = R * math:sin(T),
+ {Z0, [S2|Z1]};
+ ([S|Z]) ->
+ {Z, [S]}
+ end,
+ State = [rand:seed(exrop)],
+ stats_standard_normal(NormalS, State)
+ catch error:_ ->
+ {skip, "math:erfc/1 not supported"}
+ end.
+
+
+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))
+ catch error:_ ->
+ {skip, "math:erfc/1 not supported"}
+ end.
+%%
+stats_standard_normal(Fun, S) ->
+%%%
+%%% ct config:
+%%% {rand_SUITE, [{stats_standard_normal,[{seconds, 8}, {std_devs, 4.2}]}]}.
+%%%
+ Seconds = ct:get_config({?MODULE, ?FUNCTION_NAME, seconds}, 8),
+ StdDevs =
+ ct:get_config(
+ {?MODULE, ?FUNCTION_NAME, std_devs},
+ 4.2), % probability erfc(4.2/sqrt(2)) (1/37465) to fail a bucket
+%%%
+ ct:timetrap({seconds, Seconds + 120}),
+ %% Buckets is chosen to get a range where the the probability to land
+ %% in the top catch-all bucket is not vanishingly low, but with
+ %% these values it is about 1/25 of the probability for the low bucket
+ %% (closest to 0).
+ %%
+ %% Rounds is calculated so the expected value for the low
+ %% bucket will be at least TargetHits.
+ %%
+ InvDelta = 512,
+ Buckets = 4 * InvDelta, % 4 std devs range
+ TargetHits = 1024,
+ Sqrt2 = math:sqrt(2.0),
+ W = InvDelta * Sqrt2,
+ P0 = math:erf(1 / W),
+ Rounds = TargetHits * ceil(1.0 / P0),
+ Histogram = array:new({default, 0}),
+ StopTime = erlang:monotonic_time(second) + Seconds,
+ ct:pal(
+ "Running standard normal test against ~w std devs for ~w seconds...",
+ [StdDevs, Seconds]),
+ {PositiveHistogram, NegativeHistogram, Outlier, TotalRounds} =
+ stats_standard_normal(
+ InvDelta, Buckets, Histogram, Histogram, 0.0,
+ Fun, S, Rounds, StopTime, Rounds, 0),
+ Precision = math:sqrt(TotalRounds * P0) / StdDevs,
+ TopP = math:erfc(Buckets / W),
+ TopPrecision = math:sqrt(TotalRounds * TopP) / StdDevs,
+ OutlierProbability = math:erfc(Outlier / Sqrt2) * TotalRounds,
+ InvOP = 1.0 / OutlierProbability,
+ ct:pal(
+ "Total rounds: ~w, tolerance: 1/~.2f..1/~.2f, "
+ "outlier: ~.2f, probability 1/~.2f.",
+ [TotalRounds, Precision, TopPrecision, Outlier, InvOP]),
+ {TotalRounds, [], []} =
+ {TotalRounds,
+ check_histogram(
+ W, TotalRounds, StdDevs, PositiveHistogram, Buckets),
+ check_histogram(
+ W, TotalRounds, StdDevs, NegativeHistogram, Buckets)},
+ %% If the probability for getting this Outlier is lower than 1/50,
+ %% then this is fishy!
+ true = (1/50 =< OutlierProbability),
+ {comment, {tp, TopPrecision, op, InvOP}}.
+%%
+stats_standard_normal(
+ InvDelta, Buckets, PositiveHistogram, NegativeHistogram, Outlier,
+ Fun, S, 0, StopTime, Rounds, TotalRounds) ->
+ case erlang:monotonic_time(second) of
+ Now when Now < StopTime ->
+ stats_standard_normal(
+ InvDelta, Buckets,
+ PositiveHistogram, NegativeHistogram, Outlier,
+ Fun, S, Rounds, StopTime, Rounds, TotalRounds + Rounds);
+ _ ->
+ {PositiveHistogram, NegativeHistogram,
+ Outlier, TotalRounds + Rounds}
+ end;
+stats_standard_normal(
+ InvDelta, Buckets, PositiveHistogram, NegativeHistogram, Outlier,
+ Fun, S, Count, StopTime, Rounds, TotalRounds) ->
+ case Fun(S) of
+ {X, NewS} when 0.0 =< X ->
+ Bucket = min(Buckets, floor(X * InvDelta)),
+ stats_standard_normal(
+ InvDelta, Buckets,
+ increment_bucket(Bucket, PositiveHistogram),
+ NegativeHistogram, max(Outlier, X),
+ Fun, NewS, Count - 1, StopTime, Rounds, TotalRounds);
+ {MinusX, NewS} ->
+ X = -MinusX,
+ Bucket = min(Buckets, floor(X * InvDelta)),
+ stats_standard_normal(
+ InvDelta, Buckets,
+ PositiveHistogram,
+ increment_bucket(Bucket, NegativeHistogram), max(Outlier, X),
+ Fun, NewS, Count - 1, StopTime, Rounds, TotalRounds)
+ end.
+
+increment_bucket(Bucket, Array) ->
+ array:set(Bucket, array:get(Bucket, Array) + 1, Array).
+
+check_histogram(W, Rounds, StdDevs, Histogram, Buckets) ->
+ %%PrevBucket = 512,
+ %%Bucket = PrevBucket - 1,
+ %%P = 0.5 * math:erfc(PrevBucket / W),
+ TargetP = 0.5 * math:erfc(Buckets / W),
+ P = 0.0,
+ N = 0,
+ check_histogram(
+ W, Rounds, StdDevs, Histogram, TargetP,
+ Buckets, Buckets, P, N).
+%%
+check_histogram(
+ _W, _Rounds, _StdDevs, _Histogram, _TargetP,
+ 0, _PrevBucket, _PrevP, _PrevN) ->
+ [];
+check_histogram(
+ W, Rounds, StdDevs, Histogram, TargetP,
+ Bucket, PrevBucket, PrevP, PrevN) ->
+ N = PrevN + array:get(Bucket, Histogram),
+ P = 0.5 * math:erfc(Bucket / W),
+ BucketP = P - PrevP,
+ if
+ TargetP =< BucketP ->
+ check_histogram(
+ W, Rounds, StdDevs, Histogram, TargetP,
+ Bucket - 1, PrevBucket, PrevP, N);
+ true ->
+ Exp = BucketP * Rounds,
+ Var = Rounds * BucketP*(1.0 - BucketP),
+ Threshold = StdDevs * math:sqrt(Var),
+ LowerLimit = floor(Exp - Threshold),
+ UpperLimit = ceil(Exp + Threshold),
+ if
+ N < LowerLimit; UpperLimit < N ->
+ [#{bucket => {Bucket, PrevBucket}, n => N, exp => Exp,
+ lower => LowerLimit, upper => UpperLimit} |
+ check_histogram(
+ W, Rounds, StdDevs, Histogram, TargetP,
+ Bucket - 1, Bucket, P, 0)];
+ true ->
+ check_histogram(
+ W, Rounds, StdDevs, Histogram, TargetP,
+ Bucket - 1, Bucket, P, 0)
+ end
+ end.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% White box test of the conversion to float
+
+uniform_real_conv(Config) when is_list(Config) ->
+ [begin
+%% ct:pal("~13.16.0bx~3.16.0b: ~p~n", [M,E,Gen]),
+ uniform_real_conv_check(M, E, Gen)
+ end || {M, E, Gen} <- uniform_real_conv_data()],
+ uniform_real_scan(0),
+ uniform_real_scan(3).
+
+uniform_real_conv_data() ->
+ [{16#fffffffffffff, -1, [16#3ffffffffffffff]},
+ {16#fffffffffffff, -1, [16#3ffffffffffffe0]},
+ {16#ffffffffffffe, -1, [16#3ffffffffffffdf]},
+ %%
+ {16#0000000000000, -1, [16#200000000000000]},
+ {16#fffffffffffff, -2, [16#1ffffffffffffff]},
+ {16#fffffffffffff, -2, [16#1fffffffffffff0]},
+ {16#ffffffffffffe, -2, [16#1ffffffffffffef]},
+ %%
+ {16#0000000000000, -2, [16#100000000000000]},
+ {16#fffffffffffff, -3, [16#0ffffffffffffff]},
+ {16#fffffffffffff, -3, [16#0fffffffffffff8]},
+ {16#ffffffffffffe, -3, [16#0fffffffffffff7]},
+ %%
+ {16#0000000000000, -3, [16#080000000000000]},
+ {16#fffffffffffff, -4, [16#07fffffffffffff]},
+ {16#fffffffffffff, -4, [16#07ffffffffffffc]},
+ {16#ffffffffffffe, -4, [16#07ffffffffffffb]},
+ %%
+ {16#0000000000000, -4, [16#040000000000000]},
+ {16#fffffffffffff, -5, [16#03fffffffffffff,16#3ffffffffffffff]},
+ {16#fffffffffffff, -5, [16#03ffffffffffffe,16#200000000000000]},
+ {16#ffffffffffffe, -5, [16#03fffffffffffff,16#1ffffffffffffff]},
+ {16#ffffffffffffe, -5, [16#03fffffffffffff,16#100000000000000]},
+ %%
+ {16#0000000000001, -56, [16#000000000000007,16#00000000000007f]},
+ {16#0000000000001, -56, [16#000000000000004,16#000000000000040]},
+ {16#0000000000000, -57, [16#000000000000003,16#20000000000001f]},
+ {16#0000000000000, -57, [16#000000000000000,16#200000000000000]},
+ {16#fffffffffffff, -58, [16#000000000000003,16#1ffffffffffffff]},
+ {16#fffffffffffff, -58, [16#000000000000000,16#1fffffffffffff0]},
+ {16#ffffffffffffe, -58, [16#000000000000000,16#1ffffffffffffef]},
+ {16#ffffffffffffe, -58, [16#000000000000000,16#1ffffffffffffe0]},
+ %%
+ {16#0000000000000, -58, [16#000000000000000,16#10000000000000f]},
+ {16#0000000000000, -58, [16#000000000000000,16#100000000000000]},
+ {2#11001100000000000000000000000000000000000011000000011, % 53 bits
+ -1022,
+ [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, % 18 zeros
+ 2#1100110000000000000000000000000000000000001 bsl 2, % 43 bits
+ 2#1000000011 bsl (56-10+2)]}, % 10 bits
+ {0, -1, % 0.5 after retry
+ [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, % 18 zeros
+ 2#111111111111111111111111111111111111111111 bsl 2, % 42 bits - retry
+ 16#200000000000003]}]. % 0.5
+
+-define(UNIFORM_REAL_SCAN_PATTERN, (16#19000000000009)). % 53 bits
+-define(UNIFORM_REAL_SCAN_NUMBER, (1021)).
+
+uniform_real_scan_template(K) ->
+ <<0:?UNIFORM_REAL_SCAN_NUMBER,
+ ?UNIFORM_REAL_SCAN_PATTERN:53,K:2,0:1>>.
+
+uniform_real_scan(K) ->
+ Templ = uniform_real_scan_template(K),
+ N = ?UNIFORM_REAL_SCAN_NUMBER,
+ uniform_real_scan(Templ, N, K).
+
+uniform_real_scan(Templ, N, K) when 0 =< N ->
+ <<_:N/bits,T/bits>> = Templ,
+ Data = uniform_real_scan_data(T, K),
+ uniform_real_conv_check(
+ ?UNIFORM_REAL_SCAN_PATTERN, N - 1 - ?UNIFORM_REAL_SCAN_NUMBER, Data),
+ uniform_real_scan(Templ, N - 1, K);
+uniform_real_scan(_, _, _) ->
+ ok.
+
+uniform_real_scan_data(Templ, K) ->
+ case Templ of
+ <<X:56, T/bits>> ->
+ B = rand:bc64(X),
+ [(X bsl 2) bor K |
+ if
+ 53 =< B ->
+ [];
+ true ->
+ uniform_real_scan_data(T, K)
+ end];
+ _ ->
+ <<X:56, _/bits>> = <<Templ/bits, 0:56>>,
+ [(X bsl 2) bor K]
+ end.
+
+uniform_real_conv_check(M, E, Gen) ->
+ <<F/float>> = <<0:1, (E + 16#3ff):11, M:52>>,
+ try uniform_real_gen(Gen) of
+ F -> F;
+ FF ->
+ ct:pal(
+ "~s =/= ~s: ~s~n",
+ [rand:float2str(FF), rand:float2str(F),
+ [["16#",integer_to_list(G,16),$\s]||G<-Gen]]),
+ ct:fail({neq, FF, F})
+ catch
+ Error:Reason ->
+ ct:pal(
+ "~w:~p ~s: ~s~n",
+ [Error, Reason, rand:float2str(F),
+ [["16#",integer_to_list(G,16),$\s]||G<-Gen]]),
+ ct:fail({Error, Reason, F, erlang:get_stacktrace()})
+ end.
+
+
+uniform_real_gen(Gen) ->
+ State = rand_state(Gen),
+ {F, {#{type := rand_SUITE_list},[]}} = rand:uniform_real_s(State),
+ F.
+
+uniform_gen(Range, Gen) ->
+ State = rand_state(Gen),
+ {N, {#{type := rand_SUITE_list},[]}} = rand:uniform_s(Range, State),
+ N.
+
+%% Loaded dice for white box tests
+rand_state(Gen) ->
+ {#{type => rand_SUITE_list, bits => 58, weak_low_bits => 1,
+ next => fun ([H|T]) -> {H, T} end},
+ Gen}.
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Test that the user can write algorithms.
@@ -459,213 +807,289 @@ measure(Config) ->
{skip,{will_not_run_in_scaled_time,Scale}}
end.
+-define(CHECK_UNIFORM_RANGE(Gen, Range, X, St),
+ case (Gen) of
+ {(X), (St)} when is_integer(X), 1 =< (X), (X) =< (Range) ->
+ St
+ end).
+-define(CHECK_UNIFORM(Gen, X, St),
+ case (Gen) of
+ {(X), (St)} when is_float(X), 0.0 =< (X), (X) < 1.0 ->
+ St
+ end).
+-define(CHECK_UNIFORM_NZ(Gen, X, St),
+ case (Gen) of
+ {(X), (St)} when is_float(X), 0.0 < (X), (X) =< 1.0 ->
+ St
+ end).
+-define(CHECK_NORMAL(Gen, X, St),
+ case (Gen) of
+ {(X), (St)} when is_float(X) ->
+ St
+ end).
+
do_measure(_Config) ->
- Algos =
+ Algs =
+ algs() ++
try crypto:strong_rand_bytes(1) of
- <<_>> -> [crypto64, crypto]
+ <<_>> -> [crypto64, crypto_cache, crypto]
catch
error:low_entropy -> [];
error:undef -> []
- end ++ algs(),
+ end,
%%
- ct:pal("RNG uniform integer performance~n",[]),
- TMark1 =
+ ct:pal("~nRNG uniform integer range 10000 performance~n",[]),
+ _ =
measure_1(
- random,
fun (_) -> 10000 end,
- undefined,
- fun (Range, State) ->
- {int, random:uniform_s(Range, State)}
- end),
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
+ %%
+ ct:pal("~nRNG uniform integer 32 bit performance~n",[]),
_ =
- [measure_1(
- Algo,
- fun (_) -> 10000 end,
- TMark1,
- fun (Range, State) ->
- {int, rand:uniform_s(Range, State)}
- end) || Algo <- Algos],
+ measure_1(
+ fun (_) -> 1 bsl 32 end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
%%
ct:pal("~nRNG uniform integer half range performance~n",[]),
- HalfRangeFun = fun (State) -> half_range(State) end,
- TMark2 =
- measure_1(
- random,
- HalfRangeFun,
- undefined,
- fun (Range, State) ->
- {int, random:uniform_s(Range, State)}
- end),
_ =
- [measure_1(
- Algo,
- HalfRangeFun,
- TMark2,
- fun (Range, State) ->
- {int, rand:uniform_s(Range, State)}
- end) || Algo <- Algos],
- %%
- ct:pal("~nRNG uniform integer half range + 1 performance~n",[]),
- HalfRangePlus1Fun = fun (State) -> half_range(State) + 1 end,
- TMark3 =
measure_1(
- random,
- HalfRangePlus1Fun,
- undefined,
- fun (Range, State) ->
- {int, random:uniform_s(Range, State)}
- end),
+ fun (State) -> half_range(State) end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
+ %%
+ ct:pal("~nRNG uniform integer half range + 1 performance~n",[]),
_ =
- [measure_1(
- Algo,
- HalfRangePlus1Fun,
- TMark3,
- fun (Range, State) ->
- {int, rand:uniform_s(Range, State)}
- end) || Algo <- Algos],
+ measure_1(
+ fun (State) -> half_range(State) + 1 end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
%%
ct:pal("~nRNG uniform integer full range - 1 performance~n",[]),
- FullRangeMinus1Fun = fun (State) -> (half_range(State) bsl 1) - 1 end,
- TMark4 =
- measure_1(
- random,
- FullRangeMinus1Fun,
- undefined,
- fun (Range, State) ->
- {int, random:uniform_s(Range, State)}
- end),
_ =
- [measure_1(
- Algo,
- FullRangeMinus1Fun,
- TMark4,
- fun (Range, State) ->
- {int, rand:uniform_s(Range, State)}
- end) || Algo <- Algos],
+ measure_1(
+ fun (State) -> (half_range(State) bsl 1) - 1 end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
%%
ct:pal("~nRNG uniform integer full range performance~n",[]),
- FullRangeFun = fun (State) -> half_range(State) bsl 1 end,
- TMark5 =
- measure_1(
- random,
- FullRangeFun,
- undefined,
- fun (Range, State) ->
- {int, random:uniform_s(Range, State)}
- end),
_ =
- [measure_1(
- Algo,
- FullRangeFun,
- TMark5,
- fun (Range, State) ->
- {int, rand:uniform_s(Range, State)}
- end) || Algo <- Algos],
+ measure_1(
+ fun (State) -> half_range(State) bsl 1 end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
%%
ct:pal("~nRNG uniform integer full range + 1 performance~n",[]),
- FullRangePlus1Fun = fun (State) -> (half_range(State) bsl 1) + 1 end,
- TMark6 =
- measure_1(
- random,
- FullRangePlus1Fun,
- undefined,
- fun (Range, State) ->
- {int, random:uniform_s(Range, State)}
- end),
_ =
- [measure_1(
- Algo,
- FullRangePlus1Fun,
- TMark6,
- fun (Range, State) ->
- {int, rand:uniform_s(Range, State)}
- end) || Algo <- Algos],
+ measure_1(
+ fun (State) -> (half_range(State) bsl 1) + 1 end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
%%
ct:pal("~nRNG uniform integer double range performance~n",[]),
- DoubleRangeFun = fun (State) -> half_range(State) bsl 2 end,
- TMark7 =
- measure_1(
- random,
- DoubleRangeFun,
- undefined,
- fun (Range, State) ->
- {int, random:uniform_s(Range, State)}
- end),
_ =
- [measure_1(
- Algo,
- DoubleRangeFun,
- TMark7,
- fun (Range, State) ->
- {int, rand:uniform_s(Range, State)}
- end) || Algo <- Algos],
+ measure_1(
+ fun (State) ->
+ half_range(State) bsl 2
+ end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
%%
ct:pal("~nRNG uniform integer double range + 1 performance~n",[]),
- DoubleRangePlus1Fun = fun (State) -> (half_range(State) bsl 2) + 1 end,
- TMark8 =
+ _ =
measure_1(
- random,
- DoubleRangePlus1Fun,
- undefined,
- fun (Range, State) ->
- {int, random:uniform_s(Range, State)}
- end),
+ fun (State) ->
+ (half_range(State) bsl 2) + 1
+ end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
+ %%
+ ct:pal("~nRNG uniform integer 64 bit performance~n",[]),
_ =
- [measure_1(
- Algo,
- DoubleRangePlus1Fun,
- TMark8,
- fun (Range, State) ->
- {int, rand:uniform_s(Range, State)}
- end) || Algo <- Algos],
+ measure_1(
+ fun (_) -> 1 bsl 64 end,
+ fun (State, Range, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM_RANGE(
+ Mod:uniform_s(Range, St0), Range,
+ X, St1)
+ end,
+ State)
+ end,
+ Algs),
%%
ct:pal("~nRNG uniform float performance~n",[]),
- TMark9 =
+ _ =
measure_1(
- random,
fun (_) -> 0 end,
- undefined,
- fun (_, State) ->
- {uniform, random:uniform_s(State)}
- end),
+ fun (State, _, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM(Mod:uniform_s(St0), X, St)
+ end,
+ State)
+ end,
+ Algs),
+ %%
+ ct:pal("~nRNG uniform_real float performance~n",[]),
_ =
- [measure_1(
- Algo,
- fun (_) -> 0 end,
- TMark9,
- fun (_, State) ->
- {uniform, rand:uniform_s(State)}
- end) || Algo <- Algos],
+ measure_1(
+ fun (_) -> 0 end,
+ fun (State, _, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_UNIFORM(Mod:uniform_real_s(St0), X, St)
+ end,
+ State)
+ end,
+ Algs),
%%
ct:pal("~nRNG normal float performance~n",[]),
- io:format("~.12w: not implemented (too few bits)~n", [random]),
- _ = [measure_1(
- Algo,
- fun (_) -> 0 end,
- TMark9,
- fun (_, State) ->
- {normal, rand:normal_s(State)}
- end) || Algo <- Algos],
+ [TMarkNormalFloat|_] =
+ measure_1(
+ fun (_) -> 0 end,
+ fun (State, _, Mod) ->
+ measure_loop(
+ fun (St0) ->
+ ?CHECK_NORMAL(Mod:normal_s(St0), X, St1)
+ end,
+ State)
+ end,
+ Algs),
+ %% Just for fun try an implementation of the Box-Muller
+ %% transformation for creating normal distribution floats
+ %% to compare with our Ziggurat implementation.
+ %% Generates two numbers per call that we add so they
+ %% will not be optimized away. Hence the benchmark time
+ %% is twice what it should be.
+ TwoPi = 2 * math:pi(),
+ _ =
+ measure_1(
+ fun (_) -> 0 end,
+ fun (State, _, Mod) ->
+ measure_loop(
+ fun (State0) ->
+ {U1, State1} = Mod:uniform_real_s(State0),
+ {U2, State2} = Mod:uniform_s(State1),
+ R = math:sqrt(-2.0 * math:log(U1)),
+ T = TwoPi * U2,
+ Z0 = R * math:cos(T),
+ Z1 = R * math:sin(T),
+ ?CHECK_NORMAL({Z0 + Z1, State2}, X, State3)
+ end,
+ State)
+ end,
+ exrop, TMarkNormalFloat),
+ ok.
+
+-define(LOOP_MEASURE, (?LOOP div 5)).
+
+measure_loop(Fun, State) ->
+ measure_loop(Fun, State, ?LOOP_MEASURE).
+%%
+measure_loop(Fun, State, N) when 0 < N ->
+ measure_loop(Fun, Fun(State), N-1);
+measure_loop(_, _, _) ->
ok.
-measure_1(Algo, RangeFun, TMark, Gen) ->
+measure_1(RangeFun, Fun, Algs) ->
+ TMark = measure_1(RangeFun, Fun, hd(Algs), undefined),
+ [TMark] ++
+ [measure_1(RangeFun, Fun, Alg, TMark) || Alg <- tl(Algs)].
+
+measure_1(RangeFun, Fun, Alg, TMark) ->
Parent = self(),
- Seed =
- case Algo of
+ {Mod, State} =
+ case Alg of
crypto64 ->
- crypto64_seed();
+ {rand, crypto64_seed()};
+ crypto_cache ->
+ {rand, crypto:rand_seed_alg(crypto_cache)};
crypto ->
- crypto:rand_seed_s();
+ {rand, crypto:rand_seed_s()};
random ->
- random:seed(os:timestamp()), get(random_seed);
+ {random, random:seed(os:timestamp()), get(random_seed)};
_ ->
- rand:seed_s(Algo)
+ {rand, rand:seed_s(Alg)}
end,
- Range = RangeFun(Seed),
+ Range = RangeFun(State),
Pid = spawn_link(
fun() ->
- Fun = fun() -> measure_2(?LOOP, Range, Seed, Gen) end,
- {Time, ok} = timer:tc(Fun),
+ {Time, ok} = timer:tc(fun () -> Fun(State, Range, Mod) end),
Percent =
case TMark of
undefined -> 100;
@@ -673,7 +1097,8 @@ measure_1(Algo, RangeFun, TMark, Gen) ->
end,
io:format(
"~.12w: ~p ns ~p% [16#~.16b]~n",
- [Algo, (Time * 1000 + 500) div ?LOOP, Percent, Range]),
+ [Alg, (Time * 1000 + 500) div ?LOOP_MEASURE,
+ Percent, Range]),
Parent ! {self(), Time},
normal
end),
@@ -681,21 +1106,6 @@ measure_1(Algo, RangeFun, TMark, Gen) ->
{Pid, Msg} -> Msg
end.
-measure_2(N, Range, State0, Fun) when N > 0 ->
- case Fun(Range, State0) of
- {int, {Random, State}}
- when is_integer(Random), Random >= 1, Random =< Range ->
- measure_2(N-1, Range, State, Fun);
- {uniform, {Random, State}}
- when is_float(Random), 0.0 =< Random, Random < 1.0 ->
- measure_2(N-1, Range, State, Fun);
- {normal, {Random, State}} when is_float(Random) ->
- measure_2(N-1, Range, State, Fun);
- Res ->
- exit({error, Res, State0})
- end;
-measure_2(0, _, _, _) -> ok.
-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% The jump sequence tests has two parts
%% for those with the functional API (jump/1)