diff options
Diffstat (limited to 'lib/stdlib/test/rand_SUITE.erl')
| -rw-r--r-- | lib/stdlib/test/rand_SUITE.erl | 99 |
1 files changed, 51 insertions, 48 deletions
diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl index dbf1857a25..e256d31112 100644 --- a/lib/stdlib/test/rand_SUITE.erl +++ b/lib/stdlib/test/rand_SUITE.erl @@ -489,19 +489,21 @@ stats_standard_normal(Fun, S) -> 4.0), % probability erfc(4/sqrt(2)) (1/15787) to fail a bucket %%% ct:timetrap({seconds, Seconds + 120}), - %% InvDelta and Buckets are chosen so that the probability to land - %% in the central bucket (closest to 0) is about the same as - %% the probability to land in the top catch-all-outside bucket. + %% 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 central + %% Rounds is calculated so the expected value for the low %% bucket will be at least TargetHits. %% InvDelta = 512, - W = InvDelta * math:sqrt(2), - Buckets = 1619, % erf-1(erfc(1 / W)) * W + Buckets = 4 * InvDelta, % 4 std devs range TargetHits = 1024, - InvP0 = floor(math:ceil(1 / (0.5 * math:erf(1 / W)))), - Rounds = 2 * TargetHits * InvP0, + 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( @@ -511,20 +513,25 @@ stats_standard_normal(Fun, S) -> stats_standard_normal( InvDelta, Buckets, Histogram, Histogram, 0.0, Fun, S, Rounds, StopTime, Rounds, 0), - Precision = math:sqrt(TotalRounds / InvP0) / StdDevs, + 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, outlier: ~.2f.", - [TotalRounds, Precision, Outlier]), - ResultingTargetHits = floor(TotalRounds / 2 / InvP0), + "Total rounds: ~w, tolerance: 1/~.2f..1/~.2f, " + "outlier: ~.2f, probability 1/~.2f.", + [TotalRounds, Precision, TopPrecision, Outlier, InvOP]), {TotalRounds, [], []} = {TotalRounds, check_histogram( - W, Buckets, ResultingTargetHits, TotalRounds, - StdDevs, PositiveHistogram), + W, TotalRounds, StdDevs, PositiveHistogram, Buckets), check_histogram( - W, Buckets, ResultingTargetHits, TotalRounds, - StdDevs, NegativeHistogram)}, - ok. + W, TotalRounds, StdDevs, NegativeHistogram, Buckets)}, + %% If the probability for getting this Outlier is lower than 1/20, + %% then this is fishy! + true = (1/20 =< OutlierProbability), + {comment, {tp, TopPrecision, op, InvOP}}. %% stats_standard_normal( InvDelta, Buckets, PositiveHistogram, NegativeHistogram, Outlier, @@ -563,54 +570,50 @@ stats_standard_normal( increment_bucket(Bucket, Array) -> array:set(Bucket, array:get(Bucket, Array) + 1, Array). -check_histogram(W, Buckets, TargetHits, Rounds, StdDevs, Histogram) -> +check_histogram(W, Rounds, StdDevs, Histogram, Buckets) -> %%PrevBucket = 512, %%Bucket = PrevBucket - 1, %%P = 0.5 * math:erfc(PrevBucket / W), - PrevBucket = Buckets, - Bucket = PrevBucket, + TargetP = 0.5 * math:erfc(Buckets / W), P = 0.0, N = 0, check_histogram( - W, Bucket, TargetHits, Rounds, StdDevs, Histogram, - PrevBucket, P, N). + W, Rounds, StdDevs, Histogram, TargetP, + Buckets, Buckets, P, N). %% check_histogram( - _W, _Bucket, _TargetHits, _Rounds, _StdDevs, _Histogram, - 0, _PrevP, _PrevN) -> + _W, _Rounds, _StdDevs, _Histogram, _TargetP, + 0, _PrevBucket, _PrevP, _PrevN) -> []; check_histogram( - W, Bucket, TargetHits, Rounds, StdDevs, Histogram, - PrevBucket, PrevP, PrevN) -> + W, Rounds, StdDevs, Histogram, TargetP, + Bucket, PrevBucket, PrevP, PrevN) -> N = PrevN + array:get(Bucket, Histogram), P = 0.5 * math:erfc(Bucket / W), - DP = P - PrevP, - Exp = DP * Rounds, + BucketP = P - PrevP, if - TargetHits =< Exp -> - %% Check N - Err = N - Exp, - AbsErr = abs(Err), - Var = Rounds * DP*(1.0 - DP), - Limit = StdDevs * math:sqrt(Var), + 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 - Limit =< AbsErr -> - [#{bucket => {Bucket, PrevBucket}, - n => N, exp => Exp, err => Err, limit => Limit} | + N < LowerLimit; UpperLimit < N -> + [#{bucket => {Bucket, PrevBucket}, n => N, exp => Exp, + lower => LowerLimit, upper => UpperLimit} | check_histogram( - W, Bucket - 1, TargetHits, Rounds, StdDevs, Histogram, - Bucket, P, 0)]; - %% ct:fail( - %% {bucket, Bucket, PrevBucket, N, Exp, Err, Limit}); + W, Rounds, StdDevs, Histogram, TargetP, + Bucket - 1, Bucket, P, 0)]; true -> check_histogram( - W, Bucket - 1, TargetHits, Rounds, StdDevs, Histogram, - Bucket, P, 0) - end; - true -> - check_histogram( - W, Bucket - 1, TargetHits, Rounds, StdDevs, Histogram, - PrevBucket, PrevP, N) + W, Rounds, StdDevs, Histogram, TargetP, + Bucket - 1, Bucket, P, 0) + end end. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |