RESULTS.md

Draupnir Test Results

Here we present test results for different configurations of the Draupnir RNG.

Index

• Methodology
  • About the Constants
• Initial State = π
• Initial State = e
• Initial State = γ
• Initial State = Ω
• Initial State = 1 / π
• Initial State = 1 / e
• Initial State = 1 / γ
• Initial State = 1 / Ω
• Initial State = √2
• Initial State = √3
• Initial State = √5
• Initial State = √7
• Initial State = √11
• Initial State = 1 / √2
• Initial State = 1 / √3
• Initial State = 1 / √5
• Initial State = 1 / √7
• Initial State = 1 / √11

---

Methodology

The only parameter changed is the initial state, the width is fixed to 64 bits, the generator is fixed to the ECMA one, the initial value and xoring mask are fixed to the all-1s pattern, the soaking rounds parameter is fixed to 8, and the squeezing rounds parameter is fixed to 1.

The test results are presented as the formatted output of the results of:

dieharder -a -k 2 -Y 1 -g 201 -f draupnir.samples.bin

where draupnir.samples.bin is a 1Gb file generated by Draupnir. Only the last result of an ambiguity resolution run is shown. Any failing test is highlighted.

About the Constants

The following constants (and their inverses) are used to initialize the Draupnir RNG:

• π : the ratio of circumference to diameter (see Wikipedia, π),
• e : the base of the natural logarithms (see Wikipedia, e),
• γ : the Euler-Mascheroni constant (see Wikipedia, γ),
• Ω : the Omega constant (see Wikipedia, Ω)
• √2 : the square root of 2,
• √3 : the square root of 3,
• √5 : the square root of 5,
• √7 : the square root of 7,
• √11 : the square root of 11,

all of them were chosen because they are transcendental (or strongly suspected to be) and non-biased.

Initial State = π

Test Name	N	t samples	p samples	p-value	Assesment
diehard_birthdays	0	100	100	0.63064540	PASSED
diehard_operm5	0	1000000	100	0.03515999	PASSED
diehard_rank_32x32	0	40000	100	0.99366480	PASSED
diehard_rank_6x8	0	100000	100	0.81220479	PASSED
diehard_bitstream	0	2097152	100	0.95534811	PASSED
diehard_opso	0	2097152	100	0.94393360	PASSED
diehard_oqso	0	2097152	100	0.98087088	PASSED
diehard_dna	0	2097152	100	0.95769403	PASSED
diehard_count_1s_str	0	256000	100	0.49225429	PASSED
diehard_count_1s_byt	0	256000	100	0.88281751	PASSED
diehard_parking_lot	0	12000	100	0.43004782	PASSED
diehard_2dsphere	2	8000	100	0.51435477	PASSED
diehard_3dsphere	3	4000	100	0.28920569	PASSED
diehard_squeeze	0	100000	100	0.67876168	PASSED
diehard_sums	0	100	100	0.66044170	PASSED
diehard_runs	0	100000	100	0.04674612	PASSED
diehard_runs	0	100000	100	0.98217621	PASSED
diehard_craps	0	200000	100	0.49183776	PASSED
diehard_craps	0	200000	100	0.46006937	PASSED
marsaglia_tsang_gcd	0	10000000	100	0.20904964	PASSED
marsaglia_tsang_gcd	0	10000000	100	0.01648035	PASSED
sts_monobit	1	100000	100	0.48969331	PASSED
sts_runs	2	100000	100	0.39693806	PASSED
sts_serial	1	100000	200	0.49587339	PASSED
sts_serial	2	100000	200	0.19663377	PASSED
sts_serial	3	100000	200	0.43291004	PASSED
sts_serial	3	100000	200	0.18233658	PASSED
sts_serial	4	100000	200	0.96692485	PASSED
sts_serial	4	100000	200	0.56005169	PASSED
sts_serial	5	100000	200	0.87878990	PASSED
sts_serial	5	100000	200	0.74775083	PASSED
sts_serial	6	100000	200	0.86294971	PASSED
sts_serial	6	100000	200	0.85268807	PASSED
sts_serial	7	100000	200	0.37983973	PASSED
sts_serial	7	100000	200	0.10117355	PASSED
sts_serial	8	100000	200	0.15770631	PASSED
sts_serial	8	100000	200	0.41611920	PASSED
sts_serial	9	100000	200	0.93148930	PASSED
sts_serial	9	100000	200	0.90275330	PASSED
sts_serial	10	100000	200	0.58921179	PASSED
sts_serial	10	100000	200	0.58830610	PASSED
sts_serial	11	100000	200	0.62760477	PASSED
sts_serial	11	100000	200	0.70437632	PASSED
sts_serial	12	100000	200	0.92911851	PASSED
sts_serial	12	100000	200	0.19846138	PASSED
sts_serial	13	100000	200	0.88282809	PASSED
sts_serial	13	100000	200	0.72430544	PASSED
sts_serial	14	100000	200	0.58871871	PASSED
sts_serial	14	100000	200	0.47935487	PASSED
sts_serial	15	100000	200	0.14544557	PASSED
sts_serial	15	100000	200	0.53219509	PASSED
sts_serial	16	100000	200	0.13139076	PASSED
sts_serial	16	100000	200	0.57874754	PASSED
rgb_bitdist	1	100000	100	0.42567409	PASSED
rgb_bitdist	2	100000	100	0.55714722	PASSED
rgb_bitdist	3	100000	100	0.66063937	PASSED
rgb_bitdist	4	100000	100	0.26377560	PASSED
rgb_bitdist	5	100000	100	0.12805612	PASSED
rgb_bitdist	6	100000	100	0.47967016	PASSED
rgb_bitdist	7	100000	100	0.14175432	PASSED
rgb_bitdist	8	100000	100	0.97145223	PASSED
rgb_bitdist	9	100000	100	0.40135356	PASSED
rgb_bitdist	10	100000	100	0.32587425	PASSED
rgb_bitdist	11	100000	100	0.98519018	PASSED
rgb_bitdist	12	100000	100	0.29674658	PASSED
rgb_minimum_distance	2	10000	1000	0.76972901	PASSED
rgb_minimum_distance	3	10000	1000	0.93211566	PASSED
rgb_minimum_distance	4	10000	1000	0.39127666	PASSED
rgb_minimum_distance	5	10000	1000	0.11212254	PASSED
rgb_permutations	2	100000	100	0.72450965	PASSED
rgb_permutations	3	100000	100	0.22921651	PASSED
rgb_permutations	4	100000	100	0.34243965	PASSED
rgb_permutations	5	100000	100	0.60468421	PASSED
rgb_lagged_sum	0	1000000	100	0.81703915	PASSED
rgb_lagged_sum	1	1000000	100	0.45637948	PASSED
rgb_lagged_sum	2	1000000	100	0.95207442	PASSED
rgb_lagged_sum	3	1000000	100	0.80228102	PASSED
rgb_lagged_sum	4	1000000	100	0.39828888	PASSED
rgb_lagged_sum	5	1000000	100	0.20938165	PASSED
rgb_lagged_sum	6	1000000	100	0.56671011	PASSED
rgb_lagged_sum	7	1000000	100	0.08812106	PASSED
rgb_lagged_sum	8	1000000	100	0.17108848	PASSED
rgb_lagged_sum	9	1000000	100	0.31404455	PASSED
rgb_lagged_sum	10	1000000	100	0.98738722	PASSED
rgb_lagged_sum	11	1000000	100	0.51733467	PASSED
rgb_lagged_sum	12	1000000	100	0.91767471	PASSED
rgb_lagged_sum	13	1000000	100	0.33031728	PASSED
rgb_lagged_sum	14	1000000	100	0.32253236	PASSED
rgb_lagged_sum	15	1000000	100	0.53337340	PASSED
rgb_lagged_sum	16	1000000	100	0.67937772	PASSED
rgb_lagged_sum	17	1000000	100	0.25573759	PASSED
rgb_lagged_sum	18	1000000	100	0.60761161	PASSED
rgb_lagged_sum	19	1000000	100	0.22868094	PASSED
rgb_lagged_sum	20	1000000	100	0.46505306	PASSED
rgb_lagged_sum	21	1000000	100	0.56312916	PASSED
rgb_lagged_sum	22	1000000	100	0.48896176	PASSED
rgb_lagged_sum	23	1000000	100	0.06160357	PASSED
rgb_lagged_sum	24	1000000	100	0.71473587	PASSED
rgb_lagged_sum	25	1000000	100	0.98301624	PASSED
rgb_lagged_sum	26	1000000	100	0.20179028	PASSED
rgb_lagged_sum	27	1000000	100	0.86533400	PASSED
rgb_lagged_sum	28	1000000	100	0.63597088	PASSED
rgb_lagged_sum	29	1000000	100	0.70753809	PASSED
rgb_lagged_sum	30	1000000	100	0.21715355	PASSED
rgb_lagged_sum	31	1000000	100	0.00699472	PASSED
rgb_lagged_sum	32	1000000	100	0.57913639	PASSED
rgb_kstest_test	0	10000	1000	0.50575968	PASSED
dab_bytedistrib	0	51200000	1	0.52505240	PASSED
dab_dct	256	50000	1	0.60605756	PASSED
dab_filltree	32	15000000	1	0.16824354	PASSED
dab_filltree	32	15000000	1	0.04785636	PASSED
dab_filltree2	0	5000000	1	0.09302336	PASSED
dab_filltree2	1	5000000	1	0.10770671	PASSED
dab_monobit2	12	65000000	1	0.07515807	PASSED

Initial State = e

Test Name	N	t samples	p samples	p-value	Assesment
diehard_birthdays	0	100	100	0.26919453	PASSED
diehard_operm5	0	1000000	100	0.16884554	PASSED
diehard_rank_32x32	0	40000	100	0.27581109	PASSED
diehard_rank_6x8	0	100000	100	0.66432281	PASSED
diehard_bitstream	0	2097152	100	0.38439444	PASSED
diehard_opso	0	2097152	100	0.44277254	PASSED
diehard_oqso	0	2097152	100	0.02356951	PASSED
diehard_dna	0	2097152	100	0.33056949	PASSED
diehard_count_1s_str	0	256000	100	0.42521477	PASSED
diehard_count_1s_byt	0	256000	100	0.61012598	PASSED
diehard_parking_lot	0	12000	100	0.68180941	PASSED
diehard_2dsphere	2	8000	100	0.93858769	PASSED
diehard_3dsphere	3	4000	100	0.93666638	PASSED
diehard_squeeze	0	100000	100	0.34322281	PASSED
diehard_sums	0	100	100	0.17972349	PASSED
diehard_runs	0	100000	100	0.82283301	PASSED
diehard_runs	0	100000	100	0.81299791	PASSED
diehard_craps	0	200000	100	0.56909659	PASSED
diehard_craps	0	200000	100	0.62340713	PASSED
marsaglia_tsang_gcd	0	10000000	100	0.47039053	PASSED
marsaglia_tsang_gcd	0	10000000	100	0.27135941	PASSED
sts_monobit	1	100000	100	0.10086753	PASSED
sts_runs	2	100000	100	0.08037274	PASSED
sts_serial	1	100000	100	0.27081135	PASSED
sts_serial	2	100000	100	0.96820176	PASSED
sts_serial	3	100000	100	0.37270446	PASSED
sts_serial	3	100000	100	0.08237393	PASSED
sts_serial	4	100000	100	0.28586588	PASSED
sts_serial	4	100000	100	0.13058794	PASSED
sts_serial	5	100000	100	0.66968082	PASSED
sts_serial	5	100000	100	0.41646243	PASSED
sts_serial	6	100000	100	0.95666611	PASSED
sts_serial	6	100000	100	0.91748793	PASSED
sts_serial	7	100000	100	0.35199467	PASSED
sts_serial	7	100000	100	0.74086307	PASSED
sts_serial	8	100000	100	0.13796611	PASSED
sts_serial	8	100000	100	0.05069722	PASSED
sts_serial	9	100000	100	0.63581601	PASSED
sts_serial	9	100000	100	0.73722359	PASSED
sts_serial	10	100000	100	0.40833076	PASSED
sts_serial	10	100000	100	0.69209809	PASSED
sts_serial	11	100000	100	0.18833553	PASSED
sts_serial	11	100000	100	0.16783305	PASSED
sts_serial	12	100000	100	0.21845603	PASSED
sts_serial	12	100000	100	0.88669691	PASSED
sts_serial	13	100000	100	0.17429194	PASSED
sts_serial	13	100000	100	0.37132293	PASSED
sts_serial	14	100000	100	0.75666695	PASSED
sts_serial	14	100000	100	0.95090826	PASSED
sts_serial	15	100000	100	0.90038892	PASSED
sts_serial	15	100000	100	0.78530381	PASSED
sts_serial	16	100000	100	0.78676125	PASSED
sts_serial	16	100000	100	0.23208770	PASSED
rgb_bitdist	1	100000	100	0.25127484	PASSED
rgb_bitdist	2	100000	100	0.84999452	PASSED
rgb_bitdist	3	100000	100	0.89771832	PASSED
rgb_bitdist	4	100000	100	0.45441698	PASSED
rgb_bitdist	5	100000	100	0.61429746	PASSED
rgb_bitdist	6	100000	100	0.88113487	PASSED
rgb_bitdist	7	100000	100	0.57974761	PASSED
rgb_bitdist	8	100000	100	0.89529590	PASSED
rgb_bitdist	9	100000	100	0.94565152	PASSED
rgb_bitdist	10	100000	100	0.49196232	PASSED
rgb_bitdist	11	100000	100	0.10108980	PASSED
rgb_bitdist	12	100000	200	0.94697672	PASSED
rgb_minimum_distance	2	10000	1000	0.87670249	PASSED
rgb_minimum_distance	3	10000	1000	0.18101134	PASSED
rgb_minimum_distance	4	10000	1000	0.19003916	PASSED
rgb_minimum_distance	5	10000	1000	0.07977120	PASSED
rgb_permutations	2	100000	100	0.56047484	PASSED
rgb_permutations	3	100000	100	0.76166130	PASSED
rgb_permutations	4	100000	100	0.46830372	PASSED
rgb_permutations	5	100000	200	0.75750863	PASSED
rgb_lagged_sum	0	1000000	100	0.97892173	PASSED
rgb_lagged_sum	1	1000000	100	0.76349192	PASSED
rgb_lagged_sum	2	1000000	100	0.40145912	PASSED
rgb_lagged_sum	3	1000000	100	0.89253610	PASSED
rgb_lagged_sum	4	1000000	100	0.95886472	PASSED
rgb_lagged_sum	5	1000000	100	0.41160610	PASSED
rgb_lagged_sum	6	1000000	100	0.87348384	PASSED
rgb_lagged_sum	7	1000000	100	0.81728195	PASSED
rgb_lagged_sum	8	1000000	100	0.94655642	PASSED
rgb_lagged_sum	9	1000000	100	0.77865368	PASSED
rgb_lagged_sum	10	1000000	100	0.32911395	PASSED
rgb_lagged_sum	11	1000000	100	0.76051072	PASSED
rgb_lagged_sum	12	1000000	100	0.85088889	PASSED
rgb_lagged_sum	13	1000000	100	0.73633217	PASSED
rgb_lagged_sum	14	1000000	100	0.81211858	PASSED
rgb_lagged_sum	15	1000000	100	0.79704395	PASSED
rgb_lagged_sum	16	1000000	100	0.35199156	PASSED
rgb_lagged_sum	17	1000000	100	0.32973893	PASSED
rgb_lagged_sum	18	1000000	100	0.13043915	PASSED
rgb_lagged_sum	19	1000000	100	0.21741424	PASSED
rgb_lagged_sum	20	1000000	100	0.07393875	PASSED
rgb_lagged_sum	21	1000000	100	0.94638327	PASSED
rgb_lagged_sum	22	1000000	100	0.30391753	PASSED
rgb_lagged_sum	23	1000000	100	0.59288388	PASSED
rgb_lagged_sum	24	1000000	100	0.81374109	PASSED
rgb_lagged_sum	25	1000000	100	0.22536683	PASSED
rgb_lagged_sum	26	1000000	100	0.87509559	PASSED
rgb_lagged_sum	27	1000000	100	0.85276547	PASSED
rgb_lagged_sum	28	1000000	100	0.25947740	PASSED
rgb_lagged_sum	29	1000000	100	0.53805258	PASSED
rgb_lagged_sum	30	1000000	100	0.84417853	PASSED
rgb_lagged_sum	31	1000000	100	0.22136514	PASSED
rgb_lagged_sum	32	1000000	100	0.65164575	PASSED
rgb_kstest_test	0	10000	1000	0.55696401	PASSED
dab_bytedistrib	0	51200000	1	0.07797385	PASSED
dab_dct	256	50000	1	0.92717333	PASSED
dab_filltree	32	15000000	1	0.08584606	PASSED
dab_filltree	32	15000000	1	0.96272629	PASSED
dab_filltree2	0	5000000	1	0.49029050	PASSED
dab_filltree2	1	5000000	1	0.46930514	PASSED
dab_monobit2	12	65000000	1	0.94792086	PASSED

Initial State = γ

Initial State = Ω

Initial State = 1 / π

Initial State = 1 / e

Initial State = 1 / γ

Initial State = 1 / Ω

Initial State = √2

Initial State = √3

Initial State = √5

Initial State = √7

Initial State = √11

Initial State = 1 / √2

Initial State = 1 / √3

Initial State = 1 / √5

Initial State = 1 / √7

Initial State = 1 / √11