Test Results: The LCG as Implemented by the Sinclair ZX81

Implementation

The Sinclair ZX81 was a home computer released in 1981. It was fairly substandard for the time, being an economy model that sold for one tenth the price of its competitors.

Its pseudo random number generator was a Linear Congruent Generator, set using the following values:

• M = 65536
• a = 75
• c = 74

The use of such a small M value drastically limits this PRNG's period and possible range, which shows in the test results below.

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Test Results

Period Length Test
SEED	Number indicates how many results could be obtained before the generator fell into a loop.
1138	65536	FAIL
65535	65536	FAIL
8675309	65537	FAIL
16777216	65537	FAIL
123456789	65537	FAIL

Dice Roll Test
	This generator produced an ideal distribution of outcomes.

Dartboard Test
SEED	Minimum of 6,000 darts placed needed to pass.
1138	6239	PASS
65535	6192	PASS
8675309	6225	PASS
16777216	6196	PASS
123456789	6227	PASS

Crush Test
SEED	70% or higher required to pass.
1138	101%	PASS
65535	101%	PASS
8675309	101%	PASS
16777216	101%	PASS
123456789	101%	PASS

Plot Test
	The striped pattern indicates a serious problem with this PRNG's design.

Example Output
62450	30697	8554	51791	17716	18034	41884	61135	63146	17360	56871	5494	18902	41447	28360	29890	13566	34469	29306	35303
26319	7889	1916	12700	35056	7794	60328	2621	38	2924	22763	3337	53738	32667	25230	57288	36769	5195	62014	63534
46460	11113	47105	59488	5158	59239	52020	34891	60956	49721	59077	39870	41159	6760	48315	19164	61097	60296	221	16649
3546	3876	28626	49840	2465	53875	42942	9411	50529	54140	62817	58222	41282	15985	19283	4485	8764	2004	19300	5760
38852	30346	47766	43526	53211	58679	10020	30667	6304	14115	10107	37192	36920	16520	59408	64695	2461	53575	20442	25873
39976	49109	13177	5294	3902	30576	65016	26536	24164	42875	4386	1339	34962	744	55874	61793	46959	48538	35889	4732
27289	15102	18595	18422	5447	15377	39220	57946	20582	36373	41032	62772	54847	50305	37340	48020	62576	40147	61934	57534
55219	12668	32656	24405	60950	49271	25327	64563	58098	31982	39392	5309	5027	49414	36052	16957	26646	32414	6255	10440
62167	9472	55104	4043	41151	6160	3315	52088	39991	50234	32015	41867	59860	33058	54555	28405	33265	4543	13114	569
42749	60473	13496	29219	28778	61240	5484	18152	50734	3978	36276	33757	41443	28060	7390	30028	23916	24275	51200	38928
36046	16507	58433	57107	23194	35662	53244	61154	64571	58698	11445	6468	26415	15089	17620	10834	26180	63001	6485	27690
45177	45962	39300	63946	11823	34818	55481	32318	64592	60273	64033	18348	65434	57886	16082	26558	25814	35551	44919	26612
29864	11616	19293	5235	65014	26386	12914	51106	31878	31592	10142	39817	37184	36320	37057	26795	43589	57936	19832	45660
16650	3621	9501	57279	36094	20107	748	56174	18756	30497	59091	40920	54372	14680	52482	4004	38226	48933	65514	63886
7323	25003	40263	5097	54664	36580	56557	47481	22151	22974	19162	60947	49046	8452	44141	33799	44593	2162	31150	42529
43973	21199	17111	38196	46683	27838	56277	26481	20039	61185	1359	36462	47707	39101	49021	6577	34590	38381	60558	19871
48585	39414	6959	63240	24410	61325	11859	37518	61370	15234	28495	40015	52034	35941	8632	57641	63244	24710	18288	60934
48071	864	64874	15886	11858	37443	55745	52118	42241	22373	39624	22709	64824	12136	58293	46607	22138	21999	11574	16143
31133	41254	13885	58394	54182	430	32324	65042	28486	39340	1409	40212	1272	29937	17091	36696	65257	44611	3512	1326
33987	58693	11070	43880	14224	18282	60484	14321	25557	16276	41108	2935	23588	65212	41236	12535	22681	62724	51247	42453