Sirius64 Pseudo Random Number Generator

Sirius64 is a ultra-fast, minimalist, robust pseudo-random number generator (PRNG) designed for high-performance applications, simulations, and games.

uint64_t sirius64(uint64_t *state) 
{
	uint64_t z = (*state += 0x9e3779b97f4a7c15ull);
	z = 0x9e3779b97f4a7c15ull * (z ^ (z >> 17));
	z = (z << 32) | (z >> 32);
	return 0x9e3779b97f4a7c15ull * ((*state) ^ z ^ (z >> 17));
}

Features

Period: $2^{64}$
State: 64 bit
Output: 64 bit
Seed: all 64-bit values

SmokeRand v.0.48-gcc-linux Tests

We decided to use SmokeRand (v. 0.48-gcc-linux64) as an initial test tool rather than Dieharder as it is a new tool that we found to be more reliable and accurate.
We ran 12 full runs with 64-bit inputs; 10 runs with random seeds, and 2 runs with limit seeds (0 and MAX_UINT64).
The output files are in the test_smokerand/ directory. Each full run performs 50 tests, for a total of 600 tests. No failures were detected, and one suspect were found, a number consistent with the expected value. All runs scored a quality of 4 (good) on a scale from 0 to 4.

SmokeRand Test Summary Table

#	Seed	Anomalies
01	2369157498668639969	-
02	14269143917408480699	-
03	4380167771877769980	-
04	16790869163370235529	-
05	11162697988881170641	test: bspace8_8d_high p-value: 1 - 5.63e-04 SUSPICIOUS
06	15018305529109891896	-
07	4094093812534875946	-
08	2259750328877818529	-
09	5627138766949811142	-
10	10129161356813192160	-
11	0	-
12	MAX_UINT64	-

PractRand v.0.96 Tests

Two complementary PractRand test campaigns were performed using independently generated random seeds.
The broad campaign provides extensive seed coverage, while the deep campaign provides substantial testing depth.
Together, these approaches assess both cross-seed robustness and long-range statistical behavior.

Broad Campaign

• 200 independent RNG_test runs.
• Each run covered the range from 1 GB to 1 TB.
• Designed to evaluate consistency across a large number of initial states and seeds.
• Report available on test_practrand/practrand_test.txt

Total PractRand reports: 200
Reports without anomalies: 90
Reports with anomalies: 110
Total Test Stages: 2200
Total Tests: 646200

Anomaly Counting

Anomaly	#	Percentage	Min p-value	Max p-value
unusual	147	0.0227%	3.9e-6	1 - 3.0e-5
mildly suspicious	9	0.0014%	3.2e-5	1 - 2.4e-5
suspicious	1	0.0002%	1 - 2.5e-5	1 - 2.5e-5
very suspicious	0	0%	-	-
FAIL	0	0%	-	-
Total	157	0.0243%	-	-

Anomaly for Test Stage

Test Stage	Unusual	Mildly Suspicious	Suspicious	Very Suspicious	FAIL	Total
1 GB	7	1	0	0	0	8
2 GB	12	1	0	0	0	13
4 GB	22	4	0	0	0	26
8 GB	16	2	0	0	0	18
16 GB	16	1	0	0	0	17
32 GB	11	0	0	0	0	11
64 GB	13	0	0	0	0	13
128 GB	11	0	0	0	0	11
256 GB	19	0	1	0	0	20
512 GB	13	0	0	0	0	13
1 TB	7	0	0	0	0	7
Total	147	9	1	0	0	157

Anomaly Ranking

Show

Anomaly	#
[Low4/64]DC6-9x1Bytes-1	16
DC6-9x1Bytes-1	15
[Low16/64]DC6-9x1Bytes-1	15
[Low1/64]DC6-9x1Bytes-1	12
[Low16/64]BCFN(2+0,13-0U)	5
[Low1/64]FPF/16:cross	4
BCFN(2+1,13-0U)	4
[Low16/64]Gap-16:A	4
Gap-16:B	4
[Low16/64]BCFN(2+1,13-0U)	4
FPF/16:all	4
BCFN(2+0,13-0U)	3
[Low4/64]Gap-16:A	3
[Low4/64]FPF/16:all	3
[Low16/64]FPF/16:cross	3
[Low1/64]Gap-16:A	3
[Low1/64]Gap-16:B	3
[Low16/64]FPF/16:all	3
[Low1/64]BCFN(2+1,13-3U)	3
FPF/16:cross	3
[Low1/64]FPF/16:all	3
[Low1/64]BCFN(2+0,13-0U)	2
[Low4/64]BCFN(2+2,13-3U)	2
Gap-16:A	2
[Low1/64]BCFN(2+1,13-1U)	2
[Low4/64]BCFN(2+1,13-0U)	2
[Low4/64]BCFN(2+2,13-0U)	2
[Low4/64]BCFN(2+0,13-0U)	2
[Low4/64]mod3n(5):(0,9-1)	1
[Low4/64]BCFN(2+10,13-5U)	1
[Low4/64]FPF/16:cross	1
BRank(12):score:4096	1
[Low16/64]mod3n(5):(3,9-1)	1
[Low1/64]BCFN(2+1,13-2U)	1
BCFN(2+2,13-0U)	1
[Low4/64]BCFN(2+2,13-1U)	1
[Low1/64]BCFN(2+6,13-2U)	1
BCFN(2+5,13-0U)	1
[Low4/64]mod3n(5):(3,9-0)	1
[Low4/64]BCFN(2+3,13-0U)	1
BRank(12):score:6144	1
[Low16/64]Gap-16:B	1
BDayS2(4,24)[64+0]	1
[Low16/64]BCFN(2+2,13-0U)	1
BRank(12):score:2560	1
BRank(12):score:5120	1
[Low1/64]BCFN(2+2,13-3U)	1
[Low1/64]BCFN(2+3,13-1U)	1
[Low4/64]BCFN(2+1,13-2U)	1
[Low1/64]BCFN(2+0,13-3U)	1
[Low1/64]BCFN(2+5,13-5U)	1
[Low4/64]BCFN(2+6,13-3U)	1
[Low16/64]BCFN(2+0,13-1U)	1
[Low16/64]BCFN(2+1,13-2U)	1
Total	157

Top/Bottom p-value distribuition of anomalies

This table displays the breakdown of p-values ​​close to 1 (top) and close to 0 (bottom); in an ideal uniform distribution the values ​​should be equal.

Top	Bottom	Total
91	66	157

No reproducible weakness was observed in this campaign.

Deep Campaign

• 10 independent RNG_test runs.
• Each run covered the range from 1 GB to 64 TB.
• Designed to detect weaknesses that may emerge only at very large output volumes.

TestU01 v.1.2.3 Tests