Hawkynt

Combined LCG

Combined Linear Congruential Generator combines outputs from multiple LCG instances to produce better statistical properties than a single LCG. Developed by Pierre L’Ecuyer in 1988, the combination methods (additive, subtractive, multiplicative, XOR) significantly extend the period and improve randomness quality.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Pseudorandom Number Generator
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Pierre L’Ecuyer
Year	1988
Origin	🇨🇦 Canada
Source	`algorithms/random/combined-lcg.js`

Parameters

Parameter	Supported values
Seed sizes	1 byte (8 bits) to 32 bytes (256 bits)

Capabilities

Flag	Value
`IsDeterministic`	Yes
`IsCryptographicallySecure`	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

L’Ecuyer, P. (1988): Efficient and Portable Combined Random Number Generators (CACM 31(6):742-749,774)
L’Ecuyer, P. (1999): Good Parameters for Combined Multiple Recursive Generators (Operations Research 47(1):159-164)
Wikipedia: Linear Congruential Generator

References

Test vectors

5 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — Default PCG parameters, Additive mode, seed=1 - First 5 values

Field	Value
`seed`	`0000000000000001`
`combinationMode`	`0`
`lcg1Multiplier`	`5851f42d4c957f2d`
`lcg1Increment`	`14057b7ef767814f`
`lcg1Modulo`	`00`
`lcg2Multiplier`	`369dea0f31a53f85`
`lcg2Increment`	`255992d382208b61`
`lcg2Modulo`	`00`
`outputSize`	`40`
`input`	`null`
`expected`	`618049f4081c4420659a51615ac96cb0 c55ee230c7bb90d8d13ac8e8fa053618 925b372afca62170`

Vector 2 — Default PCG parameters, XOR mode, seed=42 - First 5 values

Field	Value
`seed`	`000000000000002a`
`combinationMode`	`3`
`lcg1Multiplier`	`5851f42d4c957f2d`
`lcg1Increment`	`14057b7ef767814f`
`lcg1Modulo`	`00`
`lcg2Multiplier`	`369dea0f31a53f85`
`lcg2Increment`	`255992d382208b61`
`lcg2Modulo`	`00`
`outputSize`	`40`
`input`	`null`
`expected`	`079c9839b884a2704981dc493c664dde 2ed1bfec97391484183722416c6399f6 3ed118fd21a09238`

Vector 3 — L’Ecuyer 1988 32-bit parameters, Additive mode, seed=12345 - First 5 values

Field	Value
`seed`	`0000000000003039`
`combinationMode`	`0`
`lcg1Multiplier`	`00009c4e`
`lcg1Increment`	`00000000`
`lcg1Modulo`	`7fffffab`
`lcg2Multiplier`	`00009ef4`
`lcg2Increment`	`00000000`
`lcg2Modulo`	`7fffff07`
`outputSize`	`40`
`input`	`null`
`expected`	`000000006265368c000000005fa82458 0000000039fd3bd5000000005bf0874e 0000000075a84d5d`

Vector 4 — Subtractive mode test, seed=1 - First 5 values

Field	Value
`seed`	`0000000000000001`
`combinationMode`	`1`
`lcg1Multiplier`	`5851f42d4c957f2d`
`lcg1Increment`	`14057b7ef767814f`
`lcg1Modulo`	`00`
`lcg2Multiplier`	`369dea0f31a53f85`
`lcg2Increment`	`255992d382208b61`
`lcg2Modulo`	`00`
`outputSize`	`40`
`input`	`null`
`expected`	`d226e9cefa38d85898c47e2167f31f06 7017c59a44754ac45cf94be0781ecaf2 97c52ce171d305f0`

Vector 5 — Multiplicative mode test, seed=100 - First 5 values

Field	Value
`seed`	`0000000000000064`
`combinationMode`	`2`
`lcg1Multiplier`	`5851f42d4c957f2d`
`lcg1Increment`	`14057b7ef767814f`
`lcg1Modulo`	`00`
`lcg2Multiplier`	`369dea0f31a53f85`
`lcg2Increment`	`255992d382208b61`
`lcg2Modulo`	`00`
`outputSize`	`40`
`input`	`null`
`expected`	`240f6b8a133e41bff80401a36365d6dc 879fb6afb278c5d7d2ec230014f07200 c6c06de607e40507`

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