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Ran0 (Numerical Recipes)

Park-Miller minimal standard PRNG from Numerical Recipes. Simple multiplicative linear congruential generator using Schrage’s method to compute (16807 × seed) mod (2^31-1) without overflow. Returns floating-point values in [0.0, 1.0). Superseded by Ran2 and Ran3, but useful for educational purposes and as a reference implementation.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Linear Congruential Generator
Security status	🎓 Educational Only
Complexity	Beginner
Inventor	Stephen K. Park and Keith W. Miller
Year	1988
Origin	🇺🇸 United States
Source	algorithms/random/ran0.js

Parameters

Parameter	Supported values
Seed sizes	1 byte (8 bits) to 4 bytes (32 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• Numerical Recipes in C: The Art of Scientific Computing (2nd Ed.), Section 7.1
• Park and Miller (1988): Random Number Generators: Good Ones Are Hard to Find
• Wikipedia: Lehmer Random Number Generator

References

• Press et al., Numerical Recipes in C (1992), pp. 278-286
• Park and Miller, CACM 31(10):1192-1201 (1988)
• Numerical Recipes Legacy Code Repository

Test vectors

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

Vector 1 — Seed=1: First 10 output values (floating-point doubles)

Field	Value
seed	00000001
outputSize	80
input	null
expected	80d32000c069e03e76ac21f13ad6c03f d65b7036eb2de83f0cb53a15865add3f dc18a2e06d0ce13fb60d38c8da06cc3f 772c30603b16a83f8572ab7f42b9e53f 9879ebd0cbbce53f02d27b1301e9ed3f

Vector 2 — Seed=123456789: First 5 output values

Field	Value
seed	075bcd15
outputSize	40
input	null
expected	43ea377921f5cb3f4f347d51279aee3f ae16f5f2568bea3fd1f2a3b868f9e13f c82835276494da3f

Vector 3 — Park-Miller canonical test: 10,000th iteration from seed=1

Field	Value
seed	00000001
count	10000
outputSize	8
input	null
expected	5934be882c1adf3f

Vector 4 — Seed=16807 (multiplier a): First value

Field	Value
seed	000041a7
outputSize	8
input	null
expected	76ac21f13ad6c03f

Vector 5 — Seed=2147483646 (max valid seed): First value

Field	Value
seed	7ffffffe
outputSize	8
input	null
expected	dfff3f96efffef3f

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