LXM Generator¶

class randomgen.lxm.LXM(seed=
None
, *, b=3037000493
)¶ Container for the LXM pseudorandom number generator.
 Parameters:¶
 seed=
None
¶ Entropy initializing the pseudorandom number generator. Can be an integer in [0, 2**64), array of integers in [0, 2**64), a SeedSequence instance or
None
(the default). If seed isNone
, then data is read from/dev/urandom
(or the Windows analog) if available. If unavailable, a hash of the time and process ID is used. b=
3037000493
¶ The additive constant in the LCG update. Must be odd, and so 1 is added if even. The default value is 3037000493.
 seed=
 lock¶
Lock instance that is shared so that the same bit git generator can be used in multiple Generators without corrupting the state. Code that generates values from a bit generator should hold the bit generator’s lock.
 Type:¶
 seed_seq¶
The SeedSequence instance used to initialize the generator if mode is “sequence” or is seed is a SeedSequence. None if mode is “legacy”.
 Type:¶
{None, SeedSequence}
Notes
The LXM generator combines two simple generators with an optional additional hashing of the output. This generator has been proposed for inclusion in Java ([1]). The first generator is a LCG of with and update
\[s = a s + b \mod 2^{64}\]where a is 2862933555777941757 and b is settable. The default value of b is 3037000493 ([5]). The second is the standard 64bit xorshift generator ([2], [3]). The output of these two is combined using addition. This sum is hashed using the Murmur3 hash function using the parameters suggested by David Stafford ([4]). Is pseudocode, each value is computed as Mix(LCG + Xorshift). While the origins of LXM are not clear from ([1]), it appears to be derived from LCG Xorshift Mix.
LXM
provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64 bit integers. These are not directly consumable in Python and must be consumed by aGenerator
or similar object that supports lowlevel access.State and Seeding
The
LXM
state vector consists of a 4element array of 64bit unsigned integers that constraint he state of the Xorshift generator and an addition 64bit unsigned integer that holds the state of the LCG.The seed value is used to create a
SeedSequence
which is then used to set the initial state.Parallel Features
LXM
can be used in parallel applications by calling the methodjumped
which provides a new instance with a state that has been updated asif \(2^{128}\) random numbers have been generated. This allows the original sequence to be split so that distinct segments can be used in each worker process. All generators should be initialized with the same seed to ensure that the segments come from the same sequence.>>> from numpy.random import Generator >>> from randomgen import LXM >>> rg = [Generator(LXM(1234))] # Advance each LXM instance by i jumps >>> for i in range(10): ... rg.append(rg[1].jumped())
Note that jumped states only alters the Xorshift state since the jump is a full cycle of the LCG.
Compatibility Guarantee
LXM
makes a guarantee that a fixed seed will always produce the same random integer stream.Examples
>>> from numpy.random import Generator >>> from randomgen import LXM >>> rg = Generator(LXM(1234)) >>> rg.standard_normal() 0.123 # random
References
Seeding and State¶

Seed the generator 
Get or set the PRNG state 
Parallel generation¶

Jumps the state asif 2**128 random numbers have been generated 

Returns a new bit generator with the state jumped 
Extending¶
CFFI interface 

ctypes interface 
Testing¶

Return randoms as generated by the underlying BitGenerator 