Recommended Generators

Introduction

Our xoshiro/xoroshiro implementations depend on up to 10 template parameters:

1. The unsigned word type used to store the state is also the generator's output type.
2. The number of words used to store the state. More words mean more state.
3. Up to three parameters, labelled \(A\), \(B\), and \(C\), which determine how the state is advanced.
4. Up to three parameters, labelled \(R\), \(S\), and \(T\), which determine how the state is scrambled to produce the required single output word.
5. Up to two indices that determine the words of the state taking part in the scrambler.

The code in xoshiro.h covers all possible cases, but typing that many parameters is not ergonomic. Moreover, while we can instantiate any generator in the family, only a limited number have been properly vetted for suitability as "good".

Therefore, we provide a few type aliases for the generators you should use in most cases.

Recommended Generators

The following type aliases cover the recommended defaults for 32-bit and 64-bit outputs:

Type Alias	Output Bits	State Bits	Synonym For
xso::rng	64	256	xso::rng64
xso::rng64	64	256	xso::xoshiro_4x64_star_star
xso::rng32	32	128	xso::xoshiro_4x32_star_star

The overall "default" xso::rng is the same thing as xso::rng64.

The 32-bit version has 128 bits of state in four 32-bit words, while the 64-bit version has 256 bits of state stored in four 64-bit words.

These generators pick specific A, B, and C parameters for the state advance method and specific R, S and T parameters for the output/scrambler function. The choices are shown in rows 11 and 14 of the table below.

Analysed Generators

Beyond the recommended and simplest type aliases above, we also provide rationally named type aliases for 17 variants, which are analysed in some detail in the original paper.

#	Type Alias	Output Bits	State Bits	State State	Output Function
1	xoroshiro_2x32_star	32	64	xoroshiro<26,9,13>	star<0x9E3779BB,0>
2	xoroshiro_2x32_star_star	32	64	xoroshiro<26,9,13>	star_star<0x9E3779BBu,5,5,0>
3	xoroshiro_2x64_plus	64	128	xoroshiro<24,16,37>	plus<0,1>
4	xoroshiro_2x64_plus_plus	64	128	xoroshiro<49,21,28>	plus_plus<17,0,1>
5	xoroshiro_2x64_star_star	64	128	xoroshiro<24,16,37>	star_star<5,7,9,0>
6	xoroshiro_16x64_star	64	1024	xoroshiro<25,27,36>	star<0x9e3779b97f4a7c13,0>
7	xoroshiro_16x64_star_star	64	1024	xoroshiro<25,27,36>	star_star<5,7,9,0>
8	xoroshiro_16x64_plus_plus	64	1024	xoroshiro<25,27,36>	plus_plus<23,15,0>
9	xoshiro_4x32_plus	32	128	xoshiro<9,11>	plus<0,3>
10	xoshiro_4x32_plus_plus	32	128	xoshiro<9,11>	plus_plus<7,0,3>
11	xoshiro_4x32_star_star	32	128	xoshiro<9,11>	plus_plus<7,0,3>
12	xoshiro_4x64_plus	64	256	xoshiro<17,45>	plus<0,3>
13	xoshiro_4x64_plus_plus	64	256	xoshiro<17,45>	plus_plus<23,0,3>
14	xoshiro_4x64_star_star	64	256	xoshiro<17,45>	star_star<5,7,9,1>
15	xoshiro_8x64_plus	64	512	xoshiro<11,21>	plus<2,0>
16	xoshiro_8x64_plus_plus	64	512	xoshiro<11,21>	plus_plus<17,2,0>
17	xoshiro_8x64_star_star	64	512	xoshiro<11,21>	star_star<5,7,9,1>

The naming convention should be fairly obvious — xoshiro or xoroshiro followed by the number of words of state and the size of those words, followed by some information about the type of output function that is used. The specific choices for the A, B, C, R, S, and T parameters are shown in the final two columns of the table.

Note: All the type aliases, engines, and output functions above are actually in the xso namespace — that has been dropped in the table for the sake of brevity.

See Also

xso::generator for information about the general implementation.