| init.sprng {rsprng} | R Documentation |
init.sprng initializes the parallel random number generator
types and seeds.
RNGkind ("user") is called if necessary so that the default RNG
is substituted with the parallel one.
init.sprng (nstream, streamno, seed = 0, kindprng = "default", para = 0)
nstream |
total number of random number streams to be initialized |
streamno |
the rank of the the random number stream
in current process (valid value is from 0 to nstream - 1) |
seed |
an integer of random number seed. It is not the starting state of the sequence; rather, it is an encoding of the starting state. The same seed for all the streams. Distinct streams are returned. Only the 31 least significant bits of seed are used in determining the initial starting state of the stream. Default value is 0 where the default seed for each random number generator is used |
kindprng |
a character string of the disired kind of parallel random number generator |
para |
additional parameters for the parallel random number
generators. If para is 0, default parameters for each PRNG
are used. When invalid parameter is given, a warning is issued and
the default paramter is used. |
The currently available PRNG kinds are given below. prngkind is
partially matched to this list. The default is "LFG".
"LFG"The recurrence relation for this sequence of random numbers is given by the following equation:
z_n = x_n mathrm{XOR} y_n
where XOR is the exclusive-or operator, x and y are sequences obtained from Lagged Fibonacci sequences X and Y of the following form:
X_n = (X_{n-k} + X_{n-l}) mathrm{ Mod } M
Y_n = (Y_{n-k} + Y_{n-l}) mathrm{ Mod } M
l and k are called the lags of the generator, and we use the convention that l > k. M is chosen to be 2^32. X_n and Y_n are 32 bit integers. x is obtained from X by setting the Least Significant Bit of the latter to 0. y is obtained from Y by shifting the latter right by one bit. This modification of the Lagged Fibonacci Generator is performed in order to avoid certain correlations that are observed in the unmodified generator.
The period of this generator is 2^31(2^l-1) where l is the lag. For the default generator with lag l = 1279, the period is approximately 2^1310. The number of distinct streams available is 2^{31(l-1)-1}. For the default generator this gives 2^39648 distinct streams.
The parameters to this generator are the values of the lags.
Allowed para values are:
para | l | k |
| 0 (default) | 1279 | 861 |
| 1 | 17 | 5 |
| 2 | 31 | 6 |
| 3 | 55 | 24 |
| 4 | 63 | 31 |
| 5 | 127 | 97 |
| 6 | 521 | 353 |
| 7 | 521 | 168 |
| 8 | 607 | 334 |
| 9 | 607 | 273 |
| 10 | 1279 | 418 |
"LCG"The recurrence relation for the sequence of random numbers produced by this generator is given by the following recurrence:
x_n = (a x_{n-1} + p ) mathrm{ Mod } M
where x_n is the n th term in the sequence, p is a prime number and a is the multiplier. The value of M for this generator is 2^48. Different random number streams are obtained by choosing different prime numbers as the addend p. The period of this generator is 2^48. The number of distinct streams available is of the order of 2^19.
The multiplier a is a parameter to this generator. Allowed
para values are 0 to 6, corresponding to 7 prefined
multipliers.
"LCG64"
The features of this generator are similar to the "LCG",
except that the arithmetic is modulo 2^64. The multipliers
and prime addends p for this generator are different from
those for the 48 bit generator.
The period of this generator is 2^64. The number of
distinct streams available is over 10^8. Allowed
para values are 0 to 2, corresponding to 3 prefine
multipliers.
"CMRG"This generator is defined by the following relation:
z_n = (x_n + y_n * 2^32 ) mathrm{ Mod } 2^64
where x_n is the sequence generated by the 64 bit Linear Congruential Generator and y_n is the sequence generated by the following prime modulus Multiple Recursive Generator:
y_n = (107374182 * y_{n-1} + 104480 * y_{n-5}) mathrm{ Mod } 2147483647
The same prime modulus generator is used for all the streams. Streams differ due to differences in the 64 bit LCG. The period of this generator is around 2^219. The number of distinct streams available is over 10^8.
The multiplier a for the 64 bit LCG is a parameter to this
generator. Allowed para values are 0 to 2, corresponding
to 3 prefine multipliers (same as "LCG64").
"MLFG"The recurrence relation for this sequence of random numbers is given by the following equation:
x_n = (x_{n-k} * x_{n-l}) mathrm{ Mod } M
l and k are called the lags of the generator, and we use the convention that l > k. M is chosen to be 2^64.
The period of this generator is 2^61(2^l-1) where l is the lag. For the default generator with lag l = 17, the period is approximately 2^81. The number of distinct streams available is 2^{63(l-1)-1}. For the default generator this gives around 2^1008 distinct streams.
The parameters to this generator are the values of the lags. Allowed
para values are:
para | l | k |
| 0 (default) | 17 | 5 |
| 1 | 31 | 6 |
| 2 | 55 | 24 |
| 3 | 63 | 31 |
| 4 | 127 | 97 |
| 5 | 521 | 353 |
| 6 | 521 | 168 |
| 7 | 607 | 334 |
| 8 | 607 | 273 |
| 9 | 1279 | 418 |
| 10 | 1279 | 861 |
"PMLCG"This generator is defined by the following relation:
x_n = ( a x_{n-1} ) mathrm{ Mod } 2^61-1
where the multiplier a differs for each stream. The mulitpler is chosen to be certain powers of 37 that give maximal period cycles of acceptable quality.
The period of this generator is 2^61-2. The number of distinct streams available is roughly 2^58.
This generator only accept the default parameter thus 0 is the
only allowed value for para.
None.
Only one active stream is allowed for each R process. Multiple streams per process can be achieved by saving (packing) the states of the streams and unpacking when needed.
Na (Michael) Li nali@umn.edu
SPRNG: Scalable Parallel Random Number Generator Library Web Page. http://sprng.cs.fsu.edu/
free.sprng, pack.sprng,
spawn.sprng, spawn.new.sprng
init.sprng (1, 0, kind = "MLFG", para = 6) runif (10) free.sprng ()