| Title: | Seeding the Default RNG with a Numeric Vector |
|---|---|
| Description: | A function setVectorSeed() is provided. Its argument is a numeric vector of an arbitrary nonzero length, whose components have integer values from [0, 2^32-1]. The input vector is transformed using AES (Advanced Encryption Standard) algorithm into an initial state of Mersenne-Twister random number generator. The function provides a better alternative to the R base function set.seed(), if the input vector is a single integer. Initializing a stream of random numbers with a vector is a convenient way to obtain several streams, each of which is identified by several integer indices. |
| Authors: | Petr Savicky |
| Maintainer: | Petr Savicky <[email protected]> |
| License: | GPL-3 |
| Version: | 0.3-3 |
| Built: | 2024-10-25 09:15:13 UTC |
| Source: | https://github.com/cranhaven/cranhaven.r-universe.dev |
The function setVectorSeed(vseed) is provided, which allows to
initialize the R base Mersenne-Twister random number generator using
a numeric vector vseed of an arbitrary nonzero length. The
transformation of vseed into the initial state of Mersenne-Twister
is computed using AES (Advanced Encryption Standard). The precise
algorithm is described in generateInitialization.
The directory "rngSetSeed/tests" contains tests, which
compare the generated random numbers to stored precomuted ones,
compare the initial states obtained using AES in C-level functions with initial states obtained using a (slow) implementation of AES in R-level functions included for test purposes.
setVectorSeed, generateInitialization.
In a typical application of the package, this function is not called
directly by the user and the function is called from setVectorSeed().
The function is made available in order to simplify testing correctness
of the package and the documentation of this function explains the exact
algorithm used by setVectorSeed().
generateInitialization(vseed, m)generateInitialization(vseed, m)
vseed |
Numeric vector of an arbitrary nonzero length, whose components
have integer values from |
m |
Numeric, the length of the required output integer vector. |
The function transforms an input vector vseed of an arbitrary length
to a random integer vector of length m using Advanced Encryption
Standard (AES) block cipher. The function setVectorSeed() calls
generateInitialization(vseed, 624) and uses its output as an initial
state of the R base Mersenne-Twister random number generator.
The vector vseed is first replaced by c(vseed, length(vseed))
in order to guarantee that if vseed1 is a prefix of vseed2,
but they have a different length, then the outputs are unrelated. If the length
of the resulting vector is not divisible by 8, the vector is padded by zeros
to the nearest larger length divisible by 8 in order to meet the requirements
of the AES algorithm. The resulting vector is splitted into blocks of length 8
and these blocks are used as 256-bit keys in AES. Each of these keys is used
to encrypt a counter sequence of length ceiling(m/4). The encrypted
values of these sequences are combined by XOR to a single sequence of
ceiling(m/4) values, each of which is a sequence of 16 bytes. These
sequences are splitted into subsequences of 4 bytes, each of which encodes
a 32-bit integer in an endianness independent way. The first m of the
obtained integers form the output.
If length(vseed) <= 7, then the above algorithm uses AES in counter
mode suggested in Fortuna random number generator as described at
https://en.wikipedia.org/wiki/Fortuna_(PRNG) with a key specified
by the user.
If length(vseed) >= 8, the algorithm uses XOR of the outputs
of several Fortuna generators with keys formed from disjoint parts of
the input vector and disjoint counter sequences.
Vector of length m of integer type suitable for substituting into
the components of .Random.seed. This means that the components
are integers from the interval [-2^31 + 1, 2^31 - 1] or NA,
which represents -2^31. If m == 624, the output vector is
suitable as the initial state of Mersenne-Twister to be copied into
.Random.seed[3:626].
If m1 < m2, then generateInitialization(vseed, m1) is equal
to the first m1 components of generateInitialization(vseed, m2).
https://en.wikipedia.org/wiki/Advanced_Encryption_Standard, https://en.wikipedia.org/wiki/Fortuna_(PRNG).
s1 <- generateInitialization(1, 3) s2 <- generateInitialization(c(1, 0), 3) s3 <- generateInitialization(c(1, 0, 0), 3) stopifnot(s1 == c(2054882070, -83320660, -37036705)) stopifnot(s2 == c(-1435341980, 1760892082, 970206446)) stopifnot(s3 == c(1941187208, 915534877, -365000103))s1 <- generateInitialization(1, 3) s2 <- generateInitialization(c(1, 0), 3) s3 <- generateInitialization(c(1, 0, 0), 3) stopifnot(s1 == c(2054882070, -83320660, -37036705)) stopifnot(s2 == c(-1435341980, 1760892082, 970206446)) stopifnot(s3 == c(1941187208, 915534877, -365000103))
Initializes Mersenne-Twister random number generator, which is
the default RNG in R, with a numeric vector
of arbitrary nonzero length, whose components are
interpreted as 32-bit integers. In order to guarantee that different input
vectors yield unrelated streams of random numbers, Fortuna random number
generator using AES (Advanced Encryption Standard) encryption
algorithm is used for the transformation of vseed to the
initial state of Mersenne-Twister. See generateInitialization
for more detail of the algorithm.
setVectorSeed(vseed)setVectorSeed(vseed)
vseed |
Numeric vector of arbitrary nonzero length with
integer values from |
The function calls RNGkind("Mersenne-Twister") and then replaces
its state with generateInitialization(vseed) as an initial state.
See generateInitialization for the description of the algorithm
computing the initialization of length 624 from vseed.
NULL invisibly.
setVectorSeed(1) x1 <- runif(5) setVectorSeed(c(1, 0)) x2 <- runif(5) stopifnot(abs(x1 - c(0.30327915, 0.93045726, 0.20716215, 0.04424525, 0.07478261)) < 1e-8) stopifnot(abs(x2 - c(0.02231465, 0.80036017, 0.27630612, 0.69594674, 0.02688734)) < 1e-8)setVectorSeed(1) x1 <- runif(5) setVectorSeed(c(1, 0)) x2 <- runif(5) stopifnot(abs(x1 - c(0.30327915, 0.93045726, 0.20716215, 0.04424525, 0.07478261)) < 1e-8) stopifnot(abs(x2 - c(0.02231465, 0.80036017, 0.27630612, 0.69594674, 0.02688734)) < 1e-8)