by Shiro Kawai (design), Arvydas Silanskas (implementation), Linas Vepštas (implementation), and John Cowan (editor and shepherd)
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This SRFI defines a set of SRFI 158 generators and generator makers that yield random data of specific ranges and distributions. It is intended to be implemented on top of SRFI 27, which provides the underlying source of random integers and floats.
Most of SRFI 27 is involved with creating and managing random
sources; there are only two generators for getting random numbers,
namely random-integer
to get a random but bounded
non-negative exact integer, and random-real
to get a
random inexact real number in the unit interval.
(When making use of a non-default random number source, the otherwise
equivalent procedures random-source-make-integers
and random-source-make-reals
can be used instead.)
However, it's very often useful to loosen these limitations, to provide random exact integers or real numbers within any desired range. In order to make them easy to use, they are exposed as generators: choose your bounds and you get a procedure which can be called without any arguments. This allows them to participate freely in the SRFI 158 infrastructure. In the same way, random booleans, random characters chosen from a seed string, and strings of random lengths up to a limit and with characters drawn from the same kind of seed string are all available.
All these use a uniform distribution of random numbers, but normal, exponential, geometric, and Poisson distributions also have their uses. Finally, if multiple generators are available, uniform and weighted choices can be made from them to produce a unified output stream.
current-random-source
An R7RS or SRFI 39
parameter that provides the random source
for all the procedures in this SRFI.
Its initial value is default-random-source
from SRFI 27.
Use parameterize
to specify a dynamic scope
in which a different SRFI 27 random source is used
when creating new generators.
The behavior of existing generators is
not affected by changes to this parameter.
(with-random-source
random-source thunk)
Binds current-random-source
to random-source
and then invokes thunk.
(make-random-source-generator
i)
Returns a generator of random sources.
Each invocation of the generator returns the random source
returned by passing the value of (current-random-source)
,
i, and successive integers j
(starting with 0) to the SRFI 27 procedure
random-source-pseudo-randomize!
.
The random sources are guaranteed to be distinct as long as i and j are not too large and the generator is not called too many times. What counts as "too large/many" depends on the SRFI 27 implementation; the sample implementation works correctly if i < 2^{63} and j < 2^{51} and no more than 2^{76} values are generated.
These generators generate uniformly distributed values of various simple Scheme types.
In the following examples, we use the generator->list
procedure to show
some concrete data from the generators.
(make-random-integer-generator
lower-bound upper-bound)
Returns a generator of exact integers between lower-bound (inclusive) and upper-bound (exclusive) uniformly. It is an error if the bounds are not exact integers or if the specified interval is empty.
;; A die roller (define die (make-random-integer-generator 1 7)) ;; Roll the die 10 times (generator->list die 10) ⇒ (6 6 2 4 2 5 5 1 2 2) |
(make-random-u1-generator
)
(make-random-u8-generator
)
(make-random-s8-generator
)
(make-random-u16-generator
)
(make-random-s16-generator
)
(make-random-u32-generator
)
(make-random-s32-generator
)
(make-random-u64-generator
)
(make-random-s64-generator
)
These procedures return generators of exact integers in the ranges of 1-bit unsigned and 8, 16, 32, and 64-bit signed and unsigned values respectively. These values can be stored in the corresponding homogeneous vectors of SRFI 160 and SRFI 178.
(generator->list (make-random-s8-generator) 10) ⇒ (20 -101 50 -99 -111 -28 -19 -61 39 110) |
(clamp-real-number
lower-bound upper-bound value)
Returns value clamped to be between lower-bound and upper-bound, inclusive. Note that this procedure works with either exact or inexact numbers, but will produce strange results with a mixture of the two. It is an error if the specified interval is empty.
(make-random-real-generator
lower-bound upper-bound)
Returns a generator that generates inexact real numbers uniformly.
(Note that this is not the same as returning all possible IEEE
floats within the stated range uniformly.)
The procedure returns reals between
lower-bound and upper-bound, both inclusive.
The similar procedure random-real
in SRFI 27
uses the exclusive bounds 0.0 and 1.0.
It is an error if the specified interval is empty.
(define uniform-100 (make-random-real-generator 0 100)) (generator->list uniform-100 3) ⇒ (81.67965004942268 81.84927577572596 53.02443813660833) |
(define generate-from-0-below-1 (gfilter (lambda (r) (not (= r 1.0))) (make-random-real-generator 0.0 1.0))) |
(make-random-rectangular-generator
real-lower-bound real-upper-bound imaginary-lower-bound imag-upper-bound)
Returns a generator that generates inexact complex numbers uniformly. The procedure returns complex numbers in a rectangle whose real part is between real-lower-bound and real-upper-bound (both inclusive), and whose imaginary part is between imag-lower-bound and imag-upper-bound (both inclusive). It is an error if either of the specified intervals is empty.
(make-random-polar-generator
[ origin ] magnitude-lower-bound magnitude-upper-bound [ angle-lower-bound angle-upper-bound ])
Returns a generator that generates inexact complex numbers uniformly. The procedure returns complex numbers in a sector of an annulus whose origin point is origin, whose magnitude is between magnitude-lower-bound and magnitude-upper-bound (both inclusive), and whose angle is between angle-lower-bound and angle-upper-bound (both inclusive). It is an error if either of the specified intervals is empty. The default value of origin is 0+0i, the default value of angle-lower-bound is 0, and the default value of angle-upper-bound is 2π. If all three are defaulted, the resulting shape is a disk centered on the origin.
(make-random-boolean-generator)
Generates boolean values (#f
and #t
) with equal probability.
(generator->list (make-random-boolean-generator) 10) ⇒ (#f #f #t #f #f #t #f #f #f #f) |
(make-random-char-generator
string)
Returns a generator that generates characters in string uniformly. Note that the characters in string need not be distinct, which allows simple weighting. It is an error if string is empty.
(define alphanumerics "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789") (define alphanumeric-chars (make-random-char-generator alphanumerics)) (generator->list alphanumeric-chars 10) ⇒ (#\f #\m #\3 #\S #\z #\m #\x #\S #\l #\y) |
(make-random-string-generator
k string)
Returns a generator that generates random strings whose characters are in string. Note that the characters in string need not be distinct, which allows simple weighting. The length of the strings is uniformly distributed between 0 (inclusive) and the length of string (exclusive). It is an error if string is empty.
(make-bernoulli-generator
p)
Returns a generator that yields 1 with probability p and 0 with probability 1 - p.
(make-binomial-generator n p)
Returns a binomial random variate generator, which conceptually is the sum of n
Bernoulli-p
random variables.
(make-categorical-generator
weight-vec)
Returns a generator that yields an exact integer n between 0 (inclusive) and the length of weight-vec (inclusive) with probability equal to the nth element of weight-vec divided by the sum of its elements. It is an error if any element of weight-vec is negative or their sum is zero.
(make-normal-generator
[ mean [ deviation ] ])
Returns a generator that yields real numbers from a normal distribution with the specified mean and deviation. The default value of mean is 0.0 and deviation is 1.0.
(make-exponential-generator
mean)
Returns a generator that yields real numbers from an exponential distribution with the specified mean.
(make-geometric-generator
p)
Returns a generator that yields integers from the geometric distribution
with success probability p (0 <= p <= 1). The mean is 1/p
and
variance is (1-p)/p^2
.
(make-poisson-generator
L)
Returns a generator that yields integers from the Poisson distribution with mean L, variance L.
(make-zipf-generator
N [ s [ q ] ])
Returns a generator that yields exact integers k from the generalized Zipf distribution 1/(k+q^{s} such that 1 ≤ k ≤ N). The default value of s is 1.0 and the default value of q is 0.0. Parameters outside the following ranges are likely to result in overflows or loss of precision: -10 < s < 100, -0.5 < q < 2^{8}, and 1 ≤ N.
The following three procedures generate points of real k-dimensional Euclidean space. These points are modeled as Scheme vectors of real numbers of length k.
(make-sphere-generator n)
(make-ellipsoid-generator axes)
(make-ball-generator dimensions)
(gsampling
generator ...)
Takes the generators and returns a new generator. Every time the resulting generator is called, it picks one of the input generators with equal probability, then calls it to get a value. When all the generators are exhausted or no generators are specified, the new generator returns an end-of-file object.
The sample implementation is in the
repository
of this SRFI and in this
.tgz
file.
An R7RS library file and a separate file containing the actual
implementation are provided, along with a test file that
works with SRFI 64.
The library itself depends on either
SRFI
121 or SRFI
158, and of course SRFI
27.
This SRFI began life as Shiro Kawai's specification for
data.random
, a Gauche library. Many of the names have
been changed to fit in better with SRFI 158 names, but the essence
is the same. John Cowan made those and other revisions, and then
put the SRFI on the back burner until he got around to implementing
it. Arvydas Silanskas began by asking why the next R7RS-large
ballot was so delayed, and ended up volunteering to write code for
the parts already specified. This SRFI is his first such implementation,
and in the process of writing it he found a number of errors in the specification
as well, which John was very glad to be told about.
During the SRFI review process, the following additional generators were added: the binomial and random-source generators written by Brad Lucier, and the Zipf, sphere, and ball generators written by Linas Vepstas.
Thanks also to the Scheme community and especially the contributors to the SRFI 194 mailing list, including Shiro Kawai and Marc Nieper-Wißkirchen.
© 2020 John Cowan.
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