/usr/share/gauche-0.9/0.9.4/lib/data/random.scm is in gauche 0.9.4-6.
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;;; data.random - Random data genarators
;;;
;;; Copyright (c) 2013-2014 Shiro Kawai <shiro@acm.org>
;;;
;;; Redistribution and use in source and binary forms, with or without
;;; modification, are permitted provided that the following conditions
;;; are met:
;;;
;;; 1. Redistributions of source code must retain the above copyright
;;; notice, this list of conditions and the following disclaimer.
;;;
;;; 2. Redistributions in binary form must reproduce the above copyright
;;; notice, this list of conditions and the following disclaimer in the
;;; documentation and/or other materials provided with the distribution.
;;;
;;; 3. Neither the name of the authors nor the names of its contributors
;;; may be used to endorse or promote products derived from this
;;; software without specific prior written permission.
;;;
;;; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
;;; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
;;; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
;;; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
;;; OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
;;; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
;;; TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
;;; PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
;;; LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
;;; NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
;;; SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
;;;
(define-module data.random
(use srfi-1)
(use srfi-14)
(use srfi-42)
(use math.const)
(use math.mt-random)
(use gauche.uvector)
(use gauche.generator)
(use gauche.parameter)
(use gauche.sequence)
(export make-random-data-state random-data-seed with-random-data-seed
integers$ integers-between$ fixnums chars$ booleans
int8s uint8s int16s uint16s int32s uint32s int64s uint64s
reals$ reals-between$ reals-normal$ reals-exponential$
integers-geometric$ integers-poisson$
default-sizer
samples-from pairs-of tuples-of lists-of vectors-of strings-of
sequences-of
permutations-of combinations-of weighted-samples-from
))
(select-module data.random)
;; Random state management
;; Random state is kept in %random-source parameter as (seed . #<mt>)
;; We use mt-random directly instead of srfi-27, for we need
;; a portable way to save and restore the random state.
;; Srfi-27's random state isn't guaranteed to be printable.
;; API
(define (make-random-data-state seed)
(cons seed (make <mersenne-twister> :seed seed)))
(define %random-data-state
(make-parameter (make-random-data-state 42)))
;; API
(define random-data-seed
(getter-with-setter
(^[] (car (%random-data-state)))
(^[seed] (%random-data-state (make-random-data-state seed)))))
;; API
(define (with-random-data-seed seed thunk)
;; create st here so that reentering thunk retains the state.
(let1 st (make-random-data-state seed)
(parameterize ([%random-data-state st])
(thunk))))
(define (%rand-int n) (mt-random-integer (cdr (%random-data-state)) n))
(define (%rand-real0) (mt-random-real0 (cdr (%random-data-state))))
(define (%rand-real) (mt-random-real (cdr (%random-data-state))))
;;;
;;; Primitive generators
;;;
;;
;; Uniform distribution
;;
;; API. Generate integers uniformly in [start, start+size)
(define (integers$ size :optional (start 0))
(^[] (+ (%rand-int size) start)))
;; API. Generate integers uniformly in [lb ub]
;; (We avoid 'integer-range', for 'range' API takes exclusive upper bound.)
(define (integers-between$ lb ub)
(let1 range (- ub lb -1)
(^[] (+ (%rand-int range) lb))))
;; API.
(define fixnums (integers-between$ (least-fixnum) (greatest-fixnum)))
(define int8s (integers$ 256 -128))
(define uint8s (integers$ 256))
(define int16s (integers$ 65536 -32768))
(define uint16s (integers$ 65536))
(define int32s (integers$ (expt 2 32) (- (expt 2 31))))
(define uint32s (integers$ (expt 2 32)))
(define int64s (integers$ (expt 2 64) (- (expt 2 64))))
(define uint64s (integers$ (expt 2 64)))
;; API.
(define booleans (^[] (zero? (%rand-int 2))))
;; API.
;; The default value of cset is debatable. We play "safe" here, limiting
;; ascii alphabets and digits, which would satisfy typical use cases without
;; worrying character encodings too much.
(define (chars$ :optional (cset #[A-Za-z0-9]))
;; We map the integer within the total # of chars in CSET into
;; the delimited ranges of characters in CSET. For example, if CSET
;; is splitted into a ranges ((48 . 57) (65 . 90) (97 . 122)),
;; the table has the following mappings:
;; 0 -> 48 (for range 48-57)
;; 10 -> (- 65 10) (for range 65-90)
;; 36 -> (- 97 36) (for range 97-122)
;; We generate a random integer in [0, 61], that is, the size same as
;; the # of chars in the CSET, then use tree-map-floor to find where it
;; belongs; that gives us an offset to add to the sample number to get
;; the char code.
;;
;; If CSET has only one range, however, we use simpler sampling
;; for optimization.
(let1 ranges ((with-module gauche.internal %char-set-ranges) cset)
(if (null? (cdr ranges))
;; simple case
(let* ([lb (caar ranges)]
[ub (cdar ranges)]
[size (- (+ ub 1) lb)])
(^[] (integer->char (+ (%rand-int size) lb))))
;; general case
(let* ([tab (make-tree-map)]
[total (do ([ranges ranges (cdr ranges)]
[cumu 0 (+ cumu (- (+ (cdar ranges) 1) (caar ranges)))])
[(null? ranges) cumu]
(tree-map-put! tab cumu (- (caar ranges) cumu)))])
(^[] (let1 p (%rand-int total)
(receive (_ off) (tree-map-floor tab p)
(integer->char (+ p off)))))))))
;; API. Extra clamp ensures fp errors won't cause out-of-range value.
;; NB: We clamp instead of rejecting the out-of-range value---since such
;; value can only be produced on the FP values on the edge, and we should
;; regard it inappropriate rounding (for our purpose). If we reject them,
;; it will skew the distribution.
(define (reals$ :optional (size 1.0) (start 0.0))
(let1 ub (+ size start)
(^[] (clamp (+ start (* size (%rand-real0))) start ub))))
(define (reals-between$ lb ub)
(let1 range (+ lb ub)
(^[] (clamp (- (* range (%rand-real0)) lb) lb ub))))
;; rational
;; complex
;;
;; Nonuniform distributions
;;
;; Normal distribution (continuous - generates real numbers)
;; Box-Muller algorithm
;; NB: We tested Ziggurat method, too (see git repo for the code),
;; only to find out Box-Muller is faster about 12% - presumably
;; the overhead of each ops is larger in Gauche than C/C++, and
;; so the difference of cost of log or sin from the primitive
;; addition/multiplication are negligible.
(define (reals-normal$ :optional (mean 0) (deviation 1))
(^[] (let ([r (%sqrt (* -2 (%log (%rand-real))))]
[theta (* 2pi (%rand-real))])
(+ mean (* deviation r (%sin theta))))))
#|
Simple test of gaussian sampling: Generate some data with this:
(with-output-to-file "tmp"
(^[] (let1 g (normal$ 2 3) (dotimes [i 1000000] (print (g))))))
Then plot with gnuplot:
binwidth=0.025
bin(x,width)=width*floor(x/width)
plot 'tmp' using (bin($1,binwidth)):(1.0) smooth freq with boxes
|#
;; Exponential distribution - continuous
(define (reals-exponential$ m)
(^[] (- (* m (log (%rand-real))))))
;; Draw from geometric distribution, with success probability p.
;; Mean is 1/p, variance is (1-p)/p^2
(define (integers-geometric$ p)
(let1 c (/ (log (- 1.0 p)))
(^[] (ceiling->exact (* c (log (%rand-real)))))))
;; Draw from poisson distribution with mean L, variance L.
;; For small L, we use Knuth's method. For larger L, we use rejection
;; method by Atkinson, The Computer Generation of Poisson Random Variables,
;; J. of the Royal Statistical Society Series C (Applied Statistics), 28(1),
;; pp29-35, 1979. The code here is a port by John D Cook's C++ implementation
;; (http://www.johndcook.com/stand_alone_code.html )
(define (integers-poisson$ L)
(if (< L 36)
(^[] (do ([exp-L (exp (- L))]
[k 0 (+ k 1)]
[p 1.0 (* p (%rand-real))])
[(<= p exp-L) (- k 1)]))
(let* ([c (- 0.767 (/ 3.36 L))]
[beta (/ pi (sqrt (* 3 L)))]
[alpha (* beta L)]
[k (- (log c) L (log beta))])
(rec (loop)
(let* ([u (%rand-real)]
[x (/ (- alpha (log (/ (- 1.0 u) u))) beta)]
[n (floor->exact (+ x 0.5))])
(if (< n 0)
(loop)
(let* ([v (%rand-real)]
[y (- alpha (* beta x))]
[t (+ 1.0 (exp y))]
[lhs (+ y (log (/ v (* t t))))]
[rhs (+ k (* n (log L)) (- (lgamma (+ n 1))))])
(if (<= lhs rhs)
n
(loop)))))))))
#|
;; This generates histograms of samples
;; e.g. (gen-hist 1000 (poisson$ 5) (poisson$ 10) (poisson$ 20) (poisson$ 50))
(define (gen-hist count . thunks)
(let ([bins (map (^_ (make-hash-table 'eqv?)) thunks)]
[maxkey 0])
(dotimes [n count]
(do-ec (:parallel (: thunk thunks)
(: bin bins))
(let1 key (thunk)
(when (> key maxkey) (set! maxkey key))
(hash-table-update! bin key (cut + <> 1) 0))))
(dotimes [n (+ maxkey 1)]
(print
(string-join (cons (x->string n)
(map (^[bin] (x->string (hash-table-get bin n 0)))
bins))
" ")))))
|#
;;;
;;; Generator combinators
;;;
;; API
(define (samples-from seq-of-gen)
(let1 s (size-of seq-of-gen)
(^[] ((~ seq-of-gen (%rand-int s))))))
;; API
;; weight&gens :: ((<real> . <generator>) ...)
(define (weighted-samples-from weight&gens)
(let* ([tab (make-tree-map)]
[total (do [(w&g weight&gens (cdr w&g))
(cumu 0 (+ cumu (caar w&g)))]
[(null? w&g) cumu]
(tree-map-put! tab cumu (cdar w&g)))])
(^[] (receive (_ gen) (tree-map-floor tab (* (%rand-real0) total))
(gen)))))
;; API
(define (pairs-of car-gen cdr-gen) (^[] (cons (car-gen) (cdr-gen))))
;; API
(define (tuples-of . gens) (^[] (map (^g (g)) gens)))
;; We accept constant integer or generator
(define-syntax %with-sizer
(syntax-rules ()
[(_ sizer . body)
(let1 sizer (if (integer? sizer) (^[] sizer) sizer)
. body)]))
(define default-sizer (make-parameter (integers-poisson$ 4)))
;; API
(define lists-of
(case-lambda
[(item-gen) (lists-of (default-sizer) item-gen)]
[(sizer item-gen)
(%with-sizer sizer (^[] (list-tabulate (sizer) (^_ (item-gen)))))]))
;; API
(define vectors-of
(case-lambda
[(item-gen) (vectors-of (default-sizer) item-gen)]
[(sizer item-gen)
(%with-sizer sizer
(^[] (let1 len (sizer)
(rlet1 vec (make-vector len)
(do-ec (: i len) (vector-set! vec i (item-gen)))))))]))
;; API
(define strings-of
(case-lambda
[() (strings-of (default-sizer) (chars$))]
[(item-gen) (strings-of (default-sizer) item-gen)]
[(sizer item-gen)
(%with-sizer sizer
(^[] (let1 len (sizer)
(with-output-to-string
(^[] (do-ec (: i len) (display (item-gen))))))))]))
;; API
(define sequences-of
(case-lambda
[(class item-gen) (sequences-of class (default-sizer) item-gen)]
[(class sizer item-gen)
(%with-sizer sizer
(^[] (let1 len (sizer)
(with-builder (class add! get :size len)
(dotimes [len] (add! (item-gen)))
(get)))))]))
;; API
(define (permutations-of seq)
(^[] (shuffle seq (cdr (%random-data-state)))))
;; API
(define (combinations-of len seq)
(let1 indices (list->vector (iota (size-of seq)))
(^[] (let1 ix (shuffle indices)
(coerce-to (class-of seq)
(list-ec (: i len) (ref seq (vector-ref ix i))))))))
|