Mersenne twister 随机数算法实现 in Scheme

这个实现基本上是从 Wiki 上的 Python 版翻译过来的，大量使用了赋值。

;; Mersenne twister algorithm from Wikipedia
;; returns a closure that returns a pseudo-random integer
;; for each call
;;
(define (make-MT19937 seed)
  ;; some bitwise procedure alias for short
  (define << bitwise-arithmetic-shift-left)
  (define >> bitwise-arithmetic-shift-right)
  (define xor bitwise-xor)

  (letrec ((mt (make-vector 624))
           (index 624)
           ;; reset index
           (twist
            (lambda ()
              (for i in (range 624)
                   (let ((y (bitwise-and
                             #xffffffff
                             (+ (bitwise-and (vector-ref mt i)
                                             #x80000000)
                                (bitwise-and (vector-ref mt (mod (+ i 1) 624))
                                             #x7fffffff)))))
                     (vector-set! mt i (xor (vector-ref mt (mod (+ i 397) 624))
                                            (>> y 1)))
                     (when (odd? y)
                           (vector-set!
                            mt i (xor (vector-ref mt i) #x9908b0df)))))
              (set! index 0)))
           ;; generates a number
           (extract_number
            (lambda ()
              (when (>= index 624)
                    (twist))
              (let ((y (vector-ref mt index)))

                (set! y (xor y (>> y 11)))
                (set! y (xor y (bitwise-and (<< y 7) 2636928640)))
                (set! y (xor y (bitwise-and (<< y 15) 4022730752)))
                (set! y (xor y (>> y 18)))
                (set! index (+ index 1))
                (bitwise-and #xffffffff y)))))

    (vector-set! mt 0 seed)

    ;; initialize the vector
    (for i in (range 1 624)
         (vector-set!
          mt
          i
          (bitwise-and (+ i
                          (* 1812433253
                             (bitwise-xor (vector-ref mt (- i 1))
                                          (>> (vector-ref mt (- i 1)) 30))))
                       #xffffffff)))
    ;; return a closure
    (lambda ()
      (extract_number))))

;; It may be better to set the seed as the system clock
;; but that involves different implementations
(define generator (make-MT19937 4294967296))  ;; the seed

(define (randint . arg)
  (if (null? arg)
      (generator)
      (mod (generator) (car arg))))

我使用了自己定义的 for 宏，以及 range 函数来实现 Python 风格的 for 循环，下面是相关的定义：

(define-syntax for
  (syntax-rules ()
    ;; loop in list
    ;; (for i in '(a b c) do something...)
    ((_ i in lst body ...)
     (let loop ((l lst))
       (unless (null? l)
               (let ((i (car l)))
                 body ...
                 (loop (cdr l))))))))

(define range
  (let ((make-range
         (lambda (first end step)
           (if (or (= step 0)
                   (> (abs (- (+ first step) end))
                      (abs (- first end))))
               (error 'range "wrong `step' leads to an infinite loop")
               (let iter ((cnt first) (result '()))
                 (cond ((or (and (> step 0) (>= cnt end))
                            (and (< step 0) (<= cnt end)))
                        (reverse result))
                       (else (iter (+ cnt step) (cons cnt result)))))))))
    (case-lambda
     ((a) (make-range 0 a 1))
     ((a b) (make-range a b 1))
     ((a b c) (make-range a b c)))))

使用了 R6RS 特有的一些函数及语法，使用时不要忘记在头部加上 (import (rnrs)，如果还依赖别的库请查阅 R6RS 文档。