src/random-numbers.lisp @ 6f72eefef02e

(in-package #:sand.random-numbers)


;;;; Types, etc
(declaim (optimize (speed 1) (safety 1) (debug 3)))

(deftype positive-fixnum () `(integer 1 ,most-positive-fixnum))
(deftype negative-fixnum () `(integer ,most-negative-fixnum -1))
(deftype nonnegative-fixnum () `(integer 1 ,most-positive-fixnum))
(deftype nonpositive-fixnum () `(integer ,most-negative-fixnum -1))


;;;; Utils
(defun +mod (x y m)
  (if (<= x (- m 1 y))
    (+ x y)
    (- x (- m y))))


;;;; Random Number Generators
(defun make-linear-congruential-rng (modulus multiplier increment seed)
  (let ((val seed))
    (lambda (msg)
      (ecase msg
        (:next (setf val (mod (+ (* multiplier val)
                                 increment)
                              modulus)))
        (:modulus modulus)))))

(defun make-linear-congruential-rng-fast% (modulus multiplier increment seed)
  (declare (optimize (speed 3) (safety 0) (debug 0)))
  (let ((val seed))
    (lambda (msg)
      (ecase msg
        (:next (setf val (mod (+ (the nonnegative-fixnum (* multiplier val))
                                 increment)
                              modulus)))
        (:modulus modulus)))))


(declaim (inline rng-next rng-modulus))

(defun rng-next (generator)
  (funcall generator :next))

(defun rng-modulus (generator)
  (funcall generator :modulus))


(define-compiler-macro make-linear-congruential-rng
    (&whole form
     modulus multiplier increment seed)
  (if (and (constantp modulus)
           (constantp multiplier)
           (<= (* multiplier (1- modulus))
               most-positive-fixnum))
    `(make-linear-congruential-rng-fast% ,modulus ,multiplier ,increment ,seed)
    form))


(defparameter *generator* (make-linear-congruential-rng 601 15 4 354))


(defun rand ()
  (rng-next *generator*))

(defun rand-float ()
  (float (/ (rng-next *generator*)
            (rng-modulus *generator*))))


;;;; Mapping
;;; The Monte Carlo method is bad because it's biased, but it's fast.
;;;
;;; Basically we take our generator that generates say 1-8, and map the range
;;; ABC onto it:
;;;
;;;    1 2 3 4 5 6 7 8
;;;    A B C A B C A B
;;;
;;; Notice that it's not uniform.
(defun monte-carlo (width)
  (mod (rng-next *generator*) width))


;;; The Las Vegas method is a bit slower, but unbiased.  We group the random
;;; numbers into contiguous buckets, with the last "partial bucket" being
;;; excess.  If we hit that one we just loop and try again:
;;;
;;;    1 2 3 4 5 6 7 8
;;;    A A B B C C retry
(defun las-vegas (width)
  (let* ((modulus (rng-modulus *generator*))
         (bucket-width (truncate (/ modulus width))))
    (iterate
      (for bucket = (truncate (/ (rng-next *generator*)
                                 bucket-width)))
      (finding bucket :such-that (< bucket width)))))


(defun rand-range-bad (min max)
  (+ min (monte-carlo (- max min))))

(defun rand-range (min max)
  (+ min (las-vegas (- max min))))