src/random-numbers.lisp @ 5cace362d318
Make Tracery
author |
Steve Losh <steve@stevelosh.com> |
date |
Mon, 09 Jan 2017 16:31:12 +0000 |
parents |
184af4c4e8fc |
children |
326c2d62fceb |
(in-package :sand.random-numbers)
;;;; Types, etc
; (declaim (optimize (speed 1) (safety 1) (debug 3)))
; (declaim (optimize (speed 3) (safety 0) (debug 0)))
(deftype positive-fixnum () `(integer 1 ,most-positive-fixnum))
(deftype negative-fixnum () `(integer ,most-negative-fixnum -1))
(deftype nonnegative-fixnum () `(integer 0 ,most-positive-fixnum))
(deftype nonpositive-fixnum () `(integer ,most-negative-fixnum 0))
;;;; Utils
(declaim (ftype (function (nonnegative-fixnum
nonnegative-fixnum
nonnegative-fixnum)
nonnegative-fixnum)
mod+)
(inline mod+))
(defun mod+ (x y m)
(if (<= x (- m 1 y))
(+ x y)
(- x (- m y))))
;;;; Random Number Generators
(defun make-linear-congruential-rng-java (modulus multiplier increment seed)
(declare (type nonnegative-fixnum seed)
(type positive-fixnum modulus multiplier increment))
(let ((val (mod (logxor seed multiplier)
modulus)))
(dlambda
(:next ()
(ldb (byte 32 16) ; java's j.u.Random only gives out 32 high-order bits
(setf val (mod (+ (* val multiplier) increment)
modulus))))
(:modulus () modulus))))
(defun make-linear-congruential-rng (modulus multiplier increment seed)
(declare (type nonnegative-fixnum seed)
(type positive-fixnum modulus multiplier increment))
(let ((val (mod (logxor seed multiplier)
modulus)))
(dlambda
(:next ()
(setf val (mod (+ (* val multiplier) increment)
modulus)))
(:modulus () modulus))))
(declaim (inline rng-next rng-modulus))
(defun rng-next (generator)
(funcall generator :next))
(defun rng-modulus (generator)
(funcall generator :modulus))
(defparameter *generator*
(make-linear-congruential-rng (expt 2 48)
25214903917
11
0))
(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))))
;;;; Spectral Test
(defun spectral ()
(spit "data"
(iterate
(repeat 1000)
(for i = (rand))
(for j :previous i)
(for k :previous j)
(when k
(format t "~d ~d ~d~%" i j k)))))
;;;; Distributions
(defun prefix-sums (list)
(iterate
(for i :in list)
(sum i :into s)
(collect s :result-type vector)))
(defun frequencies (seq &key (test 'eql))
(iterate
(with result = (make-hash-table :test test))
(for i :in-whatever seq)
(incf (gethash i result 0))
(finally (return result))))
(defun random-weighted-list (weights n)
(iterate
(with sums = (prefix-sums weights))
(with max = (elt sums (1- (length sums))))
(repeat n)
(collect (iterate
(with r = (rand-range 0 max))
(for s :in-vector sums :with-index i)
(finding i :such-that (< r s))))))
(defun random-weighted (weights)
(first (random-weighted-list weights 1)))
;;;; Scratch
; (spectral)