Scheme - レジスタ計算機での計算(レジスタ計算機の設計(レジスタ計算機シミュレータ(計算機の性能監視(命令計数))))

計算機プログラムの構造と解釈[第2版]
(翔泳社)
ハロルド エイブルソン (著)ジュリー サスマン (著)
ジェラルド・ジェイ サスマン (著)
Harold Abelson (原著)Julie Sussman (原著)
Gerald Jay Sussman (原著)和田 英一 (翻訳)

開発環境

• OS X Yosemite - Apple (OS)
• Emacs (CUI)、BBEdit - Bare Bones Software, Inc. (GUI) (Text Editor)
• Scheme (プログラミング言語)
• Gauche (処理系)

計算機プログラムの構造と解釈[第2版](ハロルド エイブルソン (著)、ジュリー サスマン (著)、ジェラルド・ジェイ サスマン (著)、Harold Abelson (原著)、Julie Sussman (原著)、Gerald Jay Sussman (原著)、和田 英一 (翻訳)、翔泳社、原書: Structure and Interpretation of Computer Programs (MIT Electrical Engineering and Computer Science)(SICP))の5(レジスタ計算機での計算)、5.2(レジスタ計算機シミュレータ)、5.2.4(計算機の性能監視)、問題 5.15.を解いてみる。

その他参考書籍

• Instructor's Manual to Accompany Structure & Interpretation of Computer Programs
• プログラミングGauche (Kahuaプロジェクト (著), 川合 史朗 (監修), オライリージャパン)
• Scheme手習い

問題 5.15.

コード(BBEdit, Emacs)

sample15.scm

#!/usr/bin/env gosh
;;-*- coding: utf-8 -*-

(load "./simulator15.scm")

(define factorial-machine
  (make-machine
   (list (list '= =) (list '- -) (list '* *))
   '((assign continue (label fact-done))
     fact-loop
     (test (op =) (reg n) (const 1))
     (branch (label base-case))
     (save continue)
     (save n)
     (assign n (op -) (reg n) (const 1))
     (assign continue (label after-fact))
     (goto (label fact-loop))
     after-fact
     (restore n)
     (restore continue)
     (assign val (op *) (reg n) (reg val))
     (goto (reg continue))
     base-case
     (assign val (const 1))
     (goto (reg continue))
     fact-done)))

(for-each
 (lambda (i)
   ((factorial-machine 'stack) 'initialize)
   (set-register-contents! factorial-machine 'n i)
   (start factorial-machine)
   (print i "! = " (get-register-contents factorial-machine 'val))
   (print-statistics factorial-machine)
   (print-instruction-counting factorial-machine)
   (initialize-instruction-counting factorial-machine))
 '(1 2 3 4 5 6 7 8 9 10))

simulator.scm

;; -*- coding: utf-8 -*-

(define (tagged-list? exp tag)
  (if (pair? exp)
      (eq? (car exp) tag)
      #f))

(define (make-machine ops controller-text)
  (let ((machine (make-new-machine)))
    ((machine 'install-operations) ops)
    ((machine 'install-instruction-sequence)
     (assemble controller-text machine))
    machine))

(define (make-register name)
  (let ((contents '*unassigned*))
    (define (dispatch message)
      (cond ((eq? message 'get) contents)
            ((eq? message 'set)
             (lambda (value) (set! contents value)))
            (else
             (error "Unknown request -- REGISTER" message))))
    dispatch))

(define (get-contents register)
  (register 'get))

(define (set-contents! register value)
  ((register 'set) value))

(define (make-stack)
  (let ((s '())
        (number-pushes 0)
        (max-depth 0)
        (current-depth 0))
    (define (push x)
      (set! s (cons x s))
      (set! number-pushes (+ 1 number-pushes))
      (set! current-depth (+ 1 current-depth))
      (set! max-depth (max current-depth max-depth)))
    (define (pop)
      (if (null? s)
          (error "Empty stack -- POP")
          (let ((top (car s)))
            (set! s (cdr s))
            (set! current-depth (- current-depth 1))
            top)))
    (define (initialize)      
      (set! s '())
      (set! number-pushes 0)
      (set! max-depth 0)
      (set! current-depth 0))
    (define (print-statistics)
      (print (list 'total-pushes '= number-pushes
                   'maximum-depth '= max-depth)))
    (define (dispatch message)
      (cond ((eq? message 'push) push)
            ((eq? message 'pop) (pop))
            ((eq? message 'initialize) (initialize))
            ((eq? message 'print-statistics)
             (print-statistics))
            (else (error "Unknown request -- STACK"
                         message))))
    dispatch))

(define (pop stack)
  (stack 'pop))

(define (push stack value)
  ((stack 'push) value))

(define (print-statistics machine)
  ((machine 'stack) 'print-statistics))

(define (make-new-machine)
  (let ((pc (make-register 'pc))
        (flag (make-register 'flag))
        (stack (make-stack))
        (the-instruction-sequence '())
        (instruction-counting 0))
    (let ((the-ops
           (list (list 'initialize-stack
                       (lambda () (stack 'initialize)))
                 (list 'print-stack-statisstics
                       (lambda () (stack 'print-statistics)))))
          (register-table
           (list (list 'pc pc) (list 'flag flag))))
      (define (allocate-register name)
        (if (assoc name register-table)
            (error "Multiply defined register: " name)
            (set! register-table
                  (cons (list name (make-register name))
                        register-table)))
        'register-allocated)
      (define (lookup-register name)
        (let ((val (assoc name register-table)))
          (if val
              (cadr val)
              (begin (allocate-register name)
                     (lookup-register name)))))
              
      (define (execute)
        (let ((insts (get-contents pc)))
          (if (null? insts)
              'done
              (begin
                (set! instruction-counting (+ instruction-counting 1))
                ((instruction-execution-proc (car insts)))
                (execute)))))
      (define (dispatch message)
        (cond ((eq? message 'start)
               (set-contents! pc the-instruction-sequence)
               (execute))
              ((eq? message 'install-instruction-sequence)
               (lambda (seq) (set! the-instruction-sequence seq)))
              ((eq? message 'allocate-register) allocate-register)
              ((eq? message 'get-register) lookup-register)
              ((eq? message 'install-operations)
               (lambda (ops) (set! the-ops (append the-ops ops))))
              ((eq? message 'stack) stack)
              ((eq? message 'operations) the-ops)
              ((eq? message 'print-instruction-counting)
               (print "(instruction-counting = " instruction-counting ")"))
              ((eq? message 'initialize-instruction-counting)
               (set! instruction-counting 0)
               'done)
              (else (error "Unknown request -- MACHINE" message))))
      dispatch)))


(define (start machine)
  (machine 'start))

(define (get-register-contents machine register-name)
  (get-contents (get-register machine register-name)))

(define (set-register-contents! machine register-name value)
  (set-contents! (get-register machine register-name) value)
  'done)

(define (get-register machine reg-name)
  ((machine 'get-register) reg-name))

(define (print-instruction-counting machine)
  (machine 'print-instruction-counting))

(define (initialize-instruction-counting machine)
  (machine 'initialize-instruction-counting))

(define (assemble controller-text machine)
  (extract-labels controller-text
                  (lambda (insts labels)
                    (update-insts! insts labels machine)
                    insts)))

(define (extract-labels text receive)
  (if (null? text)
      (receive '() '())
      (extract-labels
       (cdr text)
       (lambda (insts labels)
         (let ((next-inst (car text)))
           (if (symbol? next-inst)
               (if (assoc next-inst labels)
                   (error "Multiply defined label:" next-inst)
                   (receive insts
                            (cons (make-label-entry next-inst
                                                    insts)
                              labels)))
               (receive (cons (make-instruction next-inst)
                              insts)
                        labels)))))))

(define (update-insts! insts labels machine)
  (let ((pc (get-register machine 'pc))
        (flag (get-register machine 'flag))
        (stack (machine 'stack))
        (ops (machine 'operations)))
    (for-each
     (lambda (inst)
       (set-instruction-execution-proc!
        inst
        (make-execution-procedure
         (instruction-text inst) labels machine
         pc flag stack ops)))
     insts)))

(define (make-instruction text)
  (cons text '()))

(define (instruction-text inst)
  (car inst))

(define (instruction-execution-proc inst)
  (cdr inst))

(define (set-instruction-execution-proc! inst proc)
  (set-cdr! inst proc))

(define (make-label-entry label-name insts)
  (cons label-name insts))

(define (lookup-label labels label-name)
  (let ((val (assoc label-name labels)))
    (if val
        (cdr val)
        (error "Undefined label -- ASSEMBLE" label-name))))

(define (make-execution-procedure inst labels machine pc flag stack ops)
  (cond ((eq? (car inst) 'assign)
         (make-assign inst machine labels ops pc))
        ((eq? (car inst) 'test)
         (make-test inst machine labels ops flag pc))
        ((eq? (car inst) 'branch)
         (make-branch inst machine labels flag pc))
        ((eq? (car inst) 'goto)
         (make-goto inst machine labels pc))
        ((eq? (car inst) 'save)
         (make-save inst machine stack pc))
        ((eq? (car inst) 'restore)
         (make-restore inst machine stack pc))
        ((eq? (car inst) 'perform)
         (make-perform inst machine labels ops pc))
        ((eq? (car inst) 'del)
         ((make-del inst machine pc)))        
        (else (error "Unknown instruction type -- ASSEMBLE"
                     inst))))

(define (make-assign inst machine labels operations pc)
  (let ((target
         (get-register machine (assign-reg-name inst)))
        (value-exp (assign-value-exp inst)))
    (let ((value-proc
           (if (operation-exp? value-exp)
               (make-operation-exp
                value-exp machine labels operations)
               (make-primitive-exp
                (car value-exp) machine labels))))
      (lambda ()
        (set-contents! target (value-proc))
        (advance-pc pc)))))

(define (assign-reg-name assign-instruction)
  (cadr assign-instruction))

(define (assign-value-exp assign-instruction)
  (cddr assign-instruction))

(define (advance-pc pc)
  (set-contents! pc (cdr (get-contents pc))))

(define (make-test inst machine labels operations flag pc)
  (let ((condition (test-condition inst)))
    (if (operation-exp? condition)
        (let ((condition-proc
               (make-operation-exp
                condition machine labels operations)))
          (lambda ()
            (set-contents! flag (condition-proc))
            (advance-pc pc)))
        (error "Bad TEST instruction -- ASSEMBLE" inst))))

(define (test-condition test-instruction)
  (cdr test-instruction))

(define (make-branch inst machine labels flag pc)
  (let ((dest (branch-dest inst)))
    (if (label-exp? dest)
        (let ((insts
               (lookup-label labels (label-exp-label dest))))
          (lambda ()
            (if (get-contents flag)
                (set-contents! pc insts)
                (advance-pc pc))))
        (error "Bad BRANCH instruction -- ASSEMBLE" inst))))

(define (branch-dest branch-instruction)
  (cadr branch-instruction))

(define (make-goto inst machine labels pc)
  (let ((dest (goto-dest inst)))
    (cond ((label-exp? dest)
           (let ((insts
                  (lookup-label labels
                                (label-exp-label dest))))
             (lambda () (set-contents! pc insts))))
          ((register-exp? dest)
           (let ((reg
                  (get-register machine
                                (register-exp-reg dest))))
             (lambda ()
               (set-contents! pc (get-contents reg)))))
          (else (error "Bad GOTO instruction -- ASSEMBLE"
                       inst)))))
(define (goto-dest goto-instruction)
  (cadr goto-instruction))

(define (make-save inst machine stack pc)
  (let ((reg (get-register machine
                           (stack-inst-reg-name inst))))
    (lambda ()
      (push stack (get-contents reg))
      (advance-pc pc))))

(define (make-restore inst machine stack pc)
  (let ((reg (get-register machine
                           (stack-inst-reg-name inst))))
    (lambda ()
      (set-contents! reg (pop stack))
      (advance-pc pc))))

(define (stack-inst-reg-name stack-instruction)
  (cadr stack-instruction))

(define (make-perform inst machine labels operations pc)
  (let ((action (perform-action inst)))
    (if (operation-exp? action)
        (let ((action-proc
               (make-operation-exp
                action machine labels operations)))
          (lambda ()
            (action-proc)
            (advance-pc pc)))
        (error "Bad PERFORM instruction -- ASSEMBLE" inst))))

(define (perform-action inst) (cdr inst))

(define (make-primitive-exp exp machine labels)
  (cond ((constant-exp? exp)
         (let ((c (constant-exp-value exp)))
           (lambda () c)))
        ((label-exp? exp)
         (let ((insts
                (lookup-label labels
                              (label-exp-label exp))))
           (lambda () insts)))
        ((register-exp? exp)
         (let ((r (get-register machine
                                (register-exp-reg exp))))
           (lambda () (get-contents r))))
        (else
         (error "Unknown expression type -- ASSEMBLE" exp))))

(define (register-exp? exp) (tagged-list? exp 'reg))

(define (register-exp-reg exp) (cadr exp))

(define (constant-exp? exp) (tagged-list? exp 'const))

(define (constant-exp-value exp) (cadr exp))

(define (label-exp? exp) (tagged-list? exp 'label))

(define (label-exp-label exp) (cadr exp))

(define (make-operation-exp exp machine labels operations)
  (let ((op (lookup-prim (operation-exp-op exp) operations))
        (aprocs
         (map (lambda (e)
                (if (label-exp? e)
                    (error "Bad OPERANDS instruction -- ASSEMBLE" e)
                    (make-primitive-exp e machine labels)))
              (operation-exp-operands exp))))
    (lambda ()
      (apply op (map (lambda (p) (p)) aprocs)))))

(define (operation-exp? exp)
  (and (pair? exp) (tagged-list? (car exp) 'op)))

(define (operation-exp-op operation-exp)
  (cadr (car operation-exp)))

(define (operation-exp-operands operation-exp)
  (cdr operation-exp))

(define (lookup-prim symbol operations)
  (let ((val (assoc symbol operations)))
    (if val
        (cadr val)
        (error "Unknown operation -- ASSEMBLE" symbol))))

(define (make-del inst machine pc)
  (let ((target
         (get-register machine (del-reg-name inst))))
    (lambda ()
      (set-contents! target '*unassigned*)
      (advance-pc pc))))

(define (del-reg-name delete-instruction)
  (cadr delete-instruction))

入出力結果(Terminal(gosh), REPL(Read, Eval, Print, Loop))

$ ./sample15.scm
1! = 1
(total-pushes = 0 maximum-depth = 0)
(instruction-counting = 5)
2! = 2
(total-pushes = 2 maximum-depth = 2)
(instruction-counting = 16)
3! = 6
(total-pushes = 4 maximum-depth = 4)
(instruction-counting = 27)
4! = 24
(total-pushes = 6 maximum-depth = 6)
(instruction-counting = 38)
5! = 120
(total-pushes = 8 maximum-depth = 8)
(instruction-counting = 49)
6! = 720
(total-pushes = 10 maximum-depth = 10)
(instruction-counting = 60)
7! = 5040
(total-pushes = 12 maximum-depth = 12)
(instruction-counting = 71)
8! = 40320
(total-pushes = 14 maximum-depth = 14)
(instruction-counting = 82)
9! = 362880
(total-pushes = 16 maximum-depth = 16)
(instruction-counting = 93)
10! = 3628800
(total-pushes = 18 maximum-depth = 18)
(instruction-counting = 104)
$