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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; File: perm9.sch
; Description: memory system benchmark using Zaks's permutation generator
; Author: Lars Hansen, Will Clinger, and Gene Luks
; Created: 18-Mar-94
; Language: Scheme
; Status: Public Domain
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; 940720 / lth Added some more benchmarks for the thesis paper.
; 970215 / wdc Increased problem size from 8 to 9; improved tenperm9-benchmark.
; 970531 / wdc Cleaned up for public release.
; 000820 / wdc Added the MpermNKL benchmark; revised for new run-benchmark.
; This benchmark is in four parts. Each tests a different aspect of
; the memory system.
;
; perm storage allocation
; 10perm storage allocation and garbage collection
; sumperms traversal of a large, linked, self-sharing structure
; mergesort! side effects and write barrier
;
; The perm9 benchmark generates a list of all 362880 permutations of
; the first 9 integers, allocating 1349288 pairs (typically 10,794,304
; bytes), all of which goes into the generated list. (That is, the
; perm9 benchmark generates absolutely no garbage.) This represents
; a savings of about 63% over the storage that would be required by
; an unshared list of permutations. The generated permutations are
; in order of a grey code that bears no obvious relationship to a
; lexicographic order.
;
; The 10perm9 benchmark repeats the perm9 benchmark 10 times, so it
; allocates and reclaims 13492880 pairs (typically 107,943,040 bytes).
; The live storage peaks at twice the storage that is allocated by the
; perm9 benchmark. At the end of each iteration, the oldest half of
; the live storage becomes garbage. Object lifetimes are distributed
; uniformly between 10.3 and 20.6 megabytes.
;
; The 10perm9 benchmark is the 10perm9:2:1 special case of the
; MpermNKL benchmark, which allocates a queue of size K and then
; performs M iterations of the following operation: Fill the queue
; with individually computed copies of all permutations of a list of
; size N, and then remove the oldest L copies from the queue. At the
; end of each iteration, the oldest L/K of the live storage becomes
; garbage, and object lifetimes are distributed uniformly between two
; volumes that depend upon N, K, and L.
;
; The sumperms benchmark computes the sum of the permuted integers
; over all permutations.
;
; The mergesort! benchmark destructively sorts the generated permutations
; into lexicographic order, allocating no storage whatsoever.
;
; The benchmarks are run by calling the following procedures:
;
; (perm-benchmark n)
; (tenperm-benchmark n)
; (sumperms-benchmark n)
; (mergesort-benchmark n)
;
; The argument n may be omitted, in which case it defaults to 9.
;
; These benchmarks assume that
;
; (RUN-BENCHMARK <string> <thunk> <count>)
; (RUN-BENCHMARK <string> <count> <thunk> <predicate>)
;
; reports the time required to call <thunk> the number of times
; specified by <count>, and uses <predicate> to test whether the
; result returned by <thunk> is correct.
; Date: Thu, 17 Mar 94 19:43:32 -0800
; From: [email protected]
; To: will
; Subject: Pancake flips
;
; Procedure P_n generates a grey code of all perms of n elements
; on top of stack ending with reversal of starting sequence
;
; F_n is flip of top n elements.
;
;
; procedure P_n
;
; if n>1 then
; begin
; repeat P_{n-1},F_n n-1 times;
; P_{n-1}
; end
;
(define (permutations x)
(let ((x x)
(perms (list x)))
(define (P n)
(if (> n 1)
(do ((j (- n 1) (- j 1)))
((zero? j)
(P (- n 1)))
(P (- n 1))
(F n))))
(define (F n)
(set! x (revloop x n (list-tail x n)))
(set! perms (cons x perms)))
(define (revloop x n y)
(if (zero? n)
y
(revloop (cdr x)
(- n 1)
(cons (car x) y))))
(define (list-tail x n)
(if (zero? n)
x
(list-tail (cdr x) (- n 1))))
(P (length x))
perms))
; Given a list of lists of numbers, returns the sum of the sums
; of those lists.
;
; for (; x != NULL; x = x->rest)
; for (y = x->first; y != NULL; y = y->rest)
; sum = sum + y->first;
(define (sumlists x)
(do ((x x (cdr x))
(sum 0 (do ((y (car x) (cdr y))
(sum sum (+ sum (car y))))
((null? y) sum))))
((null? x) sum)))
; Destructive merge of two sorted lists.
; From Hansen's MS thesis.
(define (merge!! a b less?)
(define (loop r a b)
(if (less? (car b) (car a))
(begin (set-cdr! r b)
(if (null? (cdr b))
(set-cdr! b a)
(loop b a (cdr b)) ))
;; (car a) <= (car b)
(begin (set-cdr! r a)
(if (null? (cdr a))
(set-cdr! a b)
(loop a (cdr a) b)) )) )
(cond ((null? a) b)
((null? b) a)
((less? (car b) (car a))
(if (null? (cdr b))
(set-cdr! b a)
(loop b a (cdr b)))
b)
(else ; (car a) <= (car b)
(if (null? (cdr a))
(set-cdr! a b)
(loop a (cdr a) b))
a)))
;; Stable sort procedure which copies the input list and then sorts
;; the new list imperatively. On the systems we have benchmarked,
;; this generic list sort has been at least as fast and usually much
;; faster than the library's sort routine.
;; Due to Richard O'Keefe; algorithm attributed to D.H.D. Warren.
(define (sort!! seq less?)
(define (step n)
(cond ((> n 2)
(let* ((j (quotient n 2))
(a (step j))
(k (- n j))
(b (step k)))
(merge!! a b less?)))
((= n 2)
(let ((x (car seq))
(y (cadr seq))
(p seq))
(set! seq (cddr seq))
(if (less? y x)
(begin
(set-car! p y)
(set-car! (cdr p) x)))
(set-cdr! (cdr p) '())
p))
((= n 1)
(let ((p seq))
(set! seq (cdr seq))
(set-cdr! p '())
p))
(else
'())))
(step (length seq)))
(define lexicographically-less?
(lambda (x y)
(define (lexicographically-less? x y)
(cond ((null? x) (not (null? y)))
((null? y) #f)
((< (car x) (car y)) #t)
((= (car x) (car y))
(lexicographically-less? (cdr x) (cdr y)))
(else #f)))
(lexicographically-less? x y)))
; This procedure isn't used by the benchmarks,
; but is provided as a public service.
(define (internally-imperative-mergesort list less?)
(define (list-copy l)
(define (loop l prev)
(if (null? l)
#t
(let ((q (cons (car l) '())))
(set-cdr! prev q)
(loop (cdr l) q))))
(if (null? l)
l
(let ((first (cons (car l) '())))
(loop (cdr l) first)
first)))
(sort!! (list-copy list) less?))
(define *perms* '())
(define (one..n n)
(do ((n n (- n 1))
(p '() (cons n p)))
((zero? n) p)))
(define (perm-benchmark . rest)
(let ((n (if (null? rest) 9 (car rest))))
(set! *perms* '())
(run-benchmark (string-append "Perm" (number->string n))
1
(lambda ()
(set! *perms* (permutations (one..n n)))
#t)
(lambda (x) #t))))
(define (tenperm-benchmark . rest)
(let ((n (if (null? rest) 9 (car rest))))
(set! *perms* '())
(MpermNKL-benchmark 10 n 2 1)))
(define (MpermNKL-benchmark m n k ell)
(if (and (<= 0 m)
(positive? n)
(positive? k)
(<= 0 ell k))
(let ((id (string-append (number->string m)
"perm"
(number->string n)
":"
(number->string k)
":"
(number->string ell)))
(queue (make-vector k '())))
; Fills queue positions [i, j).
(define (fill-queue i j)
(if (< i j)
(begin (vector-set! queue i (permutations (one..n n)))
(fill-queue (+ i 1) j))))
; Removes ell elements from queue.
(define (flush-queue)
(let loop ((i 0))
(if (< i k)
(begin (vector-set! queue
i
(let ((j (+ i ell)))
(if (< j k)
(vector-ref queue j)
'())))
(loop (+ i 1))))))
(fill-queue 0 (- k ell))
(run-benchmark id
m
(lambda ()
(fill-queue (- k ell) k)
(flush-queue)
queue)
(lambda (q)
(let ((q0 (vector-ref q 0))
(qi (vector-ref q (max 0 (- k ell 1)))))
(or (and (null? q0) (null? qi))
(and (pair? q0)
(pair? qi)
(equal? (car q0) (car qi))))))))
(begin (display "Incorrect arguments to MpermNKL-benchmark")
(newline))))
(define (sumperms-benchmark . rest)
(let ((n (if (null? rest) 9 (car rest))))
(if (or (null? *perms*)
(not (= n (length (car *perms*)))))
(set! *perms* (permutations (one..n n))))
(run-benchmark (string-append "Sumperms" (number->string n))
1
(lambda ()
(sumlists *perms*))
(lambda (x) #t))))
(define (mergesort-benchmark . rest)
(let ((n (if (null? rest) 9 (car rest))))
(if (or (null? *perms*)
(not (= n (length (car *perms*)))))
(set! *perms* (permutations (one..n n))))
(run-benchmark (string-append "Mergesort!" (number->string n))
1
(lambda ()
(sort!! *perms* lexicographically-less?)
#t)
(lambda (x) #t))))
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