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diff --git a/test-suite/tests/srfi-67.test b/test-suite/tests/srfi-67.test new file mode 100644 index 000000000..312282e92 --- /dev/null +++ b/test-suite/tests/srfi-67.test @@ -0,0 +1,1221 @@ +;;; -*- mode: scheme; coding: utf-8; -*- + +;;; Copyright (C) 2010 Free Software Foundation, Inc. +;;; Copyright (c) 2005 Sebastian Egner and Jens Axel S{\o}gaard. +;;; +;;; This code is based on the file examples.scm in the reference +;;; implementation of SRFI-67, provided under the following license: +;;; +;;; Permission is hereby granted, free of charge, to any person obtaining +;;; a copy of this software and associated documentation files (the +;;; ``Software''), to deal in the Software without restriction, including +;;; without limitation the rights to use, copy, modify, merge, publish, +;;; distribute, sublicense, and/or sell copies of the Software, and to +;;; permit persons to whom the Software is furnished to do so, subject to +;;; the following conditions: +;;; +;;; The above copyright notice and this permission notice shall be +;;; included in all copies or substantial portions of the Software. +;;; +;;; THE SOFTWARE IS PROVIDED ``AS IS'', WITHOUT WARRANTY OF ANY KIND, +;;; EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +;;; MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +;;; NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE +;;; LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION +;;; OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION +;;; WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. +;;; + +(define-module (test-srfi-67) + #:use-module (test-suite lib) + #:use-module (srfi srfi-42) + #:use-module (srfi srfi-67)) + +; ============================================================================= + +; Test engine +; =========== +; +; We use an extended version of the checker of SRFI-42 (with +; Felix' reduction on codesize) for running a batch of tests for +; the various procedures of 'compare.scm'. Moreover, we use the +; comprehensions of SRFI-42 to generate examples systematically. + +; (my-check expr => desired-result) +; evaluates expr and compares the value with desired-result. + +(define-syntax my-check + (syntax-rules (=>) + ((my-check expr => desired-result) + (my-check-proc 'expr (lambda () expr) desired-result)))) + +(define (my-check-proc expr thunk desired-result) + (pass-if expr (equal? (thunk) desired-result))) + +; (my-check-ec <qualifier>* <ok?> <expr>) +; runs (every?-ec <qualifier>* <ok?>), counting the times <ok?> +; is evaluated as a correct example, and stopping at the first +; counter example for which <expr> provides the argument. + +(define-syntax my-check-ec + (syntax-rules (nested) + ((my-check-ec (nested q1 ...) q etc1 etc2 etc ...) + (my-check-ec (nested q1 ... q) etc1 etc2 etc ...)) + ((my-check-ec q1 q2 etc1 etc2 etc ...) + (my-check-ec (nested q1 q2) etc1 etc2 etc ...)) + ((my-check-ec ok? expr) + (my-check-ec (nested) ok? expr)) + ((my-check-ec (nested q ...) ok? expr) + (my-check-ec-proc + '(every?-ec q ... ok?) + (lambda () + (first-ec + 'ok + (nested q ...) + (:let ok ok?) + (if (not ok)) + (list expr))) + 'expr)) + ((my-check-ec q ok? expr) + (my-check-ec (nested q) ok? expr)))) + +(define (my-check-ec-proc expr thunk arg-counter-example) + (pass-if expr (eqv? (thunk) 'ok))) + +; ============================================================================= + +; Abstractions etc. +; ================= + +(define ci integer-compare) ; very frequently used + +; (result-ok? actual desired) +; tests if actual and desired specify the same ordering. + +(define (result-ok? actual desired) + (eqv? actual desired)) + +; (my-check-compare compare increasing-elements) +; evaluates (compare x y) for x, y in increasing-elements +; and checks the result against -1, 0, or 1 depending on +; the position of x and y in the list increasing-elements. + +(define-syntax my-check-compare + (syntax-rules () + ((my-check-compare compare increasing-elements) + (my-check-ec + (:list x (index ix) increasing-elements) + (:list y (index iy) increasing-elements) + (result-ok? (compare x y) (ci ix iy)) + (list x y))))) + +; sorted lists + +(define my-booleans '(#f #t)) +(define my-chars '(#\a #\b #\c)) +(define my-chars-ci '(#\a #\B #\c #\D)) +(define my-strings '("" "a" "aa" "ab" "b" "ba" "bb")) +(define my-strings-ci '("" "a" "aA" "Ab" "B" "bA" "BB")) +(define my-symbols '(a aa ab b ba bb)) + +(define my-reals + (append-ec (:range xn -6 7) + (:let x (/ xn 3)) + (list x (+ x (exact->inexact (/ 1 100)))))) + +(define my-rationals + (list-ec (:list x my-reals) + (and (exact? x) (rational? x)) + x)) + +(define my-integers + (list-ec (:list x my-reals) + (if (and (exact? x) (integer? x))) + x)) + +(define my-complexes + (list-ec (:list re-x my-reals) + (if (inexact? re-x)) + (:list im-x my-reals) + (if (inexact? im-x)) + (make-rectangular re-x im-x))) + +(define my-lists + '(() (1) (1 1) (1 2) (2) (2 1) (2 2))) + +(define my-vector-as-lists + (map list->vector my-lists)) + +(define my-list-as-vectors + '(() (1) (2) (1 1) (1 2) (2 1) (2 2))) + +(define my-vectors + (map list->vector my-list-as-vectors)) + +(define my-null-or-pairs + '(() + (1) (1 1) (1 2) (1 . 1) (1 . 2) + (2) (2 1) (2 2) (2 . 1) (2 . 2))) + +(define my-objects + (append my-null-or-pairs + my-booleans + my-chars + my-strings + my-symbols + my-integers + my-vectors)) + +; ============================================================================= + +; The checks +; ========== + +(define (check:if3) + + ; basic functionality + + (my-check (if3 -1 'n 'z 'p) => 'n) + (my-check (if3 0 'n 'z 'p) => 'z) + (my-check (if3 1 'n 'z 'p) => 'p) + + ; check arguments are evaluated only once + + (my-check + (let ((x -1)) + (if3 (let ((x0 x)) (set! x (+ x 1)) x0) 'n 'z 'p)) + => 'n) + + (my-check + (let ((x -1) (y 0)) + (if3 (let ((x0 x)) (set! x (+ x 1)) x0) + (begin (set! y (+ y 1)) y) + (begin (set! y (+ y 10)) y) + (begin (set! y (+ y 100)) y))) + => 1) + + (my-check + (let ((x 0) (y 0)) + (if3 (let ((x0 x)) (set! x (+ x 1)) x0) + (begin (set! y (+ y 1)) y) + (begin (set! y (+ y 10)) y) + (begin (set! y (+ y 100)) y))) + => 10) + + (my-check + (let ((x 1) (y 0)) + (if3 (let ((x0 x)) (set! x (+ x 1)) x0) + (begin (set! y (+ y 1)) y) + (begin (set! y (+ y 10)) y) + (begin (set! y (+ y 100)) y))) + => 100) + + ) ; check:if3 + +(define-syntax my-check-if2 + (syntax-rules () + ((my-check-if2 if-rel? rel) + (begin + ; check result + (my-check (if-rel? -1 'yes 'no) => (if (rel -1 0) 'yes 'no)) + (my-check (if-rel? 0 'yes 'no) => (if (rel 0 0) 'yes 'no)) + (my-check (if-rel? 1 'yes 'no) => (if (rel 1 0) 'yes 'no)) + + ; check result of 'laterally challenged if' + (my-check (let ((x #f)) (if-rel? -1 (set! x #t)) x) => (rel -1 0)) + (my-check (let ((x #f)) (if-rel? 0 (set! x #t)) x) => (rel 0 0)) + (my-check (let ((x #f)) (if-rel? 1 (set! x #t)) x) => (rel 1 0)) + + ; check that <c> is evaluated exactly once + (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) -1) #t #f) n) => 1) + (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) 0) #t #f) n) => 1) + (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) 1) #t #f) n) => 1) + (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) -1) #t) n) => 1) + (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) 0) #t) n) => 1) + (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) 1) #t) n) => 1) + )))) + +(define (check:ifs) + + (my-check-if2 if=? =) + (my-check-if2 if<? <) + (my-check-if2 if>? >) + (my-check-if2 if<=? <=) + (my-check-if2 if>=? >=) + (my-check-if2 if-not=? (lambda (x y) (not (= x y)))) + + ) ; check:if2 + +; <? etc. macros + +(define-syntax my-check-chain2 + (syntax-rules () + ((my-check-chain2 rel? rel) + (begin + ; all chains of length 2 + (my-check (rel? ci 0 0) => (rel 0 0)) + (my-check (rel? ci 0 1) => (rel 0 1)) + (my-check (rel? ci 1 0) => (rel 1 0)) + + ; using default-compare + (my-check (rel? 0 0) => (rel 0 0)) + (my-check (rel? 0 1) => (rel 0 1)) + (my-check (rel? 1 0) => (rel 1 0)) + + ; as a combinator + (my-check ((rel? ci) 0 0) => (rel 0 0)) + (my-check ((rel? ci) 0 1) => (rel 0 1)) + (my-check ((rel? ci) 1 0) => (rel 1 0)) + + ; using default-compare as a combinator + (my-check ((rel?) 0 0) => (rel 0 0)) + (my-check ((rel?) 0 1) => (rel 0 1)) + (my-check ((rel?) 1 0) => (rel 1 0)) + )))) + +(define (list->set xs) ; xs a list of integers + (if (null? xs) + '() + (let ((max-xs + (let max-without-apply ((m 1) (xs xs)) + (if (null? xs) + m + (max-without-apply (max m (car xs)) (cdr xs)))))) + (let ((in-xs? (make-vector (+ max-xs 1) #f))) + (do-ec (:list x xs) (vector-set! in-xs? x #t)) + (list-ec (:vector in? (index x) in-xs?) + (if in?) + x))))) + +(define-syntax arguments-used ; set of arguments (integer, >=0) used in compare + (syntax-rules () + ((arguments-used (rel1/rel2 compare arg ...)) + (let ((used '())) + (rel1/rel2 (lambda (x y) + (set! used (cons x (cons y used))) + (compare x y)) + arg ...) + (list->set used))))) + +(define-syntax my-check-chain3 + (syntax-rules () + ((my-check-chain3 rel1/rel2? rel1 rel2) + (begin + ; all chains of length 3 + (my-check (rel1/rel2? ci 0 0 0) => (and (rel1 0 0) (rel2 0 0))) + (my-check (rel1/rel2? ci 0 0 1) => (and (rel1 0 0) (rel2 0 1))) + (my-check (rel1/rel2? ci 0 1 0) => (and (rel1 0 1) (rel2 1 0))) + (my-check (rel1/rel2? ci 1 0 0) => (and (rel1 1 0) (rel2 0 0))) + (my-check (rel1/rel2? ci 1 1 0) => (and (rel1 1 1) (rel2 1 0))) + (my-check (rel1/rel2? ci 1 0 1) => (and (rel1 1 0) (rel2 0 1))) + (my-check (rel1/rel2? ci 0 1 1) => (and (rel1 0 1) (rel2 1 1))) + (my-check (rel1/rel2? ci 0 1 2) => (and (rel1 0 1) (rel2 1 2))) + (my-check (rel1/rel2? ci 0 2 1) => (and (rel1 0 2) (rel2 2 1))) + (my-check (rel1/rel2? ci 1 2 0) => (and (rel1 1 2) (rel2 2 0))) + (my-check (rel1/rel2? ci 1 0 2) => (and (rel1 1 0) (rel2 0 2))) + (my-check (rel1/rel2? ci 2 0 1) => (and (rel1 2 0) (rel2 0 1))) + (my-check (rel1/rel2? ci 2 1 0) => (and (rel1 2 1) (rel2 1 0))) + + ; using default-compare + (my-check (rel1/rel2? 0 0 0) => (and (rel1 0 0) (rel2 0 0))) + (my-check (rel1/rel2? 0 0 1) => (and (rel1 0 0) (rel2 0 1))) + (my-check (rel1/rel2? 0 1 0) => (and (rel1 0 1) (rel2 1 0))) + (my-check (rel1/rel2? 1 0 0) => (and (rel1 1 0) (rel2 0 0))) + (my-check (rel1/rel2? 1 1 0) => (and (rel1 1 1) (rel2 1 0))) + (my-check (rel1/rel2? 1 0 1) => (and (rel1 1 0) (rel2 0 1))) + (my-check (rel1/rel2? 0 1 1) => (and (rel1 0 1) (rel2 1 1))) + (my-check (rel1/rel2? 0 1 2) => (and (rel1 0 1) (rel2 1 2))) + (my-check (rel1/rel2? 0 2 1) => (and (rel1 0 2) (rel2 2 1))) + (my-check (rel1/rel2? 1 2 0) => (and (rel1 1 2) (rel2 2 0))) + (my-check (rel1/rel2? 1 0 2) => (and (rel1 1 0) (rel2 0 2))) + (my-check (rel1/rel2? 2 0 1) => (and (rel1 2 0) (rel2 0 1))) + (my-check (rel1/rel2? 2 1 0) => (and (rel1 2 1) (rel2 1 0))) + + ; as a combinator + (my-check ((rel1/rel2? ci) 0 0 0) => (and (rel1 0 0) (rel2 0 0))) + (my-check ((rel1/rel2? ci) 0 0 1) => (and (rel1 0 0) (rel2 0 1))) + (my-check ((rel1/rel2? ci) 0 1 0) => (and (rel1 0 1) (rel2 1 0))) + (my-check ((rel1/rel2? ci) 1 0 0) => (and (rel1 1 0) (rel2 0 0))) + (my-check ((rel1/rel2? ci) 1 1 0) => (and (rel1 1 1) (rel2 1 0))) + (my-check ((rel1/rel2? ci) 1 0 1) => (and (rel1 1 0) (rel2 0 1))) + (my-check ((rel1/rel2? ci) 0 1 1) => (and (rel1 0 1) (rel2 1 1))) + (my-check ((rel1/rel2? ci) 0 1 2) => (and (rel1 0 1) (rel2 1 2))) + (my-check ((rel1/rel2? ci) 0 2 1) => (and (rel1 0 2) (rel2 2 1))) + (my-check ((rel1/rel2? ci) 1 2 0) => (and (rel1 1 2) (rel2 2 0))) + (my-check ((rel1/rel2? ci) 1 0 2) => (and (rel1 1 0) (rel2 0 2))) + (my-check ((rel1/rel2? ci) 2 0 1) => (and (rel1 2 0) (rel2 0 1))) + (my-check ((rel1/rel2? ci) 2 1 0) => (and (rel1 2 1) (rel2 1 0))) + + ; as a combinator using default-compare + (my-check ((rel1/rel2?) 0 0 0) => (and (rel1 0 0) (rel2 0 0))) + (my-check ((rel1/rel2?) 0 0 1) => (and (rel1 0 0) (rel2 0 1))) + (my-check ((rel1/rel2?) 0 1 0) => (and (rel1 0 1) (rel2 1 0))) + (my-check ((rel1/rel2?) 1 0 0) => (and (rel1 1 0) (rel2 0 0))) + (my-check ((rel1/rel2?) 1 1 0) => (and (rel1 1 1) (rel2 1 0))) + (my-check ((rel1/rel2?) 1 0 1) => (and (rel1 1 0) (rel2 0 1))) + (my-check ((rel1/rel2?) 0 1 1) => (and (rel1 0 1) (rel2 1 1))) + (my-check ((rel1/rel2?) 0 1 2) => (and (rel1 0 1) (rel2 1 2))) + (my-check ((rel1/rel2?) 0 2 1) => (and (rel1 0 2) (rel2 2 1))) + (my-check ((rel1/rel2?) 1 2 0) => (and (rel1 1 2) (rel2 2 0))) + (my-check ((rel1/rel2?) 1 0 2) => (and (rel1 1 0) (rel2 0 2))) + (my-check ((rel1/rel2?) 2 0 1) => (and (rel1 2 0) (rel2 0 1))) + (my-check ((rel1/rel2?) 2 1 0) => (and (rel1 2 1) (rel2 1 0))) + + ; test if all arguments are type checked + (my-check (arguments-used (rel1/rel2? ci 0 1 2)) => '(0 1 2)) + (my-check (arguments-used (rel1/rel2? ci 0 2 1)) => '(0 1 2)) + (my-check (arguments-used (rel1/rel2? ci 1 2 0)) => '(0 1 2)) + (my-check (arguments-used (rel1/rel2? ci 1 0 2)) => '(0 1 2)) + (my-check (arguments-used (rel1/rel2? ci 2 0 1)) => '(0 1 2)) + (my-check (arguments-used (rel1/rel2? ci 2 1 0)) => '(0 1 2)) + )))) + +(define-syntax my-check-chain + (syntax-rules () + ((my-check-chain chain-rel? rel) + (begin + ; the chain of length 0 + (my-check (chain-rel? ci) => #t) + + ; a chain of length 1 + (my-check (chain-rel? ci 0) => #t) + + ; all chains of length 2 + (my-check (chain-rel? ci 0 0) => (rel 0 0)) + (my-check (chain-rel? ci 0 1) => (rel 0 1)) + (my-check (chain-rel? ci 1 0) => (rel 1 0)) + + ; all chains of length 3 + (my-check (chain-rel? ci 0 0 0) => (rel 0 0 0)) + (my-check (chain-rel? ci 0 0 1) => (rel 0 0 1)) + (my-check (chain-rel? ci 0 1 0) => (rel 0 1 0)) + (my-check (chain-rel? ci 1 0 0) => (rel 1 0 0)) + (my-check (chain-rel? ci 1 1 0) => (rel 1 1 0)) + (my-check (chain-rel? ci 1 0 1) => (rel 1 0 1)) + (my-check (chain-rel? ci 0 1 1) => (rel 0 1 1)) + (my-check (chain-rel? ci 0 1 2) => (rel 0 1 2)) + (my-check (chain-rel? ci 0 2 1) => (rel 0 2 1)) + (my-check (chain-rel? ci 1 2 0) => (rel 1 2 0)) + (my-check (chain-rel? ci 1 0 2) => (rel 1 0 2)) + (my-check (chain-rel? ci 2 0 1) => (rel 2 0 1)) + (my-check (chain-rel? ci 2 1 0) => (rel 2 1 0)) + + ; check if all arguments are used + (my-check (arguments-used (chain-rel? ci 0)) => '(0)) + (my-check (arguments-used (chain-rel? ci 0 1)) => '(0 1)) + (my-check (arguments-used (chain-rel? ci 1 0)) => '(0 1)) + (my-check (arguments-used (chain-rel? ci 0 1 2)) => '(0 1 2)) + (my-check (arguments-used (chain-rel? ci 0 2 1)) => '(0 1 2)) + (my-check (arguments-used (chain-rel? ci 1 2 0)) => '(0 1 2)) + (my-check (arguments-used (chain-rel? ci 1 0 2)) => '(0 1 2)) + (my-check (arguments-used (chain-rel? ci 2 0 1)) => '(0 1 2)) + (my-check (arguments-used (chain-rel? ci 2 1 0)) => '(0 1 2)) + )))) + +(define (check:predicates-from-compare) + + (my-check-chain2 =? =) + (my-check-chain2 <? <) + (my-check-chain2 >? >) + (my-check-chain2 <=? <=) + (my-check-chain2 >=? >=) + (my-check-chain2 not=? (lambda (x y) (not (= x y)))) + + (my-check-chain3 </<? < <) + (my-check-chain3 </<=? < <=) + (my-check-chain3 <=/<? <= <) + (my-check-chain3 <=/<=? <= <=) + + (my-check-chain3 >/>? > >) + (my-check-chain3 >/>=? > >=) + (my-check-chain3 >=/>? >= >) + (my-check-chain3 >=/>=? >= >=) + + (my-check-chain chain=? =) + (my-check-chain chain<? <) + (my-check-chain chain>? >) + (my-check-chain chain<=? <=) + (my-check-chain chain>=? >=) + + ) ; check:predicates-from-compare + +; pairwise-not=? + +(define pairwise-not=?:long-sequences + (let () + + (define (extremal-pivot-sequence r) + ; The extremal pivot sequence of order r is a + ; permutation of {0..2^(r+1)-2} such that the + ; middle element is minimal, and this property + ; holds recursively for each binary subdivision. + ; This sequence exposes a naive implementation of + ; pairwise-not=? chosing the middle element as pivot. + (if (zero? r) + '(0) + (let* ((s (extremal-pivot-sequence (- r 1))) + (ns (length s))) + (append (list-ec (:list x s) (+ x 1)) + '(0) + (list-ec (:list x s) (+ x ns 1)))))) + + (list (list-ec (: i 4096) i) + (list-ec (: i 4097 0 -1) i) + (list-ec (: i 4099) (modulo (* 1003 i) 4099)) + (extremal-pivot-sequence 11)))) + +(define pairwise-not=?:short-sequences + (let () + + (define (combinations/repeats n l) + ; return list of all sublists of l of size n, + ; the order of the elements occur in the sublists + ; of the output is the same as in the input + (let ((len (length l))) + (cond + ((= n 0) '()) + ((= n 1) (map list l)) + ((= len 1) (do ((r '() (cons (car l) r)) + (i n (- i 1))) + ((= i 0) (list r)))) + (else (append (combinations/repeats n (cdr l)) + (map (lambda (c) (cons (car l) c)) + (combinations/repeats (- n 1) l))))))) + + (define (permutations l) + ; return a list of all permutations of l + (let ((len (length l))) + (cond + ((= len 0) '(())) + ((= len 1) (list l)) + (else (apply append + (map (lambda (p) (insert-every-where (car l) p)) + (permutations (cdr l)))))))) + + (define (insert-every-where x xs) + (let loop ((result '()) (before '()) (after xs)) + (let ((new (append before (cons x after)))) + (cond + ((null? after) (cons new result)) + (else (loop (cons new result) + (append before (list (car after))) + (cdr after))))))) + + (define (sequences n max) + (apply append + (map permutations + (combinations/repeats n (list-ec (: i max) i))))) + + (append-ec (: n 5) (sequences n 5)))) + +(define (colliding-compare x y) + (ci (modulo x 3) (modulo y 3))) + +(define (naive-pairwise-not=? compare . xs) + (let ((xs (list->vector xs))) + (every?-ec (:range i (- (vector-length xs) 1)) + (:let xs-i (vector-ref xs i)) + (:range j (+ i 1) (vector-length xs)) + (:let xs-j (vector-ref xs j)) + (not=? compare xs-i xs-j)))) + +(define (check:pairwise-not=?) + + ; 0-ary, 1-ary + (my-check (pairwise-not=? ci) => #t) + (my-check (pairwise-not=? ci 0) => #t) + + ; 2-ary + (my-check (pairwise-not=? ci 0 0) => #f) + (my-check (pairwise-not=? ci 0 1) => #t) + (my-check (pairwise-not=? ci 1 0) => #t) + + ; 3-ary + (my-check (pairwise-not=? ci 0 0 0) => #f) + (my-check (pairwise-not=? ci 0 0 1) => #f) + (my-check (pairwise-not=? ci 0 1 0) => #f) + (my-check (pairwise-not=? ci 1 0 0) => #f) + (my-check (pairwise-not=? ci 1 1 0) => #f) + (my-check (pairwise-not=? ci 1 0 1) => #f) + (my-check (pairwise-not=? ci 0 1 1) => #f) + (my-check (pairwise-not=? ci 0 1 2) => #t) + (my-check (pairwise-not=? ci 0 2 1) => #t) + (my-check (pairwise-not=? ci 1 2 0) => #t) + (my-check (pairwise-not=? ci 1 0 2) => #t) + (my-check (pairwise-not=? ci 2 0 1) => #t) + (my-check (pairwise-not=? ci 2 1 0) => #t) + + ; n-ary, n large: [0..n-1], [n,n-1..1], 5^[0..96] mod 97 + (my-check (apply pairwise-not=? ci (list-ec (: i 10) i)) => #t) + (my-check (apply pairwise-not=? ci (list-ec (: i 100) i)) => #t) + (my-check (apply pairwise-not=? ci (list-ec (: i 1000) i)) => #t) + + (my-check (apply pairwise-not=? ci (list-ec (: i 10 0 -1) i)) => #t) + (my-check (apply pairwise-not=? ci (list-ec (: i 100 0 -1) i)) => #t) + (my-check (apply pairwise-not=? ci (list-ec (: i 1000 0 -1) i)) => #t) + + (my-check (apply pairwise-not=? ci + (list-ec (: i 97) (modulo (* 5 i) 97))) + => #t) + + ; bury another copy of 72 = 5^50 mod 97 in 5^[0..96] mod 97 + (my-check (apply pairwise-not=? ci + (append (list-ec (: i 0 23) (modulo (* 5 i) 97)) + '(72) + (list-ec (: i 23 97) (modulo (* 5 i) 97)))) + => #f) + (my-check (apply pairwise-not=? ci + (append (list-ec (: i 0 75) (modulo (* 5 i) 97)) + '(72) + (list-ec (: i 75 97) (modulo (* 5 i) 97)))) + => #f) + + ; check if all arguments are used + (my-check (arguments-used (pairwise-not=? ci 0)) => '(0)) + (my-check (arguments-used (pairwise-not=? ci 0 1)) => '(0 1)) + (my-check (arguments-used (pairwise-not=? ci 1 0)) => '(0 1)) + (my-check (arguments-used (pairwise-not=? ci 0 2 1)) => '(0 1 2)) + (my-check (arguments-used (pairwise-not=? ci 1 2 0)) => '(0 1 2)) + (my-check (arguments-used (pairwise-not=? ci 1 0 2)) => '(0 1 2)) + (my-check (arguments-used (pairwise-not=? ci 2 0 1)) => '(0 1 2)) + (my-check (arguments-used (pairwise-not=? ci 2 1 0)) => '(0 1 2)) + (my-check (arguments-used (pairwise-not=? ci 0 0 0 1 0 0 0 2 0 0 0 3)) + => '(0 1 2 3)) + + ; Guess if the implementation is O(n log n): + ; The test is run for 2^e pairwise unequal inputs, e >= 1, + ; and the number of calls to the compare procedure is counted. + ; all pairs: A = Binomial[2^e, 2] = 2^(2 e - 1) * (1 - 2^-e). + ; divide and conquer: D = e 2^e. + ; Since an implementation can be randomized, the actual count may + ; be a random number. We put a threshold at 100 e 2^e and choose + ; e such that A/D >= 150, i.e. e >= 12. + ; The test is applied to several inputs that are known to cause + ; trouble in simplistic sorting algorithms: (0..2^e-1), (2^e+1,2^e..1), + ; a pseudo-random permutation, and a sequence with an extremal pivot + ; at the center of each subsequence. + + (my-check-ec + (:list input pairwise-not=?:long-sequences) + (let ((compares 0)) + (apply pairwise-not=? + (lambda (x y) + (set! compares (+ compares 1)) + (ci x y)) + input) + ; (display compares) (newline) + (< compares (* 100 12 4096))) + (length input)) + + ; check many short sequences + + (my-check-ec + (:list input pairwise-not=?:short-sequences) + (eq? + (apply pairwise-not=? colliding-compare input) + (apply naive-pairwise-not=? colliding-compare input)) + input) + + ; check if the arguments are used for short sequences + + (my-check-ec + (:list input pairwise-not=?:short-sequences) + (let ((args '())) + (apply pairwise-not=? + (lambda (x y) + (set! args (cons x (cons y args))) + (colliding-compare x y)) + input) + (equal? (list->set args) (list->set input))) + input) + + ) ; check:pairwise-not=? + + +; min/max + +(define min/max:sequences + (append pairwise-not=?:short-sequences + pairwise-not=?:long-sequences)) + +(define (check:min/max) + + ; all lists of length 1,2,3 + (my-check (min-compare ci 0) => 0) + (my-check (min-compare ci 0 0) => 0) + (my-check (min-compare ci 0 1) => 0) + (my-check (min-compare ci 1 0) => 0) + (my-check (min-compare ci 0 0 0) => 0) + (my-check (min-compare ci 0 0 1) => 0) + (my-check (min-compare ci 0 1 0) => 0) + (my-check (min-compare ci 1 0 0) => 0) + (my-check (min-compare ci 1 1 0) => 0) + (my-check (min-compare ci 1 0 1) => 0) + (my-check (min-compare ci 0 1 1) => 0) + (my-check (min-compare ci 0 1 2) => 0) + (my-check (min-compare ci 0 2 1) => 0) + (my-check (min-compare ci 1 2 0) => 0) + (my-check (min-compare ci 1 0 2) => 0) + (my-check (min-compare ci 2 0 1) => 0) + (my-check (min-compare ci 2 1 0) => 0) + + (my-check (max-compare ci 0) => 0) + (my-check (max-compare ci 0 0) => 0) + (my-check (max-compare ci 0 1) => 1) + (my-check (max-compare ci 1 0) => 1) + (my-check (max-compare ci 0 0 0) => 0) + (my-check (max-compare ci 0 0 1) => 1) + (my-check (max-compare ci 0 1 0) => 1) + (my-check (max-compare ci 1 0 0) => 1) + (my-check (max-compare ci 1 1 0) => 1) + (my-check (max-compare ci 1 0 1) => 1) + (my-check (max-compare ci 0 1 1) => 1) + (my-check (max-compare ci 0 1 2) => 2) + (my-check (max-compare ci 0 2 1) => 2) + (my-check (max-compare ci 1 2 0) => 2) + (my-check (max-compare ci 1 0 2) => 2) + (my-check (max-compare ci 2 0 1) => 2) + (my-check (max-compare ci 2 1 0) => 2) + + ; check that the first minimal value is returned + (my-check (min-compare (pair-compare-car ci) + '(0 1) '(0 2) '(0 3)) + => '(0 1)) + (my-check (max-compare (pair-compare-car ci) + '(0 1) '(0 2) '(0 3)) + => '(0 1)) + + ; check for many inputs + (my-check-ec + (:list input min/max:sequences) + (= (apply min-compare ci input) + (apply min (apply max input) input)) + input) + (my-check-ec + (:list input min/max:sequences) + (= (apply max-compare ci input) + (apply max (apply min input) input)) + input) + ; Note the stupid extra argument in the apply for + ; the standard min/max makes sure the elements are + ; identical when apply truncates the arglist. + + ) ; check:min/max + + +; kth-largest + +(define kth-largest:sequences + pairwise-not=?:short-sequences) + +(define (naive-kth-largest compare k . xs) + (let ((vec (list->vector xs))) + ; bubble sort: simple, stable, O(|xs|^2) + (do-ec (:range n (- (vector-length vec) 1)) + (:range i 0 (- (- (vector-length vec) 1) n)) + (if>? (compare (vector-ref vec i) + (vector-ref vec (+ i 1))) + (let ((vec-i (vector-ref vec i))) + (vector-set! vec i (vector-ref vec (+ i 1))) + (vector-set! vec (+ i 1) vec-i)))) + (vector-ref vec (modulo k (vector-length vec))))) + +(define (check:kth-largest) + + ; check extensively against naive-kth-largest + (my-check-ec + (:list input kth-largest:sequences) + (: k (- -2 (length input)) (+ (length input) 2)) + (= (apply naive-kth-largest colliding-compare k input) + (apply kth-largest colliding-compare k input)) + (list input k)) + + ) ;check:kth-largest + +; compare-by< etc. procedures + +(define (check:compare-from-predicates) + + (my-check-compare + (compare-by< <) + my-integers) + + (my-check-compare + (compare-by> >) + my-integers) + + (my-check-compare + (compare-by<= <=) + my-integers) + + (my-check-compare + (compare-by>= >=) + my-integers) + + (my-check-compare + (compare-by=/< = <) + my-integers) + + (my-check-compare + (compare-by=/> = >) + my-integers) + + ; with explicit arguments + + (my-check-compare + (lambda (x y) (compare-by< < x y)) + my-integers) + + (my-check-compare + (lambda (x y) (compare-by> > x y)) + my-integers) + + (my-check-compare + (lambda (x y) (compare-by<= <= x y)) + my-integers) + + (my-check-compare + (lambda (x y) (compare-by>= >= x y)) + my-integers) + + (my-check-compare + (lambda (x y) (compare-by=/< = < x y)) + my-integers) + + (my-check-compare + (lambda (x y) (compare-by=/> = > x y)) + my-integers) + + ) ; check:compare-from-predicates + + +(define (check:atomic) + + (my-check-compare boolean-compare my-booleans) + + (my-check-compare char-compare my-chars) + + (my-check-compare char-compare-ci my-chars-ci) + + (my-check-compare string-compare my-strings) + + (my-check-compare string-compare-ci my-strings-ci) + + (my-check-compare symbol-compare my-symbols) + + (my-check-compare integer-compare my-integers) + + (my-check-compare rational-compare my-rationals) + + (my-check-compare real-compare my-reals) + + (my-check-compare complex-compare my-complexes) + + (my-check-compare number-compare my-complexes) + + ) ; check:atomic + +(define (check:refine-select-cond) + + ; refine-compare + + (my-check-compare + (lambda (x y) (refine-compare)) + '(#f)) + + (my-check-compare + (lambda (x y) (refine-compare (integer-compare x y))) + my-integers) + + (my-check-compare + (lambda (x y) + (refine-compare (integer-compare (car x) (car y)) + (symbol-compare (cdr x) (cdr y)))) + '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c))) + + (my-check-compare + (lambda (x y) + (refine-compare (integer-compare (car x) (car y)) + (symbol-compare (cadr x) (cadr y)) + (string-compare (caddr x) (caddr y)))) + '((1 a "a") (1 b "a") (1 b "b") (2 b "c") (2 c "a") (3 a "b") (3 c "b"))) + + ; select-compare + + (my-check-compare + (lambda (x y) (select-compare x y)) + '(#f)) + + (my-check-compare + (lambda (x y) + (select-compare x y + (integer? (ci x y)))) + my-integers) + + (my-check-compare + (lambda (x y) + (select-compare x y + (pair? (integer-compare (car x) (car y)) + (symbol-compare (cdr x) (cdr y))))) + '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c))) + + (my-check-compare + (lambda (x y) + (select-compare x y + (else (integer-compare x y)))) + my-integers) + + (my-check-compare + (lambda (x y) + (select-compare x y + (else (integer-compare (car x) (car y)) + (symbol-compare (cdr x) (cdr y))))) + '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c))) + + (my-check-compare + (lambda (x y) + (select-compare x y + (symbol? (symbol-compare x y)) + (string? (string-compare x y)))) + '(a b c "a" "b" "c" 1)) ; implicit (else 0) + + (my-check-compare + (lambda (x y) + (select-compare x y + (symbol? (symbol-compare x y)) + (else (string-compare x y)))) + '(a b c "a" "b" "c")) + + ; test if arguments are only evaluated once + + (my-check + (let ((nx 0) (ny 0) (nt 0)) + (select-compare (begin (set! nx (+ nx 1)) 1) + (begin (set! ny (+ ny 1)) 2) + ((lambda (z) (set! nt (+ nt 1)) #f) 0) + ((lambda (z) (set! nt (+ nt 10)) #f) 0) + ((lambda (z) (set! nt (+ nt 100)) #f) 0) + (else 0)) + (list nx ny nt)) + => '(1 1 222)) + + ; cond-compare + + (my-check-compare + (lambda (x y) (cond-compare)) + '(#f)) + + (my-check-compare + (lambda (x y) + (cond-compare + (((integer? x) (integer? y)) (integer-compare x y)))) + my-integers) + + (my-check-compare + (lambda (x y) + (cond-compare + (((pair? x) (pair? y)) (integer-compare (car x) (car y)) + (symbol-compare (cdr x) (cdr y))))) + '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c))) + + (my-check-compare + (lambda (x y) + (cond-compare + (else (integer-compare x y)))) + my-integers) + + (my-check-compare + (lambda (x y) + (cond-compare + (else (integer-compare (car x) (car y)) + (symbol-compare (cdr x) (cdr y))))) + '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c))) + + (my-check-compare + (lambda (x y) + (cond-compare + (((symbol? x) (symbol? y)) (symbol-compare x y)) + (((string? x) (string? y)) (string-compare x y)))) + '(a b c "a" "b" "c" 1)) ; implicit (else 0) + + (my-check-compare + (lambda (x y) + (cond-compare + (((symbol? x) (symbol? y)) (symbol-compare x y)) + (else (string-compare x y)))) + '(a b c "a" "b" "c")) + + ) ; check:refine-select-cond + + +; We define our own list/vector data structure +; as '(my-list x[1] .. x[n]), n >= 0, in order +; to make sure the default ops don't work on it. + +(define (my-list-checked obj) + (if (and (list? obj) (eqv? (car obj) 'my-list)) + obj + (error "expected my-list but received" obj))) + +(define (list->my-list list) (cons 'my-list list)) +(define (my-empty? x) (null? (cdr (my-list-checked x)))) +(define (my-head x) (cadr (my-list-checked x))) +(define (my-tail x) (cons 'my-list (cddr (my-list-checked x)))) +(define (my-size x) (- (length (my-list-checked x)) 1)) +(define (my-ref x i) (list-ref (my-list-checked x) (+ i 1))) + +(define (check:data-structures) + + (my-check-compare + (pair-compare-car ci) + '((1 . b) (2 . a) (3 . c))) + + (my-check-compare + (pair-compare-cdr ci) + '((b . 1) (a . 2) (c . 3))) + + ; pair-compare + + (my-check-compare pair-compare my-null-or-pairs) + + (my-check-compare + (lambda (x y) (pair-compare ci x y)) + my-null-or-pairs) + + (my-check-compare + (lambda (x y) (pair-compare ci symbol-compare x y)) + '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a))) + + ; list-compare + + (my-check-compare list-compare my-lists) + + (my-check-compare + (lambda (x y) (list-compare ci x y)) + my-lists) + + (my-check-compare + (lambda (x y) (list-compare x y my-empty? my-head my-tail)) + (map list->my-list my-lists)) + + (my-check-compare + (lambda (x y) (list-compare ci x y my-empty? my-head my-tail)) + (map list->my-list my-lists)) + + ; list-compare-as-vector + + (my-check-compare list-compare-as-vector my-list-as-vectors) + + (my-check-compare + (lambda (x y) (list-compare-as-vector ci x y)) + my-list-as-vectors) + + (my-check-compare + (lambda (x y) (list-compare-as-vector x y my-empty? my-head my-tail)) + (map list->my-list my-list-as-vectors)) + + (my-check-compare + (lambda (x y) (list-compare-as-vector ci x y my-empty? my-head my-tail)) + (map list->my-list my-list-as-vectors)) + + ; vector-compare + + (my-check-compare vector-compare my-vectors) + + (my-check-compare + (lambda (x y) (vector-compare ci x y)) + my-vectors) + + (my-check-compare + (lambda (x y) (vector-compare x y my-size my-ref)) + (map list->my-list my-list-as-vectors)) + + (my-check-compare + (lambda (x y) (vector-compare ci x y my-size my-ref)) + (map list->my-list my-list-as-vectors)) + + ; vector-compare-as-list + + (my-check-compare vector-compare-as-list my-vector-as-lists) + + (my-check-compare + (lambda (x y) (vector-compare-as-list ci x y)) + my-vector-as-lists) + + (my-check-compare + (lambda (x y) (vector-compare-as-list x y my-size my-ref)) + (map list->my-list my-lists)) + + (my-check-compare + (lambda (x y) (vector-compare-as-list ci x y my-size my-ref)) + (map list->my-list my-lists)) + + ) ; check:data-structures + + +(define (check:default-compare) + + (my-check-compare default-compare my-objects) + + ; check if default-compare refines pair-compare + + (my-check-ec + (:list x (index ix) my-objects) + (:list y (index iy) my-objects) + (:let c-coarse (pair-compare x y)) + (:let c-fine (default-compare x y)) + (or (eqv? c-coarse 0) (eqv? c-fine c-coarse)) + (list x y)) + + ; check if default-compare passes on debug-compare + + (my-check-compare (debug-compare default-compare) my-objects) + + ) ; check:default-compare + + +(define (sort-by-less xs pred) ; trivial quicksort + (if (or (null? xs) (null? (cdr xs))) + xs + (append + (sort-by-less (list-ec (:list x (cdr xs)) + (if (pred x (car xs))) + x) + pred) + (list (car xs)) + (sort-by-less (list-ec (:list x (cdr xs)) + (if (not (pred x (car xs)))) + x) + pred)))) + +(define (check:more-examples) + + ; define recursive order on tree type (nodes are dotted pairs) + + (my-check-compare + (letrec ((c (lambda (x y) + (cond-compare (((null? x) (null? y)) 0) + (else (pair-compare c c x y)))))) + c) + (list '() (list '()) (list '() '()) (list (list '()))) + ;'(() (() . ()) (() . (() . ())) ((() . ()) . ())) ; Chicken can't parse this ? + ) + + ; redefine default-compare using select-compare + + (my-check-compare + (letrec ((c (lambda (x y) + (select-compare x y + (null? 0) + (pair? (pair-compare c c x y)) + (boolean? (boolean-compare x y)) + (char? (char-compare x y)) + (string? (string-compare x y)) + (symbol? (symbol-compare x y)) + (number? (number-compare x y)) + (vector? (vector-compare c x y)) + (else (error "unrecognized type in c" x y)))))) + c) + my-objects) + + ; redefine default-compare using cond-compare + + (my-check-compare + (letrec ((c (lambda (x y) + (cond-compare + (((null? x) (null? y)) 0) + (((pair? x) (pair? y)) (pair-compare c c x y)) + (((boolean? x) (boolean? y)) (boolean-compare x y)) + (((char? x) (char? y)) (char-compare x y)) + (((string? x) (string? y)) (string-compare x y)) + (((symbol? x) (symbol? y)) (symbol-compare x y)) + (((number? x) (number? y)) (number-compare x y)) + (((vector? x) (vector? y)) (vector-compare c x y)) + (else (error "unrecognized type in c" x y)))))) + c) + my-objects) + + ; compare strings with character order reversed + + (my-check-compare + (lambda (x y) + (vector-compare-as-list + (lambda (x y) (char-compare y x)) + x y string-length string-ref)) + '("" "b" "bb" "ba" "a" "ab" "aa")) + + ; examples from SRFI text for <? etc. + + (my-check (>? "laugh" "LOUD") => #t) + (my-check (<? string-compare-ci "laugh" "LOUD") => #t) + (my-check (sort-by-less '(1 a "b") (<?)) => '("b" a 1)) + (my-check (sort-by-less '(1 a "b") (>?)) => '(1 a "b")) + + ) ; check:more-examples + + +; Real life examples +; ================== + +; (update/insert compare x s) +; inserts x into list s, or updates an equivalent element by x. +; It is assumed that s is sorted with respect to compare, +; i.e. (apply chain<=? compare s). The result is a list with x +; replacing the first element s[i] for which (=? compare s[i] x), +; or with x inserted in the proper place. +; The algorithm uses linear insertion from the front. + +(define (insert/update compare x s) ; insert x into list s, or update + (if (null? s) + (list x) + (if3 (compare x (car s)) + (cons x s) + (cons x (cdr s)) + (cons (car s) (insert/update compare x (cdr s)))))) + +; (index-in-vector compare vec x) +; an index i such that (=? compare vec[i] x), or #f if there is none. +; It is assumed that s is sorted with respect to compare, +; i.e. (apply chain<=? compare (vector->list s)). If there are +; several elements equivalent to x then it is unspecified which +; these is chosen. +; The algorithm uses binary search. + +(define (index-in-vector compare vec x) + (let binary-search ((lo -1) (hi (vector-length vec))) + ; invariant: vec[lo] < x < vec[hi] + (if (=? (- hi lo) 1) + #f + (let ((mi (quotient (+ lo hi) 2))) + (if3 (compare x (vector-ref vec mi)) + (binary-search lo mi) + mi + (binary-search mi hi)))))) + + +; Run the checks +; ============== + +; comment in/out as needed +(with-test-prefix "atomic" (check:atomic)) +(with-test-prefix "if3" (check:if3)) +(with-test-prefix "ifs" (check:ifs)) +(with-test-prefix "predicates-form-compare" + (check:predicates-from-compare)) +(with-test-prefix "pairwise-not=?" + (check:pairwise-not=?)) +(with-test-prefix "min/max" + (check:min/max)) +(with-test-prefix "kth-largest" + (check:kth-largest)) +(with-test-prefix "compare-from-predicates" + (check:compare-from-predicates)) +(with-test-prefix "refine-select-cond" + (check:refine-select-cond)) +(with-test-prefix "data-structures" + (check:data-structures)) +(with-test-prefix "default-compare" + (check:default-compare)) +(with-test-prefix "more-examples" + (check:more-examples)) + |