(number->string): Added tests for non-radix-10 floating point
[bpt/guile.git] / test-suite / tests / numbers.test
1 ;;;; numbers.test --- tests guile's numbers -*- scheme -*-
2 ;;;; Copyright (C) 2000, 2001, 2003, 2004 Free Software Foundation, Inc.
3 ;;;;
4 ;;;; This library is free software; you can redistribute it and/or
5 ;;;; modify it under the terms of the GNU Lesser General Public
6 ;;;; License as published by the Free Software Foundation; either
7 ;;;; version 2.1 of the License, or (at your option) any later version.
8 ;;;;
9 ;;;; This library is distributed in the hope that it will be useful,
10 ;;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
11 ;;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 ;;;; Lesser General Public License for more details.
13 ;;;;
14 ;;;; You should have received a copy of the GNU Lesser General Public
15 ;;;; License along with this library; if not, write to the Free Software
16 ;;;; Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17
18 (define-module (test-suite test-numbers)
19 #:use-module (test-suite lib)
20 #:use-module (ice-9 documentation))
21
22 ;;;
23 ;;; miscellaneous
24 ;;;
25
26 (define exception:numerical-overflow
27 (cons 'numerical-overflow "^Numerical overflow"))
28
29 (define (documented? object)
30 (not (not (object-documentation object))))
31
32 (define fixnum-bit
33 (inexact->exact (+ (/ (log (+ most-positive-fixnum 1)) (log 2)) 1)))
34
35 (define fixnum-min most-negative-fixnum)
36 (define fixnum-max most-positive-fixnum)
37
38 ;; Divine the number of bits in the mantissa of a flonum.
39 ;; We look for when 2.0^i+1.0 gets rounded, ie. the difference between that
40 ;; value and 2.0^k is not 1.0.
41 ;; Of course this assumes flonums have a fixed precision mantissa, but
42 ;; that's the case now and probably into the forseeable future.
43 ;; On an IEEE system, which means pretty much everywhere, the value here is
44 ;; the usual 53.
45 ;;
46 (define dbl-mant-dig
47 (let more ((i 1)
48 (d 2.0))
49 (if (> i 1024)
50 (error "Oops, cannot determine number of bits in mantissa of inexact"))
51 (let* ((sum (+ 1.0 d))
52 (diff (- sum d)))
53 (if (= diff 1.0)
54 (more (1+ i) (* 2.0 d))
55 i))))
56
57 ;; like ash, but working on a flonum
58 (define (ash-flo x n)
59 (while (> n 0)
60 (set! x (* 2.0 x))
61 (set! n (1- n)))
62 (while (< n 0)
63 (set! x (* 0.5 x))
64 (set! n (1+ n)))
65 x)
66
67
68 ;;;
69 ;;; exact?
70 ;;;
71
72 (with-test-prefix "exact?"
73
74 (pass-if "documented?"
75 (documented? exact?))
76
77 (with-test-prefix "integers"
78
79 (pass-if "0"
80 (exact? 0))
81
82 (pass-if "fixnum-max"
83 (exact? fixnum-max))
84
85 (pass-if "fixnum-max + 1"
86 (exact? (+ fixnum-max 1)))
87
88 (pass-if "fixnum-min"
89 (exact? fixnum-min))
90
91 (pass-if "fixnum-min - 1"
92 (exact? (- fixnum-min 1))))
93
94 (with-test-prefix "reals"
95
96 ;; (FIXME: need better examples.)
97
98 (pass-if "sqrt (fixnum-max^2 - 1)"
99 (eq? #f (exact? (sqrt (- (expt fixnum-max 2) 1)))))
100
101 (pass-if "sqrt ((fixnum-max+1)^2 - 1)"
102 (eq? #f (exact? (sqrt (- (expt (+ fixnum-max 1) 2) 1)))))))
103
104 ;;;
105 ;;; odd?
106 ;;;
107
108 (with-test-prefix "odd?"
109 (pass-if (documented? odd?))
110 (pass-if (odd? 1))
111 (pass-if (odd? -1))
112 (pass-if (not (odd? 0)))
113 (pass-if (not (odd? 2)))
114 (pass-if (not (odd? -2)))
115 (pass-if (odd? (+ (* 2 fixnum-max) 1)))
116 (pass-if (not (odd? (* 2 fixnum-max))))
117 (pass-if (odd? (- (* 2 fixnum-min) 1)))
118 (pass-if (not (odd? (* 2 fixnum-min)))))
119
120 ;;;
121 ;;; even?
122 ;;;
123
124 (with-test-prefix "even?"
125 (pass-if (documented? even?))
126 (pass-if (even? 2))
127 (pass-if (even? -2))
128 (pass-if (even? 0))
129 (pass-if (not (even? 1)))
130 (pass-if (not (even? -1)))
131 (pass-if (not (even? (+ (* 2 fixnum-max) 1))))
132 (pass-if (even? (* 2 fixnum-max)))
133 (pass-if (not (even? (- (* 2 fixnum-min) 1))))
134 (pass-if (even? (* 2 fixnum-min))))
135
136 ;;;
137 ;;; inf? and inf
138 ;;;
139
140 (with-test-prefix "inf?"
141 (pass-if (documented? inf?))
142 (pass-if (inf? (inf)))
143 ;; FIXME: what are the expected behaviors?
144 ;; (pass-if (inf? (/ 1.0 0.0))
145 ;; (pass-if (inf? (/ 1 0.0))
146 (pass-if (not (inf? 0)))
147 (pass-if (not (inf? 42.0)))
148 (pass-if (not (inf? (+ fixnum-max 1))))
149 (pass-if (not (inf? (- fixnum-min 1)))))
150
151 ;;;
152 ;;; nan? and nan
153 ;;;
154
155 (with-test-prefix "nan?"
156 (pass-if (documented? nan?))
157 (pass-if (nan? (nan)))
158 ;; FIXME: other ways we should be able to generate NaN?
159 (pass-if (not (nan? 0)))
160 (pass-if (not (nan? 42.0)))
161 (pass-if (not (nan? (+ fixnum-max 1))))
162 (pass-if (not (nan? (- fixnum-min 1)))))
163
164 ;;;
165 ;;; abs
166 ;;;
167
168 (with-test-prefix "abs"
169 (pass-if (documented? abs))
170 (pass-if (zero? (abs 0)))
171 (pass-if (= 1 (abs 1)))
172 (pass-if (= 1 (abs -1)))
173 (pass-if (= (+ fixnum-max 1) (abs (+ fixnum-max 1))))
174 (pass-if (= (+ (- fixnum-min) 1) (abs (- fixnum-min 1))))
175 (pass-if (= 0.0 (abs 0.0)))
176 (pass-if (= 1.0 (abs 1.0)))
177 (pass-if (= 1.0 (abs -1.0)))
178 (pass-if (nan? (abs +nan.0)))
179 (pass-if (= +inf.0 (abs +inf.0)))
180 (pass-if (= +inf.0 (abs -inf.0))))
181
182 ;;;
183 ;;; quotient
184 ;;;
185
186 (with-test-prefix "quotient"
187
188 (expect-fail "documented?"
189 (documented? quotient))
190
191 (with-test-prefix "0 / n"
192
193 (pass-if "n = 1"
194 (eqv? 0 (quotient 0 1)))
195
196 (pass-if "n = -1"
197 (eqv? 0 (quotient 0 -1)))
198
199 (pass-if "n = 2"
200 (eqv? 0 (quotient 0 2)))
201
202 (pass-if "n = fixnum-max"
203 (eqv? 0 (quotient 0 fixnum-max)))
204
205 (pass-if "n = fixnum-max + 1"
206 (eqv? 0 (quotient 0 (+ fixnum-max 1))))
207
208 (pass-if "n = fixnum-min"
209 (eqv? 0 (quotient 0 fixnum-min)))
210
211 (pass-if "n = fixnum-min - 1"
212 (eqv? 0 (quotient 0 (- fixnum-min 1)))))
213
214 (with-test-prefix "1 / n"
215
216 (pass-if "n = 1"
217 (eqv? 1 (quotient 1 1)))
218
219 (pass-if "n = -1"
220 (eqv? -1 (quotient 1 -1)))
221
222 (pass-if "n = 2"
223 (eqv? 0 (quotient 1 2)))
224
225 (pass-if "n = fixnum-max"
226 (eqv? 0 (quotient 1 fixnum-max)))
227
228 (pass-if "n = fixnum-max + 1"
229 (eqv? 0 (quotient 1 (+ fixnum-max 1))))
230
231 (pass-if "n = fixnum-min"
232 (eqv? 0 (quotient 1 fixnum-min)))
233
234 (pass-if "n = fixnum-min - 1"
235 (eqv? 0 (quotient 1 (- fixnum-min 1)))))
236
237 (with-test-prefix "-1 / n"
238
239 (pass-if "n = 1"
240 (eqv? -1 (quotient -1 1)))
241
242 (pass-if "n = -1"
243 (eqv? 1 (quotient -1 -1)))
244
245 (pass-if "n = 2"
246 (eqv? 0 (quotient -1 2)))
247
248 (pass-if "n = fixnum-max"
249 (eqv? 0 (quotient -1 fixnum-max)))
250
251 (pass-if "n = fixnum-max + 1"
252 (eqv? 0 (quotient -1 (+ fixnum-max 1))))
253
254 (pass-if "n = fixnum-min"
255 (eqv? 0 (quotient -1 fixnum-min)))
256
257 (pass-if "n = fixnum-min - 1"
258 (eqv? 0 (quotient -1 (- fixnum-min 1)))))
259
260 (with-test-prefix "fixnum-max / n"
261
262 (pass-if "n = 1"
263 (eqv? fixnum-max (quotient fixnum-max 1)))
264
265 (pass-if "n = -1"
266 (eqv? (- fixnum-max) (quotient fixnum-max -1)))
267
268 (pass-if "n = 2"
269 (eqv? fixnum-max (+ (* (quotient fixnum-max 2) 2) 1)))
270
271 (pass-if "n = fixnum-max"
272 (eqv? 1 (quotient fixnum-max fixnum-max)))
273
274 (pass-if "n = fixnum-max + 1"
275 (eqv? 0 (quotient fixnum-max (+ fixnum-max 1))))
276
277 (pass-if "n = fixnum-min"
278 (eqv? 0 (quotient fixnum-max fixnum-min)))
279
280 (pass-if "n = fixnum-min - 1"
281 (eqv? 0 (quotient fixnum-max (- fixnum-min 1)))))
282
283 (with-test-prefix "(fixnum-max + 1) / n"
284
285 (pass-if "n = 1"
286 (eqv? (+ fixnum-max 1) (quotient (+ fixnum-max 1) 1)))
287
288 (pass-if "n = -1"
289 (eqv? (- (+ fixnum-max 1)) (quotient (+ fixnum-max 1) -1)))
290
291 (pass-if "n = 2"
292 (eqv? (+ fixnum-max 1) (* (quotient (+ fixnum-max 1) 2) 2)))
293
294 (pass-if "n = fixnum-max"
295 (eqv? 1 (quotient (+ fixnum-max 1) fixnum-max)))
296
297 (pass-if "n = fixnum-max + 1"
298 (eqv? 1 (quotient (+ fixnum-max 1) (+ fixnum-max 1))))
299
300 (pass-if "n = fixnum-min"
301 (eqv? -1 (quotient (+ fixnum-max 1) fixnum-min)))
302
303 (pass-if "n = fixnum-min - 1"
304 (eqv? 0 (quotient (+ fixnum-max 1) (- fixnum-min 1)))))
305
306 (with-test-prefix "fixnum-min / n"
307
308 (pass-if "n = 1"
309 (eqv? fixnum-min (quotient fixnum-min 1)))
310
311 (pass-if "n = -1"
312 (eqv? (- fixnum-min) (quotient fixnum-min -1)))
313
314 (pass-if "n = 2"
315 (eqv? fixnum-min (* (quotient fixnum-min 2) 2)))
316
317 (pass-if "n = fixnum-max"
318 (eqv? -1 (quotient fixnum-min fixnum-max)))
319
320 (pass-if "n = fixnum-max + 1"
321 (eqv? -1 (quotient fixnum-min (+ fixnum-max 1))))
322
323 (pass-if "n = fixnum-min"
324 (eqv? 1 (quotient fixnum-min fixnum-min)))
325
326 (pass-if "n = fixnum-min - 1"
327 (eqv? 0 (quotient fixnum-min (- fixnum-min 1))))
328
329 (pass-if "n = - fixnum-min - 1"
330 (eqv? -1 (quotient fixnum-min (1- (- fixnum-min)))))
331
332 ;; special case, normally inum/big is zero
333 (pass-if "n = - fixnum-min"
334 (eqv? -1 (quotient fixnum-min (- fixnum-min))))
335
336 (pass-if "n = - fixnum-min + 1"
337 (eqv? 0 (quotient fixnum-min (1+ (- fixnum-min))))))
338
339 (with-test-prefix "(fixnum-min - 1) / n"
340
341 (pass-if "n = 1"
342 (eqv? (- fixnum-min 1) (quotient (- fixnum-min 1) 1)))
343
344 (pass-if "n = -1"
345 (eqv? (- (- fixnum-min 1)) (quotient (- fixnum-min 1) -1)))
346
347 (pass-if "n = 2"
348 (eqv? fixnum-min (* (quotient (- fixnum-min 1) 2) 2)))
349
350 (pass-if "n = fixnum-max"
351 (eqv? -1 (quotient (- fixnum-min 1) fixnum-max)))
352
353 (pass-if "n = fixnum-max + 1"
354 (eqv? -1 (quotient (- fixnum-min 1) (+ fixnum-max 1))))
355
356 (pass-if "n = fixnum-min"
357 (eqv? 1 (quotient (- fixnum-min 1) fixnum-min)))
358
359 (pass-if "n = fixnum-min - 1"
360 (eqv? 1 (quotient (- fixnum-min 1) (- fixnum-min 1)))))
361
362 ;; Positive dividend and divisor
363
364 (pass-if "35 / 7"
365 (eqv? 5 (quotient 35 7)))
366
367 ;; Negative dividend, positive divisor
368
369 (pass-if "-35 / 7"
370 (eqv? -5 (quotient -35 7)))
371
372 ;; Positive dividend, negative divisor
373
374 (pass-if "35 / -7"
375 (eqv? -5 (quotient 35 -7)))
376
377 ;; Negative dividend and divisor
378
379 (pass-if "-35 / -7"
380 (eqv? 5 (quotient -35 -7)))
381
382 ;; Are numerical overflows detected correctly?
383
384 (with-test-prefix "division by zero"
385
386 (pass-if-exception "(quotient 1 0)"
387 exception:numerical-overflow
388 (quotient 1 0))
389
390 (pass-if-exception "(quotient bignum 0)"
391 exception:numerical-overflow
392 (quotient (+ fixnum-max 1) 0)))
393
394 ;; Are wrong type arguments detected correctly?
395
396 )
397
398 ;;;
399 ;;; remainder
400 ;;;
401
402 (with-test-prefix "remainder"
403
404 (expect-fail "documented?"
405 (documented? remainder))
406
407 (with-test-prefix "0 / n"
408
409 (pass-if "n = 1"
410 (eqv? 0 (remainder 0 1)))
411
412 (pass-if "n = -1"
413 (eqv? 0 (remainder 0 -1)))
414
415 (pass-if "n = fixnum-max"
416 (eqv? 0 (remainder 0 fixnum-max)))
417
418 (pass-if "n = fixnum-max + 1"
419 (eqv? 0 (remainder 0 (+ fixnum-max 1))))
420
421 (pass-if "n = fixnum-min"
422 (eqv? 0 (remainder 0 fixnum-min)))
423
424 (pass-if "n = fixnum-min - 1"
425 (eqv? 0 (remainder 0 (- fixnum-min 1)))))
426
427 (with-test-prefix "1 / n"
428
429 (pass-if "n = 1"
430 (eqv? 0 (remainder 1 1)))
431
432 (pass-if "n = -1"
433 (eqv? 0 (remainder 1 -1)))
434
435 (pass-if "n = fixnum-max"
436 (eqv? 1 (remainder 1 fixnum-max)))
437
438 (pass-if "n = fixnum-max + 1"
439 (eqv? 1 (remainder 1 (+ fixnum-max 1))))
440
441 (pass-if "n = fixnum-min"
442 (eqv? 1 (remainder 1 fixnum-min)))
443
444 (pass-if "n = fixnum-min - 1"
445 (eqv? 1 (remainder 1 (- fixnum-min 1)))))
446
447 (with-test-prefix "-1 / n"
448
449 (pass-if "n = 1"
450 (eqv? 0 (remainder -1 1)))
451
452 (pass-if "n = -1"
453 (eqv? 0 (remainder -1 -1)))
454
455 (pass-if "n = fixnum-max"
456 (eqv? -1 (remainder -1 fixnum-max)))
457
458 (pass-if "n = fixnum-max + 1"
459 (eqv? -1 (remainder -1 (+ fixnum-max 1))))
460
461 (pass-if "n = fixnum-min"
462 (eqv? -1 (remainder -1 fixnum-min)))
463
464 (pass-if "n = fixnum-min - 1"
465 (eqv? -1 (remainder -1 (- fixnum-min 1)))))
466
467 (with-test-prefix "fixnum-max / n"
468
469 (pass-if "n = 1"
470 (eqv? 0 (remainder fixnum-max 1)))
471
472 (pass-if "n = -1"
473 (eqv? 0 (remainder fixnum-max -1)))
474
475 (pass-if "n = fixnum-max"
476 (eqv? 0 (remainder fixnum-max fixnum-max)))
477
478 (pass-if "n = fixnum-max + 1"
479 (eqv? fixnum-max (remainder fixnum-max (+ fixnum-max 1))))
480
481 (pass-if "n = fixnum-min"
482 (eqv? fixnum-max (remainder fixnum-max fixnum-min)))
483
484 (pass-if "n = fixnum-min - 1"
485 (eqv? fixnum-max (remainder fixnum-max (- fixnum-min 1)))))
486
487 (with-test-prefix "(fixnum-max + 1) / n"
488
489 (pass-if "n = 1"
490 (eqv? 0 (remainder (+ fixnum-max 1) 1)))
491
492 (pass-if "n = -1"
493 (eqv? 0 (remainder (+ fixnum-max 1) -1)))
494
495 (pass-if "n = fixnum-max"
496 (eqv? 1 (remainder (+ fixnum-max 1) fixnum-max)))
497
498 (pass-if "n = fixnum-max + 1"
499 (eqv? 0 (remainder (+ fixnum-max 1) (+ fixnum-max 1))))
500
501 (pass-if "n = fixnum-min"
502 (eqv? 0 (remainder (+ fixnum-max 1) fixnum-min)))
503
504 (pass-if "n = fixnum-min - 1"
505 (eqv? (+ fixnum-max 1) (remainder (+ fixnum-max 1) (- fixnum-min 1)))))
506
507 (with-test-prefix "fixnum-min / n"
508
509 (pass-if "n = 1"
510 (eqv? 0 (remainder fixnum-min 1)))
511
512 (pass-if "n = -1"
513 (eqv? 0 (remainder fixnum-min -1)))
514
515 (pass-if "n = fixnum-max"
516 (eqv? -1 (remainder fixnum-min fixnum-max)))
517
518 (pass-if "n = fixnum-max + 1"
519 (eqv? 0 (remainder fixnum-min (+ fixnum-max 1))))
520
521 (pass-if "n = fixnum-min"
522 (eqv? 0 (remainder fixnum-min fixnum-min)))
523
524 (pass-if "n = fixnum-min - 1"
525 (eqv? fixnum-min (remainder fixnum-min (- fixnum-min 1))))
526
527 (pass-if "n = - fixnum-min - 1"
528 (eqv? -1 (remainder fixnum-min (1- (- fixnum-min)))))
529
530 ;; special case, normally inum%big is the inum
531 (pass-if "n = - fixnum-min"
532 (eqv? 0 (remainder fixnum-min (- fixnum-min))))
533
534 (pass-if "n = - fixnum-min + 1"
535 (eqv? fixnum-min (remainder fixnum-min (1+ (- fixnum-min))))))
536
537 (with-test-prefix "(fixnum-min - 1) / n"
538
539 (pass-if "n = 1"
540 (eqv? 0 (remainder (- fixnum-min 1) 1)))
541
542 (pass-if "n = -1"
543 (eqv? 0 (remainder (- fixnum-min 1) -1)))
544
545 (pass-if "n = fixnum-max"
546 (eqv? -2 (remainder (- fixnum-min 1) fixnum-max)))
547
548 (pass-if "n = fixnum-max + 1"
549 (eqv? -1 (remainder (- fixnum-min 1) (+ fixnum-max 1))))
550
551 (pass-if "n = fixnum-min"
552 (eqv? -1 (remainder (- fixnum-min 1) fixnum-min)))
553
554 (pass-if "n = fixnum-min - 1"
555 (eqv? 0 (remainder (- fixnum-min 1) (- fixnum-min 1)))))
556
557 ;; Positive dividend and divisor
558
559 (pass-if "35 / 7"
560 (eqv? 0 (remainder 35 7)))
561
562 ;; Negative dividend, positive divisor
563
564 (pass-if "-35 / 7"
565 (eqv? 0 (remainder -35 7)))
566
567 ;; Positive dividend, negative divisor
568
569 (pass-if "35 / -7"
570 (eqv? 0 (remainder 35 -7)))
571
572 ;; Negative dividend and divisor
573
574 (pass-if "-35 / -7"
575 (eqv? 0 (remainder -35 -7)))
576
577 ;; Are numerical overflows detected correctly?
578
579 (with-test-prefix "division by zero"
580
581 (pass-if-exception "(remainder 1 0)"
582 exception:numerical-overflow
583 (remainder 1 0))
584
585 (pass-if-exception "(remainder bignum 0)"
586 exception:numerical-overflow
587 (remainder (+ fixnum-max 1) 0)))
588
589 ;; Are wrong type arguments detected correctly?
590
591 )
592
593 ;;;
594 ;;; modulo
595 ;;;
596
597 (with-test-prefix "modulo"
598
599 (expect-fail "documented?"
600 (documented? modulo))
601
602 (with-test-prefix "0 % n"
603
604 (pass-if "n = 1"
605 (eqv? 0 (modulo 0 1)))
606
607 (pass-if "n = -1"
608 (eqv? 0 (modulo 0 -1)))
609
610 (pass-if "n = fixnum-max"
611 (eqv? 0 (modulo 0 fixnum-max)))
612
613 (pass-if "n = fixnum-max + 1"
614 (eqv? 0 (modulo 0 (+ fixnum-max 1))))
615
616 (pass-if "n = fixnum-min"
617 (eqv? 0 (modulo 0 fixnum-min)))
618
619 (pass-if "n = fixnum-min - 1"
620 (eqv? 0 (modulo 0 (- fixnum-min 1)))))
621
622 (with-test-prefix "1 % n"
623
624 (pass-if "n = 1"
625 (eqv? 0 (modulo 1 1)))
626
627 (pass-if "n = -1"
628 (eqv? 0 (modulo 1 -1)))
629
630 (pass-if "n = fixnum-max"
631 (eqv? 1 (modulo 1 fixnum-max)))
632
633 (pass-if "n = fixnum-max + 1"
634 (eqv? 1 (modulo 1 (+ fixnum-max 1))))
635
636 (pass-if "n = fixnum-min"
637 (eqv? (+ fixnum-min 1) (modulo 1 fixnum-min)))
638
639 (pass-if "n = fixnum-min - 1"
640 (eqv? fixnum-min (modulo 1 (- fixnum-min 1)))))
641
642 (with-test-prefix "-1 % n"
643
644 (pass-if "n = 1"
645 (eqv? 0 (modulo -1 1)))
646
647 (pass-if "n = -1"
648 (eqv? 0 (modulo -1 -1)))
649
650 (pass-if "n = fixnum-max"
651 (eqv? (- fixnum-max 1) (modulo -1 fixnum-max)))
652
653 (pass-if "n = fixnum-max + 1"
654 (eqv? fixnum-max (modulo -1 (+ fixnum-max 1))))
655
656 (pass-if "n = fixnum-min"
657 (eqv? -1 (modulo -1 fixnum-min)))
658
659 (pass-if "n = fixnum-min - 1"
660 (eqv? -1 (modulo -1 (- fixnum-min 1)))))
661
662 (with-test-prefix "fixnum-max % n"
663
664 (pass-if "n = 1"
665 (eqv? 0 (modulo fixnum-max 1)))
666
667 (pass-if "n = -1"
668 (eqv? 0 (modulo fixnum-max -1)))
669
670 (pass-if "n = fixnum-max"
671 (eqv? 0 (modulo fixnum-max fixnum-max)))
672
673 (pass-if "n = fixnum-max + 1"
674 (eqv? fixnum-max (modulo fixnum-max (+ fixnum-max 1))))
675
676 (pass-if "n = fixnum-min"
677 (eqv? -1 (modulo fixnum-max fixnum-min)))
678
679 (pass-if "n = fixnum-min - 1"
680 (eqv? -2 (modulo fixnum-max (- fixnum-min 1)))))
681
682 (with-test-prefix "(fixnum-max + 1) % n"
683
684 (pass-if "n = 1"
685 (eqv? 0 (modulo (+ fixnum-max 1) 1)))
686
687 (pass-if "n = -1"
688 (eqv? 0 (modulo (+ fixnum-max 1) -1)))
689
690 (pass-if "n = fixnum-max"
691 (eqv? 1 (modulo (+ fixnum-max 1) fixnum-max)))
692
693 (pass-if "n = fixnum-max + 1"
694 (eqv? 0 (modulo (+ fixnum-max 1) (+ fixnum-max 1))))
695
696 (pass-if "n = fixnum-min"
697 (eqv? 0 (modulo (+ fixnum-max 1) fixnum-min)))
698
699 (pass-if "n = fixnum-min - 1"
700 (eqv? -1 (modulo (+ fixnum-max 1) (- fixnum-min 1)))))
701
702 (with-test-prefix "fixnum-min % n"
703
704 (pass-if "n = 1"
705 (eqv? 0 (modulo fixnum-min 1)))
706
707 (pass-if "n = -1"
708 (eqv? 0 (modulo fixnum-min -1)))
709
710 (pass-if "n = fixnum-max"
711 (eqv? (- fixnum-max 1) (modulo fixnum-min fixnum-max)))
712
713 (pass-if "n = fixnum-max + 1"
714 (eqv? 0 (modulo fixnum-min (+ fixnum-max 1))))
715
716 (pass-if "n = fixnum-min"
717 (eqv? 0 (modulo fixnum-min fixnum-min)))
718
719 (pass-if "n = fixnum-min - 1"
720 (eqv? fixnum-min (modulo fixnum-min (- fixnum-min 1)))))
721
722 (with-test-prefix "(fixnum-min - 1) % n"
723
724 (pass-if "n = 1"
725 (eqv? 0 (modulo (- fixnum-min 1) 1)))
726
727 (pass-if "n = -1"
728 (eqv? 0 (modulo (- fixnum-min 1) -1)))
729
730 (pass-if "n = fixnum-max"
731 (eqv? (- fixnum-max 2) (modulo (- fixnum-min 1) fixnum-max)))
732
733 (pass-if "n = fixnum-max + 1"
734 (eqv? fixnum-max (modulo (- fixnum-min 1) (+ fixnum-max 1))))
735
736 (pass-if "n = fixnum-min"
737 (eqv? -1 (modulo (- fixnum-min 1) fixnum-min)))
738
739 (pass-if "n = fixnum-min - 1"
740 (eqv? 0 (modulo (- fixnum-min 1) (- fixnum-min 1)))))
741
742 ;; Positive dividend and divisor
743
744 (pass-if "13 % 4"
745 (eqv? 1 (modulo 13 4)))
746
747 (pass-if "2177452800 % 86400"
748 (eqv? 0 (modulo 2177452800 86400)))
749
750 ;; Negative dividend, positive divisor
751
752 (pass-if "-13 % 4"
753 (eqv? 3 (modulo -13 4)))
754
755 (pass-if "-2177452800 % 86400"
756 (eqv? 0 (modulo -2177452800 86400)))
757
758 ;; Positive dividend, negative divisor
759
760 (pass-if "13 % -4"
761 (eqv? -3 (modulo 13 -4)))
762
763 (pass-if "2177452800 % -86400"
764 (eqv? 0 (modulo 2177452800 -86400)))
765
766 ;; Negative dividend and divisor
767
768 (pass-if "-13 % -4"
769 (eqv? -1 (modulo -13 -4)))
770
771 (pass-if "-2177452800 % -86400"
772 (eqv? 0 (modulo -2177452800 -86400)))
773
774 ;; Are numerical overflows detected correctly?
775
776 (with-test-prefix "division by zero"
777
778 (pass-if-exception "(modulo 1 0)"
779 exception:numerical-overflow
780 (modulo 1 0))
781
782 (pass-if-exception "(modulo bignum 0)"
783 exception:numerical-overflow
784 (modulo (+ fixnum-max 1) 0)))
785
786 ;; Are wrong type arguments detected correctly?
787
788 )
789
790 ;;;
791 ;;; modulo-expt
792 ;;;
793
794 (with-test-prefix "modulo-expt"
795 (pass-if (= 1 (modulo-expt 17 23 47)))
796
797 (pass-if (= 1 (modulo-expt 17 -23 47)))
798
799 (pass-if (= 17 (modulo-expt 17 -22 47)))
800
801 (pass-if (= 36 (modulo-expt 17 22 47)))
802
803 (pass-if (= 183658794479969134816674175082294846241553725240 (modulo-expt 111122223333444455556666 111122223333444455556666 1153478690012629968439432872520758982731022934717)))
804
805 (pass-if-exception
806 "Proper exception with 0 modulus"
807 (cons 'numerical-overflow "")
808 (modulo-expt 17 23 0))
809
810 (pass-if-exception
811 "Proper exception when result not invertible"
812 (cons 'numerical-overflow "")
813 (modulo-expt 10 -1 48))
814
815 (pass-if-exception
816 "Proper exception with wrong type argument"
817 (cons 'wrong-type-arg "")
818 (modulo-expt "Sam" 23 10))
819
820 (pass-if-exception
821 "Proper exception with wrong type argument"
822 (cons 'wrong-type-arg "")
823 (modulo-expt 17 9.9 10))
824
825 (pass-if-exception
826 "Proper exception with wrong type argument"
827 (cons 'wrong-type-arg "")
828 (modulo-expt 17 23 'Ethel)))
829
830 ;;;
831 ;;; gcd
832 ;;;
833
834 (with-test-prefix "gcd"
835
836 (expect-fail "documented?"
837 (documented? gcd))
838
839 (with-test-prefix "(0 n)"
840
841 (pass-if "n = 0"
842 (eqv? 0 (gcd 0 0)))
843
844 (pass-if "n = 1"
845 (eqv? 1 (gcd 0 1)))
846
847 (pass-if "n = -1"
848 (eqv? 1 (gcd 0 -1)))
849
850 (pass-if "n = fixnum-max"
851 (eqv? fixnum-max (gcd 0 fixnum-max)))
852
853 (pass-if "n = fixnum-max + 1"
854 (eqv? (+ fixnum-max 1) (gcd 0 (+ fixnum-max 1))))
855
856 (pass-if "n = fixnum-min"
857 (eqv? (- fixnum-min) (gcd 0 fixnum-min)))
858
859 (pass-if "n = fixnum-min - 1"
860 (eqv? (- (- fixnum-min 1)) (gcd 0 (- fixnum-min 1)))))
861
862 (with-test-prefix "(n 0)"
863
864 (pass-if "n = 2^128 * fixnum-max"
865 (eqv? (ash fixnum-max 128) (gcd (ash fixnum-max 128) 0))))
866
867 (with-test-prefix "(1 n)"
868
869 (pass-if "n = 0"
870 (eqv? 1 (gcd 1 0)))
871
872 (pass-if "n = 1"
873 (eqv? 1 (gcd 1 1)))
874
875 (pass-if "n = -1"
876 (eqv? 1 (gcd 1 -1)))
877
878 (pass-if "n = fixnum-max"
879 (eqv? 1 (gcd 1 fixnum-max)))
880
881 (pass-if "n = fixnum-max + 1"
882 (eqv? 1 (gcd 1 (+ fixnum-max 1))))
883
884 (pass-if "n = fixnum-min"
885 (eqv? 1 (gcd 1 fixnum-min)))
886
887 (pass-if "n = fixnum-min - 1"
888 (eqv? 1 (gcd 1 (- fixnum-min 1)))))
889
890 (with-test-prefix "(-1 n)"
891
892 (pass-if "n = 0"
893 (eqv? 1 (gcd -1 0)))
894
895 (pass-if "n = 1"
896 (eqv? 1 (gcd -1 1)))
897
898 (pass-if "n = -1"
899 (eqv? 1 (gcd -1 -1)))
900
901 (pass-if "n = fixnum-max"
902 (eqv? 1 (gcd -1 fixnum-max)))
903
904 (pass-if "n = fixnum-max + 1"
905 (eqv? 1 (gcd -1 (+ fixnum-max 1))))
906
907 (pass-if "n = fixnum-min"
908 (eqv? 1 (gcd -1 fixnum-min)))
909
910 (pass-if "n = fixnum-min - 1"
911 (eqv? 1 (gcd -1 (- fixnum-min 1)))))
912
913 (with-test-prefix "(fixnum-max n)"
914
915 (pass-if "n = 0"
916 (eqv? fixnum-max (gcd fixnum-max 0)))
917
918 (pass-if "n = 1"
919 (eqv? 1 (gcd fixnum-max 1)))
920
921 (pass-if "n = -1"
922 (eqv? 1 (gcd fixnum-max -1)))
923
924 (pass-if "n = fixnum-max"
925 (eqv? fixnum-max (gcd fixnum-max fixnum-max)))
926
927 (pass-if "n = fixnum-max + 1"
928 (eqv? 1 (gcd fixnum-max (+ fixnum-max 1))))
929
930 (pass-if "n = fixnum-min"
931 (eqv? 1 (gcd fixnum-max fixnum-min)))
932
933 (pass-if "n = fixnum-min - 1"
934 (eqv? 1 (gcd fixnum-max (- fixnum-min 1)))))
935
936 (with-test-prefix "((+ fixnum-max 1) n)"
937
938 (pass-if "n = 0"
939 (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) 0)))
940
941 (pass-if "n = 1"
942 (eqv? 1 (gcd (+ fixnum-max 1) 1)))
943
944 (pass-if "n = -1"
945 (eqv? 1 (gcd (+ fixnum-max 1) -1)))
946
947 (pass-if "n = fixnum-max"
948 (eqv? 1 (gcd (+ fixnum-max 1) fixnum-max)))
949
950 (pass-if "n = fixnum-max + 1"
951 (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) (+ fixnum-max 1))))
952
953 (pass-if "n = fixnum-min"
954 (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) fixnum-min)))
955
956 (pass-if "n = fixnum-min - 1"
957 (eqv? 1 (gcd (+ fixnum-max 1) (- fixnum-min 1)))))
958
959 (with-test-prefix "(fixnum-min n)"
960
961 (pass-if "n = 0"
962 (eqv? (- fixnum-min) (gcd fixnum-min 0)))
963
964 (pass-if "n = 1"
965 (eqv? 1 (gcd fixnum-min 1)))
966
967 (pass-if "n = -1"
968 (eqv? 1 (gcd fixnum-min -1)))
969
970 (pass-if "n = fixnum-max"
971 (eqv? 1 (gcd fixnum-min fixnum-max)))
972
973 (pass-if "n = fixnum-max + 1"
974 (eqv? (+ fixnum-max 1) (gcd fixnum-min (+ fixnum-max 1))))
975
976 (pass-if "n = fixnum-min"
977 (eqv? (- fixnum-min) (gcd fixnum-min fixnum-min)))
978
979 (pass-if "n = fixnum-min - 1"
980 (eqv? 1 (gcd fixnum-min (- fixnum-min 1)))))
981
982 (with-test-prefix "((- fixnum-min 1) n)"
983
984 (pass-if "n = 0"
985 (eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) 0)))
986
987 (pass-if "n = 1"
988 (eqv? 1 (gcd (- fixnum-min 1) 1)))
989
990 (pass-if "n = -1"
991 (eqv? 1 (gcd (- fixnum-min 1) -1)))
992
993 (pass-if "n = fixnum-max"
994 (eqv? 1 (gcd (- fixnum-min 1) fixnum-max)))
995
996 (pass-if "n = fixnum-max + 1"
997 (eqv? 1 (gcd (- fixnum-min 1) (+ fixnum-max 1))))
998
999 (pass-if "n = fixnum-min"
1000 (eqv? 1 (gcd (- fixnum-min 1) fixnum-min)))
1001
1002 (pass-if "n = fixnum-min - 1"
1003 (eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) (- fixnum-min 1)))))
1004
1005 ;; Are wrong type arguments detected correctly?
1006
1007 )
1008
1009 ;;;
1010 ;;; lcm
1011 ;;;
1012
1013 (with-test-prefix "lcm"
1014 ;; FIXME: more tests?
1015 ;; (some of these are already in r4rs.test)
1016 (expect-fail (documented? lcm))
1017 (pass-if (= (lcm) 1))
1018 (pass-if (= (lcm 32 -36) 288))
1019 (let ((big-n 115792089237316195423570985008687907853269984665640564039457584007913129639936) ; 2 ^ 256
1020 (lcm-of-big-n-and-11 1273712981610478149659280835095566986385969831322046204434033424087044426039296))
1021 (pass-if (= lcm-of-big-n-and-11 (lcm big-n 11)))
1022 (pass-if (= lcm-of-big-n-and-11 (lcm 11 big-n 11)))))
1023
1024 ;;;
1025 ;;; number->string
1026 ;;;
1027
1028 (with-test-prefix "number->string"
1029 (let ((num->str->num
1030 (lambda (n radix)
1031 (string->number (number->string n radix) radix))))
1032
1033 (pass-if (documented? number->string))
1034 (pass-if (string=? (number->string 0) "0"))
1035 (pass-if (string=? (number->string 171) "171"))
1036 (pass-if (= (+ fixnum-max 1) (num->str->num (+ fixnum-max 1) 10)))
1037 (pass-if (= (- fixnum-min 1) (num->str->num (- fixnum-min 1) 10)))
1038 (pass-if (= (inf) (num->str->num (inf) 10)))
1039 (pass-if (= 1.3 (num->str->num 1.3 10)))
1040
1041 (pass-if (string=? (number->string 35.25 36) "Z.9"))
1042 (expect-fail (string=? (number->string 0.25 2) "0.01"))
1043 (pass-if (string=? (number->string 255.0625 16) "FF.1"))
1044 (pass-if (string=? (number->string (/ 1 3) 3) "1/10"))
1045 (expect-fail (string=? (number->string 11.33333333333333333 12) "B.4"))
1046 (expect-fail (string=? (number->string 11.33333333333333333+23i 12)
1047 "B.4+1B.0i"))
1048 (expect-fail (string=? (number->string 1.324e44 16) "5.EFE0A14FAFEe24"))))
1049
1050 ;;;
1051 ;;; string->number
1052 ;;;
1053
1054 (with-test-prefix "string->number"
1055
1056 (pass-if "string->number"
1057 (documented? string->number))
1058
1059 (pass-if "non number strings"
1060 (for-each (lambda (x) (if (string->number x) (throw 'fail)))
1061 '("" "q" "1q" "6+7iq" "8+9q" "10+11" "13+" "18@19q" "20@q" "23@"
1062 "+25iq" "26i" "-q" "-iq" "i" "5#.0" "8/" "10#11" ".#" "."
1063 "#o.2" "3.4q" "15.16e17q" "18.19e+q" ".q" ".17#18" "10q" "#b2"
1064 "#b3" "#b4" "#b5" "#b6" "#b7" "#b8" "#b9" "#ba" "#bb" "#bc"
1065 "#bd" "#be" "#bf" "#q" "#b#b1" "#o#o1" "#d#d1" "#x#x1" "#e#e1"
1066 "#i#i1" "12@12+0i"))
1067 #t)
1068
1069 (pass-if "valid number strings"
1070 (for-each (lambda (couple)
1071 (apply
1072 (lambda (x y)
1073 (let ((xx (string->number x)))
1074 (if (or (eq? xx #f) (not (eqv? xx y)))
1075 (begin
1076 (pk x y)
1077 (throw 'fail)))))
1078 couple))
1079 `(;; Radix:
1080 ("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
1081 ("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
1082 ("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
1083 ("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
1084 ("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
1085 ("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
1086 ("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
1087 ("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
1088 ("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
1089 ("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
1090 ("#b1010" 10)
1091 ("#o12345670" 2739128)
1092 ("#d1234567890" 1234567890)
1093 ("#x1234567890abcdef" 1311768467294899695)
1094 ;; Exactness:
1095 ("#e1" 1) ("#e1.2" 12/10)
1096 ("#i1.1" 1.1) ("#i1" 1.0)
1097 ;; Integers:
1098 ("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1))
1099 ("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
1100 ("#b#i100" 4.0)
1101 ;; Fractions:
1102 ("1/1" 1) ("1/2" 1/2) ("-1/2" -1/2) ("1#/1" 10.0)
1103 ("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 9/10) ("#e10/1#" 1)
1104 ("#i6/8" 0.75) ("#i1/1" 1.0)
1105 ;; Decimal numbers:
1106 ;; * <uinteger 10> <suffix>
1107 ("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
1108 ("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
1109 ("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
1110 ;; * . <digit 10>+ #* <suffix>
1111 (".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
1112 (".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
1113 ;; * <digit 10>+ . <digit 10>* #* <suffix>
1114 ("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
1115 ("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
1116 ("3.1#e0" 3.1)
1117 ;; * <digit 10>+ #+ . #* <suffix>
1118 ("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
1119 ;; Complex:
1120 ("1@0" 1.0) ("1@+0" 1.0) ("1@-0" 1.0)
1121 ("2+3i" ,(+ 2 (* 3 +i))) ("4-5i" ,(- 4 (* 5 +i)))
1122 ("1+i" 1+1i) ("1-i" 1-1i) ("+1i" 0+1i) ("-1i" 0-1i)
1123 ("+i" +1i) ("-i" -1i)))
1124 #t)
1125
1126 (pass-if-exception "exponent too big"
1127 exception:out-of-range
1128 (string->number "12.13e141414")))
1129
1130 ;;;
1131 ;;; number?
1132 ;;;
1133
1134 (with-test-prefix "number?"
1135 (pass-if (documented? number?))
1136 (pass-if (number? 0))
1137 (pass-if (number? 7))
1138 (pass-if (number? -7))
1139 (pass-if (number? 1.3))
1140 (pass-if (number? (+ 1 fixnum-max)))
1141 (pass-if (number? (- 1 fixnum-min)))
1142 (pass-if (number? 3+4i))
1143 (pass-if (not (number? #\a)))
1144 (pass-if (not (number? "a")))
1145 (pass-if (not (number? (make-vector 0))))
1146 (pass-if (not (number? (cons 1 2))))
1147 (pass-if (not (number? #t)))
1148 (pass-if (not (number? (lambda () #t))))
1149 (pass-if (not (number? (current-input-port)))))
1150
1151 ;;;
1152 ;;; complex?
1153 ;;;
1154
1155 (with-test-prefix "complex?"
1156 (pass-if (documented? complex?))
1157 (pass-if (complex? 0))
1158 (pass-if (complex? 7))
1159 (pass-if (complex? -7))
1160 (pass-if (complex? (+ 1 fixnum-max)))
1161 (pass-if (complex? (- 1 fixnum-min)))
1162 (pass-if (complex? 1.3))
1163 (pass-if (complex? 3+4i))
1164 (pass-if (not (complex? #\a)))
1165 (pass-if (not (complex? "a")))
1166 (pass-if (not (complex? (make-vector 0))))
1167 (pass-if (not (complex? (cons 1 2))))
1168 (pass-if (not (complex? #t)))
1169 (pass-if (not (complex? (lambda () #t))))
1170 (pass-if (not (complex? (current-input-port)))))
1171
1172 ;;;
1173 ;;; real?
1174 ;;;
1175
1176 (with-test-prefix "real?"
1177 (pass-if (documented? real?))
1178 (pass-if (real? 0))
1179 (pass-if (real? 7))
1180 (pass-if (real? -7))
1181 (pass-if (real? (+ 1 fixnum-max)))
1182 (pass-if (real? (- 1 fixnum-min)))
1183 (pass-if (real? 1.3))
1184 (pass-if (not (real? 3+4i)))
1185 (pass-if (not (real? #\a)))
1186 (pass-if (not (real? "a")))
1187 (pass-if (not (real? (make-vector 0))))
1188 (pass-if (not (real? (cons 1 2))))
1189 (pass-if (not (real? #t)))
1190 (pass-if (not (real? (lambda () #t))))
1191 (pass-if (not (real? (current-input-port)))))
1192
1193 ;;;
1194 ;;; rational? (same as real? right now)
1195 ;;;
1196
1197 (with-test-prefix "rational?"
1198 (pass-if (documented? rational?))
1199 (pass-if (rational? 0))
1200 (pass-if (rational? 7))
1201 (pass-if (rational? -7))
1202 (pass-if (rational? (+ 1 fixnum-max)))
1203 (pass-if (rational? (- 1 fixnum-min)))
1204 (pass-if (rational? 1.3))
1205 (pass-if (not (rational? 3+4i)))
1206 (pass-if (not (rational? #\a)))
1207 (pass-if (not (rational? "a")))
1208 (pass-if (not (rational? (make-vector 0))))
1209 (pass-if (not (rational? (cons 1 2))))
1210 (pass-if (not (rational? #t)))
1211 (pass-if (not (rational? (lambda () #t))))
1212 (pass-if (not (rational? (current-input-port)))))
1213
1214 ;;;
1215 ;;; integer?
1216 ;;;
1217
1218 (with-test-prefix "integer?"
1219 (pass-if (documented? integer?))
1220 (pass-if (integer? 0))
1221 (pass-if (integer? 7))
1222 (pass-if (integer? -7))
1223 (pass-if (integer? (+ 1 fixnum-max)))
1224 (pass-if (integer? (- 1 fixnum-min)))
1225 (pass-if (and (= 3+0i (round 3+0i)) (integer? 3+0i)))
1226 (pass-if (and (= 1.0 (round 1.0)) (integer? 1.0)))
1227 (pass-if (not (integer? 1.3)))
1228 (pass-if (not (integer? 3+4i)))
1229 (pass-if (not (integer? #\a)))
1230 (pass-if (not (integer? "a")))
1231 (pass-if (not (integer? (make-vector 0))))
1232 (pass-if (not (integer? (cons 1 2))))
1233 (pass-if (not (integer? #t)))
1234 (pass-if (not (integer? (lambda () #t))))
1235 (pass-if (not (integer? (current-input-port)))))
1236
1237 ;;;
1238 ;;; inexact?
1239 ;;;
1240
1241 (with-test-prefix "inexact?"
1242 (pass-if (documented? inexact?))
1243 (pass-if (not (inexact? 0)))
1244 (pass-if (not (inexact? 7)))
1245 (pass-if (not (inexact? -7)))
1246 (pass-if (not (inexact? (+ 1 fixnum-max))))
1247 (pass-if (not (inexact? (- 1 fixnum-min))))
1248 (pass-if (inexact? 1.3))
1249 (pass-if (inexact? 3.1+4.2i))
1250 (pass-if-exception "char"
1251 exception:wrong-type-arg
1252 (not (inexact? #\a)))
1253 (pass-if-exception "string"
1254 exception:wrong-type-arg
1255 (not (inexact? "a")))
1256 (pass-if-exception "vector"
1257 exception:wrong-type-arg
1258 (not (inexact? (make-vector 0))))
1259 (pass-if-exception "cons"
1260 exception:wrong-type-arg
1261 (not (inexact? (cons 1 2))))
1262 (pass-if-exception "bool"
1263 exception:wrong-type-arg
1264 (not (inexact? #t)))
1265 (pass-if-exception "procedure"
1266 exception:wrong-type-arg
1267 (not (inexact? (lambda () #t))))
1268 (pass-if-exception "port"
1269 exception:wrong-type-arg
1270 (not (inexact? (current-input-port)))))
1271
1272 ;;;
1273 ;;; equal?
1274 ;;;
1275
1276 (with-test-prefix "equal?"
1277 (pass-if (documented? equal?))
1278 (pass-if (equal? 0 0))
1279 (pass-if (equal? 7 7))
1280 (pass-if (equal? -7 -7))
1281 (pass-if (equal? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1282 (pass-if (equal? (- fixnum-min 1) (- fixnum-min 1)))
1283 (pass-if (not (equal? 0 1)))
1284 (pass-if (not (equal? fixnum-max (+ 1 fixnum-max))))
1285 (pass-if (not (equal? (+ 1 fixnum-max) fixnum-max)))
1286 (pass-if (not (equal? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1287 (pass-if (not (equal? fixnum-min (- fixnum-min 1))))
1288 (pass-if (not (equal? (- fixnum-min 1) fixnum-min)))
1289 (pass-if (not (equal? (- fixnum-min 1) (- fixnum-min 2))))
1290 (pass-if (not (equal? (+ fixnum-max 1) (- fixnum-min 1))))
1291
1292 (pass-if (not (equal? (ash 1 256) +inf.0)))
1293 (pass-if (not (equal? +inf.0 (ash 1 256))))
1294 (pass-if (not (equal? (ash 1 256) -inf.0)))
1295 (pass-if (not (equal? -inf.0 (ash 1 256))))
1296
1297 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1298 ;; sure we've avoided that
1299 (pass-if (not (equal? (ash 1 1024) +inf.0)))
1300 (pass-if (not (equal? +inf.0 (ash 1 1024))))
1301 (pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
1302 (pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
1303
1304 (pass-if (not (equal? +nan.0 +nan.0)))
1305 (pass-if (not (equal? 0 +nan.0)))
1306 (pass-if (not (equal? +nan.0 0)))
1307 (pass-if (not (equal? 1 +nan.0)))
1308 (pass-if (not (equal? +nan.0 1)))
1309 (pass-if (not (equal? -1 +nan.0)))
1310 (pass-if (not (equal? +nan.0 -1)))
1311
1312 (pass-if (not (equal? (ash 1 256) +nan.0)))
1313 (pass-if (not (equal? +nan.0 (ash 1 256))))
1314 (pass-if (not (equal? (- (ash 1 256)) +nan.0)))
1315 (pass-if (not (equal? +nan.0 (- (ash 1 256)))))
1316
1317 (pass-if (not (equal? (ash 1 8192) +nan.0)))
1318 (pass-if (not (equal? +nan.0 (ash 1 8192))))
1319 (pass-if (not (equal? (- (ash 1 8192)) +nan.0)))
1320 (pass-if (not (equal? +nan.0 (- (ash 1 8192)))))
1321
1322 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1323 ;; sure we've avoided that
1324 (pass-if (not (equal? (ash 3 1023) +nan.0)))
1325 (pass-if (not (equal? +nan.0 (ash 3 1023)))))
1326
1327 ;;;
1328 ;;; =
1329 ;;;
1330
1331 (with-test-prefix "="
1332 (expect-fail (documented? =))
1333 (pass-if (= 0 0))
1334 (pass-if (= 7 7))
1335 (pass-if (= -7 -7))
1336 (pass-if (= (+ 1 fixnum-max) (+ 1 fixnum-max)))
1337 (pass-if (= (- fixnum-min 1) (- fixnum-min 1)))
1338 (pass-if (not (= 0 1)))
1339 (pass-if (not (= fixnum-max (+ 1 fixnum-max))))
1340 (pass-if (not (= (+ 1 fixnum-max) fixnum-max)))
1341 (pass-if (not (= (+ 1 fixnum-max) (+ 2 fixnum-max))))
1342 (pass-if (not (= fixnum-min (- fixnum-min 1))))
1343 (pass-if (not (= (- fixnum-min 1) fixnum-min)))
1344 (pass-if (not (= (- fixnum-min 1) (- fixnum-min 2))))
1345 (pass-if (not (= (+ fixnum-max 1) (- fixnum-min 1))))
1346
1347 (pass-if (not (= (ash 1 256) +inf.0)))
1348 (pass-if (not (= +inf.0 (ash 1 256))))
1349 (pass-if (not (= (ash 1 256) -inf.0)))
1350 (pass-if (not (= -inf.0 (ash 1 256))))
1351
1352 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1353 ;; sure we've avoided that
1354 (pass-if (not (= (ash 1 1024) +inf.0)))
1355 (pass-if (not (= +inf.0 (ash 1 1024))))
1356 (pass-if (not (= (- (ash 1 1024)) -inf.0)))
1357 (pass-if (not (= -inf.0 (- (ash 1 1024)))))
1358
1359 (pass-if (not (= +nan.0 +nan.0)))
1360 (pass-if (not (= 0 +nan.0)))
1361 (pass-if (not (= +nan.0 0)))
1362 (pass-if (not (= 1 +nan.0)))
1363 (pass-if (not (= +nan.0 1)))
1364 (pass-if (not (= -1 +nan.0)))
1365 (pass-if (not (= +nan.0 -1)))
1366
1367 (pass-if (not (= (ash 1 256) +nan.0)))
1368 (pass-if (not (= +nan.0 (ash 1 256))))
1369 (pass-if (not (= (- (ash 1 256)) +nan.0)))
1370 (pass-if (not (= +nan.0 (- (ash 1 256)))))
1371
1372 (pass-if (not (= (ash 1 8192) +nan.0)))
1373 (pass-if (not (= +nan.0 (ash 1 8192))))
1374 (pass-if (not (= (- (ash 1 8192)) +nan.0)))
1375 (pass-if (not (= +nan.0 (- (ash 1 8192)))))
1376
1377 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1378 ;; sure we've avoided that
1379 (pass-if (not (= (ash 3 1023) +nan.0)))
1380 (pass-if (not (= +nan.0 (ash 3 1023))))
1381
1382 (pass-if (= 1/2 0.5))
1383 (pass-if (not (= 1/3 0.333333333333333333333333333333333)))
1384 (pass-if (not (= 2/3 0.5)))
1385 (pass-if (not (= 0.5 (+ 1/2 (/ 1 (ash 1 1000))))))
1386
1387 (pass-if (= 1/2 0.5+0i))
1388 (pass-if (not (= 0.333333333333333333333333333333333 1/3)))
1389 (pass-if (not (= 2/3 0.5+0i)))
1390 (pass-if (not (= 1/2 0+0.5i)))
1391
1392 (pass-if (= 0.5 1/2))
1393 (pass-if (not (= 0.5 2/3)))
1394 (pass-if (not (= (+ 1/2 (/ 1 (ash 1 1000))) 0.5)))
1395
1396 (pass-if (= 0.5+0i 1/2))
1397 (pass-if (not (= 0.5+0i 2/3)))
1398 (pass-if (not (= 0+0.5i 1/2))))
1399
1400 ;;;
1401 ;;; <
1402 ;;;
1403
1404 (with-test-prefix "<"
1405
1406 (expect-fail "documented?"
1407 (documented? <))
1408
1409 (with-test-prefix "(< 0 n)"
1410
1411 (pass-if "n = 0"
1412 (not (< 0 0)))
1413
1414 (pass-if "n = 0.0"
1415 (not (< 0 0.0)))
1416
1417 (pass-if "n = 1"
1418 (< 0 1))
1419
1420 (pass-if "n = 1.0"
1421 (< 0 1.0))
1422
1423 (pass-if "n = -1"
1424 (not (< 0 -1)))
1425
1426 (pass-if "n = -1.0"
1427 (not (< 0 -1.0)))
1428
1429 (pass-if "n = fixnum-max"
1430 (< 0 fixnum-max))
1431
1432 (pass-if "n = fixnum-max + 1"
1433 (< 0 (+ fixnum-max 1)))
1434
1435 (pass-if "n = fixnum-min"
1436 (not (< 0 fixnum-min)))
1437
1438 (pass-if "n = fixnum-min - 1"
1439 (not (< 0 (- fixnum-min 1)))))
1440
1441 (with-test-prefix "(< 0.0 n)"
1442
1443 (pass-if "n = 0"
1444 (not (< 0.0 0)))
1445
1446 (pass-if "n = 0.0"
1447 (not (< 0.0 0.0)))
1448
1449 (pass-if "n = 1"
1450 (< 0.0 1))
1451
1452 (pass-if "n = 1.0"
1453 (< 0.0 1.0))
1454
1455 (pass-if "n = -1"
1456 (not (< 0.0 -1)))
1457
1458 (pass-if "n = -1.0"
1459 (not (< 0.0 -1.0)))
1460
1461 (pass-if "n = fixnum-max"
1462 (< 0.0 fixnum-max))
1463
1464 (pass-if "n = fixnum-max + 1"
1465 (< 0.0 (+ fixnum-max 1)))
1466
1467 (pass-if "n = fixnum-min"
1468 (not (< 0.0 fixnum-min)))
1469
1470 (pass-if "n = fixnum-min - 1"
1471 (not (< 0.0 (- fixnum-min 1)))))
1472
1473 (with-test-prefix "(< 1 n)"
1474
1475 (pass-if "n = 0"
1476 (not (< 1 0)))
1477
1478 (pass-if "n = 0.0"
1479 (not (< 1 0.0)))
1480
1481 (pass-if "n = 1"
1482 (not (< 1 1)))
1483
1484 (pass-if "n = 1.0"
1485 (not (< 1 1.0)))
1486
1487 (pass-if "n = -1"
1488 (not (< 1 -1)))
1489
1490 (pass-if "n = -1.0"
1491 (not (< 1 -1.0)))
1492
1493 (pass-if "n = fixnum-max"
1494 (< 1 fixnum-max))
1495
1496 (pass-if "n = fixnum-max + 1"
1497 (< 1 (+ fixnum-max 1)))
1498
1499 (pass-if "n = fixnum-min"
1500 (not (< 1 fixnum-min)))
1501
1502 (pass-if "n = fixnum-min - 1"
1503 (not (< 1 (- fixnum-min 1)))))
1504
1505 (with-test-prefix "(< 1.0 n)"
1506
1507 (pass-if "n = 0"
1508 (not (< 1.0 0)))
1509
1510 (pass-if "n = 0.0"
1511 (not (< 1.0 0.0)))
1512
1513 (pass-if "n = 1"
1514 (not (< 1.0 1)))
1515
1516 (pass-if "n = 1.0"
1517 (not (< 1.0 1.0)))
1518
1519 (pass-if "n = -1"
1520 (not (< 1.0 -1)))
1521
1522 (pass-if "n = -1.0"
1523 (not (< 1.0 -1.0)))
1524
1525 (pass-if "n = fixnum-max"
1526 (< 1.0 fixnum-max))
1527
1528 (pass-if "n = fixnum-max + 1"
1529 (< 1.0 (+ fixnum-max 1)))
1530
1531 (pass-if "n = fixnum-min"
1532 (not (< 1.0 fixnum-min)))
1533
1534 (pass-if "n = fixnum-min - 1"
1535 (not (< 1.0 (- fixnum-min 1)))))
1536
1537 (with-test-prefix "(< -1 n)"
1538
1539 (pass-if "n = 0"
1540 (< -1 0))
1541
1542 (pass-if "n = 0.0"
1543 (< -1 0.0))
1544
1545 (pass-if "n = 1"
1546 (< -1 1))
1547
1548 (pass-if "n = 1.0"
1549 (< -1 1.0))
1550
1551 (pass-if "n = -1"
1552 (not (< -1 -1)))
1553
1554 (pass-if "n = -1.0"
1555 (not (< -1 -1.0)))
1556
1557 (pass-if "n = fixnum-max"
1558 (< -1 fixnum-max))
1559
1560 (pass-if "n = fixnum-max + 1"
1561 (< -1 (+ fixnum-max 1)))
1562
1563 (pass-if "n = fixnum-min"
1564 (not (< -1 fixnum-min)))
1565
1566 (pass-if "n = fixnum-min - 1"
1567 (not (< -1 (- fixnum-min 1)))))
1568
1569 (with-test-prefix "(< -1.0 n)"
1570
1571 (pass-if "n = 0"
1572 (< -1.0 0))
1573
1574 (pass-if "n = 0.0"
1575 (< -1.0 0.0))
1576
1577 (pass-if "n = 1"
1578 (< -1.0 1))
1579
1580 (pass-if "n = 1.0"
1581 (< -1.0 1.0))
1582
1583 (pass-if "n = -1"
1584 (not (< -1.0 -1)))
1585
1586 (pass-if "n = -1.0"
1587 (not (< -1.0 -1.0)))
1588
1589 (pass-if "n = fixnum-max"
1590 (< -1.0 fixnum-max))
1591
1592 (pass-if "n = fixnum-max + 1"
1593 (< -1.0 (+ fixnum-max 1)))
1594
1595 (pass-if "n = fixnum-min"
1596 (not (< -1.0 fixnum-min)))
1597
1598 (pass-if "n = fixnum-min - 1"
1599 (not (< -1.0 (- fixnum-min 1)))))
1600
1601 (with-test-prefix "(< fixnum-max n)"
1602
1603 (pass-if "n = 0"
1604 (not (< fixnum-max 0)))
1605
1606 (pass-if "n = 0.0"
1607 (not (< fixnum-max 0.0)))
1608
1609 (pass-if "n = 1"
1610 (not (< fixnum-max 1)))
1611
1612 (pass-if "n = 1.0"
1613 (not (< fixnum-max 1.0)))
1614
1615 (pass-if "n = -1"
1616 (not (< fixnum-max -1)))
1617
1618 (pass-if "n = -1.0"
1619 (not (< fixnum-max -1.0)))
1620
1621 (pass-if "n = fixnum-max"
1622 (not (< fixnum-max fixnum-max)))
1623
1624 (pass-if "n = fixnum-max + 1"
1625 (< fixnum-max (+ fixnum-max 1)))
1626
1627 (pass-if "n = fixnum-min"
1628 (not (< fixnum-max fixnum-min)))
1629
1630 (pass-if "n = fixnum-min - 1"
1631 (not (< fixnum-max (- fixnum-min 1)))))
1632
1633 (with-test-prefix "(< (+ fixnum-max 1) n)"
1634
1635 (pass-if "n = 0"
1636 (not (< (+ fixnum-max 1) 0)))
1637
1638 (pass-if "n = 0.0"
1639 (not (< (+ fixnum-max 1) 0.0)))
1640
1641 (pass-if "n = 1"
1642 (not (< (+ fixnum-max 1) 1)))
1643
1644 (pass-if "n = 1.0"
1645 (not (< (+ fixnum-max 1) 1.0)))
1646
1647 (pass-if "n = -1"
1648 (not (< (+ fixnum-max 1) -1)))
1649
1650 (pass-if "n = -1.0"
1651 (not (< (+ fixnum-max 1) -1.0)))
1652
1653 (pass-if "n = fixnum-max"
1654 (not (< (+ fixnum-max 1) fixnum-max)))
1655
1656 (pass-if "n = fixnum-max + 1"
1657 (not (< (+ fixnum-max 1) (+ fixnum-max 1))))
1658
1659 (pass-if "n = fixnum-min"
1660 (not (< (+ fixnum-max 1) fixnum-min)))
1661
1662 (pass-if "n = fixnum-min - 1"
1663 (not (< (+ fixnum-max 1) (- fixnum-min 1)))))
1664
1665 (with-test-prefix "(< fixnum-min n)"
1666
1667 (pass-if "n = 0"
1668 (< fixnum-min 0))
1669
1670 (pass-if "n = 0.0"
1671 (< fixnum-min 0.0))
1672
1673 (pass-if "n = 1"
1674 (< fixnum-min 1))
1675
1676 (pass-if "n = 1.0"
1677 (< fixnum-min 1.0))
1678
1679 (pass-if "n = -1"
1680 (< fixnum-min -1))
1681
1682 (pass-if "n = -1.0"
1683 (< fixnum-min -1.0))
1684
1685 (pass-if "n = fixnum-max"
1686 (< fixnum-min fixnum-max))
1687
1688 (pass-if "n = fixnum-max + 1"
1689 (< fixnum-min (+ fixnum-max 1)))
1690
1691 (pass-if "n = fixnum-min"
1692 (not (< fixnum-min fixnum-min)))
1693
1694 (pass-if "n = fixnum-min - 1"
1695 (not (< fixnum-min (- fixnum-min 1)))))
1696
1697 (with-test-prefix "(< (- fixnum-min 1) n)"
1698
1699 (pass-if "n = 0"
1700 (< (- fixnum-min 1) 0))
1701
1702 (pass-if "n = 0.0"
1703 (< (- fixnum-min 1) 0.0))
1704
1705 (pass-if "n = 1"
1706 (< (- fixnum-min 1) 1))
1707
1708 (pass-if "n = 1.0"
1709 (< (- fixnum-min 1) 1.0))
1710
1711 (pass-if "n = -1"
1712 (< (- fixnum-min 1) -1))
1713
1714 (pass-if "n = -1.0"
1715 (< (- fixnum-min 1) -1.0))
1716
1717 (pass-if "n = fixnum-max"
1718 (< (- fixnum-min 1) fixnum-max))
1719
1720 (pass-if "n = fixnum-max + 1"
1721 (< (- fixnum-min 1) (+ fixnum-max 1)))
1722
1723 (pass-if "n = fixnum-min"
1724 (< (- fixnum-min 1) fixnum-min))
1725
1726 (pass-if "n = fixnum-min - 1"
1727 (not (< (- fixnum-min 1) (- fixnum-min 1)))))
1728
1729 (pass-if (< (ash 1 256) +inf.0))
1730 (pass-if (not (< +inf.0 (ash 1 256))))
1731 (pass-if (not (< (ash 1 256) -inf.0)))
1732 (pass-if (< -inf.0 (ash 1 256)))
1733
1734 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1735 ;; sure we've avoided that
1736 (pass-if (< (1- (ash 1 1024)) +inf.0))
1737 (pass-if (< (ash 1 1024) +inf.0))
1738 (pass-if (< (1+ (ash 1 1024)) +inf.0))
1739 (pass-if (not (< +inf.0 (1- (ash 1 1024)))))
1740 (pass-if (not (< +inf.0 (ash 1 1024))))
1741 (pass-if (not (< +inf.0 (1+ (ash 1 1024)))))
1742 (pass-if (< -inf.0 (- (1- (ash 1 1024)))))
1743 (pass-if (< -inf.0 (- (ash 1 1024))))
1744 (pass-if (< -inf.0 (- (1+ (ash 1 1024)))))
1745 (pass-if (not (< (- (1- (ash 1 1024))) -inf.0)))
1746 (pass-if (not (< (- (ash 1 1024)) -inf.0)))
1747 (pass-if (not (< (- (1+ (ash 1 1024))) -inf.0)))
1748
1749 (pass-if (not (< +nan.0 +nan.0)))
1750 (pass-if (not (< 0 +nan.0)))
1751 (pass-if (not (< +nan.0 0)))
1752 (pass-if (not (< 1 +nan.0)))
1753 (pass-if (not (< +nan.0 1)))
1754 (pass-if (not (< -1 +nan.0)))
1755 (pass-if (not (< +nan.0 -1)))
1756
1757 (pass-if (not (< (ash 1 256) +nan.0)))
1758 (pass-if (not (< +nan.0 (ash 1 256))))
1759 (pass-if (not (< (- (ash 1 256)) +nan.0)))
1760 (pass-if (not (< +nan.0 (- (ash 1 256)))))
1761
1762 (pass-if (not (< (ash 1 8192) +nan.0)))
1763 (pass-if (not (< +nan.0 (ash 1 8192))))
1764 (pass-if (not (< (- (ash 1 8192)) +nan.0)))
1765 (pass-if (not (< +nan.0 (- (ash 1 8192)))))
1766
1767 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1768 ;; sure we've avoided that
1769 (pass-if (not (< (ash 3 1023) +nan.0)))
1770 (pass-if (not (< (1+ (ash 3 1023)) +nan.0)))
1771 (pass-if (not (< (1- (ash 3 1023)) +nan.0)))
1772 (pass-if (not (< +nan.0 (ash 3 1023))))
1773 (pass-if (not (< +nan.0 (1+ (ash 3 1023)))))
1774 (pass-if (not (< +nan.0 (1- (ash 3 1023)))))
1775
1776 (with-test-prefix "inum/frac"
1777 (pass-if (< 2 9/4))
1778 (pass-if (< -2 9/4))
1779 (pass-if (< -2 7/4))
1780 (pass-if (< -2 -7/4))
1781 (pass-if (eq? #f (< 2 7/4)))
1782 (pass-if (eq? #f (< 2 -7/4)))
1783 (pass-if (eq? #f (< 2 -9/4)))
1784 (pass-if (eq? #f (< -2 -9/4))))
1785
1786 (with-test-prefix "bignum/frac"
1787 (let ((x (ash 1 2048)))
1788 (pass-if (< x (* 4/3 x)))
1789 (pass-if (< (- x) (* 4/3 x)))
1790 (pass-if (< (- x) (* 2/3 x)))
1791 (pass-if (< (- x) (* -2/3 x)))
1792 (pass-if (eq? #f (< x (* 2/3 x))))
1793 (pass-if (eq? #f (< x (* -2/3 x))))
1794 (pass-if (eq? #f (< x (* -4/3 x))))
1795 (pass-if (eq? #f (< (- x) (* -4/3 x))))))
1796
1797 (with-test-prefix "flonum/frac"
1798 (pass-if (< 0.75 4/3))
1799 (pass-if (< -0.75 4/3))
1800 (pass-if (< -0.75 2/3))
1801 (pass-if (< -0.75 -2/3))
1802 (pass-if (eq? #f (< 0.75 2/3)))
1803 (pass-if (eq? #f (< 0.75 -2/3)))
1804 (pass-if (eq? #f (< 0.75 -4/3)))
1805 (pass-if (eq? #f (< -0.75 -4/3)))
1806
1807 (pass-if (< -inf.0 4/3))
1808 (pass-if (< -inf.0 -4/3))
1809 (pass-if (eq? #f (< +inf.0 4/3)))
1810 (pass-if (eq? #f (< +inf.0 -4/3)))
1811
1812 (pass-if (eq? #f (< +nan.0 4/3)))
1813 (pass-if (eq? #f (< +nan.0 -4/3))))
1814
1815 (with-test-prefix "frac/inum"
1816 (pass-if (< 7/4 2))
1817 (pass-if (< -7/4 2))
1818 (pass-if (< -9/4 2))
1819 (pass-if (< -9/4 -2))
1820 (pass-if (eq? #f (< 9/4 2)))
1821 (pass-if (eq? #f (< 9/4 -2)))
1822 (pass-if (eq? #f (< 7/4 -2)))
1823 (pass-if (eq? #f (< -7/4 -2))))
1824
1825 (with-test-prefix "frac/bignum"
1826 (let ((x (ash 1 2048)))
1827 (pass-if (< (* 2/3 x) x))
1828 (pass-if (< (* -2/3 x) x))
1829 (pass-if (< (* -4/3 x) x))
1830 (pass-if (< (* -4/3 x) (- x)))
1831 (pass-if (eq? #f (< (* 4/3 x) x)))
1832 (pass-if (eq? #f (< (* 4/3 x) (- x))))
1833 (pass-if (eq? #f (< (* 2/3 x) (- x))))
1834 (pass-if (eq? #f (< (* -2/3 x) (- x))))))
1835
1836 (with-test-prefix "frac/flonum"
1837 (pass-if (< 2/3 0.75))
1838 (pass-if (< -2/3 0.75))
1839 (pass-if (< -4/3 0.75))
1840 (pass-if (< -4/3 -0.75))
1841 (pass-if (eq? #f (< 4/3 0.75)))
1842 (pass-if (eq? #f (< 4/3 -0.75)))
1843 (pass-if (eq? #f (< 2/3 -0.75)))
1844 (pass-if (eq? #f (< -2/3 -0.75)))
1845
1846 (pass-if (< 4/3 +inf.0))
1847 (pass-if (< -4/3 +inf.0))
1848 (pass-if (eq? #f (< 4/3 -inf.0)))
1849 (pass-if (eq? #f (< -4/3 -inf.0)))
1850
1851 (pass-if (eq? #f (< 4/3 +nan.0)))
1852 (pass-if (eq? #f (< -4/3 +nan.0))))
1853
1854 (with-test-prefix "frac/frac"
1855 (pass-if (< 2/3 6/7))
1856 (pass-if (< -2/3 6/7))
1857 (pass-if (< -4/3 6/7))
1858 (pass-if (< -4/3 -6/7))
1859 (pass-if (eq? #f (< 4/3 6/7)))
1860 (pass-if (eq? #f (< 4/3 -6/7)))
1861 (pass-if (eq? #f (< 2/3 -6/7)))
1862 (pass-if (eq? #f (< -2/3 -6/7)))))
1863
1864 ;;;
1865 ;;; >
1866 ;;;
1867
1868 ;; currently not tested -- implementation is trivial
1869 ;; (> x y) is implemented as (< y x)
1870 ;; FIXME: tests should probably be added in case we change implementation.
1871
1872 ;;;
1873 ;;; <=
1874 ;;;
1875
1876 ;; currently not tested -- implementation is trivial
1877 ;; (<= x y) is implemented as (not (< y x))
1878 ;; FIXME: tests should probably be added in case we change implementation.
1879
1880 ;;;
1881 ;;; >=
1882 ;;;
1883
1884 ;; currently not tested -- implementation is trivial
1885 ;; (>= x y) is implemented as (not (< x y))
1886 ;; FIXME: tests should probably be added in case we change implementation.
1887
1888 ;;;
1889 ;;; zero?
1890 ;;;
1891
1892 (with-test-prefix "zero?"
1893 (expect-fail (documented? zero?))
1894 (pass-if (zero? 0))
1895 (pass-if (not (zero? 7)))
1896 (pass-if (not (zero? -7)))
1897 (pass-if (not (zero? (+ 1 fixnum-max))))
1898 (pass-if (not (zero? (- 1 fixnum-min))))
1899 (pass-if (not (zero? 1.3)))
1900 (pass-if (not (zero? 3.1+4.2i))))
1901
1902 ;;;
1903 ;;; positive?
1904 ;;;
1905
1906 (with-test-prefix "positive?"
1907 (expect-fail (documented? positive?))
1908 (pass-if (positive? 1))
1909 (pass-if (positive? (+ fixnum-max 1)))
1910 (pass-if (positive? 1.3))
1911 (pass-if (not (positive? 0)))
1912 (pass-if (not (positive? -1)))
1913 (pass-if (not (positive? (- fixnum-min 1))))
1914 (pass-if (not (positive? -1.3))))
1915
1916 ;;;
1917 ;;; negative?
1918 ;;;
1919
1920 (with-test-prefix "negative?"
1921 (expect-fail (documented? negative?))
1922 (pass-if (not (negative? 1)))
1923 (pass-if (not (negative? (+ fixnum-max 1))))
1924 (pass-if (not (negative? 1.3)))
1925 (pass-if (not (negative? 0)))
1926 (pass-if (negative? -1))
1927 (pass-if (negative? (- fixnum-min 1)))
1928 (pass-if (negative? -1.3)))
1929
1930 ;;;
1931 ;;; max
1932 ;;;
1933
1934 (with-test-prefix "max"
1935 (pass-if-exception "no args" exception:wrong-num-args
1936 (max))
1937
1938 (pass-if-exception "one complex" exception:wrong-type-arg
1939 (max 1+i))
1940
1941 (pass-if-exception "inum/complex" exception:wrong-type-arg
1942 (max 123 1+i))
1943 (pass-if-exception "big/complex" exception:wrong-type-arg
1944 (max 9999999999999999999999999999999999999999 1+i))
1945 (pass-if-exception "real/complex" exception:wrong-type-arg
1946 (max 123.0 1+i))
1947 (pass-if-exception "frac/complex" exception:wrong-type-arg
1948 (max 123/456 1+i))
1949
1950 (pass-if-exception "complex/inum" exception:wrong-type-arg
1951 (max 1+i 123))
1952 (pass-if-exception "complex/big" exception:wrong-type-arg
1953 (max 1+i 9999999999999999999999999999999999999999))
1954 (pass-if-exception "complex/real" exception:wrong-type-arg
1955 (max 1+i 123.0))
1956 (pass-if-exception "complex/frac" exception:wrong-type-arg
1957 (max 1+i 123/456))
1958
1959 (let ((big*2 (* fixnum-max 2))
1960 (big*3 (* fixnum-max 3))
1961 (big*4 (* fixnum-max 4))
1962 (big*5 (* fixnum-max 5)))
1963
1964 (with-test-prefix "inum / frac"
1965 (pass-if (= 3 (max 3 5/2)))
1966 (pass-if (= 5/2 (max 2 5/2))))
1967
1968 (with-test-prefix "frac / inum"
1969 (pass-if (= 3 (max 5/2 3)))
1970 (pass-if (= 5/2 (max 5/2 2))))
1971
1972 (with-test-prefix "inum / real"
1973 (pass-if (nan? (max 123 +nan.0))))
1974
1975 (with-test-prefix "real / inum"
1976 (pass-if (nan? (max +nan.0 123))))
1977
1978 (with-test-prefix "big / frac"
1979 (pass-if (= big*2 (max big*2 5/2)))
1980 (pass-if (= 5/2 (max (- big*2) 5/2))))
1981
1982 (with-test-prefix "frac / big"
1983 (pass-if (= big*2 (max 5/2 big*2)))
1984 (pass-if (= 5/2 (max 5/2 (- big*2)))))
1985
1986 (with-test-prefix "big / real"
1987 (pass-if (nan? (max big*5 +nan.0)))
1988 (pass-if (= big*5 (max big*5 -inf.0)))
1989 (pass-if (= +inf.0 (max big*5 +inf.0)))
1990 (pass-if (= 1.0 (max (- big*5) 1.0)))
1991 (pass-if (inexact? (max big*5 1.0)))
1992 (pass-if (= (exact->inexact big*5) (max big*5 1.0))))
1993
1994 (with-test-prefix "real / big"
1995 (pass-if (nan? (max +nan.0 big*5)))
1996 (pass-if (= +inf.0 (max +inf.0 big*5)))
1997 (pass-if (= big*5 (max -inf.0 big*5)))
1998 (pass-if (= 1.0 (max 1.0 (- big*5))))
1999 (pass-if (inexact? (max 1.0 big*5)))
2000 (pass-if (= (exact->inexact big*5) (max 1.0 big*5))))
2001
2002 (with-test-prefix "frac / frac"
2003 (pass-if (= 2/3 (max 1/2 2/3)))
2004 (pass-if (= 2/3 (max 2/3 1/2)))
2005 (pass-if (= -1/2 (max -1/2 -2/3)))
2006 (pass-if (= -1/2 (max -2/3 -1/2))))
2007
2008 (with-test-prefix "real / real"
2009 (pass-if (nan? (max 123.0 +nan.0)))
2010 (pass-if (nan? (max +nan.0 123.0)))
2011 (pass-if (nan? (max +nan.0 +nan.0)))
2012 (pass-if (= 456.0 (max 123.0 456.0)))
2013 (pass-if (= 456.0 (max 456.0 123.0)))))
2014
2015 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2016 ;; sure we've avoided that
2017 (for-each (lambda (b)
2018 (pass-if (list b +inf.0)
2019 (= +inf.0 (max b +inf.0)))
2020 (pass-if (list +inf.0 b)
2021 (= +inf.0 (max b +inf.0)))
2022 (pass-if (list b -inf.0)
2023 (= (exact->inexact b) (max b -inf.0)))
2024 (pass-if (list -inf.0 b)
2025 (= (exact->inexact b) (max b -inf.0))))
2026 (list (1- (ash 1 1024))
2027 (ash 1 1024)
2028 (1+ (ash 1 1024))
2029 (- (1- (ash 1 1024)))
2030 (- (ash 1 1024))
2031 (- (1+ (ash 1 1024)))))
2032
2033 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2034 ;; sure we've avoided that
2035 (pass-if (nan? (max (ash 1 2048) +nan.0)))
2036 (pass-if (nan? (max +nan.0 (ash 1 2048)))))
2037
2038 ;;;
2039 ;;; min
2040 ;;;
2041
2042 ;; FIXME: unfinished...
2043
2044 (with-test-prefix "min"
2045 (pass-if-exception "no args" exception:wrong-num-args
2046 (min))
2047
2048 (pass-if-exception "one complex" exception:wrong-type-arg
2049 (min 1+i))
2050
2051 (pass-if-exception "inum/complex" exception:wrong-type-arg
2052 (min 123 1+i))
2053 (pass-if-exception "big/complex" exception:wrong-type-arg
2054 (min 9999999999999999999999999999999999999999 1+i))
2055 (pass-if-exception "real/complex" exception:wrong-type-arg
2056 (min 123.0 1+i))
2057 (pass-if-exception "frac/complex" exception:wrong-type-arg
2058 (min 123/456 1+i))
2059
2060 (pass-if-exception "complex/inum" exception:wrong-type-arg
2061 (min 1+i 123))
2062 (pass-if-exception "complex/big" exception:wrong-type-arg
2063 (min 1+i 9999999999999999999999999999999999999999))
2064 (pass-if-exception "complex/real" exception:wrong-type-arg
2065 (min 1+i 123.0))
2066 (pass-if-exception "complex/frac" exception:wrong-type-arg
2067 (min 1+i 123/456))
2068
2069 (let ((big*2 (* fixnum-max 2))
2070 (big*3 (* fixnum-max 3))
2071 (big*4 (* fixnum-max 4))
2072 (big*5 (* fixnum-max 5)))
2073
2074 (expect-fail (documented? min))
2075 (pass-if (= 1 (min 7 3 1 5)))
2076 (pass-if (= 1 (min 1 7 3 5)))
2077 (pass-if (= 1 (min 7 3 5 1)))
2078 (pass-if (= -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
2079 (pass-if (= -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
2080 (pass-if (= -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
2081 (pass-if (= big*2 (min big*3 big*5 big*2 big*4)))
2082 (pass-if (= big*2 (min big*2 big*3 big*5 big*4)))
2083 (pass-if (= big*2 (min big*3 big*5 big*4 big*2)))
2084 (pass-if
2085 (= (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
2086 (pass-if
2087 (= (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
2088 (pass-if
2089 (= (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
2090
2091 (with-test-prefix "inum / frac"
2092 (pass-if (= 5/2 (min 3 5/2)))
2093 (pass-if (= 2 (min 2 5/2))))
2094
2095 (with-test-prefix "frac / inum"
2096 (pass-if (= 5/2 (min 5/2 3)))
2097 (pass-if (= 2 (min 5/2 2))))
2098
2099 (with-test-prefix "inum / real"
2100 (pass-if (nan? (min 123 +nan.0))))
2101
2102 (with-test-prefix "real / inum"
2103 (pass-if (nan? (min +nan.0 123))))
2104
2105 (with-test-prefix "big / frac"
2106 (pass-if (= 5/2 (min big*2 5/2)))
2107 (pass-if (= (- big*2) (min (- big*2) 5/2))))
2108
2109 (with-test-prefix "frac / big"
2110 (pass-if (= 5/2 (min 5/2 big*2)))
2111 (pass-if (= (- big*2) (min 5/2 (- big*2)))))
2112
2113 (with-test-prefix "big / real"
2114 (pass-if (nan? (min big*5 +nan.0)))
2115 (pass-if (= big*5 (min big*5 +inf.0)))
2116 (pass-if (= -inf.0 (min big*5 -inf.0)))
2117 (pass-if (= 1.0 (min big*5 1.0)))
2118 (pass-if (inexact? (min (- big*5) 1.0)))
2119 (pass-if (= (exact->inexact (- big*5)) (min (- big*5) 1.0))))
2120
2121 (with-test-prefix "real / big"
2122 (pass-if (nan? (min +nan.0 big*5)))
2123 (pass-if (= big*5 (min +inf.0 big*5)))
2124 (pass-if (= -inf.0 (min -inf.0 big*5)))
2125 (pass-if (= 1.0 (min 1.0 big*5)))
2126 (pass-if (inexact? (min 1.0 (- big*5))))
2127 (pass-if (= (exact->inexact (- big*5)) (min 1.0 (- big*5)))))
2128
2129 (with-test-prefix "frac / frac"
2130 (pass-if (= 1/2 (min 1/2 2/3)))
2131 (pass-if (= 1/2 (min 2/3 1/2)))
2132 (pass-if (= -2/3 (min -1/2 -2/3)))
2133 (pass-if (= -2/3 (min -2/3 -1/2))))
2134
2135 (with-test-prefix "real / real"
2136 (pass-if (nan? (min 123.0 +nan.0)))
2137 (pass-if (nan? (min +nan.0 123.0)))
2138 (pass-if (nan? (min +nan.0 +nan.0)))
2139 (pass-if (= 123.0 (min 123.0 456.0)))
2140 (pass-if (= 123.0 (min 456.0 123.0)))))
2141
2142
2143 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2144 ;; sure we've avoided that
2145 (for-each (lambda (b)
2146 (pass-if (list b +inf.0)
2147 (= (exact->inexact b) (min b +inf.0)))
2148 (pass-if (list +inf.0 b)
2149 (= (exact->inexact b) (min b +inf.0)))
2150 (pass-if (list b -inf.0)
2151 (= -inf.0 (min b -inf.0)))
2152 (pass-if (list -inf.0 b)
2153 (= -inf.0 (min b -inf.0))))
2154 (list (1- (ash 1 1024))
2155 (ash 1 1024)
2156 (1+ (ash 1 1024))
2157 (- (1- (ash 1 1024)))
2158 (- (ash 1 1024))
2159 (- (1+ (ash 1 1024)))))
2160
2161 ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2162 ;; sure we've avoided that
2163 (pass-if (nan? (min (- (ash 1 2048)) (- +nan.0))))
2164 (pass-if (nan? (min (- +nan.0) (- (ash 1 2048))))))
2165
2166 ;;;
2167 ;;; +
2168 ;;;
2169
2170 (with-test-prefix "+"
2171
2172 (expect-fail "documented?"
2173 (documented? +))
2174
2175 (with-test-prefix "wrong type argument"
2176
2177 (pass-if-exception "1st argument string"
2178 exception:wrong-type-arg
2179 (+ "1" 2))
2180
2181 (pass-if-exception "2nd argument bool"
2182 exception:wrong-type-arg
2183 (+ 1 #f))))
2184 ;;;
2185 ;;; -
2186 ;;;
2187
2188 (with-test-prefix "-"
2189
2190 (pass-if "-inum - +bignum"
2191 (= #x-100000000000000000000000000000001
2192 (- -1 #x100000000000000000000000000000000)))
2193
2194 (pass-if "big - inum"
2195 (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
2196 (- #x100000000000000000000000000000000 1)))
2197
2198 (pass-if "big - -inum"
2199 (= #x100000000000000000000000000000001
2200 (- #x100000000000000000000000000000000 -1))))
2201
2202 ;;;
2203 ;;; *
2204 ;;;
2205
2206 (with-test-prefix "*"
2207
2208 (pass-if "complex * bignum"
2209 (let ((big (ash 1 90)))
2210 (= (make-rectangular big big)
2211 (* 1+1i big)))))
2212
2213 ;;;
2214 ;;; /
2215 ;;;
2216
2217 (with-test-prefix "/"
2218
2219 (expect-fail "documented?"
2220 (documented? /))
2221
2222 (with-test-prefix "division by zero"
2223
2224 (pass-if-exception "(/ 0)"
2225 exception:numerical-overflow
2226 (/ 0))
2227
2228 (pass-if "(/ 0.0)"
2229 (= +inf.0 (/ 0.0)))
2230
2231 (pass-if-exception "(/ 1 0)"
2232 exception:numerical-overflow
2233 (/ 1 0))
2234
2235 (pass-if "(/ 1 0.0)"
2236 (= +inf.0 (/ 1 0.0)))
2237
2238 (pass-if-exception "(/ bignum 0)"
2239 exception:numerical-overflow
2240 (/ (+ fixnum-max 1) 0))
2241
2242 (pass-if "(/ bignum 0.0)"
2243 (= +inf.0 (/ (+ fixnum-max 1) 0.0)))
2244
2245 (pass-if-exception "(/ 1.0 0)"
2246 exception:numerical-overflow
2247 (/ 1.0 0))
2248
2249 (pass-if "(/ 1.0 0.0)"
2250 (= +inf.0 (/ 1.0 0.0)))
2251
2252 (pass-if-exception "(/ +i 0)"
2253 exception:numerical-overflow
2254 (/ +i 0))
2255
2256 (pass-if "(/ +i 0.0)"
2257 (= +inf.0 (imag-part (/ +i 0.0)))))
2258
2259 (with-test-prefix "complex division"
2260
2261 (pass-if "(/ 3+4i)"
2262 (= (/ 3+4i) 0.12-0.16i))
2263
2264 (pass-if "(/ 4+3i)"
2265 (= (/ 4+3i) 0.16-0.12i))
2266
2267 (pass-if "(/ 25+125i 3+4i)"
2268 (= (/ 25+125i 3+4i) 23.0+11.0i))
2269
2270 (pass-if "(/ 25+125i 4+3i)"
2271 (= (/ 25+125i 4+3i) 19.0+17.0i))
2272
2273 (pass-if "(/ 25 3+4i)"
2274 (= (/ 25 3+4i) 3.0-4.0i))
2275
2276 (pass-if "(/ 25 4+3i)"
2277 (= (/ 25 4+3i) 4.0-3.0i))
2278
2279 (pass-if "(/ 1e200+1e200i)"
2280 (= (/ 1e200+1e200i) 5.0e-201-5.0e-201i))))
2281
2282 ;;;
2283 ;;; truncate
2284 ;;;
2285
2286 (with-test-prefix "truncate"
2287 (pass-if (= 1 (truncate 1.75)))
2288 (pass-if (= 1 (truncate 1.5)))
2289 (pass-if (= 1 (truncate 1.25)))
2290 (pass-if (= 0 (truncate 0.75)))
2291 (pass-if (= 0 (truncate 0.5)))
2292 (pass-if (= 0 (truncate 0.0)))
2293 (pass-if (= 0 (truncate -0.5)))
2294 (pass-if (= -1 (truncate -1.25)))
2295 (pass-if (= -1 (truncate -1.5))))
2296
2297 ;;;
2298 ;;; round
2299 ;;;
2300
2301 (with-test-prefix "round"
2302 (pass-if (= 2 (round 1.75)))
2303 (pass-if (= 2 (round 1.5)))
2304 (pass-if (= 1 (round 1.25)))
2305 (pass-if (= 1 (round 0.75)))
2306 (pass-if (= 0 (round 0.5)))
2307 (pass-if (= 0 (round 0.0)))
2308 (pass-if (= 0 (round -0.5)))
2309 (pass-if (= -1 (round -1.25)))
2310 (pass-if (= -2 (round -1.5)))
2311
2312 (with-test-prefix "inum"
2313 (pass-if "0"
2314 (and (= 0 (round 0))
2315 (exact? (round 0))))
2316
2317 (pass-if "1"
2318 (and (= 1 (round 1))
2319 (exact? (round 1))))
2320
2321 (pass-if "-1"
2322 (and (= -1 (round -1))
2323 (exact? (round -1)))))
2324
2325 (with-test-prefix "bignum"
2326 (let ((x (1+ most-positive-fixnum)))
2327 (pass-if "(1+ most-positive-fixnum)"
2328 (and (= x (round x))
2329 (exact? (round x)))))
2330
2331 (let ((x (1- most-negative-fixnum)))
2332 (pass-if "(1- most-negative-fixnum)"
2333 (and (= x (round x))
2334 (exact? (round x))))))
2335
2336 (with-test-prefix "real"
2337 (pass-if "0.0"
2338 (and (= 0.0 (round 0.0))
2339 (inexact? (round 0.0))))
2340
2341 (pass-if "1.0"
2342 (and (= 1.0 (round 1.0))
2343 (inexact? (round 1.0))))
2344
2345 (pass-if "-1.0"
2346 (and (= -1.0 (round -1.0))
2347 (inexact? (round -1.0))))
2348
2349 (pass-if "-3.1"
2350 (and (= -3.0 (round -3.1))
2351 (inexact? (round -3.1))))
2352
2353 (pass-if "3.1"
2354 (and (= 3.0 (round 3.1))
2355 (inexact? (round 3.1))))
2356
2357 (pass-if "3.9"
2358 (and (= 4.0 (round 3.9))
2359 (inexact? (round 3.9))))
2360
2361 (pass-if "-3.9"
2362 (and (= -4.0 (round -3.9))
2363 (inexact? (round -3.9))))
2364
2365 (pass-if "1.5"
2366 (and (= 2.0 (round 1.5))
2367 (inexact? (round 1.5))))
2368
2369 (pass-if "2.5"
2370 (and (= 2.0 (round 2.5))
2371 (inexact? (round 2.5))))
2372
2373 (pass-if "3.5"
2374 (and (= 4.0 (round 3.5))
2375 (inexact? (round 3.5))))
2376
2377 (pass-if "-1.5"
2378 (and (= -2.0 (round -1.5))
2379 (inexact? (round -1.5))))
2380
2381 (pass-if "-2.5"
2382 (and (= -2.0 (round -2.5))
2383 (inexact? (round -2.5))))
2384
2385 (pass-if "-3.5"
2386 (and (= -4.0 (round -3.5))
2387 (inexact? (round -3.5))))
2388
2389 ;; prior to guile 1.6.5, on an IEEE system an inexact 2^53-1 (ie. a
2390 ;; float with mantissa all ones) came out as 2^53 from `round' (except
2391 ;; on i386 and m68k systems using the coprocessor and optimizing, where
2392 ;; extra precision hid the problem)
2393 (pass-if "2^53-1"
2394 (let ((x (exact->inexact (1- (ash 1 53)))))
2395 (and (= x (round x))
2396 (inexact? (round x)))))
2397 (pass-if "-(2^53-1)"
2398 (let ((x (exact->inexact (- (1- (ash 1 53))))))
2399 (and (= x (round x))
2400 (inexact? (round x)))))))
2401
2402 ;;;
2403 ;;; exact->inexact
2404 ;;;
2405
2406 (with-test-prefix "exact->inexact"
2407
2408 ;; Test "(exact->inexact n)", expect "want".
2409 ;; "i" is a index, for diagnostic purposes.
2410 (define (try-i i n want)
2411 (with-test-prefix (list i n want)
2412 (with-test-prefix "pos"
2413 (let ((got (exact->inexact n)))
2414 (pass-if "inexact?" (inexact? got))
2415 (pass-if (list "=" got) (= want got))))
2416 (set! n (- n))
2417 (set! want (- want))
2418 (with-test-prefix "neg"
2419 (let ((got (exact->inexact n)))
2420 (pass-if "inexact?" (inexact? got))
2421 (pass-if (list "=" got) (= want got))))))
2422
2423 (with-test-prefix "2^i, no round"
2424 (do ((i 0 (1+ i))
2425 (n 1 (* 2 n))
2426 (want 1.0 (* 2.0 want)))
2427 ((> i 100))
2428 (try-i i n want)))
2429
2430 (with-test-prefix "2^i+1, no round"
2431 (do ((i 1 (1+ i))
2432 (n 3 (1- (* 2 n)))
2433 (want 3.0 (- (* 2.0 want) 1.0)))
2434 ((>= i dbl-mant-dig))
2435 (try-i i n want)))
2436
2437 (with-test-prefix "(2^i+1)*2^100, no round"
2438 (do ((i 1 (1+ i))
2439 (n 3 (1- (* 2 n)))
2440 (want 3.0 (- (* 2.0 want) 1.0)))
2441 ((>= i dbl-mant-dig))
2442 (try-i i (ash n 100) (ash-flo want 100))))
2443
2444 ;; bit pattern: 1111....11100.00
2445 ;; <-mantdig-><-i->
2446 ;;
2447 (with-test-prefix "mantdig ones then zeros, no rounding"
2448 (do ((i 0 (1+ i))
2449 (n (- (ash 1 dbl-mant-dig) 1) (* 2 n))
2450 (want (- (ash-flo 1.0 dbl-mant-dig) 1.0) (* 2.0 want)))
2451 ((> i 100))
2452 (try-i i n want)))
2453
2454 ;; bit pattern: 1111....111011..1
2455 ;; <-mantdig-> <-i->
2456 ;; This sort of value was incorrectly rounded upwards in Guile 1.6.4 when
2457 ;; i >= 11 (that's when the total is 65 or more bits).
2458 ;;
2459 (with-test-prefix "mantdig ones then 011..11, round down"
2460 (do ((i 0 (1+ i))
2461 (n (- (ash 1 (+ 1 dbl-mant-dig)) 2) (+ 1 (* 2 n)))
2462 (want (- (ash-flo 1.0 (+ 1 dbl-mant-dig)) 2.0) (* 2.0 want)))
2463 ((> i 100))
2464 (try-i i n want)))
2465
2466 ;; bit pattern: 1111....111100..001
2467 ;; <-mantdig-> <--i->
2468 ;;
2469 (with-test-prefix "mantdig ones then 100..001, round up"
2470 (do ((i 0 (1+ i))
2471 (n (- (ash 1 (+ 2 dbl-mant-dig)) 1) (1- (* 2 n)))
2472 (want (ash-flo 1.0 (+ 2 dbl-mant-dig)) (* 2.0 want)))
2473 ((> i 100))
2474 (try-i i n want)))
2475
2476 ;; bit pattern: 1000....000100..001
2477 ;; <-mantdig-> <--i->
2478 ;;
2479 (with-test-prefix "2^mantdig then 100..001, round up"
2480 (do ((i 0 (1+ i))
2481 (n (- (ash 1 (+ 2 dbl-mant-dig)) 1) (1- (* 2 n)))
2482 (want (+ (ash-flo 1.0 (+ 2 dbl-mant-dig)) 4.0) (* 2.0 want)))
2483 ((> i 100))
2484 (try-i i n want))))
2485
2486 ;;;
2487 ;;; floor
2488 ;;;
2489
2490 ;;;
2491 ;;; ceiling
2492 ;;;
2493
2494 ;;;
2495 ;;; expt
2496 ;;;
2497
2498 (with-test-prefix "expt"
2499 (pass-if "(= 1 (expt 0 0))" (= 1 (expt 0 0)))
2500 (pass-if "(= 1 (expt 0 0.0))" (= 1 (expt 0 0.0)))
2501 (pass-if "(= 1 (expt 0.0 0))" (= 1 (expt 0.0 0)))
2502 (pass-if "(= 1 (expt 0.0 0.0))" (= 1 (expt 0.0 0.0))))
2503
2504 ;;;
2505 ;;; asinh
2506 ;;;
2507
2508 (with-test-prefix "asinh"
2509 (pass-if (= 0 (asinh 0))))
2510
2511 ;;;
2512 ;;; acosh
2513 ;;;
2514
2515 (with-test-prefix "acosh"
2516 (pass-if (= 0 (acosh 1))))
2517
2518 ;;;
2519 ;;; atanh
2520 ;;;
2521
2522 (with-test-prefix "atanh"
2523 (pass-if (= 0 (atanh 0))))
2524
2525 ;;;
2526 ;;; make-rectangular
2527 ;;;
2528
2529 ;;;
2530 ;;; make-polar
2531 ;;;
2532
2533 (with-test-prefix "make-polar"
2534 (define pi 3.14159265358979323846)
2535 (define (almost= x y)
2536 (> 0.01 (magnitude (- x y))))
2537
2538 (pass-if (= 0 (make-polar 0 0)))
2539 (pass-if (= 0 (make-polar 0 123.456)))
2540 (pass-if (= 1 (make-polar 1 0)))
2541 (pass-if (= -1 (make-polar -1 0)))
2542
2543 (pass-if (almost= 0+i (make-polar 1 (* 0.5 pi))))
2544 (pass-if (almost= -1 (make-polar 1 (* 1.0 pi))))
2545 (pass-if (almost= 0-i (make-polar 1 (* 1.5 pi))))
2546 (pass-if (almost= 1 (make-polar 1 (* 2.0 pi)))))
2547
2548 ;;;
2549 ;;; real-part
2550 ;;;
2551
2552 ;;;
2553 ;;; imag-part
2554 ;;;
2555
2556 ;;;
2557 ;;; magnitude
2558 ;;;
2559
2560 (with-test-prefix "magnitude"
2561 (pass-if (= 0 (magnitude 0)))
2562 (pass-if (= 1 (magnitude 1)))
2563 (pass-if (= 1 (magnitude -1)))
2564 (pass-if (= 1 (magnitude 0+i)))
2565 (pass-if (= 1 (magnitude 0-i)))
2566 (pass-if (= 5 (magnitude 3+4i)))
2567 (pass-if (= 5 (magnitude 3-4i)))
2568 (pass-if (= 5 (magnitude -3+4i)))
2569 (pass-if (= 5 (magnitude -3-4i))))
2570
2571 ;;;
2572 ;;; angle
2573 ;;;
2574
2575 (with-test-prefix "angle"
2576 (define pi 3.14159265358979323846)
2577 (define (almost= x y)
2578 (> 0.01 (magnitude (- x y))))
2579
2580 (pass-if "inum +ve" (= 0 (angle 1)))
2581 (pass-if "inum -ve" (almost= pi (angle -1)))
2582
2583 (pass-if "bignum +ve" (= 0 (angle (1+ fixnum-max))))
2584 (pass-if "bignum -ve" (almost= pi (angle (1- fixnum-min))))
2585
2586 (pass-if "flonum +ve" (= 0 (angle 1.5)))
2587 (pass-if "flonum -ve" (almost= pi (angle -1.5))))
2588
2589 ;;;
2590 ;;; inexact->exact
2591 ;;;
2592
2593 (with-test-prefix "inexact->exact"
2594
2595 (pass-if-exception "+inf" exception:out-of-range
2596 (inexact->exact +inf.0))
2597
2598 (pass-if-exception "-inf" exception:out-of-range
2599 (inexact->exact -inf.0))
2600
2601 (pass-if-exception "nan" exception:out-of-range
2602 (inexact->exact +nan.0))
2603
2604 (with-test-prefix "2.0**i to exact and back"
2605 (do ((i 0 (1+ i))
2606 (n 1.0 (* 2.0 n)))
2607 ((> i 100))
2608 (pass-if (list i n)
2609 (= n (inexact->exact (exact->inexact n)))))))
2610
2611 ;;;
2612 ;;; integer-length
2613 ;;;
2614
2615 (with-test-prefix "integer-length"
2616
2617 (with-test-prefix "-2^i, ...11100..00"
2618 (do ((n -1 (ash n 1))
2619 (i 0 (1+ i)))
2620 ((> i 256))
2621 (pass-if (list n "expect" i)
2622 (= i (integer-length n)))))
2623
2624 (with-test-prefix "-2^i+1 ...11100..01"
2625 (do ((n -3 (logxor 3 (ash n 1)))
2626 (i 2 (1+ i)))
2627 ((> i 256))
2628 (pass-if n
2629 (= i (integer-length n)))))
2630
2631 (with-test-prefix "-2^i-1 ...111011..11"
2632 (do ((n -2 (1+ (ash n 1)))
2633 (i 1 (1+ i)))
2634 ((> i 256))
2635 (pass-if n
2636 (= i (integer-length n))))))
2637
2638 ;;;
2639 ;;; logbit?
2640 ;;;
2641
2642 (with-test-prefix "logbit?"
2643 (pass-if (eq? #f (logbit? 0 0)))
2644 (pass-if (eq? #f (logbit? 1 0)))
2645 (pass-if (eq? #f (logbit? 31 0)))
2646 (pass-if (eq? #f (logbit? 32 0)))
2647 (pass-if (eq? #f (logbit? 33 0)))
2648 (pass-if (eq? #f (logbit? 63 0)))
2649 (pass-if (eq? #f (logbit? 64 0)))
2650 (pass-if (eq? #f (logbit? 65 0)))
2651
2652 ;; prior to guile 1.6.5, testing bit 32, 64 etc of value 1 would wrap
2653 ;; around and return #t where it ought to be #f
2654 (pass-if (eq? #t (logbit? 0 1)))
2655 (pass-if (eq? #f (logbit? 1 1)))
2656 (pass-if (eq? #f (logbit? 31 1)))
2657 (pass-if (eq? #f (logbit? 32 1)))
2658 (pass-if (eq? #f (logbit? 33 1)))
2659 (pass-if (eq? #f (logbit? 63 1)))
2660 (pass-if (eq? #f (logbit? 64 1)))
2661 (pass-if (eq? #f (logbit? 65 1)))
2662 (pass-if (eq? #f (logbit? 128 1)))
2663
2664 (pass-if (eq? #t (logbit? 0 -1)))
2665 (pass-if (eq? #t (logbit? 1 -1)))
2666 (pass-if (eq? #t (logbit? 31 -1)))
2667 (pass-if (eq? #t (logbit? 32 -1)))
2668 (pass-if (eq? #t (logbit? 33 -1)))
2669 (pass-if (eq? #t (logbit? 63 -1)))
2670 (pass-if (eq? #t (logbit? 64 -1)))
2671 (pass-if (eq? #t (logbit? 65 -1))))
2672
2673 ;;;
2674 ;;; logcount
2675 ;;;
2676
2677 (with-test-prefix "logcount"
2678
2679 (with-test-prefix "-2^i, meaning ...11100..00"
2680 (do ((n -1 (ash n 1))
2681 (i 0 (1+ i)))
2682 ((> i 256))
2683 (pass-if n
2684 (= i (logcount n)))))
2685
2686 (with-test-prefix "2^i"
2687 (do ((n 1 (ash n 1))
2688 (i 0 (1+ i)))
2689 ((> i 256))
2690 (pass-if n
2691 (= 1 (logcount n)))))
2692
2693 (with-test-prefix "2^i-1"
2694 (do ((n 0 (1+ (ash n 1)))
2695 (i 0 (1+ i)))
2696 ((> i 256))
2697 (pass-if n
2698 (= i (logcount n))))))
2699
2700 ;;;
2701 ;;; lognot
2702 ;;;
2703
2704 (with-test-prefix "lognot"
2705 (pass-if (= -1 (lognot 0)))
2706 (pass-if (= 0 (lognot -1)))
2707 (pass-if (= -2 (lognot 1)))
2708 (pass-if (= 1 (lognot -2)))
2709
2710 (pass-if (= #x-100000000000000000000000000000000
2711 (lognot #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
2712 (pass-if (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
2713 (lognot #x-100000000000000000000000000000000))))