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     exception:numerical-overflow
 808     (modulo-expt 17 23 0))
 809
 810    (pass-if-exception
 811     "Proper exception when result not invertible"
 812     exception:numerical-overflow
 813     (modulo-expt 10 -1 48))
 814
 815    (pass-if-exception
 816     "Proper exception with wrong type argument"
 817     exception:wrong-type-arg
 818     (modulo-expt "Sam" 23 10))
 819
 820    (pass-if-exception
 821     "Proper exception with wrong type argument"
 822     exception:wrong-type-arg
 823     (modulo-expt 17 9.9 10))
 824
 825     (pass-if-exception
 826     "Proper exception with wrong type argument"
 827     exception: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     ;; XXX - some results depend on whether Guile is compiled optimzed
1042     ;; or not.  It is clearly undesirable to have number->string to be
1043     ;; influenced by this.
1044
1045     (pass-if (string=? (number->string 35.25 36) "Z.9"))
1046     (pass-if (or (string=? (number->string 0.25 2) "0.01")
1047                  (string=? (number->string 0.25 2) "0.010")))
1048     (pass-if (string=? (number->string 255.0625 16) "FF.1"))
1049     (pass-if (string=? (number->string (/ 1 3) 3) "1/10"))
1050     (pass-if (or (string=? (number->string 11.33333333333333333 12)
1051                            "B.4")
1052                  (string=? (number->string 11.33333333333333333 12)
1053                            "B.400000000000009")))
1054     (pass-if (or (string=? (number->string 1.324e44 16)
1055                            "5.EFE0A14FAFEe24")
1056                  (string=? (number->string 1.324e44 16)
1057                            "5.EFE0A14FAFDF8e24")))))
1058
1059 ;;;
1060 ;;; string->number
1061 ;;;
1062
1063 (with-test-prefix "string->number"
1064
1065   (pass-if "string->number"
1066     (documented? string->number))
1067
1068   (pass-if "non number strings"
1069     (for-each (lambda (x) (if (string->number x) (throw 'fail)))
1070               '("" "q" "1q" "6+7iq" "8+9q" "10+11" "13+" "18@19q" "20@q" "23@"
1071                 "+25iq" "26i" "-q" "-iq" "i" "5#.0" "8/" "10#11" ".#" "."
1072                 "#o.2" "3.4q" "15.16e17q" "18.19e+q" ".q" ".17#18" "10q" "#b2"
1073                 "#b3" "#b4" "#b5" "#b6" "#b7" "#b8" "#b9" "#ba" "#bb" "#bc"
1074                 "#bd" "#be" "#bf" "#q" "#b#b1" "#o#o1" "#d#d1" "#x#x1" "#e#e1"
1075                 "#i#i1" "12@12+0i"))
1076     #t)
1077
1078   (pass-if "valid number strings"
1079     (for-each (lambda (couple)
1080                 (apply
1081                  (lambda (x y)
1082                    (let ((xx (string->number x)))
1083                      (if (or (eq? xx #f) (not (eqv? xx y)))
1084                          (begin
1085                            (pk x y)
1086                            (throw 'fail)))))
1087                  couple))
1088               `(;; Radix:
1089                 ("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
1090                 ("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
1091                 ("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
1092                 ("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
1093                 ("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
1094                 ("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
1095                 ("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
1096                 ("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
1097                 ("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
1098                 ("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
1099                 ("#b1010" 10)
1100                 ("#o12345670" 2739128)
1101                 ("#d1234567890" 1234567890)
1102                 ("#x1234567890abcdef" 1311768467294899695)
1103                 ;; Exactness:
1104                 ("#e1" 1) ("#e1.2" 12/10)
1105                 ("#i1.1" 1.1) ("#i1" 1.0)
1106                 ;; Integers:
1107                 ("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1))
1108                 ("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
1109                 ("#b#i100" 4.0)
1110                 ;; Fractions:
1111                 ("1/1" 1) ("1/2" 1/2) ("-1/2" -1/2) ("1#/1" 10.0)
1112                 ("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 9/10) ("#e10/1#" 1)
1113                 ("#i6/8" 0.75) ("#i1/1" 1.0)
1114                 ;; Decimal numbers:
1115                 ;; * <uinteger 10> <suffix>
1116                 ("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
1117                 ("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
1118                 ("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
1119                 ;; * . <digit 10>+ #* <suffix>
1120                 (".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
1121                 (".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
1122                 ;; * <digit 10>+ . <digit 10>* #* <suffix>
1123                 ("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
1124                 ("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
1125                 ("3.1#e0" 3.1)
1126                 ;; * <digit 10>+ #+ . #* <suffix>
1127                 ("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
1128                 ;; Complex:
1129                 ("1@0" 1.0) ("1@+0" 1.0) ("1@-0" 1.0)
1130                 ("2+3i" ,(+ 2 (* 3 +i))) ("4-5i" ,(- 4 (* 5 +i)))
1131                 ("1+i" 1+1i) ("1-i" 1-1i) ("+1i" 0+1i) ("-1i" 0-1i)
1132                 ("+i" +1i) ("-i" -1i)))
1133     #t)
1134
1135   (pass-if-exception "exponent too big"
1136     exception:out-of-range
1137     (string->number "12.13e141414")))
1138
1139 ;;;
1140 ;;; number?
1141 ;;;
1142
1143 (with-test-prefix "number?"
1144   (pass-if (documented? number?))
1145   (pass-if (number? 0))
1146   (pass-if (number? 7))
1147   (pass-if (number? -7))
1148   (pass-if (number? 1.3))
1149   (pass-if (number? (+ 1 fixnum-max)))
1150   (pass-if (number? (- 1 fixnum-min)))
1151   (pass-if (number? 3+4i))
1152   (pass-if (not (number? #\a)))
1153   (pass-if (not (number? "a")))
1154   (pass-if (not (number? (make-vector 0))))
1155   (pass-if (not (number? (cons 1 2))))
1156   (pass-if (not (number? #t)))
1157   (pass-if (not (number? (lambda () #t))))
1158   (pass-if (not (number? (current-input-port)))))
1159
1160 ;;;
1161 ;;; complex?
1162 ;;;
1163
1164 (with-test-prefix "complex?"
1165   (pass-if (documented? complex?))
1166   (pass-if (complex? 0))
1167   (pass-if (complex? 7))
1168   (pass-if (complex? -7))
1169   (pass-if (complex? (+ 1 fixnum-max)))
1170   (pass-if (complex? (- 1 fixnum-min)))
1171   (pass-if (complex? 1.3))
1172   (pass-if (complex? 3+4i))
1173   (pass-if (not (complex? #\a)))
1174   (pass-if (not (complex? "a")))
1175   (pass-if (not (complex? (make-vector 0))))
1176   (pass-if (not (complex? (cons 1 2))))
1177   (pass-if (not (complex? #t)))
1178   (pass-if (not (complex? (lambda () #t))))
1179   (pass-if (not (complex? (current-input-port)))))
1180
1181 ;;;
1182 ;;; real?
1183 ;;;
1184
1185 (with-test-prefix "real?"
1186   (pass-if (documented? real?))
1187   (pass-if (real? 0))
1188   (pass-if (real? 7))
1189   (pass-if (real? -7))
1190   (pass-if (real? (+ 1 fixnum-max)))
1191   (pass-if (real? (- 1 fixnum-min)))
1192   (pass-if (real? 1.3))
1193   (pass-if (not (real? 3+4i)))
1194   (pass-if (not (real? #\a)))
1195   (pass-if (not (real? "a")))
1196   (pass-if (not (real? (make-vector 0))))
1197   (pass-if (not (real? (cons 1 2))))
1198   (pass-if (not (real? #t)))
1199   (pass-if (not (real? (lambda () #t))))
1200   (pass-if (not (real? (current-input-port)))))
1201
1202 ;;;
1203 ;;; rational? (same as real? right now)
1204 ;;;
1205
1206 (with-test-prefix "rational?"
1207   (pass-if (documented? rational?))
1208   (pass-if (rational? 0))
1209   (pass-if (rational? 7))
1210   (pass-if (rational? -7))
1211   (pass-if (rational? (+ 1 fixnum-max)))
1212   (pass-if (rational? (- 1 fixnum-min)))
1213   (pass-if (rational? 1.3))
1214   (pass-if (not (rational? 3+4i)))
1215   (pass-if (not (rational? #\a)))
1216   (pass-if (not (rational? "a")))
1217   (pass-if (not (rational? (make-vector 0))))
1218   (pass-if (not (rational? (cons 1 2))))
1219   (pass-if (not (rational? #t)))
1220   (pass-if (not (rational? (lambda () #t))))
1221   (pass-if (not (rational? (current-input-port)))))
1222
1223 ;;;
1224 ;;; integer?
1225 ;;;
1226
1227 (with-test-prefix "integer?"
1228   (pass-if (documented? integer?))
1229   (pass-if (integer? 0))
1230   (pass-if (integer? 7))
1231   (pass-if (integer? -7))
1232   (pass-if (integer? (+ 1 fixnum-max)))
1233   (pass-if (integer? (- 1 fixnum-min)))
1234   (pass-if (and (= 3+0i (round 3+0i)) (integer? 3+0i)))
1235   (pass-if (and (= 1.0 (round 1.0)) (integer? 1.0)))
1236   (pass-if (not (integer? 1.3)))
1237   (pass-if (not (integer? +inf.0)))
1238   (pass-if (not (integer? -inf.0)))
1239   (pass-if (not (integer? +nan.0)))
1240   (pass-if (not (integer? 3+4i)))
1241   (pass-if (not (integer? #\a)))
1242   (pass-if (not (integer? "a")))
1243   (pass-if (not (integer? (make-vector 0))))
1244   (pass-if (not (integer? (cons 1 2))))
1245   (pass-if (not (integer? #t)))
1246   (pass-if (not (integer? (lambda () #t))))
1247   (pass-if (not (integer? (current-input-port)))))
1248
1249 ;;;
1250 ;;; inexact?
1251 ;;;
1252
1253 (with-test-prefix "inexact?"
1254   (pass-if (documented? inexact?))
1255   (pass-if (not (inexact? 0)))
1256   (pass-if (not (inexact? 7)))
1257   (pass-if (not (inexact? -7)))
1258   (pass-if (not (inexact? (+ 1 fixnum-max))))
1259   (pass-if (not (inexact? (- 1 fixnum-min))))
1260   (pass-if (inexact? 1.3))
1261   (pass-if (inexact? 3.1+4.2i))
1262   (pass-if-exception "char"
1263                      exception:wrong-type-arg
1264                      (not (inexact? #\a)))
1265   (pass-if-exception "string"
1266                      exception:wrong-type-arg
1267                      (not (inexact? "a")))
1268   (pass-if-exception "vector"
1269                      exception:wrong-type-arg
1270                      (not (inexact? (make-vector 0))))
1271   (pass-if-exception "cons"
1272                      exception:wrong-type-arg
1273                      (not (inexact? (cons 1 2))))
1274   (pass-if-exception "bool"
1275                      exception:wrong-type-arg
1276                      (not (inexact? #t)))
1277   (pass-if-exception "procedure"
1278                      exception:wrong-type-arg
1279                      (not (inexact? (lambda () #t))))
1280   (pass-if-exception "port"
1281                      exception:wrong-type-arg
1282                      (not (inexact? (current-input-port)))))
1283
1284 ;;;
1285 ;;; equal?
1286 ;;;
1287
1288 (with-test-prefix "equal?"
1289   (pass-if (documented? equal?))
1290   (pass-if (equal? 0 0))
1291   (pass-if (equal? 7 7))
1292   (pass-if (equal? -7 -7))
1293   (pass-if (equal? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1294   (pass-if (equal? (- fixnum-min 1) (- fixnum-min 1)))
1295   (pass-if (not (equal? 0 1)))
1296   (pass-if (not (equal? fixnum-max (+ 1 fixnum-max))))
1297   (pass-if (not (equal? (+ 1 fixnum-max) fixnum-max)))
1298   (pass-if (not (equal? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1299   (pass-if (not (equal? fixnum-min (- fixnum-min 1))))
1300   (pass-if (not (equal? (- fixnum-min 1) fixnum-min)))
1301   (pass-if (not (equal? (- fixnum-min 1) (- fixnum-min 2))))
1302   (pass-if (not (equal? (+ fixnum-max 1) (- fixnum-min 1))))
1303
1304   (pass-if (not (equal? (ash 1 256) +inf.0)))
1305   (pass-if (not (equal? +inf.0 (ash 1 256))))
1306   (pass-if (not (equal? (ash 1 256) -inf.0)))
1307   (pass-if (not (equal? -inf.0 (ash 1 256))))
1308
1309   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1310   ;; sure we've avoided that
1311   (pass-if (not (equal? (ash 1 1024) +inf.0)))
1312   (pass-if (not (equal? +inf.0 (ash 1 1024))))
1313   (pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
1314   (pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
1315
1316   (pass-if (not (equal? +nan.0 +nan.0)))
1317   (pass-if (not (equal? 0 +nan.0)))
1318   (pass-if (not (equal? +nan.0 0)))
1319   (pass-if (not (equal? 1 +nan.0)))
1320   (pass-if (not (equal? +nan.0 1)))
1321   (pass-if (not (equal? -1 +nan.0)))
1322   (pass-if (not (equal? +nan.0 -1)))
1323
1324   (pass-if (not (equal? (ash 1 256) +nan.0)))
1325   (pass-if (not (equal? +nan.0 (ash 1 256))))
1326   (pass-if (not (equal? (- (ash 1 256)) +nan.0)))
1327   (pass-if (not (equal? +nan.0 (- (ash 1 256)))))
1328
1329   (pass-if (not (equal? (ash 1 8192) +nan.0)))
1330   (pass-if (not (equal? +nan.0 (ash 1 8192))))
1331   (pass-if (not (equal? (- (ash 1 8192)) +nan.0)))
1332   (pass-if (not (equal? +nan.0 (- (ash 1 8192)))))
1333
1334   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1335   ;; sure we've avoided that
1336   (pass-if (not (equal? (ash 3 1023) +nan.0)))
1337   (pass-if (not (equal? +nan.0 (ash 3 1023)))))
1338
1339 ;;;
1340 ;;; =
1341 ;;;
1342
1343 (with-test-prefix "="
1344   (expect-fail (documented? =))
1345   (pass-if (= 0 0))
1346   (pass-if (= 7 7))
1347   (pass-if (= -7 -7))
1348   (pass-if (= (+ 1 fixnum-max) (+ 1 fixnum-max)))
1349   (pass-if (= (- fixnum-min 1) (- fixnum-min 1)))
1350   (pass-if (not (= 0 1)))
1351   (pass-if (not (= fixnum-max (+ 1 fixnum-max))))
1352   (pass-if (not (= (+ 1 fixnum-max) fixnum-max)))
1353   (pass-if (not (= (+ 1 fixnum-max) (+ 2 fixnum-max))))
1354   (pass-if (not (= fixnum-min (- fixnum-min 1))))
1355   (pass-if (not (= (- fixnum-min 1) fixnum-min)))
1356   (pass-if (not (= (- fixnum-min 1) (- fixnum-min 2))))
1357   (pass-if (not (= (+ fixnum-max 1) (- fixnum-min 1))))
1358
1359   (pass-if (not (= (ash 1 256) +inf.0)))
1360   (pass-if (not (= +inf.0 (ash 1 256))))
1361   (pass-if (not (= (ash 1 256) -inf.0)))
1362   (pass-if (not (= -inf.0 (ash 1 256))))
1363
1364   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1365   ;; sure we've avoided that
1366   (pass-if (not (= (ash 1 1024) +inf.0)))
1367   (pass-if (not (= +inf.0 (ash 1 1024))))
1368   (pass-if (not (= (- (ash 1 1024)) -inf.0)))
1369   (pass-if (not (= -inf.0 (- (ash 1 1024)))))
1370
1371   (pass-if (not (= +nan.0 +nan.0)))
1372   (pass-if (not (= 0 +nan.0)))
1373   (pass-if (not (= +nan.0 0)))
1374   (pass-if (not (= 1 +nan.0)))
1375   (pass-if (not (= +nan.0 1)))
1376   (pass-if (not (= -1 +nan.0)))
1377   (pass-if (not (= +nan.0 -1)))
1378
1379   (pass-if (not (= (ash 1 256) +nan.0)))
1380   (pass-if (not (= +nan.0 (ash 1 256))))
1381   (pass-if (not (= (- (ash 1 256)) +nan.0)))
1382   (pass-if (not (= +nan.0 (- (ash 1 256)))))
1383
1384   (pass-if (not (= (ash 1 8192) +nan.0)))
1385   (pass-if (not (= +nan.0 (ash 1 8192))))
1386   (pass-if (not (= (- (ash 1 8192)) +nan.0)))
1387   (pass-if (not (= +nan.0 (- (ash 1 8192)))))
1388
1389   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1390   ;; sure we've avoided that
1391   (pass-if (not (= (ash 3 1023) +nan.0)))
1392   (pass-if (not (= +nan.0 (ash 3 1023))))
1393
1394   (pass-if (= 1/2 0.5))
1395   (pass-if (not (= 1/3 0.333333333333333333333333333333333)))
1396   (pass-if (not (= 2/3 0.5)))
1397   (pass-if (not (= 0.5 (+ 1/2 (/ 1 (ash 1 1000))))))
1398
1399   (pass-if (= 1/2 0.5+0i))
1400   (pass-if (not (= 0.333333333333333333333333333333333 1/3)))
1401   (pass-if (not (= 2/3 0.5+0i)))
1402   (pass-if (not (= 1/2 0+0.5i)))
1403
1404   (pass-if (= 0.5 1/2))
1405   (pass-if (not (= 0.5 2/3)))
1406   (pass-if (not (= (+ 1/2 (/ 1 (ash 1 1000))) 0.5)))
1407
1408   (pass-if (= 0.5+0i 1/2))
1409   (pass-if (not (= 0.5+0i 2/3)))
1410   (pass-if (not (= 0+0.5i 1/2))))
1411
1412 ;;;
1413 ;;; <
1414 ;;;
1415
1416 (with-test-prefix "<"
1417
1418   (expect-fail "documented?"
1419     (documented? <))
1420
1421   (with-test-prefix "(< 0 n)"
1422
1423     (pass-if "n = 0"
1424       (not (< 0 0)))
1425
1426     (pass-if "n = 0.0"
1427       (not (< 0 0.0)))
1428
1429     (pass-if "n = 1"
1430       (< 0 1))
1431
1432     (pass-if "n = 1.0"
1433       (< 0 1.0))
1434
1435     (pass-if "n = -1"
1436       (not (< 0 -1)))
1437
1438     (pass-if "n = -1.0"
1439       (not (< 0 -1.0)))
1440
1441     (pass-if "n = fixnum-max"
1442       (< 0 fixnum-max))
1443
1444     (pass-if "n = fixnum-max + 1"
1445       (< 0 (+ fixnum-max 1)))
1446
1447     (pass-if "n = fixnum-min"
1448       (not (< 0 fixnum-min)))
1449
1450     (pass-if "n = fixnum-min - 1"
1451       (not (< 0 (- fixnum-min 1)))))
1452
1453   (with-test-prefix "(< 0.0 n)"
1454
1455     (pass-if "n = 0"
1456       (not (< 0.0 0)))
1457
1458     (pass-if "n = 0.0"
1459       (not (< 0.0 0.0)))
1460
1461     (pass-if "n = 1"
1462       (< 0.0 1))
1463
1464     (pass-if "n = 1.0"
1465       (< 0.0 1.0))
1466
1467     (pass-if "n = -1"
1468       (not (< 0.0 -1)))
1469
1470     (pass-if "n = -1.0"
1471       (not (< 0.0 -1.0)))
1472
1473     (pass-if "n = fixnum-max"
1474       (< 0.0 fixnum-max))
1475
1476     (pass-if "n = fixnum-max + 1"
1477       (< 0.0 (+ fixnum-max 1)))
1478
1479     (pass-if "n = fixnum-min"
1480       (not (< 0.0 fixnum-min)))
1481
1482     (pass-if "n = fixnum-min - 1"
1483       (not (< 0.0 (- fixnum-min 1)))))
1484
1485   (with-test-prefix "(< 1 n)"
1486
1487     (pass-if "n = 0"
1488       (not (< 1 0)))
1489
1490     (pass-if "n = 0.0"
1491       (not (< 1 0.0)))
1492
1493     (pass-if "n = 1"
1494       (not (< 1 1)))
1495
1496     (pass-if "n = 1.0"
1497       (not (< 1 1.0)))
1498
1499     (pass-if "n = -1"
1500       (not (< 1 -1)))
1501
1502     (pass-if "n = -1.0"
1503       (not (< 1 -1.0)))
1504
1505     (pass-if "n = fixnum-max"
1506       (< 1 fixnum-max))
1507
1508     (pass-if "n = fixnum-max + 1"
1509       (< 1 (+ fixnum-max 1)))
1510
1511     (pass-if "n = fixnum-min"
1512       (not (< 1 fixnum-min)))
1513
1514     (pass-if "n = fixnum-min - 1"
1515       (not (< 1 (- fixnum-min 1)))))
1516
1517   (with-test-prefix "(< 1.0 n)"
1518
1519     (pass-if "n = 0"
1520       (not (< 1.0 0)))
1521
1522     (pass-if "n = 0.0"
1523       (not (< 1.0 0.0)))
1524
1525     (pass-if "n = 1"
1526       (not (< 1.0 1)))
1527
1528     (pass-if "n = 1.0"
1529       (not (< 1.0 1.0)))
1530
1531     (pass-if "n = -1"
1532       (not (< 1.0 -1)))
1533
1534     (pass-if "n = -1.0"
1535       (not (< 1.0 -1.0)))
1536
1537     (pass-if "n = fixnum-max"
1538       (< 1.0 fixnum-max))
1539
1540     (pass-if "n = fixnum-max + 1"
1541       (< 1.0 (+ fixnum-max 1)))
1542
1543     (pass-if "n = fixnum-min"
1544       (not (< 1.0 fixnum-min)))
1545
1546     (pass-if "n = fixnum-min - 1"
1547       (not (< 1.0 (- fixnum-min 1)))))
1548
1549   (with-test-prefix "(< -1 n)"
1550
1551     (pass-if "n = 0"
1552       (< -1 0))
1553
1554     (pass-if "n = 0.0"
1555       (< -1 0.0))
1556
1557     (pass-if "n = 1"
1558       (< -1 1))
1559
1560     (pass-if "n = 1.0"
1561       (< -1 1.0))
1562
1563     (pass-if "n = -1"
1564       (not (< -1 -1)))
1565
1566     (pass-if "n = -1.0"
1567       (not (< -1 -1.0)))
1568
1569     (pass-if "n = fixnum-max"
1570       (< -1 fixnum-max))
1571
1572     (pass-if "n = fixnum-max + 1"
1573       (< -1 (+ fixnum-max 1)))
1574
1575     (pass-if "n = fixnum-min"
1576       (not (< -1 fixnum-min)))
1577
1578     (pass-if "n = fixnum-min - 1"
1579       (not (< -1 (- fixnum-min 1)))))
1580
1581   (with-test-prefix "(< -1.0 n)"
1582
1583     (pass-if "n = 0"
1584       (< -1.0 0))
1585
1586     (pass-if "n = 0.0"
1587       (< -1.0 0.0))
1588
1589     (pass-if "n = 1"
1590       (< -1.0 1))
1591
1592     (pass-if "n = 1.0"
1593       (< -1.0 1.0))
1594
1595     (pass-if "n = -1"
1596       (not (< -1.0 -1)))
1597
1598     (pass-if "n = -1.0"
1599       (not (< -1.0 -1.0)))
1600
1601     (pass-if "n = fixnum-max"
1602       (< -1.0 fixnum-max))
1603
1604     (pass-if "n = fixnum-max + 1"
1605       (< -1.0 (+ fixnum-max 1)))
1606
1607     (pass-if "n = fixnum-min"
1608       (not (< -1.0 fixnum-min)))
1609
1610     (pass-if "n = fixnum-min - 1"
1611       (not (< -1.0 (- fixnum-min 1)))))
1612
1613   (with-test-prefix "(< fixnum-max n)"
1614
1615     (pass-if "n = 0"
1616       (not (< fixnum-max 0)))
1617
1618     (pass-if "n = 0.0"
1619       (not (< fixnum-max 0.0)))
1620
1621     (pass-if "n = 1"
1622       (not (< fixnum-max 1)))
1623
1624     (pass-if "n = 1.0"
1625       (not (< fixnum-max 1.0)))
1626
1627     (pass-if "n = -1"
1628       (not (< fixnum-max -1)))
1629
1630     (pass-if "n = -1.0"
1631       (not (< fixnum-max -1.0)))
1632
1633     (pass-if "n = fixnum-max"
1634       (not (< fixnum-max fixnum-max)))
1635
1636     (pass-if "n = fixnum-max + 1"
1637       (< fixnum-max (+ fixnum-max 1)))
1638
1639     (pass-if "n = fixnum-min"
1640       (not (< fixnum-max fixnum-min)))
1641
1642     (pass-if "n = fixnum-min - 1"
1643       (not (< fixnum-max (- fixnum-min 1)))))
1644
1645   (with-test-prefix "(< (+ fixnum-max 1) n)"
1646
1647     (pass-if "n = 0"
1648       (not (< (+ fixnum-max 1) 0)))
1649
1650     (pass-if "n = 0.0"
1651       (not (< (+ fixnum-max 1) 0.0)))
1652
1653     (pass-if "n = 1"
1654       (not (< (+ fixnum-max 1) 1)))
1655
1656     (pass-if "n = 1.0"
1657       (not (< (+ fixnum-max 1) 1.0)))
1658
1659     (pass-if "n = -1"
1660       (not (< (+ fixnum-max 1) -1)))
1661
1662     (pass-if "n = -1.0"
1663       (not (< (+ fixnum-max 1) -1.0)))
1664
1665     (pass-if "n = fixnum-max"
1666       (not (< (+ fixnum-max 1) fixnum-max)))
1667
1668     (pass-if "n = fixnum-max + 1"
1669       (not (< (+ fixnum-max 1) (+ fixnum-max 1))))
1670
1671     (pass-if "n = fixnum-min"
1672       (not (< (+ fixnum-max 1) fixnum-min)))
1673
1674     (pass-if "n = fixnum-min - 1"
1675       (not (< (+ fixnum-max 1) (- fixnum-min 1)))))
1676
1677   (with-test-prefix "(< fixnum-min n)"
1678
1679     (pass-if "n = 0"
1680       (< fixnum-min 0))
1681
1682     (pass-if "n = 0.0"
1683       (< fixnum-min 0.0))
1684
1685     (pass-if "n = 1"
1686       (< fixnum-min 1))
1687
1688     (pass-if "n = 1.0"
1689       (< fixnum-min 1.0))
1690
1691     (pass-if "n = -1"
1692       (< fixnum-min -1))
1693
1694     (pass-if "n = -1.0"
1695       (< fixnum-min -1.0))
1696
1697     (pass-if "n = fixnum-max"
1698       (< fixnum-min fixnum-max))
1699
1700     (pass-if "n = fixnum-max + 1"
1701       (< fixnum-min (+ fixnum-max 1)))
1702
1703     (pass-if "n = fixnum-min"
1704       (not (< fixnum-min fixnum-min)))
1705
1706     (pass-if "n = fixnum-min - 1"
1707       (not (< fixnum-min (- fixnum-min 1)))))
1708
1709   (with-test-prefix "(< (- fixnum-min 1) n)"
1710
1711     (pass-if "n = 0"
1712       (< (- fixnum-min 1) 0))
1713
1714     (pass-if "n = 0.0"
1715       (< (- fixnum-min 1) 0.0))
1716
1717     (pass-if "n = 1"
1718       (< (- fixnum-min 1) 1))
1719
1720     (pass-if "n = 1.0"
1721       (< (- fixnum-min 1) 1.0))
1722
1723     (pass-if "n = -1"
1724       (< (- fixnum-min 1) -1))
1725
1726     (pass-if "n = -1.0"
1727       (< (- fixnum-min 1) -1.0))
1728
1729     (pass-if "n = fixnum-max"
1730       (< (- fixnum-min 1) fixnum-max))
1731
1732     (pass-if "n = fixnum-max + 1"
1733       (< (- fixnum-min 1) (+ fixnum-max 1)))
1734
1735     (pass-if "n = fixnum-min"
1736       (< (- fixnum-min 1) fixnum-min))
1737
1738     (pass-if "n = fixnum-min - 1"
1739       (not (< (- fixnum-min 1) (- fixnum-min 1)))))
1740
1741   (pass-if (< (ash 1 256) +inf.0))
1742   (pass-if (not (< +inf.0 (ash 1 256))))
1743   (pass-if (not (< (ash 1 256) -inf.0)))
1744   (pass-if (< -inf.0 (ash 1 256)))
1745
1746   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1747   ;; sure we've avoided that
1748   (pass-if (< (1- (ash 1 1024)) +inf.0))
1749   (pass-if (<     (ash 1 1024)  +inf.0))
1750   (pass-if (< (1+ (ash 1 1024)) +inf.0))
1751   (pass-if (not (< +inf.0 (1- (ash 1 1024)))))
1752   (pass-if (not (< +inf.0     (ash 1 1024))))
1753   (pass-if (not (< +inf.0 (1+ (ash 1 1024)))))
1754   (pass-if (< -inf.0 (- (1- (ash 1 1024)))))
1755   (pass-if (< -inf.0 (-     (ash 1 1024))))
1756   (pass-if (< -inf.0 (- (1+ (ash 1 1024)))))
1757   (pass-if (not (< (- (1- (ash 1 1024))) -inf.0)))
1758   (pass-if (not (< (-     (ash 1 1024))  -inf.0)))
1759   (pass-if (not (< (- (1+ (ash 1 1024))) -inf.0)))
1760
1761   (pass-if (not (< +nan.0 +nan.0)))
1762   (pass-if (not (< 0 +nan.0)))
1763   (pass-if (not (< +nan.0 0)))
1764   (pass-if (not (< 1 +nan.0)))
1765   (pass-if (not (< +nan.0 1)))
1766   (pass-if (not (< -1 +nan.0)))
1767   (pass-if (not (< +nan.0 -1)))
1768
1769   (pass-if (not (< (ash 1 256) +nan.0)))
1770   (pass-if (not (< +nan.0 (ash 1 256))))
1771   (pass-if (not (< (- (ash 1 256)) +nan.0)))
1772   (pass-if (not (< +nan.0 (- (ash 1 256)))))
1773
1774   (pass-if (not (< (ash 1 8192) +nan.0)))
1775   (pass-if (not (< +nan.0 (ash 1 8192))))
1776   (pass-if (not (< (- (ash 1 8192)) +nan.0)))
1777   (pass-if (not (< +nan.0 (- (ash 1 8192)))))
1778
1779   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1780   ;; sure we've avoided that
1781   (pass-if (not (< (ash 3 1023) +nan.0)))
1782   (pass-if (not (< (1+ (ash 3 1023)) +nan.0)))
1783   (pass-if (not (< (1- (ash 3 1023)) +nan.0)))
1784   (pass-if (not (< +nan.0 (ash 3 1023))))
1785   (pass-if (not (< +nan.0 (1+ (ash 3 1023)))))
1786   (pass-if (not (< +nan.0 (1- (ash 3 1023)))))
1787
1788   (with-test-prefix "inum/frac"
1789     (pass-if (< 2 9/4))
1790     (pass-if (< -2 9/4))
1791     (pass-if (< -2 7/4))
1792     (pass-if (< -2 -7/4))
1793     (pass-if (eq? #f (< 2 7/4)))
1794     (pass-if (eq? #f (< 2 -7/4)))
1795     (pass-if (eq? #f (< 2 -9/4)))
1796     (pass-if (eq? #f (< -2 -9/4))))
1797
1798   (with-test-prefix "bignum/frac"
1799     (let ((x (ash 1 2048)))
1800       (pass-if (< x (* 4/3 x)))
1801       (pass-if (< (- x) (* 4/3 x)))
1802       (pass-if (< (- x) (* 2/3 x)))
1803       (pass-if (< (- x) (* -2/3 x)))
1804       (pass-if (eq? #f (< x (* 2/3 x))))
1805       (pass-if (eq? #f (< x (* -2/3 x))))
1806       (pass-if (eq? #f (< x (* -4/3 x))))
1807       (pass-if (eq? #f (< (- x) (* -4/3 x))))))
1808
1809   (with-test-prefix "flonum/frac"
1810     (pass-if (< 0.75 4/3))
1811     (pass-if (< -0.75 4/3))
1812     (pass-if (< -0.75 2/3))
1813     (pass-if (< -0.75 -2/3))
1814     (pass-if (eq? #f (< 0.75 2/3)))
1815     (pass-if (eq? #f (< 0.75 -2/3)))
1816     (pass-if (eq? #f (< 0.75 -4/3)))
1817     (pass-if (eq? #f (< -0.75 -4/3)))
1818
1819     (pass-if (< -inf.0 4/3))
1820     (pass-if (< -inf.0 -4/3))
1821     (pass-if (eq? #f (< +inf.0 4/3)))
1822     (pass-if (eq? #f (< +inf.0 -4/3)))
1823
1824     (pass-if (eq? #f (< +nan.0 4/3)))
1825     (pass-if (eq? #f (< +nan.0 -4/3))))
1826
1827   (with-test-prefix "frac/inum"
1828     (pass-if (< 7/4 2))
1829     (pass-if (< -7/4 2))
1830     (pass-if (< -9/4 2))
1831     (pass-if (< -9/4 -2))
1832     (pass-if (eq? #f (< 9/4 2)))
1833     (pass-if (eq? #f (< 9/4 -2)))
1834     (pass-if (eq? #f (< 7/4 -2)))
1835     (pass-if (eq? #f (< -7/4 -2))))
1836
1837   (with-test-prefix "frac/bignum"
1838     (let ((x (ash 1 2048)))
1839       (pass-if (< (* 2/3 x) x))
1840       (pass-if (< (* -2/3 x) x))
1841       (pass-if (< (* -4/3 x) x))
1842       (pass-if (< (* -4/3 x) (- x)))
1843       (pass-if (eq? #f (< (* 4/3 x) x)))
1844       (pass-if (eq? #f (< (* 4/3 x) (- x))))
1845       (pass-if (eq? #f (< (* 2/3 x) (- x))))
1846       (pass-if (eq? #f (< (* -2/3 x) (- x))))))
1847
1848   (with-test-prefix "frac/flonum"
1849     (pass-if (< 2/3 0.75))
1850     (pass-if (< -2/3 0.75))
1851     (pass-if (< -4/3 0.75))
1852     (pass-if (< -4/3 -0.75))
1853     (pass-if (eq? #f (< 4/3 0.75)))
1854     (pass-if (eq? #f (< 4/3 -0.75)))
1855     (pass-if (eq? #f (< 2/3 -0.75)))
1856     (pass-if (eq? #f (< -2/3 -0.75)))
1857
1858     (pass-if (< 4/3 +inf.0))
1859     (pass-if (< -4/3 +inf.0))
1860     (pass-if (eq? #f (< 4/3 -inf.0)))
1861     (pass-if (eq? #f (< -4/3 -inf.0)))
1862
1863     (pass-if (eq? #f (< 4/3 +nan.0)))
1864     (pass-if (eq? #f (< -4/3 +nan.0))))
1865
1866   (with-test-prefix "frac/frac"
1867     (pass-if (< 2/3 6/7))
1868     (pass-if (< -2/3 6/7))
1869     (pass-if (< -4/3 6/7))
1870     (pass-if (< -4/3 -6/7))
1871     (pass-if (eq? #f (< 4/3 6/7)))
1872     (pass-if (eq? #f (< 4/3 -6/7)))
1873     (pass-if (eq? #f (< 2/3 -6/7)))
1874     (pass-if (eq? #f (< -2/3 -6/7)))))
1875
1876 ;;;
1877 ;;; >
1878 ;;;
1879
1880 ;; currently not tested -- implementation is trivial
1881 ;; (> x y) is implemented as (< y x)
1882 ;; FIXME: tests should probably be added in case we change implementation.
1883
1884 ;;;
1885 ;;; <=
1886 ;;;
1887
1888 ;; currently not tested -- implementation is trivial
1889 ;; (<= x y) is implemented as (not (< y x))
1890 ;; FIXME: tests should probably be added in case we change implementation.
1891
1892 ;;;
1893 ;;; >=
1894 ;;;
1895
1896 ;; currently not tested -- implementation is trivial
1897 ;; (>= x y) is implemented as (not (< x y))
1898 ;; FIXME: tests should probably be added in case we change implementation.
1899
1900 ;;;
1901 ;;; zero?
1902 ;;;
1903
1904 (with-test-prefix "zero?"
1905   (expect-fail (documented? zero?))
1906   (pass-if (zero? 0))
1907   (pass-if (not (zero? 7)))
1908   (pass-if (not (zero? -7)))
1909   (pass-if (not (zero? (+ 1 fixnum-max))))
1910   (pass-if (not (zero? (- 1 fixnum-min))))
1911   (pass-if (not (zero? 1.3)))
1912   (pass-if (not (zero? 3.1+4.2i))))
1913
1914 ;;;
1915 ;;; positive?
1916 ;;;
1917
1918 (with-test-prefix "positive?"
1919   (expect-fail (documented? positive?))
1920   (pass-if (positive? 1))
1921   (pass-if (positive? (+ fixnum-max 1)))
1922   (pass-if (positive? 1.3))
1923   (pass-if (not (positive? 0)))
1924   (pass-if (not (positive? -1)))
1925   (pass-if (not (positive? (- fixnum-min 1))))
1926   (pass-if (not (positive? -1.3))))
1927
1928 ;;;
1929 ;;; negative?
1930 ;;;
1931
1932 (with-test-prefix "negative?"
1933   (expect-fail (documented? negative?))
1934   (pass-if (not (negative? 1)))
1935   (pass-if (not (negative? (+ fixnum-max 1))))
1936   (pass-if (not (negative? 1.3)))
1937   (pass-if (not (negative? 0)))
1938   (pass-if (negative? -1))
1939   (pass-if (negative? (- fixnum-min 1)))
1940   (pass-if (negative? -1.3)))
1941
1942 ;;;
1943 ;;; max
1944 ;;;
1945
1946 (with-test-prefix "max"
1947   (pass-if-exception "no args" exception:wrong-num-args
1948     (max))
1949
1950   (pass-if-exception "one complex" exception:wrong-type-arg
1951     (max 1+i))
1952
1953   (pass-if-exception "inum/complex" exception:wrong-type-arg
1954     (max 123 1+i))
1955   (pass-if-exception "big/complex" exception:wrong-type-arg
1956     (max 9999999999999999999999999999999999999999 1+i))
1957   (pass-if-exception "real/complex" exception:wrong-type-arg
1958     (max 123.0 1+i))
1959   (pass-if-exception "frac/complex" exception:wrong-type-arg
1960     (max 123/456 1+i))
1961
1962   (pass-if-exception "complex/inum" exception:wrong-type-arg
1963     (max 1+i 123))
1964   (pass-if-exception "complex/big" exception:wrong-type-arg
1965     (max 1+i 9999999999999999999999999999999999999999))
1966   (pass-if-exception "complex/real" exception:wrong-type-arg
1967     (max 1+i 123.0))
1968   (pass-if-exception "complex/frac" exception:wrong-type-arg
1969     (max 1+i 123/456))
1970
1971   (let ((big*2 (* fixnum-max 2))
1972         (big*3 (* fixnum-max 3))
1973         (big*4 (* fixnum-max 4))
1974         (big*5 (* fixnum-max 5)))
1975
1976     (with-test-prefix "inum / frac"
1977       (pass-if (= 3 (max 3 5/2)))
1978       (pass-if (= 5/2 (max 2 5/2))))
1979
1980     (with-test-prefix "frac / inum"
1981       (pass-if (= 3 (max 5/2 3)))
1982       (pass-if (= 5/2 (max 5/2 2))))
1983
1984     (with-test-prefix "inum / real"
1985       (pass-if (nan? (max 123 +nan.0))))
1986
1987     (with-test-prefix "real / inum"
1988       (pass-if (nan? (max +nan.0 123))))
1989
1990     (with-test-prefix "big / frac"
1991       (pass-if (= big*2 (max big*2 5/2)))
1992       (pass-if (= 5/2 (max (- big*2) 5/2))))
1993
1994     (with-test-prefix "frac / big"
1995       (pass-if (= big*2 (max 5/2 big*2)))
1996       (pass-if (= 5/2 (max 5/2 (- big*2)))))
1997
1998     (with-test-prefix "big / real"
1999       (pass-if (nan? (max big*5 +nan.0)))
2000       (pass-if (= big*5  (max big*5 -inf.0)))
2001       (pass-if (= +inf.0 (max big*5 +inf.0)))
2002       (pass-if (= 1.0 (max (- big*5) 1.0)))
2003       (pass-if (inexact? (max big*5 1.0)))
2004       (pass-if (= (exact->inexact big*5) (max big*5 1.0))))
2005
2006     (with-test-prefix "real / big"
2007       (pass-if (nan? (max +nan.0 big*5)))
2008       (pass-if (= +inf.0 (max +inf.0 big*5)))
2009       (pass-if (= big*5  (max -inf.0 big*5)))
2010       (pass-if (= 1.0 (max 1.0 (- big*5))))
2011       (pass-if (inexact? (max 1.0 big*5)))
2012       (pass-if (= (exact->inexact big*5) (max 1.0 big*5))))
2013
2014     (with-test-prefix "frac / frac"
2015       (pass-if (= 2/3 (max 1/2 2/3)))
2016       (pass-if (= 2/3 (max 2/3 1/2)))
2017       (pass-if (= -1/2 (max -1/2 -2/3)))
2018       (pass-if (= -1/2 (max -2/3 -1/2))))
2019
2020     (with-test-prefix "real / real"
2021       (pass-if (nan? (max 123.0 +nan.0)))
2022       (pass-if (nan? (max +nan.0 123.0)))
2023       (pass-if (nan? (max +nan.0 +nan.0)))
2024       (pass-if (= 456.0 (max 123.0 456.0)))
2025       (pass-if (= 456.0 (max 456.0 123.0)))))
2026
2027   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2028   ;; sure we've avoided that
2029   (for-each (lambda (b)
2030               (pass-if (list b +inf.0)
2031                 (= +inf.0 (max b +inf.0)))
2032               (pass-if (list +inf.0 b)
2033                 (= +inf.0 (max b +inf.0)))
2034               (pass-if (list b -inf.0)
2035                 (= (exact->inexact b) (max b -inf.0)))
2036               (pass-if (list -inf.0 b)
2037                 (= (exact->inexact b) (max b -inf.0))))
2038             (list (1- (ash 1 1024))
2039                   (ash 1 1024)
2040                   (1+ (ash 1 1024))
2041                   (- (1- (ash 1 1024)))
2042                   (- (ash 1 1024))
2043                   (- (1+ (ash 1 1024)))))
2044
2045   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2046   ;; sure we've avoided that
2047   (pass-if (nan? (max (ash 1 2048) +nan.0)))
2048   (pass-if (nan? (max +nan.0 (ash 1 2048)))))
2049
2050 ;;;
2051 ;;; min
2052 ;;;
2053
2054 ;; FIXME: unfinished...
2055
2056 (with-test-prefix "min"
2057   (pass-if-exception "no args" exception:wrong-num-args
2058     (min))
2059
2060   (pass-if-exception "one complex" exception:wrong-type-arg
2061     (min 1+i))
2062
2063   (pass-if-exception "inum/complex" exception:wrong-type-arg
2064     (min 123 1+i))
2065   (pass-if-exception "big/complex" exception:wrong-type-arg
2066     (min 9999999999999999999999999999999999999999 1+i))
2067   (pass-if-exception "real/complex" exception:wrong-type-arg
2068     (min 123.0 1+i))
2069   (pass-if-exception "frac/complex" exception:wrong-type-arg
2070     (min 123/456 1+i))
2071
2072   (pass-if-exception "complex/inum" exception:wrong-type-arg
2073     (min 1+i 123))
2074   (pass-if-exception "complex/big" exception:wrong-type-arg
2075     (min 1+i 9999999999999999999999999999999999999999))
2076   (pass-if-exception "complex/real" exception:wrong-type-arg
2077     (min 1+i 123.0))
2078   (pass-if-exception "complex/frac" exception:wrong-type-arg
2079     (min 1+i 123/456))
2080
2081   (let ((big*2 (* fixnum-max 2))
2082         (big*3 (* fixnum-max 3))
2083         (big*4 (* fixnum-max 4))
2084         (big*5 (* fixnum-max 5)))
2085
2086     (expect-fail (documented? min))
2087     (pass-if (= 1 (min 7 3 1 5)))
2088     (pass-if (= 1 (min 1 7 3 5)))
2089     (pass-if (= 1 (min 7 3 5 1)))
2090     (pass-if (= -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
2091     (pass-if (= -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
2092     (pass-if (= -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
2093     (pass-if (= big*2 (min big*3 big*5 big*2 big*4)))
2094     (pass-if (= big*2 (min big*2 big*3 big*5 big*4)))
2095     (pass-if (= big*2 (min big*3 big*5 big*4 big*2)))
2096     (pass-if
2097         (= (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
2098     (pass-if
2099         (= (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
2100     (pass-if
2101         (= (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
2102
2103     (with-test-prefix "inum / frac"
2104       (pass-if (= 5/2 (min 3 5/2)))
2105       (pass-if (= 2   (min 2 5/2))))
2106
2107     (with-test-prefix "frac / inum"
2108       (pass-if (= 5/2 (min 5/2 3)))
2109       (pass-if (= 2   (min 5/2 2))))
2110
2111     (with-test-prefix "inum / real"
2112       (pass-if (nan? (min 123 +nan.0))))
2113
2114     (with-test-prefix "real / inum"
2115       (pass-if (nan? (min +nan.0 123))))
2116
2117     (with-test-prefix "big / frac"
2118       (pass-if (= 5/2       (min big*2 5/2)))
2119       (pass-if (= (- big*2) (min (- big*2) 5/2))))
2120
2121     (with-test-prefix "frac / big"
2122       (pass-if (= 5/2       (min 5/2 big*2)))
2123       (pass-if (= (- big*2) (min 5/2 (- big*2)))))
2124
2125     (with-test-prefix "big / real"
2126       (pass-if (nan? (min big*5 +nan.0)))
2127       (pass-if (= big*5  (min big*5  +inf.0)))
2128       (pass-if (= -inf.0 (min big*5  -inf.0)))
2129       (pass-if (= 1.0 (min big*5 1.0)))
2130       (pass-if (inexact? (min (- big*5) 1.0)))
2131       (pass-if (= (exact->inexact (- big*5)) (min (- big*5) 1.0))))
2132
2133     (with-test-prefix "real / big"
2134       (pass-if (nan? (min +nan.0 big*5)))
2135       (pass-if (= big*5  (min +inf.0 big*5)))
2136       (pass-if (= -inf.0 (min -inf.0 big*5)))
2137       (pass-if (= 1.0 (min 1.0 big*5)))
2138       (pass-if (inexact? (min 1.0 (- big*5))))
2139       (pass-if (= (exact->inexact (- big*5)) (min 1.0 (- big*5)))))
2140
2141     (with-test-prefix "frac / frac"
2142       (pass-if (= 1/2 (min 1/2 2/3)))
2143       (pass-if (= 1/2 (min 2/3 1/2)))
2144       (pass-if (= -2/3 (min -1/2 -2/3)))
2145       (pass-if (= -2/3 (min -2/3 -1/2))))
2146
2147     (with-test-prefix "real / real"
2148       (pass-if (nan? (min 123.0 +nan.0)))
2149       (pass-if (nan? (min +nan.0 123.0)))
2150       (pass-if (nan? (min +nan.0 +nan.0)))
2151       (pass-if (= 123.0 (min 123.0 456.0)))
2152       (pass-if (= 123.0 (min 456.0 123.0)))))
2153
2154
2155   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2156   ;; sure we've avoided that
2157   (for-each (lambda (b)
2158               (pass-if (list b +inf.0)
2159                 (= (exact->inexact b) (min b +inf.0)))
2160               (pass-if (list +inf.0 b)
2161                 (= (exact->inexact b) (min b +inf.0)))
2162               (pass-if (list b -inf.0)
2163                 (= -inf.0 (min b -inf.0)))
2164               (pass-if (list -inf.0 b)
2165                 (= -inf.0 (min b -inf.0))))
2166             (list (1- (ash 1 1024))
2167                   (ash 1 1024)
2168                   (1+ (ash 1 1024))
2169                   (- (1- (ash 1 1024)))
2170                   (- (ash 1 1024))
2171                   (- (1+ (ash 1 1024)))))
2172
2173   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2174   ;; sure we've avoided that
2175   (pass-if (nan? (min (- (ash 1 2048)) (- +nan.0))))
2176   (pass-if (nan? (min (- +nan.0) (- (ash 1 2048))))))
2177
2178 ;;;
2179 ;;; +
2180 ;;;
2181
2182 (with-test-prefix "+"
2183
2184   (expect-fail "documented?"
2185     (documented? +))
2186
2187   (with-test-prefix "wrong type argument"
2188
2189     (pass-if-exception "1st argument string"
2190       exception:wrong-type-arg
2191       (+ "1" 2))
2192
2193     (pass-if-exception "2nd argument bool"
2194       exception:wrong-type-arg
2195       (+ 1 #f))))
2196 ;;;
2197 ;;; -
2198 ;;;
2199
2200 (with-test-prefix "-"
2201
2202   (pass-if "-inum - +bignum"
2203     (= #x-100000000000000000000000000000001
2204        (- -1 #x100000000000000000000000000000000)))
2205
2206   (pass-if "big - inum"
2207     (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
2208        (- #x100000000000000000000000000000000 1)))
2209
2210   (pass-if "big - -inum"
2211     (= #x100000000000000000000000000000001
2212        (- #x100000000000000000000000000000000 -1))))
2213
2214 ;;;
2215 ;;; *
2216 ;;;
2217
2218 (with-test-prefix "*"
2219
2220   (pass-if "complex * bignum"
2221     (let ((big (ash 1 90)))
2222       (= (make-rectangular big big)
2223          (* 1+1i big)))))
2224
2225 ;;;
2226 ;;; /
2227 ;;;
2228
2229 (with-test-prefix "/"
2230
2231   (expect-fail "documented?"
2232     (documented? /))
2233
2234   (with-test-prefix "division by zero"
2235
2236     (pass-if-exception "(/ 0)"
2237       exception:numerical-overflow
2238       (/ 0))
2239
2240     (pass-if "(/ 0.0)"
2241       (= +inf.0 (/ 0.0)))
2242
2243     (pass-if-exception "(/ 1 0)"
2244       exception:numerical-overflow
2245       (/ 1 0))
2246
2247     (pass-if "(/ 1 0.0)"
2248       (= +inf.0 (/ 1 0.0)))
2249
2250     (pass-if-exception "(/ bignum 0)"
2251       exception:numerical-overflow
2252       (/ (+ fixnum-max 1) 0))
2253
2254     (pass-if "(/ bignum 0.0)"
2255       (= +inf.0 (/ (+ fixnum-max 1) 0.0)))
2256
2257     (pass-if-exception "(/ 1.0 0)"
2258       exception:numerical-overflow
2259       (/ 1.0 0))
2260
2261     (pass-if "(/ 1.0 0.0)"
2262       (= +inf.0 (/ 1.0 0.0)))
2263
2264     (pass-if-exception "(/ +i 0)"
2265       exception:numerical-overflow
2266       (/ +i 0))
2267
2268     (pass-if "(/ +i 0.0)"
2269       (= +inf.0 (imag-part (/ +i 0.0)))))
2270
2271   (with-test-prefix "complex division"
2272
2273     (pass-if "(/ 3+4i)"
2274       (= (/ 3+4i) 0.12-0.16i))
2275
2276     (pass-if "(/ 4+3i)"
2277       (= (/ 4+3i) 0.16-0.12i))
2278
2279     (pass-if "(/ 25+125i 3+4i)"
2280       (= (/ 25+125i 3+4i) 23.0+11.0i))
2281
2282     (pass-if "(/ 25+125i 4+3i)"
2283       (= (/ 25+125i 4+3i) 19.0+17.0i))
2284
2285     (pass-if "(/ 25 3+4i)"
2286       (= (/ 25 3+4i) 3.0-4.0i))
2287
2288     (pass-if "(/ 25 4+3i)"
2289       (= (/ 25 4+3i) 4.0-3.0i))
2290
2291     (pass-if "(/ 1e200+1e200i)"
2292       (= (/ 1e200+1e200i) 5.0e-201-5.0e-201i))))
2293
2294 ;;;
2295 ;;; truncate
2296 ;;;
2297
2298 (with-test-prefix "truncate"
2299   (pass-if (=  1 (truncate  1.75)))
2300   (pass-if (=  1 (truncate  1.5)))
2301   (pass-if (=  1 (truncate  1.25)))
2302   (pass-if (=  0 (truncate  0.75)))
2303   (pass-if (=  0 (truncate  0.5)))
2304   (pass-if (=  0 (truncate  0.0)))
2305   (pass-if (=  0 (truncate -0.5)))
2306   (pass-if (= -1 (truncate -1.25)))
2307   (pass-if (= -1 (truncate -1.5))))
2308
2309 ;;;
2310 ;;; round
2311 ;;;
2312
2313 (with-test-prefix "round"
2314   (pass-if (=  2 (round  1.75)))
2315   (pass-if (=  2 (round  1.5)))
2316   (pass-if (=  1 (round  1.25)))
2317   (pass-if (=  1 (round  0.75)))
2318   (pass-if (=  0 (round  0.5)))
2319   (pass-if (=  0 (round  0.0)))
2320   (pass-if (=  0 (round -0.5)))
2321   (pass-if (= -1 (round -1.25)))
2322   (pass-if (= -2 (round -1.5)))
2323
2324   (with-test-prefix "inum"
2325     (pass-if "0"
2326       (and (= 0    (round 0))
2327            (exact? (round 0))))
2328
2329     (pass-if "1"
2330       (and (= 1    (round 1))
2331            (exact? (round 1))))
2332
2333     (pass-if "-1"
2334       (and (= -1   (round -1))
2335            (exact? (round -1)))))
2336
2337   (with-test-prefix "bignum"
2338     (let ((x (1+ most-positive-fixnum)))
2339       (pass-if "(1+ most-positive-fixnum)"
2340         (and (= x    (round x))
2341              (exact? (round x)))))
2342
2343     (let ((x (1- most-negative-fixnum)))
2344       (pass-if "(1- most-negative-fixnum)"
2345         (and (= x    (round x))
2346              (exact? (round x))))))
2347
2348   (with-test-prefix "real"
2349     (pass-if "0.0"
2350       (and (= 0.0    (round 0.0))
2351            (inexact? (round 0.0))))
2352
2353     (pass-if "1.0"
2354       (and (= 1.0    (round 1.0))
2355            (inexact? (round 1.0))))
2356
2357     (pass-if "-1.0"
2358       (and (= -1.0   (round -1.0))
2359            (inexact? (round -1.0))))
2360
2361     (pass-if "-3.1"
2362       (and (= -3.0   (round -3.1))
2363            (inexact? (round -3.1))))
2364
2365     (pass-if "3.1"
2366       (and (= 3.0    (round 3.1))
2367            (inexact? (round 3.1))))
2368
2369     (pass-if "3.9"
2370       (and (= 4.0    (round 3.9))
2371            (inexact? (round 3.9))))
2372
2373     (pass-if "-3.9"
2374       (and (= -4.0   (round -3.9))
2375            (inexact? (round -3.9))))
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     (pass-if "-1.5"
2390       (and (= -2.0   (round -1.5))
2391            (inexact? (round -1.5))))
2392
2393     (pass-if "-2.5"
2394       (and (= -2.0   (round -2.5))
2395            (inexact? (round -2.5))))
2396
2397     (pass-if "-3.5"
2398       (and (= -4.0   (round -3.5))
2399            (inexact? (round -3.5))))
2400
2401     ;; prior to guile 1.6.5, on an IEEE system an inexact 2^53-1 (ie. a
2402     ;; float with mantissa all ones) came out as 2^53 from `round' (except
2403     ;; on i386 and m68k systems using the coprocessor and optimizing, where
2404     ;; extra precision hid the problem)
2405     (pass-if "2^53-1"
2406       (let ((x (exact->inexact (1- (ash 1 53)))))
2407         (and (= x      (round x))
2408              (inexact? (round x)))))
2409     (pass-if "-(2^53-1)"
2410       (let ((x (exact->inexact (- (1- (ash 1 53))))))
2411         (and (= x      (round x))
2412              (inexact? (round x)))))))
2413
2414 ;;;
2415 ;;; exact->inexact
2416 ;;;
2417
2418 (with-test-prefix "exact->inexact"
2419
2420   ;; Test "(exact->inexact n)", expect "want".
2421   ;; "i" is a index, for diagnostic purposes.
2422   (define (try-i i n want)
2423     (with-test-prefix (list i n want)
2424       (with-test-prefix "pos"
2425         (let ((got (exact->inexact n)))
2426           (pass-if "inexact?" (inexact? got))
2427           (pass-if (list "=" got) (= want got))))
2428       (set! n    (- n))
2429       (set! want (- want))
2430       (with-test-prefix "neg"
2431         (let ((got (exact->inexact n)))
2432           (pass-if "inexact?" (inexact? got))
2433           (pass-if (list "=" got) (= want got))))))
2434
2435   (with-test-prefix "2^i, no round"
2436     (do ((i    0   (1+ i))
2437          (n    1   (* 2 n))
2438          (want 1.0 (* 2.0 want)))
2439         ((> i 100))
2440       (try-i i n want)))
2441
2442   (with-test-prefix "2^i+1, no round"
2443     (do ((i    1   (1+ i))
2444          (n    3   (1- (* 2 n)))
2445          (want 3.0 (- (* 2.0 want) 1.0)))
2446         ((>= i dbl-mant-dig))
2447       (try-i i n want)))
2448
2449   (with-test-prefix "(2^i+1)*2^100, no round"
2450     (do ((i    1   (1+ i))
2451          (n    3   (1- (* 2 n)))
2452          (want 3.0 (- (* 2.0 want) 1.0)))
2453         ((>= i dbl-mant-dig))
2454       (try-i i (ash n 100) (ash-flo want 100))))
2455
2456   ;; bit pattern: 1111....11100.00
2457   ;;              <-mantdig-><-i->
2458   ;;
2459   (with-test-prefix "mantdig ones then zeros, no rounding"
2460     (do ((i    0  (1+ i))
2461          (n    (- (ash     1   dbl-mant-dig) 1)   (* 2 n))
2462          (want (- (ash-flo 1.0 dbl-mant-dig) 1.0) (* 2.0 want)))
2463         ((> i 100))
2464       (try-i i n want)))
2465
2466   ;; bit pattern: 1111....111011..1
2467   ;;              <-mantdig-> <-i->
2468   ;; This sort of value was incorrectly rounded upwards in Guile 1.6.4 when
2469   ;; i >= 11 (that's when the total is 65 or more bits).
2470   ;;
2471   (with-test-prefix "mantdig ones then 011..11, round down"
2472     (do ((i    0  (1+ i))
2473          (n    (- (ash     1   (+ 1 dbl-mant-dig)) 2)   (+ 1 (* 2 n)))
2474          (want (- (ash-flo 1.0 (+ 1 dbl-mant-dig)) 2.0) (* 2.0 want)))
2475         ((> i 100))
2476       (try-i i n want)))
2477
2478   ;; bit pattern: 1111....111100..001
2479   ;;              <-mantdig-> <--i->
2480   ;;
2481   (with-test-prefix "mantdig ones then 100..001, round up"
2482     (do ((i    0  (1+ i))
2483          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)  (1- (* 2 n)))
2484          (want    (ash-flo 1.0 (+ 2 dbl-mant-dig))     (* 2.0 want)))
2485         ((> i 100))
2486       (try-i i n want)))
2487
2488   ;; bit pattern: 1000....000100..001
2489   ;;              <-mantdig-> <--i->
2490   ;;
2491   (with-test-prefix "2^mantdig then 100..001, round up"
2492     (do ((i    0  (1+ i))
2493          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)   (1- (* 2 n)))
2494          (want (+ (ash-flo 1.0 (+ 2 dbl-mant-dig)) 4.0) (* 2.0 want)))
2495         ((> i 100))
2496       (try-i i n want))))
2497
2498 ;;;
2499 ;;; floor
2500 ;;;
2501
2502 ;;;
2503 ;;; ceiling
2504 ;;;
2505
2506 ;;;
2507 ;;; expt
2508 ;;;
2509
2510 (with-test-prefix "expt"
2511   (pass-if "(= 1 (expt 0 0))" (= 1 (expt 0 0)))
2512   (pass-if "(= 1 (expt 0 0.0))" (= 1 (expt 0 0.0)))
2513   (pass-if "(= 1 (expt 0.0 0))" (= 1 (expt 0.0 0)))
2514   (pass-if "(= 1 (expt 0.0 0.0))" (= 1 (expt 0.0 0.0))))
2515
2516 ;;;
2517 ;;; asinh
2518 ;;;
2519
2520 (with-test-prefix "asinh"
2521   (pass-if (= 0 (asinh 0))))
2522
2523 ;;;
2524 ;;; acosh
2525 ;;;
2526
2527 (with-test-prefix "acosh"
2528   (pass-if (= 0 (acosh 1))))
2529
2530 ;;;
2531 ;;; atanh
2532 ;;;
2533
2534 (with-test-prefix "atanh"
2535   (pass-if (= 0 (atanh 0))))
2536
2537 ;;;
2538 ;;; make-rectangular
2539 ;;;
2540
2541 ;;;
2542 ;;; make-polar
2543 ;;;
2544
2545 (with-test-prefix "make-polar"
2546   (define pi 3.14159265358979323846)
2547   (define (almost= x y)
2548     (> 0.01 (magnitude (- x y))))
2549
2550   (pass-if (= 0 (make-polar 0 0)))
2551   (pass-if (= 0 (make-polar 0 123.456)))
2552   (pass-if (= 1 (make-polar 1 0)))
2553   (pass-if (= -1 (make-polar -1 0)))
2554
2555   (pass-if (almost= 0+i (make-polar 1 (* 0.5 pi))))
2556   (pass-if (almost= -1  (make-polar 1 (* 1.0 pi))))
2557   (pass-if (almost= 0-i (make-polar 1 (* 1.5 pi))))
2558   (pass-if (almost= 1   (make-polar 1 (* 2.0 pi)))))
2559
2560 ;;;
2561 ;;; real-part
2562 ;;;
2563
2564 ;;;
2565 ;;; imag-part
2566 ;;;
2567
2568 ;;;
2569 ;;; magnitude
2570 ;;;
2571
2572 (with-test-prefix "magnitude"
2573   (pass-if (= 0 (magnitude 0)))
2574   (pass-if (= 1 (magnitude 1)))
2575   (pass-if (= 1 (magnitude -1)))
2576   (pass-if (= 1 (magnitude 0+i)))
2577   (pass-if (= 1 (magnitude 0-i)))
2578   (pass-if (= 5 (magnitude 3+4i)))
2579   (pass-if (= 5 (magnitude 3-4i)))
2580   (pass-if (= 5 (magnitude -3+4i)))
2581   (pass-if (= 5 (magnitude -3-4i))))
2582
2583 ;;;
2584 ;;; angle
2585 ;;;
2586
2587 (with-test-prefix "angle"
2588   (define pi 3.14159265358979323846)
2589   (define (almost= x y)
2590     (> 0.01 (magnitude (- x y))))
2591
2592   (pass-if "inum +ve"   (=        0 (angle 1)))
2593   (pass-if "inum -ve"   (almost= pi (angle -1)))
2594
2595   (pass-if "bignum +ve" (=        0 (angle (1+ fixnum-max))))
2596   (pass-if "bignum -ve" (almost= pi (angle (1- fixnum-min))))
2597
2598   (pass-if "flonum +ve" (=        0 (angle 1.5)))
2599   (pass-if "flonum -ve" (almost= pi (angle -1.5))))
2600
2601 ;;;
2602 ;;; inexact->exact
2603 ;;;
2604
2605 (with-test-prefix "inexact->exact"
2606
2607   (pass-if-exception "+inf" exception:out-of-range
2608     (inexact->exact +inf.0))
2609
2610   (pass-if-exception "-inf" exception:out-of-range
2611     (inexact->exact -inf.0))
2612
2613   (pass-if-exception "nan" exception:out-of-range
2614     (inexact->exact +nan.0))
2615
2616   (with-test-prefix "2.0**i to exact and back"
2617     (do ((i 0   (1+ i))
2618          (n 1.0 (* 2.0 n)))
2619         ((> i 100))
2620       (pass-if (list i n)
2621         (= n (inexact->exact (exact->inexact n)))))))
2622
2623 ;;;
2624 ;;; integer-expt
2625 ;;;
2626
2627 (with-test-prefix "integer-expt"
2628
2629   (pass-if-exception "2^+inf" exception:wrong-type-arg
2630     (integer-expt 2 +inf.0))
2631   (pass-if-exception "2^-inf" exception:wrong-type-arg
2632     (integer-expt 2 -inf.0))
2633   (pass-if-exception "2^nan" exception:wrong-type-arg
2634     (integer-expt 2 +nan.0)))
2635
2636 ;;;
2637 ;;; integer-length
2638 ;;;
2639
2640 (with-test-prefix "integer-length"
2641
2642   (with-test-prefix "-2^i, ...11100..00"
2643     (do ((n -1 (ash n 1))
2644          (i 0  (1+ i)))
2645         ((> i 256))
2646       (pass-if (list n "expect" i)
2647         (= i (integer-length n)))))
2648
2649   (with-test-prefix "-2^i+1 ...11100..01"
2650     (do ((n -3 (logxor 3 (ash n 1)))
2651          (i 2  (1+ i)))
2652         ((> i 256))
2653       (pass-if n
2654         (= i (integer-length n)))))
2655
2656   (with-test-prefix "-2^i-1 ...111011..11"
2657     (do ((n -2 (1+ (ash n 1)))
2658          (i 1  (1+ i)))
2659         ((> i 256))
2660       (pass-if n
2661         (= i (integer-length n))))))
2662
2663 ;;;
2664 ;;; logbit?
2665 ;;;
2666
2667 (with-test-prefix "logbit?"
2668   (pass-if (eq? #f (logbit?  0 0)))
2669   (pass-if (eq? #f (logbit?  1 0)))
2670   (pass-if (eq? #f (logbit? 31 0)))
2671   (pass-if (eq? #f (logbit? 32 0)))
2672   (pass-if (eq? #f (logbit? 33 0)))
2673   (pass-if (eq? #f (logbit? 63 0)))
2674   (pass-if (eq? #f (logbit? 64 0)))
2675   (pass-if (eq? #f (logbit? 65 0)))
2676
2677   ;; prior to guile 1.6.5, testing bit 32, 64 etc of value 1 would wrap
2678   ;; around and return #t where it ought to be #f
2679   (pass-if (eq? #t (logbit?  0 1)))
2680   (pass-if (eq? #f (logbit?  1 1)))
2681   (pass-if (eq? #f (logbit? 31 1)))
2682   (pass-if (eq? #f (logbit? 32 1)))
2683   (pass-if (eq? #f (logbit? 33 1)))
2684   (pass-if (eq? #f (logbit? 63 1)))
2685   (pass-if (eq? #f (logbit? 64 1)))
2686   (pass-if (eq? #f (logbit? 65 1)))
2687   (pass-if (eq? #f (logbit? 128 1)))
2688
2689   (pass-if (eq? #t (logbit?  0 -1)))
2690   (pass-if (eq? #t (logbit?  1 -1)))
2691   (pass-if (eq? #t (logbit? 31 -1)))
2692   (pass-if (eq? #t (logbit? 32 -1)))
2693   (pass-if (eq? #t (logbit? 33 -1)))
2694   (pass-if (eq? #t (logbit? 63 -1)))
2695   (pass-if (eq? #t (logbit? 64 -1)))
2696   (pass-if (eq? #t (logbit? 65 -1))))
2697
2698 ;;;
2699 ;;; logcount
2700 ;;;
2701
2702 (with-test-prefix "logcount"
2703
2704   (with-test-prefix "-2^i, meaning ...11100..00"
2705     (do ((n -1 (ash n 1))
2706          (i 0  (1+ i)))
2707         ((> i 256))
2708       (pass-if n
2709         (= i (logcount n)))))
2710
2711   (with-test-prefix "2^i"
2712     (do ((n 1 (ash n 1))
2713          (i 0  (1+ i)))
2714         ((> i 256))
2715       (pass-if n
2716         (= 1 (logcount n)))))
2717
2718   (with-test-prefix "2^i-1"
2719     (do ((n 0 (1+ (ash n 1)))
2720          (i 0  (1+ i)))
2721         ((> i 256))
2722       (pass-if n
2723         (= i (logcount n))))))
2724
2725 ;;;
2726 ;;; lognot
2727 ;;;
2728
2729 (with-test-prefix "lognot"
2730   (pass-if (= -1 (lognot 0)))
2731   (pass-if (= 0  (lognot -1)))
2732   (pass-if (= -2 (lognot 1)))
2733   (pass-if (= 1  (lognot -2)))
2734
2735   (pass-if (= #x-100000000000000000000000000000000
2736               (lognot #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
2737   (pass-if (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
2738               (lognot #x-100000000000000000000000000000000))))