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 ;;;
1042 ;;; string->number
1043 ;;;
1044
1045 (with-test-prefix "string->number"
1046
1047   (pass-if "string->number"
1048     (documented? string->number))
1049
1050   (pass-if "non number strings"
1051     (for-each (lambda (x) (if (string->number x) (throw 'fail)))
1052               '("" "q" "1q" "6+7iq" "8+9q" "10+11" "13+" "18@19q" "20@q" "23@"
1053                 "+25iq" "26i" "-q" "-iq" "i" "5#.0" "8/" "10#11" ".#" "."
1054                 "#o.2" "3.4q" "15.16e17q" "18.19e+q" ".q" ".17#18" "10q" "#b2"
1055                 "#b3" "#b4" "#b5" "#b6" "#b7" "#b8" "#b9" "#ba" "#bb" "#bc"
1056                 "#bd" "#be" "#bf" "#q" "#b#b1" "#o#o1" "#d#d1" "#x#x1" "#e#e1"
1057                 "#i#i1" "12@12+0i"))
1058     #t)
1059
1060   (pass-if "valid number strings"
1061     (for-each (lambda (couple)
1062                 (apply
1063                  (lambda (x y)
1064                    (let ((xx (string->number x)))
1065                      (if (or (eq? xx #f) (not (eqv? xx y)))
1066                          (begin
1067                            (pk x y)
1068                            (throw 'fail)))))
1069                  couple))
1070               `(;; Radix:
1071                 ("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
1072                 ("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
1073                 ("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
1074                 ("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
1075                 ("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
1076                 ("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
1077                 ("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
1078                 ("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
1079                 ("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
1080                 ("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
1081                 ("#b1010" 10)
1082                 ("#o12345670" 2739128)
1083                 ("#d1234567890" 1234567890)
1084                 ("#x1234567890abcdef" 1311768467294899695)
1085                 ;; Exactness:
1086                 ("#e1" 1) ("#e1.2" 12/10)
1087                 ("#i1.1" 1.1) ("#i1" 1.0)
1088                 ;; Integers:
1089                 ("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1))
1090                 ("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
1091                 ("#b#i100" 4.0)
1092                 ;; Fractions:
1093                 ("1/1" 1) ("1/2" 1/2) ("-1/2" -1/2) ("1#/1" 10.0)
1094                 ("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 9/10) ("#e10/1#" 1)
1095                 ("#i6/8" 0.75) ("#i1/1" 1.0)
1096                 ;; Decimal numbers:
1097                 ;; * <uinteger 10> <suffix>
1098                 ("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
1099                 ("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
1100                 ("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
1101                 ;; * . <digit 10>+ #* <suffix>
1102                 (".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
1103                 (".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
1104                 ;; * <digit 10>+ . <digit 10>* #* <suffix>
1105                 ("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
1106                 ("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
1107                 ("3.1#e0" 3.1)
1108                 ;; * <digit 10>+ #+ . #* <suffix>
1109                 ("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
1110                 ;; Complex:
1111                 ("1@0" 1.0) ("1@+0" 1.0) ("1@-0" 1.0)
1112                 ("2+3i" ,(+ 2 (* 3 +i))) ("4-5i" ,(- 4 (* 5 +i)))
1113                 ("1+i" 1+1i) ("1-i" 1-1i) ("+1i" 0+1i) ("-1i" 0-1i)
1114                 ("+i" +1i) ("-i" -1i)))
1115     #t)
1116
1117   (pass-if-exception "exponent too big"
1118     exception:out-of-range
1119     (string->number "12.13e141414")))
1120
1121 ;;;
1122 ;;; number?
1123 ;;;
1124
1125 (with-test-prefix "number?"
1126   (pass-if (documented? number?))
1127   (pass-if (number? 0))
1128   (pass-if (number? 7))
1129   (pass-if (number? -7))
1130   (pass-if (number? 1.3))
1131   (pass-if (number? (+ 1 fixnum-max)))
1132   (pass-if (number? (- 1 fixnum-min)))
1133   (pass-if (number? 3+4i))
1134   (pass-if (not (number? #\a)))
1135   (pass-if (not (number? "a")))
1136   (pass-if (not (number? (make-vector 0))))
1137   (pass-if (not (number? (cons 1 2))))
1138   (pass-if (not (number? #t)))
1139   (pass-if (not (number? (lambda () #t))))
1140   (pass-if (not (number? (current-input-port)))))
1141
1142 ;;;
1143 ;;; complex?
1144 ;;;
1145
1146 (with-test-prefix "complex?"
1147   (pass-if (documented? complex?))
1148   (pass-if (complex? 0))
1149   (pass-if (complex? 7))
1150   (pass-if (complex? -7))
1151   (pass-if (complex? (+ 1 fixnum-max)))
1152   (pass-if (complex? (- 1 fixnum-min)))
1153   (pass-if (complex? 1.3))
1154   (pass-if (complex? 3+4i))
1155   (pass-if (not (complex? #\a)))
1156   (pass-if (not (complex? "a")))
1157   (pass-if (not (complex? (make-vector 0))))
1158   (pass-if (not (complex? (cons 1 2))))
1159   (pass-if (not (complex? #t)))
1160   (pass-if (not (complex? (lambda () #t))))
1161   (pass-if (not (complex? (current-input-port)))))
1162
1163 ;;;
1164 ;;; real?
1165 ;;;
1166
1167 (with-test-prefix "real?"
1168   (pass-if (documented? real?))
1169   (pass-if (real? 0))
1170   (pass-if (real? 7))
1171   (pass-if (real? -7))
1172   (pass-if (real? (+ 1 fixnum-max)))
1173   (pass-if (real? (- 1 fixnum-min)))
1174   (pass-if (real? 1.3))
1175   (pass-if (not (real? 3+4i)))
1176   (pass-if (not (real? #\a)))
1177   (pass-if (not (real? "a")))
1178   (pass-if (not (real? (make-vector 0))))
1179   (pass-if (not (real? (cons 1 2))))
1180   (pass-if (not (real? #t)))
1181   (pass-if (not (real? (lambda () #t))))
1182   (pass-if (not (real? (current-input-port)))))
1183
1184 ;;;
1185 ;;; rational? (same as real? right now)
1186 ;;;
1187
1188 (with-test-prefix "rational?"
1189   (pass-if (documented? rational?))
1190   (pass-if (rational? 0))
1191   (pass-if (rational? 7))
1192   (pass-if (rational? -7))
1193   (pass-if (rational? (+ 1 fixnum-max)))
1194   (pass-if (rational? (- 1 fixnum-min)))
1195   (pass-if (rational? 1.3))
1196   (pass-if (not (rational? 3+4i)))
1197   (pass-if (not (rational? #\a)))
1198   (pass-if (not (rational? "a")))
1199   (pass-if (not (rational? (make-vector 0))))
1200   (pass-if (not (rational? (cons 1 2))))
1201   (pass-if (not (rational? #t)))
1202   (pass-if (not (rational? (lambda () #t))))
1203   (pass-if (not (rational? (current-input-port)))))
1204
1205 ;;;
1206 ;;; integer?
1207 ;;;
1208
1209 (with-test-prefix "integer?"
1210   (pass-if (documented? integer?))
1211   (pass-if (integer? 0))
1212   (pass-if (integer? 7))
1213   (pass-if (integer? -7))
1214   (pass-if (integer? (+ 1 fixnum-max)))
1215   (pass-if (integer? (- 1 fixnum-min)))
1216   (pass-if (and (= 3+0i (round 3+0i)) (integer? 3+0i)))
1217   (pass-if (and (= 1.0 (round 1.0)) (integer? 1.0)))
1218   (pass-if (not (integer? 1.3)))
1219   (pass-if (not (integer? 3+4i)))
1220   (pass-if (not (integer? #\a)))
1221   (pass-if (not (integer? "a")))
1222   (pass-if (not (integer? (make-vector 0))))
1223   (pass-if (not (integer? (cons 1 2))))
1224   (pass-if (not (integer? #t)))
1225   (pass-if (not (integer? (lambda () #t))))
1226   (pass-if (not (integer? (current-input-port)))))
1227
1228 ;;;
1229 ;;; inexact?
1230 ;;;
1231
1232 (with-test-prefix "inexact?"
1233   (pass-if (documented? inexact?))
1234   (pass-if (not (inexact? 0)))
1235   (pass-if (not (inexact? 7)))
1236   (pass-if (not (inexact? -7)))
1237   (pass-if (not (inexact? (+ 1 fixnum-max))))
1238   (pass-if (not (inexact? (- 1 fixnum-min))))
1239   (pass-if (inexact? 1.3))
1240   (pass-if (inexact? 3.1+4.2i))
1241   (pass-if-exception "char"
1242                      exception:wrong-type-arg
1243                      (not (inexact? #\a)))
1244   (pass-if-exception "string"
1245                      exception:wrong-type-arg
1246                      (not (inexact? "a")))
1247   (pass-if-exception "vector"
1248                      exception:wrong-type-arg
1249                      (not (inexact? (make-vector 0))))
1250   (pass-if-exception "cons"
1251                      exception:wrong-type-arg
1252                      (not (inexact? (cons 1 2))))
1253   (pass-if-exception "bool"
1254                      exception:wrong-type-arg
1255                      (not (inexact? #t)))
1256   (pass-if-exception "procedure"
1257                      exception:wrong-type-arg
1258                      (not (inexact? (lambda () #t))))
1259   (pass-if-exception "port"
1260                      exception:wrong-type-arg
1261                      (not (inexact? (current-input-port)))))
1262
1263 ;;;
1264 ;;; equal?
1265 ;;;
1266
1267 (with-test-prefix "equal?"
1268   (pass-if (documented? equal?))
1269   (pass-if (equal? 0 0))
1270   (pass-if (equal? 7 7))
1271   (pass-if (equal? -7 -7))
1272   (pass-if (equal? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1273   (pass-if (equal? (- fixnum-min 1) (- fixnum-min 1)))
1274   (pass-if (not (equal? 0 1)))
1275   (pass-if (not (equal? fixnum-max (+ 1 fixnum-max))))
1276   (pass-if (not (equal? (+ 1 fixnum-max) fixnum-max)))
1277   (pass-if (not (equal? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1278   (pass-if (not (equal? fixnum-min (- fixnum-min 1))))
1279   (pass-if (not (equal? (- fixnum-min 1) fixnum-min)))
1280   (pass-if (not (equal? (- fixnum-min 1) (- fixnum-min 2))))
1281   (pass-if (not (equal? (+ fixnum-max 1) (- fixnum-min 1))))
1282
1283   (pass-if (not (equal? (ash 1 256) +inf.0)))
1284   (pass-if (not (equal? +inf.0 (ash 1 256))))
1285   (pass-if (not (equal? (ash 1 256) -inf.0)))
1286   (pass-if (not (equal? -inf.0 (ash 1 256))))
1287
1288   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1289   ;; sure we've avoided that
1290   (pass-if (not (equal? (ash 1 1024) +inf.0)))
1291   (pass-if (not (equal? +inf.0 (ash 1 1024))))
1292   (pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
1293   (pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
1294
1295   (pass-if (not (equal? +nan.0 +nan.0)))
1296   (pass-if (not (equal? 0 +nan.0)))
1297   (pass-if (not (equal? +nan.0 0)))
1298   (pass-if (not (equal? 1 +nan.0)))
1299   (pass-if (not (equal? +nan.0 1)))
1300   (pass-if (not (equal? -1 +nan.0)))
1301   (pass-if (not (equal? +nan.0 -1)))
1302
1303   (pass-if (not (equal? (ash 1 256) +nan.0)))
1304   (pass-if (not (equal? +nan.0 (ash 1 256))))
1305   (pass-if (not (equal? (- (ash 1 256)) +nan.0)))
1306   (pass-if (not (equal? +nan.0 (- (ash 1 256)))))
1307
1308   (pass-if (not (equal? (ash 1 8192) +nan.0)))
1309   (pass-if (not (equal? +nan.0 (ash 1 8192))))
1310   (pass-if (not (equal? (- (ash 1 8192)) +nan.0)))
1311   (pass-if (not (equal? +nan.0 (- (ash 1 8192)))))
1312
1313   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1314   ;; sure we've avoided that
1315   (pass-if (not (equal? (ash 3 1023) +nan.0)))
1316   (pass-if (not (equal? +nan.0 (ash 3 1023)))))
1317
1318 ;;;
1319 ;;; =
1320 ;;;
1321
1322 (with-test-prefix "="
1323   (expect-fail (documented? =))
1324   (pass-if (= 0 0))
1325   (pass-if (= 7 7))
1326   (pass-if (= -7 -7))
1327   (pass-if (= (+ 1 fixnum-max) (+ 1 fixnum-max)))
1328   (pass-if (= (- fixnum-min 1) (- fixnum-min 1)))
1329   (pass-if (not (= 0 1)))
1330   (pass-if (not (= fixnum-max (+ 1 fixnum-max))))
1331   (pass-if (not (= (+ 1 fixnum-max) fixnum-max)))
1332   (pass-if (not (= (+ 1 fixnum-max) (+ 2 fixnum-max))))
1333   (pass-if (not (= fixnum-min (- fixnum-min 1))))
1334   (pass-if (not (= (- fixnum-min 1) fixnum-min)))
1335   (pass-if (not (= (- fixnum-min 1) (- fixnum-min 2))))
1336   (pass-if (not (= (+ fixnum-max 1) (- fixnum-min 1))))
1337
1338   (pass-if (not (= (ash 1 256) +inf.0)))
1339   (pass-if (not (= +inf.0 (ash 1 256))))
1340   (pass-if (not (= (ash 1 256) -inf.0)))
1341   (pass-if (not (= -inf.0 (ash 1 256))))
1342
1343   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1344   ;; sure we've avoided that
1345   (pass-if (not (= (ash 1 1024) +inf.0)))
1346   (pass-if (not (= +inf.0 (ash 1 1024))))
1347   (pass-if (not (= (- (ash 1 1024)) -inf.0)))
1348   (pass-if (not (= -inf.0 (- (ash 1 1024)))))
1349
1350   (pass-if (not (= +nan.0 +nan.0)))
1351   (pass-if (not (= 0 +nan.0)))
1352   (pass-if (not (= +nan.0 0)))
1353   (pass-if (not (= 1 +nan.0)))
1354   (pass-if (not (= +nan.0 1)))
1355   (pass-if (not (= -1 +nan.0)))
1356   (pass-if (not (= +nan.0 -1)))
1357
1358   (pass-if (not (= (ash 1 256) +nan.0)))
1359   (pass-if (not (= +nan.0 (ash 1 256))))
1360   (pass-if (not (= (- (ash 1 256)) +nan.0)))
1361   (pass-if (not (= +nan.0 (- (ash 1 256)))))
1362
1363   (pass-if (not (= (ash 1 8192) +nan.0)))
1364   (pass-if (not (= +nan.0 (ash 1 8192))))
1365   (pass-if (not (= (- (ash 1 8192)) +nan.0)))
1366   (pass-if (not (= +nan.0 (- (ash 1 8192)))))
1367
1368   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1369   ;; sure we've avoided that
1370   (pass-if (not (= (ash 3 1023) +nan.0)))
1371   (pass-if (not (= +nan.0 (ash 3 1023))))
1372
1373   (pass-if (= 1/2 0.5))
1374   (pass-if (not (= 1/3 0.333333333333333333333333333333333)))
1375   (pass-if (not (= 2/3 0.5)))
1376   (pass-if (not (= 0.5 (+ 1/2 (/ 1 (ash 1 1000))))))
1377
1378   (pass-if (= 1/2 0.5+0i))
1379   (pass-if (not (= 0.333333333333333333333333333333333 1/3)))
1380   (pass-if (not (= 2/3 0.5+0i)))
1381   (pass-if (not (= 1/2 0+0.5i)))
1382
1383   (pass-if (= 0.5 1/2))
1384   (pass-if (not (= 0.5 2/3)))
1385   (pass-if (not (= (+ 1/2 (/ 1 (ash 1 1000))) 0.5)))
1386
1387   (pass-if (= 0.5+0i 1/2))
1388   (pass-if (not (= 0.5+0i 2/3)))
1389   (pass-if (not (= 0+0.5i 1/2))))
1390
1391 ;;;
1392 ;;; <
1393 ;;;
1394
1395 (with-test-prefix "<"
1396
1397   (expect-fail "documented?"
1398     (documented? <))
1399
1400   (with-test-prefix "(< 0 n)"
1401
1402     (pass-if "n = 0"
1403       (not (< 0 0)))
1404
1405     (pass-if "n = 0.0"
1406       (not (< 0 0.0)))
1407
1408     (pass-if "n = 1"
1409       (< 0 1))
1410
1411     (pass-if "n = 1.0"
1412       (< 0 1.0))
1413
1414     (pass-if "n = -1"
1415       (not (< 0 -1)))
1416
1417     (pass-if "n = -1.0"
1418       (not (< 0 -1.0)))
1419
1420     (pass-if "n = fixnum-max"
1421       (< 0 fixnum-max))
1422
1423     (pass-if "n = fixnum-max + 1"
1424       (< 0 (+ fixnum-max 1)))
1425
1426     (pass-if "n = fixnum-min"
1427       (not (< 0 fixnum-min)))
1428
1429     (pass-if "n = fixnum-min - 1"
1430       (not (< 0 (- fixnum-min 1)))))
1431
1432   (with-test-prefix "(< 0.0 n)"
1433
1434     (pass-if "n = 0"
1435       (not (< 0.0 0)))
1436
1437     (pass-if "n = 0.0"
1438       (not (< 0.0 0.0)))
1439
1440     (pass-if "n = 1"
1441       (< 0.0 1))
1442
1443     (pass-if "n = 1.0"
1444       (< 0.0 1.0))
1445
1446     (pass-if "n = -1"
1447       (not (< 0.0 -1)))
1448
1449     (pass-if "n = -1.0"
1450       (not (< 0.0 -1.0)))
1451
1452     (pass-if "n = fixnum-max"
1453       (< 0.0 fixnum-max))
1454
1455     (pass-if "n = fixnum-max + 1"
1456       (< 0.0 (+ fixnum-max 1)))
1457
1458     (pass-if "n = fixnum-min"
1459       (not (< 0.0 fixnum-min)))
1460
1461     (pass-if "n = fixnum-min - 1"
1462       (not (< 0.0 (- fixnum-min 1)))))
1463
1464   (with-test-prefix "(< 1 n)"
1465
1466     (pass-if "n = 0"
1467       (not (< 1 0)))
1468
1469     (pass-if "n = 0.0"
1470       (not (< 1 0.0)))
1471
1472     (pass-if "n = 1"
1473       (not (< 1 1)))
1474
1475     (pass-if "n = 1.0"
1476       (not (< 1 1.0)))
1477
1478     (pass-if "n = -1"
1479       (not (< 1 -1)))
1480
1481     (pass-if "n = -1.0"
1482       (not (< 1 -1.0)))
1483
1484     (pass-if "n = fixnum-max"
1485       (< 1 fixnum-max))
1486
1487     (pass-if "n = fixnum-max + 1"
1488       (< 1 (+ fixnum-max 1)))
1489
1490     (pass-if "n = fixnum-min"
1491       (not (< 1 fixnum-min)))
1492
1493     (pass-if "n = fixnum-min - 1"
1494       (not (< 1 (- fixnum-min 1)))))
1495
1496   (with-test-prefix "(< 1.0 n)"
1497
1498     (pass-if "n = 0"
1499       (not (< 1.0 0)))
1500
1501     (pass-if "n = 0.0"
1502       (not (< 1.0 0.0)))
1503
1504     (pass-if "n = 1"
1505       (not (< 1.0 1)))
1506
1507     (pass-if "n = 1.0"
1508       (not (< 1.0 1.0)))
1509
1510     (pass-if "n = -1"
1511       (not (< 1.0 -1)))
1512
1513     (pass-if "n = -1.0"
1514       (not (< 1.0 -1.0)))
1515
1516     (pass-if "n = fixnum-max"
1517       (< 1.0 fixnum-max))
1518
1519     (pass-if "n = fixnum-max + 1"
1520       (< 1.0 (+ fixnum-max 1)))
1521
1522     (pass-if "n = fixnum-min"
1523       (not (< 1.0 fixnum-min)))
1524
1525     (pass-if "n = fixnum-min - 1"
1526       (not (< 1.0 (- fixnum-min 1)))))
1527
1528   (with-test-prefix "(< -1 n)"
1529
1530     (pass-if "n = 0"
1531       (< -1 0))
1532
1533     (pass-if "n = 0.0"
1534       (< -1 0.0))
1535
1536     (pass-if "n = 1"
1537       (< -1 1))
1538
1539     (pass-if "n = 1.0"
1540       (< -1 1.0))
1541
1542     (pass-if "n = -1"
1543       (not (< -1 -1)))
1544
1545     (pass-if "n = -1.0"
1546       (not (< -1 -1.0)))
1547
1548     (pass-if "n = fixnum-max"
1549       (< -1 fixnum-max))
1550
1551     (pass-if "n = fixnum-max + 1"
1552       (< -1 (+ fixnum-max 1)))
1553
1554     (pass-if "n = fixnum-min"
1555       (not (< -1 fixnum-min)))
1556
1557     (pass-if "n = fixnum-min - 1"
1558       (not (< -1 (- fixnum-min 1)))))
1559
1560   (with-test-prefix "(< -1.0 n)"
1561
1562     (pass-if "n = 0"
1563       (< -1.0 0))
1564
1565     (pass-if "n = 0.0"
1566       (< -1.0 0.0))
1567
1568     (pass-if "n = 1"
1569       (< -1.0 1))
1570
1571     (pass-if "n = 1.0"
1572       (< -1.0 1.0))
1573
1574     (pass-if "n = -1"
1575       (not (< -1.0 -1)))
1576
1577     (pass-if "n = -1.0"
1578       (not (< -1.0 -1.0)))
1579
1580     (pass-if "n = fixnum-max"
1581       (< -1.0 fixnum-max))
1582
1583     (pass-if "n = fixnum-max + 1"
1584       (< -1.0 (+ fixnum-max 1)))
1585
1586     (pass-if "n = fixnum-min"
1587       (not (< -1.0 fixnum-min)))
1588
1589     (pass-if "n = fixnum-min - 1"
1590       (not (< -1.0 (- fixnum-min 1)))))
1591
1592   (with-test-prefix "(< fixnum-max n)"
1593
1594     (pass-if "n = 0"
1595       (not (< fixnum-max 0)))
1596
1597     (pass-if "n = 0.0"
1598       (not (< fixnum-max 0.0)))
1599
1600     (pass-if "n = 1"
1601       (not (< fixnum-max 1)))
1602
1603     (pass-if "n = 1.0"
1604       (not (< fixnum-max 1.0)))
1605
1606     (pass-if "n = -1"
1607       (not (< fixnum-max -1)))
1608
1609     (pass-if "n = -1.0"
1610       (not (< fixnum-max -1.0)))
1611
1612     (pass-if "n = fixnum-max"
1613       (not (< fixnum-max fixnum-max)))
1614
1615     (pass-if "n = fixnum-max + 1"
1616       (< fixnum-max (+ fixnum-max 1)))
1617
1618     (pass-if "n = fixnum-min"
1619       (not (< fixnum-max fixnum-min)))
1620
1621     (pass-if "n = fixnum-min - 1"
1622       (not (< fixnum-max (- fixnum-min 1)))))
1623
1624   (with-test-prefix "(< (+ fixnum-max 1) n)"
1625
1626     (pass-if "n = 0"
1627       (not (< (+ fixnum-max 1) 0)))
1628
1629     (pass-if "n = 0.0"
1630       (not (< (+ fixnum-max 1) 0.0)))
1631
1632     (pass-if "n = 1"
1633       (not (< (+ fixnum-max 1) 1)))
1634
1635     (pass-if "n = 1.0"
1636       (not (< (+ fixnum-max 1) 1.0)))
1637
1638     (pass-if "n = -1"
1639       (not (< (+ fixnum-max 1) -1)))
1640
1641     (pass-if "n = -1.0"
1642       (not (< (+ fixnum-max 1) -1.0)))
1643
1644     (pass-if "n = fixnum-max"
1645       (not (< (+ fixnum-max 1) fixnum-max)))
1646
1647     (pass-if "n = fixnum-max + 1"
1648       (not (< (+ fixnum-max 1) (+ fixnum-max 1))))
1649
1650     (pass-if "n = fixnum-min"
1651       (not (< (+ fixnum-max 1) fixnum-min)))
1652
1653     (pass-if "n = fixnum-min - 1"
1654       (not (< (+ fixnum-max 1) (- fixnum-min 1)))))
1655
1656   (with-test-prefix "(< fixnum-min n)"
1657
1658     (pass-if "n = 0"
1659       (< fixnum-min 0))
1660
1661     (pass-if "n = 0.0"
1662       (< fixnum-min 0.0))
1663
1664     (pass-if "n = 1"
1665       (< fixnum-min 1))
1666
1667     (pass-if "n = 1.0"
1668       (< fixnum-min 1.0))
1669
1670     (pass-if "n = -1"
1671       (< fixnum-min -1))
1672
1673     (pass-if "n = -1.0"
1674       (< fixnum-min -1.0))
1675
1676     (pass-if "n = fixnum-max"
1677       (< fixnum-min fixnum-max))
1678
1679     (pass-if "n = fixnum-max + 1"
1680       (< fixnum-min (+ fixnum-max 1)))
1681
1682     (pass-if "n = fixnum-min"
1683       (not (< fixnum-min fixnum-min)))
1684
1685     (pass-if "n = fixnum-min - 1"
1686       (not (< fixnum-min (- fixnum-min 1)))))
1687
1688   (with-test-prefix "(< (- fixnum-min 1) n)"
1689
1690     (pass-if "n = 0"
1691       (< (- fixnum-min 1) 0))
1692
1693     (pass-if "n = 0.0"
1694       (< (- fixnum-min 1) 0.0))
1695
1696     (pass-if "n = 1"
1697       (< (- fixnum-min 1) 1))
1698
1699     (pass-if "n = 1.0"
1700       (< (- fixnum-min 1) 1.0))
1701
1702     (pass-if "n = -1"
1703       (< (- fixnum-min 1) -1))
1704
1705     (pass-if "n = -1.0"
1706       (< (- fixnum-min 1) -1.0))
1707
1708     (pass-if "n = fixnum-max"
1709       (< (- fixnum-min 1) fixnum-max))
1710
1711     (pass-if "n = fixnum-max + 1"
1712       (< (- fixnum-min 1) (+ fixnum-max 1)))
1713
1714     (pass-if "n = fixnum-min"
1715       (< (- fixnum-min 1) fixnum-min))
1716
1717     (pass-if "n = fixnum-min - 1"
1718       (not (< (- fixnum-min 1) (- fixnum-min 1)))))
1719
1720   (pass-if (< (ash 1 256) +inf.0))
1721   (pass-if (not (< +inf.0 (ash 1 256))))
1722   (pass-if (not (< (ash 1 256) -inf.0)))
1723   (pass-if (< -inf.0 (ash 1 256)))
1724
1725   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1726   ;; sure we've avoided that
1727   (pass-if (< (1- (ash 1 1024)) +inf.0))
1728   (pass-if (<     (ash 1 1024)  +inf.0))
1729   (pass-if (< (1+ (ash 1 1024)) +inf.0))
1730   (pass-if (not (< +inf.0 (1- (ash 1 1024)))))
1731   (pass-if (not (< +inf.0     (ash 1 1024))))
1732   (pass-if (not (< +inf.0 (1+ (ash 1 1024)))))
1733   (pass-if (< -inf.0 (- (1- (ash 1 1024)))))
1734   (pass-if (< -inf.0 (-     (ash 1 1024))))
1735   (pass-if (< -inf.0 (- (1+ (ash 1 1024)))))
1736   (pass-if (not (< (- (1- (ash 1 1024))) -inf.0)))
1737   (pass-if (not (< (-     (ash 1 1024))  -inf.0)))
1738   (pass-if (not (< (- (1+ (ash 1 1024))) -inf.0)))
1739
1740   (pass-if (not (< +nan.0 +nan.0)))
1741   (pass-if (not (< 0 +nan.0)))
1742   (pass-if (not (< +nan.0 0)))
1743   (pass-if (not (< 1 +nan.0)))
1744   (pass-if (not (< +nan.0 1)))
1745   (pass-if (not (< -1 +nan.0)))
1746   (pass-if (not (< +nan.0 -1)))
1747
1748   (pass-if (not (< (ash 1 256) +nan.0)))
1749   (pass-if (not (< +nan.0 (ash 1 256))))
1750   (pass-if (not (< (- (ash 1 256)) +nan.0)))
1751   (pass-if (not (< +nan.0 (- (ash 1 256)))))
1752
1753   (pass-if (not (< (ash 1 8192) +nan.0)))
1754   (pass-if (not (< +nan.0 (ash 1 8192))))
1755   (pass-if (not (< (- (ash 1 8192)) +nan.0)))
1756   (pass-if (not (< +nan.0 (- (ash 1 8192)))))
1757
1758   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1759   ;; sure we've avoided that
1760   (pass-if (not (< (ash 3 1023) +nan.0)))
1761   (pass-if (not (< (1+ (ash 3 1023)) +nan.0)))
1762   (pass-if (not (< (1- (ash 3 1023)) +nan.0)))
1763   (pass-if (not (< +nan.0 (ash 3 1023))))
1764   (pass-if (not (< +nan.0 (1+ (ash 3 1023)))))
1765   (pass-if (not (< +nan.0 (1- (ash 3 1023)))))
1766
1767   (with-test-prefix "inum/frac"
1768     (pass-if (< 2 9/4))
1769     (pass-if (< -2 9/4))
1770     (pass-if (< -2 7/4))
1771     (pass-if (< -2 -7/4))
1772     (pass-if (eq? #f (< 2 7/4)))
1773     (pass-if (eq? #f (< 2 -7/4)))
1774     (pass-if (eq? #f (< 2 -9/4)))
1775     (pass-if (eq? #f (< -2 -9/4))))
1776
1777   (with-test-prefix "bignum/frac"
1778     (let ((x (ash 1 2048)))
1779       (pass-if (< x (* 4/3 x)))
1780       (pass-if (< (- x) (* 4/3 x)))
1781       (pass-if (< (- x) (* 2/3 x)))
1782       (pass-if (< (- x) (* -2/3 x)))
1783       (pass-if (eq? #f (< x (* 2/3 x))))
1784       (pass-if (eq? #f (< x (* -2/3 x))))
1785       (pass-if (eq? #f (< x (* -4/3 x))))
1786       (pass-if (eq? #f (< (- x) (* -4/3 x))))))
1787
1788   (with-test-prefix "flonum/frac"
1789     (pass-if (< 0.75 4/3))
1790     (pass-if (< -0.75 4/3))
1791     (pass-if (< -0.75 2/3))
1792     (pass-if (< -0.75 -2/3))
1793     (pass-if (eq? #f (< 0.75 2/3)))
1794     (pass-if (eq? #f (< 0.75 -2/3)))
1795     (pass-if (eq? #f (< 0.75 -4/3)))
1796     (pass-if (eq? #f (< -0.75 -4/3)))
1797
1798     (pass-if (< -inf.0 4/3))
1799     (pass-if (< -inf.0 -4/3))
1800     (pass-if (eq? #f (< +inf.0 4/3)))
1801     (pass-if (eq? #f (< +inf.0 -4/3)))
1802
1803     (pass-if (eq? #f (< +nan.0 4/3)))
1804     (pass-if (eq? #f (< +nan.0 -4/3))))
1805
1806   (with-test-prefix "frac/inum"
1807     (pass-if (< 7/4 2))
1808     (pass-if (< -7/4 2))
1809     (pass-if (< -9/4 2))
1810     (pass-if (< -9/4 -2))
1811     (pass-if (eq? #f (< 9/4 2)))
1812     (pass-if (eq? #f (< 9/4 -2)))
1813     (pass-if (eq? #f (< 7/4 -2)))
1814     (pass-if (eq? #f (< -7/4 -2))))
1815
1816   (with-test-prefix "frac/bignum"
1817     (let ((x (ash 1 2048)))
1818       (pass-if (< (* 2/3 x) x))
1819       (pass-if (< (* -2/3 x) x))
1820       (pass-if (< (* -4/3 x) x))
1821       (pass-if (< (* -4/3 x) (- x)))
1822       (pass-if (eq? #f (< (* 4/3 x) x)))
1823       (pass-if (eq? #f (< (* 4/3 x) (- x))))
1824       (pass-if (eq? #f (< (* 2/3 x) (- x))))
1825       (pass-if (eq? #f (< (* -2/3 x) (- x))))))
1826
1827   (with-test-prefix "frac/flonum"
1828     (pass-if (< 2/3 0.75))
1829     (pass-if (< -2/3 0.75))
1830     (pass-if (< -4/3 0.75))
1831     (pass-if (< -4/3 -0.75))
1832     (pass-if (eq? #f (< 4/3 0.75)))
1833     (pass-if (eq? #f (< 4/3 -0.75)))
1834     (pass-if (eq? #f (< 2/3 -0.75)))
1835     (pass-if (eq? #f (< -2/3 -0.75)))
1836
1837     (pass-if (< 4/3 +inf.0))
1838     (pass-if (< -4/3 +inf.0))
1839     (pass-if (eq? #f (< 4/3 -inf.0)))
1840     (pass-if (eq? #f (< -4/3 -inf.0)))
1841
1842     (pass-if (eq? #f (< 4/3 +nan.0)))
1843     (pass-if (eq? #f (< -4/3 +nan.0))))
1844
1845   (with-test-prefix "frac/frac"
1846     (pass-if (< 2/3 6/7))
1847     (pass-if (< -2/3 6/7))
1848     (pass-if (< -4/3 6/7))
1849     (pass-if (< -4/3 -6/7))
1850     (pass-if (eq? #f (< 4/3 6/7)))
1851     (pass-if (eq? #f (< 4/3 -6/7)))
1852     (pass-if (eq? #f (< 2/3 -6/7)))
1853     (pass-if (eq? #f (< -2/3 -6/7)))))
1854
1855 ;;;
1856 ;;; >
1857 ;;;
1858
1859 ;; currently not tested -- implementation is trivial
1860 ;; (> x y) is implemented as (< y x)
1861 ;; FIXME: tests should probably be added in case we change implementation.
1862
1863 ;;;
1864 ;;; <=
1865 ;;;
1866
1867 ;; currently not tested -- implementation is trivial
1868 ;; (<= x y) is implemented as (not (< y x))
1869 ;; FIXME: tests should probably be added in case we change implementation.
1870
1871 ;;;
1872 ;;; >=
1873 ;;;
1874
1875 ;; currently not tested -- implementation is trivial
1876 ;; (>= x y) is implemented as (not (< x y))
1877 ;; FIXME: tests should probably be added in case we change implementation.
1878
1879 ;;;
1880 ;;; zero?
1881 ;;;
1882
1883 (with-test-prefix "zero?"
1884   (expect-fail (documented? zero?))
1885   (pass-if (zero? 0))
1886   (pass-if (not (zero? 7)))
1887   (pass-if (not (zero? -7)))
1888   (pass-if (not (zero? (+ 1 fixnum-max))))
1889   (pass-if (not (zero? (- 1 fixnum-min))))
1890   (pass-if (not (zero? 1.3)))
1891   (pass-if (not (zero? 3.1+4.2i))))
1892
1893 ;;;
1894 ;;; positive?
1895 ;;;
1896
1897 (with-test-prefix "positive?"
1898   (expect-fail (documented? positive?))
1899   (pass-if (positive? 1))
1900   (pass-if (positive? (+ fixnum-max 1)))
1901   (pass-if (positive? 1.3))
1902   (pass-if (not (positive? 0)))
1903   (pass-if (not (positive? -1)))
1904   (pass-if (not (positive? (- fixnum-min 1))))
1905   (pass-if (not (positive? -1.3))))
1906
1907 ;;;
1908 ;;; negative?
1909 ;;;
1910
1911 (with-test-prefix "negative?"
1912   (expect-fail (documented? negative?))
1913   (pass-if (not (negative? 1)))
1914   (pass-if (not (negative? (+ fixnum-max 1))))
1915   (pass-if (not (negative? 1.3)))
1916   (pass-if (not (negative? 0)))
1917   (pass-if (negative? -1))
1918   (pass-if (negative? (- fixnum-min 1)))
1919   (pass-if (negative? -1.3)))
1920
1921 ;;;
1922 ;;; max
1923 ;;;
1924
1925 (with-test-prefix "max"
1926   (pass-if-exception "no args" exception:wrong-num-args
1927     (max))
1928
1929   (pass-if-exception "one complex" exception:wrong-type-arg
1930     (max 1+i))
1931
1932   (pass-if-exception "inum/complex" exception:wrong-type-arg
1933     (max 123 1+i))
1934   (pass-if-exception "big/complex" exception:wrong-type-arg
1935     (max 9999999999999999999999999999999999999999 1+i))
1936   (pass-if-exception "real/complex" exception:wrong-type-arg
1937     (max 123.0 1+i))
1938   (pass-if-exception "frac/complex" exception:wrong-type-arg
1939     (max 123/456 1+i))
1940
1941   (pass-if-exception "complex/inum" exception:wrong-type-arg
1942     (max 1+i 123))
1943   (pass-if-exception "complex/big" exception:wrong-type-arg
1944     (max 1+i 9999999999999999999999999999999999999999))
1945   (pass-if-exception "complex/real" exception:wrong-type-arg
1946     (max 1+i 123.0))
1947   (pass-if-exception "complex/frac" exception:wrong-type-arg
1948     (max 1+i 123/456))
1949
1950   (let ((big*2 (* fixnum-max 2))
1951         (big*3 (* fixnum-max 3))
1952         (big*4 (* fixnum-max 4))
1953         (big*5 (* fixnum-max 5)))
1954
1955     (with-test-prefix "inum / frac"
1956       (pass-if (= 3 (max 3 5/2)))
1957       (pass-if (= 5/2 (max 2 5/2))))
1958
1959     (with-test-prefix "frac / inum"
1960       (pass-if (= 3 (max 5/2 3)))
1961       (pass-if (= 5/2 (max 5/2 2))))
1962
1963     (with-test-prefix "inum / real"
1964       (pass-if (nan? (max 123 +nan.0))))
1965
1966     (with-test-prefix "real / inum"
1967       (pass-if (nan? (max +nan.0 123))))
1968
1969     (with-test-prefix "big / frac"
1970       (pass-if (= big*2 (max big*2 5/2)))
1971       (pass-if (= 5/2 (max (- big*2) 5/2))))
1972
1973     (with-test-prefix "frac / big"
1974       (pass-if (= big*2 (max 5/2 big*2)))
1975       (pass-if (= 5/2 (max 5/2 (- big*2)))))
1976
1977     (with-test-prefix "big / real"
1978       (pass-if (nan? (max big*5 +nan.0)))
1979       (pass-if (= big*5  (max big*5 -inf.0)))
1980       (pass-if (= +inf.0 (max big*5 +inf.0)))
1981       (pass-if (= 1.0 (max (- big*5) 1.0)))
1982       (pass-if (inexact? (max big*5 1.0)))
1983       (pass-if (= (exact->inexact big*5) (max big*5 1.0))))
1984
1985     (with-test-prefix "real / big"
1986       (pass-if (nan? (max +nan.0 big*5)))
1987       (pass-if (= +inf.0 (max +inf.0 big*5)))
1988       (pass-if (= big*5  (max -inf.0 big*5)))
1989       (pass-if (= 1.0 (max 1.0 (- big*5))))
1990       (pass-if (inexact? (max 1.0 big*5)))
1991       (pass-if (= (exact->inexact big*5) (max 1.0 big*5))))
1992
1993     (with-test-prefix "frac / frac"
1994       (pass-if (= 2/3 (max 1/2 2/3)))
1995       (pass-if (= 2/3 (max 2/3 1/2)))
1996       (pass-if (= -1/2 (max -1/2 -2/3)))
1997       (pass-if (= -1/2 (max -2/3 -1/2))))
1998
1999     (with-test-prefix "real / real"
2000       (pass-if (nan? (max 123.0 +nan.0)))
2001       (pass-if (nan? (max +nan.0 123.0)))
2002       (pass-if (nan? (max +nan.0 +nan.0)))
2003       (pass-if (= 456.0 (max 123.0 456.0)))
2004       (pass-if (= 456.0 (max 456.0 123.0)))))
2005
2006   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2007   ;; sure we've avoided that
2008   (for-each (lambda (b)
2009               (pass-if (list b +inf.0)
2010                 (= +inf.0 (max b +inf.0)))
2011               (pass-if (list +inf.0 b)
2012                 (= +inf.0 (max b +inf.0)))
2013               (pass-if (list b -inf.0)
2014                 (= (exact->inexact b) (max b -inf.0)))
2015               (pass-if (list -inf.0 b)
2016                 (= (exact->inexact b) (max b -inf.0))))
2017             (list (1- (ash 1 1024))
2018                   (ash 1 1024)
2019                   (1+ (ash 1 1024))
2020                   (- (1- (ash 1 1024)))
2021                   (- (ash 1 1024))
2022                   (- (1+ (ash 1 1024)))))
2023
2024   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2025   ;; sure we've avoided that
2026   (pass-if (nan? (max (ash 1 2048) +nan.0)))
2027   (pass-if (nan? (max +nan.0 (ash 1 2048)))))
2028
2029 ;;;
2030 ;;; min
2031 ;;;
2032
2033 ;; FIXME: unfinished...
2034
2035 (with-test-prefix "min"
2036   (pass-if-exception "no args" exception:wrong-num-args
2037     (min))
2038
2039   (pass-if-exception "one complex" exception:wrong-type-arg
2040     (min 1+i))
2041
2042   (pass-if-exception "inum/complex" exception:wrong-type-arg
2043     (min 123 1+i))
2044   (pass-if-exception "big/complex" exception:wrong-type-arg
2045     (min 9999999999999999999999999999999999999999 1+i))
2046   (pass-if-exception "real/complex" exception:wrong-type-arg
2047     (min 123.0 1+i))
2048   (pass-if-exception "frac/complex" exception:wrong-type-arg
2049     (min 123/456 1+i))
2050
2051   (pass-if-exception "complex/inum" exception:wrong-type-arg
2052     (min 1+i 123))
2053   (pass-if-exception "complex/big" exception:wrong-type-arg
2054     (min 1+i 9999999999999999999999999999999999999999))
2055   (pass-if-exception "complex/real" exception:wrong-type-arg
2056     (min 1+i 123.0))
2057   (pass-if-exception "complex/frac" exception:wrong-type-arg
2058     (min 1+i 123/456))
2059
2060   (let ((big*2 (* fixnum-max 2))
2061         (big*3 (* fixnum-max 3))
2062         (big*4 (* fixnum-max 4))
2063         (big*5 (* fixnum-max 5)))
2064
2065     (expect-fail (documented? max))
2066     (pass-if (= 1 (min 7 3 1 5)))
2067     (pass-if (= 1 (min 1 7 3 5)))
2068     (pass-if (= 1 (min 7 3 5 1)))
2069     (pass-if (= -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
2070     (pass-if (= -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
2071     (pass-if (= -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
2072     (pass-if (= big*2 (min big*3 big*5 big*2 big*4)))
2073     (pass-if (= big*2 (min big*2 big*3 big*5 big*4)))
2074     (pass-if (= big*2 (min big*3 big*5 big*4 big*2)))
2075     (pass-if
2076         (= (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
2077     (pass-if
2078         (= (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
2079     (pass-if
2080         (= (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
2081
2082     (with-test-prefix "inum / frac"
2083       (pass-if (= 5/2 (min 3 5/2)))
2084       (pass-if (= 2   (min 2 5/2))))
2085
2086     (with-test-prefix "frac / inum"
2087       (pass-if (= 5/2 (min 5/2 3)))
2088       (pass-if (= 2   (min 5/2 2))))
2089
2090     (with-test-prefix "inum / real"
2091       (pass-if (nan? (min 123 +nan.0))))
2092
2093     (with-test-prefix "real / inum"
2094       (pass-if (nan? (min +nan.0 123))))
2095
2096     (with-test-prefix "big / frac"
2097       (pass-if (= 5/2       (min big*2 5/2)))
2098       (pass-if (= (- big*2) (min (- big*2) 5/2))))
2099
2100     (with-test-prefix "frac / big"
2101       (pass-if (= 5/2       (min 5/2 big*2)))
2102       (pass-if (= (- big*2) (min 5/2 (- big*2)))))
2103
2104     (with-test-prefix "big / real"
2105       (pass-if (nan? (min big*5 +nan.0)))
2106       (pass-if (= big*5  (min big*5  +inf.0)))
2107       (pass-if (= -inf.0 (min big*5  -inf.0)))
2108       (pass-if (= 1.0 (min big*5 1.0)))
2109       (pass-if (inexact? (min (- big*5) 1.0)))
2110       (pass-if (= (exact->inexact (- big*5)) (min (- big*5) 1.0))))
2111
2112     (with-test-prefix "real / big"
2113       (pass-if (nan? (min +nan.0 big*5)))
2114       (pass-if (= big*5  (min +inf.0 big*5)))
2115       (pass-if (= -inf.0 (min -inf.0 big*5)))
2116       (pass-if (= 1.0 (min 1.0 big*5)))
2117       (pass-if (inexact? (min 1.0 (- big*5))))
2118       (pass-if (= (exact->inexact (- big*5)) (min 1.0 (- big*5)))))
2119
2120     (with-test-prefix "frac / frac"
2121       (pass-if (= 1/2 (min 1/2 2/3)))
2122       (pass-if (= 1/2 (min 2/3 1/2)))
2123       (pass-if (= -2/3 (min -1/2 -2/3)))
2124       (pass-if (= -2/3 (min -2/3 -1/2))))
2125
2126     (with-test-prefix "real / real"
2127       (pass-if (nan? (min 123.0 +nan.0)))
2128       (pass-if (nan? (min +nan.0 123.0)))
2129       (pass-if (nan? (min +nan.0 +nan.0)))
2130       (pass-if (= 123.0 (min 123.0 456.0)))
2131       (pass-if (= 123.0 (min 456.0 123.0)))))
2132
2133
2134   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2135   ;; sure we've avoided that
2136   (for-each (lambda (b)
2137               (pass-if (list b +inf.0)
2138                 (= (exact->inexact b) (min b +inf.0)))
2139               (pass-if (list +inf.0 b)
2140                 (= (exact->inexact b) (min b +inf.0)))
2141               (pass-if (list b -inf.0)
2142                 (= -inf.0 (min b -inf.0)))
2143               (pass-if (list -inf.0 b)
2144                 (= -inf.0 (min b -inf.0))))
2145             (list (1- (ash 1 1024))
2146                   (ash 1 1024)
2147                   (1+ (ash 1 1024))
2148                   (- (1- (ash 1 1024)))
2149                   (- (ash 1 1024))
2150                   (- (1+ (ash 1 1024)))))
2151
2152   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2153   ;; sure we've avoided that
2154   (pass-if (nan? (min (- (ash 1 2048)) (- +nan.0))))
2155   (pass-if (nan? (min (- +nan.0) (- (ash 1 2048))))))
2156
2157 ;;;
2158 ;;; +
2159 ;;;
2160
2161 (with-test-prefix "+"
2162
2163   (expect-fail "documented?"
2164     (documented? +))
2165
2166   (with-test-prefix "wrong type argument"
2167
2168     (pass-if-exception "1st argument string"
2169       exception:wrong-type-arg
2170       (+ "1" 2))
2171
2172     (pass-if-exception "2nd argument bool"
2173       exception:wrong-type-arg
2174       (+ 1 #f))))
2175 ;;;
2176 ;;; -
2177 ;;;
2178
2179 (with-test-prefix "-"
2180
2181   (pass-if "-inum - +bignum"
2182     (= #x-100000000000000000000000000000001
2183        (- -1 #x100000000000000000000000000000000)))
2184
2185   (pass-if "big - inum"
2186     (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
2187        (- #x100000000000000000000000000000000 1)))
2188
2189   (pass-if "big - -inum"
2190     (= #x100000000000000000000000000000001
2191        (- #x100000000000000000000000000000000 -1))))
2192
2193 ;;;
2194 ;;; *
2195 ;;;
2196
2197 (with-test-prefix "*"
2198
2199   (pass-if "complex * bignum"
2200     (let ((big (ash 1 90)))
2201       (= (make-rectangular big big)
2202          (* 1+1i big)))))
2203
2204 ;;;
2205 ;;; /
2206 ;;;
2207
2208 (with-test-prefix "/"
2209
2210   (expect-fail "documented?"
2211     (documented? /))
2212
2213   (with-test-prefix "division by zero"
2214
2215     (pass-if-exception "(/ 0)"
2216       exception:numerical-overflow
2217       (/ 0))
2218
2219     (pass-if "(/ 0.0)"
2220       (= +inf.0 (/ 0.0)))
2221
2222     (pass-if-exception "(/ 1 0)"
2223       exception:numerical-overflow
2224       (/ 1 0))
2225
2226     (pass-if "(/ 1 0.0)"
2227       (= +inf.0 (/ 1 0.0)))
2228
2229     (pass-if-exception "(/ bignum 0)"
2230       exception:numerical-overflow
2231       (/ (+ fixnum-max 1) 0))
2232
2233     (pass-if "(/ bignum 0.0)"
2234       (= +inf.0 (/ (+ fixnum-max 1) 0.0)))
2235
2236     (pass-if-exception "(/ 1.0 0)"
2237       exception:numerical-overflow
2238       (/ 1.0 0))
2239
2240     (pass-if "(/ 1.0 0.0)"
2241       (= +inf.0 (/ 1.0 0.0)))
2242
2243     (pass-if-exception "(/ +i 0)"
2244       exception:numerical-overflow
2245       (/ +i 0))
2246
2247     (pass-if "(/ +i 0.0)"
2248       (= +inf.0 (imag-part (/ +i 0.0)))))
2249
2250   (with-test-prefix "complex division"
2251
2252     (pass-if "(/ 3+4i)"
2253       (= (/ 3+4i) 0.12-0.16i))
2254
2255     (pass-if "(/ 4+3i)"
2256       (= (/ 4+3i) 0.16-0.12i))
2257
2258     (pass-if "(/ 25+125i 3+4i)"
2259       (= (/ 25+125i 3+4i) 23.0+11.0i))
2260
2261     (pass-if "(/ 25+125i 4+3i)"
2262       (= (/ 25+125i 4+3i) 19.0+17.0i))
2263
2264     (pass-if "(/ 25 3+4i)"
2265       (= (/ 25 3+4i) 3.0-4.0i))
2266
2267     (pass-if "(/ 25 4+3i)"
2268       (= (/ 25 4+3i) 4.0-3.0i))
2269
2270     (pass-if "(/ 1e200+1e200i)"
2271       (= (/ 1e200+1e200i) 5.0e-201-5.0e-201i))))
2272
2273 ;;;
2274 ;;; truncate
2275 ;;;
2276
2277 (with-test-prefix "truncate"
2278   (pass-if (=  1 (truncate  1.75)))
2279   (pass-if (=  1 (truncate  1.5)))
2280   (pass-if (=  1 (truncate  1.25)))
2281   (pass-if (=  0 (truncate  0.75)))
2282   (pass-if (=  0 (truncate  0.5)))
2283   (pass-if (=  0 (truncate  0.0)))
2284   (pass-if (=  0 (truncate -0.5)))
2285   (pass-if (= -1 (truncate -1.25)))
2286   (pass-if (= -1 (truncate -1.5))))
2287
2288 ;;;
2289 ;;; round
2290 ;;;
2291
2292 (with-test-prefix "round"
2293   (pass-if (=  2 (round  1.75)))
2294   (pass-if (=  2 (round  1.5)))
2295   (pass-if (=  1 (round  1.25)))
2296   (pass-if (=  1 (round  0.75)))
2297   (pass-if (=  0 (round  0.5)))
2298   (pass-if (=  0 (round  0.0)))
2299   (pass-if (=  0 (round -0.5)))
2300   (pass-if (= -1 (round -1.25)))
2301   (pass-if (= -2 (round -1.5))))
2302
2303 ;;;
2304 ;;; exact->inexact
2305 ;;;
2306
2307 (with-test-prefix "exact->inexact"
2308
2309   ;; Test "(exact->inexact n)", expect "want".
2310   ;; "i" is a index, for diagnostic purposes.
2311   (define (try-i i n want)
2312     (with-test-prefix (list i n want)
2313       (with-test-prefix "pos"
2314         (let ((got (exact->inexact n)))
2315           (pass-if "inexact?" (inexact? got))
2316           (pass-if (list "=" got) (= want got))))
2317       (set! n    (- n))
2318       (set! want (- want))
2319       (with-test-prefix "neg"
2320         (let ((got (exact->inexact n)))
2321           (pass-if "inexact?" (inexact? got))
2322           (pass-if (list "=" got) (= want got))))))
2323
2324   (with-test-prefix "2^i, no round"
2325     (do ((i    0   (1+ i))
2326          (n    1   (* 2 n))
2327          (want 1.0 (* 2.0 want)))
2328         ((> i 100))
2329       (try-i i n want)))
2330
2331   (with-test-prefix "2^i+1, no round"
2332     (do ((i    1   (1+ i))
2333          (n    3   (1- (* 2 n)))
2334          (want 3.0 (- (* 2.0 want) 1.0)))
2335         ((>= i dbl-mant-dig))
2336       (try-i i n want)))
2337
2338   (with-test-prefix "(2^i+1)*2^100, no round"
2339     (do ((i    1   (1+ i))
2340          (n    3   (1- (* 2 n)))
2341          (want 3.0 (- (* 2.0 want) 1.0)))
2342         ((>= i dbl-mant-dig))
2343       (try-i i (ash n 100) (ash-flo want 100))))
2344
2345   ;; bit pattern: 1111....11100.00
2346   ;;              <-mantdig-><-i->
2347   ;;
2348   (with-test-prefix "mantdig ones then zeros, no rounding"
2349     (do ((i    0  (1+ i))
2350          (n    (- (ash     1   dbl-mant-dig) 1)   (* 2 n))
2351          (want (- (ash-flo 1.0 dbl-mant-dig) 1.0) (* 2.0 want)))
2352         ((> i 100))
2353       (try-i i n want)))
2354
2355   ;; bit pattern: 1111....111011..1
2356   ;;              <-mantdig-> <-i->
2357   ;; This sort of value was incorrectly rounded upwards in Guile 1.6.4 when
2358   ;; i >= 11 (that's when the total is 65 or more bits).
2359   ;;
2360   (with-test-prefix "mantdig ones then 011..11, round down"
2361     (do ((i    0  (1+ i))
2362          (n    (- (ash     1   (+ 1 dbl-mant-dig)) 2)   (+ 1 (* 2 n)))
2363          (want (- (ash-flo 1.0 (+ 1 dbl-mant-dig)) 2.0) (* 2.0 want)))
2364         ((> i 100))
2365       (try-i i n want)))
2366
2367   ;; bit pattern: 1111....111100..001
2368   ;;              <-mantdig-> <--i->
2369   ;;
2370   (with-test-prefix "mantdig ones then 100..001, round up"
2371     (do ((i    0  (1+ i))
2372          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)  (1- (* 2 n)))
2373          (want    (ash-flo 1.0 (+ 2 dbl-mant-dig))     (* 2.0 want)))
2374         ((> i 100))
2375       (try-i i n want)))
2376
2377   ;; bit pattern: 1000....000100..001
2378   ;;              <-mantdig-> <--i->
2379   ;;
2380   (with-test-prefix "2^mantdig then 100..001, round up"
2381     (do ((i    0  (1+ i))
2382          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)   (1- (* 2 n)))
2383          (want (+ (ash-flo 1.0 (+ 2 dbl-mant-dig)) 4.0) (* 2.0 want)))
2384         ((> i 100))
2385       (try-i i n want))))
2386
2387 ;;;
2388 ;;; floor
2389 ;;;
2390
2391 ;;;
2392 ;;; ceiling
2393 ;;;
2394
2395 ;;;
2396 ;;; expt
2397 ;;;
2398
2399 (with-test-prefix "expt"
2400   (pass-if "(= 1 (expt 0 0))" (= 1 (expt 0 0)))
2401   (pass-if "(= 1 (expt 0 0.0))" (= 1 (expt 0 0.0)))
2402   (pass-if "(= 1 (expt 0.0 0))" (= 1 (expt 0.0 0)))
2403   (pass-if "(= 1 (expt 0.0 0.0))" (= 1 (expt 0.0 0.0))))
2404
2405 ;;;
2406 ;;; asinh
2407 ;;;
2408
2409 (with-test-prefix "asinh"
2410   (pass-if (= 0 (asinh 0))))
2411
2412 ;;;
2413 ;;; acosh
2414 ;;;
2415
2416 (with-test-prefix "acosh"
2417   (pass-if (= 0 (acosh 1))))
2418
2419 ;;;
2420 ;;; atanh
2421 ;;;
2422
2423 (with-test-prefix "atanh"
2424   (pass-if (= 0 (atanh 0))))
2425
2426 ;;;
2427 ;;; make-rectangular
2428 ;;;
2429
2430 ;;;
2431 ;;; make-polar
2432 ;;;
2433
2434 (with-test-prefix "make-polar"
2435   (define pi 3.14159265358979323846)
2436   (define (almost= x y)
2437     (> 0.01 (magnitude (- x y))))
2438
2439   (pass-if (= 0 (make-polar 0 0)))
2440   (pass-if (= 0 (make-polar 0 123.456)))
2441   (pass-if (= 1 (make-polar 1 0)))
2442   (pass-if (= -1 (make-polar -1 0)))
2443
2444   (pass-if (almost= 0+i (make-polar 1 (* 0.5 pi))))
2445   (pass-if (almost= -1  (make-polar 1 (* 1.0 pi))))
2446   (pass-if (almost= 0-i (make-polar 1 (* 1.5 pi))))
2447   (pass-if (almost= 1   (make-polar 1 (* 2.0 pi)))))
2448
2449 ;;;
2450 ;;; real-part
2451 ;;;
2452
2453 ;;;
2454 ;;; imag-part
2455 ;;;
2456
2457 ;;;
2458 ;;; magnitude
2459 ;;;
2460
2461 (with-test-prefix "magnitude"
2462   (pass-if (= 0 (magnitude 0)))
2463   (pass-if (= 1 (magnitude 1)))
2464   (pass-if (= 1 (magnitude -1)))
2465   (pass-if (= 1 (magnitude 0+i)))
2466   (pass-if (= 1 (magnitude 0-i)))
2467   (pass-if (= 5 (magnitude 3+4i)))
2468   (pass-if (= 5 (magnitude 3-4i)))
2469   (pass-if (= 5 (magnitude -3+4i)))
2470   (pass-if (= 5 (magnitude -3-4i))))
2471
2472 ;;;
2473 ;;; angle
2474 ;;;
2475
2476 (with-test-prefix "angle"
2477   (define pi 3.14159265358979323846)
2478   (define (almost= x y)
2479     (> 0.01 (magnitude (- x y))))
2480
2481   (pass-if "inum +ve"   (=        0 (angle 1)))
2482   (pass-if "inum -ve"   (almost= pi (angle -1)))
2483
2484   (pass-if "bignum +ve" (=        0 (angle (1+ fixnum-max))))
2485   (pass-if "bignum -ve" (almost= pi (angle (1- fixnum-min))))
2486
2487   (pass-if "flonum +ve" (=        0 (angle 1.5)))
2488   (pass-if "flonum -ve" (almost= pi (angle -1.5))))
2489
2490 ;;;
2491 ;;; inexact->exact
2492 ;;;
2493
2494 (with-test-prefix "inexact->exact"
2495
2496   (pass-if-exception "+inf" exception:out-of-range
2497     (inexact->exact +inf.0))
2498
2499   (pass-if-exception "-inf" exception:out-of-range
2500     (inexact->exact -inf.0))
2501
2502   (pass-if-exception "nan" exception:out-of-range
2503     (inexact->exact +nan.0))
2504
2505   (with-test-prefix "2.0**i to exact and back"
2506     (do ((i 0   (1+ i))
2507          (n 1.0 (* 2.0 n)))
2508         ((> i 100))
2509       (pass-if (list i n)
2510         (= n (inexact->exact (exact->inexact n)))))))
2511
2512 ;;;
2513 ;;; integer-length
2514 ;;;
2515
2516 (with-test-prefix "integer-length"
2517
2518   (with-test-prefix "-2^i, ...11100..00"
2519     (do ((n -1 (ash n 1))
2520          (i 0  (1+ i)))
2521         ((> i 256))
2522       (pass-if (list n "expect" i)
2523         (= i (integer-length n)))))
2524
2525   (with-test-prefix "-2^i+1 ...11100..01"
2526     (do ((n -3 (logxor 3 (ash n 1)))
2527          (i 2  (1+ i)))
2528         ((> i 256))
2529       (pass-if n
2530         (= i (integer-length n)))))
2531
2532   (with-test-prefix "-2^i-1 ...111011..11"
2533     (do ((n -2 (1+ (ash n 1)))
2534          (i 1  (1+ i)))
2535         ((> i 256))
2536       (pass-if n
2537         (= i (integer-length n))))))
2538
2539 ;;;
2540 ;;; logcount
2541 ;;;
2542
2543 (with-test-prefix "logcount"
2544
2545   (with-test-prefix "-2^i, meaning ...11100..00"
2546     (do ((n -1 (ash n 1))
2547          (i 0  (1+ i)))
2548         ((> i 256))
2549       (pass-if n
2550         (= i (logcount n)))))
2551
2552   (with-test-prefix "2^i"
2553     (do ((n 1 (ash n 1))
2554          (i 0  (1+ i)))
2555         ((> i 256))
2556       (pass-if n
2557         (= 1 (logcount n)))))
2558
2559   (with-test-prefix "2^i-1"
2560     (do ((n 0 (1+ (ash n 1)))
2561          (i 0  (1+ i)))
2562         ((> i 256))
2563       (pass-if n
2564         (= i (logcount n))))))
2565
2566 ;;;
2567 ;;; lognot
2568 ;;;
2569
2570 (with-test-prefix "lognot"
2571   (pass-if (= -1 (lognot 0)))
2572   (pass-if (= 0  (lognot -1)))
2573   (pass-if (= -2 (lognot 1)))
2574   (pass-if (= 1  (lognot -2)))
2575
2576   (pass-if (= #x-100000000000000000000000000000000
2577               (lognot #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
2578   (pass-if (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
2579               (lognot #x-100000000000000000000000000000000))))