test-suite/tests/numbers.test

   1 ;;;; numbers.test --- tests guile's numbers     -*- scheme -*-
   2 ;;;; Copyright (C) 2000, 2001, 2003, 2004, 2005, 2006, 2009 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 3 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 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 ;; `quotient' but rounded towards -infinity, like `modulo' or `ash' do
  68 ;; note only positive D supported (that's all that's currently required)
  69 (define-public (quotient-floor n d)
  70   (if (negative? n)
  71       (quotient (- n d -1) d)  ;; neg/pos
  72       (quotient n d)))         ;; pos/pos
  73
  74 ;; return true of X is in the range LO to HI, inclusive
  75 (define (within-range? lo hi x)
  76   (and (>= x (min lo hi))
  77        (<= x (max lo hi))))
  78
  79 ;; return true if GOT is within +/- 0.01 of GOT
  80 ;; for a complex number both real and imaginary parts must be in that range
  81 (define (eqv-loosely? want got)
  82   (and (within-range? (- (real-part want) 0.01)
  83                       (+ (real-part want) 0.01)
  84                       (real-part got))
  85        (within-range? (- (imag-part want) 0.01)
  86                       (+ (imag-part want) 0.01)
  87                       (imag-part got))))
  88
  89 ;; return true if OBJ is negative infinity
  90 (define (negative-infinity? obj)
  91   (and (real? obj)
  92        (negative? obj)
  93        (inf? obj)))
  94
  95 (define const-e    2.7182818284590452354)
  96 (define const-e^2  7.3890560989306502274)
  97 (define const-1/e  0.3678794411714423215)
  98
  99
 100 ;;;
 101 ;;; 1+
 102 ;;;
 103
 104 (with-test-prefix "1+"
 105
 106   (pass-if "documented?"
 107     (documented? 1+))
 108
 109   (pass-if (eqv? 1 (1+ 0)))
 110   (pass-if (eqv? 0 (1+ -1)))
 111   (pass-if (eqv? 101 (1+ 100)))
 112   (pass-if (eqv? -99 (1+ -100))))
 113
 114 ;;;
 115 ;;; 1-
 116 ;;;
 117
 118 (with-test-prefix "1-"
 119
 120   (pass-if "documented?"
 121     (documented? 1-))
 122
 123   (pass-if (eqv? -1 (1- 0)))
 124   (pass-if (eqv? 0 (1- 1)))
 125   (pass-if (eqv? 99 (1- 100)))
 126   (pass-if (eqv? -101 (1- -100))))
 127
 128 ;;;
 129 ;;; ash
 130 ;;;
 131
 132 (with-test-prefix "ash"
 133
 134   (pass-if "documented?"
 135     (documented? ash))
 136
 137   (pass-if (eqv? 0 (ash 0 0)))
 138   (pass-if (eqv? 0 (ash 0 1)))
 139   (pass-if (eqv? 0 (ash 0 1000)))
 140   (pass-if (eqv? 0 (ash 0 -1)))
 141   (pass-if (eqv? 0 (ash 0 -1000)))
 142
 143   (pass-if (eqv? 1 (ash 1 0)))
 144   (pass-if (eqv? 2 (ash 1 1)))
 145   (pass-if (eqv? 340282366920938463463374607431768211456 (ash 1 128)))
 146   (pass-if (eqv? 0 (ash 1 -1)))
 147   (pass-if (eqv? 0 (ash 1 -1000)))
 148
 149   (pass-if (eqv? -1 (ash -1 0)))
 150   (pass-if (eqv? -2 (ash -1 1)))
 151   (pass-if (eqv? -340282366920938463463374607431768211456 (ash -1 128)))
 152   (pass-if (eqv? -1 (ash -1 -1)))
 153   (pass-if (eqv? -1 (ash -1 -1000)))
 154
 155   (pass-if (eqv? -3 (ash -3 0)))
 156   (pass-if (eqv? -6 (ash -3 1)))
 157   (pass-if (eqv? -1020847100762815390390123822295304634368 (ash -3 128)))
 158   (pass-if (eqv? -2 (ash -3 -1)))
 159   (pass-if (eqv? -1 (ash -3 -1000)))
 160
 161   (pass-if (eqv? -6 (ash -23 -2)))
 162
 163   (pass-if (eqv? most-positive-fixnum       (ash most-positive-fixnum 0)))
 164   (pass-if (eqv? (* 2 most-positive-fixnum) (ash most-positive-fixnum 1)))
 165   (pass-if (eqv? (* 4 most-positive-fixnum) (ash most-positive-fixnum 2)))
 166   (pass-if
 167       (eqv? (* most-positive-fixnum 340282366920938463463374607431768211456)
 168             (ash most-positive-fixnum 128)))
 169   (pass-if (eqv? (quotient most-positive-fixnum 2)
 170                  (ash most-positive-fixnum -1)))
 171   (pass-if (eqv? 0 (ash most-positive-fixnum -1000)))
 172
 173   (let ((mpf4 (quotient most-positive-fixnum 4)))
 174     (pass-if (eqv? (* 2 mpf4) (ash mpf4 1)))
 175     (pass-if (eqv? (* 4 mpf4) (ash mpf4 2)))
 176     (pass-if (eqv? (* 8 mpf4) (ash mpf4 3))))
 177
 178   (pass-if (eqv? most-negative-fixnum       (ash most-negative-fixnum 0)))
 179   (pass-if (eqv? (* 2 most-negative-fixnum) (ash most-negative-fixnum 1)))
 180   (pass-if (eqv? (* 4 most-negative-fixnum) (ash most-negative-fixnum 2)))
 181   (pass-if
 182       (eqv? (* most-negative-fixnum 340282366920938463463374607431768211456)
 183             (ash most-negative-fixnum 128)))
 184   (pass-if (eqv? (quotient-floor most-negative-fixnum 2)
 185                  (ash most-negative-fixnum -1)))
 186   (pass-if (eqv? -1 (ash most-negative-fixnum -1000)))
 187
 188   (let ((mnf4 (quotient-floor most-negative-fixnum 4)))
 189     (pass-if (eqv? (* 2 mnf4) (ash mnf4 1)))
 190     (pass-if (eqv? (* 4 mnf4) (ash mnf4 2)))
 191     (pass-if (eqv? (* 8 mnf4) (ash mnf4 3)))))
 192
 193 ;;;
 194 ;;; exact?
 195 ;;;
 196
 197 (with-test-prefix "exact?"
 198
 199   (pass-if "documented?"
 200     (documented? exact?))
 201
 202   (with-test-prefix "integers"
 203
 204     (pass-if "0"
 205       (exact? 0))
 206
 207     (pass-if "fixnum-max"
 208       (exact? fixnum-max))
 209
 210     (pass-if "fixnum-max + 1"
 211       (exact? (+ fixnum-max 1)))
 212
 213     (pass-if "fixnum-min"
 214       (exact? fixnum-min))
 215
 216     (pass-if "fixnum-min - 1"
 217       (exact? (- fixnum-min 1))))
 218
 219   (with-test-prefix "reals"
 220
 221     ;; (FIXME: need better examples.)
 222
 223     (pass-if "sqrt (fixnum-max^2 - 1)"
 224       (eq? #f (exact? (sqrt (- (expt fixnum-max 2) 1)))))
 225
 226     (pass-if "sqrt ((fixnum-max+1)^2 - 1)"
 227       (eq? #f (exact? (sqrt (- (expt (+ fixnum-max 1) 2) 1)))))))
 228
 229 ;;;
 230 ;;; exp
 231 ;;;
 232
 233 (with-test-prefix "exp"
 234   (pass-if "documented?"
 235     (documented? exp))
 236
 237   (pass-if-exception "no args" exception:wrong-num-args
 238     (exp))
 239   (pass-if-exception "two args" exception:wrong-num-args
 240     (exp 123 456))
 241
 242   (pass-if (eqv? 0.0 (exp -inf.0)))
 243   (pass-if (eqv-loosely? 1.0 (exp 0)))
 244   (pass-if (eqv-loosely? 1.0 (exp 0.0)))
 245   (pass-if (eqv-loosely? const-e   (exp 1.0)))
 246   (pass-if (eqv-loosely? const-e^2 (exp 2.0)))
 247   (pass-if (eqv-loosely? const-1/e (exp -1)))
 248
 249   (pass-if "exp(pi*i) = -1"
 250     (eqv-loosely? -1.0 (exp 0+3.14159i)))
 251   (pass-if "exp(-pi*i) = -1"
 252     (eqv-loosely? -1.0 (exp 0-3.14159i)))
 253   (pass-if "exp(2*pi*i) = +1"
 254     (eqv-loosely? 1.0 (exp 0+6.28318i)))
 255
 256   (pass-if "exp(2-pi*i) = -e^2"
 257     (eqv-loosely? (- const-e^2) (exp 2.0-3.14159i))))
 258
 259 ;;;
 260 ;;; odd?
 261 ;;;
 262
 263 (with-test-prefix "odd?"
 264   (pass-if (documented? odd?))
 265   (pass-if (odd? 1))
 266   (pass-if (odd? -1))
 267   (pass-if (not (odd? 0)))
 268   (pass-if (not (odd? 2)))
 269   (pass-if (not (odd? -2)))
 270   (pass-if (odd? (+ (* 2 fixnum-max) 1)))
 271   (pass-if (not (odd? (* 2 fixnum-max))))
 272   (pass-if (odd? (- (* 2 fixnum-min) 1)))
 273   (pass-if (not (odd? (* 2 fixnum-min)))))
 274
 275 ;;;
 276 ;;; even?
 277 ;;;
 278
 279 (with-test-prefix "even?"
 280   (pass-if (documented? even?))
 281   (pass-if (even? 2))
 282   (pass-if (even? -2))
 283   (pass-if (even? 0))
 284   (pass-if (not (even? 1)))
 285   (pass-if (not (even? -1)))
 286   (pass-if (not (even? (+ (* 2 fixnum-max) 1))))
 287   (pass-if (even? (* 2 fixnum-max)))
 288   (pass-if (not (even? (- (* 2 fixnum-min) 1))))
 289   (pass-if (even? (* 2 fixnum-min))))
 290
 291 ;;;
 292 ;;; inf? and inf
 293 ;;;
 294
 295 (with-test-prefix "inf?"
 296   (pass-if (documented? inf?))
 297   (pass-if (inf? (inf)))
 298   ;; FIXME: what are the expected behaviors?
 299   ;; (pass-if (inf? (/ 1.0 0.0))
 300   ;; (pass-if (inf? (/ 1 0.0))
 301   (pass-if (not (inf? 0)))
 302   (pass-if (not (inf? 42.0)))
 303   (pass-if (not (inf? (+ fixnum-max 1))))
 304   (pass-if (not (inf? (- fixnum-min 1)))))
 305
 306 ;;;
 307 ;;; nan? and nan
 308 ;;;
 309
 310 (with-test-prefix "nan?"
 311   (pass-if (documented? nan?))
 312   (pass-if (nan? (nan)))
 313   ;; FIXME: other ways we should be able to generate NaN?
 314   (pass-if (not (nan? 0)))
 315   (pass-if (not (nan? 42.0)))
 316   (pass-if (not (nan? (+ fixnum-max 1))))
 317   (pass-if (not (nan? (- fixnum-min 1)))))
 318
 319 ;;;
 320 ;;; abs
 321 ;;;
 322
 323 (with-test-prefix "abs"
 324   (pass-if (documented? abs))
 325   (pass-if (zero? (abs 0)))
 326   (pass-if (= 1 (abs 1)))
 327   (pass-if (= 1 (abs -1)))
 328   (pass-if (= (+ fixnum-max 1) (abs (+ fixnum-max 1))))
 329   (pass-if (= (+ (- fixnum-min) 1) (abs (- fixnum-min 1))))
 330   (pass-if (= 0.0 (abs 0.0)))
 331   (pass-if (= 1.0 (abs 1.0)))
 332   (pass-if (= 1.0 (abs -1.0)))
 333   (pass-if (nan? (abs +nan.0)))
 334   (pass-if (= +inf.0 (abs +inf.0)))
 335   (pass-if (= +inf.0 (abs -inf.0))))
 336
 337 ;;;
 338 ;;; quotient
 339 ;;;
 340
 341 (with-test-prefix "quotient"
 342
 343   (expect-fail "documented?"
 344     (documented? quotient))
 345
 346   (with-test-prefix "0 / n"
 347
 348     (pass-if "n = 1"
 349       (eqv? 0 (quotient 0 1)))
 350
 351     (pass-if "n = -1"
 352       (eqv? 0 (quotient 0 -1)))
 353
 354     (pass-if "n = 2"
 355       (eqv? 0 (quotient 0 2)))
 356
 357     (pass-if "n = fixnum-max"
 358       (eqv? 0 (quotient 0 fixnum-max)))
 359
 360     (pass-if "n = fixnum-max + 1"
 361       (eqv? 0 (quotient 0 (+ fixnum-max 1))))
 362
 363     (pass-if "n = fixnum-min"
 364       (eqv? 0 (quotient 0 fixnum-min)))
 365
 366     (pass-if "n = fixnum-min - 1"
 367       (eqv? 0 (quotient 0 (- fixnum-min 1)))))
 368
 369   (with-test-prefix "1 / n"
 370
 371     (pass-if "n = 1"
 372       (eqv? 1 (quotient 1 1)))
 373
 374     (pass-if "n = -1"
 375       (eqv? -1 (quotient 1 -1)))
 376
 377     (pass-if "n = 2"
 378       (eqv? 0 (quotient 1 2)))
 379
 380     (pass-if "n = fixnum-max"
 381       (eqv? 0 (quotient 1 fixnum-max)))
 382
 383     (pass-if "n = fixnum-max + 1"
 384       (eqv? 0 (quotient 1 (+ fixnum-max 1))))
 385
 386     (pass-if "n = fixnum-min"
 387       (eqv? 0 (quotient 1 fixnum-min)))
 388
 389     (pass-if "n = fixnum-min - 1"
 390       (eqv? 0 (quotient 1 (- fixnum-min 1)))))
 391
 392   (with-test-prefix "-1 / n"
 393
 394     (pass-if "n = 1"
 395       (eqv? -1 (quotient -1 1)))
 396
 397     (pass-if "n = -1"
 398       (eqv? 1 (quotient -1 -1)))
 399
 400     (pass-if "n = 2"
 401       (eqv? 0 (quotient -1 2)))
 402
 403     (pass-if "n = fixnum-max"
 404       (eqv? 0 (quotient -1 fixnum-max)))
 405
 406     (pass-if "n = fixnum-max + 1"
 407       (eqv? 0 (quotient -1 (+ fixnum-max 1))))
 408
 409     (pass-if "n = fixnum-min"
 410       (eqv? 0 (quotient -1 fixnum-min)))
 411
 412     (pass-if "n = fixnum-min - 1"
 413       (eqv? 0 (quotient -1 (- fixnum-min 1)))))
 414
 415   (with-test-prefix "fixnum-max / n"
 416
 417     (pass-if "n = 1"
 418       (eqv? fixnum-max (quotient fixnum-max 1)))
 419
 420     (pass-if "n = -1"
 421       (eqv? (- fixnum-max) (quotient fixnum-max -1)))
 422
 423     (pass-if "n = 2"
 424       (eqv? fixnum-max (+ (* (quotient fixnum-max 2) 2) 1)))
 425
 426     (pass-if "n = fixnum-max"
 427       (eqv? 1 (quotient fixnum-max fixnum-max)))
 428
 429     (pass-if "n = fixnum-max + 1"
 430       (eqv? 0 (quotient fixnum-max (+ fixnum-max 1))))
 431
 432     (pass-if "n = fixnum-min"
 433       (eqv? 0 (quotient fixnum-max fixnum-min)))
 434
 435     (pass-if "n = fixnum-min - 1"
 436       (eqv? 0 (quotient fixnum-max (- fixnum-min 1)))))
 437
 438   (with-test-prefix "(fixnum-max + 1) / n"
 439
 440     (pass-if "n = 1"
 441       (eqv? (+ fixnum-max 1) (quotient (+ fixnum-max 1) 1)))
 442
 443     (pass-if "n = -1"
 444       (eqv? (- (+ fixnum-max 1)) (quotient (+ fixnum-max 1) -1)))
 445
 446     (pass-if "n = 2"
 447       (eqv? (+ fixnum-max 1) (* (quotient (+ fixnum-max 1) 2) 2)))
 448
 449     (pass-if "n = fixnum-max"
 450       (eqv? 1 (quotient (+ fixnum-max 1) fixnum-max)))
 451
 452     (pass-if "n = fixnum-max + 1"
 453       (eqv? 1 (quotient (+ fixnum-max 1) (+ fixnum-max 1))))
 454
 455     (pass-if "n = fixnum-min"
 456       (eqv? -1 (quotient (+ fixnum-max 1) fixnum-min)))
 457
 458     (pass-if "n = fixnum-min - 1"
 459       (eqv? 0 (quotient (+ fixnum-max 1) (- fixnum-min 1)))))
 460
 461   (with-test-prefix "fixnum-min / n"
 462
 463     (pass-if "n = 1"
 464       (eqv? fixnum-min (quotient fixnum-min 1)))
 465
 466     (pass-if "n = -1"
 467       (eqv? (- fixnum-min) (quotient fixnum-min -1)))
 468
 469     (pass-if "n = 2"
 470       (eqv? fixnum-min (* (quotient fixnum-min 2) 2)))
 471
 472     (pass-if "n = fixnum-max"
 473       (eqv? -1 (quotient fixnum-min fixnum-max)))
 474
 475     (pass-if "n = fixnum-max + 1"
 476       (eqv? -1 (quotient fixnum-min (+ fixnum-max 1))))
 477
 478     (pass-if "n = fixnum-min"
 479       (eqv? 1 (quotient fixnum-min fixnum-min)))
 480
 481     (pass-if "n = fixnum-min - 1"
 482       (eqv? 0 (quotient fixnum-min (- fixnum-min 1))))
 483
 484     (pass-if "n = - fixnum-min - 1"
 485       (eqv? -1 (quotient fixnum-min (1- (- fixnum-min)))))
 486
 487     ;; special case, normally inum/big is zero
 488     (pass-if "n = - fixnum-min"
 489       (eqv? -1 (quotient fixnum-min (- fixnum-min))))
 490
 491     (pass-if "n = - fixnum-min + 1"
 492       (eqv? 0 (quotient fixnum-min (1+ (- fixnum-min))))))
 493
 494   (with-test-prefix "(fixnum-min - 1) / n"
 495
 496     (pass-if "n = 1"
 497       (eqv? (- fixnum-min 1) (quotient (- fixnum-min 1) 1)))
 498
 499     (pass-if "n = -1"
 500       (eqv? (- (- fixnum-min 1)) (quotient (- fixnum-min 1) -1)))
 501
 502     (pass-if "n = 2"
 503       (eqv? fixnum-min (* (quotient (- fixnum-min 1) 2) 2)))
 504
 505     (pass-if "n = fixnum-max"
 506       (eqv? -1 (quotient (- fixnum-min 1) fixnum-max)))
 507
 508     (pass-if "n = fixnum-max + 1"
 509       (eqv? -1 (quotient (- fixnum-min 1) (+ fixnum-max 1))))
 510
 511     (pass-if "n = fixnum-min"
 512       (eqv? 1 (quotient (- fixnum-min 1) fixnum-min)))
 513
 514     (pass-if "n = fixnum-min - 1"
 515       (eqv? 1 (quotient (- fixnum-min 1) (- fixnum-min 1)))))
 516
 517   ;; Positive dividend and divisor
 518
 519   (pass-if "35 / 7"
 520     (eqv? 5 (quotient 35 7)))
 521
 522   ;; Negative dividend, positive divisor
 523
 524   (pass-if "-35 / 7"
 525     (eqv? -5 (quotient -35 7)))
 526
 527   ;; Positive dividend, negative divisor
 528
 529   (pass-if "35 / -7"
 530     (eqv? -5 (quotient 35 -7)))
 531
 532   ;; Negative dividend and divisor
 533
 534   (pass-if "-35 / -7"
 535     (eqv? 5 (quotient -35 -7)))
 536
 537   ;; Are numerical overflows detected correctly?
 538
 539   (with-test-prefix "division by zero"
 540
 541     (pass-if-exception "(quotient 1 0)"
 542       exception:numerical-overflow
 543       (quotient 1 0))
 544
 545     (pass-if-exception "(quotient bignum 0)"
 546       exception:numerical-overflow
 547       (quotient (+ fixnum-max 1) 0)))
 548
 549   ;; Are wrong type arguments detected correctly?
 550
 551   )
 552
 553 ;;;
 554 ;;; remainder
 555 ;;;
 556
 557 (with-test-prefix "remainder"
 558
 559   (expect-fail "documented?"
 560     (documented? remainder))
 561
 562   (with-test-prefix "0 / n"
 563
 564     (pass-if "n = 1"
 565       (eqv? 0 (remainder 0 1)))
 566
 567     (pass-if "n = -1"
 568       (eqv? 0 (remainder 0 -1)))
 569
 570     (pass-if "n = fixnum-max"
 571       (eqv? 0 (remainder 0 fixnum-max)))
 572
 573     (pass-if "n = fixnum-max + 1"
 574       (eqv? 0 (remainder 0 (+ fixnum-max 1))))
 575
 576     (pass-if "n = fixnum-min"
 577       (eqv? 0 (remainder 0 fixnum-min)))
 578
 579     (pass-if "n = fixnum-min - 1"
 580       (eqv? 0 (remainder 0 (- fixnum-min 1)))))
 581
 582   (with-test-prefix "1 / n"
 583
 584     (pass-if "n = 1"
 585       (eqv? 0 (remainder 1 1)))
 586
 587     (pass-if "n = -1"
 588       (eqv? 0 (remainder 1 -1)))
 589
 590     (pass-if "n = fixnum-max"
 591       (eqv? 1 (remainder 1 fixnum-max)))
 592
 593     (pass-if "n = fixnum-max + 1"
 594       (eqv? 1 (remainder 1 (+ fixnum-max 1))))
 595
 596     (pass-if "n = fixnum-min"
 597       (eqv? 1 (remainder 1 fixnum-min)))
 598
 599     (pass-if "n = fixnum-min - 1"
 600       (eqv? 1 (remainder 1 (- fixnum-min 1)))))
 601
 602   (with-test-prefix "-1 / n"
 603
 604     (pass-if "n = 1"
 605       (eqv? 0 (remainder -1 1)))
 606
 607     (pass-if "n = -1"
 608       (eqv? 0 (remainder -1 -1)))
 609
 610     (pass-if "n = fixnum-max"
 611       (eqv? -1 (remainder -1 fixnum-max)))
 612
 613     (pass-if "n = fixnum-max + 1"
 614       (eqv? -1 (remainder -1 (+ fixnum-max 1))))
 615
 616     (pass-if "n = fixnum-min"
 617       (eqv? -1 (remainder -1 fixnum-min)))
 618
 619     (pass-if "n = fixnum-min - 1"
 620       (eqv? -1 (remainder -1 (- fixnum-min 1)))))
 621
 622   (with-test-prefix "fixnum-max / n"
 623
 624     (pass-if "n = 1"
 625       (eqv? 0 (remainder fixnum-max 1)))
 626
 627     (pass-if "n = -1"
 628       (eqv? 0 (remainder fixnum-max -1)))
 629
 630     (pass-if "n = fixnum-max"
 631       (eqv? 0 (remainder fixnum-max fixnum-max)))
 632
 633     (pass-if "n = fixnum-max + 1"
 634       (eqv? fixnum-max (remainder fixnum-max (+ fixnum-max 1))))
 635
 636     (pass-if "n = fixnum-min"
 637       (eqv? fixnum-max (remainder fixnum-max fixnum-min)))
 638
 639     (pass-if "n = fixnum-min - 1"
 640       (eqv? fixnum-max (remainder fixnum-max (- fixnum-min 1)))))
 641
 642   (with-test-prefix "(fixnum-max + 1) / n"
 643
 644     (pass-if "n = 1"
 645       (eqv? 0 (remainder (+ fixnum-max 1) 1)))
 646
 647     (pass-if "n = -1"
 648       (eqv? 0 (remainder (+ fixnum-max 1) -1)))
 649
 650     (pass-if "n = fixnum-max"
 651       (eqv? 1 (remainder (+ fixnum-max 1) fixnum-max)))
 652
 653     (pass-if "n = fixnum-max + 1"
 654       (eqv? 0 (remainder (+ fixnum-max 1) (+ fixnum-max 1))))
 655
 656     (pass-if "n = fixnum-min"
 657       (eqv? 0 (remainder (+ fixnum-max 1) fixnum-min)))
 658
 659     (pass-if "n = fixnum-min - 1"
 660       (eqv? (+ fixnum-max 1) (remainder (+ fixnum-max 1) (- fixnum-min 1)))))
 661
 662   (with-test-prefix "fixnum-min / n"
 663
 664     (pass-if "n = 1"
 665       (eqv? 0 (remainder fixnum-min 1)))
 666
 667     (pass-if "n = -1"
 668       (eqv? 0 (remainder fixnum-min -1)))
 669
 670     (pass-if "n = fixnum-max"
 671       (eqv? -1 (remainder fixnum-min fixnum-max)))
 672
 673     (pass-if "n = fixnum-max + 1"
 674       (eqv? 0 (remainder fixnum-min (+ fixnum-max 1))))
 675
 676     (pass-if "n = fixnum-min"
 677       (eqv? 0 (remainder fixnum-min fixnum-min)))
 678
 679     (pass-if "n = fixnum-min - 1"
 680       (eqv? fixnum-min (remainder fixnum-min (- fixnum-min 1))))
 681
 682     (pass-if "n = - fixnum-min - 1"
 683       (eqv? -1 (remainder fixnum-min (1- (- fixnum-min)))))
 684
 685     ;; special case, normally inum%big is the inum
 686     (pass-if "n = - fixnum-min"
 687       (eqv? 0 (remainder fixnum-min (- fixnum-min))))
 688
 689     (pass-if "n = - fixnum-min + 1"
 690       (eqv? fixnum-min (remainder fixnum-min (1+ (- fixnum-min))))))
 691
 692   (with-test-prefix "(fixnum-min - 1) / n"
 693
 694     (pass-if "n = 1"
 695       (eqv? 0 (remainder (- fixnum-min 1) 1)))
 696
 697     (pass-if "n = -1"
 698       (eqv? 0 (remainder (- fixnum-min 1) -1)))
 699
 700     (pass-if "n = fixnum-max"
 701       (eqv? -2 (remainder (- fixnum-min 1) fixnum-max)))
 702
 703     (pass-if "n = fixnum-max + 1"
 704       (eqv? -1 (remainder (- fixnum-min 1) (+ fixnum-max 1))))
 705
 706     (pass-if "n = fixnum-min"
 707       (eqv? -1 (remainder (- fixnum-min 1) fixnum-min)))
 708
 709     (pass-if "n = fixnum-min - 1"
 710       (eqv? 0 (remainder (- fixnum-min 1) (- fixnum-min 1)))))
 711
 712   ;; Positive dividend and divisor
 713
 714   (pass-if "35 / 7"
 715     (eqv? 0 (remainder 35 7)))
 716
 717   ;; Negative dividend, positive divisor
 718
 719   (pass-if "-35 / 7"
 720     (eqv? 0 (remainder -35 7)))
 721
 722   ;; Positive dividend, negative divisor
 723
 724   (pass-if "35 / -7"
 725     (eqv? 0 (remainder 35 -7)))
 726
 727   ;; Negative dividend and divisor
 728
 729   (pass-if "-35 / -7"
 730     (eqv? 0 (remainder -35 -7)))
 731
 732   ;; Are numerical overflows detected correctly?
 733
 734   (with-test-prefix "division by zero"
 735
 736     (pass-if-exception "(remainder 1 0)"
 737       exception:numerical-overflow
 738       (remainder 1 0))
 739
 740     (pass-if-exception "(remainder bignum 0)"
 741       exception:numerical-overflow
 742       (remainder (+ fixnum-max 1) 0)))
 743
 744   ;; Are wrong type arguments detected correctly?
 745
 746   )
 747
 748 ;;;
 749 ;;; modulo
 750 ;;;
 751
 752 (with-test-prefix "modulo"
 753
 754   (expect-fail "documented?"
 755     (documented? modulo))
 756
 757   (with-test-prefix "0 % n"
 758
 759     (pass-if "n = 1"
 760       (eqv? 0 (modulo 0 1)))
 761
 762     (pass-if "n = -1"
 763       (eqv? 0 (modulo 0 -1)))
 764
 765     (pass-if "n = fixnum-max"
 766       (eqv? 0 (modulo 0 fixnum-max)))
 767
 768     (pass-if "n = fixnum-max + 1"
 769       (eqv? 0 (modulo 0 (+ fixnum-max 1))))
 770
 771     (pass-if "n = fixnum-min"
 772       (eqv? 0 (modulo 0 fixnum-min)))
 773
 774     (pass-if "n = fixnum-min - 1"
 775       (eqv? 0 (modulo 0 (- fixnum-min 1)))))
 776
 777   (with-test-prefix "1 % n"
 778
 779     (pass-if "n = 1"
 780       (eqv? 0 (modulo 1 1)))
 781
 782     (pass-if "n = -1"
 783       (eqv? 0 (modulo 1 -1)))
 784
 785     (pass-if "n = fixnum-max"
 786       (eqv? 1 (modulo 1 fixnum-max)))
 787
 788     (pass-if "n = fixnum-max + 1"
 789       (eqv? 1 (modulo 1 (+ fixnum-max 1))))
 790
 791     (pass-if "n = fixnum-min"
 792       (eqv? (+ fixnum-min 1) (modulo 1 fixnum-min)))
 793
 794     (pass-if "n = fixnum-min - 1"
 795       (eqv? fixnum-min (modulo 1 (- fixnum-min 1)))))
 796
 797   (with-test-prefix "-1 % n"
 798
 799     (pass-if "n = 1"
 800       (eqv? 0 (modulo -1 1)))
 801
 802     (pass-if "n = -1"
 803       (eqv? 0 (modulo -1 -1)))
 804
 805     (pass-if "n = fixnum-max"
 806       (eqv? (- fixnum-max 1) (modulo -1 fixnum-max)))
 807
 808     (pass-if "n = fixnum-max + 1"
 809       (eqv? fixnum-max (modulo -1 (+ fixnum-max 1))))
 810
 811     (pass-if "n = fixnum-min"
 812       (eqv? -1 (modulo -1 fixnum-min)))
 813
 814     (pass-if "n = fixnum-min - 1"
 815       (eqv? -1 (modulo -1 (- fixnum-min 1)))))
 816
 817   (with-test-prefix "fixnum-max % n"
 818
 819     (pass-if "n = 1"
 820       (eqv? 0 (modulo fixnum-max 1)))
 821
 822     (pass-if "n = -1"
 823       (eqv? 0 (modulo fixnum-max -1)))
 824
 825     (pass-if "n = fixnum-max"
 826       (eqv? 0 (modulo fixnum-max fixnum-max)))
 827
 828     (pass-if "n = fixnum-max + 1"
 829       (eqv? fixnum-max (modulo fixnum-max (+ fixnum-max 1))))
 830
 831     (pass-if "n = fixnum-min"
 832       (eqv? -1 (modulo fixnum-max fixnum-min)))
 833
 834     (pass-if "n = fixnum-min - 1"
 835       (eqv? -2 (modulo fixnum-max (- fixnum-min 1)))))
 836
 837   (with-test-prefix "(fixnum-max + 1) % n"
 838
 839     (pass-if "n = 1"
 840       (eqv? 0 (modulo (+ fixnum-max 1) 1)))
 841
 842     (pass-if "n = -1"
 843       (eqv? 0 (modulo (+ fixnum-max 1) -1)))
 844
 845     (pass-if "n = fixnum-max"
 846       (eqv? 1 (modulo (+ fixnum-max 1) fixnum-max)))
 847
 848     (pass-if "n = fixnum-max + 1"
 849       (eqv? 0 (modulo (+ fixnum-max 1) (+ fixnum-max 1))))
 850
 851     (pass-if "n = fixnum-min"
 852       (eqv? 0 (modulo (+ fixnum-max 1) fixnum-min)))
 853
 854     (pass-if "n = fixnum-min - 1"
 855       (eqv? -1 (modulo (+ fixnum-max 1) (- fixnum-min 1)))))
 856
 857   (with-test-prefix "fixnum-min % n"
 858
 859     (pass-if "n = 1"
 860       (eqv? 0 (modulo fixnum-min 1)))
 861
 862     (pass-if "n = -1"
 863       (eqv? 0 (modulo fixnum-min -1)))
 864
 865     (pass-if "n = fixnum-max"
 866       (eqv? (- fixnum-max 1) (modulo fixnum-min fixnum-max)))
 867
 868     (pass-if "n = fixnum-max + 1"
 869       (eqv? 0 (modulo fixnum-min (+ fixnum-max 1))))
 870
 871     (pass-if "n = fixnum-min"
 872       (eqv? 0 (modulo fixnum-min fixnum-min)))
 873
 874     (pass-if "n = fixnum-min - 1"
 875       (eqv? fixnum-min (modulo fixnum-min (- fixnum-min 1)))))
 876
 877   (with-test-prefix "(fixnum-min - 1) % n"
 878
 879     (pass-if "n = 1"
 880       (eqv? 0 (modulo (- fixnum-min 1) 1)))
 881
 882     (pass-if "n = -1"
 883       (eqv? 0 (modulo (- fixnum-min 1) -1)))
 884
 885     (pass-if "n = fixnum-max"
 886       (eqv? (- fixnum-max 2) (modulo (- fixnum-min 1) fixnum-max)))
 887
 888     (pass-if "n = fixnum-max + 1"
 889       (eqv? fixnum-max (modulo (- fixnum-min 1) (+ fixnum-max 1))))
 890
 891     (pass-if "n = fixnum-min"
 892       (eqv? -1 (modulo (- fixnum-min 1) fixnum-min)))
 893
 894     (pass-if "n = fixnum-min - 1"
 895       (eqv? 0 (modulo (- fixnum-min 1) (- fixnum-min 1)))))
 896
 897   ;; Positive dividend and divisor
 898
 899   (pass-if "13 % 4"
 900     (eqv? 1 (modulo 13 4)))
 901
 902   (pass-if "2177452800 % 86400"
 903     (eqv? 0 (modulo 2177452800 86400)))
 904
 905   ;; Negative dividend, positive divisor
 906
 907   (pass-if "-13 % 4"
 908     (eqv? 3 (modulo -13 4)))
 909
 910   (pass-if "-2177452800 % 86400"
 911     (eqv? 0 (modulo -2177452800 86400)))
 912
 913   ;; Positive dividend, negative divisor
 914
 915   (pass-if "13 % -4"
 916     (eqv? -3 (modulo 13 -4)))
 917
 918   (pass-if "2177452800 % -86400"
 919     (eqv? 0 (modulo 2177452800 -86400)))
 920
 921   ;; Negative dividend and divisor
 922
 923   (pass-if "-13 % -4"
 924     (eqv? -1 (modulo -13 -4)))
 925
 926   (pass-if "-2177452800 % -86400"
 927     (eqv? 0 (modulo -2177452800 -86400)))
 928
 929   ;; Are numerical overflows detected correctly?
 930
 931   (with-test-prefix "division by zero"
 932
 933     (pass-if-exception "(modulo 1 0)"
 934       exception:numerical-overflow
 935       (modulo 1 0))
 936
 937     (pass-if-exception "(modulo bignum 0)"
 938       exception:numerical-overflow
 939       (modulo (+ fixnum-max 1) 0)))
 940
 941   ;; Are wrong type arguments detected correctly?
 942
 943   )
 944
 945 ;;;
 946 ;;; modulo-expt
 947 ;;;
 948
 949 (with-test-prefix "modulo-expt"
 950    (pass-if (= 1 (modulo-expt 17 23 47)))
 951
 952    (pass-if (= 1 (modulo-expt 17 -23 47)))
 953
 954    (pass-if (= 17 (modulo-expt 17 -22 47)))
 955
 956    (pass-if (= 36 (modulo-expt 17 22 47)))
 957
 958    (pass-if (= 183658794479969134816674175082294846241553725240 (modulo-expt 111122223333444455556666 111122223333444455556666 1153478690012629968439432872520758982731022934717)))
 959
 960    (pass-if-exception
 961     "Proper exception with 0 modulus"
 962     exception:numerical-overflow
 963     (modulo-expt 17 23 0))
 964
 965    (pass-if-exception
 966     "Proper exception when result not invertible"
 967     exception:numerical-overflow
 968     (modulo-expt 10 -1 48))
 969
 970    (pass-if-exception
 971     "Proper exception with wrong type argument"
 972     exception:wrong-type-arg
 973     (modulo-expt "Sam" 23 10))
 974
 975    (pass-if-exception
 976     "Proper exception with wrong type argument"
 977     exception:wrong-type-arg
 978     (modulo-expt 17 9.9 10))
 979
 980     (pass-if-exception
 981     "Proper exception with wrong type argument"
 982     exception:wrong-type-arg
 983     (modulo-expt 17 23 'Ethel)))
 984
 985 ;;;
 986 ;;; numerator
 987 ;;;
 988
 989 (with-test-prefix "numerator"
 990   (pass-if "0"
 991     (eqv? 0 (numerator 0)))
 992   (pass-if "1"
 993     (eqv? 1 (numerator 1)))
 994   (pass-if "2"
 995     (eqv? 2 (numerator 2)))
 996   (pass-if "-1"
 997     (eqv? -1 (numerator -1)))
 998   (pass-if "-2"
 999     (eqv? -2 (numerator -2)))
1000
1001   (pass-if "0.0"
1002     (eqv? 0.0 (numerator 0.0)))
1003   (pass-if "1.0"
1004     (eqv? 1.0 (numerator 1.0)))
1005   (pass-if "2.0"
1006     (eqv? 2.0 (numerator 2.0)))
1007   (pass-if "-1.0"
1008     (eqv? -1.0 (numerator -1.0)))
1009   (pass-if "-2.0"
1010     (eqv? -2.0 (numerator -2.0)))
1011
1012   (pass-if "0.5"
1013     (eqv? 1.0 (numerator 0.5)))
1014   (pass-if "0.25"
1015     (eqv? 1.0 (numerator 0.25)))
1016   (pass-if "0.75"
1017     (eqv? 3.0 (numerator 0.75))))
1018
1019 ;;;
1020 ;;; denominator
1021 ;;;
1022
1023 (with-test-prefix "denominator"
1024   (pass-if "0"
1025     (eqv? 1 (denominator 0)))
1026   (pass-if "1"
1027     (eqv? 1 (denominator 1)))
1028   (pass-if "2"
1029     (eqv? 1 (denominator 2)))
1030   (pass-if "-1"
1031     (eqv? 1 (denominator -1)))
1032   (pass-if "-2"
1033     (eqv? 1 (denominator -2)))
1034
1035   (pass-if "0.0"
1036     (eqv? 1.0 (denominator 0.0)))
1037   (pass-if "1.0"
1038     (eqv? 1.0 (denominator 1.0)))
1039   (pass-if "2.0"
1040     (eqv? 1.0 (denominator 2.0)))
1041   (pass-if "-1.0"
1042     (eqv? 1.0 (denominator -1.0)))
1043   (pass-if "-2.0"
1044     (eqv? 1.0 (denominator -2.0)))
1045
1046   (pass-if "0.5"
1047     (eqv? 2.0 (denominator 0.5)))
1048   (pass-if "0.25"
1049     (eqv? 4.0 (denominator 0.25)))
1050   (pass-if "0.75"
1051     (eqv? 4.0 (denominator 0.75))))
1052
1053 ;;;
1054 ;;; gcd
1055 ;;;
1056
1057 (with-test-prefix "gcd"
1058
1059   (pass-if "documented?"
1060     (documented? gcd))
1061
1062   (with-test-prefix "(n)"
1063
1064     (pass-if "n = -2"
1065       (eqv? 2 (gcd -2))))
1066
1067   (with-test-prefix "(0 n)"
1068
1069     (pass-if "n = 0"
1070       (eqv? 0 (gcd 0 0)))
1071
1072     (pass-if "n = 1"
1073       (eqv? 1 (gcd 0 1)))
1074
1075     (pass-if "n = -1"
1076       (eqv? 1 (gcd 0 -1)))
1077
1078     (pass-if "n = fixnum-max"
1079       (eqv? fixnum-max (gcd 0 fixnum-max)))
1080
1081     (pass-if "n = fixnum-max + 1"
1082       (eqv? (+ fixnum-max 1) (gcd 0 (+ fixnum-max 1))))
1083
1084     (pass-if "n = fixnum-min"
1085       (eqv? (- fixnum-min) (gcd 0 fixnum-min)))
1086
1087     (pass-if "n = fixnum-min - 1"
1088       (eqv? (- (- fixnum-min 1)) (gcd 0 (- fixnum-min 1)))))
1089
1090   (with-test-prefix "(n 0)"
1091
1092     (pass-if "n = 2^128 * fixnum-max"
1093       (eqv? (ash fixnum-max 128) (gcd (ash fixnum-max 128) 0))))
1094
1095   (with-test-prefix "(1 n)"
1096
1097     (pass-if "n = 0"
1098       (eqv? 1 (gcd 1 0)))
1099
1100     (pass-if "n = 1"
1101       (eqv? 1 (gcd 1 1)))
1102
1103     (pass-if "n = -1"
1104       (eqv? 1 (gcd 1 -1)))
1105
1106     (pass-if "n = fixnum-max"
1107       (eqv? 1 (gcd 1 fixnum-max)))
1108
1109     (pass-if "n = fixnum-max + 1"
1110       (eqv? 1 (gcd 1 (+ fixnum-max 1))))
1111
1112     (pass-if "n = fixnum-min"
1113       (eqv? 1 (gcd 1 fixnum-min)))
1114
1115     (pass-if "n = fixnum-min - 1"
1116       (eqv? 1 (gcd 1 (- fixnum-min 1)))))
1117
1118   (with-test-prefix "(-1 n)"
1119
1120     (pass-if "n = 0"
1121       (eqv? 1 (gcd -1 0)))
1122
1123     (pass-if "n = 1"
1124       (eqv? 1 (gcd -1 1)))
1125
1126     (pass-if "n = -1"
1127       (eqv? 1 (gcd -1 -1)))
1128
1129     (pass-if "n = fixnum-max"
1130       (eqv? 1 (gcd -1 fixnum-max)))
1131
1132     (pass-if "n = fixnum-max + 1"
1133       (eqv? 1 (gcd -1 (+ fixnum-max 1))))
1134
1135     (pass-if "n = fixnum-min"
1136       (eqv? 1 (gcd -1 fixnum-min)))
1137
1138     (pass-if "n = fixnum-min - 1"
1139       (eqv? 1 (gcd -1 (- fixnum-min 1)))))
1140
1141   (with-test-prefix "(fixnum-max n)"
1142
1143     (pass-if "n = 0"
1144       (eqv? fixnum-max (gcd fixnum-max 0)))
1145
1146     (pass-if "n = 1"
1147       (eqv? 1 (gcd fixnum-max 1)))
1148
1149     (pass-if "n = -1"
1150       (eqv? 1 (gcd fixnum-max -1)))
1151
1152     (pass-if "n = fixnum-max"
1153       (eqv? fixnum-max (gcd fixnum-max fixnum-max)))
1154
1155     (pass-if "n = fixnum-max + 1"
1156       (eqv? 1 (gcd fixnum-max (+ fixnum-max 1))))
1157
1158     (pass-if "n = fixnum-min"
1159       (eqv? 1 (gcd fixnum-max fixnum-min)))
1160
1161     (pass-if "n = fixnum-min - 1"
1162       (eqv? 1 (gcd fixnum-max (- fixnum-min 1)))))
1163
1164   (with-test-prefix "((+ fixnum-max 1) n)"
1165
1166     (pass-if "n = 0"
1167       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) 0)))
1168
1169     (pass-if "n = 1"
1170       (eqv? 1 (gcd (+ fixnum-max 1) 1)))
1171
1172     (pass-if "n = -1"
1173       (eqv? 1 (gcd (+ fixnum-max 1) -1)))
1174
1175     (pass-if "n = fixnum-max"
1176       (eqv? 1 (gcd (+ fixnum-max 1) fixnum-max)))
1177
1178     (pass-if "n = fixnum-max + 1"
1179       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) (+ fixnum-max 1))))
1180
1181     (pass-if "n = fixnum-min"
1182       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) fixnum-min)))
1183
1184     (pass-if "n = fixnum-min - 1"
1185       (eqv? 1 (gcd (+ fixnum-max 1) (- fixnum-min 1)))))
1186
1187   (with-test-prefix "(fixnum-min n)"
1188
1189     (pass-if "n = 0"
1190       (eqv? (- fixnum-min) (gcd fixnum-min 0)))
1191
1192     (pass-if "n = 1"
1193       (eqv? 1 (gcd fixnum-min 1)))
1194
1195     (pass-if "n = -1"
1196       (eqv? 1 (gcd fixnum-min -1)))
1197
1198     (pass-if "n = fixnum-max"
1199       (eqv? 1 (gcd fixnum-min fixnum-max)))
1200
1201     (pass-if "n = fixnum-max + 1"
1202       (eqv? (+ fixnum-max 1) (gcd fixnum-min (+ fixnum-max 1))))
1203
1204     (pass-if "n = fixnum-min"
1205       (eqv? (- fixnum-min) (gcd fixnum-min fixnum-min)))
1206
1207     (pass-if "n = fixnum-min - 1"
1208       (eqv? 1 (gcd fixnum-min (- fixnum-min 1)))))
1209
1210   (with-test-prefix "((- fixnum-min 1) n)"
1211
1212     (pass-if "n = 0"
1213       (eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) 0)))
1214
1215     (pass-if "n = 1"
1216       (eqv? 1 (gcd (- fixnum-min 1) 1)))
1217
1218     (pass-if "n = -1"
1219       (eqv? 1 (gcd (- fixnum-min 1) -1)))
1220
1221     (pass-if "n = fixnum-max"
1222       (eqv? 1 (gcd (- fixnum-min 1) fixnum-max)))
1223
1224     (pass-if "n = fixnum-max + 1"
1225       (eqv? 1 (gcd (- fixnum-min 1) (+ fixnum-max 1))))
1226
1227     (pass-if "n = fixnum-min"
1228       (eqv? 1 (gcd (- fixnum-min 1) fixnum-min)))
1229
1230     (pass-if "n = fixnum-min - 1"
1231       (eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) (- fixnum-min 1)))))
1232
1233   ;; Are wrong type arguments detected correctly?
1234
1235   )
1236
1237 ;;;
1238 ;;; lcm
1239 ;;;
1240
1241 (with-test-prefix "lcm"
1242   ;; FIXME: more tests?
1243   ;; (some of these are already in r4rs.test)
1244   (pass-if (documented? lcm))
1245   (pass-if (= (lcm) 1))
1246   (pass-if (= (lcm 32 -36) 288))
1247   (let ((big-n 115792089237316195423570985008687907853269984665640564039457584007913129639936) ; 2 ^ 256
1248         (lcm-of-big-n-and-11 1273712981610478149659280835095566986385969831322046204434033424087044426039296))
1249     (pass-if (= lcm-of-big-n-and-11 (lcm big-n 11)))
1250     (pass-if (= lcm-of-big-n-and-11 (lcm 11 big-n 11)))))
1251
1252 ;;;
1253 ;;; number->string
1254 ;;;
1255
1256 (with-test-prefix "number->string"
1257   (let ((num->str->num
1258          (lambda (n radix)
1259            (string->number (number->string n radix) radix))))
1260
1261     (pass-if (documented? number->string))
1262     (pass-if (string=? (number->string 0) "0"))
1263     (pass-if (string=? (number->string 171) "171"))
1264     (pass-if (= (+ fixnum-max 1) (num->str->num (+ fixnum-max 1) 10)))
1265     (pass-if (= (- fixnum-min 1) (num->str->num (- fixnum-min 1) 10)))
1266     (pass-if (= (inf) (num->str->num (inf) 10)))
1267     (pass-if (= 1.3 (num->str->num 1.3 10)))
1268
1269     ;; XXX - some results depend on whether Guile is compiled optimzed
1270     ;; or not.  It is clearly undesirable to have number->string to be
1271     ;; influenced by this.
1272
1273     (pass-if (string=? (number->string 35.25 36) "Z.9"))
1274     (pass-if (or (string=? (number->string 0.25 2) "0.01")
1275                  (string=? (number->string 0.25 2) "0.010")))
1276     (pass-if (string=? (number->string 255.0625 16) "FF.1"))
1277     (pass-if (string=? (number->string (/ 1 3) 3) "1/10"))
1278
1279     ;; Numeric conversion from decimal is not precise, in its current
1280     ;; implementation, so 11.333... and 1.324... can't be expected to
1281     ;; reliably come out to precise values.  These tests did actually work
1282     ;; for a while, but something in gcc changed, affecting the conversion
1283     ;; code.
1284     ;;
1285     ;; (pass-if (or (string=? (number->string 11.33333333333333333 12)
1286     ;;                        "B.4")
1287     ;;              (string=? (number->string 11.33333333333333333 12)
1288     ;;                        "B.400000000000009")))
1289     ;; (pass-if (or (string=? (number->string 1.324e44 16)
1290     ;;                        "5.EFE0A14FAFEe24")
1291     ;;              (string=? (number->string 1.324e44 16)
1292     ;;                        "5.EFE0A14FAFDF8e24")))
1293     ))
1294
1295 ;;;
1296 ;;; string->number
1297 ;;;
1298
1299 (with-test-prefix "string->number"
1300
1301   (pass-if "documented?"
1302     (documented? string->number))
1303
1304   (pass-if "non number strings"
1305     (for-each (lambda (x) (if (string->number x) (throw 'fail)))
1306               '("" "q" "1q" "6+7iq" "8+9q" "10+11" "13+" "18@19q" "20@q" "23@"
1307                 "+25iq" "26i" "-q" "-iq" "i" "5#.0" "8/" "10#11" ".#" "."
1308                 "#o.2" "3.4q" "15.16e17q" "18.19e+q" ".q" ".17#18" "10q" "#b2"
1309                 "#b3" "#b4" "#b5" "#b6" "#b7" "#b8" "#b9" "#ba" "#bb" "#bc"
1310                 "#bd" "#be" "#bf" "#q" "#b#b1" "#o#o1" "#d#d1" "#x#x1" "#e#e1"
1311                 "#i#i1" "12@12+0i"))
1312     #t)
1313
1314   (pass-if "valid number strings"
1315     (for-each (lambda (couple)
1316                 (apply
1317                  (lambda (x y)
1318                    (let ((xx (string->number x)))
1319                      (if (or (eq? xx #f) (not (eqv? xx y)))
1320                          (begin
1321                            (pk x y)
1322                            (throw 'fail)))))
1323                  couple))
1324               `(;; Radix:
1325                 ("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
1326                 ("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
1327                 ("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
1328                 ("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
1329                 ("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
1330                 ("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
1331                 ("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
1332                 ("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
1333                 ("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
1334                 ("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
1335                 ("#b1010" 10)
1336                 ("#o12345670" 2739128)
1337                 ("#d1234567890" 1234567890)
1338                 ("#x1234567890abcdef" 1311768467294899695)
1339                 ;; Exactness:
1340                 ("#e1" 1) ("#e1.2" 12/10)
1341                 ("#i1.1" 1.1) ("#i1" 1.0)
1342                 ;; Integers:
1343                 ("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1))
1344                 ("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
1345                 ("#b#i100" 4.0)
1346                 ;; Fractions:
1347                 ("1/1" 1) ("1/2" 1/2) ("-1/2" -1/2) ("1#/1" 10.0)
1348                 ("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 9/10) ("#e10/1#" 1)
1349                 ("#i6/8" 0.75) ("#i1/1" 1.0)
1350                 ;; Decimal numbers:
1351                 ;; * <uinteger 10> <suffix>
1352                 ("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
1353                 ("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
1354                 ("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
1355                 ;; * . <digit 10>+ #* <suffix>
1356                 (".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
1357                 (".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
1358                 ;; * <digit 10>+ . <digit 10>* #* <suffix>
1359                 ("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
1360                 ("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
1361                 ("3.1#e0" 3.1)
1362                 ;; * <digit 10>+ #+ . #* <suffix>
1363                 ("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
1364                 ;; Complex:
1365                 ("1@0" 1.0) ("1@+0" 1.0) ("1@-0" 1.0)
1366                 ("2+3i" ,(+ 2 (* 3 +i))) ("4-5i" ,(- 4 (* 5 +i)))
1367                 ("1+i" 1+1i) ("1-i" 1-1i) ("+1i" 0+1i) ("-1i" 0-1i)
1368                 ("+i" +1i) ("-i" -1i)
1369                 ("1.0+.1i" 1.0+0.1i)
1370                 ("1.0-.1i" 1.0-0.1i)
1371                 (".1+.0i" 0.1)
1372                 ("1.+.0i" 1.0)
1373                 (".1+.1i" 0.1+0.1i)
1374                 ("1e1+.1i" 10+0.1i)
1375                 ))
1376     #t)
1377
1378   (pass-if-exception "exponent too big"
1379     exception:out-of-range
1380     (string->number "12.13e141414"))
1381
1382   ;; in guile 1.6.7 and earlier, bad polar forms (where the conversion of
1383   ;; the angle gave #f) caused a segv
1384   (pass-if "1@a"
1385     (eq? #f (string->number "1@a"))))
1386
1387 ;;;
1388 ;;; number?
1389 ;;;
1390
1391 (with-test-prefix "number?"
1392   (pass-if (documented? number?))
1393   (pass-if (number? 0))
1394   (pass-if (number? 7))
1395   (pass-if (number? -7))
1396   (pass-if (number? 1.3))
1397   (pass-if (number? (+ 1 fixnum-max)))
1398   (pass-if (number? (- 1 fixnum-min)))
1399   (pass-if (number? 3+4i))
1400   (pass-if (not (number? #\a)))
1401   (pass-if (not (number? "a")))
1402   (pass-if (not (number? (make-vector 0))))
1403   (pass-if (not (number? (cons 1 2))))
1404   (pass-if (not (number? #t)))
1405   (pass-if (not (number? (lambda () #t))))
1406   (pass-if (not (number? (current-input-port)))))
1407
1408 ;;;
1409 ;;; complex?
1410 ;;;
1411
1412 (with-test-prefix "complex?"
1413   (pass-if (documented? complex?))
1414   (pass-if (complex? 0))
1415   (pass-if (complex? 7))
1416   (pass-if (complex? -7))
1417   (pass-if (complex? (+ 1 fixnum-max)))
1418   (pass-if (complex? (- 1 fixnum-min)))
1419   (pass-if (complex? 1.3))
1420   (pass-if (complex? 3+4i))
1421   (pass-if (not (complex? #\a)))
1422   (pass-if (not (complex? "a")))
1423   (pass-if (not (complex? (make-vector 0))))
1424   (pass-if (not (complex? (cons 1 2))))
1425   (pass-if (not (complex? #t)))
1426   (pass-if (not (complex? (lambda () #t))))
1427   (pass-if (not (complex? (current-input-port)))))
1428
1429 ;;;
1430 ;;; real?
1431 ;;;
1432
1433 (with-test-prefix "real?"
1434   (pass-if (documented? real?))
1435   (pass-if (real? 0))
1436   (pass-if (real? 7))
1437   (pass-if (real? -7))
1438   (pass-if (real? (+ 1 fixnum-max)))
1439   (pass-if (real? (- 1 fixnum-min)))
1440   (pass-if (real? 1.3))
1441   (pass-if (not (real? 3+4i)))
1442   (pass-if (not (real? #\a)))
1443   (pass-if (not (real? "a")))
1444   (pass-if (not (real? (make-vector 0))))
1445   (pass-if (not (real? (cons 1 2))))
1446   (pass-if (not (real? #t)))
1447   (pass-if (not (real? (lambda () #t))))
1448   (pass-if (not (real? (current-input-port)))))
1449
1450 ;;;
1451 ;;; rational? (same as real? right now)
1452 ;;;
1453
1454 (with-test-prefix "rational?"
1455   (pass-if (documented? rational?))
1456   (pass-if (rational? 0))
1457   (pass-if (rational? 7))
1458   (pass-if (rational? -7))
1459   (pass-if (rational? (+ 1 fixnum-max)))
1460   (pass-if (rational? (- 1 fixnum-min)))
1461   (pass-if (rational? 1.3))
1462   (pass-if (not (rational? 3+4i)))
1463   (pass-if (not (rational? #\a)))
1464   (pass-if (not (rational? "a")))
1465   (pass-if (not (rational? (make-vector 0))))
1466   (pass-if (not (rational? (cons 1 2))))
1467   (pass-if (not (rational? #t)))
1468   (pass-if (not (rational? (lambda () #t))))
1469   (pass-if (not (rational? (current-input-port)))))
1470
1471 ;;;
1472 ;;; integer?
1473 ;;;
1474
1475 (with-test-prefix "integer?"
1476   (pass-if (documented? integer?))
1477   (pass-if (integer? 0))
1478   (pass-if (integer? 7))
1479   (pass-if (integer? -7))
1480   (pass-if (integer? (+ 1 fixnum-max)))
1481   (pass-if (integer? (- 1 fixnum-min)))
1482   (pass-if (and (= 3+0i (round 3+0i)) (integer? 3+0i)))
1483   (pass-if (and (= 1.0 (round 1.0)) (integer? 1.0)))
1484   (pass-if (not (integer? 1.3)))
1485   (pass-if (integer? +inf.0))
1486   (pass-if (integer? -inf.0))
1487   (pass-if (not (integer? +nan.0)))
1488   (pass-if (not (integer? 3+4i)))
1489   (pass-if (not (integer? #\a)))
1490   (pass-if (not (integer? "a")))
1491   (pass-if (not (integer? (make-vector 0))))
1492   (pass-if (not (integer? (cons 1 2))))
1493   (pass-if (not (integer? #t)))
1494   (pass-if (not (integer? (lambda () #t))))
1495   (pass-if (not (integer? (current-input-port)))))
1496
1497 ;;;
1498 ;;; inexact?
1499 ;;;
1500
1501 (with-test-prefix "inexact?"
1502   (pass-if (documented? inexact?))
1503   (pass-if (not (inexact? 0)))
1504   (pass-if (not (inexact? 7)))
1505   (pass-if (not (inexact? -7)))
1506   (pass-if (not (inexact? (+ 1 fixnum-max))))
1507   (pass-if (not (inexact? (- 1 fixnum-min))))
1508   (pass-if (inexact? 1.3))
1509   (pass-if (inexact? 3.1+4.2i))
1510   (pass-if-exception "char"
1511                      exception:wrong-type-arg
1512                      (not (inexact? #\a)))
1513   (pass-if-exception "string"
1514                      exception:wrong-type-arg
1515                      (not (inexact? "a")))
1516   (pass-if-exception "vector"
1517                      exception:wrong-type-arg
1518                      (not (inexact? (make-vector 0))))
1519   (pass-if-exception "cons"
1520                      exception:wrong-type-arg
1521                      (not (inexact? (cons 1 2))))
1522   (pass-if-exception "bool"
1523                      exception:wrong-type-arg
1524                      (not (inexact? #t)))
1525   (pass-if-exception "procedure"
1526                      exception:wrong-type-arg
1527                      (not (inexact? (lambda () #t))))
1528   (pass-if-exception "port"
1529                      exception:wrong-type-arg
1530                      (not (inexact? (current-input-port)))))
1531
1532 ;;;
1533 ;;; equal?
1534 ;;;
1535
1536 (with-test-prefix "equal?"
1537   (pass-if (documented? equal?))
1538   (pass-if (equal? 0 0))
1539   (pass-if (equal? 7 7))
1540   (pass-if (equal? -7 -7))
1541   (pass-if (equal? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1542   (pass-if (equal? (- fixnum-min 1) (- fixnum-min 1)))
1543   (pass-if (not (equal? 0 1)))
1544   (pass-if (not (equal? fixnum-max (+ 1 fixnum-max))))
1545   (pass-if (not (equal? (+ 1 fixnum-max) fixnum-max)))
1546   (pass-if (not (equal? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1547   (pass-if (not (equal? fixnum-min (- fixnum-min 1))))
1548   (pass-if (not (equal? (- fixnum-min 1) fixnum-min)))
1549   (pass-if (not (equal? (- fixnum-min 1) (- fixnum-min 2))))
1550   (pass-if (not (equal? (+ fixnum-max 1) (- fixnum-min 1))))
1551
1552   (pass-if (not (equal? (ash 1 256) +inf.0)))
1553   (pass-if (not (equal? +inf.0 (ash 1 256))))
1554   (pass-if (not (equal? (ash 1 256) -inf.0)))
1555   (pass-if (not (equal? -inf.0 (ash 1 256))))
1556
1557   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1558   ;; sure we've avoided that
1559   (pass-if (not (equal? (ash 1 1024) +inf.0)))
1560   (pass-if (not (equal? +inf.0 (ash 1 1024))))
1561   (pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
1562   (pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
1563
1564   (pass-if (not (equal? +nan.0 +nan.0)))
1565   (pass-if (not (equal? 0 +nan.0)))
1566   (pass-if (not (equal? +nan.0 0)))
1567   (pass-if (not (equal? 1 +nan.0)))
1568   (pass-if (not (equal? +nan.0 1)))
1569   (pass-if (not (equal? -1 +nan.0)))
1570   (pass-if (not (equal? +nan.0 -1)))
1571
1572   (pass-if (not (equal? (ash 1 256) +nan.0)))
1573   (pass-if (not (equal? +nan.0 (ash 1 256))))
1574   (pass-if (not (equal? (- (ash 1 256)) +nan.0)))
1575   (pass-if (not (equal? +nan.0 (- (ash 1 256)))))
1576
1577   (pass-if (not (equal? (ash 1 8192) +nan.0)))
1578   (pass-if (not (equal? +nan.0 (ash 1 8192))))
1579   (pass-if (not (equal? (- (ash 1 8192)) +nan.0)))
1580   (pass-if (not (equal? +nan.0 (- (ash 1 8192)))))
1581
1582   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1583   ;; sure we've avoided that
1584   (pass-if (not (equal? (ash 3 1023) +nan.0)))
1585   (pass-if (not (equal? +nan.0 (ash 3 1023)))))
1586
1587 ;;;
1588 ;;; =
1589 ;;;
1590
1591 (with-test-prefix "="
1592   (pass-if (documented? =))
1593   (pass-if (= 0 0))
1594   (pass-if (= 7 7))
1595   (pass-if (= -7 -7))
1596   (pass-if (= (+ 1 fixnum-max) (+ 1 fixnum-max)))
1597   (pass-if (= (- fixnum-min 1) (- fixnum-min 1)))
1598   (pass-if (not (= 0 1)))
1599   (pass-if (not (= fixnum-max (+ 1 fixnum-max))))
1600   (pass-if (not (= (+ 1 fixnum-max) fixnum-max)))
1601   (pass-if (not (= (+ 1 fixnum-max) (+ 2 fixnum-max))))
1602   (pass-if (not (= fixnum-min (- fixnum-min 1))))
1603   (pass-if (not (= (- fixnum-min 1) fixnum-min)))
1604   (pass-if (not (= (- fixnum-min 1) (- fixnum-min 2))))
1605   (pass-if (not (= (+ fixnum-max 1) (- fixnum-min 1))))
1606
1607   (pass-if (not (= (ash 1 256) +inf.0)))
1608   (pass-if (not (= +inf.0 (ash 1 256))))
1609   (pass-if (not (= (ash 1 256) -inf.0)))
1610   (pass-if (not (= -inf.0 (ash 1 256))))
1611
1612   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1613   ;; sure we've avoided that
1614   (pass-if (not (= (ash 1 1024) +inf.0)))
1615   (pass-if (not (= +inf.0 (ash 1 1024))))
1616   (pass-if (not (= (- (ash 1 1024)) -inf.0)))
1617   (pass-if (not (= -inf.0 (- (ash 1 1024)))))
1618
1619   (pass-if (not (= +nan.0 +nan.0)))
1620   (pass-if (not (= 0 +nan.0)))
1621   (pass-if (not (= +nan.0 0)))
1622   (pass-if (not (= 1 +nan.0)))
1623   (pass-if (not (= +nan.0 1)))
1624   (pass-if (not (= -1 +nan.0)))
1625   (pass-if (not (= +nan.0 -1)))
1626
1627   (pass-if (not (= (ash 1 256) +nan.0)))
1628   (pass-if (not (= +nan.0 (ash 1 256))))
1629   (pass-if (not (= (- (ash 1 256)) +nan.0)))
1630   (pass-if (not (= +nan.0 (- (ash 1 256)))))
1631
1632   (pass-if (not (= (ash 1 8192) +nan.0)))
1633   (pass-if (not (= +nan.0 (ash 1 8192))))
1634   (pass-if (not (= (- (ash 1 8192)) +nan.0)))
1635   (pass-if (not (= +nan.0 (- (ash 1 8192)))))
1636
1637   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1638   ;; sure we've avoided that
1639   (pass-if (not (= (ash 3 1023) +nan.0)))
1640   (pass-if (not (= +nan.0 (ash 3 1023))))
1641
1642   (pass-if (= 1/2 0.5))
1643   (pass-if (not (= 1/3 0.333333333333333333333333333333333)))
1644   (pass-if (not (= 2/3 0.5)))
1645   (pass-if (not (= 0.5 (+ 1/2 (/ 1 (ash 1 1000))))))
1646
1647   (pass-if (= 1/2 0.5+0i))
1648   (pass-if (not (= 0.333333333333333333333333333333333 1/3)))
1649   (pass-if (not (= 2/3 0.5+0i)))
1650   (pass-if (not (= 1/2 0+0.5i)))
1651
1652   (pass-if (= 0.5 1/2))
1653   (pass-if (not (= 0.5 2/3)))
1654   (pass-if (not (= (+ 1/2 (/ 1 (ash 1 1000))) 0.5)))
1655
1656   (pass-if (= 0.5+0i 1/2))
1657   (pass-if (not (= 0.5+0i 2/3)))
1658   (pass-if (not (= 0+0.5i 1/2)))
1659
1660   ;; prior to guile 1.8, inum/flonum comparisons were done just by
1661   ;; converting the inum to a double, which on a 64-bit would round making
1662   ;; say inexact 2^58 appear equal to exact 2^58+1
1663   (pass-if (= (ash-flo 1.0 58) (ash 1 58)))
1664   (pass-if (not (= (ash-flo 1.0 58) (1+ (ash 1 58)))))
1665   (pass-if (not (= (ash-flo 1.0 58) (1- (ash 1 58)))))
1666   (pass-if (= (ash 1 58) (ash-flo 1.0 58)))
1667   (pass-if (not (= (1+ (ash 1 58)) (ash-flo 1.0 58))))
1668   (pass-if (not (= (1- (ash 1 58)) (ash-flo 1.0 58)))))
1669
1670 ;;;
1671 ;;; <
1672 ;;;
1673
1674 (with-test-prefix "<"
1675
1676   (pass-if "documented?"
1677     (documented? <))
1678
1679   (with-test-prefix "(< 0 n)"
1680
1681     (pass-if "n = 0"
1682       (not (< 0 0)))
1683
1684     (pass-if "n = 0.0"
1685       (not (< 0 0.0)))
1686
1687     (pass-if "n = 1"
1688       (< 0 1))
1689
1690     (pass-if "n = 1.0"
1691       (< 0 1.0))
1692
1693     (pass-if "n = -1"
1694       (not (< 0 -1)))
1695
1696     (pass-if "n = -1.0"
1697       (not (< 0 -1.0)))
1698
1699     (pass-if "n = fixnum-max"
1700       (< 0 fixnum-max))
1701
1702     (pass-if "n = fixnum-max + 1"
1703       (< 0 (+ fixnum-max 1)))
1704
1705     (pass-if "n = fixnum-min"
1706       (not (< 0 fixnum-min)))
1707
1708     (pass-if "n = fixnum-min - 1"
1709       (not (< 0 (- fixnum-min 1)))))
1710
1711   (with-test-prefix "(< 0.0 n)"
1712
1713     (pass-if "n = 0"
1714       (not (< 0.0 0)))
1715
1716     (pass-if "n = 0.0"
1717       (not (< 0.0 0.0)))
1718
1719     (pass-if "n = 1"
1720       (< 0.0 1))
1721
1722     (pass-if "n = 1.0"
1723       (< 0.0 1.0))
1724
1725     (pass-if "n = -1"
1726       (not (< 0.0 -1)))
1727
1728     (pass-if "n = -1.0"
1729       (not (< 0.0 -1.0)))
1730
1731     (pass-if "n = fixnum-max"
1732       (< 0.0 fixnum-max))
1733
1734     (pass-if "n = fixnum-max + 1"
1735       (< 0.0 (+ fixnum-max 1)))
1736
1737     (pass-if "n = fixnum-min"
1738       (not (< 0.0 fixnum-min)))
1739
1740     (pass-if "n = fixnum-min - 1"
1741       (not (< 0.0 (- fixnum-min 1)))))
1742
1743   (with-test-prefix "(< 1 n)"
1744
1745     (pass-if "n = 0"
1746       (not (< 1 0)))
1747
1748     (pass-if "n = 0.0"
1749       (not (< 1 0.0)))
1750
1751     (pass-if "n = 1"
1752       (not (< 1 1)))
1753
1754     (pass-if "n = 1.0"
1755       (not (< 1 1.0)))
1756
1757     (pass-if "n = -1"
1758       (not (< 1 -1)))
1759
1760     (pass-if "n = -1.0"
1761       (not (< 1 -1.0)))
1762
1763     (pass-if "n = fixnum-max"
1764       (< 1 fixnum-max))
1765
1766     (pass-if "n = fixnum-max + 1"
1767       (< 1 (+ fixnum-max 1)))
1768
1769     (pass-if "n = fixnum-min"
1770       (not (< 1 fixnum-min)))
1771
1772     (pass-if "n = fixnum-min - 1"
1773       (not (< 1 (- fixnum-min 1)))))
1774
1775   (with-test-prefix "(< 1.0 n)"
1776
1777     (pass-if "n = 0"
1778       (not (< 1.0 0)))
1779
1780     (pass-if "n = 0.0"
1781       (not (< 1.0 0.0)))
1782
1783     (pass-if "n = 1"
1784       (not (< 1.0 1)))
1785
1786     (pass-if "n = 1.0"
1787       (not (< 1.0 1.0)))
1788
1789     (pass-if "n = -1"
1790       (not (< 1.0 -1)))
1791
1792     (pass-if "n = -1.0"
1793       (not (< 1.0 -1.0)))
1794
1795     (pass-if "n = fixnum-max"
1796       (< 1.0 fixnum-max))
1797
1798     (pass-if "n = fixnum-max + 1"
1799       (< 1.0 (+ fixnum-max 1)))
1800
1801     (pass-if "n = fixnum-min"
1802       (not (< 1.0 fixnum-min)))
1803
1804     (pass-if "n = fixnum-min - 1"
1805       (not (< 1.0 (- fixnum-min 1)))))
1806
1807   (with-test-prefix "(< -1 n)"
1808
1809     (pass-if "n = 0"
1810       (< -1 0))
1811
1812     (pass-if "n = 0.0"
1813       (< -1 0.0))
1814
1815     (pass-if "n = 1"
1816       (< -1 1))
1817
1818     (pass-if "n = 1.0"
1819       (< -1 1.0))
1820
1821     (pass-if "n = -1"
1822       (not (< -1 -1)))
1823
1824     (pass-if "n = -1.0"
1825       (not (< -1 -1.0)))
1826
1827     (pass-if "n = fixnum-max"
1828       (< -1 fixnum-max))
1829
1830     (pass-if "n = fixnum-max + 1"
1831       (< -1 (+ fixnum-max 1)))
1832
1833     (pass-if "n = fixnum-min"
1834       (not (< -1 fixnum-min)))
1835
1836     (pass-if "n = fixnum-min - 1"
1837       (not (< -1 (- fixnum-min 1)))))
1838
1839   (with-test-prefix "(< -1.0 n)"
1840
1841     (pass-if "n = 0"
1842       (< -1.0 0))
1843
1844     (pass-if "n = 0.0"
1845       (< -1.0 0.0))
1846
1847     (pass-if "n = 1"
1848       (< -1.0 1))
1849
1850     (pass-if "n = 1.0"
1851       (< -1.0 1.0))
1852
1853     (pass-if "n = -1"
1854       (not (< -1.0 -1)))
1855
1856     (pass-if "n = -1.0"
1857       (not (< -1.0 -1.0)))
1858
1859     (pass-if "n = fixnum-max"
1860       (< -1.0 fixnum-max))
1861
1862     (pass-if "n = fixnum-max + 1"
1863       (< -1.0 (+ fixnum-max 1)))
1864
1865     (pass-if "n = fixnum-min"
1866       (not (< -1.0 fixnum-min)))
1867
1868     (pass-if "n = fixnum-min - 1"
1869       (not (< -1.0 (- fixnum-min 1)))))
1870
1871   (with-test-prefix "(< fixnum-max n)"
1872
1873     (pass-if "n = 0"
1874       (not (< fixnum-max 0)))
1875
1876     (pass-if "n = 0.0"
1877       (not (< fixnum-max 0.0)))
1878
1879     (pass-if "n = 1"
1880       (not (< fixnum-max 1)))
1881
1882     (pass-if "n = 1.0"
1883       (not (< fixnum-max 1.0)))
1884
1885     (pass-if "n = -1"
1886       (not (< fixnum-max -1)))
1887
1888     (pass-if "n = -1.0"
1889       (not (< fixnum-max -1.0)))
1890
1891     (pass-if "n = fixnum-max"
1892       (not (< fixnum-max fixnum-max)))
1893
1894     (pass-if "n = fixnum-max + 1"
1895       (< fixnum-max (+ fixnum-max 1)))
1896
1897     (pass-if "n = fixnum-min"
1898       (not (< fixnum-max fixnum-min)))
1899
1900     (pass-if "n = fixnum-min - 1"
1901       (not (< fixnum-max (- fixnum-min 1)))))
1902
1903   (with-test-prefix "(< (+ fixnum-max 1) n)"
1904
1905     (pass-if "n = 0"
1906       (not (< (+ fixnum-max 1) 0)))
1907
1908     (pass-if "n = 0.0"
1909       (not (< (+ fixnum-max 1) 0.0)))
1910
1911     (pass-if "n = 1"
1912       (not (< (+ fixnum-max 1) 1)))
1913
1914     (pass-if "n = 1.0"
1915       (not (< (+ fixnum-max 1) 1.0)))
1916
1917     (pass-if "n = -1"
1918       (not (< (+ fixnum-max 1) -1)))
1919
1920     (pass-if "n = -1.0"
1921       (not (< (+ fixnum-max 1) -1.0)))
1922
1923     (pass-if "n = fixnum-max"
1924       (not (< (+ fixnum-max 1) fixnum-max)))
1925
1926     (pass-if "n = fixnum-max + 1"
1927       (not (< (+ fixnum-max 1) (+ fixnum-max 1))))
1928
1929     (pass-if "n = fixnum-min"
1930       (not (< (+ fixnum-max 1) fixnum-min)))
1931
1932     (pass-if "n = fixnum-min - 1"
1933       (not (< (+ fixnum-max 1) (- fixnum-min 1)))))
1934
1935   (with-test-prefix "(< fixnum-min n)"
1936
1937     (pass-if "n = 0"
1938       (< fixnum-min 0))
1939
1940     (pass-if "n = 0.0"
1941       (< fixnum-min 0.0))
1942
1943     (pass-if "n = 1"
1944       (< fixnum-min 1))
1945
1946     (pass-if "n = 1.0"
1947       (< fixnum-min 1.0))
1948
1949     (pass-if "n = -1"
1950       (< fixnum-min -1))
1951
1952     (pass-if "n = -1.0"
1953       (< fixnum-min -1.0))
1954
1955     (pass-if "n = fixnum-max"
1956       (< fixnum-min fixnum-max))
1957
1958     (pass-if "n = fixnum-max + 1"
1959       (< fixnum-min (+ fixnum-max 1)))
1960
1961     (pass-if "n = fixnum-min"
1962       (not (< fixnum-min fixnum-min)))
1963
1964     (pass-if "n = fixnum-min - 1"
1965       (not (< fixnum-min (- fixnum-min 1)))))
1966
1967   (with-test-prefix "(< (- fixnum-min 1) n)"
1968
1969     (pass-if "n = 0"
1970       (< (- fixnum-min 1) 0))
1971
1972     (pass-if "n = 0.0"
1973       (< (- fixnum-min 1) 0.0))
1974
1975     (pass-if "n = 1"
1976       (< (- fixnum-min 1) 1))
1977
1978     (pass-if "n = 1.0"
1979       (< (- fixnum-min 1) 1.0))
1980
1981     (pass-if "n = -1"
1982       (< (- fixnum-min 1) -1))
1983
1984     (pass-if "n = -1.0"
1985       (< (- fixnum-min 1) -1.0))
1986
1987     (pass-if "n = fixnum-max"
1988       (< (- fixnum-min 1) fixnum-max))
1989
1990     (pass-if "n = fixnum-max + 1"
1991       (< (- fixnum-min 1) (+ fixnum-max 1)))
1992
1993     (pass-if "n = fixnum-min"
1994       (< (- fixnum-min 1) fixnum-min))
1995
1996     (pass-if "n = fixnum-min - 1"
1997       (not (< (- fixnum-min 1) (- fixnum-min 1)))))
1998
1999   (pass-if (< (ash 1 256) +inf.0))
2000   (pass-if (not (< +inf.0 (ash 1 256))))
2001   (pass-if (not (< (ash 1 256) -inf.0)))
2002   (pass-if (< -inf.0 (ash 1 256)))
2003
2004   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2005   ;; sure we've avoided that
2006   (pass-if (< (1- (ash 1 1024)) +inf.0))
2007   (pass-if (<     (ash 1 1024)  +inf.0))
2008   (pass-if (< (1+ (ash 1 1024)) +inf.0))
2009   (pass-if (not (< +inf.0 (1- (ash 1 1024)))))
2010   (pass-if (not (< +inf.0     (ash 1 1024))))
2011   (pass-if (not (< +inf.0 (1+ (ash 1 1024)))))
2012   (pass-if (< -inf.0 (- (1- (ash 1 1024)))))
2013   (pass-if (< -inf.0 (-     (ash 1 1024))))
2014   (pass-if (< -inf.0 (- (1+ (ash 1 1024)))))
2015   (pass-if (not (< (- (1- (ash 1 1024))) -inf.0)))
2016   (pass-if (not (< (-     (ash 1 1024))  -inf.0)))
2017   (pass-if (not (< (- (1+ (ash 1 1024))) -inf.0)))
2018
2019   (pass-if (not (< +nan.0 +nan.0)))
2020   (pass-if (not (< 0 +nan.0)))
2021   (pass-if (not (< +nan.0 0)))
2022   (pass-if (not (< 1 +nan.0)))
2023   (pass-if (not (< +nan.0 1)))
2024   (pass-if (not (< -1 +nan.0)))
2025   (pass-if (not (< +nan.0 -1)))
2026
2027   (pass-if (not (< (ash 1 256) +nan.0)))
2028   (pass-if (not (< +nan.0 (ash 1 256))))
2029   (pass-if (not (< (- (ash 1 256)) +nan.0)))
2030   (pass-if (not (< +nan.0 (- (ash 1 256)))))
2031
2032   (pass-if (not (< (ash 1 8192) +nan.0)))
2033   (pass-if (not (< +nan.0 (ash 1 8192))))
2034   (pass-if (not (< (- (ash 1 8192)) +nan.0)))
2035   (pass-if (not (< +nan.0 (- (ash 1 8192)))))
2036
2037   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2038   ;; sure we've avoided that
2039   (pass-if (not (< (ash 3 1023) +nan.0)))
2040   (pass-if (not (< (1+ (ash 3 1023)) +nan.0)))
2041   (pass-if (not (< (1- (ash 3 1023)) +nan.0)))
2042   (pass-if (not (< +nan.0 (ash 3 1023))))
2043   (pass-if (not (< +nan.0 (1+ (ash 3 1023)))))
2044   (pass-if (not (< +nan.0 (1- (ash 3 1023)))))
2045
2046   (with-test-prefix "inum/frac"
2047     (pass-if (< 2 9/4))
2048     (pass-if (< -2 9/4))
2049     (pass-if (< -2 7/4))
2050     (pass-if (< -2 -7/4))
2051     (pass-if (eq? #f (< 2 7/4)))
2052     (pass-if (eq? #f (< 2 -7/4)))
2053     (pass-if (eq? #f (< 2 -9/4)))
2054     (pass-if (eq? #f (< -2 -9/4))))
2055
2056   (with-test-prefix "bignum/frac"
2057     (let ((x (ash 1 2048)))
2058       (pass-if (< x (* 4/3 x)))
2059       (pass-if (< (- x) (* 4/3 x)))
2060       (pass-if (< (- x) (* 2/3 x)))
2061       (pass-if (< (- x) (* -2/3 x)))
2062       (pass-if (eq? #f (< x (* 2/3 x))))
2063       (pass-if (eq? #f (< x (* -2/3 x))))
2064       (pass-if (eq? #f (< x (* -4/3 x))))
2065       (pass-if (eq? #f (< (- x) (* -4/3 x))))))
2066
2067   (with-test-prefix "flonum/frac"
2068     (pass-if (< 0.75 4/3))
2069     (pass-if (< -0.75 4/3))
2070     (pass-if (< -0.75 2/3))
2071     (pass-if (< -0.75 -2/3))
2072     (pass-if (eq? #f (< 0.75 2/3)))
2073     (pass-if (eq? #f (< 0.75 -2/3)))
2074     (pass-if (eq? #f (< 0.75 -4/3)))
2075     (pass-if (eq? #f (< -0.75 -4/3)))
2076
2077     (pass-if (< -inf.0 4/3))
2078     (pass-if (< -inf.0 -4/3))
2079     (pass-if (eq? #f (< +inf.0 4/3)))
2080     (pass-if (eq? #f (< +inf.0 -4/3)))
2081
2082     (pass-if (eq? #f (< +nan.0 4/3)))
2083     (pass-if (eq? #f (< +nan.0 -4/3))))
2084
2085   (with-test-prefix "frac/inum"
2086     (pass-if (< 7/4 2))
2087     (pass-if (< -7/4 2))
2088     (pass-if (< -9/4 2))
2089     (pass-if (< -9/4 -2))
2090     (pass-if (eq? #f (< 9/4 2)))
2091     (pass-if (eq? #f (< 9/4 -2)))
2092     (pass-if (eq? #f (< 7/4 -2)))
2093     (pass-if (eq? #f (< -7/4 -2))))
2094
2095   (with-test-prefix "frac/bignum"
2096     (let ((x (ash 1 2048)))
2097       (pass-if (< (* 2/3 x) x))
2098       (pass-if (< (* -2/3 x) x))
2099       (pass-if (< (* -4/3 x) x))
2100       (pass-if (< (* -4/3 x) (- x)))
2101       (pass-if (eq? #f (< (* 4/3 x) x)))
2102       (pass-if (eq? #f (< (* 4/3 x) (- x))))
2103       (pass-if (eq? #f (< (* 2/3 x) (- x))))
2104       (pass-if (eq? #f (< (* -2/3 x) (- x))))))
2105
2106   (with-test-prefix "frac/flonum"
2107     (pass-if (< 2/3 0.75))
2108     (pass-if (< -2/3 0.75))
2109     (pass-if (< -4/3 0.75))
2110     (pass-if (< -4/3 -0.75))
2111     (pass-if (eq? #f (< 4/3 0.75)))
2112     (pass-if (eq? #f (< 4/3 -0.75)))
2113     (pass-if (eq? #f (< 2/3 -0.75)))
2114     (pass-if (eq? #f (< -2/3 -0.75)))
2115
2116     (pass-if (< 4/3 +inf.0))
2117     (pass-if (< -4/3 +inf.0))
2118     (pass-if (eq? #f (< 4/3 -inf.0)))
2119     (pass-if (eq? #f (< -4/3 -inf.0)))
2120
2121     (pass-if (eq? #f (< 4/3 +nan.0)))
2122     (pass-if (eq? #f (< -4/3 +nan.0))))
2123
2124   (with-test-prefix "frac/frac"
2125     (pass-if (< 2/3 6/7))
2126     (pass-if (< -2/3 6/7))
2127     (pass-if (< -4/3 6/7))
2128     (pass-if (< -4/3 -6/7))
2129     (pass-if (eq? #f (< 4/3 6/7)))
2130     (pass-if (eq? #f (< 4/3 -6/7)))
2131     (pass-if (eq? #f (< 2/3 -6/7)))
2132     (pass-if (eq? #f (< -2/3 -6/7)))))
2133
2134 ;;;
2135 ;;; >
2136 ;;;
2137
2138 ;; currently not tested -- implementation is trivial
2139 ;; (> x y) is implemented as (< y x)
2140 ;; FIXME: tests should probably be added in case we change implementation.
2141
2142 ;;;
2143 ;;; <=
2144 ;;;
2145
2146 ;; currently not tested -- implementation is trivial
2147 ;; (<= x y) is implemented as (not (< y x))
2148 ;; FIXME: tests should probably be added in case we change implementation.
2149
2150 ;;;
2151 ;;; >=
2152 ;;;
2153
2154 ;; currently not tested -- implementation is trivial
2155 ;; (>= x y) is implemented as (not (< x y))
2156 ;; FIXME: tests should probably be added in case we change implementation.
2157
2158 ;;;
2159 ;;; zero?
2160 ;;;
2161
2162 (with-test-prefix "zero?"
2163   (expect-fail (documented? zero?))
2164   (pass-if (zero? 0))
2165   (pass-if (not (zero? 7)))
2166   (pass-if (not (zero? -7)))
2167   (pass-if (not (zero? (+ 1 fixnum-max))))
2168   (pass-if (not (zero? (- 1 fixnum-min))))
2169   (pass-if (not (zero? 1.3)))
2170   (pass-if (not (zero? 3.1+4.2i))))
2171
2172 ;;;
2173 ;;; positive?
2174 ;;;
2175
2176 (with-test-prefix "positive?"
2177   (expect-fail (documented? positive?))
2178   (pass-if (positive? 1))
2179   (pass-if (positive? (+ fixnum-max 1)))
2180   (pass-if (positive? 1.3))
2181   (pass-if (not (positive? 0)))
2182   (pass-if (not (positive? -1)))
2183   (pass-if (not (positive? (- fixnum-min 1))))
2184   (pass-if (not (positive? -1.3))))
2185
2186 ;;;
2187 ;;; negative?
2188 ;;;
2189
2190 (with-test-prefix "negative?"
2191   (expect-fail (documented? negative?))
2192   (pass-if (not (negative? 1)))
2193   (pass-if (not (negative? (+ fixnum-max 1))))
2194   (pass-if (not (negative? 1.3)))
2195   (pass-if (not (negative? 0)))
2196   (pass-if (negative? -1))
2197   (pass-if (negative? (- fixnum-min 1)))
2198   (pass-if (negative? -1.3)))
2199
2200 ;;;
2201 ;;; max
2202 ;;;
2203
2204 (with-test-prefix "max"
2205   (pass-if-exception "no args" exception:wrong-num-args
2206     (max))
2207
2208   (pass-if-exception "one complex" exception:wrong-type-arg
2209     (max 1+i))
2210
2211   (pass-if-exception "inum/complex" exception:wrong-type-arg
2212     (max 123 1+i))
2213   (pass-if-exception "big/complex" exception:wrong-type-arg
2214     (max 9999999999999999999999999999999999999999 1+i))
2215   (pass-if-exception "real/complex" exception:wrong-type-arg
2216     (max 123.0 1+i))
2217   (pass-if-exception "frac/complex" exception:wrong-type-arg
2218     (max 123/456 1+i))
2219
2220   (pass-if-exception "complex/inum" exception:wrong-type-arg
2221     (max 1+i 123))
2222   (pass-if-exception "complex/big" exception:wrong-type-arg
2223     (max 1+i 9999999999999999999999999999999999999999))
2224   (pass-if-exception "complex/real" exception:wrong-type-arg
2225     (max 1+i 123.0))
2226   (pass-if-exception "complex/frac" exception:wrong-type-arg
2227     (max 1+i 123/456))
2228
2229   (let ((big*2 (* fixnum-max 2))
2230         (big*3 (* fixnum-max 3))
2231         (big*4 (* fixnum-max 4))
2232         (big*5 (* fixnum-max 5)))
2233
2234     (with-test-prefix "inum / frac"
2235       (pass-if (= 3 (max 3 5/2)))
2236       (pass-if (= 5/2 (max 2 5/2))))
2237
2238     (with-test-prefix "frac / inum"
2239       (pass-if (= 3 (max 5/2 3)))
2240       (pass-if (= 5/2 (max 5/2 2))))
2241
2242     (with-test-prefix "inum / real"
2243       (pass-if (nan? (max 123 +nan.0))))
2244
2245     (with-test-prefix "real / inum"
2246       (pass-if (nan? (max +nan.0 123))))
2247
2248     (with-test-prefix "big / frac"
2249       (pass-if (= big*2 (max big*2 5/2)))
2250       (pass-if (= 5/2 (max (- big*2) 5/2))))
2251
2252     (with-test-prefix "frac / big"
2253       (pass-if (= big*2 (max 5/2 big*2)))
2254       (pass-if (= 5/2 (max 5/2 (- big*2)))))
2255
2256     (with-test-prefix "big / real"
2257       (pass-if (nan? (max big*5 +nan.0)))
2258       (pass-if (eqv? (exact->inexact big*5)  (max big*5 -inf.0)))
2259       (pass-if (eqv? (exact->inexact big*5)  (max big*5 1.0)))
2260       (pass-if (eqv? +inf.0                  (max big*5 +inf.0)))
2261       (pass-if (eqv? 1.0                     (max (- big*5) 1.0))))
2262
2263     (with-test-prefix "real / big"
2264       (pass-if (nan? (max +nan.0 big*5)))
2265       (pass-if (eqv? (exact->inexact big*5)  (max -inf.0 big*5)))
2266       (pass-if (eqv? (exact->inexact big*5)  (max 1.0 big*5)))
2267       (pass-if (eqv? +inf.0                  (max +inf.0 big*5)))
2268       (pass-if (eqv? 1.0                     (max 1.0 (- big*5)))))
2269
2270     (with-test-prefix "frac / frac"
2271       (pass-if (= 2/3 (max 1/2 2/3)))
2272       (pass-if (= 2/3 (max 2/3 1/2)))
2273       (pass-if (= -1/2 (max -1/2 -2/3)))
2274       (pass-if (= -1/2 (max -2/3 -1/2))))
2275
2276     (with-test-prefix "real / real"
2277       (pass-if (nan? (max 123.0 +nan.0)))
2278       (pass-if (nan? (max +nan.0 123.0)))
2279       (pass-if (nan? (max +nan.0 +nan.0)))
2280       (pass-if (= 456.0 (max 123.0 456.0)))
2281       (pass-if (= 456.0 (max 456.0 123.0)))))
2282
2283   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2284   ;; sure we've avoided that
2285   (for-each (lambda (b)
2286               (pass-if (list b +inf.0)
2287                 (= +inf.0 (max b +inf.0)))
2288               (pass-if (list +inf.0 b)
2289                 (= +inf.0 (max b +inf.0)))
2290               (pass-if (list b -inf.0)
2291                 (= (exact->inexact b) (max b -inf.0)))
2292               (pass-if (list -inf.0 b)
2293                 (= (exact->inexact b) (max b -inf.0))))
2294             (list (1- (ash 1 1024))
2295                   (ash 1 1024)
2296                   (1+ (ash 1 1024))
2297                   (- (1- (ash 1 1024)))
2298                   (- (ash 1 1024))
2299                   (- (1+ (ash 1 1024)))))
2300
2301   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2302   ;; sure we've avoided that
2303   (pass-if (nan? (max (ash 1 2048) +nan.0)))
2304   (pass-if (nan? (max +nan.0 (ash 1 2048)))))
2305
2306 ;;;
2307 ;;; min
2308 ;;;
2309
2310 ;; FIXME: unfinished...
2311
2312 (with-test-prefix "min"
2313   (pass-if-exception "no args" exception:wrong-num-args
2314     (min))
2315
2316   (pass-if-exception "one complex" exception:wrong-type-arg
2317     (min 1+i))
2318
2319   (pass-if-exception "inum/complex" exception:wrong-type-arg
2320     (min 123 1+i))
2321   (pass-if-exception "big/complex" exception:wrong-type-arg
2322     (min 9999999999999999999999999999999999999999 1+i))
2323   (pass-if-exception "real/complex" exception:wrong-type-arg
2324     (min 123.0 1+i))
2325   (pass-if-exception "frac/complex" exception:wrong-type-arg
2326     (min 123/456 1+i))
2327
2328   (pass-if-exception "complex/inum" exception:wrong-type-arg
2329     (min 1+i 123))
2330   (pass-if-exception "complex/big" exception:wrong-type-arg
2331     (min 1+i 9999999999999999999999999999999999999999))
2332   (pass-if-exception "complex/real" exception:wrong-type-arg
2333     (min 1+i 123.0))
2334   (pass-if-exception "complex/frac" exception:wrong-type-arg
2335     (min 1+i 123/456))
2336
2337   (let ((big*2 (* fixnum-max 2))
2338         (big*3 (* fixnum-max 3))
2339         (big*4 (* fixnum-max 4))
2340         (big*5 (* fixnum-max 5)))
2341
2342     (pass-if (documented? min))
2343     (pass-if (= 1 (min 7 3 1 5)))
2344     (pass-if (= 1 (min 1 7 3 5)))
2345     (pass-if (= 1 (min 7 3 5 1)))
2346     (pass-if (= -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
2347     (pass-if (= -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
2348     (pass-if (= -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
2349     (pass-if (= big*2 (min big*3 big*5 big*2 big*4)))
2350     (pass-if (= big*2 (min big*2 big*3 big*5 big*4)))
2351     (pass-if (= big*2 (min big*3 big*5 big*4 big*2)))
2352     (pass-if
2353         (= (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
2354     (pass-if
2355         (= (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
2356     (pass-if
2357         (= (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
2358
2359     (with-test-prefix "inum / frac"
2360       (pass-if (= 5/2 (min 3 5/2)))
2361       (pass-if (= 2   (min 2 5/2))))
2362
2363     (with-test-prefix "frac / inum"
2364       (pass-if (= 5/2 (min 5/2 3)))
2365       (pass-if (= 2   (min 5/2 2))))
2366
2367     (with-test-prefix "inum / real"
2368       (pass-if (nan? (min 123 +nan.0))))
2369
2370     (with-test-prefix "real / inum"
2371       (pass-if (nan? (min +nan.0 123))))
2372
2373     (with-test-prefix "big / frac"
2374       (pass-if (= 5/2       (min big*2 5/2)))
2375       (pass-if (= (- big*2) (min (- big*2) 5/2))))
2376
2377     (with-test-prefix "frac / big"
2378       (pass-if (= 5/2       (min 5/2 big*2)))
2379       (pass-if (= (- big*2) (min 5/2 (- big*2)))))
2380
2381     (with-test-prefix "big / real"
2382       (pass-if (nan? (min big*5 +nan.0)))
2383       (pass-if (eqv? (exact->inexact big*5)      (min big*5  +inf.0)))
2384       (pass-if (eqv? -inf.0                      (min big*5  -inf.0)))
2385       (pass-if (eqv? 1.0                         (min big*5 1.0)))
2386       (pass-if (eqv? (exact->inexact (- big*5))  (min (- big*5) 1.0))))
2387
2388     (with-test-prefix "real / big"
2389       (pass-if (nan? (min +nan.0 big*5)))
2390       (pass-if (eqv? (exact->inexact big*5)      (min +inf.0 big*5)))
2391       (pass-if (eqv? -inf.0                      (min -inf.0 big*5)))
2392       (pass-if (eqv? 1.0                         (min 1.0 big*5)))
2393       (pass-if (eqv? (exact->inexact (- big*5))  (min 1.0 (- big*5)))))
2394
2395     (with-test-prefix "frac / frac"
2396       (pass-if (= 1/2 (min 1/2 2/3)))
2397       (pass-if (= 1/2 (min 2/3 1/2)))
2398       (pass-if (= -2/3 (min -1/2 -2/3)))
2399       (pass-if (= -2/3 (min -2/3 -1/2))))
2400
2401     (with-test-prefix "real / real"
2402       (pass-if (nan? (min 123.0 +nan.0)))
2403       (pass-if (nan? (min +nan.0 123.0)))
2404       (pass-if (nan? (min +nan.0 +nan.0)))
2405       (pass-if (= 123.0 (min 123.0 456.0)))
2406       (pass-if (= 123.0 (min 456.0 123.0)))))
2407
2408
2409   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2410   ;; sure we've avoided that
2411   (for-each (lambda (b)
2412               (pass-if (list b +inf.0)
2413                 (= (exact->inexact b) (min b +inf.0)))
2414               (pass-if (list +inf.0 b)
2415                 (= (exact->inexact b) (min b +inf.0)))
2416               (pass-if (list b -inf.0)
2417                 (= -inf.0 (min b -inf.0)))
2418               (pass-if (list -inf.0 b)
2419                 (= -inf.0 (min b -inf.0))))
2420             (list (1- (ash 1 1024))
2421                   (ash 1 1024)
2422                   (1+ (ash 1 1024))
2423                   (- (1- (ash 1 1024)))
2424                   (- (ash 1 1024))
2425                   (- (1+ (ash 1 1024)))))
2426
2427   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2428   ;; sure we've avoided that
2429   (pass-if (nan? (min (- (ash 1 2048)) (- +nan.0))))
2430   (pass-if (nan? (min (- +nan.0) (- (ash 1 2048))))))
2431
2432 ;;;
2433 ;;; +
2434 ;;;
2435
2436 (with-test-prefix "+"
2437
2438   (pass-if "documented?"
2439     (documented? +))
2440
2441   (with-test-prefix "wrong type argument"
2442
2443     (pass-if-exception "1st argument string"
2444       exception:wrong-type-arg
2445       (+ "1" 2))
2446
2447     (pass-if-exception "2nd argument bool"
2448       exception:wrong-type-arg
2449       (+ 1 #f))))
2450 ;;;
2451 ;;; -
2452 ;;;
2453
2454 (with-test-prefix "-"
2455
2456   (pass-if "-inum - +bignum"
2457     (= #x-100000000000000000000000000000001
2458        (- -1 #x100000000000000000000000000000000)))
2459
2460   (pass-if "big - inum"
2461     (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
2462        (- #x100000000000000000000000000000000 1)))
2463
2464   (pass-if "big - -inum"
2465     (= #x100000000000000000000000000000001
2466        (- #x100000000000000000000000000000000 -1))))
2467
2468 ;;;
2469 ;;; *
2470 ;;;
2471
2472 (with-test-prefix "*"
2473
2474   (with-test-prefix "inum * bignum"
2475
2476     (pass-if "0 * 2^256 = 0"
2477       (eqv? 0 (* 0 (ash 1 256)))))
2478
2479   (with-test-prefix "inum * flonum"
2480
2481     (pass-if "0 * 1.0 = 0"
2482       (eqv? 0 (* 0 1.0))))
2483
2484   (with-test-prefix "inum * complex"
2485
2486     (pass-if "0 * 1+1i = 0"
2487       (eqv? 0 (* 0 1+1i))))
2488
2489   (with-test-prefix "inum * frac"
2490
2491     (pass-if "0 * 2/3 = 0"
2492       (eqv? 0 (* 0 2/3))))
2493
2494   (with-test-prefix "bignum * inum"
2495
2496     (pass-if "2^256 * 0 = 0"
2497       (eqv? 0 (* (ash 1 256) 0))))
2498
2499   (with-test-prefix "flonum * inum"
2500
2501     ;; in guile 1.6.8 and 1.8.1 and earlier this returned inexact 0.0
2502     (pass-if "1.0 * 0 = 0"
2503       (eqv? 0 (* 1.0 0))))
2504
2505   (with-test-prefix "complex * inum"
2506
2507     ;; in guile 1.6.8 and 1.8.1 and earlier this returned inexact 0.0
2508     (pass-if "1+1i * 0 = 0"
2509       (eqv? 0 (* 1+1i 0))))
2510
2511   (pass-if "complex * bignum"
2512     (let ((big (ash 1 90)))
2513       (= (make-rectangular big big)
2514          (* 1+1i big))))
2515
2516   (with-test-prefix "frac * inum"
2517
2518     (pass-if "2/3 * 0 = 0"
2519       (eqv? 0 (* 2/3 0)))))
2520
2521 ;;;
2522 ;;; /
2523 ;;;
2524
2525 (with-test-prefix "/"
2526
2527   (pass-if "documented?"
2528     (documented? /))
2529
2530   (with-test-prefix "division by zero"
2531
2532     (pass-if-exception "(/ 0)"
2533         exception:numerical-overflow
2534       (/ 0))
2535
2536     (pass-if "(/ 0.0)"
2537       (= +inf.0 (/ 0.0)))
2538
2539     (pass-if-exception "(/ 1 0)"
2540         exception:numerical-overflow
2541       (/ 1 0))
2542
2543     (pass-if "(/ 1 0.0)"
2544       (= +inf.0 (/ 1 0.0)))
2545
2546     (pass-if-exception "(/ bignum 0)"
2547         exception:numerical-overflow
2548       (/ (+ fixnum-max 1) 0))
2549
2550     (pass-if "(/ bignum 0.0)"
2551       (= +inf.0 (/ (+ fixnum-max 1) 0.0)))
2552
2553     (pass-if-exception "(/ 1.0 0)"
2554         exception:numerical-overflow
2555       (/ 1.0 0))
2556
2557     (pass-if "(/ 1.0 0.0)"
2558       (= +inf.0 (/ 1.0 0.0)))
2559
2560     (pass-if-exception "(/ +i 0)"
2561         exception:numerical-overflow
2562       (/ +i 0))
2563
2564     (pass-if "(/ +i 0.0)"
2565       (= +inf.0 (imag-part (/ +i 0.0)))))
2566
2567   (with-test-prefix "1/complex"
2568
2569     (pass-if "0+1i"
2570       (eqv? 0-1i (/ 0+1i)))
2571
2572     ;; in guile 1.6 through 1.6.7 this incorrectly resulted in nans
2573     (pass-if "0-1i"
2574       (eqv? 0+1i (/ 0-1i)))
2575
2576     (pass-if "1+1i"
2577       (eqv? 0.5-0.5i (/ 1+1i)))
2578
2579     (pass-if "1-1i"
2580       (eqv? 0.5+0.5i (/ 1-1i)))
2581
2582     (pass-if "-1+1i"
2583       (eqv? -0.5-0.5i (/ -1+1i)))
2584
2585     (pass-if "-1-1i"
2586       (eqv? -0.5+0.5i (/ -1-1i)))
2587
2588     (pass-if "(/ 3+4i)"
2589       (= (/ 3+4i) 0.12-0.16i))
2590
2591     (pass-if "(/ 4+3i)"
2592       (= (/ 4+3i) 0.16-0.12i))
2593
2594     (pass-if "(/ 1e200+1e200i)"
2595       (= (/ 1e200+1e200i) 5.0e-201-5.0e-201i)))
2596
2597   (with-test-prefix "inum/complex"
2598
2599     (pass-if "(/ 25 3+4i)"
2600       (= (/ 25 3+4i) 3.0-4.0i))
2601
2602     (pass-if "(/ 25 4+3i)"
2603       (= (/ 25 4+3i) 4.0-3.0i)))
2604
2605   (with-test-prefix "complex/complex"
2606
2607     (pass-if "(/ 25+125i 3+4i)"
2608       (= (/ 25+125i 3+4i) 23.0+11.0i))
2609
2610     (pass-if "(/ 25+125i 4+3i)"
2611       (= (/ 25+125i 4+3i) 19.0+17.0i))))
2612
2613 ;;;
2614 ;;; truncate
2615 ;;;
2616
2617 (with-test-prefix "truncate"
2618   (pass-if (=  1 (truncate  1.75)))
2619   (pass-if (=  1 (truncate  1.5)))
2620   (pass-if (=  1 (truncate  1.25)))
2621   (pass-if (=  0 (truncate  0.75)))
2622   (pass-if (=  0 (truncate  0.5)))
2623   (pass-if (=  0 (truncate  0.0)))
2624   (pass-if (=  0 (truncate -0.5)))
2625   (pass-if (= -1 (truncate -1.25)))
2626   (pass-if (= -1 (truncate -1.5))))
2627
2628 ;;;
2629 ;;; round
2630 ;;;
2631
2632 (with-test-prefix "round"
2633   (pass-if (=  2 (round  1.75)))
2634   (pass-if (=  2 (round  1.5)))
2635   (pass-if (=  1 (round  1.25)))
2636   (pass-if (=  1 (round  0.75)))
2637   (pass-if (=  0 (round  0.5)))
2638   (pass-if (=  0 (round  0.0)))
2639   (pass-if (=  0 (round -0.5)))
2640   (pass-if (= -1 (round -1.25)))
2641   (pass-if (= -2 (round -1.5)))
2642
2643   (with-test-prefix "inum"
2644     (pass-if "0"
2645       (and (= 0    (round 0))
2646            (exact? (round 0))))
2647
2648     (pass-if "1"
2649       (and (= 1    (round 1))
2650            (exact? (round 1))))
2651
2652     (pass-if "-1"
2653       (and (= -1   (round -1))
2654            (exact? (round -1)))))
2655
2656   (with-test-prefix "bignum"
2657     (let ((x (1+ most-positive-fixnum)))
2658       (pass-if "(1+ most-positive-fixnum)"
2659         (and (= x    (round x))
2660              (exact? (round x)))))
2661
2662     (let ((x (1- most-negative-fixnum)))
2663       (pass-if "(1- most-negative-fixnum)"
2664         (and (= x    (round x))
2665              (exact? (round x))))))
2666
2667   (with-test-prefix "frac"
2668     (define (=exact x y)
2669       (and (= x y)
2670            (exact? y)))
2671
2672     (pass-if (=exact -2 (round -7/3)))
2673     (pass-if (=exact -2 (round -5/3)))
2674     (pass-if (=exact -1 (round -4/3)))
2675     (pass-if (=exact -1 (round -2/3)))
2676     (pass-if (=exact  0 (round -1/3)))
2677     (pass-if (=exact  0 (round  1/3)))
2678     (pass-if (=exact  1 (round  2/3)))
2679     (pass-if (=exact  1 (round  4/3)))
2680     (pass-if (=exact  2 (round  5/3)))
2681     (pass-if (=exact  2 (round  7/3)))
2682
2683     (pass-if (=exact -3 (round -17/6)))
2684     (pass-if (=exact -3 (round -16/6)))
2685     (pass-if (=exact -2 (round -15/6)))
2686     (pass-if (=exact -2 (round -14/6)))
2687     (pass-if (=exact -2 (round -13/6)))
2688     (pass-if (=exact -2 (round -11/6)))
2689     (pass-if (=exact -2 (round -10/6)))
2690     (pass-if (=exact -2 (round  -9/6)))
2691     (pass-if (=exact -1 (round  -8/6)))
2692     (pass-if (=exact -1 (round  -7/6)))
2693     (pass-if (=exact -1 (round  -5/6)))
2694     (pass-if (=exact -1 (round  -4/6)))
2695     (pass-if (=exact  0 (round  -3/6)))
2696     (pass-if (=exact  0 (round  -2/6)))
2697     (pass-if (=exact  0 (round  -1/6)))
2698     (pass-if (=exact  0 (round   1/6)))
2699     (pass-if (=exact  0 (round   2/6)))
2700     (pass-if (=exact  0 (round   3/6)))
2701     (pass-if (=exact  1 (round   4/6)))
2702     (pass-if (=exact  1 (round   5/6)))
2703     (pass-if (=exact  1 (round   7/6)))
2704     (pass-if (=exact  1 (round   8/6)))
2705     (pass-if (=exact  2 (round   9/6)))
2706     (pass-if (=exact  2 (round  10/6)))
2707     (pass-if (=exact  2 (round  11/6)))
2708     (pass-if (=exact  2 (round  13/6)))
2709     (pass-if (=exact  2 (round  14/6)))
2710     (pass-if (=exact  2 (round  15/6)))
2711     (pass-if (=exact  3 (round  16/6)))
2712     (pass-if (=exact  3 (round  17/6))))
2713
2714   (with-test-prefix "real"
2715     (pass-if "0.0"
2716       (and (= 0.0    (round 0.0))
2717            (inexact? (round 0.0))))
2718
2719     (pass-if "1.0"
2720       (and (= 1.0    (round 1.0))
2721            (inexact? (round 1.0))))
2722
2723     (pass-if "-1.0"
2724       (and (= -1.0   (round -1.0))
2725            (inexact? (round -1.0))))
2726
2727     (pass-if "-3.1"
2728       (and (= -3.0   (round -3.1))
2729            (inexact? (round -3.1))))
2730
2731     (pass-if "3.1"
2732       (and (= 3.0    (round 3.1))
2733            (inexact? (round 3.1))))
2734
2735     (pass-if "3.9"
2736       (and (= 4.0    (round 3.9))
2737            (inexact? (round 3.9))))
2738
2739     (pass-if "-3.9"
2740       (and (= -4.0   (round -3.9))
2741            (inexact? (round -3.9))))
2742
2743     (pass-if "1.5"
2744       (and (= 2.0    (round 1.5))
2745            (inexact? (round 1.5))))
2746
2747     (pass-if "2.5"
2748       (and (= 2.0    (round 2.5))
2749            (inexact? (round 2.5))))
2750
2751     (pass-if "3.5"
2752       (and (= 4.0    (round 3.5))
2753            (inexact? (round 3.5))))
2754
2755     (pass-if "-1.5"
2756       (and (= -2.0   (round -1.5))
2757            (inexact? (round -1.5))))
2758
2759     (pass-if "-2.5"
2760       (and (= -2.0   (round -2.5))
2761            (inexact? (round -2.5))))
2762
2763     (pass-if "-3.5"
2764       (and (= -4.0   (round -3.5))
2765            (inexact? (round -3.5))))
2766
2767     ;; prior to guile 1.6.5, on an IEEE system an inexact 2^53-1 (ie. a
2768     ;; float with mantissa all ones) came out as 2^53 from `round' (except
2769     ;; on i386 and m68k systems using the coprocessor and optimizing, where
2770     ;; extra precision hid the problem)
2771     (pass-if "2^53-1"
2772       (let ((x (exact->inexact (1- (ash 1 53)))))
2773         (and (= x      (round x))
2774              (inexact? (round x)))))
2775     (pass-if "-(2^53-1)"
2776       (let ((x (exact->inexact (- (1- (ash 1 53))))))
2777         (and (= x      (round x))
2778              (inexact? (round x)))))))
2779
2780 ;;;
2781 ;;; exact->inexact
2782 ;;;
2783
2784 (with-test-prefix "exact->inexact"
2785
2786   ;; Test "(exact->inexact n)", expect "want".
2787   ;; "i" is a index, for diagnostic purposes.
2788   (define (try-i i n want)
2789     (with-test-prefix (list i n want)
2790       (with-test-prefix "pos"
2791         (let ((got (exact->inexact n)))
2792           (pass-if "inexact?" (inexact? got))
2793           (pass-if (list "=" got) (= want got))))
2794       (set! n    (- n))
2795       (set! want (- want))
2796       (with-test-prefix "neg"
2797         (let ((got (exact->inexact n)))
2798           (pass-if "inexact?" (inexact? got))
2799           (pass-if (list "=" got) (= want got))))))
2800
2801   (with-test-prefix "2^i, no round"
2802     (do ((i    0   (1+ i))
2803          (n    1   (* 2 n))
2804          (want 1.0 (* 2.0 want)))
2805         ((> i 100))
2806       (try-i i n want)))
2807
2808   (with-test-prefix "2^i+1, no round"
2809     (do ((i    1   (1+ i))
2810          (n    3   (1- (* 2 n)))
2811          (want 3.0 (- (* 2.0 want) 1.0)))
2812         ((>= i dbl-mant-dig))
2813       (try-i i n want)))
2814
2815   (with-test-prefix "(2^i+1)*2^100, no round"
2816     (do ((i    1   (1+ i))
2817          (n    3   (1- (* 2 n)))
2818          (want 3.0 (- (* 2.0 want) 1.0)))
2819         ((>= i dbl-mant-dig))
2820       (try-i i (ash n 100) (ash-flo want 100))))
2821
2822   ;; bit pattern: 1111....11100.00
2823   ;;              <-mantdig-><-i->
2824   ;;
2825   (with-test-prefix "mantdig ones then zeros, no rounding"
2826     (do ((i    0  (1+ i))
2827          (n    (- (ash     1   dbl-mant-dig) 1)   (* 2 n))
2828          (want (- (ash-flo 1.0 dbl-mant-dig) 1.0) (* 2.0 want)))
2829         ((> i 100))
2830       (try-i i n want)))
2831
2832   ;; bit pattern: 1111....111011..1
2833   ;;              <-mantdig-> <-i->
2834   ;; This sort of value was incorrectly rounded upwards in Guile 1.6.4 when
2835   ;; i >= 11 (that's when the total is 65 or more bits).
2836   ;;
2837   (with-test-prefix "mantdig ones then 011..11, round down"
2838     (do ((i    0  (1+ i))
2839          (n    (- (ash     1   (+ 1 dbl-mant-dig)) 2)   (+ 1 (* 2 n)))
2840          (want (- (ash-flo 1.0 (+ 1 dbl-mant-dig)) 2.0) (* 2.0 want)))
2841         ((> i 100))
2842       (try-i i n want)))
2843
2844   ;; bit pattern: 1111....111100..001
2845   ;;              <-mantdig-> <--i->
2846   ;;
2847   (with-test-prefix "mantdig ones then 100..001, round up"
2848     (do ((i    0  (1+ i))
2849          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)  (1- (* 2 n)))
2850          (want    (ash-flo 1.0 (+ 2 dbl-mant-dig))     (* 2.0 want)))
2851         ((> i 100))
2852       (try-i i n want)))
2853
2854   ;; bit pattern: 1000....000100..001
2855   ;;              <-mantdig-> <--i->
2856   ;;
2857   (with-test-prefix "2^mantdig then 100..001, round up"
2858     (do ((i    0  (1+ i))
2859          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)   (1- (* 2 n)))
2860          (want (+ (ash-flo 1.0 (+ 2 dbl-mant-dig)) 4.0) (* 2.0 want)))
2861         ((> i 100))
2862       (try-i i n want)))
2863
2864   (pass-if "frac big/big"
2865     (let ((big (ash 1 256)))
2866       (= 1.0 (exact->inexact (/ (1+ big) big)))))
2867
2868   ;; In guile 1.8.0 this failed, giving back "nan" because it tried to
2869   ;; convert the num and den to doubles, resulting in infs.
2870   (pass-if "frac big/big, exceeding double"
2871     (let ((big (ash 1 4096)))
2872       (= 1.0 (exact->inexact (/ (1+ big) big))))))
2873
2874 ;;;
2875 ;;; floor
2876 ;;;
2877
2878 ;;;
2879 ;;; ceiling
2880 ;;;
2881
2882 ;;;
2883 ;;; expt
2884 ;;;
2885
2886 (with-test-prefix "expt"
2887   (pass-if "(= 1 (expt 0 0))" (= 1 (expt 0 0)))
2888   (pass-if "(= 1 (expt 0 0.0))" (= 1 (expt 0 0.0)))
2889   (pass-if "(= 1 (expt 0.0 0))" (= 1 (expt 0.0 0)))
2890   (pass-if "(= 1 (expt 0.0 0.0))" (= 1 (expt 0.0 0.0))))
2891
2892 ;;;
2893 ;;; asinh
2894 ;;;
2895
2896 (with-test-prefix "asinh"
2897   (pass-if (= 0 (asinh 0))))
2898
2899 ;;;
2900 ;;; acosh
2901 ;;;
2902
2903 (with-test-prefix "acosh"
2904   (pass-if (= 0 (acosh 1))))
2905
2906 ;;;
2907 ;;; atanh
2908 ;;;
2909
2910 (with-test-prefix "atanh"
2911   (pass-if (= 0 (atanh 0))))
2912
2913 ;;;
2914 ;;; make-rectangular
2915 ;;;
2916
2917 ;;;
2918 ;;; make-polar
2919 ;;;
2920
2921 (with-test-prefix "make-polar"
2922   (define pi 3.14159265358979323846)
2923   (define (almost= x y)
2924     (> 0.01 (magnitude (- x y))))
2925
2926   (pass-if (= 0 (make-polar 0 0)))
2927   (pass-if (= 0 (make-polar 0 123.456)))
2928   (pass-if (= 1 (make-polar 1 0)))
2929   (pass-if (= -1 (make-polar -1 0)))
2930
2931   (pass-if (almost= 0+i (make-polar 1 (* 0.5 pi))))
2932   (pass-if (almost= -1  (make-polar 1 (* 1.0 pi))))
2933   (pass-if (almost= 0-i (make-polar 1 (* 1.5 pi))))
2934   (pass-if (almost= 1   (make-polar 1 (* 2.0 pi)))))
2935
2936 ;;;
2937 ;;; real-part
2938 ;;;
2939
2940 ;;;
2941 ;;; imag-part
2942 ;;;
2943
2944 ;;;
2945 ;;; magnitude
2946 ;;;
2947
2948 (with-test-prefix "magnitude"
2949   (pass-if (= 0 (magnitude 0)))
2950   (pass-if (= 1 (magnitude 1)))
2951   (pass-if (= 1 (magnitude -1)))
2952   (pass-if (= 1 (magnitude 0+i)))
2953   (pass-if (= 1 (magnitude 0-i)))
2954   (pass-if (= 5 (magnitude 3+4i)))
2955   (pass-if (= 5 (magnitude 3-4i)))
2956   (pass-if (= 5 (magnitude -3+4i)))
2957   (pass-if (= 5 (magnitude -3-4i))))
2958
2959 ;;;
2960 ;;; angle
2961 ;;;
2962
2963 (with-test-prefix "angle"
2964   (define pi 3.14159265358979323846)
2965   (define (almost= x y)
2966     (> 0.01 (magnitude (- x y))))
2967
2968   (pass-if "inum +ve"   (=        0 (angle 1)))
2969   (pass-if "inum -ve"   (almost= pi (angle -1)))
2970
2971   (pass-if "bignum +ve" (=        0 (angle (1+ fixnum-max))))
2972   (pass-if "bignum -ve" (almost= pi (angle (1- fixnum-min))))
2973
2974   (pass-if "flonum +ve" (=        0 (angle 1.5)))
2975   (pass-if "flonum -ve" (almost= pi (angle -1.5))))
2976
2977 ;;;
2978 ;;; inexact->exact
2979 ;;;
2980
2981 (with-test-prefix "inexact->exact"
2982
2983   (pass-if-exception "+inf" exception:out-of-range
2984     (inexact->exact +inf.0))
2985
2986   (pass-if-exception "-inf" exception:out-of-range
2987     (inexact->exact -inf.0))
2988
2989   (pass-if-exception "nan" exception:out-of-range
2990     (inexact->exact +nan.0))
2991
2992   (with-test-prefix "2.0**i to exact and back"
2993     (do ((i 0   (1+ i))
2994          (n 1.0 (* 2.0 n)))
2995         ((> i 100))
2996       (pass-if (list i n)
2997         (= n (inexact->exact (exact->inexact n)))))))
2998
2999 ;;;
3000 ;;; integer-expt
3001 ;;;
3002
3003 (with-test-prefix "integer-expt"
3004
3005   (pass-if-exception "2^+inf" exception:wrong-type-arg
3006     (integer-expt 2 +inf.0))
3007   (pass-if-exception "2^-inf" exception:wrong-type-arg
3008     (integer-expt 2 -inf.0))
3009   (pass-if-exception "2^nan" exception:wrong-type-arg
3010     (integer-expt 2 +nan.0)))
3011
3012 ;;;
3013 ;;; integer-length
3014 ;;;
3015
3016 (with-test-prefix "integer-length"
3017
3018   (with-test-prefix "-2^i, ...11100..00"
3019     (do ((n -1 (ash n 1))
3020          (i 0  (1+ i)))
3021         ((> i 256))
3022       (pass-if (list n "expect" i)
3023         (= i (integer-length n)))))
3024
3025   (with-test-prefix "-2^i+1 ...11100..01"
3026     (do ((n -3 (logxor 3 (ash n 1)))
3027          (i 2  (1+ i)))
3028         ((> i 256))
3029       (pass-if n
3030         (= i (integer-length n)))))
3031
3032   (with-test-prefix "-2^i-1 ...111011..11"
3033     (do ((n -2 (1+ (ash n 1)))
3034          (i 1  (1+ i)))
3035         ((> i 256))
3036       (pass-if n
3037         (= i (integer-length n))))))
3038
3039 ;;;
3040 ;;; log
3041 ;;;
3042
3043 (with-test-prefix "log"
3044   (pass-if "documented?"
3045     (documented? log))
3046
3047   (pass-if-exception "no args" exception:wrong-num-args
3048     (log))
3049   (pass-if-exception "two args" exception:wrong-num-args
3050     (log 123 456))
3051
3052   (pass-if (negative-infinity? (log 0)))
3053   (pass-if (negative-infinity? (log 0.0)))
3054   (pass-if (eqv? 0.0 (log 1)))
3055   (pass-if (eqv? 0.0 (log 1.0)))
3056   (pass-if (eqv-loosely? 1.0  (log const-e)))
3057   (pass-if (eqv-loosely? 2.0  (log const-e^2)))
3058   (pass-if (eqv-loosely? -1.0 (log const-1/e)))
3059
3060   (pass-if (eqv-loosely? 1.0+1.57079i (log 0+2.71828i)))
3061   (pass-if (eqv-loosely? 1.0-1.57079i (log 0-2.71828i)))
3062
3063   (pass-if (eqv-loosely? 0.0+3.14159i (log -1.0)))
3064   (pass-if (eqv-loosely? 1.0+3.14159i (log -2.71828)))
3065   (pass-if (eqv-loosely? 2.0+3.14159i (log (* -2.71828 2.71828)))))
3066
3067 ;;;
3068 ;;; log10
3069 ;;;
3070
3071 (with-test-prefix "log10"
3072   (pass-if "documented?"
3073     (documented? log10))
3074
3075   (pass-if-exception "no args" exception:wrong-num-args
3076     (log10))
3077   (pass-if-exception "two args" exception:wrong-num-args
3078     (log10 123 456))
3079
3080   (pass-if (negative-infinity? (log10 0)))
3081   (pass-if (negative-infinity? (log10 0.0)))
3082   (pass-if (eqv? 0.0 (log10 1)))
3083   (pass-if (eqv? 0.0 (log10 1.0)))
3084   (pass-if (eqv-loosely? 1.0  (log10 10.0)))
3085   (pass-if (eqv-loosely? 2.0  (log10 100.0)))
3086   (pass-if (eqv-loosely? -1.0 (log10 0.1)))
3087
3088   (pass-if (eqv-loosely? 1.0+0.68218i (log10 0+10.0i)))
3089   (pass-if (eqv-loosely? 1.0-0.68218i (log10 0-10.0i)))
3090
3091   (pass-if (eqv-loosely? 0.0+1.36437i (log10 -1)))
3092   (pass-if (eqv-loosely? 1.0+1.36437i (log10 -10)))
3093   (pass-if (eqv-loosely? 2.0+1.36437i (log10 -100))))
3094
3095 ;;;
3096 ;;; logbit?
3097 ;;;
3098
3099 (with-test-prefix "logbit?"
3100   (pass-if (eq? #f (logbit?  0 0)))
3101   (pass-if (eq? #f (logbit?  1 0)))
3102   (pass-if (eq? #f (logbit? 31 0)))
3103   (pass-if (eq? #f (logbit? 32 0)))
3104   (pass-if (eq? #f (logbit? 33 0)))
3105   (pass-if (eq? #f (logbit? 63 0)))
3106   (pass-if (eq? #f (logbit? 64 0)))
3107   (pass-if (eq? #f (logbit? 65 0)))
3108
3109   ;; prior to guile 1.6.5, testing bit 32, 64 etc of value 1 would wrap
3110   ;; around and return #t where it ought to be #f
3111   (pass-if (eq? #t (logbit?  0 1)))
3112   (pass-if (eq? #f (logbit?  1 1)))
3113   (pass-if (eq? #f (logbit? 31 1)))
3114   (pass-if (eq? #f (logbit? 32 1)))
3115   (pass-if (eq? #f (logbit? 33 1)))
3116   (pass-if (eq? #f (logbit? 63 1)))
3117   (pass-if (eq? #f (logbit? 64 1)))
3118   (pass-if (eq? #f (logbit? 65 1)))
3119   (pass-if (eq? #f (logbit? 128 1)))
3120
3121   (pass-if (eq? #t (logbit?  0 -1)))
3122   (pass-if (eq? #t (logbit?  1 -1)))
3123   (pass-if (eq? #t (logbit? 31 -1)))
3124   (pass-if (eq? #t (logbit? 32 -1)))
3125   (pass-if (eq? #t (logbit? 33 -1)))
3126   (pass-if (eq? #t (logbit? 63 -1)))
3127   (pass-if (eq? #t (logbit? 64 -1)))
3128   (pass-if (eq? #t (logbit? 65 -1))))
3129
3130 ;;;
3131 ;;; logcount
3132 ;;;
3133
3134 (with-test-prefix "logcount"
3135
3136   (with-test-prefix "-2^i, meaning ...11100..00"
3137     (do ((n -1 (ash n 1))
3138          (i 0  (1+ i)))
3139         ((> i 256))
3140       (pass-if n
3141         (= i (logcount n)))))
3142
3143   (with-test-prefix "2^i"
3144     (do ((n 1 (ash n 1))
3145          (i 0  (1+ i)))
3146         ((> i 256))
3147       (pass-if n
3148         (= 1 (logcount n)))))
3149
3150   (with-test-prefix "2^i-1"
3151     (do ((n 0 (1+ (ash n 1)))
3152          (i 0  (1+ i)))
3153         ((> i 256))
3154       (pass-if n
3155         (= i (logcount n))))))
3156
3157 ;;;
3158 ;;; logior
3159 ;;;
3160
3161 (with-test-prefix "logior"
3162   (pass-if (eqv? -1 (logior (ash -1 1) 1)))
3163
3164   ;; check that bignum or bignum+inum args will reduce to an inum
3165   (let ()
3166     (define (test x y)
3167       (pass-if (list x y '=> -1)
3168         (eqv? -1 (logior x y)))
3169       (pass-if (list y x '=> -1)
3170         (eqv? -1 (logior y x))))
3171     (test (ash -1 8) #xFF)
3172     (test (ash -1 28) #x0FFFFFFF)
3173     (test (ash -1 29) #x1FFFFFFF)
3174     (test (ash -1 30) #x3FFFFFFF)
3175     (test (ash -1 31) #x7FFFFFFF)
3176     (test (ash -1 32) #xFFFFFFFF)
3177     (test (ash -1 33) #x1FFFFFFFF)
3178     (test (ash -1 60) #x0FFFFFFFFFFFFFFF)
3179     (test (ash -1 61) #x1FFFFFFFFFFFFFFF)
3180     (test (ash -1 62) #x3FFFFFFFFFFFFFFF)
3181     (test (ash -1 63) #x7FFFFFFFFFFFFFFF)
3182     (test (ash -1 64) #xFFFFFFFFFFFFFFFF)
3183     (test (ash -1 65) #x1FFFFFFFFFFFFFFFF)
3184     (test (ash -1 128) #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
3185
3186 ;;;
3187 ;;; lognot
3188 ;;;
3189
3190 (with-test-prefix "lognot"
3191   (pass-if (= -1 (lognot 0)))
3192   (pass-if (= 0  (lognot -1)))
3193   (pass-if (= -2 (lognot 1)))
3194   (pass-if (= 1  (lognot -2)))
3195
3196   (pass-if (= #x-100000000000000000000000000000000
3197               (lognot #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
3198   (pass-if (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
3199               (lognot #x-100000000000000000000000000000000))))
3200
3201 ;;;
3202 ;;; sqrt
3203 ;;;
3204
3205 (with-test-prefix "sqrt"
3206   (pass-if "documented?"
3207     (documented? sqrt))
3208
3209   (pass-if-exception "no args" exception:wrong-num-args
3210     (sqrt))
3211   (pass-if-exception "two args" exception:wrong-num-args
3212     (sqrt 123 456))
3213
3214   (pass-if (eqv? 0.0 (sqrt 0)))
3215   (pass-if (eqv? 0.0 (sqrt 0.0)))
3216   (pass-if (eqv? 1.0 (sqrt 1.0)))
3217   (pass-if (eqv-loosely? 2.0   (sqrt 4.0)))
3218   (pass-if (eqv-loosely? 31.62 (sqrt 1000.0)))
3219
3220   (pass-if (eqv? +1.0i (sqrt -1.0)))
3221   (pass-if (eqv-loosely? +2.0i   (sqrt -4.0)))
3222   (pass-if (eqv-loosely? +31.62i (sqrt -1000.0)))
3223
3224   (pass-if "+i swings back to 45deg angle"
3225     (eqv-loosely? +0.7071+0.7071i (sqrt +1.0i)))
3226
3227   ;; Note: glibc 2.3 csqrt() had a bug affecting this test case, so if it
3228   ;; fails check whether that's the cause (there's a configure test to
3229   ;; reject it, but when cross-compiling we assume the C library is ok).
3230   (pass-if "-100i swings back to 45deg down"
3231     (eqv-loosely? +7.071-7.071i (sqrt -100.0i))))
3232
3233
3234 ;;
3235 ;; equal?
3236 ;;
3237
3238
3239 (with-test-prefix "equal?"
3240   (pass-if
3241
3242    ;; lazy reduction bit for rationals should not affect equal?
3243    (equal? 1/2 ((lambda (x) (denominator x) x) 1/2))))
3244