test-suite/tests/numbers.test

   1 ;;;; numbers.test --- tests guile's numbers     -*- scheme -*-
   2 ;;;; Copyright (C) 2000, 2001, 2003, 2004, 2005, 2006, 2009, 2010, 2011 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   #:use-module (srfi srfi-1)    ; list library
  22   #:use-module (srfi srfi-11))  ; let-values
  23
  24 ;;;
  25 ;;; miscellaneous
  26 ;;;
  27
  28 (define exception:numerical-overflow
  29   (cons 'numerical-overflow "^Numerical overflow"))
  30
  31 (define (documented? object)
  32   (not (not (object-documentation object))))
  33
  34 (define fixnum-bit
  35   (inexact->exact (+ (/ (log (+ most-positive-fixnum 1)) (log 2)) 1)))
  36
  37 (define fixnum-min most-negative-fixnum)
  38 (define fixnum-max most-positive-fixnum)
  39
  40 ;; Divine the number of bits in the mantissa of a flonum.
  41 ;; We look for when 2.0^i+1.0 gets rounded, ie. the difference between that
  42 ;; value and 2.0^k is not 1.0.
  43 ;; Of course this assumes flonums have a fixed precision mantissa, but
  44 ;; that's the case now and probably into the forseeable future.
  45 ;; On an IEEE system, which means pretty much everywhere, the value here is
  46 ;; the usual 53.
  47 ;;
  48 (define dbl-mant-dig
  49   (let more ((i 1)
  50              (d 2.0))
  51     (if (> i 1024)
  52         (error "Oops, cannot determine number of bits in mantissa of inexact"))
  53     (let* ((sum  (+ 1.0 d))
  54            (diff (- sum d)))
  55       (if (= diff 1.0)
  56           (more (1+ i) (* 2.0 d))
  57           i))))
  58
  59 ;; like ash, but working on a flonum
  60 (define (ash-flo x n)
  61   (while (> n 0)
  62     (set! x (* 2.0 x))
  63     (set! n (1- n)))
  64   (while (< n 0)
  65     (set! x (* 0.5 x))
  66     (set! n (1+ n)))
  67   x)
  68
  69 ;; `quotient' but rounded towards -infinity, like `modulo' or `ash' do
  70 ;; note only positive D supported (that's all that's currently required)
  71 (define-public (quotient-floor n d)
  72   (if (negative? n)
  73       (quotient (- n d -1) d)  ;; neg/pos
  74       (quotient n d)))         ;; pos/pos
  75
  76 ;; return true of X is in the range LO to HI, inclusive
  77 (define (within-range? lo hi x)
  78   (and (>= x (min lo hi))
  79        (<= x (max lo hi))))
  80
  81 ;; return true if GOT is within +/- 0.01 of GOT
  82 ;; for a complex number both real and imaginary parts must be in that range
  83 (define (eqv-loosely? want got)
  84   (and (within-range? (- (real-part want) 0.01)
  85                       (+ (real-part want) 0.01)
  86                       (real-part got))
  87        (within-range? (- (imag-part want) 0.01)
  88                       (+ (imag-part want) 0.01)
  89                       (imag-part got))))
  90
  91 ;; return true if OBJ is negative infinity
  92 (define (negative-infinity? obj)
  93   (and (real? obj)
  94        (negative? obj)
  95        (inf? obj)))
  96
  97 ;;
  98 ;; Tolerance used by test-eqv? for inexact numbers.
  99 ;;
 100 (define test-epsilon 1e-10)
 101
 102 ;;
 103 ;; Like eqv?, except that inexact finite numbers need only be within
 104 ;; test-epsilon (1e-10) to be considered equal.  For non-real complex
 105 ;; numbers, each component is tested according to these rules.  The
 106 ;; intent is that the known-correct value will be the first parameter.
 107 ;;
 108 (define (test-eqv? x y)
 109   (cond ((real? x)
 110          (and (real? y) (test-real-eqv? x y)))
 111         ((complex? x)
 112          (and (not (real? y))
 113               (test-real-eqv? (real-part x) (real-part y))
 114               (test-real-eqv? (imag-part x) (imag-part y))))
 115         (else (eqv? x y))))
 116
 117 ;; Auxiliary predicate used by test-eqv?
 118 (define (test-real-eqv? x y)
 119   (cond ((or (exact? x) (nan? x) (inf? x))
 120          (eqv? x y))
 121         (else (and (inexact? y) (> test-epsilon (abs (- x y)))))))
 122
 123 ;; return true if OBJ is a real NaN
 124 (define (real-nan? obj)
 125   (and (real? obj)
 126        (nan? obj)))
 127
 128 ;; return true if OBJ is a non-real complex number
 129 ;; whose real part is a nan, and whose imaginary
 130 ;; part is an inexact zero.
 131 (define (almost-real-nan? obj)
 132   (and (not (real? obj))
 133        (nan?  (real-part obj))
 134        (zero? (imag-part obj))))
 135
 136 ;; return true if both the real and imaginary
 137 ;; parts of OBJ are NaNs
 138 (define (complex-nan? obj)
 139   (and (nan? (real-part obj))
 140        (nan? (imag-part obj))))
 141
 142 ;; return true if the real part of OBJ is zero
 143 ;; and the imaginary part is a NaN.
 144 (define (imaginary-nan? obj)
 145   (and (zero? (real-part obj))
 146        (nan?  (imag-part obj))))
 147
 148 ;; return true if OBJ is a non-real complex zero
 149 (define (complex-zero? obj)
 150   (and (zero? obj)
 151        (complex? obj)
 152        (not (real? obj))))
 153
 154 (define const-e    2.7182818284590452354)
 155 (define const-e^2  7.3890560989306502274)
 156 (define const-1/e  0.3678794411714423215)
 157
 158
 159 ;;;
 160 ;;; 1+
 161 ;;;
 162
 163 (with-test-prefix/c&e "1+"
 164
 165   (pass-if "documented?"
 166     (documented? 1+))
 167
 168   (pass-if "0"   (eqv? 1 (1+ 0)))
 169   (pass-if "-1"   (eqv? 0 (1+ -1)))
 170   (pass-if "100"  (eqv? 101 (1+ 100)))
 171   (pass-if "-100" (eqv? -99 (1+ -100)))
 172
 173   ;; The maximum fixnum on a 32-bit architecture: 2^29 - 1.
 174   (pass-if "1+ fixnum = bignum (32-bit)"
 175     (eqv? 536870912 (1+ 536870911)))
 176
 177   ;; The maximum fixnum on a 64-bit architecture: 2^61 - 1.
 178   (pass-if "1+ fixnum = bignum (64-bit)"
 179     (eqv? 2305843009213693952 (1+ 2305843009213693951))))
 180
 181 ;;;
 182 ;;; 1-
 183 ;;;
 184
 185 (with-test-prefix/c&e "1-"
 186
 187   (pass-if "documented?"
 188     (documented? 1-))
 189
 190   (pass-if "0"    (eqv? -1 (1- 0)))
 191   (pass-if "1"    (eqv? 0 (1- 1)))
 192   (pass-if "100"  (eqv? 99 (1- 100)))
 193   (pass-if "-100" (eqv? -101 (1- -100)))
 194
 195   ;; The minimum fixnum on a 32-bit architecture: -2^29.
 196   (pass-if "1- fixnum = bignum (32-bit)"
 197     (eqv? -536870913 (1- -536870912)))
 198
 199   ;; The minimum fixnum on a 64-bit architecture: -2^61.
 200   (pass-if "1- fixnum = bignum (64-bit)"
 201     (eqv? -2305843009213693953 (1- -2305843009213693952))))
 202
 203 ;;;
 204 ;;; ash
 205 ;;;
 206
 207 (with-test-prefix "ash"
 208
 209   (pass-if "documented?"
 210     (documented? ash))
 211
 212   (pass-if (eqv? 0 (ash 0 0)))
 213   (pass-if (eqv? 0 (ash 0 1)))
 214   (pass-if (eqv? 0 (ash 0 1000)))
 215   (pass-if (eqv? 0 (ash 0 -1)))
 216   (pass-if (eqv? 0 (ash 0 -1000)))
 217
 218   (pass-if (eqv? 1 (ash 1 0)))
 219   (pass-if (eqv? 2 (ash 1 1)))
 220   (pass-if (eqv? 340282366920938463463374607431768211456 (ash 1 128)))
 221   (pass-if (eqv? 0 (ash 1 -1)))
 222   (pass-if (eqv? 0 (ash 1 -1000)))
 223
 224   (pass-if (eqv? -1 (ash -1 0)))
 225   (pass-if (eqv? -2 (ash -1 1)))
 226   (pass-if (eqv? -340282366920938463463374607431768211456 (ash -1 128)))
 227   (pass-if (eqv? -1 (ash -1 -1)))
 228   (pass-if (eqv? -1 (ash -1 -1000)))
 229
 230   (pass-if (eqv? -3 (ash -3 0)))
 231   (pass-if (eqv? -6 (ash -3 1)))
 232   (pass-if (eqv? -1020847100762815390390123822295304634368 (ash -3 128)))
 233   (pass-if (eqv? -2 (ash -3 -1)))
 234   (pass-if (eqv? -1 (ash -3 -1000)))
 235
 236   (pass-if (eqv? -6 (ash -23 -2)))
 237
 238   (pass-if (eqv? most-positive-fixnum       (ash most-positive-fixnum 0)))
 239   (pass-if (eqv? (* 2 most-positive-fixnum) (ash most-positive-fixnum 1)))
 240   (pass-if (eqv? (* 4 most-positive-fixnum) (ash most-positive-fixnum 2)))
 241   (pass-if
 242       (eqv? (* most-positive-fixnum 340282366920938463463374607431768211456)
 243             (ash most-positive-fixnum 128)))
 244   (pass-if (eqv? (quotient most-positive-fixnum 2)
 245                  (ash most-positive-fixnum -1)))
 246   (pass-if (eqv? 0 (ash most-positive-fixnum -1000)))
 247
 248   (let ((mpf4 (quotient most-positive-fixnum 4)))
 249     (pass-if (eqv? (* 2 mpf4) (ash mpf4 1)))
 250     (pass-if (eqv? (* 4 mpf4) (ash mpf4 2)))
 251     (pass-if (eqv? (* 8 mpf4) (ash mpf4 3))))
 252
 253   (pass-if (eqv? most-negative-fixnum       (ash most-negative-fixnum 0)))
 254   (pass-if (eqv? (* 2 most-negative-fixnum) (ash most-negative-fixnum 1)))
 255   (pass-if (eqv? (* 4 most-negative-fixnum) (ash most-negative-fixnum 2)))
 256   (pass-if
 257       (eqv? (* most-negative-fixnum 340282366920938463463374607431768211456)
 258             (ash most-negative-fixnum 128)))
 259   (pass-if (eqv? (quotient-floor most-negative-fixnum 2)
 260                  (ash most-negative-fixnum -1)))
 261   (pass-if (eqv? -1 (ash most-negative-fixnum -1000)))
 262
 263   (let ((mnf4 (quotient-floor most-negative-fixnum 4)))
 264     (pass-if (eqv? (* 2 mnf4) (ash mnf4 1)))
 265     (pass-if (eqv? (* 4 mnf4) (ash mnf4 2)))
 266     (pass-if (eqv? (* 8 mnf4) (ash mnf4 3)))))
 267
 268 ;;;
 269 ;;; exact?
 270 ;;;
 271
 272 (with-test-prefix "exact?"
 273
 274   (pass-if "documented?"
 275     (documented? exact?))
 276
 277   (with-test-prefix "integers"
 278
 279     (pass-if "0"
 280       (exact? 0))
 281
 282     (pass-if "fixnum-max"
 283       (exact? fixnum-max))
 284
 285     (pass-if "fixnum-max + 1"
 286       (exact? (+ fixnum-max 1)))
 287
 288     (pass-if "fixnum-min"
 289       (exact? fixnum-min))
 290
 291     (pass-if "fixnum-min - 1"
 292       (exact? (- fixnum-min 1))))
 293
 294   (with-test-prefix "reals"
 295
 296     ;; (FIXME: need better examples.)
 297
 298     (pass-if "sqrt (fixnum-max^2 - 1)"
 299       (eq? #f (exact? (sqrt (- (expt fixnum-max 2) 1)))))
 300
 301     (pass-if "sqrt ((fixnum-max+1)^2 - 1)"
 302       (eq? #f (exact? (sqrt (- (expt (+ fixnum-max 1) 2) 1)))))
 303
 304     (pass-if (not (exact? +inf.0)))
 305     (pass-if (not (exact? -inf.0)))
 306     (pass-if (not (exact? +nan.0)))))
 307
 308 ;;;
 309 ;;; exp
 310 ;;;
 311
 312 (with-test-prefix "exp"
 313   (pass-if (documented? exp))
 314
 315   (pass-if-exception "no args" exception:wrong-num-args
 316     (exp))
 317   (pass-if-exception "two args" exception:wrong-num-args
 318     (exp 123 456))
 319
 320   (pass-if (eqv? 0.0 (exp -inf.0)))
 321   (pass-if (eqv-loosely? 1.0 (exp 0)))
 322   (pass-if (eqv-loosely? 1.0 (exp 0.0)))
 323   (pass-if (eqv-loosely? const-e   (exp 1.0)))
 324   (pass-if (eqv-loosely? const-e^2 (exp 2.0)))
 325   (pass-if (eqv-loosely? const-1/e (exp -1)))
 326
 327   (pass-if "exp(pi*i) = -1"
 328     (eqv-loosely? -1.0 (exp 0+3.14159i)))
 329   (pass-if "exp(-pi*i) = -1"
 330     (eqv-loosely? -1.0 (exp 0-3.14159i)))
 331   (pass-if "exp(2*pi*i) = +1"
 332     (eqv-loosely? 1.0 (exp 0+6.28318i)))
 333
 334   (pass-if "exp(2-pi*i) = -e^2"
 335     (eqv-loosely? (- const-e^2) (exp 2.0-3.14159i))))
 336
 337 ;;;
 338 ;;; odd?
 339 ;;;
 340
 341 (with-test-prefix "odd?"
 342   (pass-if (documented? odd?))
 343   (pass-if (odd? 1))
 344   (pass-if (odd? -1))
 345   (pass-if (not (odd? 0)))
 346   (pass-if (not (odd? 2)))
 347   (pass-if (not (odd? -2)))
 348   (pass-if (odd? (+ (* 2 fixnum-max) 1)))
 349   (pass-if (not (odd? (* 2 fixnum-max))))
 350   (pass-if (odd? (- (* 2 fixnum-min) 1)))
 351   (pass-if (not (odd? (* 2 fixnum-min)))))
 352
 353 ;;;
 354 ;;; even?
 355 ;;;
 356
 357 (with-test-prefix "even?"
 358   (pass-if (documented? even?))
 359   (pass-if (even? 2))
 360   (pass-if (even? -2))
 361   (pass-if (even? 0))
 362   (pass-if (not (even? 1)))
 363   (pass-if (not (even? -1)))
 364   (pass-if (not (even? (+ (* 2 fixnum-max) 1))))
 365   (pass-if (even? (* 2 fixnum-max)))
 366   (pass-if (not (even? (- (* 2 fixnum-min) 1))))
 367   (pass-if (even? (* 2 fixnum-min))))
 368
 369 ;;;
 370 ;;; finite?
 371 ;;;
 372
 373 (with-test-prefix "finite?"
 374   (pass-if (documented? finite?))
 375   (pass-if (not (finite? (inf))))
 376   (pass-if (not (finite? +inf.0)))
 377   (pass-if (not (finite? -inf.0)))
 378   (pass-if-exception
 379    "complex numbers not in domain of finite?"
 380    exception:wrong-type-arg
 381    (finite? +inf.0+1i))
 382   (pass-if-exception
 383    "complex numbers not in domain of finite? (2)"
 384    exception:wrong-type-arg
 385    (finite? +1+inf.0i))
 386   (pass-if-exception
 387    "complex numbers not in domain of finite? (3)"
 388    exception:wrong-type-arg
 389    (finite? +1+1i))
 390   (pass-if (finite? 3+0i))
 391   (pass-if (not (finite? (nan))))
 392   (pass-if (not (finite? +nan.0)))
 393   (pass-if (finite? 0))
 394   (pass-if (finite? 0.0))
 395   (pass-if (finite? -0.0))
 396   (pass-if (finite? 42.0))
 397   (pass-if (finite? 1/2))
 398   (pass-if (finite? (+ fixnum-max 1)))
 399   (pass-if (finite? (- fixnum-min 1))))
 400
 401 ;;;
 402 ;;; inf? and inf
 403 ;;;
 404
 405 (with-test-prefix "inf?"
 406   (pass-if (documented? inf?))
 407   (pass-if (inf? (inf)))
 408   ;; FIXME: what are the expected behaviors?
 409   ;; (pass-if (inf? (/ 1.0 0.0))
 410   ;; (pass-if (inf? (/ 1 0.0))
 411   (pass-if-exception
 412    "complex numbers not in domain of inf?"
 413    exception:wrong-type-arg
 414    (inf? +1+inf.0i))
 415   (pass-if (inf? +inf.0+0i))
 416   (pass-if (not (inf? 0)))
 417   (pass-if (not (inf? 42.0)))
 418   (pass-if (not (inf? (+ fixnum-max 1))))
 419   (pass-if (not (inf? (- fixnum-min 1)))))
 420
 421 ;;;
 422 ;;; nan? and nan
 423 ;;;
 424
 425 (with-test-prefix "nan?"
 426   (pass-if (documented? nan?))
 427   (pass-if (nan? (nan)))
 428   ;; FIXME: other ways we should be able to generate NaN?
 429   (pass-if (not (nan? 0)))
 430   (pass-if (not (nan? 42.0)))
 431   (pass-if (not (nan? (+ fixnum-max 1))))
 432   (pass-if (not (nan? (- fixnum-min 1)))))
 433
 434 ;;;
 435 ;;; abs
 436 ;;;
 437
 438 (with-test-prefix "abs"
 439   (pass-if (documented? abs))
 440   (pass-if (eqv? 0 (abs 0)))
 441   (pass-if (eqv? 1 (abs 1)))
 442   (pass-if (eqv? 1 (abs -1)))
 443
 444   (with-test-prefix "double-negation of fixnum-min"
 445     (pass-if (eqv?   fixnum-min (- (abs fixnum-min)))))
 446
 447   (pass-if (eqv? (+    fixnum-max  1) (abs (+ fixnum-max 1))))
 448   (pass-if (eqv? (+ (- fixnum-min) 1) (abs (- fixnum-min 1))))
 449
 450   (pass-if (eqv? 0.0    (abs  0.0)))
 451   (pass-if (eqv? 0.0    (abs -0.0)))
 452   (pass-if (eqv? 1.0    (abs  1.0)))
 453   (pass-if (eqv? 1.0    (abs -1.0)))
 454   (pass-if (real-nan?   (abs +nan.0)))
 455   (pass-if (eqv? +inf.0 (abs +inf.0)))
 456   (pass-if (eqv? +inf.0 (abs -inf.0))))
 457
 458 ;;;
 459 ;;; quotient
 460 ;;;
 461
 462 (with-test-prefix "quotient"
 463   (pass-if (documented? quotient))
 464
 465   (with-test-prefix "0 / n"
 466
 467     (pass-if "n = 1"
 468       (eqv? 0 (quotient 0 1)))
 469
 470     (pass-if "n = -1"
 471       (eqv? 0 (quotient 0 -1)))
 472
 473     (pass-if "n = 2"
 474       (eqv? 0 (quotient 0 2)))
 475
 476     (pass-if "n = fixnum-max"
 477       (eqv? 0 (quotient 0 fixnum-max)))
 478
 479     (pass-if "n = fixnum-max + 1"
 480       (eqv? 0 (quotient 0 (+ fixnum-max 1))))
 481
 482     (pass-if "n = fixnum-min"
 483       (eqv? 0 (quotient 0 fixnum-min)))
 484
 485     (pass-if "n = fixnum-min - 1"
 486       (eqv? 0 (quotient 0 (- fixnum-min 1)))))
 487
 488   (with-test-prefix "1 / n"
 489
 490     (pass-if "n = 1"
 491       (eqv? 1 (quotient 1 1)))
 492
 493     (pass-if "n = -1"
 494       (eqv? -1 (quotient 1 -1)))
 495
 496     (pass-if "n = 2"
 497       (eqv? 0 (quotient 1 2)))
 498
 499     (pass-if "n = fixnum-max"
 500       (eqv? 0 (quotient 1 fixnum-max)))
 501
 502     (pass-if "n = fixnum-max + 1"
 503       (eqv? 0 (quotient 1 (+ fixnum-max 1))))
 504
 505     (pass-if "n = fixnum-min"
 506       (eqv? 0 (quotient 1 fixnum-min)))
 507
 508     (pass-if "n = fixnum-min - 1"
 509       (eqv? 0 (quotient 1 (- fixnum-min 1)))))
 510
 511   (with-test-prefix "-1 / n"
 512
 513     (pass-if "n = 1"
 514       (eqv? -1 (quotient -1 1)))
 515
 516     (pass-if "n = -1"
 517       (eqv? 1 (quotient -1 -1)))
 518
 519     (pass-if "n = 2"
 520       (eqv? 0 (quotient -1 2)))
 521
 522     (pass-if "n = fixnum-max"
 523       (eqv? 0 (quotient -1 fixnum-max)))
 524
 525     (pass-if "n = fixnum-max + 1"
 526       (eqv? 0 (quotient -1 (+ fixnum-max 1))))
 527
 528     (pass-if "n = fixnum-min"
 529       (eqv? 0 (quotient -1 fixnum-min)))
 530
 531     (pass-if "n = fixnum-min - 1"
 532       (eqv? 0 (quotient -1 (- fixnum-min 1)))))
 533
 534   (with-test-prefix "fixnum-max / n"
 535
 536     (pass-if "n = 1"
 537       (eqv? fixnum-max (quotient fixnum-max 1)))
 538
 539     (pass-if "n = -1"
 540       (eqv? (- fixnum-max) (quotient fixnum-max -1)))
 541
 542     (pass-if "n = 2"
 543       (eqv? fixnum-max (+ (* (quotient fixnum-max 2) 2) 1)))
 544
 545     (pass-if "n = fixnum-max"
 546       (eqv? 1 (quotient fixnum-max fixnum-max)))
 547
 548     (pass-if "n = fixnum-max + 1"
 549       (eqv? 0 (quotient fixnum-max (+ fixnum-max 1))))
 550
 551     (pass-if "n = fixnum-min"
 552       (eqv? 0 (quotient fixnum-max fixnum-min)))
 553
 554     (pass-if "n = fixnum-min - 1"
 555       (eqv? 0 (quotient fixnum-max (- fixnum-min 1)))))
 556
 557   (with-test-prefix "(fixnum-max + 1) / n"
 558
 559     (pass-if "n = 1"
 560       (eqv? (+ fixnum-max 1) (quotient (+ fixnum-max 1) 1)))
 561
 562     (pass-if "n = -1"
 563       (eqv? (- (+ fixnum-max 1)) (quotient (+ fixnum-max 1) -1)))
 564
 565     (pass-if "n = 2"
 566       (eqv? (+ fixnum-max 1) (* (quotient (+ fixnum-max 1) 2) 2)))
 567
 568     (pass-if "n = fixnum-max"
 569       (eqv? 1 (quotient (+ fixnum-max 1) fixnum-max)))
 570
 571     (pass-if "n = fixnum-max + 1"
 572       (eqv? 1 (quotient (+ fixnum-max 1) (+ fixnum-max 1))))
 573
 574     (pass-if "n = fixnum-min"
 575       (eqv? -1 (quotient (+ fixnum-max 1) fixnum-min)))
 576
 577     (pass-if "n = fixnum-min - 1"
 578       (eqv? 0 (quotient (+ fixnum-max 1) (- fixnum-min 1)))))
 579
 580   (with-test-prefix "fixnum-min / n"
 581
 582     (pass-if "n = 1"
 583       (eqv? fixnum-min (quotient fixnum-min 1)))
 584
 585     (pass-if "n = -1"
 586       (eqv? (- fixnum-min) (quotient fixnum-min -1)))
 587
 588     (pass-if "n = 2"
 589       (eqv? fixnum-min (* (quotient fixnum-min 2) 2)))
 590
 591     (pass-if "n = fixnum-max"
 592       (eqv? -1 (quotient fixnum-min fixnum-max)))
 593
 594     (pass-if "n = fixnum-max + 1"
 595       (eqv? -1 (quotient fixnum-min (+ fixnum-max 1))))
 596
 597     (pass-if "n = fixnum-min"
 598       (eqv? 1 (quotient fixnum-min fixnum-min)))
 599
 600     (pass-if "n = fixnum-min - 1"
 601       (eqv? 0 (quotient fixnum-min (- fixnum-min 1))))
 602
 603     (pass-if "n = - fixnum-min - 1"
 604       (eqv? -1 (quotient fixnum-min (1- (- fixnum-min)))))
 605
 606     ;; special case, normally inum/big is zero
 607     (pass-if "n = - fixnum-min"
 608       (eqv? -1 (quotient fixnum-min (- fixnum-min))))
 609
 610     (pass-if "n = - fixnum-min + 1"
 611       (eqv? 0 (quotient fixnum-min (1+ (- fixnum-min))))))
 612
 613   (with-test-prefix "(fixnum-min - 1) / n"
 614
 615     (pass-if "n = 1"
 616       (eqv? (- fixnum-min 1) (quotient (- fixnum-min 1) 1)))
 617
 618     (pass-if "n = -1"
 619       (eqv? (- (- fixnum-min 1)) (quotient (- fixnum-min 1) -1)))
 620
 621     (pass-if "n = 2"
 622       (eqv? fixnum-min (* (quotient (- fixnum-min 1) 2) 2)))
 623
 624     (pass-if "n = fixnum-max"
 625       (eqv? -1 (quotient (- fixnum-min 1) fixnum-max)))
 626
 627     (pass-if "n = fixnum-max + 1"
 628       (eqv? -1 (quotient (- fixnum-min 1) (+ fixnum-max 1))))
 629
 630     (pass-if "n = fixnum-min"
 631       (eqv? 1 (quotient (- fixnum-min 1) fixnum-min)))
 632
 633     (pass-if "n = fixnum-min - 1"
 634       (eqv? 1 (quotient (- fixnum-min 1) (- fixnum-min 1)))))
 635
 636   ;; Inexact integers
 637
 638   (pass-if (eqv? 5.0 (quotient 35.0 7.0)))
 639   (pass-if (eqv? 5.0 (quotient 35   7.0)))
 640   (pass-if (eqv? 5.0 (quotient 35.0 7  )))
 641
 642   ;; Positive dividend and divisor
 643
 644   (pass-if "35 / 7"
 645     (eqv? 5 (quotient 35 7)))
 646
 647   ;; Negative dividend, positive divisor
 648
 649   (pass-if "-35 / 7"
 650     (eqv? -5 (quotient -35 7)))
 651
 652   ;; Positive dividend, negative divisor
 653
 654   (pass-if "35 / -7"
 655     (eqv? -5 (quotient 35 -7)))
 656
 657   ;; Negative dividend and divisor
 658
 659   (pass-if "-35 / -7"
 660     (eqv? 5 (quotient -35 -7)))
 661
 662   ;; Are numerical overflows detected correctly?
 663
 664   (with-test-prefix "division by zero"
 665
 666     (pass-if-exception "(quotient 1 0)"
 667       exception:numerical-overflow
 668       (quotient 1 0))
 669
 670     (pass-if-exception "(quotient bignum 0)"
 671       exception:numerical-overflow
 672       (quotient (+ fixnum-max 1) 0)))
 673
 674   ;; Are wrong type arguments detected correctly?
 675
 676   )
 677
 678 ;;;
 679 ;;; remainder
 680 ;;;
 681
 682 (with-test-prefix "remainder"
 683   (pass-if (documented? remainder))
 684
 685   (with-test-prefix "0 / n"
 686
 687     (pass-if "n = 1"
 688       (eqv? 0 (remainder 0 1)))
 689
 690     (pass-if "n = -1"
 691       (eqv? 0 (remainder 0 -1)))
 692
 693     (pass-if "n = fixnum-max"
 694       (eqv? 0 (remainder 0 fixnum-max)))
 695
 696     (pass-if "n = fixnum-max + 1"
 697       (eqv? 0 (remainder 0 (+ fixnum-max 1))))
 698
 699     (pass-if "n = fixnum-min"
 700       (eqv? 0 (remainder 0 fixnum-min)))
 701
 702     (pass-if "n = fixnum-min - 1"
 703       (eqv? 0 (remainder 0 (- fixnum-min 1)))))
 704
 705   (with-test-prefix "1 / n"
 706
 707     (pass-if "n = 1"
 708       (eqv? 0 (remainder 1 1)))
 709
 710     (pass-if "n = -1"
 711       (eqv? 0 (remainder 1 -1)))
 712
 713     (pass-if "n = fixnum-max"
 714       (eqv? 1 (remainder 1 fixnum-max)))
 715
 716     (pass-if "n = fixnum-max + 1"
 717       (eqv? 1 (remainder 1 (+ fixnum-max 1))))
 718
 719     (pass-if "n = fixnum-min"
 720       (eqv? 1 (remainder 1 fixnum-min)))
 721
 722     (pass-if "n = fixnum-min - 1"
 723       (eqv? 1 (remainder 1 (- fixnum-min 1)))))
 724
 725   (with-test-prefix "-1 / n"
 726
 727     (pass-if "n = 1"
 728       (eqv? 0 (remainder -1 1)))
 729
 730     (pass-if "n = -1"
 731       (eqv? 0 (remainder -1 -1)))
 732
 733     (pass-if "n = fixnum-max"
 734       (eqv? -1 (remainder -1 fixnum-max)))
 735
 736     (pass-if "n = fixnum-max + 1"
 737       (eqv? -1 (remainder -1 (+ fixnum-max 1))))
 738
 739     (pass-if "n = fixnum-min"
 740       (eqv? -1 (remainder -1 fixnum-min)))
 741
 742     (pass-if "n = fixnum-min - 1"
 743       (eqv? -1 (remainder -1 (- fixnum-min 1)))))
 744
 745   (with-test-prefix "fixnum-max / n"
 746
 747     (pass-if "n = 1"
 748       (eqv? 0 (remainder fixnum-max 1)))
 749
 750     (pass-if "n = -1"
 751       (eqv? 0 (remainder fixnum-max -1)))
 752
 753     (pass-if "n = fixnum-max"
 754       (eqv? 0 (remainder fixnum-max fixnum-max)))
 755
 756     (pass-if "n = fixnum-max + 1"
 757       (eqv? fixnum-max (remainder fixnum-max (+ fixnum-max 1))))
 758
 759     (pass-if "n = fixnum-min"
 760       (eqv? fixnum-max (remainder fixnum-max fixnum-min)))
 761
 762     (pass-if "n = fixnum-min - 1"
 763       (eqv? fixnum-max (remainder fixnum-max (- fixnum-min 1)))))
 764
 765   (with-test-prefix "(fixnum-max + 1) / n"
 766
 767     (pass-if "n = 1"
 768       (eqv? 0 (remainder (+ fixnum-max 1) 1)))
 769
 770     (pass-if "n = -1"
 771       (eqv? 0 (remainder (+ fixnum-max 1) -1)))
 772
 773     (pass-if "n = fixnum-max"
 774       (eqv? 1 (remainder (+ fixnum-max 1) fixnum-max)))
 775
 776     (pass-if "n = fixnum-max + 1"
 777       (eqv? 0 (remainder (+ fixnum-max 1) (+ fixnum-max 1))))
 778
 779     (pass-if "n = fixnum-min"
 780       (eqv? 0 (remainder (+ fixnum-max 1) fixnum-min)))
 781
 782     (pass-if "n = fixnum-min - 1"
 783       (eqv? (+ fixnum-max 1) (remainder (+ fixnum-max 1) (- fixnum-min 1)))))
 784
 785   (with-test-prefix "fixnum-min / n"
 786
 787     (pass-if "n = 1"
 788       (eqv? 0 (remainder fixnum-min 1)))
 789
 790     (pass-if "n = -1"
 791       (eqv? 0 (remainder fixnum-min -1)))
 792
 793     (pass-if "n = fixnum-max"
 794       (eqv? -1 (remainder fixnum-min fixnum-max)))
 795
 796     (pass-if "n = fixnum-max + 1"
 797       (eqv? 0 (remainder fixnum-min (+ fixnum-max 1))))
 798
 799     (pass-if "n = fixnum-min"
 800       (eqv? 0 (remainder fixnum-min fixnum-min)))
 801
 802     (pass-if "n = fixnum-min - 1"
 803       (eqv? fixnum-min (remainder fixnum-min (- fixnum-min 1))))
 804
 805     (pass-if "n = - fixnum-min - 1"
 806       (eqv? -1 (remainder fixnum-min (1- (- fixnum-min)))))
 807
 808     ;; special case, normally inum%big is the inum
 809     (pass-if "n = - fixnum-min"
 810       (eqv? 0 (remainder fixnum-min (- fixnum-min))))
 811
 812     (pass-if "n = - fixnum-min + 1"
 813       (eqv? fixnum-min (remainder fixnum-min (1+ (- fixnum-min))))))
 814
 815   (with-test-prefix "(fixnum-min - 1) / n"
 816
 817     (pass-if "n = 1"
 818       (eqv? 0 (remainder (- fixnum-min 1) 1)))
 819
 820     (pass-if "n = -1"
 821       (eqv? 0 (remainder (- fixnum-min 1) -1)))
 822
 823     (pass-if "n = fixnum-max"
 824       (eqv? -2 (remainder (- fixnum-min 1) fixnum-max)))
 825
 826     (pass-if "n = fixnum-max + 1"
 827       (eqv? -1 (remainder (- fixnum-min 1) (+ fixnum-max 1))))
 828
 829     (pass-if "n = fixnum-min"
 830       (eqv? -1 (remainder (- fixnum-min 1) fixnum-min)))
 831
 832     (pass-if "n = fixnum-min - 1"
 833       (eqv? 0 (remainder (- fixnum-min 1) (- fixnum-min 1)))))
 834
 835   ;; Inexact integers
 836
 837   (pass-if (eqv? 2.0 (remainder 37.0 7.0)))
 838   (pass-if (eqv? 2.0 (remainder 37   7.0)))
 839   (pass-if (eqv? 2.0 (remainder 37.0 7  )))
 840
 841   ;; Positive dividend and divisor
 842
 843   (pass-if "35 / 7"
 844     (eqv? 0 (remainder 35 7)))
 845
 846   ;; Negative dividend, positive divisor
 847
 848   (pass-if "-35 / 7"
 849     (eqv? 0 (remainder -35 7)))
 850
 851   ;; Positive dividend, negative divisor
 852
 853   (pass-if "35 / -7"
 854     (eqv? 0 (remainder 35 -7)))
 855
 856   ;; Negative dividend and divisor
 857
 858   (pass-if "-35 / -7"
 859     (eqv? 0 (remainder -35 -7)))
 860
 861   ;; Are numerical overflows detected correctly?
 862
 863   (with-test-prefix "division by zero"
 864
 865     (pass-if-exception "(remainder 1 0)"
 866       exception:numerical-overflow
 867       (remainder 1 0))
 868
 869     (pass-if-exception "(remainder bignum 0)"
 870       exception:numerical-overflow
 871       (remainder (+ fixnum-max 1) 0)))
 872
 873   ;; Are wrong type arguments detected correctly?
 874
 875   )
 876
 877 ;;;
 878 ;;; modulo
 879 ;;;
 880
 881 (with-test-prefix "modulo"
 882   (pass-if (documented? modulo))
 883
 884   (with-test-prefix "0 % n"
 885
 886     (pass-if "n = 1"
 887       (eqv? 0 (modulo 0 1)))
 888
 889     (pass-if "n = -1"
 890       (eqv? 0 (modulo 0 -1)))
 891
 892     (pass-if "n = fixnum-max"
 893       (eqv? 0 (modulo 0 fixnum-max)))
 894
 895     (pass-if "n = fixnum-max + 1"
 896       (eqv? 0 (modulo 0 (+ fixnum-max 1))))
 897
 898     (pass-if "n = fixnum-min"
 899       (eqv? 0 (modulo 0 fixnum-min)))
 900
 901     (pass-if "n = fixnum-min - 1"
 902       (eqv? 0 (modulo 0 (- fixnum-min 1)))))
 903
 904   (with-test-prefix "1 % n"
 905
 906     (pass-if "n = 1"
 907       (eqv? 0 (modulo 1 1)))
 908
 909     (pass-if "n = -1"
 910       (eqv? 0 (modulo 1 -1)))
 911
 912     (pass-if "n = fixnum-max"
 913       (eqv? 1 (modulo 1 fixnum-max)))
 914
 915     (pass-if "n = fixnum-max + 1"
 916       (eqv? 1 (modulo 1 (+ fixnum-max 1))))
 917
 918     (pass-if "n = fixnum-min"
 919       (eqv? (+ fixnum-min 1) (modulo 1 fixnum-min)))
 920
 921     (pass-if "n = fixnum-min - 1"
 922       (eqv? fixnum-min (modulo 1 (- fixnum-min 1)))))
 923
 924   (with-test-prefix "-1 % n"
 925
 926     (pass-if "n = 1"
 927       (eqv? 0 (modulo -1 1)))
 928
 929     (pass-if "n = -1"
 930       (eqv? 0 (modulo -1 -1)))
 931
 932     (pass-if "n = fixnum-max"
 933       (eqv? (- fixnum-max 1) (modulo -1 fixnum-max)))
 934
 935     (pass-if "n = fixnum-max + 1"
 936       (eqv? fixnum-max (modulo -1 (+ fixnum-max 1))))
 937
 938     (pass-if "n = fixnum-min"
 939       (eqv? -1 (modulo -1 fixnum-min)))
 940
 941     (pass-if "n = fixnum-min - 1"
 942       (eqv? -1 (modulo -1 (- fixnum-min 1)))))
 943
 944   (with-test-prefix "fixnum-max % n"
 945
 946     (pass-if "n = 1"
 947       (eqv? 0 (modulo fixnum-max 1)))
 948
 949     (pass-if "n = -1"
 950       (eqv? 0 (modulo fixnum-max -1)))
 951
 952     (pass-if "n = fixnum-max"
 953       (eqv? 0 (modulo fixnum-max fixnum-max)))
 954
 955     (pass-if "n = fixnum-max + 1"
 956       (eqv? fixnum-max (modulo fixnum-max (+ fixnum-max 1))))
 957
 958     (pass-if "n = fixnum-min"
 959       (eqv? -1 (modulo fixnum-max fixnum-min)))
 960
 961     (pass-if "n = fixnum-min - 1"
 962       (eqv? -2 (modulo fixnum-max (- fixnum-min 1)))))
 963
 964   (with-test-prefix "(fixnum-max + 1) % n"
 965
 966     (pass-if "n = 1"
 967       (eqv? 0 (modulo (+ fixnum-max 1) 1)))
 968
 969     (pass-if "n = -1"
 970       (eqv? 0 (modulo (+ fixnum-max 1) -1)))
 971
 972     (pass-if "n = fixnum-max"
 973       (eqv? 1 (modulo (+ fixnum-max 1) fixnum-max)))
 974
 975     (pass-if "n = fixnum-max + 1"
 976       (eqv? 0 (modulo (+ fixnum-max 1) (+ fixnum-max 1))))
 977
 978     (pass-if "n = fixnum-min"
 979       (eqv? 0 (modulo (+ fixnum-max 1) fixnum-min)))
 980
 981     (pass-if "n = fixnum-min - 1"
 982       (eqv? -1 (modulo (+ fixnum-max 1) (- fixnum-min 1)))))
 983
 984   (with-test-prefix "fixnum-min % n"
 985
 986     (pass-if "n = 1"
 987       (eqv? 0 (modulo fixnum-min 1)))
 988
 989     (pass-if "n = -1"
 990       (eqv? 0 (modulo fixnum-min -1)))
 991
 992     (pass-if "n = fixnum-max"
 993       (eqv? (- fixnum-max 1) (modulo fixnum-min fixnum-max)))
 994
 995     (pass-if "n = fixnum-max + 1"
 996       (eqv? 0 (modulo fixnum-min (+ fixnum-max 1))))
 997
 998     (pass-if "n = fixnum-min"
 999       (eqv? 0 (modulo fixnum-min fixnum-min)))
1000
1001     (pass-if "n = fixnum-min - 1"
1002       (eqv? fixnum-min (modulo fixnum-min (- fixnum-min 1)))))
1003
1004   (with-test-prefix "(fixnum-min - 1) % n"
1005
1006     (pass-if "n = 1"
1007       (eqv? 0 (modulo (- fixnum-min 1) 1)))
1008
1009     (pass-if "n = -1"
1010       (eqv? 0 (modulo (- fixnum-min 1) -1)))
1011
1012     (pass-if "n = fixnum-max"
1013       (eqv? (- fixnum-max 2) (modulo (- fixnum-min 1) fixnum-max)))
1014
1015     (pass-if "n = fixnum-max + 1"
1016       (eqv? fixnum-max (modulo (- fixnum-min 1) (+ fixnum-max 1))))
1017
1018     (pass-if "n = fixnum-min"
1019       (eqv? -1 (modulo (- fixnum-min 1) fixnum-min)))
1020
1021     (pass-if "n = fixnum-min - 1"
1022       (eqv? 0 (modulo (- fixnum-min 1) (- fixnum-min 1)))))
1023
1024   ;; Inexact integers
1025
1026   (pass-if (eqv? 1.0 (modulo 13.0 4.0)))
1027   (pass-if (eqv? 1.0 (modulo 13   4.0)))
1028   (pass-if (eqv? 1.0 (modulo 13.0 4  )))
1029
1030   ;; Positive dividend and divisor
1031
1032   (pass-if "13 % 4"
1033     (eqv? 1 (modulo 13 4)))
1034
1035   (pass-if "2177452800 % 86400"
1036     (eqv? 0 (modulo 2177452800 86400)))
1037
1038   ;; Negative dividend, positive divisor
1039
1040   (pass-if "-13 % 4"
1041     (eqv? 3 (modulo -13 4)))
1042
1043   (pass-if "-2177452800 % 86400"
1044     (eqv? 0 (modulo -2177452800 86400)))
1045
1046   ;; Positive dividend, negative divisor
1047
1048   (pass-if "13 % -4"
1049     (eqv? -3 (modulo 13 -4)))
1050
1051   (pass-if "2177452800 % -86400"
1052     (eqv? 0 (modulo 2177452800 -86400)))
1053
1054   ;; Negative dividend and divisor
1055
1056   (pass-if "-13 % -4"
1057     (eqv? -1 (modulo -13 -4)))
1058
1059   (pass-if "-2177452800 % -86400"
1060     (eqv? 0 (modulo -2177452800 -86400)))
1061
1062   ;; Are numerical overflows detected correctly?
1063
1064   (with-test-prefix "division by zero"
1065
1066     (pass-if-exception "(modulo 1 0)"
1067       exception:numerical-overflow
1068       (modulo 1 0))
1069
1070     (pass-if-exception "(modulo bignum 0)"
1071       exception:numerical-overflow
1072       (modulo (+ fixnum-max 1) 0)))
1073
1074   ;; Are wrong type arguments detected correctly?
1075
1076   )
1077
1078 ;;;
1079 ;;; modulo-expt
1080 ;;;
1081
1082 (with-test-prefix "modulo-expt"
1083    (pass-if (= 1 (modulo-expt 17 23 47)))
1084
1085    (pass-if (= 1 (modulo-expt 17 -23 47)))
1086
1087    (pass-if (= 17 (modulo-expt 17 -22 47)))
1088
1089    (pass-if (= 36 (modulo-expt 17 22 47)))
1090
1091    (pass-if (= 183658794479969134816674175082294846241553725240 (modulo-expt 111122223333444455556666 111122223333444455556666 1153478690012629968439432872520758982731022934717)))
1092
1093    (pass-if-exception
1094     "Proper exception with 0 modulus"
1095     exception:numerical-overflow
1096     (modulo-expt 17 23 0))
1097
1098    (pass-if-exception
1099     "Proper exception when result not invertible"
1100     exception:numerical-overflow
1101     (modulo-expt 10 -1 48))
1102
1103    (pass-if-exception
1104     "Proper exception with wrong type argument"
1105     exception:wrong-type-arg
1106     (modulo-expt "Sam" 23 10))
1107
1108    (pass-if-exception
1109     "Proper exception with wrong type argument"
1110     exception:wrong-type-arg
1111     (modulo-expt 17 9.9 10))
1112
1113     (pass-if-exception
1114     "Proper exception with wrong type argument"
1115     exception:wrong-type-arg
1116     (modulo-expt 17 23 'Ethel)))
1117
1118 ;;;
1119 ;;; numerator
1120 ;;;
1121
1122 (with-test-prefix "numerator"
1123   (pass-if "0"
1124     (eqv? 0 (numerator 0)))
1125   (pass-if "1"
1126     (eqv? 1 (numerator 1)))
1127   (pass-if "2"
1128     (eqv? 2 (numerator 2)))
1129   (pass-if "-1"
1130     (eqv? -1 (numerator -1)))
1131   (pass-if "-2"
1132     (eqv? -2 (numerator -2)))
1133
1134   (pass-if "0.0"
1135     (eqv? 0.0 (numerator 0.0)))
1136   (pass-if "1.0"
1137     (eqv? 1.0 (numerator 1.0)))
1138   (pass-if "2.0"
1139     (eqv? 2.0 (numerator 2.0)))
1140   (pass-if "-1.0"
1141     (eqv? -1.0 (numerator -1.0)))
1142   (pass-if "-2.0"
1143     (eqv? -2.0 (numerator -2.0)))
1144
1145   (pass-if "0.5"
1146     (eqv? 1.0 (numerator 0.5)))
1147   (pass-if "0.25"
1148     (eqv? 1.0 (numerator 0.25)))
1149   (pass-if "0.75"
1150     (eqv? 3.0 (numerator 0.75))))
1151
1152 ;;;
1153 ;;; denominator
1154 ;;;
1155
1156 (with-test-prefix "denominator"
1157   (pass-if "0"
1158     (eqv? 1 (denominator 0)))
1159   (pass-if "1"
1160     (eqv? 1 (denominator 1)))
1161   (pass-if "2"
1162     (eqv? 1 (denominator 2)))
1163   (pass-if "-1"
1164     (eqv? 1 (denominator -1)))
1165   (pass-if "-2"
1166     (eqv? 1 (denominator -2)))
1167
1168   (pass-if "0.0"
1169     (eqv? 1.0 (denominator 0.0)))
1170   (pass-if "1.0"
1171     (eqv? 1.0 (denominator 1.0)))
1172   (pass-if "2.0"
1173     (eqv? 1.0 (denominator 2.0)))
1174   (pass-if "-1.0"
1175     (eqv? 1.0 (denominator -1.0)))
1176   (pass-if "-2.0"
1177     (eqv? 1.0 (denominator -2.0)))
1178
1179   (pass-if "0.5"
1180     (eqv? 2.0 (denominator 0.5)))
1181   (pass-if "0.25"
1182     (eqv? 4.0 (denominator 0.25)))
1183   (pass-if "0.75"
1184     (eqv? 4.0 (denominator 0.75))))
1185
1186 ;;;
1187 ;;; gcd
1188 ;;;
1189
1190 (with-test-prefix "gcd"
1191
1192   (pass-if "documented?"
1193     (documented? gcd))
1194
1195   (with-test-prefix "(n)"
1196
1197     (pass-if "n = -2"
1198       (eqv? 2 (gcd -2))))
1199
1200   (with-test-prefix "(0 n)"
1201
1202     (pass-if "n = 0"
1203       (eqv? 0 (gcd 0 0)))
1204
1205     (pass-if "n = 1"
1206       (eqv? 1 (gcd 0 1)))
1207
1208     (pass-if "n = -1"
1209       (eqv? 1 (gcd 0 -1)))
1210
1211     (pass-if "n = fixnum-max"
1212       (eqv? fixnum-max (gcd 0 fixnum-max)))
1213
1214     (pass-if "n = fixnum-max + 1"
1215       (eqv? (+ fixnum-max 1) (gcd 0 (+ fixnum-max 1))))
1216
1217     (pass-if "n = fixnum-min"
1218       (eqv? (- fixnum-min) (gcd 0 fixnum-min)))
1219
1220     (pass-if "n = fixnum-min - 1"
1221       (eqv? (- (- fixnum-min 1)) (gcd 0 (- fixnum-min 1)))))
1222
1223   (with-test-prefix "(n 0)"
1224
1225     (pass-if "n = 2^128 * fixnum-max"
1226       (eqv? (ash fixnum-max 128) (gcd (ash fixnum-max 128) 0))))
1227
1228   (with-test-prefix "(1 n)"
1229
1230     (pass-if "n = 0"
1231       (eqv? 1 (gcd 1 0)))
1232
1233     (pass-if "n = 1"
1234       (eqv? 1 (gcd 1 1)))
1235
1236     (pass-if "n = -1"
1237       (eqv? 1 (gcd 1 -1)))
1238
1239     (pass-if "n = fixnum-max"
1240       (eqv? 1 (gcd 1 fixnum-max)))
1241
1242     (pass-if "n = fixnum-max + 1"
1243       (eqv? 1 (gcd 1 (+ fixnum-max 1))))
1244
1245     (pass-if "n = fixnum-min"
1246       (eqv? 1 (gcd 1 fixnum-min)))
1247
1248     (pass-if "n = fixnum-min - 1"
1249       (eqv? 1 (gcd 1 (- fixnum-min 1)))))
1250
1251   (with-test-prefix "(-1 n)"
1252
1253     (pass-if "n = 0"
1254       (eqv? 1 (gcd -1 0)))
1255
1256     (pass-if "n = 1"
1257       (eqv? 1 (gcd -1 1)))
1258
1259     (pass-if "n = -1"
1260       (eqv? 1 (gcd -1 -1)))
1261
1262     (pass-if "n = fixnum-max"
1263       (eqv? 1 (gcd -1 fixnum-max)))
1264
1265     (pass-if "n = fixnum-max + 1"
1266       (eqv? 1 (gcd -1 (+ fixnum-max 1))))
1267
1268     (pass-if "n = fixnum-min"
1269       (eqv? 1 (gcd -1 fixnum-min)))
1270
1271     (pass-if "n = fixnum-min - 1"
1272       (eqv? 1 (gcd -1 (- fixnum-min 1)))))
1273
1274   (with-test-prefix "(fixnum-max n)"
1275
1276     (pass-if "n = 0"
1277       (eqv? fixnum-max (gcd fixnum-max 0)))
1278
1279     (pass-if "n = 1"
1280       (eqv? 1 (gcd fixnum-max 1)))
1281
1282     (pass-if "n = -1"
1283       (eqv? 1 (gcd fixnum-max -1)))
1284
1285     (pass-if "n = fixnum-max"
1286       (eqv? fixnum-max (gcd fixnum-max fixnum-max)))
1287
1288     (pass-if "n = fixnum-max + 1"
1289       (eqv? 1 (gcd fixnum-max (+ fixnum-max 1))))
1290
1291     (pass-if "n = fixnum-min"
1292       (eqv? 1 (gcd fixnum-max fixnum-min)))
1293
1294     (pass-if "n = fixnum-min - 1"
1295       (eqv? 1 (gcd fixnum-max (- fixnum-min 1)))))
1296
1297   (with-test-prefix "((+ fixnum-max 1) n)"
1298
1299     (pass-if "n = 0"
1300       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) 0)))
1301
1302     (pass-if "n = 1"
1303       (eqv? 1 (gcd (+ fixnum-max 1) 1)))
1304
1305     (pass-if "n = -1"
1306       (eqv? 1 (gcd (+ fixnum-max 1) -1)))
1307
1308     (pass-if "n = fixnum-max"
1309       (eqv? 1 (gcd (+ fixnum-max 1) fixnum-max)))
1310
1311     (pass-if "n = fixnum-max + 1"
1312       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) (+ fixnum-max 1))))
1313
1314     (pass-if "n = fixnum-min"
1315       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) fixnum-min)))
1316
1317     (pass-if "n = fixnum-min - 1"
1318       (eqv? 1 (gcd (+ fixnum-max 1) (- fixnum-min 1)))))
1319
1320   (with-test-prefix "(fixnum-min n)"
1321
1322     (pass-if "n = 0"
1323       (eqv? (- fixnum-min) (gcd fixnum-min 0)))
1324
1325     (pass-if "n = 1"
1326       (eqv? 1 (gcd fixnum-min 1)))
1327
1328     (pass-if "n = -1"
1329       (eqv? 1 (gcd fixnum-min -1)))
1330
1331     (pass-if "n = fixnum-max"
1332       (eqv? 1 (gcd fixnum-min fixnum-max)))
1333
1334     (pass-if "n = fixnum-max + 1"
1335       (eqv? (+ fixnum-max 1) (gcd fixnum-min (+ fixnum-max 1))))
1336
1337     (pass-if "n = fixnum-min"
1338       (eqv? (- fixnum-min) (gcd fixnum-min fixnum-min)))
1339
1340     (pass-if "n = fixnum-min - 1"
1341       (eqv? 1 (gcd fixnum-min (- fixnum-min 1)))))
1342
1343   (with-test-prefix "((- fixnum-min 1) n)"
1344
1345     (pass-if "n = 0"
1346       (eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) 0)))
1347
1348     (pass-if "n = 1"
1349       (eqv? 1 (gcd (- fixnum-min 1) 1)))
1350
1351     (pass-if "n = -1"
1352       (eqv? 1 (gcd (- fixnum-min 1) -1)))
1353
1354     (pass-if "n = fixnum-max"
1355       (eqv? 1 (gcd (- fixnum-min 1) fixnum-max)))
1356
1357     (pass-if "n = fixnum-max + 1"
1358       (eqv? 1 (gcd (- fixnum-min 1) (+ fixnum-max 1))))
1359
1360     (pass-if "n = fixnum-min"
1361       (eqv? 1 (gcd (- fixnum-min 1) fixnum-min)))
1362
1363     (pass-if "n = fixnum-min - 1"
1364       (eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) (- fixnum-min 1)))))
1365
1366   ;; Are wrong type arguments detected correctly?
1367
1368   )
1369
1370 ;;;
1371 ;;; lcm
1372 ;;;
1373
1374 (with-test-prefix "lcm"
1375   ;; FIXME: more tests?
1376   ;; (some of these are already in r4rs.test)
1377   (pass-if (documented? lcm))
1378   (pass-if (= (lcm) 1))
1379   (pass-if (= (lcm 32 -36) 288))
1380   (let ((big-n 115792089237316195423570985008687907853269984665640564039457584007913129639936) ; 2 ^ 256
1381         (lcm-of-big-n-and-11 1273712981610478149659280835095566986385969831322046204434033424087044426039296))
1382     (pass-if (= lcm-of-big-n-and-11 (lcm big-n 11)))
1383     (pass-if (= lcm-of-big-n-and-11 (lcm 11 big-n 11)))))
1384
1385 ;;;
1386 ;;; rationalize
1387 ;;;
1388 (with-test-prefix "rationalize"
1389   (pass-if (documented? rationalize))
1390   (pass-if (eqv?  2     (rationalize  4   2  )))
1391   (pass-if (eqv? -2     (rationalize -4   2  )))
1392   (pass-if (eqv?  2.0   (rationalize  4   2.0)))
1393   (pass-if (eqv? -2.0   (rationalize -4.0 2  )))
1394
1395   (pass-if (eqv?  0     (rationalize  4   8  )))
1396   (pass-if (eqv?  0     (rationalize -4   8  )))
1397   (pass-if (eqv?  0.0   (rationalize  4   8.0)))
1398   (pass-if (eqv?  0.0   (rationalize -4.0 8  )))
1399
1400   (pass-if (eqv?  0.0   (rationalize  3   +inf.0)))
1401   (pass-if (eqv?  0.0   (rationalize -3   +inf.0)))
1402
1403   (pass-if (real-nan?   (rationalize +inf.0 +inf.0)))
1404   (pass-if (real-nan?   (rationalize +nan.0 +inf.0)))
1405   (pass-if (real-nan?   (rationalize +nan.0 4)))
1406   (pass-if (eqv? +inf.0 (rationalize +inf.0 3)))
1407
1408   (pass-if (eqv?  3/10  (rationalize  3/10 0)))
1409   (pass-if (eqv? -3/10  (rationalize -3/10 0)))
1410
1411   (pass-if (eqv?  1/3   (rationalize  3/10 1/10)))
1412   (pass-if (eqv? -1/3   (rationalize -3/10 1/10)))
1413
1414   (pass-if (eqv?  1/3   (rationalize  3/10 -1/10)))
1415   (pass-if (eqv? -1/3   (rationalize -3/10 -1/10)))
1416
1417   (pass-if (test-eqv? (/  1.0 3) (rationalize  0.3  1/10)))
1418   (pass-if (test-eqv? (/ -1.0 3) (rationalize -0.3  1/10)))
1419   (pass-if (test-eqv? (/  1.0 3) (rationalize  0.3 -1/10)))
1420   (pass-if (test-eqv? (/ -1.0 3) (rationalize -0.3 -1/10))))
1421
1422 ;;;
1423 ;;; number->string
1424 ;;;
1425
1426 (with-test-prefix "number->string"
1427   (let ((num->str->num
1428          (lambda (n radix)
1429            (string->number (number->string n radix) radix))))
1430
1431     (pass-if (documented? number->string))
1432     (pass-if (string=? (number->string 0) "0"))
1433     (pass-if (string=? (number->string 171) "171"))
1434     (pass-if (= (+ fixnum-max 1) (num->str->num (+ fixnum-max 1) 10)))
1435     (pass-if (= (- fixnum-min 1) (num->str->num (- fixnum-min 1) 10)))
1436     (pass-if (= (inf) (num->str->num (inf) 10)))
1437     (pass-if (= 1.3 (num->str->num 1.3 10)))
1438
1439     ;; XXX - some results depend on whether Guile is compiled optimzed
1440     ;; or not.  It is clearly undesirable to have number->string to be
1441     ;; influenced by this.
1442
1443     (pass-if (string=? (number->string 35.25 36) "z.9"))
1444     (pass-if (or (string=? (number->string 0.25 2) "0.01")
1445                  (string=? (number->string 0.25 2) "0.010")))
1446     (pass-if (string=? (number->string 255.0625 16) "ff.1"))
1447     (pass-if (string=? (number->string (/ 1 3) 3) "1/10"))
1448
1449     (pass-if (string=? (number->string 10) "10"))
1450     (pass-if (string=? (number->string 10 11) "a"))
1451     (pass-if (string=? (number->string 36 36) "10"))
1452     (pass-if (= (num->str->num 36 36) 36))
1453     (pass-if (= (string->number "z" 36) 35))
1454     (pass-if (= (string->number "Z" 36) 35))
1455     (pass-if (not (string->number "Z" 35)))
1456     (pass-if (string=? (number->string 35 36) "z"))
1457     (pass-if (= (num->str->num 35 36) 35))
1458
1459     ;; Before Guile 2.0.1, even in the presence of a #e forced exactness
1460     ;; specifier, negative exponents were applied inexactly and then
1461     ;; later coerced to exact, yielding an incorrect fraction.
1462     (pass-if (eqv? (string->number "#e1e-10") 1/10000000000))
1463
1464     ;; Numeric conversion from decimal is not precise, in its current
1465     ;; implementation, so 11.333... and 1.324... can't be expected to
1466     ;; reliably come out to precise values.  These tests did actually work
1467     ;; for a while, but something in gcc changed, affecting the conversion
1468     ;; code.
1469     ;;
1470     ;; (pass-if (or (string=? (number->string 11.33333333333333333 12)
1471     ;;                        "B.4")
1472     ;;              (string=? (number->string 11.33333333333333333 12)
1473     ;;                        "B.400000000000009")))
1474     ;; (pass-if (or (string=? (number->string 1.324e44 16)
1475     ;;                        "5.EFE0A14FAFEe24")
1476     ;;              (string=? (number->string 1.324e44 16)
1477     ;;                        "5.EFE0A14FAFDF8e24")))
1478     ))
1479
1480 ;;;
1481 ;;; string->number
1482 ;;;
1483
1484 (with-test-prefix "string->number"
1485
1486   (pass-if "documented?"
1487     (documented? string->number))
1488
1489   (pass-if "non number strings"
1490     (for-each (lambda (x) (if (string->number x) (throw 'fail)))
1491               '("" "q" "1q" "6+7iq" "8+9q" "10+11" "13+" "18@19q" "20@q" "23@"
1492                 "+25iq" "26i" "-q" "-iq" "i" "5#.0" "8/" "10#11" ".#" "."
1493                 "#o.2" "3.4q" "15.16e17q" "18.19e+q" ".q" ".17#18" "10q" "#b2"
1494                 "#b3" "#b4" "#b5" "#b6" "#b7" "#b8" "#b9" "#ba" "#bb" "#bc"
1495                 "#bd" "#be" "#bf" "#q" "#b#b1" "#o#o1" "#d#d1" "#x#x1" "#e#e1"
1496                 "#i#i1" "12@12+0i" "3/0" "0/0" "4+3/0i" "4/0-3i" "2+0/0i"
1497                 "nan.0" "inf.0" "#e+nan.0" "#e+inf.0" "#e-inf.0"
1498                 "3@inf.0" "4@nan.0"))
1499     #t)
1500
1501   (pass-if "valid number strings"
1502     (for-each (lambda (couple)
1503                 (apply
1504                  (lambda (x y)
1505                    (let ((xx (string->number x)))
1506                      (if (or (eq? xx #f) (not (eqv? xx y)))
1507                          (begin
1508                            (pk x y)
1509                            (throw 'fail)))))
1510                  couple))
1511               `(;; Radix:
1512                 ("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
1513                 ("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
1514                 ("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
1515                 ("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
1516                 ("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
1517                 ("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
1518                 ("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
1519                 ("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
1520                 ("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
1521                 ("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
1522                 ("#b1010" 10)
1523                 ("#o12345670" 2739128)
1524                 ("#d1234567890" 1234567890)
1525                 ("#x1234567890abcdef" 1311768467294899695)
1526                 ;; Exactness:
1527                 ("#e1" 1) ("#e1.2" 12/10)
1528                 ("#i1.1" 1.1) ("#i1" 1.0)
1529                 ;; Integers:
1530                 ("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1))
1531                 ("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
1532                 ("#b#i100" 4.0)
1533                 ;; Fractions:
1534                 ("1/1" 1) ("1/2" 1/2) ("-1/2" -1/2) ("1#/1" 10.0)
1535                 ("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 9/10) ("#e10/1#" 1)
1536                 ("#i6/8" 0.75) ("#i1/1" 1.0)
1537                 ;; Infinities and NaNs:
1538                 ("+inf.0" ,(inf)) ("-inf.0" ,(- (inf)))
1539                 ("+Inf.0" ,(inf)) ("-Inf.0" ,(- (inf)))
1540                 ("+InF.0" ,(inf)) ("-InF.0" ,(- (inf)))
1541                 ("+INF.0" ,(inf)) ("-INF.0" ,(- (inf)))
1542                 ("#i+InF.0" ,(inf)) ("#i-InF.0" ,(- (inf)))
1543                 ("+nan.0" ,(nan)) ("-nan.0" ,(nan))
1544                 ("#i+nan.0" ,(nan)) ("#i-nan.0" ,(nan))
1545                 ;; Decimal numbers:
1546                 ;; * <uinteger 10> <suffix>
1547                 ("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
1548                 ("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
1549                 ("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
1550                 ;; * . <digit 10>+ #* <suffix>
1551                 (".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
1552                 (".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
1553                 ;; * <digit 10>+ . <digit 10>* #* <suffix>
1554                 ("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
1555                 ("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
1556                 ("3.1#e0" 3.1)
1557                 ;; * <digit 10>+ #+ . #* <suffix>
1558                 ("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
1559                 ))
1560     #t)
1561
1562   (pass-if "valid complex number strings"
1563     (for-each (lambda (triple)
1564                 (apply
1565                  (lambda (str re im)
1566                    (let ((z (string->number str)))
1567                      (if (or (eq? z #f)
1568                              (not (and (eqv? (real-part z) re)
1569                                        (eqv? (imag-part z) im))))
1570                          (begin
1571                            (pk str re im)
1572                            (throw 'fail)))))
1573                  triple))
1574               `(("1@0" 1 0) ("1@+0" 1 0) ("1@-0" 1 0) ("1/2@0" 1/2 0)
1575                 ("1.0@0" 1.0 0) ("1.0@-0" 1.0 0)
1576                 ("#e1@0" 1 0) ("#e1@+0" 1 0) ("#e1@-0" 1 0) ("#e0.5@0.0" 1/2 0)
1577                 ("#e1.0@0" 1 0) ("#e1.0@-0" 1 0)
1578                 ("#i1@0" 1.0 0.0) ("#i1@+0" 1.0 0.0) ("#i1@-0" 1.0 -0.0) ("#i1/2@0" 0.5 0.0)
1579                 ("#i1.0@0" 1.0 0.0) ("#i1.0@-0" 1.0 -0.0)
1580                 ("1@+0.0" 1.0 0.0) ("1.0@-0.0" 1.0 -0.0)
1581                 ("2+3i" 2.0 3.0) ("4-5i" 4.0 -5.0)
1582                 ("1+i" 1.0 1.0) ("1-i" 1.0 -1.0) ("+1i" 0.0 1.0) ("-1i" 0.0 -1.0)
1583                 ("+i" 0.0 1.0) ("-i" 0.0 -1.0)
1584                 ("1.0+.1i" 1.0 0.1) ("1.0-.1i" 1.0 -0.1)
1585                 (".1+.0i" 0.1 0.0) ("1.+.0i" 1.0 0.0) (".1+.1i" 0.1 0.1)
1586                 ("1e1+.1i" 10.0 0.1)
1587                 ("0@+nan.0" 0 0) ("0@+inf.0" 0 0) ("0@-inf.0" 0 0)
1588                 ("0.0@+nan.0" 0.0 0.0) ("0.0@+inf.0" 0.0 0.0) ("0.0@-inf.0" 0.0 0.0)
1589                 ("#i0@+nan.0" 0.0 0.0) ("#i0@+inf.0" 0.0 0.0) ("#i0@-inf.0" 0.0 0.0)
1590                 ("0.0@1" 0.0 0.0) ("0.0@2" -0.0 0.0) ("0.0@4" -0.0 -0.0) ("0.0@5" 0.0 -0.0)
1591                 ))
1592     #t)
1593
1594   (pass-if-exception "exponent too big"
1595     exception:out-of-range
1596     (string->number "12.13e141414"))
1597
1598   ;; in guile 1.6.7 and earlier, bad polar forms (where the conversion of
1599   ;; the angle gave #f) caused a segv
1600   (pass-if "1@a"
1601     (eq? #f (string->number "1@a"))))
1602
1603 ;;;
1604 ;;; number?
1605 ;;;
1606
1607 (with-test-prefix "number?"
1608   (pass-if (documented? number?))
1609   (pass-if (number? 0))
1610   (pass-if (number? 7))
1611   (pass-if (number? -7))
1612   (pass-if (number? 1.3))
1613   (pass-if (number? (+ 1 fixnum-max)))
1614   (pass-if (number? (- 1 fixnum-min)))
1615   (pass-if (number? 3+4i))
1616   (pass-if (not (number? #\a)))
1617   (pass-if (not (number? "a")))
1618   (pass-if (not (number? (make-vector 0))))
1619   (pass-if (not (number? (cons 1 2))))
1620   (pass-if (not (number? #t)))
1621   (pass-if (not (number? (lambda () #t))))
1622   (pass-if (not (number? (current-input-port)))))
1623
1624 ;;;
1625 ;;; complex?
1626 ;;;
1627
1628 (with-test-prefix "complex?"
1629   (pass-if (documented? complex?))
1630   (pass-if (complex? 0))
1631   (pass-if (complex? 7))
1632   (pass-if (complex? -7))
1633   (pass-if (complex? (+ 1 fixnum-max)))
1634   (pass-if (complex? (- 1 fixnum-min)))
1635   (pass-if (complex? 1.3))
1636   (pass-if (complex? 3+4i))
1637   (pass-if (not (complex? #\a)))
1638   (pass-if (not (complex? "a")))
1639   (pass-if (not (complex? (make-vector 0))))
1640   (pass-if (not (complex? (cons 1 2))))
1641   (pass-if (not (complex? #t)))
1642   (pass-if (not (complex? (lambda () #t))))
1643   (pass-if (not (complex? (current-input-port)))))
1644
1645 ;;;
1646 ;;; real?
1647 ;;;
1648
1649 (with-test-prefix "real?"
1650   (pass-if (documented? real?))
1651   (pass-if (real? 0))
1652   (pass-if (real? 7))
1653   (pass-if (real? -7))
1654   (pass-if (real? (+ 1 fixnum-max)))
1655   (pass-if (real? (- 1 fixnum-min)))
1656   (pass-if (real? 1.3))
1657   (pass-if (real? +inf.0))
1658   (pass-if (real? -inf.0))
1659   (pass-if (real? +nan.0))
1660   (pass-if (not (real? +inf.0-inf.0i)))
1661   (pass-if (not (real? +nan.0+nan.0i)))
1662   (pass-if (not (real? 3+4i)))
1663   (pass-if (not (real? #\a)))
1664   (pass-if (not (real? "a")))
1665   (pass-if (not (real? (make-vector 0))))
1666   (pass-if (not (real? (cons 1 2))))
1667   (pass-if (not (real? #t)))
1668   (pass-if (not (real? (lambda () #t))))
1669   (pass-if (not (real? (current-input-port)))))
1670
1671 ;;;
1672 ;;; rational?
1673 ;;;
1674
1675 (with-test-prefix "rational?"
1676   (pass-if (documented? rational?))
1677   (pass-if (rational? 0))
1678   (pass-if (rational? 7))
1679   (pass-if (rational? -7))
1680   (pass-if (rational? (+ 1 fixnum-max)))
1681   (pass-if (rational? (- 1 fixnum-min)))
1682   (pass-if (rational? 1.3))
1683   (pass-if (not (rational? +inf.0)))
1684   (pass-if (not (rational? -inf.0)))
1685   (pass-if (not (rational? +nan.0)))
1686   (pass-if (not (rational? +inf.0-inf.0i)))
1687   (pass-if (not (rational? +nan.0+nan.0i)))
1688   (pass-if (not (rational? 3+4i)))
1689   (pass-if (not (rational? #\a)))
1690   (pass-if (not (rational? "a")))
1691   (pass-if (not (rational? (make-vector 0))))
1692   (pass-if (not (rational? (cons 1 2))))
1693   (pass-if (not (rational? #t)))
1694   (pass-if (not (rational? (lambda () #t))))
1695   (pass-if (not (rational? (current-input-port)))))
1696
1697 ;;;
1698 ;;; integer?
1699 ;;;
1700
1701 (with-test-prefix "integer?"
1702   (pass-if (documented? integer?))
1703   (pass-if (integer? 0))
1704   (pass-if (integer? 7))
1705   (pass-if (integer? -7))
1706   (pass-if (integer? (+ 1 fixnum-max)))
1707   (pass-if (integer? (- 1 fixnum-min)))
1708   (pass-if (and (= 3+0i (round 3+0i)) (integer? 3+0i)))
1709   (pass-if (and (= 1.0 (round 1.0)) (integer? 1.0)))
1710   (pass-if (not (integer? 1.3)))
1711   (pass-if (not (integer? +inf.0)))
1712   (pass-if (not (integer? -inf.0)))
1713   (pass-if (not (integer? +nan.0)))
1714   (pass-if (not (integer? +inf.0-inf.0i)))
1715   (pass-if (not (integer? +nan.0+nan.0i)))
1716   (pass-if (not (integer? 3+4i)))
1717   (pass-if (not (integer? #\a)))
1718   (pass-if (not (integer? "a")))
1719   (pass-if (not (integer? (make-vector 0))))
1720   (pass-if (not (integer? (cons 1 2))))
1721   (pass-if (not (integer? #t)))
1722   (pass-if (not (integer? (lambda () #t))))
1723   (pass-if (not (integer? (current-input-port)))))
1724
1725 ;;;
1726 ;;; inexact?
1727 ;;;
1728
1729 (with-test-prefix "inexact?"
1730   (pass-if (documented? inexact?))
1731   (pass-if (not (inexact? 0)))
1732   (pass-if (not (inexact? 7)))
1733   (pass-if (not (inexact? -7)))
1734   (pass-if (not (inexact? (+ 1 fixnum-max))))
1735   (pass-if (not (inexact? (- 1 fixnum-min))))
1736   (pass-if (inexact? 1.3))
1737   (pass-if (inexact? 3.1+4.2i))
1738   (pass-if (inexact? +inf.0))
1739   (pass-if (inexact? -inf.0))
1740   (pass-if (inexact? +nan.0))
1741   (pass-if-exception "char"
1742                      exception:wrong-type-arg
1743                      (not (inexact? #\a)))
1744   (pass-if-exception "string"
1745                      exception:wrong-type-arg
1746                      (not (inexact? "a")))
1747   (pass-if-exception "vector"
1748                      exception:wrong-type-arg
1749                      (not (inexact? (make-vector 0))))
1750   (pass-if-exception "cons"
1751                      exception:wrong-type-arg
1752                      (not (inexact? (cons 1 2))))
1753   (pass-if-exception "bool"
1754                      exception:wrong-type-arg
1755                      (not (inexact? #t)))
1756   (pass-if-exception "procedure"
1757                      exception:wrong-type-arg
1758                      (not (inexact? (lambda () #t))))
1759   (pass-if-exception "port"
1760                      exception:wrong-type-arg
1761                      (not (inexact? (current-input-port)))))
1762
1763 ;;;
1764 ;;; equal?
1765 ;;;
1766
1767 (with-test-prefix "equal?"
1768   (pass-if (documented? equal?))
1769
1770   ;; The following test will fail on platforms
1771   ;; without distinct signed zeroes 0.0 and -0.0.
1772   (pass-if (not (equal? 0.0 -0.0)))
1773
1774   (pass-if (equal? 0 0))
1775   (pass-if (equal? 7 7))
1776   (pass-if (equal? -7 -7))
1777   (pass-if (equal? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1778   (pass-if (equal? (- fixnum-min 1) (- fixnum-min 1)))
1779   (pass-if (equal?  0.0  0.0))
1780   (pass-if (equal? -0.0 -0.0))
1781   (pass-if (equal?  0.0+0.0i  0.0+0.0i))
1782   (pass-if (equal?  0.0-0.0i  0.0-0.0i))
1783   (pass-if (equal? -0.0+0.0i -0.0+0.0i))
1784   (pass-if (not (equal? 0 1)))
1785   (pass-if (not (equal? 0 0.0)))
1786   (pass-if (not (equal? 1 1.0)))
1787   (pass-if (not (equal? 0.0 0)))
1788   (pass-if (not (equal? 1.0 1)))
1789   (pass-if (not (equal? -1.0 -1)))
1790   (pass-if (not (equal? 1.0 1.0+0.0i)))
1791   (pass-if (not (equal? 0.0 0.0+0.0i)))
1792   (pass-if (not (equal? 0.0+0.0i  0.0-0.0i)))
1793   (pass-if (not (equal? 0.0+0.0i -0.0+0.0i)))
1794   (pass-if (not (equal? fixnum-max (+ 1 fixnum-max))))
1795   (pass-if (not (equal? (+ 1 fixnum-max) fixnum-max)))
1796   (pass-if (not (equal? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1797   (pass-if (not (equal? fixnum-min (- fixnum-min 1))))
1798   (pass-if (not (equal? (- fixnum-min 1) fixnum-min)))
1799   (pass-if (not (equal? (- fixnum-min 1) (- fixnum-min 2))))
1800   (pass-if (not (equal? (+ fixnum-max 1) (- fixnum-min 1))))
1801
1802   (pass-if (not (equal? (ash 1 256) +inf.0)))
1803   (pass-if (not (equal? +inf.0 (ash 1 256))))
1804   (pass-if (not (equal? (ash 1 256) -inf.0)))
1805   (pass-if (not (equal? -inf.0 (ash 1 256))))
1806
1807   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1808   ;; sure we've avoided that
1809   (pass-if (not (equal? (ash 1 1024) +inf.0)))
1810   (pass-if (not (equal? +inf.0 (ash 1 1024))))
1811   (pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
1812   (pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
1813
1814   (pass-if (equal? +nan.0 +nan.0))
1815   (pass-if (equal? +nan.0 +nan.0))
1816   (pass-if (not (equal? +nan.0 0.0+nan.0i)))
1817
1818   (pass-if (not (equal? 0 +nan.0)))
1819   (pass-if (not (equal? +nan.0 0)))
1820   (pass-if (not (equal? 1 +nan.0)))
1821   (pass-if (not (equal? +nan.0 1)))
1822   (pass-if (not (equal? -1 +nan.0)))
1823   (pass-if (not (equal? +nan.0 -1)))
1824
1825   (pass-if (not (equal? (ash 1 256) +nan.0)))
1826   (pass-if (not (equal? +nan.0 (ash 1 256))))
1827   (pass-if (not (equal? (- (ash 1 256)) +nan.0)))
1828   (pass-if (not (equal? +nan.0 (- (ash 1 256)))))
1829
1830   (pass-if (not (equal? (ash 1 8192) +nan.0)))
1831   (pass-if (not (equal? +nan.0 (ash 1 8192))))
1832   (pass-if (not (equal? (- (ash 1 8192)) +nan.0)))
1833   (pass-if (not (equal? +nan.0 (- (ash 1 8192)))))
1834
1835   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1836   ;; sure we've avoided that
1837   (pass-if (not (equal? (ash 3 1023) +nan.0)))
1838   (pass-if (not (equal? +nan.0 (ash 3 1023)))))
1839
1840 ;;;
1841 ;;; eqv?
1842 ;;;
1843
1844 (with-test-prefix "eqv?"
1845   (pass-if (documented? eqv?))
1846
1847   ;; The following test will fail on platforms
1848   ;; without distinct signed zeroes 0.0 and -0.0.
1849   (pass-if (not (eqv? 0.0 -0.0)))
1850
1851   (pass-if (eqv? 0 0))
1852   (pass-if (eqv? 7 7))
1853   (pass-if (eqv? -7 -7))
1854   (pass-if (eqv? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1855   (pass-if (eqv? (- fixnum-min 1) (- fixnum-min 1)))
1856   (pass-if (eqv?  0.0  0.0))
1857   (pass-if (eqv? -0.0 -0.0))
1858   (pass-if (eqv?  0.0+0.0i  0.0+0.0i))
1859   (pass-if (eqv?  0.0-0.0i  0.0-0.0i))
1860   (pass-if (eqv? -0.0+0.0i -0.0+0.0i))
1861   (pass-if (not (eqv? 0.0 -0.0)))
1862   (pass-if (not (eqv? 0.0  0.0+0.0i)))
1863   (pass-if (not (eqv? 0.0+0.0i  0.0-0.0i)))
1864   (pass-if (not (eqv? 0.0+0.0i -0.0+0.0i)))
1865   (pass-if (not (eqv? 0 1)))
1866   (pass-if (not (eqv? 0 0.0)))
1867   (pass-if (not (eqv? 1 1.0)))
1868   (pass-if (not (eqv? 0.0 0)))
1869   (pass-if (not (eqv? 1.0 1)))
1870   (pass-if (not (eqv? -1.0 -1)))
1871   (pass-if (not (eqv? 1.0 1.0+0.0i)))
1872   (pass-if (not (eqv? 0.0 0.0+0.0i)))
1873   (pass-if (not (eqv? fixnum-max (+ 1 fixnum-max))))
1874   (pass-if (not (eqv? (+ 1 fixnum-max) fixnum-max)))
1875   (pass-if (not (eqv? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1876   (pass-if (not (eqv? fixnum-min (- fixnum-min 1))))
1877   (pass-if (not (eqv? (- fixnum-min 1) fixnum-min)))
1878   (pass-if (not (eqv? (- fixnum-min 1) (- fixnum-min 2))))
1879   (pass-if (not (eqv? (+ fixnum-max 1) (- fixnum-min 1))))
1880
1881   (pass-if (not (eqv? (ash 1 256) +inf.0)))
1882   (pass-if (not (eqv? +inf.0 (ash 1 256))))
1883   (pass-if (not (eqv? (ash 1 256) -inf.0)))
1884   (pass-if (not (eqv? -inf.0 (ash 1 256))))
1885
1886   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1887   ;; sure we've avoided that
1888   (pass-if (not (eqv? (ash 1 1024) +inf.0)))
1889   (pass-if (not (eqv? +inf.0 (ash 1 1024))))
1890   (pass-if (not (eqv? (- (ash 1 1024)) -inf.0)))
1891   (pass-if (not (eqv? -inf.0 (- (ash 1 1024)))))
1892
1893   (pass-if (eqv? +nan.0 +nan.0))
1894   (pass-if (not (eqv? +nan.0 0.0+nan.0i)))
1895
1896   (pass-if (not (eqv? 0 +nan.0)))
1897   (pass-if (not (eqv? +nan.0 0)))
1898   (pass-if (not (eqv? 1 +nan.0)))
1899   (pass-if (not (eqv? +nan.0 1)))
1900   (pass-if (not (eqv? -1 +nan.0)))
1901   (pass-if (not (eqv? +nan.0 -1)))
1902
1903   (pass-if (not (eqv? (ash 1 256) +nan.0)))
1904   (pass-if (not (eqv? +nan.0 (ash 1 256))))
1905   (pass-if (not (eqv? (- (ash 1 256)) +nan.0)))
1906   (pass-if (not (eqv? +nan.0 (- (ash 1 256)))))
1907
1908   (pass-if (not (eqv? (ash 1 8192) +nan.0)))
1909   (pass-if (not (eqv? +nan.0 (ash 1 8192))))
1910   (pass-if (not (eqv? (- (ash 1 8192)) +nan.0)))
1911   (pass-if (not (eqv? +nan.0 (- (ash 1 8192)))))
1912
1913   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1914   ;; sure we've avoided that
1915   (pass-if (not (eqv? (ash 3 1023) +nan.0)))
1916   (pass-if (not (eqv? +nan.0 (ash 3 1023)))))
1917
1918 ;;;
1919 ;;; =
1920 ;;;
1921
1922 (with-test-prefix "="
1923   (pass-if (documented? =))
1924   (pass-if (= 7 7))
1925   (pass-if (= -7 -7))
1926   (pass-if (= 1.0 1))
1927   (pass-if (= 1 1.0))
1928   (pass-if (= -1 -1.0))
1929   (pass-if (= 0.0  0.0))
1930   (pass-if (= 0.0 -0.0))
1931   (pass-if (= 1 1.0+0.0i))
1932
1933   (pass-if (= 0  0))
1934   (pass-if (= 0  0.0))
1935   (pass-if (= 0 -0.0))
1936   (pass-if (= 0  0.0+0.0i))
1937   (pass-if (= 0  0.0-0.0i))
1938   (pass-if (= 0  0.0+0.0i))
1939   (pass-if (= 0 -0.0-0.0i))
1940
1941   (pass-if (=  0        0))
1942   (pass-if (=  0.0      0))
1943   (pass-if (= -0.0      0))
1944   (pass-if (=  0.0+0.0i 0))
1945   (pass-if (=  0.0-0.0i 0))
1946   (pass-if (=  0.0+0.0i 0))
1947   (pass-if (= -0.0-0.0i 0))
1948
1949   (pass-if (= 0.0+0.0i  0.0-0.0i))
1950   (pass-if (= 0.0+0.0i -0.0+0.0i))
1951
1952   (pass-if (= (+ 1 fixnum-max) (+ 1 fixnum-max)))
1953   (pass-if (= (- fixnum-min 1) (- fixnum-min 1)))
1954   (pass-if (not (= 0 1)))
1955   (pass-if (not (= fixnum-max (+ 1 fixnum-max))))
1956   (pass-if (not (= (+ 1 fixnum-max) fixnum-max)))
1957   (pass-if (not (= (+ 1 fixnum-max) (+ 2 fixnum-max))))
1958   (pass-if (not (= fixnum-min (- fixnum-min 1))))
1959   (pass-if (not (= (- fixnum-min 1) fixnum-min)))
1960   (pass-if (not (= (- fixnum-min 1) (- fixnum-min 2))))
1961   (pass-if (not (= (+ fixnum-max 1) (- fixnum-min 1))))
1962
1963   (pass-if (not (= (ash 1 256) +inf.0)))
1964   (pass-if (not (= +inf.0 (ash 1 256))))
1965   (pass-if (not (= (ash 1 256) -inf.0)))
1966   (pass-if (not (= -inf.0 (ash 1 256))))
1967
1968   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1969   ;; sure we've avoided that
1970   (pass-if (not (= (ash 1 1024) +inf.0)))
1971   (pass-if (not (= +inf.0 (ash 1 1024))))
1972   (pass-if (not (= (- (ash 1 1024)) -inf.0)))
1973   (pass-if (not (= -inf.0 (- (ash 1 1024)))))
1974
1975   (pass-if (not (= +nan.0 +nan.0)))
1976   (pass-if (not (= 0 +nan.0)))
1977   (pass-if (not (= +nan.0 0)))
1978   (pass-if (not (= 1 +nan.0)))
1979   (pass-if (not (= +nan.0 1)))
1980   (pass-if (not (= -1 +nan.0)))
1981   (pass-if (not (= +nan.0 -1)))
1982
1983   (pass-if (not (= (ash 1 256) +nan.0)))
1984   (pass-if (not (= +nan.0 (ash 1 256))))
1985   (pass-if (not (= (- (ash 1 256)) +nan.0)))
1986   (pass-if (not (= +nan.0 (- (ash 1 256)))))
1987
1988   (pass-if (not (= (ash 1 8192) +nan.0)))
1989   (pass-if (not (= +nan.0 (ash 1 8192))))
1990   (pass-if (not (= (- (ash 1 8192)) +nan.0)))
1991   (pass-if (not (= +nan.0 (- (ash 1 8192)))))
1992
1993   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1994   ;; sure we've avoided that
1995   (pass-if (not (= (ash 3 1023) +nan.0)))
1996   (pass-if (not (= +nan.0 (ash 3 1023))))
1997
1998   (pass-if (= 1/2 0.5))
1999   (pass-if (not (= 1/3 0.333333333333333333333333333333333)))
2000   (pass-if (not (= 2/3 0.5)))
2001   (pass-if (not (= 0.5 (+ 1/2 (/ 1 (ash 1 1000))))))
2002
2003   (pass-if (= 1/2 0.5+0i))
2004   (pass-if (not (= 0.333333333333333333333333333333333 1/3)))
2005   (pass-if (not (= 2/3 0.5+0i)))
2006   (pass-if (not (= 1/2 0+0.5i)))
2007
2008   (pass-if (= 0.5 1/2))
2009   (pass-if (not (= 0.5 2/3)))
2010   (pass-if (not (= (+ 1/2 (/ 1 (ash 1 1000))) 0.5)))
2011
2012   (pass-if (= 0.5+0i 1/2))
2013   (pass-if (not (= 0.5+0i 2/3)))
2014   (pass-if (not (= 0+0.5i 1/2)))
2015
2016   ;; prior to guile 1.8, inum/flonum comparisons were done just by
2017   ;; converting the inum to a double, which on a 64-bit would round making
2018   ;; say inexact 2^58 appear equal to exact 2^58+1
2019   (pass-if (= (ash-flo 1.0 58) (ash 1 58)))
2020   (pass-if (not (= (ash-flo 1.0 58) (1+ (ash 1 58)))))
2021   (pass-if (not (= (ash-flo 1.0 58) (1- (ash 1 58)))))
2022   (pass-if (= (ash 1 58) (ash-flo 1.0 58)))
2023   (pass-if (not (= (1+ (ash 1 58)) (ash-flo 1.0 58))))
2024   (pass-if (not (= (1- (ash 1 58)) (ash-flo 1.0 58)))))
2025
2026 ;;;
2027 ;;; <
2028 ;;;
2029
2030 (with-test-prefix "<"
2031
2032   (pass-if "documented?"
2033     (documented? <))
2034
2035   (with-test-prefix "(< 0 n)"
2036
2037     (pass-if "n = 0"
2038       (not (< 0 0)))
2039
2040     (pass-if "n = 0.0"
2041       (not (< 0 0.0)))
2042
2043     (pass-if "n = 1"
2044       (< 0 1))
2045
2046     (pass-if "n = 1.0"
2047       (< 0 1.0))
2048
2049     (pass-if "n = -1"
2050       (not (< 0 -1)))
2051
2052     (pass-if "n = -1.0"
2053       (not (< 0 -1.0)))
2054
2055     (pass-if "n = fixnum-max"
2056       (< 0 fixnum-max))
2057
2058     (pass-if "n = fixnum-max + 1"
2059       (< 0 (+ fixnum-max 1)))
2060
2061     (pass-if "n = fixnum-min"
2062       (not (< 0 fixnum-min)))
2063
2064     (pass-if "n = fixnum-min - 1"
2065       (not (< 0 (- fixnum-min 1)))))
2066
2067   (with-test-prefix "(< 0.0 n)"
2068
2069     (pass-if "n = 0"
2070       (not (< 0.0 0)))
2071
2072     (pass-if "n = 0.0"
2073       (not (< 0.0 0.0)))
2074
2075     (pass-if "n = 1"
2076       (< 0.0 1))
2077
2078     (pass-if "n = 1.0"
2079       (< 0.0 1.0))
2080
2081     (pass-if "n = -1"
2082       (not (< 0.0 -1)))
2083
2084     (pass-if "n = -1.0"
2085       (not (< 0.0 -1.0)))
2086
2087     (pass-if "n = fixnum-max"
2088       (< 0.0 fixnum-max))
2089
2090     (pass-if "n = fixnum-max + 1"
2091       (< 0.0 (+ fixnum-max 1)))
2092
2093     (pass-if "n = fixnum-min"
2094       (not (< 0.0 fixnum-min)))
2095
2096     (pass-if "n = fixnum-min - 1"
2097       (not (< 0.0 (- fixnum-min 1)))))
2098
2099   (with-test-prefix "(< 1 n)"
2100
2101     (pass-if "n = 0"
2102       (not (< 1 0)))
2103
2104     (pass-if "n = 0.0"
2105       (not (< 1 0.0)))
2106
2107     (pass-if "n = 1"
2108       (not (< 1 1)))
2109
2110     (pass-if "n = 1.0"
2111       (not (< 1 1.0)))
2112
2113     (pass-if "n = -1"
2114       (not (< 1 -1)))
2115
2116     (pass-if "n = -1.0"
2117       (not (< 1 -1.0)))
2118
2119     (pass-if "n = fixnum-max"
2120       (< 1 fixnum-max))
2121
2122     (pass-if "n = fixnum-max + 1"
2123       (< 1 (+ fixnum-max 1)))
2124
2125     (pass-if "n = fixnum-min"
2126       (not (< 1 fixnum-min)))
2127
2128     (pass-if "n = fixnum-min - 1"
2129       (not (< 1 (- fixnum-min 1)))))
2130
2131   (with-test-prefix "(< 1.0 n)"
2132
2133     (pass-if "n = 0"
2134       (not (< 1.0 0)))
2135
2136     (pass-if "n = 0.0"
2137       (not (< 1.0 0.0)))
2138
2139     (pass-if "n = 1"
2140       (not (< 1.0 1)))
2141
2142     (pass-if "n = 1.0"
2143       (not (< 1.0 1.0)))
2144
2145     (pass-if "n = -1"
2146       (not (< 1.0 -1)))
2147
2148     (pass-if "n = -1.0"
2149       (not (< 1.0 -1.0)))
2150
2151     (pass-if "n = fixnum-max"
2152       (< 1.0 fixnum-max))
2153
2154     (pass-if "n = fixnum-max + 1"
2155       (< 1.0 (+ fixnum-max 1)))
2156
2157     (pass-if "n = fixnum-min"
2158       (not (< 1.0 fixnum-min)))
2159
2160     (pass-if "n = fixnum-min - 1"
2161       (not (< 1.0 (- fixnum-min 1)))))
2162
2163   (with-test-prefix "(< -1 n)"
2164
2165     (pass-if "n = 0"
2166       (< -1 0))
2167
2168     (pass-if "n = 0.0"
2169       (< -1 0.0))
2170
2171     (pass-if "n = 1"
2172       (< -1 1))
2173
2174     (pass-if "n = 1.0"
2175       (< -1 1.0))
2176
2177     (pass-if "n = -1"
2178       (not (< -1 -1)))
2179
2180     (pass-if "n = -1.0"
2181       (not (< -1 -1.0)))
2182
2183     (pass-if "n = fixnum-max"
2184       (< -1 fixnum-max))
2185
2186     (pass-if "n = fixnum-max + 1"
2187       (< -1 (+ fixnum-max 1)))
2188
2189     (pass-if "n = fixnum-min"
2190       (not (< -1 fixnum-min)))
2191
2192     (pass-if "n = fixnum-min - 1"
2193       (not (< -1 (- fixnum-min 1)))))
2194
2195   (with-test-prefix "(< -1.0 n)"
2196
2197     (pass-if "n = 0"
2198       (< -1.0 0))
2199
2200     (pass-if "n = 0.0"
2201       (< -1.0 0.0))
2202
2203     (pass-if "n = 1"
2204       (< -1.0 1))
2205
2206     (pass-if "n = 1.0"
2207       (< -1.0 1.0))
2208
2209     (pass-if "n = -1"
2210       (not (< -1.0 -1)))
2211
2212     (pass-if "n = -1.0"
2213       (not (< -1.0 -1.0)))
2214
2215     (pass-if "n = fixnum-max"
2216       (< -1.0 fixnum-max))
2217
2218     (pass-if "n = fixnum-max + 1"
2219       (< -1.0 (+ fixnum-max 1)))
2220
2221     (pass-if "n = fixnum-min"
2222       (not (< -1.0 fixnum-min)))
2223
2224     (pass-if "n = fixnum-min - 1"
2225       (not (< -1.0 (- fixnum-min 1)))))
2226
2227   (with-test-prefix "(< fixnum-max n)"
2228
2229     (pass-if "n = 0"
2230       (not (< fixnum-max 0)))
2231
2232     (pass-if "n = 0.0"
2233       (not (< fixnum-max 0.0)))
2234
2235     (pass-if "n = 1"
2236       (not (< fixnum-max 1)))
2237
2238     (pass-if "n = 1.0"
2239       (not (< fixnum-max 1.0)))
2240
2241     (pass-if "n = -1"
2242       (not (< fixnum-max -1)))
2243
2244     (pass-if "n = -1.0"
2245       (not (< fixnum-max -1.0)))
2246
2247     (pass-if "n = fixnum-max"
2248       (not (< fixnum-max fixnum-max)))
2249
2250     (pass-if "n = fixnum-max + 1"
2251       (< fixnum-max (+ fixnum-max 1)))
2252
2253     (pass-if "n = fixnum-min"
2254       (not (< fixnum-max fixnum-min)))
2255
2256     (pass-if "n = fixnum-min - 1"
2257       (not (< fixnum-max (- fixnum-min 1)))))
2258
2259   (with-test-prefix "(< (+ fixnum-max 1) n)"
2260
2261     (pass-if "n = 0"
2262       (not (< (+ fixnum-max 1) 0)))
2263
2264     (pass-if "n = 0.0"
2265       (not (< (+ fixnum-max 1) 0.0)))
2266
2267     (pass-if "n = 1"
2268       (not (< (+ fixnum-max 1) 1)))
2269
2270     (pass-if "n = 1.0"
2271       (not (< (+ fixnum-max 1) 1.0)))
2272
2273     (pass-if "n = -1"
2274       (not (< (+ fixnum-max 1) -1)))
2275
2276     (pass-if "n = -1.0"
2277       (not (< (+ fixnum-max 1) -1.0)))
2278
2279     (pass-if "n = fixnum-max"
2280       (not (< (+ fixnum-max 1) fixnum-max)))
2281
2282     (pass-if "n = fixnum-max + 1"
2283       (not (< (+ fixnum-max 1) (+ fixnum-max 1))))
2284
2285     (pass-if "n = fixnum-min"
2286       (not (< (+ fixnum-max 1) fixnum-min)))
2287
2288     (pass-if "n = fixnum-min - 1"
2289       (not (< (+ fixnum-max 1) (- fixnum-min 1)))))
2290
2291   (with-test-prefix "(< fixnum-min n)"
2292
2293     (pass-if "n = 0"
2294       (< fixnum-min 0))
2295
2296     (pass-if "n = 0.0"
2297       (< fixnum-min 0.0))
2298
2299     (pass-if "n = 1"
2300       (< fixnum-min 1))
2301
2302     (pass-if "n = 1.0"
2303       (< fixnum-min 1.0))
2304
2305     (pass-if "n = -1"
2306       (< fixnum-min -1))
2307
2308     (pass-if "n = -1.0"
2309       (< fixnum-min -1.0))
2310
2311     (pass-if "n = fixnum-max"
2312       (< fixnum-min fixnum-max))
2313
2314     (pass-if "n = fixnum-max + 1"
2315       (< fixnum-min (+ fixnum-max 1)))
2316
2317     (pass-if "n = fixnum-min"
2318       (not (< fixnum-min fixnum-min)))
2319
2320     (pass-if "n = fixnum-min - 1"
2321       (not (< fixnum-min (- fixnum-min 1)))))
2322
2323   (with-test-prefix "(< (- fixnum-min 1) n)"
2324
2325     (pass-if "n = 0"
2326       (< (- fixnum-min 1) 0))
2327
2328     (pass-if "n = 0.0"
2329       (< (- fixnum-min 1) 0.0))
2330
2331     (pass-if "n = 1"
2332       (< (- fixnum-min 1) 1))
2333
2334     (pass-if "n = 1.0"
2335       (< (- fixnum-min 1) 1.0))
2336
2337     (pass-if "n = -1"
2338       (< (- fixnum-min 1) -1))
2339
2340     (pass-if "n = -1.0"
2341       (< (- fixnum-min 1) -1.0))
2342
2343     (pass-if "n = fixnum-max"
2344       (< (- fixnum-min 1) fixnum-max))
2345
2346     (pass-if "n = fixnum-max + 1"
2347       (< (- fixnum-min 1) (+ fixnum-max 1)))
2348
2349     (pass-if "n = fixnum-min"
2350       (< (- fixnum-min 1) fixnum-min))
2351
2352     (pass-if "n = fixnum-min - 1"
2353       (not (< (- fixnum-min 1) (- fixnum-min 1)))))
2354
2355   (pass-if (< (ash 1 256) +inf.0))
2356   (pass-if (not (< +inf.0 (ash 1 256))))
2357   (pass-if (not (< (ash 1 256) -inf.0)))
2358   (pass-if (< -inf.0 (ash 1 256)))
2359
2360   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2361   ;; sure we've avoided that
2362   (pass-if (< (1- (ash 1 1024)) +inf.0))
2363   (pass-if (<     (ash 1 1024)  +inf.0))
2364   (pass-if (< (1+ (ash 1 1024)) +inf.0))
2365   (pass-if (not (< +inf.0 (1- (ash 1 1024)))))
2366   (pass-if (not (< +inf.0     (ash 1 1024))))
2367   (pass-if (not (< +inf.0 (1+ (ash 1 1024)))))
2368   (pass-if (< -inf.0 (- (1- (ash 1 1024)))))
2369   (pass-if (< -inf.0 (-     (ash 1 1024))))
2370   (pass-if (< -inf.0 (- (1+ (ash 1 1024)))))
2371   (pass-if (not (< (- (1- (ash 1 1024))) -inf.0)))
2372   (pass-if (not (< (-     (ash 1 1024))  -inf.0)))
2373   (pass-if (not (< (- (1+ (ash 1 1024))) -inf.0)))
2374
2375   (pass-if (not (< +nan.0 +nan.0)))
2376   (pass-if (not (< 0 +nan.0)))
2377   (pass-if (not (< +nan.0 0)))
2378   (pass-if (not (< 1 +nan.0)))
2379   (pass-if (not (< +nan.0 1)))
2380   (pass-if (not (< -1 +nan.0)))
2381   (pass-if (not (< +nan.0 -1)))
2382
2383   (pass-if (not (< (ash 1 256) +nan.0)))
2384   (pass-if (not (< +nan.0 (ash 1 256))))
2385   (pass-if (not (< (- (ash 1 256)) +nan.0)))
2386   (pass-if (not (< +nan.0 (- (ash 1 256)))))
2387
2388   (pass-if (not (< (ash 1 8192) +nan.0)))
2389   (pass-if (not (< +nan.0 (ash 1 8192))))
2390   (pass-if (not (< (- (ash 1 8192)) +nan.0)))
2391   (pass-if (not (< +nan.0 (- (ash 1 8192)))))
2392
2393   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2394   ;; sure we've avoided that
2395   (pass-if (not (< (ash 3 1023) +nan.0)))
2396   (pass-if (not (< (1+ (ash 3 1023)) +nan.0)))
2397   (pass-if (not (< (1- (ash 3 1023)) +nan.0)))
2398   (pass-if (not (< +nan.0 (ash 3 1023))))
2399   (pass-if (not (< +nan.0 (1+ (ash 3 1023)))))
2400   (pass-if (not (< +nan.0 (1- (ash 3 1023)))))
2401
2402   (with-test-prefix "inum/frac"
2403     (pass-if (< 2 9/4))
2404     (pass-if (< -2 9/4))
2405     (pass-if (< -2 7/4))
2406     (pass-if (< -2 -7/4))
2407     (pass-if (eq? #f (< 2 7/4)))
2408     (pass-if (eq? #f (< 2 -7/4)))
2409     (pass-if (eq? #f (< 2 -9/4)))
2410     (pass-if (eq? #f (< -2 -9/4))))
2411
2412   (with-test-prefix "bignum/frac"
2413     (let ((x (ash 1 2048)))
2414       (pass-if (< x (* 4/3 x)))
2415       (pass-if (< (- x) (* 4/3 x)))
2416       (pass-if (< (- x) (* 2/3 x)))
2417       (pass-if (< (- x) (* -2/3 x)))
2418       (pass-if (eq? #f (< x (* 2/3 x))))
2419       (pass-if (eq? #f (< x (* -2/3 x))))
2420       (pass-if (eq? #f (< x (* -4/3 x))))
2421       (pass-if (eq? #f (< (- x) (* -4/3 x))))))
2422
2423   (with-test-prefix "flonum/frac"
2424     (pass-if (< 0.75 4/3))
2425     (pass-if (< -0.75 4/3))
2426     (pass-if (< -0.75 2/3))
2427     (pass-if (< -0.75 -2/3))
2428     (pass-if (eq? #f (< 0.75 2/3)))
2429     (pass-if (eq? #f (< 0.75 -2/3)))
2430     (pass-if (eq? #f (< 0.75 -4/3)))
2431     (pass-if (eq? #f (< -0.75 -4/3)))
2432
2433     (pass-if (< -inf.0 4/3))
2434     (pass-if (< -inf.0 -4/3))
2435     (pass-if (eq? #f (< +inf.0 4/3)))
2436     (pass-if (eq? #f (< +inf.0 -4/3)))
2437
2438     (pass-if (eq? #f (< +nan.0 4/3)))
2439     (pass-if (eq? #f (< +nan.0 -4/3))))
2440
2441   (with-test-prefix "frac/inum"
2442     (pass-if (< 7/4 2))
2443     (pass-if (< -7/4 2))
2444     (pass-if (< -9/4 2))
2445     (pass-if (< -9/4 -2))
2446     (pass-if (eq? #f (< 9/4 2)))
2447     (pass-if (eq? #f (< 9/4 -2)))
2448     (pass-if (eq? #f (< 7/4 -2)))
2449     (pass-if (eq? #f (< -7/4 -2))))
2450
2451   (with-test-prefix "frac/bignum"
2452     (let ((x (ash 1 2048)))
2453       (pass-if (< (* 2/3 x) x))
2454       (pass-if (< (* -2/3 x) x))
2455       (pass-if (< (* -4/3 x) x))
2456       (pass-if (< (* -4/3 x) (- x)))
2457       (pass-if (eq? #f (< (* 4/3 x) x)))
2458       (pass-if (eq? #f (< (* 4/3 x) (- x))))
2459       (pass-if (eq? #f (< (* 2/3 x) (- x))))
2460       (pass-if (eq? #f (< (* -2/3 x) (- x))))))
2461
2462   (with-test-prefix "frac/flonum"
2463     (pass-if (< 2/3 0.75))
2464     (pass-if (< -2/3 0.75))
2465     (pass-if (< -4/3 0.75))
2466     (pass-if (< -4/3 -0.75))
2467     (pass-if (eq? #f (< 4/3 0.75)))
2468     (pass-if (eq? #f (< 4/3 -0.75)))
2469     (pass-if (eq? #f (< 2/3 -0.75)))
2470     (pass-if (eq? #f (< -2/3 -0.75)))
2471
2472     (pass-if (< 4/3 +inf.0))
2473     (pass-if (< -4/3 +inf.0))
2474     (pass-if (eq? #f (< 4/3 -inf.0)))
2475     (pass-if (eq? #f (< -4/3 -inf.0)))
2476
2477     (pass-if (eq? #f (< 4/3 +nan.0)))
2478     (pass-if (eq? #f (< -4/3 +nan.0))))
2479
2480   (with-test-prefix "frac/frac"
2481     (pass-if (< 2/3 6/7))
2482     (pass-if (< -2/3 6/7))
2483     (pass-if (< -4/3 6/7))
2484     (pass-if (< -4/3 -6/7))
2485     (pass-if (eq? #f (< 4/3 6/7)))
2486     (pass-if (eq? #f (< 4/3 -6/7)))
2487     (pass-if (eq? #f (< 2/3 -6/7)))
2488     (pass-if (eq? #f (< -2/3 -6/7)))))
2489
2490 ;;;
2491 ;;; >
2492 ;;;
2493
2494 ;; currently not tested -- implementation is trivial
2495 ;; (> x y) is implemented as (< y x)
2496 ;; FIXME: tests should probably be added in case we change implementation.
2497
2498 ;;;
2499 ;;; <=
2500 ;;;
2501
2502 ;; currently not tested -- implementation is trivial
2503 ;; (<= x y) is implemented as (not (< y x))
2504 ;; FIXME: tests should probably be added in case we change implementation.
2505
2506 ;;;
2507 ;;; >=
2508 ;;;
2509
2510 ;; currently not tested -- implementation is trivial
2511 ;; (>= x y) is implemented as (not (< x y))
2512 ;; FIXME: tests should probably be added in case we change implementation.
2513
2514 ;;;
2515 ;;; zero?
2516 ;;;
2517
2518 (with-test-prefix "zero?"
2519   (pass-if (documented? zero?))
2520
2521   (pass-if (zero?  0))
2522   (pass-if (zero?  0.0))
2523   (pass-if (zero? -0.0))
2524
2525   (pass-if (zero?  0.0+0.0i))
2526   (pass-if (zero?  0.0-0.0i))
2527   (pass-if (zero?  0.0+0.0i))
2528   (pass-if (zero? -0.0-0.0i))
2529
2530   (pass-if (not (zero?  7)))
2531   (pass-if (not (zero? -7)))
2532   (pass-if (not (zero? 1/7)))
2533   (pass-if (not (zero? -inf.0)))
2534   (pass-if (not (zero? +inf.0)))
2535   (pass-if (not (zero? +nan.0)))
2536   (pass-if (not (zero? (+ 1 fixnum-max))))
2537   (pass-if (not (zero? (- 1 fixnum-min))))
2538   (pass-if (not (zero? 1.3)))
2539   (pass-if (not (zero? 3.1+4.2i)))
2540   (pass-if (not (zero? 1.0+0.0i)))
2541   (pass-if (not (zero? 0.0-1.0i))))
2542
2543 ;;;
2544 ;;; positive?
2545 ;;;
2546
2547 (with-test-prefix "positive?"
2548   (pass-if (documented? positive?))
2549   (pass-if (positive? 1))
2550   (pass-if (positive? (+ fixnum-max 1)))
2551   (pass-if (positive? 1.3))
2552   (pass-if (not (positive? 0)))
2553   (pass-if (not (positive? -1)))
2554   (pass-if (not (positive? (- fixnum-min 1))))
2555   (pass-if (not (positive? -1.3))))
2556
2557 ;;;
2558 ;;; negative?
2559 ;;;
2560
2561 (with-test-prefix "negative?"
2562   (pass-if (documented? negative?))
2563   (pass-if (not (negative? 1)))
2564   (pass-if (not (negative? (+ fixnum-max 1))))
2565   (pass-if (not (negative? 1.3)))
2566   (pass-if (not (negative? 0)))
2567   (pass-if (negative? -1))
2568   (pass-if (negative? (- fixnum-min 1)))
2569   (pass-if (negative? -1.3)))
2570
2571 ;;;
2572 ;;; max
2573 ;;;
2574
2575 (with-test-prefix "max"
2576   (pass-if-exception "no args" exception:wrong-num-args
2577     (max))
2578
2579   (pass-if-exception "one complex" exception:wrong-type-arg
2580     (max 1+i))
2581
2582   (pass-if-exception "inum/complex" exception:wrong-type-arg
2583     (max 123 1+i))
2584   (pass-if-exception "big/complex" exception:wrong-type-arg
2585     (max 9999999999999999999999999999999999999999 1+i))
2586   (pass-if-exception "real/complex" exception:wrong-type-arg
2587     (max 123.0 1+i))
2588   (pass-if-exception "frac/complex" exception:wrong-type-arg
2589     (max 123/456 1+i))
2590
2591   (pass-if-exception "complex/inum" exception:wrong-type-arg
2592     (max 1+i 123))
2593   (pass-if-exception "complex/big" exception:wrong-type-arg
2594     (max 1+i 9999999999999999999999999999999999999999))
2595   (pass-if-exception "complex/real" exception:wrong-type-arg
2596     (max 1+i 123.0))
2597   (pass-if-exception "complex/frac" exception:wrong-type-arg
2598     (max 1+i 123/456))
2599
2600   (let ((big*2 (* fixnum-max 2))
2601         (big*3 (* fixnum-max 3))
2602         (big*4 (* fixnum-max 4))
2603         (big*5 (* fixnum-max 5)))
2604
2605     (with-test-prefix "inum / frac"
2606       (pass-if (eqv? 3 (max 3 5/2)))
2607       (pass-if (eqv? 5/2 (max 2 5/2))))
2608
2609     (with-test-prefix "frac / inum"
2610       (pass-if (eqv? 3 (max 5/2 3)))
2611       (pass-if (eqv? 5/2 (max 5/2 2))))
2612
2613     (with-test-prefix "infinities and NaNs"
2614       ;; +inf.0 beats everything else, including NaNs
2615       (pass-if (eqv?  +inf.0   (max   +inf.0    123   )))
2616       (pass-if (eqv?  +inf.0   (max    123     +inf.0 )))
2617       (pass-if (eqv?  +inf.0   (max   +inf.0   -123.3 )))
2618       (pass-if (eqv?  +inf.0   (max   -123.3   +inf.0 )))
2619       (pass-if (eqv?  +inf.0   (max   +inf.0   -7/2   )))
2620       (pass-if (eqv?  +inf.0   (max   -7/2     +inf.0 )))
2621       (pass-if (eqv?  +inf.0   (max   +inf.0  -1e20   )))
2622       (pass-if (eqv?  +inf.0   (max  -1e20     +inf.0 )))
2623       (pass-if (eqv?  +inf.0   (max   +inf.0 (- big*2))))
2624       (pass-if (eqv?  +inf.0   (max (- big*2)  +inf.0 )))
2625       (pass-if (eqv?  +inf.0   (max   +inf.0   +inf.0 )))
2626       (pass-if (eqv?  +inf.0   (max   +inf.0   +inf.0 )))
2627       (pass-if (eqv?  +inf.0   (max   +inf.0   +nan.0 )))
2628       (pass-if (eqv?  +inf.0   (max   +nan.0   +inf.0 )))
2629       (pass-if (eqv?  +inf.0   (max   +inf.0   +inf.0 )))
2630
2631       ;; NaNs beat everything except +inf.0
2632       (pass-if (real-nan?      (max   +nan.0    123   )))
2633       (pass-if (real-nan?      (max    123     +nan.0 )))
2634       (pass-if (real-nan?      (max   +nan.0    123.3 )))
2635       (pass-if (real-nan?      (max    123.3   +nan.0 )))
2636       (pass-if (real-nan?      (max   +nan.0   -7/2   )))
2637       (pass-if (real-nan?      (max   -7/2     +nan.0 )))
2638       (pass-if (real-nan?      (max   +nan.0  -1e20   )))
2639       (pass-if (real-nan?      (max  -1e20     +nan.0 )))
2640       (pass-if (real-nan?      (max   +nan.0 (- big*2))))
2641       (pass-if (real-nan?      (max (- big*2)  +nan.0 )))
2642       (pass-if (real-nan?      (max   +nan.0   -inf.0 )))
2643       (pass-if (real-nan?      (max   -inf.0   +nan.0 )))
2644       (pass-if (real-nan?      (max   +nan.0   +nan.0 )))
2645
2646       ;; -inf.0 always loses, except against itself
2647       (pass-if (eqv?   -inf.0  (max   -inf.0   -inf.0 )))
2648       (pass-if (eqv?   -123.0  (max   -inf.0   -123   )))
2649       (pass-if (eqv?   -123.0  (max   -123     -inf.0 )))
2650       (pass-if (eqv?   -123.3  (max   -inf.0   -123.3 )))
2651       (pass-if (eqv?   -123.3  (max   -123.3   -inf.0 )))
2652       (pass-if (eqv?     -3.5  (max   -inf.0   -7/2   )))
2653       (pass-if (eqv?     -3.5  (max   -7/2     -inf.0 )))
2654       (pass-if (eqv?  -1.0e20  (max   -inf.0  -1e20   )))
2655       (pass-if (eqv?  -1.0e20  (max  -1e20     -inf.0 )))
2656       (pass-if (eqv? (exact->inexact (- big*2))
2657                      (max   -inf.0 (- big*2))))
2658       (pass-if (eqv? (exact->inexact (- big*2))
2659                      (max (- big*2)  -inf.0 ))))
2660
2661     (with-test-prefix "signed zeroes"
2662       (pass-if (eqv?  0.0  (max  0.0  0.0)))
2663       (pass-if (eqv?  0.0  (max  0.0 -0.0)))
2664       (pass-if (eqv?  0.0  (max -0.0  0.0)))
2665       (pass-if (eqv? -0.0  (max -0.0 -0.0)))
2666       (pass-if (eqv?  0.0  (max -0.0  0  )))
2667       (pass-if (eqv?  0.0  (max  0.0  0  )))
2668       (pass-if (eqv?  0.0  (max  0   -0.0)))
2669       (pass-if (eqv?  0.0  (max  0    0.0)))
2670       (pass-if (eqv?  0    (min  0    0  ))))
2671
2672     (with-test-prefix "big / frac"
2673       (pass-if (eqv? big*2 (max big*2 5/2)))
2674       (pass-if (eqv? 5/2 (max (- big*2) 5/2))))
2675
2676     (with-test-prefix "frac / big"
2677       (pass-if (eqv? big*2 (max 5/2 big*2)))
2678       (pass-if (eqv? 5/2 (max 5/2 (- big*2)))))
2679
2680     (with-test-prefix "big / real"
2681       (pass-if (real-nan? (max big*5 +nan.0)))
2682       (pass-if (eqv? (exact->inexact big*5)  (max big*5 -inf.0)))
2683       (pass-if (eqv? (exact->inexact big*5)  (max big*5 1.0)))
2684       (pass-if (eqv? +inf.0                  (max big*5 +inf.0)))
2685       (pass-if (eqv? 1.0                     (max (- big*5) 1.0))))
2686
2687     (with-test-prefix "real / big"
2688       (pass-if (real-nan? (max +nan.0 big*5)))
2689       (pass-if (eqv? (exact->inexact big*5)  (max -inf.0 big*5)))
2690       (pass-if (eqv? (exact->inexact big*5)  (max 1.0 big*5)))
2691       (pass-if (eqv? +inf.0                  (max +inf.0 big*5)))
2692       (pass-if (eqv? 1.0                     (max 1.0 (- big*5)))))
2693
2694     (with-test-prefix "frac / frac"
2695       (pass-if (eqv? 2/3 (max 1/2 2/3)))
2696       (pass-if (eqv? 2/3 (max 2/3 1/2)))
2697       (pass-if (eqv? -1/2 (max -1/2 -2/3)))
2698       (pass-if (eqv? -1/2 (max -2/3 -1/2))))
2699
2700     (with-test-prefix "real / real"
2701       (pass-if (real-nan? (max 123.0 +nan.0)))
2702       (pass-if (real-nan? (max +nan.0 123.0)))
2703       (pass-if (real-nan? (max +nan.0 +nan.0)))
2704       (pass-if (eqv? 456.0 (max 123.0 456.0)))
2705       (pass-if (eqv? 456.0 (max 456.0 123.0)))))
2706
2707   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2708   ;; sure we've avoided that
2709   (for-each (lambda (b)
2710               (pass-if (list b +inf.0)
2711                 (eqv? +inf.0 (max b +inf.0)))
2712               (pass-if (list +inf.0 b)
2713                 (eqv? +inf.0 (max b +inf.0)))
2714               (pass-if (list b -inf.0)
2715                 (eqv? (exact->inexact b) (max b -inf.0)))
2716               (pass-if (list -inf.0 b)
2717                 (eqv? (exact->inexact b) (max b -inf.0))))
2718             (list (1- (ash 1 1024))
2719                   (ash 1 1024)
2720                   (1+ (ash 1 1024))
2721                   (- (1- (ash 1 1024)))
2722                   (- (ash 1 1024))
2723                   (- (1+ (ash 1 1024)))))
2724
2725   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2726   ;; sure we've avoided that
2727   (pass-if (real-nan? (max (ash 1 2048) +nan.0)))
2728   (pass-if (real-nan? (max +nan.0 (ash 1 2048)))))
2729
2730 ;;;
2731 ;;; min
2732 ;;;
2733
2734 ;; FIXME: unfinished...
2735
2736 (with-test-prefix "min"
2737   (pass-if-exception "no args" exception:wrong-num-args
2738     (min))
2739
2740   (pass-if-exception "one complex" exception:wrong-type-arg
2741     (min 1+i))
2742
2743   (pass-if-exception "inum/complex" exception:wrong-type-arg
2744     (min 123 1+i))
2745   (pass-if-exception "big/complex" exception:wrong-type-arg
2746     (min 9999999999999999999999999999999999999999 1+i))
2747   (pass-if-exception "real/complex" exception:wrong-type-arg
2748     (min 123.0 1+i))
2749   (pass-if-exception "frac/complex" exception:wrong-type-arg
2750     (min 123/456 1+i))
2751
2752   (pass-if-exception "complex/inum" exception:wrong-type-arg
2753     (min 1+i 123))
2754   (pass-if-exception "complex/big" exception:wrong-type-arg
2755     (min 1+i 9999999999999999999999999999999999999999))
2756   (pass-if-exception "complex/real" exception:wrong-type-arg
2757     (min 1+i 123.0))
2758   (pass-if-exception "complex/frac" exception:wrong-type-arg
2759     (min 1+i 123/456))
2760
2761   (let ((big*2 (* fixnum-max 2))
2762         (big*3 (* fixnum-max 3))
2763         (big*4 (* fixnum-max 4))
2764         (big*5 (* fixnum-max 5)))
2765
2766     (pass-if (documented? min))
2767     (pass-if (eqv? 1 (min 7 3 1 5)))
2768     (pass-if (eqv? 1 (min 1 7 3 5)))
2769     (pass-if (eqv? 1 (min 7 3 5 1)))
2770     (pass-if (eqv? -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
2771     (pass-if (eqv? -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
2772     (pass-if (eqv? -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
2773     (pass-if (eqv? big*2 (min big*3 big*5 big*2 big*4)))
2774     (pass-if (eqv? big*2 (min big*2 big*3 big*5 big*4)))
2775     (pass-if (eqv? big*2 (min big*3 big*5 big*4 big*2)))
2776     (pass-if
2777         (eqv? (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
2778     (pass-if
2779         (eqv? (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
2780     (pass-if
2781         (eqv? (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
2782
2783     (with-test-prefix "inum / frac"
2784       (pass-if (eqv? 5/2 (min 3 5/2)))
2785       (pass-if (eqv? 2   (min 2 5/2))))
2786
2787     (with-test-prefix "frac / inum"
2788       (pass-if (eqv? 5/2 (min 5/2 3)))
2789       (pass-if (eqv? 2   (min 5/2 2))))
2790
2791     (with-test-prefix "infinities and NaNs"
2792       ;; -inf.0 beats everything else, including NaNs
2793       (pass-if (eqv?  -inf.0   (min   -inf.0    123   )))
2794       (pass-if (eqv?  -inf.0   (min    123     -inf.0 )))
2795       (pass-if (eqv?  -inf.0   (min   -inf.0   -123.3 )))
2796       (pass-if (eqv?  -inf.0   (min   -123.3   -inf.0 )))
2797       (pass-if (eqv?  -inf.0   (min   -inf.0   -7/2   )))
2798       (pass-if (eqv?  -inf.0   (min   -7/2     -inf.0 )))
2799       (pass-if (eqv?  -inf.0   (min   -inf.0  -1e20   )))
2800       (pass-if (eqv?  -inf.0   (min  -1e20     -inf.0 )))
2801       (pass-if (eqv?  -inf.0   (min   -inf.0 (- big*2))))
2802       (pass-if (eqv?  -inf.0   (min (- big*2)  -inf.0 )))
2803       (pass-if (eqv?  -inf.0   (min   -inf.0   +inf.0 )))
2804       (pass-if (eqv?  -inf.0   (min   +inf.0   -inf.0 )))
2805       (pass-if (eqv?  -inf.0   (min   -inf.0   +nan.0 )))
2806       (pass-if (eqv?  -inf.0   (min   +nan.0   -inf.0 )))
2807       (pass-if (eqv?  -inf.0   (min   -inf.0   -inf.0 )))
2808
2809       ;; NaNs beat everything except -inf.0
2810       (pass-if (real-nan?      (min   +nan.0    123   )))
2811       (pass-if (real-nan?      (min    123     +nan.0 )))
2812       (pass-if (real-nan?      (min   +nan.0    123.3 )))
2813       (pass-if (real-nan?      (min    123.3   +nan.0 )))
2814       (pass-if (real-nan?      (min   +nan.0   -7/2   )))
2815       (pass-if (real-nan?      (min   -7/2     +nan.0 )))
2816       (pass-if (real-nan?      (min   +nan.0  -1e20   )))
2817       (pass-if (real-nan?      (min  -1e20     +nan.0 )))
2818       (pass-if (real-nan?      (min   +nan.0 (- big*2))))
2819       (pass-if (real-nan?      (min (- big*2)  +nan.0 )))
2820       (pass-if (real-nan?      (min   +nan.0   +inf.0 )))
2821       (pass-if (real-nan?      (min   +inf.0   +nan.0 )))
2822       (pass-if (real-nan?      (min   +nan.0   +nan.0 )))
2823
2824       ;; +inf.0 always loses, except against itself
2825       (pass-if (eqv?   +inf.0  (min   +inf.0   +inf.0 )))
2826       (pass-if (eqv?   -123.0  (min   +inf.0   -123   )))
2827       (pass-if (eqv?   -123.0  (min   -123     +inf.0 )))
2828       (pass-if (eqv?   -123.3  (min   +inf.0   -123.3 )))
2829       (pass-if (eqv?   -123.3  (min   -123.3   +inf.0 )))
2830       (pass-if (eqv?     -3.5  (min   +inf.0   -7/2   )))
2831       (pass-if (eqv?     -3.5  (min   -7/2     +inf.0 )))
2832       (pass-if (eqv?  -1.0e20  (min   +inf.0  -1e20   )))
2833       (pass-if (eqv?  -1.0e20  (min  -1e20     +inf.0 )))
2834       (pass-if (eqv? (exact->inexact (- big*2))
2835                      (min   +inf.0 (- big*2))))
2836       (pass-if (eqv? (exact->inexact (- big*2))
2837                      (min (- big*2)  +inf.0 ))))
2838
2839     (with-test-prefix "signed zeroes"
2840       (pass-if (eqv?  0.0  (min  0.0  0.0)))
2841       (pass-if (eqv? -0.0  (min  0.0 -0.0)))
2842       (pass-if (eqv? -0.0  (min -0.0  0.0)))
2843       (pass-if (eqv? -0.0  (min -0.0 -0.0)))
2844       (pass-if (eqv? -0.0  (min -0.0  0  )))
2845       (pass-if (eqv?  0.0  (min  0.0  0  )))
2846       (pass-if (eqv? -0.0  (min  0   -0.0)))
2847       (pass-if (eqv?  0.0  (min  0    0.0)))
2848       (pass-if (eqv?  0    (min  0    0  ))))
2849
2850     (with-test-prefix "big / frac"
2851       (pass-if (eqv? 5/2       (min big*2 5/2)))
2852       (pass-if (eqv? (- big*2) (min (- big*2) 5/2))))
2853
2854     (with-test-prefix "frac / big"
2855       (pass-if (eqv? 5/2       (min 5/2 big*2)))
2856       (pass-if (eqv? (- big*2) (min 5/2 (- big*2)))))
2857
2858     (with-test-prefix "big / real"
2859       (pass-if (real-nan? (min big*5 +nan.0)))
2860       (pass-if (eqv? (exact->inexact big*5)      (min big*5  +inf.0)))
2861       (pass-if (eqv? -inf.0                      (min big*5  -inf.0)))
2862       (pass-if (eqv? 1.0                         (min big*5 1.0)))
2863       (pass-if (eqv? (exact->inexact (- big*5))  (min (- big*5) 1.0))))
2864
2865     (with-test-prefix "real / big"
2866       (pass-if (real-nan? (min +nan.0 big*5)))
2867       (pass-if (eqv? (exact->inexact big*5)      (min +inf.0 big*5)))
2868       (pass-if (eqv? -inf.0                      (min -inf.0 big*5)))
2869       (pass-if (eqv? 1.0                         (min 1.0 big*5)))
2870       (pass-if (eqv? (exact->inexact (- big*5))  (min 1.0 (- big*5)))))
2871
2872     (with-test-prefix "frac / frac"
2873       (pass-if (eqv? 1/2 (min 1/2 2/3)))
2874       (pass-if (eqv? 1/2 (min 2/3 1/2)))
2875       (pass-if (eqv? -2/3 (min -1/2 -2/3)))
2876       (pass-if (eqv? -2/3 (min -2/3 -1/2))))
2877
2878     (with-test-prefix "real / real"
2879       (pass-if (real-nan? (min 123.0 +nan.0)))
2880       (pass-if (real-nan? (min +nan.0 123.0)))
2881       (pass-if (real-nan? (min +nan.0 +nan.0)))
2882       (pass-if (eqv? 123.0 (min 123.0 456.0)))
2883       (pass-if (eqv? 123.0 (min 456.0 123.0)))))
2884
2885
2886   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2887   ;; sure we've avoided that
2888   (for-each (lambda (b)
2889               (pass-if (list b +inf.0)
2890                 (eqv? (exact->inexact b) (min b +inf.0)))
2891               (pass-if (list +inf.0 b)
2892                 (eqv? (exact->inexact b) (min b +inf.0)))
2893               (pass-if (list b -inf.0)
2894                 (eqv? -inf.0 (min b -inf.0)))
2895               (pass-if (list -inf.0 b)
2896                 (eqv? -inf.0 (min b -inf.0))))
2897             (list (1- (ash 1 1024))
2898                   (ash 1 1024)
2899                   (1+ (ash 1 1024))
2900                   (- (1- (ash 1 1024)))
2901                   (- (ash 1 1024))
2902                   (- (1+ (ash 1 1024)))))
2903
2904   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2905   ;; sure we've avoided that
2906   (pass-if (real-nan? (min (- (ash 1 2048)) (- +nan.0))))
2907   (pass-if (real-nan? (min (- +nan.0) (- (ash 1 2048))))))
2908
2909 ;;;
2910 ;;; +
2911 ;;;
2912
2913 (with-test-prefix/c&e "+"
2914
2915   (pass-if "documented?"
2916     (documented? +))
2917
2918   (pass-if "simple"
2919     (and (eqv?  7 (+ 3 4))
2920          (eqv?  3 (+ 3))
2921          (eqv?  0 (+))))
2922
2923   (pass-if "exactness propagation"
2924     (and (eqv?  8   (+ 3 5))
2925          (eqv?  8.0 (+ 3 5.0))
2926          (eqv?  8.0 (+ 3.0 5))
2927          (eqv?  8.0 (+ 3.0 5.0))
2928
2929          (eqv?  5/6  (+ 1/2 1/3))
2930          (eqv?  5.5  (+ 1/2 5.0))
2931          (eqv?  3.25 (+ 3.0 1/4))))
2932
2933   (pass-if "signed zeroes"
2934     (and (eqv?  0.0 (+  0.0))
2935          (eqv? -0.0 (+ -0.0))
2936          (eqv?  0.0 (+  0.0  0.0))
2937          (eqv?  0.0 (+  0.0 -0.0))
2938          (eqv?  0.0 (+ -0.0  0.0))
2939          (eqv? -0.0 (+ -0.0 -0.0))))
2940
2941   (pass-if "NaNs"
2942     (and (real-nan?  (+ +nan.0 +nan.0))
2943          (real-nan?  (+ 0 +nan.0))
2944          (real-nan?  (+ +nan.0 0))
2945          (real-nan?  (+ 1 +nan.0))
2946          (real-nan?  (+ +nan.0 1))
2947          (real-nan?  (+ -1 +nan.0))
2948          (real-nan?  (+ +nan.0 -1))
2949          (real-nan?  (+ -7/2 +nan.0))
2950          (real-nan?  (+ +nan.0 -7/2))
2951          (real-nan?  (+ 1e20 +nan.0))
2952          (real-nan?  (+ +nan.0 1e20))
2953          (real-nan?  (+ +inf.0 +nan.0))
2954          (real-nan?  (+ +nan.0 +inf.0))
2955          (real-nan?  (+ -inf.0 +nan.0))
2956          (real-nan?  (+ +nan.0 -inf.0))
2957          (real-nan?  (+ (* fixnum-max 2) +nan.0))
2958          (real-nan?  (+ +nan.0 (* fixnum-max 2)))))
2959
2960   (pass-if "infinities"
2961     (and (eqv? +inf.0 (+ +inf.0 +inf.0))
2962          (eqv? -inf.0 (+ -inf.0 -inf.0))
2963          (real-nan?   (+ +inf.0 -inf.0))
2964          (real-nan?   (+ -inf.0 +inf.0))))
2965
2966   ;; The maximum fixnum on a 32-bit architecture: 2^29 - 1.
2967   (pass-if "fixnum + fixnum = bignum (32-bit)"
2968     (eqv? 536870912 (+ 536870910 2)))
2969
2970   ;; The maximum fixnum on a 64-bit architecture: 2^61 - 1.
2971   (pass-if "fixnum + fixnum = bignum (64-bit)"
2972     (eqv? 2305843009213693952 (+ 2305843009213693950 2)))
2973
2974   (pass-if "bignum + fixnum = fixnum"
2975     (eqv? 0 (+ (1+ most-positive-fixnum) most-negative-fixnum))))
2976
2977 ;;;
2978 ;;; -
2979 ;;;
2980
2981 (with-test-prefix/c&e "-"
2982
2983   (pass-if "double-negation of fixnum-min: ="
2984     (=      fixnum-min (- (- fixnum-min))))
2985   (pass-if "double-negation of fixnum-min: eqv?"
2986     (eqv?   fixnum-min (- (- fixnum-min))))
2987   (pass-if "double-negation of fixnum-min: equal?"
2988     (equal? fixnum-min (- (- fixnum-min))))
2989
2990   (pass-if "binary double-negation of fixnum-min: ="
2991     (=      fixnum-min (- 0 (- 0 fixnum-min))))
2992   (pass-if "binary double-negation of fixnum-min: eqv?"
2993     (eqv?   fixnum-min (- 0 (- 0 fixnum-min))))
2994   (pass-if "binary double-negation of fixnum-min: equal?"
2995     (equal? fixnum-min (- 0 (- 0 fixnum-min))))
2996
2997   (pass-if "signed zeroes"
2998     (and (eqv? +0.0 (- -0.0))
2999          (eqv? -0.0 (- +0.0))
3000          (eqv?  0.0 (-  0.0  0.0))
3001          (eqv?  0.0 (-  0.0 -0.0))
3002          (eqv?  0.0 (- -0.0 -0.0))
3003          (eqv? -0.0 (- -0.0  0.0))))
3004
3005   (pass-if "exactness propagation"
3006     (and (eqv?  3   (- 8 5))
3007          (eqv?  3.0 (- 8 5.0))
3008          (eqv?  3.0 (- 8.0 5))
3009          (eqv?  3.0 (- 8.0 5.0))
3010          (eqv? -1/6  (- 1/3 1/2))
3011          (eqv? -4.5  (- 1/2 5.0))
3012          (eqv?  2.75 (- 3.0 1/4))))
3013
3014   (pass-if "infinities"
3015     (and (eqv? +inf.0 (- +inf.0 -inf.0))
3016          (eqv? -inf.0 (- -inf.0 +inf.0))
3017          (real-nan?   (- +inf.0 +inf.0))
3018          (real-nan?   (- -inf.0 -inf.0))))
3019
3020   (pass-if "NaNs"
3021     (and (real-nan?  (- +nan.0 +nan.0))
3022          (real-nan?  (- 0 +nan.0))
3023          (real-nan?  (- +nan.0 0))
3024          (real-nan?  (- 1 +nan.0))
3025          (real-nan?  (- +nan.0 1))
3026          (real-nan?  (- -1 +nan.0))
3027          (real-nan?  (- +nan.0 -1))
3028          (real-nan?  (- -7/2 +nan.0))
3029          (real-nan?  (- +nan.0 -7/2))
3030          (real-nan?  (- 1e20 +nan.0))
3031          (real-nan?  (- +nan.0 1e20))
3032          (real-nan?  (- +inf.0 +nan.0))
3033          (real-nan?  (- +nan.0 +inf.0))
3034          (real-nan?  (- -inf.0 +nan.0))
3035          (real-nan?  (- +nan.0 -inf.0))
3036          (real-nan?  (- (* fixnum-max 2) +nan.0))
3037          (real-nan?  (- +nan.0 (* fixnum-max 2)))))
3038
3039   (pass-if "(eqv? fixnum-min (- (- fixnum-min)))"
3040     (eqv? fixnum-min (- (- fixnum-min))))
3041   (pass-if "(eqv? fixnum-min (- 0 (- 0 fixnum-min)))"
3042     (eqv? fixnum-min (- 0 (- 0 fixnum-min))))
3043   (pass-if "(eqv? fixnum-num (apply - (list (apply - (list fixnum-min)))))"
3044     (eqv? fixnum-min (apply - (list (apply - (list fixnum-min))))))
3045
3046   (pass-if "-inum - +bignum"
3047     (= #x-100000000000000000000000000000001
3048        (- -1 #x100000000000000000000000000000000)))
3049
3050   (pass-if "big - inum"
3051     (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
3052        (- #x100000000000000000000000000000000 1)))
3053
3054   (pass-if "big - -inum"
3055     (= #x100000000000000000000000000000001
3056        (- #x100000000000000000000000000000000 -1)))
3057
3058   ;; The mininum fixnum on a 32-bit architecture: -2^29.
3059   (pass-if "fixnum - fixnum = bignum (32-bit)"
3060     (eqv? -536870912 (- -536870910 2)))
3061
3062   ;; The minimum fixnum on a 64-bit architecture: -2^61.
3063   (pass-if "fixnum - fixnum = bignum (64-bit)"
3064     (eqv? -2305843009213693952 (- -2305843009213693950 2)))
3065
3066   (pass-if "bignum - fixnum = fixnum"
3067     (eqv? most-positive-fixnum (- (1+ most-positive-fixnum) 1))))
3068
3069 ;;;
3070 ;;; *
3071 ;;;
3072
3073 (with-test-prefix "*"
3074
3075   (with-test-prefix "double-negation of fixnum-min"
3076     (pass-if (=      fixnum-min (* -1 (* -1 fixnum-min))))
3077     (pass-if (eqv?   fixnum-min (* -1 (* -1 fixnum-min))))
3078     (pass-if (equal? fixnum-min (* -1 (* -1 fixnum-min))))
3079     (pass-if (=      fixnum-min (* (* fixnum-min -1) -1)))
3080     (pass-if (eqv?   fixnum-min (* (* fixnum-min -1) -1)))
3081     (pass-if (equal? fixnum-min (* (* fixnum-min -1) -1))))
3082
3083   (with-test-prefix "signed fixnum overflow"
3084     (pass-if (eqv? (* 65536 65536) 4294967296))
3085     (pass-if (eqv? (* -65536 65536) -4294967296))
3086     (pass-if (eqv? (* 65536 -65536) -4294967296))
3087     (pass-if (eqv? (* -65536 -65536) 4294967296))
3088     (pass-if (eqv? (* 4294967296 4294967296) 18446744073709551616))
3089     (pass-if (eqv? (* -4294967296 4294967296) -18446744073709551616))
3090     (pass-if (eqv? (* 4294967296 -4294967296) -18446744073709551616))
3091     (pass-if (eqv? (* -4294967296 -4294967296) 18446744073709551616)))
3092
3093   (with-test-prefix "signed zeroes"
3094     (pass-if (eqv? +0.0 (* +0.0 +0.0)))
3095     (pass-if (eqv? -0.0 (* -0.0 +0.0)))
3096     (pass-if (eqv? +0.0 (* -0.0 -0.0)))
3097     (pass-if (eqv? -0.0 (* +0.0 -0.0)))
3098     (pass-if (eqv? +0.0+0.0i (* +i +0.0)))
3099     (pass-if (eqv? +0.0-0.0i (* -i +0.0)))
3100     (pass-if (eqv? -0.0-0.0i (* +i -0.0)))
3101     (pass-if (eqv? -0.0+0.0i (* -i -0.0))))
3102
3103   (with-test-prefix "exactness propagation"
3104     (pass-if (eqv? -0.0 (*  0 -1.0 )))
3105     (pass-if (eqv?  0.0 (*  0  1.0 )))
3106     (pass-if (eqv? -0.0 (* -1.0  0 )))
3107     (pass-if (eqv?  0.0 (*  1.0  0 )))
3108     (pass-if (eqv?  0   (*  0  1/2 )))
3109     (pass-if (eqv?  0   (*  1/2  0 )))
3110     (pass-if (eqv?  0.0+0.0i (*  0  1+i )))
3111     (pass-if (eqv?  0.0+0.0i (*  1+i  0 )))
3112     (pass-if (eqv? -1.0 (*  1 -1.0 )))
3113     (pass-if (eqv?  1.0 (*  1  1.0 )))
3114     (pass-if (eqv? -1.0 (* -1.0  1 )))
3115     (pass-if (eqv?  1.0 (*  1.0  1 )))
3116     (pass-if (eqv?  1/2 (*  1  1/2 )))
3117     (pass-if (eqv?  1/2 (*  1/2  1 )))
3118     (pass-if (eqv?  1+i (*  1  1+i )))
3119     (pass-if (eqv?  1+i (*  1+i  1 ))))
3120
3121   (with-test-prefix "propagation of NaNs"
3122     (pass-if (real-nan?      (* +nan.0 +nan.0)))
3123     (pass-if (real-nan?      (* +nan.0    1  )))
3124     (pass-if (real-nan?      (* +nan.0   -1  )))
3125     (pass-if (real-nan?      (* +nan.0 -7/2  )))
3126     (pass-if (real-nan?      (* +nan.0 1e20  )))
3127     (pass-if (real-nan?      (*  1     +nan.0)))
3128     (pass-if (real-nan?      (* -1     +nan.0)))
3129     (pass-if (real-nan?      (* -7/2   +nan.0)))
3130     (pass-if (real-nan?      (* 1e20   +nan.0)))
3131     (pass-if (real-nan?      (* +inf.0 +nan.0)))
3132     (pass-if (real-nan?      (* +nan.0 +inf.0)))
3133     (pass-if (real-nan?      (* -inf.0 +nan.0)))
3134     (pass-if (real-nan?      (* +nan.0 -inf.0)))
3135     (pass-if (real-nan?      (* (* fixnum-max 2) +nan.0)))
3136     (pass-if (real-nan?      (* +nan.0 (* fixnum-max 2))))
3137
3138     (pass-if (real-nan?        (*     0     +nan.0  )))
3139     (pass-if (real-nan?        (*  +nan.0      0    )))
3140     (pass-if (almost-real-nan? (*     0     +nan.0+i)))
3141     (pass-if (almost-real-nan? (*  +nan.0+i    0    )))
3142
3143     (pass-if (imaginary-nan? (*     0     +nan.0i )))
3144     (pass-if (imaginary-nan? (*  +nan.0i     0    )))
3145     (pass-if (imaginary-nan? (*     0    1+nan.0i )))
3146     (pass-if (imaginary-nan? (* 1+nan.0i     0    )))
3147
3148     (pass-if (complex-nan?   (* 0   +nan.0+nan.0i )))
3149     (pass-if (complex-nan?   (* +nan.0+nan.0i   0 ))))
3150
3151   (with-test-prefix "infinities"
3152     (pass-if (eqv?   +inf.0  (* +inf.0  5  )))
3153     (pass-if (eqv?   -inf.0  (* +inf.0 -5  )))
3154     (pass-if (eqv?   +inf.0  (* +inf.0 73.1)))
3155     (pass-if (eqv?   -inf.0  (* +inf.0 -9.2)))
3156     (pass-if (eqv?   +inf.0  (* +inf.0  5/2)))
3157     (pass-if (eqv?   -inf.0  (* +inf.0 -5/2)))
3158     (pass-if (eqv?   -inf.0  (* -5   +inf.0)))
3159     (pass-if (eqv?   +inf.0  (* 73.1 +inf.0)))
3160     (pass-if (eqv?   -inf.0  (* -9.2 +inf.0)))
3161     (pass-if (eqv?   +inf.0  (*  5/2 +inf.0)))
3162     (pass-if (eqv?   -inf.0  (* -5/2 +inf.0)))
3163
3164     (pass-if (eqv?   -inf.0  (* -inf.0  5  )))
3165     (pass-if (eqv?   +inf.0  (* -inf.0 -5  )))
3166     (pass-if (eqv?   -inf.0  (* -inf.0 73.1)))
3167     (pass-if (eqv?   +inf.0  (* -inf.0 -9.2)))
3168     (pass-if (eqv?   -inf.0  (* -inf.0  5/2)))
3169     (pass-if (eqv?   +inf.0  (* -inf.0 -5/2)))
3170     (pass-if (eqv?   +inf.0  (* -5   -inf.0)))
3171     (pass-if (eqv?   -inf.0  (* 73.1 -inf.0)))
3172     (pass-if (eqv?   +inf.0  (* -9.2 -inf.0)))
3173     (pass-if (eqv?   -inf.0  (* 5/2  -inf.0)))
3174     (pass-if (eqv?   +inf.0  (* -5/2 -inf.0)))
3175
3176     (pass-if (real-nan?      (*    0.0 +inf.0)))
3177     (pass-if (real-nan?      (*   -0.0 +inf.0)))
3178     (pass-if (real-nan?      (* +inf.0    0.0)))
3179     (pass-if (real-nan?      (* +inf.0   -0.0)))
3180
3181     (pass-if (real-nan?      (*    0.0 -inf.0)))
3182     (pass-if (real-nan?      (*   -0.0 -inf.0)))
3183     (pass-if (real-nan?      (* -inf.0    0.0)))
3184     (pass-if (real-nan?      (* -inf.0   -0.0)))
3185
3186     (pass-if (real-nan?      (*     0     +inf.0  )))
3187     (pass-if (real-nan?      (*  +inf.0      0    )))
3188     (pass-if (real-nan?      (*     0     -inf.0  )))
3189     (pass-if (real-nan?      (*  -inf.0      0    )))
3190
3191     (pass-if (almost-real-nan? (*     0     +inf.0+i)))
3192     (pass-if (almost-real-nan? (*  +inf.0+i    0    )))
3193     (pass-if (almost-real-nan? (*     0     -inf.0+i)))
3194     (pass-if (almost-real-nan? (*  -inf.0+i    0    )))
3195
3196     (pass-if (imaginary-nan? (*     0     +inf.0i )))
3197     (pass-if (imaginary-nan? (*  +inf.0i     0    )))
3198     (pass-if (imaginary-nan? (*     0    1+inf.0i )))
3199     (pass-if (imaginary-nan? (* 1+inf.0i     0    )))
3200
3201     (pass-if (imaginary-nan? (*     0     -inf.0i )))
3202     (pass-if (imaginary-nan? (*  -inf.0i     0    )))
3203     (pass-if (imaginary-nan? (*     0    1-inf.0i )))
3204     (pass-if (imaginary-nan? (* 1-inf.0i     0    )))
3205
3206     (pass-if (complex-nan?   (* 0   +inf.0+inf.0i )))
3207     (pass-if (complex-nan?   (* +inf.0+inf.0i   0 )))
3208
3209     (pass-if (complex-nan?   (* 0   +inf.0-inf.0i )))
3210     (pass-if (complex-nan?   (* -inf.0+inf.0i   0 ))))
3211
3212   (with-test-prefix "inum * bignum"
3213
3214     (pass-if "0 * 2^256 = 0"
3215       (eqv? 0 (* 0 (ash 1 256)))))
3216
3217   (with-test-prefix "inum * flonum"
3218
3219     (pass-if "0 * 1.0 = 0.0"
3220       (eqv? 0.0 (* 0 1.0))))
3221
3222   (with-test-prefix "inum * complex"
3223
3224     (pass-if "0 * 1+1i = 0.0+0.0i"
3225       (eqv? 0.0+0.0i (* 0 1+1i))))
3226
3227   (with-test-prefix "inum * frac"
3228
3229     (pass-if "0 * 2/3 = 0"
3230       (eqv? 0 (* 0 2/3))))
3231
3232   (with-test-prefix "bignum * inum"
3233
3234     (pass-if "2^256 * 0 = 0"
3235       (eqv? 0 (* (ash 1 256) 0))))
3236
3237   (with-test-prefix "flonum * inum"
3238     (pass-if "1.0 * 0 = 0.0"
3239       (eqv? 0.0 (* 1.0 0))))
3240
3241   (with-test-prefix "complex * inum"
3242     (pass-if "1+1i * 0 = 0.0+0.0i"
3243       (eqv? 0.0+0.0i (* 1+1i 0))))
3244
3245   (pass-if "complex * bignum"
3246     (let ((big (ash 1 90)))
3247       (= (make-rectangular big big)
3248          (* 1+1i big))))
3249
3250   (with-test-prefix "frac * inum"
3251
3252     (pass-if "2/3 * 0 = 0"
3253       (eqv? 0 (* 2/3 0)))))
3254
3255 ;;;
3256 ;;; /
3257 ;;;
3258
3259 (with-test-prefix "/"
3260
3261   (with-test-prefix "double-negation of fixnum-min"
3262     (pass-if (=      fixnum-min (/ (/ fixnum-min -1) -1)))
3263     (pass-if (eqv?   fixnum-min (/ (/ fixnum-min -1) -1)))
3264     (pass-if (equal? fixnum-min (/ (/ fixnum-min -1) -1))))
3265
3266   (pass-if "documented?"
3267     (documented? /))
3268
3269   (with-test-prefix "division by zero"
3270
3271     (pass-if-exception "(/ 0)"
3272         exception:numerical-overflow
3273       (/ 0))
3274
3275     (pass-if "(/ 0.0)"
3276       (= +inf.0 (/ 0.0)))
3277
3278     (pass-if-exception "(/ 1 0)"
3279         exception:numerical-overflow
3280       (/ 1 0))
3281
3282     (pass-if "(/ 1 0.0)"
3283       (= +inf.0 (/ 1 0.0)))
3284
3285     (pass-if-exception "(/ bignum 0)"
3286         exception:numerical-overflow
3287       (/ (+ fixnum-max 1) 0))
3288
3289     (pass-if "(/ bignum 0.0)"
3290       (= +inf.0 (/ (+ fixnum-max 1) 0.0)))
3291
3292     (pass-if-exception "(/ 1.0 0)"
3293         exception:numerical-overflow
3294       (/ 1.0 0))
3295
3296     (pass-if "(/ 1.0 0.0)"
3297       (= +inf.0 (/ 1.0 0.0)))
3298
3299     (pass-if-exception "(/ +i 0)"
3300         exception:numerical-overflow
3301       (/ +i 0))
3302
3303     (pass-if "(/ +i 0.0)"
3304       (= +inf.0 (imag-part (/ +i 0.0)))))
3305
3306   (with-test-prefix "1/complex"
3307
3308     (pass-if "0+1i"
3309       (eqv? 0-1i (/ 0+1i)))
3310
3311     ;; in guile 1.6 through 1.6.7 this incorrectly resulted in nans
3312     (pass-if "0-1i"
3313       (eqv? 0+1i (/ 0-1i)))
3314
3315     (pass-if "1+1i"
3316       (eqv? 0.5-0.5i (/ 1+1i)))
3317
3318     (pass-if "1-1i"
3319       (eqv? 0.5+0.5i (/ 1-1i)))
3320
3321     (pass-if "-1+1i"
3322       (eqv? -0.5-0.5i (/ -1+1i)))
3323
3324     (pass-if "-1-1i"
3325       (eqv? -0.5+0.5i (/ -1-1i)))
3326
3327     (pass-if "(/ 3+4i)"
3328       (= (/ 3+4i) 0.12-0.16i))
3329
3330     (pass-if "(/ 4+3i)"
3331       (= (/ 4+3i) 0.16-0.12i))
3332
3333     (pass-if "(/ 1e200+1e200i)"
3334       (= (/ 1e200+1e200i) 5.0e-201-5.0e-201i)))
3335
3336   (with-test-prefix "inum/complex"
3337
3338     (pass-if "(/ 25 3+4i)"
3339       (= (/ 25 3+4i) 3.0-4.0i))
3340
3341     (pass-if "(/ 25 4+3i)"
3342       (= (/ 25 4+3i) 4.0-3.0i)))
3343
3344   (with-test-prefix "complex/complex"
3345
3346     (pass-if "(/ 25+125i 3+4i)"
3347       (= (/ 25+125i 3+4i) 23.0+11.0i))
3348
3349     (pass-if "(/ 25+125i 4+3i)"
3350       (= (/ 25+125i 4+3i) 19.0+17.0i))))
3351
3352 ;;;
3353 ;;; floor
3354 ;;;
3355
3356 (with-test-prefix "floor"
3357   (pass-if (=  1 (floor  1.75)))
3358   (pass-if (=  1 (floor  1.5)))
3359   (pass-if (=  1 (floor  1.25)))
3360   (pass-if (=  0 (floor  0.75)))
3361   (pass-if (=  0 (floor  0.5)))
3362   (pass-if (=  0 (floor  0.0)))
3363   (pass-if (= -1 (floor -0.5)))
3364   (pass-if (= -2 (floor -1.25)))
3365   (pass-if (= -2 (floor -1.5)))
3366
3367   (with-test-prefix "inum"
3368     (pass-if "0"
3369       (and (= 0    (floor 0))
3370            (exact? (floor 0))))
3371
3372     (pass-if "1"
3373       (and (= 1    (floor 1))
3374            (exact? (floor 1))))
3375
3376     (pass-if "-1"
3377       (and (= -1   (floor -1))
3378            (exact? (floor -1)))))
3379
3380   (with-test-prefix "bignum"
3381     (let ((x (1+ most-positive-fixnum)))
3382       (pass-if "(1+ most-positive-fixnum)"
3383         (and (= x    (floor x))
3384              (exact? (floor x)))))
3385
3386     (let ((x (1- most-negative-fixnum)))
3387       (pass-if "(1- most-negative-fixnum)"
3388         (and (= x    (floor x))
3389              (exact? (floor x))))))
3390
3391   (with-test-prefix "frac"
3392     (define (=exact x y)
3393       (and (= x y)
3394            (exact? y)))
3395
3396     (pass-if (=exact -3 (floor -7/3)))
3397     (pass-if (=exact -2 (floor -5/3)))
3398     (pass-if (=exact -2 (floor -4/3)))
3399     (pass-if (=exact -1 (floor -2/3)))
3400     (pass-if (=exact -1 (floor -1/3)))
3401     (pass-if (=exact  0 (floor  1/3)))
3402     (pass-if (=exact  0 (floor  2/3)))
3403     (pass-if (=exact  1 (floor  4/3)))
3404     (pass-if (=exact  1 (floor  5/3)))
3405     (pass-if (=exact  2 (floor  7/3)))
3406
3407     (pass-if (=exact -3 (floor -17/6)))
3408     (pass-if (=exact -3 (floor -16/6)))
3409     (pass-if (=exact -3 (floor -15/6)))
3410     (pass-if (=exact -3 (floor -14/6)))
3411     (pass-if (=exact -3 (floor -13/6)))
3412     (pass-if (=exact -2 (floor -11/6)))
3413     (pass-if (=exact -2 (floor -10/6)))
3414     (pass-if (=exact -2 (floor  -9/6)))
3415     (pass-if (=exact -2 (floor  -8/6)))
3416     (pass-if (=exact -2 (floor  -7/6)))
3417     (pass-if (=exact -1 (floor  -5/6)))
3418     (pass-if (=exact -1 (floor  -4/6)))
3419     (pass-if (=exact -1 (floor  -3/6)))
3420     (pass-if (=exact -1 (floor  -2/6)))
3421     (pass-if (=exact -1 (floor  -1/6)))
3422     (pass-if (=exact  0 (floor   1/6)))
3423     (pass-if (=exact  0 (floor   2/6)))
3424     (pass-if (=exact  0 (floor   3/6)))
3425     (pass-if (=exact  0 (floor   4/6)))
3426     (pass-if (=exact  0 (floor   5/6)))
3427     (pass-if (=exact  1 (floor   7/6)))
3428     (pass-if (=exact  1 (floor   8/6)))
3429     (pass-if (=exact  1 (floor   9/6)))
3430     (pass-if (=exact  1 (floor  10/6)))
3431     (pass-if (=exact  1 (floor  11/6)))
3432     (pass-if (=exact  2 (floor  13/6)))
3433     (pass-if (=exact  2 (floor  14/6)))
3434     (pass-if (=exact  2 (floor  15/6)))
3435     (pass-if (=exact  2 (floor  16/6)))
3436     (pass-if (=exact  2 (floor  17/6))))
3437
3438   (with-test-prefix "real"
3439     (pass-if "0.0"
3440       (and (= 0.0    (floor 0.0))
3441            (inexact? (floor 0.0))))
3442
3443     (pass-if "1.0"
3444       (and (= 1.0    (floor 1.0))
3445            (inexact? (floor 1.0))))
3446
3447     (pass-if "-1.0"
3448       (and (= -1.0   (floor -1.0))
3449            (inexact? (floor -1.0))))
3450
3451     (pass-if "-3.1"
3452       (and (= -4.0   (floor -3.1))
3453            (inexact? (floor -3.1))))
3454
3455     (pass-if "3.1"
3456       (and (= 3.0    (floor 3.1))
3457            (inexact? (floor 3.1))))
3458
3459     (pass-if "3.9"
3460       (and (= 3.0    (floor 3.9))
3461            (inexact? (floor 3.9))))
3462
3463     (pass-if "-3.9"
3464       (and (= -4.0   (floor -3.9))
3465            (inexact? (floor -3.9))))
3466
3467     (pass-if "1.5"
3468       (and (= 1.0    (floor 1.5))
3469            (inexact? (floor 1.5))))
3470
3471     (pass-if "2.5"
3472       (and (= 2.0    (floor 2.5))
3473            (inexact? (floor 2.5))))
3474
3475     (pass-if "3.5"
3476       (and (= 3.0    (floor 3.5))
3477            (inexact? (floor 3.5))))
3478
3479     (pass-if "-1.5"
3480       (and (= -2.0   (floor -1.5))
3481            (inexact? (floor -1.5))))
3482
3483     (pass-if "-2.5"
3484       (and (= -3.0   (floor -2.5))
3485            (inexact? (floor -2.5))))
3486
3487     (pass-if "-3.5"
3488       (and (= -4.0   (floor -3.5))
3489            (inexact? (floor -3.5))))))
3490
3491 ;;;
3492 ;;; ceiling
3493 ;;;
3494
3495 (with-test-prefix "ceiling"
3496   (pass-if (=  2 (ceiling  1.75)))
3497   (pass-if (=  2 (ceiling  1.5)))
3498   (pass-if (=  2 (ceiling  1.25)))
3499   (pass-if (=  1 (ceiling  0.75)))
3500   (pass-if (=  1 (ceiling  0.5)))
3501   (pass-if (=  0 (ceiling  0.0)))
3502   (pass-if (=  0 (ceiling -0.5)))
3503   (pass-if (= -1 (ceiling -1.25)))
3504   (pass-if (= -1 (ceiling -1.5)))
3505
3506   (with-test-prefix "inum"
3507     (pass-if "0"
3508       (and (= 0    (ceiling 0))
3509            (exact? (ceiling 0))))
3510
3511     (pass-if "1"
3512       (and (= 1    (ceiling 1))
3513            (exact? (ceiling 1))))
3514
3515     (pass-if "-1"
3516       (and (= -1   (ceiling -1))
3517            (exact? (ceiling -1)))))
3518
3519   (with-test-prefix "bignum"
3520     (let ((x (1+ most-positive-fixnum)))
3521       (pass-if "(1+ most-positive-fixnum)"
3522         (and (= x    (ceiling x))
3523              (exact? (ceiling x)))))
3524
3525     (let ((x (1- most-negative-fixnum)))
3526       (pass-if "(1- most-negative-fixnum)"
3527         (and (= x    (ceiling x))
3528              (exact? (ceiling x))))))
3529
3530   (with-test-prefix "frac"
3531     (define (=exact x y)
3532       (and (= x y)
3533            (exact? y)))
3534
3535     (pass-if (=exact -2 (ceiling -7/3)))
3536     (pass-if (=exact -1 (ceiling -5/3)))
3537     (pass-if (=exact -1 (ceiling -4/3)))
3538     (pass-if (=exact  0 (ceiling -2/3)))
3539     (pass-if (=exact  0 (ceiling -1/3)))
3540     (pass-if (=exact  1 (ceiling  1/3)))
3541     (pass-if (=exact  1 (ceiling  2/3)))
3542     (pass-if (=exact  2 (ceiling  4/3)))
3543     (pass-if (=exact  2 (ceiling  5/3)))
3544     (pass-if (=exact  3 (ceiling  7/3)))
3545
3546     (pass-if (=exact -2 (ceiling -17/6)))
3547     (pass-if (=exact -2 (ceiling -16/6)))
3548     (pass-if (=exact -2 (ceiling -15/6)))
3549     (pass-if (=exact -2 (ceiling -14/6)))
3550     (pass-if (=exact -2 (ceiling -13/6)))
3551     (pass-if (=exact -1 (ceiling -11/6)))
3552     (pass-if (=exact -1 (ceiling -10/6)))
3553     (pass-if (=exact -1 (ceiling  -9/6)))
3554     (pass-if (=exact -1 (ceiling  -8/6)))
3555     (pass-if (=exact -1 (ceiling  -7/6)))
3556     (pass-if (=exact  0 (ceiling  -5/6)))
3557     (pass-if (=exact  0 (ceiling  -4/6)))
3558     (pass-if (=exact  0 (ceiling  -3/6)))
3559     (pass-if (=exact  0 (ceiling  -2/6)))
3560     (pass-if (=exact  0 (ceiling  -1/6)))
3561     (pass-if (=exact  1 (ceiling   1/6)))
3562     (pass-if (=exact  1 (ceiling   2/6)))
3563     (pass-if (=exact  1 (ceiling   3/6)))
3564     (pass-if (=exact  1 (ceiling   4/6)))
3565     (pass-if (=exact  1 (ceiling   5/6)))
3566     (pass-if (=exact  2 (ceiling   7/6)))
3567     (pass-if (=exact  2 (ceiling   8/6)))
3568     (pass-if (=exact  2 (ceiling   9/6)))
3569     (pass-if (=exact  2 (ceiling  10/6)))
3570     (pass-if (=exact  2 (ceiling  11/6)))
3571     (pass-if (=exact  3 (ceiling  13/6)))
3572     (pass-if (=exact  3 (ceiling  14/6)))
3573     (pass-if (=exact  3 (ceiling  15/6)))
3574     (pass-if (=exact  3 (ceiling  16/6)))
3575     (pass-if (=exact  3 (ceiling  17/6))))
3576
3577   (with-test-prefix "real"
3578     (pass-if "0.0"
3579       (and (= 0.0    (ceiling 0.0))
3580            (inexact? (ceiling 0.0))))
3581
3582     (pass-if "1.0"
3583       (and (= 1.0    (ceiling 1.0))
3584            (inexact? (ceiling 1.0))))
3585
3586     (pass-if "-1.0"
3587       (and (= -1.0   (ceiling -1.0))
3588            (inexact? (ceiling -1.0))))
3589
3590     (pass-if "-3.1"
3591       (and (= -3.0   (ceiling -3.1))
3592            (inexact? (ceiling -3.1))))
3593
3594     (pass-if "3.1"
3595       (and (= 4.0    (ceiling 3.1))
3596            (inexact? (ceiling 3.1))))
3597
3598     (pass-if "3.9"
3599       (and (= 4.0    (ceiling 3.9))
3600            (inexact? (ceiling 3.9))))
3601
3602     (pass-if "-3.9"
3603       (and (= -3.0   (ceiling -3.9))
3604            (inexact? (ceiling -3.9))))
3605
3606     (pass-if "1.5"
3607       (and (= 2.0    (ceiling 1.5))
3608            (inexact? (ceiling 1.5))))
3609
3610     (pass-if "2.5"
3611       (and (= 3.0    (ceiling 2.5))
3612            (inexact? (ceiling 2.5))))
3613
3614     (pass-if "3.5"
3615       (and (= 4.0    (ceiling 3.5))
3616            (inexact? (ceiling 3.5))))
3617
3618     (pass-if "-1.5"
3619       (and (= -1.0   (ceiling -1.5))
3620            (inexact? (ceiling -1.5))))
3621
3622     (pass-if "-2.5"
3623       (and (= -2.0   (ceiling -2.5))
3624            (inexact? (ceiling -2.5))))
3625
3626     (pass-if "-3.5"
3627       (and (= -3.0   (ceiling -3.5))
3628            (inexact? (ceiling -3.5))))))
3629
3630 ;;;
3631 ;;; truncate
3632 ;;;
3633
3634 (with-test-prefix "truncate"
3635   (pass-if (=  1 (truncate  1.75)))
3636   (pass-if (=  1 (truncate  1.5)))
3637   (pass-if (=  1 (truncate  1.25)))
3638   (pass-if (=  0 (truncate  0.75)))
3639   (pass-if (=  0 (truncate  0.5)))
3640   (pass-if (=  0 (truncate  0.0)))
3641   (pass-if (=  0 (truncate -0.5)))
3642   (pass-if (= -1 (truncate -1.25)))
3643   (pass-if (= -1 (truncate -1.5)))
3644
3645   (with-test-prefix "inum"
3646     (pass-if "0"
3647       (and (= 0    (truncate 0))
3648            (exact? (truncate 0))))
3649
3650     (pass-if "1"
3651       (and (= 1    (truncate 1))
3652            (exact? (truncate 1))))
3653
3654     (pass-if "-1"
3655       (and (= -1   (truncate -1))
3656            (exact? (truncate -1)))))
3657
3658   (with-test-prefix "bignum"
3659     (let ((x (1+ most-positive-fixnum)))
3660       (pass-if "(1+ most-positive-fixnum)"
3661         (and (= x    (truncate x))
3662              (exact? (truncate x)))))
3663
3664     (let ((x (1- most-negative-fixnum)))
3665       (pass-if "(1- most-negative-fixnum)"
3666         (and (= x    (truncate x))
3667              (exact? (truncate x))))))
3668
3669   (with-test-prefix "frac"
3670     (define (=exact x y)
3671       (and (= x y)
3672            (exact? y)))
3673
3674     (pass-if (=exact -2 (truncate -7/3)))
3675     (pass-if (=exact -1 (truncate -5/3)))
3676     (pass-if (=exact -1 (truncate -4/3)))
3677     (pass-if (=exact  0 (truncate -2/3)))
3678     (pass-if (=exact  0 (truncate -1/3)))
3679     (pass-if (=exact  0 (truncate  1/3)))
3680     (pass-if (=exact  0 (truncate  2/3)))
3681     (pass-if (=exact  1 (truncate  4/3)))
3682     (pass-if (=exact  1 (truncate  5/3)))
3683     (pass-if (=exact  2 (truncate  7/3)))
3684
3685     (pass-if (=exact -2 (truncate -17/6)))
3686     (pass-if (=exact -2 (truncate -16/6)))
3687     (pass-if (=exact -2 (truncate -15/6)))
3688     (pass-if (=exact -2 (truncate -14/6)))
3689     (pass-if (=exact -2 (truncate -13/6)))
3690     (pass-if (=exact -1 (truncate -11/6)))
3691     (pass-if (=exact -1 (truncate -10/6)))
3692     (pass-if (=exact -1 (truncate  -9/6)))
3693     (pass-if (=exact -1 (truncate  -8/6)))
3694     (pass-if (=exact -1 (truncate  -7/6)))
3695     (pass-if (=exact  0 (truncate  -5/6)))
3696     (pass-if (=exact  0 (truncate  -4/6)))
3697     (pass-if (=exact  0 (truncate  -3/6)))
3698     (pass-if (=exact  0 (truncate  -2/6)))
3699     (pass-if (=exact  0 (truncate  -1/6)))
3700     (pass-if (=exact  0 (truncate   1/6)))
3701     (pass-if (=exact  0 (truncate   2/6)))
3702     (pass-if (=exact  0 (truncate   3/6)))
3703     (pass-if (=exact  0 (truncate   4/6)))
3704     (pass-if (=exact  0 (truncate   5/6)))
3705     (pass-if (=exact  1 (truncate   7/6)))
3706     (pass-if (=exact  1 (truncate   8/6)))
3707     (pass-if (=exact  1 (truncate   9/6)))
3708     (pass-if (=exact  1 (truncate  10/6)))
3709     (pass-if (=exact  1 (truncate  11/6)))
3710     (pass-if (=exact  2 (truncate  13/6)))
3711     (pass-if (=exact  2 (truncate  14/6)))
3712     (pass-if (=exact  2 (truncate  15/6)))
3713     (pass-if (=exact  2 (truncate  16/6)))
3714     (pass-if (=exact  2 (truncate  17/6))))
3715
3716   (with-test-prefix "real"
3717     (pass-if "0.0"
3718       (and (= 0.0    (truncate 0.0))
3719            (inexact? (truncate 0.0))))
3720
3721     (pass-if "1.0"
3722       (and (= 1.0    (truncate 1.0))
3723            (inexact? (truncate 1.0))))
3724
3725     (pass-if "-1.0"
3726       (and (= -1.0   (truncate -1.0))
3727            (inexact? (truncate -1.0))))
3728
3729     (pass-if "-3.1"
3730       (and (= -3.0   (truncate -3.1))
3731            (inexact? (truncate -3.1))))
3732
3733     (pass-if "3.1"
3734       (and (= 3.0    (truncate 3.1))
3735            (inexact? (truncate 3.1))))
3736
3737     (pass-if "3.9"
3738       (and (= 3.0    (truncate 3.9))
3739            (inexact? (truncate 3.9))))
3740
3741     (pass-if "-3.9"
3742       (and (= -3.0   (truncate -3.9))
3743            (inexact? (truncate -3.9))))
3744
3745     (pass-if "1.5"
3746       (and (= 1.0    (truncate 1.5))
3747            (inexact? (truncate 1.5))))
3748
3749     (pass-if "2.5"
3750       (and (= 2.0    (truncate 2.5))
3751            (inexact? (truncate 2.5))))
3752
3753     (pass-if "3.5"
3754       (and (= 3.0    (truncate 3.5))
3755            (inexact? (truncate 3.5))))
3756
3757     (pass-if "-1.5"
3758       (and (= -1.0   (truncate -1.5))
3759            (inexact? (truncate -1.5))))
3760
3761     (pass-if "-2.5"
3762       (and (= -2.0   (truncate -2.5))
3763            (inexact? (truncate -2.5))))
3764
3765     (pass-if "-3.5"
3766       (and (= -3.0   (truncate -3.5))
3767            (inexact? (truncate -3.5))))))
3768
3769 ;;;
3770 ;;; round
3771 ;;;
3772
3773 (with-test-prefix "round"
3774   (pass-if (=  2 (round  1.75)))
3775   (pass-if (=  2 (round  1.5)))
3776   (pass-if (=  1 (round  1.25)))
3777   (pass-if (=  1 (round  0.75)))
3778   (pass-if (=  0 (round  0.5)))
3779   (pass-if (=  0 (round  0.0)))
3780   (pass-if (=  0 (round -0.5)))
3781   (pass-if (= -1 (round -1.25)))
3782   (pass-if (= -2 (round -1.5)))
3783
3784   (with-test-prefix "inum"
3785     (pass-if "0"
3786       (and (= 0    (round 0))
3787            (exact? (round 0))))
3788
3789     (pass-if "1"
3790       (and (= 1    (round 1))
3791            (exact? (round 1))))
3792
3793     (pass-if "-1"
3794       (and (= -1   (round -1))
3795            (exact? (round -1)))))
3796
3797   (with-test-prefix "bignum"
3798     (let ((x (1+ most-positive-fixnum)))
3799       (pass-if "(1+ most-positive-fixnum)"
3800         (and (= x    (round x))
3801              (exact? (round x)))))
3802
3803     (let ((x (1- most-negative-fixnum)))
3804       (pass-if "(1- most-negative-fixnum)"
3805         (and (= x    (round x))
3806              (exact? (round x))))))
3807
3808   (with-test-prefix "frac"
3809     (define (=exact x y)
3810       (and (= x y)
3811            (exact? y)))
3812
3813     (pass-if (=exact -2 (round -7/3)))
3814     (pass-if (=exact -2 (round -5/3)))
3815     (pass-if (=exact -1 (round -4/3)))
3816     (pass-if (=exact -1 (round -2/3)))
3817     (pass-if (=exact  0 (round -1/3)))
3818     (pass-if (=exact  0 (round  1/3)))
3819     (pass-if (=exact  1 (round  2/3)))
3820     (pass-if (=exact  1 (round  4/3)))
3821     (pass-if (=exact  2 (round  5/3)))
3822     (pass-if (=exact  2 (round  7/3)))
3823
3824     (pass-if (=exact -3 (round -17/6)))
3825     (pass-if (=exact -3 (round -16/6)))
3826     (pass-if (=exact -2 (round -15/6)))
3827     (pass-if (=exact -2 (round -14/6)))
3828     (pass-if (=exact -2 (round -13/6)))
3829     (pass-if (=exact -2 (round -11/6)))
3830     (pass-if (=exact -2 (round -10/6)))
3831     (pass-if (=exact -2 (round  -9/6)))
3832     (pass-if (=exact -1 (round  -8/6)))
3833     (pass-if (=exact -1 (round  -7/6)))
3834     (pass-if (=exact -1 (round  -5/6)))
3835     (pass-if (=exact -1 (round  -4/6)))
3836     (pass-if (=exact  0 (round  -3/6)))
3837     (pass-if (=exact  0 (round  -2/6)))
3838     (pass-if (=exact  0 (round  -1/6)))
3839     (pass-if (=exact  0 (round   1/6)))
3840     (pass-if (=exact  0 (round   2/6)))
3841     (pass-if (=exact  0 (round   3/6)))
3842     (pass-if (=exact  1 (round   4/6)))
3843     (pass-if (=exact  1 (round   5/6)))
3844     (pass-if (=exact  1 (round   7/6)))
3845     (pass-if (=exact  1 (round   8/6)))
3846     (pass-if (=exact  2 (round   9/6)))
3847     (pass-if (=exact  2 (round  10/6)))
3848     (pass-if (=exact  2 (round  11/6)))
3849     (pass-if (=exact  2 (round  13/6)))
3850     (pass-if (=exact  2 (round  14/6)))
3851     (pass-if (=exact  2 (round  15/6)))
3852     (pass-if (=exact  3 (round  16/6)))
3853     (pass-if (=exact  3 (round  17/6))))
3854
3855   (with-test-prefix "real"
3856     (pass-if "0.0"
3857       (and (= 0.0    (round 0.0))
3858            (inexact? (round 0.0))))
3859
3860     (pass-if "1.0"
3861       (and (= 1.0    (round 1.0))
3862            (inexact? (round 1.0))))
3863
3864     (pass-if "-1.0"
3865       (and (= -1.0   (round -1.0))
3866            (inexact? (round -1.0))))
3867
3868     (pass-if "-3.1"
3869       (and (= -3.0   (round -3.1))
3870            (inexact? (round -3.1))))
3871
3872     (pass-if "3.1"
3873       (and (= 3.0    (round 3.1))
3874            (inexact? (round 3.1))))
3875
3876     (pass-if "3.9"
3877       (and (= 4.0    (round 3.9))
3878            (inexact? (round 3.9))))
3879
3880     (pass-if "-3.9"
3881       (and (= -4.0   (round -3.9))
3882            (inexact? (round -3.9))))
3883
3884     (pass-if "1.5"
3885       (and (= 2.0    (round 1.5))
3886            (inexact? (round 1.5))))
3887
3888     (pass-if "2.5"
3889       (and (= 2.0    (round 2.5))
3890            (inexact? (round 2.5))))
3891
3892     (pass-if "3.5"
3893       (and (= 4.0    (round 3.5))
3894            (inexact? (round 3.5))))
3895
3896     (pass-if "-1.5"
3897       (and (= -2.0   (round -1.5))
3898            (inexact? (round -1.5))))
3899
3900     (pass-if "-2.5"
3901       (and (= -2.0   (round -2.5))
3902            (inexact? (round -2.5))))
3903
3904     (pass-if "-3.5"
3905       (and (= -4.0   (round -3.5))
3906            (inexact? (round -3.5))))
3907
3908     ;; prior to guile 1.6.5, on an IEEE system an inexact 2^53-1 (ie. a
3909     ;; float with mantissa all ones) came out as 2^53 from `round' (except
3910     ;; on i386 and m68k systems using the coprocessor and optimizing, where
3911     ;; extra precision hid the problem)
3912     (pass-if "2^53-1"
3913       (let ((x (exact->inexact (1- (ash 1 53)))))
3914         (and (= x      (round x))
3915              (inexact? (round x)))))
3916     (pass-if "-(2^53-1)"
3917       (let ((x (exact->inexact (- (1- (ash 1 53))))))
3918         (and (= x      (round x))
3919              (inexact? (round x)))))))
3920
3921 ;;;
3922 ;;; exact->inexact
3923 ;;;
3924
3925 (with-test-prefix "exact->inexact"
3926
3927   ;; Test "(exact->inexact n)", expect "want".
3928   ;; "i" is a index, for diagnostic purposes.
3929   (define (try-i i n want)
3930     (with-test-prefix (list i n want)
3931       (with-test-prefix "pos"
3932         (let ((got (exact->inexact n)))
3933           (pass-if "inexact?" (inexact? got))
3934           (pass-if (list "=" got) (= want got))))
3935       (set! n    (- n))
3936       (set! want (- want))
3937       (with-test-prefix "neg"
3938         (let ((got (exact->inexact n)))
3939           (pass-if "inexact?" (inexact? got))
3940           (pass-if (list "=" got) (= want got))))))
3941
3942   (with-test-prefix "2^i, no round"
3943     (do ((i    0   (1+ i))
3944          (n    1   (* 2 n))
3945          (want 1.0 (* 2.0 want)))
3946         ((> i 100))
3947       (try-i i n want)))
3948
3949   (with-test-prefix "2^i+1, no round"
3950     (do ((i    1   (1+ i))
3951          (n    3   (1- (* 2 n)))
3952          (want 3.0 (- (* 2.0 want) 1.0)))
3953         ((>= i dbl-mant-dig))
3954       (try-i i n want)))
3955
3956   (with-test-prefix "(2^i+1)*2^100, no round"
3957     (do ((i    1   (1+ i))
3958          (n    3   (1- (* 2 n)))
3959          (want 3.0 (- (* 2.0 want) 1.0)))
3960         ((>= i dbl-mant-dig))
3961       (try-i i (ash n 100) (ash-flo want 100))))
3962
3963   ;; bit pattern: 1111....11100.00
3964   ;;              <-mantdig-><-i->
3965   ;;
3966   (with-test-prefix "mantdig ones then zeros, no rounding"
3967     (do ((i    0  (1+ i))
3968          (n    (- (ash     1   dbl-mant-dig) 1)   (* 2 n))
3969          (want (- (ash-flo 1.0 dbl-mant-dig) 1.0) (* 2.0 want)))
3970         ((> i 100))
3971       (try-i i n want)))
3972
3973   ;; bit pattern: 1111....111011..1
3974   ;;              <-mantdig-> <-i->
3975   ;; This sort of value was incorrectly rounded upwards in Guile 1.6.4 when
3976   ;; i >= 11 (that's when the total is 65 or more bits).
3977   ;;
3978   (with-test-prefix "mantdig ones then 011..11, round down"
3979     (do ((i    0  (1+ i))
3980          (n    (- (ash     1   (+ 1 dbl-mant-dig)) 2)   (+ 1 (* 2 n)))
3981          (want (- (ash-flo 1.0 (+ 1 dbl-mant-dig)) 2.0) (* 2.0 want)))
3982         ((> i 100))
3983       (try-i i n want)))
3984
3985   ;; bit pattern: 1111....111100..001
3986   ;;              <-mantdig-> <--i->
3987   ;;
3988   (with-test-prefix "mantdig ones then 100..001, round up"
3989     (do ((i    0  (1+ i))
3990          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)  (1- (* 2 n)))
3991          (want    (ash-flo 1.0 (+ 2 dbl-mant-dig))     (* 2.0 want)))
3992         ((> i 100))
3993       (try-i i n want)))
3994
3995   ;; bit pattern: 1000....000100..001
3996   ;;              <-mantdig-> <--i->
3997   ;;
3998   (with-test-prefix "2^mantdig then 100..001, round up"
3999     (do ((i    0  (1+ i))
4000          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)   (1- (* 2 n)))
4001          (want (+ (ash-flo 1.0 (+ 2 dbl-mant-dig)) 4.0) (* 2.0 want)))
4002         ((> i 100))
4003       (try-i i n want)))
4004
4005   (pass-if "frac big/big"
4006     (let ((big (ash 1 256)))
4007       (= 1.0 (exact->inexact (/ (1+ big) big)))))
4008
4009   ;; In guile 1.8.0 this failed, giving back "nan" because it tried to
4010   ;; convert the num and den to doubles, resulting in infs.
4011   (pass-if "frac big/big, exceeding double"
4012     (let ((big (ash 1 4096)))
4013       (= 1.0 (exact->inexact (/ (1+ big) big))))))
4014
4015 ;;;
4016 ;;; expt
4017 ;;;
4018
4019 (with-test-prefix "expt"
4020   (pass-if (documented? expt))
4021
4022   ;;
4023   ;; expt no longer requires its first argument to be a scheme number,
4024   ;; for the sake of extensibility, and expt calls integer-expt for
4025   ;; integer powers.  To raise to a positive power, all that is required
4026   ;; is that it can be multiplied using `*'.  For negative powers we
4027   ;; must also be able to find the reciprocal.  If we try to raise #t to
4028   ;; any power other than 0 or 1 it may throw an exception, depending on
4029   ;; whether * has been defined for #t.  However, when raising to the 0
4030   ;; or 1 power, the first argument is not manipulated at all.
4031   ;;
4032   ;; (pass-if-exception "non-numeric base" exception:wrong-type-arg
4033   ;;                    (expt #t 0))
4034   ;;
4035
4036   (pass-if (eqv? 1 (expt 0 0)))
4037   (pass-if (eqv? 1 (expt 0.0 0)))
4038   (pass-if (eqv? 1.0 (expt 0 0.0)))
4039   (pass-if (eqv? 1.0 (expt 0.0 0.0)))
4040   (pass-if (real-nan? (expt 0 -1)))
4041   (pass-if (real-nan? (expt 0 -1.0)))
4042   (pass-if (real-nan? (expt 0.0 -1)))
4043   (pass-if (real-nan? (expt 0.0 -1.0)))
4044   (pass-if (eqv? 0 (expt 0 3)))
4045   (pass-if (= 0 (expt 0 4.0)))
4046   (pass-if (eqv? 0.0 (expt 0.0 5)))
4047   (pass-if (eqv? 0.0 (expt 0.0 6.0)))
4048   (pass-if (eqv? -2742638075.5 (expt -2742638075.5 1)))
4049   (pass-if (eqv? (* -2742638075.5 -2742638075.5)
4050                  (expt -2742638075.5 2)))
4051   (pass-if (eqv? 4.0 (expt -2.0 2.0)))
4052   (pass-if (eqv? -1/8 (expt -2 -3)))
4053   (pass-if (eqv? -0.125 (expt -2.0 -3)))
4054   (pass-if (eqv? -0.125 (expt -2 -3.0)))
4055   (pass-if (eqv? -0.125 (expt -2.0 -3.0)))
4056   (pass-if (eqv? 0.25 (expt 2.0 -2.0)))
4057   (pass-if (eqv? 32/243 (expt 2/3 5)))
4058   (pass-if (eqv? 243/32 (expt 2/3 -5)))
4059   (pass-if (eqv? 32 (expt 1/2 -5)))
4060   (pass-if (test-eqv? (* -1.0+0.0i 12398 12398) (expt +12398i 2.0)))
4061   (pass-if (eqv-loosely? +i (expt -1 0.5)))
4062   (pass-if (eqv-loosely? +i (expt -1 1/2)))
4063   (pass-if (eqv-loosely? 1.0+1.7320508075688i (expt -8 1/3)))
4064   (pass-if (eqv? +inf.0 (expt 2 +inf.0)))
4065   (pass-if (eqv? +inf.0 (expt 2.0 +inf.0)))
4066   (pass-if (eqv? 0.0 (expt 2 -inf.0)))
4067   (pass-if (eqv? 0.0 (expt 2.0 -inf.0))))
4068
4069
4070 ;;;
4071 ;;; sin
4072 ;;;
4073
4074 (with-test-prefix "sin"
4075   (pass-if (eqv? 0   (sin 0)))
4076   (pass-if (eqv? 0.0 (sin 0.0)))
4077   (pass-if (eqv-loosely? 1.0 (sin 1.57)))
4078   (pass-if (eqv-loosely? +1.175i (sin +i)))
4079   (pass-if (real-nan? (sin +nan.0)))
4080   (pass-if (real-nan? (sin +inf.0)))
4081   (pass-if (real-nan? (sin -inf.0))))
4082
4083 ;;;
4084 ;;; cos
4085 ;;;
4086
4087 (with-test-prefix "cos"
4088   (pass-if (eqv? 1   (cos 0)))
4089   (pass-if (eqv? 1.0 (cos 0.0)))
4090   (pass-if (eqv-loosely? 0.0 (cos 1.57)))
4091   (pass-if (eqv-loosely? 1.543 (cos +i)))
4092   (pass-if (real-nan? (cos +nan.0)))
4093   (pass-if (real-nan? (cos +inf.0)))
4094   (pass-if (real-nan? (cos -inf.0))))
4095
4096 ;;;
4097 ;;; tan
4098 ;;;
4099
4100 (with-test-prefix "tan"
4101   (pass-if (eqv? 0   (tan 0)))
4102   (pass-if (eqv? 0.0 (tan 0.0)))
4103   (pass-if (eqv-loosely? 1.0 (tan 0.785)))
4104   (pass-if (eqv-loosely? +0.76i (tan +i)))
4105   (pass-if (real-nan? (tan +nan.0)))
4106   (pass-if (real-nan? (tan +inf.0)))
4107   (pass-if (real-nan? (tan -inf.0))))
4108
4109 ;;;
4110 ;;; asin
4111 ;;;
4112
4113 (with-test-prefix "asin"
4114   (pass-if (complex-nan? (asin +nan.0)))
4115   (pass-if (eqv? 0 (asin 0)))
4116   (pass-if (eqv? 0.0 (asin 0.0))))
4117
4118 ;;;
4119 ;;; acos
4120 ;;;
4121
4122 (with-test-prefix "acos"
4123   (pass-if (complex-nan? (acos +nan.0)))
4124   (pass-if (eqv? 0 (acos 1)))
4125   (pass-if (eqv? 0.0 (acos 1.0))))
4126
4127 ;;;
4128 ;;; atan
4129 ;;;
4130 ;;; FIXME: add tests for two-argument atan
4131 ;;;
4132 (with-test-prefix "atan"
4133   (pass-if (real-nan? (atan +nan.0)))
4134   (pass-if (eqv? 0 (atan 0)))
4135   (pass-if (eqv? 0.0 (atan 0.0)))
4136   (pass-if (eqv-loosely?  1.57 (atan +inf.0)))
4137   (pass-if (eqv-loosely? -1.57 (atan -inf.0))))
4138
4139 ;;;
4140 ;;; sinh
4141 ;;;
4142
4143 (with-test-prefix "sinh"
4144   (pass-if (= 0 (sinh 0)))
4145   (pass-if (= 0.0 (sinh 0.0))))
4146
4147 ;;;
4148 ;;; cosh
4149 ;;;
4150
4151 (with-test-prefix "cosh"
4152   (pass-if (= 1 (cosh 0)))
4153   (pass-if (= 1.0 (cosh 0.0))))
4154
4155 ;;;
4156 ;;; tanh
4157 ;;;
4158
4159 (with-test-prefix "tanh"
4160   (pass-if (= 0 (tanh 0)))
4161   (pass-if (= 0.0 (tanh 0.0))))
4162
4163 ;;;
4164 ;;; asinh
4165 ;;;
4166
4167 (with-test-prefix "asinh"
4168   (pass-if (= 0 (asinh 0)))
4169   (pass-if (= 0.0 (asinh 0.0))))
4170
4171 ;;;
4172 ;;; acosh
4173 ;;;
4174
4175 (with-test-prefix "acosh"
4176   (pass-if (= 0 (acosh 1)))
4177   (pass-if (= 0.0 (acosh 1.0))))
4178
4179 ;;;
4180 ;;; atanh
4181 ;;;
4182
4183 (with-test-prefix "atanh"
4184   (pass-if (= 0 (atanh 0)))
4185   (pass-if (= 0.0 (atanh 0.0))))
4186
4187 ;;;
4188 ;;; make-rectangular
4189 ;;;
4190
4191 (with-test-prefix "make-rectangular"
4192   (pass-if (real?      (make-rectangular 5.0  0  )))
4193   (pass-if (not (real? (make-rectangular 5.0  0.0))))
4194   (pass-if (not (real? (make-rectangular 5.0 -0.0)))))
4195
4196 ;;;
4197 ;;; make-polar
4198 ;;;
4199
4200 (with-test-prefix "make-polar"
4201   (define pi 3.14159265358979323846)
4202   (define (almost= x y)
4203     (> 0.01 (magnitude (- x y))))
4204
4205   (pass-if (real?      (make-polar 0    1.0)))
4206   (pass-if (real?      (make-polar 5.0  0  )))
4207   (pass-if (not (real? (make-polar 5.0  0.0))))
4208   (pass-if (not (real? (make-polar 5.0 -0.0))))
4209
4210   (pass-if (eqv?  0 (make-polar  0 0)))
4211   (pass-if (eqv?  0 (make-polar  0 123.456)))
4212   (pass-if (eqv?  1 (make-polar  1 0)))
4213   (pass-if (eqv? -1 (make-polar -1 0)))
4214
4215   (pass-if (almost= 0+i (make-polar 1 (* 0.5 pi))))
4216   (pass-if (almost= -1  (make-polar 1 (* 1.0 pi))))
4217   (pass-if (almost= 0-i (make-polar 1 (* 1.5 pi))))
4218   (pass-if (almost= 1   (make-polar 1 (* 2.0 pi)))))
4219
4220 ;;;
4221 ;;; real-part
4222 ;;;
4223
4224 (with-test-prefix "real-part"
4225   (pass-if (documented? real-part))
4226   (pass-if (eqv? 5.0 (real-part  5.0)))
4227   (pass-if (eqv? 0.0 (real-part +5.0i)))
4228   (pass-if (eqv? 5   (real-part  5)))
4229   (pass-if (eqv? 1/5 (real-part  1/5)))
4230   (pass-if (eqv? (1+ fixnum-max) (real-part (1+ fixnum-max)))))
4231
4232 ;;;
4233 ;;; imag-part
4234 ;;;
4235
4236 (with-test-prefix "imag-part"
4237   (pass-if (documented? imag-part))
4238   (pass-if (eqv? 0   (imag-part  5.0)))
4239   (pass-if (eqv? 5.0 (imag-part +5.0i)))
4240   (pass-if (eqv? 0   (imag-part  5)))
4241   (pass-if (eqv? 0   (imag-part  1/5)))
4242   (pass-if (eqv? 0   (imag-part (1+ fixnum-max)))))
4243
4244 ;;;
4245 ;;; magnitude
4246 ;;;
4247
4248 (with-test-prefix "magnitude"
4249   (pass-if (documented? magnitude))
4250   (pass-if (= 0 (magnitude 0)))
4251   (pass-if (= 1 (magnitude 1)))
4252   (pass-if (= 1 (magnitude -1)))
4253   (pass-if (= 1 (magnitude 0+i)))
4254   (pass-if (= 1 (magnitude 0-i)))
4255   (pass-if (= 5 (magnitude 3+4i)))
4256   (pass-if (= 5 (magnitude 3-4i)))
4257   (pass-if (= 5 (magnitude -3+4i)))
4258   (pass-if (= 5 (magnitude -3-4i))))
4259
4260 ;;;
4261 ;;; angle
4262 ;;;
4263
4264 (with-test-prefix "angle"
4265   (define pi 3.14159265358979323846)
4266   (define (almost= x y)
4267     (> 0.000001 (magnitude (- x y))))
4268
4269   (pass-if (documented? angle))
4270
4271   (pass-if "inum +ve"   (=        0 (angle 1)))
4272   (pass-if "inum -ve"   (almost= pi (angle -1)))
4273
4274   (pass-if "bignum +ve" (=        0 (angle (1+ fixnum-max))))
4275   (pass-if "bignum -ve" (almost= pi (angle (1- fixnum-min))))
4276
4277   (pass-if "flonum +ve" (=        0 (angle 1.5)))
4278   (pass-if "flonum -ve" (almost= pi (angle -1.5)))
4279
4280   (pass-if "signed zero +ve" (=        0 (angle 0.0)))
4281   (pass-if "signed zero -ve" (almost= pi (angle -0.0))))
4282
4283 ;;;
4284 ;;; inexact->exact
4285 ;;;
4286
4287 (with-test-prefix "inexact->exact"
4288   (pass-if (documented? inexact->exact))
4289
4290   (pass-if-exception "+inf" exception:out-of-range
4291     (inexact->exact +inf.0))
4292
4293   (pass-if-exception "-inf" exception:out-of-range
4294     (inexact->exact -inf.0))
4295
4296   (pass-if-exception "nan" exception:out-of-range
4297     (inexact->exact +nan.0))
4298
4299   (with-test-prefix "2.0**i to exact and back"
4300     (do ((i 0   (1+ i))
4301          (n 1.0 (* 2.0 n)))
4302         ((> i 100))
4303       (pass-if (list i n)
4304         (= n (inexact->exact (exact->inexact n)))))))
4305
4306 ;;;
4307 ;;; integer-expt
4308 ;;;
4309
4310 (with-test-prefix "integer-expt"
4311   (pass-if (documented? integer-expt))
4312
4313   (pass-if-exception "2^+inf" exception:wrong-type-arg
4314     (integer-expt 2 +inf.0))
4315   (pass-if-exception "2^-inf" exception:wrong-type-arg
4316     (integer-expt 2 -inf.0))
4317   (pass-if-exception "2^nan" exception:wrong-type-arg
4318     (integer-expt 2 +nan.0))
4319
4320   (pass-if (eqv? 1 (integer-expt 0 0)))
4321   (pass-if (eqv? 1 (integer-expt 0.0 0)))
4322   (pass-if (real-nan? (integer-expt 0 -1)))
4323   (pass-if (real-nan? (integer-expt 0.0 -1)))
4324   (pass-if (eqv? 0 (integer-expt 0 3)))
4325   (pass-if (eqv? 0.0 (integer-expt 0.0 5)))
4326   (pass-if (eqv? -2742638075.5 (integer-expt -2742638075.5 1)))
4327   (pass-if (eqv? (* -2742638075.5 -2742638075.5)
4328                  (integer-expt -2742638075.5 2)))
4329   (pass-if (eqv? 4.0 (integer-expt -2.0 2)))
4330   (pass-if (eqv? -1/8 (integer-expt -2 -3)))
4331   (pass-if (eqv? -0.125 (integer-expt -2.0 -3)))
4332   (pass-if (eqv? 0.25 (integer-expt 2.0 -2)))
4333   (pass-if (eqv? 32/243 (integer-expt 2/3 5)))
4334   (pass-if (eqv? 243/32 (integer-expt 2/3 -5)))
4335   (pass-if (eqv? 32 (integer-expt 1/2 -5)))
4336   (pass-if (test-eqv? (* -1.0+0.0i 12398 12398) (integer-expt +12398.0i 2))))
4337
4338
4339 ;;;
4340 ;;; integer-length
4341 ;;;
4342
4343 (with-test-prefix "integer-length"
4344   (pass-if (documented? integer-length))
4345
4346   (with-test-prefix "-2^i, ...11100..00"
4347     (do ((n -1 (ash n 1))
4348          (i 0  (1+ i)))
4349         ((> i 256))
4350       (pass-if (list n "expect" i)
4351         (= i (integer-length n)))))
4352
4353   (with-test-prefix "-2^i+1 ...11100..01"
4354     (do ((n -3 (logxor 3 (ash n 1)))
4355          (i 2  (1+ i)))
4356         ((> i 256))
4357       (pass-if n
4358         (= i (integer-length n)))))
4359
4360   (with-test-prefix "-2^i-1 ...111011..11"
4361     (do ((n -2 (1+ (ash n 1)))
4362          (i 1  (1+ i)))
4363         ((> i 256))
4364       (pass-if n
4365         (= i (integer-length n))))))
4366
4367 ;;;
4368 ;;; log
4369 ;;;
4370
4371 (with-test-prefix "log"
4372   (pass-if (documented? log))
4373
4374   (pass-if-exception "no args" exception:wrong-num-args
4375     (log))
4376   (pass-if-exception "two args" exception:wrong-num-args
4377     (log 123 456))
4378   (pass-if-exception "(log 0)" exception:numerical-overflow
4379     (log 0))
4380
4381   (pass-if (test-eqv? -inf.0 (log 0.0)))
4382   (pass-if (test-eqv? +inf.0 (log +inf.0)))
4383   (pass-if (test-eqv? -inf.0+3.14159265358979i (log -0.0)))
4384   (pass-if (test-eqv? +inf.0+3.14159265358979i (log -inf.0)))
4385   (pass-if (test-eqv?  0.0 (log 1  )))
4386   (pass-if (test-eqv?  0.0 (log 1.0)))
4387   (pass-if (test-eqv?  1.0 (log const-e)))
4388   (pass-if (test-eqv?  2.0 (log const-e^2)))
4389   (pass-if (test-eqv? -1.0 (log const-1/e)))
4390   (pass-if (test-eqv? -1.0+3.14159265358979i (log (- const-1/e))))
4391   (pass-if (test-eqv?  2.30258509299405 (log 10)))
4392   (pass-if (test-eqv?  2.30258509299405+3.14159265358979i (log -10)))
4393
4394   (pass-if (test-eqv?  1.0+0.0i (log (+ const-e +0.0i))))
4395   (pass-if (test-eqv?  1.0-0.0i (log (+ const-e -0.0i))))
4396
4397   (pass-if (eqv-loosely?  230258.509299405 (log (expt 10  100000))))
4398   (pass-if (eqv-loosely? -230258.509299405 (log (expt 10 -100000))))
4399   (pass-if (eqv-loosely?  230257.410687116 (log (/ (expt 10 100000) 3))))
4400   (pass-if (eqv-loosely?  230258.509299405+3.14159265358979i
4401                           (log (- (expt 10 100000)))))
4402   (pass-if (eqv-loosely? -230258.509299405+3.14159265358979i
4403                           (log (- (expt 10 -100000)))))
4404   (pass-if (eqv-loosely?  230257.410687116+3.14159265358979i
4405                           (log (- (/ (expt 10 100000) 3)))))
4406   (pass-if (test-eqv?  3.05493636349961e-151
4407                        (log (/ (1+ (expt 2 500)) (expt 2 500)))))
4408
4409   (pass-if (eqv-loosely? 1.0+1.57079i (log 0+2.71828i)))
4410   (pass-if (eqv-loosely? 1.0-1.57079i (log 0-2.71828i)))
4411
4412   (pass-if (eqv-loosely? 0.0+3.14159i (log -1.0)))
4413   (pass-if (eqv-loosely? 1.0+3.14159i (log -2.71828)))
4414   (pass-if (eqv-loosely? 2.0+3.14159i (log (* -2.71828 2.71828)))))
4415
4416 ;;;
4417 ;;; log10
4418 ;;;
4419
4420 (with-test-prefix "log10"
4421   (pass-if (documented? log10))
4422
4423   (pass-if-exception "no args" exception:wrong-num-args
4424     (log10))
4425   (pass-if-exception "two args" exception:wrong-num-args
4426     (log10 123 456))
4427   (pass-if-exception "(log10 0)" exception:numerical-overflow
4428     (log10 0))
4429
4430   (pass-if (test-eqv? -inf.0 (log10 0.0)))
4431   (pass-if (test-eqv? +inf.0 (log10 +inf.0)))
4432   (pass-if (test-eqv? -inf.0+1.36437635384184i (log10 -0.0)))
4433   (pass-if (test-eqv? +inf.0+1.36437635384184i (log10 -inf.0)))
4434   (pass-if (test-eqv?  0.0 (log10   1  )))
4435   (pass-if (test-eqv?  0.0 (log10   1.0)))
4436   (pass-if (test-eqv?  1.0 (log10  10  )))
4437   (pass-if (test-eqv?  1.0 (log10  10.0)))
4438   (pass-if (test-eqv?  2.0 (log10 100.0)))
4439   (pass-if (test-eqv? -1.0 (log10   0.1)))
4440   (pass-if (test-eqv? -1.0+1.36437635384184i (log10  -0.1)))
4441   (pass-if (test-eqv?  1.0+1.36437635384184i (log10 -10  )))
4442
4443   (pass-if (test-eqv?  1.0+0.0i (log10  10.0+0.0i)))
4444   (pass-if (test-eqv?  1.0-0.0i (log10  10.0-0.0i)))
4445
4446   (pass-if (eqv-loosely?  100000.0 (log10 (expt 10  100000))))
4447   (pass-if (eqv-loosely? -100000.0 (log10 (expt 10 -100000))))
4448   (pass-if (eqv-loosely?   99999.5228787453 (log10 (/ (expt 10 100000) 3))))
4449   (pass-if (eqv-loosely?  100000.0+1.36437635384184i
4450                           (log10 (- (expt 10 100000)))))
4451   (pass-if (eqv-loosely? -100000.0+1.36437635384184i
4452                           (log10 (- (expt 10 -100000)))))
4453   (pass-if (eqv-loosely?   99999.5228787453+1.36437635384184i
4454                           (log10 (- (/ (expt 10 100000) 3)))))
4455   (pass-if (test-eqv?  1.32674200523347e-151
4456                        (log10 (/ (1+ (expt 2 500)) (expt 2 500)))))
4457
4458   (pass-if (eqv-loosely? 1.0+0.68218i (log10 0+10.0i)))
4459   (pass-if (eqv-loosely? 1.0-0.68218i (log10 0-10.0i)))
4460
4461   (pass-if (eqv-loosely? 0.0+1.36437i (log10   -1)))
4462   (pass-if (eqv-loosely? 1.0+1.36437i (log10  -10)))
4463   (pass-if (eqv-loosely? 2.0+1.36437i (log10 -100))))
4464
4465 ;;;
4466 ;;; logbit?
4467 ;;;
4468
4469 (with-test-prefix "logbit?"
4470   (pass-if (documented? logbit?))
4471
4472   (pass-if (eq? #f (logbit?  0 0)))
4473   (pass-if (eq? #f (logbit?  1 0)))
4474   (pass-if (eq? #f (logbit? 31 0)))
4475   (pass-if (eq? #f (logbit? 32 0)))
4476   (pass-if (eq? #f (logbit? 33 0)))
4477   (pass-if (eq? #f (logbit? 63 0)))
4478   (pass-if (eq? #f (logbit? 64 0)))
4479   (pass-if (eq? #f (logbit? 65 0)))
4480
4481   ;; prior to guile 1.6.5, testing bit 32, 64 etc of value 1 would wrap
4482   ;; around and return #t where it ought to be #f
4483   (pass-if (eq? #t (logbit?  0 1)))
4484   (pass-if (eq? #f (logbit?  1 1)))
4485   (pass-if (eq? #f (logbit? 31 1)))
4486   (pass-if (eq? #f (logbit? 32 1)))
4487   (pass-if (eq? #f (logbit? 33 1)))
4488   (pass-if (eq? #f (logbit? 63 1)))
4489   (pass-if (eq? #f (logbit? 64 1)))
4490   (pass-if (eq? #f (logbit? 65 1)))
4491   (pass-if (eq? #f (logbit? 128 1)))
4492
4493   (pass-if (eq? #t (logbit?  0 -1)))
4494   (pass-if (eq? #t (logbit?  1 -1)))
4495   (pass-if (eq? #t (logbit? 31 -1)))
4496   (pass-if (eq? #t (logbit? 32 -1)))
4497   (pass-if (eq? #t (logbit? 33 -1)))
4498   (pass-if (eq? #t (logbit? 63 -1)))
4499   (pass-if (eq? #t (logbit? 64 -1)))
4500   (pass-if (eq? #t (logbit? 65 -1))))
4501
4502 ;;;
4503 ;;; logcount
4504 ;;;
4505
4506 (with-test-prefix "logcount"
4507   (pass-if (documented? logcount))
4508
4509   (with-test-prefix "-2^i, meaning ...11100..00"
4510     (do ((n -1 (ash n 1))
4511          (i 0  (1+ i)))
4512         ((> i 256))
4513       (pass-if n
4514         (= i (logcount n)))))
4515
4516   (with-test-prefix "2^i"
4517     (do ((n 1 (ash n 1))
4518          (i 0  (1+ i)))
4519         ((> i 256))
4520       (pass-if n
4521         (= 1 (logcount n)))))
4522
4523   (with-test-prefix "2^i-1"
4524     (do ((n 0 (1+ (ash n 1)))
4525          (i 0  (1+ i)))
4526         ((> i 256))
4527       (pass-if n
4528         (= i (logcount n))))))
4529
4530 ;;;
4531 ;;; logior
4532 ;;;
4533
4534 (with-test-prefix "logior"
4535   (pass-if (documented? logior))
4536
4537   (pass-if (eqv? -1 (logior (ash -1 1) 1)))
4538
4539   ;; check that bignum or bignum+inum args will reduce to an inum
4540   (let ()
4541     (define (test x y)
4542       (pass-if (list x y '=> -1)
4543         (eqv? -1 (logior x y)))
4544       (pass-if (list y x '=> -1)
4545         (eqv? -1 (logior y x))))
4546     (test (ash -1 8) #xFF)
4547     (test (ash -1 28) #x0FFFFFFF)
4548     (test (ash -1 29) #x1FFFFFFF)
4549     (test (ash -1 30) #x3FFFFFFF)
4550     (test (ash -1 31) #x7FFFFFFF)
4551     (test (ash -1 32) #xFFFFFFFF)
4552     (test (ash -1 33) #x1FFFFFFFF)
4553     (test (ash -1 60) #x0FFFFFFFFFFFFFFF)
4554     (test (ash -1 61) #x1FFFFFFFFFFFFFFF)
4555     (test (ash -1 62) #x3FFFFFFFFFFFFFFF)
4556     (test (ash -1 63) #x7FFFFFFFFFFFFFFF)
4557     (test (ash -1 64) #xFFFFFFFFFFFFFFFF)
4558     (test (ash -1 65) #x1FFFFFFFFFFFFFFFF)
4559     (test (ash -1 128) #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
4560
4561 ;;;
4562 ;;; lognot
4563 ;;;
4564
4565 (with-test-prefix "lognot"
4566   (pass-if (documented? lognot))
4567
4568   (pass-if (= -1 (lognot 0)))
4569   (pass-if (= 0  (lognot -1)))
4570   (pass-if (= -2 (lognot 1)))
4571   (pass-if (= 1  (lognot -2)))
4572
4573   (pass-if (= #x-100000000000000000000000000000000
4574               (lognot #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
4575   (pass-if (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
4576               (lognot #x-100000000000000000000000000000000))))
4577
4578 ;;;
4579 ;;; exact-integer-sqrt
4580 ;;;
4581
4582 (with-test-prefix "exact-integer-sqrt"
4583   (define (non-negative-exact-integer? k)
4584     (and (integer? k) (exact? k) (>= k 0)))
4585
4586   (define (test k)
4587     (pass-if k (let-values (((s r) (exact-integer-sqrt k)))
4588                  (and (non-negative-exact-integer? s)
4589                       (non-negative-exact-integer? r)
4590                       (= k (+ r (* s s)))
4591                       (< k (* (1+ s) (1+ s)))))))
4592
4593   (define (test-wrong-type-arg k)
4594     (pass-if-exception k exception:wrong-type-arg
4595                        (let-values (((s r) (exact-integer-sqrt k)))
4596                          #t)))
4597
4598   (pass-if (documented? exact-integer-sqrt))
4599
4600   (pass-if-exception "no args" exception:wrong-num-args
4601     (exact-integer-sqrt))
4602   (pass-if-exception "two args" exception:wrong-num-args
4603     (exact-integer-sqrt 123 456))
4604
4605   (test 0)
4606   (test 1)
4607   (test 9)
4608   (test 10)
4609   (test fixnum-max)
4610   (test (1+ fixnum-max))
4611   (test (* fixnum-max fixnum-max))
4612   (test (+ 1 (* fixnum-max fixnum-max)))
4613   (test (expt 10 100))
4614   (test (+ 3 (expt 10 100)))
4615
4616   (test-wrong-type-arg -1)
4617   (test-wrong-type-arg 1/9)
4618   (test-wrong-type-arg fixnum-min)
4619   (test-wrong-type-arg (1- fixnum-min))
4620   (test-wrong-type-arg 1.0)
4621   (test-wrong-type-arg 1.5)
4622   (test-wrong-type-arg "foo")
4623   (test-wrong-type-arg 'foo))
4624
4625
4626 ;;;
4627 ;;; sqrt
4628 ;;;
4629
4630 (with-test-prefix "sqrt"
4631   (pass-if (documented? sqrt))
4632
4633   (pass-if-exception "no args" exception:wrong-num-args
4634     (sqrt))
4635   (pass-if-exception "two args" exception:wrong-num-args
4636     (sqrt 123 456))
4637
4638   (pass-if (eqv? 0.0 (sqrt 0)))
4639   (pass-if (eqv? 0.0 (sqrt 0.0)))
4640   (pass-if (eqv? 1.0 (sqrt 1.0)))
4641   (pass-if (eqv-loosely? 2.0   (sqrt 4.0)))
4642   (pass-if (eqv-loosely? 31.62 (sqrt 1000.0)))
4643
4644   (pass-if (eqv? +1.0i (sqrt -1.0)))
4645   (pass-if (eqv-loosely? +2.0i   (sqrt -4.0)))
4646   (pass-if (eqv-loosely? +31.62i (sqrt -1000.0)))
4647
4648   (pass-if "+i swings back to 45deg angle"
4649     (eqv-loosely? +0.7071+0.7071i (sqrt +1.0i)))
4650
4651   ;; Note: glibc 2.3 csqrt() had a bug affecting this test case, so if it
4652   ;; fails check whether that's the cause (there's a configure test to
4653   ;; reject it, but when cross-compiling we assume the C library is ok).
4654   (pass-if "-100i swings back to 45deg down"
4655     (eqv-loosely? +7.071-7.071i (sqrt -100.0i))))
4656
4657
4658 ;;;
4659 ;;; Tests for number-theoretic division operators:
4660 ;;;
4661 ;;; euclidean/
4662 ;;; euclidean-quotient
4663 ;;; euclidean-remainder
4664 ;;; floor/
4665 ;;; floor-quotient
4666 ;;; floor-remainder
4667 ;;; ceiling/
4668 ;;; ceiling-quotient
4669 ;;; ceiling-remainder
4670 ;;; truncate/
4671 ;;; truncate-quotient
4672 ;;; truncate-remainder
4673 ;;; centered/
4674 ;;; centered-quotient
4675 ;;; centered-remainder
4676 ;;; round/
4677 ;;; round-quotient
4678 ;;; round-remainder
4679 ;;;
4680
4681 (with-test-prefix "Number-theoretic division"
4682
4683   ;; Tests that (lo <1 x <2 hi),
4684   ;; but allowing for imprecision
4685   ;; if x is inexact.
4686   (define (test-within-range? lo <1 x <2 hi)
4687     (if (exact? x)
4688         (and (<1 lo x) (<2 x hi))
4689         (let ((lo (- lo test-epsilon))
4690               (hi (+ hi test-epsilon)))
4691           (<= lo x hi))))
4692
4693   (define (valid-euclidean-answer? x y q r)
4694     (and (eq? (exact? q)
4695               (exact? r)
4696               (and (exact? x) (exact? y)))
4697          (test-eqv? r (- x (* q y)))
4698          (if (and (finite? x) (finite? y))
4699              (and (integer? q)
4700                   (test-within-range? 0 <= r < (abs y)))
4701              (test-eqv? q (/ x y)))))
4702
4703   (define (valid-floor-answer? x y q r)
4704     (and (eq? (exact? q)
4705               (exact? r)
4706               (and (exact? x) (exact? y)))
4707          (test-eqv? r (- x (* q y)))
4708          (if (and (finite? x) (finite? y))
4709              (and (integer? q)
4710                   (if (> y 0)
4711                       (test-within-range? 0 <= r < y)
4712                       (test-within-range? y < r <= 0)))
4713              (test-eqv? q (/ x y)))))
4714
4715   (define (valid-ceiling-answer? x y q r)
4716     (and (eq? (exact? q)
4717               (exact? r)
4718               (and (exact? x) (exact? y)))
4719          (test-eqv? r (- x (* q y)))
4720          (if (and (finite? x) (finite? y))
4721              (and (integer? q)
4722                   (if (> y 0)
4723                       (test-within-range? (- y) < r <= 0)
4724                       (test-within-range?    0 <= r < (- y))))
4725              (test-eqv? q (/ x y)))))
4726
4727   (define (valid-truncate-answer? x y q r)
4728     (and (eq? (exact? q)
4729               (exact? r)
4730               (and (exact? x) (exact? y)))
4731          (test-eqv? r (- x (* q y)))
4732          (if (and (finite? x) (finite? y))
4733              (and (integer? q)
4734                   (if (> x 0)
4735                       (test-within-range?          0 <= r < (abs y))
4736                       (test-within-range? (- (abs y)) < r <= 0)))
4737              (test-eqv? q (/ x y)))))
4738
4739   (define (valid-centered-answer? x y q r)
4740     (and (eq? (exact? q)
4741               (exact? r)
4742               (and (exact? x) (exact? y)))
4743          (test-eqv? r (- x (* q y)))
4744          (if (and (finite? x) (finite? y))
4745              (and (integer? q)
4746                   (test-within-range?
4747                    (* -1/2 (abs y)) <= r < (* +1/2 (abs y))))
4748              (test-eqv? q (/ x y)))))
4749
4750   (define (valid-round-answer? x y q r)
4751     (and (eq? (exact? q)
4752               (exact? r)
4753               (and (exact? x) (exact? y)))
4754          (test-eqv? r (- x (* q y)))
4755          (if (and (finite? x) (finite? y))
4756              (and (integer? q)
4757                   (let ((ay/2 (/ (abs y) 2)))
4758                     (if (even? q)
4759                         (test-within-range? (- ay/2) <= r <= ay/2)
4760                         (test-within-range? (- ay/2) <  r <  ay/2))))
4761              (test-eqv? q (/ x y)))))
4762
4763   (define (for lsts f) (apply for-each f lsts))
4764
4765   (define big (expt 10 (1+ (inexact->exact (ceiling (log10 fixnum-max))))))
4766
4767   (define (run-division-tests quo+rem quo rem valid-answer?)
4768     (define (test n d)
4769       (run-test (list n d) #t
4770                 (lambda ()
4771                   (let-values (((q r) (quo+rem n d)))
4772                     (and (test-eqv? q (quo n d))
4773                          (test-eqv? r (rem n d))
4774                          (valid-answer? n d q r))))))
4775     (define (test+/- n d)
4776       (test n    d )
4777       (test n (- d))
4778       (cond ((not (zero? n))
4779              (test (- n)    d )
4780              (test (- n) (- d)))))
4781
4782     (define (test-for-exception n d exception)
4783       (let ((name (list n d)))
4784         (pass-if-exception name exception (quo+rem n d))
4785         (pass-if-exception name exception (quo n d))
4786         (pass-if-exception name exception (rem n d))))
4787
4788     (run-test "documented?" #t
4789               (lambda ()
4790                 (and (documented? quo+rem)
4791                      (documented? quo)
4792                      (documented? rem))))
4793
4794     (with-test-prefix "inum / inum"
4795       (with-test-prefix "fixnum-min / -1"
4796         (test fixnum-min -1))
4797       (for '((1 2 5 10))  ;; denominators
4798            (lambda (d)
4799              (for '((0 1 2 5 10))  ;; multiples
4800                   (lambda (m)
4801                     (for '((-2 -1 0 1 2 3 4 5 7 10
4802                                12 15 16 19 20))  ;; offsets
4803                          (lambda (b)
4804                            (test+/- (+ b (* m d))
4805                                     d))))))))
4806
4807     (with-test-prefix "inum / big"
4808       (with-test-prefix "fixnum-min / -fixnum-min"
4809         (test fixnum-min (- fixnum-min)))
4810       (with-test-prefix "fixnum-max / (2*fixnum-max)"
4811         (test+/- fixnum-max (* 2 fixnum-max)))
4812       (for `((0 1 2 10 ,(1- fixnum-max) ,fixnum-max))
4813            (lambda (n)
4814              (test    n  (1+ fixnum-max))
4815              (test (- n) (1+ fixnum-max))
4816              (test    n  (1- fixnum-min))
4817              (test (- n) (1- fixnum-min)))))
4818
4819     (with-test-prefix "big / inum"
4820       (with-test-prefix "-fixnum-min / fixnum-min"
4821         (test (- fixnum-min) fixnum-min))
4822       (for '((1 4 5 10))  ;; denominators
4823            (lambda (d)
4824              (for `((1 2 5 ,@(if (even? d)
4825                                  '(1/2 3/2 5/2)
4826                                  '())))  ;; multiples
4827                   (lambda (m)
4828                     (for '((-2 -1 0 1 2))  ;; offsets
4829                          (lambda (b)
4830                            (test+/- (+ b (* m d big))
4831                                     d))))))))
4832
4833     (with-test-prefix "big / big"
4834       (for `((,big ,(1+ big)))  ;; denominators
4835            (lambda (d)
4836              (for `((1 2 5 ,@(if (even? d)
4837                                  '(1/2 3/2 5/2)
4838                                  '())))  ;; multiples
4839                   (lambda (m)
4840                     (for '((-2 -1 0 1 2))  ;; offsets
4841                          (lambda (b)
4842                            (test+/- (+ b (* m d))
4843                                     d))))))))
4844
4845     (with-test-prefix "inexact"
4846       (for '((0.5 1.5 2.25 5.75))  ;; denominators
4847            (lambda (d)
4848              (for '((0 1 2 5 1/2 3/2 5/2))  ;; multiples
4849                   (lambda (m)
4850                     (for '((-2 -1 0 1 2))  ;; offsets
4851                          (lambda (b)
4852                            (test+/- (+ b (* m d))
4853                                     d))))))))
4854
4855     (with-test-prefix "fractions"
4856       (for '((1/10 16/3 10/7))  ;; denominators
4857            (lambda (d)
4858              (for '((0 1 2 5 1/2 3/2 5/2))  ;; multiples
4859                   (lambda (m)
4860                     (for '((-2/9 -1/11 0 1/3 2/3))  ;; offsets
4861                          (lambda (b)
4862                            (test+/- (+ b (* m d))
4863                                     d))))))))
4864
4865     (with-test-prefix "mixed types"
4866       (for `((10 ,big 12.0 10/7 +inf.0 -inf.0 +nan.0))  ;; denominators
4867            (lambda (d)
4868              (for `((25 ,(* 3/2 big) 130.0 15/7
4869                         0 0.0 -0.0 +inf.0 -inf.0 +nan.0))  ;; numerators
4870                   (lambda (n)
4871                     (test+/- n d))))))
4872
4873     (with-test-prefix "divide by zero"
4874       (for `((0 0.0 -0.0))  ;; denominators
4875            (lambda (d)
4876              (for `((15 ,(* 3/2 big) 18.0 33/7
4877                         0 0.0 -0.0 +inf.0 -inf.0 +nan.0))  ;; numerators
4878                   (lambda (n)
4879                     (test-for-exception
4880                      n d exception:numerical-overflow)))))))
4881
4882   (with-test-prefix "euclidean/"
4883     (run-division-tests euclidean/
4884                         euclidean-quotient
4885                         euclidean-remainder
4886                         valid-euclidean-answer?))
4887
4888   (with-test-prefix "floor/"
4889     (run-division-tests floor/
4890                         floor-quotient
4891                         floor-remainder
4892                         valid-floor-answer?))
4893
4894   (with-test-prefix "ceiling/"
4895     (run-division-tests ceiling/
4896                         ceiling-quotient
4897                         ceiling-remainder
4898                         valid-ceiling-answer?))
4899
4900   (with-test-prefix "truncate/"
4901     (run-division-tests truncate/
4902                         truncate-quotient
4903                         truncate-remainder
4904                         valid-truncate-answer?))
4905
4906   (with-test-prefix "centered/"
4907     (run-division-tests centered/
4908                         centered-quotient
4909                         centered-remainder
4910                         valid-centered-answer?))
4911
4912   (with-test-prefix "round/"
4913     (run-division-tests round/
4914                         round-quotient
4915                         round-remainder
4916                         valid-round-answer?)))