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"))
1497     #t)
1498
1499   (pass-if "valid number strings"
1500     (for-each (lambda (couple)
1501                 (apply
1502                  (lambda (x y)
1503                    (let ((xx (string->number x)))
1504                      (if (or (eq? xx #f) (not (eqv? xx y)))
1505                          (begin
1506                            (pk x y)
1507                            (throw 'fail)))))
1508                  couple))
1509               `(;; Radix:
1510                 ("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
1511                 ("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
1512                 ("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
1513                 ("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
1514                 ("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
1515                 ("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
1516                 ("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
1517                 ("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
1518                 ("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
1519                 ("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
1520                 ("#b1010" 10)
1521                 ("#o12345670" 2739128)
1522                 ("#d1234567890" 1234567890)
1523                 ("#x1234567890abcdef" 1311768467294899695)
1524                 ;; Exactness:
1525                 ("#e1" 1) ("#e1.2" 12/10)
1526                 ("#i1.1" 1.1) ("#i1" 1.0)
1527                 ;; Integers:
1528                 ("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1))
1529                 ("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
1530                 ("#b#i100" 4.0)
1531                 ;; Fractions:
1532                 ("1/1" 1) ("1/2" 1/2) ("-1/2" -1/2) ("1#/1" 10.0)
1533                 ("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 9/10) ("#e10/1#" 1)
1534                 ("#i6/8" 0.75) ("#i1/1" 1.0)
1535                 ;; Decimal numbers:
1536                 ;; * <uinteger 10> <suffix>
1537                 ("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
1538                 ("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
1539                 ("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
1540                 ;; * . <digit 10>+ #* <suffix>
1541                 (".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
1542                 (".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
1543                 ;; * <digit 10>+ . <digit 10>* #* <suffix>
1544                 ("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
1545                 ("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
1546                 ("3.1#e0" 3.1)
1547                 ;; * <digit 10>+ #+ . #* <suffix>
1548                 ("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
1549                 ))
1550     #t)
1551
1552   (pass-if "valid complex number strings"
1553     (for-each (lambda (triple)
1554                 (apply
1555                  (lambda (str re im)
1556                    (let ((z (string->number str)))
1557                      (if (or (eq? z #f)
1558                              (not (and (eqv? (real-part z) re)
1559                                        (eqv? (imag-part z) im))))
1560                          (begin
1561                            (pk str re im)
1562                            (throw 'fail)))))
1563                  triple))
1564               `(("1@0" 1 0) ("1@+0" 1 0) ("1@-0" 1 0) ("1/2@0" 1/2 0)
1565                 ("1.0@0" 1.0 0) ("1.0@-0" 1.0 0)
1566                 ("#e1@0" 1 0) ("#e1@+0" 1 0) ("#e1@-0" 1 0) ("#e0.5@0.0" 1/2 0)
1567                 ("#e1.0@0" 1 0) ("#e1.0@-0" 1 0)
1568                 ("#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)
1569                 ("#i1.0@0" 1.0 0.0) ("#i1.0@-0" 1.0 -0.0)
1570                 ("1@+0.0" 1.0 0.0) ("1.0@-0.0" 1.0 -0.0)
1571                 ("2+3i" 2.0 3.0) ("4-5i" 4.0 -5.0)
1572                 ("1+i" 1.0 1.0) ("1-i" 1.0 -1.0) ("+1i" 0.0 1.0) ("-1i" 0.0 -1.0)
1573                 ("+i" 0.0 1.0) ("-i" 0.0 -1.0)
1574                 ("1.0+.1i" 1.0 0.1) ("1.0-.1i" 1.0 -0.1)
1575                 (".1+.0i" 0.1 0.0) ("1.+.0i" 1.0 0.0) (".1+.1i" 0.1 0.1)
1576                 ("1e1+.1i" 10.0 0.1)
1577                 ("0@+nan.0" 0 0) ("0@+inf.0" 0 0) ("0@-inf.0" 0 0)
1578                 ("0.0@+nan.0" 0.0 0.0) ("0.0@+inf.0" 0.0 0.0) ("0.0@-inf.0" 0.0 0.0)
1579                 ("#i0@+nan.0" 0.0 0.0) ("#i0@+inf.0" 0.0 0.0) ("#i0@-inf.0" 0.0 0.0)
1580                 ("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)
1581                 ))
1582     #t)
1583
1584   (pass-if-exception "exponent too big"
1585     exception:out-of-range
1586     (string->number "12.13e141414"))
1587
1588   ;; in guile 1.6.7 and earlier, bad polar forms (where the conversion of
1589   ;; the angle gave #f) caused a segv
1590   (pass-if "1@a"
1591     (eq? #f (string->number "1@a"))))
1592
1593 ;;;
1594 ;;; number?
1595 ;;;
1596
1597 (with-test-prefix "number?"
1598   (pass-if (documented? number?))
1599   (pass-if (number? 0))
1600   (pass-if (number? 7))
1601   (pass-if (number? -7))
1602   (pass-if (number? 1.3))
1603   (pass-if (number? (+ 1 fixnum-max)))
1604   (pass-if (number? (- 1 fixnum-min)))
1605   (pass-if (number? 3+4i))
1606   (pass-if (not (number? #\a)))
1607   (pass-if (not (number? "a")))
1608   (pass-if (not (number? (make-vector 0))))
1609   (pass-if (not (number? (cons 1 2))))
1610   (pass-if (not (number? #t)))
1611   (pass-if (not (number? (lambda () #t))))
1612   (pass-if (not (number? (current-input-port)))))
1613
1614 ;;;
1615 ;;; complex?
1616 ;;;
1617
1618 (with-test-prefix "complex?"
1619   (pass-if (documented? complex?))
1620   (pass-if (complex? 0))
1621   (pass-if (complex? 7))
1622   (pass-if (complex? -7))
1623   (pass-if (complex? (+ 1 fixnum-max)))
1624   (pass-if (complex? (- 1 fixnum-min)))
1625   (pass-if (complex? 1.3))
1626   (pass-if (complex? 3+4i))
1627   (pass-if (not (complex? #\a)))
1628   (pass-if (not (complex? "a")))
1629   (pass-if (not (complex? (make-vector 0))))
1630   (pass-if (not (complex? (cons 1 2))))
1631   (pass-if (not (complex? #t)))
1632   (pass-if (not (complex? (lambda () #t))))
1633   (pass-if (not (complex? (current-input-port)))))
1634
1635 ;;;
1636 ;;; real?
1637 ;;;
1638
1639 (with-test-prefix "real?"
1640   (pass-if (documented? real?))
1641   (pass-if (real? 0))
1642   (pass-if (real? 7))
1643   (pass-if (real? -7))
1644   (pass-if (real? (+ 1 fixnum-max)))
1645   (pass-if (real? (- 1 fixnum-min)))
1646   (pass-if (real? 1.3))
1647   (pass-if (real? +inf.0))
1648   (pass-if (real? -inf.0))
1649   (pass-if (real? +nan.0))
1650   (pass-if (not (real? +inf.0-inf.0i)))
1651   (pass-if (not (real? +nan.0+nan.0i)))
1652   (pass-if (not (real? 3+4i)))
1653   (pass-if (not (real? #\a)))
1654   (pass-if (not (real? "a")))
1655   (pass-if (not (real? (make-vector 0))))
1656   (pass-if (not (real? (cons 1 2))))
1657   (pass-if (not (real? #t)))
1658   (pass-if (not (real? (lambda () #t))))
1659   (pass-if (not (real? (current-input-port)))))
1660
1661 ;;;
1662 ;;; rational?
1663 ;;;
1664
1665 (with-test-prefix "rational?"
1666   (pass-if (documented? rational?))
1667   (pass-if (rational? 0))
1668   (pass-if (rational? 7))
1669   (pass-if (rational? -7))
1670   (pass-if (rational? (+ 1 fixnum-max)))
1671   (pass-if (rational? (- 1 fixnum-min)))
1672   (pass-if (rational? 1.3))
1673   (pass-if (not (rational? +inf.0)))
1674   (pass-if (not (rational? -inf.0)))
1675   (pass-if (not (rational? +nan.0)))
1676   (pass-if (not (rational? +inf.0-inf.0i)))
1677   (pass-if (not (rational? +nan.0+nan.0i)))
1678   (pass-if (not (rational? 3+4i)))
1679   (pass-if (not (rational? #\a)))
1680   (pass-if (not (rational? "a")))
1681   (pass-if (not (rational? (make-vector 0))))
1682   (pass-if (not (rational? (cons 1 2))))
1683   (pass-if (not (rational? #t)))
1684   (pass-if (not (rational? (lambda () #t))))
1685   (pass-if (not (rational? (current-input-port)))))
1686
1687 ;;;
1688 ;;; integer?
1689 ;;;
1690
1691 (with-test-prefix "integer?"
1692   (pass-if (documented? integer?))
1693   (pass-if (integer? 0))
1694   (pass-if (integer? 7))
1695   (pass-if (integer? -7))
1696   (pass-if (integer? (+ 1 fixnum-max)))
1697   (pass-if (integer? (- 1 fixnum-min)))
1698   (pass-if (and (= 3+0i (round 3+0i)) (integer? 3+0i)))
1699   (pass-if (and (= 1.0 (round 1.0)) (integer? 1.0)))
1700   (pass-if (not (integer? 1.3)))
1701   (pass-if (not (integer? +inf.0)))
1702   (pass-if (not (integer? -inf.0)))
1703   (pass-if (not (integer? +nan.0)))
1704   (pass-if (not (integer? +inf.0-inf.0i)))
1705   (pass-if (not (integer? +nan.0+nan.0i)))
1706   (pass-if (not (integer? 3+4i)))
1707   (pass-if (not (integer? #\a)))
1708   (pass-if (not (integer? "a")))
1709   (pass-if (not (integer? (make-vector 0))))
1710   (pass-if (not (integer? (cons 1 2))))
1711   (pass-if (not (integer? #t)))
1712   (pass-if (not (integer? (lambda () #t))))
1713   (pass-if (not (integer? (current-input-port)))))
1714
1715 ;;;
1716 ;;; inexact?
1717 ;;;
1718
1719 (with-test-prefix "inexact?"
1720   (pass-if (documented? inexact?))
1721   (pass-if (not (inexact? 0)))
1722   (pass-if (not (inexact? 7)))
1723   (pass-if (not (inexact? -7)))
1724   (pass-if (not (inexact? (+ 1 fixnum-max))))
1725   (pass-if (not (inexact? (- 1 fixnum-min))))
1726   (pass-if (inexact? 1.3))
1727   (pass-if (inexact? 3.1+4.2i))
1728   (pass-if (inexact? +inf.0))
1729   (pass-if (inexact? -inf.0))
1730   (pass-if (inexact? +nan.0))
1731   (pass-if-exception "char"
1732                      exception:wrong-type-arg
1733                      (not (inexact? #\a)))
1734   (pass-if-exception "string"
1735                      exception:wrong-type-arg
1736                      (not (inexact? "a")))
1737   (pass-if-exception "vector"
1738                      exception:wrong-type-arg
1739                      (not (inexact? (make-vector 0))))
1740   (pass-if-exception "cons"
1741                      exception:wrong-type-arg
1742                      (not (inexact? (cons 1 2))))
1743   (pass-if-exception "bool"
1744                      exception:wrong-type-arg
1745                      (not (inexact? #t)))
1746   (pass-if-exception "procedure"
1747                      exception:wrong-type-arg
1748                      (not (inexact? (lambda () #t))))
1749   (pass-if-exception "port"
1750                      exception:wrong-type-arg
1751                      (not (inexact? (current-input-port)))))
1752
1753 ;;;
1754 ;;; equal?
1755 ;;;
1756
1757 (with-test-prefix "equal?"
1758   (pass-if (documented? equal?))
1759
1760   ;; The following test will fail on platforms
1761   ;; without distinct signed zeroes 0.0 and -0.0.
1762   (pass-if (not (equal? 0.0 -0.0)))
1763
1764   (pass-if (equal? 0 0))
1765   (pass-if (equal? 7 7))
1766   (pass-if (equal? -7 -7))
1767   (pass-if (equal? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1768   (pass-if (equal? (- fixnum-min 1) (- fixnum-min 1)))
1769   (pass-if (equal?  0.0  0.0))
1770   (pass-if (equal? -0.0 -0.0))
1771   (pass-if (equal?  0.0+0.0i  0.0+0.0i))
1772   (pass-if (equal?  0.0-0.0i  0.0-0.0i))
1773   (pass-if (equal? -0.0+0.0i -0.0+0.0i))
1774   (pass-if (not (equal? 0 1)))
1775   (pass-if (not (equal? 0 0.0)))
1776   (pass-if (not (equal? 1 1.0)))
1777   (pass-if (not (equal? 0.0 0)))
1778   (pass-if (not (equal? 1.0 1)))
1779   (pass-if (not (equal? -1.0 -1)))
1780   (pass-if (not (equal? 1.0 1.0+0.0i)))
1781   (pass-if (not (equal? 0.0 0.0+0.0i)))
1782   (pass-if (not (equal? 0.0+0.0i  0.0-0.0i)))
1783   (pass-if (not (equal? 0.0+0.0i -0.0+0.0i)))
1784   (pass-if (not (equal? fixnum-max (+ 1 fixnum-max))))
1785   (pass-if (not (equal? (+ 1 fixnum-max) fixnum-max)))
1786   (pass-if (not (equal? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1787   (pass-if (not (equal? fixnum-min (- fixnum-min 1))))
1788   (pass-if (not (equal? (- fixnum-min 1) fixnum-min)))
1789   (pass-if (not (equal? (- fixnum-min 1) (- fixnum-min 2))))
1790   (pass-if (not (equal? (+ fixnum-max 1) (- fixnum-min 1))))
1791
1792   (pass-if (not (equal? (ash 1 256) +inf.0)))
1793   (pass-if (not (equal? +inf.0 (ash 1 256))))
1794   (pass-if (not (equal? (ash 1 256) -inf.0)))
1795   (pass-if (not (equal? -inf.0 (ash 1 256))))
1796
1797   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1798   ;; sure we've avoided that
1799   (pass-if (not (equal? (ash 1 1024) +inf.0)))
1800   (pass-if (not (equal? +inf.0 (ash 1 1024))))
1801   (pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
1802   (pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
1803
1804   (pass-if (equal? +nan.0 +nan.0))
1805   (pass-if (equal? +nan.0 +nan.0))
1806   (pass-if (not (equal? +nan.0 0.0+nan.0i)))
1807
1808   (pass-if (not (equal? 0 +nan.0)))
1809   (pass-if (not (equal? +nan.0 0)))
1810   (pass-if (not (equal? 1 +nan.0)))
1811   (pass-if (not (equal? +nan.0 1)))
1812   (pass-if (not (equal? -1 +nan.0)))
1813   (pass-if (not (equal? +nan.0 -1)))
1814
1815   (pass-if (not (equal? (ash 1 256) +nan.0)))
1816   (pass-if (not (equal? +nan.0 (ash 1 256))))
1817   (pass-if (not (equal? (- (ash 1 256)) +nan.0)))
1818   (pass-if (not (equal? +nan.0 (- (ash 1 256)))))
1819
1820   (pass-if (not (equal? (ash 1 8192) +nan.0)))
1821   (pass-if (not (equal? +nan.0 (ash 1 8192))))
1822   (pass-if (not (equal? (- (ash 1 8192)) +nan.0)))
1823   (pass-if (not (equal? +nan.0 (- (ash 1 8192)))))
1824
1825   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1826   ;; sure we've avoided that
1827   (pass-if (not (equal? (ash 3 1023) +nan.0)))
1828   (pass-if (not (equal? +nan.0 (ash 3 1023)))))
1829
1830 ;;;
1831 ;;; eqv?
1832 ;;;
1833
1834 (with-test-prefix "eqv?"
1835   (pass-if (documented? eqv?))
1836
1837   ;; The following test will fail on platforms
1838   ;; without distinct signed zeroes 0.0 and -0.0.
1839   (pass-if (not (eqv? 0.0 -0.0)))
1840
1841   (pass-if (eqv? 0 0))
1842   (pass-if (eqv? 7 7))
1843   (pass-if (eqv? -7 -7))
1844   (pass-if (eqv? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1845   (pass-if (eqv? (- fixnum-min 1) (- fixnum-min 1)))
1846   (pass-if (eqv?  0.0  0.0))
1847   (pass-if (eqv? -0.0 -0.0))
1848   (pass-if (eqv?  0.0+0.0i  0.0+0.0i))
1849   (pass-if (eqv?  0.0-0.0i  0.0-0.0i))
1850   (pass-if (eqv? -0.0+0.0i -0.0+0.0i))
1851   (pass-if (not (eqv? 0.0 -0.0)))
1852   (pass-if (not (eqv? 0.0  0.0+0.0i)))
1853   (pass-if (not (eqv? 0.0+0.0i  0.0-0.0i)))
1854   (pass-if (not (eqv? 0.0+0.0i -0.0+0.0i)))
1855   (pass-if (not (eqv? 0 1)))
1856   (pass-if (not (eqv? 0 0.0)))
1857   (pass-if (not (eqv? 1 1.0)))
1858   (pass-if (not (eqv? 0.0 0)))
1859   (pass-if (not (eqv? 1.0 1)))
1860   (pass-if (not (eqv? -1.0 -1)))
1861   (pass-if (not (eqv? 1.0 1.0+0.0i)))
1862   (pass-if (not (eqv? 0.0 0.0+0.0i)))
1863   (pass-if (not (eqv? fixnum-max (+ 1 fixnum-max))))
1864   (pass-if (not (eqv? (+ 1 fixnum-max) fixnum-max)))
1865   (pass-if (not (eqv? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1866   (pass-if (not (eqv? fixnum-min (- fixnum-min 1))))
1867   (pass-if (not (eqv? (- fixnum-min 1) fixnum-min)))
1868   (pass-if (not (eqv? (- fixnum-min 1) (- fixnum-min 2))))
1869   (pass-if (not (eqv? (+ fixnum-max 1) (- fixnum-min 1))))
1870
1871   (pass-if (not (eqv? (ash 1 256) +inf.0)))
1872   (pass-if (not (eqv? +inf.0 (ash 1 256))))
1873   (pass-if (not (eqv? (ash 1 256) -inf.0)))
1874   (pass-if (not (eqv? -inf.0 (ash 1 256))))
1875
1876   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1877   ;; sure we've avoided that
1878   (pass-if (not (eqv? (ash 1 1024) +inf.0)))
1879   (pass-if (not (eqv? +inf.0 (ash 1 1024))))
1880   (pass-if (not (eqv? (- (ash 1 1024)) -inf.0)))
1881   (pass-if (not (eqv? -inf.0 (- (ash 1 1024)))))
1882
1883   (pass-if (eqv? +nan.0 +nan.0))
1884   (pass-if (not (eqv? +nan.0 0.0+nan.0i)))
1885
1886   (pass-if (not (eqv? 0 +nan.0)))
1887   (pass-if (not (eqv? +nan.0 0)))
1888   (pass-if (not (eqv? 1 +nan.0)))
1889   (pass-if (not (eqv? +nan.0 1)))
1890   (pass-if (not (eqv? -1 +nan.0)))
1891   (pass-if (not (eqv? +nan.0 -1)))
1892
1893   (pass-if (not (eqv? (ash 1 256) +nan.0)))
1894   (pass-if (not (eqv? +nan.0 (ash 1 256))))
1895   (pass-if (not (eqv? (- (ash 1 256)) +nan.0)))
1896   (pass-if (not (eqv? +nan.0 (- (ash 1 256)))))
1897
1898   (pass-if (not (eqv? (ash 1 8192) +nan.0)))
1899   (pass-if (not (eqv? +nan.0 (ash 1 8192))))
1900   (pass-if (not (eqv? (- (ash 1 8192)) +nan.0)))
1901   (pass-if (not (eqv? +nan.0 (- (ash 1 8192)))))
1902
1903   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1904   ;; sure we've avoided that
1905   (pass-if (not (eqv? (ash 3 1023) +nan.0)))
1906   (pass-if (not (eqv? +nan.0 (ash 3 1023)))))
1907
1908 ;;;
1909 ;;; =
1910 ;;;
1911
1912 (with-test-prefix "="
1913   (pass-if (documented? =))
1914   (pass-if (= 7 7))
1915   (pass-if (= -7 -7))
1916   (pass-if (= 1.0 1))
1917   (pass-if (= 1 1.0))
1918   (pass-if (= -1 -1.0))
1919   (pass-if (= 0.0  0.0))
1920   (pass-if (= 0.0 -0.0))
1921   (pass-if (= 1 1.0+0.0i))
1922
1923   (pass-if (= 0  0))
1924   (pass-if (= 0  0.0))
1925   (pass-if (= 0 -0.0))
1926   (pass-if (= 0  0.0+0.0i))
1927   (pass-if (= 0  0.0-0.0i))
1928   (pass-if (= 0  0.0+0.0i))
1929   (pass-if (= 0 -0.0-0.0i))
1930
1931   (pass-if (=  0        0))
1932   (pass-if (=  0.0      0))
1933   (pass-if (= -0.0      0))
1934   (pass-if (=  0.0+0.0i 0))
1935   (pass-if (=  0.0-0.0i 0))
1936   (pass-if (=  0.0+0.0i 0))
1937   (pass-if (= -0.0-0.0i 0))
1938
1939   (pass-if (= 0.0+0.0i  0.0-0.0i))
1940   (pass-if (= 0.0+0.0i -0.0+0.0i))
1941
1942   (pass-if (= (+ 1 fixnum-max) (+ 1 fixnum-max)))
1943   (pass-if (= (- fixnum-min 1) (- fixnum-min 1)))
1944   (pass-if (not (= 0 1)))
1945   (pass-if (not (= fixnum-max (+ 1 fixnum-max))))
1946   (pass-if (not (= (+ 1 fixnum-max) fixnum-max)))
1947   (pass-if (not (= (+ 1 fixnum-max) (+ 2 fixnum-max))))
1948   (pass-if (not (= fixnum-min (- fixnum-min 1))))
1949   (pass-if (not (= (- fixnum-min 1) fixnum-min)))
1950   (pass-if (not (= (- fixnum-min 1) (- fixnum-min 2))))
1951   (pass-if (not (= (+ fixnum-max 1) (- fixnum-min 1))))
1952
1953   (pass-if (not (= (ash 1 256) +inf.0)))
1954   (pass-if (not (= +inf.0 (ash 1 256))))
1955   (pass-if (not (= (ash 1 256) -inf.0)))
1956   (pass-if (not (= -inf.0 (ash 1 256))))
1957
1958   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1959   ;; sure we've avoided that
1960   (pass-if (not (= (ash 1 1024) +inf.0)))
1961   (pass-if (not (= +inf.0 (ash 1 1024))))
1962   (pass-if (not (= (- (ash 1 1024)) -inf.0)))
1963   (pass-if (not (= -inf.0 (- (ash 1 1024)))))
1964
1965   (pass-if (not (= +nan.0 +nan.0)))
1966   (pass-if (not (= 0 +nan.0)))
1967   (pass-if (not (= +nan.0 0)))
1968   (pass-if (not (= 1 +nan.0)))
1969   (pass-if (not (= +nan.0 1)))
1970   (pass-if (not (= -1 +nan.0)))
1971   (pass-if (not (= +nan.0 -1)))
1972
1973   (pass-if (not (= (ash 1 256) +nan.0)))
1974   (pass-if (not (= +nan.0 (ash 1 256))))
1975   (pass-if (not (= (- (ash 1 256)) +nan.0)))
1976   (pass-if (not (= +nan.0 (- (ash 1 256)))))
1977
1978   (pass-if (not (= (ash 1 8192) +nan.0)))
1979   (pass-if (not (= +nan.0 (ash 1 8192))))
1980   (pass-if (not (= (- (ash 1 8192)) +nan.0)))
1981   (pass-if (not (= +nan.0 (- (ash 1 8192)))))
1982
1983   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1984   ;; sure we've avoided that
1985   (pass-if (not (= (ash 3 1023) +nan.0)))
1986   (pass-if (not (= +nan.0 (ash 3 1023))))
1987
1988   (pass-if (= 1/2 0.5))
1989   (pass-if (not (= 1/3 0.333333333333333333333333333333333)))
1990   (pass-if (not (= 2/3 0.5)))
1991   (pass-if (not (= 0.5 (+ 1/2 (/ 1 (ash 1 1000))))))
1992
1993   (pass-if (= 1/2 0.5+0i))
1994   (pass-if (not (= 0.333333333333333333333333333333333 1/3)))
1995   (pass-if (not (= 2/3 0.5+0i)))
1996   (pass-if (not (= 1/2 0+0.5i)))
1997
1998   (pass-if (= 0.5 1/2))
1999   (pass-if (not (= 0.5 2/3)))
2000   (pass-if (not (= (+ 1/2 (/ 1 (ash 1 1000))) 0.5)))
2001
2002   (pass-if (= 0.5+0i 1/2))
2003   (pass-if (not (= 0.5+0i 2/3)))
2004   (pass-if (not (= 0+0.5i 1/2)))
2005
2006   ;; prior to guile 1.8, inum/flonum comparisons were done just by
2007   ;; converting the inum to a double, which on a 64-bit would round making
2008   ;; say inexact 2^58 appear equal to exact 2^58+1
2009   (pass-if (= (ash-flo 1.0 58) (ash 1 58)))
2010   (pass-if (not (= (ash-flo 1.0 58) (1+ (ash 1 58)))))
2011   (pass-if (not (= (ash-flo 1.0 58) (1- (ash 1 58)))))
2012   (pass-if (= (ash 1 58) (ash-flo 1.0 58)))
2013   (pass-if (not (= (1+ (ash 1 58)) (ash-flo 1.0 58))))
2014   (pass-if (not (= (1- (ash 1 58)) (ash-flo 1.0 58)))))
2015
2016 ;;;
2017 ;;; <
2018 ;;;
2019
2020 (with-test-prefix "<"
2021
2022   (pass-if "documented?"
2023     (documented? <))
2024
2025   (with-test-prefix "(< 0 n)"
2026
2027     (pass-if "n = 0"
2028       (not (< 0 0)))
2029
2030     (pass-if "n = 0.0"
2031       (not (< 0 0.0)))
2032
2033     (pass-if "n = 1"
2034       (< 0 1))
2035
2036     (pass-if "n = 1.0"
2037       (< 0 1.0))
2038
2039     (pass-if "n = -1"
2040       (not (< 0 -1)))
2041
2042     (pass-if "n = -1.0"
2043       (not (< 0 -1.0)))
2044
2045     (pass-if "n = fixnum-max"
2046       (< 0 fixnum-max))
2047
2048     (pass-if "n = fixnum-max + 1"
2049       (< 0 (+ fixnum-max 1)))
2050
2051     (pass-if "n = fixnum-min"
2052       (not (< 0 fixnum-min)))
2053
2054     (pass-if "n = fixnum-min - 1"
2055       (not (< 0 (- fixnum-min 1)))))
2056
2057   (with-test-prefix "(< 0.0 n)"
2058
2059     (pass-if "n = 0"
2060       (not (< 0.0 0)))
2061
2062     (pass-if "n = 0.0"
2063       (not (< 0.0 0.0)))
2064
2065     (pass-if "n = 1"
2066       (< 0.0 1))
2067
2068     (pass-if "n = 1.0"
2069       (< 0.0 1.0))
2070
2071     (pass-if "n = -1"
2072       (not (< 0.0 -1)))
2073
2074     (pass-if "n = -1.0"
2075       (not (< 0.0 -1.0)))
2076
2077     (pass-if "n = fixnum-max"
2078       (< 0.0 fixnum-max))
2079
2080     (pass-if "n = fixnum-max + 1"
2081       (< 0.0 (+ fixnum-max 1)))
2082
2083     (pass-if "n = fixnum-min"
2084       (not (< 0.0 fixnum-min)))
2085
2086     (pass-if "n = fixnum-min - 1"
2087       (not (< 0.0 (- fixnum-min 1)))))
2088
2089   (with-test-prefix "(< 1 n)"
2090
2091     (pass-if "n = 0"
2092       (not (< 1 0)))
2093
2094     (pass-if "n = 0.0"
2095       (not (< 1 0.0)))
2096
2097     (pass-if "n = 1"
2098       (not (< 1 1)))
2099
2100     (pass-if "n = 1.0"
2101       (not (< 1 1.0)))
2102
2103     (pass-if "n = -1"
2104       (not (< 1 -1)))
2105
2106     (pass-if "n = -1.0"
2107       (not (< 1 -1.0)))
2108
2109     (pass-if "n = fixnum-max"
2110       (< 1 fixnum-max))
2111
2112     (pass-if "n = fixnum-max + 1"
2113       (< 1 (+ fixnum-max 1)))
2114
2115     (pass-if "n = fixnum-min"
2116       (not (< 1 fixnum-min)))
2117
2118     (pass-if "n = fixnum-min - 1"
2119       (not (< 1 (- fixnum-min 1)))))
2120
2121   (with-test-prefix "(< 1.0 n)"
2122
2123     (pass-if "n = 0"
2124       (not (< 1.0 0)))
2125
2126     (pass-if "n = 0.0"
2127       (not (< 1.0 0.0)))
2128
2129     (pass-if "n = 1"
2130       (not (< 1.0 1)))
2131
2132     (pass-if "n = 1.0"
2133       (not (< 1.0 1.0)))
2134
2135     (pass-if "n = -1"
2136       (not (< 1.0 -1)))
2137
2138     (pass-if "n = -1.0"
2139       (not (< 1.0 -1.0)))
2140
2141     (pass-if "n = fixnum-max"
2142       (< 1.0 fixnum-max))
2143
2144     (pass-if "n = fixnum-max + 1"
2145       (< 1.0 (+ fixnum-max 1)))
2146
2147     (pass-if "n = fixnum-min"
2148       (not (< 1.0 fixnum-min)))
2149
2150     (pass-if "n = fixnum-min - 1"
2151       (not (< 1.0 (- fixnum-min 1)))))
2152
2153   (with-test-prefix "(< -1 n)"
2154
2155     (pass-if "n = 0"
2156       (< -1 0))
2157
2158     (pass-if "n = 0.0"
2159       (< -1 0.0))
2160
2161     (pass-if "n = 1"
2162       (< -1 1))
2163
2164     (pass-if "n = 1.0"
2165       (< -1 1.0))
2166
2167     (pass-if "n = -1"
2168       (not (< -1 -1)))
2169
2170     (pass-if "n = -1.0"
2171       (not (< -1 -1.0)))
2172
2173     (pass-if "n = fixnum-max"
2174       (< -1 fixnum-max))
2175
2176     (pass-if "n = fixnum-max + 1"
2177       (< -1 (+ fixnum-max 1)))
2178
2179     (pass-if "n = fixnum-min"
2180       (not (< -1 fixnum-min)))
2181
2182     (pass-if "n = fixnum-min - 1"
2183       (not (< -1 (- fixnum-min 1)))))
2184
2185   (with-test-prefix "(< -1.0 n)"
2186
2187     (pass-if "n = 0"
2188       (< -1.0 0))
2189
2190     (pass-if "n = 0.0"
2191       (< -1.0 0.0))
2192
2193     (pass-if "n = 1"
2194       (< -1.0 1))
2195
2196     (pass-if "n = 1.0"
2197       (< -1.0 1.0))
2198
2199     (pass-if "n = -1"
2200       (not (< -1.0 -1)))
2201
2202     (pass-if "n = -1.0"
2203       (not (< -1.0 -1.0)))
2204
2205     (pass-if "n = fixnum-max"
2206       (< -1.0 fixnum-max))
2207
2208     (pass-if "n = fixnum-max + 1"
2209       (< -1.0 (+ fixnum-max 1)))
2210
2211     (pass-if "n = fixnum-min"
2212       (not (< -1.0 fixnum-min)))
2213
2214     (pass-if "n = fixnum-min - 1"
2215       (not (< -1.0 (- fixnum-min 1)))))
2216
2217   (with-test-prefix "(< fixnum-max n)"
2218
2219     (pass-if "n = 0"
2220       (not (< fixnum-max 0)))
2221
2222     (pass-if "n = 0.0"
2223       (not (< fixnum-max 0.0)))
2224
2225     (pass-if "n = 1"
2226       (not (< fixnum-max 1)))
2227
2228     (pass-if "n = 1.0"
2229       (not (< fixnum-max 1.0)))
2230
2231     (pass-if "n = -1"
2232       (not (< fixnum-max -1)))
2233
2234     (pass-if "n = -1.0"
2235       (not (< fixnum-max -1.0)))
2236
2237     (pass-if "n = fixnum-max"
2238       (not (< fixnum-max fixnum-max)))
2239
2240     (pass-if "n = fixnum-max + 1"
2241       (< fixnum-max (+ fixnum-max 1)))
2242
2243     (pass-if "n = fixnum-min"
2244       (not (< fixnum-max fixnum-min)))
2245
2246     (pass-if "n = fixnum-min - 1"
2247       (not (< fixnum-max (- fixnum-min 1)))))
2248
2249   (with-test-prefix "(< (+ fixnum-max 1) n)"
2250
2251     (pass-if "n = 0"
2252       (not (< (+ fixnum-max 1) 0)))
2253
2254     (pass-if "n = 0.0"
2255       (not (< (+ fixnum-max 1) 0.0)))
2256
2257     (pass-if "n = 1"
2258       (not (< (+ fixnum-max 1) 1)))
2259
2260     (pass-if "n = 1.0"
2261       (not (< (+ fixnum-max 1) 1.0)))
2262
2263     (pass-if "n = -1"
2264       (not (< (+ fixnum-max 1) -1)))
2265
2266     (pass-if "n = -1.0"
2267       (not (< (+ fixnum-max 1) -1.0)))
2268
2269     (pass-if "n = fixnum-max"
2270       (not (< (+ fixnum-max 1) fixnum-max)))
2271
2272     (pass-if "n = fixnum-max + 1"
2273       (not (< (+ fixnum-max 1) (+ fixnum-max 1))))
2274
2275     (pass-if "n = fixnum-min"
2276       (not (< (+ fixnum-max 1) fixnum-min)))
2277
2278     (pass-if "n = fixnum-min - 1"
2279       (not (< (+ fixnum-max 1) (- fixnum-min 1)))))
2280
2281   (with-test-prefix "(< fixnum-min n)"
2282
2283     (pass-if "n = 0"
2284       (< fixnum-min 0))
2285
2286     (pass-if "n = 0.0"
2287       (< fixnum-min 0.0))
2288
2289     (pass-if "n = 1"
2290       (< fixnum-min 1))
2291
2292     (pass-if "n = 1.0"
2293       (< fixnum-min 1.0))
2294
2295     (pass-if "n = -1"
2296       (< fixnum-min -1))
2297
2298     (pass-if "n = -1.0"
2299       (< fixnum-min -1.0))
2300
2301     (pass-if "n = fixnum-max"
2302       (< fixnum-min fixnum-max))
2303
2304     (pass-if "n = fixnum-max + 1"
2305       (< fixnum-min (+ fixnum-max 1)))
2306
2307     (pass-if "n = fixnum-min"
2308       (not (< fixnum-min fixnum-min)))
2309
2310     (pass-if "n = fixnum-min - 1"
2311       (not (< fixnum-min (- fixnum-min 1)))))
2312
2313   (with-test-prefix "(< (- fixnum-min 1) n)"
2314
2315     (pass-if "n = 0"
2316       (< (- fixnum-min 1) 0))
2317
2318     (pass-if "n = 0.0"
2319       (< (- fixnum-min 1) 0.0))
2320
2321     (pass-if "n = 1"
2322       (< (- fixnum-min 1) 1))
2323
2324     (pass-if "n = 1.0"
2325       (< (- fixnum-min 1) 1.0))
2326
2327     (pass-if "n = -1"
2328       (< (- fixnum-min 1) -1))
2329
2330     (pass-if "n = -1.0"
2331       (< (- fixnum-min 1) -1.0))
2332
2333     (pass-if "n = fixnum-max"
2334       (< (- fixnum-min 1) fixnum-max))
2335
2336     (pass-if "n = fixnum-max + 1"
2337       (< (- fixnum-min 1) (+ fixnum-max 1)))
2338
2339     (pass-if "n = fixnum-min"
2340       (< (- fixnum-min 1) fixnum-min))
2341
2342     (pass-if "n = fixnum-min - 1"
2343       (not (< (- fixnum-min 1) (- fixnum-min 1)))))
2344
2345   (pass-if (< (ash 1 256) +inf.0))
2346   (pass-if (not (< +inf.0 (ash 1 256))))
2347   (pass-if (not (< (ash 1 256) -inf.0)))
2348   (pass-if (< -inf.0 (ash 1 256)))
2349
2350   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2351   ;; sure we've avoided that
2352   (pass-if (< (1- (ash 1 1024)) +inf.0))
2353   (pass-if (<     (ash 1 1024)  +inf.0))
2354   (pass-if (< (1+ (ash 1 1024)) +inf.0))
2355   (pass-if (not (< +inf.0 (1- (ash 1 1024)))))
2356   (pass-if (not (< +inf.0     (ash 1 1024))))
2357   (pass-if (not (< +inf.0 (1+ (ash 1 1024)))))
2358   (pass-if (< -inf.0 (- (1- (ash 1 1024)))))
2359   (pass-if (< -inf.0 (-     (ash 1 1024))))
2360   (pass-if (< -inf.0 (- (1+ (ash 1 1024)))))
2361   (pass-if (not (< (- (1- (ash 1 1024))) -inf.0)))
2362   (pass-if (not (< (-     (ash 1 1024))  -inf.0)))
2363   (pass-if (not (< (- (1+ (ash 1 1024))) -inf.0)))
2364
2365   (pass-if (not (< +nan.0 +nan.0)))
2366   (pass-if (not (< 0 +nan.0)))
2367   (pass-if (not (< +nan.0 0)))
2368   (pass-if (not (< 1 +nan.0)))
2369   (pass-if (not (< +nan.0 1)))
2370   (pass-if (not (< -1 +nan.0)))
2371   (pass-if (not (< +nan.0 -1)))
2372
2373   (pass-if (not (< (ash 1 256) +nan.0)))
2374   (pass-if (not (< +nan.0 (ash 1 256))))
2375   (pass-if (not (< (- (ash 1 256)) +nan.0)))
2376   (pass-if (not (< +nan.0 (- (ash 1 256)))))
2377
2378   (pass-if (not (< (ash 1 8192) +nan.0)))
2379   (pass-if (not (< +nan.0 (ash 1 8192))))
2380   (pass-if (not (< (- (ash 1 8192)) +nan.0)))
2381   (pass-if (not (< +nan.0 (- (ash 1 8192)))))
2382
2383   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2384   ;; sure we've avoided that
2385   (pass-if (not (< (ash 3 1023) +nan.0)))
2386   (pass-if (not (< (1+ (ash 3 1023)) +nan.0)))
2387   (pass-if (not (< (1- (ash 3 1023)) +nan.0)))
2388   (pass-if (not (< +nan.0 (ash 3 1023))))
2389   (pass-if (not (< +nan.0 (1+ (ash 3 1023)))))
2390   (pass-if (not (< +nan.0 (1- (ash 3 1023)))))
2391
2392   (with-test-prefix "inum/frac"
2393     (pass-if (< 2 9/4))
2394     (pass-if (< -2 9/4))
2395     (pass-if (< -2 7/4))
2396     (pass-if (< -2 -7/4))
2397     (pass-if (eq? #f (< 2 7/4)))
2398     (pass-if (eq? #f (< 2 -7/4)))
2399     (pass-if (eq? #f (< 2 -9/4)))
2400     (pass-if (eq? #f (< -2 -9/4))))
2401
2402   (with-test-prefix "bignum/frac"
2403     (let ((x (ash 1 2048)))
2404       (pass-if (< x (* 4/3 x)))
2405       (pass-if (< (- x) (* 4/3 x)))
2406       (pass-if (< (- x) (* 2/3 x)))
2407       (pass-if (< (- x) (* -2/3 x)))
2408       (pass-if (eq? #f (< x (* 2/3 x))))
2409       (pass-if (eq? #f (< x (* -2/3 x))))
2410       (pass-if (eq? #f (< x (* -4/3 x))))
2411       (pass-if (eq? #f (< (- x) (* -4/3 x))))))
2412
2413   (with-test-prefix "flonum/frac"
2414     (pass-if (< 0.75 4/3))
2415     (pass-if (< -0.75 4/3))
2416     (pass-if (< -0.75 2/3))
2417     (pass-if (< -0.75 -2/3))
2418     (pass-if (eq? #f (< 0.75 2/3)))
2419     (pass-if (eq? #f (< 0.75 -2/3)))
2420     (pass-if (eq? #f (< 0.75 -4/3)))
2421     (pass-if (eq? #f (< -0.75 -4/3)))
2422
2423     (pass-if (< -inf.0 4/3))
2424     (pass-if (< -inf.0 -4/3))
2425     (pass-if (eq? #f (< +inf.0 4/3)))
2426     (pass-if (eq? #f (< +inf.0 -4/3)))
2427
2428     (pass-if (eq? #f (< +nan.0 4/3)))
2429     (pass-if (eq? #f (< +nan.0 -4/3))))
2430
2431   (with-test-prefix "frac/inum"
2432     (pass-if (< 7/4 2))
2433     (pass-if (< -7/4 2))
2434     (pass-if (< -9/4 2))
2435     (pass-if (< -9/4 -2))
2436     (pass-if (eq? #f (< 9/4 2)))
2437     (pass-if (eq? #f (< 9/4 -2)))
2438     (pass-if (eq? #f (< 7/4 -2)))
2439     (pass-if (eq? #f (< -7/4 -2))))
2440
2441   (with-test-prefix "frac/bignum"
2442     (let ((x (ash 1 2048)))
2443       (pass-if (< (* 2/3 x) x))
2444       (pass-if (< (* -2/3 x) x))
2445       (pass-if (< (* -4/3 x) x))
2446       (pass-if (< (* -4/3 x) (- x)))
2447       (pass-if (eq? #f (< (* 4/3 x) x)))
2448       (pass-if (eq? #f (< (* 4/3 x) (- x))))
2449       (pass-if (eq? #f (< (* 2/3 x) (- x))))
2450       (pass-if (eq? #f (< (* -2/3 x) (- x))))))
2451
2452   (with-test-prefix "frac/flonum"
2453     (pass-if (< 2/3 0.75))
2454     (pass-if (< -2/3 0.75))
2455     (pass-if (< -4/3 0.75))
2456     (pass-if (< -4/3 -0.75))
2457     (pass-if (eq? #f (< 4/3 0.75)))
2458     (pass-if (eq? #f (< 4/3 -0.75)))
2459     (pass-if (eq? #f (< 2/3 -0.75)))
2460     (pass-if (eq? #f (< -2/3 -0.75)))
2461
2462     (pass-if (< 4/3 +inf.0))
2463     (pass-if (< -4/3 +inf.0))
2464     (pass-if (eq? #f (< 4/3 -inf.0)))
2465     (pass-if (eq? #f (< -4/3 -inf.0)))
2466
2467     (pass-if (eq? #f (< 4/3 +nan.0)))
2468     (pass-if (eq? #f (< -4/3 +nan.0))))
2469
2470   (with-test-prefix "frac/frac"
2471     (pass-if (< 2/3 6/7))
2472     (pass-if (< -2/3 6/7))
2473     (pass-if (< -4/3 6/7))
2474     (pass-if (< -4/3 -6/7))
2475     (pass-if (eq? #f (< 4/3 6/7)))
2476     (pass-if (eq? #f (< 4/3 -6/7)))
2477     (pass-if (eq? #f (< 2/3 -6/7)))
2478     (pass-if (eq? #f (< -2/3 -6/7)))))
2479
2480 ;;;
2481 ;;; >
2482 ;;;
2483
2484 ;; currently not tested -- implementation is trivial
2485 ;; (> x y) is implemented as (< y x)
2486 ;; FIXME: tests should probably be added in case we change implementation.
2487
2488 ;;;
2489 ;;; <=
2490 ;;;
2491
2492 ;; currently not tested -- implementation is trivial
2493 ;; (<= x y) is implemented as (not (< y x))
2494 ;; FIXME: tests should probably be added in case we change implementation.
2495
2496 ;;;
2497 ;;; >=
2498 ;;;
2499
2500 ;; currently not tested -- implementation is trivial
2501 ;; (>= x y) is implemented as (not (< x y))
2502 ;; FIXME: tests should probably be added in case we change implementation.
2503
2504 ;;;
2505 ;;; zero?
2506 ;;;
2507
2508 (with-test-prefix "zero?"
2509   (pass-if (documented? zero?))
2510
2511   (pass-if (zero?  0))
2512   (pass-if (zero?  0.0))
2513   (pass-if (zero? -0.0))
2514
2515   (pass-if (zero?  0.0+0.0i))
2516   (pass-if (zero?  0.0-0.0i))
2517   (pass-if (zero?  0.0+0.0i))
2518   (pass-if (zero? -0.0-0.0i))
2519
2520   (pass-if (not (zero?  7)))
2521   (pass-if (not (zero? -7)))
2522   (pass-if (not (zero? 1/7)))
2523   (pass-if (not (zero? -inf.0)))
2524   (pass-if (not (zero? +inf.0)))
2525   (pass-if (not (zero? +nan.0)))
2526   (pass-if (not (zero? (+ 1 fixnum-max))))
2527   (pass-if (not (zero? (- 1 fixnum-min))))
2528   (pass-if (not (zero? 1.3)))
2529   (pass-if (not (zero? 3.1+4.2i)))
2530   (pass-if (not (zero? 1.0+0.0i)))
2531   (pass-if (not (zero? 0.0-1.0i))))
2532
2533 ;;;
2534 ;;; positive?
2535 ;;;
2536
2537 (with-test-prefix "positive?"
2538   (pass-if (documented? positive?))
2539   (pass-if (positive? 1))
2540   (pass-if (positive? (+ fixnum-max 1)))
2541   (pass-if (positive? 1.3))
2542   (pass-if (not (positive? 0)))
2543   (pass-if (not (positive? -1)))
2544   (pass-if (not (positive? (- fixnum-min 1))))
2545   (pass-if (not (positive? -1.3))))
2546
2547 ;;;
2548 ;;; negative?
2549 ;;;
2550
2551 (with-test-prefix "negative?"
2552   (pass-if (documented? negative?))
2553   (pass-if (not (negative? 1)))
2554   (pass-if (not (negative? (+ fixnum-max 1))))
2555   (pass-if (not (negative? 1.3)))
2556   (pass-if (not (negative? 0)))
2557   (pass-if (negative? -1))
2558   (pass-if (negative? (- fixnum-min 1)))
2559   (pass-if (negative? -1.3)))
2560
2561 ;;;
2562 ;;; max
2563 ;;;
2564
2565 (with-test-prefix "max"
2566   (pass-if-exception "no args" exception:wrong-num-args
2567     (max))
2568
2569   (pass-if-exception "one complex" exception:wrong-type-arg
2570     (max 1+i))
2571
2572   (pass-if-exception "inum/complex" exception:wrong-type-arg
2573     (max 123 1+i))
2574   (pass-if-exception "big/complex" exception:wrong-type-arg
2575     (max 9999999999999999999999999999999999999999 1+i))
2576   (pass-if-exception "real/complex" exception:wrong-type-arg
2577     (max 123.0 1+i))
2578   (pass-if-exception "frac/complex" exception:wrong-type-arg
2579     (max 123/456 1+i))
2580
2581   (pass-if-exception "complex/inum" exception:wrong-type-arg
2582     (max 1+i 123))
2583   (pass-if-exception "complex/big" exception:wrong-type-arg
2584     (max 1+i 9999999999999999999999999999999999999999))
2585   (pass-if-exception "complex/real" exception:wrong-type-arg
2586     (max 1+i 123.0))
2587   (pass-if-exception "complex/frac" exception:wrong-type-arg
2588     (max 1+i 123/456))
2589
2590   (let ((big*2 (* fixnum-max 2))
2591         (big*3 (* fixnum-max 3))
2592         (big*4 (* fixnum-max 4))
2593         (big*5 (* fixnum-max 5)))
2594
2595     (with-test-prefix "inum / frac"
2596       (pass-if (eqv? 3 (max 3 5/2)))
2597       (pass-if (eqv? 5/2 (max 2 5/2))))
2598
2599     (with-test-prefix "frac / inum"
2600       (pass-if (eqv? 3 (max 5/2 3)))
2601       (pass-if (eqv? 5/2 (max 5/2 2))))
2602
2603     (with-test-prefix "infinities and NaNs"
2604       ;; +inf.0 beats everything else, including NaNs
2605       (pass-if (eqv?  +inf.0   (max   +inf.0    123   )))
2606       (pass-if (eqv?  +inf.0   (max    123     +inf.0 )))
2607       (pass-if (eqv?  +inf.0   (max   +inf.0   -123.3 )))
2608       (pass-if (eqv?  +inf.0   (max   -123.3   +inf.0 )))
2609       (pass-if (eqv?  +inf.0   (max   +inf.0   -7/2   )))
2610       (pass-if (eqv?  +inf.0   (max   -7/2     +inf.0 )))
2611       (pass-if (eqv?  +inf.0   (max   +inf.0  -1e20   )))
2612       (pass-if (eqv?  +inf.0   (max  -1e20     +inf.0 )))
2613       (pass-if (eqv?  +inf.0   (max   +inf.0 (- big*2))))
2614       (pass-if (eqv?  +inf.0   (max (- big*2)  +inf.0 )))
2615       (pass-if (eqv?  +inf.0   (max   +inf.0   +inf.0 )))
2616       (pass-if (eqv?  +inf.0   (max   +inf.0   +inf.0 )))
2617       (pass-if (eqv?  +inf.0   (max   +inf.0   +nan.0 )))
2618       (pass-if (eqv?  +inf.0   (max   +nan.0   +inf.0 )))
2619       (pass-if (eqv?  +inf.0   (max   +inf.0   +inf.0 )))
2620
2621       ;; NaNs beat everything except +inf.0
2622       (pass-if (real-nan?      (max   +nan.0    123   )))
2623       (pass-if (real-nan?      (max    123     +nan.0 )))
2624       (pass-if (real-nan?      (max   +nan.0    123.3 )))
2625       (pass-if (real-nan?      (max    123.3   +nan.0 )))
2626       (pass-if (real-nan?      (max   +nan.0   -7/2   )))
2627       (pass-if (real-nan?      (max   -7/2     +nan.0 )))
2628       (pass-if (real-nan?      (max   +nan.0  -1e20   )))
2629       (pass-if (real-nan?      (max  -1e20     +nan.0 )))
2630       (pass-if (real-nan?      (max   +nan.0 (- big*2))))
2631       (pass-if (real-nan?      (max (- big*2)  +nan.0 )))
2632       (pass-if (real-nan?      (max   +nan.0   -inf.0 )))
2633       (pass-if (real-nan?      (max   -inf.0   +nan.0 )))
2634       (pass-if (real-nan?      (max   +nan.0   +nan.0 )))
2635
2636       ;; -inf.0 always loses, except against itself
2637       (pass-if (eqv?   -inf.0  (max   -inf.0   -inf.0 )))
2638       (pass-if (eqv?   -123.0  (max   -inf.0   -123   )))
2639       (pass-if (eqv?   -123.0  (max   -123     -inf.0 )))
2640       (pass-if (eqv?   -123.3  (max   -inf.0   -123.3 )))
2641       (pass-if (eqv?   -123.3  (max   -123.3   -inf.0 )))
2642       (pass-if (eqv?     -3.5  (max   -inf.0   -7/2   )))
2643       (pass-if (eqv?     -3.5  (max   -7/2     -inf.0 )))
2644       (pass-if (eqv?  -1.0e20  (max   -inf.0  -1e20   )))
2645       (pass-if (eqv?  -1.0e20  (max  -1e20     -inf.0 )))
2646       (pass-if (eqv? (exact->inexact (- big*2))
2647                      (max   -inf.0 (- big*2))))
2648       (pass-if (eqv? (exact->inexact (- big*2))
2649                      (max (- big*2)  -inf.0 ))))
2650
2651     (with-test-prefix "signed zeroes"
2652       (pass-if (eqv?  0.0  (max  0.0  0.0)))
2653       (pass-if (eqv?  0.0  (max  0.0 -0.0)))
2654       (pass-if (eqv?  0.0  (max -0.0  0.0)))
2655       (pass-if (eqv? -0.0  (max -0.0 -0.0)))
2656       (pass-if (eqv?  0.0  (max -0.0  0  )))
2657       (pass-if (eqv?  0.0  (max  0.0  0  )))
2658       (pass-if (eqv?  0.0  (max  0   -0.0)))
2659       (pass-if (eqv?  0.0  (max  0    0.0)))
2660       (pass-if (eqv?  0    (min  0    0  ))))
2661
2662     (with-test-prefix "big / frac"
2663       (pass-if (eqv? big*2 (max big*2 5/2)))
2664       (pass-if (eqv? 5/2 (max (- big*2) 5/2))))
2665
2666     (with-test-prefix "frac / big"
2667       (pass-if (eqv? big*2 (max 5/2 big*2)))
2668       (pass-if (eqv? 5/2 (max 5/2 (- big*2)))))
2669
2670     (with-test-prefix "big / real"
2671       (pass-if (real-nan? (max big*5 +nan.0)))
2672       (pass-if (eqv? (exact->inexact big*5)  (max big*5 -inf.0)))
2673       (pass-if (eqv? (exact->inexact big*5)  (max big*5 1.0)))
2674       (pass-if (eqv? +inf.0                  (max big*5 +inf.0)))
2675       (pass-if (eqv? 1.0                     (max (- big*5) 1.0))))
2676
2677     (with-test-prefix "real / big"
2678       (pass-if (real-nan? (max +nan.0 big*5)))
2679       (pass-if (eqv? (exact->inexact big*5)  (max -inf.0 big*5)))
2680       (pass-if (eqv? (exact->inexact big*5)  (max 1.0 big*5)))
2681       (pass-if (eqv? +inf.0                  (max +inf.0 big*5)))
2682       (pass-if (eqv? 1.0                     (max 1.0 (- big*5)))))
2683
2684     (with-test-prefix "frac / frac"
2685       (pass-if (eqv? 2/3 (max 1/2 2/3)))
2686       (pass-if (eqv? 2/3 (max 2/3 1/2)))
2687       (pass-if (eqv? -1/2 (max -1/2 -2/3)))
2688       (pass-if (eqv? -1/2 (max -2/3 -1/2))))
2689
2690     (with-test-prefix "real / real"
2691       (pass-if (real-nan? (max 123.0 +nan.0)))
2692       (pass-if (real-nan? (max +nan.0 123.0)))
2693       (pass-if (real-nan? (max +nan.0 +nan.0)))
2694       (pass-if (eqv? 456.0 (max 123.0 456.0)))
2695       (pass-if (eqv? 456.0 (max 456.0 123.0)))))
2696
2697   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2698   ;; sure we've avoided that
2699   (for-each (lambda (b)
2700               (pass-if (list b +inf.0)
2701                 (eqv? +inf.0 (max b +inf.0)))
2702               (pass-if (list +inf.0 b)
2703                 (eqv? +inf.0 (max b +inf.0)))
2704               (pass-if (list b -inf.0)
2705                 (eqv? (exact->inexact b) (max b -inf.0)))
2706               (pass-if (list -inf.0 b)
2707                 (eqv? (exact->inexact b) (max b -inf.0))))
2708             (list (1- (ash 1 1024))
2709                   (ash 1 1024)
2710                   (1+ (ash 1 1024))
2711                   (- (1- (ash 1 1024)))
2712                   (- (ash 1 1024))
2713                   (- (1+ (ash 1 1024)))))
2714
2715   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2716   ;; sure we've avoided that
2717   (pass-if (real-nan? (max (ash 1 2048) +nan.0)))
2718   (pass-if (real-nan? (max +nan.0 (ash 1 2048)))))
2719
2720 ;;;
2721 ;;; min
2722 ;;;
2723
2724 ;; FIXME: unfinished...
2725
2726 (with-test-prefix "min"
2727   (pass-if-exception "no args" exception:wrong-num-args
2728     (min))
2729
2730   (pass-if-exception "one complex" exception:wrong-type-arg
2731     (min 1+i))
2732
2733   (pass-if-exception "inum/complex" exception:wrong-type-arg
2734     (min 123 1+i))
2735   (pass-if-exception "big/complex" exception:wrong-type-arg
2736     (min 9999999999999999999999999999999999999999 1+i))
2737   (pass-if-exception "real/complex" exception:wrong-type-arg
2738     (min 123.0 1+i))
2739   (pass-if-exception "frac/complex" exception:wrong-type-arg
2740     (min 123/456 1+i))
2741
2742   (pass-if-exception "complex/inum" exception:wrong-type-arg
2743     (min 1+i 123))
2744   (pass-if-exception "complex/big" exception:wrong-type-arg
2745     (min 1+i 9999999999999999999999999999999999999999))
2746   (pass-if-exception "complex/real" exception:wrong-type-arg
2747     (min 1+i 123.0))
2748   (pass-if-exception "complex/frac" exception:wrong-type-arg
2749     (min 1+i 123/456))
2750
2751   (let ((big*2 (* fixnum-max 2))
2752         (big*3 (* fixnum-max 3))
2753         (big*4 (* fixnum-max 4))
2754         (big*5 (* fixnum-max 5)))
2755
2756     (pass-if (documented? min))
2757     (pass-if (eqv? 1 (min 7 3 1 5)))
2758     (pass-if (eqv? 1 (min 1 7 3 5)))
2759     (pass-if (eqv? 1 (min 7 3 5 1)))
2760     (pass-if (eqv? -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
2761     (pass-if (eqv? -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
2762     (pass-if (eqv? -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
2763     (pass-if (eqv? big*2 (min big*3 big*5 big*2 big*4)))
2764     (pass-if (eqv? big*2 (min big*2 big*3 big*5 big*4)))
2765     (pass-if (eqv? big*2 (min big*3 big*5 big*4 big*2)))
2766     (pass-if
2767         (eqv? (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
2768     (pass-if
2769         (eqv? (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
2770     (pass-if
2771         (eqv? (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
2772
2773     (with-test-prefix "inum / frac"
2774       (pass-if (eqv? 5/2 (min 3 5/2)))
2775       (pass-if (eqv? 2   (min 2 5/2))))
2776
2777     (with-test-prefix "frac / inum"
2778       (pass-if (eqv? 5/2 (min 5/2 3)))
2779       (pass-if (eqv? 2   (min 5/2 2))))
2780
2781     (with-test-prefix "infinities and NaNs"
2782       ;; -inf.0 beats everything else, including NaNs
2783       (pass-if (eqv?  -inf.0   (min   -inf.0    123   )))
2784       (pass-if (eqv?  -inf.0   (min    123     -inf.0 )))
2785       (pass-if (eqv?  -inf.0   (min   -inf.0   -123.3 )))
2786       (pass-if (eqv?  -inf.0   (min   -123.3   -inf.0 )))
2787       (pass-if (eqv?  -inf.0   (min   -inf.0   -7/2   )))
2788       (pass-if (eqv?  -inf.0   (min   -7/2     -inf.0 )))
2789       (pass-if (eqv?  -inf.0   (min   -inf.0  -1e20   )))
2790       (pass-if (eqv?  -inf.0   (min  -1e20     -inf.0 )))
2791       (pass-if (eqv?  -inf.0   (min   -inf.0 (- big*2))))
2792       (pass-if (eqv?  -inf.0   (min (- big*2)  -inf.0 )))
2793       (pass-if (eqv?  -inf.0   (min   -inf.0   +inf.0 )))
2794       (pass-if (eqv?  -inf.0   (min   +inf.0   -inf.0 )))
2795       (pass-if (eqv?  -inf.0   (min   -inf.0   +nan.0 )))
2796       (pass-if (eqv?  -inf.0   (min   +nan.0   -inf.0 )))
2797       (pass-if (eqv?  -inf.0   (min   -inf.0   -inf.0 )))
2798
2799       ;; NaNs beat everything except -inf.0
2800       (pass-if (real-nan?      (min   +nan.0    123   )))
2801       (pass-if (real-nan?      (min    123     +nan.0 )))
2802       (pass-if (real-nan?      (min   +nan.0    123.3 )))
2803       (pass-if (real-nan?      (min    123.3   +nan.0 )))
2804       (pass-if (real-nan?      (min   +nan.0   -7/2   )))
2805       (pass-if (real-nan?      (min   -7/2     +nan.0 )))
2806       (pass-if (real-nan?      (min   +nan.0  -1e20   )))
2807       (pass-if (real-nan?      (min  -1e20     +nan.0 )))
2808       (pass-if (real-nan?      (min   +nan.0 (- big*2))))
2809       (pass-if (real-nan?      (min (- big*2)  +nan.0 )))
2810       (pass-if (real-nan?      (min   +nan.0   +inf.0 )))
2811       (pass-if (real-nan?      (min   +inf.0   +nan.0 )))
2812       (pass-if (real-nan?      (min   +nan.0   +nan.0 )))
2813
2814       ;; +inf.0 always loses, except against itself
2815       (pass-if (eqv?   +inf.0  (min   +inf.0   +inf.0 )))
2816       (pass-if (eqv?   -123.0  (min   +inf.0   -123   )))
2817       (pass-if (eqv?   -123.0  (min   -123     +inf.0 )))
2818       (pass-if (eqv?   -123.3  (min   +inf.0   -123.3 )))
2819       (pass-if (eqv?   -123.3  (min   -123.3   +inf.0 )))
2820       (pass-if (eqv?     -3.5  (min   +inf.0   -7/2   )))
2821       (pass-if (eqv?     -3.5  (min   -7/2     +inf.0 )))
2822       (pass-if (eqv?  -1.0e20  (min   +inf.0  -1e20   )))
2823       (pass-if (eqv?  -1.0e20  (min  -1e20     +inf.0 )))
2824       (pass-if (eqv? (exact->inexact (- big*2))
2825                      (min   +inf.0 (- big*2))))
2826       (pass-if (eqv? (exact->inexact (- big*2))
2827                      (min (- big*2)  +inf.0 ))))
2828
2829     (with-test-prefix "signed zeroes"
2830       (pass-if (eqv?  0.0  (min  0.0  0.0)))
2831       (pass-if (eqv? -0.0  (min  0.0 -0.0)))
2832       (pass-if (eqv? -0.0  (min -0.0  0.0)))
2833       (pass-if (eqv? -0.0  (min -0.0 -0.0)))
2834       (pass-if (eqv? -0.0  (min -0.0  0  )))
2835       (pass-if (eqv?  0.0  (min  0.0  0  )))
2836       (pass-if (eqv? -0.0  (min  0   -0.0)))
2837       (pass-if (eqv?  0.0  (min  0    0.0)))
2838       (pass-if (eqv?  0    (min  0    0  ))))
2839
2840     (with-test-prefix "big / frac"
2841       (pass-if (eqv? 5/2       (min big*2 5/2)))
2842       (pass-if (eqv? (- big*2) (min (- big*2) 5/2))))
2843
2844     (with-test-prefix "frac / big"
2845       (pass-if (eqv? 5/2       (min 5/2 big*2)))
2846       (pass-if (eqv? (- big*2) (min 5/2 (- big*2)))))
2847
2848     (with-test-prefix "big / real"
2849       (pass-if (real-nan? (min big*5 +nan.0)))
2850       (pass-if (eqv? (exact->inexact big*5)      (min big*5  +inf.0)))
2851       (pass-if (eqv? -inf.0                      (min big*5  -inf.0)))
2852       (pass-if (eqv? 1.0                         (min big*5 1.0)))
2853       (pass-if (eqv? (exact->inexact (- big*5))  (min (- big*5) 1.0))))
2854
2855     (with-test-prefix "real / big"
2856       (pass-if (real-nan? (min +nan.0 big*5)))
2857       (pass-if (eqv? (exact->inexact big*5)      (min +inf.0 big*5)))
2858       (pass-if (eqv? -inf.0                      (min -inf.0 big*5)))
2859       (pass-if (eqv? 1.0                         (min 1.0 big*5)))
2860       (pass-if (eqv? (exact->inexact (- big*5))  (min 1.0 (- big*5)))))
2861
2862     (with-test-prefix "frac / frac"
2863       (pass-if (eqv? 1/2 (min 1/2 2/3)))
2864       (pass-if (eqv? 1/2 (min 2/3 1/2)))
2865       (pass-if (eqv? -2/3 (min -1/2 -2/3)))
2866       (pass-if (eqv? -2/3 (min -2/3 -1/2))))
2867
2868     (with-test-prefix "real / real"
2869       (pass-if (real-nan? (min 123.0 +nan.0)))
2870       (pass-if (real-nan? (min +nan.0 123.0)))
2871       (pass-if (real-nan? (min +nan.0 +nan.0)))
2872       (pass-if (eqv? 123.0 (min 123.0 456.0)))
2873       (pass-if (eqv? 123.0 (min 456.0 123.0)))))
2874
2875
2876   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2877   ;; sure we've avoided that
2878   (for-each (lambda (b)
2879               (pass-if (list b +inf.0)
2880                 (eqv? (exact->inexact b) (min b +inf.0)))
2881               (pass-if (list +inf.0 b)
2882                 (eqv? (exact->inexact b) (min b +inf.0)))
2883               (pass-if (list b -inf.0)
2884                 (eqv? -inf.0 (min b -inf.0)))
2885               (pass-if (list -inf.0 b)
2886                 (eqv? -inf.0 (min b -inf.0))))
2887             (list (1- (ash 1 1024))
2888                   (ash 1 1024)
2889                   (1+ (ash 1 1024))
2890                   (- (1- (ash 1 1024)))
2891                   (- (ash 1 1024))
2892                   (- (1+ (ash 1 1024)))))
2893
2894   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2895   ;; sure we've avoided that
2896   (pass-if (real-nan? (min (- (ash 1 2048)) (- +nan.0))))
2897   (pass-if (real-nan? (min (- +nan.0) (- (ash 1 2048))))))
2898
2899 ;;;
2900 ;;; +
2901 ;;;
2902
2903 (with-test-prefix/c&e "+"
2904
2905   (pass-if "documented?"
2906     (documented? +))
2907
2908   (pass-if "simple"
2909     (and (eqv?  7 (+ 3 4))
2910          (eqv?  3 (+ 3))
2911          (eqv?  0 (+))))
2912
2913   (pass-if "exactness propagation"
2914     (and (eqv?  8   (+ 3 5))
2915          (eqv?  8.0 (+ 3 5.0))
2916          (eqv?  8.0 (+ 3.0 5))
2917          (eqv?  8.0 (+ 3.0 5.0))
2918
2919          (eqv?  5/6  (+ 1/2 1/3))
2920          (eqv?  5.5  (+ 1/2 5.0))
2921          (eqv?  3.25 (+ 3.0 1/4))))
2922
2923   (pass-if "signed zeroes"
2924     (and (eqv?  0.0 (+  0.0))
2925          (eqv? -0.0 (+ -0.0))
2926          (eqv?  0.0 (+  0.0  0.0))
2927          (eqv?  0.0 (+  0.0 -0.0))
2928          (eqv?  0.0 (+ -0.0  0.0))
2929          (eqv? -0.0 (+ -0.0 -0.0))))
2930
2931   (pass-if "NaNs"
2932     (and (real-nan?  (+ +nan.0 +nan.0))
2933          (real-nan?  (+ 0 +nan.0))
2934          (real-nan?  (+ +nan.0 0))
2935          (real-nan?  (+ 1 +nan.0))
2936          (real-nan?  (+ +nan.0 1))
2937          (real-nan?  (+ -1 +nan.0))
2938          (real-nan?  (+ +nan.0 -1))
2939          (real-nan?  (+ -7/2 +nan.0))
2940          (real-nan?  (+ +nan.0 -7/2))
2941          (real-nan?  (+ 1e20 +nan.0))
2942          (real-nan?  (+ +nan.0 1e20))
2943          (real-nan?  (+ +inf.0 +nan.0))
2944          (real-nan?  (+ +nan.0 +inf.0))
2945          (real-nan?  (+ -inf.0 +nan.0))
2946          (real-nan?  (+ +nan.0 -inf.0))
2947          (real-nan?  (+ (* fixnum-max 2) +nan.0))
2948          (real-nan?  (+ +nan.0 (* fixnum-max 2)))))
2949
2950   (pass-if "infinities"
2951     (and (eqv? +inf.0 (+ +inf.0 +inf.0))
2952          (eqv? -inf.0 (+ -inf.0 -inf.0))
2953          (real-nan?   (+ +inf.0 -inf.0))
2954          (real-nan?   (+ -inf.0 +inf.0))))
2955
2956   ;; The maximum fixnum on a 32-bit architecture: 2^29 - 1.
2957   (pass-if "fixnum + fixnum = bignum (32-bit)"
2958     (eqv? 536870912 (+ 536870910 2)))
2959
2960   ;; The maximum fixnum on a 64-bit architecture: 2^61 - 1.
2961   (pass-if "fixnum + fixnum = bignum (64-bit)"
2962     (eqv? 2305843009213693952 (+ 2305843009213693950 2)))
2963
2964   (pass-if "bignum + fixnum = fixnum"
2965     (eqv? 0 (+ (1+ most-positive-fixnum) most-negative-fixnum))))
2966
2967 ;;;
2968 ;;; -
2969 ;;;
2970
2971 (with-test-prefix/c&e "-"
2972
2973   (pass-if "double-negation of fixnum-min: ="
2974     (=      fixnum-min (- (- fixnum-min))))
2975   (pass-if "double-negation of fixnum-min: eqv?"
2976     (eqv?   fixnum-min (- (- fixnum-min))))
2977   (pass-if "double-negation of fixnum-min: equal?"
2978     (equal? fixnum-min (- (- fixnum-min))))
2979
2980   (pass-if "binary double-negation of fixnum-min: ="
2981     (=      fixnum-min (- 0 (- 0 fixnum-min))))
2982   (pass-if "binary double-negation of fixnum-min: eqv?"
2983     (eqv?   fixnum-min (- 0 (- 0 fixnum-min))))
2984   (pass-if "binary double-negation of fixnum-min: equal?"
2985     (equal? fixnum-min (- 0 (- 0 fixnum-min))))
2986
2987   (pass-if "signed zeroes"
2988     (and (eqv? +0.0 (- -0.0))
2989          (eqv? -0.0 (- +0.0))
2990          (eqv?  0.0 (-  0.0  0.0))
2991          (eqv?  0.0 (-  0.0 -0.0))
2992          (eqv?  0.0 (- -0.0 -0.0))
2993          (eqv? -0.0 (- -0.0  0.0))))
2994
2995   (pass-if "exactness propagation"
2996     (and (eqv?  3   (- 8 5))
2997          (eqv?  3.0 (- 8 5.0))
2998          (eqv?  3.0 (- 8.0 5))
2999          (eqv?  3.0 (- 8.0 5.0))
3000          (eqv? -1/6  (- 1/3 1/2))
3001          (eqv? -4.5  (- 1/2 5.0))
3002          (eqv?  2.75 (- 3.0 1/4))))
3003
3004   (pass-if "infinities"
3005     (and (eqv? +inf.0 (- +inf.0 -inf.0))
3006          (eqv? -inf.0 (- -inf.0 +inf.0))
3007          (real-nan?   (- +inf.0 +inf.0))
3008          (real-nan?   (- -inf.0 -inf.0))))
3009
3010   (pass-if "NaNs"
3011     (and (real-nan?  (- +nan.0 +nan.0))
3012          (real-nan?  (- 0 +nan.0))
3013          (real-nan?  (- +nan.0 0))
3014          (real-nan?  (- 1 +nan.0))
3015          (real-nan?  (- +nan.0 1))
3016          (real-nan?  (- -1 +nan.0))
3017          (real-nan?  (- +nan.0 -1))
3018          (real-nan?  (- -7/2 +nan.0))
3019          (real-nan?  (- +nan.0 -7/2))
3020          (real-nan?  (- 1e20 +nan.0))
3021          (real-nan?  (- +nan.0 1e20))
3022          (real-nan?  (- +inf.0 +nan.0))
3023          (real-nan?  (- +nan.0 +inf.0))
3024          (real-nan?  (- -inf.0 +nan.0))
3025          (real-nan?  (- +nan.0 -inf.0))
3026          (real-nan?  (- (* fixnum-max 2) +nan.0))
3027          (real-nan?  (- +nan.0 (* fixnum-max 2)))))
3028
3029   (pass-if "(eqv? fixnum-min (- (- fixnum-min)))"
3030     (eqv? fixnum-min (- (- fixnum-min))))
3031   (pass-if "(eqv? fixnum-min (- 0 (- 0 fixnum-min)))"
3032     (eqv? fixnum-min (- 0 (- 0 fixnum-min))))
3033   (pass-if "(eqv? fixnum-num (apply - (list (apply - (list fixnum-min)))))"
3034     (eqv? fixnum-min (apply - (list (apply - (list fixnum-min))))))
3035
3036   (pass-if "-inum - +bignum"
3037     (= #x-100000000000000000000000000000001
3038        (- -1 #x100000000000000000000000000000000)))
3039
3040   (pass-if "big - inum"
3041     (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
3042        (- #x100000000000000000000000000000000 1)))
3043
3044   (pass-if "big - -inum"
3045     (= #x100000000000000000000000000000001
3046        (- #x100000000000000000000000000000000 -1)))
3047
3048   ;; The mininum fixnum on a 32-bit architecture: -2^29.
3049   (pass-if "fixnum - fixnum = bignum (32-bit)"
3050     (eqv? -536870912 (- -536870910 2)))
3051
3052   ;; The minimum fixnum on a 64-bit architecture: -2^61.
3053   (pass-if "fixnum - fixnum = bignum (64-bit)"
3054     (eqv? -2305843009213693952 (- -2305843009213693950 2)))
3055
3056   (pass-if "bignum - fixnum = fixnum"
3057     (eqv? most-positive-fixnum (- (1+ most-positive-fixnum) 1))))
3058
3059 ;;;
3060 ;;; *
3061 ;;;
3062
3063 (with-test-prefix "*"
3064
3065   (with-test-prefix "double-negation of fixnum-min"
3066     (pass-if (=      fixnum-min (* -1 (* -1 fixnum-min))))
3067     (pass-if (eqv?   fixnum-min (* -1 (* -1 fixnum-min))))
3068     (pass-if (equal? fixnum-min (* -1 (* -1 fixnum-min))))
3069     (pass-if (=      fixnum-min (* (* fixnum-min -1) -1)))
3070     (pass-if (eqv?   fixnum-min (* (* fixnum-min -1) -1)))
3071     (pass-if (equal? fixnum-min (* (* fixnum-min -1) -1))))
3072
3073   (with-test-prefix "signed zeroes"
3074     (pass-if (eqv? +0.0 (* +0.0 +0.0)))
3075     (pass-if (eqv? -0.0 (* -0.0 +0.0)))
3076     (pass-if (eqv? +0.0 (* -0.0 -0.0)))
3077     (pass-if (eqv? -0.0 (* +0.0 -0.0)))
3078     (pass-if (eqv? +0.0+0.0i (* +i +0.0)))
3079     (pass-if (eqv? +0.0-0.0i (* -i +0.0)))
3080     (pass-if (eqv? -0.0-0.0i (* +i -0.0)))
3081     (pass-if (eqv? -0.0+0.0i (* -i -0.0))))
3082
3083   (with-test-prefix "exactness propagation"
3084     (pass-if (eqv? -0.0 (*  0 -1.0 )))
3085     (pass-if (eqv?  0.0 (*  0  1.0 )))
3086     (pass-if (eqv? -0.0 (* -1.0  0 )))
3087     (pass-if (eqv?  0.0 (*  1.0  0 )))
3088     (pass-if (eqv?  0   (*  0  1/2 )))
3089     (pass-if (eqv?  0   (*  1/2  0 )))
3090     (pass-if (eqv?  0.0+0.0i (*  0  1+i )))
3091     (pass-if (eqv?  0.0+0.0i (*  1+i  0 )))
3092     (pass-if (eqv? -1.0 (*  1 -1.0 )))
3093     (pass-if (eqv?  1.0 (*  1  1.0 )))
3094     (pass-if (eqv? -1.0 (* -1.0  1 )))
3095     (pass-if (eqv?  1.0 (*  1.0  1 )))
3096     (pass-if (eqv?  1/2 (*  1  1/2 )))
3097     (pass-if (eqv?  1/2 (*  1/2  1 )))
3098     (pass-if (eqv?  1+i (*  1  1+i )))
3099     (pass-if (eqv?  1+i (*  1+i  1 ))))
3100
3101   (with-test-prefix "propagation of NaNs"
3102     (pass-if (real-nan?      (* +nan.0 +nan.0)))
3103     (pass-if (real-nan?      (* +nan.0    1  )))
3104     (pass-if (real-nan?      (* +nan.0   -1  )))
3105     (pass-if (real-nan?      (* +nan.0 -7/2  )))
3106     (pass-if (real-nan?      (* +nan.0 1e20  )))
3107     (pass-if (real-nan?      (*  1     +nan.0)))
3108     (pass-if (real-nan?      (* -1     +nan.0)))
3109     (pass-if (real-nan?      (* -7/2   +nan.0)))
3110     (pass-if (real-nan?      (* 1e20   +nan.0)))
3111     (pass-if (real-nan?      (* +inf.0 +nan.0)))
3112     (pass-if (real-nan?      (* +nan.0 +inf.0)))
3113     (pass-if (real-nan?      (* -inf.0 +nan.0)))
3114     (pass-if (real-nan?      (* +nan.0 -inf.0)))
3115     (pass-if (real-nan?      (* (* fixnum-max 2) +nan.0)))
3116     (pass-if (real-nan?      (* +nan.0 (* fixnum-max 2))))
3117
3118     (pass-if (real-nan?        (*     0     +nan.0  )))
3119     (pass-if (real-nan?        (*  +nan.0      0    )))
3120     (pass-if (almost-real-nan? (*     0     +nan.0+i)))
3121     (pass-if (almost-real-nan? (*  +nan.0+i    0    )))
3122
3123     (pass-if (imaginary-nan? (*     0     +nan.0i )))
3124     (pass-if (imaginary-nan? (*  +nan.0i     0    )))
3125     (pass-if (imaginary-nan? (*     0    1+nan.0i )))
3126     (pass-if (imaginary-nan? (* 1+nan.0i     0    )))
3127
3128     (pass-if (complex-nan?   (* 0   +nan.0+nan.0i )))
3129     (pass-if (complex-nan?   (* +nan.0+nan.0i   0 ))))
3130
3131   (with-test-prefix "infinities"
3132     (pass-if (eqv?   +inf.0  (* +inf.0  5  )))
3133     (pass-if (eqv?   -inf.0  (* +inf.0 -5  )))
3134     (pass-if (eqv?   +inf.0  (* +inf.0 73.1)))
3135     (pass-if (eqv?   -inf.0  (* +inf.0 -9.2)))
3136     (pass-if (eqv?   +inf.0  (* +inf.0  5/2)))
3137     (pass-if (eqv?   -inf.0  (* +inf.0 -5/2)))
3138     (pass-if (eqv?   -inf.0  (* -5   +inf.0)))
3139     (pass-if (eqv?   +inf.0  (* 73.1 +inf.0)))
3140     (pass-if (eqv?   -inf.0  (* -9.2 +inf.0)))
3141     (pass-if (eqv?   +inf.0  (*  5/2 +inf.0)))
3142     (pass-if (eqv?   -inf.0  (* -5/2 +inf.0)))
3143
3144     (pass-if (eqv?   -inf.0  (* -inf.0  5  )))
3145     (pass-if (eqv?   +inf.0  (* -inf.0 -5  )))
3146     (pass-if (eqv?   -inf.0  (* -inf.0 73.1)))
3147     (pass-if (eqv?   +inf.0  (* -inf.0 -9.2)))
3148     (pass-if (eqv?   -inf.0  (* -inf.0  5/2)))
3149     (pass-if (eqv?   +inf.0  (* -inf.0 -5/2)))
3150     (pass-if (eqv?   +inf.0  (* -5   -inf.0)))
3151     (pass-if (eqv?   -inf.0  (* 73.1 -inf.0)))
3152     (pass-if (eqv?   +inf.0  (* -9.2 -inf.0)))
3153     (pass-if (eqv?   -inf.0  (* 5/2  -inf.0)))
3154     (pass-if (eqv?   +inf.0  (* -5/2 -inf.0)))
3155
3156     (pass-if (real-nan?      (*    0.0 +inf.0)))
3157     (pass-if (real-nan?      (*   -0.0 +inf.0)))
3158     (pass-if (real-nan?      (* +inf.0    0.0)))
3159     (pass-if (real-nan?      (* +inf.0   -0.0)))
3160
3161     (pass-if (real-nan?      (*    0.0 -inf.0)))
3162     (pass-if (real-nan?      (*   -0.0 -inf.0)))
3163     (pass-if (real-nan?      (* -inf.0    0.0)))
3164     (pass-if (real-nan?      (* -inf.0   -0.0)))
3165
3166     (pass-if (real-nan?      (*     0     +inf.0  )))
3167     (pass-if (real-nan?      (*  +inf.0      0    )))
3168     (pass-if (real-nan?      (*     0     -inf.0  )))
3169     (pass-if (real-nan?      (*  -inf.0      0    )))
3170
3171     (pass-if (almost-real-nan? (*     0     +inf.0+i)))
3172     (pass-if (almost-real-nan? (*  +inf.0+i    0    )))
3173     (pass-if (almost-real-nan? (*     0     -inf.0+i)))
3174     (pass-if (almost-real-nan? (*  -inf.0+i    0    )))
3175
3176     (pass-if (imaginary-nan? (*     0     +inf.0i )))
3177     (pass-if (imaginary-nan? (*  +inf.0i     0    )))
3178     (pass-if (imaginary-nan? (*     0    1+inf.0i )))
3179     (pass-if (imaginary-nan? (* 1+inf.0i     0    )))
3180
3181     (pass-if (imaginary-nan? (*     0     -inf.0i )))
3182     (pass-if (imaginary-nan? (*  -inf.0i     0    )))
3183     (pass-if (imaginary-nan? (*     0    1-inf.0i )))
3184     (pass-if (imaginary-nan? (* 1-inf.0i     0    )))
3185
3186     (pass-if (complex-nan?   (* 0   +inf.0+inf.0i )))
3187     (pass-if (complex-nan?   (* +inf.0+inf.0i   0 )))
3188
3189     (pass-if (complex-nan?   (* 0   +inf.0-inf.0i )))
3190     (pass-if (complex-nan?   (* -inf.0+inf.0i   0 ))))
3191
3192   (with-test-prefix "inum * bignum"
3193
3194     (pass-if "0 * 2^256 = 0"
3195       (eqv? 0 (* 0 (ash 1 256)))))
3196
3197   (with-test-prefix "inum * flonum"
3198
3199     (pass-if "0 * 1.0 = 0.0"
3200       (eqv? 0.0 (* 0 1.0))))
3201
3202   (with-test-prefix "inum * complex"
3203
3204     (pass-if "0 * 1+1i = 0.0+0.0i"
3205       (eqv? 0.0+0.0i (* 0 1+1i))))
3206
3207   (with-test-prefix "inum * frac"
3208
3209     (pass-if "0 * 2/3 = 0"
3210       (eqv? 0 (* 0 2/3))))
3211
3212   (with-test-prefix "bignum * inum"
3213
3214     (pass-if "2^256 * 0 = 0"
3215       (eqv? 0 (* (ash 1 256) 0))))
3216
3217   (with-test-prefix "flonum * inum"
3218     (pass-if "1.0 * 0 = 0.0"
3219       (eqv? 0.0 (* 1.0 0))))
3220
3221   (with-test-prefix "complex * inum"
3222     (pass-if "1+1i * 0 = 0.0+0.0i"
3223       (eqv? 0.0+0.0i (* 1+1i 0))))
3224
3225   (pass-if "complex * bignum"
3226     (let ((big (ash 1 90)))
3227       (= (make-rectangular big big)
3228          (* 1+1i big))))
3229
3230   (with-test-prefix "frac * inum"
3231
3232     (pass-if "2/3 * 0 = 0"
3233       (eqv? 0 (* 2/3 0)))))
3234
3235 ;;;
3236 ;;; /
3237 ;;;
3238
3239 (with-test-prefix "/"
3240
3241   (with-test-prefix "double-negation of fixnum-min"
3242     (pass-if (=      fixnum-min (/ (/ fixnum-min -1) -1)))
3243     (pass-if (eqv?   fixnum-min (/ (/ fixnum-min -1) -1)))
3244     (pass-if (equal? fixnum-min (/ (/ fixnum-min -1) -1))))
3245
3246   (pass-if "documented?"
3247     (documented? /))
3248
3249   (with-test-prefix "division by zero"
3250
3251     (pass-if-exception "(/ 0)"
3252         exception:numerical-overflow
3253       (/ 0))
3254
3255     (pass-if "(/ 0.0)"
3256       (= +inf.0 (/ 0.0)))
3257
3258     (pass-if-exception "(/ 1 0)"
3259         exception:numerical-overflow
3260       (/ 1 0))
3261
3262     (pass-if "(/ 1 0.0)"
3263       (= +inf.0 (/ 1 0.0)))
3264
3265     (pass-if-exception "(/ bignum 0)"
3266         exception:numerical-overflow
3267       (/ (+ fixnum-max 1) 0))
3268
3269     (pass-if "(/ bignum 0.0)"
3270       (= +inf.0 (/ (+ fixnum-max 1) 0.0)))
3271
3272     (pass-if-exception "(/ 1.0 0)"
3273         exception:numerical-overflow
3274       (/ 1.0 0))
3275
3276     (pass-if "(/ 1.0 0.0)"
3277       (= +inf.0 (/ 1.0 0.0)))
3278
3279     (pass-if-exception "(/ +i 0)"
3280         exception:numerical-overflow
3281       (/ +i 0))
3282
3283     (pass-if "(/ +i 0.0)"
3284       (= +inf.0 (imag-part (/ +i 0.0)))))
3285
3286   (with-test-prefix "1/complex"
3287
3288     (pass-if "0+1i"
3289       (eqv? 0-1i (/ 0+1i)))
3290
3291     ;; in guile 1.6 through 1.6.7 this incorrectly resulted in nans
3292     (pass-if "0-1i"
3293       (eqv? 0+1i (/ 0-1i)))
3294
3295     (pass-if "1+1i"
3296       (eqv? 0.5-0.5i (/ 1+1i)))
3297
3298     (pass-if "1-1i"
3299       (eqv? 0.5+0.5i (/ 1-1i)))
3300
3301     (pass-if "-1+1i"
3302       (eqv? -0.5-0.5i (/ -1+1i)))
3303
3304     (pass-if "-1-1i"
3305       (eqv? -0.5+0.5i (/ -1-1i)))
3306
3307     (pass-if "(/ 3+4i)"
3308       (= (/ 3+4i) 0.12-0.16i))
3309
3310     (pass-if "(/ 4+3i)"
3311       (= (/ 4+3i) 0.16-0.12i))
3312
3313     (pass-if "(/ 1e200+1e200i)"
3314       (= (/ 1e200+1e200i) 5.0e-201-5.0e-201i)))
3315
3316   (with-test-prefix "inum/complex"
3317
3318     (pass-if "(/ 25 3+4i)"
3319       (= (/ 25 3+4i) 3.0-4.0i))
3320
3321     (pass-if "(/ 25 4+3i)"
3322       (= (/ 25 4+3i) 4.0-3.0i)))
3323
3324   (with-test-prefix "complex/complex"
3325
3326     (pass-if "(/ 25+125i 3+4i)"
3327       (= (/ 25+125i 3+4i) 23.0+11.0i))
3328
3329     (pass-if "(/ 25+125i 4+3i)"
3330       (= (/ 25+125i 4+3i) 19.0+17.0i))))
3331
3332 ;;;
3333 ;;; floor
3334 ;;;
3335
3336 (with-test-prefix "floor"
3337   (pass-if (=  1 (floor  1.75)))
3338   (pass-if (=  1 (floor  1.5)))
3339   (pass-if (=  1 (floor  1.25)))
3340   (pass-if (=  0 (floor  0.75)))
3341   (pass-if (=  0 (floor  0.5)))
3342   (pass-if (=  0 (floor  0.0)))
3343   (pass-if (= -1 (floor -0.5)))
3344   (pass-if (= -2 (floor -1.25)))
3345   (pass-if (= -2 (floor -1.5)))
3346
3347   (with-test-prefix "inum"
3348     (pass-if "0"
3349       (and (= 0    (floor 0))
3350            (exact? (floor 0))))
3351
3352     (pass-if "1"
3353       (and (= 1    (floor 1))
3354            (exact? (floor 1))))
3355
3356     (pass-if "-1"
3357       (and (= -1   (floor -1))
3358            (exact? (floor -1)))))
3359
3360   (with-test-prefix "bignum"
3361     (let ((x (1+ most-positive-fixnum)))
3362       (pass-if "(1+ most-positive-fixnum)"
3363         (and (= x    (floor x))
3364              (exact? (floor x)))))
3365
3366     (let ((x (1- most-negative-fixnum)))
3367       (pass-if "(1- most-negative-fixnum)"
3368         (and (= x    (floor x))
3369              (exact? (floor x))))))
3370
3371   (with-test-prefix "frac"
3372     (define (=exact x y)
3373       (and (= x y)
3374            (exact? y)))
3375
3376     (pass-if (=exact -3 (floor -7/3)))
3377     (pass-if (=exact -2 (floor -5/3)))
3378     (pass-if (=exact -2 (floor -4/3)))
3379     (pass-if (=exact -1 (floor -2/3)))
3380     (pass-if (=exact -1 (floor -1/3)))
3381     (pass-if (=exact  0 (floor  1/3)))
3382     (pass-if (=exact  0 (floor  2/3)))
3383     (pass-if (=exact  1 (floor  4/3)))
3384     (pass-if (=exact  1 (floor  5/3)))
3385     (pass-if (=exact  2 (floor  7/3)))
3386
3387     (pass-if (=exact -3 (floor -17/6)))
3388     (pass-if (=exact -3 (floor -16/6)))
3389     (pass-if (=exact -3 (floor -15/6)))
3390     (pass-if (=exact -3 (floor -14/6)))
3391     (pass-if (=exact -3 (floor -13/6)))
3392     (pass-if (=exact -2 (floor -11/6)))
3393     (pass-if (=exact -2 (floor -10/6)))
3394     (pass-if (=exact -2 (floor  -9/6)))
3395     (pass-if (=exact -2 (floor  -8/6)))
3396     (pass-if (=exact -2 (floor  -7/6)))
3397     (pass-if (=exact -1 (floor  -5/6)))
3398     (pass-if (=exact -1 (floor  -4/6)))
3399     (pass-if (=exact -1 (floor  -3/6)))
3400     (pass-if (=exact -1 (floor  -2/6)))
3401     (pass-if (=exact -1 (floor  -1/6)))
3402     (pass-if (=exact  0 (floor   1/6)))
3403     (pass-if (=exact  0 (floor   2/6)))
3404     (pass-if (=exact  0 (floor   3/6)))
3405     (pass-if (=exact  0 (floor   4/6)))
3406     (pass-if (=exact  0 (floor   5/6)))
3407     (pass-if (=exact  1 (floor   7/6)))
3408     (pass-if (=exact  1 (floor   8/6)))
3409     (pass-if (=exact  1 (floor   9/6)))
3410     (pass-if (=exact  1 (floor  10/6)))
3411     (pass-if (=exact  1 (floor  11/6)))
3412     (pass-if (=exact  2 (floor  13/6)))
3413     (pass-if (=exact  2 (floor  14/6)))
3414     (pass-if (=exact  2 (floor  15/6)))
3415     (pass-if (=exact  2 (floor  16/6)))
3416     (pass-if (=exact  2 (floor  17/6))))
3417
3418   (with-test-prefix "real"
3419     (pass-if "0.0"
3420       (and (= 0.0    (floor 0.0))
3421            (inexact? (floor 0.0))))
3422
3423     (pass-if "1.0"
3424       (and (= 1.0    (floor 1.0))
3425            (inexact? (floor 1.0))))
3426
3427     (pass-if "-1.0"
3428       (and (= -1.0   (floor -1.0))
3429            (inexact? (floor -1.0))))
3430
3431     (pass-if "-3.1"
3432       (and (= -4.0   (floor -3.1))
3433            (inexact? (floor -3.1))))
3434
3435     (pass-if "3.1"
3436       (and (= 3.0    (floor 3.1))
3437            (inexact? (floor 3.1))))
3438
3439     (pass-if "3.9"
3440       (and (= 3.0    (floor 3.9))
3441            (inexact? (floor 3.9))))
3442
3443     (pass-if "-3.9"
3444       (and (= -4.0   (floor -3.9))
3445            (inexact? (floor -3.9))))
3446
3447     (pass-if "1.5"
3448       (and (= 1.0    (floor 1.5))
3449            (inexact? (floor 1.5))))
3450
3451     (pass-if "2.5"
3452       (and (= 2.0    (floor 2.5))
3453            (inexact? (floor 2.5))))
3454
3455     (pass-if "3.5"
3456       (and (= 3.0    (floor 3.5))
3457            (inexact? (floor 3.5))))
3458
3459     (pass-if "-1.5"
3460       (and (= -2.0   (floor -1.5))
3461            (inexact? (floor -1.5))))
3462
3463     (pass-if "-2.5"
3464       (and (= -3.0   (floor -2.5))
3465            (inexact? (floor -2.5))))
3466
3467     (pass-if "-3.5"
3468       (and (= -4.0   (floor -3.5))
3469            (inexact? (floor -3.5))))))
3470
3471 ;;;
3472 ;;; ceiling
3473 ;;;
3474
3475 (with-test-prefix "ceiling"
3476   (pass-if (=  2 (ceiling  1.75)))
3477   (pass-if (=  2 (ceiling  1.5)))
3478   (pass-if (=  2 (ceiling  1.25)))
3479   (pass-if (=  1 (ceiling  0.75)))
3480   (pass-if (=  1 (ceiling  0.5)))
3481   (pass-if (=  0 (ceiling  0.0)))
3482   (pass-if (=  0 (ceiling -0.5)))
3483   (pass-if (= -1 (ceiling -1.25)))
3484   (pass-if (= -1 (ceiling -1.5)))
3485
3486   (with-test-prefix "inum"
3487     (pass-if "0"
3488       (and (= 0    (ceiling 0))
3489            (exact? (ceiling 0))))
3490
3491     (pass-if "1"
3492       (and (= 1    (ceiling 1))
3493            (exact? (ceiling 1))))
3494
3495     (pass-if "-1"
3496       (and (= -1   (ceiling -1))
3497            (exact? (ceiling -1)))))
3498
3499   (with-test-prefix "bignum"
3500     (let ((x (1+ most-positive-fixnum)))
3501       (pass-if "(1+ most-positive-fixnum)"
3502         (and (= x    (ceiling x))
3503              (exact? (ceiling x)))))
3504
3505     (let ((x (1- most-negative-fixnum)))
3506       (pass-if "(1- most-negative-fixnum)"
3507         (and (= x    (ceiling x))
3508              (exact? (ceiling x))))))
3509
3510   (with-test-prefix "frac"
3511     (define (=exact x y)
3512       (and (= x y)
3513            (exact? y)))
3514
3515     (pass-if (=exact -2 (ceiling -7/3)))
3516     (pass-if (=exact -1 (ceiling -5/3)))
3517     (pass-if (=exact -1 (ceiling -4/3)))
3518     (pass-if (=exact  0 (ceiling -2/3)))
3519     (pass-if (=exact  0 (ceiling -1/3)))
3520     (pass-if (=exact  1 (ceiling  1/3)))
3521     (pass-if (=exact  1 (ceiling  2/3)))
3522     (pass-if (=exact  2 (ceiling  4/3)))
3523     (pass-if (=exact  2 (ceiling  5/3)))
3524     (pass-if (=exact  3 (ceiling  7/3)))
3525
3526     (pass-if (=exact -2 (ceiling -17/6)))
3527     (pass-if (=exact -2 (ceiling -16/6)))
3528     (pass-if (=exact -2 (ceiling -15/6)))
3529     (pass-if (=exact -2 (ceiling -14/6)))
3530     (pass-if (=exact -2 (ceiling -13/6)))
3531     (pass-if (=exact -1 (ceiling -11/6)))
3532     (pass-if (=exact -1 (ceiling -10/6)))
3533     (pass-if (=exact -1 (ceiling  -9/6)))
3534     (pass-if (=exact -1 (ceiling  -8/6)))
3535     (pass-if (=exact -1 (ceiling  -7/6)))
3536     (pass-if (=exact  0 (ceiling  -5/6)))
3537     (pass-if (=exact  0 (ceiling  -4/6)))
3538     (pass-if (=exact  0 (ceiling  -3/6)))
3539     (pass-if (=exact  0 (ceiling  -2/6)))
3540     (pass-if (=exact  0 (ceiling  -1/6)))
3541     (pass-if (=exact  1 (ceiling   1/6)))
3542     (pass-if (=exact  1 (ceiling   2/6)))
3543     (pass-if (=exact  1 (ceiling   3/6)))
3544     (pass-if (=exact  1 (ceiling   4/6)))
3545     (pass-if (=exact  1 (ceiling   5/6)))
3546     (pass-if (=exact  2 (ceiling   7/6)))
3547     (pass-if (=exact  2 (ceiling   8/6)))
3548     (pass-if (=exact  2 (ceiling   9/6)))
3549     (pass-if (=exact  2 (ceiling  10/6)))
3550     (pass-if (=exact  2 (ceiling  11/6)))
3551     (pass-if (=exact  3 (ceiling  13/6)))
3552     (pass-if (=exact  3 (ceiling  14/6)))
3553     (pass-if (=exact  3 (ceiling  15/6)))
3554     (pass-if (=exact  3 (ceiling  16/6)))
3555     (pass-if (=exact  3 (ceiling  17/6))))
3556
3557   (with-test-prefix "real"
3558     (pass-if "0.0"
3559       (and (= 0.0    (ceiling 0.0))
3560            (inexact? (ceiling 0.0))))
3561
3562     (pass-if "1.0"
3563       (and (= 1.0    (ceiling 1.0))
3564            (inexact? (ceiling 1.0))))
3565
3566     (pass-if "-1.0"
3567       (and (= -1.0   (ceiling -1.0))
3568            (inexact? (ceiling -1.0))))
3569
3570     (pass-if "-3.1"
3571       (and (= -3.0   (ceiling -3.1))
3572            (inexact? (ceiling -3.1))))
3573
3574     (pass-if "3.1"
3575       (and (= 4.0    (ceiling 3.1))
3576            (inexact? (ceiling 3.1))))
3577
3578     (pass-if "3.9"
3579       (and (= 4.0    (ceiling 3.9))
3580            (inexact? (ceiling 3.9))))
3581
3582     (pass-if "-3.9"
3583       (and (= -3.0   (ceiling -3.9))
3584            (inexact? (ceiling -3.9))))
3585
3586     (pass-if "1.5"
3587       (and (= 2.0    (ceiling 1.5))
3588            (inexact? (ceiling 1.5))))
3589
3590     (pass-if "2.5"
3591       (and (= 3.0    (ceiling 2.5))
3592            (inexact? (ceiling 2.5))))
3593
3594     (pass-if "3.5"
3595       (and (= 4.0    (ceiling 3.5))
3596            (inexact? (ceiling 3.5))))
3597
3598     (pass-if "-1.5"
3599       (and (= -1.0   (ceiling -1.5))
3600            (inexact? (ceiling -1.5))))
3601
3602     (pass-if "-2.5"
3603       (and (= -2.0   (ceiling -2.5))
3604            (inexact? (ceiling -2.5))))
3605
3606     (pass-if "-3.5"
3607       (and (= -3.0   (ceiling -3.5))
3608            (inexact? (ceiling -3.5))))))
3609
3610 ;;;
3611 ;;; truncate
3612 ;;;
3613
3614 (with-test-prefix "truncate"
3615   (pass-if (=  1 (truncate  1.75)))
3616   (pass-if (=  1 (truncate  1.5)))
3617   (pass-if (=  1 (truncate  1.25)))
3618   (pass-if (=  0 (truncate  0.75)))
3619   (pass-if (=  0 (truncate  0.5)))
3620   (pass-if (=  0 (truncate  0.0)))
3621   (pass-if (=  0 (truncate -0.5)))
3622   (pass-if (= -1 (truncate -1.25)))
3623   (pass-if (= -1 (truncate -1.5)))
3624
3625   (with-test-prefix "inum"
3626     (pass-if "0"
3627       (and (= 0    (truncate 0))
3628            (exact? (truncate 0))))
3629
3630     (pass-if "1"
3631       (and (= 1    (truncate 1))
3632            (exact? (truncate 1))))
3633
3634     (pass-if "-1"
3635       (and (= -1   (truncate -1))
3636            (exact? (truncate -1)))))
3637
3638   (with-test-prefix "bignum"
3639     (let ((x (1+ most-positive-fixnum)))
3640       (pass-if "(1+ most-positive-fixnum)"
3641         (and (= x    (truncate x))
3642              (exact? (truncate x)))))
3643
3644     (let ((x (1- most-negative-fixnum)))
3645       (pass-if "(1- most-negative-fixnum)"
3646         (and (= x    (truncate x))
3647              (exact? (truncate x))))))
3648
3649   (with-test-prefix "frac"
3650     (define (=exact x y)
3651       (and (= x y)
3652            (exact? y)))
3653
3654     (pass-if (=exact -2 (truncate -7/3)))
3655     (pass-if (=exact -1 (truncate -5/3)))
3656     (pass-if (=exact -1 (truncate -4/3)))
3657     (pass-if (=exact  0 (truncate -2/3)))
3658     (pass-if (=exact  0 (truncate -1/3)))
3659     (pass-if (=exact  0 (truncate  1/3)))
3660     (pass-if (=exact  0 (truncate  2/3)))
3661     (pass-if (=exact  1 (truncate  4/3)))
3662     (pass-if (=exact  1 (truncate  5/3)))
3663     (pass-if (=exact  2 (truncate  7/3)))
3664
3665     (pass-if (=exact -2 (truncate -17/6)))
3666     (pass-if (=exact -2 (truncate -16/6)))
3667     (pass-if (=exact -2 (truncate -15/6)))
3668     (pass-if (=exact -2 (truncate -14/6)))
3669     (pass-if (=exact -2 (truncate -13/6)))
3670     (pass-if (=exact -1 (truncate -11/6)))
3671     (pass-if (=exact -1 (truncate -10/6)))
3672     (pass-if (=exact -1 (truncate  -9/6)))
3673     (pass-if (=exact -1 (truncate  -8/6)))
3674     (pass-if (=exact -1 (truncate  -7/6)))
3675     (pass-if (=exact  0 (truncate  -5/6)))
3676     (pass-if (=exact  0 (truncate  -4/6)))
3677     (pass-if (=exact  0 (truncate  -3/6)))
3678     (pass-if (=exact  0 (truncate  -2/6)))
3679     (pass-if (=exact  0 (truncate  -1/6)))
3680     (pass-if (=exact  0 (truncate   1/6)))
3681     (pass-if (=exact  0 (truncate   2/6)))
3682     (pass-if (=exact  0 (truncate   3/6)))
3683     (pass-if (=exact  0 (truncate   4/6)))
3684     (pass-if (=exact  0 (truncate   5/6)))
3685     (pass-if (=exact  1 (truncate   7/6)))
3686     (pass-if (=exact  1 (truncate   8/6)))
3687     (pass-if (=exact  1 (truncate   9/6)))
3688     (pass-if (=exact  1 (truncate  10/6)))
3689     (pass-if (=exact  1 (truncate  11/6)))
3690     (pass-if (=exact  2 (truncate  13/6)))
3691     (pass-if (=exact  2 (truncate  14/6)))
3692     (pass-if (=exact  2 (truncate  15/6)))
3693     (pass-if (=exact  2 (truncate  16/6)))
3694     (pass-if (=exact  2 (truncate  17/6))))
3695
3696   (with-test-prefix "real"
3697     (pass-if "0.0"
3698       (and (= 0.0    (truncate 0.0))
3699            (inexact? (truncate 0.0))))
3700
3701     (pass-if "1.0"
3702       (and (= 1.0    (truncate 1.0))
3703            (inexact? (truncate 1.0))))
3704
3705     (pass-if "-1.0"
3706       (and (= -1.0   (truncate -1.0))
3707            (inexact? (truncate -1.0))))
3708
3709     (pass-if "-3.1"
3710       (and (= -3.0   (truncate -3.1))
3711            (inexact? (truncate -3.1))))
3712
3713     (pass-if "3.1"
3714       (and (= 3.0    (truncate 3.1))
3715            (inexact? (truncate 3.1))))
3716
3717     (pass-if "3.9"
3718       (and (= 3.0    (truncate 3.9))
3719            (inexact? (truncate 3.9))))
3720
3721     (pass-if "-3.9"
3722       (and (= -3.0   (truncate -3.9))
3723            (inexact? (truncate -3.9))))
3724
3725     (pass-if "1.5"
3726       (and (= 1.0    (truncate 1.5))
3727            (inexact? (truncate 1.5))))
3728
3729     (pass-if "2.5"
3730       (and (= 2.0    (truncate 2.5))
3731            (inexact? (truncate 2.5))))
3732
3733     (pass-if "3.5"
3734       (and (= 3.0    (truncate 3.5))
3735            (inexact? (truncate 3.5))))
3736
3737     (pass-if "-1.5"
3738       (and (= -1.0   (truncate -1.5))
3739            (inexact? (truncate -1.5))))
3740
3741     (pass-if "-2.5"
3742       (and (= -2.0   (truncate -2.5))
3743            (inexact? (truncate -2.5))))
3744
3745     (pass-if "-3.5"
3746       (and (= -3.0   (truncate -3.5))
3747            (inexact? (truncate -3.5))))))
3748
3749 ;;;
3750 ;;; round
3751 ;;;
3752
3753 (with-test-prefix "round"
3754   (pass-if (=  2 (round  1.75)))
3755   (pass-if (=  2 (round  1.5)))
3756   (pass-if (=  1 (round  1.25)))
3757   (pass-if (=  1 (round  0.75)))
3758   (pass-if (=  0 (round  0.5)))
3759   (pass-if (=  0 (round  0.0)))
3760   (pass-if (=  0 (round -0.5)))
3761   (pass-if (= -1 (round -1.25)))
3762   (pass-if (= -2 (round -1.5)))
3763
3764   (with-test-prefix "inum"
3765     (pass-if "0"
3766       (and (= 0    (round 0))
3767            (exact? (round 0))))
3768
3769     (pass-if "1"
3770       (and (= 1    (round 1))
3771            (exact? (round 1))))
3772
3773     (pass-if "-1"
3774       (and (= -1   (round -1))
3775            (exact? (round -1)))))
3776
3777   (with-test-prefix "bignum"
3778     (let ((x (1+ most-positive-fixnum)))
3779       (pass-if "(1+ most-positive-fixnum)"
3780         (and (= x    (round x))
3781              (exact? (round x)))))
3782
3783     (let ((x (1- most-negative-fixnum)))
3784       (pass-if "(1- most-negative-fixnum)"
3785         (and (= x    (round x))
3786              (exact? (round x))))))
3787
3788   (with-test-prefix "frac"
3789     (define (=exact x y)
3790       (and (= x y)
3791            (exact? y)))
3792
3793     (pass-if (=exact -2 (round -7/3)))
3794     (pass-if (=exact -2 (round -5/3)))
3795     (pass-if (=exact -1 (round -4/3)))
3796     (pass-if (=exact -1 (round -2/3)))
3797     (pass-if (=exact  0 (round -1/3)))
3798     (pass-if (=exact  0 (round  1/3)))
3799     (pass-if (=exact  1 (round  2/3)))
3800     (pass-if (=exact  1 (round  4/3)))
3801     (pass-if (=exact  2 (round  5/3)))
3802     (pass-if (=exact  2 (round  7/3)))
3803
3804     (pass-if (=exact -3 (round -17/6)))
3805     (pass-if (=exact -3 (round -16/6)))
3806     (pass-if (=exact -2 (round -15/6)))
3807     (pass-if (=exact -2 (round -14/6)))
3808     (pass-if (=exact -2 (round -13/6)))
3809     (pass-if (=exact -2 (round -11/6)))
3810     (pass-if (=exact -2 (round -10/6)))
3811     (pass-if (=exact -2 (round  -9/6)))
3812     (pass-if (=exact -1 (round  -8/6)))
3813     (pass-if (=exact -1 (round  -7/6)))
3814     (pass-if (=exact -1 (round  -5/6)))
3815     (pass-if (=exact -1 (round  -4/6)))
3816     (pass-if (=exact  0 (round  -3/6)))
3817     (pass-if (=exact  0 (round  -2/6)))
3818     (pass-if (=exact  0 (round  -1/6)))
3819     (pass-if (=exact  0 (round   1/6)))
3820     (pass-if (=exact  0 (round   2/6)))
3821     (pass-if (=exact  0 (round   3/6)))
3822     (pass-if (=exact  1 (round   4/6)))
3823     (pass-if (=exact  1 (round   5/6)))
3824     (pass-if (=exact  1 (round   7/6)))
3825     (pass-if (=exact  1 (round   8/6)))
3826     (pass-if (=exact  2 (round   9/6)))
3827     (pass-if (=exact  2 (round  10/6)))
3828     (pass-if (=exact  2 (round  11/6)))
3829     (pass-if (=exact  2 (round  13/6)))
3830     (pass-if (=exact  2 (round  14/6)))
3831     (pass-if (=exact  2 (round  15/6)))
3832     (pass-if (=exact  3 (round  16/6)))
3833     (pass-if (=exact  3 (round  17/6))))
3834
3835   (with-test-prefix "real"
3836     (pass-if "0.0"
3837       (and (= 0.0    (round 0.0))
3838            (inexact? (round 0.0))))
3839
3840     (pass-if "1.0"
3841       (and (= 1.0    (round 1.0))
3842            (inexact? (round 1.0))))
3843
3844     (pass-if "-1.0"
3845       (and (= -1.0   (round -1.0))
3846            (inexact? (round -1.0))))
3847
3848     (pass-if "-3.1"
3849       (and (= -3.0   (round -3.1))
3850            (inexact? (round -3.1))))
3851
3852     (pass-if "3.1"
3853       (and (= 3.0    (round 3.1))
3854            (inexact? (round 3.1))))
3855
3856     (pass-if "3.9"
3857       (and (= 4.0    (round 3.9))
3858            (inexact? (round 3.9))))
3859
3860     (pass-if "-3.9"
3861       (and (= -4.0   (round -3.9))
3862            (inexact? (round -3.9))))
3863
3864     (pass-if "1.5"
3865       (and (= 2.0    (round 1.5))
3866            (inexact? (round 1.5))))
3867
3868     (pass-if "2.5"
3869       (and (= 2.0    (round 2.5))
3870            (inexact? (round 2.5))))
3871
3872     (pass-if "3.5"
3873       (and (= 4.0    (round 3.5))
3874            (inexact? (round 3.5))))
3875
3876     (pass-if "-1.5"
3877       (and (= -2.0   (round -1.5))
3878            (inexact? (round -1.5))))
3879
3880     (pass-if "-2.5"
3881       (and (= -2.0   (round -2.5))
3882            (inexact? (round -2.5))))
3883
3884     (pass-if "-3.5"
3885       (and (= -4.0   (round -3.5))
3886            (inexact? (round -3.5))))
3887
3888     ;; prior to guile 1.6.5, on an IEEE system an inexact 2^53-1 (ie. a
3889     ;; float with mantissa all ones) came out as 2^53 from `round' (except
3890     ;; on i386 and m68k systems using the coprocessor and optimizing, where
3891     ;; extra precision hid the problem)
3892     (pass-if "2^53-1"
3893       (let ((x (exact->inexact (1- (ash 1 53)))))
3894         (and (= x      (round x))
3895              (inexact? (round x)))))
3896     (pass-if "-(2^53-1)"
3897       (let ((x (exact->inexact (- (1- (ash 1 53))))))
3898         (and (= x      (round x))
3899              (inexact? (round x)))))))
3900
3901 ;;;
3902 ;;; exact->inexact
3903 ;;;
3904
3905 (with-test-prefix "exact->inexact"
3906
3907   ;; Test "(exact->inexact n)", expect "want".
3908   ;; "i" is a index, for diagnostic purposes.
3909   (define (try-i i n want)
3910     (with-test-prefix (list i n want)
3911       (with-test-prefix "pos"
3912         (let ((got (exact->inexact n)))
3913           (pass-if "inexact?" (inexact? got))
3914           (pass-if (list "=" got) (= want got))))
3915       (set! n    (- n))
3916       (set! want (- want))
3917       (with-test-prefix "neg"
3918         (let ((got (exact->inexact n)))
3919           (pass-if "inexact?" (inexact? got))
3920           (pass-if (list "=" got) (= want got))))))
3921
3922   (with-test-prefix "2^i, no round"
3923     (do ((i    0   (1+ i))
3924          (n    1   (* 2 n))
3925          (want 1.0 (* 2.0 want)))
3926         ((> i 100))
3927       (try-i i n want)))
3928
3929   (with-test-prefix "2^i+1, no round"
3930     (do ((i    1   (1+ i))
3931          (n    3   (1- (* 2 n)))
3932          (want 3.0 (- (* 2.0 want) 1.0)))
3933         ((>= i dbl-mant-dig))
3934       (try-i i n want)))
3935
3936   (with-test-prefix "(2^i+1)*2^100, no round"
3937     (do ((i    1   (1+ i))
3938          (n    3   (1- (* 2 n)))
3939          (want 3.0 (- (* 2.0 want) 1.0)))
3940         ((>= i dbl-mant-dig))
3941       (try-i i (ash n 100) (ash-flo want 100))))
3942
3943   ;; bit pattern: 1111....11100.00
3944   ;;              <-mantdig-><-i->
3945   ;;
3946   (with-test-prefix "mantdig ones then zeros, no rounding"
3947     (do ((i    0  (1+ i))
3948          (n    (- (ash     1   dbl-mant-dig) 1)   (* 2 n))
3949          (want (- (ash-flo 1.0 dbl-mant-dig) 1.0) (* 2.0 want)))
3950         ((> i 100))
3951       (try-i i n want)))
3952
3953   ;; bit pattern: 1111....111011..1
3954   ;;              <-mantdig-> <-i->
3955   ;; This sort of value was incorrectly rounded upwards in Guile 1.6.4 when
3956   ;; i >= 11 (that's when the total is 65 or more bits).
3957   ;;
3958   (with-test-prefix "mantdig ones then 011..11, round down"
3959     (do ((i    0  (1+ i))
3960          (n    (- (ash     1   (+ 1 dbl-mant-dig)) 2)   (+ 1 (* 2 n)))
3961          (want (- (ash-flo 1.0 (+ 1 dbl-mant-dig)) 2.0) (* 2.0 want)))
3962         ((> i 100))
3963       (try-i i n want)))
3964
3965   ;; bit pattern: 1111....111100..001
3966   ;;              <-mantdig-> <--i->
3967   ;;
3968   (with-test-prefix "mantdig ones then 100..001, round up"
3969     (do ((i    0  (1+ i))
3970          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)  (1- (* 2 n)))
3971          (want    (ash-flo 1.0 (+ 2 dbl-mant-dig))     (* 2.0 want)))
3972         ((> i 100))
3973       (try-i i n want)))
3974
3975   ;; bit pattern: 1000....000100..001
3976   ;;              <-mantdig-> <--i->
3977   ;;
3978   (with-test-prefix "2^mantdig then 100..001, round up"
3979     (do ((i    0  (1+ i))
3980          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)   (1- (* 2 n)))
3981          (want (+ (ash-flo 1.0 (+ 2 dbl-mant-dig)) 4.0) (* 2.0 want)))
3982         ((> i 100))
3983       (try-i i n want)))
3984
3985   (pass-if "frac big/big"
3986     (let ((big (ash 1 256)))
3987       (= 1.0 (exact->inexact (/ (1+ big) big)))))
3988
3989   ;; In guile 1.8.0 this failed, giving back "nan" because it tried to
3990   ;; convert the num and den to doubles, resulting in infs.
3991   (pass-if "frac big/big, exceeding double"
3992     (let ((big (ash 1 4096)))
3993       (= 1.0 (exact->inexact (/ (1+ big) big))))))
3994
3995 ;;;
3996 ;;; expt
3997 ;;;
3998
3999 (with-test-prefix "expt"
4000   (pass-if (documented? expt))
4001
4002   ;;
4003   ;; expt no longer requires its first argument to be a scheme number,
4004   ;; for the sake of extensibility, and expt calls integer-expt for
4005   ;; integer powers.  To raise to a positive power, all that is required
4006   ;; is that it can be multiplied using `*'.  For negative powers we
4007   ;; must also be able to find the reciprocal.  If we try to raise #t to
4008   ;; any power other than 0 or 1 it may throw an exception, depending on
4009   ;; whether * has been defined for #t.  However, when raising to the 0
4010   ;; or 1 power, the first argument is not manipulated at all.
4011   ;;
4012   ;; (pass-if-exception "non-numeric base" exception:wrong-type-arg
4013   ;;                    (expt #t 0))
4014   ;;
4015
4016   (pass-if (eqv? 1 (expt 0 0)))
4017   (pass-if (eqv? 1 (expt 0.0 0)))
4018   (pass-if (eqv? 1.0 (expt 0 0.0)))
4019   (pass-if (eqv? 1.0 (expt 0.0 0.0)))
4020   (pass-if (real-nan? (expt 0 -1)))
4021   (pass-if (real-nan? (expt 0 -1.0)))
4022   (pass-if (real-nan? (expt 0.0 -1)))
4023   (pass-if (real-nan? (expt 0.0 -1.0)))
4024   (pass-if (eqv? 0 (expt 0 3)))
4025   (pass-if (= 0 (expt 0 4.0)))
4026   (pass-if (eqv? 0.0 (expt 0.0 5)))
4027   (pass-if (eqv? 0.0 (expt 0.0 6.0)))
4028   (pass-if (eqv? -2742638075.5 (expt -2742638075.5 1)))
4029   (pass-if (eqv? (* -2742638075.5 -2742638075.5)
4030                  (expt -2742638075.5 2)))
4031   (pass-if (eqv? 4.0 (expt -2.0 2.0)))
4032   (pass-if (eqv? -1/8 (expt -2 -3)))
4033   (pass-if (eqv? -0.125 (expt -2.0 -3)))
4034   (pass-if (eqv? -0.125 (expt -2 -3.0)))
4035   (pass-if (eqv? -0.125 (expt -2.0 -3.0)))
4036   (pass-if (eqv? 0.25 (expt 2.0 -2.0)))
4037   (pass-if (test-eqv? (* -1.0+0.0i 12398 12398) (expt +12398i 2.0)))
4038   (pass-if (eqv-loosely? +i (expt -1 0.5)))
4039   (pass-if (eqv-loosely? +i (expt -1 1/2)))
4040   (pass-if (eqv-loosely? 1.0+1.7320508075688i (expt -8 1/3)))
4041   (pass-if (eqv? +inf.0 (expt 2 +inf.0)))
4042   (pass-if (eqv? +inf.0 (expt 2.0 +inf.0)))
4043   (pass-if (eqv? 0.0 (expt 2 -inf.0)))
4044   (pass-if (eqv? 0.0 (expt 2.0 -inf.0))))
4045
4046
4047 ;;;
4048 ;;; sin
4049 ;;;
4050
4051 (with-test-prefix "sin"
4052   (pass-if (eqv? 0   (sin 0)))
4053   (pass-if (eqv? 0.0 (sin 0.0)))
4054   (pass-if (eqv-loosely? 1.0 (sin 1.57)))
4055   (pass-if (eqv-loosely? +1.175i (sin +i)))
4056   (pass-if (real-nan? (sin +nan.0)))
4057   (pass-if (real-nan? (sin +inf.0)))
4058   (pass-if (real-nan? (sin -inf.0))))
4059
4060 ;;;
4061 ;;; cos
4062 ;;;
4063
4064 (with-test-prefix "cos"
4065   (pass-if (eqv? 1   (cos 0)))
4066   (pass-if (eqv? 1.0 (cos 0.0)))
4067   (pass-if (eqv-loosely? 0.0 (cos 1.57)))
4068   (pass-if (eqv-loosely? 1.543 (cos +i)))
4069   (pass-if (real-nan? (cos +nan.0)))
4070   (pass-if (real-nan? (cos +inf.0)))
4071   (pass-if (real-nan? (cos -inf.0))))
4072
4073 ;;;
4074 ;;; tan
4075 ;;;
4076
4077 (with-test-prefix "tan"
4078   (pass-if (eqv? 0   (tan 0)))
4079   (pass-if (eqv? 0.0 (tan 0.0)))
4080   (pass-if (eqv-loosely? 1.0 (tan 0.785)))
4081   (pass-if (eqv-loosely? +0.76i (tan +i)))
4082   (pass-if (real-nan? (tan +nan.0)))
4083   (pass-if (real-nan? (tan +inf.0)))
4084   (pass-if (real-nan? (tan -inf.0))))
4085
4086 ;;;
4087 ;;; asin
4088 ;;;
4089
4090 (with-test-prefix "asin"
4091   (pass-if (complex-nan? (asin +nan.0)))
4092   (pass-if (eqv? 0 (asin 0)))
4093   (pass-if (eqv? 0.0 (asin 0.0))))
4094
4095 ;;;
4096 ;;; acos
4097 ;;;
4098
4099 (with-test-prefix "acos"
4100   (pass-if (complex-nan? (acos +nan.0)))
4101   (pass-if (eqv? 0 (acos 1)))
4102   (pass-if (eqv? 0.0 (acos 1.0))))
4103
4104 ;;;
4105 ;;; atan
4106 ;;;
4107 ;;; FIXME: add tests for two-argument atan
4108 ;;;
4109 (with-test-prefix "atan"
4110   (pass-if (real-nan? (atan +nan.0)))
4111   (pass-if (eqv? 0 (atan 0)))
4112   (pass-if (eqv? 0.0 (atan 0.0)))
4113   (pass-if (eqv-loosely?  1.57 (atan +inf.0)))
4114   (pass-if (eqv-loosely? -1.57 (atan -inf.0))))
4115
4116 ;;;
4117 ;;; sinh
4118 ;;;
4119
4120 (with-test-prefix "sinh"
4121   (pass-if (= 0 (sinh 0)))
4122   (pass-if (= 0.0 (sinh 0.0))))
4123
4124 ;;;
4125 ;;; cosh
4126 ;;;
4127
4128 (with-test-prefix "cosh"
4129   (pass-if (= 1 (cosh 0)))
4130   (pass-if (= 1.0 (cosh 0.0))))
4131
4132 ;;;
4133 ;;; tanh
4134 ;;;
4135
4136 (with-test-prefix "tanh"
4137   (pass-if (= 0 (tanh 0)))
4138   (pass-if (= 0.0 (tanh 0.0))))
4139
4140 ;;;
4141 ;;; asinh
4142 ;;;
4143
4144 (with-test-prefix "asinh"
4145   (pass-if (= 0 (asinh 0)))
4146   (pass-if (= 0.0 (asinh 0.0))))
4147
4148 ;;;
4149 ;;; acosh
4150 ;;;
4151
4152 (with-test-prefix "acosh"
4153   (pass-if (= 0 (acosh 1)))
4154   (pass-if (= 0.0 (acosh 1.0))))
4155
4156 ;;;
4157 ;;; atanh
4158 ;;;
4159
4160 (with-test-prefix "atanh"
4161   (pass-if (= 0 (atanh 0)))
4162   (pass-if (= 0.0 (atanh 0.0))))
4163
4164 ;;;
4165 ;;; make-rectangular
4166 ;;;
4167
4168 (with-test-prefix "make-rectangular"
4169   (pass-if (real?      (make-rectangular 5.0  0  )))
4170   (pass-if (not (real? (make-rectangular 5.0  0.0))))
4171   (pass-if (not (real? (make-rectangular 5.0 -0.0)))))
4172
4173 ;;;
4174 ;;; make-polar
4175 ;;;
4176
4177 (with-test-prefix "make-polar"
4178   (define pi 3.14159265358979323846)
4179   (define (almost= x y)
4180     (> 0.01 (magnitude (- x y))))
4181
4182   (pass-if (real?      (make-polar 0    1.0)))
4183   (pass-if (real?      (make-polar 5.0  0  )))
4184   (pass-if (not (real? (make-polar 5.0  0.0))))
4185   (pass-if (not (real? (make-polar 5.0 -0.0))))
4186
4187   (pass-if (eqv?  0 (make-polar  0 0)))
4188   (pass-if (eqv?  0 (make-polar  0 123.456)))
4189   (pass-if (eqv?  1 (make-polar  1 0)))
4190   (pass-if (eqv? -1 (make-polar -1 0)))
4191
4192   (pass-if (almost= 0+i (make-polar 1 (* 0.5 pi))))
4193   (pass-if (almost= -1  (make-polar 1 (* 1.0 pi))))
4194   (pass-if (almost= 0-i (make-polar 1 (* 1.5 pi))))
4195   (pass-if (almost= 1   (make-polar 1 (* 2.0 pi)))))
4196
4197 ;;;
4198 ;;; real-part
4199 ;;;
4200
4201 (with-test-prefix "real-part"
4202   (pass-if (documented? real-part))
4203   (pass-if (eqv? 5.0 (real-part  5.0)))
4204   (pass-if (eqv? 0.0 (real-part +5.0i)))
4205   (pass-if (eqv? 5   (real-part  5)))
4206   (pass-if (eqv? 1/5 (real-part  1/5)))
4207   (pass-if (eqv? (1+ fixnum-max) (real-part (1+ fixnum-max)))))
4208
4209 ;;;
4210 ;;; imag-part
4211 ;;;
4212
4213 (with-test-prefix "imag-part"
4214   (pass-if (documented? imag-part))
4215   (pass-if (eqv? 0   (imag-part  5.0)))
4216   (pass-if (eqv? 5.0 (imag-part +5.0i)))
4217   (pass-if (eqv? 0   (imag-part  5)))
4218   (pass-if (eqv? 0   (imag-part  1/5)))
4219   (pass-if (eqv? 0   (imag-part (1+ fixnum-max)))))
4220
4221 ;;;
4222 ;;; magnitude
4223 ;;;
4224
4225 (with-test-prefix "magnitude"
4226   (pass-if (documented? magnitude))
4227   (pass-if (= 0 (magnitude 0)))
4228   (pass-if (= 1 (magnitude 1)))
4229   (pass-if (= 1 (magnitude -1)))
4230   (pass-if (= 1 (magnitude 0+i)))
4231   (pass-if (= 1 (magnitude 0-i)))
4232   (pass-if (= 5 (magnitude 3+4i)))
4233   (pass-if (= 5 (magnitude 3-4i)))
4234   (pass-if (= 5 (magnitude -3+4i)))
4235   (pass-if (= 5 (magnitude -3-4i))))
4236
4237 ;;;
4238 ;;; angle
4239 ;;;
4240
4241 (with-test-prefix "angle"
4242   (define pi 3.14159265358979323846)
4243   (define (almost= x y)
4244     (> 0.01 (magnitude (- x y))))
4245
4246   (pass-if (documented? angle))
4247
4248   (pass-if "inum +ve"   (=        0 (angle 1)))
4249   (pass-if "inum -ve"   (almost= pi (angle -1)))
4250
4251   (pass-if "bignum +ve" (=        0 (angle (1+ fixnum-max))))
4252   (pass-if "bignum -ve" (almost= pi (angle (1- fixnum-min))))
4253
4254   (pass-if "flonum +ve" (=        0 (angle 1.5)))
4255   (pass-if "flonum -ve" (almost= pi (angle -1.5))))
4256
4257 ;;;
4258 ;;; inexact->exact
4259 ;;;
4260
4261 (with-test-prefix "inexact->exact"
4262   (pass-if (documented? inexact->exact))
4263
4264   (pass-if-exception "+inf" exception:out-of-range
4265     (inexact->exact +inf.0))
4266
4267   (pass-if-exception "-inf" exception:out-of-range
4268     (inexact->exact -inf.0))
4269
4270   (pass-if-exception "nan" exception:out-of-range
4271     (inexact->exact +nan.0))
4272
4273   (with-test-prefix "2.0**i to exact and back"
4274     (do ((i 0   (1+ i))
4275          (n 1.0 (* 2.0 n)))
4276         ((> i 100))
4277       (pass-if (list i n)
4278         (= n (inexact->exact (exact->inexact n)))))))
4279
4280 ;;;
4281 ;;; integer-expt
4282 ;;;
4283
4284 (with-test-prefix "integer-expt"
4285   (pass-if (documented? integer-expt))
4286
4287   (pass-if-exception "2^+inf" exception:wrong-type-arg
4288     (integer-expt 2 +inf.0))
4289   (pass-if-exception "2^-inf" exception:wrong-type-arg
4290     (integer-expt 2 -inf.0))
4291   (pass-if-exception "2^nan" exception:wrong-type-arg
4292     (integer-expt 2 +nan.0))
4293
4294   (pass-if (eqv? 1 (integer-expt 0 0)))
4295   (pass-if (eqv? 1 (integer-expt 0.0 0)))
4296   (pass-if (real-nan? (integer-expt 0 -1)))
4297   (pass-if (real-nan? (integer-expt 0.0 -1)))
4298   (pass-if (eqv? 0 (integer-expt 0 3)))
4299   (pass-if (eqv? 0.0 (integer-expt 0.0 5)))
4300   (pass-if (eqv? -2742638075.5 (integer-expt -2742638075.5 1)))
4301   (pass-if (eqv? (* -2742638075.5 -2742638075.5)
4302                  (integer-expt -2742638075.5 2)))
4303   (pass-if (eqv? 4.0 (integer-expt -2.0 2)))
4304   (pass-if (eqv? -1/8 (integer-expt -2 -3)))
4305   (pass-if (eqv? -0.125 (integer-expt -2.0 -3)))
4306   (pass-if (eqv? 0.25 (integer-expt 2.0 -2)))
4307   (pass-if (test-eqv? (* -1.0+0.0i 12398 12398) (integer-expt +12398.0i 2))))
4308
4309
4310 ;;;
4311 ;;; integer-length
4312 ;;;
4313
4314 (with-test-prefix "integer-length"
4315   (pass-if (documented? integer-length))
4316
4317   (with-test-prefix "-2^i, ...11100..00"
4318     (do ((n -1 (ash n 1))
4319          (i 0  (1+ i)))
4320         ((> i 256))
4321       (pass-if (list n "expect" i)
4322         (= i (integer-length n)))))
4323
4324   (with-test-prefix "-2^i+1 ...11100..01"
4325     (do ((n -3 (logxor 3 (ash n 1)))
4326          (i 2  (1+ i)))
4327         ((> i 256))
4328       (pass-if n
4329         (= i (integer-length n)))))
4330
4331   (with-test-prefix "-2^i-1 ...111011..11"
4332     (do ((n -2 (1+ (ash n 1)))
4333          (i 1  (1+ i)))
4334         ((> i 256))
4335       (pass-if n
4336         (= i (integer-length n))))))
4337
4338 ;;;
4339 ;;; log
4340 ;;;
4341
4342 (with-test-prefix "log"
4343   (pass-if (documented? log))
4344
4345   (pass-if-exception "no args" exception:wrong-num-args
4346     (log))
4347   (pass-if-exception "two args" exception:wrong-num-args
4348     (log 123 456))
4349   (pass-if-exception "(log 0)" exception:numerical-overflow
4350     (log 0))
4351
4352   (pass-if (test-eqv? -inf.0 (log 0.0)))
4353   (pass-if (test-eqv? +inf.0 (log +inf.0)))
4354   (pass-if (test-eqv? -inf.0+3.14159265358979i (log -0.0)))
4355   (pass-if (test-eqv? +inf.0+3.14159265358979i (log -inf.0)))
4356   (pass-if (test-eqv?  0.0 (log 1  )))
4357   (pass-if (test-eqv?  0.0 (log 1.0)))
4358   (pass-if (test-eqv?  1.0 (log const-e)))
4359   (pass-if (test-eqv?  2.0 (log const-e^2)))
4360   (pass-if (test-eqv? -1.0 (log const-1/e)))
4361   (pass-if (test-eqv? -1.0+3.14159265358979i (log (- const-1/e))))
4362   (pass-if (test-eqv?  2.30258509299405 (log 10)))
4363   (pass-if (test-eqv?  2.30258509299405+3.14159265358979i (log -10)))
4364
4365   (pass-if (test-eqv?  1.0+0.0i (log (+ const-e +0.0i))))
4366   (pass-if (test-eqv?  1.0-0.0i (log (+ const-e -0.0i))))
4367
4368   (pass-if (eqv-loosely?  230258.509299405 (log (expt 10  100000))))
4369   (pass-if (eqv-loosely? -230258.509299405 (log (expt 10 -100000))))
4370   (pass-if (eqv-loosely?  230257.410687116 (log (/ (expt 10 100000) 3))))
4371   (pass-if (eqv-loosely?  230258.509299405+3.14159265358979i
4372                           (log (- (expt 10 100000)))))
4373   (pass-if (eqv-loosely? -230258.509299405+3.14159265358979i
4374                           (log (- (expt 10 -100000)))))
4375   (pass-if (eqv-loosely?  230257.410687116+3.14159265358979i
4376                           (log (- (/ (expt 10 100000) 3)))))
4377   (pass-if (test-eqv?  3.05493636349961e-151
4378                        (log (/ (1+ (expt 2 500)) (expt 2 500)))))
4379
4380   (pass-if (eqv-loosely? 1.0+1.57079i (log 0+2.71828i)))
4381   (pass-if (eqv-loosely? 1.0-1.57079i (log 0-2.71828i)))
4382
4383   (pass-if (eqv-loosely? 0.0+3.14159i (log -1.0)))
4384   (pass-if (eqv-loosely? 1.0+3.14159i (log -2.71828)))
4385   (pass-if (eqv-loosely? 2.0+3.14159i (log (* -2.71828 2.71828)))))
4386
4387 ;;;
4388 ;;; log10
4389 ;;;
4390
4391 (with-test-prefix "log10"
4392   (pass-if (documented? log10))
4393
4394   (pass-if-exception "no args" exception:wrong-num-args
4395     (log10))
4396   (pass-if-exception "two args" exception:wrong-num-args
4397     (log10 123 456))
4398   (pass-if-exception "(log10 0)" exception:numerical-overflow
4399     (log10 0))
4400
4401   (pass-if (test-eqv? -inf.0 (log10 0.0)))
4402   (pass-if (test-eqv? +inf.0 (log10 +inf.0)))
4403   (pass-if (test-eqv? -inf.0+1.36437635384184i (log10 -0.0)))
4404   (pass-if (test-eqv? +inf.0+1.36437635384184i (log10 -inf.0)))
4405   (pass-if (test-eqv?  0.0 (log10   1  )))
4406   (pass-if (test-eqv?  0.0 (log10   1.0)))
4407   (pass-if (test-eqv?  1.0 (log10  10  )))
4408   (pass-if (test-eqv?  1.0 (log10  10.0)))
4409   (pass-if (test-eqv?  2.0 (log10 100.0)))
4410   (pass-if (test-eqv? -1.0 (log10   0.1)))
4411   (pass-if (test-eqv? -1.0+1.36437635384184i (log10  -0.1)))
4412   (pass-if (test-eqv?  1.0+1.36437635384184i (log10 -10  )))
4413
4414   (pass-if (test-eqv?  1.0+0.0i (log10  10.0+0.0i)))
4415   (pass-if (test-eqv?  1.0-0.0i (log10  10.0-0.0i)))
4416
4417   (pass-if (eqv-loosely?  100000.0 (log10 (expt 10  100000))))
4418   (pass-if (eqv-loosely? -100000.0 (log10 (expt 10 -100000))))
4419   (pass-if (eqv-loosely?   99999.5228787453 (log10 (/ (expt 10 100000) 3))))
4420   (pass-if (eqv-loosely?  100000.0+1.36437635384184i
4421                           (log10 (- (expt 10 100000)))))
4422   (pass-if (eqv-loosely? -100000.0+1.36437635384184i
4423                           (log10 (- (expt 10 -100000)))))
4424   (pass-if (eqv-loosely?   99999.5228787453+1.36437635384184i
4425                           (log10 (- (/ (expt 10 100000) 3)))))
4426   (pass-if (test-eqv?  1.32674200523347e-151
4427                        (log10 (/ (1+ (expt 2 500)) (expt 2 500)))))
4428
4429   (pass-if (eqv-loosely? 1.0+0.68218i (log10 0+10.0i)))
4430   (pass-if (eqv-loosely? 1.0-0.68218i (log10 0-10.0i)))
4431
4432   (pass-if (eqv-loosely? 0.0+1.36437i (log10   -1)))
4433   (pass-if (eqv-loosely? 1.0+1.36437i (log10  -10)))
4434   (pass-if (eqv-loosely? 2.0+1.36437i (log10 -100))))
4435
4436 ;;;
4437 ;;; logbit?
4438 ;;;
4439
4440 (with-test-prefix "logbit?"
4441   (pass-if (documented? logbit?))
4442
4443   (pass-if (eq? #f (logbit?  0 0)))
4444   (pass-if (eq? #f (logbit?  1 0)))
4445   (pass-if (eq? #f (logbit? 31 0)))
4446   (pass-if (eq? #f (logbit? 32 0)))
4447   (pass-if (eq? #f (logbit? 33 0)))
4448   (pass-if (eq? #f (logbit? 63 0)))
4449   (pass-if (eq? #f (logbit? 64 0)))
4450   (pass-if (eq? #f (logbit? 65 0)))
4451
4452   ;; prior to guile 1.6.5, testing bit 32, 64 etc of value 1 would wrap
4453   ;; around and return #t where it ought to be #f
4454   (pass-if (eq? #t (logbit?  0 1)))
4455   (pass-if (eq? #f (logbit?  1 1)))
4456   (pass-if (eq? #f (logbit? 31 1)))
4457   (pass-if (eq? #f (logbit? 32 1)))
4458   (pass-if (eq? #f (logbit? 33 1)))
4459   (pass-if (eq? #f (logbit? 63 1)))
4460   (pass-if (eq? #f (logbit? 64 1)))
4461   (pass-if (eq? #f (logbit? 65 1)))
4462   (pass-if (eq? #f (logbit? 128 1)))
4463
4464   (pass-if (eq? #t (logbit?  0 -1)))
4465   (pass-if (eq? #t (logbit?  1 -1)))
4466   (pass-if (eq? #t (logbit? 31 -1)))
4467   (pass-if (eq? #t (logbit? 32 -1)))
4468   (pass-if (eq? #t (logbit? 33 -1)))
4469   (pass-if (eq? #t (logbit? 63 -1)))
4470   (pass-if (eq? #t (logbit? 64 -1)))
4471   (pass-if (eq? #t (logbit? 65 -1))))
4472
4473 ;;;
4474 ;;; logcount
4475 ;;;
4476
4477 (with-test-prefix "logcount"
4478   (pass-if (documented? logcount))
4479
4480   (with-test-prefix "-2^i, meaning ...11100..00"
4481     (do ((n -1 (ash n 1))
4482          (i 0  (1+ i)))
4483         ((> i 256))
4484       (pass-if n
4485         (= i (logcount n)))))
4486
4487   (with-test-prefix "2^i"
4488     (do ((n 1 (ash n 1))
4489          (i 0  (1+ i)))
4490         ((> i 256))
4491       (pass-if n
4492         (= 1 (logcount n)))))
4493
4494   (with-test-prefix "2^i-1"
4495     (do ((n 0 (1+ (ash n 1)))
4496          (i 0  (1+ i)))
4497         ((> i 256))
4498       (pass-if n
4499         (= i (logcount n))))))
4500
4501 ;;;
4502 ;;; logior
4503 ;;;
4504
4505 (with-test-prefix "logior"
4506   (pass-if (documented? logior))
4507
4508   (pass-if (eqv? -1 (logior (ash -1 1) 1)))
4509
4510   ;; check that bignum or bignum+inum args will reduce to an inum
4511   (let ()
4512     (define (test x y)
4513       (pass-if (list x y '=> -1)
4514         (eqv? -1 (logior x y)))
4515       (pass-if (list y x '=> -1)
4516         (eqv? -1 (logior y x))))
4517     (test (ash -1 8) #xFF)
4518     (test (ash -1 28) #x0FFFFFFF)
4519     (test (ash -1 29) #x1FFFFFFF)
4520     (test (ash -1 30) #x3FFFFFFF)
4521     (test (ash -1 31) #x7FFFFFFF)
4522     (test (ash -1 32) #xFFFFFFFF)
4523     (test (ash -1 33) #x1FFFFFFFF)
4524     (test (ash -1 60) #x0FFFFFFFFFFFFFFF)
4525     (test (ash -1 61) #x1FFFFFFFFFFFFFFF)
4526     (test (ash -1 62) #x3FFFFFFFFFFFFFFF)
4527     (test (ash -1 63) #x7FFFFFFFFFFFFFFF)
4528     (test (ash -1 64) #xFFFFFFFFFFFFFFFF)
4529     (test (ash -1 65) #x1FFFFFFFFFFFFFFFF)
4530     (test (ash -1 128) #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
4531
4532 ;;;
4533 ;;; lognot
4534 ;;;
4535
4536 (with-test-prefix "lognot"
4537   (pass-if (documented? lognot))
4538
4539   (pass-if (= -1 (lognot 0)))
4540   (pass-if (= 0  (lognot -1)))
4541   (pass-if (= -2 (lognot 1)))
4542   (pass-if (= 1  (lognot -2)))
4543
4544   (pass-if (= #x-100000000000000000000000000000000
4545               (lognot #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
4546   (pass-if (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
4547               (lognot #x-100000000000000000000000000000000))))
4548
4549 ;;;
4550 ;;; exact-integer-sqrt
4551 ;;;
4552
4553 (with-test-prefix "exact-integer-sqrt"
4554   (define (non-negative-exact-integer? k)
4555     (and (integer? k) (exact? k) (>= k 0)))
4556
4557   (define (test k)
4558     (pass-if k (let-values (((s r) (exact-integer-sqrt k)))
4559                  (and (non-negative-exact-integer? s)
4560                       (non-negative-exact-integer? r)
4561                       (= k (+ r (* s s)))
4562                       (< k (* (1+ s) (1+ s)))))))
4563
4564   (define (test-wrong-type-arg k)
4565     (pass-if-exception k exception:wrong-type-arg
4566                        (let-values (((s r) (exact-integer-sqrt k)))
4567                          #t)))
4568
4569   (pass-if (documented? exact-integer-sqrt))
4570
4571   (pass-if-exception "no args" exception:wrong-num-args
4572     (exact-integer-sqrt))
4573   (pass-if-exception "two args" exception:wrong-num-args
4574     (exact-integer-sqrt 123 456))
4575
4576   (test 0)
4577   (test 1)
4578   (test 9)
4579   (test 10)
4580   (test fixnum-max)
4581   (test (1+ fixnum-max))
4582   (test (* fixnum-max fixnum-max))
4583   (test (+ 1 (* fixnum-max fixnum-max)))
4584   (test (expt 10 100))
4585   (test (+ 3 (expt 10 100)))
4586
4587   (test-wrong-type-arg -1)
4588   (test-wrong-type-arg 1/9)
4589   (test-wrong-type-arg fixnum-min)
4590   (test-wrong-type-arg (1- fixnum-min))
4591   (test-wrong-type-arg 1.0)
4592   (test-wrong-type-arg 1.5)
4593   (test-wrong-type-arg "foo")
4594   (test-wrong-type-arg 'foo))
4595
4596
4597 ;;;
4598 ;;; sqrt
4599 ;;;
4600
4601 (with-test-prefix "sqrt"
4602   (pass-if (documented? sqrt))
4603
4604   (pass-if-exception "no args" exception:wrong-num-args
4605     (sqrt))
4606   (pass-if-exception "two args" exception:wrong-num-args
4607     (sqrt 123 456))
4608
4609   (pass-if (eqv? 0.0 (sqrt 0)))
4610   (pass-if (eqv? 0.0 (sqrt 0.0)))
4611   (pass-if (eqv? 1.0 (sqrt 1.0)))
4612   (pass-if (eqv-loosely? 2.0   (sqrt 4.0)))
4613   (pass-if (eqv-loosely? 31.62 (sqrt 1000.0)))
4614
4615   (pass-if (eqv? +1.0i (sqrt -1.0)))
4616   (pass-if (eqv-loosely? +2.0i   (sqrt -4.0)))
4617   (pass-if (eqv-loosely? +31.62i (sqrt -1000.0)))
4618
4619   (pass-if "+i swings back to 45deg angle"
4620     (eqv-loosely? +0.7071+0.7071i (sqrt +1.0i)))
4621
4622   ;; Note: glibc 2.3 csqrt() had a bug affecting this test case, so if it
4623   ;; fails check whether that's the cause (there's a configure test to
4624   ;; reject it, but when cross-compiling we assume the C library is ok).
4625   (pass-if "-100i swings back to 45deg down"
4626     (eqv-loosely? +7.071-7.071i (sqrt -100.0i))))
4627
4628
4629 ;;;
4630 ;;; Tests for number-theoretic division operators:
4631 ;;;
4632 ;;; euclidean/
4633 ;;; euclidean-quotient
4634 ;;; euclidean-remainder
4635 ;;; floor/
4636 ;;; floor-quotient
4637 ;;; floor-remainder
4638 ;;; ceiling/
4639 ;;; ceiling-quotient
4640 ;;; ceiling-remainder
4641 ;;; truncate/
4642 ;;; truncate-quotient
4643 ;;; truncate-remainder
4644 ;;; centered/
4645 ;;; centered-quotient
4646 ;;; centered-remainder
4647 ;;; round/
4648 ;;; round-quotient
4649 ;;; round-remainder
4650 ;;;
4651
4652 (with-test-prefix "Number-theoretic division"
4653
4654   ;; Tests that (lo <1 x <2 hi),
4655   ;; but allowing for imprecision
4656   ;; if x is inexact.
4657   (define (test-within-range? lo <1 x <2 hi)
4658     (if (exact? x)
4659         (and (<1 lo x) (<2 x hi))
4660         (let ((lo (- lo test-epsilon))
4661               (hi (+ hi test-epsilon)))
4662           (<= lo x hi))))
4663
4664   (define (valid-euclidean-answer? x y q r)
4665     (and (eq? (exact? q)
4666               (exact? r)
4667               (and (exact? x) (exact? y)))
4668          (test-eqv? r (- x (* q y)))
4669          (if (and (finite? x) (finite? y))
4670              (and (integer? q)
4671                   (test-within-range? 0 <= r < (abs y)))
4672              (test-eqv? q (/ x y)))))
4673
4674   (define (valid-floor-answer? x y q r)
4675     (and (eq? (exact? q)
4676               (exact? r)
4677               (and (exact? x) (exact? y)))
4678          (test-eqv? r (- x (* q y)))
4679          (if (and (finite? x) (finite? y))
4680              (and (integer? q)
4681                   (if (> y 0)
4682                       (test-within-range? 0 <= r < y)
4683                       (test-within-range? y < r <= 0)))
4684              (test-eqv? q (/ x y)))))
4685
4686   (define (valid-ceiling-answer? x y q r)
4687     (and (eq? (exact? q)
4688               (exact? r)
4689               (and (exact? x) (exact? y)))
4690          (test-eqv? r (- x (* q y)))
4691          (if (and (finite? x) (finite? y))
4692              (and (integer? q)
4693                   (if (> y 0)
4694                       (test-within-range? (- y) < r <= 0)
4695                       (test-within-range?    0 <= r < (- y))))
4696              (test-eqv? q (/ x y)))))
4697
4698   (define (valid-truncate-answer? x y q r)
4699     (and (eq? (exact? q)
4700               (exact? r)
4701               (and (exact? x) (exact? y)))
4702          (test-eqv? r (- x (* q y)))
4703          (if (and (finite? x) (finite? y))
4704              (and (integer? q)
4705                   (if (> x 0)
4706                       (test-within-range?          0 <= r < (abs y))
4707                       (test-within-range? (- (abs y)) < r <= 0)))
4708              (test-eqv? q (/ x y)))))
4709
4710   (define (valid-centered-answer? x y q r)
4711     (and (eq? (exact? q)
4712               (exact? r)
4713               (and (exact? x) (exact? y)))
4714          (test-eqv? r (- x (* q y)))
4715          (if (and (finite? x) (finite? y))
4716              (and (integer? q)
4717                   (test-within-range?
4718                    (* -1/2 (abs y)) <= r < (* +1/2 (abs y))))
4719              (test-eqv? q (/ x y)))))
4720
4721   (define (valid-round-answer? x y q r)
4722     (and (eq? (exact? q)
4723               (exact? r)
4724               (and (exact? x) (exact? y)))
4725          (test-eqv? r (- x (* q y)))
4726          (if (and (finite? x) (finite? y))
4727              (and (integer? q)
4728                   (let ((ay/2 (/ (abs y) 2)))
4729                     (if (even? q)
4730                         (test-within-range? (- ay/2) <= r <= ay/2)
4731                         (test-within-range? (- ay/2) <  r <  ay/2))))
4732              (test-eqv? q (/ x y)))))
4733
4734   (define (for lsts f) (apply for-each f lsts))
4735
4736   (define big (expt 10 (1+ (inexact->exact (ceiling (log10 fixnum-max))))))
4737
4738   (define (run-division-tests quo+rem quo rem valid-answer?)
4739     (define (test n d)
4740       (run-test (list n d) #t
4741                 (lambda ()
4742                   (let-values (((q r) (quo+rem n d)))
4743                     (and (test-eqv? q (quo n d))
4744                          (test-eqv? r (rem n d))
4745                          (valid-answer? n d q r))))))
4746     (define (test+/- n d)
4747       (test n    d )
4748       (test n (- d))
4749       (cond ((not (zero? n))
4750              (test (- n)    d )
4751              (test (- n) (- d)))))
4752
4753     (define (test-for-exception n d exception)
4754       (let ((name (list n d)))
4755         (pass-if-exception name exception (quo+rem n d))
4756         (pass-if-exception name exception (quo n d))
4757         (pass-if-exception name exception (rem n d))))
4758
4759     (run-test "documented?" #t
4760               (lambda ()
4761                 (and (documented? quo+rem)
4762                      (documented? quo)
4763                      (documented? rem))))
4764
4765     (with-test-prefix "inum / inum"
4766       (with-test-prefix "fixnum-min / -1"
4767         (test fixnum-min -1))
4768       (for '((1 2 5 10))  ;; denominators
4769            (lambda (d)
4770              (for '((0 1 2 5 10))  ;; multiples
4771                   (lambda (m)
4772                     (for '((-2 -1 0 1 2 3 4 5 7 10
4773                                12 15 16 19 20))  ;; offsets
4774                          (lambda (b)
4775                            (test+/- (+ b (* m d))
4776                                     d))))))))
4777
4778     (with-test-prefix "inum / big"
4779       (with-test-prefix "fixnum-min / -fixnum-min"
4780         (test fixnum-min (- fixnum-min)))
4781       (with-test-prefix "fixnum-max / (2*fixnum-max)"
4782         (test+/- fixnum-max (* 2 fixnum-max)))
4783       (for `((0 1 2 10 ,(1- fixnum-max) ,fixnum-max))
4784            (lambda (n)
4785              (test    n  (1+ fixnum-max))
4786              (test (- n) (1+ fixnum-max))
4787              (test    n  (1- fixnum-min))
4788              (test (- n) (1- fixnum-min)))))
4789
4790     (with-test-prefix "big / inum"
4791       (with-test-prefix "-fixnum-min / fixnum-min"
4792         (test (- fixnum-min) fixnum-min))
4793       (for '((1 4 5 10))  ;; denominators
4794            (lambda (d)
4795              (for `((1 2 5 ,@(if (even? d)
4796                                  '(1/2 3/2 5/2)
4797                                  '())))  ;; multiples
4798                   (lambda (m)
4799                     (for '((-2 -1 0 1 2))  ;; offsets
4800                          (lambda (b)
4801                            (test+/- (+ b (* m d big))
4802                                     d))))))))
4803
4804     (with-test-prefix "big / big"
4805       (for `((,big ,(1+ big)))  ;; denominators
4806            (lambda (d)
4807              (for `((1 2 5 ,@(if (even? d)
4808                                  '(1/2 3/2 5/2)
4809                                  '())))  ;; multiples
4810                   (lambda (m)
4811                     (for '((-2 -1 0 1 2))  ;; offsets
4812                          (lambda (b)
4813                            (test+/- (+ b (* m d))
4814                                     d))))))))
4815
4816     (with-test-prefix "inexact"
4817       (for '((0.5 1.5 2.25 5.75))  ;; denominators
4818            (lambda (d)
4819              (for '((0 1 2 5 1/2 3/2 5/2))  ;; multiples
4820                   (lambda (m)
4821                     (for '((-2 -1 0 1 2))  ;; offsets
4822                          (lambda (b)
4823                            (test+/- (+ b (* m d))
4824                                     d))))))))
4825
4826     (with-test-prefix "fractions"
4827       (for '((1/10 16/3 10/7))  ;; denominators
4828            (lambda (d)
4829              (for '((0 1 2 5 1/2 3/2 5/2))  ;; multiples
4830                   (lambda (m)
4831                     (for '((-2/9 -1/11 0 1/3 2/3))  ;; offsets
4832                          (lambda (b)
4833                            (test+/- (+ b (* m d))
4834                                     d))))))))
4835
4836     (with-test-prefix "mixed types"
4837       (for `((10 ,big 12.0 10/7 +inf.0 -inf.0 +nan.0))  ;; denominators
4838            (lambda (d)
4839              (for `((25 ,(* 3/2 big) 130.0 15/7
4840                         0 0.0 -0.0 +inf.0 -inf.0 +nan.0))  ;; numerators
4841                   (lambda (n)
4842                     (test+/- n d))))))
4843
4844     (with-test-prefix "divide by zero"
4845       (for `((0 0.0 +0.0))  ;; denominators
4846            (lambda (d)
4847              (for `((15 ,(* 3/2 big) 18.0 33/7
4848                         0 0.0 -0.0 +inf.0 -inf.0 +nan.0))  ;; numerators
4849                   (lambda (n)
4850                     (test-for-exception
4851                      n d exception:numerical-overflow)))))))
4852
4853   (with-test-prefix "euclidean/"
4854     (run-division-tests euclidean/
4855                         euclidean-quotient
4856                         euclidean-remainder
4857                         valid-euclidean-answer?))
4858
4859   (with-test-prefix "floor/"
4860     (run-division-tests floor/
4861                         floor-quotient
4862                         floor-remainder
4863                         valid-floor-answer?))
4864
4865   (with-test-prefix "ceiling/"
4866     (run-division-tests ceiling/
4867                         ceiling-quotient
4868                         ceiling-remainder
4869                         valid-ceiling-answer?))
4870
4871   (with-test-prefix "truncate/"
4872     (run-division-tests truncate/
4873                         truncate-quotient
4874                         truncate-remainder
4875                         valid-truncate-answer?))
4876
4877   (with-test-prefix "centered/"
4878     (run-division-tests centered/
4879                         centered-quotient
4880                         centered-remainder
4881                         valid-centered-answer?))
4882
4883   (with-test-prefix "round/"
4884     (run-division-tests round/
4885                         round-quotient
4886                         round-remainder
4887                         valid-round-answer?)))