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
  22 ;;;
  23 ;;; miscellaneous
  24 ;;;
  25
  26 (define exception:numerical-overflow
  27   (cons 'numerical-overflow "^Numerical overflow"))
  28
  29 (define (documented? object)
  30   (not (not (object-documentation object))))
  31
  32 (define fixnum-bit
  33   (inexact->exact (+ (/ (log (+ most-positive-fixnum 1)) (log 2)) 1)))
  34
  35 (define fixnum-min most-negative-fixnum)
  36 (define fixnum-max most-positive-fixnum)
  37
  38 ;; Divine the number of bits in the mantissa of a flonum.
  39 ;; We look for when 2.0^i+1.0 gets rounded, ie. the difference between that
  40 ;; value and 2.0^k is not 1.0.
  41 ;; Of course this assumes flonums have a fixed precision mantissa, but
  42 ;; that's the case now and probably into the forseeable future.
  43 ;; On an IEEE system, which means pretty much everywhere, the value here is
  44 ;; the usual 53.
  45 ;;
  46 (define dbl-mant-dig
  47   (let more ((i 1)
  48              (d 2.0))
  49     (if (> i 1024)
  50         (error "Oops, cannot determine number of bits in mantissa of inexact"))
  51     (let* ((sum  (+ 1.0 d))
  52            (diff (- sum d)))
  53       (if (= diff 1.0)
  54           (more (1+ i) (* 2.0 d))
  55           i))))
  56
  57 ;; like ash, but working on a flonum
  58 (define (ash-flo x n)
  59   (while (> n 0)
  60     (set! x (* 2.0 x))
  61     (set! n (1- n)))
  62   (while (< n 0)
  63     (set! x (* 0.5 x))
  64     (set! n (1+ n)))
  65   x)
  66
  67 ;; `quotient' but rounded towards -infinity, like `modulo' or `ash' do
  68 ;; note only positive D supported (that's all that's currently required)
  69 (define-public (quotient-floor n d)
  70   (if (negative? n)
  71       (quotient (- n d -1) d)  ;; neg/pos
  72       (quotient n d)))         ;; pos/pos
  73
  74 ;; return true of X is in the range LO to HI, inclusive
  75 (define (within-range? lo hi x)
  76   (and (>= x (min lo hi))
  77        (<= x (max lo hi))))
  78
  79 ;; return true if GOT is within +/- 0.01 of GOT
  80 ;; for a complex number both real and imaginary parts must be in that range
  81 (define (eqv-loosely? want got)
  82   (and (within-range? (- (real-part want) 0.01)
  83                       (+ (real-part want) 0.01)
  84                       (real-part got))
  85        (within-range? (- (imag-part want) 0.01)
  86                       (+ (imag-part want) 0.01)
  87                       (imag-part got))))
  88
  89 ;; return true if OBJ is negative infinity
  90 (define (negative-infinity? obj)
  91   (and (real? obj)
  92        (negative? obj)
  93        (inf? obj)))
  94
  95 (define const-e    2.7182818284590452354)
  96 (define const-e^2  7.3890560989306502274)
  97 (define const-1/e  0.3678794411714423215)
  98
  99
 100 ;;;
 101 ;;; 1+
 102 ;;;
 103
 104 (with-test-prefix/c&e "1+"
 105
 106   (pass-if "documented?"
 107     (documented? 1+))
 108
 109   (pass-if "0"   (eqv? 1 (1+ 0)))
 110   (pass-if "-1"   (eqv? 0 (1+ -1)))
 111   (pass-if "100"  (eqv? 101 (1+ 100)))
 112   (pass-if "-100" (eqv? -99 (1+ -100)))
 113
 114   ;; The maximum fixnum on a 32-bit architecture: 2^29 - 1.
 115   (pass-if "1+ fixnum = bignum (32-bit)"
 116     (eqv? 536870912 (1+ 536870911)))
 117
 118   ;; The maximum fixnum on a 64-bit architecture: 2^61 - 1.
 119   (pass-if "1+ fixnum = bignum (64-bit)"
 120     (eqv? 2305843009213693952 (1+ 2305843009213693951))))
 121
 122 ;;;
 123 ;;; 1-
 124 ;;;
 125
 126 (with-test-prefix/c&e "1-"
 127
 128   (pass-if "documented?"
 129     (documented? 1-))
 130
 131   (pass-if "0"    (eqv? -1 (1- 0)))
 132   (pass-if "1"    (eqv? 0 (1- 1)))
 133   (pass-if "100"  (eqv? 99 (1- 100)))
 134   (pass-if "-100" (eqv? -101 (1- -100)))
 135
 136   ;; The minimum fixnum on a 32-bit architecture: -2^29.
 137   (pass-if "1- fixnum = bignum (32-bit)"
 138     (eqv? -536870913 (1- -536870912)))
 139
 140   ;; The minimum fixnum on a 64-bit architecture: -2^61.
 141   (pass-if "1- fixnum = bignum (64-bit)"
 142     (eqv? -2305843009213693953 (1- -2305843009213693952))))
 143
 144 ;;;
 145 ;;; ash
 146 ;;;
 147
 148 (with-test-prefix "ash"
 149
 150   (pass-if "documented?"
 151     (documented? ash))
 152
 153   (pass-if (eqv? 0 (ash 0 0)))
 154   (pass-if (eqv? 0 (ash 0 1)))
 155   (pass-if (eqv? 0 (ash 0 1000)))
 156   (pass-if (eqv? 0 (ash 0 -1)))
 157   (pass-if (eqv? 0 (ash 0 -1000)))
 158
 159   (pass-if (eqv? 1 (ash 1 0)))
 160   (pass-if (eqv? 2 (ash 1 1)))
 161   (pass-if (eqv? 340282366920938463463374607431768211456 (ash 1 128)))
 162   (pass-if (eqv? 0 (ash 1 -1)))
 163   (pass-if (eqv? 0 (ash 1 -1000)))
 164
 165   (pass-if (eqv? -1 (ash -1 0)))
 166   (pass-if (eqv? -2 (ash -1 1)))
 167   (pass-if (eqv? -340282366920938463463374607431768211456 (ash -1 128)))
 168   (pass-if (eqv? -1 (ash -1 -1)))
 169   (pass-if (eqv? -1 (ash -1 -1000)))
 170
 171   (pass-if (eqv? -3 (ash -3 0)))
 172   (pass-if (eqv? -6 (ash -3 1)))
 173   (pass-if (eqv? -1020847100762815390390123822295304634368 (ash -3 128)))
 174   (pass-if (eqv? -2 (ash -3 -1)))
 175   (pass-if (eqv? -1 (ash -3 -1000)))
 176
 177   (pass-if (eqv? -6 (ash -23 -2)))
 178
 179   (pass-if (eqv? most-positive-fixnum       (ash most-positive-fixnum 0)))
 180   (pass-if (eqv? (* 2 most-positive-fixnum) (ash most-positive-fixnum 1)))
 181   (pass-if (eqv? (* 4 most-positive-fixnum) (ash most-positive-fixnum 2)))
 182   (pass-if
 183       (eqv? (* most-positive-fixnum 340282366920938463463374607431768211456)
 184             (ash most-positive-fixnum 128)))
 185   (pass-if (eqv? (quotient most-positive-fixnum 2)
 186                  (ash most-positive-fixnum -1)))
 187   (pass-if (eqv? 0 (ash most-positive-fixnum -1000)))
 188
 189   (let ((mpf4 (quotient most-positive-fixnum 4)))
 190     (pass-if (eqv? (* 2 mpf4) (ash mpf4 1)))
 191     (pass-if (eqv? (* 4 mpf4) (ash mpf4 2)))
 192     (pass-if (eqv? (* 8 mpf4) (ash mpf4 3))))
 193
 194   (pass-if (eqv? most-negative-fixnum       (ash most-negative-fixnum 0)))
 195   (pass-if (eqv? (* 2 most-negative-fixnum) (ash most-negative-fixnum 1)))
 196   (pass-if (eqv? (* 4 most-negative-fixnum) (ash most-negative-fixnum 2)))
 197   (pass-if
 198       (eqv? (* most-negative-fixnum 340282366920938463463374607431768211456)
 199             (ash most-negative-fixnum 128)))
 200   (pass-if (eqv? (quotient-floor most-negative-fixnum 2)
 201                  (ash most-negative-fixnum -1)))
 202   (pass-if (eqv? -1 (ash most-negative-fixnum -1000)))
 203
 204   (let ((mnf4 (quotient-floor most-negative-fixnum 4)))
 205     (pass-if (eqv? (* 2 mnf4) (ash mnf4 1)))
 206     (pass-if (eqv? (* 4 mnf4) (ash mnf4 2)))
 207     (pass-if (eqv? (* 8 mnf4) (ash mnf4 3)))))
 208
 209 ;;;
 210 ;;; exact?
 211 ;;;
 212
 213 (with-test-prefix "exact?"
 214
 215   (pass-if "documented?"
 216     (documented? exact?))
 217
 218   (with-test-prefix "integers"
 219
 220     (pass-if "0"
 221       (exact? 0))
 222
 223     (pass-if "fixnum-max"
 224       (exact? fixnum-max))
 225
 226     (pass-if "fixnum-max + 1"
 227       (exact? (+ fixnum-max 1)))
 228
 229     (pass-if "fixnum-min"
 230       (exact? fixnum-min))
 231
 232     (pass-if "fixnum-min - 1"
 233       (exact? (- fixnum-min 1))))
 234
 235   (with-test-prefix "reals"
 236
 237     ;; (FIXME: need better examples.)
 238
 239     (pass-if "sqrt (fixnum-max^2 - 1)"
 240       (eq? #f (exact? (sqrt (- (expt fixnum-max 2) 1)))))
 241
 242     (pass-if "sqrt ((fixnum-max+1)^2 - 1)"
 243       (eq? #f (exact? (sqrt (- (expt (+ fixnum-max 1) 2) 1)))))))
 244
 245 ;;;
 246 ;;; exp
 247 ;;;
 248
 249 (with-test-prefix "exp"
 250   (pass-if "documented?"
 251     (documented? exp))
 252
 253   (pass-if-exception "no args" exception:wrong-num-args
 254     (exp))
 255   (pass-if-exception "two args" exception:wrong-num-args
 256     (exp 123 456))
 257
 258   (pass-if (eqv? 0.0 (exp -inf.0)))
 259   (pass-if (eqv-loosely? 1.0 (exp 0)))
 260   (pass-if (eqv-loosely? 1.0 (exp 0.0)))
 261   (pass-if (eqv-loosely? const-e   (exp 1.0)))
 262   (pass-if (eqv-loosely? const-e^2 (exp 2.0)))
 263   (pass-if (eqv-loosely? const-1/e (exp -1)))
 264
 265   (pass-if "exp(pi*i) = -1"
 266     (eqv-loosely? -1.0 (exp 0+3.14159i)))
 267   (pass-if "exp(-pi*i) = -1"
 268     (eqv-loosely? -1.0 (exp 0-3.14159i)))
 269   (pass-if "exp(2*pi*i) = +1"
 270     (eqv-loosely? 1.0 (exp 0+6.28318i)))
 271
 272   (pass-if "exp(2-pi*i) = -e^2"
 273     (eqv-loosely? (- const-e^2) (exp 2.0-3.14159i))))
 274
 275 ;;;
 276 ;;; odd?
 277 ;;;
 278
 279 (with-test-prefix "odd?"
 280   (pass-if (documented? odd?))
 281   (pass-if (odd? 1))
 282   (pass-if (odd? -1))
 283   (pass-if (not (odd? 0)))
 284   (pass-if (not (odd? 2)))
 285   (pass-if (not (odd? -2)))
 286   (pass-if (odd? (+ (* 2 fixnum-max) 1)))
 287   (pass-if (not (odd? (* 2 fixnum-max))))
 288   (pass-if (odd? (- (* 2 fixnum-min) 1)))
 289   (pass-if (not (odd? (* 2 fixnum-min)))))
 290
 291 ;;;
 292 ;;; even?
 293 ;;;
 294
 295 (with-test-prefix "even?"
 296   (pass-if (documented? even?))
 297   (pass-if (even? 2))
 298   (pass-if (even? -2))
 299   (pass-if (even? 0))
 300   (pass-if (not (even? 1)))
 301   (pass-if (not (even? -1)))
 302   (pass-if (not (even? (+ (* 2 fixnum-max) 1))))
 303   (pass-if (even? (* 2 fixnum-max)))
 304   (pass-if (not (even? (- (* 2 fixnum-min) 1))))
 305   (pass-if (even? (* 2 fixnum-min))))
 306
 307 ;;;
 308 ;;; inf? and inf
 309 ;;;
 310
 311 (with-test-prefix "inf?"
 312   (pass-if (documented? inf?))
 313   (pass-if (inf? (inf)))
 314   ;; FIXME: what are the expected behaviors?
 315   ;; (pass-if (inf? (/ 1.0 0.0))
 316   ;; (pass-if (inf? (/ 1 0.0))
 317   (pass-if (not (inf? 0)))
 318   (pass-if (not (inf? 42.0)))
 319   (pass-if (not (inf? (+ fixnum-max 1))))
 320   (pass-if (not (inf? (- fixnum-min 1)))))
 321
 322 ;;;
 323 ;;; nan? and nan
 324 ;;;
 325
 326 (with-test-prefix "nan?"
 327   (pass-if (documented? nan?))
 328   (pass-if (nan? (nan)))
 329   ;; FIXME: other ways we should be able to generate NaN?
 330   (pass-if (not (nan? 0)))
 331   (pass-if (not (nan? 42.0)))
 332   (pass-if (not (nan? (+ fixnum-max 1))))
 333   (pass-if (not (nan? (- fixnum-min 1)))))
 334
 335 ;;;
 336 ;;; abs
 337 ;;;
 338
 339 (with-test-prefix "abs"
 340   (pass-if (documented? abs))
 341   (pass-if (zero? (abs 0)))
 342   (pass-if (= 1 (abs 1)))
 343   (pass-if (= 1 (abs -1)))
 344   (pass-if (= (+ fixnum-max 1) (abs (+ fixnum-max 1))))
 345   (pass-if (= (+ (- fixnum-min) 1) (abs (- fixnum-min 1))))
 346   (pass-if (= 0.0 (abs 0.0)))
 347   (pass-if (= 1.0 (abs 1.0)))
 348   (pass-if (= 1.0 (abs -1.0)))
 349   (pass-if (nan? (abs +nan.0)))
 350   (pass-if (= +inf.0 (abs +inf.0)))
 351   (pass-if (= +inf.0 (abs -inf.0))))
 352
 353 ;;;
 354 ;;; quotient
 355 ;;;
 356
 357 (with-test-prefix "quotient"
 358
 359   (expect-fail "documented?"
 360     (documented? quotient))
 361
 362   (with-test-prefix "0 / n"
 363
 364     (pass-if "n = 1"
 365       (eqv? 0 (quotient 0 1)))
 366
 367     (pass-if "n = -1"
 368       (eqv? 0 (quotient 0 -1)))
 369
 370     (pass-if "n = 2"
 371       (eqv? 0 (quotient 0 2)))
 372
 373     (pass-if "n = fixnum-max"
 374       (eqv? 0 (quotient 0 fixnum-max)))
 375
 376     (pass-if "n = fixnum-max + 1"
 377       (eqv? 0 (quotient 0 (+ fixnum-max 1))))
 378
 379     (pass-if "n = fixnum-min"
 380       (eqv? 0 (quotient 0 fixnum-min)))
 381
 382     (pass-if "n = fixnum-min - 1"
 383       (eqv? 0 (quotient 0 (- fixnum-min 1)))))
 384
 385   (with-test-prefix "1 / n"
 386
 387     (pass-if "n = 1"
 388       (eqv? 1 (quotient 1 1)))
 389
 390     (pass-if "n = -1"
 391       (eqv? -1 (quotient 1 -1)))
 392
 393     (pass-if "n = 2"
 394       (eqv? 0 (quotient 1 2)))
 395
 396     (pass-if "n = fixnum-max"
 397       (eqv? 0 (quotient 1 fixnum-max)))
 398
 399     (pass-if "n = fixnum-max + 1"
 400       (eqv? 0 (quotient 1 (+ fixnum-max 1))))
 401
 402     (pass-if "n = fixnum-min"
 403       (eqv? 0 (quotient 1 fixnum-min)))
 404
 405     (pass-if "n = fixnum-min - 1"
 406       (eqv? 0 (quotient 1 (- fixnum-min 1)))))
 407
 408   (with-test-prefix "-1 / n"
 409
 410     (pass-if "n = 1"
 411       (eqv? -1 (quotient -1 1)))
 412
 413     (pass-if "n = -1"
 414       (eqv? 1 (quotient -1 -1)))
 415
 416     (pass-if "n = 2"
 417       (eqv? 0 (quotient -1 2)))
 418
 419     (pass-if "n = fixnum-max"
 420       (eqv? 0 (quotient -1 fixnum-max)))
 421
 422     (pass-if "n = fixnum-max + 1"
 423       (eqv? 0 (quotient -1 (+ fixnum-max 1))))
 424
 425     (pass-if "n = fixnum-min"
 426       (eqv? 0 (quotient -1 fixnum-min)))
 427
 428     (pass-if "n = fixnum-min - 1"
 429       (eqv? 0 (quotient -1 (- fixnum-min 1)))))
 430
 431   (with-test-prefix "fixnum-max / n"
 432
 433     (pass-if "n = 1"
 434       (eqv? fixnum-max (quotient fixnum-max 1)))
 435
 436     (pass-if "n = -1"
 437       (eqv? (- fixnum-max) (quotient fixnum-max -1)))
 438
 439     (pass-if "n = 2"
 440       (eqv? fixnum-max (+ (* (quotient fixnum-max 2) 2) 1)))
 441
 442     (pass-if "n = fixnum-max"
 443       (eqv? 1 (quotient fixnum-max fixnum-max)))
 444
 445     (pass-if "n = fixnum-max + 1"
 446       (eqv? 0 (quotient fixnum-max (+ fixnum-max 1))))
 447
 448     (pass-if "n = fixnum-min"
 449       (eqv? 0 (quotient fixnum-max fixnum-min)))
 450
 451     (pass-if "n = fixnum-min - 1"
 452       (eqv? 0 (quotient fixnum-max (- fixnum-min 1)))))
 453
 454   (with-test-prefix "(fixnum-max + 1) / n"
 455
 456     (pass-if "n = 1"
 457       (eqv? (+ fixnum-max 1) (quotient (+ fixnum-max 1) 1)))
 458
 459     (pass-if "n = -1"
 460       (eqv? (- (+ fixnum-max 1)) (quotient (+ fixnum-max 1) -1)))
 461
 462     (pass-if "n = 2"
 463       (eqv? (+ fixnum-max 1) (* (quotient (+ fixnum-max 1) 2) 2)))
 464
 465     (pass-if "n = fixnum-max"
 466       (eqv? 1 (quotient (+ fixnum-max 1) fixnum-max)))
 467
 468     (pass-if "n = fixnum-max + 1"
 469       (eqv? 1 (quotient (+ fixnum-max 1) (+ fixnum-max 1))))
 470
 471     (pass-if "n = fixnum-min"
 472       (eqv? -1 (quotient (+ fixnum-max 1) fixnum-min)))
 473
 474     (pass-if "n = fixnum-min - 1"
 475       (eqv? 0 (quotient (+ fixnum-max 1) (- fixnum-min 1)))))
 476
 477   (with-test-prefix "fixnum-min / n"
 478
 479     (pass-if "n = 1"
 480       (eqv? fixnum-min (quotient fixnum-min 1)))
 481
 482     (pass-if "n = -1"
 483       (eqv? (- fixnum-min) (quotient fixnum-min -1)))
 484
 485     (pass-if "n = 2"
 486       (eqv? fixnum-min (* (quotient fixnum-min 2) 2)))
 487
 488     (pass-if "n = fixnum-max"
 489       (eqv? -1 (quotient fixnum-min fixnum-max)))
 490
 491     (pass-if "n = fixnum-max + 1"
 492       (eqv? -1 (quotient fixnum-min (+ fixnum-max 1))))
 493
 494     (pass-if "n = fixnum-min"
 495       (eqv? 1 (quotient fixnum-min fixnum-min)))
 496
 497     (pass-if "n = fixnum-min - 1"
 498       (eqv? 0 (quotient fixnum-min (- fixnum-min 1))))
 499
 500     (pass-if "n = - fixnum-min - 1"
 501       (eqv? -1 (quotient fixnum-min (1- (- fixnum-min)))))
 502
 503     ;; special case, normally inum/big is zero
 504     (pass-if "n = - fixnum-min"
 505       (eqv? -1 (quotient fixnum-min (- fixnum-min))))
 506
 507     (pass-if "n = - fixnum-min + 1"
 508       (eqv? 0 (quotient fixnum-min (1+ (- fixnum-min))))))
 509
 510   (with-test-prefix "(fixnum-min - 1) / n"
 511
 512     (pass-if "n = 1"
 513       (eqv? (- fixnum-min 1) (quotient (- fixnum-min 1) 1)))
 514
 515     (pass-if "n = -1"
 516       (eqv? (- (- fixnum-min 1)) (quotient (- fixnum-min 1) -1)))
 517
 518     (pass-if "n = 2"
 519       (eqv? fixnum-min (* (quotient (- fixnum-min 1) 2) 2)))
 520
 521     (pass-if "n = fixnum-max"
 522       (eqv? -1 (quotient (- fixnum-min 1) fixnum-max)))
 523
 524     (pass-if "n = fixnum-max + 1"
 525       (eqv? -1 (quotient (- fixnum-min 1) (+ fixnum-max 1))))
 526
 527     (pass-if "n = fixnum-min"
 528       (eqv? 1 (quotient (- fixnum-min 1) fixnum-min)))
 529
 530     (pass-if "n = fixnum-min - 1"
 531       (eqv? 1 (quotient (- fixnum-min 1) (- fixnum-min 1)))))
 532
 533   ;; Positive dividend and divisor
 534
 535   (pass-if "35 / 7"
 536     (eqv? 5 (quotient 35 7)))
 537
 538   ;; Negative dividend, positive divisor
 539
 540   (pass-if "-35 / 7"
 541     (eqv? -5 (quotient -35 7)))
 542
 543   ;; Positive dividend, negative divisor
 544
 545   (pass-if "35 / -7"
 546     (eqv? -5 (quotient 35 -7)))
 547
 548   ;; Negative dividend and divisor
 549
 550   (pass-if "-35 / -7"
 551     (eqv? 5 (quotient -35 -7)))
 552
 553   ;; Are numerical overflows detected correctly?
 554
 555   (with-test-prefix "division by zero"
 556
 557     (pass-if-exception "(quotient 1 0)"
 558       exception:numerical-overflow
 559       (quotient 1 0))
 560
 561     (pass-if-exception "(quotient bignum 0)"
 562       exception:numerical-overflow
 563       (quotient (+ fixnum-max 1) 0)))
 564
 565   ;; Are wrong type arguments detected correctly?
 566
 567   )
 568
 569 ;;;
 570 ;;; remainder
 571 ;;;
 572
 573 (with-test-prefix "remainder"
 574
 575   (expect-fail "documented?"
 576     (documented? remainder))
 577
 578   (with-test-prefix "0 / n"
 579
 580     (pass-if "n = 1"
 581       (eqv? 0 (remainder 0 1)))
 582
 583     (pass-if "n = -1"
 584       (eqv? 0 (remainder 0 -1)))
 585
 586     (pass-if "n = fixnum-max"
 587       (eqv? 0 (remainder 0 fixnum-max)))
 588
 589     (pass-if "n = fixnum-max + 1"
 590       (eqv? 0 (remainder 0 (+ fixnum-max 1))))
 591
 592     (pass-if "n = fixnum-min"
 593       (eqv? 0 (remainder 0 fixnum-min)))
 594
 595     (pass-if "n = fixnum-min - 1"
 596       (eqv? 0 (remainder 0 (- fixnum-min 1)))))
 597
 598   (with-test-prefix "1 / n"
 599
 600     (pass-if "n = 1"
 601       (eqv? 0 (remainder 1 1)))
 602
 603     (pass-if "n = -1"
 604       (eqv? 0 (remainder 1 -1)))
 605
 606     (pass-if "n = fixnum-max"
 607       (eqv? 1 (remainder 1 fixnum-max)))
 608
 609     (pass-if "n = fixnum-max + 1"
 610       (eqv? 1 (remainder 1 (+ fixnum-max 1))))
 611
 612     (pass-if "n = fixnum-min"
 613       (eqv? 1 (remainder 1 fixnum-min)))
 614
 615     (pass-if "n = fixnum-min - 1"
 616       (eqv? 1 (remainder 1 (- fixnum-min 1)))))
 617
 618   (with-test-prefix "-1 / n"
 619
 620     (pass-if "n = 1"
 621       (eqv? 0 (remainder -1 1)))
 622
 623     (pass-if "n = -1"
 624       (eqv? 0 (remainder -1 -1)))
 625
 626     (pass-if "n = fixnum-max"
 627       (eqv? -1 (remainder -1 fixnum-max)))
 628
 629     (pass-if "n = fixnum-max + 1"
 630       (eqv? -1 (remainder -1 (+ fixnum-max 1))))
 631
 632     (pass-if "n = fixnum-min"
 633       (eqv? -1 (remainder -1 fixnum-min)))
 634
 635     (pass-if "n = fixnum-min - 1"
 636       (eqv? -1 (remainder -1 (- fixnum-min 1)))))
 637
 638   (with-test-prefix "fixnum-max / n"
 639
 640     (pass-if "n = 1"
 641       (eqv? 0 (remainder fixnum-max 1)))
 642
 643     (pass-if "n = -1"
 644       (eqv? 0 (remainder fixnum-max -1)))
 645
 646     (pass-if "n = fixnum-max"
 647       (eqv? 0 (remainder fixnum-max fixnum-max)))
 648
 649     (pass-if "n = fixnum-max + 1"
 650       (eqv? fixnum-max (remainder fixnum-max (+ fixnum-max 1))))
 651
 652     (pass-if "n = fixnum-min"
 653       (eqv? fixnum-max (remainder fixnum-max fixnum-min)))
 654
 655     (pass-if "n = fixnum-min - 1"
 656       (eqv? fixnum-max (remainder fixnum-max (- fixnum-min 1)))))
 657
 658   (with-test-prefix "(fixnum-max + 1) / n"
 659
 660     (pass-if "n = 1"
 661       (eqv? 0 (remainder (+ fixnum-max 1) 1)))
 662
 663     (pass-if "n = -1"
 664       (eqv? 0 (remainder (+ fixnum-max 1) -1)))
 665
 666     (pass-if "n = fixnum-max"
 667       (eqv? 1 (remainder (+ fixnum-max 1) fixnum-max)))
 668
 669     (pass-if "n = fixnum-max + 1"
 670       (eqv? 0 (remainder (+ fixnum-max 1) (+ fixnum-max 1))))
 671
 672     (pass-if "n = fixnum-min"
 673       (eqv? 0 (remainder (+ fixnum-max 1) fixnum-min)))
 674
 675     (pass-if "n = fixnum-min - 1"
 676       (eqv? (+ fixnum-max 1) (remainder (+ fixnum-max 1) (- fixnum-min 1)))))
 677
 678   (with-test-prefix "fixnum-min / n"
 679
 680     (pass-if "n = 1"
 681       (eqv? 0 (remainder fixnum-min 1)))
 682
 683     (pass-if "n = -1"
 684       (eqv? 0 (remainder fixnum-min -1)))
 685
 686     (pass-if "n = fixnum-max"
 687       (eqv? -1 (remainder fixnum-min fixnum-max)))
 688
 689     (pass-if "n = fixnum-max + 1"
 690       (eqv? 0 (remainder fixnum-min (+ fixnum-max 1))))
 691
 692     (pass-if "n = fixnum-min"
 693       (eqv? 0 (remainder fixnum-min fixnum-min)))
 694
 695     (pass-if "n = fixnum-min - 1"
 696       (eqv? fixnum-min (remainder fixnum-min (- fixnum-min 1))))
 697
 698     (pass-if "n = - fixnum-min - 1"
 699       (eqv? -1 (remainder fixnum-min (1- (- fixnum-min)))))
 700
 701     ;; special case, normally inum%big is the inum
 702     (pass-if "n = - fixnum-min"
 703       (eqv? 0 (remainder fixnum-min (- fixnum-min))))
 704
 705     (pass-if "n = - fixnum-min + 1"
 706       (eqv? fixnum-min (remainder fixnum-min (1+ (- fixnum-min))))))
 707
 708   (with-test-prefix "(fixnum-min - 1) / n"
 709
 710     (pass-if "n = 1"
 711       (eqv? 0 (remainder (- fixnum-min 1) 1)))
 712
 713     (pass-if "n = -1"
 714       (eqv? 0 (remainder (- fixnum-min 1) -1)))
 715
 716     (pass-if "n = fixnum-max"
 717       (eqv? -2 (remainder (- fixnum-min 1) fixnum-max)))
 718
 719     (pass-if "n = fixnum-max + 1"
 720       (eqv? -1 (remainder (- fixnum-min 1) (+ fixnum-max 1))))
 721
 722     (pass-if "n = fixnum-min"
 723       (eqv? -1 (remainder (- fixnum-min 1) fixnum-min)))
 724
 725     (pass-if "n = fixnum-min - 1"
 726       (eqv? 0 (remainder (- fixnum-min 1) (- fixnum-min 1)))))
 727
 728   ;; Positive dividend and divisor
 729
 730   (pass-if "35 / 7"
 731     (eqv? 0 (remainder 35 7)))
 732
 733   ;; Negative dividend, positive divisor
 734
 735   (pass-if "-35 / 7"
 736     (eqv? 0 (remainder -35 7)))
 737
 738   ;; Positive dividend, negative divisor
 739
 740   (pass-if "35 / -7"
 741     (eqv? 0 (remainder 35 -7)))
 742
 743   ;; Negative dividend and divisor
 744
 745   (pass-if "-35 / -7"
 746     (eqv? 0 (remainder -35 -7)))
 747
 748   ;; Are numerical overflows detected correctly?
 749
 750   (with-test-prefix "division by zero"
 751
 752     (pass-if-exception "(remainder 1 0)"
 753       exception:numerical-overflow
 754       (remainder 1 0))
 755
 756     (pass-if-exception "(remainder bignum 0)"
 757       exception:numerical-overflow
 758       (remainder (+ fixnum-max 1) 0)))
 759
 760   ;; Are wrong type arguments detected correctly?
 761
 762   )
 763
 764 ;;;
 765 ;;; modulo
 766 ;;;
 767
 768 (with-test-prefix "modulo"
 769
 770   (expect-fail "documented?"
 771     (documented? modulo))
 772
 773   (with-test-prefix "0 % n"
 774
 775     (pass-if "n = 1"
 776       (eqv? 0 (modulo 0 1)))
 777
 778     (pass-if "n = -1"
 779       (eqv? 0 (modulo 0 -1)))
 780
 781     (pass-if "n = fixnum-max"
 782       (eqv? 0 (modulo 0 fixnum-max)))
 783
 784     (pass-if "n = fixnum-max + 1"
 785       (eqv? 0 (modulo 0 (+ fixnum-max 1))))
 786
 787     (pass-if "n = fixnum-min"
 788       (eqv? 0 (modulo 0 fixnum-min)))
 789
 790     (pass-if "n = fixnum-min - 1"
 791       (eqv? 0 (modulo 0 (- fixnum-min 1)))))
 792
 793   (with-test-prefix "1 % n"
 794
 795     (pass-if "n = 1"
 796       (eqv? 0 (modulo 1 1)))
 797
 798     (pass-if "n = -1"
 799       (eqv? 0 (modulo 1 -1)))
 800
 801     (pass-if "n = fixnum-max"
 802       (eqv? 1 (modulo 1 fixnum-max)))
 803
 804     (pass-if "n = fixnum-max + 1"
 805       (eqv? 1 (modulo 1 (+ fixnum-max 1))))
 806
 807     (pass-if "n = fixnum-min"
 808       (eqv? (+ fixnum-min 1) (modulo 1 fixnum-min)))
 809
 810     (pass-if "n = fixnum-min - 1"
 811       (eqv? fixnum-min (modulo 1 (- fixnum-min 1)))))
 812
 813   (with-test-prefix "-1 % n"
 814
 815     (pass-if "n = 1"
 816       (eqv? 0 (modulo -1 1)))
 817
 818     (pass-if "n = -1"
 819       (eqv? 0 (modulo -1 -1)))
 820
 821     (pass-if "n = fixnum-max"
 822       (eqv? (- fixnum-max 1) (modulo -1 fixnum-max)))
 823
 824     (pass-if "n = fixnum-max + 1"
 825       (eqv? fixnum-max (modulo -1 (+ fixnum-max 1))))
 826
 827     (pass-if "n = fixnum-min"
 828       (eqv? -1 (modulo -1 fixnum-min)))
 829
 830     (pass-if "n = fixnum-min - 1"
 831       (eqv? -1 (modulo -1 (- fixnum-min 1)))))
 832
 833   (with-test-prefix "fixnum-max % n"
 834
 835     (pass-if "n = 1"
 836       (eqv? 0 (modulo fixnum-max 1)))
 837
 838     (pass-if "n = -1"
 839       (eqv? 0 (modulo fixnum-max -1)))
 840
 841     (pass-if "n = fixnum-max"
 842       (eqv? 0 (modulo fixnum-max fixnum-max)))
 843
 844     (pass-if "n = fixnum-max + 1"
 845       (eqv? fixnum-max (modulo fixnum-max (+ fixnum-max 1))))
 846
 847     (pass-if "n = fixnum-min"
 848       (eqv? -1 (modulo fixnum-max fixnum-min)))
 849
 850     (pass-if "n = fixnum-min - 1"
 851       (eqv? -2 (modulo fixnum-max (- fixnum-min 1)))))
 852
 853   (with-test-prefix "(fixnum-max + 1) % n"
 854
 855     (pass-if "n = 1"
 856       (eqv? 0 (modulo (+ fixnum-max 1) 1)))
 857
 858     (pass-if "n = -1"
 859       (eqv? 0 (modulo (+ fixnum-max 1) -1)))
 860
 861     (pass-if "n = fixnum-max"
 862       (eqv? 1 (modulo (+ fixnum-max 1) fixnum-max)))
 863
 864     (pass-if "n = fixnum-max + 1"
 865       (eqv? 0 (modulo (+ fixnum-max 1) (+ fixnum-max 1))))
 866
 867     (pass-if "n = fixnum-min"
 868       (eqv? 0 (modulo (+ fixnum-max 1) fixnum-min)))
 869
 870     (pass-if "n = fixnum-min - 1"
 871       (eqv? -1 (modulo (+ fixnum-max 1) (- fixnum-min 1)))))
 872
 873   (with-test-prefix "fixnum-min % n"
 874
 875     (pass-if "n = 1"
 876       (eqv? 0 (modulo fixnum-min 1)))
 877
 878     (pass-if "n = -1"
 879       (eqv? 0 (modulo fixnum-min -1)))
 880
 881     (pass-if "n = fixnum-max"
 882       (eqv? (- fixnum-max 1) (modulo fixnum-min fixnum-max)))
 883
 884     (pass-if "n = fixnum-max + 1"
 885       (eqv? 0 (modulo fixnum-min (+ fixnum-max 1))))
 886
 887     (pass-if "n = fixnum-min"
 888       (eqv? 0 (modulo fixnum-min fixnum-min)))
 889
 890     (pass-if "n = fixnum-min - 1"
 891       (eqv? fixnum-min (modulo fixnum-min (- fixnum-min 1)))))
 892
 893   (with-test-prefix "(fixnum-min - 1) % n"
 894
 895     (pass-if "n = 1"
 896       (eqv? 0 (modulo (- fixnum-min 1) 1)))
 897
 898     (pass-if "n = -1"
 899       (eqv? 0 (modulo (- fixnum-min 1) -1)))
 900
 901     (pass-if "n = fixnum-max"
 902       (eqv? (- fixnum-max 2) (modulo (- fixnum-min 1) fixnum-max)))
 903
 904     (pass-if "n = fixnum-max + 1"
 905       (eqv? fixnum-max (modulo (- fixnum-min 1) (+ fixnum-max 1))))
 906
 907     (pass-if "n = fixnum-min"
 908       (eqv? -1 (modulo (- fixnum-min 1) fixnum-min)))
 909
 910     (pass-if "n = fixnum-min - 1"
 911       (eqv? 0 (modulo (- fixnum-min 1) (- fixnum-min 1)))))
 912
 913   ;; Positive dividend and divisor
 914
 915   (pass-if "13 % 4"
 916     (eqv? 1 (modulo 13 4)))
 917
 918   (pass-if "2177452800 % 86400"
 919     (eqv? 0 (modulo 2177452800 86400)))
 920
 921   ;; Negative dividend, positive divisor
 922
 923   (pass-if "-13 % 4"
 924     (eqv? 3 (modulo -13 4)))
 925
 926   (pass-if "-2177452800 % 86400"
 927     (eqv? 0 (modulo -2177452800 86400)))
 928
 929   ;; Positive dividend, negative divisor
 930
 931   (pass-if "13 % -4"
 932     (eqv? -3 (modulo 13 -4)))
 933
 934   (pass-if "2177452800 % -86400"
 935     (eqv? 0 (modulo 2177452800 -86400)))
 936
 937   ;; Negative dividend and divisor
 938
 939   (pass-if "-13 % -4"
 940     (eqv? -1 (modulo -13 -4)))
 941
 942   (pass-if "-2177452800 % -86400"
 943     (eqv? 0 (modulo -2177452800 -86400)))
 944
 945   ;; Are numerical overflows detected correctly?
 946
 947   (with-test-prefix "division by zero"
 948
 949     (pass-if-exception "(modulo 1 0)"
 950       exception:numerical-overflow
 951       (modulo 1 0))
 952
 953     (pass-if-exception "(modulo bignum 0)"
 954       exception:numerical-overflow
 955       (modulo (+ fixnum-max 1) 0)))
 956
 957   ;; Are wrong type arguments detected correctly?
 958
 959   )
 960
 961 ;;;
 962 ;;; modulo-expt
 963 ;;;
 964
 965 (with-test-prefix "modulo-expt"
 966    (pass-if (= 1 (modulo-expt 17 23 47)))
 967
 968    (pass-if (= 1 (modulo-expt 17 -23 47)))
 969
 970    (pass-if (= 17 (modulo-expt 17 -22 47)))
 971
 972    (pass-if (= 36 (modulo-expt 17 22 47)))
 973
 974    (pass-if (= 183658794479969134816674175082294846241553725240 (modulo-expt 111122223333444455556666 111122223333444455556666 1153478690012629968439432872520758982731022934717)))
 975
 976    (pass-if-exception
 977     "Proper exception with 0 modulus"
 978     exception:numerical-overflow
 979     (modulo-expt 17 23 0))
 980
 981    (pass-if-exception
 982     "Proper exception when result not invertible"
 983     exception:numerical-overflow
 984     (modulo-expt 10 -1 48))
 985
 986    (pass-if-exception
 987     "Proper exception with wrong type argument"
 988     exception:wrong-type-arg
 989     (modulo-expt "Sam" 23 10))
 990
 991    (pass-if-exception
 992     "Proper exception with wrong type argument"
 993     exception:wrong-type-arg
 994     (modulo-expt 17 9.9 10))
 995
 996     (pass-if-exception
 997     "Proper exception with wrong type argument"
 998     exception:wrong-type-arg
 999     (modulo-expt 17 23 'Ethel)))
1000
1001 ;;;
1002 ;;; numerator
1003 ;;;
1004
1005 (with-test-prefix "numerator"
1006   (pass-if "0"
1007     (eqv? 0 (numerator 0)))
1008   (pass-if "1"
1009     (eqv? 1 (numerator 1)))
1010   (pass-if "2"
1011     (eqv? 2 (numerator 2)))
1012   (pass-if "-1"
1013     (eqv? -1 (numerator -1)))
1014   (pass-if "-2"
1015     (eqv? -2 (numerator -2)))
1016
1017   (pass-if "0.0"
1018     (eqv? 0.0 (numerator 0.0)))
1019   (pass-if "1.0"
1020     (eqv? 1.0 (numerator 1.0)))
1021   (pass-if "2.0"
1022     (eqv? 2.0 (numerator 2.0)))
1023   (pass-if "-1.0"
1024     (eqv? -1.0 (numerator -1.0)))
1025   (pass-if "-2.0"
1026     (eqv? -2.0 (numerator -2.0)))
1027
1028   (pass-if "0.5"
1029     (eqv? 1.0 (numerator 0.5)))
1030   (pass-if "0.25"
1031     (eqv? 1.0 (numerator 0.25)))
1032   (pass-if "0.75"
1033     (eqv? 3.0 (numerator 0.75))))
1034
1035 ;;;
1036 ;;; denominator
1037 ;;;
1038
1039 (with-test-prefix "denominator"
1040   (pass-if "0"
1041     (eqv? 1 (denominator 0)))
1042   (pass-if "1"
1043     (eqv? 1 (denominator 1)))
1044   (pass-if "2"
1045     (eqv? 1 (denominator 2)))
1046   (pass-if "-1"
1047     (eqv? 1 (denominator -1)))
1048   (pass-if "-2"
1049     (eqv? 1 (denominator -2)))
1050
1051   (pass-if "0.0"
1052     (eqv? 1.0 (denominator 0.0)))
1053   (pass-if "1.0"
1054     (eqv? 1.0 (denominator 1.0)))
1055   (pass-if "2.0"
1056     (eqv? 1.0 (denominator 2.0)))
1057   (pass-if "-1.0"
1058     (eqv? 1.0 (denominator -1.0)))
1059   (pass-if "-2.0"
1060     (eqv? 1.0 (denominator -2.0)))
1061
1062   (pass-if "0.5"
1063     (eqv? 2.0 (denominator 0.5)))
1064   (pass-if "0.25"
1065     (eqv? 4.0 (denominator 0.25)))
1066   (pass-if "0.75"
1067     (eqv? 4.0 (denominator 0.75))))
1068
1069 ;;;
1070 ;;; gcd
1071 ;;;
1072
1073 (with-test-prefix "gcd"
1074
1075   (pass-if "documented?"
1076     (documented? gcd))
1077
1078   (with-test-prefix "(n)"
1079
1080     (pass-if "n = -2"
1081       (eqv? 2 (gcd -2))))
1082
1083   (with-test-prefix "(0 n)"
1084
1085     (pass-if "n = 0"
1086       (eqv? 0 (gcd 0 0)))
1087
1088     (pass-if "n = 1"
1089       (eqv? 1 (gcd 0 1)))
1090
1091     (pass-if "n = -1"
1092       (eqv? 1 (gcd 0 -1)))
1093
1094     (pass-if "n = fixnum-max"
1095       (eqv? fixnum-max (gcd 0 fixnum-max)))
1096
1097     (pass-if "n = fixnum-max + 1"
1098       (eqv? (+ fixnum-max 1) (gcd 0 (+ fixnum-max 1))))
1099
1100     (pass-if "n = fixnum-min"
1101       (eqv? (- fixnum-min) (gcd 0 fixnum-min)))
1102
1103     (pass-if "n = fixnum-min - 1"
1104       (eqv? (- (- fixnum-min 1)) (gcd 0 (- fixnum-min 1)))))
1105
1106   (with-test-prefix "(n 0)"
1107
1108     (pass-if "n = 2^128 * fixnum-max"
1109       (eqv? (ash fixnum-max 128) (gcd (ash fixnum-max 128) 0))))
1110
1111   (with-test-prefix "(1 n)"
1112
1113     (pass-if "n = 0"
1114       (eqv? 1 (gcd 1 0)))
1115
1116     (pass-if "n = 1"
1117       (eqv? 1 (gcd 1 1)))
1118
1119     (pass-if "n = -1"
1120       (eqv? 1 (gcd 1 -1)))
1121
1122     (pass-if "n = fixnum-max"
1123       (eqv? 1 (gcd 1 fixnum-max)))
1124
1125     (pass-if "n = fixnum-max + 1"
1126       (eqv? 1 (gcd 1 (+ fixnum-max 1))))
1127
1128     (pass-if "n = fixnum-min"
1129       (eqv? 1 (gcd 1 fixnum-min)))
1130
1131     (pass-if "n = fixnum-min - 1"
1132       (eqv? 1 (gcd 1 (- fixnum-min 1)))))
1133
1134   (with-test-prefix "(-1 n)"
1135
1136     (pass-if "n = 0"
1137       (eqv? 1 (gcd -1 0)))
1138
1139     (pass-if "n = 1"
1140       (eqv? 1 (gcd -1 1)))
1141
1142     (pass-if "n = -1"
1143       (eqv? 1 (gcd -1 -1)))
1144
1145     (pass-if "n = fixnum-max"
1146       (eqv? 1 (gcd -1 fixnum-max)))
1147
1148     (pass-if "n = fixnum-max + 1"
1149       (eqv? 1 (gcd -1 (+ fixnum-max 1))))
1150
1151     (pass-if "n = fixnum-min"
1152       (eqv? 1 (gcd -1 fixnum-min)))
1153
1154     (pass-if "n = fixnum-min - 1"
1155       (eqv? 1 (gcd -1 (- fixnum-min 1)))))
1156
1157   (with-test-prefix "(fixnum-max n)"
1158
1159     (pass-if "n = 0"
1160       (eqv? fixnum-max (gcd fixnum-max 0)))
1161
1162     (pass-if "n = 1"
1163       (eqv? 1 (gcd fixnum-max 1)))
1164
1165     (pass-if "n = -1"
1166       (eqv? 1 (gcd fixnum-max -1)))
1167
1168     (pass-if "n = fixnum-max"
1169       (eqv? fixnum-max (gcd fixnum-max fixnum-max)))
1170
1171     (pass-if "n = fixnum-max + 1"
1172       (eqv? 1 (gcd fixnum-max (+ fixnum-max 1))))
1173
1174     (pass-if "n = fixnum-min"
1175       (eqv? 1 (gcd fixnum-max fixnum-min)))
1176
1177     (pass-if "n = fixnum-min - 1"
1178       (eqv? 1 (gcd fixnum-max (- fixnum-min 1)))))
1179
1180   (with-test-prefix "((+ fixnum-max 1) n)"
1181
1182     (pass-if "n = 0"
1183       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) 0)))
1184
1185     (pass-if "n = 1"
1186       (eqv? 1 (gcd (+ fixnum-max 1) 1)))
1187
1188     (pass-if "n = -1"
1189       (eqv? 1 (gcd (+ fixnum-max 1) -1)))
1190
1191     (pass-if "n = fixnum-max"
1192       (eqv? 1 (gcd (+ fixnum-max 1) fixnum-max)))
1193
1194     (pass-if "n = fixnum-max + 1"
1195       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) (+ fixnum-max 1))))
1196
1197     (pass-if "n = fixnum-min"
1198       (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) fixnum-min)))
1199
1200     (pass-if "n = fixnum-min - 1"
1201       (eqv? 1 (gcd (+ fixnum-max 1) (- fixnum-min 1)))))
1202
1203   (with-test-prefix "(fixnum-min n)"
1204
1205     (pass-if "n = 0"
1206       (eqv? (- fixnum-min) (gcd fixnum-min 0)))
1207
1208     (pass-if "n = 1"
1209       (eqv? 1 (gcd fixnum-min 1)))
1210
1211     (pass-if "n = -1"
1212       (eqv? 1 (gcd fixnum-min -1)))
1213
1214     (pass-if "n = fixnum-max"
1215       (eqv? 1 (gcd fixnum-min fixnum-max)))
1216
1217     (pass-if "n = fixnum-max + 1"
1218       (eqv? (+ fixnum-max 1) (gcd fixnum-min (+ fixnum-max 1))))
1219
1220     (pass-if "n = fixnum-min"
1221       (eqv? (- fixnum-min) (gcd fixnum-min fixnum-min)))
1222
1223     (pass-if "n = fixnum-min - 1"
1224       (eqv? 1 (gcd fixnum-min (- fixnum-min 1)))))
1225
1226   (with-test-prefix "((- fixnum-min 1) n)"
1227
1228     (pass-if "n = 0"
1229       (eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) 0)))
1230
1231     (pass-if "n = 1"
1232       (eqv? 1 (gcd (- fixnum-min 1) 1)))
1233
1234     (pass-if "n = -1"
1235       (eqv? 1 (gcd (- fixnum-min 1) -1)))
1236
1237     (pass-if "n = fixnum-max"
1238       (eqv? 1 (gcd (- fixnum-min 1) fixnum-max)))
1239
1240     (pass-if "n = fixnum-max + 1"
1241       (eqv? 1 (gcd (- fixnum-min 1) (+ fixnum-max 1))))
1242
1243     (pass-if "n = fixnum-min"
1244       (eqv? 1 (gcd (- fixnum-min 1) fixnum-min)))
1245
1246     (pass-if "n = fixnum-min - 1"
1247       (eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) (- fixnum-min 1)))))
1248
1249   ;; Are wrong type arguments detected correctly?
1250
1251   )
1252
1253 ;;;
1254 ;;; lcm
1255 ;;;
1256
1257 (with-test-prefix "lcm"
1258   ;; FIXME: more tests?
1259   ;; (some of these are already in r4rs.test)
1260   (pass-if (documented? lcm))
1261   (pass-if (= (lcm) 1))
1262   (pass-if (= (lcm 32 -36) 288))
1263   (let ((big-n 115792089237316195423570985008687907853269984665640564039457584007913129639936) ; 2 ^ 256
1264         (lcm-of-big-n-and-11 1273712981610478149659280835095566986385969831322046204434033424087044426039296))
1265     (pass-if (= lcm-of-big-n-and-11 (lcm big-n 11)))
1266     (pass-if (= lcm-of-big-n-and-11 (lcm 11 big-n 11)))))
1267
1268 ;;;
1269 ;;; number->string
1270 ;;;
1271
1272 (with-test-prefix "number->string"
1273   (let ((num->str->num
1274          (lambda (n radix)
1275            (string->number (number->string n radix) radix))))
1276
1277     (pass-if (documented? number->string))
1278     (pass-if (string=? (number->string 0) "0"))
1279     (pass-if (string=? (number->string 171) "171"))
1280     (pass-if (= (+ fixnum-max 1) (num->str->num (+ fixnum-max 1) 10)))
1281     (pass-if (= (- fixnum-min 1) (num->str->num (- fixnum-min 1) 10)))
1282     (pass-if (= (inf) (num->str->num (inf) 10)))
1283     (pass-if (= 1.3 (num->str->num 1.3 10)))
1284
1285     ;; XXX - some results depend on whether Guile is compiled optimzed
1286     ;; or not.  It is clearly undesirable to have number->string to be
1287     ;; influenced by this.
1288
1289     (pass-if (string=? (number->string 35.25 36) "z.9"))
1290     (pass-if (or (string=? (number->string 0.25 2) "0.01")
1291                  (string=? (number->string 0.25 2) "0.010")))
1292     (pass-if (string=? (number->string 255.0625 16) "ff.1"))
1293     (pass-if (string=? (number->string (/ 1 3) 3) "1/10"))
1294
1295     (pass-if (string=? (number->string 10) "10"))
1296     (pass-if (string=? (number->string 10 11) "a"))
1297     (pass-if (string=? (number->string 36 36) "10"))
1298     (pass-if (= (num->str->num 36 36) 36))
1299     (pass-if (= (string->number "z" 36) 35))
1300     (pass-if (= (string->number "Z" 36) 35))
1301     (pass-if (not (string->number "Z" 35)))
1302     (pass-if (string=? (number->string 35 36) "z"))
1303     (pass-if (= (num->str->num 35 36) 35))
1304
1305     ;; Numeric conversion from decimal is not precise, in its current
1306     ;; implementation, so 11.333... and 1.324... can't be expected to
1307     ;; reliably come out to precise values.  These tests did actually work
1308     ;; for a while, but something in gcc changed, affecting the conversion
1309     ;; code.
1310     ;;
1311     ;; (pass-if (or (string=? (number->string 11.33333333333333333 12)
1312     ;;                        "B.4")
1313     ;;              (string=? (number->string 11.33333333333333333 12)
1314     ;;                        "B.400000000000009")))
1315     ;; (pass-if (or (string=? (number->string 1.324e44 16)
1316     ;;                        "5.EFE0A14FAFEe24")
1317     ;;              (string=? (number->string 1.324e44 16)
1318     ;;                        "5.EFE0A14FAFDF8e24")))
1319     ))
1320
1321 ;;;
1322 ;;; string->number
1323 ;;;
1324
1325 (with-test-prefix "string->number"
1326
1327   (pass-if "documented?"
1328     (documented? string->number))
1329
1330   (pass-if "non number strings"
1331     (for-each (lambda (x) (if (string->number x) (throw 'fail)))
1332               '("" "q" "1q" "6+7iq" "8+9q" "10+11" "13+" "18@19q" "20@q" "23@"
1333                 "+25iq" "26i" "-q" "-iq" "i" "5#.0" "8/" "10#11" ".#" "."
1334                 "#o.2" "3.4q" "15.16e17q" "18.19e+q" ".q" ".17#18" "10q" "#b2"
1335                 "#b3" "#b4" "#b5" "#b6" "#b7" "#b8" "#b9" "#ba" "#bb" "#bc"
1336                 "#bd" "#be" "#bf" "#q" "#b#b1" "#o#o1" "#d#d1" "#x#x1" "#e#e1"
1337                 "#i#i1" "12@12+0i"))
1338     #t)
1339
1340   (pass-if "valid number strings"
1341     (for-each (lambda (couple)
1342                 (apply
1343                  (lambda (x y)
1344                    (let ((xx (string->number x)))
1345                      (if (or (eq? xx #f) (not (eqv? xx y)))
1346                          (begin
1347                            (pk x y)
1348                            (throw 'fail)))))
1349                  couple))
1350               `(;; Radix:
1351                 ("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
1352                 ("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
1353                 ("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
1354                 ("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
1355                 ("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
1356                 ("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
1357                 ("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
1358                 ("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
1359                 ("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
1360                 ("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
1361                 ("#b1010" 10)
1362                 ("#o12345670" 2739128)
1363                 ("#d1234567890" 1234567890)
1364                 ("#x1234567890abcdef" 1311768467294899695)
1365                 ;; Exactness:
1366                 ("#e1" 1) ("#e1.2" 12/10)
1367                 ("#i1.1" 1.1) ("#i1" 1.0)
1368                 ;; Integers:
1369                 ("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1))
1370                 ("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
1371                 ("#b#i100" 4.0)
1372                 ;; Fractions:
1373                 ("1/1" 1) ("1/2" 1/2) ("-1/2" -1/2) ("1#/1" 10.0)
1374                 ("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 9/10) ("#e10/1#" 1)
1375                 ("#i6/8" 0.75) ("#i1/1" 1.0)
1376                 ;; Decimal numbers:
1377                 ;; * <uinteger 10> <suffix>
1378                 ("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
1379                 ("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
1380                 ("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
1381                 ;; * . <digit 10>+ #* <suffix>
1382                 (".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
1383                 (".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
1384                 ;; * <digit 10>+ . <digit 10>* #* <suffix>
1385                 ("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
1386                 ("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
1387                 ("3.1#e0" 3.1)
1388                 ;; * <digit 10>+ #+ . #* <suffix>
1389                 ("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
1390                 ;; Complex:
1391                 ("1@0" 1.0) ("1@+0" 1.0) ("1@-0" 1.0)
1392                 ("2+3i" ,(+ 2 (* 3 +i))) ("4-5i" ,(- 4 (* 5 +i)))
1393                 ("1+i" 1+1i) ("1-i" 1-1i) ("+1i" 0+1i) ("-1i" 0-1i)
1394                 ("+i" +1i) ("-i" -1i)
1395                 ("1.0+.1i" 1.0+0.1i)
1396                 ("1.0-.1i" 1.0-0.1i)
1397                 (".1+.0i" 0.1)
1398                 ("1.+.0i" 1.0)
1399                 (".1+.1i" 0.1+0.1i)
1400                 ("1e1+.1i" 10+0.1i)
1401                 ))
1402     #t)
1403
1404   (pass-if-exception "exponent too big"
1405     exception:out-of-range
1406     (string->number "12.13e141414"))
1407
1408   ;; in guile 1.6.7 and earlier, bad polar forms (where the conversion of
1409   ;; the angle gave #f) caused a segv
1410   (pass-if "1@a"
1411     (eq? #f (string->number "1@a"))))
1412
1413 ;;;
1414 ;;; number?
1415 ;;;
1416
1417 (with-test-prefix "number?"
1418   (pass-if (documented? number?))
1419   (pass-if (number? 0))
1420   (pass-if (number? 7))
1421   (pass-if (number? -7))
1422   (pass-if (number? 1.3))
1423   (pass-if (number? (+ 1 fixnum-max)))
1424   (pass-if (number? (- 1 fixnum-min)))
1425   (pass-if (number? 3+4i))
1426   (pass-if (not (number? #\a)))
1427   (pass-if (not (number? "a")))
1428   (pass-if (not (number? (make-vector 0))))
1429   (pass-if (not (number? (cons 1 2))))
1430   (pass-if (not (number? #t)))
1431   (pass-if (not (number? (lambda () #t))))
1432   (pass-if (not (number? (current-input-port)))))
1433
1434 ;;;
1435 ;;; complex?
1436 ;;;
1437
1438 (with-test-prefix "complex?"
1439   (pass-if (documented? complex?))
1440   (pass-if (complex? 0))
1441   (pass-if (complex? 7))
1442   (pass-if (complex? -7))
1443   (pass-if (complex? (+ 1 fixnum-max)))
1444   (pass-if (complex? (- 1 fixnum-min)))
1445   (pass-if (complex? 1.3))
1446   (pass-if (complex? 3+4i))
1447   (pass-if (not (complex? #\a)))
1448   (pass-if (not (complex? "a")))
1449   (pass-if (not (complex? (make-vector 0))))
1450   (pass-if (not (complex? (cons 1 2))))
1451   (pass-if (not (complex? #t)))
1452   (pass-if (not (complex? (lambda () #t))))
1453   (pass-if (not (complex? (current-input-port)))))
1454
1455 ;;;
1456 ;;; real?
1457 ;;;
1458
1459 (with-test-prefix "real?"
1460   (pass-if (documented? real?))
1461   (pass-if (real? 0))
1462   (pass-if (real? 7))
1463   (pass-if (real? -7))
1464   (pass-if (real? (+ 1 fixnum-max)))
1465   (pass-if (real? (- 1 fixnum-min)))
1466   (pass-if (real? 1.3))
1467   (pass-if (not (real? 3+4i)))
1468   (pass-if (not (real? #\a)))
1469   (pass-if (not (real? "a")))
1470   (pass-if (not (real? (make-vector 0))))
1471   (pass-if (not (real? (cons 1 2))))
1472   (pass-if (not (real? #t)))
1473   (pass-if (not (real? (lambda () #t))))
1474   (pass-if (not (real? (current-input-port)))))
1475
1476 ;;;
1477 ;;; rational? (same as real? right now)
1478 ;;;
1479
1480 (with-test-prefix "rational?"
1481   (pass-if (documented? rational?))
1482   (pass-if (rational? 0))
1483   (pass-if (rational? 7))
1484   (pass-if (rational? -7))
1485   (pass-if (rational? (+ 1 fixnum-max)))
1486   (pass-if (rational? (- 1 fixnum-min)))
1487   (pass-if (rational? 1.3))
1488   (pass-if (not (rational? 3+4i)))
1489   (pass-if (not (rational? #\a)))
1490   (pass-if (not (rational? "a")))
1491   (pass-if (not (rational? (make-vector 0))))
1492   (pass-if (not (rational? (cons 1 2))))
1493   (pass-if (not (rational? #t)))
1494   (pass-if (not (rational? (lambda () #t))))
1495   (pass-if (not (rational? (current-input-port)))))
1496
1497 ;;;
1498 ;;; integer?
1499 ;;;
1500
1501 (with-test-prefix "integer?"
1502   (pass-if (documented? integer?))
1503   (pass-if (integer? 0))
1504   (pass-if (integer? 7))
1505   (pass-if (integer? -7))
1506   (pass-if (integer? (+ 1 fixnum-max)))
1507   (pass-if (integer? (- 1 fixnum-min)))
1508   (pass-if (and (= 3+0i (round 3+0i)) (integer? 3+0i)))
1509   (pass-if (and (= 1.0 (round 1.0)) (integer? 1.0)))
1510   (pass-if (not (integer? 1.3)))
1511   (pass-if (not (integer? +inf.0)))
1512   (pass-if (not (integer? -inf.0)))
1513   (pass-if (not (integer? +nan.0)))
1514   (pass-if (not (integer? 3+4i)))
1515   (pass-if (not (integer? #\a)))
1516   (pass-if (not (integer? "a")))
1517   (pass-if (not (integer? (make-vector 0))))
1518   (pass-if (not (integer? (cons 1 2))))
1519   (pass-if (not (integer? #t)))
1520   (pass-if (not (integer? (lambda () #t))))
1521   (pass-if (not (integer? (current-input-port)))))
1522
1523 ;;;
1524 ;;; inexact?
1525 ;;;
1526
1527 (with-test-prefix "inexact?"
1528   (pass-if (documented? inexact?))
1529   (pass-if (not (inexact? 0)))
1530   (pass-if (not (inexact? 7)))
1531   (pass-if (not (inexact? -7)))
1532   (pass-if (not (inexact? (+ 1 fixnum-max))))
1533   (pass-if (not (inexact? (- 1 fixnum-min))))
1534   (pass-if (inexact? 1.3))
1535   (pass-if (inexact? 3.1+4.2i))
1536   (pass-if-exception "char"
1537                      exception:wrong-type-arg
1538                      (not (inexact? #\a)))
1539   (pass-if-exception "string"
1540                      exception:wrong-type-arg
1541                      (not (inexact? "a")))
1542   (pass-if-exception "vector"
1543                      exception:wrong-type-arg
1544                      (not (inexact? (make-vector 0))))
1545   (pass-if-exception "cons"
1546                      exception:wrong-type-arg
1547                      (not (inexact? (cons 1 2))))
1548   (pass-if-exception "bool"
1549                      exception:wrong-type-arg
1550                      (not (inexact? #t)))
1551   (pass-if-exception "procedure"
1552                      exception:wrong-type-arg
1553                      (not (inexact? (lambda () #t))))
1554   (pass-if-exception "port"
1555                      exception:wrong-type-arg
1556                      (not (inexact? (current-input-port)))))
1557
1558 ;;;
1559 ;;; equal?
1560 ;;;
1561
1562 (with-test-prefix "equal?"
1563   (pass-if (documented? equal?))
1564   (pass-if (equal? 0 0))
1565   (pass-if (equal? 7 7))
1566   (pass-if (equal? -7 -7))
1567   (pass-if (equal? (+ 1 fixnum-max) (+ 1 fixnum-max)))
1568   (pass-if (equal? (- fixnum-min 1) (- fixnum-min 1)))
1569   (pass-if (not (equal? 0 1)))
1570   (pass-if (not (equal? fixnum-max (+ 1 fixnum-max))))
1571   (pass-if (not (equal? (+ 1 fixnum-max) fixnum-max)))
1572   (pass-if (not (equal? (+ 1 fixnum-max) (+ 2 fixnum-max))))
1573   (pass-if (not (equal? fixnum-min (- fixnum-min 1))))
1574   (pass-if (not (equal? (- fixnum-min 1) fixnum-min)))
1575   (pass-if (not (equal? (- fixnum-min 1) (- fixnum-min 2))))
1576   (pass-if (not (equal? (+ fixnum-max 1) (- fixnum-min 1))))
1577
1578   (pass-if (not (equal? (ash 1 256) +inf.0)))
1579   (pass-if (not (equal? +inf.0 (ash 1 256))))
1580   (pass-if (not (equal? (ash 1 256) -inf.0)))
1581   (pass-if (not (equal? -inf.0 (ash 1 256))))
1582
1583   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1584   ;; sure we've avoided that
1585   (pass-if (not (equal? (ash 1 1024) +inf.0)))
1586   (pass-if (not (equal? +inf.0 (ash 1 1024))))
1587   (pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
1588   (pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
1589
1590   (pass-if (not (equal? +nan.0 +nan.0)))
1591   (pass-if (not (equal? 0 +nan.0)))
1592   (pass-if (not (equal? +nan.0 0)))
1593   (pass-if (not (equal? 1 +nan.0)))
1594   (pass-if (not (equal? +nan.0 1)))
1595   (pass-if (not (equal? -1 +nan.0)))
1596   (pass-if (not (equal? +nan.0 -1)))
1597
1598   (pass-if (not (equal? (ash 1 256) +nan.0)))
1599   (pass-if (not (equal? +nan.0 (ash 1 256))))
1600   (pass-if (not (equal? (- (ash 1 256)) +nan.0)))
1601   (pass-if (not (equal? +nan.0 (- (ash 1 256)))))
1602
1603   (pass-if (not (equal? (ash 1 8192) +nan.0)))
1604   (pass-if (not (equal? +nan.0 (ash 1 8192))))
1605   (pass-if (not (equal? (- (ash 1 8192)) +nan.0)))
1606   (pass-if (not (equal? +nan.0 (- (ash 1 8192)))))
1607
1608   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1609   ;; sure we've avoided that
1610   (pass-if (not (equal? (ash 3 1023) +nan.0)))
1611   (pass-if (not (equal? +nan.0 (ash 3 1023)))))
1612
1613 ;;;
1614 ;;; =
1615 ;;;
1616
1617 (with-test-prefix "="
1618   (pass-if (documented? =))
1619   (pass-if (= 0 0))
1620   (pass-if (= 7 7))
1621   (pass-if (= -7 -7))
1622   (pass-if (= (+ 1 fixnum-max) (+ 1 fixnum-max)))
1623   (pass-if (= (- fixnum-min 1) (- fixnum-min 1)))
1624   (pass-if (not (= 0 1)))
1625   (pass-if (not (= fixnum-max (+ 1 fixnum-max))))
1626   (pass-if (not (= (+ 1 fixnum-max) fixnum-max)))
1627   (pass-if (not (= (+ 1 fixnum-max) (+ 2 fixnum-max))))
1628   (pass-if (not (= fixnum-min (- fixnum-min 1))))
1629   (pass-if (not (= (- fixnum-min 1) fixnum-min)))
1630   (pass-if (not (= (- fixnum-min 1) (- fixnum-min 2))))
1631   (pass-if (not (= (+ fixnum-max 1) (- fixnum-min 1))))
1632
1633   (pass-if (not (= (ash 1 256) +inf.0)))
1634   (pass-if (not (= +inf.0 (ash 1 256))))
1635   (pass-if (not (= (ash 1 256) -inf.0)))
1636   (pass-if (not (= -inf.0 (ash 1 256))))
1637
1638   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
1639   ;; sure we've avoided that
1640   (pass-if (not (= (ash 1 1024) +inf.0)))
1641   (pass-if (not (= +inf.0 (ash 1 1024))))
1642   (pass-if (not (= (- (ash 1 1024)) -inf.0)))
1643   (pass-if (not (= -inf.0 (- (ash 1 1024)))))
1644
1645   (pass-if (not (= +nan.0 +nan.0)))
1646   (pass-if (not (= 0 +nan.0)))
1647   (pass-if (not (= +nan.0 0)))
1648   (pass-if (not (= 1 +nan.0)))
1649   (pass-if (not (= +nan.0 1)))
1650   (pass-if (not (= -1 +nan.0)))
1651   (pass-if (not (= +nan.0 -1)))
1652
1653   (pass-if (not (= (ash 1 256) +nan.0)))
1654   (pass-if (not (= +nan.0 (ash 1 256))))
1655   (pass-if (not (= (- (ash 1 256)) +nan.0)))
1656   (pass-if (not (= +nan.0 (- (ash 1 256)))))
1657
1658   (pass-if (not (= (ash 1 8192) +nan.0)))
1659   (pass-if (not (= +nan.0 (ash 1 8192))))
1660   (pass-if (not (= (- (ash 1 8192)) +nan.0)))
1661   (pass-if (not (= +nan.0 (- (ash 1 8192)))))
1662
1663   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
1664   ;; sure we've avoided that
1665   (pass-if (not (= (ash 3 1023) +nan.0)))
1666   (pass-if (not (= +nan.0 (ash 3 1023))))
1667
1668   (pass-if (= 1/2 0.5))
1669   (pass-if (not (= 1/3 0.333333333333333333333333333333333)))
1670   (pass-if (not (= 2/3 0.5)))
1671   (pass-if (not (= 0.5 (+ 1/2 (/ 1 (ash 1 1000))))))
1672
1673   (pass-if (= 1/2 0.5+0i))
1674   (pass-if (not (= 0.333333333333333333333333333333333 1/3)))
1675   (pass-if (not (= 2/3 0.5+0i)))
1676   (pass-if (not (= 1/2 0+0.5i)))
1677
1678   (pass-if (= 0.5 1/2))
1679   (pass-if (not (= 0.5 2/3)))
1680   (pass-if (not (= (+ 1/2 (/ 1 (ash 1 1000))) 0.5)))
1681
1682   (pass-if (= 0.5+0i 1/2))
1683   (pass-if (not (= 0.5+0i 2/3)))
1684   (pass-if (not (= 0+0.5i 1/2)))
1685
1686   ;; prior to guile 1.8, inum/flonum comparisons were done just by
1687   ;; converting the inum to a double, which on a 64-bit would round making
1688   ;; say inexact 2^58 appear equal to exact 2^58+1
1689   (pass-if (= (ash-flo 1.0 58) (ash 1 58)))
1690   (pass-if (not (= (ash-flo 1.0 58) (1+ (ash 1 58)))))
1691   (pass-if (not (= (ash-flo 1.0 58) (1- (ash 1 58)))))
1692   (pass-if (= (ash 1 58) (ash-flo 1.0 58)))
1693   (pass-if (not (= (1+ (ash 1 58)) (ash-flo 1.0 58))))
1694   (pass-if (not (= (1- (ash 1 58)) (ash-flo 1.0 58)))))
1695
1696 ;;;
1697 ;;; <
1698 ;;;
1699
1700 (with-test-prefix "<"
1701
1702   (pass-if "documented?"
1703     (documented? <))
1704
1705   (with-test-prefix "(< 0 n)"
1706
1707     (pass-if "n = 0"
1708       (not (< 0 0)))
1709
1710     (pass-if "n = 0.0"
1711       (not (< 0 0.0)))
1712
1713     (pass-if "n = 1"
1714       (< 0 1))
1715
1716     (pass-if "n = 1.0"
1717       (< 0 1.0))
1718
1719     (pass-if "n = -1"
1720       (not (< 0 -1)))
1721
1722     (pass-if "n = -1.0"
1723       (not (< 0 -1.0)))
1724
1725     (pass-if "n = fixnum-max"
1726       (< 0 fixnum-max))
1727
1728     (pass-if "n = fixnum-max + 1"
1729       (< 0 (+ fixnum-max 1)))
1730
1731     (pass-if "n = fixnum-min"
1732       (not (< 0 fixnum-min)))
1733
1734     (pass-if "n = fixnum-min - 1"
1735       (not (< 0 (- fixnum-min 1)))))
1736
1737   (with-test-prefix "(< 0.0 n)"
1738
1739     (pass-if "n = 0"
1740       (not (< 0.0 0)))
1741
1742     (pass-if "n = 0.0"
1743       (not (< 0.0 0.0)))
1744
1745     (pass-if "n = 1"
1746       (< 0.0 1))
1747
1748     (pass-if "n = 1.0"
1749       (< 0.0 1.0))
1750
1751     (pass-if "n = -1"
1752       (not (< 0.0 -1)))
1753
1754     (pass-if "n = -1.0"
1755       (not (< 0.0 -1.0)))
1756
1757     (pass-if "n = fixnum-max"
1758       (< 0.0 fixnum-max))
1759
1760     (pass-if "n = fixnum-max + 1"
1761       (< 0.0 (+ fixnum-max 1)))
1762
1763     (pass-if "n = fixnum-min"
1764       (not (< 0.0 fixnum-min)))
1765
1766     (pass-if "n = fixnum-min - 1"
1767       (not (< 0.0 (- fixnum-min 1)))))
1768
1769   (with-test-prefix "(< 1 n)"
1770
1771     (pass-if "n = 0"
1772       (not (< 1 0)))
1773
1774     (pass-if "n = 0.0"
1775       (not (< 1 0.0)))
1776
1777     (pass-if "n = 1"
1778       (not (< 1 1)))
1779
1780     (pass-if "n = 1.0"
1781       (not (< 1 1.0)))
1782
1783     (pass-if "n = -1"
1784       (not (< 1 -1)))
1785
1786     (pass-if "n = -1.0"
1787       (not (< 1 -1.0)))
1788
1789     (pass-if "n = fixnum-max"
1790       (< 1 fixnum-max))
1791
1792     (pass-if "n = fixnum-max + 1"
1793       (< 1 (+ fixnum-max 1)))
1794
1795     (pass-if "n = fixnum-min"
1796       (not (< 1 fixnum-min)))
1797
1798     (pass-if "n = fixnum-min - 1"
1799       (not (< 1 (- fixnum-min 1)))))
1800
1801   (with-test-prefix "(< 1.0 n)"
1802
1803     (pass-if "n = 0"
1804       (not (< 1.0 0)))
1805
1806     (pass-if "n = 0.0"
1807       (not (< 1.0 0.0)))
1808
1809     (pass-if "n = 1"
1810       (not (< 1.0 1)))
1811
1812     (pass-if "n = 1.0"
1813       (not (< 1.0 1.0)))
1814
1815     (pass-if "n = -1"
1816       (not (< 1.0 -1)))
1817
1818     (pass-if "n = -1.0"
1819       (not (< 1.0 -1.0)))
1820
1821     (pass-if "n = fixnum-max"
1822       (< 1.0 fixnum-max))
1823
1824     (pass-if "n = fixnum-max + 1"
1825       (< 1.0 (+ fixnum-max 1)))
1826
1827     (pass-if "n = fixnum-min"
1828       (not (< 1.0 fixnum-min)))
1829
1830     (pass-if "n = fixnum-min - 1"
1831       (not (< 1.0 (- fixnum-min 1)))))
1832
1833   (with-test-prefix "(< -1 n)"
1834
1835     (pass-if "n = 0"
1836       (< -1 0))
1837
1838     (pass-if "n = 0.0"
1839       (< -1 0.0))
1840
1841     (pass-if "n = 1"
1842       (< -1 1))
1843
1844     (pass-if "n = 1.0"
1845       (< -1 1.0))
1846
1847     (pass-if "n = -1"
1848       (not (< -1 -1)))
1849
1850     (pass-if "n = -1.0"
1851       (not (< -1 -1.0)))
1852
1853     (pass-if "n = fixnum-max"
1854       (< -1 fixnum-max))
1855
1856     (pass-if "n = fixnum-max + 1"
1857       (< -1 (+ fixnum-max 1)))
1858
1859     (pass-if "n = fixnum-min"
1860       (not (< -1 fixnum-min)))
1861
1862     (pass-if "n = fixnum-min - 1"
1863       (not (< -1 (- fixnum-min 1)))))
1864
1865   (with-test-prefix "(< -1.0 n)"
1866
1867     (pass-if "n = 0"
1868       (< -1.0 0))
1869
1870     (pass-if "n = 0.0"
1871       (< -1.0 0.0))
1872
1873     (pass-if "n = 1"
1874       (< -1.0 1))
1875
1876     (pass-if "n = 1.0"
1877       (< -1.0 1.0))
1878
1879     (pass-if "n = -1"
1880       (not (< -1.0 -1)))
1881
1882     (pass-if "n = -1.0"
1883       (not (< -1.0 -1.0)))
1884
1885     (pass-if "n = fixnum-max"
1886       (< -1.0 fixnum-max))
1887
1888     (pass-if "n = fixnum-max + 1"
1889       (< -1.0 (+ fixnum-max 1)))
1890
1891     (pass-if "n = fixnum-min"
1892       (not (< -1.0 fixnum-min)))
1893
1894     (pass-if "n = fixnum-min - 1"
1895       (not (< -1.0 (- fixnum-min 1)))))
1896
1897   (with-test-prefix "(< fixnum-max n)"
1898
1899     (pass-if "n = 0"
1900       (not (< fixnum-max 0)))
1901
1902     (pass-if "n = 0.0"
1903       (not (< fixnum-max 0.0)))
1904
1905     (pass-if "n = 1"
1906       (not (< fixnum-max 1)))
1907
1908     (pass-if "n = 1.0"
1909       (not (< fixnum-max 1.0)))
1910
1911     (pass-if "n = -1"
1912       (not (< fixnum-max -1)))
1913
1914     (pass-if "n = -1.0"
1915       (not (< fixnum-max -1.0)))
1916
1917     (pass-if "n = fixnum-max"
1918       (not (< fixnum-max fixnum-max)))
1919
1920     (pass-if "n = fixnum-max + 1"
1921       (< fixnum-max (+ fixnum-max 1)))
1922
1923     (pass-if "n = fixnum-min"
1924       (not (< fixnum-max fixnum-min)))
1925
1926     (pass-if "n = fixnum-min - 1"
1927       (not (< fixnum-max (- fixnum-min 1)))))
1928
1929   (with-test-prefix "(< (+ fixnum-max 1) n)"
1930
1931     (pass-if "n = 0"
1932       (not (< (+ fixnum-max 1) 0)))
1933
1934     (pass-if "n = 0.0"
1935       (not (< (+ fixnum-max 1) 0.0)))
1936
1937     (pass-if "n = 1"
1938       (not (< (+ fixnum-max 1) 1)))
1939
1940     (pass-if "n = 1.0"
1941       (not (< (+ fixnum-max 1) 1.0)))
1942
1943     (pass-if "n = -1"
1944       (not (< (+ fixnum-max 1) -1)))
1945
1946     (pass-if "n = -1.0"
1947       (not (< (+ fixnum-max 1) -1.0)))
1948
1949     (pass-if "n = fixnum-max"
1950       (not (< (+ fixnum-max 1) fixnum-max)))
1951
1952     (pass-if "n = fixnum-max + 1"
1953       (not (< (+ fixnum-max 1) (+ fixnum-max 1))))
1954
1955     (pass-if "n = fixnum-min"
1956       (not (< (+ fixnum-max 1) fixnum-min)))
1957
1958     (pass-if "n = fixnum-min - 1"
1959       (not (< (+ fixnum-max 1) (- fixnum-min 1)))))
1960
1961   (with-test-prefix "(< fixnum-min n)"
1962
1963     (pass-if "n = 0"
1964       (< fixnum-min 0))
1965
1966     (pass-if "n = 0.0"
1967       (< fixnum-min 0.0))
1968
1969     (pass-if "n = 1"
1970       (< fixnum-min 1))
1971
1972     (pass-if "n = 1.0"
1973       (< fixnum-min 1.0))
1974
1975     (pass-if "n = -1"
1976       (< fixnum-min -1))
1977
1978     (pass-if "n = -1.0"
1979       (< fixnum-min -1.0))
1980
1981     (pass-if "n = fixnum-max"
1982       (< fixnum-min fixnum-max))
1983
1984     (pass-if "n = fixnum-max + 1"
1985       (< fixnum-min (+ fixnum-max 1)))
1986
1987     (pass-if "n = fixnum-min"
1988       (not (< fixnum-min fixnum-min)))
1989
1990     (pass-if "n = fixnum-min - 1"
1991       (not (< fixnum-min (- fixnum-min 1)))))
1992
1993   (with-test-prefix "(< (- fixnum-min 1) n)"
1994
1995     (pass-if "n = 0"
1996       (< (- fixnum-min 1) 0))
1997
1998     (pass-if "n = 0.0"
1999       (< (- fixnum-min 1) 0.0))
2000
2001     (pass-if "n = 1"
2002       (< (- fixnum-min 1) 1))
2003
2004     (pass-if "n = 1.0"
2005       (< (- fixnum-min 1) 1.0))
2006
2007     (pass-if "n = -1"
2008       (< (- fixnum-min 1) -1))
2009
2010     (pass-if "n = -1.0"
2011       (< (- fixnum-min 1) -1.0))
2012
2013     (pass-if "n = fixnum-max"
2014       (< (- fixnum-min 1) fixnum-max))
2015
2016     (pass-if "n = fixnum-max + 1"
2017       (< (- fixnum-min 1) (+ fixnum-max 1)))
2018
2019     (pass-if "n = fixnum-min"
2020       (< (- fixnum-min 1) fixnum-min))
2021
2022     (pass-if "n = fixnum-min - 1"
2023       (not (< (- fixnum-min 1) (- fixnum-min 1)))))
2024
2025   (pass-if (< (ash 1 256) +inf.0))
2026   (pass-if (not (< +inf.0 (ash 1 256))))
2027   (pass-if (not (< (ash 1 256) -inf.0)))
2028   (pass-if (< -inf.0 (ash 1 256)))
2029
2030   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2031   ;; sure we've avoided that
2032   (pass-if (< (1- (ash 1 1024)) +inf.0))
2033   (pass-if (<     (ash 1 1024)  +inf.0))
2034   (pass-if (< (1+ (ash 1 1024)) +inf.0))
2035   (pass-if (not (< +inf.0 (1- (ash 1 1024)))))
2036   (pass-if (not (< +inf.0     (ash 1 1024))))
2037   (pass-if (not (< +inf.0 (1+ (ash 1 1024)))))
2038   (pass-if (< -inf.0 (- (1- (ash 1 1024)))))
2039   (pass-if (< -inf.0 (-     (ash 1 1024))))
2040   (pass-if (< -inf.0 (- (1+ (ash 1 1024)))))
2041   (pass-if (not (< (- (1- (ash 1 1024))) -inf.0)))
2042   (pass-if (not (< (-     (ash 1 1024))  -inf.0)))
2043   (pass-if (not (< (- (1+ (ash 1 1024))) -inf.0)))
2044
2045   (pass-if (not (< +nan.0 +nan.0)))
2046   (pass-if (not (< 0 +nan.0)))
2047   (pass-if (not (< +nan.0 0)))
2048   (pass-if (not (< 1 +nan.0)))
2049   (pass-if (not (< +nan.0 1)))
2050   (pass-if (not (< -1 +nan.0)))
2051   (pass-if (not (< +nan.0 -1)))
2052
2053   (pass-if (not (< (ash 1 256) +nan.0)))
2054   (pass-if (not (< +nan.0 (ash 1 256))))
2055   (pass-if (not (< (- (ash 1 256)) +nan.0)))
2056   (pass-if (not (< +nan.0 (- (ash 1 256)))))
2057
2058   (pass-if (not (< (ash 1 8192) +nan.0)))
2059   (pass-if (not (< +nan.0 (ash 1 8192))))
2060   (pass-if (not (< (- (ash 1 8192)) +nan.0)))
2061   (pass-if (not (< +nan.0 (- (ash 1 8192)))))
2062
2063   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2064   ;; sure we've avoided that
2065   (pass-if (not (< (ash 3 1023) +nan.0)))
2066   (pass-if (not (< (1+ (ash 3 1023)) +nan.0)))
2067   (pass-if (not (< (1- (ash 3 1023)) +nan.0)))
2068   (pass-if (not (< +nan.0 (ash 3 1023))))
2069   (pass-if (not (< +nan.0 (1+ (ash 3 1023)))))
2070   (pass-if (not (< +nan.0 (1- (ash 3 1023)))))
2071
2072   (with-test-prefix "inum/frac"
2073     (pass-if (< 2 9/4))
2074     (pass-if (< -2 9/4))
2075     (pass-if (< -2 7/4))
2076     (pass-if (< -2 -7/4))
2077     (pass-if (eq? #f (< 2 7/4)))
2078     (pass-if (eq? #f (< 2 -7/4)))
2079     (pass-if (eq? #f (< 2 -9/4)))
2080     (pass-if (eq? #f (< -2 -9/4))))
2081
2082   (with-test-prefix "bignum/frac"
2083     (let ((x (ash 1 2048)))
2084       (pass-if (< x (* 4/3 x)))
2085       (pass-if (< (- x) (* 4/3 x)))
2086       (pass-if (< (- x) (* 2/3 x)))
2087       (pass-if (< (- x) (* -2/3 x)))
2088       (pass-if (eq? #f (< x (* 2/3 x))))
2089       (pass-if (eq? #f (< x (* -2/3 x))))
2090       (pass-if (eq? #f (< x (* -4/3 x))))
2091       (pass-if (eq? #f (< (- x) (* -4/3 x))))))
2092
2093   (with-test-prefix "flonum/frac"
2094     (pass-if (< 0.75 4/3))
2095     (pass-if (< -0.75 4/3))
2096     (pass-if (< -0.75 2/3))
2097     (pass-if (< -0.75 -2/3))
2098     (pass-if (eq? #f (< 0.75 2/3)))
2099     (pass-if (eq? #f (< 0.75 -2/3)))
2100     (pass-if (eq? #f (< 0.75 -4/3)))
2101     (pass-if (eq? #f (< -0.75 -4/3)))
2102
2103     (pass-if (< -inf.0 4/3))
2104     (pass-if (< -inf.0 -4/3))
2105     (pass-if (eq? #f (< +inf.0 4/3)))
2106     (pass-if (eq? #f (< +inf.0 -4/3)))
2107
2108     (pass-if (eq? #f (< +nan.0 4/3)))
2109     (pass-if (eq? #f (< +nan.0 -4/3))))
2110
2111   (with-test-prefix "frac/inum"
2112     (pass-if (< 7/4 2))
2113     (pass-if (< -7/4 2))
2114     (pass-if (< -9/4 2))
2115     (pass-if (< -9/4 -2))
2116     (pass-if (eq? #f (< 9/4 2)))
2117     (pass-if (eq? #f (< 9/4 -2)))
2118     (pass-if (eq? #f (< 7/4 -2)))
2119     (pass-if (eq? #f (< -7/4 -2))))
2120
2121   (with-test-prefix "frac/bignum"
2122     (let ((x (ash 1 2048)))
2123       (pass-if (< (* 2/3 x) x))
2124       (pass-if (< (* -2/3 x) x))
2125       (pass-if (< (* -4/3 x) x))
2126       (pass-if (< (* -4/3 x) (- x)))
2127       (pass-if (eq? #f (< (* 4/3 x) x)))
2128       (pass-if (eq? #f (< (* 4/3 x) (- x))))
2129       (pass-if (eq? #f (< (* 2/3 x) (- x))))
2130       (pass-if (eq? #f (< (* -2/3 x) (- x))))))
2131
2132   (with-test-prefix "frac/flonum"
2133     (pass-if (< 2/3 0.75))
2134     (pass-if (< -2/3 0.75))
2135     (pass-if (< -4/3 0.75))
2136     (pass-if (< -4/3 -0.75))
2137     (pass-if (eq? #f (< 4/3 0.75)))
2138     (pass-if (eq? #f (< 4/3 -0.75)))
2139     (pass-if (eq? #f (< 2/3 -0.75)))
2140     (pass-if (eq? #f (< -2/3 -0.75)))
2141
2142     (pass-if (< 4/3 +inf.0))
2143     (pass-if (< -4/3 +inf.0))
2144     (pass-if (eq? #f (< 4/3 -inf.0)))
2145     (pass-if (eq? #f (< -4/3 -inf.0)))
2146
2147     (pass-if (eq? #f (< 4/3 +nan.0)))
2148     (pass-if (eq? #f (< -4/3 +nan.0))))
2149
2150   (with-test-prefix "frac/frac"
2151     (pass-if (< 2/3 6/7))
2152     (pass-if (< -2/3 6/7))
2153     (pass-if (< -4/3 6/7))
2154     (pass-if (< -4/3 -6/7))
2155     (pass-if (eq? #f (< 4/3 6/7)))
2156     (pass-if (eq? #f (< 4/3 -6/7)))
2157     (pass-if (eq? #f (< 2/3 -6/7)))
2158     (pass-if (eq? #f (< -2/3 -6/7)))))
2159
2160 ;;;
2161 ;;; >
2162 ;;;
2163
2164 ;; currently not tested -- implementation is trivial
2165 ;; (> x y) is implemented as (< y x)
2166 ;; FIXME: tests should probably be added in case we change implementation.
2167
2168 ;;;
2169 ;;; <=
2170 ;;;
2171
2172 ;; currently not tested -- implementation is trivial
2173 ;; (<= x y) is implemented as (not (< y x))
2174 ;; FIXME: tests should probably be added in case we change implementation.
2175
2176 ;;;
2177 ;;; >=
2178 ;;;
2179
2180 ;; currently not tested -- implementation is trivial
2181 ;; (>= x y) is implemented as (not (< x y))
2182 ;; FIXME: tests should probably be added in case we change implementation.
2183
2184 ;;;
2185 ;;; zero?
2186 ;;;
2187
2188 (with-test-prefix "zero?"
2189   (expect-fail (documented? zero?))
2190   (pass-if (zero? 0))
2191   (pass-if (not (zero? 7)))
2192   (pass-if (not (zero? -7)))
2193   (pass-if (not (zero? (+ 1 fixnum-max))))
2194   (pass-if (not (zero? (- 1 fixnum-min))))
2195   (pass-if (not (zero? 1.3)))
2196   (pass-if (not (zero? 3.1+4.2i))))
2197
2198 ;;;
2199 ;;; positive?
2200 ;;;
2201
2202 (with-test-prefix "positive?"
2203   (expect-fail (documented? positive?))
2204   (pass-if (positive? 1))
2205   (pass-if (positive? (+ fixnum-max 1)))
2206   (pass-if (positive? 1.3))
2207   (pass-if (not (positive? 0)))
2208   (pass-if (not (positive? -1)))
2209   (pass-if (not (positive? (- fixnum-min 1))))
2210   (pass-if (not (positive? -1.3))))
2211
2212 ;;;
2213 ;;; negative?
2214 ;;;
2215
2216 (with-test-prefix "negative?"
2217   (expect-fail (documented? negative?))
2218   (pass-if (not (negative? 1)))
2219   (pass-if (not (negative? (+ fixnum-max 1))))
2220   (pass-if (not (negative? 1.3)))
2221   (pass-if (not (negative? 0)))
2222   (pass-if (negative? -1))
2223   (pass-if (negative? (- fixnum-min 1)))
2224   (pass-if (negative? -1.3)))
2225
2226 ;;;
2227 ;;; max
2228 ;;;
2229
2230 (with-test-prefix "max"
2231   (pass-if-exception "no args" exception:wrong-num-args
2232     (max))
2233
2234   (pass-if-exception "one complex" exception:wrong-type-arg
2235     (max 1+i))
2236
2237   (pass-if-exception "inum/complex" exception:wrong-type-arg
2238     (max 123 1+i))
2239   (pass-if-exception "big/complex" exception:wrong-type-arg
2240     (max 9999999999999999999999999999999999999999 1+i))
2241   (pass-if-exception "real/complex" exception:wrong-type-arg
2242     (max 123.0 1+i))
2243   (pass-if-exception "frac/complex" exception:wrong-type-arg
2244     (max 123/456 1+i))
2245
2246   (pass-if-exception "complex/inum" exception:wrong-type-arg
2247     (max 1+i 123))
2248   (pass-if-exception "complex/big" exception:wrong-type-arg
2249     (max 1+i 9999999999999999999999999999999999999999))
2250   (pass-if-exception "complex/real" exception:wrong-type-arg
2251     (max 1+i 123.0))
2252   (pass-if-exception "complex/frac" exception:wrong-type-arg
2253     (max 1+i 123/456))
2254
2255   (let ((big*2 (* fixnum-max 2))
2256         (big*3 (* fixnum-max 3))
2257         (big*4 (* fixnum-max 4))
2258         (big*5 (* fixnum-max 5)))
2259
2260     (with-test-prefix "inum / frac"
2261       (pass-if (= 3 (max 3 5/2)))
2262       (pass-if (= 5/2 (max 2 5/2))))
2263
2264     (with-test-prefix "frac / inum"
2265       (pass-if (= 3 (max 5/2 3)))
2266       (pass-if (= 5/2 (max 5/2 2))))
2267
2268     (with-test-prefix "inum / real"
2269       (pass-if (nan? (max 123 +nan.0))))
2270
2271     (with-test-prefix "real / inum"
2272       (pass-if (nan? (max +nan.0 123))))
2273
2274     (with-test-prefix "big / frac"
2275       (pass-if (= big*2 (max big*2 5/2)))
2276       (pass-if (= 5/2 (max (- big*2) 5/2))))
2277
2278     (with-test-prefix "frac / big"
2279       (pass-if (= big*2 (max 5/2 big*2)))
2280       (pass-if (= 5/2 (max 5/2 (- big*2)))))
2281
2282     (with-test-prefix "big / real"
2283       (pass-if (nan? (max big*5 +nan.0)))
2284       (pass-if (eqv? (exact->inexact big*5)  (max big*5 -inf.0)))
2285       (pass-if (eqv? (exact->inexact big*5)  (max big*5 1.0)))
2286       (pass-if (eqv? +inf.0                  (max big*5 +inf.0)))
2287       (pass-if (eqv? 1.0                     (max (- big*5) 1.0))))
2288
2289     (with-test-prefix "real / big"
2290       (pass-if (nan? (max +nan.0 big*5)))
2291       (pass-if (eqv? (exact->inexact big*5)  (max -inf.0 big*5)))
2292       (pass-if (eqv? (exact->inexact big*5)  (max 1.0 big*5)))
2293       (pass-if (eqv? +inf.0                  (max +inf.0 big*5)))
2294       (pass-if (eqv? 1.0                     (max 1.0 (- big*5)))))
2295
2296     (with-test-prefix "frac / frac"
2297       (pass-if (= 2/3 (max 1/2 2/3)))
2298       (pass-if (= 2/3 (max 2/3 1/2)))
2299       (pass-if (= -1/2 (max -1/2 -2/3)))
2300       (pass-if (= -1/2 (max -2/3 -1/2))))
2301
2302     (with-test-prefix "real / real"
2303       (pass-if (nan? (max 123.0 +nan.0)))
2304       (pass-if (nan? (max +nan.0 123.0)))
2305       (pass-if (nan? (max +nan.0 +nan.0)))
2306       (pass-if (= 456.0 (max 123.0 456.0)))
2307       (pass-if (= 456.0 (max 456.0 123.0)))))
2308
2309   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2310   ;; sure we've avoided that
2311   (for-each (lambda (b)
2312               (pass-if (list b +inf.0)
2313                 (= +inf.0 (max b +inf.0)))
2314               (pass-if (list +inf.0 b)
2315                 (= +inf.0 (max b +inf.0)))
2316               (pass-if (list b -inf.0)
2317                 (= (exact->inexact b) (max b -inf.0)))
2318               (pass-if (list -inf.0 b)
2319                 (= (exact->inexact b) (max b -inf.0))))
2320             (list (1- (ash 1 1024))
2321                   (ash 1 1024)
2322                   (1+ (ash 1 1024))
2323                   (- (1- (ash 1 1024)))
2324                   (- (ash 1 1024))
2325                   (- (1+ (ash 1 1024)))))
2326
2327   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2328   ;; sure we've avoided that
2329   (pass-if (nan? (max (ash 1 2048) +nan.0)))
2330   (pass-if (nan? (max +nan.0 (ash 1 2048)))))
2331
2332 ;;;
2333 ;;; min
2334 ;;;
2335
2336 ;; FIXME: unfinished...
2337
2338 (with-test-prefix "min"
2339   (pass-if-exception "no args" exception:wrong-num-args
2340     (min))
2341
2342   (pass-if-exception "one complex" exception:wrong-type-arg
2343     (min 1+i))
2344
2345   (pass-if-exception "inum/complex" exception:wrong-type-arg
2346     (min 123 1+i))
2347   (pass-if-exception "big/complex" exception:wrong-type-arg
2348     (min 9999999999999999999999999999999999999999 1+i))
2349   (pass-if-exception "real/complex" exception:wrong-type-arg
2350     (min 123.0 1+i))
2351   (pass-if-exception "frac/complex" exception:wrong-type-arg
2352     (min 123/456 1+i))
2353
2354   (pass-if-exception "complex/inum" exception:wrong-type-arg
2355     (min 1+i 123))
2356   (pass-if-exception "complex/big" exception:wrong-type-arg
2357     (min 1+i 9999999999999999999999999999999999999999))
2358   (pass-if-exception "complex/real" exception:wrong-type-arg
2359     (min 1+i 123.0))
2360   (pass-if-exception "complex/frac" exception:wrong-type-arg
2361     (min 1+i 123/456))
2362
2363   (let ((big*2 (* fixnum-max 2))
2364         (big*3 (* fixnum-max 3))
2365         (big*4 (* fixnum-max 4))
2366         (big*5 (* fixnum-max 5)))
2367
2368     (pass-if (documented? min))
2369     (pass-if (= 1 (min 7 3 1 5)))
2370     (pass-if (= 1 (min 1 7 3 5)))
2371     (pass-if (= 1 (min 7 3 5 1)))
2372     (pass-if (= -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
2373     (pass-if (= -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
2374     (pass-if (= -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
2375     (pass-if (= big*2 (min big*3 big*5 big*2 big*4)))
2376     (pass-if (= big*2 (min big*2 big*3 big*5 big*4)))
2377     (pass-if (= big*2 (min big*3 big*5 big*4 big*2)))
2378     (pass-if
2379         (= (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
2380     (pass-if
2381         (= (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
2382     (pass-if
2383         (= (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
2384
2385     (with-test-prefix "inum / frac"
2386       (pass-if (= 5/2 (min 3 5/2)))
2387       (pass-if (= 2   (min 2 5/2))))
2388
2389     (with-test-prefix "frac / inum"
2390       (pass-if (= 5/2 (min 5/2 3)))
2391       (pass-if (= 2   (min 5/2 2))))
2392
2393     (with-test-prefix "inum / real"
2394       (pass-if (nan? (min 123 +nan.0))))
2395
2396     (with-test-prefix "real / inum"
2397       (pass-if (nan? (min +nan.0 123))))
2398
2399     (with-test-prefix "big / frac"
2400       (pass-if (= 5/2       (min big*2 5/2)))
2401       (pass-if (= (- big*2) (min (- big*2) 5/2))))
2402
2403     (with-test-prefix "frac / big"
2404       (pass-if (= 5/2       (min 5/2 big*2)))
2405       (pass-if (= (- big*2) (min 5/2 (- big*2)))))
2406
2407     (with-test-prefix "big / real"
2408       (pass-if (nan? (min big*5 +nan.0)))
2409       (pass-if (eqv? (exact->inexact big*5)      (min big*5  +inf.0)))
2410       (pass-if (eqv? -inf.0                      (min big*5  -inf.0)))
2411       (pass-if (eqv? 1.0                         (min big*5 1.0)))
2412       (pass-if (eqv? (exact->inexact (- big*5))  (min (- big*5) 1.0))))
2413
2414     (with-test-prefix "real / big"
2415       (pass-if (nan? (min +nan.0 big*5)))
2416       (pass-if (eqv? (exact->inexact big*5)      (min +inf.0 big*5)))
2417       (pass-if (eqv? -inf.0                      (min -inf.0 big*5)))
2418       (pass-if (eqv? 1.0                         (min 1.0 big*5)))
2419       (pass-if (eqv? (exact->inexact (- big*5))  (min 1.0 (- big*5)))))
2420
2421     (with-test-prefix "frac / frac"
2422       (pass-if (= 1/2 (min 1/2 2/3)))
2423       (pass-if (= 1/2 (min 2/3 1/2)))
2424       (pass-if (= -2/3 (min -1/2 -2/3)))
2425       (pass-if (= -2/3 (min -2/3 -1/2))))
2426
2427     (with-test-prefix "real / real"
2428       (pass-if (nan? (min 123.0 +nan.0)))
2429       (pass-if (nan? (min +nan.0 123.0)))
2430       (pass-if (nan? (min +nan.0 +nan.0)))
2431       (pass-if (= 123.0 (min 123.0 456.0)))
2432       (pass-if (= 123.0 (min 456.0 123.0)))))
2433
2434
2435   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
2436   ;; sure we've avoided that
2437   (for-each (lambda (b)
2438               (pass-if (list b +inf.0)
2439                 (= (exact->inexact b) (min b +inf.0)))
2440               (pass-if (list +inf.0 b)
2441                 (= (exact->inexact b) (min b +inf.0)))
2442               (pass-if (list b -inf.0)
2443                 (= -inf.0 (min b -inf.0)))
2444               (pass-if (list -inf.0 b)
2445                 (= -inf.0 (min b -inf.0))))
2446             (list (1- (ash 1 1024))
2447                   (ash 1 1024)
2448                   (1+ (ash 1 1024))
2449                   (- (1- (ash 1 1024)))
2450                   (- (ash 1 1024))
2451                   (- (1+ (ash 1 1024)))))
2452
2453   ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
2454   ;; sure we've avoided that
2455   (pass-if (nan? (min (- (ash 1 2048)) (- +nan.0))))
2456   (pass-if (nan? (min (- +nan.0) (- (ash 1 2048))))))
2457
2458 ;;;
2459 ;;; +
2460 ;;;
2461
2462 (with-test-prefix/c&e "+"
2463
2464   (pass-if "documented?"
2465     (documented? +))
2466
2467   ;; The maximum fixnum on a 32-bit architecture: 2^29 - 1.
2468   (pass-if "fixnum + fixnum = bignum (32-bit)"
2469     (eqv? 536870912 (+ 536870910 2)))
2470
2471   ;; The maximum fixnum on a 64-bit architecture: 2^61 - 1.
2472   (pass-if "fixnum + fixnum = bignum (64-bit)"
2473     (eqv? 2305843009213693952 (+ 2305843009213693950 2)))
2474
2475   (pass-if "bignum + fixnum = fixnum"
2476     (eqv? 0 (+ (1+ most-positive-fixnum) most-negative-fixnum))))
2477
2478 ;;;
2479 ;;; -
2480 ;;;
2481
2482 (with-test-prefix/c&e "-"
2483
2484   (pass-if "-inum - +bignum"
2485     (= #x-100000000000000000000000000000001
2486        (- -1 #x100000000000000000000000000000000)))
2487
2488   (pass-if "big - inum"
2489     (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
2490        (- #x100000000000000000000000000000000 1)))
2491
2492   (pass-if "big - -inum"
2493     (= #x100000000000000000000000000000001
2494        (- #x100000000000000000000000000000000 -1)))
2495
2496   ;; The mininum fixnum on a 32-bit architecture: -2^29.
2497   (pass-if "fixnum - fixnum = bignum (32-bit)"
2498     (eqv? -536870912 (- -536870910 2)))
2499
2500   ;; The minimum fixnum on a 64-bit architecture: -2^61.
2501   (pass-if "fixnum - fixnum = bignum (64-bit)"
2502     (eqv? -2305843009213693952 (- -2305843009213693950 2)))
2503
2504   (pass-if "bignum - fixnum = fixnum"
2505     (eqv? most-positive-fixnum (- (1+ most-positive-fixnum) 1))))
2506
2507 ;;;
2508 ;;; *
2509 ;;;
2510
2511 (with-test-prefix "*"
2512
2513   (with-test-prefix "inum * bignum"
2514
2515     (pass-if "0 * 2^256 = 0"
2516       (eqv? 0 (* 0 (ash 1 256)))))
2517
2518   (with-test-prefix "inum * flonum"
2519
2520     (pass-if "0 * 1.0 = 0"
2521       (eqv? 0 (* 0 1.0))))
2522
2523   (with-test-prefix "inum * complex"
2524
2525     (pass-if "0 * 1+1i = 0"
2526       (eqv? 0 (* 0 1+1i))))
2527
2528   (with-test-prefix "inum * frac"
2529
2530     (pass-if "0 * 2/3 = 0"
2531       (eqv? 0 (* 0 2/3))))
2532
2533   (with-test-prefix "bignum * inum"
2534
2535     (pass-if "2^256 * 0 = 0"
2536       (eqv? 0 (* (ash 1 256) 0))))
2537
2538   (with-test-prefix "flonum * inum"
2539
2540     ;; in guile 1.6.8 and 1.8.1 and earlier this returned inexact 0.0
2541     (pass-if "1.0 * 0 = 0"
2542       (eqv? 0 (* 1.0 0))))
2543
2544   (with-test-prefix "complex * inum"
2545
2546     ;; in guile 1.6.8 and 1.8.1 and earlier this returned inexact 0.0
2547     (pass-if "1+1i * 0 = 0"
2548       (eqv? 0 (* 1+1i 0))))
2549
2550   (pass-if "complex * bignum"
2551     (let ((big (ash 1 90)))
2552       (= (make-rectangular big big)
2553          (* 1+1i big))))
2554
2555   (with-test-prefix "frac * inum"
2556
2557     (pass-if "2/3 * 0 = 0"
2558       (eqv? 0 (* 2/3 0)))))
2559
2560 ;;;
2561 ;;; /
2562 ;;;
2563
2564 (with-test-prefix "/"
2565
2566   (pass-if "documented?"
2567     (documented? /))
2568
2569   (with-test-prefix "division by zero"
2570
2571     (pass-if-exception "(/ 0)"
2572         exception:numerical-overflow
2573       (/ 0))
2574
2575     (pass-if "(/ 0.0)"
2576       (= +inf.0 (/ 0.0)))
2577
2578     (pass-if-exception "(/ 1 0)"
2579         exception:numerical-overflow
2580       (/ 1 0))
2581
2582     (pass-if "(/ 1 0.0)"
2583       (= +inf.0 (/ 1 0.0)))
2584
2585     (pass-if-exception "(/ bignum 0)"
2586         exception:numerical-overflow
2587       (/ (+ fixnum-max 1) 0))
2588
2589     (pass-if "(/ bignum 0.0)"
2590       (= +inf.0 (/ (+ fixnum-max 1) 0.0)))
2591
2592     (pass-if-exception "(/ 1.0 0)"
2593         exception:numerical-overflow
2594       (/ 1.0 0))
2595
2596     (pass-if "(/ 1.0 0.0)"
2597       (= +inf.0 (/ 1.0 0.0)))
2598
2599     (pass-if-exception "(/ +i 0)"
2600         exception:numerical-overflow
2601       (/ +i 0))
2602
2603     (pass-if "(/ +i 0.0)"
2604       (= +inf.0 (imag-part (/ +i 0.0)))))
2605
2606   (with-test-prefix "1/complex"
2607
2608     (pass-if "0+1i"
2609       (eqv? 0-1i (/ 0+1i)))
2610
2611     ;; in guile 1.6 through 1.6.7 this incorrectly resulted in nans
2612     (pass-if "0-1i"
2613       (eqv? 0+1i (/ 0-1i)))
2614
2615     (pass-if "1+1i"
2616       (eqv? 0.5-0.5i (/ 1+1i)))
2617
2618     (pass-if "1-1i"
2619       (eqv? 0.5+0.5i (/ 1-1i)))
2620
2621     (pass-if "-1+1i"
2622       (eqv? -0.5-0.5i (/ -1+1i)))
2623
2624     (pass-if "-1-1i"
2625       (eqv? -0.5+0.5i (/ -1-1i)))
2626
2627     (pass-if "(/ 3+4i)"
2628       (= (/ 3+4i) 0.12-0.16i))
2629
2630     (pass-if "(/ 4+3i)"
2631       (= (/ 4+3i) 0.16-0.12i))
2632
2633     (pass-if "(/ 1e200+1e200i)"
2634       (= (/ 1e200+1e200i) 5.0e-201-5.0e-201i)))
2635
2636   (with-test-prefix "inum/complex"
2637
2638     (pass-if "(/ 25 3+4i)"
2639       (= (/ 25 3+4i) 3.0-4.0i))
2640
2641     (pass-if "(/ 25 4+3i)"
2642       (= (/ 25 4+3i) 4.0-3.0i)))
2643
2644   (with-test-prefix "complex/complex"
2645
2646     (pass-if "(/ 25+125i 3+4i)"
2647       (= (/ 25+125i 3+4i) 23.0+11.0i))
2648
2649     (pass-if "(/ 25+125i 4+3i)"
2650       (= (/ 25+125i 4+3i) 19.0+17.0i))))
2651
2652 ;;;
2653 ;;; truncate
2654 ;;;
2655
2656 (with-test-prefix "truncate"
2657   (pass-if (=  1 (truncate  1.75)))
2658   (pass-if (=  1 (truncate  1.5)))
2659   (pass-if (=  1 (truncate  1.25)))
2660   (pass-if (=  0 (truncate  0.75)))
2661   (pass-if (=  0 (truncate  0.5)))
2662   (pass-if (=  0 (truncate  0.0)))
2663   (pass-if (=  0 (truncate -0.5)))
2664   (pass-if (= -1 (truncate -1.25)))
2665   (pass-if (= -1 (truncate -1.5))))
2666
2667 ;;;
2668 ;;; round
2669 ;;;
2670
2671 (with-test-prefix "round"
2672   (pass-if (=  2 (round  1.75)))
2673   (pass-if (=  2 (round  1.5)))
2674   (pass-if (=  1 (round  1.25)))
2675   (pass-if (=  1 (round  0.75)))
2676   (pass-if (=  0 (round  0.5)))
2677   (pass-if (=  0 (round  0.0)))
2678   (pass-if (=  0 (round -0.5)))
2679   (pass-if (= -1 (round -1.25)))
2680   (pass-if (= -2 (round -1.5)))
2681
2682   (with-test-prefix "inum"
2683     (pass-if "0"
2684       (and (= 0    (round 0))
2685            (exact? (round 0))))
2686
2687     (pass-if "1"
2688       (and (= 1    (round 1))
2689            (exact? (round 1))))
2690
2691     (pass-if "-1"
2692       (and (= -1   (round -1))
2693            (exact? (round -1)))))
2694
2695   (with-test-prefix "bignum"
2696     (let ((x (1+ most-positive-fixnum)))
2697       (pass-if "(1+ most-positive-fixnum)"
2698         (and (= x    (round x))
2699              (exact? (round x)))))
2700
2701     (let ((x (1- most-negative-fixnum)))
2702       (pass-if "(1- most-negative-fixnum)"
2703         (and (= x    (round x))
2704              (exact? (round x))))))
2705
2706   (with-test-prefix "frac"
2707     (define (=exact x y)
2708       (and (= x y)
2709            (exact? y)))
2710
2711     (pass-if (=exact -2 (round -7/3)))
2712     (pass-if (=exact -2 (round -5/3)))
2713     (pass-if (=exact -1 (round -4/3)))
2714     (pass-if (=exact -1 (round -2/3)))
2715     (pass-if (=exact  0 (round -1/3)))
2716     (pass-if (=exact  0 (round  1/3)))
2717     (pass-if (=exact  1 (round  2/3)))
2718     (pass-if (=exact  1 (round  4/3)))
2719     (pass-if (=exact  2 (round  5/3)))
2720     (pass-if (=exact  2 (round  7/3)))
2721
2722     (pass-if (=exact -3 (round -17/6)))
2723     (pass-if (=exact -3 (round -16/6)))
2724     (pass-if (=exact -2 (round -15/6)))
2725     (pass-if (=exact -2 (round -14/6)))
2726     (pass-if (=exact -2 (round -13/6)))
2727     (pass-if (=exact -2 (round -11/6)))
2728     (pass-if (=exact -2 (round -10/6)))
2729     (pass-if (=exact -2 (round  -9/6)))
2730     (pass-if (=exact -1 (round  -8/6)))
2731     (pass-if (=exact -1 (round  -7/6)))
2732     (pass-if (=exact -1 (round  -5/6)))
2733     (pass-if (=exact -1 (round  -4/6)))
2734     (pass-if (=exact  0 (round  -3/6)))
2735     (pass-if (=exact  0 (round  -2/6)))
2736     (pass-if (=exact  0 (round  -1/6)))
2737     (pass-if (=exact  0 (round   1/6)))
2738     (pass-if (=exact  0 (round   2/6)))
2739     (pass-if (=exact  0 (round   3/6)))
2740     (pass-if (=exact  1 (round   4/6)))
2741     (pass-if (=exact  1 (round   5/6)))
2742     (pass-if (=exact  1 (round   7/6)))
2743     (pass-if (=exact  1 (round   8/6)))
2744     (pass-if (=exact  2 (round   9/6)))
2745     (pass-if (=exact  2 (round  10/6)))
2746     (pass-if (=exact  2 (round  11/6)))
2747     (pass-if (=exact  2 (round  13/6)))
2748     (pass-if (=exact  2 (round  14/6)))
2749     (pass-if (=exact  2 (round  15/6)))
2750     (pass-if (=exact  3 (round  16/6)))
2751     (pass-if (=exact  3 (round  17/6))))
2752
2753   (with-test-prefix "real"
2754     (pass-if "0.0"
2755       (and (= 0.0    (round 0.0))
2756            (inexact? (round 0.0))))
2757
2758     (pass-if "1.0"
2759       (and (= 1.0    (round 1.0))
2760            (inexact? (round 1.0))))
2761
2762     (pass-if "-1.0"
2763       (and (= -1.0   (round -1.0))
2764            (inexact? (round -1.0))))
2765
2766     (pass-if "-3.1"
2767       (and (= -3.0   (round -3.1))
2768            (inexact? (round -3.1))))
2769
2770     (pass-if "3.1"
2771       (and (= 3.0    (round 3.1))
2772            (inexact? (round 3.1))))
2773
2774     (pass-if "3.9"
2775       (and (= 4.0    (round 3.9))
2776            (inexact? (round 3.9))))
2777
2778     (pass-if "-3.9"
2779       (and (= -4.0   (round -3.9))
2780            (inexact? (round -3.9))))
2781
2782     (pass-if "1.5"
2783       (and (= 2.0    (round 1.5))
2784            (inexact? (round 1.5))))
2785
2786     (pass-if "2.5"
2787       (and (= 2.0    (round 2.5))
2788            (inexact? (round 2.5))))
2789
2790     (pass-if "3.5"
2791       (and (= 4.0    (round 3.5))
2792            (inexact? (round 3.5))))
2793
2794     (pass-if "-1.5"
2795       (and (= -2.0   (round -1.5))
2796            (inexact? (round -1.5))))
2797
2798     (pass-if "-2.5"
2799       (and (= -2.0   (round -2.5))
2800            (inexact? (round -2.5))))
2801
2802     (pass-if "-3.5"
2803       (and (= -4.0   (round -3.5))
2804            (inexact? (round -3.5))))
2805
2806     ;; prior to guile 1.6.5, on an IEEE system an inexact 2^53-1 (ie. a
2807     ;; float with mantissa all ones) came out as 2^53 from `round' (except
2808     ;; on i386 and m68k systems using the coprocessor and optimizing, where
2809     ;; extra precision hid the problem)
2810     (pass-if "2^53-1"
2811       (let ((x (exact->inexact (1- (ash 1 53)))))
2812         (and (= x      (round x))
2813              (inexact? (round x)))))
2814     (pass-if "-(2^53-1)"
2815       (let ((x (exact->inexact (- (1- (ash 1 53))))))
2816         (and (= x      (round x))
2817              (inexact? (round x)))))))
2818
2819 ;;;
2820 ;;; exact->inexact
2821 ;;;
2822
2823 (with-test-prefix "exact->inexact"
2824
2825   ;; Test "(exact->inexact n)", expect "want".
2826   ;; "i" is a index, for diagnostic purposes.
2827   (define (try-i i n want)
2828     (with-test-prefix (list i n want)
2829       (with-test-prefix "pos"
2830         (let ((got (exact->inexact n)))
2831           (pass-if "inexact?" (inexact? got))
2832           (pass-if (list "=" got) (= want got))))
2833       (set! n    (- n))
2834       (set! want (- want))
2835       (with-test-prefix "neg"
2836         (let ((got (exact->inexact n)))
2837           (pass-if "inexact?" (inexact? got))
2838           (pass-if (list "=" got) (= want got))))))
2839
2840   (with-test-prefix "2^i, no round"
2841     (do ((i    0   (1+ i))
2842          (n    1   (* 2 n))
2843          (want 1.0 (* 2.0 want)))
2844         ((> i 100))
2845       (try-i i n want)))
2846
2847   (with-test-prefix "2^i+1, no round"
2848     (do ((i    1   (1+ i))
2849          (n    3   (1- (* 2 n)))
2850          (want 3.0 (- (* 2.0 want) 1.0)))
2851         ((>= i dbl-mant-dig))
2852       (try-i i n want)))
2853
2854   (with-test-prefix "(2^i+1)*2^100, no round"
2855     (do ((i    1   (1+ i))
2856          (n    3   (1- (* 2 n)))
2857          (want 3.0 (- (* 2.0 want) 1.0)))
2858         ((>= i dbl-mant-dig))
2859       (try-i i (ash n 100) (ash-flo want 100))))
2860
2861   ;; bit pattern: 1111....11100.00
2862   ;;              <-mantdig-><-i->
2863   ;;
2864   (with-test-prefix "mantdig ones then zeros, no rounding"
2865     (do ((i    0  (1+ i))
2866          (n    (- (ash     1   dbl-mant-dig) 1)   (* 2 n))
2867          (want (- (ash-flo 1.0 dbl-mant-dig) 1.0) (* 2.0 want)))
2868         ((> i 100))
2869       (try-i i n want)))
2870
2871   ;; bit pattern: 1111....111011..1
2872   ;;              <-mantdig-> <-i->
2873   ;; This sort of value was incorrectly rounded upwards in Guile 1.6.4 when
2874   ;; i >= 11 (that's when the total is 65 or more bits).
2875   ;;
2876   (with-test-prefix "mantdig ones then 011..11, round down"
2877     (do ((i    0  (1+ i))
2878          (n    (- (ash     1   (+ 1 dbl-mant-dig)) 2)   (+ 1 (* 2 n)))
2879          (want (- (ash-flo 1.0 (+ 1 dbl-mant-dig)) 2.0) (* 2.0 want)))
2880         ((> i 100))
2881       (try-i i n want)))
2882
2883   ;; bit pattern: 1111....111100..001
2884   ;;              <-mantdig-> <--i->
2885   ;;
2886   (with-test-prefix "mantdig ones then 100..001, round up"
2887     (do ((i    0  (1+ i))
2888          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)  (1- (* 2 n)))
2889          (want    (ash-flo 1.0 (+ 2 dbl-mant-dig))     (* 2.0 want)))
2890         ((> i 100))
2891       (try-i i n want)))
2892
2893   ;; bit pattern: 1000....000100..001
2894   ;;              <-mantdig-> <--i->
2895   ;;
2896   (with-test-prefix "2^mantdig then 100..001, round up"
2897     (do ((i    0  (1+ i))
2898          (n    (- (ash     1   (+ 2 dbl-mant-dig)) 1)   (1- (* 2 n)))
2899          (want (+ (ash-flo 1.0 (+ 2 dbl-mant-dig)) 4.0) (* 2.0 want)))
2900         ((> i 100))
2901       (try-i i n want)))
2902
2903   (pass-if "frac big/big"
2904     (let ((big (ash 1 256)))
2905       (= 1.0 (exact->inexact (/ (1+ big) big)))))
2906
2907   ;; In guile 1.8.0 this failed, giving back "nan" because it tried to
2908   ;; convert the num and den to doubles, resulting in infs.
2909   (pass-if "frac big/big, exceeding double"
2910     (let ((big (ash 1 4096)))
2911       (= 1.0 (exact->inexact (/ (1+ big) big))))))
2912
2913 ;;;
2914 ;;; floor
2915 ;;;
2916
2917 ;;;
2918 ;;; ceiling
2919 ;;;
2920
2921 ;;;
2922 ;;; expt
2923 ;;;
2924
2925 (with-test-prefix "expt"
2926   (pass-if-exception "non-numeric base" exception:wrong-type-arg
2927                      (expt #t 0))
2928   (pass-if (eqv? 1 (expt 0 0)))
2929   (pass-if (eqv? 1 (expt 0.0 0)))
2930   (pass-if (eqv? 1.0 (expt 0 0.0)))
2931   (pass-if (eqv? 1.0 (expt 0.0 0.0)))
2932   (pass-if (nan? (expt 0 -1)))
2933   (pass-if (nan? (expt 0 -1.0)))
2934   (pass-if (nan? (expt 0.0 -1)))
2935   (pass-if (nan? (expt 0.0 -1.0)))
2936   (pass-if (eqv? 0 (expt 0 3)))
2937   (pass-if (= 0 (expt 0 4.0)))
2938   (pass-if (eqv? 0.0 (expt 0.0 5)))
2939   (pass-if (eqv? 0.0 (expt 0.0 6.0)))
2940   (pass-if (eqv? -2742638075.5 (expt -2742638075.5 1)))
2941   (pass-if (eqv? (* -2742638075.5 -2742638075.5)
2942                  (expt -2742638075.5 2)))
2943   (pass-if (eqv? 4.0 (expt -2.0 2.0)))
2944   (pass-if (eqv? -1/8 (expt -2 -3)))
2945   (pass-if (eqv? -0.125 (expt -2.0 -3)))
2946   (pass-if (eqv? -0.125 (expt -2 -3.0)))
2947   (pass-if (eqv? -0.125 (expt -2.0 -3.0)))
2948   (pass-if (eqv? 0.25 (expt 2.0 -2.0)))
2949   (pass-if (eqv? (* -1.0 12398 12398) (expt +12398i 2.0)))
2950   (pass-if (eqv-loosely? +i (expt -1 0.5)))
2951   (pass-if (eqv-loosely? +i (expt -1 1/2)))
2952   (pass-if (eqv-loosely? 1.0+1.7320508075688i (expt -8 1/3)))
2953   (pass-if (eqv? +inf.0 (expt 2 +inf.0)))
2954   (pass-if (eqv? +inf.0 (expt 2.0 +inf.0)))
2955   (pass-if (eqv? 0.0 (expt 2 -inf.0)))
2956   (pass-if (eqv? 0.0 (expt 2.0 -inf.0))))
2957
2958
2959 ;;;
2960 ;;; asinh
2961 ;;;
2962
2963 (with-test-prefix "asinh"
2964   (pass-if (= 0 (asinh 0))))
2965
2966 ;;;
2967 ;;; acosh
2968 ;;;
2969
2970 (with-test-prefix "acosh"
2971   (pass-if (= 0 (acosh 1))))
2972
2973 ;;;
2974 ;;; atanh
2975 ;;;
2976
2977 (with-test-prefix "atanh"
2978   (pass-if (= 0 (atanh 0))))
2979
2980 ;;;
2981 ;;; make-rectangular
2982 ;;;
2983
2984 ;;;
2985 ;;; make-polar
2986 ;;;
2987
2988 (with-test-prefix "make-polar"
2989   (define pi 3.14159265358979323846)
2990   (define (almost= x y)
2991     (> 0.01 (magnitude (- x y))))
2992
2993   (pass-if (= 0 (make-polar 0 0)))
2994   (pass-if (= 0 (make-polar 0 123.456)))
2995   (pass-if (= 1 (make-polar 1 0)))
2996   (pass-if (= -1 (make-polar -1 0)))
2997
2998   (pass-if (almost= 0+i (make-polar 1 (* 0.5 pi))))
2999   (pass-if (almost= -1  (make-polar 1 (* 1.0 pi))))
3000   (pass-if (almost= 0-i (make-polar 1 (* 1.5 pi))))
3001   (pass-if (almost= 1   (make-polar 1 (* 2.0 pi)))))
3002
3003 ;;;
3004 ;;; real-part
3005 ;;;
3006
3007 ;;;
3008 ;;; imag-part
3009 ;;;
3010
3011 ;;;
3012 ;;; magnitude
3013 ;;;
3014
3015 (with-test-prefix "magnitude"
3016   (pass-if (= 0 (magnitude 0)))
3017   (pass-if (= 1 (magnitude 1)))
3018   (pass-if (= 1 (magnitude -1)))
3019   (pass-if (= 1 (magnitude 0+i)))
3020   (pass-if (= 1 (magnitude 0-i)))
3021   (pass-if (= 5 (magnitude 3+4i)))
3022   (pass-if (= 5 (magnitude 3-4i)))
3023   (pass-if (= 5 (magnitude -3+4i)))
3024   (pass-if (= 5 (magnitude -3-4i))))
3025
3026 ;;;
3027 ;;; angle
3028 ;;;
3029
3030 (with-test-prefix "angle"
3031   (define pi 3.14159265358979323846)
3032   (define (almost= x y)
3033     (> 0.01 (magnitude (- x y))))
3034
3035   (pass-if "inum +ve"   (=        0 (angle 1)))
3036   (pass-if "inum -ve"   (almost= pi (angle -1)))
3037
3038   (pass-if "bignum +ve" (=        0 (angle (1+ fixnum-max))))
3039   (pass-if "bignum -ve" (almost= pi (angle (1- fixnum-min))))
3040
3041   (pass-if "flonum +ve" (=        0 (angle 1.5)))
3042   (pass-if "flonum -ve" (almost= pi (angle -1.5))))
3043
3044 ;;;
3045 ;;; inexact->exact
3046 ;;;
3047
3048 (with-test-prefix "inexact->exact"
3049
3050   (pass-if-exception "+inf" exception:out-of-range
3051     (inexact->exact +inf.0))
3052
3053   (pass-if-exception "-inf" exception:out-of-range
3054     (inexact->exact -inf.0))
3055
3056   (pass-if-exception "nan" exception:out-of-range
3057     (inexact->exact +nan.0))
3058
3059   (with-test-prefix "2.0**i to exact and back"
3060     (do ((i 0   (1+ i))
3061          (n 1.0 (* 2.0 n)))
3062         ((> i 100))
3063       (pass-if (list i n)
3064         (= n (inexact->exact (exact->inexact n)))))))
3065
3066 ;;;
3067 ;;; integer-expt
3068 ;;;
3069
3070 (with-test-prefix "integer-expt"
3071
3072   (pass-if-exception "non-numeric base" exception:wrong-type-arg
3073                      (integer-expt #t 0))
3074   (pass-if-exception "2^+inf" exception:wrong-type-arg
3075     (integer-expt 2 +inf.0))
3076   (pass-if-exception "2^-inf" exception:wrong-type-arg
3077     (integer-expt 2 -inf.0))
3078   (pass-if-exception "2^nan" exception:wrong-type-arg
3079     (integer-expt 2 +nan.0))
3080
3081   (pass-if (eqv? 1 (integer-expt 0 0)))
3082   (pass-if (eqv? 1 (integer-expt 0.0 0)))
3083   (pass-if (nan? (integer-expt 0 -1)))
3084   (pass-if (nan? (integer-expt 0.0 -1)))
3085   (pass-if (eqv? 0 (integer-expt 0 3)))
3086   (pass-if (eqv? 0.0 (integer-expt 0.0 5)))
3087   (pass-if (eqv? -2742638075.5 (integer-expt -2742638075.5 1)))
3088   (pass-if (eqv? (* -2742638075.5 -2742638075.5)
3089                  (integer-expt -2742638075.5 2)))
3090   (pass-if (eqv? 4.0 (integer-expt -2.0 2)))
3091   (pass-if (eqv? -1/8 (integer-expt -2 -3)))
3092   (pass-if (eqv? -0.125 (integer-expt -2.0 -3)))
3093   (pass-if (eqv? 0.25 (integer-expt 2.0 -2)))
3094   (pass-if (eqv? (* -1.0 12398 12398) (integer-expt +12398.0i 2))))
3095
3096
3097 ;;;
3098 ;;; integer-length
3099 ;;;
3100
3101 (with-test-prefix "integer-length"
3102
3103   (with-test-prefix "-2^i, ...11100..00"
3104     (do ((n -1 (ash n 1))
3105          (i 0  (1+ i)))
3106         ((> i 256))
3107       (pass-if (list n "expect" i)
3108         (= i (integer-length n)))))
3109
3110   (with-test-prefix "-2^i+1 ...11100..01"
3111     (do ((n -3 (logxor 3 (ash n 1)))
3112          (i 2  (1+ i)))
3113         ((> i 256))
3114       (pass-if n
3115         (= i (integer-length n)))))
3116
3117   (with-test-prefix "-2^i-1 ...111011..11"
3118     (do ((n -2 (1+ (ash n 1)))
3119          (i 1  (1+ i)))
3120         ((> i 256))
3121       (pass-if n
3122         (= i (integer-length n))))))
3123
3124 ;;;
3125 ;;; log
3126 ;;;
3127
3128 (with-test-prefix "log"
3129   (pass-if "documented?"
3130     (documented? log))
3131
3132   (pass-if-exception "no args" exception:wrong-num-args
3133     (log))
3134   (pass-if-exception "two args" exception:wrong-num-args
3135     (log 123 456))
3136
3137   (pass-if (negative-infinity? (log 0)))
3138   (pass-if (negative-infinity? (log 0.0)))
3139   (pass-if (eqv? 0.0 (log 1)))
3140   (pass-if (eqv? 0.0 (log 1.0)))
3141   (pass-if (eqv-loosely? 1.0  (log const-e)))
3142   (pass-if (eqv-loosely? 2.0  (log const-e^2)))
3143   (pass-if (eqv-loosely? -1.0 (log const-1/e)))
3144
3145   (pass-if (eqv-loosely? 1.0+1.57079i (log 0+2.71828i)))
3146   (pass-if (eqv-loosely? 1.0-1.57079i (log 0-2.71828i)))
3147
3148   (pass-if (eqv-loosely? 0.0+3.14159i (log -1.0)))
3149   (pass-if (eqv-loosely? 1.0+3.14159i (log -2.71828)))
3150   (pass-if (eqv-loosely? 2.0+3.14159i (log (* -2.71828 2.71828)))))
3151
3152 ;;;
3153 ;;; log10
3154 ;;;
3155
3156 (with-test-prefix "log10"
3157   (pass-if "documented?"
3158     (documented? log10))
3159
3160   (pass-if-exception "no args" exception:wrong-num-args
3161     (log10))
3162   (pass-if-exception "two args" exception:wrong-num-args
3163     (log10 123 456))
3164
3165   (pass-if (negative-infinity? (log10 0)))
3166   (pass-if (negative-infinity? (log10 0.0)))
3167   (pass-if (eqv? 0.0 (log10 1)))
3168   (pass-if (eqv? 0.0 (log10 1.0)))
3169   (pass-if (eqv-loosely? 1.0  (log10 10.0)))
3170   (pass-if (eqv-loosely? 2.0  (log10 100.0)))
3171   (pass-if (eqv-loosely? -1.0 (log10 0.1)))
3172
3173   (pass-if (eqv-loosely? 1.0+0.68218i (log10 0+10.0i)))
3174   (pass-if (eqv-loosely? 1.0-0.68218i (log10 0-10.0i)))
3175
3176   (pass-if (eqv-loosely? 0.0+1.36437i (log10 -1)))
3177   (pass-if (eqv-loosely? 1.0+1.36437i (log10 -10)))
3178   (pass-if (eqv-loosely? 2.0+1.36437i (log10 -100))))
3179
3180 ;;;
3181 ;;; logbit?
3182 ;;;
3183
3184 (with-test-prefix "logbit?"
3185   (pass-if (eq? #f (logbit?  0 0)))
3186   (pass-if (eq? #f (logbit?  1 0)))
3187   (pass-if (eq? #f (logbit? 31 0)))
3188   (pass-if (eq? #f (logbit? 32 0)))
3189   (pass-if (eq? #f (logbit? 33 0)))
3190   (pass-if (eq? #f (logbit? 63 0)))
3191   (pass-if (eq? #f (logbit? 64 0)))
3192   (pass-if (eq? #f (logbit? 65 0)))
3193
3194   ;; prior to guile 1.6.5, testing bit 32, 64 etc of value 1 would wrap
3195   ;; around and return #t where it ought to be #f
3196   (pass-if (eq? #t (logbit?  0 1)))
3197   (pass-if (eq? #f (logbit?  1 1)))
3198   (pass-if (eq? #f (logbit? 31 1)))
3199   (pass-if (eq? #f (logbit? 32 1)))
3200   (pass-if (eq? #f (logbit? 33 1)))
3201   (pass-if (eq? #f (logbit? 63 1)))
3202   (pass-if (eq? #f (logbit? 64 1)))
3203   (pass-if (eq? #f (logbit? 65 1)))
3204   (pass-if (eq? #f (logbit? 128 1)))
3205
3206   (pass-if (eq? #t (logbit?  0 -1)))
3207   (pass-if (eq? #t (logbit?  1 -1)))
3208   (pass-if (eq? #t (logbit? 31 -1)))
3209   (pass-if (eq? #t (logbit? 32 -1)))
3210   (pass-if (eq? #t (logbit? 33 -1)))
3211   (pass-if (eq? #t (logbit? 63 -1)))
3212   (pass-if (eq? #t (logbit? 64 -1)))
3213   (pass-if (eq? #t (logbit? 65 -1))))
3214
3215 ;;;
3216 ;;; logcount
3217 ;;;
3218
3219 (with-test-prefix "logcount"
3220
3221   (with-test-prefix "-2^i, meaning ...11100..00"
3222     (do ((n -1 (ash n 1))
3223          (i 0  (1+ i)))
3224         ((> i 256))
3225       (pass-if n
3226         (= i (logcount n)))))
3227
3228   (with-test-prefix "2^i"
3229     (do ((n 1 (ash n 1))
3230          (i 0  (1+ i)))
3231         ((> i 256))
3232       (pass-if n
3233         (= 1 (logcount n)))))
3234
3235   (with-test-prefix "2^i-1"
3236     (do ((n 0 (1+ (ash n 1)))
3237          (i 0  (1+ i)))
3238         ((> i 256))
3239       (pass-if n
3240         (= i (logcount n))))))
3241
3242 ;;;
3243 ;;; logior
3244 ;;;
3245
3246 (with-test-prefix "logior"
3247   (pass-if (eqv? -1 (logior (ash -1 1) 1)))
3248
3249   ;; check that bignum or bignum+inum args will reduce to an inum
3250   (let ()
3251     (define (test x y)
3252       (pass-if (list x y '=> -1)
3253         (eqv? -1 (logior x y)))
3254       (pass-if (list y x '=> -1)
3255         (eqv? -1 (logior y x))))
3256     (test (ash -1 8) #xFF)
3257     (test (ash -1 28) #x0FFFFFFF)
3258     (test (ash -1 29) #x1FFFFFFF)
3259     (test (ash -1 30) #x3FFFFFFF)
3260     (test (ash -1 31) #x7FFFFFFF)
3261     (test (ash -1 32) #xFFFFFFFF)
3262     (test (ash -1 33) #x1FFFFFFFF)
3263     (test (ash -1 60) #x0FFFFFFFFFFFFFFF)
3264     (test (ash -1 61) #x1FFFFFFFFFFFFFFF)
3265     (test (ash -1 62) #x3FFFFFFFFFFFFFFF)
3266     (test (ash -1 63) #x7FFFFFFFFFFFFFFF)
3267     (test (ash -1 64) #xFFFFFFFFFFFFFFFF)
3268     (test (ash -1 65) #x1FFFFFFFFFFFFFFFF)
3269     (test (ash -1 128) #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
3270
3271 ;;;
3272 ;;; lognot
3273 ;;;
3274
3275 (with-test-prefix "lognot"
3276   (pass-if (= -1 (lognot 0)))
3277   (pass-if (= 0  (lognot -1)))
3278   (pass-if (= -2 (lognot 1)))
3279   (pass-if (= 1  (lognot -2)))
3280
3281   (pass-if (= #x-100000000000000000000000000000000
3282               (lognot #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
3283   (pass-if (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
3284               (lognot #x-100000000000000000000000000000000))))
3285
3286 ;;;
3287 ;;; sqrt
3288 ;;;
3289
3290 (with-test-prefix "sqrt"
3291   (pass-if "documented?"
3292     (documented? sqrt))
3293
3294   (pass-if-exception "no args" exception:wrong-num-args
3295     (sqrt))
3296   (pass-if-exception "two args" exception:wrong-num-args
3297     (sqrt 123 456))
3298
3299   (pass-if (eqv? 0.0 (sqrt 0)))
3300   (pass-if (eqv? 0.0 (sqrt 0.0)))
3301   (pass-if (eqv? 1.0 (sqrt 1.0)))
3302   (pass-if (eqv-loosely? 2.0   (sqrt 4.0)))
3303   (pass-if (eqv-loosely? 31.62 (sqrt 1000.0)))
3304
3305   (pass-if (eqv? +1.0i (sqrt -1.0)))
3306   (pass-if (eqv-loosely? +2.0i   (sqrt -4.0)))
3307   (pass-if (eqv-loosely? +31.62i (sqrt -1000.0)))
3308
3309   (pass-if "+i swings back to 45deg angle"
3310     (eqv-loosely? +0.7071+0.7071i (sqrt +1.0i)))
3311
3312   ;; Note: glibc 2.3 csqrt() had a bug affecting this test case, so if it
3313   ;; fails check whether that's the cause (there's a configure test to
3314   ;; reject it, but when cross-compiling we assume the C library is ok).
3315   (pass-if "-100i swings back to 45deg down"
3316     (eqv-loosely? +7.071-7.071i (sqrt -100.0i))))
3317
3318
3319 ;;
3320 ;; equal?
3321 ;;
3322
3323
3324 (with-test-prefix "equal?"
3325   (pass-if
3326
3327    ;; lazy reduction bit for rationals should not affect equal?
3328    (equal? 1/2 ((lambda (x) (denominator x) x) 1/2))))
3329