tests/arith.pure.lisp

   1 ;;;; arithmetic tests with no side effects
   2
   3 ;;;; This software is part of the SBCL system. See the README file for
   4 ;;;; more information.
   5 ;;;;
   6 ;;;; While most of SBCL is derived from the CMU CL system, the test
   7 ;;;; files (like this one) were written from scratch after the fork
   8 ;;;; from CMU CL.
   9 ;;;;
  10 ;;;; This software is in the public domain and is provided with
  11 ;;;; absolutely no warranty. See the COPYING and CREDITS files for
  12 ;;;; more information.
  13
  14 (cl:in-package :cl-user)
  15
  16 ;;; Once upon a time, in the process of porting CMUCL's SPARC backend
  17 ;;; to SBCL, multiplications were excitingly broken.  While it's
  18 ;;; unlikely that anything with such fundamental arithmetic errors as
  19 ;;; these are going to get this far, it's probably worth checking.
  20 (macrolet ((test (op res1 res2)
  21              `(progn
  22                (assert (= (,op 4 2) ,res1))
  23                (assert (= (,op 2 4) ,res2))
  24                (assert (= (funcall (compile nil '(lambda (x y) (,op x y))) 4 2)
  25                         ,res1))
  26                (assert (= (funcall (compile nil '(lambda (x y) (,op x y))) 2 4)
  27                         ,res2)))))
  28   (test + 6 6)
  29   (test - 2 -2)
  30   (test * 8 8)
  31   (test / 2 1/2)
  32   (test expt 16 16))
  33
  34 ;;; In a bug reported by Wolfhard Buss on cmucl-imp 2002-06-18 (BUG
  35 ;;; 184), sbcl didn't catch all divisions by zero, notably divisions
  36 ;;; of bignums and ratios by 0.  Fixed in sbcl-0.7.6.13.
  37 (assert-error (/ 2/3 0) division-by-zero)
  38 (assert-error (/ (1+ most-positive-fixnum) 0) division-by-zero)
  39
  40 ;;; In a bug reported by Raymond Toy on cmucl-imp 2002-07-18, (COERCE
  41 ;;; <RATIONAL> '(COMPLEX FLOAT)) was failing to return a complex
  42 ;;; float; a patch was given by Wolfhard Buss cmucl-imp 2002-07-19.
  43 (assert (= (coerce 1 '(complex float)) #c(1.0 0.0)))
  44 (assert (= (coerce 1/2 '(complex float)) #c(0.5 0.0)))
  45 (assert (= (coerce 1.0d0 '(complex float)) #c(1.0d0 0.0d0)))
  46
  47 ;;; (COERCE #c(<RATIONAL> <RATIONAL>) '(complex float)) resulted in
  48 ;;; an error up to 0.8.17.31
  49 (assert (= (coerce #c(1 2) '(complex float)) #c(1.0 2.0)))
  50
  51 ;;; COERCE also sometimes failed to verify that a particular coercion
  52 ;;; was possible (in particular coercing rationals to bounded float
  53 ;;; types.
  54 (assert-error (coerce 1 '(float 2.0 3.0)) type-error)
  55 (assert-error (coerce 1 '(single-float -1.0 0.0)) type-error)
  56 (assert (eql (coerce 1 '(single-float -1.0 2.0)) 1.0))
  57
  58 ;;; ANSI says MIN and MAX should signal TYPE-ERROR if any argument
  59 ;;; isn't REAL. SBCL 0.7.7 didn't in the 1-arg case. (reported as a
  60 ;;; bug in CMU CL on #lisp IRC by lrasinen 2002-09-01)
  61 (assert (null (ignore-errors (min '(1 2 3)))))
  62 (assert (= (min -1) -1))
  63 (assert (null (ignore-errors (min 1 #(1 2 3)))))
  64 (assert (= (min 10 11) 10))
  65 (assert (null (ignore-errors (min (find-package "CL") -5.0))))
  66 (assert (= (min 5.0 -3) -3))
  67 (assert (null (ignore-errors (max #c(4 3)))))
  68 (assert (= (max 0) 0))
  69 (assert (null (ignore-errors (max "MIX" 3))))
  70 (assert (= (max -1 10.0) 10.0))
  71 (assert (null (ignore-errors (max 3 #'max))))
  72 (assert (= (max -3 0) 0))
  73
  74 ;;; (CEILING x 2^k) was optimized incorrectly
  75 (loop for divisor in '(-4 4)
  76       for ceiler = (compile nil `(lambda (x)
  77                                    (declare (fixnum x))
  78                                    (declare (optimize (speed 3)))
  79                                    (ceiling x ,divisor)))
  80       do (loop for i from -5 to 5
  81                for exact-q = (/ i divisor)
  82                do (multiple-value-bind (q r)
  83                       (funcall ceiler i)
  84                     (assert (= (+ (* q divisor) r) i))
  85                     (assert (<= exact-q q))
  86                     (assert (< q (1+ exact-q))))))
  87
  88 ;;; (TRUNCATE x 2^k) was optimized incorrectly
  89 (loop for divisor in '(-4 4)
  90       for truncater = (compile nil `(lambda (x)
  91                                       (declare (fixnum x))
  92                                       (declare (optimize (speed 3)))
  93                                       (truncate x ,divisor)))
  94       do (loop for i from -9 to 9
  95                for exact-q = (/ i divisor)
  96                do (multiple-value-bind (q r)
  97                       (funcall truncater i)
  98                     (assert (= (+ (* q divisor) r) i))
  99                     (assert (<= (abs q) (abs exact-q)))
 100                     (assert (< (abs exact-q) (1+ (abs q)))))))
 101
 102 ;;; CEILING had a corner case, spotted by Paul Dietz
 103 (assert (= (ceiling most-negative-fixnum (1+ most-positive-fixnum)) -1))
 104
 105 ;;; give any optimizers of constant multiplication a light testing.
 106 ;;; 100 may seem low, but (a) it caught CSR's initial errors, and (b)
 107 ;;; before checking in, CSR tested with 10000.  So one hundred
 108 ;;; checkins later, we'll have doubled the coverage.
 109 (dotimes (i 100)
 110   (let* ((x (random most-positive-fixnum))
 111          (x2 (* x 2))
 112          (x3 (* x 3)))
 113     (let ((fn (handler-bind ((sb-ext:compiler-note
 114                               (lambda (c)
 115                                 (when (<= x3 most-positive-fixnum)
 116                                   (error c)))))
 117                 (compile nil
 118                          `(lambda (y)
 119                             (declare (optimize speed) (type (integer 0 3) y))
 120                             (* y ,x))))))
 121       (unless (and (= (funcall fn 0) 0)
 122                    (= (funcall fn 1) x)
 123                    (= (funcall fn 2) x2)
 124                    (= (funcall fn 3) x3))
 125         (error "bad results for ~D" x)))))
 126
 127 ;;; Bugs reported by Paul Dietz:
 128
 129 ;;; (GCD 0 x) must return (abs x)
 130 (dolist (x (list -10 (* 3 most-negative-fixnum)))
 131   (assert (= (gcd 0 x) (abs x))))
 132 ;;; LCM returns a non-negative number
 133 (assert (= (lcm 4 -10) 20))
 134 (assert (= (lcm 0 0) 0))
 135
 136 ;;; PPC bignum arithmetic bug:
 137 (multiple-value-bind (quo rem)
 138     (truncate 291351647815394962053040658028983955 10000000000000000000000000)
 139   (assert (= quo 29135164781))
 140   (assert (= rem 5394962053040658028983955)))
 141
 142 ;;; x86 LEA bug:
 143 (assert (= (funcall
 144             (compile nil '(lambda (x) (declare (bit x)) (+ x #xf0000000)))
 145             1)
 146            #xf0000001))
 147
 148 ;;; LOGBITP on bignums:
 149 (dolist (x '(((1+ most-positive-fixnum) 1 nil)
 150              ((1+ most-positive-fixnum) -1 t)
 151              ((1+ most-positive-fixnum) (1+ most-positive-fixnum) nil)
 152              ((1+ most-positive-fixnum) (1- most-negative-fixnum) t)
 153              (1 (ash most-negative-fixnum 1) nil)
 154              (#.(- sb-vm:n-word-bits sb-vm:n-fixnum-tag-bits 1) most-negative-fixnum t)
 155              (#.(1+ (- sb-vm:n-word-bits sb-vm:n-fixnum-tag-bits 1)) (ash most-negative-fixnum 1) t)
 156              (#.(+ 2 (- sb-vm:n-word-bits sb-vm:n-fixnum-tag-bits 1)) (ash most-negative-fixnum 1) t)
 157              (#.(+ sb-vm:n-word-bits 32) (ash most-negative-fixnum #.(+ 32 sb-vm:n-fixnum-tag-bits 2)) nil)
 158              (#.(+ sb-vm:n-word-bits 33) (ash most-negative-fixnum #.(+ 32 sb-vm:n-fixnum-tag-bits 2)) t)))
 159   (destructuring-bind (index int result) x
 160     (assert (eq (eval `(logbitp ,index ,int)) result))))
 161
 162 ;;; off-by-1 type inference error for %DPB and %DEPOSIT-FIELD:
 163 (let ((f (compile nil '(lambda (b)
 164                         (integer-length (dpb b (byte 4 28) -1005))))))
 165   (assert (= (funcall f 1230070) 32)))
 166 (let ((f (compile nil '(lambda (b)
 167                         (integer-length (deposit-field b (byte 4 28) -1005))))))
 168   (assert (= (funcall f 1230070) 32)))
 169
 170 ;;; type inference leading to an internal compiler error:
 171 (let ((f (compile nil '(lambda (x)
 172                         (declare (type fixnum x))
 173                         (ldb (byte 0 0) x)))))
 174   (assert (= (funcall f 1) 0))
 175   (assert (= (funcall f most-positive-fixnum) 0))
 176   (assert (= (funcall f -1) 0)))
 177
 178 ;;; Alpha bignum arithmetic bug:
 179 (assert (= (* 966082078641 419216044685) 404997107848943140073085))
 180
 181 ;;; Alpha smallnum arithmetic bug:
 182 (assert (= (ash -129876 -1026) -1))
 183
 184 ;;; Alpha middlenum (yes, really! Affecting numbers between 2^32 and
 185 ;;; 2^64 :) arithmetic bug
 186 (let ((fn (compile nil '(LAMBDA (A B C D)
 187           (DECLARE (TYPE (INTEGER -1621 -513) A)
 188                    (TYPE (INTEGER -3 34163) B)
 189                    (TYPE (INTEGER -9485132993 81272960) C)
 190                    (TYPE (INTEGER -255340814 519943) D)
 191                    (IGNORABLE A B C D)
 192                    (OPTIMIZE (SPEED 3) (SAFETY 1) (DEBUG 1)))
 193           (TRUNCATE C (MIN -100 4149605))))))
 194   (assert (= (funcall fn -1332 5864 -6963328729 -43789079) 69633287)))
 195
 196 ;;; Here's another fantastic Alpha backend bug: the code to load
 197 ;;; immediate 64-bit constants into a register was wrong.
 198 (let ((fn (compile nil '(LAMBDA (A B C D)
 199           (DECLARE (TYPE (INTEGER -3563 2733564) A)
 200                    (TYPE (INTEGER -548947 7159) B)
 201                    (TYPE (INTEGER -19 0) C)
 202                    (TYPE (INTEGER -2546009 0) D)
 203                    (IGNORABLE A B C D)
 204                    (OPTIMIZE (SPEED 3) (SAFETY 1) (DEBUG 1)))
 205           (CASE A
 206             ((89 125 16) (ASH A (MIN 18 -706)))
 207             (T (DPB -3 (BYTE 30 30) -1)))))))
 208   (assert (= (funcall fn 1227072 -529823 -18 -792831) -2147483649)))
 209
 210 ;;; ASH of a negative bignum by a bignum count would erroneously
 211 ;;; return 0 prior to sbcl-0.8.4.4
 212 (assert (= (ash (1- most-negative-fixnum) (1- most-negative-fixnum)) -1))
 213
 214 ;;; Whoops.  Too much optimization in division operators for 0
 215 ;;; divisor.
 216 (macrolet ((frob (name)
 217              `(let ((fn (compile nil '(lambda (x)
 218                                        (declare (optimize speed) (fixnum x))
 219                                        (,name x 0)))))
 220                 (assert-error (funcall fn 1) division-by-zero))))
 221   (frob mod)
 222   (frob truncate)
 223   (frob rem)
 224   (frob /)
 225   (frob floor)
 226   (frob ceiling))
 227
 228 ;; Check that the logic in SB-KERNEL::BASIC-COMPARE for doing fixnum/float
 229 ;; comparisons without rationalizing the floats still gives the right anwers
 230 ;; in the edge cases (had a fencepost error).
 231 (macrolet ((test (range type sign)
 232              `(let (ints
 233                     floats
 234                     (start (- ,(find-symbol (format nil
 235                                                     "MOST-~A-EXACTLY-~A-FIXNUM"
 236                                                     sign type)
 237                                             :sb-kernel)
 238                               ,range)))
 239                 (dotimes (i (1+ (* ,range 2)))
 240                   (let* ((x (+ start i))
 241                          (y (coerce x ',type)))
 242                     (push x ints)
 243                     (push y floats)))
 244                 (dolist (i ints)
 245                   (dolist (f floats)
 246                     (dolist (op '(< <= = >= >))
 247                       (unless (eq (funcall op i f)
 248                                   (funcall op i (rationalize f)))
 249                         (error "(not (eq (~a ~a ~f) (~a ~a ~a)))~%"
 250                                op i f
 251                                op i (rationalize f)))
 252                       (unless (eq (funcall op f i)
 253                                   (funcall op (rationalize f) i))
 254                         (error "(not (eq (~a ~f ~a) (~a ~a ~a)))~%"
 255                                op f i
 256                                op (rationalize f) i))))))))
 257   (test 32 double-float negative)
 258   (test 32 double-float positive)
 259   (test 32 single-float negative)
 260   (test 32 single-float positive))
 261
 262 ;; x86-64 sign-extension bug found using pfdietz's random tester.
 263 (assert (= 286142502
 264            (funcall (lambda ()
 265                       (declare (notinline logxor))
 266                       (min (logxor 0 0 0 286142502))))))
 267
 268 ;; Small bugs in LOGCOUNT can still allow SBCL to be built and thus go
 269 ;; unnoticed, so check more thoroughly here.
 270 (with-test (:name :logcount)
 271   (flet ((test (x n)
 272            (unless (= (logcount x) n)
 273              (error "logcount failure for ~a" x))))
 274     ;; Test with some patterns with well known number of ones/zeroes ...
 275     (dotimes (i 128)
 276       (let ((x (ash 1 i)))
 277         (test x 1)
 278         (test (- x) i)
 279         (test (1- x) i)))
 280     ;; ... and with some random integers of varying length.
 281     (flet ((test-logcount (x)
 282              (declare (type integer x))
 283              (do ((result 0 (1+ result))
 284                   (x (if (minusp x)
 285                          (lognot x)
 286                          x)
 287                      (logand x (1- x))))
 288                  ((zerop x) result))))
 289       (dotimes (i 200)
 290         (let ((x (random (ash 1 i))))
 291           (test x (test-logcount x))
 292           (test (- x) (test-logcount (- x))))))))
 293
 294 ;; 1.0 had a broken ATANH on win32
 295 (with-test (:name :atanh)
 296   (assert (= (atanh 0.9d0) 1.4722194895832204d0)))
 297
 298 ;; Test some cases of integer operations with constant arguments
 299 (with-test (:name :constant-integers)
 300   (labels ((test-forms (op x y header &rest forms)
 301              (let ((val (funcall op x y)))
 302                (dolist (form forms)
 303                  (let ((new-val (funcall (compile nil (append header form)) x y)))
 304                    (unless (eql val new-val)
 305                      (error "~S /= ~S: ~S ~S ~S~%" val new-val (append header form) x y))))))
 306            (test-case (op x y type)
 307              (test-forms op x y `(lambda (x y &aux z)
 308                                    (declare (type ,type x y)
 309                                             (ignorable x y z)
 310                                             (notinline identity)
 311                                             (optimize speed (safety 0))))
 312                          `((,op x ,y))
 313                          `((setf z (,op x ,y))
 314                            (identity x)
 315                            z)
 316                          `((values (,op x ,y) x))
 317                          `((,op ,x y))
 318                          `((setf z (,op ,x y))
 319                            (identity y)
 320                            z)
 321                          `((values (,op ,x y) y))
 322
 323                          `((identity x)
 324                            (,op x ,y))
 325                          `((identity x)
 326                            (setf z (,op x ,y))
 327                            (identity x)
 328                            z)
 329                          `((identity x)
 330                            (values (,op x ,y) x))
 331                          `((identity y)
 332                            (,op ,x y))
 333                          `((identity y)
 334                            (setf z (,op ,x y))
 335                            (identity y)
 336                            z)
 337                          `((identity y)
 338                            (values (,op ,x y) y))))
 339            (test-op (op)
 340              (let ((ub `(unsigned-byte ,sb-vm:n-word-bits))
 341                    (sb `(signed-byte ,sb-vm:n-word-bits)))
 342                (loop for (x y type)
 343                      in `((2 1 fixnum)
 344                           (2 1 ,ub)
 345                           (2 1 ,sb)
 346                           (,(1+ (ash 1 28)) ,(1- (ash 1 28)) fixnum)
 347                           (,(+ 3 (ash 1 30)) ,(+ 2 (ash 1 30)) ,ub)
 348                           (,(- -2 (ash 1 29)) ,(- 3 (ash 1 29)) ,sb)
 349                           ,@(when (> sb-vm:n-word-bits 32)
 350                               `((,(1+ (ash 1 29)) ,(1- (ash 1 29)) fixnum)
 351                                 (,(1+ (ash 1 31)) ,(1- (ash 1 31)) ,ub)
 352                                 (,(- -2 (ash 1 31)) ,(- 3 (ash 1 30)) ,sb)
 353                                 (,(ash 1 40) ,(ash 1 39) fixnum)
 354                                 (,(ash 1 40) ,(ash 1 39) ,ub)
 355                                 (,(ash 1 40) ,(ash 1 39) ,sb)))
 356                           ;; fixnums that can be represented as 32-bit
 357                           ;; sign-extended immediates on x86-64
 358                           ,@(when (and (> sb-vm:n-word-bits 32)
 359                                        (< sb-vm:n-fixnum-tag-bits 3))
 360                               `((,(1+ (ash 1 (- 31 sb-vm:n-fixnum-tag-bits)))
 361                                  ,(1- (ash 1 (- 32 sb-vm:n-fixnum-tag-bits)))
 362                                  fixnum))))
 363                      do
 364                   (test-case op x y type)
 365                   (test-case op x x type)))))
 366     (mapc #'test-op '(+ - * truncate
 367                       < <= = >= >
 368                       eql
 369                       eq))))
 370
 371 ;; GCD used to sometimes return negative values. The following did, on 32 bit
 372 ;; builds.
 373 (with-test (:name :gcd)
 374   ;; from lp#413680
 375   (assert (plusp (gcd 20286123923750474264166990598656
 376                       680564733841876926926749214863536422912)))
 377   ;; from lp#516750
 378   (assert (plusp (gcd 2596102012663483082521318626691873
 379                       2596148429267413814265248164610048))))
 380
 381 (with-test (:name :expt-zero-zero)
 382   ;; Check that (expt 0.0 0.0) and (expt 0 0.0) signal error, but (expt 0.0 0)
 383   ;; returns 1.0
 384   (assert-error (expt 0.0 0.0) sb-int:arguments-out-of-domain-error)
 385   (assert-error (expt 0 0.0) sb-int:arguments-out-of-domain-error)
 386   (assert (eql (expt 0.0 0) 1.0)))
 387
 388 (with-test (:name :multiple-constant-folding)
 389   (let ((*random-state* (make-random-state t)))
 390     (flet ((make-args ()
 391              (let (args vars)
 392                (loop repeat (1+ (random 12))
 393                      do (if (zerop (random 2))
 394                             (let ((var (gensym)))
 395                               (push var args)
 396                               (push var vars))
 397                             (push (- (random 21) 10) args)))
 398                (values args vars))))
 399       (dolist (op '(+ * logior logxor logand logeqv gcd lcm - /))
 400         (loop repeat 10
 401               do (multiple-value-bind (args vars) (make-args)
 402                    (let ((fast (compile nil `(lambda ,vars
 403                                                (,op ,@args))))
 404                          (slow (compile nil `(lambda ,vars
 405                                                (declare (notinline ,op))
 406                                                (,op ,@args)))))
 407                      (loop repeat 3
 408                            do (let* ((call-args (loop repeat (length vars)
 409                                                       collect (- (random 21) 10)))
 410                                      (fast-result (handler-case
 411                                                       (apply fast call-args)
 412                                                     (division-by-zero () :div0)))
 413                                      (slow-result (handler-case
 414                                                       (apply slow call-args)
 415                                                     (division-by-zero () :div0))))
 416                                 (if (eql fast-result slow-result)
 417                                     (print (list :ok `(,op ,@args) :=> fast-result))
 418                                     (error "oops: ~S, ~S" args call-args)))))))))))
 419
 420 ;;; (TRUNCATE <unsigned-word> <constant unsigned-word>) is optimized
 421 ;;; to use multiplication instead of division. This propagates to FLOOR,
 422 ;;; MOD and REM. Test that the transform is indeed triggered and test
 423 ;;; several cases for correct results.
 424 (with-test (:name (:integer-division-using-multiplication :used)
 425                   :skipped-on '(not (or :x86-64 :x86)))
 426   (dolist (fun '(truncate floor ceiling mod rem))
 427     (let* ((foo (compile nil `(lambda (x)
 428                                 (declare (optimize (speed 3)
 429                                                    (space 1)
 430                                                    (compilation-speed 0))
 431                                          (type (unsigned-byte
 432                                                 ,sb-vm:n-word-bits) x))
 433                                 (,fun x 9))))
 434            (disassembly (with-output-to-string (s)
 435                           (disassemble foo :stream s))))
 436       ;; KLUDGE copied from test :float-division-using-exact-reciprocal
 437       ;; in compiler.pure.lisp.
 438       (assert (and (not (search "DIV" disassembly))
 439                    (search "MUL" disassembly))))))
 440
 441 (with-test (:name (:integer-division-using-multiplication :correctness))
 442   (let ((*random-state* (make-random-state t)))
 443     (dolist (dividend-type `((unsigned-byte ,sb-vm:n-word-bits)
 444                              (and fixnum unsigned-byte)
 445                              (integer 10000 10100)))
 446       (dolist (divisor `(;; Some special cases from the paper
 447                          7 10 14 641 274177
 448                          ;; Range extremes
 449                          3
 450                          ,most-positive-fixnum
 451                          ,(1- (expt 2 sb-vm:n-word-bits))
 452                          ;; Some random values
 453                          ,@(loop for i from 8 to sb-vm:n-word-bits
 454                                  for r = (random (expt 2 i))
 455                                  ;; We don't want 0, 1 and powers of 2.
 456                                  when (not (zerop (logand r (1- r))))
 457                                  collect r)))
 458         (dolist (fun '(truncate ceiling floor mod rem))
 459           (let ((foo (compile nil `(lambda (x)
 460                                      (declare (optimize (speed 3)
 461                                                         (space 1)
 462                                                         (compilation-speed 0))
 463                                               (type ,dividend-type x))
 464                                      (,fun x ,divisor)))))
 465             (dolist (dividend `(0 1 ,most-positive-fixnum
 466                                 ,(1- divisor) ,divisor
 467                                 ,(1- (* divisor 2)) ,(* divisor 2)
 468                                 ,@(loop repeat 4
 469                                         collect (+ 10000 (random 101)))
 470                                 ,@(loop for i from 4 to sb-vm:n-word-bits
 471                                         for pow = (expt 2 (1- i))
 472                                         for r = (+ pow (random pow))
 473                                         collect r)))
 474               (when (typep dividend dividend-type)
 475                 (multiple-value-bind (q1 r1)
 476                     (funcall foo dividend)
 477                   (multiple-value-bind (q2 r2)
 478                       (funcall fun dividend divisor)
 479                     (unless (and (= q1 q2)
 480                                  (eql r1 r2))
 481                       (error "bad results for ~s with dividend type ~s"
 482                              (list fun dividend divisor)
 483                              dividend-type))))))))))))
 484
 485 ;; The fast path for logbitp underestimated sb!vm:n-positive-fixnum-bits
 486 ;; for > 61 bit fixnums.
 487 (with-test (:name :logbitp-wide-fixnum)
 488   (assert (not (logbitp (1- (integer-length most-positive-fixnum))
 489                         most-negative-fixnum))))
 490
 491 ;; EXPT dispatches in a complicated way on the types of its arguments.
 492 ;; Check that all possible combinations are covered.
 493 (with-test (:name (:expt :argument-type-combinations))
 494   (let ((numbers '(2                 ; fixnum
 495                    3/5               ; ratio
 496                    1.2f0             ; single-float
 497                    2.0d0             ; double-float
 498                    #c(3/5 1/7)       ; complex rational
 499                    #c(1.2f0 1.3f0)   ; complex single-float
 500                    #c(2.0d0 3.0d0))) ; complex double-float
 501         (bignum (expt 2 64))
 502         results)
 503     (dolist (base (cons bignum numbers))
 504       (dolist (power numbers)
 505         (format t "(expt ~s ~s) => " base power)
 506         (let ((result (expt base power)))
 507           (format t "~s~%" result)
 508           (push result results))))
 509     (assert (every #'numberp results))))
 510
 511 (with-test (:name :bug-741564)
 512   ;; The bug was that in (expt <fixnum> <(complex double-float)>) the
 513   ;; calculation was partially done only to single-float precision,
 514   ;; making the complex double-float result too unprecise. Some other
 515   ;; combinations of argument types were affected, too; test that all
 516   ;; of them are good to double-float precision.
 517   (labels ((nearly-equal-p (x y)
 518              "Are the arguments equal to nearly double-float precision?"
 519              (declare (type double-float x y))
 520              (< (/ (abs (- x y)) (abs y))
 521                 (* double-float-epsilon 4))) ; Differences in the two least
 522                                              ; significant mantissa bits
 523                                              ; are OK.
 524            (test-complex (x y)
 525              (and (nearly-equal-p (realpart x) (realpart y))
 526                   (nearly-equal-p (imagpart x) (imagpart y))))
 527            (print-result (msg base power got expected)
 528              (format t "~a (expt ~s ~s)~%got      ~s~%expected ~s~%"
 529                      msg base power got expected)))
 530     (let ((n-broken 0))
 531       (flet ((test (base power coerce-to-type)
 532                (let* ((got (expt base power))
 533                       (expected (expt (coerce base coerce-to-type) power))
 534                       (result (test-complex got expected)))
 535                  (print-result (if result "Good:" "Bad:")
 536                                base power got expected)
 537                  (unless result
 538                    (incf n-broken)))))
 539         (dolist (base (list 2                    ; fixnum
 540                             (expt 2 64)          ; bignum
 541                             3/5                  ; ratio
 542                             2.0f0))              ; single-float
 543           (let ((power #c(-2.5d0 -4.5d0)))       ; complex double-float
 544             (test base power 'double-float)))
 545         (dolist (base (list #c(2.0f0 3.0f0)      ; complex single-float
 546                             #c(2 3)              ; complex fixnum
 547                             (complex (expt 2 64) (expt 2 65))
 548                                                  ; complex bignum
 549                             #c(3/5 1/7)))        ; complex ratio
 550           (dolist (power (list #c(-2.5d0 -4.5d0) ; complex double-float
 551                                -2.5d0))          ; double-float
 552             (test base power '(complex double-float)))))
 553       (when (> n-broken 0)
 554         (error "Number of broken combinations: ~a" n-broken)))))
 555
 556 (with-test (:name (:ldb :rlwinm :ppc))
 557   (let ((one (compile nil '(lambda (a) (ldb (byte 9 27) a))))
 558         (two (compile nil '(lambda (a)
 559                             (declare (type (integer -3 57216651) a))
 560                             (ldb (byte 9 27) a)))))
 561     (assert (= 0 (- (funcall one 10) (funcall two 10))))))
 562
 563 ;; The ISQRT implementation is sufficiently complicated that it should
 564 ;; be tested.
 565 (with-test (:name :isqrt)
 566   (labels ((test (x)
 567              (let* ((r (isqrt x))
 568                     (r2 (expt r 2))
 569                     (s2 (expt (1+ r) 2)))
 570                (unless (and (<= r2 x)
 571                             (> s2 x))
 572                  (error "isqrt failure for ~a" x))))
 573            (tests (x)
 574              (test x)
 575              (let ((x2 (expt x 2)))
 576                (test x2)
 577                (test (1+ x2))
 578                (test (1- x2)))))
 579     (test most-positive-fixnum)
 580     (test (1+ most-positive-fixnum))
 581     (loop for i from 1 to 200
 582           for pow = (expt 2 (1- i))
 583           for j = (+ pow (random pow))
 584           do
 585           (tests i)
 586           (tests j))
 587     (dotimes (i 10)
 588       (tests (random (expt 2 (+ 1000 (random 10000))))))))
 589
 590 ;; bug 1026634 (reported by Eric Marsden on sbcl-devel)
 591 (with-test (:name :recursive-cut-to-width)
 592   (assert (eql (funcall
 593                 (compile nil
 594                          `(lambda (x)
 595                             (declare (optimize (space 3))
 596                                      (type (integer 12417236377505266230
 597                                                     12417274239874990070) x))
 598                             (logand 8459622733968096971 x)))
 599                 12417237222845306758)
 600                2612793697039849090)))
 601
 602 ;; Also reported by Eric Marsden on sbcl-devel (2013-06-06)
 603 (with-test (:name :more-recursive-cut-to-width)
 604   (assert (eql (funcall
 605                 (compile nil `(lambda (a b)
 606                                 (declare (optimize (speed 2) (safety 0)))
 607                                 (logand (the (eql 16779072918521075607) a)
 608                                         (the (integer 21371810342718833225 21371810343571293860) b))))
 609                 16779072918521075607 21371810342718833263)
 610                2923729245085762055)))
 611
 612 (with-test (:name :complicated-logand-identity)
 613   (loop for k from -8 upto 8 do
 614     (loop for min from -16 upto 16 do
 615       (loop for max from min upto 16 do
 616         (let ((f (compile nil `(lambda (x)
 617                                  (declare (type (integer ,min ,max) x))
 618                                  (logand x ,k)))))
 619           (loop for x from min upto max do
 620             (assert (eql (logand x k) (funcall f x)))))))))
 621
 622 (with-test (:name :complicated-logior-identity)
 623   (loop for k from -8 upto 8 do
 624     (loop for min from -16 upto 16 do
 625       (loop for max from min upto 16 do
 626         (let ((f (compile nil `(lambda (x)
 627                                  (declare (type (integer ,min ,max) x))
 628                                  (logior x ,k)))))
 629           (loop for x from min upto max do
 630             (assert (eql (logior x k) (funcall f x)))))))))
 631
 632 (with-test (:name :ldb-negative-index-no-error)
 633   (assert-error
 634    (funcall (compile nil
 635                      `(lambda (x y)
 636                         (ldb (byte x y) 100)))
 637             -1 -2))
 638   (assert-error
 639    (funcall (compile nil
 640                      `(lambda (x y)
 641                         (mask-field (byte x y) 100)))
 642             -1 -2))
 643   (assert-error
 644    (funcall (compile nil
 645                      `(lambda (x y)
 646                         (dpb 0 (byte x y) 100)))
 647             -1 -2))
 648   (assert-error
 649    (funcall (compile nil
 650                      `(lambda (x y)
 651                         (deposit-field 0 (byte x y) 100)))
 652             -1 -2)))