lib/Math/BigInt/t/upgrade.inc

   1 #include this file into another for subclass testing
   2
   3 # This file is nearly identical to bigintpm.t, except that certain results
   4 # are _requird_ to be different due to "upgrading" or "promoting" to BigFloat.
   5 # The reverse is not true, any unmarked results can be either BigInt or
   6 # BigFloat, depending on how good the internal optimization is.
   7
   8 # Plaese note that the testcount goes up by two for each extra result marked
   9 # with ^, since then we test whether it has the proper class and that it left
  10 # the upgrade variable alone.
  11
  12 my $version = ${"$class\::VERSION"};
  13
  14 ##############################################################################
  15 # for testing inheritance of _swap
  16
  17 package Math::Foo;
  18
  19 use Math::BigInt lib => $main::CL;
  20 use vars qw/@ISA/;
  21 @ISA = (qw/Math::BigInt/);
  22
  23 use overload
  24 # customized overload for sub, since original does not use swap there
  25 '-'     =>      sub { my @a = ref($_[0])->_swap(@_);
  26                    $a[0]->bsub($a[1])};
  27
  28 sub _swap
  29   {
  30   # a fake _swap, which reverses the params
  31   my $self = shift;                     # for override in subclass
  32   if ($_[2])
  33     {
  34     my $c = ref ($_[0] ) || 'Math::Foo';
  35     return ( $_[0]->copy(), $_[1] );
  36     }
  37   else
  38     {
  39     return ( Math::Foo->new($_[1]), $_[0] );
  40     }
  41   }
  42
  43 ##############################################################################
  44 package main;
  45
  46 my $CALC = $class->config()->{lib}; ok ($CALC,$CL);
  47
  48 my ($f,$z,$a,$exp,@a,$m,$e,$round_mode,$expected_class);
  49
  50 while (<DATA>)
  51   {
  52   chop;
  53   next if /^#/; # skip comments
  54   if (s/^&//)
  55     {
  56     $f = $_; next;
  57     }
  58   elsif (/^\$/)
  59     {
  60     $round_mode = $_; $round_mode =~ s/^\$/$class\->/; next;
  61     }
  62
  63   @args = split(/:/,$_,99); $ans = pop(@args);
  64   $expected_class = $class;
  65   if ($ans =~ /\^$/)
  66     {
  67     $expected_class = $ECL; $ans =~ s/\^$//;
  68     }
  69   $try = "\$x = $class->new(\"$args[0]\");";
  70   if ($f eq "bnorm")
  71     {
  72     $try = "\$x = $class->bnorm(\"$args[0]\");";
  73   # some is_xxx tests
  74    } elsif ($f =~ /^is_(zero|one|odd|even|negative|positive|nan|int)$/) {
  75     $try .= "\$x->$f();";
  76    } elsif ($f eq "as_hex") {
  77     $try .= '$x->as_hex();';
  78    } elsif ($f eq "as_bin") {
  79     $try .= '$x->as_bin();';
  80    } elsif ($f eq "is_inf") {
  81     $try .= "\$x->is_inf('$args[1]');";
  82    } elsif ($f eq "binf") {
  83     $try .= "\$x->binf('$args[1]');";
  84    } elsif ($f eq "bone") {
  85     $try .= "\$x->bone('$args[1]');";
  86    # some unary ops
  87    } elsif ($f =~ /^b(nan|floor|ceil|sstr|neg|abs|inc|dec|not|sqrt|fac)$/) {
  88     $try .= "\$x->$f();";
  89    } elsif ($f eq "length") {
  90     $try .= '$x->length();';
  91    } elsif ($f eq "exponent"){
  92     # ->bstr() to see if an object is returned
  93     $try .= '$x = $x->exponent()->bstr();';
  94    } elsif ($f eq "mantissa"){
  95     # ->bstr() to see if an object is returned
  96     $try .= '$x = $x->mantissa()->bstr();';
  97    } elsif ($f eq "parts"){
  98     $try .= '($m,$e) = $x->parts();';
  99     # ->bstr() to see if an object is returned
 100     $try .= '$m = $m->bstr(); $m = "NaN" if !defined $m;';
 101     $try .= '$e = $e->bstr(); $e = "NaN" if !defined $e;';
 102     $try .= '"$m,$e";';
 103    } else {
 104     $try .= "\$y = $class->new('$args[1]');";
 105     if ($f eq "bcmp")
 106       {
 107       $try .= '$x <=> $y;';
 108       } elsif ($f eq "bround") {
 109       $try .= "$round_mode; \$x->bround(\$y);";
 110       } elsif ($f eq "bacmp"){
 111       $try .= '$x->bacmp($y);';
 112       } elsif ($f eq "badd"){
 113       $try .= '$x + $y;';
 114       } elsif ($f eq "bsub"){
 115       $try .= '$x - $y;';
 116       } elsif ($f eq "bmul"){
 117       $try .= '$x * $y;';
 118       } elsif ($f eq "bdiv"){
 119       $try .= '$x / $y;';
 120       } elsif ($f eq "bdiv-list"){
 121       $try .= 'join (",",$x->bdiv($y));';
 122       # overload via x=
 123       } elsif ($f =~ /^.=$/){
 124       $try .= "\$x $f \$y;";
 125       # overload via x
 126       } elsif ($f =~ /^.$/){
 127       $try .= "\$x $f \$y;";
 128       } elsif ($f eq "bmod"){
 129       $try .= '$x % $y;';
 130       } elsif ($f eq "bgcd")
 131         {
 132         if (defined $args[2])
 133           {
 134           $try .= " \$z = $class->new('$args[2]'); ";
 135           }
 136         $try .= "$class\::bgcd(\$x, \$y";
 137         $try .= ", \$z" if (defined $args[2]);
 138         $try .= " );";
 139         }
 140       elsif ($f eq "blcm")
 141         {
 142         if (defined $args[2])
 143           {
 144           $try .= " \$z = $class->new('$args[2]'); ";
 145           }
 146         $try .= "$class\::blcm(\$x, \$y";
 147         $try .= ", \$z" if (defined $args[2]);
 148         $try .= " );";
 149       }elsif ($f eq "blsft"){
 150         if (defined $args[2])
 151           {
 152           $try .= "\$x->blsft(\$y,$args[2]);";
 153           }
 154         else
 155           {
 156           $try .= "\$x << \$y;";
 157           }
 158       }elsif ($f eq "brsft"){
 159         if (defined $args[2])
 160           {
 161           $try .= "\$x->brsft(\$y,$args[2]);";
 162           }
 163         else
 164           {
 165           $try .= "\$x >> \$y;";
 166           }
 167       }elsif ($f eq "band"){
 168         $try .= "\$x & \$y;";
 169       }elsif ($f eq "bior"){
 170         $try .= "\$x | \$y;";
 171       }elsif ($f eq "bxor"){
 172         $try .= "\$x ^ \$y;";
 173       }elsif ($f eq "bpow"){
 174         $try .= "\$x ** \$y;";
 175       }elsif ($f eq "digit"){
 176         $try = "\$x = $class->new('$args[0]'); \$x->digit($args[1]);";
 177       } else { warn "Unknown op '$f'"; }
 178     } # end else all other ops
 179
 180   $ans1 = eval $try;
 181   # convert hex/binary targets to decimal
 182   if ($ans =~ /^(0x0x|0b0b)/)
 183     {
 184     $ans =~ s/^0[xb]//; $ans = Math::BigInt->new($ans)->bstr();
 185     }
 186   if ($ans eq "")
 187     {
 188     ok_undef ($ans1);
 189     }
 190   else
 191     {
 192     # print "try: $try ans: $ans1 $ans\n";
 193     print "# Tried: '$try'\n" if !ok ($ans1, $ans);
 194     if ($expected_class ne $class)
 195       {
 196       ok (ref($ans1),$expected_class);  # also checks that it really is ref!
 197       ok ($Math::BigInt::upgrade,'Math::BigFloat');     # still okay?
 198       }
 199     }
 200   # check internal state of number objects
 201   is_valid($ans1,$f) if ref $ans1;
 202   } # endwhile data tests
 203 close DATA;
 204
 205 # all tests done
 206
 207 1;
 208
 209 ###############################################################################
 210 ###############################################################################
 211 # Perl 5.005 does not like ok ($x,undef)
 212
 213 sub ok_undef
 214   {
 215   my $x = shift;
 216
 217   ok (1,1) and return if !defined $x;
 218   ok ($x,'undef');
 219   }
 220
 221 ###############################################################################
 222 # sub to check validity of a BigInt internally, to ensure that no op leaves a
 223 # number object in an invalid state (f.i. "-0")
 224
 225 sub is_valid
 226   {
 227   my ($x,$f,$c) = @_;
 228
 229   # The checks here are loosened a bit to allow BigInt or BigFloats to pass
 230
 231   my $e = 0;                    # error?
 232   # ok as reference?
 233   # $e = "Not a reference to $c" if (ref($x) || '') ne $c;
 234
 235   # has ok sign?
 236   $e = "Illegal sign $x->{sign} (expected: '+', '-', '-inf', '+inf' or 'NaN'"
 237    if $e eq '0' && $x->{sign} !~ /^(\+|-|\+inf|-inf|NaN)$/;
 238
 239   $e = "-0 is invalid!" if $e ne '0' && $x->{sign} eq '-' && $x == 0;
 240   #$e = $CALC->_check($x->{value}) if $e eq '0';
 241
 242   # test done, see if error did crop up
 243   ok (1,1), return if ($e eq '0');
 244
 245   ok (1,$e." after op '$f'");
 246   }
 247
 248 __DATA__
 249 &.=
 250 1234:-345:1234-345
 251 &+=
 252 1:2:3
 253 -1:-2:-3
 254 &-=
 255 1:2:-1
 256 -1:-2:1
 257 &*=
 258 2:3:6
 259 -1:5:-5
 260 &%=
 261 100:3:1
 262 8:9:8
 263 &/=
 264 100:3:33
 265 -8:2:-4
 266 &|=
 267 2:1:3
 268 &&=
 269 5:7:5
 270 &^=
 271 5:7:2
 272 &is_negative
 273 0:0
 274 -1:1
 275 1:0
 276 +inf:0
 277 -inf:1
 278 NaNneg:0
 279 &is_positive
 280 0:1
 281 -1:0
 282 1:1
 283 +inf:1
 284 -inf:0
 285 NaNneg:0
 286 &is_odd
 287 abc:0
 288 0:0
 289 1:1
 290 3:1
 291 -1:1
 292 -3:1
 293 10000001:1
 294 10000002:0
 295 2:0
 296 120:0
 297 121:1
 298 &is_int
 299 NaN:0
 300 inf:0
 301 -inf:0
 302 1:1
 303 12:1
 304 123e12:1
 305 &is_even
 306 abc:0
 307 0:1
 308 1:0
 309 3:0
 310 -1:0
 311 -3:0
 312 10000001:0
 313 10000002:1
 314 2:1
 315 120:1
 316 121:0
 317 &bacmp
 318 +0:-0:0
 319 +0:+1:-1
 320 -1:+1:0
 321 +1:-1:0
 322 -1:+2:-1
 323 +2:-1:1
 324 -123456789:+987654321:-1
 325 +123456789:-987654321:-1
 326 +987654321:+123456789:1
 327 -987654321:+123456789:1
 328 -123:+4567889:-1
 329 # NaNs
 330 acmpNaN:123:
 331 123:acmpNaN:
 332 acmpNaN:acmpNaN:
 333 # infinity
 334 +inf:+inf:0
 335 -inf:-inf:0
 336 +inf:-inf:0
 337 -inf:+inf:0
 338 +inf:123:1
 339 -inf:123:1
 340 +inf:-123:1
 341 -inf:-123:1
 342 # return undef
 343 +inf:NaN:
 344 NaN:inf:
 345 -inf:NaN:
 346 NaN:-inf:
 347 &bnorm
 348 123:123
 349 12.3:12.3^
 350 # binary input
 351 0babc:NaN
 352 0b123:NaN
 353 0b0:0
 354 -0b0:0
 355 -0b1:-1
 356 0b0001:1
 357 0b001:1
 358 0b011:3
 359 0b101:5
 360 0b1001:9
 361 0b10001:17
 362 0b100001:33
 363 0b1000001:65
 364 0b10000001:129
 365 0b100000001:257
 366 0b1000000001:513
 367 0b10000000001:1025
 368 0b100000000001:2049
 369 0b1000000000001:4097
 370 0b10000000000001:8193
 371 0b100000000000001:16385
 372 0b1000000000000001:32769
 373 0b10000000000000001:65537
 374 0b100000000000000001:131073
 375 0b1000000000000000001:262145
 376 0b10000000000000000001:524289
 377 0b100000000000000000001:1048577
 378 0b1000000000000000000001:2097153
 379 0b10000000000000000000001:4194305
 380 0b100000000000000000000001:8388609
 381 0b1000000000000000000000001:16777217
 382 0b10000000000000000000000001:33554433
 383 0b100000000000000000000000001:67108865
 384 0b1000000000000000000000000001:134217729
 385 0b10000000000000000000000000001:268435457
 386 0b100000000000000000000000000001:536870913
 387 0b1000000000000000000000000000001:1073741825
 388 0b10000000000000000000000000000001:2147483649
 389 0b100000000000000000000000000000001:4294967297
 390 0b1000000000000000000000000000000001:8589934593
 391 0b10000000000000000000000000000000001:17179869185
 392 0b_101:NaN
 393 0b1_0_1:5
 394 0b0_0_0_1:1
 395 # hex input
 396 -0x0:0
 397 0xabcdefgh:NaN
 398 0x1234:4660
 399 0xabcdef:11259375
 400 -0xABCDEF:-11259375
 401 -0x1234:-4660
 402 0x12345678:305419896
 403 0x1_2_3_4_56_78:305419896
 404 0xa_b_c_d_e_f:11259375
 405 0x_123:NaN
 406 0x9:9
 407 0x11:17
 408 0x21:33
 409 0x41:65
 410 0x81:129
 411 0x101:257
 412 0x201:513
 413 0x401:1025
 414 0x801:2049
 415 0x1001:4097
 416 0x2001:8193
 417 0x4001:16385
 418 0x8001:32769
 419 0x10001:65537
 420 0x20001:131073
 421 0x40001:262145
 422 0x80001:524289
 423 0x100001:1048577
 424 0x200001:2097153
 425 0x400001:4194305
 426 0x800001:8388609
 427 0x1000001:16777217
 428 0x2000001:33554433
 429 0x4000001:67108865
 430 0x8000001:134217729
 431 0x10000001:268435457
 432 0x20000001:536870913
 433 0x40000001:1073741825
 434 0x80000001:2147483649
 435 0x100000001:4294967297
 436 0x200000001:8589934593
 437 0x400000001:17179869185
 438 0x800000001:34359738369
 439 # inf input
 440 inf:inf
 441 +inf:inf
 442 -inf:-inf
 443 0inf:NaN
 444 # abnormal input
 445 :NaN
 446 abc:NaN
 447    1 a:NaN
 448 1bcd2:NaN
 449 11111b:NaN
 450 +1z:NaN
 451 -1z:NaN
 452 # only one underscore between two digits
 453 _123:NaN
 454 _123_:NaN
 455 123_:NaN
 456 1__23:NaN
 457 1E1__2:NaN
 458 1_E12:NaN
 459 1E_12:NaN
 460 1_E_12:NaN
 461 +_1E12:NaN
 462 +0_1E2:100
 463 +0_0_1E2:100
 464 -0_0_1E2:-100
 465 -0_0_1E+0_0_2:-100
 466 E1:NaN
 467 E23:NaN
 468 1.23E1:12.3^
 469 1.23E-1:0.123^
 470 # bug with two E's in number beeing valid
 471 1e2e3:NaN
 472 1e2r:NaN
 473 1e2.0:NaN
 474 # leading zeros
 475 012:12
 476 0123:123
 477 01234:1234
 478 012345:12345
 479 0123456:123456
 480 01234567:1234567
 481 012345678:12345678
 482 0123456789:123456789
 483 01234567891:1234567891
 484 012345678912:12345678912
 485 0123456789123:123456789123
 486 01234567891234:1234567891234
 487 # normal input
 488 0:0
 489 +0:0
 490 +00:0
 491 +000:0
 492 000000000000000000:0
 493 -0:0
 494 -0000:0
 495 +1:1
 496 +01:1
 497 +001:1
 498 +00000100000:100000
 499 123456789:123456789
 500 -1:-1
 501 -01:-1
 502 -001:-1
 503 -123456789:-123456789
 504 -00000100000:-100000
 505 1_2_3:123
 506 10000000000E-1_0:1
 507 1E2:100
 508 1E1:10
 509 1E0:1
 510 1.23E2:123
 511 100E-1:10
 512 # floating point input
 513 # .2e2:20
 514 1.E3:1000
 515 1.01E2:101
 516 1010E-1:101
 517 -1010E0:-1010
 518 -1010E1:-10100
 519 1234.00:1234
 520 # non-integer numbers
 521 -1010E-2:-10.1^
 522 -1.01E+1:-10.1^
 523 -1.01E-1:-0.101^
 524 &bnan
 525 1:NaN
 526 2:NaN
 527 abc:NaN
 528 &bone
 529 2:+:1
 530 2:-:-1
 531 boneNaN:-:-1
 532 boneNaN:+:1
 533 2:abc:1
 534 3::1
 535 &binf
 536 1:+:inf
 537 2:-:-inf
 538 3:abc:inf
 539 &is_nan
 540 123:0
 541 abc:1
 542 NaN:1
 543 -123:0
 544 &is_inf
 545 +inf::1
 546 -inf::1
 547 abc::0
 548 1::0
 549 NaN::0
 550 -1::0
 551 +inf:-:0
 552 +inf:+:1
 553 -inf:-:1
 554 -inf:+:0
 555 # it must be exactly /^[+-]inf$/
 556 +infinity::0
 557 -infinity::0
 558 &blsft
 559 abc:abc:NaN
 560 +2:+2:8
 561 +1:+32:4294967296
 562 +1:+48:281474976710656
 563 +8:-2:NaN
 564 # excercise base 10
 565 +12345:4:10:123450000
 566 -1234:0:10:-1234
 567 +1234:0:10:1234
 568 +2:2:10:200
 569 +12:2:10:1200
 570 +1234:-3:10:NaN
 571 1234567890123:12:10:1234567890123000000000000
 572 &brsft
 573 abc:abc:NaN
 574 +8:+2:2
 575 +4294967296:+32:1
 576 +281474976710656:+48:1
 577 +2:-2:NaN
 578 # excercise base 10
 579 -1234:0:10:-1234
 580 +1234:0:10:1234
 581 +200:2:10:2
 582 +1234:3:10:1
 583 +1234:2:10:12
 584 +1234:-3:10:NaN
 585 310000:4:10:31
 586 12300000:5:10:123
 587 1230000000000:10:10:123
 588 09876123456789067890:12:10:9876123
 589 1234561234567890123:13:10:123456
 590 &bsstr
 591 1e+34:1e+34
 592 123.456E3:123456e+0
 593 100:1e+2
 594 abc:NaN
 595 &bneg
 596 bnegNaN:NaN
 597 +inf:-inf
 598 -inf:inf
 599 abd:NaN
 600 0:0
 601 1:-1
 602 -1:1
 603 +123456789:-123456789
 604 -123456789:123456789
 605 &babs
 606 babsNaN:NaN
 607 +inf:inf
 608 -inf:inf
 609 0:0
 610 1:1
 611 -1:1
 612 +123456789:123456789
 613 -123456789:123456789
 614 &bcmp
 615 bcmpNaN:bcmpNaN:
 616 bcmpNaN:0:
 617 0:bcmpNaN:
 618 0:0:0
 619 -1:0:-1
 620 0:-1:1
 621 1:0:1
 622 0:1:-1
 623 -1:1:-1
 624 1:-1:1
 625 -1:-1:0
 626 1:1:0
 627 123:123:0
 628 123:12:1
 629 12:123:-1
 630 -123:-123:0
 631 -123:-12:-1
 632 -12:-123:1
 633 123:124:-1
 634 124:123:1
 635 -123:-124:1
 636 -124:-123:-1
 637 100:5:1
 638 -123456789:987654321:-1
 639 +123456789:-987654321:1
 640 -987654321:123456789:-1
 641 -inf:5432112345:-1
 642 +inf:5432112345:1
 643 -inf:-5432112345:-1
 644 +inf:-5432112345:1
 645 +inf:+inf:0
 646 -inf:-inf:0
 647 +inf:-inf:1
 648 -inf:+inf:-1
 649 5:inf:-1
 650 5:inf:-1
 651 -5:-inf:1
 652 -5:-inf:1
 653 # return undef
 654 +inf:NaN:
 655 NaN:inf:
 656 -inf:NaN:
 657 NaN:-inf:
 658 &binc
 659 abc:NaN
 660 +inf:inf
 661 -inf:-inf
 662 +0:1
 663 +1:2
 664 -1:0
 665 &bdec
 666 abc:NaN
 667 +inf:inf
 668 -inf:-inf
 669 +0:-1
 670 +1:0
 671 -1:-2
 672 &badd
 673 abc:abc:NaN
 674 abc:0:NaN
 675 +0:abc:NaN
 676 +inf:-inf:NaN
 677 -inf:+inf:NaN
 678 +inf:+inf:inf
 679 -inf:-inf:-inf
 680 baddNaN:+inf:NaN
 681 baddNaN:+inf:NaN
 682 +inf:baddNaN:NaN
 683 -inf:baddNaN:NaN
 684 0:0:0
 685 1:0:1
 686 0:1:1
 687 1:1:2
 688 -1:0:-1
 689 0:-1:-1
 690 -1:-1:-2
 691 -1:+1:0
 692 +1:-1:0
 693 +9:+1:10
 694 +99:+1:100
 695 +999:+1:1000
 696 +9999:+1:10000
 697 +99999:+1:100000
 698 +999999:+1:1000000
 699 +9999999:+1:10000000
 700 +99999999:+1:100000000
 701 +999999999:+1:1000000000
 702 +9999999999:+1:10000000000
 703 +99999999999:+1:100000000000
 704 +10:-1:9
 705 +100:-1:99
 706 +1000:-1:999
 707 +10000:-1:9999
 708 +100000:-1:99999
 709 +1000000:-1:999999
 710 +10000000:-1:9999999
 711 +100000000:-1:99999999
 712 +1000000000:-1:999999999
 713 +10000000000:-1:9999999999
 714 +123456789:987654321:1111111110
 715 -123456789:987654321:864197532
 716 -123456789:-987654321:-1111111110
 717 +123456789:-987654321:-864197532
 718 #2:2.5:4.5^
 719 #-123:-1.5:-124.5^
 720 #-1.2:1:-0.2^
 721 &bsub
 722 abc:abc:NaN
 723 abc:+0:NaN
 724 +0:abc:NaN
 725 +inf:-inf:inf
 726 -inf:+inf:-inf
 727 +inf:+inf:NaN
 728 -inf:-inf:NaN
 729 +0:+0:0
 730 +1:+0:1
 731 +0:+1:-1
 732 +1:+1:0
 733 -1:+0:-1
 734 +0:-1:1
 735 -1:-1:0
 736 -1:+1:-2
 737 +1:-1:2
 738 +9:+1:8
 739 +99:+1:98
 740 +999:+1:998
 741 +9999:+1:9998
 742 +99999:+1:99998
 743 +999999:+1:999998
 744 +9999999:+1:9999998
 745 +99999999:+1:99999998
 746 +999999999:+1:999999998
 747 +9999999999:+1:9999999998
 748 +99999999999:+1:99999999998
 749 +10:-1:11
 750 +100:-1:101
 751 +1000:-1:1001
 752 +10000:-1:10001
 753 +100000:-1:100001
 754 +1000000:-1:1000001
 755 +10000000:-1:10000001
 756 +100000000:-1:100000001
 757 +1000000000:-1:1000000001
 758 +10000000000:-1:10000000001
 759 +123456789:+987654321:-864197532
 760 -123456789:+987654321:-1111111110
 761 -123456789:-987654321:864197532
 762 +123456789:-987654321:1111111110
 763 &bmul
 764 abc:abc:NaN
 765 abc:+0:NaN
 766 +0:abc:NaN
 767 NaNmul:+inf:NaN
 768 NaNmul:-inf:NaN
 769 -inf:NaNmul:NaN
 770 +inf:NaNmul:NaN
 771 +inf:+inf:inf
 772 +inf:-inf:-inf
 773 -inf:+inf:-inf
 774 -inf:-inf:inf
 775 +0:+0:0
 776 +0:+1:0
 777 +1:+0:0
 778 +0:-1:0
 779 -1:+0:0
 780 123456789123456789:0:0
 781 0:123456789123456789:0
 782 -1:-1:1
 783 -1:+1:-1
 784 +1:-1:-1
 785 +1:+1:1
 786 +2:+3:6
 787 -2:+3:-6
 788 +2:-3:-6
 789 -2:-3:6
 790 111:111:12321
 791 10101:10101:102030201
 792 1001001:1001001:1002003002001
 793 100010001:100010001:10002000300020001
 794 10000100001:10000100001:100002000030000200001
 795 11111111111:9:99999999999
 796 22222222222:9:199999999998
 797 33333333333:9:299999999997
 798 44444444444:9:399999999996
 799 55555555555:9:499999999995
 800 66666666666:9:599999999994
 801 77777777777:9:699999999993
 802 88888888888:9:799999999992
 803 99999999999:9:899999999991
 804 +25:+25:625
 805 +12345:+12345:152399025
 806 +99999:+11111:1111088889
 807 9999:10000:99990000
 808 99999:100000:9999900000
 809 999999:1000000:999999000000
 810 9999999:10000000:99999990000000
 811 99999999:100000000:9999999900000000
 812 999999999:1000000000:999999999000000000
 813 9999999999:10000000000:99999999990000000000
 814 99999999999:100000000000:9999999999900000000000
 815 999999999999:1000000000000:999999999999000000000000
 816 9999999999999:10000000000000:99999999999990000000000000
 817 99999999999999:100000000000000:9999999999999900000000000000
 818 999999999999999:1000000000000000:999999999999999000000000000000
 819 9999999999999999:10000000000000000:99999999999999990000000000000000
 820 99999999999999999:100000000000000000:9999999999999999900000000000000000
 821 999999999999999999:1000000000000000000:999999999999999999000000000000000000
 822 9999999999999999999:10000000000000000000:99999999999999999990000000000000000000
 823 &bdiv-list
 824 100:20:5,0
 825 4095:4095:1,0
 826 -4095:-4095:1,0
 827 4095:-4095:-1,0
 828 -4095:4095:-1,0
 829 123:2:61,1
 830 9:5:1,4
 831 9:4:2,1
 832 # inf handling and general remainder
 833 5:8:0.625,5
 834 0:8:0,0
 835 11:2:5,1
 836 11:-2:-5,-1
 837 -11:2:-5,1
 838 # see table in documentation in MBI
 839 0:inf:0,0
 840 0:-inf:0,0
 841 5:inf:0,5
 842 5:-inf:0,5
 843 -5:inf:0,-5
 844 -5:-inf:0,-5
 845 inf:5:inf,0
 846 -inf:5:-inf,0
 847 inf:-5:-inf,0
 848 -inf:-5:inf,0
 849 5:5:1,0
 850 -5:-5:1,0
 851 inf:inf:NaN,NaN
 852 -inf:-inf:NaN,NaN
 853 -inf:inf:NaN,NaN
 854 inf:-inf:NaN,NaN
 855 8:0:inf,8
 856 inf:0:inf,inf
 857 # exceptions to reminder rule
 858 -8:0:-inf,-8
 859 -inf:0:-inf,-inf
 860 0:0:NaN,NaN
 861 &bdiv
 862 abc:abc:NaN
 863 abc:1:NaN
 864 1:abc:NaN
 865 0:0:NaN
 866 # inf handling (see table in doc)
 867 0:inf:0
 868 0:-inf:0
 869 5:inf:0
 870 5:-inf:0
 871 -5:inf:0
 872 -5:-inf:0
 873 inf:5:inf
 874 -inf:5:-inf
 875 inf:-5:-inf
 876 -inf:-5:inf
 877 5:5:1
 878 -5:-5:1
 879 inf:inf:NaN
 880 -inf:-inf:NaN
 881 -inf:inf:NaN
 882 inf:-inf:NaN
 883 8:0:inf
 884 inf:0:inf
 885 -8:0:-inf
 886 -inf:0:-inf
 887 0:0:NaN
 888 11:2:5
 889 -11:-2:5
 890 -11:2:-5
 891 11:-2:-5
 892 0:1:0
 893 0:-1:0
 894 1:1:1
 895 -1:-1:1
 896 1:-1:-1
 897 -1:1:-1
 898 1:2:0.5^
 899 2:1:2
 900 1000000000:9:111111111
 901 2000000000:9:222222222
 902 3000000000:9:333333333
 903 4000000000:9:444444444
 904 5000000000:9:555555555
 905 6000000000:9:666666666
 906 7000000000:9:777777777
 907 8000000000:9:888888888
 908 9000000000:9:1000000000
 909 35500000:113:314159
 910 71000000:226:314159
 911 106500000:339:314159
 912 1000000000:3:333333333
 913 +10:+5:2
 914 +100:+4:25
 915 +1000:+8:125
 916 +10000:+16:625
 917 999999999999:9:111111111111
 918 999999999999:99:10101010101
 919 999999999999:999:1001001001
 920 999999999999:9999:100010001
 921 999999999999999:99999:10000100001
 922 +1111088889:99999:11111
 923 -5:-3:1
 924 -5:3:-1
 925 4:3:1
 926 4:-3:-1
 927 1:3:0.3333333333333333333333333333333333333333
 928 1:-3:-0.3333333333333333333333333333333333333333
 929 -2:-3:0.6666666666666666666666666666666666666667
 930 -2:3:-0.6666666666666666666666666666666666666667
 931 #8:5:1.6^
 932 #-8:5:-1.6^
 933 8:5:1
 934 -8:5:-1
 935 14:-3:-4
 936 -14:3:-4
 937 -14:-3:4
 938 14:3:4
 939 # bug in Calc with '99999' vs $BASE-1
 940 10000000000000000000000000000000000000000000000000000000000000000000000000000000000:10000000375084540248994272022843165711074:999999962491547381984643365663244474111576
 941 12:24:0.5^
 942 &bmod
 943 # inf handling, see table in doc
 944 0:inf:0
 945 0:-inf:0
 946 5:inf:5
 947 5:-inf:5
 948 -5:inf:-5
 949 -5:-inf:-5
 950 inf:5:0
 951 -inf:5:0
 952 inf:-5:0
 953 -inf:-5:0
 954 5:5:0
 955 -5:-5:0
 956 inf:inf:NaN
 957 -inf:-inf:NaN
 958 -inf:inf:NaN
 959 inf:-inf:NaN
 960 8:0:8
 961 inf:0:inf
 962 # exceptions to reminder rule
 963 -inf:0:-inf
 964 -8:0:-8
 965 0:0:NaN
 966 abc:abc:NaN
 967 abc:1:abc:NaN
 968 1:abc:NaN
 969 0:0:NaN
 970 0:1:0
 971 1:0:1
 972 0:-1:0
 973 -1:0:-1
 974 1:1:0
 975 -1:-1:0
 976 1:-1:0
 977 -1:1:0
 978 1:2:1
 979 2:1:0
 980 1000000000:9:1
 981 2000000000:9:2
 982 3000000000:9:3
 983 4000000000:9:4
 984 5000000000:9:5
 985 6000000000:9:6
 986 7000000000:9:7
 987 8000000000:9:8
 988 9000000000:9:0
 989 35500000:113:33
 990 71000000:226:66
 991 106500000:339:99
 992 1000000000:3:1
 993 10:5:0
 994 100:4:0
 995 1000:8:0
 996 10000:16:0
 997 999999999999:9:0
 998 999999999999:99:0
 999 999999999999:999:0
1000 999999999999:9999:0
1001 999999999999999:99999:0
1002 -9:+5:1
1003 +9:-5:-1
1004 -9:-5:-4
1005 -5:3:1
1006 -2:3:1
1007 4:3:1
1008 1:3:1
1009 -5:-3:-2
1010 -2:-3:-2
1011 4:-3:-2
1012 1:-3:-2
1013 4095:4095:0
1014 100041000510123:3:0
1015 152403346:12345:4321
1016 9:5:4
1017 &bgcd
1018 abc:abc:NaN
1019 abc:+0:NaN
1020 +0:abc:NaN
1021 +0:+0:0
1022 +0:+1:1
1023 +1:+0:1
1024 +1:+1:1
1025 +2:+3:1
1026 +3:+2:1
1027 -3:+2:1
1028 100:625:25
1029 4096:81:1
1030 1034:804:2
1031 27:90:56:1
1032 27:90:54:9
1033 &blcm
1034 abc:abc:NaN
1035 abc:+0:NaN
1036 +0:abc:NaN
1037 +0:+0:NaN
1038 +1:+0:0
1039 +0:+1:0
1040 +27:+90:270
1041 +1034:+804:415668
1042 &band
1043 abc:abc:NaN
1044 abc:0:NaN
1045 0:abc:NaN
1046 1:2:0
1047 3:2:2
1048 +8:+2:0
1049 +281474976710656:0:0
1050 +281474976710656:1:0
1051 +281474976710656:+281474976710656:281474976710656
1052 -2:-3:-4
1053 -1:-1:-1
1054 -6:-6:-6
1055 -7:-4:-8
1056 -7:4:0
1057 -4:7:4
1058 # equal arguments are treated special, so also do some test with unequal ones
1059 0xFFFF:0xFFFF:0x0xFFFF
1060 0xFFFFFF:0xFFFFFF:0x0xFFFFFF
1061 0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF
1062 0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF
1063 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
1064 0xF0F0:0xF0F0:0x0xF0F0
1065 0x0F0F:0x0F0F:0x0x0F0F
1066 0xF0F0F0:0xF0F0F0:0x0xF0F0F0
1067 0x0F0F0F:0x0F0F0F:0x0x0F0F0F
1068 0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0
1069 0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F
1070 0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0
1071 0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F
1072 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0
1073 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F
1074 0x1F0F0F0F0F0F:0x3F0F0F0F0F0F:0x0x1F0F0F0F0F0F
1075 &bior
1076 abc:abc:NaN
1077 abc:0:NaN
1078 0:abc:NaN
1079 1:2:3
1080 +8:+2:10
1081 +281474976710656:0:281474976710656
1082 +281474976710656:1:281474976710657
1083 +281474976710656:281474976710656:281474976710656
1084 -2:-3:-1
1085 -1:-1:-1
1086 -6:-6:-6
1087 -7:4:-3
1088 -4:7:-1
1089 # equal arguments are treated special, so also do some test with unequal ones
1090 0xFFFF:0xFFFF:0x0xFFFF
1091 0xFFFFFF:0xFFFFFF:0x0xFFFFFF
1092 0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF
1093 0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF
1094 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
1095 0:0xFFFF:0x0xFFFF
1096 0:0xFFFFFF:0x0xFFFFFF
1097 0:0xFFFFFFFF:0x0xFFFFFFFF
1098 0:0xFFFFFFFFFF:0x0xFFFFFFFFFF
1099 0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
1100 0xFFFF:0:0x0xFFFF
1101 0xFFFFFF:0:0x0xFFFFFF
1102 0xFFFFFFFF:0:0x0xFFFFFFFF
1103 0xFFFFFFFFFF:0:0x0xFFFFFFFFFF
1104 0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF
1105 0xF0F0:0xF0F0:0x0xF0F0
1106 0x0F0F:0x0F0F:0x0x0F0F
1107 0xF0F0:0x0F0F:0x0xFFFF
1108 0xF0F0F0:0xF0F0F0:0x0xF0F0F0
1109 0x0F0F0F:0x0F0F0F:0x0x0F0F0F
1110 0x0F0F0F:0xF0F0F0:0x0xFFFFFF
1111 0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0
1112 0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F
1113 0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF
1114 0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0
1115 0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F
1116 0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF
1117 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0
1118 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F
1119 0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
1120 0x1F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
1121 &bxor
1122 abc:abc:NaN
1123 abc:0:NaN
1124 0:abc:NaN
1125 1:2:3
1126 +8:+2:10
1127 +281474976710656:0:281474976710656
1128 +281474976710656:1:281474976710657
1129 +281474976710656:281474976710656:0
1130 -2:-3:3
1131 -1:-1:0
1132 -6:-6:0
1133 -7:4:-3
1134 -4:7:-5
1135 4:-7:-3
1136 -4:-7:5
1137 # equal arguments are treated special, so also do some test with unequal ones
1138 0xFFFF:0xFFFF:0
1139 0xFFFFFF:0xFFFFFF:0
1140 0xFFFFFFFF:0xFFFFFFFF:0
1141 0xFFFFFFFFFF:0xFFFFFFFFFF:0
1142 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0
1143 0:0xFFFF:0x0xFFFF
1144 0:0xFFFFFF:0x0xFFFFFF
1145 0:0xFFFFFFFF:0x0xFFFFFFFF
1146 0:0xFFFFFFFFFF:0x0xFFFFFFFFFF
1147 0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
1148 0xFFFF:0:0x0xFFFF
1149 0xFFFFFF:0:0x0xFFFFFF
1150 0xFFFFFFFF:0:0x0xFFFFFFFF
1151 0xFFFFFFFFFF:0:0x0xFFFFFFFFFF
1152 0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF
1153 0xF0F0:0xF0F0:0
1154 0x0F0F:0x0F0F:0
1155 0xF0F0:0x0F0F:0x0xFFFF
1156 0xF0F0F0:0xF0F0F0:0
1157 0x0F0F0F:0x0F0F0F:0
1158 0x0F0F0F:0xF0F0F0:0x0xFFFFFF
1159 0xF0F0F0F0:0xF0F0F0F0:0
1160 0x0F0F0F0F:0x0F0F0F0F:0
1161 0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF
1162 0xF0F0F0F0F0:0xF0F0F0F0F0:0
1163 0x0F0F0F0F0F:0x0F0F0F0F0F:0
1164 0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF
1165 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0
1166 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0
1167 0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
1168 &bnot
1169 abc:NaN
1170 +0:-1
1171 +8:-9
1172 +281474976710656:-281474976710657
1173 -1:0
1174 -2:1
1175 -12:11
1176 &digit
1177 0:0:0
1178 12:0:2
1179 12:1:1
1180 123:0:3
1181 123:1:2
1182 123:2:1
1183 123:-1:1
1184 123:-2:2
1185 123:-3:3
1186 123456:0:6
1187 123456:1:5
1188 123456:2:4
1189 123456:3:3
1190 123456:4:2
1191 123456:5:1
1192 123456:-1:1
1193 123456:-2:2
1194 123456:-3:3
1195 100000:-3:0
1196 100000:0:0
1197 100000:1:0
1198 &mantissa
1199 abc:NaN
1200 1e4:1
1201 2e0:2
1202 123:123
1203 -1:-1
1204 -2:-2
1205 +inf:inf
1206 -inf:-inf
1207 &exponent
1208 abc:NaN
1209 1e4:4
1210 2e0:0
1211 123:0
1212 -1:0
1213 -2:0
1214 0:1
1215 +inf:inf
1216 -inf:inf
1217 &parts
1218 abc:NaN,NaN
1219 1e4:1,4
1220 2e0:2,0
1221 123:123,0
1222 -1:-1,0
1223 -2:-2,0
1224 0:0,1
1225 +inf:inf,inf
1226 -inf:-inf,inf
1227 &bfac
1228 -1:NaN
1229 NaNfac:NaN
1230 +inf:NaN
1231 -inf:NaN
1232 0:1
1233 1:1
1234 2:2
1235 3:6
1236 4:24
1237 5:120
1238 6:720
1239 10:3628800
1240 11:39916800
1241 12:479001600
1242 &bpow
1243 abc:12:NaN
1244 12:abc:NaN
1245 0:0:1
1246 0:1:0
1247 0:2:0
1248 0:-1:NaN
1249 0:-2:NaN
1250 1:0:1
1251 1:1:1
1252 1:2:1
1253 1:3:1
1254 1:-1:1
1255 1:-2:1
1256 1:-3:1
1257 2:0:1
1258 2:1:2
1259 2:2:4
1260 2:3:8
1261 3:3:27
1262 2:-1:NaN
1263 -2:-1:NaN
1264 2:-2:NaN
1265 -2:-2:NaN
1266 +inf:1234500012:inf
1267 -inf:1234500012:-inf
1268 +inf:-12345000123:inf
1269 -inf:-12345000123:-inf
1270 # 1 ** -x => 1 / (1 ** x)
1271 -1:0:1
1272 -2:0:1
1273 -1:1:-1
1274 -1:2:1
1275 -1:3:-1
1276 -1:4:1
1277 -1:5:-1
1278 -1:-1:-1
1279 -1:-2:1
1280 -1:-3:-1
1281 -1:-4:1
1282 10:2:100
1283 10:3:1000
1284 10:4:10000
1285 10:5:100000
1286 10:6:1000000
1287 10:7:10000000
1288 10:8:100000000
1289 10:9:1000000000
1290 10:20:100000000000000000000
1291 123456:2:15241383936
1292 &length
1293 100:3
1294 10:2
1295 1:1
1296 0:1
1297 12345:5
1298 10000000000000000:17
1299 -123:3
1300 215960156869840440586892398248:30
1301 &bsqrt
1302 145:12.04159457879229548012824103037860805243^
1303 144:12^
1304 143:11.95826074310139802112984075619561661399^
1305 16:4
1306 170:13.03840481040529742916594311485836883306^
1307 169:13
1308 168:12.96148139681572046193193487217599331541^
1309 4:2
1310 3:1.732050807568877293527446341505872366943^
1311 2:1.41421356237309504880168872420969807857^
1312 9:3
1313 12:3.464101615137754587054892683011744733886^
1314 256:16
1315 100000000:10000
1316 4000000000000:2000000
1317 152399026:12345.00004050222755607815159966235881398^
1318 152399025:12345
1319 152399024:12344.99995949777231103967404745303741942^
1320 1:1
1321 0:0
1322 -2:NaN
1323 -123:NaN
1324 Nan:NaN
1325 +inf:NaN
1326 &bround
1327 $round_mode('trunc')
1328 0:12:0
1329 NaNbround:12:NaN
1330 +inf:12:inf
1331 -inf:12:-inf
1332 1234:0:1234
1333 1234:2:1200
1334 123456:4:123400
1335 123456:5:123450
1336 123456:6:123456
1337 +10123456789:5:10123000000
1338 -10123456789:5:-10123000000
1339 +10123456789:9:10123456700
1340 -10123456789:9:-10123456700
1341 +101234500:6:101234000
1342 -101234500:6:-101234000
1343 #+101234500:-4:101234000
1344 #-101234500:-4:-101234000
1345 $round_mode('zero')
1346 +20123456789:5:20123000000
1347 -20123456789:5:-20123000000
1348 +20123456789:9:20123456800
1349 -20123456789:9:-20123456800
1350 +201234500:6:201234000
1351 -201234500:6:-201234000
1352 #+201234500:-4:201234000
1353 #-201234500:-4:-201234000
1354 +12345000:4:12340000
1355 -12345000:4:-12340000
1356 $round_mode('+inf')
1357 +30123456789:5:30123000000
1358 -30123456789:5:-30123000000
1359 +30123456789:9:30123456800
1360 -30123456789:9:-30123456800
1361 +301234500:6:301235000
1362 -301234500:6:-301234000
1363 #+301234500:-4:301235000
1364 #-301234500:-4:-301234000
1365 +12345000:4:12350000
1366 -12345000:4:-12340000
1367 $round_mode('-inf')
1368 +40123456789:5:40123000000
1369 -40123456789:5:-40123000000
1370 +40123456789:9:40123456800
1371 -40123456789:9:-40123456800
1372 +401234500:6:401234000
1373 +401234500:6:401234000
1374 #-401234500:-4:-401235000
1375 #-401234500:-4:-401235000
1376 +12345000:4:12340000
1377 -12345000:4:-12350000
1378 $round_mode('odd')
1379 +50123456789:5:50123000000
1380 -50123456789:5:-50123000000
1381 +50123456789:9:50123456800
1382 -50123456789:9:-50123456800
1383 +501234500:6:501235000
1384 -501234500:6:-501235000
1385 #+501234500:-4:501235000
1386 #-501234500:-4:-501235000
1387 +12345000:4:12350000
1388 -12345000:4:-12350000
1389 $round_mode('even')
1390 +60123456789:5:60123000000
1391 -60123456789:5:-60123000000
1392 +60123456789:9:60123456800
1393 -60123456789:9:-60123456800
1394 +601234500:6:601234000
1395 -601234500:6:-601234000
1396 #+601234500:-4:601234000
1397 #-601234500:-4:-601234000
1398 #-601234500:-9:0
1399 #-501234500:-9:0
1400 #-601234500:-8:0
1401 #-501234500:-8:0
1402 +1234567:7:1234567
1403 +1234567:6:1234570
1404 +12345000:4:12340000
1405 -12345000:4:-12340000
1406 &is_zero
1407 0:1
1408 NaNzero:0
1409 +inf:0
1410 -inf:0
1411 123:0
1412 -1:0
1413 1:0
1414 &is_one
1415 0:0
1416 NaNone:0
1417 +inf:0
1418 -inf:0
1419 1:1
1420 2:0
1421 -1:0
1422 -2:0
1423 # floor and ceil tests are pretty pointless in integer space...but play safe
1424 &bfloor
1425 0:0
1426 NaNfloor:NaN
1427 +inf:inf
1428 -inf:-inf
1429 -1:-1
1430 -2:-2
1431 2:2
1432 3:3
1433 abc:NaN
1434 &bceil
1435 NaNceil:NaN
1436 +inf:inf
1437 -inf:-inf
1438 0:0
1439 -1:-1
1440 -2:-2
1441 2:2
1442 3:3
1443 abc:NaN
1444 &as_hex
1445 128:0x80
1446 -128:-0x80
1447 0:0x0
1448 -0:0x0
1449 1:0x1
1450 0x123456789123456789:0x123456789123456789
1451 +inf:inf
1452 -inf:-inf
1453 NaNas_hex:NaN
1454 &as_bin
1455 128:0b10000000
1456 -128:-0b10000000
1457 0:0b0
1458 -0:0b0
1459 1:0b1
1460 0b1010111101010101010110110110110110101:0b1010111101010101010110110110110110101
1461 +inf:inf
1462 -inf:-inf
1463 NaNas_bin:NaN