| 1 | |
| 2 | =head1 NAME |
| 3 | |
| 4 | Bit::Vector - Efficient bit vector, set of integers and "big int" math library |
| 5 | |
| 6 | =head1 SYNOPSIS |
| 7 | |
| 8 | =head2 OVERLOADED OPERATORS |
| 9 | |
| 10 | See L<Bit::Vector::Overload(3)>. |
| 11 | |
| 12 | =head2 MORE STRING IMPORT/EXPORT |
| 13 | |
| 14 | See L<Bit::Vector::String(3)>. |
| 15 | |
| 16 | =head2 CLASS METHODS |
| 17 | |
| 18 | Version |
| 19 | $version = Bit::Vector->Version(); |
| 20 | |
| 21 | Word_Bits |
| 22 | $bits = Bit::Vector->Word_Bits(); # bits in a machine word |
| 23 | |
| 24 | Long_Bits |
| 25 | $bits = Bit::Vector->Long_Bits(); # bits in an unsigned long |
| 26 | |
| 27 | new |
| 28 | $vector = Bit::Vector->new($bits); # bit vector constructor |
| 29 | |
| 30 | @veclist = Bit::Vector->new($bits,$count); |
| 31 | |
| 32 | new_Hex |
| 33 | $vector = Bit::Vector->new_Hex($bits,$string); |
| 34 | |
| 35 | new_Bin |
| 36 | $vector = Bit::Vector->new_Bin($bits,$string); |
| 37 | |
| 38 | new_Dec |
| 39 | $vector = Bit::Vector->new_Dec($bits,$string); |
| 40 | |
| 41 | new_Enum |
| 42 | $vector = Bit::Vector->new_Enum($bits,$string); |
| 43 | |
| 44 | Concat_List |
| 45 | $vector = Bit::Vector->Concat_List(@vectors); |
| 46 | |
| 47 | =head2 OBJECT METHODS |
| 48 | |
| 49 | new |
| 50 | $vec2 = $vec1->new($bits); # alternative call of constructor |
| 51 | |
| 52 | @veclist = $vec->new($bits,$count); |
| 53 | |
| 54 | Shadow |
| 55 | $vec2 = $vec1->Shadow(); # new vector, same size but empty |
| 56 | |
| 57 | Clone |
| 58 | $vec2 = $vec1->Clone(); # new vector, exact duplicate |
| 59 | |
| 60 | Concat |
| 61 | $vector = $vec1->Concat($vec2); |
| 62 | |
| 63 | Concat_List |
| 64 | $vector = $vec1->Concat_List($vec2,$vec3,...); |
| 65 | |
| 66 | Size |
| 67 | $bits = $vector->Size(); |
| 68 | |
| 69 | Resize |
| 70 | $vector->Resize($bits); |
| 71 | $vector->Resize($vector->Size()+5); |
| 72 | $vector->Resize($vector->Size()-5); |
| 73 | |
| 74 | Copy |
| 75 | $vec2->Copy($vec1); |
| 76 | |
| 77 | Empty |
| 78 | $vector->Empty(); |
| 79 | |
| 80 | Fill |
| 81 | $vector->Fill(); |
| 82 | |
| 83 | Flip |
| 84 | $vector->Flip(); |
| 85 | |
| 86 | Primes |
| 87 | $vector->Primes(); # Sieve of Erathostenes |
| 88 | |
| 89 | Reverse |
| 90 | $vec2->Reverse($vec1); |
| 91 | |
| 92 | Interval_Empty |
| 93 | $vector->Interval_Empty($min,$max); |
| 94 | |
| 95 | Interval_Fill |
| 96 | $vector->Interval_Fill($min,$max); |
| 97 | |
| 98 | Interval_Flip |
| 99 | $vector->Interval_Flip($min,$max); |
| 100 | |
| 101 | Interval_Reverse |
| 102 | $vector->Interval_Reverse($min,$max); |
| 103 | |
| 104 | Interval_Scan_inc |
| 105 | if (($min,$max) = $vector->Interval_Scan_inc($start)) |
| 106 | |
| 107 | Interval_Scan_dec |
| 108 | if (($min,$max) = $vector->Interval_Scan_dec($start)) |
| 109 | |
| 110 | Interval_Copy |
| 111 | $vec2->Interval_Copy($vec1,$offset2,$offset1,$length); |
| 112 | |
| 113 | Interval_Substitute |
| 114 | $vec2->Interval_Substitute($vec1,$off2,$len2,$off1,$len1); |
| 115 | |
| 116 | is_empty |
| 117 | if ($vector->is_empty()) |
| 118 | |
| 119 | is_full |
| 120 | if ($vector->is_full()) |
| 121 | |
| 122 | equal |
| 123 | if ($vec1->equal($vec2)) |
| 124 | |
| 125 | Lexicompare (unsigned) |
| 126 | if ($vec1->Lexicompare($vec2) == 0) |
| 127 | if ($vec1->Lexicompare($vec2) != 0) |
| 128 | if ($vec1->Lexicompare($vec2) < 0) |
| 129 | if ($vec1->Lexicompare($vec2) <= 0) |
| 130 | if ($vec1->Lexicompare($vec2) > 0) |
| 131 | if ($vec1->Lexicompare($vec2) >= 0) |
| 132 | |
| 133 | Compare (signed) |
| 134 | if ($vec1->Compare($vec2) == 0) |
| 135 | if ($vec1->Compare($vec2) != 0) |
| 136 | if ($vec1->Compare($vec2) < 0) |
| 137 | if ($vec1->Compare($vec2) <= 0) |
| 138 | if ($vec1->Compare($vec2) > 0) |
| 139 | if ($vec1->Compare($vec2) >= 0) |
| 140 | |
| 141 | to_Hex |
| 142 | $string = $vector->to_Hex(); |
| 143 | |
| 144 | from_Hex |
| 145 | $vector->from_Hex($string); |
| 146 | |
| 147 | to_Bin |
| 148 | $string = $vector->to_Bin(); |
| 149 | |
| 150 | from_Bin |
| 151 | $vector->from_Bin($string); |
| 152 | |
| 153 | to_Dec |
| 154 | $string = $vector->to_Dec(); |
| 155 | |
| 156 | from_Dec |
| 157 | $vector->from_Dec($string); |
| 158 | |
| 159 | to_Enum |
| 160 | $string = $vector->to_Enum(); # e.g. "2,3,5-7,11,13-19" |
| 161 | |
| 162 | from_Enum |
| 163 | $vector->from_Enum($string); |
| 164 | |
| 165 | Bit_Off |
| 166 | $vector->Bit_Off($index); |
| 167 | |
| 168 | Bit_On |
| 169 | $vector->Bit_On($index); |
| 170 | |
| 171 | bit_flip |
| 172 | $bit = $vector->bit_flip($index); |
| 173 | |
| 174 | bit_test |
| 175 | contains |
| 176 | $bit = $vector->bit_test($index); |
| 177 | $bit = $vector->contains($index); |
| 178 | if ($vector->bit_test($index)) |
| 179 | if ($vector->contains($index)) |
| 180 | |
| 181 | Bit_Copy |
| 182 | $vector->Bit_Copy($index,$bit); |
| 183 | |
| 184 | LSB (least significant bit) |
| 185 | $vector->LSB($bit); |
| 186 | |
| 187 | MSB (most significant bit) |
| 188 | $vector->MSB($bit); |
| 189 | |
| 190 | lsb (least significant bit) |
| 191 | $bit = $vector->lsb(); |
| 192 | |
| 193 | msb (most significant bit) |
| 194 | $bit = $vector->msb(); |
| 195 | |
| 196 | rotate_left |
| 197 | $carry = $vector->rotate_left(); |
| 198 | |
| 199 | rotate_right |
| 200 | $carry = $vector->rotate_right(); |
| 201 | |
| 202 | shift_left |
| 203 | $carry = $vector->shift_left($carry); |
| 204 | |
| 205 | shift_right |
| 206 | $carry = $vector->shift_right($carry); |
| 207 | |
| 208 | Move_Left |
| 209 | $vector->Move_Left($bits); # shift left "$bits" positions |
| 210 | |
| 211 | Move_Right |
| 212 | $vector->Move_Right($bits); # shift right "$bits" positions |
| 213 | |
| 214 | Insert |
| 215 | $vector->Insert($offset,$bits); |
| 216 | |
| 217 | Delete |
| 218 | $vector->Delete($offset,$bits); |
| 219 | |
| 220 | increment |
| 221 | $carry = $vector->increment(); |
| 222 | |
| 223 | decrement |
| 224 | $carry = $vector->decrement(); |
| 225 | |
| 226 | inc |
| 227 | $overflow = $vec2->inc($vec1); |
| 228 | |
| 229 | dec |
| 230 | $overflow = $vec2->dec($vec1); |
| 231 | |
| 232 | add |
| 233 | $carry = $vec3->add($vec1,$vec2,$carry); |
| 234 | ($carry,$overflow) = $vec3->add($vec1,$vec2,$carry); |
| 235 | |
| 236 | subtract |
| 237 | $carry = $vec3->subtract($vec1,$vec2,$carry); |
| 238 | ($carry,$overflow) = $vec3->subtract($vec1,$vec2,$carry); |
| 239 | |
| 240 | Neg |
| 241 | Negate |
| 242 | $vec2->Neg($vec1); |
| 243 | $vec2->Negate($vec1); |
| 244 | |
| 245 | Abs |
| 246 | Absolute |
| 247 | $vec2->Abs($vec1); |
| 248 | $vec2->Absolute($vec1); |
| 249 | |
| 250 | Sign |
| 251 | if ($vector->Sign() == 0) |
| 252 | if ($vector->Sign() != 0) |
| 253 | if ($vector->Sign() < 0) |
| 254 | if ($vector->Sign() <= 0) |
| 255 | if ($vector->Sign() > 0) |
| 256 | if ($vector->Sign() >= 0) |
| 257 | |
| 258 | Multiply |
| 259 | $vec3->Multiply($vec1,$vec2); |
| 260 | |
| 261 | Divide |
| 262 | $quot->Divide($vec1,$vec2,$rest); |
| 263 | |
| 264 | GCD (Greatest Common Divisor) |
| 265 | $vecgcd->GCD($veca,$vecb); |
| 266 | $vecgcd->GCD($vecx,$vecy,$veca,$vecb); |
| 267 | |
| 268 | Power |
| 269 | $vec3->Power($vec1,$vec2); |
| 270 | |
| 271 | Block_Store |
| 272 | $vector->Block_Store($buffer); |
| 273 | |
| 274 | Block_Read |
| 275 | $buffer = $vector->Block_Read(); |
| 276 | |
| 277 | Word_Size |
| 278 | $size = $vector->Word_Size(); # number of words in "$vector" |
| 279 | |
| 280 | Word_Store |
| 281 | $vector->Word_Store($offset,$word); |
| 282 | |
| 283 | Word_Read |
| 284 | $word = $vector->Word_Read($offset); |
| 285 | |
| 286 | Word_List_Store |
| 287 | $vector->Word_List_Store(@words); |
| 288 | |
| 289 | Word_List_Read |
| 290 | @words = $vector->Word_List_Read(); |
| 291 | |
| 292 | Word_Insert |
| 293 | $vector->Word_Insert($offset,$count); |
| 294 | |
| 295 | Word_Delete |
| 296 | $vector->Word_Delete($offset,$count); |
| 297 | |
| 298 | Chunk_Store |
| 299 | $vector->Chunk_Store($chunksize,$offset,$chunk); |
| 300 | |
| 301 | Chunk_Read |
| 302 | $chunk = $vector->Chunk_Read($chunksize,$offset); |
| 303 | |
| 304 | Chunk_List_Store |
| 305 | $vector->Chunk_List_Store($chunksize,@chunks); |
| 306 | |
| 307 | Chunk_List_Read |
| 308 | @chunks = $vector->Chunk_List_Read($chunksize); |
| 309 | |
| 310 | Index_List_Remove |
| 311 | $vector->Index_List_Remove(@indices); |
| 312 | |
| 313 | Index_List_Store |
| 314 | $vector->Index_List_Store(@indices); |
| 315 | |
| 316 | Index_List_Read |
| 317 | @indices = $vector->Index_List_Read(); |
| 318 | |
| 319 | Or |
| 320 | Union |
| 321 | $vec3->Or($vec1,$vec2); |
| 322 | $set3->Union($set1,$set2); |
| 323 | |
| 324 | And |
| 325 | Intersection |
| 326 | $vec3->And($vec1,$vec2); |
| 327 | $set3->Intersection($set1,$set2); |
| 328 | |
| 329 | AndNot |
| 330 | Difference |
| 331 | $vec3->AndNot($vec1,$vec2); |
| 332 | $set3->Difference($set1,$set2); |
| 333 | |
| 334 | Xor |
| 335 | ExclusiveOr |
| 336 | $vec3->Xor($vec1,$vec2); |
| 337 | $set3->ExclusiveOr($set1,$set2); |
| 338 | |
| 339 | Not |
| 340 | Complement |
| 341 | $vec2->Not($vec1); |
| 342 | $set2->Complement($set1); |
| 343 | |
| 344 | subset |
| 345 | if ($set1->subset($set2)) # true if $set1 is subset of $set2 |
| 346 | |
| 347 | Norm |
| 348 | $norm = $set->Norm(); |
| 349 | $norm = $set->Norm2(); |
| 350 | $norm = $set->Norm3(); |
| 351 | |
| 352 | Min |
| 353 | $min = $set->Min(); |
| 354 | |
| 355 | Max |
| 356 | $max = $set->Max(); |
| 357 | |
| 358 | Multiplication |
| 359 | $matrix3->Multiplication($rows3,$cols3, |
| 360 | $matrix1,$rows1,$cols1, |
| 361 | $matrix2,$rows2,$cols2); |
| 362 | |
| 363 | Product |
| 364 | $matrix3->Product($rows3,$cols3, |
| 365 | $matrix1,$rows1,$cols1, |
| 366 | $matrix2,$rows2,$cols2); |
| 367 | |
| 368 | Closure |
| 369 | $matrix->Closure($rows,$cols); |
| 370 | |
| 371 | Transpose |
| 372 | $matrix2->Transpose($rows2,$cols2,$matrix1,$rows1,$cols1); |
| 373 | |
| 374 | =head1 IMPORTANT NOTES |
| 375 | |
| 376 | =over 2 |
| 377 | |
| 378 | =item * |
| 379 | |
| 380 | Method naming conventions |
| 381 | |
| 382 | Method names completely in lower case indicate a boolean return value. |
| 383 | |
| 384 | (Except for the bit vector constructor method "C<new()>", of course.) |
| 385 | |
| 386 | =item * |
| 387 | |
| 388 | Boolean values |
| 389 | |
| 390 | Boolean values in this module are always a numeric zero ("C<0>") for |
| 391 | "false" and a numeric one ("C<1>") for "true". |
| 392 | |
| 393 | =item * |
| 394 | |
| 395 | Negative numbers |
| 396 | |
| 397 | All numeric input parameters passed to any of the methods in this module |
| 398 | are regarded as being B<UNSIGNED> (as opposed to the contents of the |
| 399 | bit vectors themselves, which are usually considered to be B<SIGNED>). |
| 400 | |
| 401 | As a consequence, whenever you pass a negative number as an argument to |
| 402 | some method of this module, it will be treated as a (usually very large) |
| 403 | positive number due to its internal two's complement binary representation, |
| 404 | usually resulting in an "index out of range" error message and program |
| 405 | abortion. |
| 406 | |
| 407 | =item * |
| 408 | |
| 409 | Bit order |
| 410 | |
| 411 | Note that bit vectors are stored least order bit and least order word first |
| 412 | internally. |
| 413 | |
| 414 | I.e., bit #0 of any given bit vector corresponds to bit #0 of word #0 in the |
| 415 | array of machine words representing the bit vector. |
| 416 | |
| 417 | (Where word #0 comes first in memory, i.e., it is stored at the least memory |
| 418 | address in the allocated block of memory holding the given bit vector.) |
| 419 | |
| 420 | Note however that machine words can be stored least order byte first or last, |
| 421 | depending on your system's implementation. |
| 422 | |
| 423 | When you are exporting or importing a whole bit vector at once using the |
| 424 | methods "C<Block_Read()>" and "C<Block_Store()>" (the only time in this |
| 425 | module where this could make any difference), however, a conversion to and |
| 426 | from "least order byte first" order is automatically supplied. |
| 427 | |
| 428 | In other words, what "C<Block_Read()>" provides and what "C<Block_Store()>" |
| 429 | expects is always in "least order byte first" order, regardless of the order |
| 430 | in which words are stored internally on your machine. |
| 431 | |
| 432 | This is to make sure that what you export on one machine using "C<Block_Read()>" |
| 433 | can always be read in correctly with "C<Block_Store()>" on a different machine. |
| 434 | |
| 435 | Note further that whenever bit vectors are converted to and from (binary or |
| 436 | hexadecimal) strings, the B<RIGHTMOST> bit is always the B<LEAST SIGNIFICANT> |
| 437 | one, and the B<LEFTMOST> bit is always the B<MOST SIGNIFICANT> bit. |
| 438 | |
| 439 | This is because in our western culture, numbers are always represented in this |
| 440 | way (least significant to most significant digits go from right to left). |
| 441 | |
| 442 | Of course this requires an internal reversion of order, which the corresponding |
| 443 | conversion methods perform automatically (without any additional overhead, it's |
| 444 | just a matter of starting the internal loop at the bottom or the top end). |
| 445 | |
| 446 | =item * |
| 447 | |
| 448 | "Word" related methods |
| 449 | |
| 450 | Note that all methods whose names begin with "C<Word_>" are |
| 451 | B<MACHINE-DEPENDENT>! |
| 452 | |
| 453 | They depend on the size (number of bits) of an "unsigned int" (C type) on |
| 454 | your machine. |
| 455 | |
| 456 | Therefore, you should only use these methods if you are B<ABSOLUTELY CERTAIN> |
| 457 | that portability of your code is not an issue! |
| 458 | |
| 459 | Note that you can use arbitrarily large chunks (i.e., fragments of bit vectors) |
| 460 | of up to 32 bits B<IN A PORTABLE WAY> using the methods whose names begin with |
| 461 | "C<Chunk_>". |
| 462 | |
| 463 | =item * |
| 464 | |
| 465 | Chunk sizes |
| 466 | |
| 467 | Note that legal chunk sizes for all methods whose names begin with "C<Chunk_>" |
| 468 | range from "C<1>" to "C<Bit::Vector-E<gt>Long_Bits();>" bits ("C<0>" is B<NOT> |
| 469 | allowed!). |
| 470 | |
| 471 | In order to make your programs portable, however, you shouldn't use chunk sizes |
| 472 | larger than 32 bits, since this is the minimum size of an "unsigned long" |
| 473 | (C type) on all systems, as prescribed by S<ANSI C>. |
| 474 | |
| 475 | =item * |
| 476 | |
| 477 | Matching sizes |
| 478 | |
| 479 | In general, for methods involving several bit vectors at the same time, all |
| 480 | bit vector arguments must have identical sizes (number of bits), or a fatal |
| 481 | "size mismatch" error will occur. |
| 482 | |
| 483 | Exceptions from this rule are the methods "C<Concat()>", "C<Concat_List()>", |
| 484 | "C<Copy()>", "C<Interval_Copy()>" and "C<Interval_Substitute()>", where no |
| 485 | conditions at all are imposed on the size of their bit vector arguments. |
| 486 | |
| 487 | In method "C<Multiply()>", all three bit vector arguments must in principle |
| 488 | obey the rule of matching sizes, but the bit vector in which the result of |
| 489 | the multiplication is to be stored may be larger than the two bit vector |
| 490 | arguments containing the factors for the multiplication. |
| 491 | |
| 492 | In method "C<Power()>", the bit vector for the result must be the same |
| 493 | size or greater than the base of the exponentiation term. The exponent |
| 494 | can be any size. |
| 495 | |
| 496 | =item * |
| 497 | |
| 498 | Index ranges |
| 499 | |
| 500 | All indices for any given bits must lie between "C<0>" and |
| 501 | "C<$vector-E<gt>Size()-1>", or a fatal "index out of range" |
| 502 | error will occur. |
| 503 | |
| 504 | =back |
| 505 | |
| 506 | =head1 DESCRIPTION |
| 507 | |
| 508 | =head2 OVERLOADED OPERATORS |
| 509 | |
| 510 | See L<Bit::Vector::Overload(3)>. |
| 511 | |
| 512 | =head2 MORE STRING IMPORT/EXPORT |
| 513 | |
| 514 | See L<Bit::Vector::String(3)>. |
| 515 | |
| 516 | =head2 CLASS METHODS |
| 517 | |
| 518 | =over 2 |
| 519 | |
| 520 | =item * |
| 521 | |
| 522 | C<$version = Bit::Vector-E<gt>Version();> |
| 523 | |
| 524 | Returns the current version number of this module. |
| 525 | |
| 526 | =item * |
| 527 | |
| 528 | C<$bits = Bit::Vector-E<gt>Word_Bits();> |
| 529 | |
| 530 | Returns the number of bits of an "unsigned int" (C type) |
| 531 | on your machine. |
| 532 | |
| 533 | (An "unsigned int" is also called a "machine word", |
| 534 | hence the name of this method.) |
| 535 | |
| 536 | =item * |
| 537 | |
| 538 | C<$bits = Bit::Vector-E<gt>Long_Bits();> |
| 539 | |
| 540 | Returns the number of bits of an "unsigned long" (C type) |
| 541 | on your machine. |
| 542 | |
| 543 | =item * |
| 544 | |
| 545 | C<$vector = Bit::Vector-E<gt>new($bits);> |
| 546 | |
| 547 | This is the bit vector constructor method. |
| 548 | |
| 549 | Call this method to create a new bit vector containing "C<$bits>" |
| 550 | bits (with indices ranging from "C<0>" to "C<$bits-1>"). |
| 551 | |
| 552 | Note that - in contrast to previous versions - bit vectors |
| 553 | of length zero (i.e., with C<$bits = 0>) are permitted now. |
| 554 | |
| 555 | The method returns a reference to the newly created bit vector. |
| 556 | |
| 557 | A new bit vector is always initialized so that all bits are cleared |
| 558 | (turned off). |
| 559 | |
| 560 | An exception will be raised if the method is unable to allocate the |
| 561 | necessary memory. |
| 562 | |
| 563 | Note that if you specify a negative number for "C<$bits>" it will be |
| 564 | interpreted as a large positive number due to its internal two's |
| 565 | complement binary representation. |
| 566 | |
| 567 | In such a case, the bit vector constructor method will obediently attempt |
| 568 | to create a bit vector of that size, probably resulting in an exception, |
| 569 | as explained above. |
| 570 | |
| 571 | =item * |
| 572 | |
| 573 | C<@veclist = Bit::Vector-E<gt>new($bits,$count);> |
| 574 | |
| 575 | You can also create more than one bit vector at a time if you specify the |
| 576 | optional second parameter "C<$count>". |
| 577 | |
| 578 | The method returns a list of "C<$count>" bit vectors which all have the |
| 579 | same number of bits "C<$bits>" (and which are all initialized, i.e., |
| 580 | all bits are cleared). |
| 581 | |
| 582 | If "C<$count>" is zero, an empty list is returned. |
| 583 | |
| 584 | If "C<$bits>" is zero, a list of null-sized bit vectors is returned. |
| 585 | |
| 586 | Note again that if you specify a negative number for "C<$count>" it will |
| 587 | be interpreted as a large positive number due to its internal two's |
| 588 | complement binary representation. |
| 589 | |
| 590 | In such a case, the bit vector constructor method will obediently attempt |
| 591 | to create that many bit vectors, probably resulting in an exception ("out |
| 592 | of memory"). |
| 593 | |
| 594 | =item * |
| 595 | |
| 596 | C<$vector = Bit::Vector-E<gt>new_Hex($bits,$string);> |
| 597 | |
| 598 | This method is an alternative constructor which allows you to create |
| 599 | a new bit vector object (with "C<$bits>" bits) and to initialize it |
| 600 | all in one go. |
| 601 | |
| 602 | The method internally first calls the bit vector constructor method |
| 603 | "C<new()>" and then passes the given string to the method "C<from_Hex()>". |
| 604 | |
| 605 | However, this method is more efficient than performing these two steps |
| 606 | separately: First because in this method, the memory area occupied by |
| 607 | the new bit vector is not initialized to zeros (which is pointless in |
| 608 | this case), and second because it saves you from the associated overhead |
| 609 | of one additional method invocation. |
| 610 | |
| 611 | An exception will be raised if the necessary memory cannot be allocated |
| 612 | (see the description of the method "C<new()>" immediately above for |
| 613 | possible causes) or if the given string cannot be converted successfully |
| 614 | (see the description of the method "C<from_Hex()>" further below for |
| 615 | details). |
| 616 | |
| 617 | In the latter case, the memory occupied by the new bit vector is |
| 618 | released first (i.e., "free"d) before the exception is actually |
| 619 | raised. |
| 620 | |
| 621 | =item * |
| 622 | |
| 623 | C<$vector = Bit::Vector-E<gt>new_Bin($bits,$string);> |
| 624 | |
| 625 | This method is an alternative constructor which allows you to create |
| 626 | a new bit vector object (with "C<$bits>" bits) and to initialize it |
| 627 | all in one go. |
| 628 | |
| 629 | The method internally first calls the bit vector constructor method |
| 630 | "C<new()>" and then passes the given string to the method "C<from_Bin()>". |
| 631 | |
| 632 | However, this method is more efficient than performing these two steps |
| 633 | separately: First because in this method, the memory area occupied by |
| 634 | the new bit vector is not initialized to zeros (which is pointless in |
| 635 | this case), and second because it saves you from the associated overhead |
| 636 | of one additional method invocation. |
| 637 | |
| 638 | An exception will be raised if the necessary memory cannot be allocated |
| 639 | (see the description of the method "C<new()>" above for possible causes) |
| 640 | or if the given string cannot be converted successfully (see the |
| 641 | description of the method "C<from_Bin()>" further below for details). |
| 642 | |
| 643 | In the latter case, the memory occupied by the new bit vector is |
| 644 | released first (i.e., "free"d) before the exception is actually |
| 645 | raised. |
| 646 | |
| 647 | =item * |
| 648 | |
| 649 | C<$vector = Bit::Vector-E<gt>new_Dec($bits,$string);> |
| 650 | |
| 651 | This method is an alternative constructor which allows you to create |
| 652 | a new bit vector object (with "C<$bits>" bits) and to initialize it |
| 653 | all in one go. |
| 654 | |
| 655 | The method internally first calls the bit vector constructor method |
| 656 | "C<new()>" and then passes the given string to the method "C<from_Dec()>". |
| 657 | |
| 658 | However, this method is more efficient than performing these two steps |
| 659 | separately: First because in this method, "C<new()>" does not initialize |
| 660 | the memory area occupied by the new bit vector with zeros (which is |
| 661 | pointless in this case, because "C<from_Dec()>" will do it anyway), |
| 662 | and second because it saves you from the associated overhead of one |
| 663 | additional method invocation. |
| 664 | |
| 665 | An exception will be raised if the necessary memory cannot be allocated |
| 666 | (see the description of the method "C<new()>" above for possible causes) |
| 667 | or if the given string cannot be converted successfully (see the |
| 668 | description of the method "C<from_Dec()>" further below for details). |
| 669 | |
| 670 | In the latter case, the memory occupied by the new bit vector is |
| 671 | released first (i.e., "free"d) before the exception is actually |
| 672 | raised. |
| 673 | |
| 674 | =item * |
| 675 | |
| 676 | C<$vector = Bit::Vector-E<gt>new_Enum($bits,$string);> |
| 677 | |
| 678 | This method is an alternative constructor which allows you to create |
| 679 | a new bit vector object (with "C<$bits>" bits) and to initialize it |
| 680 | all in one go. |
| 681 | |
| 682 | The method internally first calls the bit vector constructor method |
| 683 | "C<new()>" and then passes the given string to the method "C<from_Enum()>". |
| 684 | |
| 685 | However, this method is more efficient than performing these two steps |
| 686 | separately: First because in this method, "C<new()>" does not initialize |
| 687 | the memory area occupied by the new bit vector with zeros (which is |
| 688 | pointless in this case, because "C<from_Enum()>" will do it anyway), |
| 689 | and second because it saves you from the associated overhead of one |
| 690 | additional method invocation. |
| 691 | |
| 692 | An exception will be raised if the necessary memory cannot be allocated |
| 693 | (see the description of the method "C<new()>" above for possible causes) |
| 694 | or if the given string cannot be converted successfully (see the |
| 695 | description of the method "C<from_Enum()>" further below for details). |
| 696 | |
| 697 | In the latter case, the memory occupied by the new bit vector is |
| 698 | released first (i.e., "free"d) before the exception is actually |
| 699 | raised. |
| 700 | |
| 701 | =item * |
| 702 | |
| 703 | C<$vector = Bit::Vector-E<gt>Concat_List(@vectors);> |
| 704 | |
| 705 | This method creates a new vector containing all bit vectors from the |
| 706 | argument list in concatenated form. |
| 707 | |
| 708 | The argument list may contain any number of arguments (including |
| 709 | zero); the only condition is that all arguments must be bit vectors. |
| 710 | |
| 711 | There is no condition concerning the length (in number of bits) of |
| 712 | these arguments. |
| 713 | |
| 714 | The vectors from the argument list are not changed in any way. |
| 715 | |
| 716 | If the argument list is empty or if all arguments have length zero, |
| 717 | the resulting bit vector will also have length zero. |
| 718 | |
| 719 | Note that the B<RIGHTMOST> bit vector from the argument list will |
| 720 | become the B<LEAST> significant part of the resulting bit vector, |
| 721 | and the B<LEFTMOST> bit vector from the argument list will |
| 722 | become the B<MOST> significant part of the resulting bit vector. |
| 723 | |
| 724 | =back |
| 725 | |
| 726 | =head2 OBJECT METHODS |
| 727 | |
| 728 | =over 2 |
| 729 | |
| 730 | =item * |
| 731 | |
| 732 | C<$vec2 = $vec1-E<gt>new($bits);> |
| 733 | |
| 734 | C<@veclist = $vec-E<gt>new($bits);> |
| 735 | |
| 736 | This is an alternative way of calling the bit vector constructor method. |
| 737 | |
| 738 | Vector "C<$vec1>" (or "C<$vec>") is not affected by this, it just serves |
| 739 | as an anchor for the method invocation mechanism. |
| 740 | |
| 741 | In fact B<ALL> class methods in this module can be called this way, |
| 742 | even though this is probably considered to be "politically incorrect" |
| 743 | by OO ("object-orientation") aficionados. ;-) |
| 744 | |
| 745 | So even if you are too lazy to type "C<Bit::Vector-E<gt>>" instead of |
| 746 | "C<$vec1-E<gt>>" (and even though laziness is - allegedly - a programmer's |
| 747 | virtue C<:-)>), maybe it is better not to use this feature if you don't |
| 748 | want to get booed at. ;-) |
| 749 | |
| 750 | =item * |
| 751 | |
| 752 | C<$vec2 = $vec1-E<gt>Shadow();> |
| 753 | |
| 754 | Creates a B<NEW> bit vector "C<$vec2>" of the B<SAME SIZE> as "C<$vec1>" |
| 755 | but which is B<EMPTY>. |
| 756 | |
| 757 | Just like a shadow that has the same shape as the object it |
| 758 | originates from, but is flat and has no volume, i.e., contains |
| 759 | nothing. |
| 760 | |
| 761 | =item * |
| 762 | |
| 763 | C<$vec2 = $vec1-E<gt>Clone();> |
| 764 | |
| 765 | Creates a B<NEW> bit vector "C<$vec2>" of the B<SAME SIZE> as "C<$vec1>" |
| 766 | which is an B<EXACT COPY> of "C<$vec1>". |
| 767 | |
| 768 | =item * |
| 769 | |
| 770 | C<$vector = $vec1-E<gt>Concat($vec2);> |
| 771 | |
| 772 | This method returns a new bit vector object which is the result of the |
| 773 | concatenation of the contents of "C<$vec1>" and "C<$vec2>". |
| 774 | |
| 775 | Note that the contents of "C<$vec1>" become the B<MOST> significant part |
| 776 | of the resulting bit vector, and "C<$vec2>" the B<LEAST> significant part. |
| 777 | |
| 778 | If both bit vector arguments have length zero, the resulting bit vector |
| 779 | will also have length zero. |
| 780 | |
| 781 | =item * |
| 782 | |
| 783 | C<$vector = $vec1-E<gt>Concat_List($vec2,$vec3,...);> |
| 784 | |
| 785 | This is an alternative way of calling this (class) method as an |
| 786 | object method. |
| 787 | |
| 788 | The method returns a new bit vector object which is the result of |
| 789 | the concatenation of the contents of C<$vec1 . $vec2 . $vec3 . ...> |
| 790 | |
| 791 | See the section "class methods" above for a detailed description of |
| 792 | this method. |
| 793 | |
| 794 | Note that the argument list may be empty and that all arguments |
| 795 | must be bit vectors if it isn't. |
| 796 | |
| 797 | =item * |
| 798 | |
| 799 | C<$bits = $vector-E<gt>Size();> |
| 800 | |
| 801 | Returns the size (number of bits) the given vector was created with |
| 802 | (or "C<Resize()>"d to). |
| 803 | |
| 804 | =item * |
| 805 | |
| 806 | C<$vector-E<gt>Resize($bits);> |
| 807 | |
| 808 | Changes the size of the given vector to the specified number of bits. |
| 809 | |
| 810 | This method allows you to change the size of an existing bit vector, |
| 811 | preserving as many bits from the old vector as will fit into the |
| 812 | new one (i.e., all bits with indices smaller than the minimum of the |
| 813 | sizes of both vectors, old and new). |
| 814 | |
| 815 | If the number of machine words needed to store the new vector is smaller |
| 816 | than or equal to the number of words needed to store the old vector, the |
| 817 | memory allocated for the old vector is reused for the new one, and only |
| 818 | the relevant book-keeping information is adjusted accordingly. |
| 819 | |
| 820 | This means that even if the number of bits increases, new memory is not |
| 821 | necessarily being allocated (i.e., if the old and the new number of bits |
| 822 | fit into the same number of machine words). |
| 823 | |
| 824 | If the number of machine words needed to store the new vector is greater |
| 825 | than the number of words needed to store the old vector, new memory is |
| 826 | allocated for the new vector, the old vector is copied to the new one, |
| 827 | the remaining bits in the new vector are cleared (turned off) and the old |
| 828 | vector is deleted, i.e., the memory that was allocated for it is released. |
| 829 | |
| 830 | (An exception will be raised if the method is unable to allocate the |
| 831 | necessary memory for the new vector.) |
| 832 | |
| 833 | As a consequence, if you decrease the size of a given vector so that |
| 834 | it will use fewer machine words, and increase it again later so that it |
| 835 | will use more words than immediately before but still less than the |
| 836 | original vector, new memory will be allocated anyway because the |
| 837 | information about the size of the original vector is lost whenever |
| 838 | you resize it. |
| 839 | |
| 840 | Note also that if you specify a negative number for "C<$bits>" it will |
| 841 | be interpreted as a large positive number due to its internal two's |
| 842 | complement binary representation. |
| 843 | |
| 844 | In such a case, "Resize()" will obediently attempt to create a bit |
| 845 | vector of that size, probably resulting in an exception, as explained |
| 846 | above. |
| 847 | |
| 848 | Finally, note that - in contrast to previous versions - resizing a bit |
| 849 | vector to a size of zero bits (length zero) is now permitted. |
| 850 | |
| 851 | =item * |
| 852 | |
| 853 | C<$vec2-E<gt>Copy($vec1);> |
| 854 | |
| 855 | Copies the contents of bit vector "C<$vec1>" to bit vector "C<$vec2>". |
| 856 | |
| 857 | The previous contents of bit vector "C<$vec2>" get overwritten, i.e., |
| 858 | are lost. |
| 859 | |
| 860 | Both vectors must exist beforehand, i.e., this method does not B<CREATE> |
| 861 | any new bit vector object. |
| 862 | |
| 863 | The two vectors may be of any size. |
| 864 | |
| 865 | If the source bit vector is larger than the target, this method will copy |
| 866 | as much of the least significant bits of the source vector as will fit into |
| 867 | the target vector, thereby discarding any extraneous most significant bits. |
| 868 | |
| 869 | BEWARE that this causes a brutal cutoff in the middle of your data, and it |
| 870 | will also leave you with an almost unpredictable sign if subsequently the |
| 871 | number in the target vector is going to be interpreted as a number! (You |
| 872 | have been warned!) |
| 873 | |
| 874 | If the target bit vector is larger than the source, this method fills up |
| 875 | the remaining most significant bits in the target bit vector with either |
| 876 | 0's or 1's, depending on the sign (= the most significant bit) of the |
| 877 | source bit vector. This is also known as "sign extension". |
| 878 | |
| 879 | This makes it possible to copy numbers from a smaller bit vector into |
| 880 | a larger one while preserving the number's absolute value as well as |
| 881 | its sign (due to the two's complement binary representation of numbers). |
| 882 | |
| 883 | =item * |
| 884 | |
| 885 | C<$vector-E<gt>Empty();> |
| 886 | |
| 887 | Clears all bits in the given vector. |
| 888 | |
| 889 | =item * |
| 890 | |
| 891 | C<$vector-E<gt>Fill();> |
| 892 | |
| 893 | Sets all bits in the given vector. |
| 894 | |
| 895 | =item * |
| 896 | |
| 897 | C<$vector-E<gt>Flip();> |
| 898 | |
| 899 | Flips (i.e., complements) all bits in the given vector. |
| 900 | |
| 901 | =item * |
| 902 | |
| 903 | C<$vector-E<gt>Primes();> |
| 904 | |
| 905 | Clears the given bit vector and sets all bits whose |
| 906 | indices are prime numbers. |
| 907 | |
| 908 | This method uses the algorithm known as the "Sieve of |
| 909 | Erathostenes" internally. |
| 910 | |
| 911 | =item * |
| 912 | |
| 913 | C<$vec2-E<gt>Reverse($vec1);> |
| 914 | |
| 915 | This method copies the given vector "C<$vec1>" to |
| 916 | the vector "C<$vec2>", thereby reversing the order |
| 917 | of all bits. |
| 918 | |
| 919 | I.e., the least significant bit of "C<$vec1>" becomes the |
| 920 | most significant bit of "C<$vec2>", whereas the most |
| 921 | significant bit of "C<$vec1>" becomes the least |
| 922 | significant bit of "C<$vec2>", and so forth |
| 923 | for all bits in between. |
| 924 | |
| 925 | Note that in-place processing is also possible, i.e., |
| 926 | "C<$vec1>" and "C<$vec2>" may be identical. |
| 927 | |
| 928 | (Internally, this is the same as |
| 929 | C<$vec1-E<gt>Interval_Reverse(0,$vec1-E<gt>Size()-1);>.) |
| 930 | |
| 931 | =item * |
| 932 | |
| 933 | C<$vector-E<gt>Interval_Empty($min,$max);> |
| 934 | |
| 935 | Clears all bits in the interval C<[$min..$max]> (including both limits) |
| 936 | in the given vector. |
| 937 | |
| 938 | "C<$min>" and "C<$max>" may have the same value; this is the same |
| 939 | as clearing a single bit with "C<Bit_Off()>" (but less efficient). |
| 940 | |
| 941 | Note that C<$vector-E<gt>Interval_Empty(0,$vector-E<gt>Size()-1);> |
| 942 | is the same as C<$vector-E<gt>Empty();> (but less efficient). |
| 943 | |
| 944 | =item * |
| 945 | |
| 946 | C<$vector-E<gt>Interval_Fill($min,$max);> |
| 947 | |
| 948 | Sets all bits in the interval C<[$min..$max]> (including both limits) |
| 949 | in the given vector. |
| 950 | |
| 951 | "C<$min>" and "C<$max>" may have the same value; this is the same |
| 952 | as setting a single bit with "C<Bit_On()>" (but less efficient). |
| 953 | |
| 954 | Note that C<$vector-E<gt>Interval_Fill(0,$vector-E<gt>Size()-1);> |
| 955 | is the same as C<$vector-E<gt>Fill();> (but less efficient). |
| 956 | |
| 957 | =item * |
| 958 | |
| 959 | C<$vector-E<gt>Interval_Flip($min,$max);> |
| 960 | |
| 961 | Flips (i.e., complements) all bits in the interval C<[$min..$max]> |
| 962 | (including both limits) in the given vector. |
| 963 | |
| 964 | "C<$min>" and "C<$max>" may have the same value; this is the same |
| 965 | as flipping a single bit with "C<bit_flip()>" (but less efficient). |
| 966 | |
| 967 | Note that C<$vector-E<gt>Interval_Flip(0,$vector-E<gt>Size()-1);> |
| 968 | is the same as C<$vector-E<gt>Flip();> and |
| 969 | C<$vector-E<gt>Complement($vector);> |
| 970 | (but less efficient). |
| 971 | |
| 972 | =item * |
| 973 | |
| 974 | C<$vector-E<gt>Interval_Reverse($min,$max);> |
| 975 | |
| 976 | Reverses the order of all bits in the interval C<[$min..$max]> |
| 977 | (including both limits) in the given vector. |
| 978 | |
| 979 | I.e., bits "C<$min>" and "C<$max>" swap places, and so forth |
| 980 | for all bits in between. |
| 981 | |
| 982 | "C<$min>" and "C<$max>" may have the same value; this has no |
| 983 | effect whatsoever, though. |
| 984 | |
| 985 | =item * |
| 986 | |
| 987 | C<if (($min,$max) = $vector-E<gt>Interval_Scan_inc($start))> |
| 988 | |
| 989 | Returns the minimum and maximum indices of the next contiguous block |
| 990 | of set bits (i.e., bits in the "on" state). |
| 991 | |
| 992 | The search starts at index "C<$start>" (i.e., C<"$min" E<gt>= "$start">) |
| 993 | and proceeds upwards (i.e., C<"$max" E<gt>= "$min">), thus repeatedly |
| 994 | increments the search pointer "C<$start>" (internally). |
| 995 | |
| 996 | Note though that the contents of the variable (or scalar literal value) |
| 997 | "C<$start>" is B<NOT> altered. I.e., you have to set it to the desired |
| 998 | value yourself prior to each call to "C<Interval_Scan_inc()>" (see also |
| 999 | the example given below). |
| 1000 | |
| 1001 | Actually, the bit vector is not searched bit by bit, but one machine |
| 1002 | word at a time, in order to speed up execution (which means that this |
| 1003 | method is quite efficient). |
| 1004 | |
| 1005 | An empty list is returned if no such block can be found. |
| 1006 | |
| 1007 | Note that a single set bit (surrounded by cleared bits) is a valid |
| 1008 | block by this definition. In that case the return values for "C<$min>" |
| 1009 | and "C<$max>" are the same. |
| 1010 | |
| 1011 | Typical use: |
| 1012 | |
| 1013 | $start = 0; |
| 1014 | while (($start < $vector->Size()) && |
| 1015 | (($min,$max) = $vector->Interval_Scan_inc($start))) |
| 1016 | { |
| 1017 | $start = $max + 2; |
| 1018 | |
| 1019 | # do something with $min and $max |
| 1020 | } |
| 1021 | |
| 1022 | =item * |
| 1023 | |
| 1024 | C<if (($min,$max) = $vector-E<gt>Interval_Scan_dec($start))> |
| 1025 | |
| 1026 | Returns the minimum and maximum indices of the next contiguous block |
| 1027 | of set bits (i.e., bits in the "on" state). |
| 1028 | |
| 1029 | The search starts at index "C<$start>" (i.e., C<"$max" E<lt>= "$start">) |
| 1030 | and proceeds downwards (i.e., C<"$min" E<lt>= "$max">), thus repeatedly |
| 1031 | decrements the search pointer "C<$start>" (internally). |
| 1032 | |
| 1033 | Note though that the contents of the variable (or scalar literal value) |
| 1034 | "C<$start>" is B<NOT> altered. I.e., you have to set it to the desired |
| 1035 | value yourself prior to each call to "C<Interval_Scan_dec()>" (see also |
| 1036 | the example given below). |
| 1037 | |
| 1038 | Actually, the bit vector is not searched bit by bit, but one machine |
| 1039 | word at a time, in order to speed up execution (which means that this |
| 1040 | method is quite efficient). |
| 1041 | |
| 1042 | An empty list is returned if no such block can be found. |
| 1043 | |
| 1044 | Note that a single set bit (surrounded by cleared bits) is a valid |
| 1045 | block by this definition. In that case the return values for "C<$min>" |
| 1046 | and "C<$max>" are the same. |
| 1047 | |
| 1048 | Typical use: |
| 1049 | |
| 1050 | $start = $vector->Size() - 1; |
| 1051 | while (($start >= 0) && |
| 1052 | (($min,$max) = $vector->Interval_Scan_dec($start))) |
| 1053 | { |
| 1054 | $start = $min - 2; |
| 1055 | |
| 1056 | # do something with $min and $max |
| 1057 | } |
| 1058 | |
| 1059 | =item * |
| 1060 | |
| 1061 | C<$vec2-E<gt>Interval_Copy($vec1,$offset2,$offset1,$length);> |
| 1062 | |
| 1063 | This method allows you to copy a stretch of contiguous bits (starting |
| 1064 | at any position "C<$offset1>" you choose, with a length of "C<$length>" |
| 1065 | bits) from a given "source" bit vector "C<$vec1>" to another position |
| 1066 | "C<$offset2>" in a "target" bit vector "C<$vec2>". |
| 1067 | |
| 1068 | Note that the two bit vectors "C<$vec1>" and "C<$vec2>" do B<NOT> |
| 1069 | need to have the same (matching) size! |
| 1070 | |
| 1071 | Consequently, any of the two terms "C<$offset1 + $length>" and |
| 1072 | "C<$offset2 + $length>" (or both) may exceed the actual length |
| 1073 | of its corresponding bit vector ("C<$vec1-E<gt>Size()>" and |
| 1074 | "C<$vec2-E<gt>Size()>", respectively). |
| 1075 | |
| 1076 | In such a case, the "C<$length>" parameter is automatically reduced |
| 1077 | internally so that both terms above are bounded by the number of bits |
| 1078 | of their corresponding bit vector. |
| 1079 | |
| 1080 | This may even result in a length of zero, in which case nothing is |
| 1081 | copied at all. |
| 1082 | |
| 1083 | (Of course the value of the "C<$length>" parameter, supplied by you |
| 1084 | in the initial method call, may also be zero right from the start!) |
| 1085 | |
| 1086 | Note also that "C<$offset1>" and "C<$offset2>" must lie within the |
| 1087 | range "C<0>" and, respectively, "C<$vec1-E<gt>Size()-1>" or |
| 1088 | "C<$vec2-E<gt>Size()-1>", or a fatal "offset out of range" error |
| 1089 | will occur. |
| 1090 | |
| 1091 | Note further that "C<$vec1>" and "C<$vec2>" may be identical, i.e., |
| 1092 | you may copy a stretch of contiguous bits from one part of a given |
| 1093 | bit vector to another part. |
| 1094 | |
| 1095 | The source and the target interval may even overlap, in which case |
| 1096 | the copying is automatically performed in ascending or descending |
| 1097 | order (depending on the direction of the copy - downwards or upwards |
| 1098 | in the bit vector, respectively) to handle this situation correctly, |
| 1099 | i.e., so that no bits are being overwritten before they have been |
| 1100 | copied themselves. |
| 1101 | |
| 1102 | =item * |
| 1103 | |
| 1104 | C<$vec2-E<gt>Interval_Substitute($vec1,$off2,$len2,$off1,$len1);> |
| 1105 | |
| 1106 | This method is (roughly) the same for bit vectors (i.e., arrays |
| 1107 | of booleans) as what the "splice" function in Perl is for lists |
| 1108 | (i.e., arrays of scalars). |
| 1109 | |
| 1110 | (See L<perlfunc/splice> for more details about this function.) |
| 1111 | |
| 1112 | The method allows you to substitute a stretch of contiguous bits |
| 1113 | (defined by a position (offset) "C<$off1>" and a length of "C<$len1>" |
| 1114 | bits) from a given "source" bit vector "C<$vec1>" for a different |
| 1115 | stretch of contiguous bits (defined by a position (offset) "C<$off2>" |
| 1116 | and a length of "C<$len2>" bits) in another, "target" bit vector |
| 1117 | "C<$vec2>". |
| 1118 | |
| 1119 | Note that the two bit vectors "C<$vec1>" and "C<$vec2>" do B<NOT> |
| 1120 | need to have the same (matching) size! |
| 1121 | |
| 1122 | Note further that "C<$off1>" and "C<$off2>" must lie within the |
| 1123 | range "C<0>" and, respectively, "C<$vec1-E<gt>Size()>" or |
| 1124 | "C<$vec2-E<gt>Size()>", or a fatal "offset out of range" error |
| 1125 | will occur. |
| 1126 | |
| 1127 | Alert readers will have noticed that these upper limits are B<NOT> |
| 1128 | "C<$vec1-E<gt>Size()-1>" and "C<$vec2-E<gt>Size()-1>", as they would |
| 1129 | be for any other method in this module, but that these offsets may |
| 1130 | actually point to one position B<PAST THE END> of the corresponding |
| 1131 | bit vector. |
| 1132 | |
| 1133 | This is necessary in order to make it possible to B<APPEND> a given |
| 1134 | stretch of bits to the target bit vector instead of B<REPLACING> |
| 1135 | something in it. |
| 1136 | |
| 1137 | For reasons of symmetry and generality, the same applies to the offset |
| 1138 | in the source bit vector, even though such an offset (one position past |
| 1139 | the end of the bit vector) does not serve any practical purpose there |
| 1140 | (but does not cause any harm either). |
| 1141 | |
| 1142 | (Actually this saves you from the need of testing for this special case, |
| 1143 | in certain circumstances.) |
| 1144 | |
| 1145 | Note that whenever the term "C<$off1 + $len1>" exceeds the size |
| 1146 | "C<$vec1-E<gt>Size()>" of bit vector "C<$vec1>" (or if "C<$off2 + $len2>" |
| 1147 | exceeds "C<$vec2-E<gt>Size()>"), the corresponding length ("C<$len1>" |
| 1148 | or "C<$len2>", respectively) is automatically reduced internally |
| 1149 | so that "C<$off1 + $len1 E<lt>= $vec1-E<gt>Size()>" (and |
| 1150 | "C<$off2 + $len2 E<lt>= $vec2-E<gt>Size()>") holds. |
| 1151 | |
| 1152 | (Note that this does B<NOT> alter the intended result, even though |
| 1153 | this may seem counter-intuitive at first!) |
| 1154 | |
| 1155 | This may even result in a length ("C<$len1>" or "C<$len2>") of zero. |
| 1156 | |
| 1157 | A length of zero for the interval in the B<SOURCE> bit vector |
| 1158 | ("C<$len1 == 0>") means that the indicated stretch of bits in |
| 1159 | the target bit vector (starting at position "C<$off2>") is to |
| 1160 | be replaced by B<NOTHING>, i.e., is to be B<DELETED>. |
| 1161 | |
| 1162 | A length of zero for the interval in the B<TARGET> bit vector |
| 1163 | ("C<$len2> == 0") means that B<NOTHING> is replaced, and that the |
| 1164 | stretch of bits from the source bit vector is simply B<INSERTED> |
| 1165 | into the target bit vector at the indicated position ("C<$off2>"). |
| 1166 | |
| 1167 | If both length parameters are zero, nothing is done at all. |
| 1168 | |
| 1169 | Note that in contrast to any other method in this module (especially |
| 1170 | "C<Interval_Copy()>", "C<Insert()>" and "C<Delete()>"), this method |
| 1171 | B<IMPLICITLY> and B<AUTOMATICALLY> adapts the length of the resulting |
| 1172 | bit vector as needed, as given by |
| 1173 | |
| 1174 | $size = $vec2->Size(); # before |
| 1175 | $size += $len1 - $len2; # after |
| 1176 | |
| 1177 | (The only other method in this module that changes the size of a bit |
| 1178 | vector is the method "C<Resize()>".) |
| 1179 | |
| 1180 | In other words, replacing a given interval of bits in the target bit |
| 1181 | vector with a longer or shorter stretch of bits from the source bit |
| 1182 | vector, or simply inserting ("C<$len2 == 0>") a stretch of bits into |
| 1183 | or deleting ("C<$len1 == 0>") an interval of bits from the target bit |
| 1184 | vector will automatically increase or decrease, respectively, the size |
| 1185 | of the target bit vector accordingly. |
| 1186 | |
| 1187 | For the sake of generality, this may even result in a bit vector with |
| 1188 | a size of zero (containing no bits at all). |
| 1189 | |
| 1190 | This is also the reason why bit vectors of length zero are permitted |
| 1191 | in this module in the first place, starting with version 5.0. |
| 1192 | |
| 1193 | Finally, note that "C<$vec1>" and "C<$vec2>" may be identical, i.e., |
| 1194 | in-place processing is possible. |
| 1195 | |
| 1196 | (If you think about that for a while or if you look at the code, |
| 1197 | you will see that this is far from trivial!) |
| 1198 | |
| 1199 | =item * |
| 1200 | |
| 1201 | C<if ($vector-E<gt>is_empty())> |
| 1202 | |
| 1203 | Tests whether the given bit vector is empty, i.e., whether B<ALL> of |
| 1204 | its bits are cleared (in the "off" state). |
| 1205 | |
| 1206 | In "big integer" arithmetic, this is equivalent to testing whether |
| 1207 | the number stored in the bit vector is zero ("C<0>"). |
| 1208 | |
| 1209 | Returns "true" ("C<1>") if the bit vector is empty and "false" ("C<0>") |
| 1210 | otherwise. |
| 1211 | |
| 1212 | Note that this method also returns "true" ("C<1>") if the given bit |
| 1213 | vector has a length of zero, i.e., if it contains no bits at all. |
| 1214 | |
| 1215 | =item * |
| 1216 | |
| 1217 | C<if ($vector-E<gt>is_full())> |
| 1218 | |
| 1219 | Tests whether the given bit vector is full, i.e., whether B<ALL> of |
| 1220 | its bits are set (in the "on" state). |
| 1221 | |
| 1222 | In "big integer" arithmetic, this is equivalent to testing whether |
| 1223 | the number stored in the bit vector is minus one ("-1"). |
| 1224 | |
| 1225 | Returns "true" ("C<1>") if the bit vector is full and "false" ("C<0>") |
| 1226 | otherwise. |
| 1227 | |
| 1228 | If the given bit vector has a length of zero (i.e., if it contains |
| 1229 | no bits at all), this method returns "false" ("C<0>"). |
| 1230 | |
| 1231 | =item * |
| 1232 | |
| 1233 | C<if ($vec1-E<gt>equal($vec2))> |
| 1234 | |
| 1235 | Tests the two given bit vectors for equality. |
| 1236 | |
| 1237 | Returns "true" ("C<1>") if the two bit vectors are exact |
| 1238 | copies of one another and "false" ("C<0>") otherwise. |
| 1239 | |
| 1240 | =item * |
| 1241 | |
| 1242 | C<$cmp = $vec1-E<gt>Lexicompare($vec2);> |
| 1243 | |
| 1244 | Compares the two given bit vectors, which are |
| 1245 | regarded as B<UNSIGNED> numbers in binary representation. |
| 1246 | |
| 1247 | The method returns "C<-1>" if the first bit vector is smaller |
| 1248 | than the second bit vector, "C<0>" if the two bit vectors are |
| 1249 | exact copies of one another and "C<1>" if the first bit vector |
| 1250 | is greater than the second bit vector. |
| 1251 | |
| 1252 | =item * |
| 1253 | |
| 1254 | C<$cmp = $vec1-E<gt>Compare($vec2);> |
| 1255 | |
| 1256 | Compares the two given bit vectors, which are |
| 1257 | regarded as B<SIGNED> numbers in binary representation. |
| 1258 | |
| 1259 | The method returns "C<-1>" if the first bit vector is smaller |
| 1260 | than the second bit vector, "C<0>" if the two bit vectors are |
| 1261 | exact copies of one another and "C<1>" if the first bit vector |
| 1262 | is greater than the second bit vector. |
| 1263 | |
| 1264 | =item * |
| 1265 | |
| 1266 | C<$string = $vector-E<gt>to_Hex();> |
| 1267 | |
| 1268 | Returns a hexadecimal string representing the given bit vector. |
| 1269 | |
| 1270 | Note that this representation is quite compact, in that it only |
| 1271 | needs at most twice the number of bytes needed to store the bit |
| 1272 | vector itself, internally. |
| 1273 | |
| 1274 | Note also that since a hexadecimal digit is always worth four bits, |
| 1275 | the length of the resulting string is always a multiple of four bits, |
| 1276 | regardless of the true length (in bits) of the given bit vector. |
| 1277 | |
| 1278 | Finally, note that the B<LEAST> significant hexadecimal digit is |
| 1279 | located at the B<RIGHT> end of the resulting string, and the B<MOST> |
| 1280 | significant digit at the B<LEFT> end. |
| 1281 | |
| 1282 | =item * |
| 1283 | |
| 1284 | C<$vector-E<gt>from_Hex($string);> |
| 1285 | |
| 1286 | Allows to read in the contents of a bit vector from a hexadecimal |
| 1287 | string, such as returned by the method "C<to_Hex()>" (see above). |
| 1288 | |
| 1289 | Remember that the least significant bits are always to the right of a |
| 1290 | hexadecimal string, and the most significant bits to the left. Therefore, |
| 1291 | the string is actually read in from right to left while the bit vector |
| 1292 | is filled accordingly, 4 bits at a time, starting with the least significant |
| 1293 | bits and going upward to the most significant bits. |
| 1294 | |
| 1295 | If the given string contains less hexadecimal digits than are needed |
| 1296 | to completely fill the given bit vector, the remaining (most significant) |
| 1297 | bits are all cleared. |
| 1298 | |
| 1299 | This also means that, even if the given string does not contain enough digits |
| 1300 | to completely fill the given bit vector, the previous contents of the |
| 1301 | bit vector are erased completely. |
| 1302 | |
| 1303 | If the given string is longer than it needs to fill the given bit vector, |
| 1304 | the superfluous characters are simply ignored. |
| 1305 | |
| 1306 | (In fact they are ignored completely - they are not even checked for |
| 1307 | proper syntax. See also below for more about that.) |
| 1308 | |
| 1309 | This behaviour is intentional so that you may read in the string |
| 1310 | representing one bit vector into another bit vector of different |
| 1311 | size, i.e., as much of it as will fit. |
| 1312 | |
| 1313 | If during the process of reading the given string any character is |
| 1314 | encountered which is not a hexadecimal digit, a fatal syntax error |
| 1315 | ensues ("input string syntax error"). |
| 1316 | |
| 1317 | =item * |
| 1318 | |
| 1319 | C<$string = $vector-E<gt>to_Bin();> |
| 1320 | |
| 1321 | Returns a binary string representing the given bit vector. |
| 1322 | |
| 1323 | Example: |
| 1324 | |
| 1325 | $vector = Bit::Vector->new(8); |
| 1326 | $vector->Primes(); |
| 1327 | $string = $vector->to_Bin(); |
| 1328 | print "'$string'\n"; |
| 1329 | |
| 1330 | This prints: |
| 1331 | |
| 1332 | '10101100' |
| 1333 | |
| 1334 | (Bits #7, #5, #3 and #2 are set.) |
| 1335 | |
| 1336 | Note that the B<LEAST> significant bit is located at the B<RIGHT> |
| 1337 | end of the resulting string, and the B<MOST> significant bit at |
| 1338 | the B<LEFT> end. |
| 1339 | |
| 1340 | =item * |
| 1341 | |
| 1342 | C<$vector-E<gt>from_Bin($string);> |
| 1343 | |
| 1344 | This method allows you to read in the contents of a bit vector from a |
| 1345 | binary string, such as returned by the method "C<to_Bin()>" (see above). |
| 1346 | |
| 1347 | Note that this method assumes that the B<LEAST> significant bit is located at |
| 1348 | the B<RIGHT> end of the binary string, and the B<MOST> significant bit at the |
| 1349 | B<LEFT> end. Therefore, the string is actually read in from right to left |
| 1350 | while the bit vector is filled accordingly, one bit at a time, starting with |
| 1351 | the least significant bit and going upward to the most significant bit. |
| 1352 | |
| 1353 | If the given string contains less binary digits ("C<0>" and "C<1>") than are |
| 1354 | needed to completely fill the given bit vector, the remaining (most significant) |
| 1355 | bits are all cleared. |
| 1356 | |
| 1357 | This also means that, even if the given string does not contain enough digits |
| 1358 | to completely fill the given bit vector, the previous contents of the |
| 1359 | bit vector are erased completely. |
| 1360 | |
| 1361 | If the given string is longer than it needs to fill the given bit vector, |
| 1362 | the superfluous characters are simply ignored. |
| 1363 | |
| 1364 | (In fact they are ignored completely - they are not even checked for |
| 1365 | proper syntax. See also below for more about that.) |
| 1366 | |
| 1367 | This behaviour is intentional so that you may read in the string |
| 1368 | representing one bit vector into another bit vector of different |
| 1369 | size, i.e., as much of it as will fit. |
| 1370 | |
| 1371 | If during the process of reading the given string any character is |
| 1372 | encountered which is not either "C<0>" or "C<1>", a fatal syntax error |
| 1373 | ensues ("input string syntax error"). |
| 1374 | |
| 1375 | =item * |
| 1376 | |
| 1377 | C<$string = $vector-E<gt>to_Dec();> |
| 1378 | |
| 1379 | This method returns a string representing the contents of the given bit |
| 1380 | vector converted to decimal (base C<10>). |
| 1381 | |
| 1382 | Note that this method assumes the given bit vector to be B<SIGNED> (and |
| 1383 | to contain a number in two's complement binary representation). |
| 1384 | |
| 1385 | Consequently, whenever the most significant bit of the given bit vector |
| 1386 | is set, the number stored in it is regarded as being B<NEGATIVE>. |
| 1387 | |
| 1388 | The resulting string can be fed into "C<from_Dec()>" (see below) in order |
| 1389 | to copy the contents of this bit vector to another one (or to restore the |
| 1390 | contents of this one). This is not advisable, though, since this would be |
| 1391 | very inefficient (there are much more efficient methods for storing and |
| 1392 | copying bit vectors in this module). |
| 1393 | |
| 1394 | Note that such conversion from binary to decimal is inherently slow |
| 1395 | since the bit vector has to be repeatedly divided by C<10> with remainder |
| 1396 | until the quotient becomes C<0> (each remainder in turn represents a single |
| 1397 | decimal digit of the resulting string). |
| 1398 | |
| 1399 | This is also true for the implementation of this method in this module, |
| 1400 | even though a considerable effort has been made to speed it up: instead of |
| 1401 | repeatedly dividing by C<10>, the bit vector is repeatedly divided by the |
| 1402 | largest power of C<10> that will fit into a machine word. The remainder is |
| 1403 | then repeatedly divided by C<10> using only machine word arithmetics, which |
| 1404 | is much faster than dividing the whole bit vector ("divide and rule" principle). |
| 1405 | |
| 1406 | According to my own measurements, this resulted in an 8-fold speed increase |
| 1407 | over the straightforward approach. |
| 1408 | |
| 1409 | Still, conversion to decimal should be used only where absolutely necessary. |
| 1410 | |
| 1411 | Keep the resulting string stored in some variable if you need it again, |
| 1412 | instead of converting the bit vector all over again. |
| 1413 | |
| 1414 | Beware that if you set the configuration for overloaded operators to |
| 1415 | "output=decimal", this method will be called for every bit vector |
| 1416 | enclosed in double quotes! |
| 1417 | |
| 1418 | =item * |
| 1419 | |
| 1420 | C<$vector-E<gt>from_Dec($string);> |
| 1421 | |
| 1422 | This method allows you to convert a given decimal number, which may be |
| 1423 | positive or negative, into two's complement binary representation, which |
| 1424 | is then stored in the given bit vector. |
| 1425 | |
| 1426 | The decimal number should always be provided as a string, to avoid possible |
| 1427 | truncation (due to the limited precision of integers in Perl) or formatting |
| 1428 | (due to Perl's use of scientific notation for large numbers), which would |
| 1429 | lead to errors. |
| 1430 | |
| 1431 | If the binary representation of the given decimal number is too big to fit |
| 1432 | into the given bit vector (if the given bit vector does not contain enough |
| 1433 | bits to hold it), a fatal "numeric overflow error" occurs. |
| 1434 | |
| 1435 | If the input string contains other characters than decimal digits (C<0-9>) |
| 1436 | and an optional leading sign ("C<+>" or "C<->"), a fatal "input string |
| 1437 | syntax error" occurs. |
| 1438 | |
| 1439 | Beware that large positive numbers which cause the most significant bit to |
| 1440 | be set (e.g. "255" in a bit vector with 8 bits) will be printed as negative |
| 1441 | numbers when converted back to decimal using the method "to_Dec()" (e.g. |
| 1442 | "-1", in our example), because numbers with the most significant bit set |
| 1443 | are considered to be negative in two's complement binary representation. |
| 1444 | |
| 1445 | Note also that while it is possible to thusly enter negative numbers as |
| 1446 | large positive numbers (e.g. "255" for "-1" in a bit vector with 8 bits), |
| 1447 | the contrary isn't, i.e., you cannot enter "-255" for "+1", in our example. |
| 1448 | A fatal "numeric overflow error" will occur if you try to do so. |
| 1449 | |
| 1450 | If possible program abortion is unwanted or intolerable, use |
| 1451 | "C<eval>", like this: |
| 1452 | |
| 1453 | eval { $vector->from_Dec("1152921504606846976"); }; |
| 1454 | if ($@) |
| 1455 | { |
| 1456 | # an error occurred |
| 1457 | } |
| 1458 | |
| 1459 | There are four possible error messages: |
| 1460 | |
| 1461 | if ($@ =~ /item is not a string/) |
| 1462 | |
| 1463 | if ($@ =~ /input string syntax error/) |
| 1464 | |
| 1465 | if ($@ =~ /numeric overflow error/) |
| 1466 | |
| 1467 | if ($@ =~ /unable to allocate memory/) |
| 1468 | |
| 1469 | Note that the conversion from decimal to binary is costly in terms of |
| 1470 | processing time, since a lot of multiplications have to be carried out |
| 1471 | (in principle, each decimal digit must be multiplied with the binary |
| 1472 | representation of the power of C<10> corresponding to its position in |
| 1473 | the decimal number, i.e., 1, 10, 100, 1000, 10000 and so on). |
| 1474 | |
| 1475 | This is not as time consuming as the opposite conversion, from binary |
| 1476 | to decimal (where successive divisions have to be carried out, which |
| 1477 | are even more expensive than multiplications), but still noticeable. |
| 1478 | |
| 1479 | Again (as in the case of "C<to_Dec()>"), the implementation of this |
| 1480 | method in this module uses the principle of "divide and rule" in order |
| 1481 | to speed up the conversion, i.e., as many decimal digits as possible |
| 1482 | are first accumulated (converted) in a machine word and only then |
| 1483 | stored in the given bit vector. |
| 1484 | |
| 1485 | Even so, use this method only where absolutely necessary if speed is |
| 1486 | an important consideration in your application. |
| 1487 | |
| 1488 | Beware that if you set the configuration for overloaded operators to |
| 1489 | "input=decimal", this method will be called for every scalar operand |
| 1490 | you use! |
| 1491 | |
| 1492 | =item * |
| 1493 | |
| 1494 | C<$string = $vector-E<gt>to_Enum();> |
| 1495 | |
| 1496 | Converts the given bit vector or set into an enumeration of single |
| 1497 | indices and ranges of indices (".newsrc" style), representing the |
| 1498 | bits that are set ("C<1>") in the bit vector. |
| 1499 | |
| 1500 | Example: |
| 1501 | |
| 1502 | $vector = Bit::Vector->new(20); |
| 1503 | $vector->Bit_On(2); |
| 1504 | $vector->Bit_On(3); |
| 1505 | $vector->Bit_On(11); |
| 1506 | $vector->Interval_Fill(5,7); |
| 1507 | $vector->Interval_Fill(13,19); |
| 1508 | print "'", $vector->to_Enum(), "'\n"; |
| 1509 | |
| 1510 | which prints |
| 1511 | |
| 1512 | '2,3,5-7,11,13-19' |
| 1513 | |
| 1514 | If the given bit vector is empty, the resulting string will |
| 1515 | also be empty. |
| 1516 | |
| 1517 | Note, by the way, that the above example can also be written |
| 1518 | a little handier, perhaps, as follows: |
| 1519 | |
| 1520 | Bit::Vector->Configuration("out=enum"); |
| 1521 | $vector = Bit::Vector->new(20); |
| 1522 | $vector->Index_List_Store(2,3,5,6,7,11,13,14,15,16,17,18,19); |
| 1523 | print "'$vector'\n"; |
| 1524 | |
| 1525 | =item * |
| 1526 | |
| 1527 | C<$vector-E<gt>from_Enum($string);> |
| 1528 | |
| 1529 | This method first empties the given bit vector and then tries to |
| 1530 | set the bits and ranges of bits specified in the given string. |
| 1531 | |
| 1532 | The string "C<$string>" must only contain unsigned integers |
| 1533 | or ranges of integers (two unsigned integers separated by a |
| 1534 | dash "-"), separated by commas (","). |
| 1535 | |
| 1536 | All other characters are disallowed (including white space!) |
| 1537 | and will lead to a fatal "input string syntax error". |
| 1538 | |
| 1539 | In each range, the first integer (the lower limit of the range) |
| 1540 | must always be less than or equal to the second integer (the |
| 1541 | upper limit), or a fatal "minimum > maximum index" error occurs. |
| 1542 | |
| 1543 | All integers must lie in the permitted range for the given |
| 1544 | bit vector, i.e., they must lie between "C<0>" and |
| 1545 | "C<$vector-E<gt>Size()-1>". |
| 1546 | |
| 1547 | If this condition is not met, a fatal "index out of range" |
| 1548 | error occurs. |
| 1549 | |
| 1550 | If possible program abortion is unwanted or intolerable, use |
| 1551 | "C<eval>", like this: |
| 1552 | |
| 1553 | eval { $vector->from_Enum("2,3,5-7,11,13-19"); }; |
| 1554 | if ($@) |
| 1555 | { |
| 1556 | # an error occurred |
| 1557 | } |
| 1558 | |
| 1559 | There are four possible error messages: |
| 1560 | |
| 1561 | if ($@ =~ /item is not a string/) |
| 1562 | |
| 1563 | if ($@ =~ /input string syntax error/) |
| 1564 | |
| 1565 | if ($@ =~ /index out of range/) |
| 1566 | |
| 1567 | if ($@ =~ /minimum > maximum index/) |
| 1568 | |
| 1569 | Note that the order of the indices and ranges is irrelevant, |
| 1570 | i.e., |
| 1571 | |
| 1572 | eval { $vector->from_Enum("11,5-7,3,13-19,2"); }; |
| 1573 | |
| 1574 | results in the same vector as in the example above. |
| 1575 | |
| 1576 | Ranges and indices may also overlap. |
| 1577 | |
| 1578 | This is because each (single) index in the string is passed |
| 1579 | to the method "C<Bit_On()>", internally, and each range to |
| 1580 | the method "C<Interval_Fill()>". |
| 1581 | |
| 1582 | This means that the resulting bit vector is just the union |
| 1583 | of all the indices and ranges specified in the given string. |
| 1584 | |
| 1585 | =item * |
| 1586 | |
| 1587 | C<$vector-E<gt>Bit_Off($index);> |
| 1588 | |
| 1589 | Clears the bit with index "C<$index>" in the given vector. |
| 1590 | |
| 1591 | =item * |
| 1592 | |
| 1593 | C<$vector-E<gt>Bit_On($index);> |
| 1594 | |
| 1595 | Sets the bit with index "C<$index>" in the given vector. |
| 1596 | |
| 1597 | =item * |
| 1598 | |
| 1599 | C<$vector-E<gt>bit_flip($index)> |
| 1600 | |
| 1601 | Flips (i.e., complements) the bit with index "C<$index>" |
| 1602 | in the given vector. |
| 1603 | |
| 1604 | Moreover, this method returns the B<NEW> state of the |
| 1605 | bit in question, i.e., it returns "C<0>" if the bit is |
| 1606 | cleared or "C<1>" if the bit is set (B<AFTER> flipping it). |
| 1607 | |
| 1608 | =item * |
| 1609 | |
| 1610 | C<if ($vector-E<gt>bit_test($index))> |
| 1611 | |
| 1612 | C<if ($vector-E<gt>contains($index))> |
| 1613 | |
| 1614 | Returns the current state of the bit with index "C<$index>" |
| 1615 | in the given vector, i.e., returns "C<0>" if it is cleared |
| 1616 | (in the "off" state) or "C<1>" if it is set (in the "on" state). |
| 1617 | |
| 1618 | =item * |
| 1619 | |
| 1620 | C<$vector-E<gt>Bit_Copy($index,$bit);> |
| 1621 | |
| 1622 | Sets the bit with index "C<$index>" in the given vector either |
| 1623 | to "C<0>" or "C<1>" depending on the boolean value "C<$bit>". |
| 1624 | |
| 1625 | =item * |
| 1626 | |
| 1627 | C<$vector-E<gt>LSB($bit);> |
| 1628 | |
| 1629 | Allows you to set the least significant bit in the given bit |
| 1630 | vector to the value given by the boolean parameter "C<$bit>". |
| 1631 | |
| 1632 | This is a (faster) shortcut for "C<$vector-E<gt>Bit_Copy(0,$bit);>". |
| 1633 | |
| 1634 | =item * |
| 1635 | |
| 1636 | C<$vector-E<gt>MSB($bit);> |
| 1637 | |
| 1638 | Allows you to set the most significant bit in the given bit |
| 1639 | vector to the value given by the boolean parameter "C<$bit>". |
| 1640 | |
| 1641 | This is a (faster) shortcut for |
| 1642 | "C<$vector-E<gt>Bit_Copy($vector-E<gt>Size()-1,$bit);>". |
| 1643 | |
| 1644 | =item * |
| 1645 | |
| 1646 | C<$bit = $vector-E<gt>lsb();> |
| 1647 | |
| 1648 | Returns the least significant bit of the given bit vector. |
| 1649 | |
| 1650 | This is a (faster) shortcut for "C<$bit = $vector-E<gt>bit_test(0);>". |
| 1651 | |
| 1652 | =item * |
| 1653 | |
| 1654 | C<$bit = $vector-E<gt>msb();> |
| 1655 | |
| 1656 | Returns the most significant bit of the given bit vector. |
| 1657 | |
| 1658 | This is a (faster) shortcut for |
| 1659 | "C<$bit = $vector-E<gt>bit_test($vector-E<gt>Size()-1);>". |
| 1660 | |
| 1661 | =item * |
| 1662 | |
| 1663 | C<$carry_out = $vector-E<gt>rotate_left();> |
| 1664 | |
| 1665 | carry MSB vector: LSB |
| 1666 | out: |
| 1667 | +---+ +---+---+---+--- ---+---+---+---+ |
| 1668 | | | <---+--- | | | | ... | | | | <---+ |
| 1669 | +---+ | +---+---+---+--- ---+---+---+---+ | |
| 1670 | | | |
| 1671 | +------------------------------------------------+ |
| 1672 | |
| 1673 | The least significant bit (LSB) is the bit with index "C<0>", the most |
| 1674 | significant bit (MSB) is the bit with index "C<$vector-E<gt>Size()-1>". |
| 1675 | |
| 1676 | =item * |
| 1677 | |
| 1678 | C<$carry_out = $vector-E<gt>rotate_right();> |
| 1679 | |
| 1680 | MSB vector: LSB carry |
| 1681 | out: |
| 1682 | +---+---+---+--- ---+---+---+---+ +---+ |
| 1683 | +---> | | | | ... | | | | ---+---> | | |
| 1684 | | +---+---+---+--- ---+---+---+---+ | +---+ |
| 1685 | | | |
| 1686 | +------------------------------------------------+ |
| 1687 | |
| 1688 | The least significant bit (LSB) is the bit with index "C<0>", the most |
| 1689 | significant bit (MSB) is the bit with index "C<$vector-E<gt>Size()-1>". |
| 1690 | |
| 1691 | =item * |
| 1692 | |
| 1693 | C<$carry_out = $vector-E<gt>shift_left($carry_in);> |
| 1694 | |
| 1695 | carry MSB vector: LSB carry |
| 1696 | out: in: |
| 1697 | +---+ +---+---+---+--- ---+---+---+---+ +---+ |
| 1698 | | | <--- | | | | ... | | | | <--- | | |
| 1699 | +---+ +---+---+---+--- ---+---+---+---+ +---+ |
| 1700 | |
| 1701 | The least significant bit (LSB) is the bit with index "C<0>", the most |
| 1702 | significant bit (MSB) is the bit with index "C<$vector-E<gt>Size()-1>". |
| 1703 | |
| 1704 | =item * |
| 1705 | |
| 1706 | C<$carry_out = $vector-E<gt>shift_right($carry_in);> |
| 1707 | |
| 1708 | carry MSB vector: LSB carry |
| 1709 | in: out: |
| 1710 | +---+ +---+---+---+--- ---+---+---+---+ +---+ |
| 1711 | | | ---> | | | | ... | | | | ---> | | |
| 1712 | +---+ +---+---+---+--- ---+---+---+---+ +---+ |
| 1713 | |
| 1714 | The least significant bit (LSB) is the bit with index "C<0>", the most |
| 1715 | significant bit (MSB) is the bit with index "C<$vector-E<gt>Size()-1>". |
| 1716 | |
| 1717 | =item * |
| 1718 | |
| 1719 | C<$vector-E<gt>Move_Left($bits);> |
| 1720 | |
| 1721 | Shifts the given bit vector left by "C<$bits>" bits, i.e., inserts "C<$bits>" |
| 1722 | new bits at the lower end (least significant bit) of the bit vector, moving |
| 1723 | all other bits up by "C<$bits>" places, thereby losing the "C<$bits>" most |
| 1724 | significant bits. |
| 1725 | |
| 1726 | The inserted new bits are all cleared (set to the "off" state). |
| 1727 | |
| 1728 | This method does nothing if "C<$bits>" is equal to zero. |
| 1729 | |
| 1730 | Beware that the whole bit vector is cleared B<WITHOUT WARNING> if |
| 1731 | "C<$bits>" is greater than or equal to the size of the given bit vector! |
| 1732 | |
| 1733 | In fact this method is equivalent to |
| 1734 | |
| 1735 | for ( $i = 0; $i < $bits; $i++ ) { $vector->shift_left(0); } |
| 1736 | |
| 1737 | except that it is much more efficient (for "C<$bits>" greater than or |
| 1738 | equal to the number of bits in a machine word on your system) than |
| 1739 | this straightforward approach. |
| 1740 | |
| 1741 | =item * |
| 1742 | |
| 1743 | C<$vector-E<gt>Move_Right($bits);> |
| 1744 | |
| 1745 | Shifts the given bit vector right by "C<$bits>" bits, i.e., deletes the |
| 1746 | "C<$bits>" least significant bits of the bit vector, moving all other bits |
| 1747 | down by "C<$bits>" places, thereby creating "C<$bits>" new bits at the upper |
| 1748 | end (most significant bit) of the bit vector. |
| 1749 | |
| 1750 | These new bits are all cleared (set to the "off" state). |
| 1751 | |
| 1752 | This method does nothing if "C<$bits>" is equal to zero. |
| 1753 | |
| 1754 | Beware that the whole bit vector is cleared B<WITHOUT WARNING> if |
| 1755 | "C<$bits>" is greater than or equal to the size of the given bit vector! |
| 1756 | |
| 1757 | In fact this method is equivalent to |
| 1758 | |
| 1759 | for ( $i = 0; $i < $bits; $i++ ) { $vector->shift_right(0); } |
| 1760 | |
| 1761 | except that it is much more efficient (for "C<$bits>" greater than or |
| 1762 | equal to the number of bits in a machine word on your system) than |
| 1763 | this straightforward approach. |
| 1764 | |
| 1765 | =item * |
| 1766 | |
| 1767 | C<$vector-E<gt>Insert($offset,$bits);> |
| 1768 | |
| 1769 | This method inserts "C<$bits>" fresh new bits at position "C<$offset>" |
| 1770 | in the given bit vector. |
| 1771 | |
| 1772 | The "C<$bits>" most significant bits are lost, and all bits starting |
| 1773 | with bit number "C<$offset>" up to and including bit number |
| 1774 | "C<$vector-E<gt>Size()-$bits-1>" are moved up by "C<$bits>" places. |
| 1775 | |
| 1776 | The now vacant "C<$bits>" bits starting at bit number "C<$offset>" |
| 1777 | (up to and including bit number "C<$offset+$bits-1>") are then set |
| 1778 | to zero (cleared). |
| 1779 | |
| 1780 | Note that this method does B<NOT> increase the size of the given bit |
| 1781 | vector, i.e., the bit vector is B<NOT> extended at its upper end to |
| 1782 | "rescue" the "C<$bits>" uppermost (most significant) bits - instead, |
| 1783 | these bits are lost forever. |
| 1784 | |
| 1785 | If you don't want this to happen, you have to increase the size of the |
| 1786 | given bit vector B<EXPLICITLY> and B<BEFORE> you perform the "Insert" |
| 1787 | operation, with a statement such as the following: |
| 1788 | |
| 1789 | $vector->Resize($vector->Size() + $bits); |
| 1790 | |
| 1791 | Or use the method "C<Interval_Substitute()>" instead of "C<Insert()>", |
| 1792 | which performs automatic growing and shrinking of its target bit vector. |
| 1793 | |
| 1794 | Note also that "C<$offset>" must lie in the permitted range between |
| 1795 | "C<0>" and "C<$vector-E<gt>Size()-1>", or a fatal "offset out of range" |
| 1796 | error will occur. |
| 1797 | |
| 1798 | If the term "C<$offset + $bits>" exceeds "C<$vector-E<gt>Size()-1>", |
| 1799 | all the bits starting with bit number "C<$offset>" up to bit number |
| 1800 | "C<$vector-E<gt>Size()-1>" are simply cleared. |
| 1801 | |
| 1802 | =item * |
| 1803 | |
| 1804 | C<$vector-E<gt>Delete($offset,$bits);> |
| 1805 | |
| 1806 | This method deletes, i.e., removes the bits starting at position |
| 1807 | "C<$offset>" up to and including bit number "C<$offset+$bits-1>" |
| 1808 | from the given bit vector. |
| 1809 | |
| 1810 | The remaining uppermost bits (starting at position "C<$offset+$bits>" |
| 1811 | up to and including bit number "C<$vector-E<gt>Size()-1>") are moved |
| 1812 | down by "C<$bits>" places. |
| 1813 | |
| 1814 | The now vacant uppermost (most significant) "C<$bits>" bits are then |
| 1815 | set to zero (cleared). |
| 1816 | |
| 1817 | Note that this method does B<NOT> decrease the size of the given bit |
| 1818 | vector, i.e., the bit vector is B<NOT> clipped at its upper end to |
| 1819 | "get rid of" the vacant "C<$bits>" uppermost bits. |
| 1820 | |
| 1821 | If you don't want this, i.e., if you want the bit vector to shrink |
| 1822 | accordingly, you have to do so B<EXPLICITLY> and B<AFTER> the "Delete" |
| 1823 | operation, with a couple of statements such as these: |
| 1824 | |
| 1825 | $size = $vector->Size(); |
| 1826 | if ($bits > $size) { $bits = $size; } |
| 1827 | $vector->Resize($size - $bits); |
| 1828 | |
| 1829 | Or use the method "C<Interval_Substitute()>" instead of "C<Delete()>", |
| 1830 | which performs automatic growing and shrinking of its target bit vector. |
| 1831 | |
| 1832 | Note also that "C<$offset>" must lie in the permitted range between |
| 1833 | "C<0>" and "C<$vector-E<gt>Size()-1>", or a fatal "offset out of range" |
| 1834 | error will occur. |
| 1835 | |
| 1836 | If the term "C<$offset + $bits>" exceeds "C<$vector-E<gt>Size()-1>", |
| 1837 | all the bits starting with bit number "C<$offset>" up to bit number |
| 1838 | "C<$vector-E<gt>Size()-1>" are simply cleared. |
| 1839 | |
| 1840 | =item * |
| 1841 | |
| 1842 | C<$carry = $vector-E<gt>increment();> |
| 1843 | |
| 1844 | This method increments the given bit vector. |
| 1845 | |
| 1846 | Note that this method regards bit vectors as being unsigned, |
| 1847 | i.e., the largest possible positive number is directly |
| 1848 | followed by the smallest possible (or greatest possible, |
| 1849 | speaking in absolute terms) negative number: |
| 1850 | |
| 1851 | before: 2 ^ (b-1) - 1 (= "0111...1111") |
| 1852 | after: 2 ^ (b-1) (= "1000...0000") |
| 1853 | |
| 1854 | where "C<b>" is the number of bits of the given bit vector. |
| 1855 | |
| 1856 | The method returns "false" ("C<0>") in all cases except when a |
| 1857 | carry over occurs (in which case it returns "true", i.e., "C<1>"), |
| 1858 | which happens when the number "1111...1111" is incremented, |
| 1859 | which gives "0000...0000" plus a carry over to the next higher |
| 1860 | (binary) digit. |
| 1861 | |
| 1862 | This can be used for the terminating condition of a "while" loop, |
| 1863 | for instance, in order to cycle through all possible values the |
| 1864 | bit vector can assume. |
| 1865 | |
| 1866 | =item * |
| 1867 | |
| 1868 | C<$carry = $vector-E<gt>decrement();> |
| 1869 | |
| 1870 | This method decrements the given bit vector. |
| 1871 | |
| 1872 | Note that this method regards bit vectors as being unsigned, |
| 1873 | i.e., the smallest possible (or greatest possible, speaking |
| 1874 | in absolute terms) negative number is directly followed by |
| 1875 | the largest possible positive number: |
| 1876 | |
| 1877 | before: 2 ^ (b-1) (= "1000...0000") |
| 1878 | after: 2 ^ (b-1) - 1 (= "0111...1111") |
| 1879 | |
| 1880 | where "C<b>" is the number of bits of the given bit vector. |
| 1881 | |
| 1882 | The method returns "false" ("C<0>") in all cases except when a |
| 1883 | carry over occurs (in which case it returns "true", i.e., "C<1>"), |
| 1884 | which happens when the number "0000...0000" is decremented, |
| 1885 | which gives "1111...1111" minus a carry over to the next higher |
| 1886 | (binary) digit. |
| 1887 | |
| 1888 | This can be used for the terminating condition of a "while" loop, |
| 1889 | for instance, in order to cycle through all possible values the |
| 1890 | bit vector can assume. |
| 1891 | |
| 1892 | =item * |
| 1893 | |
| 1894 | C<$overflow = $vec2-E<gt>inc($vec1);> |
| 1895 | |
| 1896 | This method copies the contents of bit vector "C<$vec1>" to bit |
| 1897 | vector "C<$vec2>" and increments the copy (not the original). |
| 1898 | |
| 1899 | If by incrementing the number its sign becomes invalid, the return |
| 1900 | value ("overflow" flag) will be true ("C<1>"), or false ("C<0>") |
| 1901 | if not. (See the description of the method "add()" below for |
| 1902 | a more in-depth explanation of what "overflow" means). |
| 1903 | |
| 1904 | Note that in-place operation is also possible, i.e., "C<$vec1>" |
| 1905 | and "C<$vec2>" may be identical. |
| 1906 | |
| 1907 | =item * |
| 1908 | |
| 1909 | C<$overflow = $vec2-E<gt>dec($vec1);> |
| 1910 | |
| 1911 | This method copies the contents of bit vector "C<$vec1>" to bit |
| 1912 | vector "C<$vec2>" and decrements the copy (not the original). |
| 1913 | |
| 1914 | If by decrementing the number its sign becomes invalid, the return |
| 1915 | value ("overflow" flag) will be true ("C<1>"), or false ("C<0>") |
| 1916 | if not. (See the description of the method "subtract()" below |
| 1917 | for a more in-depth explanation of what "overflow" means). |
| 1918 | |
| 1919 | Note that in-place operation is also possible, i.e., "C<$vec1>" |
| 1920 | and "C<$vec2>" may be identical. |
| 1921 | |
| 1922 | =item * |
| 1923 | |
| 1924 | C<$carry = $vec3-E<gt>add($vec1,$vec2,$carry);> |
| 1925 | |
| 1926 | C<($carry,$overflow) = $vec3-E<gt>add($vec1,$vec2,$carry);> |
| 1927 | |
| 1928 | This method adds the two numbers contained in bit vector "C<$vec1>" |
| 1929 | and "C<$vec2>" with carry "C<$carry>" and stores the result in |
| 1930 | bit vector "C<$vec3>". |
| 1931 | |
| 1932 | I.e., |
| 1933 | $vec3 = $vec1 + $vec2 + $carry |
| 1934 | |
| 1935 | Note that the "C<$carry>" parameter is a boolean value, i.e., |
| 1936 | only its least significant bit is taken into account. (Think of |
| 1937 | it as though "C<$carry &= 1;>" was always executed internally.) |
| 1938 | |
| 1939 | In scalar context, the method returns a boolean value which |
| 1940 | indicates if a carry over (to the next higher bit position) |
| 1941 | has occured. In list context, the method returns the carry |
| 1942 | and the overflow flag (in this order). |
| 1943 | |
| 1944 | The overflow flag is true ("C<1>") if the sign (i.e., the most |
| 1945 | significant bit) of the result is wrong. This can happen when |
| 1946 | adding two very large positive numbers or when adding two (by |
| 1947 | their absolute value) very large negative numbers. See also |
| 1948 | further below. |
| 1949 | |
| 1950 | The carry in- and output is needed mainly for cascading, i.e., |
| 1951 | to add numbers that are fragmented into several pieces. |
| 1952 | |
| 1953 | Example: |
| 1954 | |
| 1955 | # initialize |
| 1956 | |
| 1957 | for ( $i = 0; $i < $n; $i++ ) |
| 1958 | { |
| 1959 | $a[$i] = Bit::Vector->new($bits); |
| 1960 | $b[$i] = Bit::Vector->new($bits); |
| 1961 | $c[$i] = Bit::Vector->new($bits); |
| 1962 | } |
| 1963 | |
| 1964 | # fill @a and @b |
| 1965 | |
| 1966 | # $a[ 0 ] is low order part, |
| 1967 | # $a[$n-1] is high order part, |
| 1968 | # and same for @b |
| 1969 | |
| 1970 | # add |
| 1971 | |
| 1972 | $carry = 0; |
| 1973 | for ( $i = 0; $i < $n; $i++ ) |
| 1974 | { |
| 1975 | $carry = $c[$i]->add($a[$i],$b[$i],$carry); |
| 1976 | } |
| 1977 | |
| 1978 | Note that it makes no difference to this method whether the numbers |
| 1979 | in "C<$vec1>" and "C<$vec2>" are unsigned or signed (i.e., in two's |
| 1980 | complement binary representation). |
| 1981 | |
| 1982 | Note however that the return value (carry flag) is not meaningful |
| 1983 | when the numbers are B<SIGNED>. |
| 1984 | |
| 1985 | Moreover, when the numbers are signed, a special type of error can |
| 1986 | occur which is commonly called an "overflow error". |
| 1987 | |
| 1988 | An overflow error occurs when the sign of the result (its most |
| 1989 | significant bit) is flipped (i.e., falsified) by a carry over |
| 1990 | from the next-lower bit position ("MSB-1"). |
| 1991 | |
| 1992 | In fact matters are a bit more complicated than that: the overflow |
| 1993 | flag is set to "true" whenever there is a carry over from bit |
| 1994 | position MSB-1 to the most significant bit (MSB) but no carry |
| 1995 | over from the MSB to the output carry flag, or vice-versa, i.e., |
| 1996 | when there is no carry over from bit position MSB-1 to the most |
| 1997 | significant bit (MSB) but a carry over to the output carry flag. |
| 1998 | |
| 1999 | Thus the overflow flag is the result of an exclusive-or operation |
| 2000 | between incoming and outgoing carry over at the most significant |
| 2001 | bit position. |
| 2002 | |
| 2003 | =item * |
| 2004 | |
| 2005 | C<$carry = $vec3-E<gt>subtract($vec1,$vec2,$carry);> |
| 2006 | |
| 2007 | C<($carry,$overflow) = $vec3-E<gt>subtract($vec1,$vec2,$carry);> |
| 2008 | |
| 2009 | This method subtracts the two numbers contained in bit vector |
| 2010 | "C<$vec1>" and "C<$vec2>" with carry "C<$carry>" and stores the |
| 2011 | result in bit vector "C<$vec3>". |
| 2012 | |
| 2013 | I.e., |
| 2014 | $vec3 = $vec1 - $vec2 - $carry |
| 2015 | |
| 2016 | Note that the "C<$carry>" parameter is a boolean value, i.e., |
| 2017 | only its least significant bit is taken into account. (Think of |
| 2018 | it as though "C<$carry &= 1;>" was always executed internally.) |
| 2019 | |
| 2020 | In scalar context, the method returns a boolean value which |
| 2021 | indicates if a carry over (to the next higher bit position) |
| 2022 | has occured. In list context, the method returns the carry |
| 2023 | and the overflow flag (in this order). |
| 2024 | |
| 2025 | The overflow flag is true ("C<1>") if the sign (i.e., the most |
| 2026 | significant bit) of the result is wrong. This can happen when |
| 2027 | subtracting a very large negative number from a very large |
| 2028 | positive number or vice-versa. See also further below. |
| 2029 | |
| 2030 | The carry in- and output is needed mainly for cascading, i.e., |
| 2031 | to subtract numbers that are fragmented into several pieces. |
| 2032 | |
| 2033 | Example: |
| 2034 | |
| 2035 | # initialize |
| 2036 | |
| 2037 | for ( $i = 0; $i < $n; $i++ ) |
| 2038 | { |
| 2039 | $a[$i] = Bit::Vector->new($bits); |
| 2040 | $b[$i] = Bit::Vector->new($bits); |
| 2041 | $c[$i] = Bit::Vector->new($bits); |
| 2042 | } |
| 2043 | |
| 2044 | # fill @a and @b |
| 2045 | |
| 2046 | # $a[ 0 ] is low order part, |
| 2047 | # $a[$n-1] is high order part, |
| 2048 | # and same for @b |
| 2049 | |
| 2050 | # subtract |
| 2051 | |
| 2052 | $carry = 0; |
| 2053 | for ( $i = 0; $i < $n; $i++ ) |
| 2054 | { |
| 2055 | $carry = $c[$i]->subtract($a[$i],$b[$i],$carry); |
| 2056 | } |
| 2057 | |
| 2058 | Note that it makes no difference to this method whether the numbers |
| 2059 | in "C<$vec1>" and "C<$vec2>" are unsigned or signed (i.e., in two's |
| 2060 | complement binary representation). |
| 2061 | |
| 2062 | Note however that the return value (carry flag) is not meaningful |
| 2063 | when the numbers are B<SIGNED>. |
| 2064 | |
| 2065 | Moreover, when the numbers are signed, a special type of error can |
| 2066 | occur which is commonly called an "overflow error". |
| 2067 | |
| 2068 | An overflow error occurs when the sign of the result (its most |
| 2069 | significant bit) is flipped (i.e., falsified) by a carry over |
| 2070 | from the next-lower bit position ("MSB-1"). |
| 2071 | |
| 2072 | In fact matters are a bit more complicated than that: the overflow |
| 2073 | flag is set to "true" whenever there is a carry over from bit |
| 2074 | position MSB-1 to the most significant bit (MSB) but no carry |
| 2075 | over from the MSB to the output carry flag, or vice-versa, i.e., |
| 2076 | when there is no carry over from bit position MSB-1 to the most |
| 2077 | significant bit (MSB) but a carry over to the output carry flag. |
| 2078 | |
| 2079 | Thus the overflow flag is the result of an exclusive-or operation |
| 2080 | between incoming and outgoing carry over at the most significant |
| 2081 | bit position. |
| 2082 | |
| 2083 | =item * |
| 2084 | |
| 2085 | C<$vec2-E<gt>Neg($vec1);> |
| 2086 | |
| 2087 | C<$vec2-E<gt>Negate($vec1);> |
| 2088 | |
| 2089 | This method calculates the two's complement of the number in bit |
| 2090 | vector "C<$vec1>" and stores the result in bit vector "C<$vec2>". |
| 2091 | |
| 2092 | Calculating the two's complement of a given number in binary representation |
| 2093 | consists of inverting all bits and incrementing the result by one. |
| 2094 | |
| 2095 | This is the same as changing the sign of the given number from "C<+>" to |
| 2096 | "C<->" or vice-versa. In other words, applying this method twice on a given |
| 2097 | number yields the original number again. |
| 2098 | |
| 2099 | Note that in-place processing is also possible, i.e., "C<$vec1>" and |
| 2100 | "C<$vec2>" may be identical. |
| 2101 | |
| 2102 | Most importantly, beware that this method produces a counter-intuitive |
| 2103 | result if the number contained in bit vector "C<$vec1>" is C<2 ^ (n-1)> |
| 2104 | (i.e., "1000...0000"), where "C<n>" is the number of bits the given bit |
| 2105 | vector contains: The negated value of this number is the number itself! |
| 2106 | |
| 2107 | =item * |
| 2108 | |
| 2109 | C<$vec2-E<gt>Abs($vec1);> |
| 2110 | |
| 2111 | C<$vec2-E<gt>Absolute($vec1);> |
| 2112 | |
| 2113 | Depending on the sign (i.e., the most significant bit) of the number in |
| 2114 | bit vector "C<$vec1>", the contents of bit vector "C<$vec1>" are copied |
| 2115 | to bit vector "C<$vec2>" either with the method "C<Copy()>" (if the number |
| 2116 | in bit vector "C<$vec1>" is positive), or with "C<Negate()>" (if the number |
| 2117 | in bit vector "C<$vec1>" is negative). |
| 2118 | |
| 2119 | In other words, this method calculates the absolute value of the number |
| 2120 | in bit vector "C<$vec1>" and stores the result in bit vector "C<$vec2>". |
| 2121 | |
| 2122 | Note that in-place processing is also possible, i.e., "C<$vec1>" and |
| 2123 | "C<$vec2>" may be identical. |
| 2124 | |
| 2125 | Most importantly, beware that this method produces a counter-intuitive |
| 2126 | result if the number contained in bit vector "C<$vec1>" is C<2 ^ (n-1)> |
| 2127 | (i.e., "1000...0000"), where "C<n>" is the number of bits the given bit |
| 2128 | vector contains: The absolute value of this number is the number itself, |
| 2129 | even though this number is still negative by definition (the most |
| 2130 | significant bit is still set)! |
| 2131 | |
| 2132 | =item * |
| 2133 | |
| 2134 | C<$sign = $vector-E<gt>Sign();> |
| 2135 | |
| 2136 | This method returns "C<0>" if all bits in the given bit vector are cleared, |
| 2137 | i.e., if the given bit vector contains the number "C<0>", or if the given |
| 2138 | bit vector has a length of zero (contains no bits at all). |
| 2139 | |
| 2140 | If not all bits are cleared, this method returns "C<-1>" if the most |
| 2141 | significant bit is set (i.e., if the bit vector contains a negative |
| 2142 | number), or "C<1>" otherwise (i.e., if the bit vector contains a |
| 2143 | positive number). |
| 2144 | |
| 2145 | =item * |
| 2146 | |
| 2147 | C<$vec3-E<gt>Multiply($vec1,$vec2);> |
| 2148 | |
| 2149 | This method multiplies the two numbers contained in bit vector "C<$vec1>" |
| 2150 | and "C<$vec2>" and stores the result in bit vector "C<$vec3>". |
| 2151 | |
| 2152 | Note that this method regards its arguments as B<SIGNED>. |
| 2153 | |
| 2154 | If you want to make sure that a large number can never be treated as being |
| 2155 | negative by mistake, make your bit vectors at least one bit longer than the |
| 2156 | largest number you wish to represent, right from the start, or proceed as |
| 2157 | follows: |
| 2158 | |
| 2159 | $msb1 = $vec1->msb(); |
| 2160 | $msb2 = $vec2->msb(); |
| 2161 | $vec1->Resize($vec1->Size()+1); |
| 2162 | $vec2->Resize($vec2->Size()+1); |
| 2163 | $vec3->Resize($vec3->Size()+1); |
| 2164 | $vec1->MSB($msb1); |
| 2165 | $vec2->MSB($msb2); |
| 2166 | $vec3->Multiply($vec1,$vec2); |
| 2167 | |
| 2168 | Note also that all three bit vector arguments must in principle obey the |
| 2169 | rule of matching sizes, but that the bit vector "C<$vec3>" may be larger |
| 2170 | than the two factors "C<$vec1>" and "C<$vec2>". |
| 2171 | |
| 2172 | In fact multiplying two binary numbers with "C<n>" bits may yield a result |
| 2173 | which is at most "C<2n>" bits long. |
| 2174 | |
| 2175 | Therefore, it is usually a good idea to let bit vector "C<$vec3>" have |
| 2176 | twice the size of bit vector "C<$vec1>" and "C<$vec2>", unless you are |
| 2177 | absolutely sure that the result will fit into a bit vector of the same |
| 2178 | size as the two factors. |
| 2179 | |
| 2180 | If you are wrong, a fatal "numeric overflow error" will occur. |
| 2181 | |
| 2182 | Finally, note that in-place processing is possible, i.e., "C<$vec3>" |
| 2183 | may be identical with "C<$vec1>" or "C<$vec2>", or both. |
| 2184 | |
| 2185 | =item * |
| 2186 | |
| 2187 | C<$quot-E<gt>Divide($vec1,$vec2,$rest);> |
| 2188 | |
| 2189 | This method divides the two numbers contained in bit vector "C<$vec1>" |
| 2190 | and "C<$vec2>" and stores the quotient in bit vector "C<$quot>" and |
| 2191 | the remainder in bit vector "C<$rest>". |
| 2192 | |
| 2193 | I.e., |
| 2194 | $quot = $vec1 / $vec2; # div |
| 2195 | $rest = $vec1 % $vec2; # mod |
| 2196 | |
| 2197 | Therefore, "C<$quot>" and "C<$rest>" must be two B<DISTINCT> bit vectors, |
| 2198 | or a fatal "result vector(s) must be distinct" error will occur. |
| 2199 | |
| 2200 | Note also that a fatal "division by zero error" will occur if "C<$vec2>" |
| 2201 | is equal to zero. |
| 2202 | |
| 2203 | Note further that this method regards its arguments as B<SIGNED>. |
| 2204 | |
| 2205 | If you want to make sure that a large number can never be treated as being |
| 2206 | negative by mistake, make your bit vectors at least one bit longer than the |
| 2207 | largest number you wish to represent, right from the start, or proceed as |
| 2208 | follows: |
| 2209 | |
| 2210 | $msb1 = $vec1->msb(); |
| 2211 | $msb2 = $vec2->msb(); |
| 2212 | $vec1->Resize($vec1->Size()+1); |
| 2213 | $vec2->Resize($vec2->Size()+1); |
| 2214 | $quot->Resize($quot->Size()+1); |
| 2215 | $rest->Resize($rest->Size()+1); |
| 2216 | $vec1->MSB($msb1); |
| 2217 | $vec2->MSB($msb2); |
| 2218 | $quot->Divide($vec1,$vec2,$rest); |
| 2219 | |
| 2220 | Finally, note that in-place processing is possible, i.e., "C<$quot>" |
| 2221 | may be identical with "C<$vec1>" or "C<$vec2>" or both, and "C<$rest>" |
| 2222 | may also be identical with "C<$vec1>" or "C<$vec2>" or both, as long |
| 2223 | as "C<$quot>" and "C<$rest>" are distinct. (!) |
| 2224 | |
| 2225 | =item * |
| 2226 | |
| 2227 | C<$vecgcd-E<gt>GCD($veca,$vecb);> |
| 2228 | |
| 2229 | This method calculates the "Greatest Common Divisor" of the two numbers |
| 2230 | contained in bit vector "C<$veca>" and "C<$vecb>" and stores the result |
| 2231 | in bit vector "C<$vecgcd>". |
| 2232 | |
| 2233 | The method uses Euklid's algorithm internally: |
| 2234 | |
| 2235 | int GCD(int a, int b) |
| 2236 | { |
| 2237 | int t; |
| 2238 | |
| 2239 | while (b != 0) |
| 2240 | { |
| 2241 | t = a % b; /* = remainder of (a div b) */ |
| 2242 | a = b; |
| 2243 | b = t; |
| 2244 | } |
| 2245 | return(a); |
| 2246 | } |
| 2247 | |
| 2248 | Note that C<GCD(z,0) == GCD(0,z) == z>. |
| 2249 | |
| 2250 | =item * |
| 2251 | |
| 2252 | C<$vecgcd-E<gt>GCD($vecx,$vecy,$veca,$vecb);> |
| 2253 | |
| 2254 | This variant of the "GCD" method calculates the "Greatest Common Divisor" |
| 2255 | of the two numbers contained in bit vector "C<$veca>" and "C<$vecb>" and |
| 2256 | stores the result in bit vector "C<$vecgcd>". |
| 2257 | |
| 2258 | Moreover, it determines the two factors which are necessary in order to |
| 2259 | represent the greatest common divisor as a linear combination of its two |
| 2260 | arguments, i.e., the two factors C<"x"> and C<"y"> so that |
| 2261 | C<GCD(a,b) == x * a + y * b>, and stores them in bit vector "C<$vecx>" |
| 2262 | and "C<$vecy>", respectively. |
| 2263 | |
| 2264 | For example: |
| 2265 | |
| 2266 | a = 2322 |
| 2267 | b = 654 |
| 2268 | |
| 2269 | GCD( 2322, 654 ) == 6 |
| 2270 | |
| 2271 | x = 20 |
| 2272 | y = -71 |
| 2273 | |
| 2274 | 20 * 2322 - 71 * 654 == 6 |
| 2275 | |
| 2276 | Please see http://www.cut-the-knot.org/blue/extension.shtml |
| 2277 | for an explanation of how this extension of Euklid's algorithm works. |
| 2278 | |
| 2279 | =item * |
| 2280 | |
| 2281 | C<$vec3-E<gt>Power($vec1,$vec2);> |
| 2282 | |
| 2283 | This method calculates the exponentiation of base "C<$vec1>" elevated to |
| 2284 | the "C<$vec2>" power, i.e., "C<$vec1 ** $vec2>", and stores the result |
| 2285 | in bit vector "C<$vec3>". |
| 2286 | |
| 2287 | The method uses an efficient divide-and-conquer algorithm: |
| 2288 | |
| 2289 | Suppose the exponent is (decimal) 13, for example. The binary |
| 2290 | representation of this exponent is "1101". |
| 2291 | |
| 2292 | This means we want to calculate |
| 2293 | |
| 2294 | $vec1 * $vec1 * $vec1 * $vec1 * $vec1 * $vec1 * $vec1 * $vec1 * |
| 2295 | $vec1 * $vec1 * $vec1 * $vec1 * |
| 2296 | $vec1 |
| 2297 | |
| 2298 | That is, "C<$vec1>" multiplied with itself 13 times. The grouping |
| 2299 | into lines above is no coincidence. The first line comprises 8 |
| 2300 | factors, the second contains 4, and the last line just one. This |
| 2301 | just happens to be the binary representation of 13. C<;-)> |
| 2302 | |
| 2303 | We then calculate a series of squares (of squares of squares...) of |
| 2304 | the base, i.e., |
| 2305 | |
| 2306 | $power[0] = $vec1; |
| 2307 | $power[1] = $vec1 * $vec1; |
| 2308 | $power[2] = $power[1] * $power[1]; |
| 2309 | $power[3] = $power[2] * $power[2]; |
| 2310 | etc. |
| 2311 | |
| 2312 | To calculate the power of our example, we simply initialize our result |
| 2313 | with 1 and consecutively multiply it with the items of the series of |
| 2314 | powers we just calculated, if the corresponding bit of the binary |
| 2315 | representation of the exponent is set: |
| 2316 | |
| 2317 | $result = 1; |
| 2318 | $result *= $power[0] if ($vec2 & 1); |
| 2319 | $result *= $power[1] if ($vec2 & 2); |
| 2320 | $result *= $power[2] if ($vec2 & 4); |
| 2321 | $result *= $power[3] if ($vec2 & 8); |
| 2322 | etc. |
| 2323 | |
| 2324 | The bit vector "C<$vec3>" must be of the same size as the base |
| 2325 | "C<$vec1>" or greater. "C<$vec3>" and "C<$vec1>" may be the same |
| 2326 | vector (i.e., in-place calculation as in "C<$vec1 **= $vec2;>" is |
| 2327 | possible), but "C<$vec3>" and "C<$vec2>" must be distinct. Finally, |
| 2328 | the exponent "C<$vec2>" must be positive. A fatal error occurs if |
| 2329 | any of these conditions is not met. |
| 2330 | |
| 2331 | =item * |
| 2332 | |
| 2333 | C<$vector-E<gt>Block_Store($buffer);> |
| 2334 | |
| 2335 | This method allows you to load the contents of a given bit vector in |
| 2336 | one go. |
| 2337 | |
| 2338 | This is useful when you store the contents of a bit vector in a file, |
| 2339 | for instance (using method "C<Block_Read()>"), and when you want to |
| 2340 | restore the previously saved bit vector. |
| 2341 | |
| 2342 | For this, "C<$buffer>" B<MUST> be a string (B<NO> automatic conversion |
| 2343 | from numeric to string is provided here as would normally in Perl!) |
| 2344 | containing the bit vector in "low order byte first" order. |
| 2345 | |
| 2346 | If the given string is shorter than what is needed to completely fill |
| 2347 | the given bit vector, the remaining (most significant) bytes of the |
| 2348 | bit vector are filled with zeros, i.e., the previous contents of the |
| 2349 | bit vector are always erased completely. |
| 2350 | |
| 2351 | If the given string is longer than what is needed to completely fill |
| 2352 | the given bit vector, the superfluous bytes are simply ignored. |
| 2353 | |
| 2354 | See L<perlfunc/sysread> for how to read in the contents of "C<$buffer>" |
| 2355 | from a file prior to passing it to this method. |
| 2356 | |
| 2357 | =item * |
| 2358 | |
| 2359 | C<$buffer = $vector-E<gt>Block_Read();> |
| 2360 | |
| 2361 | This method allows you to export the contents of a given bit vector in |
| 2362 | one block. |
| 2363 | |
| 2364 | This is useful when you want to save the contents of a bit vector for |
| 2365 | later, for instance in a file. |
| 2366 | |
| 2367 | The advantage of this method is that it allows you to do so in the |
| 2368 | compactest possible format, in binary. |
| 2369 | |
| 2370 | The method returns a Perl string which contains an exact copy of the |
| 2371 | contents of the given bit vector in "low order byte first" order. |
| 2372 | |
| 2373 | See L<perlfunc/syswrite> for how to write the data from this string |
| 2374 | to a file. |
| 2375 | |
| 2376 | =item * |
| 2377 | |
| 2378 | C<$size = $vector-E<gt>Word_Size();> |
| 2379 | |
| 2380 | Each bit vector is internally organized as an array of machine words. |
| 2381 | |
| 2382 | The methods whose names begin with "Word_" allow you to access this |
| 2383 | internal array of machine words. |
| 2384 | |
| 2385 | Note that because the size of a machine word may vary from system to |
| 2386 | system, these methods are inherently B<MACHINE-DEPENDENT>! |
| 2387 | |
| 2388 | Therefore, B<DO NOT USE> these methods unless you are absolutely certain |
| 2389 | that portability of your code is not an issue! |
| 2390 | |
| 2391 | You have been warned! |
| 2392 | |
| 2393 | To be machine-independent, use the methods whose names begin with "C<Chunk_>" |
| 2394 | instead, with chunk sizes no greater than 32 bits. |
| 2395 | |
| 2396 | The method "C<Word_Size()>" returns the number of machine words that the |
| 2397 | internal array of words of the given bit vector contains. |
| 2398 | |
| 2399 | This is similar in function to the term "C<scalar(@array)>" for a Perl array. |
| 2400 | |
| 2401 | =item * |
| 2402 | |
| 2403 | C<$vector-E<gt>Word_Store($offset,$word);> |
| 2404 | |
| 2405 | This method allows you to store a given value "C<$word>" at a given |
| 2406 | position "C<$offset>" in the internal array of words of the given |
| 2407 | bit vector. |
| 2408 | |
| 2409 | Note that "C<$offset>" must lie in the permitted range between "C<0>" |
| 2410 | and "C<$vector-E<gt>Word_Size()-1>", or a fatal "offset out of range" |
| 2411 | error will occur. |
| 2412 | |
| 2413 | This method is similar in function to the expression |
| 2414 | "C<$array[$offset] = $word;>" for a Perl array. |
| 2415 | |
| 2416 | =item * |
| 2417 | |
| 2418 | C<$word = $vector-E<gt>Word_Read($offset);> |
| 2419 | |
| 2420 | This method allows you to access the value of a given machine word |
| 2421 | at position "C<$offset>" in the internal array of words of the given |
| 2422 | bit vector. |
| 2423 | |
| 2424 | Note that "C<$offset>" must lie in the permitted range between "C<0>" |
| 2425 | and "C<$vector-E<gt>Word_Size()-1>", or a fatal "offset out of range" |
| 2426 | error will occur. |
| 2427 | |
| 2428 | This method is similar in function to the expression |
| 2429 | "C<$word = $array[$offset];>" for a Perl array. |
| 2430 | |
| 2431 | =item * |
| 2432 | |
| 2433 | C<$vector-E<gt>Word_List_Store(@words);> |
| 2434 | |
| 2435 | This method allows you to store a list of values "C<@words>" in the |
| 2436 | internal array of machine words of the given bit vector. |
| 2437 | |
| 2438 | Thereby the B<LEFTMOST> value in the list ("C<$words[0]>") is stored |
| 2439 | in the B<LEAST> significant word of the internal array of words (the |
| 2440 | one with offset "C<0>"), the next value from the list ("C<$words[1]>") |
| 2441 | is stored in the word with offset "C<1>", and so on, as intuitively |
| 2442 | expected. |
| 2443 | |
| 2444 | If the list "C<@words>" contains fewer elements than the internal |
| 2445 | array of words of the given bit vector contains machine words, |
| 2446 | the remaining (most significant) words are filled with zeros. |
| 2447 | |
| 2448 | If the list "C<@words>" contains more elements than the internal |
| 2449 | array of words of the given bit vector contains machine words, |
| 2450 | the superfluous values are simply ignored. |
| 2451 | |
| 2452 | This method is comparable in function to the expression |
| 2453 | "C<@array = @words;>" for a Perl array. |
| 2454 | |
| 2455 | =item * |
| 2456 | |
| 2457 | C<@words = $vector-E<gt>Word_List_Read();> |
| 2458 | |
| 2459 | This method allows you to retrieve the internal array of machine |
| 2460 | words of the given bit vector all at once. |
| 2461 | |
| 2462 | Thereby the B<LEFTMOST> value in the returned list ("C<$words[0]>") |
| 2463 | is the B<LEAST> significant word from the given bit vector, and the |
| 2464 | B<RIGHTMOST> value in the returned list ("C<$words[$#words]>") is |
| 2465 | the B<MOST> significant word of the given bit vector. |
| 2466 | |
| 2467 | This method is similar in function to the expression |
| 2468 | "C<@words = @array;>" for a Perl array. |
| 2469 | |
| 2470 | =item * |
| 2471 | |
| 2472 | C<$vector-E<gt>Word_Insert($offset,$count);> |
| 2473 | |
| 2474 | This method inserts "C<$count>" empty new machine words at position |
| 2475 | "C<$offset>" in the internal array of words of the given bit vector. |
| 2476 | |
| 2477 | The "C<$count>" most significant words are lost, and all words starting |
| 2478 | with word number "C<$offset>" up to and including word number |
| 2479 | "C<$vector-E<gt>Word_Size()-$count-1>" are moved up by "C<$count>" places. |
| 2480 | |
| 2481 | The now vacant "C<$count>" words starting at word number "C<$offset>" |
| 2482 | (up to and including word number "C<$offset+$count-1>") are then set |
| 2483 | to zero (cleared). |
| 2484 | |
| 2485 | Note that this method does B<NOT> increase the size of the given bit |
| 2486 | vector, i.e., the bit vector is B<NOT> extended at its upper end to |
| 2487 | "rescue" the "C<$count>" uppermost (most significant) words - instead, |
| 2488 | these words are lost forever. |
| 2489 | |
| 2490 | If you don't want this to happen, you have to increase the size of the |
| 2491 | given bit vector B<EXPLICITLY> and B<BEFORE> you perform the "Insert" |
| 2492 | operation, with a statement such as the following: |
| 2493 | |
| 2494 | $vector->Resize($vector->Size() + $count * Bit::Vector->Word_Bits()); |
| 2495 | |
| 2496 | Note also that "C<$offset>" must lie in the permitted range between |
| 2497 | "C<0>" and "C<$vector-E<gt>Word_Size()-1>", or a fatal "offset out |
| 2498 | of range" error will occur. |
| 2499 | |
| 2500 | If the term "C<$offset + $count>" exceeds "C<$vector-E<gt>Word_Size()-1>", |
| 2501 | all the words starting with word number "C<$offset>" up to word number |
| 2502 | "C<$vector-E<gt>Word_Size()-1>" are simply cleared. |
| 2503 | |
| 2504 | =item * |
| 2505 | |
| 2506 | C<$vector-E<gt>Word_Delete($offset,$count);> |
| 2507 | |
| 2508 | This method deletes, i.e., removes the words starting at position |
| 2509 | "C<$offset>" up to and including word number "C<$offset+$count-1>" |
| 2510 | from the internal array of machine words of the given bit vector. |
| 2511 | |
| 2512 | The remaining uppermost words (starting at position "C<$offset+$count>" |
| 2513 | up to and including word number "C<$vector-E<gt>Word_Size()-1>") are |
| 2514 | moved down by "C<$count>" places. |
| 2515 | |
| 2516 | The now vacant uppermost (most significant) "C<$count>" words are then |
| 2517 | set to zero (cleared). |
| 2518 | |
| 2519 | Note that this method does B<NOT> decrease the size of the given bit |
| 2520 | vector, i.e., the bit vector is B<NOT> clipped at its upper end to |
| 2521 | "get rid of" the vacant "C<$count>" uppermost words. |
| 2522 | |
| 2523 | If you don't want this, i.e., if you want the bit vector to shrink |
| 2524 | accordingly, you have to do so B<EXPLICITLY> and B<AFTER> the "Delete" |
| 2525 | operation, with a couple of statements such as these: |
| 2526 | |
| 2527 | $bits = $vector->Size(); |
| 2528 | $count *= Bit::Vector->Word_Bits(); |
| 2529 | if ($count > $bits) { $count = $bits; } |
| 2530 | $vector->Resize($bits - $count); |
| 2531 | |
| 2532 | Note also that "C<$offset>" must lie in the permitted range between |
| 2533 | "C<0>" and "C<$vector-E<gt>Word_Size()-1>", or a fatal "offset out |
| 2534 | of range" error will occur. |
| 2535 | |
| 2536 | If the term "C<$offset + $count>" exceeds "C<$vector-E<gt>Word_Size()-1>", |
| 2537 | all the words starting with word number "C<$offset>" up to word number |
| 2538 | "C<$vector-E<gt>Word_Size()-1>" are simply cleared. |
| 2539 | |
| 2540 | =item * |
| 2541 | |
| 2542 | C<$vector-E<gt>Chunk_Store($chunksize,$offset,$chunk);> |
| 2543 | |
| 2544 | This method allows you to set more than one bit at a time with |
| 2545 | different values. |
| 2546 | |
| 2547 | You can access chunks (i.e., ranges of contiguous bits) between |
| 2548 | one and at most "C<Bit::Vector-E<gt>Long_Bits()>" bits wide. |
| 2549 | |
| 2550 | In order to be portable, though, you should never use chunk sizes |
| 2551 | larger than 32 bits. |
| 2552 | |
| 2553 | If the given "C<$chunksize>" does not lie between "C<1>" and |
| 2554 | "C<Bit::Vector-E<gt>Long_Bits()>", a fatal "chunk size out of range" |
| 2555 | error will occur. |
| 2556 | |
| 2557 | The method copies the "C<$chunksize>" least significant bits |
| 2558 | from the value "C<$chunk>" to the given bit vector, starting at |
| 2559 | bit position "C<$offset>" and proceeding upwards until bit number |
| 2560 | "C<$offset+$chunksize-1>". |
| 2561 | |
| 2562 | (I.e., bit number "C<0>" of "C<$chunk>" becomes bit number "C<$offset>" |
| 2563 | in the given bit vector, and bit number "C<$chunksize-1>" becomes |
| 2564 | bit number "C<$offset+$chunksize-1>".) |
| 2565 | |
| 2566 | If the term "C<$offset+$chunksize-1>" exceeds "C<$vector-E<gt>Size()-1>", |
| 2567 | the corresponding superfluous (most significant) bits from "C<$chunk>" |
| 2568 | are simply ignored. |
| 2569 | |
| 2570 | Note that "C<$offset>" itself must lie in the permitted range between |
| 2571 | "C<0>" and "C<$vector-E<gt>Size()-1>", or a fatal "offset out of range" |
| 2572 | error will occur. |
| 2573 | |
| 2574 | This method (as well as the other "C<Chunk_>" methods) is useful, for |
| 2575 | example, when you are reading in data in chunks of, say, 8 bits, which |
| 2576 | you need to access later, say, using 16 bits at a time (like audio CD |
| 2577 | wave files, for instance). |
| 2578 | |
| 2579 | =item * |
| 2580 | |
| 2581 | C<$chunk = $vector-E<gt>Chunk_Read($chunksize,$offset);> |
| 2582 | |
| 2583 | This method allows you to read the values of more than one bit at |
| 2584 | a time. |
| 2585 | |
| 2586 | You can read chunks (i.e., ranges of contiguous bits) between |
| 2587 | one and at most "C<Bit::Vector-E<gt>Long_Bits()>" bits wide. |
| 2588 | |
| 2589 | In order to be portable, though, you should never use chunk sizes |
| 2590 | larger than 32 bits. |
| 2591 | |
| 2592 | If the given "C<$chunksize>" does not lie between "C<1>" and |
| 2593 | "C<Bit::Vector-E<gt>Long_Bits()>", a fatal "chunk size out of range" |
| 2594 | error will occur. |
| 2595 | |
| 2596 | The method returns the "C<$chunksize>" bits from the given bit vector |
| 2597 | starting at bit position "C<$offset>" and proceeding upwards until |
| 2598 | bit number "C<$offset+$chunksize-1>". |
| 2599 | |
| 2600 | (I.e., bit number "C<$offset>" of the given bit vector becomes bit number |
| 2601 | "C<0>" of the returned value, and bit number "C<$offset+$chunksize-1>" |
| 2602 | becomes bit number "C<$chunksize-1>".) |
| 2603 | |
| 2604 | If the term "C<$offset+$chunksize-1>" exceeds "C<$vector-E<gt>Size()-1>", |
| 2605 | the non-existent bits are simply not returned. |
| 2606 | |
| 2607 | Note that "C<$offset>" itself must lie in the permitted range between |
| 2608 | "C<0>" and "C<$vector-E<gt>Size()-1>", or a fatal "offset out of range" |
| 2609 | error will occur. |
| 2610 | |
| 2611 | =item * |
| 2612 | |
| 2613 | C<$vector-E<gt>Chunk_List_Store($chunksize,@chunks);> |
| 2614 | |
| 2615 | This method allows you to fill the given bit vector with a list of |
| 2616 | data packets ("chunks") of any size ("C<$chunksize>") you like |
| 2617 | (within certain limits). |
| 2618 | |
| 2619 | In fact the given "C<$chunksize>" must lie in the range between "C<1>" |
| 2620 | and "C<Bit::Vector-E<gt>Long_Bits()>", or a fatal "chunk size out of |
| 2621 | range" error will occur. |
| 2622 | |
| 2623 | In order to be portable, though, you should never use chunk sizes |
| 2624 | larger than 32 bits. |
| 2625 | |
| 2626 | The given bit vector is thereby filled in ascending order: The first |
| 2627 | chunk from the list (i.e., "C<$chunks[0]>") fills the "C<$chunksize>" |
| 2628 | least significant bits, the next chunk from the list ("C<$chunks[1]>") |
| 2629 | fills the bits number "C<$chunksize>" to number "C<2*$chunksize-1>", |
| 2630 | the third chunk ("C<$chunks[2]>") fills the bits number "C<2*$chunksize>", |
| 2631 | to number "C<3*$chunksize-1>", and so on. |
| 2632 | |
| 2633 | If there a less chunks in the list than are needed to fill the entire |
| 2634 | bit vector, the remaining (most significant) bits are cleared, i.e., |
| 2635 | the previous contents of the given bit vector are always erased completely. |
| 2636 | |
| 2637 | If there are more chunks in the list than are needed to fill the entire |
| 2638 | bit vector, and/or if a chunk extends beyond "C<$vector-E<gt>Size()-1>" |
| 2639 | (which happens whenever "C<$vector-E<gt>Size()>" is not a multiple of |
| 2640 | "C<$chunksize>"), the superfluous chunks and/or bits are simply ignored. |
| 2641 | |
| 2642 | The method is useful, for example (and among many other applications), |
| 2643 | for the conversion of packet sizes in a data stream. |
| 2644 | |
| 2645 | This method can also be used to store an octal string in a given |
| 2646 | bit vector: |
| 2647 | |
| 2648 | $vector->Chunk_List_Store(3, split(//, reverse $string)); |
| 2649 | |
| 2650 | Note however that unlike the conversion methods "C<from_Hex()>", |
| 2651 | "C<from_Bin()>", "C<from_Dec()>" and "C<from_Enum()>", |
| 2652 | this statement does not include any syntax checking, i.e., |
| 2653 | it may fail silently, without warning. |
| 2654 | |
| 2655 | To perform syntax checking, add the following statements: |
| 2656 | |
| 2657 | if ($string =~ /^[0-7]+$/) |
| 2658 | { |
| 2659 | # okay, go ahead with conversion as shown above |
| 2660 | } |
| 2661 | else |
| 2662 | { |
| 2663 | # error, string contains other than octal characters |
| 2664 | } |
| 2665 | |
| 2666 | Another application is to store a repetitive pattern in a given |
| 2667 | bit vector: |
| 2668 | |
| 2669 | $pattern = 0xDEADBEEF; |
| 2670 | $length = 32; # = length of $pattern in bits |
| 2671 | $size = $vector->Size(); |
| 2672 | $factor = int($size / $length); |
| 2673 | if ($size % $length) { $factor++; } |
| 2674 | $vector->Chunk_List_Store($length, ($pattern) x $factor); |
| 2675 | |
| 2676 | =item * |
| 2677 | |
| 2678 | C<@chunks = $vector-E<gt>Chunk_List_Read($chunksize);> |
| 2679 | |
| 2680 | This method allows you to access the contents of the given bit vector in |
| 2681 | form of a list of data packets ("chunks") of a size ("C<$chunksize>") |
| 2682 | of your choosing (within certain limits). |
| 2683 | |
| 2684 | In fact the given "C<$chunksize>" must lie in the range between "C<1>" |
| 2685 | and "C<Bit::Vector-E<gt>Long_Bits()>", or a fatal "chunk size out of |
| 2686 | range" error will occur. |
| 2687 | |
| 2688 | In order to be portable, though, you should never use chunk sizes |
| 2689 | larger than 32 bits. |
| 2690 | |
| 2691 | The given bit vector is thereby read in ascending order: The |
| 2692 | "C<$chunksize>" least significant bits (bits number "C<0>" to |
| 2693 | "C<$chunksize-1>") become the first chunk in the returned list |
| 2694 | (i.e., "C<$chunks[0]>"). The bits number "C<$chunksize>" to |
| 2695 | "C<2*$chunksize-1>" become the next chunk in the list |
| 2696 | ("C<$chunks[1]>"), and so on. |
| 2697 | |
| 2698 | If "C<$vector-E<gt>Size()>" is not a multiple of "C<$chunksize>", |
| 2699 | the last chunk in the list will contain fewer bits than "C<$chunksize>". |
| 2700 | |
| 2701 | B<BEWARE> that for large bit vectors and/or small values of "C<$chunksize>", |
| 2702 | the number of returned list elements can be extremely large! B<BE CAREFUL!> |
| 2703 | |
| 2704 | You could blow up your application with lack of memory (each list element |
| 2705 | is a full-grown Perl scalar, internally, with an associated memory overhead |
| 2706 | for its administration!) or at least cause a noticeable, more or less |
| 2707 | long-lasting "freeze" of your application! |
| 2708 | |
| 2709 | Possible applications: |
| 2710 | |
| 2711 | The method is especially useful in the conversion of packet sizes in |
| 2712 | a data stream. |
| 2713 | |
| 2714 | This method can also be used to convert a given bit vector to a string |
| 2715 | of octal numbers: |
| 2716 | |
| 2717 | $string = reverse join('', $vector->Chunk_List_Read(3)); |
| 2718 | |
| 2719 | =item * |
| 2720 | |
| 2721 | C<$vector-E<gt>Index_List_Remove(@indices);> |
| 2722 | |
| 2723 | This method allows you to specify a list of indices of bits which |
| 2724 | should be turned off in the given bit vector. |
| 2725 | |
| 2726 | In fact this method is a shortcut for |
| 2727 | |
| 2728 | foreach $index (@indices) |
| 2729 | { |
| 2730 | $vector->Bit_Off($index); |
| 2731 | } |
| 2732 | |
| 2733 | In contrast to all other import methods in this module, this method |
| 2734 | does B<NOT> clear the given bit vector before processing its list |
| 2735 | of arguments. |
| 2736 | |
| 2737 | Instead, this method allows you to accumulate the results of various |
| 2738 | consecutive calls. |
| 2739 | |
| 2740 | (The same holds for the method "C<Index_List_Store()>". As a |
| 2741 | consequence, you can "wipe out" what you did using the method |
| 2742 | "C<Index_List_Remove()>" by passing the identical argument list |
| 2743 | to the method "C<Index_List_Store()>".) |
| 2744 | |
| 2745 | =item * |
| 2746 | |
| 2747 | C<$vector-E<gt>Index_List_Store(@indices);> |
| 2748 | |
| 2749 | This method allows you to specify a list of indices of bits which |
| 2750 | should be turned on in the given bit vector. |
| 2751 | |
| 2752 | In fact this method is a shortcut for |
| 2753 | |
| 2754 | foreach $index (@indices) |
| 2755 | { |
| 2756 | $vector->Bit_On($index); |
| 2757 | } |
| 2758 | |
| 2759 | In contrast to all other import methods in this module, this method |
| 2760 | does B<NOT> clear the given bit vector before processing its list |
| 2761 | of arguments. |
| 2762 | |
| 2763 | Instead, this method allows you to accumulate the results of various |
| 2764 | consecutive calls. |
| 2765 | |
| 2766 | (The same holds for the method "C<Index_List_Remove()>". As a |
| 2767 | consequence, you can "wipe out" what you did using the method |
| 2768 | "C<Index_List_Store()>" by passing the identical argument list |
| 2769 | to the method "C<Index_List_Remove()>".) |
| 2770 | |
| 2771 | =item * |
| 2772 | |
| 2773 | C<@indices = $vector-E<gt>Index_List_Read();> |
| 2774 | |
| 2775 | This method returns a list of Perl scalars. |
| 2776 | |
| 2777 | The list contains one scalar for each set bit in the given |
| 2778 | bit vector. |
| 2779 | |
| 2780 | B<BEWARE> that for large bit vectors, this can result in a literally |
| 2781 | overwhelming number of list elements! B<BE CAREFUL!> You could run |
| 2782 | out of memory or slow down your application considerably! |
| 2783 | |
| 2784 | Each scalar contains the number of the index corresponding to |
| 2785 | the bit in question. |
| 2786 | |
| 2787 | These indices are always returned in ascending order. |
| 2788 | |
| 2789 | If the given bit vector is empty (contains only cleared bits) |
| 2790 | or if it has a length of zero (if it contains no bits at all), |
| 2791 | the method returns an empty list. |
| 2792 | |
| 2793 | This method can be useful, for instance, to obtain a list of |
| 2794 | prime numbers: |
| 2795 | |
| 2796 | $limit = 1000; # or whatever |
| 2797 | $vector = Bit::Vector->new($limit+1); |
| 2798 | $vector->Primes(); |
| 2799 | @primes = $vector->Index_List_Read(); |
| 2800 | |
| 2801 | =item * |
| 2802 | |
| 2803 | C<$vec3-E<gt>Or($vec1,$vec2);> |
| 2804 | |
| 2805 | C<$set3-E<gt>Union($set1,$set2);> |
| 2806 | |
| 2807 | This method calculates the union of "C<$set1>" and "C<$set2>" and stores |
| 2808 | the result in "C<$set3>". |
| 2809 | |
| 2810 | This is usually written as "C<$set3 = $set1 u $set2>" in set theory |
| 2811 | (where "u" is the "cup" operator). |
| 2812 | |
| 2813 | (On systems where the "cup" character is unavailable this operator |
| 2814 | is often denoted by a plus sign "+".) |
| 2815 | |
| 2816 | In-place calculation is also possible, i.e., "C<$set3>" may be identical |
| 2817 | with "C<$set1>" or "C<$set2>" or both. |
| 2818 | |
| 2819 | =item * |
| 2820 | |
| 2821 | C<$vec3-E<gt>And($vec1,$vec2);> |
| 2822 | |
| 2823 | C<$set3-E<gt>Intersection($set1,$set2);> |
| 2824 | |
| 2825 | This method calculates the intersection of "C<$set1>" and "C<$set2>" and |
| 2826 | stores the result in "C<$set3>". |
| 2827 | |
| 2828 | This is usually written as "C<$set3 = $set1 n $set2>" in set theory |
| 2829 | (where "n" is the "cap" operator). |
| 2830 | |
| 2831 | (On systems where the "cap" character is unavailable this operator |
| 2832 | is often denoted by an asterisk "*".) |
| 2833 | |
| 2834 | In-place calculation is also possible, i.e., "C<$set3>" may be identical |
| 2835 | with "C<$set1>" or "C<$set2>" or both. |
| 2836 | |
| 2837 | =item * |
| 2838 | |
| 2839 | C<$vec3-E<gt>AndNot($vec1,$vec2);> |
| 2840 | |
| 2841 | C<$set3-E<gt>Difference($set1,$set2);> |
| 2842 | |
| 2843 | This method calculates the difference of "C<$set1>" less "C<$set2>" and |
| 2844 | stores the result in "C<$set3>". |
| 2845 | |
| 2846 | This is usually written as "C<$set3 = $set1 \ $set2>" in set theory |
| 2847 | (where "\" is the "less" operator). |
| 2848 | |
| 2849 | In-place calculation is also possible, i.e., "C<$set3>" may be identical |
| 2850 | with "C<$set1>" or "C<$set2>" or both. |
| 2851 | |
| 2852 | =item * |
| 2853 | |
| 2854 | C<$vec3-E<gt>Xor($vec1,$vec2);> |
| 2855 | |
| 2856 | C<$set3-E<gt>ExclusiveOr($set1,$set2);> |
| 2857 | |
| 2858 | This method calculates the symmetric difference of "C<$set1>" and "C<$set2>" |
| 2859 | and stores the result in "C<$set3>". |
| 2860 | |
| 2861 | This can be written as "C<$set3 = ($set1 u $set2) \ ($set1 n $set2)>" in set |
| 2862 | theory (the union of the two sets less their intersection). |
| 2863 | |
| 2864 | When sets are implemented as bit vectors then the above formula is |
| 2865 | equivalent to the exclusive-or between corresponding bits of the two |
| 2866 | bit vectors (hence the name of this method). |
| 2867 | |
| 2868 | Note that this method is also much more efficient than evaluating the |
| 2869 | above formula explicitly since it uses a built-in machine language |
| 2870 | instruction internally. |
| 2871 | |
| 2872 | In-place calculation is also possible, i.e., "C<$set3>" may be identical |
| 2873 | with "C<$set1>" or "C<$set2>" or both. |
| 2874 | |
| 2875 | =item * |
| 2876 | |
| 2877 | C<$vec2-E<gt>Not($vec1);> |
| 2878 | |
| 2879 | C<$set2-E<gt>Complement($set1);> |
| 2880 | |
| 2881 | This method calculates the complement of "C<$set1>" and stores the result |
| 2882 | in "C<$set2>". |
| 2883 | |
| 2884 | In "big integer" arithmetic, this is equivalent to calculating the one's |
| 2885 | complement of the number stored in the bit vector "C<$set1>" in binary |
| 2886 | representation. |
| 2887 | |
| 2888 | In-place calculation is also possible, i.e., "C<$set2>" may be identical |
| 2889 | with "C<$set1>". |
| 2890 | |
| 2891 | =item * |
| 2892 | |
| 2893 | C<if ($set1-E<gt>subset($set2))> |
| 2894 | |
| 2895 | Returns "true" ("C<1>") if "C<$set1>" is a subset of "C<$set2>" |
| 2896 | (i.e., completely contained in "C<$set2>") and "false" ("C<0>") |
| 2897 | otherwise. |
| 2898 | |
| 2899 | This means that any bit which is set ("C<1>") in "C<$set1>" must |
| 2900 | also be set in "C<$set2>", but "C<$set2>" may contain set bits |
| 2901 | which are not set in "C<$set1>", in order for the condition |
| 2902 | of subset relationship to be true between these two sets. |
| 2903 | |
| 2904 | Note that by definition, if two sets are identical, they are |
| 2905 | also subsets (and also supersets) of each other. |
| 2906 | |
| 2907 | =item * |
| 2908 | |
| 2909 | C<$norm = $set-E<gt>Norm();> |
| 2910 | |
| 2911 | Returns the norm (number of bits which are set) of the given vector. |
| 2912 | |
| 2913 | This is equivalent to the number of elements contained in the given |
| 2914 | set. |
| 2915 | |
| 2916 | Uses a byte lookup table for calculating the number of set bits |
| 2917 | per byte, and thus needs a time for evaluation (and a number of |
| 2918 | loops) linearly proportional to the length of the given bit vector |
| 2919 | (in bytes). |
| 2920 | |
| 2921 | This should be the fastest algorithm on average. |
| 2922 | |
| 2923 | =item * |
| 2924 | |
| 2925 | C<$norm = $set-E<gt>Norm2();> |
| 2926 | |
| 2927 | Returns the norm (number of bits which are set) of the given vector. |
| 2928 | |
| 2929 | This is equivalent to the number of elements contained in the given |
| 2930 | set. |
| 2931 | |
| 2932 | This does the same as the method "C<Norm()>" above, only with a |
| 2933 | different algorithm: |
| 2934 | |
| 2935 | This method counts the number of set and cleared bits at the same |
| 2936 | time and will stop when either of them has been exhausted, thus |
| 2937 | needing at most half as many loops per machine word as the total |
| 2938 | number of bits in a machine word - in fact it will need a number |
| 2939 | of loops equal to the minimum of the number of set bits and the |
| 2940 | number of cleared bits. |
| 2941 | |
| 2942 | This might be a faster algorithm than of the method "C<Norm()>" |
| 2943 | above on some systems, depending on the system's architecture |
| 2944 | and the compiler and optimisation used, for bit vectors with |
| 2945 | sparse set bits and for bit vectors with sparse cleared bits |
| 2946 | (i.e., predominantly set bits). |
| 2947 | |
| 2948 | =item * |
| 2949 | |
| 2950 | C<$norm = $set-E<gt>Norm3();> |
| 2951 | |
| 2952 | Returns the norm (number of bits which are set) of the given vector. |
| 2953 | |
| 2954 | This is equivalent to the number of elements contained in the given |
| 2955 | set. |
| 2956 | |
| 2957 | This does the same as the two methods "C<Norm()>" and "C<Norm2()>" |
| 2958 | above, however with a different algorithm. |
| 2959 | |
| 2960 | In fact this is the implementation of the method "C<Norm()>" used |
| 2961 | in previous versions of this module. |
| 2962 | |
| 2963 | The method needs a number of loops per machine word equal to the |
| 2964 | number of set bits in that machine word. |
| 2965 | |
| 2966 | Only for bit vectors with sparse set bits will this method be |
| 2967 | fast; it will depend on a system's architecture and compiler |
| 2968 | whether the method will be faster than any of the two methods |
| 2969 | above in such cases. |
| 2970 | |
| 2971 | On average however, this is probably the slowest method of the |
| 2972 | three. |
| 2973 | |
| 2974 | =item * |
| 2975 | |
| 2976 | C<$min = $set-E<gt>Min();> |
| 2977 | |
| 2978 | Returns the minimum of the given set, i.e., the minimum of all |
| 2979 | indices of all set bits in the given bit vector "C<$set>". |
| 2980 | |
| 2981 | If the set is empty (no set bits), plus infinity (represented |
| 2982 | by the constant "MAX_LONG" on your system) is returned. |
| 2983 | |
| 2984 | (This constant is usually S<2 ^ (n-1) - 1>, where "C<n>" is the |
| 2985 | number of bits of an unsigned long on your machine.) |
| 2986 | |
| 2987 | =item * |
| 2988 | |
| 2989 | C<$max = $set-E<gt>Max();> |
| 2990 | |
| 2991 | Returns the maximum of the given set, i.e., the maximum of all |
| 2992 | indices of all set bits in the given bit vector "C<$set>". |
| 2993 | |
| 2994 | If the set is empty (no set bits), minus infinity (represented |
| 2995 | by the constant "MIN_LONG" on your system) is returned. |
| 2996 | |
| 2997 | (This constant is usually S<-(2 ^ (n-1) - 1)> or S<-(2 ^ (n-1))>, |
| 2998 | where "C<n>" is the number of bits of an unsigned long on your machine.) |
| 2999 | |
| 3000 | =item * |
| 3001 | |
| 3002 | C<$m3-E<gt>Multiplication($r3,$c3,$m1,$r1,$c1,$m2,$r2,$c2);> |
| 3003 | |
| 3004 | This method multiplies two boolean matrices (stored as bit vectors) |
| 3005 | "C<$m1>" and "C<$m2>" and stores the result in matrix "C<$m3>". |
| 3006 | |
| 3007 | The method uses the binary "xor" operation ("C<^>") as the boolean |
| 3008 | addition operator ("C<+>"). |
| 3009 | |
| 3010 | An exception is raised if the product of the number of rows and |
| 3011 | columns of any of the three matrices differs from the actual size |
| 3012 | of their underlying bit vector. |
| 3013 | |
| 3014 | An exception is also raised if the numbers of rows and columns |
| 3015 | of the three matrices do not harmonize in the required manner: |
| 3016 | |
| 3017 | rows3 == rows1 |
| 3018 | cols3 == cols2 |
| 3019 | cols1 == rows2 |
| 3020 | |
| 3021 | This method is used by the module "Math::MatrixBool". |
| 3022 | |
| 3023 | See L<Math::MatrixBool(3)> for details. |
| 3024 | |
| 3025 | =item * |
| 3026 | |
| 3027 | C<$m3-E<gt>Product($r3,$c3,$m1,$r1,$c1,$m2,$r2,$c2);> |
| 3028 | |
| 3029 | This method multiplies two boolean matrices (stored as bit vectors) |
| 3030 | "C<$m1>" and "C<$m2>" and stores the result in matrix "C<$m3>". |
| 3031 | |
| 3032 | This special method uses the binary "or" operation ("C<|>") as the |
| 3033 | boolean addition operator ("C<+>"). |
| 3034 | |
| 3035 | An exception is raised if the product of the number of rows and |
| 3036 | columns of any of the three matrices differs from the actual size |
| 3037 | of their underlying bit vector. |
| 3038 | |
| 3039 | An exception is also raised if the numbers of rows and columns |
| 3040 | of the three matrices do not harmonize in the required manner: |
| 3041 | |
| 3042 | rows3 == rows1 |
| 3043 | cols3 == cols2 |
| 3044 | cols1 == rows2 |
| 3045 | |
| 3046 | This method is used by the module "Math::MatrixBool". |
| 3047 | |
| 3048 | See L<Math::MatrixBool(3)> for details. |
| 3049 | |
| 3050 | =item * |
| 3051 | |
| 3052 | C<$matrix-E<gt>Closure($rows,$cols);> |
| 3053 | |
| 3054 | This method calculates the reflexive transitive closure of the |
| 3055 | given boolean matrix (stored as a bit vector) using Kleene's |
| 3056 | algoritm. |
| 3057 | |
| 3058 | (See L<Math::Kleene(3)> for a brief introduction into the |
| 3059 | theory behind Kleene's algorithm.) |
| 3060 | |
| 3061 | The reflexive transitive closure answers the question whether |
| 3062 | a path exists between any two vertices of a graph whose edges |
| 3063 | are given as a matrix: |
| 3064 | |
| 3065 | If a (directed) edge exists going from vertex "i" to vertex "j", |
| 3066 | then the element in the matrix with coordinates (i,j) is set to |
| 3067 | "C<1>" (otherwise it remains set to "C<0>"). |
| 3068 | |
| 3069 | If the edges are undirected, the resulting matrix is symmetric, |
| 3070 | i.e., elements (i,j) and (j,i) always contain the same value. |
| 3071 | |
| 3072 | The matrix representing the edges of the graph only answers the |
| 3073 | question whether an B<EDGE> exists between any two vertices of |
| 3074 | the graph or not, whereas the reflexive transitive closure |
| 3075 | answers the question whether a B<PATH> (a series of adjacent |
| 3076 | edges) exists between any two vertices of the graph! |
| 3077 | |
| 3078 | Note that the contents of the given matrix are modified by |
| 3079 | this method, so make a copy of the initial matrix in time |
| 3080 | if you are going to need it again later. |
| 3081 | |
| 3082 | An exception is raised if the given matrix is not quadratic, |
| 3083 | i.e., if the number of rows and columns of the given matrix |
| 3084 | is not identical. |
| 3085 | |
| 3086 | An exception is also raised if the product of the number of |
| 3087 | rows and columns of the given matrix differs from the actual |
| 3088 | size of its underlying bit vector. |
| 3089 | |
| 3090 | This method is used by the module "Math::MatrixBool". |
| 3091 | |
| 3092 | See L<Math::MatrixBool(3)> for details. |
| 3093 | |
| 3094 | =item * |
| 3095 | |
| 3096 | C<$matrix2-E<gt>Transpose($rows2,$cols2,$matrix1,$rows1,$cols1);> |
| 3097 | |
| 3098 | This method calculates the transpose of a boolean matrix "C<$matrix1>" |
| 3099 | (stored as a bit vector) and stores the result in matrix "C<$matrix2>". |
| 3100 | |
| 3101 | The transpose of a boolean matrix, representing the edges of a graph, |
| 3102 | can be used for finding the strongly connected components of that graph. |
| 3103 | |
| 3104 | An exception is raised if the product of the number of rows and |
| 3105 | columns of any of the two matrices differs from the actual size |
| 3106 | of its underlying bit vector. |
| 3107 | |
| 3108 | An exception is also raised if the following conditions are not |
| 3109 | met: |
| 3110 | |
| 3111 | rows2 == cols1 |
| 3112 | cols2 == rows1 |
| 3113 | |
| 3114 | Note that in-place processing ("C<$matrix1>" and "C<$matrix2>" are |
| 3115 | identical) is only possible if the matrix is quadratic. Otherwise, |
| 3116 | a fatal "matrix is not quadratic" error will occur. |
| 3117 | |
| 3118 | This method is used by the module "Math::MatrixBool". |
| 3119 | |
| 3120 | See L<Math::MatrixBool(3)> for details. |
| 3121 | |
| 3122 | =back |
| 3123 | |
| 3124 | =head1 SEE ALSO |
| 3125 | |
| 3126 | Bit::Vector::Overload(3), |
| 3127 | Bit::Vector::String(3). |
| 3128 | |
| 3129 | Set::IntRange(3), |
| 3130 | Math::MatrixBool(3), |
| 3131 | Math::MatrixReal(3), |
| 3132 | DFA::Kleene(3), |
| 3133 | Math::Kleene(3), |
| 3134 | Graph::Kruskal(3). |
| 3135 | |
| 3136 | =head1 VERSION |
| 3137 | |
| 3138 | This man page documents "Bit::Vector" version 6.4. |
| 3139 | |
| 3140 | =head1 AUTHOR |
| 3141 | |
| 3142 | Steffen Beyer |
| 3143 | mailto:sb@engelschall.com |
| 3144 | http://www.engelschall.com/u/sb/download/ |
| 3145 | |
| 3146 | =head1 COPYRIGHT |
| 3147 | |
| 3148 | Copyright (c) 1995 - 2004 by Steffen Beyer. All rights reserved. |
| 3149 | |
| 3150 | =head1 LICENSE |
| 3151 | |
| 3152 | This package is free software; you can redistribute it and/or |
| 3153 | modify it under the same terms as Perl itself, i.e., under the |
| 3154 | terms of the "Artistic License" or the "GNU General Public License". |
| 3155 | |
| 3156 | The C library at the core of this Perl module can additionally |
| 3157 | be redistributed and/or modified under the terms of the "GNU |
| 3158 | Library General Public License". |
| 3159 | |
| 3160 | Please refer to the files "Artistic.txt", "GNU_GPL.txt" and |
| 3161 | "GNU_LGPL.txt" in this distribution for details! |
| 3162 | |
| 3163 | =head1 DISCLAIMER |
| 3164 | |
| 3165 | This package is distributed in the hope that it will be useful, |
| 3166 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 3167 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. |
| 3168 | |
| 3169 | See the "GNU General Public License" for more details. |
| 3170 | |