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| 128 | .rm #[ #] #H #V #F C |
| 129 | .\" ======================================================================== |
| 130 | .\" |
| 131 | .IX Title "bignum 3" |
| 132 | .TH bignum 3 "2001-09-21" "perl v5.8.8" "Perl Programmers Reference Guide" |
| 133 | .SH "NAME" |
| 134 | bignum \- Transparent BigNumber support for Perl |
| 135 | .SH "SYNOPSIS" |
| 136 | .IX Header "SYNOPSIS" |
| 137 | .Vb 1 |
| 138 | \& use bignum; |
| 139 | .Ve |
| 140 | .PP |
| 141 | .Vb 4 |
| 142 | \& $x = 2 + 4.5,"\en"; # BigFloat 6.5 |
| 143 | \& print 2 ** 512 * 0.1,"\en"; # really is what you think it is |
| 144 | \& print inf * inf,"\en"; # prints inf |
| 145 | \& print NaN * 3,"\en"; # prints NaN |
| 146 | .Ve |
| 147 | .SH "DESCRIPTION" |
| 148 | .IX Header "DESCRIPTION" |
| 149 | All operators (including basic math operations) are overloaded. Integer and |
| 150 | floating-point constants are created as proper BigInts or BigFloats, |
| 151 | respectively. |
| 152 | .PP |
| 153 | If you do |
| 154 | .PP |
| 155 | .Vb 1 |
| 156 | \& use bignum; |
| 157 | .Ve |
| 158 | .PP |
| 159 | at the top of your script, Math::BigFloat and Math::BigInt will be loaded |
| 160 | and any constant number will be converted to an object (Math::BigFloat for |
| 161 | floats like 3.1415 and Math::BigInt for integers like 1234). |
| 162 | .PP |
| 163 | So, the following line: |
| 164 | .PP |
| 165 | .Vb 1 |
| 166 | \& $x = 1234; |
| 167 | .Ve |
| 168 | .PP |
| 169 | creates actually a Math::BigInt and stores a reference to in \f(CW$x\fR. |
| 170 | This happens transparently and behind your back, so to speak. |
| 171 | .PP |
| 172 | You can see this with the following: |
| 173 | .PP |
| 174 | .Vb 1 |
| 175 | \& perl -Mbignum -le 'print ref(1234)' |
| 176 | .Ve |
| 177 | .PP |
| 178 | Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite |
| 179 | if it is installed since it is faster for some operations. It will be |
| 180 | automatically upgraded to BigInt whenever neccessary: |
| 181 | .PP |
| 182 | .Vb 1 |
| 183 | \& perl -Mbignum -le 'print ref(2**255)' |
| 184 | .Ve |
| 185 | .PP |
| 186 | This also means it is a bad idea to check for some specific package, since |
| 187 | the actual contents of \f(CW$x\fR might be something unexpected. Due to the |
| 188 | transparent way of bignum \f(CW\*(C`ref()\*(C'\fR should not be neccessary, anyway. |
| 189 | .PP |
| 190 | Since Math::BigInt and BigFloat also overload the normal math operations, |
| 191 | the following line will still work: |
| 192 | .PP |
| 193 | .Vb 1 |
| 194 | \& perl -Mbignum -le 'print ref(1234+1234)' |
| 195 | .Ve |
| 196 | .PP |
| 197 | Since numbers are actually objects, you can call all the usual methods from |
| 198 | BigInt/BigFloat on them. This even works to some extent on expressions: |
| 199 | .PP |
| 200 | .Vb 4 |
| 201 | \& perl -Mbignum -le '$x = 1234; print $x->bdec()' |
| 202 | \& perl -Mbignum -le 'print 1234->binc();' |
| 203 | \& perl -Mbignum -le 'print 1234->binc->badd(6);' |
| 204 | \& perl -Mbignum -le 'print +(1234)->binc()' |
| 205 | .Ve |
| 206 | .PP |
| 207 | (Note that print doesn't do what you expect if the expression starts with |
| 208 | \&'(' hence the \f(CW\*(C`+\*(C'\fR) |
| 209 | .PP |
| 210 | You can even chain the operations together as usual: |
| 211 | .PP |
| 212 | .Vb 2 |
| 213 | \& perl -Mbignum -le 'print 1234->binc->badd(6);' |
| 214 | \& 1241 |
| 215 | .Ve |
| 216 | .PP |
| 217 | Under bignum (or bigint or bigrat), Perl will \*(L"upgrade\*(R" the numbers |
| 218 | appropriately. This means that: |
| 219 | .PP |
| 220 | .Vb 2 |
| 221 | \& perl -Mbignum -le 'print 1234+4.5' |
| 222 | \& 1238.5 |
| 223 | .Ve |
| 224 | .PP |
| 225 | will work correctly. These mixed cases don't do always work when using |
| 226 | Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl |
| 227 | scalars work. |
| 228 | .PP |
| 229 | If you do want to work with large integers like under \f(CW\*(C`use integer;\*(C'\fR, try |
| 230 | \&\f(CW\*(C`use bigint;\*(C'\fR: |
| 231 | .PP |
| 232 | .Vb 2 |
| 233 | \& perl -Mbigint -le 'print 1234.5+4.5' |
| 234 | \& 1238 |
| 235 | .Ve |
| 236 | .PP |
| 237 | There is also \f(CW\*(C`use bigrat;\*(C'\fR which gives you big rationals: |
| 238 | .PP |
| 239 | .Vb 2 |
| 240 | \& perl -Mbigrat -le 'print 1234+4.1' |
| 241 | \& 12381/10 |
| 242 | .Ve |
| 243 | .PP |
| 244 | The entire upgrading/downgrading is still experimental and might not work |
| 245 | as you expect or may even have bugs. |
| 246 | .PP |
| 247 | You might get errors like this: |
| 248 | .PP |
| 249 | .Vb 2 |
| 250 | \& Can't use an undefined value as an ARRAY reference at |
| 251 | \& /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864 |
| 252 | .Ve |
| 253 | .PP |
| 254 | This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or |
| 255 | vice versa) and the upgrade/downgrad path was missing. This is a bug, please |
| 256 | report it so that we can fix it. |
| 257 | .PP |
| 258 | You might consider using just Math::BigInt or Math::BigFloat, since they |
| 259 | allow you finer control over what get's done in which module/space. For |
| 260 | instance, simple loop counters will be Math::BigInts under \f(CW\*(C`use bignum;\*(C'\fR and |
| 261 | this is slower than keeping them as Perl scalars: |
| 262 | .PP |
| 263 | .Vb 1 |
| 264 | \& perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }' |
| 265 | .Ve |
| 266 | .PP |
| 267 | Please note the following does not work as expected (prints nothing), since |
| 268 | overloading of '..' is not yet possible in Perl (as of v5.8.0): |
| 269 | .PP |
| 270 | .Vb 1 |
| 271 | \& perl -Mbignum -le 'for (1..2) { print ref($_); }' |
| 272 | .Ve |
| 273 | .Sh "Options" |
| 274 | .IX Subsection "Options" |
| 275 | bignum recognizes some options that can be passed while loading it via use. |
| 276 | The options can (currently) be either a single letter form, or the long form. |
| 277 | The following options exist: |
| 278 | .IP "a or accuracy" 2 |
| 279 | .IX Item "a or accuracy" |
| 280 | This sets the accuracy for all math operations. The argument must be greater |
| 281 | than or equal to zero. See Math::BigInt's \fIbround()\fR function for details. |
| 282 | .Sp |
| 283 | .Vb 1 |
| 284 | \& perl -Mbignum=a,50 -le 'print sqrt(20)' |
| 285 | .Ve |
| 286 | .IP "p or precision" 2 |
| 287 | .IX Item "p or precision" |
| 288 | This sets the precision for all math operations. The argument can be any |
| 289 | integer. Negative values mean a fixed number of digits after the dot, while |
| 290 | a positive value rounds to this digit left from the dot. 0 or 1 mean round to |
| 291 | integer. See Math::BigInt's \fIbfround()\fR function for details. |
| 292 | .Sp |
| 293 | .Vb 1 |
| 294 | \& perl -Mbignum=p,-50 -le 'print sqrt(20)' |
| 295 | .Ve |
| 296 | .IP "t or trace" 2 |
| 297 | .IX Item "t or trace" |
| 298 | This enables a trace mode and is primarily for debugging bignum or |
| 299 | Math::BigInt/Math::BigFloat. |
| 300 | .IP "l or lib" 2 |
| 301 | .IX Item "l or lib" |
| 302 | Load a different math lib, see \*(L"\s-1MATH\s0 \s-1LIBRARY\s0\*(R". |
| 303 | .Sp |
| 304 | .Vb 1 |
| 305 | \& perl -Mbignum=l,GMP -e 'print 2 ** 512' |
| 306 | .Ve |
| 307 | .Sp |
| 308 | Currently there is no way to specify more than one library on the command |
| 309 | line. This will be hopefully fixed soon ;) |
| 310 | .IP "v or version" 2 |
| 311 | .IX Item "v or version" |
| 312 | This prints out the name and version of all modules used and then exits. |
| 313 | .Sp |
| 314 | .Vb 1 |
| 315 | \& perl -Mbignum=v |
| 316 | .Ve |
| 317 | .Sh "Methods" |
| 318 | .IX Subsection "Methods" |
| 319 | Beside \fIimport()\fR and \s-1\fIAUTOLOAD\s0()\fR there are only a few other methods. |
| 320 | .Sp |
| 321 | Since all numbers are now objects, you can use all functions that are part of |
| 322 | the BigInt or BigFloat \s-1API\s0. It is wise to use only the \fIbxxx()\fR notation, and not |
| 323 | the \fIfxxx()\fR notation, though. This makes it possible that the underlying object |
| 324 | might morph into a different class than BigFloat. |
| 325 | .Sh "Caveat" |
| 326 | .IX Subsection "Caveat" |
| 327 | But a warning is in order. When using the following to make a copy of a number, |
| 328 | only a shallow copy will be made. |
| 329 | .Sp |
| 330 | .Vb 2 |
| 331 | \& $x = 9; $y = $x; |
| 332 | \& $x = $y = 7; |
| 333 | .Ve |
| 334 | .Sp |
| 335 | If you want to make a real copy, use the following: |
| 336 | .Sp |
| 337 | .Vb 1 |
| 338 | \& $y = $x->copy(); |
| 339 | .Ve |
| 340 | .Sp |
| 341 | Using the copy or the original with overloaded math is okay, e.g. the |
| 342 | following work: |
| 343 | .Sp |
| 344 | .Vb 2 |
| 345 | \& $x = 9; $y = $x; |
| 346 | \& print $x + 1, " ", $y,"\en"; # prints 10 9 |
| 347 | .Ve |
| 348 | .Sp |
| 349 | but calling any method that modifies the number directly will result in |
| 350 | \&\fBboth\fR the original and the copy beeing destroyed: |
| 351 | .Sp |
| 352 | .Vb 2 |
| 353 | \& $x = 9; $y = $x; |
| 354 | \& print $x->badd(1), " ", $y,"\en"; # prints 10 10 |
| 355 | .Ve |
| 356 | .Sp |
| 357 | .Vb 2 |
| 358 | \& $x = 9; $y = $x; |
| 359 | \& print $x->binc(1), " ", $y,"\en"; # prints 10 10 |
| 360 | .Ve |
| 361 | .Sp |
| 362 | .Vb 2 |
| 363 | \& $x = 9; $y = $x; |
| 364 | \& print $x->bmul(2), " ", $y,"\en"; # prints 18 18 |
| 365 | .Ve |
| 366 | .Sp |
| 367 | Using methods that do not modify, but testthe contents works: |
| 368 | .Sp |
| 369 | .Vb 2 |
| 370 | \& $x = 9; $y = $x; |
| 371 | \& $z = 9 if $x->is_zero(); # works fine |
| 372 | .Ve |
| 373 | .Sp |
| 374 | See the documentation about the copy constructor and \f(CW\*(C`=\*(C'\fR in overload, as |
| 375 | well as the documentation in BigInt for further details. |
| 376 | .RS 2 |
| 377 | .IP "\fIinf()\fR" 2 |
| 378 | .IX Item "inf()" |
| 379 | A shortcut to return Math::BigInt\->\fIbinf()\fR. Usefull because Perl does not always |
| 380 | handle bareword \f(CW\*(C`inf\*(C'\fR properly. |
| 381 | .IP "\fINaN()\fR" 2 |
| 382 | .IX Item "NaN()" |
| 383 | A shortcut to return Math::BigInt\->\fIbnan()\fR. Usefull because Perl does not always |
| 384 | handle bareword \f(CW\*(C`NaN\*(C'\fR properly. |
| 385 | .IP "\fIupgrade()\fR" 2 |
| 386 | .IX Item "upgrade()" |
| 387 | Return the class that numbers are upgraded to, is in fact returning |
| 388 | \&\f(CW$Math::BigInt::upgrade\fR. |
| 389 | .RE |
| 390 | .RS 2 |
| 391 | .Sh "\s-1MATH\s0 \s-1LIBRARY\s0" |
| 392 | .IX Subsection "MATH LIBRARY" |
| 393 | Math with the numbers is done (by default) by a module called |
| 394 | Math::BigInt::Calc. This is equivalent to saying: |
| 395 | .Sp |
| 396 | .Vb 1 |
| 397 | \& use bignum lib => 'Calc'; |
| 398 | .Ve |
| 399 | .Sp |
| 400 | You can change this by using: |
| 401 | .Sp |
| 402 | .Vb 1 |
| 403 | \& use bignum lib => 'BitVect'; |
| 404 | .Ve |
| 405 | .Sp |
| 406 | The following would first try to find Math::BigInt::Foo, then |
| 407 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
| 408 | .Sp |
| 409 | .Vb 1 |
| 410 | \& use bignum lib => 'Foo,Math::BigInt::Bar'; |
| 411 | .Ve |
| 412 | .Sp |
| 413 | Please see respective module documentation for further details. |
| 414 | .Sh "\s-1INTERNAL\s0 \s-1FORMAT\s0" |
| 415 | .IX Subsection "INTERNAL FORMAT" |
| 416 | The numbers are stored as objects, and their internals might change at anytime, |
| 417 | especially between math operations. The objects also might belong to different |
| 418 | classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even |
| 419 | with normal scalars is not extraordinary, but normal and expected. |
| 420 | .Sp |
| 421 | You should not depend on the internal format, all accesses must go through |
| 422 | accessor methods. E.g. looking at \f(CW$x\fR\->{sign} is not a bright idea since there |
| 423 | is no guaranty that the object in question has such a hashkey, nor is a hash |
| 424 | underneath at all. |
| 425 | .Sh "\s-1SIGN\s0" |
| 426 | .IX Subsection "SIGN" |
| 427 | The sign is either '+', '\-', 'NaN', '+inf' or '\-inf' and stored seperately. |
| 428 | You can access it with the \fIsign()\fR method. |
| 429 | .Sp |
| 430 | A sign of 'NaN' is used to represent the result when input arguments are not |
| 431 | numbers or as a result of 0/0. '+inf' and '\-inf' represent plus respectively |
| 432 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
| 433 | \&'\-inf' when dividing any negative number by 0. |
| 434 | .SH "MODULES USED" |
| 435 | .IX Header "MODULES USED" |
| 436 | \&\f(CW\*(C`bignum\*(C'\fR is just a thin wrapper around various modules of the Math::BigInt |
| 437 | family. Think of it as the head of the family, who runs the shop, and orders |
| 438 | the others to do the work. |
| 439 | .Sp |
| 440 | The following modules are currently used by bignum: |
| 441 | .Sp |
| 442 | .Vb 3 |
| 443 | \& Math::BigInt::Lite (for speed, and only if it is loadable) |
| 444 | \& Math::BigInt |
| 445 | \& Math::BigFloat |
| 446 | .Ve |
| 447 | .SH "EXAMPLES" |
| 448 | .IX Header "EXAMPLES" |
| 449 | Some cool command line examples to impress the Python crowd ;) |
| 450 | .Sp |
| 451 | .Vb 8 |
| 452 | \& perl -Mbignum -le 'print sqrt(33)' |
| 453 | \& perl -Mbignum -le 'print 2*255' |
| 454 | \& perl -Mbignum -le 'print 4.5+2*255' |
| 455 | \& perl -Mbignum -le 'print 3/7 + 5/7 + 8/3' |
| 456 | \& perl -Mbignum -le 'print 123->is_odd()' |
| 457 | \& perl -Mbignum -le 'print log(2)' |
| 458 | \& perl -Mbignum -le 'print 2 ** 0.5' |
| 459 | \& perl -Mbignum=a,65 -le 'print 2 ** 0.2' |
| 460 | .Ve |
| 461 | .SH "LICENSE" |
| 462 | .IX Header "LICENSE" |
| 463 | This program is free software; you may redistribute it and/or modify it under |
| 464 | the same terms as Perl itself. |
| 465 | .SH "SEE ALSO" |
| 466 | .IX Header "SEE ALSO" |
| 467 | Especially bigrat as in \f(CW\*(C`perl \-Mbigrat \-le 'print 1/3+1/4'\*(C'\fR. |
| 468 | .Sp |
| 469 | Math::BigFloat, Math::BigInt, Math::BigRat and Math::Big as well |
| 470 | as Math::BigInt::BitVect, Math::BigInt::Pari and Math::BigInt::GMP. |
| 471 | .SH "AUTHORS" |
| 472 | .IX Header "AUTHORS" |
| 473 | (C) by Tels <http://bloodgate.com/> in early 2002, 2003. |