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| 129 | .\" ======================================================================== |
| 130 | .\" |
| 131 | .IX Title "Math::BigRat 3" |
| 132 | .TH Math::BigRat 3 "2001-09-21" "perl v5.8.8" "Perl Programmers Reference Guide" |
| 133 | .SH "NAME" |
| 134 | Math::BigRat \- Arbitrary big rational numbers |
| 135 | .SH "SYNOPSIS" |
| 136 | .IX Header "SYNOPSIS" |
| 137 | .Vb 1 |
| 138 | \& use Math::BigRat; |
| 139 | .Ve |
| 140 | .PP |
| 141 | .Vb 1 |
| 142 | \& my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
| 143 | .Ve |
| 144 | .PP |
| 145 | .Vb 2 |
| 146 | \& print $x->bstr(),"\en"; |
| 147 | \& print $x ** 2,"\en"; |
| 148 | .Ve |
| 149 | .PP |
| 150 | .Vb 2 |
| 151 | \& my $y = Math::BigRat->new('inf'); |
| 152 | \& print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\en"; |
| 153 | .Ve |
| 154 | .PP |
| 155 | .Vb 1 |
| 156 | \& my $z = Math::BigRat->new(144); $z->bsqrt(); |
| 157 | .Ve |
| 158 | .SH "DESCRIPTION" |
| 159 | .IX Header "DESCRIPTION" |
| 160 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
| 161 | for arbitrary big rational numbers. |
| 162 | .Sh "\s-1MATH\s0 \s-1LIBRARY\s0" |
| 163 | .IX Subsection "MATH LIBRARY" |
| 164 | Math with the numbers is done (by default) by a module called |
| 165 | Math::BigInt::Calc. This is equivalent to saying: |
| 166 | .PP |
| 167 | .Vb 1 |
| 168 | \& use Math::BigRat lib => 'Calc'; |
| 169 | .Ve |
| 170 | .PP |
| 171 | You can change this by using: |
| 172 | .PP |
| 173 | .Vb 1 |
| 174 | \& use Math::BigRat lib => 'BitVect'; |
| 175 | .Ve |
| 176 | .PP |
| 177 | The following would first try to find Math::BigInt::Foo, then |
| 178 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
| 179 | .PP |
| 180 | .Vb 1 |
| 181 | \& use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
| 182 | .Ve |
| 183 | .PP |
| 184 | Calc.pm uses as internal format an array of elements of some decimal base |
| 185 | (usually 1e7, but this might be different for some systems) with the least |
| 186 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
| 187 | significant bit first. Other modules might use even different means of |
| 188 | representing the numbers. See the respective module documentation for further |
| 189 | details. |
| 190 | .PP |
| 191 | Currently the following replacement libraries exist, search for them at \s-1CPAN:\s0 |
| 192 | .PP |
| 193 | .Vb 4 |
| 194 | \& Math::BigInt::BitVect |
| 195 | \& Math::BigInt::GMP |
| 196 | \& Math::BigInt::Pari |
| 197 | \& Math::BigInt::FastCalc |
| 198 | .Ve |
| 199 | .SH "METHODS" |
| 200 | .IX Header "METHODS" |
| 201 | Any methods not listed here are dervied from Math::BigFloat (or |
| 202 | Math::BigInt), so make sure you check these two modules for further |
| 203 | information. |
| 204 | .Sh "\fInew()\fP" |
| 205 | .IX Subsection "new()" |
| 206 | .Vb 1 |
| 207 | \& $x = Math::BigRat->new('1/3'); |
| 208 | .Ve |
| 209 | .PP |
| 210 | Create a new Math::BigRat object. Input can come in various forms: |
| 211 | .PP |
| 212 | .Vb 9 |
| 213 | \& $x = Math::BigRat->new(123); # scalars |
| 214 | \& $x = Math::BigRat->new('inf'); # infinity |
| 215 | \& $x = Math::BigRat->new('123.3'); # float |
| 216 | \& $x = Math::BigRat->new('1/3'); # simple string |
| 217 | \& $x = Math::BigRat->new('1 / 3'); # spaced |
| 218 | \& $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
| 219 | \& $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
| 220 | \& $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
| 221 | \& $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
| 222 | .Ve |
| 223 | .PP |
| 224 | .Vb 5 |
| 225 | \& # You can also give D and N as different objects: |
| 226 | \& $x = Math::BigRat->new( |
| 227 | \& Math::BigInt->new(-123), |
| 228 | \& Math::BigInt->new(7), |
| 229 | \& ); # => -123/7 |
| 230 | .Ve |
| 231 | .Sh "\fInumerator()\fP" |
| 232 | .IX Subsection "numerator()" |
| 233 | .Vb 1 |
| 234 | \& $n = $x->numerator(); |
| 235 | .Ve |
| 236 | .PP |
| 237 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
| 238 | .Sh "\fIdenominator()\fP" |
| 239 | .IX Subsection "denominator()" |
| 240 | .Vb 1 |
| 241 | \& $d = $x->denominator(); |
| 242 | .Ve |
| 243 | .PP |
| 244 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
| 245 | .Sh "\fIparts()\fP" |
| 246 | .IX Subsection "parts()" |
| 247 | .Vb 1 |
| 248 | \& ($n,$d) = $x->parts(); |
| 249 | .Ve |
| 250 | .PP |
| 251 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
| 252 | BigInts. |
| 253 | .Sh "\fIas_int()\fP" |
| 254 | .IX Subsection "as_int()" |
| 255 | .Vb 2 |
| 256 | \& $x = Math::BigRat->new('13/7'); |
| 257 | \& print $x->as_int(),"\en"; # '1' |
| 258 | .Ve |
| 259 | .PP |
| 260 | Returns a copy of the object as BigInt, truncated to an integer. |
| 261 | .PP |
| 262 | \&\f(CW\*(C`as_number()\*(C'\fR is an alias for \f(CW\*(C`as_int()\*(C'\fR. |
| 263 | .Sh "\fIas_hex()\fP" |
| 264 | .IX Subsection "as_hex()" |
| 265 | .Vb 2 |
| 266 | \& $x = Math::BigRat->new('13'); |
| 267 | \& print $x->as_hex(),"\en"; # '0xd' |
| 268 | .Ve |
| 269 | .PP |
| 270 | Returns the BigRat as hexadecimal string. Works only for integers. |
| 271 | .Sh "\fIas_bin()\fP" |
| 272 | .IX Subsection "as_bin()" |
| 273 | .Vb 2 |
| 274 | \& $x = Math::BigRat->new('13'); |
| 275 | \& print $x->as_bin(),"\en"; # '0x1101' |
| 276 | .Ve |
| 277 | .PP |
| 278 | Returns the BigRat as binary string. Works only for integers. |
| 279 | .Sh "\fIbfac()\fP" |
| 280 | .IX Subsection "bfac()" |
| 281 | .Vb 1 |
| 282 | \& $x->bfac(); |
| 283 | .Ve |
| 284 | .PP |
| 285 | Calculates the factorial of \f(CW$x\fR. For instance: |
| 286 | .PP |
| 287 | .Vb 2 |
| 288 | \& print Math::BigRat->new('3/1')->bfac(),"\en"; # 1*2*3 |
| 289 | \& print Math::BigRat->new('5/1')->bfac(),"\en"; # 1*2*3*4*5 |
| 290 | .Ve |
| 291 | .PP |
| 292 | Works currently only for integers. |
| 293 | .Sh "\fIblog()\fP" |
| 294 | .IX Subsection "blog()" |
| 295 | Is not yet implemented. |
| 296 | .Sh "\fIbround()\fP/\fIround()\fP/\fIbfround()\fP" |
| 297 | .IX Subsection "bround()/round()/bfround()" |
| 298 | Are not yet implemented. |
| 299 | .Sh "\fIbmod()\fP" |
| 300 | .IX Subsection "bmod()" |
| 301 | .Vb 4 |
| 302 | \& use Math::BigRat; |
| 303 | \& my $x = Math::BigRat->new('7/4'); |
| 304 | \& my $y = Math::BigRat->new('4/3'); |
| 305 | \& print $x->bmod($y); |
| 306 | .Ve |
| 307 | .PP |
| 308 | Set \f(CW$x\fR to the remainder of the division of \f(CW$x\fR by \f(CW$y\fR. |
| 309 | .Sh "\fIis_one()\fP" |
| 310 | .IX Subsection "is_one()" |
| 311 | .Vb 1 |
| 312 | \& print "$x is 1\en" if $x->is_one(); |
| 313 | .Ve |
| 314 | .PP |
| 315 | Return true if \f(CW$x\fR is exactly one, otherwise false. |
| 316 | .Sh "\fIis_zero()\fP" |
| 317 | .IX Subsection "is_zero()" |
| 318 | .Vb 1 |
| 319 | \& print "$x is 0\en" if $x->is_zero(); |
| 320 | .Ve |
| 321 | .PP |
| 322 | Return true if \f(CW$x\fR is exactly zero, otherwise false. |
| 323 | .Sh "\fIis_pos()\fP" |
| 324 | .IX Subsection "is_pos()" |
| 325 | .Vb 1 |
| 326 | \& print "$x is >= 0\en" if $x->is_positive(); |
| 327 | .Ve |
| 328 | .PP |
| 329 | Return true if \f(CW$x\fR is positive (greater than or equal to zero), otherwise |
| 330 | false. Please note that '+inf' is also positive, while 'NaN' and '\-inf' aren't. |
| 331 | .PP |
| 332 | \&\f(CW\*(C`is_positive()\*(C'\fR is an alias for \f(CW\*(C`is_pos()\*(C'\fR. |
| 333 | .Sh "\fIis_neg()\fP" |
| 334 | .IX Subsection "is_neg()" |
| 335 | .Vb 1 |
| 336 | \& print "$x is < 0\en" if $x->is_negative(); |
| 337 | .Ve |
| 338 | .PP |
| 339 | Return true if \f(CW$x\fR is negative (smaller than zero), otherwise false. Please |
| 340 | note that '\-inf' is also negative, while 'NaN' and '+inf' aren't. |
| 341 | .PP |
| 342 | \&\f(CW\*(C`is_negative()\*(C'\fR is an alias for \f(CW\*(C`is_neg()\*(C'\fR. |
| 343 | .Sh "\fIis_int()\fP" |
| 344 | .IX Subsection "is_int()" |
| 345 | .Vb 1 |
| 346 | \& print "$x is an integer\en" if $x->is_int(); |
| 347 | .Ve |
| 348 | .PP |
| 349 | Return true if \f(CW$x\fR has a denominator of 1 (e.g. no fraction parts), otherwise |
| 350 | false. Please note that '\-inf', 'inf' and 'NaN' aren't integer. |
| 351 | .Sh "\fIis_odd()\fP" |
| 352 | .IX Subsection "is_odd()" |
| 353 | .Vb 1 |
| 354 | \& print "$x is odd\en" if $x->is_odd(); |
| 355 | .Ve |
| 356 | .PP |
| 357 | Return true if \f(CW$x\fR is odd, otherwise false. |
| 358 | .Sh "\fIis_even()\fP" |
| 359 | .IX Subsection "is_even()" |
| 360 | .Vb 1 |
| 361 | \& print "$x is even\en" if $x->is_even(); |
| 362 | .Ve |
| 363 | .PP |
| 364 | Return true if \f(CW$x\fR is even, otherwise false. |
| 365 | .Sh "\fIbceil()\fP" |
| 366 | .IX Subsection "bceil()" |
| 367 | .Vb 1 |
| 368 | \& $x->bceil(); |
| 369 | .Ve |
| 370 | .PP |
| 371 | Set \f(CW$x\fR to the next bigger integer value (e.g. truncate the number to integer |
| 372 | and then increment it by one). |
| 373 | .Sh "\fIbfloor()\fP" |
| 374 | .IX Subsection "bfloor()" |
| 375 | .Vb 1 |
| 376 | \& $x->bfloor(); |
| 377 | .Ve |
| 378 | .PP |
| 379 | Truncate \f(CW$x\fR to an integer value. |
| 380 | .Sh "\fIbsqrt()\fP" |
| 381 | .IX Subsection "bsqrt()" |
| 382 | .Vb 1 |
| 383 | \& $x->bsqrt(); |
| 384 | .Ve |
| 385 | .PP |
| 386 | Calculate the square root of \f(CW$x\fR. |
| 387 | .Sh "config" |
| 388 | .IX Subsection "config" |
| 389 | .Vb 1 |
| 390 | \& use Data::Dumper; |
| 391 | .Ve |
| 392 | .PP |
| 393 | .Vb 2 |
| 394 | \& print Dumper ( Math::BigRat->config() ); |
| 395 | \& print Math::BigRat->config()->{lib},"\en"; |
| 396 | .Ve |
| 397 | .PP |
| 398 | Returns a hash containing the configuration, e.g. the version number, lib |
| 399 | loaded etc. The following hash keys are currently filled in with the |
| 400 | appropriate information. |
| 401 | .PP |
| 402 | .Vb 27 |
| 403 | \& key RO/RW Description |
| 404 | \& Example |
| 405 | \& ============================================================ |
| 406 | \& lib RO Name of the Math library |
| 407 | \& Math::BigInt::Calc |
| 408 | \& lib_version RO Version of 'lib' |
| 409 | \& 0.30 |
| 410 | \& class RO The class of config you just called |
| 411 | \& Math::BigRat |
| 412 | \& version RO version number of the class you used |
| 413 | \& 0.10 |
| 414 | \& upgrade RW To which class numbers are upgraded |
| 415 | \& undef |
| 416 | \& downgrade RW To which class numbers are downgraded |
| 417 | \& undef |
| 418 | \& precision RW Global precision |
| 419 | \& undef |
| 420 | \& accuracy RW Global accuracy |
| 421 | \& undef |
| 422 | \& round_mode RW Global round mode |
| 423 | \& even |
| 424 | \& div_scale RW Fallback acccuracy for div |
| 425 | \& 40 |
| 426 | \& trap_nan RW Trap creation of NaN (undef = no) |
| 427 | \& undef |
| 428 | \& trap_inf RW Trap creation of +inf/-inf (undef = no) |
| 429 | \& undef |
| 430 | .Ve |
| 431 | .PP |
| 432 | By passing a reference to a hash you may set the configuration values. This |
| 433 | works only for values that a marked with a \f(CW\*(C`RW\*(C'\fR above, anything else is |
| 434 | read\-only. |
| 435 | .SH "BUGS" |
| 436 | .IX Header "BUGS" |
| 437 | Some things are not yet implemented, or only implemented half\-way: |
| 438 | .IP "inf handling (partial)" 2 |
| 439 | .IX Item "inf handling (partial)" |
| 440 | .PD 0 |
| 441 | .IP "NaN handling (partial)" 2 |
| 442 | .IX Item "NaN handling (partial)" |
| 443 | .IP "rounding (not implemented except for bceil/bfloor)" 2 |
| 444 | .IX Item "rounding (not implemented except for bceil/bfloor)" |
| 445 | .ie n .IP "$x ** $y\fR where \f(CW$y is not an integer" 2 |
| 446 | .el .IP "$x ** \f(CW$y\fR where \f(CW$y\fR is not an integer" 2 |
| 447 | .IX Item "$x ** $y where $y is not an integer" |
| 448 | .IP "\fIbmod()\fR, \fIblog()\fR, \fIbmodinv()\fR and \fIbmodpow()\fR (partial)" 2 |
| 449 | .IX Item "bmod(), blog(), bmodinv() and bmodpow() (partial)" |
| 450 | .PD |
| 451 | .SH "LICENSE" |
| 452 | .IX Header "LICENSE" |
| 453 | This program is free software; you may redistribute it and/or modify it under |
| 454 | the same terms as Perl itself. |
| 455 | .SH "SEE ALSO" |
| 456 | .IX Header "SEE ALSO" |
| 457 | Math::BigFloat and Math::Big as well as Math::BigInt::BitVect, |
| 458 | Math::BigInt::Pari and Math::BigInt::GMP. |
| 459 | .PP |
| 460 | See <http://search.cpan.org/search?dist=bignum> for a way to use |
| 461 | Math::BigRat. |
| 462 | .PP |
| 463 | The package at <http://search.cpan.org/search?dist=Math%3A%3ABigRat> |
| 464 | may contain more documentation and examples as well as testcases. |
| 465 | .SH "AUTHORS" |
| 466 | .IX Header "AUTHORS" |
| 467 | (C) by Tels <http://bloodgate.com/> 2001 \- 2005. |