projects / OpenSPARC-T2-SAM / blame
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| 129 | .\" ======================================================================== | |
| 130 | .\" | |
| 131 | .IX Title "Math::BigFloat 3" | |
| 132 | .TH Math::BigFloat 3 "2001-09-21" "perl v5.8.8" "Perl Programmers Reference Guide" | |
| 133 | .SH "NAME" | |
| 134 | Math::BigFloat \- Arbitrary size floating point math package | |
| 135 | .SH "SYNOPSIS" | |
| 136 | .IX Header "SYNOPSIS" | |
| 137 | .Vb 1 | |
| 138 | \& use Math::BigFloat; | |
| 139 | .Ve | |
| 140 | .PP | |
| 141 | .Vb 8 | |
| 142 | \& # Number creation | |
| 143 | \& $x = Math::BigFloat->new($str); # defaults to 0 | |
| 144 | \& $nan = Math::BigFloat->bnan(); # create a NotANumber | |
| 145 | \& $zero = Math::BigFloat->bzero(); # create a +0 | |
| 146 | \& $inf = Math::BigFloat->binf(); # create a +inf | |
| 147 | \& $inf = Math::BigFloat->binf('-'); # create a -inf | |
| 148 | \& $one = Math::BigFloat->bone(); # create a +1 | |
| 149 | \& $one = Math::BigFloat->bone('-'); # create a -1 | |
| 150 | .Ve | |
| 151 | .PP | |
| 152 | .Vb 10 | |
| 153 | \& # Testing | |
| 154 | \& $x->is_zero(); # true if arg is +0 | |
| 155 | \& $x->is_nan(); # true if arg is NaN | |
| 156 | \& $x->is_one(); # true if arg is +1 | |
| 157 | \& $x->is_one('-'); # true if arg is -1 | |
| 158 | \& $x->is_odd(); # true if odd, false for even | |
| 159 | \& $x->is_even(); # true if even, false for odd | |
| 160 | \& $x->is_pos(); # true if >= 0 | |
| 161 | \& $x->is_neg(); # true if < 0 | |
| 162 | \& $x->is_inf(sign); # true if +inf, or -inf (default is '+') | |
| 163 | .Ve | |
| 164 | .PP | |
| 165 | .Vb 5 | |
| 166 | \& $x->bcmp($y); # compare numbers (undef,<0,=0,>0) | |
| 167 | \& $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
| 168 | \& $x->sign(); # return the sign, either +,- or NaN | |
| 169 | \& $x->digit($n); # return the nth digit, counting from right | |
| 170 | \& $x->digit(-$n); # return the nth digit, counting from left | |
| 171 | .Ve | |
| 172 | .PP | |
| 173 | .Vb 3 | |
| 174 | \& # The following all modify their first argument. If you want to preserve | |
| 175 | \& # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is | |
| 176 | \& # neccessary when mixing $a = $b assigments with non-overloaded math. | |
| 177 | .Ve | |
| 178 | .PP | |
| 179 | .Vb 7 | |
| 180 | \& # set | |
| 181 | \& $x->bzero(); # set $i to 0 | |
| 182 | \& $x->bnan(); # set $i to NaN | |
| 183 | \& $x->bone(); # set $x to +1 | |
| 184 | \& $x->bone('-'); # set $x to -1 | |
| 185 | \& $x->binf(); # set $x to inf | |
| 186 | \& $x->binf('-'); # set $x to -inf | |
| 187 | .Ve | |
| 188 | .PP | |
| 189 | .Vb 6 | |
| 190 | \& $x->bneg(); # negation | |
| 191 | \& $x->babs(); # absolute value | |
| 192 | \& $x->bnorm(); # normalize (no-op) | |
| 193 | \& $x->bnot(); # two's complement (bit wise not) | |
| 194 | \& $x->binc(); # increment x by 1 | |
| 195 | \& $x->bdec(); # decrement x by 1 | |
| 196 | .Ve | |
| 197 | .PP | |
| 198 | .Vb 5 | |
| 199 | \& $x->badd($y); # addition (add $y to $x) | |
| 200 | \& $x->bsub($y); # subtraction (subtract $y from $x) | |
| 201 | \& $x->bmul($y); # multiplication (multiply $x by $y) | |
| 202 | \& $x->bdiv($y); # divide, set $x to quotient | |
| 203 | \& # return (quo,rem) or quo if scalar | |
| 204 | .Ve | |
| 205 | .PP | |
| 206 | .Vb 5 | |
| 207 | \& $x->bmod($y); # modulus ($x % $y) | |
| 208 | \& $x->bpow($y); # power of arguments ($x ** $y) | |
| 209 | \& $x->blsft($y); # left shift | |
| 210 | \& $x->brsft($y); # right shift | |
| 211 | \& # return (quo,rem) or quo if scalar | |
| 212 | .Ve | |
| 213 | .PP | |
| 214 | .Vb 2 | |
| 215 | \& $x->blog(); # logarithm of $x to base e (Euler's number) | |
| 216 | \& $x->blog($base); # logarithm of $x to base $base (f.i. 2) | |
| 217 | .Ve | |
| 218 | .PP | |
| 219 | .Vb 4 | |
| 220 | \& $x->band($y); # bit-wise and | |
| 221 | \& $x->bior($y); # bit-wise inclusive or | |
| 222 | \& $x->bxor($y); # bit-wise exclusive or | |
| 223 | \& $x->bnot(); # bit-wise not (two's complement) | |
| 224 | .Ve | |
| 225 | .PP | |
| 226 | .Vb 3 | |
| 227 | \& $x->bsqrt(); # calculate square-root | |
| 228 | \& $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) | |
| 229 | \& $x->bfac(); # factorial of $x (1*2*3*4*..$x) | |
| 230 | .Ve | |
| 231 | .PP | |
| 232 | .Vb 2 | |
| 233 | \& $x->bround($N); # accuracy: preserve $N digits | |
| 234 | \& $x->bfround($N); # precision: round to the $Nth digit | |
| 235 | .Ve | |
| 236 | .PP | |
| 237 | .Vb 2 | |
| 238 | \& $x->bfloor(); # return integer less or equal than $x | |
| 239 | \& $x->bceil(); # return integer greater or equal than $x | |
| 240 | .Ve | |
| 241 | .PP | |
| 242 | .Vb 1 | |
| 243 | \& # The following do not modify their arguments: | |
| 244 | .Ve | |
| 245 | .PP | |
| 246 | .Vb 2 | |
| 247 | \& bgcd(@values); # greatest common divisor | |
| 248 | \& blcm(@values); # lowest common multiplicator | |
| 249 | .Ve | |
| 250 | .PP | |
| 251 | .Vb 2 | |
| 252 | \& $x->bstr(); # return string | |
| 253 | \& $x->bsstr(); # return string in scientific notation | |
| 254 | .Ve | |
| 255 | .PP | |
| 256 | .Vb 4 | |
| 257 | \& $x->as_int(); # return $x as BigInt | |
| 258 | \& $x->exponent(); # return exponent as BigInt | |
| 259 | \& $x->mantissa(); # return mantissa as BigInt | |
| 260 | \& $x->parts(); # return (mantissa,exponent) as BigInt | |
| 261 | .Ve | |
| 262 | .PP | |
| 263 | .Vb 2 | |
| 264 | \& $x->length(); # number of digits (w/o sign and '.') | |
| 265 | \& ($l,$f) = $x->length(); # number of digits, and length of fraction | |
| 266 | .Ve | |
| 267 | .PP | |
| 268 | .Vb 4 | |
| 269 | \& $x->precision(); # return P of $x (or global, if P of $x undef) | |
| 270 | \& $x->precision($n); # set P of $x to $n | |
| 271 | \& $x->accuracy(); # return A of $x (or global, if A of $x undef) | |
| 272 | \& $x->accuracy($n); # set A $x to $n | |
| 273 | .Ve | |
| 274 | .PP | |
| 275 | .Vb 4 | |
| 276 | \& # these get/set the appropriate global value for all BigFloat objects | |
| 277 | \& Math::BigFloat->precision(); # Precision | |
| 278 | \& Math::BigFloat->accuracy(); # Accuracy | |
| 279 | \& Math::BigFloat->round_mode(); # rounding mode | |
| 280 | .Ve | |
| 281 | .SH "DESCRIPTION" | |
| 282 | .IX Header "DESCRIPTION" | |
| 283 | All operators (inlcuding basic math operations) are overloaded if you | |
| 284 | declare your big floating point numbers as | |
| 285 | .PP | |
| 286 | .Vb 1 | |
| 287 | \& $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; | |
| 288 | .Ve | |
| 289 | .PP | |
| 290 | Operations with overloaded operators preserve the arguments, which is | |
| 291 | exactly what you expect. | |
| 292 | .Sh "Canonical notation" | |
| 293 | .IX Subsection "Canonical notation" | |
| 294 | Input to these routines are either BigFloat objects, or strings of the | |
| 295 | following four forms: | |
| 296 | .IP "\(bu" 2 | |
| 297 | \&\f(CW\*(C`/^[+\-]\ed+$/\*(C'\fR | |
| 298 | .IP "\(bu" 2 | |
| 299 | \&\f(CW\*(C`/^[+\-]\ed+\e.\ed*$/\*(C'\fR | |
| 300 | .IP "\(bu" 2 | |
| 301 | \&\f(CW\*(C`/^[+\-]\ed+E[+\-]?\ed+$/\*(C'\fR | |
| 302 | .IP "\(bu" 2 | |
| 303 | \&\f(CW\*(C`/^[+\-]\ed*\e.\ed+E[+\-]?\ed+$/\*(C'\fR | |
| 304 | .PP | |
| 305 | all with optional leading and trailing zeros and/or spaces. Additonally, | |
| 306 | numbers are allowed to have an underscore between any two digits. | |
| 307 | .PP | |
| 308 | Empty strings as well as other illegal numbers results in 'NaN'. | |
| 309 | .PP | |
| 310 | \&\fIbnorm()\fR on a BigFloat object is now effectively a no\-op, since the numbers | |
| 311 | are always stored in normalized form. On a string, it creates a BigFloat | |
| 312 | object. | |
| 313 | .Sh "Output" | |
| 314 | .IX Subsection "Output" | |
| 315 | Output values are BigFloat objects (normalized), except for \fIbstr()\fR and \fIbsstr()\fR. | |
| 316 | .PP | |
| 317 | The string output will always have leading and trailing zeros stripped and drop | |
| 318 | a plus sign. \f(CW\*(C`bstr()\*(C'\fR will give you always the form with a decimal point, | |
| 319 | while \f(CW\*(C`bsstr()\*(C'\fR (s for scientific) gives you the scientific notation. | |
| 320 | .PP | |
| 321 | .Vb 6 | |
| 322 | \& Input bstr() bsstr() | |
| 323 | \& '-0' '0' '0E1' | |
| 324 | \& ' -123 123 123' '-123123123' '-123123123E0' | |
| 325 | \& '00.0123' '0.0123' '123E-4' | |
| 326 | \& '123.45E-2' '1.2345' '12345E-4' | |
| 327 | \& '10E+3' '10000' '1E4' | |
| 328 | .Ve | |
| 329 | .PP | |
| 330 | Some routines (\f(CW\*(C`is_odd()\*(C'\fR, \f(CW\*(C`is_even()\*(C'\fR, \f(CW\*(C`is_zero()\*(C'\fR, \f(CW\*(C`is_one()\*(C'\fR, | |
| 331 | \&\f(CW\*(C`is_nan()\*(C'\fR) return true or false, while others (\f(CW\*(C`bcmp()\*(C'\fR, \f(CW\*(C`bacmp()\*(C'\fR) | |
| 332 | return either undef, <0, 0 or >0 and are suited for sort. | |
| 333 | .PP | |
| 334 | Actual math is done by using the class defined with \f(CW\*(C`with =\*(C'\fR Class;> (which | |
| 335 | defaults to BigInts) to represent the mantissa and exponent. | |
| 336 | .PP | |
| 337 | The sign \f(CW\*(C`/^[+\-]$/\*(C'\fR is stored separately. The string 'NaN' is used to | |
| 338 | represent the result when input arguments are not numbers, as well as | |
| 339 | the result of dividing by zero. | |
| 340 | .ie n .Sh """mantissa()""\fP, \f(CW""exponent()""\fP and \f(CW""parts()""" | |
| 341 | .el .Sh "\f(CWmantissa()\fP, \f(CWexponent()\fP and \f(CWparts()\fP" | |
| 342 | .IX Subsection "mantissa(), exponent() and parts()" | |
| 343 | \&\f(CW\*(C`mantissa()\*(C'\fR and \f(CW\*(C`exponent()\*(C'\fR return the said parts of the BigFloat | |
| 344 | as BigInts such that: | |
| 345 | .PP | |
| 346 | .Vb 4 | |
| 347 | \& $m = $x->mantissa(); | |
| 348 | \& $e = $x->exponent(); | |
| 349 | \& $y = $m * ( 10 ** $e ); | |
| 350 | \& print "ok\en" if $x == $y; | |
| 351 | .Ve | |
| 352 | .PP | |
| 353 | \&\f(CW\*(C`($m,$e) = $x\->parts();\*(C'\fR is just a shortcut giving you both of them. | |
| 354 | .PP | |
| 355 | A zero is represented and returned as \f(CW0E1\fR, \fBnot\fR \f(CW0E0\fR (after Knuth). | |
| 356 | .PP | |
| 357 | Currently the mantissa is reduced as much as possible, favouring higher | |
| 358 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). | |
| 359 | This might change in the future, so do not depend on it. | |
| 360 | .Sh "Accuracy vs. Precision" | |
| 361 | .IX Subsection "Accuracy vs. Precision" | |
| 362 | See also: Rounding. | |
| 363 | .PP | |
| 364 | Math::BigFloat supports both precision (rounding to a certain place before or | |
| 365 | after the dot) and accuracy (rounding to a certain number of digits). For a | |
| 366 | full documentation, examples and tips on these topics please see the large | |
| 367 | section about rounding in Math::BigInt. | |
| 368 | .PP | |
| 369 | Since things like \f(CWsqrt(2)\fR or \f(CW\*(C`1 / 3\*(C'\fR must presented with a limited | |
| 370 | accuracy lest a operation consumes all resources, each operation produces | |
| 371 | no more than the requested number of digits. | |
| 372 | .PP | |
| 373 | If there is no gloabl precision or accuracy set, \fBand\fR the operation in | |
| 374 | question was not called with a requested precision or accuracy, \fBand\fR the | |
| 375 | input \f(CW$x\fR has no accuracy or precision set, then a fallback parameter will | |
| 376 | be used. For historical reasons, it is called \f(CW\*(C`div_scale\*(C'\fR and can be accessed | |
| 377 | via: | |
| 378 | .PP | |
| 379 | .Vb 2 | |
| 380 | \& $d = Math::BigFloat->div_scale(); # query | |
| 381 | \& Math::BigFloat->div_scale($n); # set to $n digits | |
| 382 | .Ve | |
| 383 | .PP | |
| 384 | The default value for \f(CW\*(C`div_scale\*(C'\fR is 40. | |
| 385 | .PP | |
| 386 | In case the result of one operation has more digits than specified, | |
| 387 | it is rounded. The rounding mode taken is either the default mode, or the one | |
| 388 | supplied to the operation after the \fIscale\fR: | |
| 389 | .PP | |
| 390 | .Vb 7 | |
| 391 | \& $x = Math::BigFloat->new(2); | |
| 392 | \& Math::BigFloat->accuracy(5); # 5 digits max | |
| 393 | \& $y = $x->copy()->bdiv(3); # will give 0.66667 | |
| 394 | \& $y = $x->copy()->bdiv(3,6); # will give 0.666667 | |
| 395 | \& $y = $x->copy()->bdiv(3,6,undef,'odd'); # will give 0.666667 | |
| 396 | \& Math::BigFloat->round_mode('zero'); | |
| 397 | \& $y = $x->copy()->bdiv(3,6); # will also give 0.666667 | |
| 398 | .Ve | |
| 399 | .PP | |
| 400 | Note that \f(CW\*(C`Math::BigFloat\->accuracy()\*(C'\fR and \f(CW\*(C`Math::BigFloat\->precision()\*(C'\fR | |
| 401 | set the global variables, and thus \fBany\fR newly created number will be subject | |
| 402 | to the global rounding \fBimmidiately\fR. This means that in the examples above, the | |
| 403 | \&\f(CW3\fR as argument to \f(CW\*(C`bdiv()\*(C'\fR will also get an accuracy of \fB5\fR. | |
| 404 | .PP | |
| 405 | It is less confusing to either calculate the result fully, and afterwards | |
| 406 | round it explicitely, or use the additional parameters to the math | |
| 407 | functions like so: | |
| 408 | .PP | |
| 409 | .Vb 4 | |
| 410 | \& use Math::BigFloat; | |
| 411 | \& $x = Math::BigFloat->new(2); | |
| 412 | \& $y = $x->copy()->bdiv(3); | |
| 413 | \& print $y->bround(5),"\en"; # will give 0.66667 | |
| 414 | .Ve | |
| 415 | .PP | |
| 416 | .Vb 1 | |
| 417 | \& or | |
| 418 | .Ve | |
| 419 | .PP | |
| 420 | .Vb 4 | |
| 421 | \& use Math::BigFloat; | |
| 422 | \& $x = Math::BigFloat->new(2); | |
| 423 | \& $y = $x->copy()->bdiv(3,5); # will give 0.66667 | |
| 424 | \& print "$y\en"; | |
| 425 | .Ve | |
| 426 | .Sh "Rounding" | |
| 427 | .IX Subsection "Rounding" | |
| 428 | .IP "ffround ( +$scale )" 2 | |
| 429 | .IX Item "ffround ( +$scale )" | |
| 430 | Rounds to the \f(CW$scale\fR'th place left from the '.', counting from the dot. | |
| 431 | The first digit is numbered 1. | |
| 432 | .IP "ffround ( \-$scale )" 2 | |
| 433 | .IX Item "ffround ( -$scale )" | |
| 434 | Rounds to the \f(CW$scale\fR'th place right from the '.', counting from the dot. | |
| 435 | .IP "ffround ( 0 )" 2 | |
| 436 | .IX Item "ffround ( 0 )" | |
| 437 | Rounds to an integer. | |
| 438 | .IP "fround ( +$scale )" 2 | |
| 439 | .IX Item "fround ( +$scale )" | |
| 440 | Preserves accuracy to \f(CW$scale\fR digits from the left (aka significant digits) | |
| 441 | and pads the rest with zeros. If the number is between 1 and \-1, the | |
| 442 | significant digits count from the first non-zero after the '.' | |
| 443 | .IP "fround ( \-$scale ) and fround ( 0 )" 2 | |
| 444 | .IX Item "fround ( -$scale ) and fround ( 0 )" | |
| 445 | These are effectively no\-ops. | |
| 446 | .PP | |
| 447 | All rounding functions take as a second parameter a rounding mode from one of | |
| 448 | the following: 'even', 'odd', '+inf', '\-inf', 'zero' or 'trunc'. | |
| 449 | .PP | |
| 450 | The default rounding mode is 'even'. By using | |
| 451 | \&\f(CW\*(C`Math::BigFloat\->round_mode($round_mode);\*(C'\fR you can get and set the default | |
| 452 | mode for subsequent rounding. The usage of \f(CW\*(C`$Math::BigFloat::$round_mode\*(C'\fR is | |
| 453 | no longer supported. | |
| 454 | The second parameter to the round functions then overrides the default | |
| 455 | temporarily. | |
| 456 | .PP | |
| 457 | The \f(CW\*(C`as_number()\*(C'\fR function returns a BigInt from a Math::BigFloat. It uses | |
| 458 | \&'trunc' as rounding mode to make it equivalent to: | |
| 459 | .PP | |
| 460 | .Vb 2 | |
| 461 | \& $x = 2.5; | |
| 462 | \& $y = int($x) + 2; | |
| 463 | .Ve | |
| 464 | .PP | |
| 465 | You can override this by passing the desired rounding mode as parameter to | |
| 466 | \&\f(CW\*(C`as_number()\*(C'\fR: | |
| 467 | .PP | |
| 468 | .Vb 2 | |
| 469 | \& $x = Math::BigFloat->new(2.5); | |
| 470 | \& $y = $x->as_number('odd'); # $y = 3 | |
| 471 | .Ve | |
| 472 | .SH "METHODS" | |
| 473 | .IX Header "METHODS" | |
| 474 | .Sh "accuracy" | |
| 475 | .IX Subsection "accuracy" | |
| 476 | .Vb 3 | |
| 477 | \& $x->accuracy(5); # local for $x | |
| 478 | \& CLASS->accuracy(5); # global for all members of CLASS | |
| 479 | \& # Note: This also applies to new()! | |
| 480 | .Ve | |
| 481 | .PP | |
| 482 | .Vb 2 | |
| 483 | \& $A = $x->accuracy(); # read out accuracy that affects $x | |
| 484 | \& $A = CLASS->accuracy(); # read out global accuracy | |
| 485 | .Ve | |
| 486 | .PP | |
| 487 | Set or get the global or local accuracy, aka how many significant digits the | |
| 488 | results have. If you set a global accuracy, then this also applies to \fInew()\fR! | |
| 489 | .PP | |
| 490 | Warning! The accuracy \fIsticks\fR, e.g. once you created a number under the | |
| 491 | influence of \f(CW\*(C`CLASS\->accuracy($A)\*(C'\fR, all results from math operations with | |
| 492 | that number will also be rounded. | |
| 493 | .PP | |
| 494 | In most cases, you should probably round the results explicitely using one of | |
| 495 | \&\fIround()\fR, \fIbround()\fR or \fIbfround()\fR or by passing the desired accuracy | |
| 496 | to the math operation as additional parameter: | |
| 497 | .PP | |
| 498 | .Vb 4 | |
| 499 | \& my $x = Math::BigInt->new(30000); | |
| 500 | \& my $y = Math::BigInt->new(7); | |
| 501 | \& print scalar $x->copy()->bdiv($y, 2); # print 4300 | |
| 502 | \& print scalar $x->copy()->bdiv($y)->bround(2); # print 4300 | |
| 503 | .Ve | |
| 504 | .Sh "\fIprecision()\fP" | |
| 505 | .IX Subsection "precision()" | |
| 506 | .Vb 2 | |
| 507 | \& $x->precision(-2); # local for $x, round at the second digit right of the dot | |
| 508 | \& $x->precision(2); # ditto, round at the second digit left of the dot | |
| 509 | .Ve | |
| 510 | .PP | |
| 511 | .Vb 3 | |
| 512 | \& CLASS->precision(5); # Global for all members of CLASS | |
| 513 | \& # This also applies to new()! | |
| 514 | \& CLASS->precision(-5); # ditto | |
| 515 | .Ve | |
| 516 | .PP | |
| 517 | .Vb 2 | |
| 518 | \& $P = CLASS->precision(); # read out global precision | |
| 519 | \& $P = $x->precision(); # read out precision that affects $x | |
| 520 | .Ve | |
| 521 | .PP | |
| 522 | Note: You probably want to use \fIaccuracy()\fR instead. With accuracy you | |
| 523 | set the number of digits each result should have, with precision you | |
| 524 | set the place where to round! | |
| 525 | .SH "Autocreating constants" | |
| 526 | .IX Header "Autocreating constants" | |
| 527 | After \f(CW\*(C`use Math::BigFloat ':constant'\*(C'\fR all the floating point constants | |
| 528 | in the given scope are converted to \f(CW\*(C`Math::BigFloat\*(C'\fR. This conversion | |
| 529 | happens at compile time. | |
| 530 | .PP | |
| 531 | In particular | |
| 532 | .PP | |
| 533 | .Vb 1 | |
| 534 | \& perl -MMath::BigFloat=:constant -e 'print 2E-100,"\en"' | |
| 535 | .Ve | |
| 536 | .PP | |
| 537 | prints the value of \f(CW\*(C`2E\-100\*(C'\fR. Note that without conversion of | |
| 538 | constants the expression 2E\-100 will be calculated as normal floating point | |
| 539 | number. | |
| 540 | .PP | |
| 541 | Please note that ':constant' does not affect integer constants, nor binary | |
| 542 | nor hexadecimal constants. Use bignum or Math::BigInt to get this to | |
| 543 | work. | |
| 544 | .Sh "Math library" | |
| 545 | .IX Subsection "Math library" | |
| 546 | Math with the numbers is done (by default) by a module called | |
| 547 | Math::BigInt::Calc. This is equivalent to saying: | |
| 548 | .PP | |
| 549 | .Vb 1 | |
| 550 | \& use Math::BigFloat lib => 'Calc'; | |
| 551 | .Ve | |
| 552 | .PP | |
| 553 | You can change this by using: | |
| 554 | .PP | |
| 555 | .Vb 1 | |
| 556 | \& use Math::BigFloat lib => 'BitVect'; | |
| 557 | .Ve | |
| 558 | .PP | |
| 559 | The following would first try to find Math::BigInt::Foo, then | |
| 560 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
| 561 | .PP | |
| 562 | .Vb 1 | |
| 563 | \& use Math::BigFloat lib => 'Foo,Math::BigInt::Bar'; | |
| 564 | .Ve | |
| 565 | .PP | |
| 566 | Calc.pm uses as internal format an array of elements of some decimal base | |
| 567 | (usually 1e7, but this might be differen for some systems) with the least | |
| 568 | significant digit first, while BitVect.pm uses a bit vector of base 2, most | |
| 569 | significant bit first. Other modules might use even different means of | |
| 570 | representing the numbers. See the respective module documentation for further | |
| 571 | details. | |
| 572 | .PP | |
| 573 | Please note that Math::BigFloat does \fBnot\fR use the denoted library itself, | |
| 574 | but it merely passes the lib argument to Math::BigInt. So, instead of the need | |
| 575 | to do: | |
| 576 | .PP | |
| 577 | .Vb 2 | |
| 578 | \& use Math::BigInt lib => 'GMP'; | |
| 579 | \& use Math::BigFloat; | |
| 580 | .Ve | |
| 581 | .PP | |
| 582 | you can roll it all into one line: | |
| 583 | .PP | |
| 584 | .Vb 1 | |
| 585 | \& use Math::BigFloat lib => 'GMP'; | |
| 586 | .Ve | |
| 587 | .PP | |
| 588 | It is also possible to just require Math::BigFloat: | |
| 589 | .PP | |
| 590 | .Vb 1 | |
| 591 | \& require Math::BigFloat; | |
| 592 | .Ve | |
| 593 | .PP | |
| 594 | This will load the neccessary things (like BigInt) when they are needed, and | |
| 595 | automatically. | |
| 596 | .PP | |
| 597 | Use the lib, Luke! And see \*(L"Using Math::BigInt::Lite\*(R" for more details than | |
| 598 | you ever wanted to know about loading a different library. | |
| 599 | .Sh "Using Math::BigInt::Lite" | |
| 600 | .IX Subsection "Using Math::BigInt::Lite" | |
| 601 | It is possible to use Math::BigInt::Lite with Math::BigFloat: | |
| 602 | .PP | |
| 603 | .Vb 2 | |
| 604 | \& # 1 | |
| 605 | \& use Math::BigFloat with => 'Math::BigInt::Lite'; | |
| 606 | .Ve | |
| 607 | .PP | |
| 608 | There is no need to \*(L"use Math::BigInt\*(R" or \*(L"use Math::BigInt::Lite\*(R", but you | |
| 609 | can combine these if you want. For instance, you may want to use | |
| 610 | Math::BigInt objects in your main script, too. | |
| 611 | .PP | |
| 612 | .Vb 3 | |
| 613 | \& # 2 | |
| 614 | \& use Math::BigInt; | |
| 615 | \& use Math::BigFloat with => 'Math::BigInt::Lite'; | |
| 616 | .Ve | |
| 617 | .PP | |
| 618 | Of course, you can combine this with the \f(CW\*(C`lib\*(C'\fR parameter. | |
| 619 | .PP | |
| 620 | .Vb 2 | |
| 621 | \& # 3 | |
| 622 | \& use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; | |
| 623 | .Ve | |
| 624 | .PP | |
| 625 | There is no need for a \*(L"use Math::BigInt;\*(R" statement, even if you want to | |
| 626 | use Math::BigInt's, since Math::BigFloat will needs Math::BigInt and thus | |
| 627 | always loads it. But if you add it, add it \fBbefore\fR: | |
| 628 | .PP | |
| 629 | .Vb 3 | |
| 630 | \& # 4 | |
| 631 | \& use Math::BigInt; | |
| 632 | \& use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; | |
| 633 | .Ve | |
| 634 | .PP | |
| 635 | Notice that the module with the last \f(CW\*(C`lib\*(C'\fR will \*(L"win\*(R" and thus | |
| 636 | it's lib will be used if the lib is available: | |
| 637 | .PP | |
| 638 | .Vb 3 | |
| 639 | \& # 5 | |
| 640 | \& use Math::BigInt lib => 'Bar,Baz'; | |
| 641 | \& use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo'; | |
| 642 | .Ve | |
| 643 | .PP | |
| 644 | That would try to load Foo, Bar, Baz and Calc (in that order). Or in other | |
| 645 | words, Math::BigFloat will try to retain previously loaded libs when you | |
| 646 | don't specify it onem but if you specify one, it will try to load them. | |
| 647 | .PP | |
| 648 | Actually, the lib loading order would be \*(L"Bar,Baz,Calc\*(R", and then | |
| 649 | \&\*(L"Foo,Bar,Baz,Calc\*(R", but independend of which lib exists, the result is the | |
| 650 | same as trying the latter load alone, except for the fact that one of Bar or | |
| 651 | Baz might be loaded needlessly in an intermidiate step (and thus hang around | |
| 652 | and waste memory). If neither Bar nor Baz exist (or don't work/compile), they | |
| 653 | will still be tried to be loaded, but this is not as time/memory consuming as | |
| 654 | actually loading one of them. Still, this type of usage is not recommended due | |
| 655 | to these issues. | |
| 656 | .PP | |
| 657 | The old way (loading the lib only in BigInt) still works though: | |
| 658 | .PP | |
| 659 | .Vb 3 | |
| 660 | \& # 6 | |
| 661 | \& use Math::BigInt lib => 'Bar,Baz'; | |
| 662 | \& use Math::BigFloat; | |
| 663 | .Ve | |
| 664 | .PP | |
| 665 | You can even load Math::BigInt afterwards: | |
| 666 | .PP | |
| 667 | .Vb 3 | |
| 668 | \& # 7 | |
| 669 | \& use Math::BigFloat; | |
| 670 | \& use Math::BigInt lib => 'Bar,Baz'; | |
| 671 | .Ve | |
| 672 | .PP | |
| 673 | But this has the same problems like #5, it will first load Calc | |
| 674 | (Math::BigFloat needs Math::BigInt and thus loads it) and then later Bar or | |
| 675 | Baz, depending on which of them works and is usable/loadable. Since this | |
| 676 | loads Calc unnecc., it is not recommended. | |
| 677 | .PP | |
| 678 | Since it also possible to just require Math::BigFloat, this poses the question | |
| 679 | about what libary this will use: | |
| 680 | .PP | |
| 681 | .Vb 2 | |
| 682 | \& require Math::BigFloat; | |
| 683 | \& my $x = Math::BigFloat->new(123); $x += 123; | |
| 684 | .Ve | |
| 685 | .PP | |
| 686 | It will use Calc. Please note that the call to \fIimport()\fR is still done, but | |
| 687 | only when you use for the first time some Math::BigFloat math (it is triggered | |
| 688 | via any constructor, so the first time you create a Math::BigFloat, the load | |
| 689 | will happen in the background). This means: | |
| 690 | .PP | |
| 691 | .Vb 2 | |
| 692 | \& require Math::BigFloat; | |
| 693 | \& Math::BigFloat->import ( lib => 'Foo,Bar' ); | |
| 694 | .Ve | |
| 695 | .PP | |
| 696 | would be the same as: | |
| 697 | .PP | |
| 698 | .Vb 1 | |
| 699 | \& use Math::BigFloat lib => 'Foo, Bar'; | |
| 700 | .Ve | |
| 701 | .PP | |
| 702 | But don't try to be clever to insert some operations in between: | |
| 703 | .PP | |
| 704 | .Vb 4 | |
| 705 | \& require Math::BigFloat; | |
| 706 | \& my $x = Math::BigFloat->bone() + 4; # load BigInt and Calc | |
| 707 | \& Math::BigFloat->import( lib => 'Pari' ); # load Pari, too | |
| 708 | \& $x = Math::BigFloat->bone()+4; # now use Pari | |
| 709 | .Ve | |
| 710 | .PP | |
| 711 | While this works, it loads Calc needlessly. But maybe you just wanted that? | |
| 712 | .PP | |
| 713 | \&\fBExamples #3 is highly recommended\fR for daily usage. | |
| 714 | .SH "BUGS" | |
| 715 | .IX Header "BUGS" | |
| 716 | Please see the file \s-1BUGS\s0 in the \s-1CPAN\s0 distribution Math::BigInt for known bugs. | |
| 717 | .SH "CAVEATS" | |
| 718 | .IX Header "CAVEATS" | |
| 719 | .IP "stringify, \fIbstr()\fR" 1 | |
| 720 | .IX Item "stringify, bstr()" | |
| 721 | Both stringify and \fIbstr()\fR now drop the leading '+'. The old code would return | |
| 722 | \&'+1.23', the new returns '1.23'. See the documentation in Math::BigInt for | |
| 723 | reasoning and details. | |
| 724 | .IP "bdiv" 1 | |
| 725 | .IX Item "bdiv" | |
| 726 | The following will probably not do what you expect: | |
| 727 | .Sp | |
| 728 | .Vb 1 | |
| 729 | \& print $c->bdiv(123.456),"\en"; | |
| 730 | .Ve | |
| 731 | .Sp | |
| 732 | It prints both quotient and reminder since print works in list context. Also, | |
| 733 | \&\fIbdiv()\fR will modify \f(CW$c\fR, so be carefull. You probably want to use | |
| 734 | .Sp | |
| 735 | .Vb 2 | |
| 736 | \& print $c / 123.456,"\en"; | |
| 737 | \& print scalar $c->bdiv(123.456),"\en"; # or if you want to modify $c | |
| 738 | .Ve | |
| 739 | .Sp | |
| 740 | instead. | |
| 741 | .IP "Modifying and =" 1 | |
| 742 | .IX Item "Modifying and =" | |
| 743 | Beware of: | |
| 744 | .Sp | |
| 745 | .Vb 2 | |
| 746 | \& $x = Math::BigFloat->new(5); | |
| 747 | \& $y = $x; | |
| 748 | .Ve | |
| 749 | .Sp | |
| 750 | It will not do what you think, e.g. making a copy of \f(CW$x\fR. Instead it just makes | |
| 751 | a second reference to the \fBsame\fR object and stores it in \f(CW$y\fR. Thus anything | |
| 752 | that modifies \f(CW$x\fR will modify \f(CW$y\fR (except overloaded math operators), and vice | |
| 753 | versa. See Math::BigInt for details and how to avoid that. | |
| 754 | .IP "bpow" 1 | |
| 755 | .IX Item "bpow" | |
| 756 | \&\f(CW\*(C`bpow()\*(C'\fR now modifies the first argument, unlike the old code which left | |
| 757 | it alone and only returned the result. This is to be consistent with | |
| 758 | \&\f(CW\*(C`badd()\*(C'\fR etc. The first will modify \f(CW$x\fR, the second one won't: | |
| 759 | .Sp | |
| 760 | .Vb 3 | |
| 761 | \& print bpow($x,$i),"\en"; # modify $x | |
| 762 | \& print $x->bpow($i),"\en"; # ditto | |
| 763 | \& print $x ** $i,"\en"; # leave $x alone | |
| 764 | .Ve | |
| 765 | .IP "\fIprecision()\fR vs. \fIaccuracy()\fR" 1 | |
| 766 | .IX Item "precision() vs. accuracy()" | |
| 767 | A common pitfall is to use \fIprecision()\fR when you want to round a result to | |
| 768 | a certain number of digits: | |
| 769 | .Sp | |
| 770 | .Vb 1 | |
| 771 | \& use Math::BigFloat; | |
| 772 | .Ve | |
| 773 | .Sp | |
| 774 | .Vb 8 | |
| 775 | \& Math::BigFloat->precision(4); # does not do what you think it does | |
| 776 | \& my $x = Math::BigFloat->new(12345); # rounds $x to "12000"! | |
| 777 | \& print "$x\en"; # print "12000" | |
| 778 | \& my $y = Math::BigFloat->new(3); # rounds $y to "0"! | |
| 779 | \& print "$y\en"; # print "0" | |
| 780 | \& $z = $x / $y; # 12000 / 0 => NaN! | |
| 781 | \& print "$z\en"; | |
| 782 | \& print $z->precision(),"\en"; # 4 | |
| 783 | .Ve | |
| 784 | .Sp | |
| 785 | Replacing precision with accuracy is probably not what you want, either: | |
| 786 | .Sp | |
| 787 | .Vb 1 | |
| 788 | \& use Math::BigFloat; | |
| 789 | .Ve | |
| 790 | .Sp | |
| 791 | .Vb 7 | |
| 792 | \& Math::BigFloat->accuracy(4); # enables global rounding: | |
| 793 | \& my $x = Math::BigFloat->new(123456); # rounded immidiately to "12350" | |
| 794 | \& print "$x\en"; # print "123500" | |
| 795 | \& my $y = Math::BigFloat->new(3); # rounded to "3 | |
| 796 | \& print "$y\en"; # print "3" | |
| 797 | \& print $z = $x->copy()->bdiv($y),"\en"; # 41170 | |
| 798 | \& print $z->accuracy(),"\en"; # 4 | |
| 799 | .Ve | |
| 800 | .Sp | |
| 801 | What you want to use instead is: | |
| 802 | .Sp | |
| 803 | .Vb 1 | |
| 804 | \& use Math::BigFloat; | |
| 805 | .Ve | |
| 806 | .Sp | |
| 807 | .Vb 6 | |
| 808 | \& my $x = Math::BigFloat->new(123456); # no rounding | |
| 809 | \& print "$x\en"; # print "123456" | |
| 810 | \& my $y = Math::BigFloat->new(3); # no rounding | |
| 811 | \& print "$y\en"; # print "3" | |
| 812 | \& print $z = $x->copy()->bdiv($y,4),"\en"; # 41150 | |
| 813 | \& print $z->accuracy(),"\en"; # undef | |
| 814 | .Ve | |
| 815 | .Sp | |
| 816 | In addition to computing what you expected, the last example also does \fBnot\fR | |
| 817 | \&\*(L"taint\*(R" the result with an accuracy or precision setting, which would | |
| 818 | influence any further operation. | |
| 819 | .SH "SEE ALSO" | |
| 820 | .IX Header "SEE ALSO" | |
| 821 | Math::BigInt, Math::BigRat and Math::Big as well as | |
| 822 | Math::BigInt::BitVect, Math::BigInt::Pari and Math::BigInt::GMP. | |
| 823 | .PP | |
| 824 | The pragmas bignum, bigint and bigrat might also be of interest | |
| 825 | because they solve the autoupgrading/downgrading issue, at least partly. | |
| 826 | .PP | |
| 827 | The package at | |
| 828 | <http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains | |
| 829 | more documentation including a full version history, testcases, empty | |
| 830 | subclass files and benchmarks. | |
| 831 | .SH "LICENSE" | |
| 832 | .IX Header "LICENSE" | |
| 833 | This program is free software; you may redistribute it and/or modify it under | |
| 834 | the same terms as Perl itself. | |
| 835 | .SH "AUTHORS" | |
| 836 | .IX Header "AUTHORS" | |
| 837 | Mark Biggar, overloaded interface by Ilya Zakharevich. | |
| 838 | Completely rewritten by Tels <http://bloodgate.com> in 2001 \- 2004, and still | |
| 839 | at it in 2005. |