lib/perl5/5.8.8/bignum.pm

   1 package bignum;
   2 require 5.005;
   3
   4 $VERSION = '0.17';
   5 use Exporter;
   6 @EXPORT_OK      = qw( );
   7 @EXPORT         = qw( inf NaN );
   8 @ISA            = qw( Exporter );
   9
  10 use strict;
  11
  12 ##############################################################################
  13
  14 # These are all alike, and thus faked by AUTOLOAD
  15
  16 my @faked = qw/round_mode accuracy precision div_scale/;
  17 use vars qw/$VERSION $AUTOLOAD $_lite/;         # _lite for testsuite
  18
  19 sub AUTOLOAD
  20   {
  21   my $name = $AUTOLOAD;
  22
  23   $name =~ s/.*:://;    # split package
  24   no strict 'refs';
  25   foreach my $n (@faked)
  26     {
  27     if ($n eq $name)
  28       {
  29       *{"bignum::$name"} = sub
  30         {
  31         my $self = shift;
  32         no strict 'refs';
  33         if (defined $_[0])
  34           {
  35           Math::BigInt->$name($_[0]);
  36           return Math::BigFloat->$name($_[0]);
  37           }
  38         return Math::BigInt->$name();
  39         };
  40       return &$name;
  41       }
  42     }
  43
  44   # delayed load of Carp and avoid recursion
  45   require Carp;
  46   Carp::croak ("Can't call bignum\-\>$name, not a valid method");
  47   }
  48
  49 sub upgrade
  50   {
  51   my $self = shift;
  52   no strict 'refs';
  53 #  if (defined $_[0])
  54 #    {
  55 #    $Math::BigInt::upgrade = $_[0];
  56 #    $Math::BigFloat::upgrade = $_[0];
  57 #    }
  58   return $Math::BigInt::upgrade;
  59   }
  60
  61 sub import
  62   {
  63   my $self = shift;
  64
  65   # some defaults
  66   my $lib = '';
  67   my $upgrade = 'Math::BigFloat';
  68   my $downgrade = 'Math::BigInt';
  69
  70   my @import = ( ':constant' );                         # drive it w/ constant
  71   my @a = @_; my $l = scalar @_; my $j = 0;
  72   my ($ver,$trace);                                     # version? trace?
  73   my ($a,$p);                                           # accuracy, precision
  74   for ( my $i = 0; $i < $l ; $i++,$j++ )
  75     {
  76     if ($_[$i] eq 'upgrade')
  77       {
  78       # this causes upgrading
  79       $upgrade = $_[$i+1];              # or undef to disable
  80       my $s = 2; $s = 1 if @a-$j < 2;   # avoid "can not modify non-existant..."
  81       splice @a, $j, $s; $j -= $s; $i++;
  82       }
  83     elsif ($_[$i] eq 'downgrade')
  84       {
  85       # this causes downgrading
  86       $downgrade = $_[$i+1];            # or undef to disable
  87       my $s = 2; $s = 1 if @a-$j < 2;   # avoid "can not modify non-existant..."
  88       splice @a, $j, $s; $j -= $s; $i++;
  89       }
  90     elsif ($_[$i] =~ /^(l|lib)$/)
  91       {
  92       # this causes a different low lib to take care...
  93       $lib = $_[$i+1] || '';
  94       my $s = 2; $s = 1 if @a-$j < 2;   # avoid "can not modify non-existant..."
  95       splice @a, $j, $s; $j -= $s; $i++;
  96       }
  97     elsif ($_[$i] =~ /^(a|accuracy)$/)
  98       {
  99       $a = $_[$i+1];
 100       my $s = 2; $s = 1 if @a-$j < 2;   # avoid "can not modify non-existant..."
 101       splice @a, $j, $s; $j -= $s; $i++;
 102       }
 103     elsif ($_[$i] =~ /^(p|precision)$/)
 104       {
 105       $p = $_[$i+1];
 106       my $s = 2; $s = 1 if @a-$j < 2;   # avoid "can not modify non-existant..."
 107       splice @a, $j, $s; $j -= $s; $i++;
 108       }
 109     elsif ($_[$i] =~ /^(v|version)$/)
 110       {
 111       $ver = 1;
 112       splice @a, $j, 1; $j --;
 113       }
 114     elsif ($_[$i] =~ /^(t|trace)$/)
 115       {
 116       $trace = 1;
 117       splice @a, $j, 1; $j --;
 118       }
 119     else { die "unknown option $_[$i]"; }
 120     }
 121   my $class;
 122   $_lite = 0;                                   # using M::BI::L ?
 123   if ($trace)
 124     {
 125     require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
 126     $upgrade = 'Math::BigFloat::Trace';
 127     }
 128   else
 129     {
 130     # see if we can find Math::BigInt::Lite
 131     if (!defined $a && !defined $p)             # rounding won't work to well
 132       {
 133       eval 'require Math::BigInt::Lite;';
 134       if ($@ eq '')
 135         {
 136         @import = ( );                          # :constant in Lite, not MBI
 137         Math::BigInt::Lite->import( ':constant' );
 138         $_lite= 1;                              # signal okay
 139         }
 140       }
 141     require Math::BigInt if $_lite == 0;        # not already loaded?
 142     $class = 'Math::BigInt';                    # regardless of MBIL or not
 143     }
 144   push @import, 'lib' => $lib if $lib ne '';
 145   # Math::BigInt::Trace or plain Math::BigInt
 146   $class->import(@import, upgrade => $upgrade);
 147
 148   if ($trace)
 149     {
 150     require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
 151     $downgrade = 'Math::BigInt::Trace';
 152     }
 153   else
 154     {
 155     require Math::BigFloat; $class = 'Math::BigFloat';
 156     }
 157   $class->import(':constant','downgrade',$downgrade);
 158
 159   bignum->accuracy($a) if defined $a;
 160   bignum->precision($p) if defined $p;
 161   if ($ver)
 162     {
 163     print "bignum\t\t\t v$VERSION\n";
 164     print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
 165     print "Math::BigInt\t\t v$Math::BigInt::VERSION";
 166     my $config = Math::BigInt->config();
 167     print " lib => $config->{lib} v$config->{lib_version}\n";
 168     print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
 169     exit;
 170     }
 171   $self->export_to_level(1,$self,@a);           # export inf and NaN
 172   }
 173
 174 sub inf () { Math::BigInt->binf(); }
 175 sub NaN () { Math::BigInt->bnan(); }
 176
 177 1;
 178
 179 __END__
 180
 181 =head1 NAME
 182
 183 bignum - Transparent BigNumber support for Perl
 184
 185 =head1 SYNOPSIS
 186
 187   use bignum;
 188
 189   $x = 2 + 4.5,"\n";                    # BigFloat 6.5
 190   print 2 ** 512 * 0.1,"\n";            # really is what you think it is
 191   print inf * inf,"\n";                 # prints inf
 192   print NaN * 3,"\n";                   # prints NaN
 193
 194 =head1 DESCRIPTION
 195
 196 All operators (including basic math operations) are overloaded. Integer and
 197 floating-point constants are created as proper BigInts or BigFloats,
 198 respectively.
 199
 200 If you do
 201
 202         use bignum;
 203
 204 at the top of your script, Math::BigFloat and Math::BigInt will be loaded
 205 and any constant number will be converted to an object (Math::BigFloat for
 206 floats like 3.1415 and Math::BigInt for integers like 1234).
 207
 208 So, the following line:
 209
 210         $x = 1234;
 211
 212 creates actually a Math::BigInt and stores a reference to in $x.
 213 This happens transparently and behind your back, so to speak.
 214
 215 You can see this with the following:
 216
 217         perl -Mbignum -le 'print ref(1234)'
 218
 219 Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
 220 if it is installed since it is faster for some operations. It will be
 221 automatically upgraded to BigInt whenever neccessary:
 222
 223         perl -Mbignum -le 'print ref(2**255)'
 224
 225 This also means it is a bad idea to check for some specific package, since
 226 the actual contents of $x might be something unexpected. Due to the
 227 transparent way of bignum C<ref()> should not be neccessary, anyway.
 228
 229 Since Math::BigInt and BigFloat also overload the normal math operations,
 230 the following line will still work:
 231
 232         perl -Mbignum -le 'print ref(1234+1234)'
 233
 234 Since numbers are actually objects, you can call all the usual methods from
 235 BigInt/BigFloat on them. This even works to some extent on expressions:
 236
 237         perl -Mbignum -le '$x = 1234; print $x->bdec()'
 238         perl -Mbignum -le 'print 1234->binc();'
 239         perl -Mbignum -le 'print 1234->binc->badd(6);'
 240         perl -Mbignum -le 'print +(1234)->binc()'
 241
 242 (Note that print doesn't do what you expect if the expression starts with
 243 '(' hence the C<+>)
 244
 245 You can even chain the operations together as usual:
 246
 247         perl -Mbignum -le 'print 1234->binc->badd(6);'
 248         1241
 249
 250 Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
 251 appropriately. This means that:
 252
 253         perl -Mbignum -le 'print 1234+4.5'
 254         1238.5
 255
 256 will work correctly. These mixed cases don't do always work when using
 257 Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
 258 scalars work.
 259
 260 If you do want to work with large integers like under C<use integer;>, try
 261 C<use bigint;>:
 262
 263         perl -Mbigint -le 'print 1234.5+4.5'
 264         1238
 265
 266 There is also C<use bigrat;> which gives you big rationals:
 267
 268         perl -Mbigrat -le 'print 1234+4.1'
 269         12381/10
 270
 271 The entire upgrading/downgrading is still experimental and might not work
 272 as you expect or may even have bugs.
 273
 274 You might get errors like this:
 275
 276         Can't use an undefined value as an ARRAY reference at
 277         /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
 278
 279 This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
 280 vice versa) and the upgrade/downgrad path was missing. This is a bug, please
 281 report it so that we can fix it.
 282
 283 You might consider using just Math::BigInt or Math::BigFloat, since they
 284 allow you finer control over what get's done in which module/space. For
 285 instance, simple loop counters will be Math::BigInts under C<use bignum;> and
 286 this is slower than keeping them as Perl scalars:
 287
 288         perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
 289
 290 Please note the following does not work as expected (prints nothing), since
 291 overloading of '..' is not yet possible in Perl (as of v5.8.0):
 292
 293         perl -Mbignum -le 'for (1..2) { print ref($_); }'
 294
 295 =head2 Options
 296
 297 bignum recognizes some options that can be passed while loading it via use.
 298 The options can (currently) be either a single letter form, or the long form.
 299 The following options exist:
 300
 301 =over 2
 302
 303 =item a or accuracy
 304
 305 This sets the accuracy for all math operations. The argument must be greater
 306 than or equal to zero. See Math::BigInt's bround() function for details.
 307
 308         perl -Mbignum=a,50 -le 'print sqrt(20)'
 309
 310 =item p or precision
 311
 312 This sets the precision for all math operations. The argument can be any
 313 integer. Negative values mean a fixed number of digits after the dot, while
 314 a positive value rounds to this digit left from the dot. 0 or 1 mean round to
 315 integer. See Math::BigInt's bfround() function for details.
 316
 317         perl -Mbignum=p,-50 -le 'print sqrt(20)'
 318
 319 =item t or trace
 320
 321 This enables a trace mode and is primarily for debugging bignum or
 322 Math::BigInt/Math::BigFloat.
 323
 324 =item l or lib
 325
 326 Load a different math lib, see L<MATH LIBRARY>.
 327
 328         perl -Mbignum=l,GMP -e 'print 2 ** 512'
 329
 330 Currently there is no way to specify more than one library on the command
 331 line. This will be hopefully fixed soon ;)
 332
 333 =item v or version
 334
 335 This prints out the name and version of all modules used and then exits.
 336
 337         perl -Mbignum=v
 338
 339 =head2 Methods
 340
 341 Beside import() and AUTOLOAD() there are only a few other methods.
 342
 343 Since all numbers are now objects, you can use all functions that are part of
 344 the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
 345 the fxxx() notation, though. This makes it possible that the underlying object
 346 might morph into a different class than BigFloat.
 347
 348 =head2 Caveat
 349
 350 But a warning is in order. When using the following to make a copy of a number,
 351 only a shallow copy will be made.
 352
 353         $x = 9; $y = $x;
 354         $x = $y = 7;
 355
 356 If you want to make a real copy, use the following:
 357
 358         $y = $x->copy();
 359
 360 Using the copy or the original with overloaded math is okay, e.g. the
 361 following work:
 362
 363         $x = 9; $y = $x;
 364         print $x + 1, " ", $y,"\n";     # prints 10 9
 365
 366 but calling any method that modifies the number directly will result in
 367 B<both> the original and the copy beeing destroyed:
 368
 369         $x = 9; $y = $x;
 370         print $x->badd(1), " ", $y,"\n";        # prints 10 10
 371
 372         $x = 9; $y = $x;
 373         print $x->binc(1), " ", $y,"\n";        # prints 10 10
 374
 375         $x = 9; $y = $x;
 376         print $x->bmul(2), " ", $y,"\n";        # prints 18 18
 377
 378 Using methods that do not modify, but testthe contents works:
 379
 380         $x = 9; $y = $x;
 381         $z = 9 if $x->is_zero();                # works fine
 382
 383 See the documentation about the copy constructor and C<=> in overload, as
 384 well as the documentation in BigInt for further details.
 385
 386 =over 2
 387
 388 =item inf()
 389
 390 A shortcut to return Math::BigInt->binf(). Usefull because Perl does not always
 391 handle bareword C<inf> properly.
 392
 393 =item NaN()
 394
 395 A shortcut to return Math::BigInt->bnan(). Usefull because Perl does not always
 396 handle bareword C<NaN> properly.
 397
 398 =item upgrade()
 399
 400 Return the class that numbers are upgraded to, is in fact returning
 401 C<$Math::BigInt::upgrade>.
 402
 403 =back
 404
 405 =head2 MATH LIBRARY
 406
 407 Math with the numbers is done (by default) by a module called
 408 Math::BigInt::Calc. This is equivalent to saying:
 409
 410         use bignum lib => 'Calc';
 411
 412 You can change this by using:
 413
 414         use bignum lib => 'BitVect';
 415
 416 The following would first try to find Math::BigInt::Foo, then
 417 Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
 418
 419         use bignum lib => 'Foo,Math::BigInt::Bar';
 420
 421 Please see respective module documentation for further details.
 422
 423 =head2 INTERNAL FORMAT
 424
 425 The numbers are stored as objects, and their internals might change at anytime,
 426 especially between math operations. The objects also might belong to different
 427 classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
 428 with normal scalars is not extraordinary, but normal and expected.
 429
 430 You should not depend on the internal format, all accesses must go through
 431 accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
 432 is no guaranty that the object in question has such a hashkey, nor is a hash
 433 underneath at all.
 434
 435 =head2 SIGN
 436
 437 The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
 438 You can access it with the sign() method.
 439
 440 A sign of 'NaN' is used to represent the result when input arguments are not
 441 numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
 442 minus infinity. You will get '+inf' when dividing a positive number by 0, and
 443 '-inf' when dividing any negative number by 0.
 444
 445 =head1 MODULES USED
 446
 447 C<bignum> is just a thin wrapper around various modules of the Math::BigInt
 448 family. Think of it as the head of the family, who runs the shop, and orders
 449 the others to do the work.
 450
 451 The following modules are currently used by bignum:
 452
 453         Math::BigInt::Lite      (for speed, and only if it is loadable)
 454         Math::BigInt
 455         Math::BigFloat
 456
 457 =head1 EXAMPLES
 458
 459 Some cool command line examples to impress the Python crowd ;)
 460
 461         perl -Mbignum -le 'print sqrt(33)'
 462         perl -Mbignum -le 'print 2*255'
 463         perl -Mbignum -le 'print 4.5+2*255'
 464         perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
 465         perl -Mbignum -le 'print 123->is_odd()'
 466         perl -Mbignum -le 'print log(2)'
 467         perl -Mbignum -le 'print 2 ** 0.5'
 468         perl -Mbignum=a,65 -le 'print 2 ** 0.2'
 469
 470 =head1 LICENSE
 471
 472 This program is free software; you may redistribute it and/or modify it under
 473 the same terms as Perl itself.
 474
 475 =head1 SEE ALSO
 476
 477 Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
 478
 479 L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
 480 as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and  L<Math::BigInt::GMP>.
 481
 482 =head1 AUTHORS
 483
 484 (C) by Tels L<http://bloodgate.com/> in early 2002, 2003.
 485
 486 =cut