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1 | package bigint; |
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2 | use 5.006002; |
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3 | |
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4 | $VERSION = '0.22'; |
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5 | use Exporter; |
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6 | @ISA = qw( Exporter ); |
7 | @EXPORT_OK = qw( ); |
8 | @EXPORT = qw( inf NaN ); |
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9 | |
10 | use strict; |
11 | use overload; |
12 | |
13 | ############################################################################## |
14 | |
15 | # These are all alike, and thus faked by AUTOLOAD |
16 | |
17 | my @faked = qw/round_mode accuracy precision div_scale/; |
18 | use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite |
19 | |
20 | sub AUTOLOAD |
21 | { |
22 | my $name = $AUTOLOAD; |
23 | |
24 | $name =~ s/.*:://; # split package |
25 | no strict 'refs'; |
26 | foreach my $n (@faked) |
27 | { |
28 | if ($n eq $name) |
29 | { |
30 | *{"bigint::$name"} = sub |
31 | { |
32 | my $self = shift; |
33 | no strict 'refs'; |
34 | if (defined $_[0]) |
35 | { |
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36 | return Math::BigInt->$name($_[0]); |
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37 | } |
38 | return Math::BigInt->$name(); |
39 | }; |
40 | return &$name; |
41 | } |
42 | } |
43 | |
44 | # delayed load of Carp and avoid recursion |
45 | require Carp; |
46 | Carp::croak ("Can't call bigint\-\>$name, not a valid method"); |
47 | } |
48 | |
49 | sub upgrade |
50 | { |
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51 | $Math::BigInt::upgrade; |
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52 | } |
53 | |
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54 | sub _binary_constant |
55 | { |
56 | # this takes a binary/hexadecimal/octal constant string and returns it |
57 | # as string suitable for new. Basically it converts octal to decimal, and |
58 | # passes every thing else unmodified back. |
59 | my $string = shift; |
60 | |
61 | return Math::BigInt->new($string) if $string =~ /^0[bx]/; |
62 | |
63 | # so it must be an octal constant |
64 | Math::BigInt->from_oct($string); |
65 | } |
66 | |
67 | sub _float_constant |
126f3c5f |
68 | { |
69 | # this takes a floating point constant string and returns it truncated to |
70 | # integer. For instance, '4.5' => '4', '1.234e2' => '123' etc |
71 | my $float = shift; |
72 | |
73 | # some simple cases first |
74 | return $float if ($float =~ /^[+-]?[0-9]+$/); # '+123','-1','0' etc |
75 | return $float |
76 | if ($float =~ /^[+-]?[0-9]+\.?[eE]\+?[0-9]+$/); # 123e2, 123.e+2 |
77 | return '0' if ($float =~ /^[+-]?[0]*\.[0-9]+$/); # .2, 0.2, -.1 |
78 | if ($float =~ /^[+-]?[0-9]+\.[0-9]*$/) # 1., 1.23, -1.2 etc |
79 | { |
80 | $float =~ s/\..*//; |
81 | return $float; |
82 | } |
9b924220 |
83 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split($float); |
126f3c5f |
84 | return $float if !defined $mis; # doesn't look like a number to me |
85 | my $ec = int($$ev); |
86 | my $sign = $$mis; $sign = '' if $sign eq '+'; |
87 | if ($$es eq '-') |
88 | { |
89 | # ignore fraction part entirely |
90 | if ($ec >= length($$miv)) # 123.23E-4 |
91 | { |
92 | return '0'; |
93 | } |
94 | return $sign . substr ($$miv,0,length($$miv)-$ec); # 1234.45E-2 = 12 |
95 | } |
96 | # xE+y |
97 | if ($ec >= length($$mfv)) |
98 | { |
99 | $ec -= length($$mfv); |
100 | return $sign.$$miv.$$mfv if $ec == 0; # 123.45E+2 => 12345 |
101 | return $sign.$$miv.$$mfv.'E'.$ec; # 123.45e+3 => 12345e1 |
102 | } |
103 | $mfv = substr($$mfv,0,$ec); |
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104 | $sign.$$miv.$mfv; # 123.45e+1 => 1234 |
126f3c5f |
105 | } |
106 | |
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107 | sub unimport |
108 | { |
109 | $^H{bigint} = undef; # no longer in effect |
110 | overload::remove_constant('binary','','float','','integer'); |
111 | } |
112 | |
113 | sub in_effect |
114 | { |
115 | my $level = shift || 0; |
116 | my $hinthash = (caller($level))[10]; |
117 | $hinthash->{bigint}; |
118 | } |
119 | |
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120 | ############################################################################# |
121 | # the following two routines are for "use bigint qw/hex oct/;": |
122 | |
123 | sub _hex_global |
124 | { |
125 | my $i = $_[0]; |
126 | $i = '0x'.$i unless $i =~ /^0x/; |
127 | Math::BigInt->new($i); |
128 | } |
129 | |
130 | sub _oct_global |
131 | { |
132 | my $i = $_[0]; |
133 | return Math::BigInt->from_oct($i) if $i =~ /^0[0-7]/; |
134 | Math::BigInt->new($i); |
135 | } |
136 | |
137 | ############################################################################# |
138 | # the following two routines are for Perl 5.9.4 or later and are lexical |
139 | |
140 | sub _hex |
141 | { |
142 | return CORE::hex($_[0]) unless in_effect(1); |
143 | my $i = $_[0]; |
144 | $i = '0x'.$i unless $i =~ /^0x/; |
145 | Math::BigInt->new($i); |
146 | } |
147 | |
148 | sub _oct |
149 | { |
150 | return CORE::oct($_[0]) unless in_effect(1); |
151 | my $i = $_[0]; |
152 | return Math::BigInt->from_oct($i) if $i =~ /^0[0-7]/; |
153 | Math::BigInt->new($i); |
154 | } |
155 | |
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156 | sub import |
157 | { |
158 | my $self = shift; |
159 | |
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160 | $^H{bigint} = 1; # we are in effect |
161 | |
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162 | my ($hex,$oct); |
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163 | # for newer Perls always override hex() and oct() with a lexical version: |
164 | if ($] > 5.009004) |
165 | { |
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166 | $oct = \&_oct; |
167 | $hex = \&_hex; |
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168 | } |
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169 | # some defaults |
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170 | my $lib = ''; my $lib_kind = 'try'; |
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171 | |
172 | my @import = ( ':constant' ); # drive it w/ constant |
173 | my @a = @_; my $l = scalar @_; my $j = 0; |
174 | my ($ver,$trace); # version? trace? |
175 | my ($a,$p); # accuracy, precision |
176 | for ( my $i = 0; $i < $l ; $i++,$j++ ) |
177 | { |
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178 | if ($_[$i] =~ /^(l|lib|try|only)$/) |
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179 | { |
180 | # this causes a different low lib to take care... |
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181 | $lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l'; |
126f3c5f |
182 | $lib = $_[$i+1] || ''; |
183 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
184 | splice @a, $j, $s; $j -= $s; $i++; |
185 | } |
186 | elsif ($_[$i] =~ /^(a|accuracy)$/) |
187 | { |
188 | $a = $_[$i+1]; |
189 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
190 | splice @a, $j, $s; $j -= $s; $i++; |
191 | } |
192 | elsif ($_[$i] =~ /^(p|precision)$/) |
193 | { |
194 | $p = $_[$i+1]; |
195 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
196 | splice @a, $j, $s; $j -= $s; $i++; |
197 | } |
198 | elsif ($_[$i] =~ /^(v|version)$/) |
199 | { |
200 | $ver = 1; |
201 | splice @a, $j, 1; $j --; |
202 | } |
203 | elsif ($_[$i] =~ /^(t|trace)$/) |
204 | { |
205 | $trace = 1; |
206 | splice @a, $j, 1; $j --; |
207 | } |
d1a15766 |
208 | elsif ($_[$i] eq 'hex') |
209 | { |
210 | splice @a, $j, 1; $j --; |
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211 | $hex = \&_hex_global; |
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212 | } |
213 | elsif ($_[$i] eq 'oct') |
214 | { |
215 | splice @a, $j, 1; $j --; |
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216 | $oct = \&_oct_global; |
d1a15766 |
217 | } |
126f3c5f |
218 | else { die "unknown option $_[$i]"; } |
219 | } |
220 | my $class; |
221 | $_lite = 0; # using M::BI::L ? |
222 | if ($trace) |
223 | { |
224 | require Math::BigInt::Trace; $class = 'Math::BigInt::Trace'; |
126f3c5f |
225 | } |
226 | else |
227 | { |
228 | # see if we can find Math::BigInt::Lite |
229 | if (!defined $a && !defined $p) # rounding won't work to well |
230 | { |
231 | eval 'require Math::BigInt::Lite;'; |
232 | if ($@ eq '') |
233 | { |
234 | @import = ( ); # :constant in Lite, not MBI |
235 | Math::BigInt::Lite->import( ':constant' ); |
236 | $_lite= 1; # signal okay |
237 | } |
238 | } |
239 | require Math::BigInt if $_lite == 0; # not already loaded? |
240 | $class = 'Math::BigInt'; # regardless of MBIL or not |
233f7bc0 |
241 | } |
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242 | push @import, $lib_kind => $lib if $lib ne ''; |
126f3c5f |
243 | # Math::BigInt::Trace or plain Math::BigInt |
233f7bc0 |
244 | $class->import(@import); |
126f3c5f |
245 | |
246 | bigint->accuracy($a) if defined $a; |
247 | bigint->precision($p) if defined $p; |
248 | if ($ver) |
249 | { |
250 | print "bigint\t\t\t v$VERSION\n"; |
251 | print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite; |
252 | print "Math::BigInt\t\t v$Math::BigInt::VERSION"; |
253 | my $config = Math::BigInt->config(); |
254 | print " lib => $config->{lib} v$config->{lib_version}\n"; |
255 | exit; |
256 | } |
257 | # we take care of floating point constants, since BigFloat isn't available |
258 | # and BigInt doesn't like them: |
95a2d02c |
259 | overload::constant float => sub { Math::BigInt->new( _float_constant(shift) ); }; |
260 | # Take care of octal/hexadecimal constants |
261 | overload::constant binary => sub { _binary_constant(shift) }; |
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262 | |
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263 | # if another big* was already loaded: |
264 | my ($package) = caller(); |
265 | |
266 | no strict 'refs'; |
267 | if (!defined *{"${package}::inf"}) |
268 | { |
269 | $self->export_to_level(1,$self,@a); # export inf and NaN |
270 | } |
075d4edd |
271 | { |
272 | no warnings 'redefine'; |
273 | *CORE::GLOBAL::oct = $oct if $oct; |
274 | *CORE::GLOBAL::hex = $hex if $hex; |
275 | } |
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276 | } |
277 | |
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278 | sub inf () { Math::BigInt->binf(); } |
279 | sub NaN () { Math::BigInt->bnan(); } |
280 | |
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281 | 1; |
282 | |
283 | __END__ |
284 | |
285 | =head1 NAME |
286 | |
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287 | bigint - Transparent BigInteger support for Perl |
126f3c5f |
288 | |
289 | =head1 SYNOPSIS |
290 | |
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291 | use bigint; |
126f3c5f |
292 | |
293 | $x = 2 + 4.5,"\n"; # BigInt 6 |
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294 | print 2 ** 512,"\n"; # really is what you think it is |
295 | print inf + 42,"\n"; # inf |
296 | print NaN * 7,"\n"; # NaN |
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297 | print hex("0x1234567890123490"),"\n"; # Perl v5.9.4 or later |
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298 | |
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299 | { |
300 | no bigint; |
301 | print 2 ** 256,"\n"; # a normal Perl scalar now |
302 | } |
303 | |
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304 | # Note that this will be global: |
305 | use bigint qw/hex oct/; |
306 | print hex("0x1234567890123490"),"\n"; |
307 | print oct("01234567890123490"),"\n"; |
308 | |
126f3c5f |
309 | =head1 DESCRIPTION |
310 | |
311 | All operators (including basic math operations) are overloaded. Integer |
312 | constants are created as proper BigInts. |
313 | |
1ad2138d |
314 | Floating point constants are truncated to integer. All parts and results of |
315 | expressions are also truncated. |
316 | |
317 | Unlike L<integer>, this pragma creates integer constants that are only |
318 | limited in their size by the available memory and CPU time. |
319 | |
320 | =head2 use integer vs. use bigint |
321 | |
322 | There is one small difference between C<use integer> and C<use bigint>: the |
323 | former will not affect assignments to variables and the return value of |
324 | some functions. C<bigint> truncates these results to integer too: |
325 | |
326 | # perl -Minteger -wle 'print 3.2' |
327 | 3.2 |
328 | # perl -Minteger -wle 'print 3.2 + 0' |
329 | 3 |
330 | # perl -Mbigint -wle 'print 3.2' |
331 | 3 |
332 | # perl -Mbigint -wle 'print 3.2 + 0' |
333 | 3 |
334 | |
335 | # perl -Mbigint -wle 'print exp(1) + 0' |
336 | 2 |
337 | # perl -Mbigint -wle 'print exp(1)' |
338 | 2 |
d1a15766 |
339 | # perl -Minteger -wle 'print exp(1)' |
1ad2138d |
340 | 2.71828182845905 |
d1a15766 |
341 | # perl -Minteger -wle 'print exp(1) + 0' |
1ad2138d |
342 | 2 |
343 | |
344 | In practice this makes seldom a difference as B<parts and results> of |
345 | expressions will be truncated anyway, but this can, for instance, affect the |
346 | return value of subroutines: |
347 | |
348 | sub three_integer { use integer; return 3.2; } |
349 | sub three_bigint { use bigint; return 3.2; } |
350 | |
351 | print three_integer(), " ", three_bigint(),"\n"; # prints "3.2 3" |
126f3c5f |
352 | |
b68b7ab1 |
353 | =head2 Options |
126f3c5f |
354 | |
355 | bigint recognizes some options that can be passed while loading it via use. |
356 | The options can (currently) be either a single letter form, or the long form. |
357 | The following options exist: |
358 | |
359 | =over 2 |
360 | |
361 | =item a or accuracy |
362 | |
363 | This sets the accuracy for all math operations. The argument must be greater |
364 | than or equal to zero. See Math::BigInt's bround() function for details. |
365 | |
366 | perl -Mbigint=a,2 -le 'print 12345+1' |
367 | |
95a2d02c |
368 | Note that setting precision and accurary at the same time is not possible. |
369 | |
126f3c5f |
370 | =item p or precision |
371 | |
372 | This sets the precision for all math operations. The argument can be any |
373 | integer. Negative values mean a fixed number of digits after the dot, and |
374 | are <B>ignored</B> since all operations happen in integer space. |
375 | A positive value rounds to this digit left from the dot. 0 or 1 mean round to |
376 | integer and are ignore like negative values. |
377 | |
378 | See Math::BigInt's bfround() function for details. |
379 | |
380 | perl -Mbignum=p,5 -le 'print 123456789+123' |
381 | |
95a2d02c |
382 | Note that setting precision and accurary at the same time is not possible. |
383 | |
126f3c5f |
384 | =item t or trace |
385 | |
386 | This enables a trace mode and is primarily for debugging bigint or |
387 | Math::BigInt. |
388 | |
d1a15766 |
389 | =item hex |
390 | |
391 | Override the build-in hex() method with a version that can handle big |
392 | integers. Note that under Perl v5.9.4 or ealier, this will be global |
393 | and cannot be disabled with "no bigint;". |
394 | |
395 | =item oct |
396 | |
397 | Override the build-in oct() method with a version that can handle big |
398 | integers. Note that under Perl v5.9.4 or ealier, this will be global |
399 | and cannot be disabled with "no bigint;". |
400 | |
bd49aa09 |
401 | =item l, lib, try or only |
126f3c5f |
402 | |
bd49aa09 |
403 | Load a different math lib, see L<Math Library>. |
126f3c5f |
404 | |
bd49aa09 |
405 | perl -Mbigint=lib,GMP -e 'print 2 ** 512' |
406 | perl -Mbigint=try,GMP -e 'print 2 ** 512' |
407 | perl -Mbigint=only,GMP -e 'print 2 ** 512' |
126f3c5f |
408 | |
409 | Currently there is no way to specify more than one library on the command |
95a2d02c |
410 | line. This means the following does not work: |
411 | |
412 | perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512' |
413 | |
414 | This will be hopefully fixed soon ;) |
126f3c5f |
415 | |
416 | =item v or version |
417 | |
418 | This prints out the name and version of all modules used and then exits. |
419 | |
b68b7ab1 |
420 | perl -Mbigint=v |
126f3c5f |
421 | |
95a2d02c |
422 | =back |
423 | |
b68b7ab1 |
424 | =head2 Math Library |
126f3c5f |
425 | |
426 | Math with the numbers is done (by default) by a module called |
427 | Math::BigInt::Calc. This is equivalent to saying: |
428 | |
429 | use bigint lib => 'Calc'; |
430 | |
431 | You can change this by using: |
432 | |
bd49aa09 |
433 | use bignum lib => 'GMP'; |
126f3c5f |
434 | |
435 | The following would first try to find Math::BigInt::Foo, then |
436 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
437 | |
438 | use bigint lib => 'Foo,Math::BigInt::Bar'; |
439 | |
bd49aa09 |
440 | Using C<lib> warns if none of the specified libraries can be found and |
441 | L<Math::BigInt> did fall back to one of the default libraries. |
442 | To supress this warning, use C<try> instead: |
443 | |
444 | use bignum try => 'GMP'; |
445 | |
446 | If you want the code to die instead of falling back, use C<only> instead: |
447 | |
448 | use bignum only => 'GMP'; |
449 | |
126f3c5f |
450 | Please see respective module documentation for further details. |
451 | |
b68b7ab1 |
452 | =head2 Internal Format |
126f3c5f |
453 | |
454 | The numbers are stored as objects, and their internals might change at anytime, |
455 | especially between math operations. The objects also might belong to different |
456 | classes, like Math::BigInt, or Math::BigInt::Lite. Mixing them together, even |
457 | with normal scalars is not extraordinary, but normal and expected. |
458 | |
459 | You should not depend on the internal format, all accesses must go through |
990fb837 |
460 | accessor methods. E.g. looking at $x->{sign} is not a good idea since there |
126f3c5f |
461 | is no guaranty that the object in question has such a hash key, nor is a hash |
462 | underneath at all. |
463 | |
b68b7ab1 |
464 | =head2 Sign |
126f3c5f |
465 | |
b68b7ab1 |
466 | The sign is either '+', '-', 'NaN', '+inf' or '-inf'. |
126f3c5f |
467 | You can access it with the sign() method. |
468 | |
469 | A sign of 'NaN' is used to represent the result when input arguments are not |
470 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively |
471 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
472 | '-inf' when dividing any negative number by 0. |
473 | |
b68b7ab1 |
474 | =head2 Methods |
126f3c5f |
475 | |
476 | Since all numbers are now objects, you can use all functions that are part of |
477 | the BigInt API. You can only use the bxxx() notation, and not the fxxx() |
478 | notation, though. |
479 | |
95a2d02c |
480 | =over 2 |
481 | |
482 | =item inf() |
483 | |
484 | A shortcut to return Math::BigInt->binf(). Useful because Perl does not always |
485 | handle bareword C<inf> properly. |
486 | |
487 | =item NaN() |
488 | |
489 | A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always |
490 | handle bareword C<NaN> properly. |
491 | |
492 | =item upgrade() |
493 | |
494 | Return the class that numbers are upgraded to, is in fact returning |
495 | C<$Math::BigInt::upgrade>. |
496 | |
4440d13a |
497 | =item in_effect() |
498 | |
499 | use bigint; |
500 | |
501 | print "in effect\n" if bigint::in_effect; # true |
502 | { |
503 | no bigint; |
504 | print "in effect\n" if bigint::in_effect; # false |
505 | } |
506 | |
507 | Returns true or false if C<bigint> is in effect in the current scope. |
508 | |
509 | This method only works on Perl v5.9.4 or later. |
510 | |
95a2d02c |
511 | =back |
512 | |
513 | =head2 MATH LIBRARY |
514 | |
515 | Math with the numbers is done (by default) by a module called |
516 | |
b68b7ab1 |
517 | =head2 Caveat |
990fb837 |
518 | |
519 | But a warning is in order. When using the following to make a copy of a number, |
520 | only a shallow copy will be made. |
521 | |
522 | $x = 9; $y = $x; |
523 | $x = $y = 7; |
524 | |
525 | Using the copy or the original with overloaded math is okay, e.g. the |
526 | following work: |
527 | |
528 | $x = 9; $y = $x; |
529 | print $x + 1, " ", $y,"\n"; # prints 10 9 |
530 | |
531 | but calling any method that modifies the number directly will result in |
3c4b39be |
532 | B<both> the original and the copy being destroyed: |
990fb837 |
533 | |
534 | $x = 9; $y = $x; |
535 | print $x->badd(1), " ", $y,"\n"; # prints 10 10 |
536 | |
537 | $x = 9; $y = $x; |
538 | print $x->binc(1), " ", $y,"\n"; # prints 10 10 |
539 | |
540 | $x = 9; $y = $x; |
541 | print $x->bmul(2), " ", $y,"\n"; # prints 18 18 |
542 | |
543 | Using methods that do not modify, but testthe contents works: |
544 | |
545 | $x = 9; $y = $x; |
546 | $z = 9 if $x->is_zero(); # works fine |
547 | |
548 | See the documentation about the copy constructor and C<=> in overload, as |
549 | well as the documentation in BigInt for further details. |
550 | |
d1a15766 |
551 | =head1 CAVAETS |
552 | |
553 | =over 2 |
554 | |
555 | =item in_effect() |
556 | |
557 | This method only works on Perl v5.9.4 or later. |
558 | |
559 | =item hex()/oct() |
560 | |
561 | C<bigint> overrides these routines with versions that can also handle |
562 | big integer values. Under Perl prior to version v5.9.4, however, this |
563 | will not happen unless you specifically ask for it with the two |
564 | import tags "hex" and "oct" - and then it will be global and cannot be |
565 | disabled inside a scope with "no bigint": |
566 | |
567 | use bigint qw/hex oct/; |
568 | |
569 | print hex("0x1234567890123456"); |
570 | { |
571 | no bigint; |
572 | print hex("0x1234567890123456"); |
573 | } |
574 | |
575 | The second call to hex() will warn about a non-portable constant. |
576 | |
577 | Compare this to: |
578 | |
579 | use bigint; |
580 | |
581 | # will warn only under Perl older than v5.9.4 |
582 | print hex("0x1234567890123456"); |
583 | |
584 | =back |
585 | |
126f3c5f |
586 | =head1 MODULES USED |
587 | |
588 | C<bigint> is just a thin wrapper around various modules of the Math::BigInt |
589 | family. Think of it as the head of the family, who runs the shop, and orders |
590 | the others to do the work. |
591 | |
592 | The following modules are currently used by bigint: |
593 | |
594 | Math::BigInt::Lite (for speed, and only if it is loadable) |
595 | Math::BigInt |
596 | |
597 | =head1 EXAMPLES |
598 | |
599 | Some cool command line examples to impress the Python crowd ;) You might want |
600 | to compare them to the results under -Mbignum or -Mbigrat: |
601 | |
602 | perl -Mbigint -le 'print sqrt(33)' |
603 | perl -Mbigint -le 'print 2*255' |
604 | perl -Mbigint -le 'print 4.5+2*255' |
605 | perl -Mbigint -le 'print 3/7 + 5/7 + 8/3' |
606 | perl -Mbigint -le 'print 123->is_odd()' |
607 | perl -Mbigint -le 'print log(2)' |
608 | perl -Mbigint -le 'print 2 ** 0.5' |
609 | perl -Mbigint=a,65 -le 'print 2 ** 0.2' |
95a2d02c |
610 | perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777' |
126f3c5f |
611 | |
612 | =head1 LICENSE |
613 | |
614 | This program is free software; you may redistribute it and/or modify it under |
615 | the same terms as Perl itself. |
616 | |
617 | =head1 SEE ALSO |
618 | |
619 | Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'> and |
620 | L<bignum> as in C<perl -Mbignum -le 'print sqrt(2)'>. |
621 | |
622 | L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well |
623 | as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
624 | |
625 | =head1 AUTHORS |
626 | |
95a2d02c |
627 | (C) by Tels L<http://bloodgate.com/> in early 2002 - 2007. |
126f3c5f |
628 | |
629 | =cut |