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920dae64 AT |
1 | package Math::BigInt; |
2 | ||
3 | # | |
4 | # "Mike had an infinite amount to do and a negative amount of time in which | |
5 | # to do it." - Before and After | |
6 | # | |
7 | ||
8 | # The following hash values are used: | |
9 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) | |
10 | # sign : +,-,NaN,+inf,-inf | |
11 | # _a : accuracy | |
12 | # _p : precision | |
13 | # _f : flags, used by MBF to flag parts of a float as untouchable | |
14 | ||
15 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since | |
16 | # underlying lib might change the reference! | |
17 | ||
18 | my $class = "Math::BigInt"; | |
19 | require 5.005; | |
20 | ||
21 | $VERSION = '1.77'; | |
22 | ||
23 | @ISA = qw(Exporter); | |
24 | @EXPORT_OK = qw(objectify bgcd blcm); | |
25 | ||
26 | # _trap_inf and _trap_nan are internal and should never be accessed from the | |
27 | # outside | |
28 | use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode | |
29 | $upgrade $downgrade $_trap_nan $_trap_inf/; | |
30 | use strict; | |
31 | ||
32 | # Inside overload, the first arg is always an object. If the original code had | |
33 | # it reversed (like $x = 2 * $y), then the third paramater is true. | |
34 | # In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes | |
35 | # no difference, but in some cases it does. | |
36 | ||
37 | # For overloaded ops with only one argument we simple use $_[0]->copy() to | |
38 | # preserve the argument. | |
39 | ||
40 | # Thus inheritance of overload operators becomes possible and transparent for | |
41 | # our subclasses without the need to repeat the entire overload section there. | |
42 | ||
43 | use overload | |
44 | '=' => sub { $_[0]->copy(); }, | |
45 | ||
46 | # some shortcuts for speed (assumes that reversed order of arguments is routed | |
47 | # to normal '+' and we thus can always modify first arg. If this is changed, | |
48 | # this breaks and must be adjusted.) | |
49 | '+=' => sub { $_[0]->badd($_[1]); }, | |
50 | '-=' => sub { $_[0]->bsub($_[1]); }, | |
51 | '*=' => sub { $_[0]->bmul($_[1]); }, | |
52 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, | |
53 | '%=' => sub { $_[0]->bmod($_[1]); }, | |
54 | '^=' => sub { $_[0]->bxor($_[1]); }, | |
55 | '&=' => sub { $_[0]->band($_[1]); }, | |
56 | '|=' => sub { $_[0]->bior($_[1]); }, | |
57 | ||
58 | '**=' => sub { $_[0]->bpow($_[1]); }, | |
59 | '<<=' => sub { $_[0]->blsft($_[1]); }, | |
60 | '>>=' => sub { $_[0]->brsft($_[1]); }, | |
61 | ||
62 | # not supported by Perl yet | |
63 | '..' => \&_pointpoint, | |
64 | ||
65 | # we might need '==' and '!=' to get things like "NaN == NaN" right | |
66 | '<=>' => sub { $_[2] ? | |
67 | ref($_[0])->bcmp($_[1],$_[0]) : | |
68 | $_[0]->bcmp($_[1]); }, | |
69 | 'cmp' => sub { | |
70 | $_[2] ? | |
71 | "$_[1]" cmp $_[0]->bstr() : | |
72 | $_[0]->bstr() cmp "$_[1]" }, | |
73 | ||
74 | # make cos()/sin()/exp() "work" with BigInt's or subclasses | |
75 | 'cos' => sub { cos($_[0]->numify()) }, | |
76 | 'sin' => sub { sin($_[0]->numify()) }, | |
77 | 'exp' => sub { exp($_[0]->numify()) }, | |
78 | 'atan2' => sub { $_[2] ? | |
79 | atan2($_[1],$_[0]->numify()) : | |
80 | atan2($_[0]->numify(),$_[1]) }, | |
81 | ||
82 | # are not yet overloadable | |
83 | #'hex' => sub { print "hex"; $_[0]; }, | |
84 | #'oct' => sub { print "oct"; $_[0]; }, | |
85 | ||
86 | 'log' => sub { $_[0]->copy()->blog($_[1]); }, | |
87 | 'int' => sub { $_[0]->copy(); }, | |
88 | 'neg' => sub { $_[0]->copy()->bneg(); }, | |
89 | 'abs' => sub { $_[0]->copy()->babs(); }, | |
90 | 'sqrt' => sub { $_[0]->copy()->bsqrt(); }, | |
91 | '~' => sub { $_[0]->copy()->bnot(); }, | |
92 | ||
93 | # for subtract it's a bit tricky to not modify b: b-a => -a+b | |
94 | '-' => sub { my $c = $_[0]->copy; $_[2] ? | |
95 | $c->bneg()->badd( $_[1]) : | |
96 | $c->bsub( $_[1]) }, | |
97 | '+' => sub { $_[0]->copy()->badd($_[1]); }, | |
98 | '*' => sub { $_[0]->copy()->bmul($_[1]); }, | |
99 | ||
100 | '/' => sub { | |
101 | $_[2] ? ref($_[0])->new($_[1])->bdiv($_[0]) : $_[0]->copy->bdiv($_[1]); | |
102 | }, | |
103 | '%' => sub { | |
104 | $_[2] ? ref($_[0])->new($_[1])->bmod($_[0]) : $_[0]->copy->bmod($_[1]); | |
105 | }, | |
106 | '**' => sub { | |
107 | $_[2] ? ref($_[0])->new($_[1])->bpow($_[0]) : $_[0]->copy->bpow($_[1]); | |
108 | }, | |
109 | '<<' => sub { | |
110 | $_[2] ? ref($_[0])->new($_[1])->blsft($_[0]) : $_[0]->copy->blsft($_[1]); | |
111 | }, | |
112 | '>>' => sub { | |
113 | $_[2] ? ref($_[0])->new($_[1])->brsft($_[0]) : $_[0]->copy->brsft($_[1]); | |
114 | }, | |
115 | '&' => sub { | |
116 | $_[2] ? ref($_[0])->new($_[1])->band($_[0]) : $_[0]->copy->band($_[1]); | |
117 | }, | |
118 | '|' => sub { | |
119 | $_[2] ? ref($_[0])->new($_[1])->bior($_[0]) : $_[0]->copy->bior($_[1]); | |
120 | }, | |
121 | '^' => sub { | |
122 | $_[2] ? ref($_[0])->new($_[1])->bxor($_[0]) : $_[0]->copy->bxor($_[1]); | |
123 | }, | |
124 | ||
125 | # can modify arg of ++ and --, so avoid a copy() for speed, but don't | |
126 | # use $_[0]->bone(), it would modify $_[0] to be 1! | |
127 | '++' => sub { $_[0]->binc() }, | |
128 | '--' => sub { $_[0]->bdec() }, | |
129 | ||
130 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers | |
131 | 'bool' => sub { | |
132 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ | |
133 | # v5.6.1 dumps on this: return !$_[0]->is_zero() || undef; :-( | |
134 | my $t = undef; | |
135 | $t = 1 if !$_[0]->is_zero(); | |
136 | $t; | |
137 | }, | |
138 | ||
139 | # the original qw() does not work with the TIESCALAR below, why? | |
140 | # Order of arguments unsignificant | |
141 | '""' => sub { $_[0]->bstr(); }, | |
142 | '0+' => sub { $_[0]->numify(); } | |
143 | ; | |
144 | ||
145 | ############################################################################## | |
146 | # global constants, flags and accessory | |
147 | ||
148 | # These vars are public, but their direct usage is not recommended, use the | |
149 | # accessor methods instead | |
150 | ||
151 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' | |
152 | $accuracy = undef; | |
153 | $precision = undef; | |
154 | $div_scale = 40; | |
155 | ||
156 | $upgrade = undef; # default is no upgrade | |
157 | $downgrade = undef; # default is no downgrade | |
158 | ||
159 | # These are internally, and not to be used from the outside at all | |
160 | ||
161 | $_trap_nan = 0; # are NaNs ok? set w/ config() | |
162 | $_trap_inf = 0; # are infs ok? set w/ config() | |
163 | my $nan = 'NaN'; # constants for easier life | |
164 | ||
165 | my $CALC = 'Math::BigInt::FastCalc'; # module to do the low level math | |
166 | # default is FastCalc.pm | |
167 | my $IMPORT = 0; # was import() called yet? | |
168 | # used to make require work | |
169 | my %WARN; # warn only once for low-level libs | |
170 | my %CAN; # cache for $CALC->can(...) | |
171 | my %CALLBACKS; # callbacks to notify on lib loads | |
172 | my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math | |
173 | ||
174 | ############################################################################## | |
175 | # the old code had $rnd_mode, so we need to support it, too | |
176 | ||
177 | $rnd_mode = 'even'; | |
178 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } | |
179 | sub FETCH { return $round_mode; } | |
180 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } | |
181 | ||
182 | BEGIN | |
183 | { | |
184 | # tie to enable $rnd_mode to work transparently | |
185 | tie $rnd_mode, 'Math::BigInt'; | |
186 | ||
187 | # set up some handy alias names | |
188 | *as_int = \&as_number; | |
189 | *is_pos = \&is_positive; | |
190 | *is_neg = \&is_negative; | |
191 | } | |
192 | ||
193 | ############################################################################## | |
194 | ||
195 | sub round_mode | |
196 | { | |
197 | no strict 'refs'; | |
198 | # make Class->round_mode() work | |
199 | my $self = shift; | |
200 | my $class = ref($self) || $self || __PACKAGE__; | |
201 | if (defined $_[0]) | |
202 | { | |
203 | my $m = shift; | |
204 | if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/) | |
205 | { | |
206 | require Carp; Carp::croak ("Unknown round mode '$m'"); | |
207 | } | |
208 | return ${"${class}::round_mode"} = $m; | |
209 | } | |
210 | ${"${class}::round_mode"}; | |
211 | } | |
212 | ||
213 | sub upgrade | |
214 | { | |
215 | no strict 'refs'; | |
216 | # make Class->upgrade() work | |
217 | my $self = shift; | |
218 | my $class = ref($self) || $self || __PACKAGE__; | |
219 | # need to set new value? | |
220 | if (@_ > 0) | |
221 | { | |
222 | return ${"${class}::upgrade"} = $_[0]; | |
223 | } | |
224 | ${"${class}::upgrade"}; | |
225 | } | |
226 | ||
227 | sub downgrade | |
228 | { | |
229 | no strict 'refs'; | |
230 | # make Class->downgrade() work | |
231 | my $self = shift; | |
232 | my $class = ref($self) || $self || __PACKAGE__; | |
233 | # need to set new value? | |
234 | if (@_ > 0) | |
235 | { | |
236 | return ${"${class}::downgrade"} = $_[0]; | |
237 | } | |
238 | ${"${class}::downgrade"}; | |
239 | } | |
240 | ||
241 | sub div_scale | |
242 | { | |
243 | no strict 'refs'; | |
244 | # make Class->div_scale() work | |
245 | my $self = shift; | |
246 | my $class = ref($self) || $self || __PACKAGE__; | |
247 | if (defined $_[0]) | |
248 | { | |
249 | if ($_[0] < 0) | |
250 | { | |
251 | require Carp; Carp::croak ('div_scale must be greater than zero'); | |
252 | } | |
253 | ${"${class}::div_scale"} = $_[0]; | |
254 | } | |
255 | ${"${class}::div_scale"}; | |
256 | } | |
257 | ||
258 | sub accuracy | |
259 | { | |
260 | # $x->accuracy($a); ref($x) $a | |
261 | # $x->accuracy(); ref($x) | |
262 | # Class->accuracy(); class | |
263 | # Class->accuracy($a); class $a | |
264 | ||
265 | my $x = shift; | |
266 | my $class = ref($x) || $x || __PACKAGE__; | |
267 | ||
268 | no strict 'refs'; | |
269 | # need to set new value? | |
270 | if (@_ > 0) | |
271 | { | |
272 | my $a = shift; | |
273 | # convert objects to scalars to avoid deep recursion. If object doesn't | |
274 | # have numify(), then hopefully it will have overloading for int() and | |
275 | # boolean test without wandering into a deep recursion path... | |
276 | $a = $a->numify() if ref($a) && $a->can('numify'); | |
277 | ||
278 | if (defined $a) | |
279 | { | |
280 | # also croak on non-numerical | |
281 | if (!$a || $a <= 0) | |
282 | { | |
283 | require Carp; | |
284 | Carp::croak ('Argument to accuracy must be greater than zero'); | |
285 | } | |
286 | if (int($a) != $a) | |
287 | { | |
288 | require Carp; Carp::croak ('Argument to accuracy must be an integer'); | |
289 | } | |
290 | } | |
291 | if (ref($x)) | |
292 | { | |
293 | # $object->accuracy() or fallback to global | |
294 | $x->bround($a) if $a; # not for undef, 0 | |
295 | $x->{_a} = $a; # set/overwrite, even if not rounded | |
296 | delete $x->{_p}; # clear P | |
297 | $a = ${"${class}::accuracy"} unless defined $a; # proper return value | |
298 | } | |
299 | else | |
300 | { | |
301 | ${"${class}::accuracy"} = $a; # set global A | |
302 | ${"${class}::precision"} = undef; # clear global P | |
303 | } | |
304 | return $a; # shortcut | |
305 | } | |
306 | ||
307 | my $a; | |
308 | # $object->accuracy() or fallback to global | |
309 | $a = $x->{_a} if ref($x); | |
310 | # but don't return global undef, when $x's accuracy is 0! | |
311 | $a = ${"${class}::accuracy"} if !defined $a; | |
312 | $a; | |
313 | } | |
314 | ||
315 | sub precision | |
316 | { | |
317 | # $x->precision($p); ref($x) $p | |
318 | # $x->precision(); ref($x) | |
319 | # Class->precision(); class | |
320 | # Class->precision($p); class $p | |
321 | ||
322 | my $x = shift; | |
323 | my $class = ref($x) || $x || __PACKAGE__; | |
324 | ||
325 | no strict 'refs'; | |
326 | if (@_ > 0) | |
327 | { | |
328 | my $p = shift; | |
329 | # convert objects to scalars to avoid deep recursion. If object doesn't | |
330 | # have numify(), then hopefully it will have overloading for int() and | |
331 | # boolean test without wandering into a deep recursion path... | |
332 | $p = $p->numify() if ref($p) && $p->can('numify'); | |
333 | if ((defined $p) && (int($p) != $p)) | |
334 | { | |
335 | require Carp; Carp::croak ('Argument to precision must be an integer'); | |
336 | } | |
337 | if (ref($x)) | |
338 | { | |
339 | # $object->precision() or fallback to global | |
340 | $x->bfround($p) if $p; # not for undef, 0 | |
341 | $x->{_p} = $p; # set/overwrite, even if not rounded | |
342 | delete $x->{_a}; # clear A | |
343 | $p = ${"${class}::precision"} unless defined $p; # proper return value | |
344 | } | |
345 | else | |
346 | { | |
347 | ${"${class}::precision"} = $p; # set global P | |
348 | ${"${class}::accuracy"} = undef; # clear global A | |
349 | } | |
350 | return $p; # shortcut | |
351 | } | |
352 | ||
353 | my $p; | |
354 | # $object->precision() or fallback to global | |
355 | $p = $x->{_p} if ref($x); | |
356 | # but don't return global undef, when $x's precision is 0! | |
357 | $p = ${"${class}::precision"} if !defined $p; | |
358 | $p; | |
359 | } | |
360 | ||
361 | sub config | |
362 | { | |
363 | # return (or set) configuration data as hash ref | |
364 | my $class = shift || 'Math::BigInt'; | |
365 | ||
366 | no strict 'refs'; | |
367 | if (@_ > 0) | |
368 | { | |
369 | # try to set given options as arguments from hash | |
370 | ||
371 | my $args = $_[0]; | |
372 | if (ref($args) ne 'HASH') | |
373 | { | |
374 | $args = { @_ }; | |
375 | } | |
376 | # these values can be "set" | |
377 | my $set_args = {}; | |
378 | foreach my $key ( | |
379 | qw/trap_inf trap_nan | |
380 | upgrade downgrade precision accuracy round_mode div_scale/ | |
381 | ) | |
382 | { | |
383 | $set_args->{$key} = $args->{$key} if exists $args->{$key}; | |
384 | delete $args->{$key}; | |
385 | } | |
386 | if (keys %$args > 0) | |
387 | { | |
388 | require Carp; | |
389 | Carp::croak ("Illegal key(s) '", | |
390 | join("','",keys %$args),"' passed to $class\->config()"); | |
391 | } | |
392 | foreach my $key (keys %$set_args) | |
393 | { | |
394 | if ($key =~ /^trap_(inf|nan)\z/) | |
395 | { | |
396 | ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0); | |
397 | next; | |
398 | } | |
399 | # use a call instead of just setting the $variable to check argument | |
400 | $class->$key($set_args->{$key}); | |
401 | } | |
402 | } | |
403 | ||
404 | # now return actual configuration | |
405 | ||
406 | my $cfg = { | |
407 | lib => $CALC, | |
408 | lib_version => ${"${CALC}::VERSION"}, | |
409 | class => $class, | |
410 | trap_nan => ${"${class}::_trap_nan"}, | |
411 | trap_inf => ${"${class}::_trap_inf"}, | |
412 | version => ${"${class}::VERSION"}, | |
413 | }; | |
414 | foreach my $key (qw/ | |
415 | upgrade downgrade precision accuracy round_mode div_scale | |
416 | /) | |
417 | { | |
418 | $cfg->{$key} = ${"${class}::$key"}; | |
419 | }; | |
420 | $cfg; | |
421 | } | |
422 | ||
423 | sub _scale_a | |
424 | { | |
425 | # select accuracy parameter based on precedence, | |
426 | # used by bround() and bfround(), may return undef for scale (means no op) | |
427 | my ($x,$scale,$mode) = @_; | |
428 | ||
429 | $scale = $x->{_a} unless defined $scale; | |
430 | ||
431 | no strict 'refs'; | |
432 | my $class = ref($x); | |
433 | ||
434 | $scale = ${ $class . '::accuracy' } unless defined $scale; | |
435 | $mode = ${ $class . '::round_mode' } unless defined $mode; | |
436 | ||
437 | ($scale,$mode); | |
438 | } | |
439 | ||
440 | sub _scale_p | |
441 | { | |
442 | # select precision parameter based on precedence, | |
443 | # used by bround() and bfround(), may return undef for scale (means no op) | |
444 | my ($x,$scale,$mode) = @_; | |
445 | ||
446 | $scale = $x->{_p} unless defined $scale; | |
447 | ||
448 | no strict 'refs'; | |
449 | my $class = ref($x); | |
450 | ||
451 | $scale = ${ $class . '::precision' } unless defined $scale; | |
452 | $mode = ${ $class . '::round_mode' } unless defined $mode; | |
453 | ||
454 | ($scale,$mode); | |
455 | } | |
456 | ||
457 | ############################################################################## | |
458 | # constructors | |
459 | ||
460 | sub copy | |
461 | { | |
462 | my ($c,$x); | |
463 | if (@_ > 1) | |
464 | { | |
465 | # if two arguments, the first one is the class to "swallow" subclasses | |
466 | ($c,$x) = @_; | |
467 | } | |
468 | else | |
469 | { | |
470 | $x = shift; | |
471 | $c = ref($x); | |
472 | } | |
473 | return unless ref($x); # only for objects | |
474 | ||
475 | my $self = bless {}, $c; | |
476 | ||
477 | $self->{sign} = $x->{sign}; | |
478 | $self->{value} = $CALC->_copy($x->{value}); | |
479 | $self->{_a} = $x->{_a} if defined $x->{_a}; | |
480 | $self->{_p} = $x->{_p} if defined $x->{_p}; | |
481 | $self; | |
482 | } | |
483 | ||
484 | sub new | |
485 | { | |
486 | # create a new BigInt object from a string or another BigInt object. | |
487 | # see hash keys documented at top | |
488 | ||
489 | # the argument could be an object, so avoid ||, && etc on it, this would | |
490 | # cause costly overloaded code to be called. The only allowed ops are | |
491 | # ref() and defined. | |
492 | ||
493 | my ($class,$wanted,$a,$p,$r) = @_; | |
494 | ||
495 | # avoid numify-calls by not using || on $wanted! | |
496 | return $class->bzero($a,$p) if !defined $wanted; # default to 0 | |
497 | return $class->copy($wanted,$a,$p,$r) | |
498 | if ref($wanted) && $wanted->isa($class); # MBI or subclass | |
499 | ||
500 | $class->import() if $IMPORT == 0; # make require work | |
501 | ||
502 | my $self = bless {}, $class; | |
503 | ||
504 | # shortcut for "normal" numbers | |
505 | if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/)) | |
506 | { | |
507 | $self->{sign} = $1 || '+'; | |
508 | ||
509 | if ($wanted =~ /^[+-]/) | |
510 | { | |
511 | # remove sign without touching wanted to make it work with constants | |
512 | my $t = $wanted; $t =~ s/^[+-]//; | |
513 | $self->{value} = $CALC->_new($t); | |
514 | } | |
515 | else | |
516 | { | |
517 | $self->{value} = $CALC->_new($wanted); | |
518 | } | |
519 | no strict 'refs'; | |
520 | if ( (defined $a) || (defined $p) | |
521 | || (defined ${"${class}::precision"}) | |
522 | || (defined ${"${class}::accuracy"}) | |
523 | ) | |
524 | { | |
525 | $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p); | |
526 | } | |
527 | return $self; | |
528 | } | |
529 | ||
530 | # handle '+inf', '-inf' first | |
531 | if ($wanted =~ /^[+-]?inf\z/) | |
532 | { | |
533 | $self->{sign} = $wanted; # set a default sign for bstr() | |
534 | return $self->binf($wanted); | |
535 | } | |
536 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign | |
537 | my ($mis,$miv,$mfv,$es,$ev) = _split($wanted); | |
538 | if (!ref $mis) | |
539 | { | |
540 | if ($_trap_nan) | |
541 | { | |
542 | require Carp; Carp::croak("$wanted is not a number in $class"); | |
543 | } | |
544 | $self->{value} = $CALC->_zero(); | |
545 | $self->{sign} = $nan; | |
546 | return $self; | |
547 | } | |
548 | if (!ref $miv) | |
549 | { | |
550 | # _from_hex or _from_bin | |
551 | $self->{value} = $mis->{value}; | |
552 | $self->{sign} = $mis->{sign}; | |
553 | return $self; # throw away $mis | |
554 | } | |
555 | # make integer from mantissa by adjusting exp, then convert to bigint | |
556 | $self->{sign} = $$mis; # store sign | |
557 | $self->{value} = $CALC->_zero(); # for all the NaN cases | |
558 | my $e = int("$$es$$ev"); # exponent (avoid recursion) | |
559 | if ($e > 0) | |
560 | { | |
561 | my $diff = $e - CORE::length($$mfv); | |
562 | if ($diff < 0) # Not integer | |
563 | { | |
564 | if ($_trap_nan) | |
565 | { | |
566 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
567 | } | |
568 | #print "NOI 1\n"; | |
569 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; | |
570 | $self->{sign} = $nan; | |
571 | } | |
572 | else # diff >= 0 | |
573 | { | |
574 | # adjust fraction and add it to value | |
575 | #print "diff > 0 $$miv\n"; | |
576 | $$miv = $$miv . ($$mfv . '0' x $diff); | |
577 | } | |
578 | } | |
579 | else | |
580 | { | |
581 | if ($$mfv ne '') # e <= 0 | |
582 | { | |
583 | # fraction and negative/zero E => NOI | |
584 | if ($_trap_nan) | |
585 | { | |
586 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
587 | } | |
588 | #print "NOI 2 \$\$mfv '$$mfv'\n"; | |
589 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; | |
590 | $self->{sign} = $nan; | |
591 | } | |
592 | elsif ($e < 0) | |
593 | { | |
594 | # xE-y, and empty mfv | |
595 | #print "xE-y\n"; | |
596 | $e = abs($e); | |
597 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? | |
598 | { | |
599 | if ($_trap_nan) | |
600 | { | |
601 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
602 | } | |
603 | #print "NOI 3\n"; | |
604 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; | |
605 | $self->{sign} = $nan; | |
606 | } | |
607 | } | |
608 | } | |
609 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 | |
610 | $self->{value} = $CALC->_new($$miv) if $self->{sign} =~ /^[+-]$/; | |
611 | # if any of the globals is set, use them to round and store them inside $self | |
612 | # do not round for new($x,undef,undef) since that is used by MBF to signal | |
613 | # no rounding | |
614 | $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p; | |
615 | $self; | |
616 | } | |
617 | ||
618 | sub bnan | |
619 | { | |
620 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' | |
621 | my $self = shift; | |
622 | $self = $class if !defined $self; | |
623 | if (!ref($self)) | |
624 | { | |
625 | my $c = $self; $self = {}; bless $self, $c; | |
626 | } | |
627 | no strict 'refs'; | |
628 | if (${"${class}::_trap_nan"}) | |
629 | { | |
630 | require Carp; | |
631 | Carp::croak ("Tried to set $self to NaN in $class\::bnan()"); | |
632 | } | |
633 | $self->import() if $IMPORT == 0; # make require work | |
634 | return if $self->modify('bnan'); | |
635 | if ($self->can('_bnan')) | |
636 | { | |
637 | # use subclass to initialize | |
638 | $self->_bnan(); | |
639 | } | |
640 | else | |
641 | { | |
642 | # otherwise do our own thing | |
643 | $self->{value} = $CALC->_zero(); | |
644 | } | |
645 | $self->{sign} = $nan; | |
646 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly | |
647 | $self; | |
648 | } | |
649 | ||
650 | sub binf | |
651 | { | |
652 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' | |
653 | # the sign is either '+', or if given, used from there | |
654 | my $self = shift; | |
655 | my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/; | |
656 | $self = $class if !defined $self; | |
657 | if (!ref($self)) | |
658 | { | |
659 | my $c = $self; $self = {}; bless $self, $c; | |
660 | } | |
661 | no strict 'refs'; | |
662 | if (${"${class}::_trap_inf"}) | |
663 | { | |
664 | require Carp; | |
665 | Carp::croak ("Tried to set $self to +-inf in $class\::binf()"); | |
666 | } | |
667 | $self->import() if $IMPORT == 0; # make require work | |
668 | return if $self->modify('binf'); | |
669 | if ($self->can('_binf')) | |
670 | { | |
671 | # use subclass to initialize | |
672 | $self->_binf(); | |
673 | } | |
674 | else | |
675 | { | |
676 | # otherwise do our own thing | |
677 | $self->{value} = $CALC->_zero(); | |
678 | } | |
679 | $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf | |
680 | $self->{sign} = $sign; | |
681 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding | |
682 | $self; | |
683 | } | |
684 | ||
685 | sub bzero | |
686 | { | |
687 | # create a bigint '+0', if given a BigInt, set it to 0 | |
688 | my $self = shift; | |
689 | $self = __PACKAGE__ if !defined $self; | |
690 | ||
691 | if (!ref($self)) | |
692 | { | |
693 | my $c = $self; $self = {}; bless $self, $c; | |
694 | } | |
695 | $self->import() if $IMPORT == 0; # make require work | |
696 | return if $self->modify('bzero'); | |
697 | ||
698 | if ($self->can('_bzero')) | |
699 | { | |
700 | # use subclass to initialize | |
701 | $self->_bzero(); | |
702 | } | |
703 | else | |
704 | { | |
705 | # otherwise do our own thing | |
706 | $self->{value} = $CALC->_zero(); | |
707 | } | |
708 | $self->{sign} = '+'; | |
709 | if (@_ > 0) | |
710 | { | |
711 | if (@_ > 3) | |
712 | { | |
713 | # call like: $x->bzero($a,$p,$r,$y); | |
714 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); | |
715 | } | |
716 | else | |
717 | { | |
718 | $self->{_a} = $_[0] | |
719 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); | |
720 | $self->{_p} = $_[1] | |
721 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); | |
722 | } | |
723 | } | |
724 | $self; | |
725 | } | |
726 | ||
727 | sub bone | |
728 | { | |
729 | # create a bigint '+1' (or -1 if given sign '-'), | |
730 | # if given a BigInt, set it to +1 or -1, respecively | |
731 | my $self = shift; | |
732 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; | |
733 | $self = $class if !defined $self; | |
734 | ||
735 | if (!ref($self)) | |
736 | { | |
737 | my $c = $self; $self = {}; bless $self, $c; | |
738 | } | |
739 | $self->import() if $IMPORT == 0; # make require work | |
740 | return if $self->modify('bone'); | |
741 | ||
742 | if ($self->can('_bone')) | |
743 | { | |
744 | # use subclass to initialize | |
745 | $self->_bone(); | |
746 | } | |
747 | else | |
748 | { | |
749 | # otherwise do our own thing | |
750 | $self->{value} = $CALC->_one(); | |
751 | } | |
752 | $self->{sign} = $sign; | |
753 | if (@_ > 0) | |
754 | { | |
755 | if (@_ > 3) | |
756 | { | |
757 | # call like: $x->bone($sign,$a,$p,$r,$y); | |
758 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); | |
759 | } | |
760 | else | |
761 | { | |
762 | # call like: $x->bone($sign,$a,$p,$r); | |
763 | $self->{_a} = $_[0] | |
764 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); | |
765 | $self->{_p} = $_[1] | |
766 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); | |
767 | } | |
768 | } | |
769 | $self; | |
770 | } | |
771 | ||
772 | ############################################################################## | |
773 | # string conversation | |
774 | ||
775 | sub bsstr | |
776 | { | |
777 | # (ref to BFLOAT or num_str ) return num_str | |
778 | # Convert number from internal format to scientific string format. | |
779 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") | |
780 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
781 | ||
782 | if ($x->{sign} !~ /^[+-]$/) | |
783 | { | |
784 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
785 | return 'inf'; # +inf | |
786 | } | |
787 | my ($m,$e) = $x->parts(); | |
788 | #$m->bstr() . 'e+' . $e->bstr(); # e can only be positive in BigInt | |
789 | # 'e+' because E can only be positive in BigInt | |
790 | $m->bstr() . 'e+' . $CALC->_str($e->{value}); | |
791 | } | |
792 | ||
793 | sub bstr | |
794 | { | |
795 | # make a string from bigint object | |
796 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
797 | ||
798 | if ($x->{sign} !~ /^[+-]$/) | |
799 | { | |
800 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
801 | return 'inf'; # +inf | |
802 | } | |
803 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; | |
804 | $es.$CALC->_str($x->{value}); | |
805 | } | |
806 | ||
807 | sub numify | |
808 | { | |
809 | # Make a "normal" scalar from a BigInt object | |
810 | my $x = shift; $x = $class->new($x) unless ref $x; | |
811 | ||
812 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; | |
813 | my $num = $CALC->_num($x->{value}); | |
814 | return -$num if $x->{sign} eq '-'; | |
815 | $num; | |
816 | } | |
817 | ||
818 | ############################################################################## | |
819 | # public stuff (usually prefixed with "b") | |
820 | ||
821 | sub sign | |
822 | { | |
823 | # return the sign of the number: +/-/-inf/+inf/NaN | |
824 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
825 | ||
826 | $x->{sign}; | |
827 | } | |
828 | ||
829 | sub _find_round_parameters | |
830 | { | |
831 | # After any operation or when calling round(), the result is rounded by | |
832 | # regarding the A & P from arguments, local parameters, or globals. | |
833 | ||
834 | # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!! | |
835 | ||
836 | # This procedure finds the round parameters, but it is for speed reasons | |
837 | # duplicated in round. Otherwise, it is tested by the testsuite and used | |
838 | # by fdiv(). | |
839 | ||
840 | # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P | |
841 | # were requested/defined (locally or globally or both) | |
842 | ||
843 | my ($self,$a,$p,$r,@args) = @_; | |
844 | # $a accuracy, if given by caller | |
845 | # $p precision, if given by caller | |
846 | # $r round_mode, if given by caller | |
847 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
848 | ||
849 | my $c = ref($self); # find out class of argument(s) | |
850 | no strict 'refs'; | |
851 | ||
852 | # now pick $a or $p, but only if we have got "arguments" | |
853 | if (!defined $a) | |
854 | { | |
855 | foreach ($self,@args) | |
856 | { | |
857 | # take the defined one, or if both defined, the one that is smaller | |
858 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
859 | } | |
860 | } | |
861 | if (!defined $p) | |
862 | { | |
863 | # even if $a is defined, take $p, to signal error for both defined | |
864 | foreach ($self,@args) | |
865 | { | |
866 | # take the defined one, or if both defined, the one that is bigger | |
867 | # -2 > -3, and 3 > 2 | |
868 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
869 | } | |
870 | } | |
871 | # if still none defined, use globals (#2) | |
872 | $a = ${"$c\::accuracy"} unless defined $a; | |
873 | $p = ${"$c\::precision"} unless defined $p; | |
874 | ||
875 | # A == 0 is useless, so undef it to signal no rounding | |
876 | $a = undef if defined $a && $a == 0; | |
877 | ||
878 | # no rounding today? | |
879 | return ($self) unless defined $a || defined $p; # early out | |
880 | ||
881 | # set A and set P is an fatal error | |
882 | return ($self->bnan()) if defined $a && defined $p; # error | |
883 | ||
884 | $r = ${"$c\::round_mode"} unless defined $r; | |
885 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/) | |
886 | { | |
887 | require Carp; Carp::croak ("Unknown round mode '$r'"); | |
888 | } | |
889 | ||
890 | ($self,$a,$p,$r); | |
891 | } | |
892 | ||
893 | sub round | |
894 | { | |
895 | # Round $self according to given parameters, or given second argument's | |
896 | # parameters or global defaults | |
897 | ||
898 | # for speed reasons, _find_round_parameters is embeded here: | |
899 | ||
900 | my ($self,$a,$p,$r,@args) = @_; | |
901 | # $a accuracy, if given by caller | |
902 | # $p precision, if given by caller | |
903 | # $r round_mode, if given by caller | |
904 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
905 | ||
906 | my $c = ref($self); # find out class of argument(s) | |
907 | no strict 'refs'; | |
908 | ||
909 | # now pick $a or $p, but only if we have got "arguments" | |
910 | if (!defined $a) | |
911 | { | |
912 | foreach ($self,@args) | |
913 | { | |
914 | # take the defined one, or if both defined, the one that is smaller | |
915 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
916 | } | |
917 | } | |
918 | if (!defined $p) | |
919 | { | |
920 | # even if $a is defined, take $p, to signal error for both defined | |
921 | foreach ($self,@args) | |
922 | { | |
923 | # take the defined one, or if both defined, the one that is bigger | |
924 | # -2 > -3, and 3 > 2 | |
925 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
926 | } | |
927 | } | |
928 | # if still none defined, use globals (#2) | |
929 | $a = ${"$c\::accuracy"} unless defined $a; | |
930 | $p = ${"$c\::precision"} unless defined $p; | |
931 | ||
932 | # A == 0 is useless, so undef it to signal no rounding | |
933 | $a = undef if defined $a && $a == 0; | |
934 | ||
935 | # no rounding today? | |
936 | return $self unless defined $a || defined $p; # early out | |
937 | ||
938 | # set A and set P is an fatal error | |
939 | return $self->bnan() if defined $a && defined $p; | |
940 | ||
941 | $r = ${"$c\::round_mode"} unless defined $r; | |
942 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/) | |
943 | { | |
944 | require Carp; Carp::croak ("Unknown round mode '$r'"); | |
945 | } | |
946 | ||
947 | # now round, by calling either fround or ffround: | |
948 | if (defined $a) | |
949 | { | |
950 | $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a; | |
951 | } | |
952 | else # both can't be undefined due to early out | |
953 | { | |
954 | $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p; | |
955 | } | |
956 | # bround() or bfround() already callled bnorm() if necc. | |
957 | $self; | |
958 | } | |
959 | ||
960 | sub bnorm | |
961 | { | |
962 | # (numstr or BINT) return BINT | |
963 | # Normalize number -- no-op here | |
964 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
965 | $x; | |
966 | } | |
967 | ||
968 | sub babs | |
969 | { | |
970 | # (BINT or num_str) return BINT | |
971 | # make number absolute, or return absolute BINT from string | |
972 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
973 | ||
974 | return $x if $x->modify('babs'); | |
975 | # post-normalized abs for internal use (does nothing for NaN) | |
976 | $x->{sign} =~ s/^-/+/; | |
977 | $x; | |
978 | } | |
979 | ||
980 | sub bneg | |
981 | { | |
982 | # (BINT or num_str) return BINT | |
983 | # negate number or make a negated number from string | |
984 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
985 | ||
986 | return $x if $x->modify('bneg'); | |
987 | ||
988 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN' | |
989 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value})); | |
990 | $x; | |
991 | } | |
992 | ||
993 | sub bcmp | |
994 | { | |
995 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
996 | # (BINT or num_str, BINT or num_str) return cond_code | |
997 | ||
998 | # set up parameters | |
999 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1000 | ||
1001 | # objectify is costly, so avoid it | |
1002 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1003 | { | |
1004 | ($self,$x,$y) = objectify(2,@_); | |
1005 | } | |
1006 | ||
1007 | return $upgrade->bcmp($x,$y) if defined $upgrade && | |
1008 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1009 | ||
1010 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1011 | { | |
1012 | # handle +-inf and NaN | |
1013 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1014 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; | |
1015 | return +1 if $x->{sign} eq '+inf'; | |
1016 | return -1 if $x->{sign} eq '-inf'; | |
1017 | return -1 if $y->{sign} eq '+inf'; | |
1018 | return +1; | |
1019 | } | |
1020 | # check sign for speed first | |
1021 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
1022 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
1023 | ||
1024 | # have same sign, so compare absolute values. Don't make tests for zero here | |
1025 | # because it's actually slower than testin in Calc (especially w/ Pari et al) | |
1026 | ||
1027 | # post-normalized compare for internal use (honors signs) | |
1028 | if ($x->{sign} eq '+') | |
1029 | { | |
1030 | # $x and $y both > 0 | |
1031 | return $CALC->_acmp($x->{value},$y->{value}); | |
1032 | } | |
1033 | ||
1034 | # $x && $y both < 0 | |
1035 | $CALC->_acmp($y->{value},$x->{value}); # swaped acmp (lib returns 0,1,-1) | |
1036 | } | |
1037 | ||
1038 | sub bacmp | |
1039 | { | |
1040 | # Compares 2 values, ignoring their signs. | |
1041 | # Returns one of undef, <0, =0, >0. (suitable for sort) | |
1042 | # (BINT, BINT) return cond_code | |
1043 | ||
1044 | # set up parameters | |
1045 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1046 | # objectify is costly, so avoid it | |
1047 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1048 | { | |
1049 | ($self,$x,$y) = objectify(2,@_); | |
1050 | } | |
1051 | ||
1052 | return $upgrade->bacmp($x,$y) if defined $upgrade && | |
1053 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1054 | ||
1055 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1056 | { | |
1057 | # handle +-inf and NaN | |
1058 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1059 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
1060 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; | |
1061 | return -1; | |
1062 | } | |
1063 | $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1 | |
1064 | } | |
1065 | ||
1066 | sub badd | |
1067 | { | |
1068 | # add second arg (BINT or string) to first (BINT) (modifies first) | |
1069 | # return result as BINT | |
1070 | ||
1071 | # set up parameters | |
1072 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1073 | # objectify is costly, so avoid it | |
1074 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1075 | { | |
1076 | ($self,$x,$y,@r) = objectify(2,@_); | |
1077 | } | |
1078 | ||
1079 | return $x if $x->modify('badd'); | |
1080 | return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade && | |
1081 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1082 | ||
1083 | $r[3] = $y; # no push! | |
1084 | # inf and NaN handling | |
1085 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1086 | { | |
1087 | # NaN first | |
1088 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1089 | # inf handling | |
1090 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
1091 | { | |
1092 | # +inf++inf or -inf+-inf => same, rest is NaN | |
1093 | return $x if $x->{sign} eq $y->{sign}; | |
1094 | return $x->bnan(); | |
1095 | } | |
1096 | # +-inf + something => +inf | |
1097 | # something +-inf => +-inf | |
1098 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; | |
1099 | return $x; | |
1100 | } | |
1101 | ||
1102 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs | |
1103 | ||
1104 | if ($sx eq $sy) | |
1105 | { | |
1106 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add | |
1107 | } | |
1108 | else | |
1109 | { | |
1110 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare | |
1111 | if ($a > 0) | |
1112 | { | |
1113 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap | |
1114 | $x->{sign} = $sy; | |
1115 | } | |
1116 | elsif ($a == 0) | |
1117 | { | |
1118 | # speedup, if equal, set result to 0 | |
1119 | $x->{value} = $CALC->_zero(); | |
1120 | $x->{sign} = '+'; | |
1121 | } | |
1122 | else # a < 0 | |
1123 | { | |
1124 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub | |
1125 | } | |
1126 | } | |
1127 | $x->round(@r); | |
1128 | } | |
1129 | ||
1130 | sub bsub | |
1131 | { | |
1132 | # (BINT or num_str, BINT or num_str) return BINT | |
1133 | # subtract second arg from first, modify first | |
1134 | ||
1135 | # set up parameters | |
1136 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1137 | # objectify is costly, so avoid it | |
1138 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1139 | { | |
1140 | ($self,$x,$y,@r) = objectify(2,@_); | |
1141 | } | |
1142 | ||
1143 | return $x if $x->modify('bsub'); | |
1144 | ||
1145 | return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade && | |
1146 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1147 | ||
1148 | return $x->round(@r) if $y->is_zero(); | |
1149 | ||
1150 | # To correctly handle the lone special case $x->bsub($x), we note the sign | |
1151 | # of $x, then flip the sign from $y, and if the sign of $x did change, too, | |
1152 | # then we caught the special case: | |
1153 | my $xsign = $x->{sign}; | |
1154 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN | |
1155 | if ($xsign ne $x->{sign}) | |
1156 | { | |
1157 | # special case of $x->bsub($x) results in 0 | |
1158 | return $x->bzero(@r) if $xsign =~ /^[+-]$/; | |
1159 | return $x->bnan(); # NaN, -inf, +inf | |
1160 | } | |
1161 | $x->badd($y,@r); # badd does not leave internal zeros | |
1162 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) | |
1163 | $x; # already rounded by badd() or no round necc. | |
1164 | } | |
1165 | ||
1166 | sub binc | |
1167 | { | |
1168 | # increment arg by one | |
1169 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
1170 | return $x if $x->modify('binc'); | |
1171 | ||
1172 | if ($x->{sign} eq '+') | |
1173 | { | |
1174 | $x->{value} = $CALC->_inc($x->{value}); | |
1175 | return $x->round($a,$p,$r); | |
1176 | } | |
1177 | elsif ($x->{sign} eq '-') | |
1178 | { | |
1179 | $x->{value} = $CALC->_dec($x->{value}); | |
1180 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 | |
1181 | return $x->round($a,$p,$r); | |
1182 | } | |
1183 | # inf, nan handling etc | |
1184 | $x->badd($self->bone(),$a,$p,$r); # badd does round | |
1185 | } | |
1186 | ||
1187 | sub bdec | |
1188 | { | |
1189 | # decrement arg by one | |
1190 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
1191 | return $x if $x->modify('bdec'); | |
1192 | ||
1193 | if ($x->{sign} eq '-') | |
1194 | { | |
1195 | # x already < 0 | |
1196 | $x->{value} = $CALC->_inc($x->{value}); | |
1197 | } | |
1198 | else | |
1199 | { | |
1200 | return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf or NaN | |
1201 | # >= 0 | |
1202 | if ($CALC->_is_zero($x->{value})) | |
1203 | { | |
1204 | # == 0 | |
1205 | $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1 | |
1206 | } | |
1207 | else | |
1208 | { | |
1209 | # > 0 | |
1210 | $x->{value} = $CALC->_dec($x->{value}); | |
1211 | } | |
1212 | } | |
1213 | $x->round(@r); | |
1214 | } | |
1215 | ||
1216 | sub blog | |
1217 | { | |
1218 | # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base | |
1219 | # $base of $x) | |
1220 | ||
1221 | # set up parameters | |
1222 | my ($self,$x,$base,@r) = (undef,@_); | |
1223 | # objectify is costly, so avoid it | |
1224 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1225 | { | |
1226 | ($self,$x,$base,@r) = objectify(1,ref($x),@_); | |
1227 | } | |
1228 | ||
1229 | return $x if $x->modify('blog'); | |
1230 | ||
1231 | # inf, -inf, NaN, <0 => NaN | |
1232 | return $x->bnan() | |
1233 | if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+'); | |
1234 | ||
1235 | return $upgrade->blog($upgrade->new($x),$base,@r) if | |
1236 | defined $upgrade; | |
1237 | ||
1238 | my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value}); | |
1239 | return $x->bnan() unless defined $rc; # not possible to take log? | |
1240 | $x->{value} = $rc; | |
1241 | $x->round(@r); | |
1242 | } | |
1243 | ||
1244 | sub blcm | |
1245 | { | |
1246 | # (BINT or num_str, BINT or num_str) return BINT | |
1247 | # does not modify arguments, but returns new object | |
1248 | # Lowest Common Multiplicator | |
1249 | ||
1250 | my $y = shift; my ($x); | |
1251 | if (ref($y)) | |
1252 | { | |
1253 | $x = $y->copy(); | |
1254 | } | |
1255 | else | |
1256 | { | |
1257 | $x = $class->new($y); | |
1258 | } | |
1259 | my $self = ref($x); | |
1260 | while (@_) | |
1261 | { | |
1262 | my $y = shift; $y = $self->new($y) if !ref ($y); | |
1263 | $x = __lcm($x,$y); | |
1264 | } | |
1265 | $x; | |
1266 | } | |
1267 | ||
1268 | sub bgcd | |
1269 | { | |
1270 | # (BINT or num_str, BINT or num_str) return BINT | |
1271 | # does not modify arguments, but returns new object | |
1272 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) | |
1273 | ||
1274 | my $y = shift; | |
1275 | $y = $class->new($y) if !ref($y); | |
1276 | my $self = ref($y); | |
1277 | my $x = $y->copy()->babs(); # keep arguments | |
1278 | return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN? | |
1279 | ||
1280 | while (@_) | |
1281 | { | |
1282 | $y = shift; $y = $self->new($y) if !ref($y); | |
1283 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? | |
1284 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); | |
1285 | last if $CALC->_is_one($x->{value}); | |
1286 | } | |
1287 | $x; | |
1288 | } | |
1289 | ||
1290 | sub bnot | |
1291 | { | |
1292 | # (num_str or BINT) return BINT | |
1293 | # represent ~x as twos-complement number | |
1294 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster | |
1295 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1296 | ||
1297 | return $x if $x->modify('bnot'); | |
1298 | $x->binc()->bneg(); # binc already does round | |
1299 | } | |
1300 | ||
1301 | ############################################################################## | |
1302 | # is_foo test routines | |
1303 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster | |
1304 | ||
1305 | sub is_zero | |
1306 | { | |
1307 | # return true if arg (BINT or num_str) is zero (array '+', '0') | |
1308 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1309 | ||
1310 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't | |
1311 | $CALC->_is_zero($x->{value}); | |
1312 | } | |
1313 | ||
1314 | sub is_nan | |
1315 | { | |
1316 | # return true if arg (BINT or num_str) is NaN | |
1317 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1318 | ||
1319 | $x->{sign} eq $nan ? 1 : 0; | |
1320 | } | |
1321 | ||
1322 | sub is_inf | |
1323 | { | |
1324 | # return true if arg (BINT or num_str) is +-inf | |
1325 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1326 | ||
1327 | if (defined $sign) | |
1328 | { | |
1329 | $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf | |
1330 | $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-' | |
1331 | return $x->{sign} =~ /^$sign$/ ? 1 : 0; | |
1332 | } | |
1333 | $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity | |
1334 | } | |
1335 | ||
1336 | sub is_one | |
1337 | { | |
1338 | # return true if arg (BINT or num_str) is +1, or -1 if sign is given | |
1339 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1340 | ||
1341 | $sign = '+' if !defined $sign || $sign ne '-'; | |
1342 | ||
1343 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either | |
1344 | $CALC->_is_one($x->{value}); | |
1345 | } | |
1346 | ||
1347 | sub is_odd | |
1348 | { | |
1349 | # return true when arg (BINT or num_str) is odd, false for even | |
1350 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1351 | ||
1352 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't | |
1353 | $CALC->_is_odd($x->{value}); | |
1354 | } | |
1355 | ||
1356 | sub is_even | |
1357 | { | |
1358 | # return true when arg (BINT or num_str) is even, false for odd | |
1359 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1360 | ||
1361 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't | |
1362 | $CALC->_is_even($x->{value}); | |
1363 | } | |
1364 | ||
1365 | sub is_positive | |
1366 | { | |
1367 | # return true when arg (BINT or num_str) is positive (>= 0) | |
1368 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1369 | ||
1370 | return 1 if $x->{sign} eq '+inf'; # +inf is positive | |
1371 | ||
1372 | # 0+ is neither positive nor negative | |
1373 | ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0; | |
1374 | } | |
1375 | ||
1376 | sub is_negative | |
1377 | { | |
1378 | # return true when arg (BINT or num_str) is negative (< 0) | |
1379 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1380 | ||
1381 | $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not | |
1382 | } | |
1383 | ||
1384 | sub is_int | |
1385 | { | |
1386 | # return true when arg (BINT or num_str) is an integer | |
1387 | # always true for BigInt, but different for BigFloats | |
1388 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1389 | ||
1390 | $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't | |
1391 | } | |
1392 | ||
1393 | ############################################################################### | |
1394 | ||
1395 | sub bmul | |
1396 | { | |
1397 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 | |
1398 | # (BINT or num_str, BINT or num_str) return BINT | |
1399 | ||
1400 | # set up parameters | |
1401 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1402 | # objectify is costly, so avoid it | |
1403 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1404 | { | |
1405 | ($self,$x,$y,@r) = objectify(2,@_); | |
1406 | } | |
1407 | ||
1408 | return $x if $x->modify('bmul'); | |
1409 | ||
1410 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1411 | ||
1412 | # inf handling | |
1413 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1414 | { | |
1415 | return $x->bnan() if $x->is_zero() || $y->is_zero(); | |
1416 | # result will always be +-inf: | |
1417 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
1418 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
1419 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
1420 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
1421 | return $x->binf('-'); | |
1422 | } | |
1423 | ||
1424 | return $upgrade->bmul($x,$upgrade->new($y),@r) | |
1425 | if defined $upgrade && !$y->isa($self); | |
1426 | ||
1427 | $r[3] = $y; # no push here | |
1428 | ||
1429 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + | |
1430 | ||
1431 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math | |
1432 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 | |
1433 | ||
1434 | $x->round(@r); | |
1435 | } | |
1436 | ||
1437 | sub _div_inf | |
1438 | { | |
1439 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code | |
1440 | my ($self,$x,$y) = @_; | |
1441 | ||
1442 | # NaN if x == NaN or y == NaN or x==y==0 | |
1443 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() | |
1444 | if (($x->is_nan() || $y->is_nan()) || | |
1445 | ($x->is_zero() && $y->is_zero())); | |
1446 | ||
1447 | # +-inf / +-inf == NaN, reminder also NaN | |
1448 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
1449 | { | |
1450 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan(); | |
1451 | } | |
1452 | # x / +-inf => 0, remainder x (works even if x == 0) | |
1453 | if ($y->{sign} =~ /^[+-]inf$/) | |
1454 | { | |
1455 | my $t = $x->copy(); # bzero clobbers up $x | |
1456 | return wantarray ? ($x->bzero(),$t) : $x->bzero() | |
1457 | } | |
1458 | ||
1459 | # 5 / 0 => +inf, -6 / 0 => -inf | |
1460 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf | |
1461 | # exception: -8 / 0 has remainder -8, not 8 | |
1462 | # exception: -inf / 0 has remainder -inf, not inf | |
1463 | if ($y->is_zero()) | |
1464 | { | |
1465 | # +-inf / 0 => special case for -inf | |
1466 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); | |
1467 | if (!$x->is_zero() && !$x->is_inf()) | |
1468 | { | |
1469 | my $t = $x->copy(); # binf clobbers up $x | |
1470 | return wantarray ? | |
1471 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) | |
1472 | } | |
1473 | } | |
1474 | ||
1475 | # last case: +-inf / ordinary number | |
1476 | my $sign = '+inf'; | |
1477 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; | |
1478 | $x->{sign} = $sign; | |
1479 | return wantarray ? ($x,$self->bzero()) : $x; | |
1480 | } | |
1481 | ||
1482 | sub bdiv | |
1483 | { | |
1484 | # (dividend: BINT or num_str, divisor: BINT or num_str) return | |
1485 | # (BINT,BINT) (quo,rem) or BINT (only rem) | |
1486 | ||
1487 | # set up parameters | |
1488 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1489 | # objectify is costly, so avoid it | |
1490 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1491 | { | |
1492 | ($self,$x,$y,@r) = objectify(2,@_); | |
1493 | } | |
1494 | ||
1495 | return $x if $x->modify('bdiv'); | |
1496 | ||
1497 | return $self->_div_inf($x,$y) | |
1498 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
1499 | ||
1500 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) | |
1501 | if defined $upgrade; | |
1502 | ||
1503 | $r[3] = $y; # no push! | |
1504 | ||
1505 | # calc new sign and in case $y == +/- 1, return $x | |
1506 | my $xsign = $x->{sign}; # keep | |
1507 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); | |
1508 | ||
1509 | if (wantarray) | |
1510 | { | |
1511 | my $rem = $self->bzero(); | |
1512 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); | |
1513 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
1514 | $rem->{_a} = $x->{_a}; | |
1515 | $rem->{_p} = $x->{_p}; | |
1516 | $x->round(@r); | |
1517 | if (! $CALC->_is_zero($rem->{value})) | |
1518 | { | |
1519 | $rem->{sign} = $y->{sign}; | |
1520 | $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-' | |
1521 | } | |
1522 | else | |
1523 | { | |
1524 | $rem->{sign} = '+'; # dont leave -0 | |
1525 | } | |
1526 | $rem->round(@r); | |
1527 | return ($x,$rem); | |
1528 | } | |
1529 | ||
1530 | $x->{value} = $CALC->_div($x->{value},$y->{value}); | |
1531 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
1532 | ||
1533 | $x->round(@r); | |
1534 | } | |
1535 | ||
1536 | ############################################################################### | |
1537 | # modulus functions | |
1538 | ||
1539 | sub bmod | |
1540 | { | |
1541 | # modulus (or remainder) | |
1542 | # (BINT or num_str, BINT or num_str) return BINT | |
1543 | ||
1544 | # set up parameters | |
1545 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1546 | # objectify is costly, so avoid it | |
1547 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1548 | { | |
1549 | ($self,$x,$y,@r) = objectify(2,@_); | |
1550 | } | |
1551 | ||
1552 | return $x if $x->modify('bmod'); | |
1553 | $r[3] = $y; # no push! | |
1554 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) | |
1555 | { | |
1556 | my ($d,$r) = $self->_div_inf($x,$y); | |
1557 | $x->{sign} = $r->{sign}; | |
1558 | $x->{value} = $r->{value}; | |
1559 | return $x->round(@r); | |
1560 | } | |
1561 | ||
1562 | # calc new sign and in case $y == +/- 1, return $x | |
1563 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); | |
1564 | if (!$CALC->_is_zero($x->{value})) | |
1565 | { | |
1566 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1) # $y-$x | |
1567 | if ($x->{sign} ne $y->{sign}); | |
1568 | $x->{sign} = $y->{sign}; | |
1569 | } | |
1570 | else | |
1571 | { | |
1572 | $x->{sign} = '+'; # dont leave -0 | |
1573 | } | |
1574 | $x->round(@r); | |
1575 | } | |
1576 | ||
1577 | sub bmodinv | |
1578 | { | |
1579 | # Modular inverse. given a number which is (hopefully) relatively | |
1580 | # prime to the modulus, calculate its inverse using Euclid's | |
1581 | # alogrithm. If the number is not relatively prime to the modulus | |
1582 | # (i.e. their gcd is not one) then NaN is returned. | |
1583 | ||
1584 | # set up parameters | |
1585 | my ($self,$x,$y,@r) = (undef,@_); | |
1586 | # objectify is costly, so avoid it | |
1587 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1588 | { | |
1589 | ($self,$x,$y,@r) = objectify(2,@_); | |
1590 | } | |
1591 | ||
1592 | return $x if $x->modify('bmodinv'); | |
1593 | ||
1594 | return $x->bnan() | |
1595 | if ($y->{sign} ne '+' # -, NaN, +inf, -inf | |
1596 | || $x->is_zero() # or num == 0 | |
1597 | || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf | |
1598 | ); | |
1599 | ||
1600 | # put least residue into $x if $x was negative, and thus make it positive | |
1601 | $x->bmod($y) if $x->{sign} eq '-'; | |
1602 | ||
1603 | my $sign; | |
1604 | ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value}); | |
1605 | return $x->bnan() if !defined $x->{value}; # in case no GCD found | |
1606 | return $x if !defined $sign; # already real result | |
1607 | $x->{sign} = $sign; # flip/flop see below | |
1608 | $x->bmod($y); # calc real result | |
1609 | $x; | |
1610 | } | |
1611 | ||
1612 | sub bmodpow | |
1613 | { | |
1614 | # takes a very large number to a very large exponent in a given very | |
1615 | # large modulus, quickly, thanks to binary exponentation. supports | |
1616 | # negative exponents. | |
1617 | my ($self,$num,$exp,$mod,@r) = objectify(3,@_); | |
1618 | ||
1619 | return $num if $num->modify('bmodpow'); | |
1620 | ||
1621 | # check modulus for valid values | |
1622 | return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf | |
1623 | || $mod->is_zero()); | |
1624 | ||
1625 | # check exponent for valid values | |
1626 | if ($exp->{sign} =~ /\w/) | |
1627 | { | |
1628 | # i.e., if it's NaN, +inf, or -inf... | |
1629 | return $num->bnan(); | |
1630 | } | |
1631 | ||
1632 | $num->bmodinv ($mod) if ($exp->{sign} eq '-'); | |
1633 | ||
1634 | # check num for valid values (also NaN if there was no inverse but $exp < 0) | |
1635 | return $num->bnan() if $num->{sign} !~ /^[+-]$/; | |
1636 | ||
1637 | # $mod is positive, sign on $exp is ignored, result also positive | |
1638 | $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value}); | |
1639 | $num; | |
1640 | } | |
1641 | ||
1642 | ############################################################################### | |
1643 | ||
1644 | sub bfac | |
1645 | { | |
1646 | # (BINT or num_str, BINT or num_str) return BINT | |
1647 | # compute factorial number from $x, modify $x in place | |
1648 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1649 | ||
1650 | return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf | |
1651 | return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN | |
1652 | ||
1653 | $x->{value} = $CALC->_fac($x->{value}); | |
1654 | $x->round(@r); | |
1655 | } | |
1656 | ||
1657 | sub bpow | |
1658 | { | |
1659 | # (BINT or num_str, BINT or num_str) return BINT | |
1660 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 | |
1661 | # modifies first argument | |
1662 | ||
1663 | # set up parameters | |
1664 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1665 | # objectify is costly, so avoid it | |
1666 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1667 | { | |
1668 | ($self,$x,$y,@r) = objectify(2,@_); | |
1669 | } | |
1670 | ||
1671 | return $x if $x->modify('bpow'); | |
1672 | ||
1673 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; | |
1674 | ||
1675 | # inf handling | |
1676 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1677 | { | |
1678 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
1679 | { | |
1680 | # +-inf ** +-inf | |
1681 | return $x->bnan(); | |
1682 | } | |
1683 | # +-inf ** Y | |
1684 | if ($x->{sign} =~ /^[+-]inf/) | |
1685 | { | |
1686 | # +inf ** 0 => NaN | |
1687 | return $x->bnan() if $y->is_zero(); | |
1688 | # -inf ** -1 => 1/inf => 0 | |
1689 | return $x->bzero() if $y->is_one('-') && $x->is_negative(); | |
1690 | ||
1691 | # +inf ** Y => inf | |
1692 | return $x if $x->{sign} eq '+inf'; | |
1693 | ||
1694 | # -inf ** Y => -inf if Y is odd | |
1695 | return $x if $y->is_odd(); | |
1696 | return $x->babs(); | |
1697 | } | |
1698 | # X ** +-inf | |
1699 | ||
1700 | # 1 ** +inf => 1 | |
1701 | return $x if $x->is_one(); | |
1702 | ||
1703 | # 0 ** inf => 0 | |
1704 | return $x if $x->is_zero() && $y->{sign} =~ /^[+]/; | |
1705 | ||
1706 | # 0 ** -inf => inf | |
1707 | return $x->binf() if $x->is_zero(); | |
1708 | ||
1709 | # -1 ** -inf => NaN | |
1710 | return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/; | |
1711 | ||
1712 | # -X ** -inf => 0 | |
1713 | return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/; | |
1714 | ||
1715 | # -1 ** inf => NaN | |
1716 | return $x->bnan() if $x->{sign} eq '-'; | |
1717 | ||
1718 | # X ** inf => inf | |
1719 | return $x->binf() if $y->{sign} =~ /^[+]/; | |
1720 | # X ** -inf => 0 | |
1721 | return $x->bzero(); | |
1722 | } | |
1723 | ||
1724 | return $upgrade->bpow($upgrade->new($x),$y,@r) | |
1725 | if defined $upgrade && !$y->isa($self); | |
1726 | ||
1727 | $r[3] = $y; # no push! | |
1728 | ||
1729 | # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu | |
1730 | ||
1731 | my $new_sign = '+'; | |
1732 | $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+'); | |
1733 | ||
1734 | # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf | |
1735 | return $x->binf() | |
1736 | if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value}); | |
1737 | # 1 ** -y => 1 / (1 ** |y|) | |
1738 | # so do test for negative $y after above's clause | |
1739 | return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value}); | |
1740 | ||
1741 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); | |
1742 | $x->{sign} = $new_sign; | |
1743 | $x->{sign} = '+' if $CALC->_is_zero($y->{value}); | |
1744 | $x->round(@r); | |
1745 | } | |
1746 | ||
1747 | sub blsft | |
1748 | { | |
1749 | # (BINT or num_str, BINT or num_str) return BINT | |
1750 | # compute x << y, base n, y >= 0 | |
1751 | ||
1752 | # set up parameters | |
1753 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); | |
1754 | # objectify is costly, so avoid it | |
1755 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1756 | { | |
1757 | ($self,$x,$y,$n,@r) = objectify(2,@_); | |
1758 | } | |
1759 | ||
1760 | return $x if $x->modify('blsft'); | |
1761 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
1762 | return $x->round(@r) if $y->is_zero(); | |
1763 | ||
1764 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; | |
1765 | ||
1766 | $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n); | |
1767 | $x->round(@r); | |
1768 | } | |
1769 | ||
1770 | sub brsft | |
1771 | { | |
1772 | # (BINT or num_str, BINT or num_str) return BINT | |
1773 | # compute x >> y, base n, y >= 0 | |
1774 | ||
1775 | # set up parameters | |
1776 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); | |
1777 | # objectify is costly, so avoid it | |
1778 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1779 | { | |
1780 | ($self,$x,$y,$n,@r) = objectify(2,@_); | |
1781 | } | |
1782 | ||
1783 | return $x if $x->modify('brsft'); | |
1784 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
1785 | return $x->round(@r) if $y->is_zero(); | |
1786 | return $x->bzero(@r) if $x->is_zero(); # 0 => 0 | |
1787 | ||
1788 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; | |
1789 | ||
1790 | # this only works for negative numbers when shifting in base 2 | |
1791 | if (($x->{sign} eq '-') && ($n == 2)) | |
1792 | { | |
1793 | return $x->round(@r) if $x->is_one('-'); # -1 => -1 | |
1794 | if (!$y->is_one()) | |
1795 | { | |
1796 | # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al | |
1797 | # but perhaps there is a better emulation for two's complement shift... | |
1798 | # if $y != 1, we must simulate it by doing: | |
1799 | # convert to bin, flip all bits, shift, and be done | |
1800 | $x->binc(); # -3 => -2 | |
1801 | my $bin = $x->as_bin(); | |
1802 | $bin =~ s/^-0b//; # strip '-0b' prefix | |
1803 | $bin =~ tr/10/01/; # flip bits | |
1804 | # now shift | |
1805 | if (CORE::length($bin) <= $y) | |
1806 | { | |
1807 | $bin = '0'; # shifting to far right creates -1 | |
1808 | # 0, because later increment makes | |
1809 | # that 1, attached '-' makes it '-1' | |
1810 | # because -1 >> x == -1 ! | |
1811 | } | |
1812 | else | |
1813 | { | |
1814 | $bin =~ s/.{$y}$//; # cut off at the right side | |
1815 | $bin = '1' . $bin; # extend left side by one dummy '1' | |
1816 | $bin =~ tr/10/01/; # flip bits back | |
1817 | } | |
1818 | my $res = $self->new('0b'.$bin); # add prefix and convert back | |
1819 | $res->binc(); # remember to increment | |
1820 | $x->{value} = $res->{value}; # take over value | |
1821 | return $x->round(@r); # we are done now, magic, isn't? | |
1822 | } | |
1823 | # x < 0, n == 2, y == 1 | |
1824 | $x->bdec(); # n == 2, but $y == 1: this fixes it | |
1825 | } | |
1826 | ||
1827 | $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n); | |
1828 | $x->round(@r); | |
1829 | } | |
1830 | ||
1831 | sub band | |
1832 | { | |
1833 | #(BINT or num_str, BINT or num_str) return BINT | |
1834 | # compute x & y | |
1835 | ||
1836 | # set up parameters | |
1837 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1838 | # objectify is costly, so avoid it | |
1839 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1840 | { | |
1841 | ($self,$x,$y,@r) = objectify(2,@_); | |
1842 | } | |
1843 | ||
1844 | return $x if $x->modify('band'); | |
1845 | ||
1846 | $r[3] = $y; # no push! | |
1847 | ||
1848 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
1849 | ||
1850 | my $sx = $x->{sign} eq '+' ? 1 : -1; | |
1851 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
1852 | ||
1853 | if ($sx == 1 && $sy == 1) | |
1854 | { | |
1855 | $x->{value} = $CALC->_and($x->{value},$y->{value}); | |
1856 | return $x->round(@r); | |
1857 | } | |
1858 | ||
1859 | if ($CAN{signed_and}) | |
1860 | { | |
1861 | $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy); | |
1862 | return $x->round(@r); | |
1863 | } | |
1864 | ||
1865 | require $EMU_LIB; | |
1866 | __emu_band($self,$x,$y,$sx,$sy,@r); | |
1867 | } | |
1868 | ||
1869 | sub bior | |
1870 | { | |
1871 | #(BINT or num_str, BINT or num_str) return BINT | |
1872 | # compute x | y | |
1873 | ||
1874 | # set up parameters | |
1875 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1876 | # objectify is costly, so avoid it | |
1877 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1878 | { | |
1879 | ($self,$x,$y,@r) = objectify(2,@_); | |
1880 | } | |
1881 | ||
1882 | return $x if $x->modify('bior'); | |
1883 | $r[3] = $y; # no push! | |
1884 | ||
1885 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
1886 | ||
1887 | my $sx = $x->{sign} eq '+' ? 1 : -1; | |
1888 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
1889 | ||
1890 | # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior() | |
1891 | ||
1892 | # don't use lib for negative values | |
1893 | if ($sx == 1 && $sy == 1) | |
1894 | { | |
1895 | $x->{value} = $CALC->_or($x->{value},$y->{value}); | |
1896 | return $x->round(@r); | |
1897 | } | |
1898 | ||
1899 | # if lib can do negative values, let it handle this | |
1900 | if ($CAN{signed_or}) | |
1901 | { | |
1902 | $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy); | |
1903 | return $x->round(@r); | |
1904 | } | |
1905 | ||
1906 | require $EMU_LIB; | |
1907 | __emu_bior($self,$x,$y,$sx,$sy,@r); | |
1908 | } | |
1909 | ||
1910 | sub bxor | |
1911 | { | |
1912 | #(BINT or num_str, BINT or num_str) return BINT | |
1913 | # compute x ^ y | |
1914 | ||
1915 | # set up parameters | |
1916 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1917 | # objectify is costly, so avoid it | |
1918 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1919 | { | |
1920 | ($self,$x,$y,@r) = objectify(2,@_); | |
1921 | } | |
1922 | ||
1923 | return $x if $x->modify('bxor'); | |
1924 | $r[3] = $y; # no push! | |
1925 | ||
1926 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
1927 | ||
1928 | my $sx = $x->{sign} eq '+' ? 1 : -1; | |
1929 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
1930 | ||
1931 | # don't use lib for negative values | |
1932 | if ($sx == 1 && $sy == 1) | |
1933 | { | |
1934 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); | |
1935 | return $x->round(@r); | |
1936 | } | |
1937 | ||
1938 | # if lib can do negative values, let it handle this | |
1939 | if ($CAN{signed_xor}) | |
1940 | { | |
1941 | $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy); | |
1942 | return $x->round(@r); | |
1943 | } | |
1944 | ||
1945 | require $EMU_LIB; | |
1946 | __emu_bxor($self,$x,$y,$sx,$sy,@r); | |
1947 | } | |
1948 | ||
1949 | sub length | |
1950 | { | |
1951 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1952 | ||
1953 | my $e = $CALC->_len($x->{value}); | |
1954 | wantarray ? ($e,0) : $e; | |
1955 | } | |
1956 | ||
1957 | sub digit | |
1958 | { | |
1959 | # return the nth decimal digit, negative values count backward, 0 is right | |
1960 | my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1961 | ||
1962 | $n = $n->numify() if ref($n); | |
1963 | $CALC->_digit($x->{value},$n||0); | |
1964 | } | |
1965 | ||
1966 | sub _trailing_zeros | |
1967 | { | |
1968 | # return the amount of trailing zeros in $x (as scalar) | |
1969 | my $x = shift; | |
1970 | $x = $class->new($x) unless ref $x; | |
1971 | ||
1972 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc | |
1973 | ||
1974 | $CALC->_zeros($x->{value}); # must handle odd values, 0 etc | |
1975 | } | |
1976 | ||
1977 | sub bsqrt | |
1978 | { | |
1979 | # calculate square root of $x | |
1980 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1981 | ||
1982 | return $x if $x->modify('bsqrt'); | |
1983 | ||
1984 | return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN | |
1985 | return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf | |
1986 | ||
1987 | return $upgrade->bsqrt($x,@r) if defined $upgrade; | |
1988 | ||
1989 | $x->{value} = $CALC->_sqrt($x->{value}); | |
1990 | $x->round(@r); | |
1991 | } | |
1992 | ||
1993 | sub broot | |
1994 | { | |
1995 | # calculate $y'th root of $x | |
1996 | ||
1997 | # set up parameters | |
1998 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1999 | ||
2000 | $y = $self->new(2) unless defined $y; | |
2001 | ||
2002 | # objectify is costly, so avoid it | |
2003 | if ((!ref($x)) || (ref($x) ne ref($y))) | |
2004 | { | |
2005 | ($self,$x,$y,@r) = objectify(2,$self || $class,@_); | |
2006 | } | |
2007 | ||
2008 | return $x if $x->modify('broot'); | |
2009 | ||
2010 | # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0 | |
2011 | return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() || | |
2012 | $y->{sign} !~ /^\+$/; | |
2013 | ||
2014 | return $x->round(@r) | |
2015 | if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one(); | |
2016 | ||
2017 | return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade; | |
2018 | ||
2019 | $x->{value} = $CALC->_root($x->{value},$y->{value}); | |
2020 | $x->round(@r); | |
2021 | } | |
2022 | ||
2023 | sub exponent | |
2024 | { | |
2025 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) | |
2026 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
2027 | ||
2028 | if ($x->{sign} !~ /^[+-]$/) | |
2029 | { | |
2030 | my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf | |
2031 | return $self->new($s); | |
2032 | } | |
2033 | return $self->bone() if $x->is_zero(); | |
2034 | ||
2035 | $self->new($x->_trailing_zeros()); | |
2036 | } | |
2037 | ||
2038 | sub mantissa | |
2039 | { | |
2040 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) | |
2041 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
2042 | ||
2043 | if ($x->{sign} !~ /^[+-]$/) | |
2044 | { | |
2045 | # for NaN, +inf, -inf: keep the sign | |
2046 | return $self->new($x->{sign}); | |
2047 | } | |
2048 | my $m = $x->copy(); delete $m->{_p}; delete $m->{_a}; | |
2049 | # that's a bit inefficient: | |
2050 | my $zeros = $m->_trailing_zeros(); | |
2051 | $m->brsft($zeros,10) if $zeros != 0; | |
2052 | $m; | |
2053 | } | |
2054 | ||
2055 | sub parts | |
2056 | { | |
2057 | # return a copy of both the exponent and the mantissa | |
2058 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
2059 | ||
2060 | ($x->mantissa(),$x->exponent()); | |
2061 | } | |
2062 | ||
2063 | ############################################################################## | |
2064 | # rounding functions | |
2065 | ||
2066 | sub bfround | |
2067 | { | |
2068 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' | |
2069 | # $n == 0 || $n == 1 => round to integer | |
2070 | my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x; | |
2071 | ||
2072 | my ($scale,$mode) = $x->_scale_p(@_); | |
2073 | ||
2074 | return $x if !defined $scale || $x->modify('bfround'); # no-op | |
2075 | ||
2076 | # no-op for BigInts if $n <= 0 | |
2077 | $x->bround( $x->length()-$scale, $mode) if $scale > 0; | |
2078 | ||
2079 | delete $x->{_a}; # delete to save memory | |
2080 | $x->{_p} = $scale; # store new _p | |
2081 | $x; | |
2082 | } | |
2083 | ||
2084 | sub _scan_for_nonzero | |
2085 | { | |
2086 | # internal, used by bround() to scan for non-zeros after a '5' | |
2087 | my ($x,$pad,$xs,$len) = @_; | |
2088 | ||
2089 | return 0 if $len == 1; # "5" is trailed by invisible zeros | |
2090 | my $follow = $pad - 1; | |
2091 | return 0 if $follow > $len || $follow < 1; | |
2092 | ||
2093 | # use the string form to check whether only '0's follow or not | |
2094 | substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0; | |
2095 | } | |
2096 | ||
2097 | sub fround | |
2098 | { | |
2099 | # Exists to make life easier for switch between MBF and MBI (should we | |
2100 | # autoload fxxx() like MBF does for bxxx()?) | |
2101 | my $x = shift; $x = $class->new($x) unless ref $x; | |
2102 | $x->bround(@_); | |
2103 | } | |
2104 | ||
2105 | sub bround | |
2106 | { | |
2107 | # accuracy: +$n preserve $n digits from left, | |
2108 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) | |
2109 | # no-op for $n == 0 | |
2110 | # and overwrite the rest with 0's, return normalized number | |
2111 | # do not return $x->bnorm(), but $x | |
2112 | ||
2113 | my $x = shift; $x = $class->new($x) unless ref $x; | |
2114 | my ($scale,$mode) = $x->_scale_a(@_); | |
2115 | return $x if !defined $scale || $x->modify('bround'); # no-op | |
2116 | ||
2117 | if ($x->is_zero() || $scale == 0) | |
2118 | { | |
2119 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 | |
2120 | return $x; | |
2121 | } | |
2122 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN | |
2123 | ||
2124 | # we have fewer digits than we want to scale to | |
2125 | my $len = $x->length(); | |
2126 | # convert $scale to a scalar in case it is an object (put's a limit on the | |
2127 | # number length, but this would already limited by memory constraints), makes | |
2128 | # it faster | |
2129 | $scale = $scale->numify() if ref ($scale); | |
2130 | ||
2131 | # scale < 0, but > -len (not >=!) | |
2132 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) | |
2133 | { | |
2134 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 | |
2135 | return $x; | |
2136 | } | |
2137 | ||
2138 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 | |
2139 | my ($pad,$digit_round,$digit_after); | |
2140 | $pad = $len - $scale; | |
2141 | $pad = abs($scale-1) if $scale < 0; | |
2142 | ||
2143 | # do not use digit(), it is very costly for binary => decimal | |
2144 | # getting the entire string is also costly, but we need to do it only once | |
2145 | my $xs = $CALC->_str($x->{value}); | |
2146 | my $pl = -$pad-1; | |
2147 | ||
2148 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 | |
2149 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 | |
2150 | $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len; | |
2151 | $pl++; $pl ++ if $pad >= $len; | |
2152 | $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0; | |
2153 | ||
2154 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look | |
2155 | # closer at the remaining digits of the original $x, remember decision | |
2156 | my $round_up = 1; # default round up | |
2157 | $round_up -- if | |
2158 | ($mode eq 'trunc') || # trunc by round down | |
2159 | ($digit_after =~ /[01234]/) || # round down anyway, | |
2160 | # 6789 => round up | |
2161 | ($digit_after eq '5') && # not 5000...0000 | |
2162 | ($x->_scan_for_nonzero($pad,$xs,$len) == 0) && | |
2163 | ( | |
2164 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || | |
2165 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || | |
2166 | ($mode eq '+inf') && ($x->{sign} eq '-') || | |
2167 | ($mode eq '-inf') && ($x->{sign} eq '+') || | |
2168 | ($mode eq 'zero') # round down if zero, sign adjusted below | |
2169 | ); | |
2170 | my $put_back = 0; # not yet modified | |
2171 | ||
2172 | if (($pad > 0) && ($pad <= $len)) | |
2173 | { | |
2174 | substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...' | |
2175 | $put_back = 1; # need to put back | |
2176 | } | |
2177 | elsif ($pad > $len) | |
2178 | { | |
2179 | $x->bzero(); # round to '0' | |
2180 | } | |
2181 | ||
2182 | if ($round_up) # what gave test above? | |
2183 | { | |
2184 | $put_back = 1; # need to put back | |
2185 | $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0 | |
2186 | ||
2187 | # we modify directly the string variant instead of creating a number and | |
2188 | # adding it, since that is faster (we already have the string) | |
2189 | my $c = 0; $pad ++; # for $pad == $len case | |
2190 | while ($pad <= $len) | |
2191 | { | |
2192 | $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10'; | |
2193 | substr($xs,-$pad,1) = $c; $pad++; | |
2194 | last if $c != 0; # no overflow => early out | |
2195 | } | |
2196 | $xs = '1'.$xs if $c == 0; | |
2197 | ||
2198 | } | |
2199 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed | |
2200 | ||
2201 | $x->{_a} = $scale if $scale >= 0; | |
2202 | if ($scale < 0) | |
2203 | { | |
2204 | $x->{_a} = $len+$scale; | |
2205 | $x->{_a} = 0 if $scale < -$len; | |
2206 | } | |
2207 | $x; | |
2208 | } | |
2209 | ||
2210 | sub bfloor | |
2211 | { | |
2212 | # return integer less or equal then number; no-op since it's already integer | |
2213 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
2214 | ||
2215 | $x->round(@r); | |
2216 | } | |
2217 | ||
2218 | sub bceil | |
2219 | { | |
2220 | # return integer greater or equal then number; no-op since it's already int | |
2221 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
2222 | ||
2223 | $x->round(@r); | |
2224 | } | |
2225 | ||
2226 | sub as_number | |
2227 | { | |
2228 | # An object might be asked to return itself as bigint on certain overloaded | |
2229 | # operations, this does exactly this, so that sub classes can simple inherit | |
2230 | # it or override with their own integer conversion routine. | |
2231 | $_[0]->copy(); | |
2232 | } | |
2233 | ||
2234 | sub as_hex | |
2235 | { | |
2236 | # return as hex string, with prefixed 0x | |
2237 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2238 | ||
2239 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2240 | ||
2241 | my $s = ''; | |
2242 | $s = $x->{sign} if $x->{sign} eq '-'; | |
2243 | $s . $CALC->_as_hex($x->{value}); | |
2244 | } | |
2245 | ||
2246 | sub as_bin | |
2247 | { | |
2248 | # return as binary string, with prefixed 0b | |
2249 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2250 | ||
2251 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2252 | ||
2253 | my $s = ''; $s = $x->{sign} if $x->{sign} eq '-'; | |
2254 | return $s . $CALC->_as_bin($x->{value}); | |
2255 | } | |
2256 | ||
2257 | ############################################################################## | |
2258 | # private stuff (internal use only) | |
2259 | ||
2260 | sub objectify | |
2261 | { | |
2262 | # check for strings, if yes, return objects instead | |
2263 | ||
2264 | # the first argument is number of args objectify() should look at it will | |
2265 | # return $count+1 elements, the first will be a classname. This is because | |
2266 | # overloaded '""' calls bstr($object,undef,undef) and this would result in | |
2267 | # useless objects beeing created and thrown away. So we cannot simple loop | |
2268 | # over @_. If the given count is 0, all arguments will be used. | |
2269 | ||
2270 | # If the second arg is a ref, use it as class. | |
2271 | # If not, try to use it as classname, unless undef, then use $class | |
2272 | # (aka Math::BigInt). The latter shouldn't happen,though. | |
2273 | ||
2274 | # caller: gives us: | |
2275 | # $x->badd(1); => ref x, scalar y | |
2276 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y | |
2277 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y | |
2278 | # Math::BigInt::badd(1,2); => scalar x, scalar y | |
2279 | # In the last case we check number of arguments to turn it silently into | |
2280 | # $class,1,2. (We can not take '1' as class ;o) | |
2281 | # badd($class,1) is not supported (it should, eventually, try to add undef) | |
2282 | # currently it tries 'Math::BigInt' + 1, which will not work. | |
2283 | ||
2284 | # some shortcut for the common cases | |
2285 | # $x->unary_op(); | |
2286 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); | |
2287 | ||
2288 | my $count = abs(shift || 0); | |
2289 | ||
2290 | my (@a,$k,$d); # resulting array, temp, and downgrade | |
2291 | if (ref $_[0]) | |
2292 | { | |
2293 | # okay, got object as first | |
2294 | $a[0] = ref $_[0]; | |
2295 | } | |
2296 | else | |
2297 | { | |
2298 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) | |
2299 | $a[0] = $class; | |
2300 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? | |
2301 | } | |
2302 | ||
2303 | no strict 'refs'; | |
2304 | # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats | |
2305 | if (defined ${"$a[0]::downgrade"}) | |
2306 | { | |
2307 | $d = ${"$a[0]::downgrade"}; | |
2308 | ${"$a[0]::downgrade"} = undef; | |
2309 | } | |
2310 | ||
2311 | my $up = ${"$a[0]::upgrade"}; | |
2312 | #print "Now in objectify, my class is today $a[0], count = $count\n"; | |
2313 | if ($count == 0) | |
2314 | { | |
2315 | while (@_) | |
2316 | { | |
2317 | $k = shift; | |
2318 | if (!ref($k)) | |
2319 | { | |
2320 | $k = $a[0]->new($k); | |
2321 | } | |
2322 | elsif (!defined $up && ref($k) ne $a[0]) | |
2323 | { | |
2324 | # foreign object, try to convert to integer | |
2325 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
2326 | } | |
2327 | push @a,$k; | |
2328 | } | |
2329 | } | |
2330 | else | |
2331 | { | |
2332 | while ($count > 0) | |
2333 | { | |
2334 | $count--; | |
2335 | $k = shift; | |
2336 | if (!ref($k)) | |
2337 | { | |
2338 | $k = $a[0]->new($k); | |
2339 | } | |
2340 | elsif (!defined $up && ref($k) ne $a[0]) | |
2341 | { | |
2342 | # foreign object, try to convert to integer | |
2343 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
2344 | } | |
2345 | push @a,$k; | |
2346 | } | |
2347 | push @a,@_; # return other params, too | |
2348 | } | |
2349 | if (! wantarray) | |
2350 | { | |
2351 | require Carp; Carp::croak ("$class objectify needs list context"); | |
2352 | } | |
2353 | ${"$a[0]::downgrade"} = $d; | |
2354 | @a; | |
2355 | } | |
2356 | ||
2357 | sub _register_callback | |
2358 | { | |
2359 | my ($class,$callback) = @_; | |
2360 | ||
2361 | if (ref($callback) ne 'CODE') | |
2362 | { | |
2363 | require Carp; | |
2364 | Carp::croak ("$callback is not a coderef"); | |
2365 | } | |
2366 | $CALLBACKS{$class} = $callback; | |
2367 | } | |
2368 | ||
2369 | sub import | |
2370 | { | |
2371 | my $self = shift; | |
2372 | ||
2373 | $IMPORT++; # remember we did import() | |
2374 | my @a; my $l = scalar @_; | |
2375 | for ( my $i = 0; $i < $l ; $i++ ) | |
2376 | { | |
2377 | if ($_[$i] eq ':constant') | |
2378 | { | |
2379 | # this causes overlord er load to step in | |
2380 | overload::constant | |
2381 | integer => sub { $self->new(shift) }, | |
2382 | binary => sub { $self->new(shift) }; | |
2383 | } | |
2384 | elsif ($_[$i] eq 'upgrade') | |
2385 | { | |
2386 | # this causes upgrading | |
2387 | $upgrade = $_[$i+1]; # or undef to disable | |
2388 | $i++; | |
2389 | } | |
2390 | elsif ($_[$i] =~ /^lib$/i) | |
2391 | { | |
2392 | # this causes a different low lib to take care... | |
2393 | $CALC = $_[$i+1] || ''; | |
2394 | $i++; | |
2395 | } | |
2396 | else | |
2397 | { | |
2398 | push @a, $_[$i]; | |
2399 | } | |
2400 | } | |
2401 | # any non :constant stuff is handled by our parent, Exporter | |
2402 | if (@a > 0) | |
2403 | { | |
2404 | require Exporter; | |
2405 | ||
2406 | $self->SUPER::import(@a); # need it for subclasses | |
2407 | $self->export_to_level(1,$self,@a); # need it for MBF | |
2408 | } | |
2409 | ||
2410 | # try to load core math lib | |
2411 | my @c = split /\s*,\s*/,$CALC; | |
2412 | foreach (@c) | |
2413 | { | |
2414 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters | |
2415 | } | |
2416 | push @c, 'FastCalc', 'Calc'; # if all fail, try these | |
2417 | $CALC = ''; # signal error | |
2418 | foreach my $lib (@c) | |
2419 | { | |
2420 | next if ($lib || '') eq ''; | |
2421 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; | |
2422 | $lib =~ s/\.pm$//; | |
2423 | if ($] < 5.006) | |
2424 | { | |
2425 | # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is | |
2426 | # used in the same script, or eval("") inside import(). | |
2427 | my @parts = split /::/, $lib; # Math::BigInt => Math BigInt | |
2428 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm | |
2429 | require File::Spec; | |
2430 | $file = File::Spec->catfile (@parts, $file); | |
2431 | eval { require "$file"; $lib->import( @c ); } | |
2432 | } | |
2433 | else | |
2434 | { | |
2435 | eval "use $lib qw/@c/;"; | |
2436 | } | |
2437 | if ($@ eq '') | |
2438 | { | |
2439 | my $ok = 1; | |
2440 | # loaded it ok, see if the api_version() is high enough | |
2441 | if ($lib->can('api_version') && $lib->api_version() >= 1.0) | |
2442 | { | |
2443 | $ok = 0; | |
2444 | # api_version matches, check if it really provides anything we need | |
2445 | for my $method (qw/ | |
2446 | one two ten | |
2447 | str num | |
2448 | add mul div sub dec inc | |
2449 | acmp len digit is_one is_zero is_even is_odd | |
2450 | is_two is_ten | |
2451 | new copy check from_hex from_bin as_hex as_bin zeros | |
2452 | rsft lsft xor and or | |
2453 | mod sqrt root fac pow modinv modpow log_int gcd | |
2454 | /) | |
2455 | { | |
2456 | if (!$lib->can("_$method")) | |
2457 | { | |
2458 | if (($WARN{$lib}||0) < 2) | |
2459 | { | |
2460 | require Carp; | |
2461 | Carp::carp ("$lib is missing method '_$method'"); | |
2462 | $WARN{$lib} = 1; # still warn about the lib | |
2463 | } | |
2464 | $ok++; last; | |
2465 | } | |
2466 | } | |
2467 | } | |
2468 | if ($ok == 0) | |
2469 | { | |
2470 | $CALC = $lib; | |
2471 | last; # found a usable one, break | |
2472 | } | |
2473 | else | |
2474 | { | |
2475 | if (($WARN{$lib}||0) < 2) | |
2476 | { | |
2477 | my $ver = eval "\$$lib\::VERSION" || 'unknown'; | |
2478 | require Carp; | |
2479 | Carp::carp ("Cannot load outdated $lib v$ver, please upgrade"); | |
2480 | $WARN{$lib} = 2; # never warn again | |
2481 | } | |
2482 | } | |
2483 | } | |
2484 | } | |
2485 | if ($CALC eq '') | |
2486 | { | |
2487 | require Carp; | |
2488 | Carp::croak ("Couldn't load any math lib, not even 'Calc.pm'"); | |
2489 | } | |
2490 | ||
2491 | # notify callbacks | |
2492 | foreach my $class (keys %CALLBACKS) | |
2493 | { | |
2494 | &{$CALLBACKS{$class}}($CALC); | |
2495 | } | |
2496 | ||
2497 | # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib | |
2498 | # functions | |
2499 | ||
2500 | %CAN = (); | |
2501 | for my $method (qw/ signed_and signed_or signed_xor /) | |
2502 | { | |
2503 | $CAN{$method} = $CALC->can("_$method") ? 1 : 0; | |
2504 | } | |
2505 | ||
2506 | # import done | |
2507 | } | |
2508 | ||
2509 | sub __from_hex | |
2510 | { | |
2511 | # internal | |
2512 | # convert a (ref to) big hex string to BigInt, return undef for error | |
2513 | my $hs = shift; | |
2514 | ||
2515 | my $x = Math::BigInt->bzero(); | |
2516 | ||
2517 | # strip underscores | |
2518 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
2519 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
2520 | ||
2521 | return $x->bnan() if $hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; | |
2522 | ||
2523 | my $sign = '+'; $sign = '-' if $hs =~ /^-/; | |
2524 | ||
2525 | $hs =~ s/^[+-]//; # strip sign | |
2526 | $x->{value} = $CALC->_from_hex($hs); | |
2527 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' | |
2528 | $x; | |
2529 | } | |
2530 | ||
2531 | sub __from_bin | |
2532 | { | |
2533 | # internal | |
2534 | # convert a (ref to) big binary string to BigInt, return undef for error | |
2535 | my $bs = shift; | |
2536 | ||
2537 | my $x = Math::BigInt->bzero(); | |
2538 | # strip underscores | |
2539 | $bs =~ s/([01])_([01])/$1$2/g; | |
2540 | $bs =~ s/([01])_([01])/$1$2/g; | |
2541 | return $x->bnan() if $bs !~ /^[+-]?0b[01]+$/; | |
2542 | ||
2543 | my $sign = '+'; $sign = '-' if $bs =~ /^\-/; | |
2544 | $bs =~ s/^[+-]//; # strip sign | |
2545 | ||
2546 | $x->{value} = $CALC->_from_bin($bs); | |
2547 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' | |
2548 | $x; | |
2549 | } | |
2550 | ||
2551 | sub _split | |
2552 | { | |
2553 | # input: num_str; output: undef for invalid or | |
2554 | # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,\$exp_sign,\$exp_value) | |
2555 | # Internal, take apart a string and return the pieces. | |
2556 | # Strip leading/trailing whitespace, leading zeros, underscore and reject | |
2557 | # invalid input. | |
2558 | my $x = shift; | |
2559 | ||
2560 | # strip white space at front, also extranous leading zeros | |
2561 | $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' | |
2562 | $x =~ s/^\s+//; # but this will | |
2563 | $x =~ s/\s+$//g; # strip white space at end | |
2564 | ||
2565 | # shortcut, if nothing to split, return early | |
2566 | if ($x =~ /^[+-]?\d+\z/) | |
2567 | { | |
2568 | $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; | |
2569 | return (\$sign, \$x, \'', \'', \0); | |
2570 | } | |
2571 | ||
2572 | # invalid starting char? | |
2573 | return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; | |
2574 | ||
2575 | return __from_hex($x) if $x =~ /^[\-\+]?0x/; # hex string | |
2576 | return __from_bin($x) if $x =~ /^[\-\+]?0b/; # binary string | |
2577 | ||
2578 | # strip underscores between digits | |
2579 | $x =~ s/(\d)_(\d)/$1$2/g; | |
2580 | $x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 | |
2581 | ||
2582 | # some possible inputs: | |
2583 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 | |
2584 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999 | |
2585 | ||
2586 | my ($m,$e,$last) = split /[Ee]/,$x; | |
2587 | return if defined $last; # last defined => 1e2E3 or others | |
2588 | $e = '0' if !defined $e || $e eq ""; | |
2589 | ||
2590 | # sign,value for exponent,mantint,mantfrac | |
2591 | my ($es,$ev,$mis,$miv,$mfv); | |
2592 | # valid exponent? | |
2593 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros | |
2594 | { | |
2595 | $es = $1; $ev = $2; | |
2596 | # valid mantissa? | |
2597 | return if $m eq '.' || $m eq ''; | |
2598 | my ($mi,$mf,$lastf) = split /\./,$m; | |
2599 | return if defined $lastf; # lastf defined => 1.2.3 or others | |
2600 | $mi = '0' if !defined $mi; | |
2601 | $mi .= '0' if $mi =~ /^[\-\+]?$/; | |
2602 | $mf = '0' if !defined $mf || $mf eq ''; | |
2603 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros | |
2604 | { | |
2605 | $mis = $1||'+'; $miv = $2; | |
2606 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros | |
2607 | $mfv = $1; | |
2608 | # handle the 0e999 case here | |
2609 | $ev = 0 if $miv eq '0' && $mfv eq ''; | |
2610 | return (\$mis,\$miv,\$mfv,\$es,\$ev); | |
2611 | } | |
2612 | } | |
2613 | return; # NaN, not a number | |
2614 | } | |
2615 | ||
2616 | ############################################################################## | |
2617 | # internal calculation routines (others are in Math::BigInt::Calc etc) | |
2618 | ||
2619 | sub __lcm | |
2620 | { | |
2621 | # (BINT or num_str, BINT or num_str) return BINT | |
2622 | # does modify first argument | |
2623 | # LCM | |
2624 | ||
2625 | my ($x,$ty) = @_; | |
2626 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); | |
2627 | my $method = ref($x) . '::bgcd'; | |
2628 | no strict 'refs'; | |
2629 | $x * $ty / &$method($x,$ty); | |
2630 | } | |
2631 | ||
2632 | ############################################################################### | |
2633 | # this method returns 0 if the object can be modified, or 1 if not. | |
2634 | # We use a fast constant sub() here, to avoid costly calls. Subclasses | |
2635 | # may override it with special code (f.i. Math::BigInt::Constant does so) | |
2636 | ||
2637 | sub modify () { 0; } | |
2638 | ||
2639 | 1; | |
2640 | __END__ | |
2641 | ||
2642 | =pod | |
2643 | ||
2644 | =head1 NAME | |
2645 | ||
2646 | Math::BigInt - Arbitrary size integer/float math package | |
2647 | ||
2648 | =head1 SYNOPSIS | |
2649 | ||
2650 | use Math::BigInt; | |
2651 | ||
2652 | # or make it faster: install (optional) Math::BigInt::GMP | |
2653 | # and always use (it will fall back to pure Perl if the | |
2654 | # GMP library is not installed): | |
2655 | ||
2656 | use Math::BigInt lib => 'GMP'; | |
2657 | ||
2658 | my $str = '1234567890'; | |
2659 | my @values = (64,74,18); | |
2660 | my $n = 1; my $sign = '-'; | |
2661 | ||
2662 | # Number creation | |
2663 | $x = Math::BigInt->new($str); # defaults to 0 | |
2664 | $y = $x->copy(); # make a true copy | |
2665 | $nan = Math::BigInt->bnan(); # create a NotANumber | |
2666 | $zero = Math::BigInt->bzero(); # create a +0 | |
2667 | $inf = Math::BigInt->binf(); # create a +inf | |
2668 | $inf = Math::BigInt->binf('-'); # create a -inf | |
2669 | $one = Math::BigInt->bone(); # create a +1 | |
2670 | $one = Math::BigInt->bone('-'); # create a -1 | |
2671 | ||
2672 | # Testing (don't modify their arguments) | |
2673 | # (return true if the condition is met, otherwise false) | |
2674 | ||
2675 | $x->is_zero(); # if $x is +0 | |
2676 | $x->is_nan(); # if $x is NaN | |
2677 | $x->is_one(); # if $x is +1 | |
2678 | $x->is_one('-'); # if $x is -1 | |
2679 | $x->is_odd(); # if $x is odd | |
2680 | $x->is_even(); # if $x is even | |
2681 | $x->is_pos(); # if $x >= 0 | |
2682 | $x->is_neg(); # if $x < 0 | |
2683 | $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+') | |
2684 | $x->is_int(); # if $x is an integer (not a float) | |
2685 | ||
2686 | # comparing and digit/sign extration | |
2687 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) | |
2688 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
2689 | $x->sign(); # return the sign, either +,- or NaN | |
2690 | $x->digit($n); # return the nth digit, counting from right | |
2691 | $x->digit(-$n); # return the nth digit, counting from left | |
2692 | ||
2693 | # The following all modify their first argument. If you want to preserve | |
2694 | # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is | |
2695 | # neccessary when mixing $a = $b assigments with non-overloaded math. | |
2696 | ||
2697 | $x->bzero(); # set $x to 0 | |
2698 | $x->bnan(); # set $x to NaN | |
2699 | $x->bone(); # set $x to +1 | |
2700 | $x->bone('-'); # set $x to -1 | |
2701 | $x->binf(); # set $x to inf | |
2702 | $x->binf('-'); # set $x to -inf | |
2703 | ||
2704 | $x->bneg(); # negation | |
2705 | $x->babs(); # absolute value | |
2706 | $x->bnorm(); # normalize (no-op in BigInt) | |
2707 | $x->bnot(); # two's complement (bit wise not) | |
2708 | $x->binc(); # increment $x by 1 | |
2709 | $x->bdec(); # decrement $x by 1 | |
2710 | ||
2711 | $x->badd($y); # addition (add $y to $x) | |
2712 | $x->bsub($y); # subtraction (subtract $y from $x) | |
2713 | $x->bmul($y); # multiplication (multiply $x by $y) | |
2714 | $x->bdiv($y); # divide, set $x to quotient | |
2715 | # return (quo,rem) or quo if scalar | |
2716 | ||
2717 | $x->bmod($y); # modulus (x % y) | |
2718 | $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod)) | |
2719 | $x->bmodinv($mod); # the inverse of $x in the given modulus $mod | |
2720 | ||
2721 | $x->bpow($y); # power of arguments (x ** y) | |
2722 | $x->blsft($y); # left shift | |
2723 | $x->brsft($y); # right shift | |
2724 | $x->blsft($y,$n); # left shift, by base $n (like 10) | |
2725 | $x->brsft($y,$n); # right shift, by base $n (like 10) | |
2726 | ||
2727 | $x->band($y); # bitwise and | |
2728 | $x->bior($y); # bitwise inclusive or | |
2729 | $x->bxor($y); # bitwise exclusive or | |
2730 | $x->bnot(); # bitwise not (two's complement) | |
2731 | ||
2732 | $x->bsqrt(); # calculate square-root | |
2733 | $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) | |
2734 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) | |
2735 | ||
2736 | $x->round($A,$P,$mode); # round to accuracy or precision using mode $mode | |
2737 | $x->bround($n); # accuracy: preserve $n digits | |
2738 | $x->bfround($n); # round to $nth digit, no-op for BigInts | |
2739 | ||
2740 | # The following do not modify their arguments in BigInt (are no-ops), | |
2741 | # but do so in BigFloat: | |
2742 | ||
2743 | $x->bfloor(); # return integer less or equal than $x | |
2744 | $x->bceil(); # return integer greater or equal than $x | |
2745 | ||
2746 | # The following do not modify their arguments: | |
2747 | ||
2748 | # greatest common divisor (no OO style) | |
2749 | my $gcd = Math::BigInt::bgcd(@values); | |
2750 | # lowest common multiplicator (no OO style) | |
2751 | my $lcm = Math::BigInt::blcm(@values); | |
2752 | ||
2753 | $x->length(); # return number of digits in number | |
2754 | ($xl,$f) = $x->length(); # length of number and length of fraction part, | |
2755 | # latter is always 0 digits long for BigInts | |
2756 | ||
2757 | $x->exponent(); # return exponent as BigInt | |
2758 | $x->mantissa(); # return (signed) mantissa as BigInt | |
2759 | $x->parts(); # return (mantissa,exponent) as BigInt | |
2760 | $x->copy(); # make a true copy of $x (unlike $y = $x;) | |
2761 | $x->as_int(); # return as BigInt (in BigInt: same as copy()) | |
2762 | $x->numify(); # return as scalar (might overflow!) | |
2763 | ||
2764 | # conversation to string (do not modify their argument) | |
2765 | $x->bstr(); # normalized string (e.g. '3') | |
2766 | $x->bsstr(); # norm. string in scientific notation (e.g. '3E0') | |
2767 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x | |
2768 | $x->as_bin(); # as signed binary string with prefixed 0b | |
2769 | ||
2770 | ||
2771 | # precision and accuracy (see section about rounding for more) | |
2772 | $x->precision(); # return P of $x (or global, if P of $x undef) | |
2773 | $x->precision($n); # set P of $x to $n | |
2774 | $x->accuracy(); # return A of $x (or global, if A of $x undef) | |
2775 | $x->accuracy($n); # set A $x to $n | |
2776 | ||
2777 | # Global methods | |
2778 | Math::BigInt->precision(); # get/set global P for all BigInt objects | |
2779 | Math::BigInt->accuracy(); # get/set global A for all BigInt objects | |
2780 | Math::BigInt->round_mode(); # get/set global round mode, one of | |
2781 | # 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' | |
2782 | Math::BigInt->config(); # return hash containing configuration | |
2783 | ||
2784 | =head1 DESCRIPTION | |
2785 | ||
2786 | All operators (inlcuding basic math operations) are overloaded if you | |
2787 | declare your big integers as | |
2788 | ||
2789 | $i = new Math::BigInt '123_456_789_123_456_789'; | |
2790 | ||
2791 | Operations with overloaded operators preserve the arguments which is | |
2792 | exactly what you expect. | |
2793 | ||
2794 | =over 2 | |
2795 | ||
2796 | =item Input | |
2797 | ||
2798 | Input values to these routines may be any string, that looks like a number | |
2799 | and results in an integer, including hexadecimal and binary numbers. | |
2800 | ||
2801 | Scalars holding numbers may also be passed, but note that non-integer numbers | |
2802 | may already have lost precision due to the conversation to float. Quote | |
2803 | your input if you want BigInt to see all the digits: | |
2804 | ||
2805 | $x = Math::BigInt->new(12345678890123456789); # bad | |
2806 | $x = Math::BigInt->new('12345678901234567890'); # good | |
2807 | ||
2808 | You can include one underscore between any two digits. | |
2809 | ||
2810 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. | |
2811 | Non-integer values result in NaN. | |
2812 | ||
2813 | Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('') | |
2814 | results in 'NaN'. This might change in the future, so use always the following | |
2815 | explicit forms to get a zero or NaN: | |
2816 | ||
2817 | $zero = Math::BigInt->bzero(); | |
2818 | $nan = Math::BigInt->bnan(); | |
2819 | ||
2820 | C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers | |
2821 | are always stored in normalized form. If passed a string, creates a BigInt | |
2822 | object from the input. | |
2823 | ||
2824 | =item Output | |
2825 | ||
2826 | Output values are BigInt objects (normalized), except for the methods which | |
2827 | return a string (see L<SYNOPSIS>). | |
2828 | ||
2829 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, | |
2830 | C<is_nan()>, etc.) return true or false, while others (C<bcmp()>, C<bacmp()>) | |
2831 | return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort. | |
2832 | ||
2833 | =back | |
2834 | ||
2835 | =head1 METHODS | |
2836 | ||
2837 | Each of the methods below (except config(), accuracy() and precision()) | |
2838 | accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R> | |
2839 | are C<accuracy>, C<precision> and C<round_mode>. Please see the section about | |
2840 | L<ACCURACY and PRECISION> for more information. | |
2841 | ||
2842 | =head2 config | |
2843 | ||
2844 | use Data::Dumper; | |
2845 | ||
2846 | print Dumper ( Math::BigInt->config() ); | |
2847 | print Math::BigInt->config()->{lib},"\n"; | |
2848 | ||
2849 | Returns a hash containing the configuration, e.g. the version number, lib | |
2850 | loaded etc. The following hash keys are currently filled in with the | |
2851 | appropriate information. | |
2852 | ||
2853 | key Description | |
2854 | Example | |
2855 | ============================================================ | |
2856 | lib Name of the low-level math library | |
2857 | Math::BigInt::Calc | |
2858 | lib_version Version of low-level math library (see 'lib') | |
2859 | 0.30 | |
2860 | class The class name of config() you just called | |
2861 | Math::BigInt | |
2862 | upgrade To which class math operations might be upgraded | |
2863 | Math::BigFloat | |
2864 | downgrade To which class math operations might be downgraded | |
2865 | undef | |
2866 | precision Global precision | |
2867 | undef | |
2868 | accuracy Global accuracy | |
2869 | undef | |
2870 | round_mode Global round mode | |
2871 | even | |
2872 | version version number of the class you used | |
2873 | 1.61 | |
2874 | div_scale Fallback acccuracy for div | |
2875 | 40 | |
2876 | trap_nan If true, traps creation of NaN via croak() | |
2877 | 1 | |
2878 | trap_inf If true, traps creation of +inf/-inf via croak() | |
2879 | 1 | |
2880 | ||
2881 | The following values can be set by passing C<config()> a reference to a hash: | |
2882 | ||
2883 | trap_inf trap_nan | |
2884 | upgrade downgrade precision accuracy round_mode div_scale | |
2885 | ||
2886 | Example: | |
2887 | ||
2888 | $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } ); | |
2889 | ||
2890 | =head2 accuracy | |
2891 | ||
2892 | $x->accuracy(5); # local for $x | |
2893 | CLASS->accuracy(5); # global for all members of CLASS | |
2894 | # Note: This also applies to new()! | |
2895 | ||
2896 | $A = $x->accuracy(); # read out accuracy that affects $x | |
2897 | $A = CLASS->accuracy(); # read out global accuracy | |
2898 | ||
2899 | Set or get the global or local accuracy, aka how many significant digits the | |
2900 | results have. If you set a global accuracy, then this also applies to new()! | |
2901 | ||
2902 | Warning! The accuracy I<sticks>, e.g. once you created a number under the | |
2903 | influence of C<< CLASS->accuracy($A) >>, all results from math operations with | |
2904 | that number will also be rounded. | |
2905 | ||
2906 | In most cases, you should probably round the results explicitely using one of | |
2907 | L<round()>, L<bround()> or L<bfround()> or by passing the desired accuracy | |
2908 | to the math operation as additional parameter: | |
2909 | ||
2910 | my $x = Math::BigInt->new(30000); | |
2911 | my $y = Math::BigInt->new(7); | |
2912 | print scalar $x->copy()->bdiv($y, 2); # print 4300 | |
2913 | print scalar $x->copy()->bdiv($y)->bround(2); # print 4300 | |
2914 | ||
2915 | Please see the section about L<ACCURACY AND PRECISION> for further details. | |
2916 | ||
2917 | Value must be greater than zero. Pass an undef value to disable it: | |
2918 | ||
2919 | $x->accuracy(undef); | |
2920 | Math::BigInt->accuracy(undef); | |
2921 | ||
2922 | Returns the current accuracy. For C<$x->accuracy()> it will return either the | |
2923 | local accuracy, or if not defined, the global. This means the return value | |
2924 | represents the accuracy that will be in effect for $x: | |
2925 | ||
2926 | $y = Math::BigInt->new(1234567); # unrounded | |
2927 | print Math::BigInt->accuracy(4),"\n"; # set 4, print 4 | |
2928 | $x = Math::BigInt->new(123456); # $x will be automatically rounded! | |
2929 | print "$x $y\n"; # '123500 1234567' | |
2930 | print $x->accuracy(),"\n"; # will be 4 | |
2931 | print $y->accuracy(),"\n"; # also 4, since global is 4 | |
2932 | print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5 | |
2933 | print $x->accuracy(),"\n"; # still 4 | |
2934 | print $y->accuracy(),"\n"; # 5, since global is 5 | |
2935 | ||
2936 | Note: Works also for subclasses like Math::BigFloat. Each class has it's own | |
2937 | globals separated from Math::BigInt, but it is possible to subclass | |
2938 | Math::BigInt and make the globals of the subclass aliases to the ones from | |
2939 | Math::BigInt. | |
2940 | ||
2941 | =head2 precision | |
2942 | ||
2943 | $x->precision(-2); # local for $x, round at the second digit right of the dot | |
2944 | $x->precision(2); # ditto, round at the second digit left of the dot | |
2945 | ||
2946 | CLASS->precision(5); # Global for all members of CLASS | |
2947 | # This also applies to new()! | |
2948 | CLASS->precision(-5); # ditto | |
2949 | ||
2950 | $P = CLASS->precision(); # read out global precision | |
2951 | $P = $x->precision(); # read out precision that affects $x | |
2952 | ||
2953 | Note: You probably want to use L<accuracy()> instead. With L<accuracy> you | |
2954 | set the number of digits each result should have, with L<precision> you | |
2955 | set the place where to round! | |
2956 | ||
2957 | C<precision()> sets or gets the global or local precision, aka at which digit | |
2958 | before or after the dot to round all results. A set global precision also | |
2959 | applies to all newly created numbers! | |
2960 | ||
2961 | In Math::BigInt, passing a negative number precision has no effect since no | |
2962 | numbers have digits after the dot. In L<Math::BigFloat>, it will round all | |
2963 | results to P digits after the dot. | |
2964 | ||
2965 | Please see the section about L<ACCURACY AND PRECISION> for further details. | |
2966 | ||
2967 | Pass an undef value to disable it: | |
2968 | ||
2969 | $x->precision(undef); | |
2970 | Math::BigInt->precision(undef); | |
2971 | ||
2972 | Returns the current precision. For C<$x->precision()> it will return either the | |
2973 | local precision of $x, or if not defined, the global. This means the return | |
2974 | value represents the prevision that will be in effect for $x: | |
2975 | ||
2976 | $y = Math::BigInt->new(1234567); # unrounded | |
2977 | print Math::BigInt->precision(4),"\n"; # set 4, print 4 | |
2978 | $x = Math::BigInt->new(123456); # will be automatically rounded | |
2979 | print $x; # print "120000"! | |
2980 | ||
2981 | Note: Works also for subclasses like L<Math::BigFloat>. Each class has its | |
2982 | own globals separated from Math::BigInt, but it is possible to subclass | |
2983 | Math::BigInt and make the globals of the subclass aliases to the ones from | |
2984 | Math::BigInt. | |
2985 | ||
2986 | =head2 brsft | |
2987 | ||
2988 | $x->brsft($y,$n); | |
2989 | ||
2990 | Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and | |
2991 | 2, but others work, too. | |
2992 | ||
2993 | Right shifting usually amounts to dividing $x by $n ** $y and truncating the | |
2994 | result: | |
2995 | ||
2996 | ||
2997 | $x = Math::BigInt->new(10); | |
2998 | $x->brsft(1); # same as $x >> 1: 5 | |
2999 | $x = Math::BigInt->new(1234); | |
3000 | $x->brsft(2,10); # result 12 | |
3001 | ||
3002 | There is one exception, and that is base 2 with negative $x: | |
3003 | ||
3004 | ||
3005 | $x = Math::BigInt->new(-5); | |
3006 | print $x->brsft(1); | |
3007 | ||
3008 | This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the | |
3009 | result). | |
3010 | ||
3011 | =head2 new | |
3012 | ||
3013 | $x = Math::BigInt->new($str,$A,$P,$R); | |
3014 | ||
3015 | Creates a new BigInt object from a scalar or another BigInt object. The | |
3016 | input is accepted as decimal, hex (with leading '0x') or binary (with leading | |
3017 | '0b'). | |
3018 | ||
3019 | See L<Input> for more info on accepted input formats. | |
3020 | ||
3021 | =head2 bnan | |
3022 | ||
3023 | $x = Math::BigInt->bnan(); | |
3024 | ||
3025 | Creates a new BigInt object representing NaN (Not A Number). | |
3026 | If used on an object, it will set it to NaN: | |
3027 | ||
3028 | $x->bnan(); | |
3029 | ||
3030 | =head2 bzero | |
3031 | ||
3032 | $x = Math::BigInt->bzero(); | |
3033 | ||
3034 | Creates a new BigInt object representing zero. | |
3035 | If used on an object, it will set it to zero: | |
3036 | ||
3037 | $x->bzero(); | |
3038 | ||
3039 | =head2 binf | |
3040 | ||
3041 | $x = Math::BigInt->binf($sign); | |
3042 | ||
3043 | Creates a new BigInt object representing infinity. The optional argument is | |
3044 | either '-' or '+', indicating whether you want infinity or minus infinity. | |
3045 | If used on an object, it will set it to infinity: | |
3046 | ||
3047 | $x->binf(); | |
3048 | $x->binf('-'); | |
3049 | ||
3050 | =head2 bone | |
3051 | ||
3052 | $x = Math::BigInt->binf($sign); | |
3053 | ||
3054 | Creates a new BigInt object representing one. The optional argument is | |
3055 | either '-' or '+', indicating whether you want one or minus one. | |
3056 | If used on an object, it will set it to one: | |
3057 | ||
3058 | $x->bone(); # +1 | |
3059 | $x->bone('-'); # -1 | |
3060 | ||
3061 | =head2 is_one()/is_zero()/is_nan()/is_inf() | |
3062 | ||
3063 | ||
3064 | $x->is_zero(); # true if arg is +0 | |
3065 | $x->is_nan(); # true if arg is NaN | |
3066 | $x->is_one(); # true if arg is +1 | |
3067 | $x->is_one('-'); # true if arg is -1 | |
3068 | $x->is_inf(); # true if +inf | |
3069 | $x->is_inf('-'); # true if -inf (sign is default '+') | |
3070 | ||
3071 | These methods all test the BigInt for beeing one specific value and return | |
3072 | true or false depending on the input. These are faster than doing something | |
3073 | like: | |
3074 | ||
3075 | if ($x == 0) | |
3076 | ||
3077 | =head2 is_pos()/is_neg() | |
3078 | ||
3079 | $x->is_pos(); # true if > 0 | |
3080 | $x->is_neg(); # true if < 0 | |
3081 | ||
3082 | The methods return true if the argument is positive or negative, respectively. | |
3083 | C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and | |
3084 | C<-inf> is negative. A C<zero> is neither positive nor negative. | |
3085 | ||
3086 | These methods are only testing the sign, and not the value. | |
3087 | ||
3088 | C<is_positive()> and C<is_negative()> are aliase to C<is_pos()> and | |
3089 | C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were | |
3090 | introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced | |
3091 | in v1.68. | |
3092 | ||
3093 | =head2 is_odd()/is_even()/is_int() | |
3094 | ||
3095 | $x->is_odd(); # true if odd, false for even | |
3096 | $x->is_even(); # true if even, false for odd | |
3097 | $x->is_int(); # true if $x is an integer | |
3098 | ||
3099 | The return true when the argument satisfies the condition. C<NaN>, C<+inf>, | |
3100 | C<-inf> are not integers and are neither odd nor even. | |
3101 | ||
3102 | In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers. | |
3103 | ||
3104 | =head2 bcmp | |
3105 | ||
3106 | $x->bcmp($y); | |
3107 | ||
3108 | Compares $x with $y and takes the sign into account. | |
3109 | Returns -1, 0, 1 or undef. | |
3110 | ||
3111 | =head2 bacmp | |
3112 | ||
3113 | $x->bacmp($y); | |
3114 | ||
3115 | Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef. | |
3116 | ||
3117 | =head2 sign | |
3118 | ||
3119 | $x->sign(); | |
3120 | ||
3121 | Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN. | |
3122 | ||
3123 | If you want $x to have a certain sign, use one of the following methods: | |
3124 | ||
3125 | $x->babs(); # '+' | |
3126 | $x->babs()->bneg(); # '-' | |
3127 | $x->bnan(); # 'NaN' | |
3128 | $x->binf(); # '+inf' | |
3129 | $x->binf('-'); # '-inf' | |
3130 | ||
3131 | =head2 digit | |
3132 | ||
3133 | $x->digit($n); # return the nth digit, counting from right | |
3134 | ||
3135 | If C<$n> is negative, returns the digit counting from left. | |
3136 | ||
3137 | =head2 bneg | |
3138 | ||
3139 | $x->bneg(); | |
3140 | ||
3141 | Negate the number, e.g. change the sign between '+' and '-', or between '+inf' | |
3142 | and '-inf', respectively. Does nothing for NaN or zero. | |
3143 | ||
3144 | =head2 babs | |
3145 | ||
3146 | $x->babs(); | |
3147 | ||
3148 | Set the number to it's absolute value, e.g. change the sign from '-' to '+' | |
3149 | and from '-inf' to '+inf', respectively. Does nothing for NaN or positive | |
3150 | numbers. | |
3151 | ||
3152 | =head2 bnorm | |
3153 | ||
3154 | $x->bnorm(); # normalize (no-op) | |
3155 | ||
3156 | =head2 bnot | |
3157 | ||
3158 | $x->bnot(); | |
3159 | ||
3160 | Two's complement (bit wise not). This is equivalent to | |
3161 | ||
3162 | $x->binc()->bneg(); | |
3163 | ||
3164 | but faster. | |
3165 | ||
3166 | =head2 binc | |
3167 | ||
3168 | $x->binc(); # increment x by 1 | |
3169 | ||
3170 | =head2 bdec | |
3171 | ||
3172 | $x->bdec(); # decrement x by 1 | |
3173 | ||
3174 | =head2 badd | |
3175 | ||
3176 | $x->badd($y); # addition (add $y to $x) | |
3177 | ||
3178 | =head2 bsub | |
3179 | ||
3180 | $x->bsub($y); # subtraction (subtract $y from $x) | |
3181 | ||
3182 | =head2 bmul | |
3183 | ||
3184 | $x->bmul($y); # multiplication (multiply $x by $y) | |
3185 | ||
3186 | =head2 bdiv | |
3187 | ||
3188 | $x->bdiv($y); # divide, set $x to quotient | |
3189 | # return (quo,rem) or quo if scalar | |
3190 | ||
3191 | =head2 bmod | |
3192 | ||
3193 | $x->bmod($y); # modulus (x % y) | |
3194 | ||
3195 | =head2 bmodinv | |
3196 | ||
3197 | num->bmodinv($mod); # modular inverse | |
3198 | ||
3199 | Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is | |
3200 | returned unless C<$num> is relatively prime to C<$mod>, i.e. unless | |
3201 | C<bgcd($num, $mod)==1>. | |
3202 | ||
3203 | =head2 bmodpow | |
3204 | ||
3205 | $num->bmodpow($exp,$mod); # modular exponentation | |
3206 | # ($num**$exp % $mod) | |
3207 | ||
3208 | Returns the value of C<$num> taken to the power C<$exp> in the modulus | |
3209 | C<$mod> using binary exponentation. C<bmodpow> is far superior to | |
3210 | writing | |
3211 | ||
3212 | $num ** $exp % $mod | |
3213 | ||
3214 | because it is much faster - it reduces internal variables into | |
3215 | the modulus whenever possible, so it operates on smaller numbers. | |
3216 | ||
3217 | C<bmodpow> also supports negative exponents. | |
3218 | ||
3219 | bmodpow($num, -1, $mod) | |
3220 | ||
3221 | is exactly equivalent to | |
3222 | ||
3223 | bmodinv($num, $mod) | |
3224 | ||
3225 | =head2 bpow | |
3226 | ||
3227 | $x->bpow($y); # power of arguments (x ** y) | |
3228 | ||
3229 | =head2 blsft | |
3230 | ||
3231 | $x->blsft($y); # left shift | |
3232 | $x->blsft($y,$n); # left shift, in base $n (like 10) | |
3233 | ||
3234 | =head2 brsft | |
3235 | ||
3236 | $x->brsft($y); # right shift | |
3237 | $x->brsft($y,$n); # right shift, in base $n (like 10) | |
3238 | ||
3239 | =head2 band | |
3240 | ||
3241 | $x->band($y); # bitwise and | |
3242 | ||
3243 | =head2 bior | |
3244 | ||
3245 | $x->bior($y); # bitwise inclusive or | |
3246 | ||
3247 | =head2 bxor | |
3248 | ||
3249 | $x->bxor($y); # bitwise exclusive or | |
3250 | ||
3251 | =head2 bnot | |
3252 | ||
3253 | $x->bnot(); # bitwise not (two's complement) | |
3254 | ||
3255 | =head2 bsqrt | |
3256 | ||
3257 | $x->bsqrt(); # calculate square-root | |
3258 | ||
3259 | =head2 bfac | |
3260 | ||
3261 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) | |
3262 | ||
3263 | =head2 round | |
3264 | ||
3265 | $x->round($A,$P,$round_mode); | |
3266 | ||
3267 | Round $x to accuracy C<$A> or precision C<$P> using the round mode | |
3268 | C<$round_mode>. | |
3269 | ||
3270 | =head2 bround | |
3271 | ||
3272 | $x->bround($N); # accuracy: preserve $N digits | |
3273 | ||
3274 | =head2 bfround | |
3275 | ||
3276 | $x->bfround($N); # round to $Nth digit, no-op for BigInts | |
3277 | ||
3278 | =head2 bfloor | |
3279 | ||
3280 | $x->bfloor(); | |
3281 | ||
3282 | Set $x to the integer less or equal than $x. This is a no-op in BigInt, but | |
3283 | does change $x in BigFloat. | |
3284 | ||
3285 | =head2 bceil | |
3286 | ||
3287 | $x->bceil(); | |
3288 | ||
3289 | Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but | |
3290 | does change $x in BigFloat. | |
3291 | ||
3292 | =head2 bgcd | |
3293 | ||
3294 | bgcd(@values); # greatest common divisor (no OO style) | |
3295 | ||
3296 | =head2 blcm | |
3297 | ||
3298 | blcm(@values); # lowest common multiplicator (no OO style) | |
3299 | ||
3300 | head2 length | |
3301 | ||
3302 | $x->length(); | |
3303 | ($xl,$fl) = $x->length(); | |
3304 | ||
3305 | Returns the number of digits in the decimal representation of the number. | |
3306 | In list context, returns the length of the integer and fraction part. For | |
3307 | BigInt's, the length of the fraction part will always be 0. | |
3308 | ||
3309 | =head2 exponent | |
3310 | ||
3311 | $x->exponent(); | |
3312 | ||
3313 | Return the exponent of $x as BigInt. | |
3314 | ||
3315 | =head2 mantissa | |
3316 | ||
3317 | $x->mantissa(); | |
3318 | ||
3319 | Return the signed mantissa of $x as BigInt. | |
3320 | ||
3321 | =head2 parts | |
3322 | ||
3323 | $x->parts(); # return (mantissa,exponent) as BigInt | |
3324 | ||
3325 | =head2 copy | |
3326 | ||
3327 | $x->copy(); # make a true copy of $x (unlike $y = $x;) | |
3328 | ||
3329 | =head2 as_int | |
3330 | ||
3331 | $x->as_int(); | |
3332 | ||
3333 | Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as | |
3334 | C<copy()>. | |
3335 | ||
3336 | C<as_number()> is an alias to this method. C<as_number> was introduced in | |
3337 | v1.22, while C<as_int()> was only introduced in v1.68. | |
3338 | ||
3339 | =head2 bstr | |
3340 | ||
3341 | $x->bstr(); | |
3342 | ||
3343 | Returns a normalized string represantation of C<$x>. | |
3344 | ||
3345 | =head2 bsstr | |
3346 | ||
3347 | $x->bsstr(); # normalized string in scientific notation | |
3348 | ||
3349 | =head2 as_hex | |
3350 | ||
3351 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x | |
3352 | ||
3353 | =head2 as_bin | |
3354 | ||
3355 | $x->as_bin(); # as signed binary string with prefixed 0b | |
3356 | ||
3357 | =head1 ACCURACY and PRECISION | |
3358 | ||
3359 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for | |
3360 | accuracy and precision based rounding, both automatically after every | |
3361 | operation, as well as manually. | |
3362 | ||
3363 | This section describes the accuracy/precision handling in Math::Big* as it | |
3364 | used to be and as it is now, complete with an explanation of all terms and | |
3365 | abbreviations. | |
3366 | ||
3367 | Not yet implemented things (but with correct description) are marked with '!', | |
3368 | things that need to be answered are marked with '?'. | |
3369 | ||
3370 | In the next paragraph follows a short description of terms used here (because | |
3371 | these may differ from terms used by others people or documentation). | |
3372 | ||
3373 | During the rest of this document, the shortcuts A (for accuracy), P (for | |
3374 | precision), F (fallback) and R (rounding mode) will be used. | |
3375 | ||
3376 | =head2 Precision P | |
3377 | ||
3378 | A fixed number of digits before (positive) or after (negative) | |
3379 | the decimal point. For example, 123.45 has a precision of -2. 0 means an | |
3380 | integer like 123 (or 120). A precision of 2 means two digits to the left | |
3381 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that | |
3382 | numbers with zeros before the decimal point may have different precisions, | |
3383 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value | |
3384 | was). It could also have p < 0, when the digits after the decimal point | |
3385 | are zero. | |
3386 | ||
3387 | The string output (of floating point numbers) will be padded with zeros: | |
3388 | ||
3389 | Initial value P A Result String | |
3390 | ------------------------------------------------------------ | |
3391 | 1234.01 -3 1000 1000 | |
3392 | 1234 -2 1200 1200 | |
3393 | 1234.5 -1 1230 1230 | |
3394 | 1234.001 1 1234 1234.0 | |
3395 | 1234.01 0 1234 1234 | |
3396 | 1234.01 2 1234.01 1234.01 | |
3397 | 1234.01 5 1234.01 1234.01000 | |
3398 | ||
3399 | For BigInts, no padding occurs. | |
3400 | ||
3401 | =head2 Accuracy A | |
3402 | ||
3403 | Number of significant digits. Leading zeros are not counted. A | |
3404 | number may have an accuracy greater than the non-zero digits | |
3405 | when there are zeros in it or trailing zeros. For example, 123.456 has | |
3406 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. | |
3407 | ||
3408 | The string output (of floating point numbers) will be padded with zeros: | |
3409 | ||
3410 | Initial value P A Result String | |
3411 | ------------------------------------------------------------ | |
3412 | 1234.01 3 1230 1230 | |
3413 | 1234.01 6 1234.01 1234.01 | |
3414 | 1234.1 8 1234.1 1234.1000 | |
3415 | ||
3416 | For BigInts, no padding occurs. | |
3417 | ||
3418 | =head2 Fallback F | |
3419 | ||
3420 | When both A and P are undefined, this is used as a fallback accuracy when | |
3421 | dividing numbers. | |
3422 | ||
3423 | =head2 Rounding mode R | |
3424 | ||
3425 | When rounding a number, different 'styles' or 'kinds' | |
3426 | of rounding are possible. (Note that random rounding, as in | |
3427 | Math::Round, is not implemented.) | |
3428 | ||
3429 | =over 2 | |
3430 | ||
3431 | =item 'trunc' | |
3432 | ||
3433 | truncation invariably removes all digits following the | |
3434 | rounding place, replacing them with zeros. Thus, 987.65 rounded | |
3435 | to tens (P=1) becomes 980, and rounded to the fourth sigdig | |
3436 | becomes 987.6 (A=4). 123.456 rounded to the second place after the | |
3437 | decimal point (P=-2) becomes 123.46. | |
3438 | ||
3439 | All other implemented styles of rounding attempt to round to the | |
3440 | "nearest digit." If the digit D immediately to the right of the | |
3441 | rounding place (skipping the decimal point) is greater than 5, the | |
3442 | number is incremented at the rounding place (possibly causing a | |
3443 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds | |
3444 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly | |
3445 | truncated at the rounding place: e.g. when rounding to units, 0.4 | |
3446 | rounds to 0, and -19.4 rounds to -19. | |
3447 | ||
3448 | However the results of other styles of rounding differ if the | |
3449 | digit immediately to the right of the rounding place (skipping the | |
3450 | decimal point) is 5 and if there are no digits, or no digits other | |
3451 | than 0, after that 5. In such cases: | |
3452 | ||
3453 | =item 'even' | |
3454 | ||
3455 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 | |
3456 | if it is not already. E.g., when rounding to the first sigdig, 0.45 | |
3457 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. | |
3458 | ||
3459 | =item 'odd' | |
3460 | ||
3461 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if | |
3462 | it is not already. E.g., when rounding to the first sigdig, 0.45 | |
3463 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. | |
3464 | ||
3465 | =item '+inf' | |
3466 | ||
3467 | round to plus infinity, i.e. always round up. E.g., when | |
3468 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, | |
3469 | and 0.4501 also becomes 0.5. | |
3470 | ||
3471 | =item '-inf' | |
3472 | ||
3473 | round to minus infinity, i.e. always round down. E.g., when | |
3474 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, | |
3475 | but 0.4501 becomes 0.5. | |
3476 | ||
3477 | =item 'zero' | |
3478 | ||
3479 | round to zero, i.e. positive numbers down, negative ones up. | |
3480 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 | |
3481 | becomes -0.5, but 0.4501 becomes 0.5. | |
3482 | ||
3483 | =back | |
3484 | ||
3485 | The handling of A & P in MBI/MBF (the old core code shipped with Perl | |
3486 | versions <= 5.7.2) is like this: | |
3487 | ||
3488 | =over 2 | |
3489 | ||
3490 | =item Precision | |
3491 | ||
3492 | * ffround($p) is able to round to $p number of digits after the decimal | |
3493 | point | |
3494 | * otherwise P is unused | |
3495 | ||
3496 | =item Accuracy (significant digits) | |
3497 | ||
3498 | * fround($a) rounds to $a significant digits | |
3499 | * only fdiv() and fsqrt() take A as (optional) paramater | |
3500 | + other operations simply create the same number (fneg etc), or more (fmul) | |
3501 | of digits | |
3502 | + rounding/truncating is only done when explicitly calling one of fround | |
3503 | or ffround, and never for BigInt (not implemented) | |
3504 | * fsqrt() simply hands its accuracy argument over to fdiv. | |
3505 | * the documentation and the comment in the code indicate two different ways | |
3506 | on how fdiv() determines the maximum number of digits it should calculate, | |
3507 | and the actual code does yet another thing | |
3508 | POD: | |
3509 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) | |
3510 | Comment: | |
3511 | result has at most max(scale, length(dividend), length(divisor)) digits | |
3512 | Actual code: | |
3513 | scale = max(scale, length(dividend)-1,length(divisor)-1); | |
3514 | scale += length(divisior) - length(dividend); | |
3515 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). | |
3516 | Actually, the 'difference' added to the scale is calculated from the | |
3517 | number of "significant digits" in dividend and divisor, which is derived | |
3518 | by looking at the length of the mantissa. Which is wrong, since it includes | |
3519 | the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops | |
3520 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange | |
3521 | assumption that 124 has 3 significant digits, while 120/7 will get you | |
3522 | '17', not '17.1' since 120 is thought to have 2 significant digits. | |
3523 | The rounding after the division then uses the remainder and $y to determine | |
3524 | wether it must round up or down. | |
3525 | ? I have no idea which is the right way. That's why I used a slightly more | |
3526 | ? simple scheme and tweaked the few failing testcases to match it. | |
3527 | ||
3528 | =back | |
3529 | ||
3530 | This is how it works now: | |
3531 | ||
3532 | =over 2 | |
3533 | ||
3534 | =item Setting/Accessing | |
3535 | ||
3536 | * You can set the A global via C<< Math::BigInt->accuracy() >> or | |
3537 | C<< Math::BigFloat->accuracy() >> or whatever class you are using. | |
3538 | * You can also set P globally by using C<< Math::SomeClass->precision() >> | |
3539 | likewise. | |
3540 | * Globals are classwide, and not inherited by subclasses. | |
3541 | * to undefine A, use C<< Math::SomeCLass->accuracy(undef); >> | |
3542 | * to undefine P, use C<< Math::SomeClass->precision(undef); >> | |
3543 | * Setting C<< Math::SomeClass->accuracy() >> clears automatically | |
3544 | C<< Math::SomeClass->precision() >>, and vice versa. | |
3545 | * To be valid, A must be > 0, P can have any value. | |
3546 | * If P is negative, this means round to the P'th place to the right of the | |
3547 | decimal point; positive values mean to the left of the decimal point. | |
3548 | P of 0 means round to integer. | |
3549 | * to find out the current global A, use C<< Math::SomeClass->accuracy() >> | |
3550 | * to find out the current global P, use C<< Math::SomeClass->precision() >> | |
3551 | * use C<< $x->accuracy() >> respective C<< $x->precision() >> for the local | |
3552 | setting of C<< $x >>. | |
3553 | * Please note that C<< $x->accuracy() >> respecive C<< $x->precision() >> | |
3554 | return eventually defined global A or P, when C<< $x >>'s A or P is not | |
3555 | set. | |
3556 | ||
3557 | =item Creating numbers | |
3558 | ||
3559 | * When you create a number, you can give it's desired A or P via: | |
3560 | $x = Math::BigInt->new($number,$A,$P); | |
3561 | * Only one of A or P can be defined, otherwise the result is NaN | |
3562 | * If no A or P is give ($x = Math::BigInt->new($number) form), then the | |
3563 | globals (if set) will be used. Thus changing the global defaults later on | |
3564 | will not change the A or P of previously created numbers (i.e., A and P of | |
3565 | $x will be what was in effect when $x was created) | |
3566 | * If given undef for A and P, B<no> rounding will occur, and the globals will | |
3567 | B<not> be used. This is used by subclasses to create numbers without | |
3568 | suffering rounding in the parent. Thus a subclass is able to have it's own | |
3569 | globals enforced upon creation of a number by using | |
3570 | C<< $x = Math::BigInt->new($number,undef,undef) >>: | |
3571 | ||
3572 | use Math::BigInt::SomeSubclass; | |
3573 | use Math::BigInt; | |
3574 | ||
3575 | Math::BigInt->accuracy(2); | |
3576 | Math::BigInt::SomeSubClass->accuracy(3); | |
3577 | $x = Math::BigInt::SomeSubClass->new(1234); | |
3578 | ||
3579 | $x is now 1230, and not 1200. A subclass might choose to implement | |
3580 | this otherwise, e.g. falling back to the parent's A and P. | |
3581 | ||
3582 | =item Usage | |
3583 | ||
3584 | * If A or P are enabled/defined, they are used to round the result of each | |
3585 | operation according to the rules below | |
3586 | * Negative P is ignored in Math::BigInt, since BigInts never have digits | |
3587 | after the decimal point | |
3588 | * Math::BigFloat uses Math::BigInt internally, but setting A or P inside | |
3589 | Math::BigInt as globals does not tamper with the parts of a BigFloat. | |
3590 | A flag is used to mark all Math::BigFloat numbers as 'never round'. | |
3591 | ||
3592 | =item Precedence | |
3593 | ||
3594 | * It only makes sense that a number has only one of A or P at a time. | |
3595 | If you set either A or P on one object, or globally, the other one will | |
3596 | be automatically cleared. | |
3597 | * If two objects are involved in an operation, and one of them has A in | |
3598 | effect, and the other P, this results in an error (NaN). | |
3599 | * A takes precendence over P (Hint: A comes before P). | |
3600 | If neither of them is defined, nothing is used, i.e. the result will have | |
3601 | as many digits as it can (with an exception for fdiv/fsqrt) and will not | |
3602 | be rounded. | |
3603 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of | |
3604 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. | |
3605 | If either the dividend's or the divisor's mantissa has more digits than | |
3606 | the value of F, the higher value will be used instead of F. | |
3607 | This is to limit the digits (A) of the result (just consider what would | |
3608 | happen with unlimited A and P in the case of 1/3 :-) | |
3609 | * fdiv will calculate (at least) 4 more digits than required (determined by | |
3610 | A, P or F), and, if F is not used, round the result | |
3611 | (this will still fail in the case of a result like 0.12345000000001 with A | |
3612 | or P of 5, but this can not be helped - or can it?) | |
3613 | * Thus you can have the math done by on Math::Big* class in two modi: | |
3614 | + never round (this is the default): | |
3615 | This is done by setting A and P to undef. No math operation | |
3616 | will round the result, with fdiv() and fsqrt() as exceptions to guard | |
3617 | against overflows. You must explicitely call bround(), bfround() or | |
3618 | round() (the latter with parameters). | |
3619 | Note: Once you have rounded a number, the settings will 'stick' on it | |
3620 | and 'infect' all other numbers engaged in math operations with it, since | |
3621 | local settings have the highest precedence. So, to get SaferRound[tm], | |
3622 | use a copy() before rounding like this: | |
3623 | ||
3624 | $x = Math::BigFloat->new(12.34); | |
3625 | $y = Math::BigFloat->new(98.76); | |
3626 | $z = $x * $y; # 1218.6984 | |
3627 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) | |
3628 | $z = $x * $y; # still 1218.6984, without | |
3629 | # copy would have been 1210! | |
3630 | ||
3631 | + round after each op: | |
3632 | After each single operation (except for testing like is_zero()), the | |
3633 | method round() is called and the result is rounded appropriately. By | |
3634 | setting proper values for A and P, you can have all-the-same-A or | |
3635 | all-the-same-P modes. For example, Math::Currency might set A to undef, | |
3636 | and P to -2, globally. | |
3637 | ||
3638 | ?Maybe an extra option that forbids local A & P settings would be in order, | |
3639 | ?so that intermediate rounding does not 'poison' further math? | |
3640 | ||
3641 | =item Overriding globals | |
3642 | ||
3643 | * you will be able to give A, P and R as an argument to all the calculation | |
3644 | routines; the second parameter is A, the third one is P, and the fourth is | |
3645 | R (shift right by one for binary operations like badd). P is used only if | |
3646 | the first parameter (A) is undefined. These three parameters override the | |
3647 | globals in the order detailed as follows, i.e. the first defined value | |
3648 | wins: | |
3649 | (local: per object, global: global default, parameter: argument to sub) | |
3650 | + parameter A | |
3651 | + parameter P | |
3652 | + local A (if defined on both of the operands: smaller one is taken) | |
3653 | + local P (if defined on both of the operands: bigger one is taken) | |
3654 | + global A | |
3655 | + global P | |
3656 | + global F | |
3657 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two | |
3658 | arguments (A and P) instead of one | |
3659 | ||
3660 | =item Local settings | |
3661 | ||
3662 | * You can set A or P locally by using C<< $x->accuracy() >> or | |
3663 | C<< $x->precision() >> | |
3664 | and thus force different A and P for different objects/numbers. | |
3665 | * Setting A or P this way immediately rounds $x to the new value. | |
3666 | * C<< $x->accuracy() >> clears C<< $x->precision() >>, and vice versa. | |
3667 | ||
3668 | =item Rounding | |
3669 | ||
3670 | * the rounding routines will use the respective global or local settings. | |
3671 | fround()/bround() is for accuracy rounding, while ffround()/bfround() | |
3672 | is for precision | |
3673 | * the two rounding functions take as the second parameter one of the | |
3674 | following rounding modes (R): | |
3675 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' | |
3676 | * you can set/get the global R by using C<< Math::SomeClass->round_mode() >> | |
3677 | or by setting C<< $Math::SomeClass::round_mode >> | |
3678 | * after each operation, C<< $result->round() >> is called, and the result may | |
3679 | eventually be rounded (that is, if A or P were set either locally, | |
3680 | globally or as parameter to the operation) | |
3681 | * to manually round a number, call C<< $x->round($A,$P,$round_mode); >> | |
3682 | this will round the number by using the appropriate rounding function | |
3683 | and then normalize it. | |
3684 | * rounding modifies the local settings of the number: | |
3685 | ||
3686 | $x = Math::BigFloat->new(123.456); | |
3687 | $x->accuracy(5); | |
3688 | $x->bround(4); | |
3689 | ||
3690 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() | |
3691 | will be 4 from now on. | |
3692 | ||
3693 | =item Default values | |
3694 | ||
3695 | * R: 'even' | |
3696 | * F: 40 | |
3697 | * A: undef | |
3698 | * P: undef | |
3699 | ||
3700 | =item Remarks | |
3701 | ||
3702 | * The defaults are set up so that the new code gives the same results as | |
3703 | the old code (except in a few cases on fdiv): | |
3704 | + Both A and P are undefined and thus will not be used for rounding | |
3705 | after each operation. | |
3706 | + round() is thus a no-op, unless given extra parameters A and P | |
3707 | ||
3708 | =back | |
3709 | ||
3710 | =head1 Infinity and Not a Number | |
3711 | ||
3712 | While BigInt has extensive handling of inf and NaN, certain quirks remain. | |
3713 | ||
3714 | =over 2 | |
3715 | ||
3716 | =item oct()/hex() | |
3717 | ||
3718 | These perl routines currently (as of Perl v.5.8.6) cannot handle passed | |
3719 | inf. | |
3720 | ||
3721 | te@linux:~> perl -wle 'print 2 ** 3333' | |
3722 | inf | |
3723 | te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333' | |
3724 | 1 | |
3725 | te@linux:~> perl -wle 'print oct(2 ** 3333)' | |
3726 | 0 | |
3727 | te@linux:~> perl -wle 'print hex(2 ** 3333)' | |
3728 | Illegal hexadecimal digit 'i' ignored at -e line 1. | |
3729 | 0 | |
3730 | ||
3731 | The same problems occur if you pass them Math::BigInt->binf() objects. Since | |
3732 | overloading these routines is not possible, this cannot be fixed from BigInt. | |
3733 | ||
3734 | =item ==, !=, <, >, <=, >= with NaNs | |
3735 | ||
3736 | BigInt's bcmp() routine currently returns undef to signal that a NaN was | |
3737 | involved in a comparisation. However, the overload code turns that into | |
3738 | either 1 or '' and thus operations like C<< NaN != NaN >> might return | |
3739 | wrong values. | |
3740 | ||
3741 | =item log(-inf) | |
3742 | ||
3743 | C<< log(-inf) >> is highly weird. Since log(-x)=pi*i+log(x), then | |
3744 | log(-inf)=pi*i+inf. However, since the imaginary part is finite, the real | |
3745 | infinity "overshadows" it, so the number might as well just be infinity. | |
3746 | However, the result is a complex number, and since BigInt/BigFloat can only | |
3747 | have real numbers as results, the result is NaN. | |
3748 | ||
3749 | =item exp(), cos(), sin(), atan2() | |
3750 | ||
3751 | These all might have problems handling infinity right. | |
3752 | ||
3753 | =back | |
3754 | ||
3755 | =head1 INTERNALS | |
3756 | ||
3757 | The actual numbers are stored as unsigned big integers (with seperate sign). | |
3758 | ||
3759 | You should neither care about nor depend on the internal representation; it | |
3760 | might change without notice. Use B<ONLY> method calls like C<< $x->sign(); >> | |
3761 | instead relying on the internal representation. | |
3762 | ||
3763 | =head2 MATH LIBRARY | |
3764 | ||
3765 | Math with the numbers is done (by default) by a module called | |
3766 | C<Math::BigInt::Calc>. This is equivalent to saying: | |
3767 | ||
3768 | use Math::BigInt lib => 'Calc'; | |
3769 | ||
3770 | You can change this by using: | |
3771 | ||
3772 | use Math::BigInt lib => 'BitVect'; | |
3773 | ||
3774 | The following would first try to find Math::BigInt::Foo, then | |
3775 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
3776 | ||
3777 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; | |
3778 | ||
3779 | Since Math::BigInt::GMP is in almost all cases faster than Calc (especially in | |
3780 | math involving really big numbers, where it is B<much> faster), and there is | |
3781 | no penalty if Math::BigInt::GMP is not installed, it is a good idea to always | |
3782 | use the following: | |
3783 | ||
3784 | use Math::BigInt lib => 'GMP'; | |
3785 | ||
3786 | Different low-level libraries use different formats to store the | |
3787 | numbers. You should B<NOT> depend on the number having a specific format | |
3788 | internally. | |
3789 | ||
3790 | See the respective math library module documentation for further details. | |
3791 | ||
3792 | =head2 SIGN | |
3793 | ||
3794 | The sign is either '+', '-', 'NaN', '+inf' or '-inf'. | |
3795 | ||
3796 | A sign of 'NaN' is used to represent the result when input arguments are not | |
3797 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively | |
3798 | minus infinity. You will get '+inf' when dividing a positive number by 0, and | |
3799 | '-inf' when dividing any negative number by 0. | |
3800 | ||
3801 | =head2 mantissa(), exponent() and parts() | |
3802 | ||
3803 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such | |
3804 | that: | |
3805 | ||
3806 | $m = $x->mantissa(); | |
3807 | $e = $x->exponent(); | |
3808 | $y = $m * ( 10 ** $e ); | |
3809 | print "ok\n" if $x == $y; | |
3810 | ||
3811 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them | |
3812 | in one go. Both the returned mantissa and exponent have a sign. | |
3813 | ||
3814 | Currently, for BigInts C<$e> is always 0, except for NaN, +inf and -inf, | |
3815 | where it is C<NaN>; and for C<$x == 0>, where it is C<1> (to be compatible | |
3816 | with Math::BigFloat's internal representation of a zero as C<0E1>). | |
3817 | ||
3818 | C<$m> is currently just a copy of the original number. The relation between | |
3819 | C<$e> and C<$m> will stay always the same, though their real values might | |
3820 | change. | |
3821 | ||
3822 | =head1 EXAMPLES | |
3823 | ||
3824 | use Math::BigInt; | |
3825 | ||
3826 | sub bint { Math::BigInt->new(shift); } | |
3827 | ||
3828 | $x = Math::BigInt->bstr("1234") # string "1234" | |
3829 | $x = "$x"; # same as bstr() | |
3830 | $x = Math::BigInt->bneg("1234"); # BigInt "-1234" | |
3831 | $x = Math::BigInt->babs("-12345"); # BigInt "12345" | |
3832 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" | |
3833 | $x = bint(1) + bint(2); # BigInt "3" | |
3834 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") | |
3835 | $x = bint(1); # BigInt "1" | |
3836 | $x = $x + 5 / 2; # BigInt "3" | |
3837 | $x = $x ** 3; # BigInt "27" | |
3838 | $x *= 2; # BigInt "54" | |
3839 | $x = Math::BigInt->new(0); # BigInt "0" | |
3840 | $x--; # BigInt "-1" | |
3841 | $x = Math::BigInt->badd(4,5) # BigInt "9" | |
3842 | print $x->bsstr(); # 9e+0 | |
3843 | ||
3844 | Examples for rounding: | |
3845 | ||
3846 | use Math::BigFloat; | |
3847 | use Test; | |
3848 | ||
3849 | $x = Math::BigFloat->new(123.4567); | |
3850 | $y = Math::BigFloat->new(123.456789); | |
3851 | Math::BigFloat->accuracy(4); # no more A than 4 | |
3852 | ||
3853 | ok ($x->copy()->fround(),123.4); # even rounding | |
3854 | print $x->copy()->fround(),"\n"; # 123.4 | |
3855 | Math::BigFloat->round_mode('odd'); # round to odd | |
3856 | print $x->copy()->fround(),"\n"; # 123.5 | |
3857 | Math::BigFloat->accuracy(5); # no more A than 5 | |
3858 | Math::BigFloat->round_mode('odd'); # round to odd | |
3859 | print $x->copy()->fround(),"\n"; # 123.46 | |
3860 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 | |
3861 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 | |
3862 | ||
3863 | Math::BigFloat->accuracy(undef); # A not important now | |
3864 | Math::BigFloat->precision(2); # P important | |
3865 | print $x->copy()->bnorm(),"\n"; # 123.46 | |
3866 | print $x->copy()->fround(),"\n"; # 123.46 | |
3867 | ||
3868 | Examples for converting: | |
3869 | ||
3870 | my $x = Math::BigInt->new('0b1'.'01' x 123); | |
3871 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; | |
3872 | ||
3873 | =head1 Autocreating constants | |
3874 | ||
3875 | After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal | |
3876 | and binary constants in the given scope are converted to C<Math::BigInt>. | |
3877 | This conversion happens at compile time. | |
3878 | ||
3879 | In particular, | |
3880 | ||
3881 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' | |
3882 | ||
3883 | prints the integer value of C<2**100>. Note that without conversion of | |
3884 | constants the expression 2**100 will be calculated as perl scalar. | |
3885 | ||
3886 | Please note that strings and floating point constants are not affected, | |
3887 | so that | |
3888 | ||
3889 | use Math::BigInt qw/:constant/; | |
3890 | ||
3891 | $x = 1234567890123456789012345678901234567890 | |
3892 | + 123456789123456789; | |
3893 | $y = '1234567890123456789012345678901234567890' | |
3894 | + '123456789123456789'; | |
3895 | ||
3896 | do not work. You need an explicit Math::BigInt->new() around one of the | |
3897 | operands. You should also quote large constants to protect loss of precision: | |
3898 | ||
3899 | use Math::BigInt; | |
3900 | ||
3901 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); | |
3902 | ||
3903 | Without the quotes Perl would convert the large number to a floating point | |
3904 | constant at compile time and then hand the result to BigInt, which results in | |
3905 | an truncated result or a NaN. | |
3906 | ||
3907 | This also applies to integers that look like floating point constants: | |
3908 | ||
3909 | use Math::BigInt ':constant'; | |
3910 | ||
3911 | print ref(123e2),"\n"; | |
3912 | print ref(123.2e2),"\n"; | |
3913 | ||
3914 | will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat> | |
3915 | to get this to work. | |
3916 | ||
3917 | =head1 PERFORMANCE | |
3918 | ||
3919 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x | |
3920 | must be made in the second case. For long numbers, the copy can eat up to 20% | |
3921 | of the work (in the case of addition/subtraction, less for | |
3922 | multiplication/division). If $y is very small compared to $x, the form | |
3923 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes | |
3924 | more time then the actual addition. | |
3925 | ||
3926 | With a technique called copy-on-write, the cost of copying with overload could | |
3927 | be minimized or even completely avoided. A test implementation of COW did show | |
3928 | performance gains for overloaded math, but introduced a performance loss due | |
3929 | to a constant overhead for all other operatons. So Math::BigInt does currently | |
3930 | not COW. | |
3931 | ||
3932 | The rewritten version of this module (vs. v0.01) is slower on certain | |
3933 | operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it | |
3934 | does now more work and handles much more cases. The time spent in these | |
3935 | operations is usually gained in the other math operations so that code on | |
3936 | the average should get (much) faster. If they don't, please contact the author. | |
3937 | ||
3938 | Some operations may be slower for small numbers, but are significantly faster | |
3939 | for big numbers. Other operations are now constant (O(1), like C<bneg()>, | |
3940 | C<babs()> etc), instead of O(N) and thus nearly always take much less time. | |
3941 | These optimizations were done on purpose. | |
3942 | ||
3943 | If you find the Calc module to slow, try to install any of the replacement | |
3944 | modules and see if they help you. | |
3945 | ||
3946 | =head2 Alternative math libraries | |
3947 | ||
3948 | You can use an alternative library to drive Math::BigInt via: | |
3949 | ||
3950 | use Math::BigInt lib => 'Module'; | |
3951 | ||
3952 | See L<MATH LIBRARY> for more information. | |
3953 | ||
3954 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. | |
3955 | ||
3956 | =head2 SUBCLASSING | |
3957 | ||
3958 | =head1 Subclassing Math::BigInt | |
3959 | ||
3960 | The basic design of Math::BigInt allows simple subclasses with very little | |
3961 | work, as long as a few simple rules are followed: | |
3962 | ||
3963 | =over 2 | |
3964 | ||
3965 | =item * | |
3966 | ||
3967 | The public API must remain consistent, i.e. if a sub-class is overloading | |
3968 | addition, the sub-class must use the same name, in this case badd(). The | |
3969 | reason for this is that Math::BigInt is optimized to call the object methods | |
3970 | directly. | |
3971 | ||
3972 | =item * | |
3973 | ||
3974 | The private object hash keys like C<$x->{sign}> may not be changed, but | |
3975 | additional keys can be added, like C<$x->{_custom}>. | |
3976 | ||
3977 | =item * | |
3978 | ||
3979 | Accessor functions are available for all existing object hash keys and should | |
3980 | be used instead of directly accessing the internal hash keys. The reason for | |
3981 | this is that Math::BigInt itself has a pluggable interface which permits it | |
3982 | to support different storage methods. | |
3983 | ||
3984 | =back | |
3985 | ||
3986 | More complex sub-classes may have to replicate more of the logic internal of | |
3987 | Math::BigInt if they need to change more basic behaviors. A subclass that | |
3988 | needs to merely change the output only needs to overload C<bstr()>. | |
3989 | ||
3990 | All other object methods and overloaded functions can be directly inherited | |
3991 | from the parent class. | |
3992 | ||
3993 | At the very minimum, any subclass will need to provide it's own C<new()> and can | |
3994 | store additional hash keys in the object. There are also some package globals | |
3995 | that must be defined, e.g.: | |
3996 | ||
3997 | # Globals | |
3998 | $accuracy = undef; | |
3999 | $precision = -2; # round to 2 decimal places | |
4000 | $round_mode = 'even'; | |
4001 | $div_scale = 40; | |
4002 | ||
4003 | Additionally, you might want to provide the following two globals to allow | |
4004 | auto-upgrading and auto-downgrading to work correctly: | |
4005 | ||
4006 | $upgrade = undef; | |
4007 | $downgrade = undef; | |
4008 | ||
4009 | This allows Math::BigInt to correctly retrieve package globals from the | |
4010 | subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or | |
4011 | t/Math/BigFloat/SubClass.pm completely functional subclass examples. | |
4012 | ||
4013 | Don't forget to | |
4014 | ||
4015 | use overload; | |
4016 | ||
4017 | in your subclass to automatically inherit the overloading from the parent. If | |
4018 | you like, you can change part of the overloading, look at Math::String for an | |
4019 | example. | |
4020 | ||
4021 | =head1 UPGRADING | |
4022 | ||
4023 | When used like this: | |
4024 | ||
4025 | use Math::BigInt upgrade => 'Foo::Bar'; | |
4026 | ||
4027 | certain operations will 'upgrade' their calculation and thus the result to | |
4028 | the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat: | |
4029 | ||
4030 | use Math::BigInt upgrade => 'Math::BigFloat'; | |
4031 | ||
4032 | As a shortcut, you can use the module C<bignum>: | |
4033 | ||
4034 | use bignum; | |
4035 | ||
4036 | Also good for oneliners: | |
4037 | ||
4038 | perl -Mbignum -le 'print 2 ** 255' | |
4039 | ||
4040 | This makes it possible to mix arguments of different classes (as in 2.5 + 2) | |
4041 | as well es preserve accuracy (as in sqrt(3)). | |
4042 | ||
4043 | Beware: This feature is not fully implemented yet. | |
4044 | ||
4045 | =head2 Auto-upgrade | |
4046 | ||
4047 | The following methods upgrade themselves unconditionally; that is if upgrade | |
4048 | is in effect, they will always hand up their work: | |
4049 | ||
4050 | =over 2 | |
4051 | ||
4052 | =item bsqrt() | |
4053 | ||
4054 | =item div() | |
4055 | ||
4056 | =item blog() | |
4057 | ||
4058 | =back | |
4059 | ||
4060 | Beware: This list is not complete. | |
4061 | ||
4062 | All other methods upgrade themselves only when one (or all) of their | |
4063 | arguments are of the class mentioned in $upgrade (This might change in later | |
4064 | versions to a more sophisticated scheme): | |
4065 | ||
4066 | =head1 BUGS | |
4067 | ||
4068 | =over 2 | |
4069 | ||
4070 | =item broot() does not work | |
4071 | ||
4072 | The broot() function in BigInt may only work for small values. This will be | |
4073 | fixed in a later version. | |
4074 | ||
4075 | =item Out of Memory! | |
4076 | ||
4077 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and | |
4078 | C<eval()> in your code will crash with "Out of memory". This is probably an | |
4079 | overload/exporter bug. You can workaround by not having C<eval()> | |
4080 | and ':constant' at the same time or upgrade your Perl to a newer version. | |
4081 | ||
4082 | =item Fails to load Calc on Perl prior 5.6.0 | |
4083 | ||
4084 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt | |
4085 | will fall back to eval { require ... } when loading the math lib on Perls | |
4086 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on | |
4087 | filesystems using a different seperator. | |
4088 | ||
4089 | =back | |
4090 | ||
4091 | =head1 CAVEATS | |
4092 | ||
4093 | Some things might not work as you expect them. Below is documented what is | |
4094 | known to be troublesome: | |
4095 | ||
4096 | =over 1 | |
4097 | ||
4098 | =item bstr(), bsstr() and 'cmp' | |
4099 | ||
4100 | Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now | |
4101 | drop the leading '+'. The old code would return '+3', the new returns '3'. | |
4102 | This is to be consistent with Perl and to make C<cmp> (especially with | |
4103 | overloading) to work as you expect. It also solves problems with C<Test.pm>, | |
4104 | because it's C<ok()> uses 'eq' internally. | |
4105 | ||
4106 | Mark Biggar said, when asked about to drop the '+' altogether, or make only | |
4107 | C<cmp> work: | |
4108 | ||
4109 | I agree (with the first alternative), don't add the '+' on positive | |
4110 | numbers. It's not as important anymore with the new internal | |
4111 | form for numbers. It made doing things like abs and neg easier, | |
4112 | but those have to be done differently now anyway. | |
4113 | ||
4114 | So, the following examples will now work all as expected: | |
4115 | ||
4116 | use Test; | |
4117 | BEGIN { plan tests => 1 } | |
4118 | use Math::BigInt; | |
4119 | ||
4120 | my $x = new Math::BigInt 3*3; | |
4121 | my $y = new Math::BigInt 3*3; | |
4122 | ||
4123 | ok ($x,3*3); | |
4124 | print "$x eq 9" if $x eq $y; | |
4125 | print "$x eq 9" if $x eq '9'; | |
4126 | print "$x eq 9" if $x eq 3*3; | |
4127 | ||
4128 | Additionally, the following still works: | |
4129 | ||
4130 | print "$x == 9" if $x == $y; | |
4131 | print "$x == 9" if $x == 9; | |
4132 | print "$x == 9" if $x == 3*3; | |
4133 | ||
4134 | There is now a C<bsstr()> method to get the string in scientific notation aka | |
4135 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() | |
4136 | for comparisation, but Perl will represent some numbers as 100 and others | |
4137 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before | |
4138 | comparing them as strings: | |
4139 | ||
4140 | use Test; | |
4141 | BEGIN { plan tests => 3 } | |
4142 | use Math::BigInt; | |
4143 | ||
4144 | $x = Math::BigInt->new('1e56'); $y = 1e56; | |
4145 | ok ($x,$y); # will fail | |
4146 | ok ($x->bsstr(),$y); # okay | |
4147 | $y = Math::BigInt->new($y); | |
4148 | ok ($x,$y); # okay | |
4149 | ||
4150 | Alternatively, simple use C<< <=> >> for comparisations, this will get it | |
4151 | always right. There is not yet a way to get a number automatically represented | |
4152 | as a string that matches exactly the way Perl represents it. | |
4153 | ||
4154 | See also the section about L<Infinity and Not a Number> for problems in | |
4155 | comparing NaNs. | |
4156 | ||
4157 | =item int() | |
4158 | ||
4159 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a | |
4160 | Perl scalar: | |
4161 | ||
4162 | $x = Math::BigInt->new(123); | |
4163 | $y = int($x); # BigInt 123 | |
4164 | $x = Math::BigFloat->new(123.45); | |
4165 | $y = int($x); # BigInt 123 | |
4166 | ||
4167 | In all Perl versions you can use C<as_number()> or C<as_int> for the same | |
4168 | effect: | |
4169 | ||
4170 | $x = Math::BigFloat->new(123.45); | |
4171 | $y = $x->as_number(); # BigInt 123 | |
4172 | $y = $x->as_int(); # ditto | |
4173 | ||
4174 | This also works for other subclasses, like Math::String. | |
4175 | ||
4176 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. | |
4177 | ||
4178 | If you want a real Perl scalar, use C<numify()>: | |
4179 | ||
4180 | $y = $x->numify(); # 123 as scalar | |
4181 | ||
4182 | This is seldom necessary, though, because this is done automatically, like | |
4183 | when you access an array: | |
4184 | ||
4185 | $z = $array[$x]; # does work automatically | |
4186 | ||
4187 | =item length | |
4188 | ||
4189 | The following will probably not do what you expect: | |
4190 | ||
4191 | $c = Math::BigInt->new(123); | |
4192 | print $c->length(),"\n"; # prints 30 | |
4193 | ||
4194 | It prints both the number of digits in the number and in the fraction part | |
4195 | since print calls C<length()> in list context. Use something like: | |
4196 | ||
4197 | print scalar $c->length(),"\n"; # prints 3 | |
4198 | ||
4199 | =item bdiv | |
4200 | ||
4201 | The following will probably not do what you expect: | |
4202 | ||
4203 | print $c->bdiv(10000),"\n"; | |
4204 | ||
4205 | It prints both quotient and remainder since print calls C<bdiv()> in list | |
4206 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want | |
4207 | to use | |
4208 | ||
4209 | print $c / 10000,"\n"; | |
4210 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c | |
4211 | ||
4212 | instead. | |
4213 | ||
4214 | The quotient is always the greatest integer less than or equal to the | |
4215 | real-valued quotient of the two operands, and the remainder (when it is | |
4216 | nonzero) always has the same sign as the second operand; so, for | |
4217 | example, | |
4218 | ||
4219 | 1 / 4 => ( 0, 1) | |
4220 | 1 / -4 => (-1,-3) | |
4221 | -3 / 4 => (-1, 1) | |
4222 | -3 / -4 => ( 0,-3) | |
4223 | -11 / 2 => (-5,1) | |
4224 | 11 /-2 => (-5,-1) | |
4225 | ||
4226 | As a consequence, the behavior of the operator % agrees with the | |
4227 | behavior of Perl's built-in % operator (as documented in the perlop | |
4228 | manpage), and the equation | |
4229 | ||
4230 | $x == ($x / $y) * $y + ($x % $y) | |
4231 | ||
4232 | holds true for any $x and $y, which justifies calling the two return | |
4233 | values of bdiv() the quotient and remainder. The only exception to this rule | |
4234 | are when $y == 0 and $x is negative, then the remainder will also be | |
4235 | negative. See below under "infinity handling" for the reasoning behing this. | |
4236 | ||
4237 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will | |
4238 | not change BigInt's way to do things. This is because under 'use integer' Perl | |
4239 | will do what the underlying C thinks is right and this is different for each | |
4240 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug | |
4241 | the author to implement it ;) | |
4242 | ||
4243 | =item infinity handling | |
4244 | ||
4245 | Here are some examples that explain the reasons why certain results occur while | |
4246 | handling infinity: | |
4247 | ||
4248 | The following table shows the result of the division and the remainder, so that | |
4249 | the equation above holds true. Some "ordinary" cases are strewn in to show more | |
4250 | clearly the reasoning: | |
4251 | ||
4252 | A / B = C, R so that C * B + R = A | |
4253 | ========================================================= | |
4254 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 | |
4255 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 | |
4256 | 0 / inf = 0, 0 0 * inf + 0 = 0 | |
4257 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 | |
4258 | 5 / inf = 0, 5 0 * inf + 5 = 5 | |
4259 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 | |
4260 | -5/ inf = 0, -5 0 * inf + -5 = -5 | |
4261 | -5/-inf = 0, -5 0 * -inf + -5 = -5 | |
4262 | inf/ 5 = inf, 0 inf * 5 + 0 = inf | |
4263 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf | |
4264 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf | |
4265 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf | |
4266 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 | |
4267 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 | |
4268 | inf/ inf = 1, 0 1 * inf + 0 = inf | |
4269 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf | |
4270 | inf/-inf = -1, 0 -1 * -inf + 0 = inf | |
4271 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf | |
4272 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 | |
4273 | inf/ 0 = inf, inf inf * 0 + inf = inf | |
4274 | 0/ 0 = NaN | |
4275 | ||
4276 | These cases below violate the "remainder has the sign of the second of the two | |
4277 | arguments", since they wouldn't match up otherwise. | |
4278 | ||
4279 | A / B = C, R so that C * B + R = A | |
4280 | ======================================================== | |
4281 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf | |
4282 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 | |
4283 | ||
4284 | =item Modifying and = | |
4285 | ||
4286 | Beware of: | |
4287 | ||
4288 | $x = Math::BigFloat->new(5); | |
4289 | $y = $x; | |
4290 | ||
4291 | It will not do what you think, e.g. making a copy of $x. Instead it just makes | |
4292 | a second reference to the B<same> object and stores it in $y. Thus anything | |
4293 | that modifies $x (except overloaded operators) will modify $y, and vice versa. | |
4294 | Or in other words, C<=> is only safe if you modify your BigInts only via | |
4295 | overloaded math. As soon as you use a method call it breaks: | |
4296 | ||
4297 | $x->bmul(2); | |
4298 | print "$x, $y\n"; # prints '10, 10' | |
4299 | ||
4300 | If you want a true copy of $x, use: | |
4301 | ||
4302 | $y = $x->copy(); | |
4303 | ||
4304 | You can also chain the calls like this, this will make first a copy and then | |
4305 | multiply it by 2: | |
4306 | ||
4307 | $y = $x->copy()->bmul(2); | |
4308 | ||
4309 | See also the documentation for overload.pm regarding C<=>. | |
4310 | ||
4311 | =item bpow | |
4312 | ||
4313 | C<bpow()> (and the rounding functions) now modifies the first argument and | |
4314 | returns it, unlike the old code which left it alone and only returned the | |
4315 | result. This is to be consistent with C<badd()> etc. The first three will | |
4316 | modify $x, the last one won't: | |
4317 | ||
4318 | print bpow($x,$i),"\n"; # modify $x | |
4319 | print $x->bpow($i),"\n"; # ditto | |
4320 | print $x **= $i,"\n"; # the same | |
4321 | print $x ** $i,"\n"; # leave $x alone | |
4322 | ||
4323 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. | |
4324 | ||
4325 | =item Overloading -$x | |
4326 | ||
4327 | The following: | |
4328 | ||
4329 | $x = -$x; | |
4330 | ||
4331 | is slower than | |
4332 | ||
4333 | $x->bneg(); | |
4334 | ||
4335 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant | |
4336 | needs to preserve $x since it does not know that it later will get overwritten. | |
4337 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). | |
4338 | ||
4339 | =item Mixing different object types | |
4340 | ||
4341 | In Perl you will get a floating point value if you do one of the following: | |
4342 | ||
4343 | $float = 5.0 + 2; | |
4344 | $float = 2 + 5.0; | |
4345 | $float = 5 / 2; | |
4346 | ||
4347 | With overloaded math, only the first two variants will result in a BigFloat: | |
4348 | ||
4349 | use Math::BigInt; | |
4350 | use Math::BigFloat; | |
4351 | ||
4352 | $mbf = Math::BigFloat->new(5); | |
4353 | $mbi2 = Math::BigInteger->new(5); | |
4354 | $mbi = Math::BigInteger->new(2); | |
4355 | ||
4356 | # what actually gets called: | |
4357 | $float = $mbf + $mbi; # $mbf->badd() | |
4358 | $float = $mbf / $mbi; # $mbf->bdiv() | |
4359 | $integer = $mbi + $mbf; # $mbi->badd() | |
4360 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() | |
4361 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() | |
4362 | ||
4363 | This is because math with overloaded operators follows the first (dominating) | |
4364 | operand, and the operation of that is called and returns thus the result. So, | |
4365 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether | |
4366 | the result should be a Math::BigFloat or the second operant is one. | |
4367 | ||
4368 | To get a Math::BigFloat you either need to call the operation manually, | |
4369 | make sure the operands are already of the proper type or casted to that type | |
4370 | via Math::BigFloat->new(): | |
4371 | ||
4372 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 | |
4373 | ||
4374 | Beware of simple "casting" the entire expression, this would only convert | |
4375 | the already computed result: | |
4376 | ||
4377 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! | |
4378 | ||
4379 | Beware also of the order of more complicated expressions like: | |
4380 | ||
4381 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int | |
4382 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto | |
4383 | ||
4384 | If in doubt, break the expression into simpler terms, or cast all operands | |
4385 | to the desired resulting type. | |
4386 | ||
4387 | Scalar values are a bit different, since: | |
4388 | ||
4389 | $float = 2 + $mbf; | |
4390 | $float = $mbf + 2; | |
4391 | ||
4392 | will both result in the proper type due to the way the overloaded math works. | |
4393 | ||
4394 | This section also applies to other overloaded math packages, like Math::String. | |
4395 | ||
4396 | One solution to you problem might be autoupgrading|upgrading. See the | |
4397 | pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this. | |
4398 | ||
4399 | =item bsqrt() | |
4400 | ||
4401 | C<bsqrt()> works only good if the result is a big integer, e.g. the square | |
4402 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding | |
4403 | mode. The reason is that the result is always truncated to an integer. | |
4404 | ||
4405 | If you want a better approximation of the square root, then use: | |
4406 | ||
4407 | $x = Math::BigFloat->new(12); | |
4408 | Math::BigFloat->precision(0); | |
4409 | Math::BigFloat->round_mode('even'); | |
4410 | print $x->copy->bsqrt(),"\n"; # 4 | |
4411 | ||
4412 | Math::BigFloat->precision(2); | |
4413 | print $x->bsqrt(),"\n"; # 3.46 | |
4414 | print $x->bsqrt(3),"\n"; # 3.464 | |
4415 | ||
4416 | =item brsft() | |
4417 | ||
4418 | For negative numbers in base see also L<brsft|brsft>. | |
4419 | ||
4420 | =back | |
4421 | ||
4422 | =head1 LICENSE | |
4423 | ||
4424 | This program is free software; you may redistribute it and/or modify it under | |
4425 | the same terms as Perl itself. | |
4426 | ||
4427 | =head1 SEE ALSO | |
4428 | ||
4429 | L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as | |
4430 | L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
4431 | ||
4432 | The pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest | |
4433 | because they solve the autoupgrading/downgrading issue, at least partly. | |
4434 | ||
4435 | The package at | |
4436 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains | |
4437 | more documentation including a full version history, testcases, empty | |
4438 | subclass files and benchmarks. | |
4439 | ||
4440 | =head1 AUTHORS | |
4441 | ||
4442 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. | |
4443 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2004 | |
4444 | and still at it in 2005. | |
4445 | ||
4446 | Many people contributed in one or more ways to the final beast, see the file | |
4447 | CREDITS for an (uncomplete) list. If you miss your name, please drop me a | |
4448 | mail. Thank you! | |
4449 | ||
4450 | =cut |