Commit | Line | Data |
58cde26e |
1 | #!/usr/bin/perl -w |
2 | |
58cde26e |
3 | # The following hash values are used: |
0716bf9b |
4 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) |
58cde26e |
5 | # sign : +,-,NaN,+inf,-inf |
6 | # _a : accuracy |
7 | # _p : precision |
0716bf9b |
8 | # _f : flags, used by MBF to flag parts of a float as untouchable |
b4f14daa |
9 | |
574bacfe |
10 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since |
11 | # underlying lib might change the reference! |
12 | |
58cde26e |
13 | package Math::BigInt; |
14 | my $class = "Math::BigInt"; |
0716bf9b |
15 | require 5.005; |
58cde26e |
16 | |
61f5c3f5 |
17 | $VERSION = '1.49'; |
58cde26e |
18 | use Exporter; |
19 | @ISA = qw( Exporter ); |
61f5c3f5 |
20 | @EXPORT_OK = qw( objectify _swap bgcd blcm); |
027dc388 |
21 | use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/; |
58cde26e |
22 | use strict; |
23 | |
24 | # Inside overload, the first arg is always an object. If the original code had |
25 | # it reversed (like $x = 2 * $y), then the third paramater indicates this |
26 | # swapping. To make it work, we use a helper routine which not only reswaps the |
27 | # params, but also makes a new object in this case. See _swap() for details, |
28 | # especially the cases of operators with different classes. |
29 | |
30 | # For overloaded ops with only one argument we simple use $_[0]->copy() to |
31 | # preserve the argument. |
32 | |
33 | # Thus inheritance of overload operators becomes possible and transparent for |
34 | # our subclasses without the need to repeat the entire overload section there. |
a0d0e21e |
35 | |
a5f75d66 |
36 | use overload |
58cde26e |
37 | '=' => sub { $_[0]->copy(); }, |
38 | |
39 | # '+' and '-' do not use _swap, since it is a triffle slower. If you want to |
40 | # override _swap (if ever), then override overload of '+' and '-', too! |
41 | # for sub it is a bit tricky to keep b: b-a => -a+b |
42 | '-' => sub { my $c = $_[0]->copy; $_[2] ? |
43 | $c->bneg()->badd($_[1]) : |
44 | $c->bsub( $_[1]) }, |
45 | '+' => sub { $_[0]->copy()->badd($_[1]); }, |
46 | |
47 | # some shortcuts for speed (assumes that reversed order of arguments is routed |
48 | # to normal '+' and we thus can always modify first arg. If this is changed, |
49 | # this breaks and must be adjusted.) |
50 | '+=' => sub { $_[0]->badd($_[1]); }, |
51 | '-=' => sub { $_[0]->bsub($_[1]); }, |
52 | '*=' => sub { $_[0]->bmul($_[1]); }, |
53 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, |
027dc388 |
54 | '%=' => sub { $_[0]->bmod($_[1]); }, |
55 | '^=' => sub { $_[0]->bxor($_[1]); }, |
56 | '&=' => sub { $_[0]->band($_[1]); }, |
57 | '|=' => sub { $_[0]->bior($_[1]); }, |
58cde26e |
58 | '**=' => sub { $_[0]->bpow($_[1]); }, |
59 | |
027dc388 |
60 | '..' => \&_pointpoint, |
61 | |
58cde26e |
62 | '<=>' => sub { $_[2] ? |
bd05a461 |
63 | ref($_[0])->bcmp($_[1],$_[0]) : |
64 | ref($_[0])->bcmp($_[0],$_[1])}, |
027dc388 |
65 | 'cmp' => sub { |
58cde26e |
66 | $_[2] ? |
67 | $_[1] cmp $_[0]->bstr() : |
68 | $_[0]->bstr() cmp $_[1] }, |
69 | |
61f5c3f5 |
70 | 'log' => sub { $_[0]->copy()->blog(); }, |
58cde26e |
71 | 'int' => sub { $_[0]->copy(); }, |
72 | 'neg' => sub { $_[0]->copy()->bneg(); }, |
73 | 'abs' => sub { $_[0]->copy()->babs(); }, |
74 | '~' => sub { $_[0]->copy()->bnot(); }, |
75 | |
76 | '*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); }, |
77 | '/' => sub { my @a = ref($_[0])->_swap(@_);scalar $a[0]->bdiv($a[1]);}, |
78 | '%' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmod($a[1]); }, |
79 | '**' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bpow($a[1]); }, |
80 | '<<' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->blsft($a[1]); }, |
81 | '>>' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->brsft($a[1]); }, |
82 | |
83 | '&' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->band($a[1]); }, |
84 | '|' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bior($a[1]); }, |
85 | '^' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bxor($a[1]); }, |
86 | |
87 | # can modify arg of ++ and --, so avoid a new-copy for speed, but don't |
574bacfe |
88 | # use $_[0]->__one(), it modifies $_[0] to be 1! |
58cde26e |
89 | '++' => sub { $_[0]->binc() }, |
90 | '--' => sub { $_[0]->bdec() }, |
91 | |
92 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers |
93 | 'bool' => sub { |
94 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ |
95 | # v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-( |
96 | my $t = !$_[0]->is_zero(); |
97 | undef $t if $t == 0; |
98 | return $t; |
99 | }, |
a0d0e21e |
100 | |
027dc388 |
101 | # the original qw() does not work with the TIESCALAR below, why? |
102 | # Order of arguments unsignificant |
103 | '""' => sub { $_[0]->bstr(); }, |
104 | '0+' => sub { $_[0]->numify(); } |
a5f75d66 |
105 | ; |
a0d0e21e |
106 | |
58cde26e |
107 | ############################################################################## |
108 | # global constants, flags and accessory |
109 | |
0716bf9b |
110 | use constant MB_NEVER_ROUND => 0x0001; |
111 | |
112 | my $NaNOK=1; # are NaNs ok? |
113 | my $nan = 'NaN'; # constants for easier life |
114 | |
115 | my $CALC = 'Math::BigInt::Calc'; # module to do low level math |
61f5c3f5 |
116 | my $IMPORT = 0; # did import() yet? |
0716bf9b |
117 | sub _core_lib () { return $CALC; } # for test suite |
118 | |
ee15d750 |
119 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
120 | $accuracy = undef; |
121 | $precision = undef; |
122 | $div_scale = 40; |
58cde26e |
123 | |
027dc388 |
124 | ############################################################################## |
125 | # the old code had $rnd_mode, so we need to support it, too |
126 | |
127 | $rnd_mode = 'even'; |
128 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
129 | sub FETCH { return $round_mode; } |
130 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
131 | |
132 | BEGIN { tie $rnd_mode, 'Math::BigInt'; } |
133 | |
134 | ############################################################################## |
135 | |
58cde26e |
136 | sub round_mode |
137 | { |
ee15d750 |
138 | no strict 'refs'; |
58cde26e |
139 | # make Class->round_mode() work |
ee15d750 |
140 | my $self = shift; |
141 | my $class = ref($self) || $self || __PACKAGE__; |
58cde26e |
142 | if (defined $_[0]) |
143 | { |
144 | my $m = shift; |
145 | die "Unknown round mode $m" |
146 | if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
ee15d750 |
147 | ${"${class}::round_mode"} = $m; return $m; |
58cde26e |
148 | } |
ee15d750 |
149 | return ${"${class}::round_mode"}; |
150 | } |
151 | |
152 | sub div_scale |
153 | { |
154 | no strict 'refs'; |
155 | # make Class->round_mode() work |
156 | my $self = shift; |
157 | my $class = ref($self) || $self || __PACKAGE__; |
158 | if (defined $_[0]) |
159 | { |
160 | die ('div_scale must be greater than zero') if $_[0] < 0; |
161 | ${"${class}::div_scale"} = shift; |
162 | } |
163 | return ${"${class}::div_scale"}; |
58cde26e |
164 | } |
165 | |
166 | sub accuracy |
167 | { |
ee15d750 |
168 | # $x->accuracy($a); ref($x) $a |
169 | # $x->accuracy(); ref($x) |
170 | # Class->accuracy(); class |
171 | # Class->accuracy($a); class $a |
58cde26e |
172 | |
ee15d750 |
173 | my $x = shift; |
174 | my $class = ref($x) || $x || __PACKAGE__; |
58cde26e |
175 | |
ee15d750 |
176 | no strict 'refs'; |
177 | # need to set new value? |
58cde26e |
178 | if (@_ > 0) |
179 | { |
ee15d750 |
180 | my $a = shift; |
181 | die ('accuracy must not be zero') if defined $a && $a == 0; |
182 | if (ref($x)) |
183 | { |
184 | # $object->accuracy() or fallback to global |
185 | $x->bround($a) if defined $a; |
186 | $x->{_a} = $a; # set/overwrite, even if not rounded |
187 | $x->{_p} = undef; # clear P |
188 | } |
189 | else |
190 | { |
191 | # set global |
192 | ${"${class}::accuracy"} = $a; |
193 | } |
194 | return $a; # shortcut |
195 | } |
196 | |
197 | if (ref($x)) |
198 | { |
199 | # $object->accuracy() or fallback to global |
200 | return $x->{_a} || ${"${class}::accuracy"}; |
58cde26e |
201 | } |
ee15d750 |
202 | return ${"${class}::accuracy"}; |
58cde26e |
203 | } |
204 | |
205 | sub precision |
206 | { |
ee15d750 |
207 | # $x->precision($p); ref($x) $p |
208 | # $x->precision(); ref($x) |
209 | # Class->precision(); class |
210 | # Class->precision($p); class $p |
58cde26e |
211 | |
ee15d750 |
212 | my $x = shift; |
213 | my $class = ref($x) || $x || __PACKAGE__; |
58cde26e |
214 | |
ee15d750 |
215 | no strict 'refs'; |
216 | # need to set new value? |
58cde26e |
217 | if (@_ > 0) |
218 | { |
ee15d750 |
219 | my $p = shift; |
220 | if (ref($x)) |
221 | { |
222 | # $object->precision() or fallback to global |
223 | $x->bfround($p) if defined $p; |
224 | $x->{_p} = $p; # set/overwrite, even if not rounded |
225 | $x->{_a} = undef; # clear P |
226 | } |
227 | else |
228 | { |
229 | # set global |
230 | ${"${class}::precision"} = $p; |
231 | } |
232 | return $p; # shortcut |
58cde26e |
233 | } |
ee15d750 |
234 | |
235 | if (ref($x)) |
236 | { |
237 | # $object->precision() or fallback to global |
238 | return $x->{_p} || ${"${class}::precision"}; |
239 | } |
240 | return ${"${class}::precision"}; |
58cde26e |
241 | } |
242 | |
243 | sub _scale_a |
244 | { |
245 | # select accuracy parameter based on precedence, |
246 | # used by bround() and bfround(), may return undef for scale (means no op) |
247 | my ($x,$s,$m,$scale,$mode) = @_; |
248 | $scale = $x->{_a} if !defined $scale; |
249 | $scale = $s if (!defined $scale); |
250 | $mode = $m if !defined $mode; |
251 | return ($scale,$mode); |
252 | } |
253 | |
254 | sub _scale_p |
255 | { |
256 | # select precision parameter based on precedence, |
257 | # used by bround() and bfround(), may return undef for scale (means no op) |
258 | my ($x,$s,$m,$scale,$mode) = @_; |
259 | $scale = $x->{_p} if !defined $scale; |
260 | $scale = $s if (!defined $scale); |
261 | $mode = $m if !defined $mode; |
262 | return ($scale,$mode); |
263 | } |
264 | |
265 | ############################################################################## |
266 | # constructors |
267 | |
268 | sub copy |
269 | { |
270 | my ($c,$x); |
271 | if (@_ > 1) |
272 | { |
273 | # if two arguments, the first one is the class to "swallow" subclasses |
274 | ($c,$x) = @_; |
275 | } |
276 | else |
277 | { |
278 | $x = shift; |
279 | $c = ref($x); |
280 | } |
281 | return unless ref($x); # only for objects |
282 | |
283 | my $self = {}; bless $self,$c; |
394e6ffb |
284 | my $r; |
58cde26e |
285 | foreach my $k (keys %$x) |
286 | { |
0716bf9b |
287 | if ($k eq 'value') |
288 | { |
394e6ffb |
289 | $self->{value} = $CALC->_copy($x->{value}); next; |
290 | } |
291 | if (!($r = ref($x->{$k}))) |
292 | { |
293 | $self->{$k} = $x->{$k}; next; |
0716bf9b |
294 | } |
394e6ffb |
295 | if ($r eq 'SCALAR') |
0716bf9b |
296 | { |
297 | $self->{$k} = \${$x->{$k}}; |
298 | } |
394e6ffb |
299 | elsif ($r eq 'ARRAY') |
58cde26e |
300 | { |
301 | $self->{$k} = [ @{$x->{$k}} ]; |
302 | } |
394e6ffb |
303 | elsif ($r eq 'HASH') |
58cde26e |
304 | { |
305 | # only one level deep! |
306 | foreach my $h (keys %{$x->{$k}}) |
307 | { |
308 | $self->{$k}->{$h} = $x->{$k}->{$h}; |
309 | } |
310 | } |
394e6ffb |
311 | else # normal ref |
58cde26e |
312 | { |
61f5c3f5 |
313 | my $xk = $x->{$k}; |
394e6ffb |
314 | if ($xk->can('copy')) |
315 | { |
316 | $self->{$k} = $xk->copy(); |
317 | } |
318 | else |
319 | { |
320 | $self->{$k} = $xk->new($xk); |
321 | } |
58cde26e |
322 | } |
323 | } |
324 | $self; |
325 | } |
326 | |
327 | sub new |
328 | { |
b22b3e31 |
329 | # create a new BigInt object from a string or another BigInt object. |
0716bf9b |
330 | # see hash keys documented at top |
58cde26e |
331 | |
332 | # the argument could be an object, so avoid ||, && etc on it, this would |
b22b3e31 |
333 | # cause costly overloaded code to be called. The only allowed ops are |
334 | # ref() and defined. |
58cde26e |
335 | |
61f5c3f5 |
336 | my ($class,$wanted,$a,$p,$r) = @_; |
58cde26e |
337 | |
61f5c3f5 |
338 | # avoid numify-calls by not using || on $wanted! |
339 | return $class->bzero($a,$p) if !defined $wanted; # default to 0 |
340 | return $class->copy($wanted,$a,$p,$r) if ref($wanted); |
58cde26e |
341 | |
61f5c3f5 |
342 | $class->import() if $IMPORT == 0; # make require work |
343 | |
58cde26e |
344 | my $self = {}; bless $self, $class; |
345 | # handle '+inf', '-inf' first |
ee15d750 |
346 | if ($wanted =~ /^[+-]?inf$/) |
58cde26e |
347 | { |
0716bf9b |
348 | $self->{value} = $CALC->_zero(); |
ee15d750 |
349 | $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
58cde26e |
350 | return $self; |
351 | } |
352 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign |
353 | my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted); |
58cde26e |
354 | if (!ref $mis) |
355 | { |
356 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
357 | #print "NaN 1\n"; |
0716bf9b |
358 | $self->{value} = $CALC->_zero(); |
58cde26e |
359 | $self->{sign} = $nan; |
360 | return $self; |
361 | } |
574bacfe |
362 | if (!ref $miv) |
363 | { |
364 | # _from_hex or _from_bin |
365 | $self->{value} = $mis->{value}; |
366 | $self->{sign} = $mis->{sign}; |
367 | return $self; # throw away $mis |
368 | } |
58cde26e |
369 | # make integer from mantissa by adjusting exp, then convert to bigint |
370 | $self->{sign} = $$mis; # store sign |
0716bf9b |
371 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
58cde26e |
372 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
373 | if ($e > 0) |
374 | { |
375 | my $diff = $e - CORE::length($$mfv); |
376 | if ($diff < 0) # Not integer |
377 | { |
378 | #print "NOI 1\n"; |
379 | $self->{sign} = $nan; |
380 | } |
381 | else # diff >= 0 |
382 | { |
383 | # adjust fraction and add it to value |
384 | # print "diff > 0 $$miv\n"; |
385 | $$miv = $$miv . ($$mfv . '0' x $diff); |
386 | } |
387 | } |
388 | else |
389 | { |
390 | if ($$mfv ne '') # e <= 0 |
391 | { |
392 | # fraction and negative/zero E => NOI |
393 | #print "NOI 2 \$\$mfv '$$mfv'\n"; |
394 | $self->{sign} = $nan; |
395 | } |
396 | elsif ($e < 0) |
397 | { |
398 | # xE-y, and empty mfv |
399 | #print "xE-y\n"; |
400 | $e = abs($e); |
401 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? |
402 | { |
403 | #print "NOI 3\n"; |
404 | $self->{sign} = $nan; |
405 | } |
406 | } |
407 | } |
408 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 |
0716bf9b |
409 | $self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/; |
0716bf9b |
410 | # if any of the globals is set, use them to round and store them inside $self |
61f5c3f5 |
411 | # do not round for new($x,undef,undef) since that is used by MBF to signal |
412 | # no rounding |
413 | $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p; |
58cde26e |
414 | return $self; |
415 | } |
416 | |
58cde26e |
417 | sub bnan |
418 | { |
419 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' |
b4f14daa |
420 | my $self = shift; |
58cde26e |
421 | $self = $class if !defined $self; |
422 | if (!ref($self)) |
423 | { |
424 | my $c = $self; $self = {}; bless $self, $c; |
425 | } |
61f5c3f5 |
426 | $self->import() if $IMPORT == 0; # make require work |
58cde26e |
427 | return if $self->modify('bnan'); |
0716bf9b |
428 | $self->{value} = $CALC->_zero(); |
58cde26e |
429 | $self->{sign} = $nan; |
394e6ffb |
430 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly |
58cde26e |
431 | return $self; |
b4f14daa |
432 | } |
58cde26e |
433 | |
434 | sub binf |
435 | { |
436 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' |
437 | # the sign is either '+', or if given, used from there |
438 | my $self = shift; |
439 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
440 | $self = $class if !defined $self; |
441 | if (!ref($self)) |
442 | { |
443 | my $c = $self; $self = {}; bless $self, $c; |
444 | } |
61f5c3f5 |
445 | $self->import() if $IMPORT == 0; # make require work |
58cde26e |
446 | return if $self->modify('binf'); |
0716bf9b |
447 | $self->{value} = $CALC->_zero(); |
58cde26e |
448 | $self->{sign} = $sign.'inf'; |
394e6ffb |
449 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
58cde26e |
450 | return $self; |
451 | } |
452 | |
453 | sub bzero |
454 | { |
455 | # create a bigint '+0', if given a BigInt, set it to 0 |
456 | my $self = shift; |
457 | $self = $class if !defined $self; |
0716bf9b |
458 | |
58cde26e |
459 | if (!ref($self)) |
460 | { |
461 | my $c = $self; $self = {}; bless $self, $c; |
462 | } |
61f5c3f5 |
463 | $self->import() if $IMPORT == 0; # make require work |
58cde26e |
464 | return if $self->modify('bzero'); |
0716bf9b |
465 | $self->{value} = $CALC->_zero(); |
58cde26e |
466 | $self->{sign} = '+'; |
61f5c3f5 |
467 | if (@_ > 0) |
468 | { |
469 | $self->{_a} = $_[0] |
470 | if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a}); |
471 | $self->{_p} = $_[1] |
472 | if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p}); |
473 | } |
58cde26e |
474 | return $self; |
475 | } |
476 | |
574bacfe |
477 | sub bone |
478 | { |
479 | # create a bigint '+1' (or -1 if given sign '-'), |
480 | # if given a BigInt, set it to +1 or -1, respecively |
481 | my $self = shift; |
482 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
483 | $self = $class if !defined $self; |
394e6ffb |
484 | |
574bacfe |
485 | if (!ref($self)) |
486 | { |
487 | my $c = $self; $self = {}; bless $self, $c; |
488 | } |
61f5c3f5 |
489 | $self->import() if $IMPORT == 0; # make require work |
574bacfe |
490 | return if $self->modify('bone'); |
491 | $self->{value} = $CALC->_one(); |
492 | $self->{sign} = $sign; |
61f5c3f5 |
493 | if (@_ > 0) |
494 | { |
495 | $self->{_a} = $_[0] |
496 | if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a}); |
497 | $self->{_p} = $_[1] |
498 | if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p}); |
499 | } |
574bacfe |
500 | return $self; |
501 | } |
502 | |
58cde26e |
503 | ############################################################################## |
504 | # string conversation |
505 | |
506 | sub bsstr |
507 | { |
508 | # (ref to BFLOAT or num_str ) return num_str |
509 | # Convert number from internal format to scientific string format. |
510 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
dccbb853 |
511 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
512 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
513 | |
574bacfe |
514 | if ($x->{sign} !~ /^[+-]$/) |
515 | { |
516 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
517 | return 'inf'; # +inf |
518 | } |
58cde26e |
519 | my ($m,$e) = $x->parts(); |
574bacfe |
520 | # e can only be positive |
58cde26e |
521 | my $sign = 'e+'; |
522 | # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s; |
523 | return $m->bstr().$sign.$e->bstr(); |
524 | } |
525 | |
526 | sub bstr |
527 | { |
0716bf9b |
528 | # make a string from bigint object |
ee15d750 |
529 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
530 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
027dc388 |
531 | |
574bacfe |
532 | if ($x->{sign} !~ /^[+-]$/) |
533 | { |
534 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
535 | return 'inf'; # +inf |
536 | } |
0716bf9b |
537 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
538 | return $es.${$CALC->_str($x->{value})}; |
58cde26e |
539 | } |
540 | |
541 | sub numify |
542 | { |
394e6ffb |
543 | # Make a "normal" scalar from a BigInt object |
58cde26e |
544 | my $x = shift; $x = $class->new($x) unless ref $x; |
0716bf9b |
545 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
546 | my $num = $CALC->_num($x->{value}); |
547 | return -$num if $x->{sign} eq '-'; |
58cde26e |
548 | return $num; |
549 | } |
550 | |
551 | ############################################################################## |
552 | # public stuff (usually prefixed with "b") |
553 | |
554 | sub sign |
555 | { |
556 | # return the sign of the number: +/-/NaN |
ee15d750 |
557 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
558 | |
58cde26e |
559 | return $x->{sign}; |
560 | } |
561 | |
ee15d750 |
562 | sub _find_round_parameters |
58cde26e |
563 | { |
564 | # After any operation or when calling round(), the result is rounded by |
565 | # regarding the A & P from arguments, local parameters, or globals. |
61f5c3f5 |
566 | |
567 | # This procedure finds the round parameters, but it is for speed reasons |
568 | # duplicated in round. Otherwise, it is tested by the testsuite and used |
569 | # by fdiv(). |
570 | |
394e6ffb |
571 | my ($self,$a,$p,$r,@args) = @_; |
572 | # $a accuracy, if given by caller |
573 | # $p precision, if given by caller |
574 | # $r round_mode, if given by caller |
575 | # @args all 'other' arguments (0 for unary, 1 for binary ops) |
58cde26e |
576 | |
17baacb7 |
577 | # leave bigfloat parts alone |
ee15d750 |
578 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
17baacb7 |
579 | |
394e6ffb |
580 | my $c = ref($self); # find out class of argument(s) |
574bacfe |
581 | no strict 'refs'; |
574bacfe |
582 | |
58cde26e |
583 | # now pick $a or $p, but only if we have got "arguments" |
61f5c3f5 |
584 | if (!defined $a) |
58cde26e |
585 | { |
61f5c3f5 |
586 | foreach ($self,@args) |
58cde26e |
587 | { |
588 | # take the defined one, or if both defined, the one that is smaller |
589 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); |
590 | } |
61f5c3f5 |
591 | } |
592 | if (!defined $p) |
ee15d750 |
593 | { |
61f5c3f5 |
594 | # even if $a is defined, take $p, to signal error for both defined |
595 | foreach ($self,@args) |
596 | { |
597 | # take the defined one, or if both defined, the one that is bigger |
598 | # -2 > -3, and 3 > 2 |
599 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); |
600 | } |
ee15d750 |
601 | } |
61f5c3f5 |
602 | # if still none defined, use globals (#2) |
603 | $a = ${"$c\::accuracy"} unless defined $a; |
604 | $p = ${"$c\::precision"} unless defined $p; |
605 | |
606 | # no rounding today? |
607 | return ($self) unless defined $a || defined $p; # early out |
608 | |
609 | # set A and set P is an fatal error |
610 | return ($self->bnan()) if defined $a && defined $p; |
611 | |
612 | $r = ${"$c\::round_mode"} unless defined $r; |
613 | die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
614 | |
615 | return ($self,$a,$p,$r); |
ee15d750 |
616 | } |
617 | |
618 | sub round |
619 | { |
61f5c3f5 |
620 | # Round $self according to given parameters, or given second argument's |
ee15d750 |
621 | # parameters or global defaults |
ee15d750 |
622 | |
61f5c3f5 |
623 | # for speed reasons, _find_round_parameters is embeded here: |
624 | |
625 | my ($self,$a,$p,$r,@args) = @_; |
626 | # $a accuracy, if given by caller |
627 | # $p precision, if given by caller |
628 | # $r round_mode, if given by caller |
629 | # @args all 'other' arguments (0 for unary, 1 for binary ops) |
630 | |
631 | # leave bigfloat parts alone |
632 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
633 | |
634 | my $c = ref($self); # find out class of argument(s) |
635 | no strict 'refs'; |
636 | |
637 | # now pick $a or $p, but only if we have got "arguments" |
638 | if (!defined $a) |
58cde26e |
639 | { |
61f5c3f5 |
640 | foreach ($self,@args) |
641 | { |
642 | # take the defined one, or if both defined, the one that is smaller |
643 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); |
644 | } |
58cde26e |
645 | } |
61f5c3f5 |
646 | if (!defined $p) |
647 | { |
648 | # even if $a is defined, take $p, to signal error for both defined |
649 | foreach ($self,@args) |
650 | { |
651 | # take the defined one, or if both defined, the one that is bigger |
652 | # -2 > -3, and 3 > 2 |
653 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); |
654 | } |
655 | } |
656 | # if still none defined, use globals (#2) |
657 | $a = ${"$c\::accuracy"} unless defined $a; |
658 | $p = ${"$c\::precision"} unless defined $p; |
659 | |
660 | # no rounding today? |
661 | return $self unless defined $a || defined $p; # early out |
662 | |
663 | # set A and set P is an fatal error |
664 | return $self->bnan() if defined $a && defined $p; |
665 | |
666 | $r = ${"$c\::round_mode"} unless defined $r; |
667 | die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
668 | |
669 | # now round, by calling either fround or ffround: |
670 | if (defined $a) |
671 | { |
672 | $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a; |
673 | } |
674 | else # both can't be undefined due to early out |
58cde26e |
675 | { |
61f5c3f5 |
676 | $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p; |
58cde26e |
677 | } |
61f5c3f5 |
678 | $self->bnorm(); # after round, normalize |
58cde26e |
679 | } |
680 | |
17baacb7 |
681 | sub bnorm |
58cde26e |
682 | { |
027dc388 |
683 | # (numstr or BINT) return BINT |
58cde26e |
684 | # Normalize number -- no-op here |
dccbb853 |
685 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
686 | return $x; |
58cde26e |
687 | } |
688 | |
689 | sub babs |
690 | { |
691 | # (BINT or num_str) return BINT |
692 | # make number absolute, or return absolute BINT from string |
ee15d750 |
693 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
694 | |
58cde26e |
695 | return $x if $x->modify('babs'); |
696 | # post-normalized abs for internal use (does nothing for NaN) |
697 | $x->{sign} =~ s/^-/+/; |
698 | $x; |
699 | } |
700 | |
701 | sub bneg |
702 | { |
703 | # (BINT or num_str) return BINT |
704 | # negate number or make a negated number from string |
ee15d750 |
705 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
706 | |
58cde26e |
707 | return $x if $x->modify('bneg'); |
708 | # for +0 dont negate (to have always normalized) |
709 | return $x if $x->is_zero(); |
394e6ffb |
710 | $x->{sign} =~ tr/+-/-+/; # does nothing for NaN |
58cde26e |
711 | $x; |
712 | } |
713 | |
714 | sub bcmp |
715 | { |
716 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
717 | # (BINT or num_str, BINT or num_str) return cond_code |
718 | my ($self,$x,$y) = objectify(2,@_); |
0716bf9b |
719 | |
720 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
721 | { |
722 | # handle +-inf and NaN |
723 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
574bacfe |
724 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b |
725 | return +1 if $x->{sign} eq '+inf'; |
726 | return -1 if $x->{sign} eq '-inf'; |
727 | return -1 if $y->{sign} eq '+inf'; |
728 | return +1 if $y->{sign} eq '-inf'; |
729 | } |
574bacfe |
730 | # check sign for speed first |
731 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
732 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
733 | |
734 | # shortcut |
735 | my $xz = $x->is_zero(); |
736 | my $yz = $y->is_zero(); |
737 | return 0 if $xz && $yz; # 0 <=> 0 |
738 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
739 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
dccbb853 |
740 | |
741 | # post-normalized compare for internal use (honors signs) |
742 | if ($x->{sign} eq '+') |
743 | { |
744 | return 1 if $y->{sign} eq '-'; # 0 check handled above |
745 | return $CALC->_acmp($x->{value},$y->{value}); |
746 | } |
747 | |
748 | # $x->{sign} eq '-' |
749 | return -1 if $y->{sign} eq '+'; |
750 | return $CALC->_acmp($y->{value},$x->{value}); # swaped |
751 | |
752 | # &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0; |
58cde26e |
753 | } |
754 | |
755 | sub bacmp |
756 | { |
757 | # Compares 2 values, ignoring their signs. |
758 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
759 | # (BINT, BINT) return cond_code |
760 | my ($self,$x,$y) = objectify(2,@_); |
574bacfe |
761 | |
762 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
763 | { |
764 | # handle +-inf and NaN |
765 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
766 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
767 | return +1; # inf is always bigger |
768 | } |
0716bf9b |
769 | $CALC->_acmp($x->{value},$y->{value}) <=> 0; |
58cde26e |
770 | } |
771 | |
772 | sub badd |
773 | { |
774 | # add second arg (BINT or string) to first (BINT) (modifies first) |
775 | # return result as BINT |
61f5c3f5 |
776 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e |
777 | |
778 | return $x if $x->modify('badd'); |
58cde26e |
779 | |
61f5c3f5 |
780 | $r[3] = $y; # no push! |
574bacfe |
781 | # inf and NaN handling |
782 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
783 | { |
784 | # NaN first |
785 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
786 | # inf handline |
787 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
788 | { |
789 | # + and + => +, - and - => -, + and - => 0, - and + => 0 |
61f5c3f5 |
790 | return $x->bzero(@r) if $x->{sign} ne $y->{sign}; |
574bacfe |
791 | return $x; |
792 | } |
793 | # +-inf + something => +inf |
794 | # something +-inf => +-inf |
795 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
796 | return $x; |
797 | } |
798 | |
58cde26e |
799 | # speed: no add for 0+y or x+0 |
61f5c3f5 |
800 | return $x->round(@r) if $y->is_zero(); # x+0 |
58cde26e |
801 | if ($x->is_zero()) # 0+y |
802 | { |
803 | # make copy, clobbering up x |
0716bf9b |
804 | $x->{value} = $CALC->_copy($y->{value}); |
58cde26e |
805 | $x->{sign} = $y->{sign} || $nan; |
61f5c3f5 |
806 | return $x->round(@r); |
58cde26e |
807 | } |
808 | |
58cde26e |
809 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
810 | |
811 | if ($sx eq $sy) |
812 | { |
574bacfe |
813 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e |
814 | $x->{sign} = $sx; |
815 | } |
816 | else |
817 | { |
574bacfe |
818 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e |
819 | if ($a > 0) |
820 | { |
821 | #print "swapped sub (a=$a)\n"; |
574bacfe |
822 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e |
823 | $x->{sign} = $sy; |
824 | } |
825 | elsif ($a == 0) |
826 | { |
827 | # speedup, if equal, set result to 0 |
0716bf9b |
828 | #print "equal sub, result = 0\n"; |
829 | $x->{value} = $CALC->_zero(); |
58cde26e |
830 | $x->{sign} = '+'; |
831 | } |
832 | else # a < 0 |
833 | { |
834 | #print "unswapped sub (a=$a)\n"; |
574bacfe |
835 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
58cde26e |
836 | $x->{sign} = $sx; |
a0d0e21e |
837 | } |
a0d0e21e |
838 | } |
61f5c3f5 |
839 | $x->round(@r); |
58cde26e |
840 | } |
841 | |
842 | sub bsub |
843 | { |
844 | # (BINT or num_str, BINT or num_str) return num_str |
845 | # subtract second arg from first, modify first |
846 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
847 | |
58cde26e |
848 | return $x if $x->modify('bsub'); |
e745a66c |
849 | |
850 | if (!$y->is_zero()) # don't need to do anything if $y is 0 |
851 | { |
852 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
853 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros |
854 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
855 | } |
61f5c3f5 |
856 | $x; # already rounded by badd() or no round necc. |
58cde26e |
857 | } |
858 | |
859 | sub binc |
860 | { |
861 | # increment arg by one |
ee15d750 |
862 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
863 | return $x if $x->modify('binc'); |
e745a66c |
864 | |
865 | if ($x->{sign} eq '+') |
866 | { |
867 | $x->{value} = $CALC->_inc($x->{value}); |
868 | return $x->round($a,$p,$r); |
869 | } |
870 | elsif ($x->{sign} eq '-') |
871 | { |
872 | $x->{value} = $CALC->_dec($x->{value}); |
873 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 |
874 | return $x->round($a,$p,$r); |
875 | } |
876 | # inf, nan handling etc |
61f5c3f5 |
877 | $x->badd($self->__one(),$a,$p,$r); # badd does round |
58cde26e |
878 | } |
879 | |
880 | sub bdec |
881 | { |
882 | # decrement arg by one |
ee15d750 |
883 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
884 | return $x if $x->modify('bdec'); |
e745a66c |
885 | |
886 | my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+'; |
887 | # <= 0 |
888 | if (($x->{sign} eq '-') || $zero) |
889 | { |
890 | $x->{value} = $CALC->_inc($x->{value}); |
891 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
892 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 |
893 | return $x->round($a,$p,$r); |
894 | } |
895 | # > 0 |
896 | elsif ($x->{sign} eq '+') |
897 | { |
898 | $x->{value} = $CALC->_dec($x->{value}); |
899 | return $x->round($a,$p,$r); |
900 | } |
901 | # inf, nan handling etc |
61f5c3f5 |
902 | $x->badd($self->__one('-'),$a,$p,$r); # badd does round |
58cde26e |
903 | } |
904 | |
61f5c3f5 |
905 | sub blog |
906 | { |
907 | # not implemented yet |
908 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
909 | |
910 | return $x->bnan(); |
911 | } |
912 | |
58cde26e |
913 | sub blcm |
914 | { |
915 | # (BINT or num_str, BINT or num_str) return BINT |
916 | # does not modify arguments, but returns new object |
917 | # Lowest Common Multiplicator |
58cde26e |
918 | |
0716bf9b |
919 | my $y = shift; my ($x); |
920 | if (ref($y)) |
921 | { |
922 | $x = $y->copy(); |
923 | } |
924 | else |
925 | { |
926 | $x = $class->new($y); |
927 | } |
dccbb853 |
928 | while (@_) { $x = __lcm($x,shift); } |
58cde26e |
929 | $x; |
930 | } |
931 | |
932 | sub bgcd |
933 | { |
934 | # (BINT or num_str, BINT or num_str) return BINT |
935 | # does not modify arguments, but returns new object |
936 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) |
0716bf9b |
937 | |
dccbb853 |
938 | my $y = shift; |
939 | $y = __PACKAGE__->new($y) if !ref($y); |
940 | my $self = ref($y); |
941 | my $x = $y->copy(); # keep arguments |
0716bf9b |
942 | if ($CALC->can('_gcd')) |
943 | { |
944 | while (@_) |
945 | { |
dccbb853 |
946 | $y = shift; $y = $self->new($y) if !ref($y); |
0716bf9b |
947 | next if $y->is_zero(); |
948 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? |
949 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one(); |
950 | } |
951 | } |
952 | else |
953 | { |
954 | while (@_) |
955 | { |
dccbb853 |
956 | $y = shift; $y = $self->new($y) if !ref($y); |
957 | $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN |
0716bf9b |
958 | } |
959 | } |
960 | $x->babs(); |
58cde26e |
961 | } |
962 | |
58cde26e |
963 | sub bnot |
964 | { |
965 | # (num_str or BINT) return BINT |
966 | # represent ~x as twos-complement number |
ee15d750 |
967 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
968 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
969 | |
58cde26e |
970 | return $x if $x->modify('bnot'); |
61f5c3f5 |
971 | $x->bneg()->bdec(); # bdec already does round |
58cde26e |
972 | } |
973 | |
974 | sub is_zero |
975 | { |
976 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
ee15d750 |
977 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
978 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
979 | |
574bacfe |
980 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 |
981 | $CALC->_is_zero($x->{value}); |
58cde26e |
982 | } |
983 | |
984 | sub is_nan |
985 | { |
986 | # return true if arg (BINT or num_str) is NaN |
ee15d750 |
987 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
988 | |
989 | return 1 if $x->{sign} eq $nan; |
990 | return 0; |
58cde26e |
991 | } |
992 | |
993 | sub is_inf |
994 | { |
995 | # return true if arg (BINT or num_str) is +-inf |
ee15d750 |
996 | my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
997 | |
998 | $sign = '' if !defined $sign; |
999 | return 0 if $sign !~ /^([+-]|)$/; |
58cde26e |
1000 | |
ee15d750 |
1001 | if ($sign eq '') |
1002 | { |
1003 | return 1 if ($x->{sign} =~ /^[+-]inf$/); |
1004 | return 0; |
1005 | } |
1006 | $sign = quotemeta($sign.'inf'); |
1007 | return 1 if ($x->{sign} =~ /^$sign$/); |
1008 | return 0; |
58cde26e |
1009 | } |
1010 | |
1011 | sub is_one |
1012 | { |
b22b3e31 |
1013 | # return true if arg (BINT or num_str) is +1 |
1014 | # or -1 if sign is given |
ee15d750 |
1015 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1016 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
1017 | |
1018 | $sign = '' if !defined $sign; $sign = '+' if $sign ne '-'; |
0716bf9b |
1019 | |
ee15d750 |
1020 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
394e6ffb |
1021 | $CALC->_is_one($x->{value}); |
58cde26e |
1022 | } |
1023 | |
1024 | sub is_odd |
1025 | { |
1026 | # return true when arg (BINT or num_str) is odd, false for even |
ee15d750 |
1027 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1028 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
1029 | |
b22b3e31 |
1030 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb |
1031 | $CALC->_is_odd($x->{value}); |
58cde26e |
1032 | } |
1033 | |
1034 | sub is_even |
1035 | { |
1036 | # return true when arg (BINT or num_str) is even, false for odd |
ee15d750 |
1037 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1038 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b |
1039 | |
b22b3e31 |
1040 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb |
1041 | $CALC->_is_even($x->{value}); |
0716bf9b |
1042 | } |
1043 | |
1044 | sub is_positive |
1045 | { |
1046 | # return true when arg (BINT or num_str) is positive (>= 0) |
ee15d750 |
1047 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1048 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1049 | |
1050 | return 1 if $x->{sign} =~ /^\+/; |
394e6ffb |
1051 | 0; |
0716bf9b |
1052 | } |
1053 | |
1054 | sub is_negative |
1055 | { |
1056 | # return true when arg (BINT or num_str) is negative (< 0) |
ee15d750 |
1057 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1058 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1059 | |
1060 | return 1 if ($x->{sign} =~ /^-/); |
394e6ffb |
1061 | 0; |
58cde26e |
1062 | } |
1063 | |
0716bf9b |
1064 | ############################################################################### |
1065 | |
58cde26e |
1066 | sub bmul |
1067 | { |
1068 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
1069 | # (BINT or num_str, BINT or num_str) return BINT |
61f5c3f5 |
1070 | my ($self,$x,$y,@r) = objectify(2,@_); |
0716bf9b |
1071 | |
58cde26e |
1072 | return $x if $x->modify('bmul'); |
61f5c3f5 |
1073 | |
1074 | $r[3] = $y; # no push here |
1075 | |
574bacfe |
1076 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1077 | # handle result = 0 |
61f5c3f5 |
1078 | return $x->round(@r) if $x->is_zero(); |
1079 | return $x->bzero()->round(@r) if $y->is_zero(); |
574bacfe |
1080 | # inf handling |
1081 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
1082 | { |
1083 | # result will always be +-inf: |
1084 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
1085 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
1086 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
1087 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
1088 | return $x->binf('-'); |
1089 | } |
58cde26e |
1090 | |
0716bf9b |
1091 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
dccbb853 |
1092 | |
574bacfe |
1093 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
61f5c3f5 |
1094 | return $x->round(@r); |
dccbb853 |
1095 | } |
1096 | |
1097 | sub _div_inf |
1098 | { |
1099 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code |
1100 | my ($self,$x,$y) = @_; |
1101 | |
1102 | # NaN if x == NaN or y == NaN or x==y==0 |
1103 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() |
1104 | if (($x->is_nan() || $y->is_nan()) || |
1105 | ($x->is_zero() && $y->is_zero())); |
1106 | |
1107 | # +inf / +inf == -inf / -inf == 1, remainder is 0 (A / A = 1, remainder 0) |
1108 | if (($x->{sign} eq $y->{sign}) && |
1109 | ($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
1110 | { |
1111 | return wantarray ? ($x->bone(),$self->bzero()) : $x->bone(); |
1112 | } |
1113 | # +inf / -inf == -inf / +inf == -1, remainder 0 |
1114 | if (($x->{sign} ne $y->{sign}) && |
1115 | ($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
1116 | { |
1117 | return wantarray ? ($x->bone('-'),$self->bzero()) : $x->bone('-'); |
1118 | } |
1119 | # x / +-inf => 0, remainder x (works even if x == 0) |
1120 | if ($y->{sign} =~ /^[+-]inf$/) |
1121 | { |
1122 | my $t = $x->copy(); # binf clobbers up $x |
1123 | return wantarray ? ($x->bzero(),$t) : $x->bzero() |
1124 | } |
1125 | |
1126 | # 5 / 0 => +inf, -6 / 0 => -inf |
1127 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf |
1128 | # exception: -8 / 0 has remainder -8, not 8 |
1129 | # exception: -inf / 0 has remainder -inf, not inf |
1130 | if ($y->is_zero()) |
1131 | { |
1132 | # +-inf / 0 => special case for -inf |
1133 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); |
1134 | if (!$x->is_zero() && !$x->is_inf()) |
1135 | { |
1136 | my $t = $x->copy(); # binf clobbers up $x |
1137 | return wantarray ? |
1138 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) |
1139 | } |
1140 | } |
1141 | |
1142 | # last case: +-inf / ordinary number |
1143 | my $sign = '+inf'; |
1144 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; |
1145 | $x->{sign} = $sign; |
1146 | return wantarray ? ($x,$self->bzero()) : $x; |
58cde26e |
1147 | } |
1148 | |
1149 | sub bdiv |
1150 | { |
1151 | # (dividend: BINT or num_str, divisor: BINT or num_str) return |
1152 | # (BINT,BINT) (quo,rem) or BINT (only rem) |
61f5c3f5 |
1153 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e |
1154 | |
1155 | return $x if $x->modify('bdiv'); |
1156 | |
dccbb853 |
1157 | return $self->_div_inf($x,$y) |
1158 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
58cde26e |
1159 | |
61f5c3f5 |
1160 | $r[3] = $y; # no push! |
1161 | |
58cde26e |
1162 | # 0 / something |
61f5c3f5 |
1163 | return |
1164 | wantarray ? ($x->round(@r),$self->bzero(@r)):$x->round(@r) if $x->is_zero(); |
58cde26e |
1165 | |
1166 | # Is $x in the interval [0, $y) ? |
0716bf9b |
1167 | my $cmp = $CALC->_acmp($x->{value},$y->{value}); |
58cde26e |
1168 | if (($cmp < 0) and ($x->{sign} eq $y->{sign})) |
1169 | { |
61f5c3f5 |
1170 | return $x->bzero()->round(@r) unless wantarray; |
58cde26e |
1171 | my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x |
61f5c3f5 |
1172 | return ($x->bzero()->round(@r),$t); |
58cde26e |
1173 | } |
1174 | elsif ($cmp == 0) |
1175 | { |
1176 | # shortcut, both are the same, so set to +/- 1 |
574bacfe |
1177 | $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') ); |
58cde26e |
1178 | return $x unless wantarray; |
61f5c3f5 |
1179 | return ($x->round(@r),$self->bzero(@r)); |
58cde26e |
1180 | } |
1181 | |
1182 | # calc new sign and in case $y == +/- 1, return $x |
dccbb853 |
1183 | my $xsign = $x->{sign}; # keep |
58cde26e |
1184 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
1185 | # check for / +-1 (cant use $y->is_one due to '-' |
394e6ffb |
1186 | if ($CALC->_is_one($y->{value})) |
58cde26e |
1187 | { |
61f5c3f5 |
1188 | return wantarray ? ($x->round(@r),$self->bzero(@r)) : $x->round(@r); |
58cde26e |
1189 | } |
1190 | |
394e6ffb |
1191 | my $rem; |
58cde26e |
1192 | if (wantarray) |
1193 | { |
394e6ffb |
1194 | my $rem = $self->bzero(); |
1195 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); |
1196 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); |
61f5c3f5 |
1197 | $x->round(@r); |
dccbb853 |
1198 | if (! $CALC->_is_zero($rem->{value})) |
1199 | { |
1200 | $rem->{sign} = $y->{sign}; |
1201 | $rem = $y-$rem if $xsign ne $y->{sign}; # one of them '-' |
1202 | } |
1203 | else |
1204 | { |
1205 | $rem->{sign} = '+'; # dont leave -0 |
1206 | } |
61f5c3f5 |
1207 | $rem->round(@r); |
58cde26e |
1208 | return ($x,$rem); |
1209 | } |
394e6ffb |
1210 | |
1211 | $x->{value} = $CALC->_div($x->{value},$y->{value}); |
1212 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); |
61f5c3f5 |
1213 | $x->round(@r); |
1214 | $x; |
58cde26e |
1215 | } |
1216 | |
dccbb853 |
1217 | sub bmod |
1218 | { |
1219 | # modulus (or remainder) |
1220 | # (BINT or num_str, BINT or num_str) return BINT |
61f5c3f5 |
1221 | my ($self,$x,$y,@r) = objectify(2,@_); |
1222 | |
dccbb853 |
1223 | return $x if $x->modify('bmod'); |
61f5c3f5 |
1224 | $r[3] = $y; # no push! |
dccbb853 |
1225 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) |
1226 | { |
1227 | my ($d,$r) = $self->_div_inf($x,$y); |
61f5c3f5 |
1228 | return $r->round(@r); |
dccbb853 |
1229 | } |
1230 | |
1231 | if ($CALC->can('_mod')) |
1232 | { |
1233 | # calc new sign and in case $y == +/- 1, return $x |
1234 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); |
1235 | my $xsign = $x->{sign}; |
1236 | if (!$CALC->_is_zero($x->{value})) |
1237 | { |
1238 | $x->{sign} = $y->{sign}; |
1239 | $x = $y-$x if $xsign ne $y->{sign}; # one of them '-' |
1240 | } |
1241 | else |
1242 | { |
1243 | $x->{sign} = '+'; # dont leave -0 |
1244 | } |
61f5c3f5 |
1245 | return $x->round(@r); |
dccbb853 |
1246 | } |
61f5c3f5 |
1247 | $x = (&bdiv($self,$x,$y,@r))[1]; # slow way (also rounds) |
dccbb853 |
1248 | } |
1249 | |
58cde26e |
1250 | sub bpow |
1251 | { |
1252 | # (BINT or num_str, BINT or num_str) return BINT |
1253 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 |
1254 | # modifies first argument |
61f5c3f5 |
1255 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e |
1256 | |
1257 | return $x if $x->modify('bpow'); |
1258 | |
61f5c3f5 |
1259 | $r[3] = $y; # no push! |
0716bf9b |
1260 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
58cde26e |
1261 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
61f5c3f5 |
1262 | return $x->bone(@r) if $y->is_zero(); |
1263 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
0716bf9b |
1264 | if ($x->{sign} eq '-' && $CALC->_is_one($x->{value})) |
58cde26e |
1265 | { |
1266 | # if $x == -1 and odd/even y => +1/-1 |
61f5c3f5 |
1267 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
574bacfe |
1268 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
58cde26e |
1269 | } |
574bacfe |
1270 | # 1 ** -y => 1 / (1 ** |y|) |
1271 | # so do test for negative $y after above's clause |
58cde26e |
1272 | return $x->bnan() if $y->{sign} eq '-'; |
61f5c3f5 |
1273 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
58cde26e |
1274 | |
0716bf9b |
1275 | if ($CALC->can('_pow')) |
58cde26e |
1276 | { |
574bacfe |
1277 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
61f5c3f5 |
1278 | return $x->round(@r); |
58cde26e |
1279 | } |
027dc388 |
1280 | |
1281 | # based on the assumption that shifting in base 10 is fast, and that mul |
1282 | # works faster if numbers are small: we count trailing zeros (this step is |
1283 | # O(1)..O(N), but in case of O(N) we save much more time due to this), |
1284 | # stripping them out of the multiplication, and add $count * $y zeros |
1285 | # afterwards like this: |
1286 | # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6 |
1287 | # creates deep recursion? |
574bacfe |
1288 | # my $zeros = $x->_trailing_zeros(); |
1289 | # if ($zeros > 0) |
1290 | # { |
1291 | # $x->brsft($zeros,10); # remove zeros |
1292 | # $x->bpow($y); # recursion (will not branch into here again) |
1293 | # $zeros = $y * $zeros; # real number of zeros to add |
1294 | # $x->blsft($zeros,10); |
1295 | # return $x->round($a,$p,$r); |
1296 | # } |
1297 | |
1298 | my $pow2 = $self->__one(); |
58cde26e |
1299 | my $y1 = $class->new($y); |
dccbb853 |
1300 | my $two = $self->new(2); |
58cde26e |
1301 | while (!$y1->is_one()) |
1302 | { |
dccbb853 |
1303 | $pow2->bmul($x) if $y1->is_odd(); |
1304 | $y1->bdiv($two); |
027dc388 |
1305 | $x->bmul($x); |
58cde26e |
1306 | } |
dccbb853 |
1307 | $x->bmul($pow2) unless $pow2->is_one(); |
61f5c3f5 |
1308 | return $x->round(@r); |
58cde26e |
1309 | } |
1310 | |
1311 | sub blsft |
1312 | { |
1313 | # (BINT or num_str, BINT or num_str) return BINT |
1314 | # compute x << y, base n, y >= 0 |
1315 | my ($self,$x,$y,$n) = objectify(2,@_); |
1316 | |
1317 | return $x if $x->modify('blsft'); |
1318 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1319 | |
574bacfe |
1320 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1321 | |
027dc388 |
1322 | my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft'); |
574bacfe |
1323 | if (defined $t) |
1324 | { |
1325 | $x->{value} = $t; return $x; |
1326 | } |
1327 | # fallback |
1328 | return $x->bmul( $self->bpow($n, $y) ); |
58cde26e |
1329 | } |
1330 | |
1331 | sub brsft |
1332 | { |
1333 | # (BINT or num_str, BINT or num_str) return BINT |
1334 | # compute x >> y, base n, y >= 0 |
1335 | my ($self,$x,$y,$n) = objectify(2,@_); |
1336 | |
1337 | return $x if $x->modify('brsft'); |
1338 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1339 | |
1340 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
574bacfe |
1341 | |
027dc388 |
1342 | my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft'); |
574bacfe |
1343 | if (defined $t) |
1344 | { |
1345 | $x->{value} = $t; return $x; |
1346 | } |
1347 | # fallback |
1348 | return scalar bdiv($x, $self->bpow($n, $y)); |
58cde26e |
1349 | } |
1350 | |
1351 | sub band |
1352 | { |
1353 | #(BINT or num_str, BINT or num_str) return BINT |
1354 | # compute x & y |
0716bf9b |
1355 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1356 | |
1357 | return $x if $x->modify('band'); |
1358 | |
1359 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
394e6ffb |
1360 | return $x->bzero() if $y->is_zero() || $x->is_zero(); |
0716bf9b |
1361 | |
574bacfe |
1362 | my $sign = 0; # sign of result |
1363 | $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-'); |
1364 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1365 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1366 | |
1367 | if ($CALC->can('_and') && $sx == 1 && $sy == 1) |
0716bf9b |
1368 | { |
574bacfe |
1369 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
0716bf9b |
1370 | return $x->round($a,$p,$r); |
1371 | } |
574bacfe |
1372 | |
394e6ffb |
1373 | my $m = Math::BigInt->bone(); my ($xr,$yr); |
574bacfe |
1374 | my $x10000 = new Math::BigInt (0x1000); |
1375 | my $y1 = copy(ref($x),$y); # make copy |
1376 | $y1->babs(); # and positive |
1377 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1378 | use integer; # need this for negative bools |
0716bf9b |
1379 | while (!$x1->is_zero() && !$y1->is_zero()) |
58cde26e |
1380 | { |
0716bf9b |
1381 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e |
1382 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe |
1383 | # make both op's numbers! |
1384 | $x->badd( bmul( $class->new( |
1385 | abs($sx*int($xr->numify()) & $sy*int($yr->numify()))), |
1386 | $m)); |
58cde26e |
1387 | $m->bmul($x10000); |
1388 | } |
574bacfe |
1389 | $x->bneg() if $sign; |
0716bf9b |
1390 | return $x->round($a,$p,$r); |
58cde26e |
1391 | } |
1392 | |
1393 | sub bior |
1394 | { |
1395 | #(BINT or num_str, BINT or num_str) return BINT |
1396 | # compute x | y |
0716bf9b |
1397 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1398 | |
1399 | return $x if $x->modify('bior'); |
1400 | |
1401 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1402 | return $x if $y->is_zero(); |
574bacfe |
1403 | |
1404 | my $sign = 0; # sign of result |
1405 | $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-'); |
1406 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1407 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1408 | |
1409 | # don't use lib for negative values |
1410 | if ($CALC->can('_or') && $sx == 1 && $sy == 1) |
0716bf9b |
1411 | { |
574bacfe |
1412 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
0716bf9b |
1413 | return $x->round($a,$p,$r); |
1414 | } |
1415 | |
394e6ffb |
1416 | my $m = Math::BigInt->bone(); my ($xr,$yr); |
1417 | my $x10000 = Math::BigInt->new(0x10000); |
574bacfe |
1418 | my $y1 = copy(ref($x),$y); # make copy |
1419 | $y1->babs(); # and positive |
1420 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1421 | use integer; # need this for negative bools |
0716bf9b |
1422 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e |
1423 | { |
0716bf9b |
1424 | ($x1, $xr) = bdiv($x1,$x10000); |
58cde26e |
1425 | ($y1, $yr) = bdiv($y1,$x10000); |
574bacfe |
1426 | # make both op's numbers! |
1427 | $x->badd( bmul( $class->new( |
1428 | abs($sx*int($xr->numify()) | $sy*int($yr->numify()))), |
1429 | $m)); |
58cde26e |
1430 | $m->bmul($x10000); |
1431 | } |
574bacfe |
1432 | $x->bneg() if $sign; |
0716bf9b |
1433 | return $x->round($a,$p,$r); |
58cde26e |
1434 | } |
1435 | |
1436 | sub bxor |
1437 | { |
1438 | #(BINT or num_str, BINT or num_str) return BINT |
1439 | # compute x ^ y |
0716bf9b |
1440 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1441 | |
1442 | return $x if $x->modify('bxor'); |
1443 | |
0716bf9b |
1444 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
58cde26e |
1445 | return $x if $y->is_zero(); |
0716bf9b |
1446 | |
574bacfe |
1447 | my $sign = 0; # sign of result |
1448 | $sign = 1 if $x->{sign} ne $y->{sign}; |
1449 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1450 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1451 | |
1452 | # don't use lib for negative values |
1453 | if ($CALC->can('_xor') && $sx == 1 && $sy == 1) |
0716bf9b |
1454 | { |
574bacfe |
1455 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
0716bf9b |
1456 | return $x->round($a,$p,$r); |
1457 | } |
1458 | |
394e6ffb |
1459 | my $m = $self->bone(); my ($xr,$yr); |
1460 | my $x10000 = Math::BigInt->new(0x10000); |
58cde26e |
1461 | my $y1 = copy(ref($x),$y); # make copy |
574bacfe |
1462 | $y1->babs(); # and positive |
1463 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1464 | use integer; # need this for negative bools |
0716bf9b |
1465 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e |
1466 | { |
0716bf9b |
1467 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e |
1468 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe |
1469 | # make both op's numbers! |
1470 | $x->badd( bmul( $class->new( |
1471 | abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))), |
1472 | $m)); |
58cde26e |
1473 | $m->bmul($x10000); |
1474 | } |
574bacfe |
1475 | $x->bneg() if $sign; |
0716bf9b |
1476 | return $x->round($a,$p,$r); |
58cde26e |
1477 | } |
1478 | |
1479 | sub length |
1480 | { |
ee15d750 |
1481 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1482 | |
0716bf9b |
1483 | my $e = $CALC->_len($x->{value}); |
0716bf9b |
1484 | return wantarray ? ($e,0) : $e; |
58cde26e |
1485 | } |
1486 | |
1487 | sub digit |
1488 | { |
0716bf9b |
1489 | # return the nth decimal digit, negative values count backward, 0 is right |
58cde26e |
1490 | my $x = shift; |
1491 | my $n = shift || 0; |
1492 | |
0716bf9b |
1493 | return $CALC->_digit($x->{value},$n); |
58cde26e |
1494 | } |
1495 | |
1496 | sub _trailing_zeros |
1497 | { |
1498 | # return the amount of trailing zeros in $x |
1499 | my $x = shift; |
1500 | $x = $class->new($x) unless ref $x; |
1501 | |
dccbb853 |
1502 | return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/; |
0716bf9b |
1503 | |
1504 | return $CALC->_zeros($x->{value}) if $CALC->can('_zeros'); |
1505 | |
b22b3e31 |
1506 | # if not: since we do not know underlying internal representation: |
0716bf9b |
1507 | my $es = "$x"; $es =~ /([0]*)$/; |
0716bf9b |
1508 | return 0 if !defined $1; # no zeros |
1509 | return CORE::length("$1"); # as string, not as +0! |
58cde26e |
1510 | } |
1511 | |
1512 | sub bsqrt |
1513 | { |
394e6ffb |
1514 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1515 | |
394e6ffb |
1516 | return $x->bnan() if $x->{sign} ne '+'; # -x or inf or NaN => NaN |
1517 | return $x->bzero($a,$p) if $x->is_zero(); # 0 => 0 |
1518 | return $x->round($a,$p,$r) if $x->is_one(); # 1 => 1 |
1519 | return $x->bone($a,$p) if $x < 4; # 2,3 => 1 |
58cde26e |
1520 | |
394e6ffb |
1521 | if ($CALC->can('_sqrt')) |
1522 | { |
1523 | $x->{value} = $CALC->_sqrt($x->{value}); |
1524 | return $x->round($a,$p,$r); |
1525 | } |
1526 | |
1527 | my $y = $x->copy(); |
58cde26e |
1528 | my $l = int($x->length()/2); |
1529 | |
394e6ffb |
1530 | $x->bone(); # keep ref($x), but modify it |
1531 | $x->blsft($l,10); |
58cde26e |
1532 | |
1533 | my $last = $self->bzero(); |
394e6ffb |
1534 | my $two = $self->new(2); |
1535 | my $lastlast = $x+$two; |
1536 | while ($last != $x && $lastlast != $x) |
58cde26e |
1537 | { |
394e6ffb |
1538 | $lastlast = $last; $last = $x; |
58cde26e |
1539 | $x += $y / $x; |
394e6ffb |
1540 | $x /= $two; |
58cde26e |
1541 | } |
394e6ffb |
1542 | $x-- if $x * $x > $y; # overshot? |
1543 | return $x->round($a,$p,$r); |
58cde26e |
1544 | } |
1545 | |
1546 | sub exponent |
1547 | { |
1548 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) |
ee15d750 |
1549 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1550 | |
ee15d750 |
1551 | if ($x->{sign} !~ /^[+-]$/) |
1552 | { |
1553 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
1554 | return $self->new($s); # -inf,+inf => inf |
1555 | } |
58cde26e |
1556 | my $e = $class->bzero(); |
1557 | return $e->binc() if $x->is_zero(); |
1558 | $e += $x->_trailing_zeros(); |
1559 | return $e; |
1560 | } |
1561 | |
1562 | sub mantissa |
1563 | { |
ee15d750 |
1564 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
1565 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1566 | |
ee15d750 |
1567 | if ($x->{sign} !~ /^[+-]$/) |
1568 | { |
1569 | my $s = $x->{sign}; $s =~ s/^[+]//; |
1570 | return $self->new($s); # +inf => inf |
1571 | } |
58cde26e |
1572 | my $m = $x->copy(); |
1573 | # that's inefficient |
1574 | my $zeros = $m->_trailing_zeros(); |
1575 | $m /= 10 ** $zeros if $zeros != 0; |
1576 | return $m; |
1577 | } |
1578 | |
1579 | sub parts |
1580 | { |
ee15d750 |
1581 | # return a copy of both the exponent and the mantissa |
1582 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e |
1583 | |
ee15d750 |
1584 | return ($x->mantissa(),$x->exponent()); |
58cde26e |
1585 | } |
1586 | |
1587 | ############################################################################## |
1588 | # rounding functions |
1589 | |
1590 | sub bfround |
1591 | { |
1592 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
ee15d750 |
1593 | # $n == 0 || $n == 1 => round to integer |
58cde26e |
1594 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 |
1595 | my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_); |
58cde26e |
1596 | return $x if !defined $scale; # no-op |
1597 | |
1598 | # no-op for BigInts if $n <= 0 |
ee15d750 |
1599 | if ($scale <= 0) |
1600 | { |
61f5c3f5 |
1601 | $x->{_a} = undef; # clear an eventual set A |
ee15d750 |
1602 | $x->{_p} = $scale; return $x; |
1603 | } |
58cde26e |
1604 | |
1605 | $x->bround( $x->length()-$scale, $mode); |
ee15d750 |
1606 | $x->{_a} = undef; # bround sets {_a} |
1607 | $x->{_p} = $scale; # so correct it |
1608 | $x; |
58cde26e |
1609 | } |
1610 | |
1611 | sub _scan_for_nonzero |
1612 | { |
1613 | my $x = shift; |
1614 | my $pad = shift; |
0716bf9b |
1615 | my $xs = shift; |
58cde26e |
1616 | |
1617 | my $len = $x->length(); |
1618 | return 0 if $len == 1; # '5' is trailed by invisible zeros |
1619 | my $follow = $pad - 1; |
1620 | return 0 if $follow > $len || $follow < 1; |
0716bf9b |
1621 | |
b22b3e31 |
1622 | # since we do not know underlying represention of $x, use decimal string |
0716bf9b |
1623 | #my $r = substr ($$xs,-$follow); |
58cde26e |
1624 | my $r = substr ("$x",-$follow); |
1625 | return 1 if $r =~ /[^0]/; return 0; |
58cde26e |
1626 | } |
1627 | |
1628 | sub fround |
1629 | { |
1630 | # to make life easier for switch between MBF and MBI (autoload fxxx() |
1631 | # like MBF does for bxxx()?) |
1632 | my $x = shift; |
1633 | return $x->bround(@_); |
1634 | } |
1635 | |
1636 | sub bround |
1637 | { |
1638 | # accuracy: +$n preserve $n digits from left, |
1639 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) |
1640 | # no-op for $n == 0 |
1641 | # and overwrite the rest with 0's, return normalized number |
1642 | # do not return $x->bnorm(), but $x |
61f5c3f5 |
1643 | |
58cde26e |
1644 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 |
1645 | my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_); |
61f5c3f5 |
1646 | return $x if !defined $scale; # no-op |
58cde26e |
1647 | |
61f5c3f5 |
1648 | if ($x->is_zero() || $scale == 0) |
1649 | { |
1650 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
1651 | return $x; |
1652 | } |
1653 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN |
58cde26e |
1654 | |
1655 | # we have fewer digits than we want to scale to |
1656 | my $len = $x->length(); |
ee15d750 |
1657 | # scale < 0, but > -len (not >=!) |
1658 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) |
1659 | { |
61f5c3f5 |
1660 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
ee15d750 |
1661 | return $x; |
1662 | } |
58cde26e |
1663 | |
1664 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 |
1665 | my ($pad,$digit_round,$digit_after); |
1666 | $pad = $len - $scale; |
ee15d750 |
1667 | $pad = abs($scale-1) if $scale < 0; |
1668 | |
0716bf9b |
1669 | # do not use digit(), it is costly for binary => decimal |
ee15d750 |
1670 | |
0716bf9b |
1671 | my $xs = $CALC->_str($x->{value}); |
1672 | my $pl = -$pad-1; |
ee15d750 |
1673 | |
0716bf9b |
1674 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
1675 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 |
1676 | $digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len; |
1677 | $pl++; $pl ++ if $pad >= $len; |
61f5c3f5 |
1678 | $digit_after = '0'; $digit_after = substr($$xs,$pl,1) if $pad > 0; |
ee15d750 |
1679 | |
1680 | # print "$pad $pl $$xs dr $digit_round da $digit_after\n"; |
58cde26e |
1681 | |
1682 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look |
1683 | # closer at the remaining digits of the original $x, remember decision |
1684 | my $round_up = 1; # default round up |
1685 | $round_up -- if |
1686 | ($mode eq 'trunc') || # trunc by round down |
1687 | ($digit_after =~ /[01234]/) || # round down anyway, |
1688 | # 6789 => round up |
1689 | ($digit_after eq '5') && # not 5000...0000 |
0716bf9b |
1690 | ($x->_scan_for_nonzero($pad,$xs) == 0) && |
58cde26e |
1691 | ( |
1692 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || |
1693 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || |
1694 | ($mode eq '+inf') && ($x->{sign} eq '-') || |
1695 | ($mode eq '-inf') && ($x->{sign} eq '+') || |
1696 | ($mode eq 'zero') # round down if zero, sign adjusted below |
1697 | ); |
61f5c3f5 |
1698 | my $put_back = 0; # not yet modified |
1699 | |
1700 | # old code, depend on internal representation |
1701 | # split mantissa at $pad and then pad with zeros |
1702 | #my $s5 = int($pad / 5); |
1703 | #my $i = 0; |
1704 | #while ($i < $s5) |
1705 | # { |
1706 | # $x->{value}->[$i++] = 0; # replace with 5 x 0 |
1707 | # } |
1708 | #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0 |
1709 | #my $rem = $pad % 5; # so much left over |
1710 | #if ($rem > 0) |
1711 | # { |
1712 | # #print "remainder $rem\n"; |
1713 | ## #print "elem $x->{value}->[$s5]\n"; |
1714 | # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0' |
1715 | # } |
1716 | #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5' |
1717 | #print ${$CALC->_str($pad->{value})}," $len\n"; |
1718 | |
1719 | if (($pad > 0) && ($pad <= $len)) |
1720 | { |
1721 | substr($$xs,-$pad,$pad) = '0' x $pad; |
1722 | $put_back = 1; |
58cde26e |
1723 | } |
61f5c3f5 |
1724 | elsif ($pad > $len) |
1725 | { |
1726 | $x->bzero(); # round to '0' |
1727 | } |
1728 | |
58cde26e |
1729 | if ($round_up) # what gave test above? |
1730 | { |
61f5c3f5 |
1731 | $put_back = 1; |
1732 | $pad = $len, $$xs = '0'x$pad if $scale < 0; # tlr: whack 0.51=>1.0 |
1733 | |
1734 | # we modify directly the string variant instead of creating a number and |
1735 | # adding it |
1736 | my $c = 0; $pad ++; # for $pad == $len case |
1737 | while ($pad <= $len) |
1738 | { |
1739 | $c = substr($$xs,-$pad,1) + 1; $c = '0' if $c eq '10'; |
1740 | substr($$xs,-$pad,1) = $c; $pad++; |
1741 | last if $c != 0; # no overflow => early out |
1742 | } |
1743 | $$xs = '1'.$$xs if $c == 0; |
1744 | |
1745 | # $x->badd( Math::BigInt->new($x->{sign}.'1'. '0' x $pad) ); |
58cde26e |
1746 | } |
61f5c3f5 |
1747 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back in |
ee15d750 |
1748 | |
1749 | $x->{_a} = $scale if $scale >= 0; |
1750 | if ($scale < 0) |
1751 | { |
1752 | $x->{_a} = $len+$scale; |
1753 | $x->{_a} = 0 if $scale < -$len; |
1754 | } |
58cde26e |
1755 | $x; |
1756 | } |
1757 | |
1758 | sub bfloor |
1759 | { |
1760 | # return integer less or equal then number, since it is already integer, |
1761 | # always returns $self |
ee15d750 |
1762 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1763 | |
1764 | # not needed: return $x if $x->modify('bfloor'); |
58cde26e |
1765 | return $x->round($a,$p,$r); |
1766 | } |
1767 | |
1768 | sub bceil |
1769 | { |
1770 | # return integer greater or equal then number, since it is already integer, |
1771 | # always returns $self |
ee15d750 |
1772 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e |
1773 | |
1774 | # not needed: return $x if $x->modify('bceil'); |
58cde26e |
1775 | return $x->round($a,$p,$r); |
1776 | } |
1777 | |
1778 | ############################################################################## |
1779 | # private stuff (internal use only) |
1780 | |
574bacfe |
1781 | sub __one |
58cde26e |
1782 | { |
1783 | # internal speedup, set argument to 1, or create a +/- 1 |
1784 | my $self = shift; |
dccbb853 |
1785 | my $x = $self->bone(); # $x->{value} = $CALC->_one(); |
0716bf9b |
1786 | $x->{sign} = shift || '+'; |
1787 | return $x; |
58cde26e |
1788 | } |
1789 | |
1790 | sub _swap |
1791 | { |
1792 | # Overload will swap params if first one is no object ref so that the first |
1793 | # one is always an object ref. In this case, third param is true. |
1794 | # This routine is to overcome the effect of scalar,$object creating an object |
1795 | # of the class of this package, instead of the second param $object. This |
1796 | # happens inside overload, when the overload section of this package is |
1797 | # inherited by sub classes. |
1798 | # For overload cases (and this is used only there), we need to preserve the |
1799 | # args, hence the copy(). |
1800 | # You can override this method in a subclass, the overload section will call |
1801 | # $object->_swap() to make sure it arrives at the proper subclass, with some |
394e6ffb |
1802 | # exceptions like '+' and '-'. To make '+' and '-' work, you also need to |
1803 | # specify your own overload for them. |
58cde26e |
1804 | |
1805 | # object, (object|scalar) => preserve first and make copy |
1806 | # scalar, object => swapped, re-swap and create new from first |
1807 | # (using class of second object, not $class!!) |
1808 | my $self = shift; # for override in subclass |
58cde26e |
1809 | if ($_[2]) |
1810 | { |
1811 | my $c = ref ($_[0]) || $class; # fallback $class should not happen |
1812 | return ( $c->new($_[1]), $_[0] ); |
1813 | } |
17baacb7 |
1814 | return ( $_[0]->copy(), $_[1] ); |
58cde26e |
1815 | } |
1816 | |
1817 | sub objectify |
1818 | { |
1819 | # check for strings, if yes, return objects instead |
1820 | |
1821 | # the first argument is number of args objectify() should look at it will |
1822 | # return $count+1 elements, the first will be a classname. This is because |
1823 | # overloaded '""' calls bstr($object,undef,undef) and this would result in |
1824 | # useless objects beeing created and thrown away. So we cannot simple loop |
1825 | # over @_. If the given count is 0, all arguments will be used. |
1826 | |
1827 | # If the second arg is a ref, use it as class. |
1828 | # If not, try to use it as classname, unless undef, then use $class |
1829 | # (aka Math::BigInt). The latter shouldn't happen,though. |
1830 | |
1831 | # caller: gives us: |
1832 | # $x->badd(1); => ref x, scalar y |
1833 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y |
1834 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y |
1835 | # Math::BigInt::badd(1,2); => scalar x, scalar y |
1836 | # In the last case we check number of arguments to turn it silently into |
574bacfe |
1837 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e |
1838 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
1839 | # currently it tries 'Math::BigInt' + 1, which will not work. |
ee15d750 |
1840 | |
1841 | # some shortcut for the common cases |
1842 | |
1843 | # $x->unary_op(); |
1844 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); |
1845 | # $x->binary_op($y); |
1846 | #return (ref($_[1]),$_[1],$_[2]) if (@_ == 3) && ($_[0]||0 == 2) |
1847 | # && ref($_[1]) && ref($_[2]); |
1848 | |
58cde26e |
1849 | my $count = abs(shift || 0); |
1850 | |
58cde26e |
1851 | my @a; # resulting array |
1852 | if (ref $_[0]) |
1853 | { |
1854 | # okay, got object as first |
1855 | $a[0] = ref $_[0]; |
1856 | } |
1857 | else |
1858 | { |
1859 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) |
1860 | $a[0] = $class; |
58cde26e |
1861 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
1862 | } |
58cde26e |
1863 | # print "Now in objectify, my class is today $a[0]\n"; |
1864 | my $k; |
1865 | if ($count == 0) |
1866 | { |
1867 | while (@_) |
1868 | { |
1869 | $k = shift; |
1870 | if (!ref($k)) |
1871 | { |
1872 | $k = $a[0]->new($k); |
1873 | } |
1874 | elsif (ref($k) ne $a[0]) |
1875 | { |
1876 | # foreign object, try to convert to integer |
1877 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 |
1878 | } |
58cde26e |
1879 | push @a,$k; |
1880 | } |
1881 | } |
1882 | else |
1883 | { |
1884 | while ($count > 0) |
1885 | { |
58cde26e |
1886 | $count--; |
1887 | $k = shift; |
1888 | if (!ref($k)) |
1889 | { |
1890 | $k = $a[0]->new($k); |
1891 | } |
1892 | elsif (ref($k) ne $a[0]) |
1893 | { |
1894 | # foreign object, try to convert to integer |
1895 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 |
1896 | } |
58cde26e |
1897 | push @a,$k; |
1898 | } |
1899 | push @a,@_; # return other params, too |
1900 | } |
58cde26e |
1901 | die "$class objectify needs list context" unless wantarray; |
1902 | @a; |
1903 | } |
1904 | |
1905 | sub import |
1906 | { |
1907 | my $self = shift; |
61f5c3f5 |
1908 | |
1909 | $IMPORT++; |
0716bf9b |
1910 | my @a = @_; my $l = scalar @_; my $j = 0; |
1911 | for ( my $i = 0; $i < $l ; $i++,$j++ ) |
58cde26e |
1912 | { |
0716bf9b |
1913 | if ($_[$i] eq ':constant') |
58cde26e |
1914 | { |
0716bf9b |
1915 | # this causes overlord er load to step in |
58cde26e |
1916 | overload::constant integer => sub { $self->new(shift) }; |
0716bf9b |
1917 | splice @a, $j, 1; $j --; |
1918 | } |
1919 | elsif ($_[$i] =~ /^lib$/i) |
1920 | { |
1921 | # this causes a different low lib to take care... |
61f5c3f5 |
1922 | $CALC = $_[$i+1] || ''; |
574bacfe |
1923 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
0716bf9b |
1924 | splice @a, $j, $s; $j -= $s; |
58cde26e |
1925 | } |
1926 | } |
1927 | # any non :constant stuff is handled by our parent, Exporter |
1928 | # even if @_ is empty, to give it a chance |
dccbb853 |
1929 | $self->SUPER::import(@a); # need it for subclasses |
1930 | $self->export_to_level(1,$self,@a); # need it for MBF |
58cde26e |
1931 | |
574bacfe |
1932 | # try to load core math lib |
1933 | my @c = split /\s*,\s*/,$CALC; |
1934 | push @c,'Calc'; # if all fail, try this |
61f5c3f5 |
1935 | $CALC = ''; # signal error |
574bacfe |
1936 | foreach my $lib (@c) |
1937 | { |
1938 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
1939 | $lib =~ s/\.pm$//; |
61f5c3f5 |
1940 | if ($] < 5.006) |
574bacfe |
1941 | { |
1942 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
1943 | # used in the same script, or eval inside import(). |
1944 | (my $mod = $lib . '.pm') =~ s!::!/!g; |
1945 | # require does not automatically :: => /, so portability problems arise |
bd05a461 |
1946 | eval { require $mod; $lib->import( @c ); } |
574bacfe |
1947 | } |
1948 | else |
1949 | { |
61f5c3f5 |
1950 | eval "use $lib qw/@c/;"; |
574bacfe |
1951 | } |
bd05a461 |
1952 | $CALC = $lib, last if $@ eq ''; # no error in loading lib? |
574bacfe |
1953 | } |
61f5c3f5 |
1954 | die "Couldn't load any math lib, not even the default" if $CALC eq ''; |
58cde26e |
1955 | } |
1956 | |
574bacfe |
1957 | sub __from_hex |
58cde26e |
1958 | { |
1959 | # convert a (ref to) big hex string to BigInt, return undef for error |
1960 | my $hs = shift; |
1961 | |
1962 | my $x = Math::BigInt->bzero(); |
394e6ffb |
1963 | |
1964 | # strip underscores |
1965 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
1966 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
1967 | |
58cde26e |
1968 | return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
1969 | |
b22b3e31 |
1970 | my $sign = '+'; $sign = '-' if ($$hs =~ /^-/); |
58cde26e |
1971 | |
b22b3e31 |
1972 | $$hs =~ s/^[+-]//; # strip sign |
0716bf9b |
1973 | if ($CALC->can('_from_hex')) |
58cde26e |
1974 | { |
0716bf9b |
1975 | $x->{value} = $CALC->_from_hex($hs); |
58cde26e |
1976 | } |
0716bf9b |
1977 | else |
58cde26e |
1978 | { |
0716bf9b |
1979 | # fallback to pure perl |
1980 | my $mul = Math::BigInt->bzero(); $mul++; |
1981 | my $x65536 = Math::BigInt->new(65536); |
1982 | my $len = CORE::length($$hs)-2; |
1983 | $len = int($len/4); # 4-digit parts, w/o '0x' |
1984 | my $val; my $i = -4; |
1985 | while ($len >= 0) |
1986 | { |
1987 | $val = substr($$hs,$i,4); |
b22b3e31 |
1988 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because |
0716bf9b |
1989 | $val = hex($val); # hex does not like wrong chars |
0716bf9b |
1990 | $i -= 4; $len --; |
1991 | $x += $mul * $val if $val != 0; |
1992 | $mul *= $x65536 if $len >= 0; # skip last mul |
1993 | } |
58cde26e |
1994 | } |
0716bf9b |
1995 | $x->{sign} = $sign if !$x->is_zero(); # no '-0' |
58cde26e |
1996 | return $x; |
1997 | } |
1998 | |
574bacfe |
1999 | sub __from_bin |
58cde26e |
2000 | { |
2001 | # convert a (ref to) big binary string to BigInt, return undef for error |
2002 | my $bs = shift; |
2003 | |
2004 | my $x = Math::BigInt->bzero(); |
394e6ffb |
2005 | # strip underscores |
2006 | $$bs =~ s/([01])_([01])/$1$2/g; |
2007 | $$bs =~ s/([01])_([01])/$1$2/g; |
b22b3e31 |
2008 | return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/; |
58cde26e |
2009 | |
2010 | my $mul = Math::BigInt->bzero(); $mul++; |
2011 | my $x256 = Math::BigInt->new(256); |
2012 | |
0716bf9b |
2013 | my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/); |
b22b3e31 |
2014 | $$bs =~ s/^[+-]//; # strip sign |
0716bf9b |
2015 | if ($CALC->can('_from_bin')) |
58cde26e |
2016 | { |
0716bf9b |
2017 | $x->{value} = $CALC->_from_bin($bs); |
58cde26e |
2018 | } |
0716bf9b |
2019 | else |
58cde26e |
2020 | { |
0716bf9b |
2021 | my $len = CORE::length($$bs)-2; |
2022 | $len = int($len/8); # 8-digit parts, w/o '0b' |
2023 | my $val; my $i = -8; |
2024 | while ($len >= 0) |
2025 | { |
2026 | $val = substr($$bs,$i,8); |
b22b3e31 |
2027 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only |
2028 | #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0 |
394e6ffb |
2029 | # slower: |
2030 | # $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8; |
2031 | $val = ord(pack('B8',substr('00000000'.$val,-8,8))); |
0716bf9b |
2032 | $i -= 8; $len --; |
2033 | $x += $mul * $val if $val != 0; |
2034 | $mul *= $x256 if $len >= 0; # skip last mul |
2035 | } |
58cde26e |
2036 | } |
2037 | $x->{sign} = $sign if !$x->is_zero(); |
2038 | return $x; |
2039 | } |
2040 | |
2041 | sub _split |
2042 | { |
2043 | # (ref to num_str) return num_str |
2044 | # internal, take apart a string and return the pieces |
dccbb853 |
2045 | # strip leading/trailing whitespace, leading zeros, underscore and reject |
574bacfe |
2046 | # invalid input |
58cde26e |
2047 | my $x = shift; |
2048 | |
574bacfe |
2049 | # strip white space at front, also extranous leading zeros |
2050 | $$x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' |
2051 | $$x =~ s/^\s+//; # but this will |
58cde26e |
2052 | $$x =~ s/\s+$//g; # strip white space at end |
58cde26e |
2053 | |
574bacfe |
2054 | # shortcut, if nothing to split, return early |
2055 | if ($$x =~ /^[+-]?\d+$/) |
2056 | { |
2057 | $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; |
2058 | return (\$sign, $x, \'', \'', \0); |
2059 | } |
58cde26e |
2060 | |
574bacfe |
2061 | # invalid starting char? |
2062 | return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; |
58cde26e |
2063 | |
574bacfe |
2064 | return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string |
2065 | return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string |
394e6ffb |
2066 | |
2067 | # strip underscores between digits |
2068 | $$x =~ s/(\d)_(\d)/$1$2/g; |
2069 | $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 |
574bacfe |
2070 | |
58cde26e |
2071 | # some possible inputs: |
2072 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 |
2073 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 |
2074 | |
027dc388 |
2075 | return if $$x =~ /[Ee].*[Ee]/; # more than one E => error |
2076 | |
58cde26e |
2077 | my ($m,$e) = split /[Ee]/,$$x; |
2078 | $e = '0' if !defined $e || $e eq ""; |
58cde26e |
2079 | # sign,value for exponent,mantint,mantfrac |
2080 | my ($es,$ev,$mis,$miv,$mfv); |
2081 | # valid exponent? |
2082 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
2083 | { |
2084 | $es = $1; $ev = $2; |
58cde26e |
2085 | # valid mantissa? |
2086 | return if $m eq '.' || $m eq ''; |
2087 | my ($mi,$mf) = split /\./,$m; |
2088 | $mi = '0' if !defined $mi; |
2089 | $mi .= '0' if $mi =~ /^[\-\+]?$/; |
2090 | $mf = '0' if !defined $mf || $mf eq ''; |
2091 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
2092 | { |
2093 | $mis = $1||'+'; $miv = $2; |
58cde26e |
2094 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros |
2095 | $mfv = $1; |
58cde26e |
2096 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
2097 | } |
2098 | } |
2099 | return; # NaN, not a number |
2100 | } |
2101 | |
58cde26e |
2102 | sub as_number |
2103 | { |
2104 | # an object might be asked to return itself as bigint on certain overloaded |
2105 | # operations, this does exactly this, so that sub classes can simple inherit |
2106 | # it or override with their own integer conversion routine |
2107 | my $self = shift; |
2108 | |
17baacb7 |
2109 | $self->copy(); |
58cde26e |
2110 | } |
2111 | |
bd05a461 |
2112 | sub as_hex |
2113 | { |
2114 | # return as hex string, with prefixed 0x |
2115 | my $x = shift; $x = $class->new($x) if !ref($x); |
2116 | |
2117 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
2118 | return '0x0' if $x->is_zero(); |
2119 | |
2120 | my $es = ''; my $s = ''; |
2121 | $s = $x->{sign} if $x->{sign} eq '-'; |
bd05a461 |
2122 | if ($CALC->can('_as_hex')) |
2123 | { |
ee15d750 |
2124 | $es = ${$CALC->_as_hex($x->{value})}; |
bd05a461 |
2125 | } |
2126 | else |
2127 | { |
2128 | my $x1 = $x->copy()->babs(); my $xr; |
61f5c3f5 |
2129 | my $x10000 = Math::BigInt->new (0x10000); |
bd05a461 |
2130 | while (!$x1->is_zero()) |
2131 | { |
61f5c3f5 |
2132 | ($x1, $xr) = bdiv($x1,$x10000); |
2133 | $es .= unpack('h4',pack('v',$xr->numify())); |
bd05a461 |
2134 | } |
2135 | $es = reverse $es; |
2136 | $es =~ s/^[0]+//; # strip leading zeros |
ee15d750 |
2137 | $s .= '0x'; |
bd05a461 |
2138 | } |
2139 | $s . $es; |
2140 | } |
2141 | |
2142 | sub as_bin |
2143 | { |
2144 | # return as binary string, with prefixed 0b |
2145 | my $x = shift; $x = $class->new($x) if !ref($x); |
2146 | |
2147 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
2148 | return '0b0' if $x->is_zero(); |
2149 | |
2150 | my $es = ''; my $s = ''; |
2151 | $s = $x->{sign} if $x->{sign} eq '-'; |
bd05a461 |
2152 | if ($CALC->can('_as_bin')) |
2153 | { |
ee15d750 |
2154 | $es = ${$CALC->_as_bin($x->{value})}; |
bd05a461 |
2155 | } |
2156 | else |
2157 | { |
2158 | my $x1 = $x->copy()->babs(); my $xr; |
61f5c3f5 |
2159 | my $x10000 = Math::BigInt->new (0x10000); |
bd05a461 |
2160 | while (!$x1->is_zero()) |
2161 | { |
61f5c3f5 |
2162 | ($x1, $xr) = bdiv($x1,$x10000); |
2163 | $es .= unpack('b16',pack('v',$xr->numify())); |
bd05a461 |
2164 | } |
2165 | $es = reverse $es; |
2166 | $es =~ s/^[0]+//; # strip leading zeros |
ee15d750 |
2167 | $s .= '0b'; |
bd05a461 |
2168 | } |
2169 | $s . $es; |
2170 | } |
2171 | |
58cde26e |
2172 | ############################################################################## |
0716bf9b |
2173 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e |
2174 | |
dccbb853 |
2175 | sub __lcm |
58cde26e |
2176 | { |
2177 | # (BINT or num_str, BINT or num_str) return BINT |
2178 | # does modify first argument |
2179 | # LCM |
2180 | |
2181 | my $x = shift; my $ty = shift; |
2182 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); |
2183 | return $x * $ty / bgcd($x,$ty); |
2184 | } |
2185 | |
574bacfe |
2186 | sub __gcd |
58cde26e |
2187 | { |
2188 | # (BINT or num_str, BINT or num_str) return BINT |
dccbb853 |
2189 | # does modify both arguments |
58cde26e |
2190 | # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296 |
dccbb853 |
2191 | my ($x,$ty) = @_; |
2192 | |
0716bf9b |
2193 | return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/; |
58cde26e |
2194 | |
2195 | while (!$ty->is_zero()) |
2196 | { |
2197 | ($x, $ty) = ($ty,bmod($x,$ty)); |
2198 | } |
2199 | $x; |
2200 | } |
2201 | |
58cde26e |
2202 | ############################################################################### |
2203 | # this method return 0 if the object can be modified, or 1 for not |
2204 | # We use a fast use constant statement here, to avoid costly calls. Subclasses |
2205 | # may override it with special code (f.i. Math::BigInt::Constant does so) |
2206 | |
0716bf9b |
2207 | sub modify () { 0; } |
e16b8f49 |
2208 | |
a0d0e21e |
2209 | 1; |
a5f75d66 |
2210 | __END__ |
2211 | |
2212 | =head1 NAME |
2213 | |
2214 | Math::BigInt - Arbitrary size integer math package |
2215 | |
2216 | =head1 SYNOPSIS |
2217 | |
2218 | use Math::BigInt; |
58cde26e |
2219 | |
2220 | # Number creation |
574bacfe |
2221 | $x = Math::BigInt->new($str); # defaults to 0 |
2222 | $nan = Math::BigInt->bnan(); # create a NotANumber |
2223 | $zero = Math::BigInt->bzero(); # create a +0 |
2224 | $inf = Math::BigInt->binf(); # create a +inf |
2225 | $inf = Math::BigInt->binf('-'); # create a -inf |
2226 | $one = Math::BigInt->bone(); # create a +1 |
2227 | $one = Math::BigInt->bone('-'); # create a -1 |
58cde26e |
2228 | |
2229 | # Testing |
574bacfe |
2230 | $x->is_zero(); # true if arg is +0 |
2231 | $x->is_nan(); # true if arg is NaN |
0716bf9b |
2232 | $x->is_one(); # true if arg is +1 |
2233 | $x->is_one('-'); # true if arg is -1 |
2234 | $x->is_odd(); # true if odd, false for even |
2235 | $x->is_even(); # true if even, false for odd |
2236 | $x->is_positive(); # true if >= 0 |
2237 | $x->is_negative(); # true if < 0 |
2238 | $x->is_inf(sign); # true if +inf, or -inf (sign is default '+') |
2239 | |
58cde26e |
2240 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
2241 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
2242 | $x->sign(); # return the sign, either +,- or NaN |
2243 | $x->digit($n); # return the nth digit, counting from right |
2244 | $x->digit(-$n); # return the nth digit, counting from left |
2245 | |
2246 | # The following all modify their first argument: |
2247 | |
2248 | # set |
2249 | $x->bzero(); # set $x to 0 |
2250 | $x->bnan(); # set $x to NaN |
574bacfe |
2251 | $x->bone(); # set $x to +1 |
2252 | $x->bone('-'); # set $x to -1 |
58cde26e |
2253 | |
2254 | $x->bneg(); # negation |
2255 | $x->babs(); # absolute value |
2256 | $x->bnorm(); # normalize (no-op) |
2257 | $x->bnot(); # two's complement (bit wise not) |
2258 | $x->binc(); # increment x by 1 |
2259 | $x->bdec(); # decrement x by 1 |
2260 | |
2261 | $x->badd($y); # addition (add $y to $x) |
2262 | $x->bsub($y); # subtraction (subtract $y from $x) |
2263 | $x->bmul($y); # multiplication (multiply $x by $y) |
2264 | $x->bdiv($y); # divide, set $x to quotient |
2265 | # return (quo,rem) or quo if scalar |
2266 | |
2267 | $x->bmod($y); # modulus (x % y) |
2268 | $x->bpow($y); # power of arguments (x ** y) |
2269 | $x->blsft($y); # left shift |
2270 | $x->brsft($y); # right shift |
2271 | $x->blsft($y,$n); # left shift, by base $n (like 10) |
2272 | $x->brsft($y,$n); # right shift, by base $n (like 10) |
2273 | |
2274 | $x->band($y); # bitwise and |
2275 | $x->bior($y); # bitwise inclusive or |
2276 | $x->bxor($y); # bitwise exclusive or |
2277 | $x->bnot(); # bitwise not (two's complement) |
2278 | |
2279 | $x->bsqrt(); # calculate square-root |
2280 | |
2281 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r |
2282 | $x->bround($N); # accuracy: preserve $N digits |
2283 | $x->bfround($N); # round to $Nth digit, no-op for BigInts |
2284 | |
2285 | # The following do not modify their arguments in BigInt, but do in BigFloat: |
2286 | $x->bfloor(); # return integer less or equal than $x |
2287 | $x->bceil(); # return integer greater or equal than $x |
2288 | |
2289 | # The following do not modify their arguments: |
2290 | |
dccbb853 |
2291 | bgcd(@values); # greatest common divisor (no OO style) |
2292 | blcm(@values); # lowest common multiplicator (no OO style) |
bd05a461 |
2293 | |
58cde26e |
2294 | $x->length(); # return number of digits in number |
bd05a461 |
2295 | ($x,$f) = $x->length(); # length of number and length of fraction part, |
2296 | # latter is always 0 digits long for BigInt's |
58cde26e |
2297 | |
2298 | $x->exponent(); # return exponent as BigInt |
ee15d750 |
2299 | $x->mantissa(); # return (signed) mantissa as BigInt |
58cde26e |
2300 | $x->parts(); # return (mantissa,exponent) as BigInt |
0716bf9b |
2301 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
2302 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) |
bd05a461 |
2303 | |
2304 | # conversation to string |
2305 | $x->bstr(); # normalized string |
2306 | $x->bsstr(); # normalized string in scientific notation |
2307 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
2308 | $x->as_bin(); # as signed binary string with prefixed 0b |
2309 | |
a5f75d66 |
2310 | =head1 DESCRIPTION |
2311 | |
58cde26e |
2312 | All operators (inlcuding basic math operations) are overloaded if you |
2313 | declare your big integers as |
a5f75d66 |
2314 | |
58cde26e |
2315 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 |
2316 | |
58cde26e |
2317 | Operations with overloaded operators preserve the arguments which is |
2318 | exactly what you expect. |
a5f75d66 |
2319 | |
2320 | =over 2 |
2321 | |
2322 | =item Canonical notation |
2323 | |
58cde26e |
2324 | Big integer values are strings of the form C</^[+-]\d+$/> with leading |
a5f75d66 |
2325 | zeros suppressed. |
2326 | |
58cde26e |
2327 | '-0' canonical value '-0', normalized '0' |
2328 | ' -123_123_123' canonical value '-123123123' |
2329 | '1_23_456_7890' canonical value '1234567890' |
2330 | |
a5f75d66 |
2331 | =item Input |
2332 | |
58cde26e |
2333 | Input values to these routines may be either Math::BigInt objects or |
2334 | strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>. |
2335 | |
2336 | You can include one underscore between any two digits. |
2337 | |
2338 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. |
2339 | Non integer values result in NaN. |
2340 | |
2341 | Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results |
2342 | in 'NaN'. |
2343 | |
2344 | bnorm() on a BigInt object is now effectively a no-op, since the numbers |
2345 | are always stored in normalized form. On a string, it creates a BigInt |
2346 | object. |
a5f75d66 |
2347 | |
2348 | =item Output |
2349 | |
58cde26e |
2350 | Output values are BigInt objects (normalized), except for bstr(), which |
2351 | returns a string in normalized form. |
2352 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
2353 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
2354 | return either undef, <0, 0 or >0 and are suited for sort. |
a5f75d66 |
2355 | |
2356 | =back |
2357 | |
0716bf9b |
2358 | =head1 ACCURACY and PRECISION |
2359 | |
b22b3e31 |
2360 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b |
2361 | accuracy and precision based rounding, both automatically after every |
b22b3e31 |
2362 | operation as well as manually. |
0716bf9b |
2363 | |
2364 | This section describes the accuracy/precision handling in Math::Big* as it |
b22b3e31 |
2365 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b |
2366 | abbreviations. |
2367 | |
2368 | Not yet implemented things (but with correct description) are marked with '!', |
2369 | things that need to be answered are marked with '?'. |
2370 | |
2371 | In the next paragraph follows a short description of terms used here (because |
574bacfe |
2372 | these may differ from terms used by others people or documentation). |
0716bf9b |
2373 | |
b22b3e31 |
2374 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b |
2375 | precision), F (fallback) and R (rounding mode) will be used. |
2376 | |
2377 | =head2 Precision P |
2378 | |
2379 | A fixed number of digits before (positive) or after (negative) |
b22b3e31 |
2380 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
2381 | integer like 123 (or 120). A precision of 2 means two digits to the left |
2382 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that |
2383 | numbers with zeros before the decimal point may have different precisions, |
2384 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value |
2385 | was). It could also have p < 0, when the digits after the decimal point |
2386 | are zero. |
0716bf9b |
2387 | |
574bacfe |
2388 | The string output (of floating point numbers) will be padded with zeros: |
2389 | |
2390 | Initial value P A Result String |
2391 | ------------------------------------------------------------ |
2392 | 1234.01 -3 1000 1000 |
2393 | 1234 -2 1200 1200 |
2394 | 1234.5 -1 1230 1230 |
2395 | 1234.001 1 1234 1234.0 |
2396 | 1234.01 0 1234 1234 |
2397 | 1234.01 2 1234.01 1234.01 |
2398 | 1234.01 5 1234.01 1234.01000 |
2399 | |
2400 | For BigInts, no padding occurs. |
0716bf9b |
2401 | |
2402 | =head2 Accuracy A |
2403 | |
2404 | Number of significant digits. Leading zeros are not counted. A |
2405 | number may have an accuracy greater than the non-zero digits |
b22b3e31 |
2406 | when there are zeros in it or trailing zeros. For example, 123.456 has |
2407 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. |
0716bf9b |
2408 | |
574bacfe |
2409 | The string output (of floating point numbers) will be padded with zeros: |
2410 | |
2411 | Initial value P A Result String |
2412 | ------------------------------------------------------------ |
2413 | 1234.01 3 1230 1230 |
2414 | 1234.01 6 1234.01 1234.01 |
2415 | 1234.1 8 1234.1 1234.1000 |
2416 | |
2417 | For BigInts, no padding occurs. |
2418 | |
0716bf9b |
2419 | =head2 Fallback F |
a5f75d66 |
2420 | |
574bacfe |
2421 | When both A and P are undefined, this is used as a fallback accuracy when |
2422 | dividing numbers. |
0716bf9b |
2423 | |
2424 | =head2 Rounding mode R |
2425 | |
2426 | When rounding a number, different 'styles' or 'kinds' |
2427 | of rounding are possible. (Note that random rounding, as in |
2428 | Math::Round, is not implemented.) |
58cde26e |
2429 | |
2430 | =over 2 |
a5f75d66 |
2431 | |
0716bf9b |
2432 | =item 'trunc' |
2433 | |
2434 | truncation invariably removes all digits following the |
2435 | rounding place, replacing them with zeros. Thus, 987.65 rounded |
b22b3e31 |
2436 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b |
2437 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 |
2438 | decimal point (P=-2) becomes 123.46. |
0716bf9b |
2439 | |
2440 | All other implemented styles of rounding attempt to round to the |
2441 | "nearest digit." If the digit D immediately to the right of the |
2442 | rounding place (skipping the decimal point) is greater than 5, the |
2443 | number is incremented at the rounding place (possibly causing a |
2444 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds |
2445 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly |
2446 | truncated at the rounding place: e.g. when rounding to units, 0.4 |
2447 | rounds to 0, and -19.4 rounds to -19. |
2448 | |
2449 | However the results of other styles of rounding differ if the |
2450 | digit immediately to the right of the rounding place (skipping the |
2451 | decimal point) is 5 and if there are no digits, or no digits other |
2452 | than 0, after that 5. In such cases: |
2453 | |
2454 | =item 'even' |
2455 | |
2456 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 |
2457 | if it is not already. E.g., when rounding to the first sigdig, 0.45 |
2458 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. |
2459 | |
2460 | =item 'odd' |
2461 | |
2462 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if |
2463 | it is not already. E.g., when rounding to the first sigdig, 0.45 |
2464 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. |
2465 | |
2466 | =item '+inf' |
2467 | |
2468 | round to plus infinity, i.e. always round up. E.g., when |
2469 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, |
b22b3e31 |
2470 | and 0.4501 also becomes 0.5. |
0716bf9b |
2471 | |
2472 | =item '-inf' |
2473 | |
2474 | round to minus infinity, i.e. always round down. E.g., when |
2475 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, |
2476 | but 0.4501 becomes 0.5. |
2477 | |
2478 | =item 'zero' |
2479 | |
2480 | round to zero, i.e. positive numbers down, negative ones up. |
2481 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 |
2482 | becomes -0.5, but 0.4501 becomes 0.5. |
2483 | |
2484 | =back |
2485 | |
2486 | The handling of A & P in MBI/MBF (the old core code shipped with Perl |
2487 | versions <= 5.7.2) is like this: |
2488 | |
2489 | =over 2 |
a5f75d66 |
2490 | |
0716bf9b |
2491 | =item Precision |
2492 | |
b22b3e31 |
2493 | * ffround($p) is able to round to $p number of digits after the decimal |
2494 | point |
0716bf9b |
2495 | * otherwise P is unused |
2496 | |
2497 | =item Accuracy (significant digits) |
2498 | |
2499 | * fround($a) rounds to $a significant digits |
2500 | * only fdiv() and fsqrt() take A as (optional) paramater |
b22b3e31 |
2501 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b |
2502 | of digits |
2503 | + rounding/truncating is only done when explicitly calling one of fround |
2504 | or ffround, and never for BigInt (not implemented) |
b22b3e31 |
2505 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b |
2506 | * the documentation and the comment in the code indicate two different ways |
2507 | on how fdiv() determines the maximum number of digits it should calculate, |
2508 | and the actual code does yet another thing |
2509 | POD: |
2510 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) |
2511 | Comment: |
2512 | result has at most max(scale, length(dividend), length(divisor)) digits |
2513 | Actual code: |
2514 | scale = max(scale, length(dividend)-1,length(divisor)-1); |
2515 | scale += length(divisior) - length(dividend); |
b22b3e31 |
2516 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b |
2517 | Actually, the 'difference' added to the scale is calculated from the |
2518 | number of "significant digits" in dividend and divisor, which is derived |
2519 | by looking at the length of the mantissa. Which is wrong, since it includes |
2520 | the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups |
2521 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange |
2522 | assumption that 124 has 3 significant digits, while 120/7 will get you |
2523 | '17', not '17.1' since 120 is thought to have 2 significant digits. |
dccbb853 |
2524 | The rounding after the division then uses the remainder and $y to determine |
0716bf9b |
2525 | wether it must round up or down. |
b22b3e31 |
2526 | ? I have no idea which is the right way. That's why I used a slightly more |
2527 | ? simple scheme and tweaked the few failing testcases to match it. |
58cde26e |
2528 | |
0716bf9b |
2529 | =back |
5dc6f178 |
2530 | |
0716bf9b |
2531 | This is how it works now: |
5dc6f178 |
2532 | |
0716bf9b |
2533 | =over 2 |
5dc6f178 |
2534 | |
0716bf9b |
2535 | =item Setting/Accessing |
2536 | |
2537 | * You can set the A global via $Math::BigInt::accuracy or |
2538 | $Math::BigFloat::accuracy or whatever class you are using. |
2539 | * You can also set P globally by using $Math::SomeClass::precision likewise. |
2540 | * Globals are classwide, and not inherited by subclasses. |
2541 | * to undefine A, use $Math::SomeCLass::accuracy = undef |
2542 | * to undefine P, use $Math::SomeClass::precision = undef |
2543 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 |
2544 | * If P is negative, this means round to the P'th place to the right of the |
2545 | decimal point; positive values mean to the left of the decimal point. |
2546 | P of 0 means round to integer. |
0716bf9b |
2547 | * to find out the current global A, take $Math::SomeClass::accuracy |
2548 | * use $x->accuracy() for the local setting of $x. |
2549 | * to find out the current global P, take $Math::SomeClass::precision |
2550 | * use $x->precision() for the local setting |
2551 | |
2552 | =item Creating numbers |
2553 | |
b22b3e31 |
2554 | !* When you create a number, there should be a way to define its A & P |
0716bf9b |
2555 | * When a number without specific A or P is created, but the globals are |
b22b3e31 |
2556 | defined, these should be used to round the number immediately and also |
2557 | stored locally with the number. Thus changing the global defaults later on |
2558 | will not change the A or P of previously created numbers (i.e., A and P of |
0716bf9b |
2559 | $x will be what was in effect when $x was created) |
2560 | |
2561 | =item Usage |
2562 | |
b22b3e31 |
2563 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b |
2564 | operation according to the rules below |
b22b3e31 |
2565 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
2566 | after the decimal point |
574bacfe |
2567 | * Math::BigFloat uses Math::BigInts internally, but setting A or P inside |
2568 | Math::BigInt as globals should not tamper with the parts of a BigFloat. |
2569 | Thus a flag is used to mark all Math::BigFloat numbers as 'never round' |
0716bf9b |
2570 | |
2571 | =item Precedence |
2572 | |
b22b3e31 |
2573 | * It only makes sense that a number has only one of A or P at a time. |
2574 | Since you can set/get both A and P, there is a rule that will practically |
2575 | enforce only A or P to be in effect at a time, even if both are set. |
2576 | This is called precedence. |
2577 | !* If two objects are involved in an operation, and one of them has A in |
0716bf9b |
2578 | ! effect, and the other P, this should result in a warning or an error, |
2579 | ! probably in NaN. |
2580 | * A takes precendence over P (Hint: A comes before P). If A is defined, it |
b22b3e31 |
2581 | is used, otherwise P is used. If neither of them is defined, nothing is |
2582 | used, i.e. the result will have as many digits as it can (with an |
2583 | exception for fdiv/fsqrt) and will not be rounded. |
2584 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of |
2585 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. |
2586 | If either the dividend's or the divisor's mantissa has more digits than |
2587 | the value of F, the higher value will be used instead of F. |
2588 | This is to limit the digits (A) of the result (just consider what would |
2589 | happen with unlimited A and P in the case of 1/3 :-) |
2590 | * fdiv will calculate 1 more digit than required (determined by |
0716bf9b |
2591 | A, P or F), and, if F is not used, round the result |
b22b3e31 |
2592 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe |
2593 | or P of 5, but this can not be helped - or can it?) |
b22b3e31 |
2594 | * Thus you can have the math done by on Math::Big* class in three modes: |
0716bf9b |
2595 | + never round (this is the default): |
2596 | This is done by setting A and P to undef. No math operation |
b22b3e31 |
2597 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
0716bf9b |
2598 | against overflows. You must explicitely call bround(), bfround() or |
b22b3e31 |
2599 | round() (the latter with parameters). |
2600 | Note: Once you have rounded a number, the settings will 'stick' on it |
2601 | and 'infect' all other numbers engaged in math operations with it, since |
0716bf9b |
2602 | local settings have the highest precedence. So, to get SaferRound[tm], |
2603 | use a copy() before rounding like this: |
2604 | |
2605 | $x = Math::BigFloat->new(12.34); |
2606 | $y = Math::BigFloat->new(98.76); |
2607 | $z = $x * $y; # 1218.6984 |
2608 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) |
2609 | $z = $x * $y; # still 1218.6984, without |
2610 | # copy would have been 1210! |
2611 | |
2612 | + round after each op: |
b22b3e31 |
2613 | After each single operation (except for testing like is_zero()), the |
2614 | method round() is called and the result is rounded appropriately. By |
0716bf9b |
2615 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 |
2616 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
2617 | and P to -2, globally. |
0716bf9b |
2618 | |
b22b3e31 |
2619 | ?Maybe an extra option that forbids local A & P settings would be in order, |
2620 | ?so that intermediate rounding does not 'poison' further math? |
0716bf9b |
2621 | |
2622 | =item Overriding globals |
2623 | |
2624 | * you will be able to give A, P and R as an argument to all the calculation |
b22b3e31 |
2625 | routines; the second parameter is A, the third one is P, and the fourth is |
0716bf9b |
2626 | R (shift place by one for binary operations like add). P is used only if |
b22b3e31 |
2627 | the first parameter (A) is undefined. These three parameters override the |
2628 | globals in the order detailed as follows, i.e. the first defined value |
0716bf9b |
2629 | wins: |
b22b3e31 |
2630 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b |
2631 | + parameter A |
2632 | + parameter P |
2633 | + local A (if defined on both of the operands: smaller one is taken) |
2634 | + local P (if defined on both of the operands: smaller one is taken) |
2635 | + global A |
2636 | + global P |
2637 | + global F |
b22b3e31 |
2638 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b |
2639 | arguments (A and P) instead of one |
2640 | |
2641 | =item Local settings |
2642 | |
2643 | * You can set A and P locally by using $x->accuracy() and $x->precision() |
2644 | and thus force different A and P for different objects/numbers. |
b22b3e31 |
2645 | * Setting A or P this way immediately rounds $x to the new value. |
0716bf9b |
2646 | |
2647 | =item Rounding |
2648 | |
b22b3e31 |
2649 | * the rounding routines will use the respective global or local settings. |
0716bf9b |
2650 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
2651 | is for precision |
2652 | * the two rounding functions take as the second parameter one of the |
2653 | following rounding modes (R): |
2654 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' |
2655 | * you can set and get the global R by using Math::SomeClass->round_mode() |
ee15d750 |
2656 | or by setting $Math::SomeClass::round_mode |
0716bf9b |
2657 | * after each operation, $result->round() is called, and the result may |
b22b3e31 |
2658 | eventually be rounded (that is, if A or P were set either locally, |
2659 | globally or as parameter to the operation) |
ee15d750 |
2660 | * to manually round a number, call $x->round($A,$P,$round_mode); |
b22b3e31 |
2661 | this will round the number by using the appropriate rounding function |
0716bf9b |
2662 | and then normalize it. |
b22b3e31 |
2663 | * rounding modifies the local settings of the number: |
0716bf9b |
2664 | |
2665 | $x = Math::BigFloat->new(123.456); |
2666 | $x->accuracy(5); |
2667 | $x->bround(4); |
2668 | |
2669 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() |
2670 | will be 4 from now on. |
2671 | |
2672 | =item Default values |
2673 | |
2674 | * R: 'even' |
2675 | * F: 40 |
2676 | * A: undef |
2677 | * P: undef |
2678 | |
2679 | =item Remarks |
2680 | |
2681 | * The defaults are set up so that the new code gives the same results as |
2682 | the old code (except in a few cases on fdiv): |
2683 | + Both A and P are undefined and thus will not be used for rounding |
2684 | after each operation. |
2685 | + round() is thus a no-op, unless given extra parameters A and P |
58cde26e |
2686 | |
2687 | =back |
2688 | |
0716bf9b |
2689 | =head1 INTERNALS |
2690 | |
574bacfe |
2691 | The actual numbers are stored as unsigned big integers (with seperate sign). |
2692 | You should neither care about nor depend on the internal representation; it |
2693 | might change without notice. Use only method calls like C<< $x->sign(); >> |
2694 | instead relying on the internal hash keys like in C<< $x->{sign}; >>. |
2695 | |
2696 | =head2 MATH LIBRARY |
58cde26e |
2697 | |
574bacfe |
2698 | Math with the numbers is done (by default) by a module called |
2699 | Math::BigInt::Calc. This is equivalent to saying: |
2700 | |
2701 | use Math::BigInt lib => 'Calc'; |
58cde26e |
2702 | |
0716bf9b |
2703 | You can change this by using: |
58cde26e |
2704 | |
0716bf9b |
2705 | use Math::BigInt lib => 'BitVect'; |
58cde26e |
2706 | |
574bacfe |
2707 | The following would first try to find Math::BigInt::Foo, then |
2708 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
0716bf9b |
2709 | |
574bacfe |
2710 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
58cde26e |
2711 | |
574bacfe |
2712 | Calc.pm uses as internal format an array of elements of some decimal base |
2713 | (usually 1e5, but this might change to 1e7) with the least significant digit |
2714 | first, while BitVect.pm uses a bit vector of base 2, most significant bit |
2715 | first. Other modules might use even different means of representing the |
2716 | numbers. See the respective module documentation for further details. |
58cde26e |
2717 | |
574bacfe |
2718 | =head2 SIGN |
2719 | |
2720 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. |
2721 | |
2722 | A sign of 'NaN' is used to represent the result when input arguments are not |
2723 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively |
2724 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
2725 | '-inf' when dividing any negative number by 0. |
58cde26e |
2726 | |
2727 | =head2 mantissa(), exponent() and parts() |
2728 | |
2729 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such |
2730 | that: |
2731 | |
2732 | $m = $x->mantissa(); |
2733 | $e = $x->exponent(); |
2734 | $y = $m * ( 10 ** $e ); |
2735 | print "ok\n" if $x == $y; |
2736 | |
b22b3e31 |
2737 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
2738 | in one go. Both the returned mantissa and exponent have a sign. |
58cde26e |
2739 | |
574bacfe |
2740 | Currently, for BigInts C<$e> will be always 0, except for NaN, +inf and -inf, |
2741 | where it will be NaN; and for $x == 0, where it will be 1 |
2742 | (to be compatible with Math::BigFloat's internal representation of a zero as |
2743 | C<0E1>). |
58cde26e |
2744 | |
2745 | C<$m> will always be a copy of the original number. The relation between $e |
b22b3e31 |
2746 | and $m might change in the future, but will always be equivalent in a |
0716bf9b |
2747 | numerical sense, e.g. $m might get minimized. |
2748 | |
58cde26e |
2749 | =head1 EXAMPLES |
2750 | |
394e6ffb |
2751 | use Math::BigInt; |
574bacfe |
2752 | |
2753 | sub bint { Math::BigInt->new(shift); } |
2754 | |
394e6ffb |
2755 | $x = Math::BigInt->bstr("1234") # string "1234" |
58cde26e |
2756 | $x = "$x"; # same as bstr() |
58cde26e |
2757 | $x = Math::BigInt->bneg("1234"); # Bigint "-1234" |
2758 | $x = Math::BigInt->babs("-12345"); # Bigint "12345" |
2759 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" |
2760 | $x = bint(1) + bint(2); # BigInt "3" |
2761 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") |
2762 | $x = bint(1); # BigInt "1" |
2763 | $x = $x + 5 / 2; # BigInt "3" |
2764 | $x = $x ** 3; # BigInt "27" |
2765 | $x *= 2; # BigInt "54" |
394e6ffb |
2766 | $x = Math::BigInt->new(0); # BigInt "0" |
58cde26e |
2767 | $x--; # BigInt "-1" |
2768 | $x = Math::BigInt->badd(4,5) # BigInt "9" |
58cde26e |
2769 | print $x->bsstr(); # 9e+0 |
a5f75d66 |
2770 | |
0716bf9b |
2771 | Examples for rounding: |
2772 | |
2773 | use Math::BigFloat; |
2774 | use Test; |
2775 | |
2776 | $x = Math::BigFloat->new(123.4567); |
2777 | $y = Math::BigFloat->new(123.456789); |
394e6ffb |
2778 | Math::BigFloat->accuracy(4); # no more A than 4 |
0716bf9b |
2779 | |
2780 | ok ($x->copy()->fround(),123.4); # even rounding |
2781 | print $x->copy()->fround(),"\n"; # 123.4 |
2782 | Math::BigFloat->round_mode('odd'); # round to odd |
2783 | print $x->copy()->fround(),"\n"; # 123.5 |
394e6ffb |
2784 | Math::BigFloat->accuracy(5); # no more A than 5 |
0716bf9b |
2785 | Math::BigFloat->round_mode('odd'); # round to odd |
2786 | print $x->copy()->fround(),"\n"; # 123.46 |
2787 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 |
2788 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 |
2789 | |
394e6ffb |
2790 | Math::BigFloat->accuracy(undef); # A not important now |
2791 | Math::BigFloat->precision(2); # P important |
2792 | print $x->copy()->bnorm(),"\n"; # 123.46 |
2793 | print $x->copy()->fround(),"\n"; # 123.46 |
0716bf9b |
2794 | |
bd05a461 |
2795 | Examples for converting: |
2796 | |
2797 | my $x = Math::BigInt->new('0b1'.'01' x 123); |
2798 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; |
2799 | |
b3ac6de7 |
2800 | =head1 Autocreating constants |
2801 | |
58cde26e |
2802 | After C<use Math::BigInt ':constant'> all the B<integer> decimal constants |
2803 | in the given scope are converted to C<Math::BigInt>. This conversion |
b3ac6de7 |
2804 | happens at compile time. |
2805 | |
b22b3e31 |
2806 | In particular, |
b3ac6de7 |
2807 | |
58cde26e |
2808 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
2809 | |
2810 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b |
2811 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e |
2812 | |
2813 | Please note that strings and floating point constants are not affected, |
2814 | so that |
2815 | |
2816 | use Math::BigInt qw/:constant/; |
2817 | |
2818 | $x = 1234567890123456789012345678901234567890 |
2819 | + 123456789123456789; |
b22b3e31 |
2820 | $y = '1234567890123456789012345678901234567890' |
58cde26e |
2821 | + '123456789123456789'; |
b3ac6de7 |
2822 | |
b22b3e31 |
2823 | do not work. You need an explicit Math::BigInt->new() around one of the |
394e6ffb |
2824 | operands. You should also quote large constants to protect loss of precision: |
2825 | |
2826 | use Math::Bigint; |
2827 | |
2828 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); |
2829 | |
2830 | Without the quotes Perl would convert the large number to a floating point |
2831 | constant at compile time and then hand the result to BigInt, which results in |
2832 | an truncated result or a NaN. |
58cde26e |
2833 | |
2834 | =head1 PERFORMANCE |
2835 | |
2836 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x |
2837 | must be made in the second case. For long numbers, the copy can eat up to 20% |
b22b3e31 |
2838 | of the work (in the case of addition/subtraction, less for |
58cde26e |
2839 | multiplication/division). If $y is very small compared to $x, the form |
2840 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes |
2841 | more time then the actual addition. |
2842 | |
b22b3e31 |
2843 | With a technique called copy-on-write, the cost of copying with overload could |
394e6ffb |
2844 | be minimized or even completely avoided. A test implementation of COW did show |
2845 | performance gains for overloaded math, but introduced a performance loss due |
2846 | to a constant overhead for all other operatons. |
2847 | |
2848 | The rewritten version of this module is slower on certain operations, like |
2849 | new(), bstr() and numify(). The reason are that it does now more work and |
2850 | handles more cases. The time spent in these operations is usually gained in |
2851 | the other operations so that programs on the average should get faster. If |
2852 | they don't, please contect the author. |
58cde26e |
2853 | |
394e6ffb |
2854 | Some operations may be slower for small numbers, but are significantly faster |
2855 | for big numbers. Other operations are now constant (O(1), like bneg(), babs() |
2856 | etc), instead of O(N) and thus nearly always take much less time. These |
2857 | optimizations were done on purpose. |
58cde26e |
2858 | |
574bacfe |
2859 | If you find the Calc module to slow, try to install any of the replacement |
2860 | modules and see if they help you. |
b3ac6de7 |
2861 | |
574bacfe |
2862 | =head2 Alternative math libraries |
0716bf9b |
2863 | |
2864 | You can use an alternative library to drive Math::BigInt via: |
2865 | |
2866 | use Math::BigInt lib => 'Module'; |
2867 | |
394e6ffb |
2868 | See L<MATH LIBRARY> for more information. |
0716bf9b |
2869 | |
394e6ffb |
2870 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. |
574bacfe |
2871 | |
a5f75d66 |
2872 | =head1 BUGS |
2873 | |
58cde26e |
2874 | =over 2 |
2875 | |
574bacfe |
2876 | =item Out of Memory! |
58cde26e |
2877 | |
2878 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and |
2879 | C<eval()> in your code will crash with "Out of memory". This is probably an |
2880 | overload/exporter bug. You can workaround by not having C<eval()> |
574bacfe |
2881 | and ':constant' at the same time or upgrade your Perl to a newer version. |
2882 | |
2883 | =item Fails to load Calc on Perl prior 5.6.0 |
2884 | |
2885 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt |
2886 | will fall back to eval { require ... } when loading the math lib on Perls |
2887 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on |
2888 | filesystems using a different seperator. |
58cde26e |
2889 | |
2890 | =back |
2891 | |
2892 | =head1 CAVEATS |
2893 | |
2894 | Some things might not work as you expect them. Below is documented what is |
2895 | known to be troublesome: |
2896 | |
2897 | =over 1 |
2898 | |
2899 | =item stringify, bstr(), bsstr() and 'cmp' |
2900 | |
2901 | Both stringify and bstr() now drop the leading '+'. The old code would return |
2902 | '+3', the new returns '3'. This is to be consistent with Perl and to make |
2903 | cmp (especially with overloading) to work as you expect. It also solves |
2904 | problems with Test.pm, it's ok() uses 'eq' internally. |
2905 | |
2906 | Mark said, when asked about to drop the '+' altogether, or make only cmp work: |
2907 | |
2908 | I agree (with the first alternative), don't add the '+' on positive |
2909 | numbers. It's not as important anymore with the new internal |
2910 | form for numbers. It made doing things like abs and neg easier, |
2911 | but those have to be done differently now anyway. |
2912 | |
2913 | So, the following examples will now work all as expected: |
2914 | |
2915 | use Test; |
2916 | BEGIN { plan tests => 1 } |
2917 | use Math::BigInt; |
2918 | |
2919 | my $x = new Math::BigInt 3*3; |
2920 | my $y = new Math::BigInt 3*3; |
2921 | |
2922 | ok ($x,3*3); |
2923 | print "$x eq 9" if $x eq $y; |
2924 | print "$x eq 9" if $x eq '9'; |
2925 | print "$x eq 9" if $x eq 3*3; |
2926 | |
2927 | Additionally, the following still works: |
2928 | |
2929 | print "$x == 9" if $x == $y; |
2930 | print "$x == 9" if $x == 9; |
2931 | print "$x == 9" if $x == 3*3; |
2932 | |
2933 | There is now a C<bsstr()> method to get the string in scientific notation aka |
2934 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() |
2935 | for comparisation, but Perl will represent some numbers as 100 and others |
2936 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before doing eq: |
2937 | |
2938 | use Test; |
2939 | BEGIN { plan tests => 3 } |
2940 | use Math::BigInt; |
2941 | |
2942 | $x = Math::BigInt->new('1e56'); $y = 1e56; |
2943 | ok ($x,$y); # will fail |
2944 | ok ($x->bsstr(),$y); # okay |
2945 | $y = Math::BigInt->new($y); |
2946 | ok ($x,$y); # okay |
2947 | |
394e6ffb |
2948 | Alternatively, simple use <=> for comparisations, that will get it always |
2949 | right. There is not yet a way to get a number automatically represented as |
2950 | a string that matches exactly the way Perl represents it. |
574bacfe |
2951 | |
58cde26e |
2952 | =item int() |
2953 | |
2954 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a |
2955 | Perl scalar: |
2956 | |
2957 | $x = Math::BigInt->new(123); |
2958 | $y = int($x); # BigInt 123 |
2959 | $x = Math::BigFloat->new(123.45); |
2960 | $y = int($x); # BigInt 123 |
2961 | |
2962 | In all Perl versions you can use C<as_number()> for the same effect: |
2963 | |
2964 | $x = Math::BigFloat->new(123.45); |
2965 | $y = $x->as_number(); # BigInt 123 |
2966 | |
2967 | This also works for other subclasses, like Math::String. |
2968 | |
574bacfe |
2969 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. |
2970 | |
dccbb853 |
2971 | =item length |
58cde26e |
2972 | |
2973 | The following will probably not do what you expect: |
2974 | |
bd05a461 |
2975 | $c = Math::BigInt->new(123); |
2976 | print $c->length(),"\n"; # prints 30 |
2977 | |
2978 | It prints both the number of digits in the number and in the fraction part |
2979 | since print calls C<length()> in list context. Use something like: |
2980 | |
2981 | print scalar $c->length(),"\n"; # prints 3 |
2982 | |
2983 | =item bdiv |
2984 | |
2985 | The following will probably not do what you expect: |
2986 | |
58cde26e |
2987 | print $c->bdiv(10000),"\n"; |
2988 | |
dccbb853 |
2989 | It prints both quotient and remainder since print calls C<bdiv()> in list |
58cde26e |
2990 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want |
2991 | to use |
2992 | |
2993 | print $c / 10000,"\n"; |
2994 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c |
2995 | |
2996 | instead. |
2997 | |
2998 | The quotient is always the greatest integer less than or equal to the |
2999 | real-valued quotient of the two operands, and the remainder (when it is |
3000 | nonzero) always has the same sign as the second operand; so, for |
3001 | example, |
3002 | |
dccbb853 |
3003 | 1 / 4 => ( 0, 1) |
3004 | 1 / -4 => (-1,-3) |
3005 | -3 / 4 => (-1, 1) |
3006 | -3 / -4 => ( 0,-3) |
3007 | -11 / 2 => (-5,1) |
3008 | 11 /-2 => (-5,-1) |
58cde26e |
3009 | |
3010 | As a consequence, the behavior of the operator % agrees with the |
3011 | behavior of Perl's built-in % operator (as documented in the perlop |
3012 | manpage), and the equation |
3013 | |
3014 | $x == ($x / $y) * $y + ($x % $y) |
3015 | |
3016 | holds true for any $x and $y, which justifies calling the two return |
dccbb853 |
3017 | values of bdiv() the quotient and remainder. The only exception to this rule |
3018 | are when $y == 0 and $x is negative, then the remainder will also be |
3019 | negative. See below under "infinity handling" for the reasoning behing this. |
58cde26e |
3020 | |
3021 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will |
3022 | not change BigInt's way to do things. This is because under 'use integer' Perl |
3023 | will do what the underlying C thinks is right and this is different for each |
3024 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug |
3025 | the author to implement it ;) |
3026 | |
dccbb853 |
3027 | =item infinity handling |
3028 | |
3029 | Here are some examples that explain the reasons why certain results occur while |
3030 | handling infinity: |
3031 | |
3032 | The following table shows the result of the division and the remainder, so that |
3033 | the equation above holds true. Some "ordinary" cases are strewn in to show more |
3034 | clearly the reasoning: |
3035 | |
3036 | A / B = C, R so that C * B + R = A |
3037 | ========================================================= |
3038 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 |
3039 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 |
3040 | 0 / inf = 0, 0 0 * inf + 0 = 0 |
3041 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 |
3042 | 5 / inf = 0, 5 0 * inf + 5 = 5 |
3043 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 |
3044 | -5/ inf = 0, -5 0 * inf + -5 = -5 |
3045 | -5/-inf = 0, -5 0 * -inf + -5 = -5 |
3046 | inf/ 5 = inf, 0 inf * 5 + 0 = inf |
3047 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf |
3048 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf |
3049 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf |
3050 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 |
3051 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 |
3052 | inf/ inf = 1, 0 1 * inf + 0 = inf |
3053 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf |
3054 | inf/-inf = -1, 0 -1 * -inf + 0 = inf |
3055 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf |
3056 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 |
3057 | inf/ 0 = inf, inf inf * 0 + inf = inf |
3058 | 0/ 0 = NaN |
3059 | |
3060 | These cases below violate the "remainder has the sign of the second of the two |
3061 | arguments", since they wouldn't match up otherwise. |
3062 | |
3063 | A / B = C, R so that C * B + R = A |
3064 | ======================================================== |
3065 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf |
3066 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 |
3067 | |
58cde26e |
3068 | =item Modifying and = |
3069 | |
3070 | Beware of: |
3071 | |
3072 | $x = Math::BigFloat->new(5); |
3073 | $y = $x; |
3074 | |
3075 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
3076 | a second reference to the B<same> object and stores it in $y. Thus anything |
17baacb7 |
3077 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
3078 | Or in other words, C<=> is only safe if you modify your BigInts only via |
3079 | overloaded math. As soon as you use a method call it breaks: |
58cde26e |
3080 | |
3081 | $x->bmul(2); |
3082 | print "$x, $y\n"; # prints '10, 10' |
3083 | |
3084 | If you want a true copy of $x, use: |
3085 | |
3086 | $y = $x->copy(); |
3087 | |
17baacb7 |
3088 | You can also chain the calls like this, this will make first a copy and then |
3089 | multiply it by 2: |
3090 | |
3091 | $y = $x->copy()->bmul(2); |
3092 | |
b22b3e31 |
3093 | See also the documentation for overload.pm regarding C<=>. |
58cde26e |
3094 | |
3095 | =item bpow |
3096 | |
3097 | C<bpow()> (and the rounding functions) now modifies the first argument and |
574bacfe |
3098 | returns it, unlike the old code which left it alone and only returned the |
58cde26e |
3099 | result. This is to be consistent with C<badd()> etc. The first three will |
3100 | modify $x, the last one won't: |
3101 | |
3102 | print bpow($x,$i),"\n"; # modify $x |
3103 | print $x->bpow($i),"\n"; # ditto |
3104 | print $x **= $i,"\n"; # the same |
3105 | print $x ** $i,"\n"; # leave $x alone |
3106 | |
3107 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. |
3108 | |
3109 | =item Overloading -$x |
3110 | |
3111 | The following: |
3112 | |
3113 | $x = -$x; |
3114 | |
3115 | is slower than |
3116 | |
3117 | $x->bneg(); |
3118 | |
3119 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant |
3120 | needs to preserve $x since it does not know that it later will get overwritten. |
0716bf9b |
3121 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e |
3122 | |
394e6ffb |
3123 | With Copy-On-Write, this issue would be gone, but C-o-W is not implemented |
3124 | since it is slower for all other things. |
58cde26e |
3125 | |
3126 | =item Mixing different object types |
3127 | |
3128 | In Perl you will get a floating point value if you do one of the following: |
3129 | |
3130 | $float = 5.0 + 2; |
3131 | $float = 2 + 5.0; |
3132 | $float = 5 / 2; |
3133 | |
3134 | With overloaded math, only the first two variants will result in a BigFloat: |
3135 | |
3136 | use Math::BigInt; |
3137 | use Math::BigFloat; |
3138 | |
3139 | $mbf = Math::BigFloat->new(5); |
3140 | $mbi2 = Math::BigInteger->new(5); |
3141 | $mbi = Math::BigInteger->new(2); |
3142 | |
3143 | # what actually gets called: |
3144 | $float = $mbf + $mbi; # $mbf->badd() |
3145 | $float = $mbf / $mbi; # $mbf->bdiv() |
3146 | $integer = $mbi + $mbf; # $mbi->badd() |
3147 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() |
3148 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() |
3149 | |
3150 | This is because math with overloaded operators follows the first (dominating) |
394e6ffb |
3151 | operand, and the operation of that is called and returns thus the result. So, |
58cde26e |
3152 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
3153 | the result should be a Math::BigFloat or the second operant is one. |
3154 | |
3155 | To get a Math::BigFloat you either need to call the operation manually, |
3156 | make sure the operands are already of the proper type or casted to that type |
3157 | via Math::BigFloat->new(): |
3158 | |
3159 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 |
3160 | |
3161 | Beware of simple "casting" the entire expression, this would only convert |
3162 | the already computed result: |
3163 | |
3164 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! |
3165 | |
0716bf9b |
3166 | Beware also of the order of more complicated expressions like: |
58cde26e |
3167 | |
3168 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int |
3169 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto |
3170 | |
3171 | If in doubt, break the expression into simpler terms, or cast all operands |
3172 | to the desired resulting type. |
3173 | |
3174 | Scalar values are a bit different, since: |
3175 | |
3176 | $float = 2 + $mbf; |
3177 | $float = $mbf + 2; |
3178 | |
3179 | will both result in the proper type due to the way the overloaded math works. |
3180 | |
3181 | This section also applies to other overloaded math packages, like Math::String. |
3182 | |
3183 | =item bsqrt() |
3184 | |
394e6ffb |
3185 | C<bsqrt()> works only good if the result is a big integer, e.g. the square |
58cde26e |
3186 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
3187 | mode. |
3188 | |
3189 | If you want a better approximation of the square root, then use: |
3190 | |
3191 | $x = Math::BigFloat->new(12); |
394e6ffb |
3192 | Math::BigFloat->precision(0); |
58cde26e |
3193 | Math::BigFloat->round_mode('even'); |
3194 | print $x->copy->bsqrt(),"\n"; # 4 |
3195 | |
394e6ffb |
3196 | Math::BigFloat->precision(2); |
58cde26e |
3197 | print $x->bsqrt(),"\n"; # 3.46 |
3198 | print $x->bsqrt(3),"\n"; # 3.464 |
3199 | |
3200 | =back |
3201 | |
3202 | =head1 LICENSE |
3203 | |
3204 | This program is free software; you may redistribute it and/or modify it under |
3205 | the same terms as Perl itself. |
a5f75d66 |
3206 | |
0716bf9b |
3207 | =head1 SEE ALSO |
3208 | |
027dc388 |
3209 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
3210 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
0716bf9b |
3211 | |
027dc388 |
3212 | The package at |
3213 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains |
3214 | more documentation including a full version history, testcases, empty |
3215 | subclass files and benchmarks. |
574bacfe |
3216 | |
58cde26e |
3217 | =head1 AUTHORS |
a5f75d66 |
3218 | |
58cde26e |
3219 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
3220 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001. |
a5f75d66 |
3221 | |
3222 | =cut |