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1 | #!/usr/bin/perl -w |
2 | |
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3 | # Qs: what exactly happens on numify of HUGE numbers? overflow? |
4 | # $a = -$a is much slower (making copy of $a) than $a->bneg(), hm!? |
5 | # (copy_on_write will help there, but that is not yet implemented) |
6 | |
7 | # The following hash values are used: |
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8 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) |
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9 | # sign : +,-,NaN,+inf,-inf |
10 | # _a : accuracy |
11 | # _p : precision |
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12 | # _f : flags, used by MBF to flag parts of a float as untouchable |
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13 | # _cow : copy on write: number of objects that share the data (NRY) |
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14 | |
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15 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since |
16 | # underlying lib might change the reference! |
17 | |
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18 | package Math::BigInt; |
19 | my $class = "Math::BigInt"; |
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20 | require 5.005; |
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21 | |
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22 | $VERSION = '1.42'; |
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23 | use Exporter; |
24 | @ISA = qw( Exporter ); |
25 | @EXPORT_OK = qw( bneg babs bcmp badd bmul bdiv bmod bnorm bsub |
26 | bgcd blcm |
27 | bround |
28 | blsft brsft band bior bxor bnot bpow bnan bzero |
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29 | bacmp bstr bsstr binc bdec binf bfloor bceil |
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30 | is_odd is_even is_zero is_one is_nan is_inf sign |
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31 | is_positive is_negative |
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32 | length as_number |
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33 | objectify _swap |
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34 | ); |
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35 | #@EXPORT = qw( ); |
36 | use vars qw/$rnd_mode $accuracy $precision $div_scale/; |
37 | use strict; |
38 | |
39 | # Inside overload, the first arg is always an object. If the original code had |
40 | # it reversed (like $x = 2 * $y), then the third paramater indicates this |
41 | # swapping. To make it work, we use a helper routine which not only reswaps the |
42 | # params, but also makes a new object in this case. See _swap() for details, |
43 | # especially the cases of operators with different classes. |
44 | |
45 | # For overloaded ops with only one argument we simple use $_[0]->copy() to |
46 | # preserve the argument. |
47 | |
48 | # Thus inheritance of overload operators becomes possible and transparent for |
49 | # our subclasses without the need to repeat the entire overload section there. |
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50 | |
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51 | use overload |
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52 | '=' => sub { $_[0]->copy(); }, |
53 | |
54 | # '+' and '-' do not use _swap, since it is a triffle slower. If you want to |
55 | # override _swap (if ever), then override overload of '+' and '-', too! |
56 | # for sub it is a bit tricky to keep b: b-a => -a+b |
57 | '-' => sub { my $c = $_[0]->copy; $_[2] ? |
58 | $c->bneg()->badd($_[1]) : |
59 | $c->bsub( $_[1]) }, |
60 | '+' => sub { $_[0]->copy()->badd($_[1]); }, |
61 | |
62 | # some shortcuts for speed (assumes that reversed order of arguments is routed |
63 | # to normal '+' and we thus can always modify first arg. If this is changed, |
64 | # this breaks and must be adjusted.) |
65 | '+=' => sub { $_[0]->badd($_[1]); }, |
66 | '-=' => sub { $_[0]->bsub($_[1]); }, |
67 | '*=' => sub { $_[0]->bmul($_[1]); }, |
68 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, |
69 | '**=' => sub { $_[0]->bpow($_[1]); }, |
70 | |
71 | '<=>' => sub { $_[2] ? |
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72 | ref($_[0])->bcmp($_[1],$_[0]) : |
73 | ref($_[0])->bcmp($_[0],$_[1])}, |
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74 | 'cmp' => sub { |
75 | $_[2] ? |
76 | $_[1] cmp $_[0]->bstr() : |
77 | $_[0]->bstr() cmp $_[1] }, |
78 | |
79 | 'int' => sub { $_[0]->copy(); }, |
80 | 'neg' => sub { $_[0]->copy()->bneg(); }, |
81 | 'abs' => sub { $_[0]->copy()->babs(); }, |
82 | '~' => sub { $_[0]->copy()->bnot(); }, |
83 | |
84 | '*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); }, |
85 | '/' => sub { my @a = ref($_[0])->_swap(@_);scalar $a[0]->bdiv($a[1]);}, |
86 | '%' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmod($a[1]); }, |
87 | '**' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bpow($a[1]); }, |
88 | '<<' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->blsft($a[1]); }, |
89 | '>>' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->brsft($a[1]); }, |
90 | |
91 | '&' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->band($a[1]); }, |
92 | '|' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bior($a[1]); }, |
93 | '^' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bxor($a[1]); }, |
94 | |
95 | # can modify arg of ++ and --, so avoid a new-copy for speed, but don't |
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96 | # use $_[0]->__one(), it modifies $_[0] to be 1! |
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97 | '++' => sub { $_[0]->binc() }, |
98 | '--' => sub { $_[0]->bdec() }, |
99 | |
100 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers |
101 | 'bool' => sub { |
102 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ |
103 | # v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-( |
104 | my $t = !$_[0]->is_zero(); |
105 | undef $t if $t == 0; |
106 | return $t; |
107 | }, |
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108 | |
109 | qw( |
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110 | "" bstr |
111 | 0+ numify), # Order of arguments unsignificant |
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112 | ; |
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113 | |
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114 | ############################################################################## |
115 | # global constants, flags and accessory |
116 | |
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117 | use constant MB_NEVER_ROUND => 0x0001; |
118 | |
119 | my $NaNOK=1; # are NaNs ok? |
120 | my $nan = 'NaN'; # constants for easier life |
121 | |
122 | my $CALC = 'Math::BigInt::Calc'; # module to do low level math |
123 | sub _core_lib () { return $CALC; } # for test suite |
124 | |
125 | # Rounding modes, one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
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126 | $rnd_mode = 'even'; |
127 | $accuracy = undef; |
128 | $precision = undef; |
129 | $div_scale = 40; |
130 | |
131 | sub round_mode |
132 | { |
133 | # make Class->round_mode() work |
134 | my $self = shift || $class; |
135 | # shift @_ if defined $_[0] && $_[0] eq $class; |
136 | if (defined $_[0]) |
137 | { |
138 | my $m = shift; |
139 | die "Unknown round mode $m" |
140 | if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
141 | $rnd_mode = $m; return; |
142 | } |
143 | return $rnd_mode; |
144 | } |
145 | |
146 | sub accuracy |
147 | { |
148 | # $x->accuracy($a); ref($x) a |
149 | # $x->accuracy(); ref($x); |
150 | # Class::accuracy(); # not supported |
151 | #print "MBI @_ ($class)\n"; |
152 | my $x = shift; |
153 | |
154 | die ("accuracy() needs reference to object as first parameter.") |
155 | if !ref $x; |
156 | |
157 | if (@_ > 0) |
158 | { |
159 | $x->{_a} = shift; |
160 | $x->round() if defined $x->{_a}; |
161 | } |
162 | return $x->{_a}; |
163 | } |
164 | |
165 | sub precision |
166 | { |
167 | my $x = shift; |
168 | |
169 | die ("precision() needs reference to object as first parameter.") |
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170 | if !ref $x; |
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171 | |
172 | if (@_ > 0) |
173 | { |
174 | $x->{_p} = shift; |
175 | $x->round() if defined $x->{_p}; |
176 | } |
177 | return $x->{_p}; |
178 | } |
179 | |
180 | sub _scale_a |
181 | { |
182 | # select accuracy parameter based on precedence, |
183 | # used by bround() and bfround(), may return undef for scale (means no op) |
184 | my ($x,$s,$m,$scale,$mode) = @_; |
185 | $scale = $x->{_a} if !defined $scale; |
186 | $scale = $s if (!defined $scale); |
187 | $mode = $m if !defined $mode; |
188 | return ($scale,$mode); |
189 | } |
190 | |
191 | sub _scale_p |
192 | { |
193 | # select precision parameter based on precedence, |
194 | # used by bround() and bfround(), may return undef for scale (means no op) |
195 | my ($x,$s,$m,$scale,$mode) = @_; |
196 | $scale = $x->{_p} if !defined $scale; |
197 | $scale = $s if (!defined $scale); |
198 | $mode = $m if !defined $mode; |
199 | return ($scale,$mode); |
200 | } |
201 | |
202 | ############################################################################## |
203 | # constructors |
204 | |
205 | sub copy |
206 | { |
207 | my ($c,$x); |
208 | if (@_ > 1) |
209 | { |
210 | # if two arguments, the first one is the class to "swallow" subclasses |
211 | ($c,$x) = @_; |
212 | } |
213 | else |
214 | { |
215 | $x = shift; |
216 | $c = ref($x); |
217 | } |
218 | return unless ref($x); # only for objects |
219 | |
220 | my $self = {}; bless $self,$c; |
221 | foreach my $k (keys %$x) |
222 | { |
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223 | if ($k eq 'value') |
224 | { |
225 | $self->{$k} = $CALC->_copy($x->{$k}); |
226 | } |
227 | elsif (ref($x->{$k}) eq 'SCALAR') |
228 | { |
229 | $self->{$k} = \${$x->{$k}}; |
230 | } |
231 | elsif (ref($x->{$k}) eq 'ARRAY') |
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232 | { |
233 | $self->{$k} = [ @{$x->{$k}} ]; |
234 | } |
235 | elsif (ref($x->{$k}) eq 'HASH') |
236 | { |
237 | # only one level deep! |
238 | foreach my $h (keys %{$x->{$k}}) |
239 | { |
240 | $self->{$k}->{$h} = $x->{$k}->{$h}; |
241 | } |
242 | } |
243 | elsif (ref($x->{$k})) |
244 | { |
245 | my $c = ref($x->{$k}); |
246 | $self->{$k} = $c->new($x->{$k}); # no copy() due to deep rec |
247 | } |
248 | else |
249 | { |
250 | $self->{$k} = $x->{$k}; |
251 | } |
252 | } |
253 | $self; |
254 | } |
255 | |
256 | sub new |
257 | { |
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258 | # create a new BigInt object from a string or another BigInt object. |
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259 | # see hash keys documented at top |
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260 | |
261 | # the argument could be an object, so avoid ||, && etc on it, this would |
b22b3e31 |
262 | # cause costly overloaded code to be called. The only allowed ops are |
263 | # ref() and defined. |
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264 | |
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265 | my $class = shift; |
266 | |
267 | my $wanted = shift; # avoid numify call by not using || here |
268 | return $class->bzero() if !defined $wanted; # default to 0 |
269 | return $class->copy($wanted) if ref($wanted); |
270 | |
271 | my $self = {}; bless $self, $class; |
272 | # handle '+inf', '-inf' first |
273 | if ($wanted =~ /^[+-]inf$/) |
274 | { |
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275 | $self->{value} = $CALC->_zero(); |
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276 | $self->{sign} = $wanted; |
277 | return $self; |
278 | } |
279 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign |
280 | my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted); |
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281 | if (!ref $mis) |
282 | { |
283 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
284 | #print "NaN 1\n"; |
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285 | $self->{value} = $CALC->_zero(); |
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286 | $self->{sign} = $nan; |
287 | return $self; |
288 | } |
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289 | if (!ref $miv) |
290 | { |
291 | # _from_hex or _from_bin |
292 | $self->{value} = $mis->{value}; |
293 | $self->{sign} = $mis->{sign}; |
294 | return $self; # throw away $mis |
295 | } |
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296 | # make integer from mantissa by adjusting exp, then convert to bigint |
297 | $self->{sign} = $$mis; # store sign |
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298 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
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299 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
300 | if ($e > 0) |
301 | { |
302 | my $diff = $e - CORE::length($$mfv); |
303 | if ($diff < 0) # Not integer |
304 | { |
305 | #print "NOI 1\n"; |
306 | $self->{sign} = $nan; |
307 | } |
308 | else # diff >= 0 |
309 | { |
310 | # adjust fraction and add it to value |
311 | # print "diff > 0 $$miv\n"; |
312 | $$miv = $$miv . ($$mfv . '0' x $diff); |
313 | } |
314 | } |
315 | else |
316 | { |
317 | if ($$mfv ne '') # e <= 0 |
318 | { |
319 | # fraction and negative/zero E => NOI |
320 | #print "NOI 2 \$\$mfv '$$mfv'\n"; |
321 | $self->{sign} = $nan; |
322 | } |
323 | elsif ($e < 0) |
324 | { |
325 | # xE-y, and empty mfv |
326 | #print "xE-y\n"; |
327 | $e = abs($e); |
328 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? |
329 | { |
330 | #print "NOI 3\n"; |
331 | $self->{sign} = $nan; |
332 | } |
333 | } |
334 | } |
335 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 |
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336 | $self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/; |
337 | #print "$wanted => $self->{sign}\n"; |
338 | # if any of the globals is set, use them to round and store them inside $self |
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339 | $self->round($accuracy,$precision,$rnd_mode) |
340 | if defined $accuracy || defined $precision; |
341 | return $self; |
342 | } |
343 | |
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344 | sub bnan |
345 | { |
346 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' |
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347 | my $self = shift; |
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348 | $self = $class if !defined $self; |
349 | if (!ref($self)) |
350 | { |
351 | my $c = $self; $self = {}; bless $self, $c; |
352 | } |
353 | return if $self->modify('bnan'); |
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354 | $self->{value} = $CALC->_zero(); |
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355 | $self->{sign} = $nan; |
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356 | return $self; |
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357 | } |
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358 | |
359 | sub binf |
360 | { |
361 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' |
362 | # the sign is either '+', or if given, used from there |
363 | my $self = shift; |
364 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
365 | $self = $class if !defined $self; |
366 | if (!ref($self)) |
367 | { |
368 | my $c = $self; $self = {}; bless $self, $c; |
369 | } |
370 | return if $self->modify('binf'); |
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371 | $self->{value} = $CALC->_zero(); |
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372 | $self->{sign} = $sign.'inf'; |
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373 | return $self; |
374 | } |
375 | |
376 | sub bzero |
377 | { |
378 | # create a bigint '+0', if given a BigInt, set it to 0 |
379 | my $self = shift; |
380 | $self = $class if !defined $self; |
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381 | |
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382 | if (!ref($self)) |
383 | { |
384 | my $c = $self; $self = {}; bless $self, $c; |
385 | } |
386 | return if $self->modify('bzero'); |
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387 | $self->{value} = $CALC->_zero(); |
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388 | $self->{sign} = '+'; |
0716bf9b |
389 | #print "result: $self\n"; |
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390 | return $self; |
391 | } |
392 | |
574bacfe |
393 | sub bone |
394 | { |
395 | # create a bigint '+1' (or -1 if given sign '-'), |
396 | # if given a BigInt, set it to +1 or -1, respecively |
397 | my $self = shift; |
398 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
399 | $self = $class if !defined $self; |
400 | #print "bone $self\n"; |
401 | |
402 | if (!ref($self)) |
403 | { |
404 | my $c = $self; $self = {}; bless $self, $c; |
405 | } |
406 | return if $self->modify('bone'); |
407 | $self->{value} = $CALC->_one(); |
408 | $self->{sign} = $sign; |
409 | #print "result: $self\n"; |
410 | return $self; |
411 | } |
412 | |
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413 | ############################################################################## |
414 | # string conversation |
415 | |
416 | sub bsstr |
417 | { |
418 | # (ref to BFLOAT or num_str ) return num_str |
419 | # Convert number from internal format to scientific string format. |
420 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
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421 | my ($self,$x) = objectify(1,@_); |
422 | |
574bacfe |
423 | if ($x->{sign} !~ /^[+-]$/) |
424 | { |
425 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
426 | return 'inf'; # +inf |
427 | } |
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428 | my ($m,$e) = $x->parts(); |
574bacfe |
429 | # e can only be positive |
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430 | my $sign = 'e+'; |
431 | # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s; |
432 | return $m->bstr().$sign.$e->bstr(); |
433 | } |
434 | |
435 | sub bstr |
436 | { |
0716bf9b |
437 | # make a string from bigint object |
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438 | my $x = shift; $x = $class->new($x) unless ref $x; |
574bacfe |
439 | if ($x->{sign} !~ /^[+-]$/) |
440 | { |
441 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
442 | return 'inf'; # +inf |
443 | } |
0716bf9b |
444 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
445 | return $es.${$CALC->_str($x->{value})}; |
58cde26e |
446 | } |
447 | |
448 | sub numify |
449 | { |
450 | # Make a number from a BigInt object |
58cde26e |
451 | my $x = shift; $x = $class->new($x) unless ref $x; |
0716bf9b |
452 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
453 | my $num = $CALC->_num($x->{value}); |
454 | return -$num if $x->{sign} eq '-'; |
58cde26e |
455 | return $num; |
456 | } |
457 | |
458 | ############################################################################## |
459 | # public stuff (usually prefixed with "b") |
460 | |
461 | sub sign |
462 | { |
463 | # return the sign of the number: +/-/NaN |
464 | my ($self,$x) = objectify(1,@_); |
465 | return $x->{sign}; |
466 | } |
467 | |
468 | sub round |
469 | { |
470 | # After any operation or when calling round(), the result is rounded by |
471 | # regarding the A & P from arguments, local parameters, or globals. |
472 | # The result's A or P are set by the rounding, but not inspected beforehand |
473 | # (aka only the arguments enter into it). This works because the given |
474 | # 'first' argument is both the result and true first argument with unchanged |
475 | # A and P settings. |
476 | # This does not yet handle $x with A, and $y with P (which should be an |
477 | # error). |
478 | my $self = shift; |
479 | my $a = shift; # accuracy, if given by caller |
480 | my $p = shift; # precision, if given by caller |
481 | my $r = shift; # round_mode, if given by caller |
482 | my @args = @_; # all 'other' arguments (0 for unary, 1 for binary ops) |
483 | |
574bacfe |
484 | $self = new($self) unless ref($self); # if not object, make one |
485 | my $c = ref($args[0]); # find out class of argument |
486 | unshift @args,$self; # add 'first' argument |
487 | |
17baacb7 |
488 | # leave bigfloat parts alone |
489 | return $self if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
490 | |
574bacfe |
491 | no strict 'refs'; |
492 | my $z = "$c\::accuracy"; my $aa = $$z; my $ap = undef; |
493 | if (!defined $aa) |
494 | { |
495 | $z = "$c\::precision"; $ap = $$z; |
496 | } |
497 | |
58cde26e |
498 | # now pick $a or $p, but only if we have got "arguments" |
499 | if ((!defined $a) && (!defined $p) && (@args > 0)) |
500 | { |
501 | foreach (@args) |
502 | { |
503 | # take the defined one, or if both defined, the one that is smaller |
504 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); |
505 | } |
506 | if (!defined $a) # if it still is not defined, take p |
507 | { |
508 | foreach (@args) |
509 | { |
510 | # take the defined one, or if both defined, the one that is smaller |
511 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} < $p); |
1f45ae4a |
512 | } |
58cde26e |
513 | # if none defined, use globals (#2) |
514 | if (!defined $p) |
515 | { |
574bacfe |
516 | $a = $aa; $p = $ap; # save the check: if !defined $a; |
1f45ae4a |
517 | } |
58cde26e |
518 | } # endif !$a |
519 | } # endif !$a || !$P && args > 0 |
520 | # for clearity, this is not merged at place (#2) |
521 | # now round, by calling fround or ffround: |
522 | if (defined $a) |
523 | { |
524 | $self->{_a} = $a; $self->bround($a,$r); |
525 | } |
526 | elsif (defined $p) |
527 | { |
528 | $self->{_p} = $p; $self->bfround($p,$r); |
529 | } |
530 | return $self->bnorm(); |
531 | } |
532 | |
17baacb7 |
533 | sub bnorm |
58cde26e |
534 | { |
535 | # (num_str or BINT) return BINT |
536 | # Normalize number -- no-op here |
574bacfe |
537 | return $_[0]; |
58cde26e |
538 | } |
539 | |
540 | sub babs |
541 | { |
542 | # (BINT or num_str) return BINT |
543 | # make number absolute, or return absolute BINT from string |
58cde26e |
544 | my $x = shift; $x = $class->new($x) unless ref $x; |
545 | return $x if $x->modify('babs'); |
546 | # post-normalized abs for internal use (does nothing for NaN) |
547 | $x->{sign} =~ s/^-/+/; |
548 | $x; |
549 | } |
550 | |
551 | sub bneg |
552 | { |
553 | # (BINT or num_str) return BINT |
554 | # negate number or make a negated number from string |
574bacfe |
555 | my $x = shift; $x = $class->new($x) unless ref $x; |
58cde26e |
556 | return $x if $x->modify('bneg'); |
557 | # for +0 dont negate (to have always normalized) |
558 | return $x if $x->is_zero(); |
559 | $x->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
58cde26e |
560 | $x; |
561 | } |
562 | |
563 | sub bcmp |
564 | { |
565 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
566 | # (BINT or num_str, BINT or num_str) return cond_code |
567 | my ($self,$x,$y) = objectify(2,@_); |
0716bf9b |
568 | |
569 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
570 | { |
571 | # handle +-inf and NaN |
572 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
574bacfe |
573 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b |
574 | return +1 if $x->{sign} eq '+inf'; |
575 | return -1 if $x->{sign} eq '-inf'; |
576 | return -1 if $y->{sign} eq '+inf'; |
577 | return +1 if $y->{sign} eq '-inf'; |
578 | } |
574bacfe |
579 | # check sign for speed first |
580 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
581 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
582 | |
583 | # shortcut |
584 | my $xz = $x->is_zero(); |
585 | my $yz = $y->is_zero(); |
586 | return 0 if $xz && $yz; # 0 <=> 0 |
587 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
588 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
0716bf9b |
589 | # normal compare now |
58cde26e |
590 | &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0; |
591 | } |
592 | |
593 | sub bacmp |
594 | { |
595 | # Compares 2 values, ignoring their signs. |
596 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
597 | # (BINT, BINT) return cond_code |
598 | my ($self,$x,$y) = objectify(2,@_); |
574bacfe |
599 | |
600 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
601 | { |
602 | # handle +-inf and NaN |
603 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
604 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
605 | return +1; # inf is always bigger |
606 | } |
0716bf9b |
607 | $CALC->_acmp($x->{value},$y->{value}) <=> 0; |
58cde26e |
608 | } |
609 | |
610 | sub badd |
611 | { |
612 | # add second arg (BINT or string) to first (BINT) (modifies first) |
613 | # return result as BINT |
58cde26e |
614 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
615 | |
616 | return $x if $x->modify('badd'); |
58cde26e |
617 | |
574bacfe |
618 | # inf and NaN handling |
619 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
620 | { |
621 | # NaN first |
622 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
623 | # inf handline |
624 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
625 | { |
626 | # + and + => +, - and - => -, + and - => 0, - and + => 0 |
627 | return $x->bzero() if $x->{sign} ne $y->{sign}; |
628 | return $x; |
629 | } |
630 | # +-inf + something => +inf |
631 | # something +-inf => +-inf |
632 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
633 | return $x; |
634 | } |
635 | |
0716bf9b |
636 | my @bn = ($a,$p,$r,$y); # make array for round calls |
58cde26e |
637 | # speed: no add for 0+y or x+0 |
0716bf9b |
638 | return $x->round(@bn) if $y->is_zero(); # x+0 |
58cde26e |
639 | if ($x->is_zero()) # 0+y |
640 | { |
641 | # make copy, clobbering up x |
0716bf9b |
642 | $x->{value} = $CALC->_copy($y->{value}); |
58cde26e |
643 | $x->{sign} = $y->{sign} || $nan; |
644 | return $x->round(@bn); |
645 | } |
646 | |
58cde26e |
647 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
648 | |
649 | if ($sx eq $sy) |
650 | { |
574bacfe |
651 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e |
652 | $x->{sign} = $sx; |
653 | } |
654 | else |
655 | { |
574bacfe |
656 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e |
657 | if ($a > 0) |
658 | { |
659 | #print "swapped sub (a=$a)\n"; |
574bacfe |
660 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e |
661 | $x->{sign} = $sy; |
662 | } |
663 | elsif ($a == 0) |
664 | { |
665 | # speedup, if equal, set result to 0 |
0716bf9b |
666 | #print "equal sub, result = 0\n"; |
667 | $x->{value} = $CALC->_zero(); |
58cde26e |
668 | $x->{sign} = '+'; |
669 | } |
670 | else # a < 0 |
671 | { |
672 | #print "unswapped sub (a=$a)\n"; |
574bacfe |
673 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
58cde26e |
674 | $x->{sign} = $sx; |
a0d0e21e |
675 | } |
a0d0e21e |
676 | } |
58cde26e |
677 | return $x->round(@bn); |
678 | } |
679 | |
680 | sub bsub |
681 | { |
682 | # (BINT or num_str, BINT or num_str) return num_str |
683 | # subtract second arg from first, modify first |
684 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
685 | |
58cde26e |
686 | return $x if $x->modify('bsub'); |
687 | $x->badd($y->bneg()); # badd does not leave internal zeros |
688 | $y->bneg(); # refix y, assumes no one reads $y in between |
689 | return $x->round($a,$p,$r,$y); |
690 | } |
691 | |
692 | sub binc |
693 | { |
694 | # increment arg by one |
695 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
696 | # my $x = shift; $x = $class->new($x) unless ref $x; my $self = ref($x); |
58cde26e |
697 | return $x if $x->modify('binc'); |
574bacfe |
698 | $x->badd($self->__one())->round($a,$p,$r); |
58cde26e |
699 | } |
700 | |
701 | sub bdec |
702 | { |
703 | # decrement arg by one |
704 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
58cde26e |
705 | return $x if $x->modify('bdec'); |
574bacfe |
706 | $x->badd($self->__one('-'))->round($a,$p,$r); |
58cde26e |
707 | } |
708 | |
709 | sub blcm |
710 | { |
711 | # (BINT or num_str, BINT or num_str) return BINT |
712 | # does not modify arguments, but returns new object |
713 | # Lowest Common Multiplicator |
58cde26e |
714 | |
0716bf9b |
715 | my $y = shift; my ($x); |
716 | if (ref($y)) |
717 | { |
718 | $x = $y->copy(); |
719 | } |
720 | else |
721 | { |
722 | $x = $class->new($y); |
723 | } |
724 | while (@_) { $x = _lcm($x,shift); } |
58cde26e |
725 | $x; |
726 | } |
727 | |
728 | sub bgcd |
729 | { |
730 | # (BINT or num_str, BINT or num_str) return BINT |
731 | # does not modify arguments, but returns new object |
732 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) |
0716bf9b |
733 | |
734 | my $y = shift; my ($x); |
735 | if (ref($y)) |
58cde26e |
736 | { |
0716bf9b |
737 | $x = $y->copy(); |
738 | } |
739 | else |
740 | { |
741 | $x = $class->new($y); |
742 | } |
743 | |
744 | if ($CALC->can('_gcd')) |
745 | { |
746 | while (@_) |
747 | { |
748 | $y = shift; $y = $class->new($y) if !ref($y); |
749 | next if $y->is_zero(); |
750 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? |
751 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one(); |
752 | } |
753 | } |
754 | else |
755 | { |
756 | while (@_) |
757 | { |
574bacfe |
758 | $x = __gcd($x,shift); last if $x->is_one(); # _gcd handles NaN |
0716bf9b |
759 | } |
760 | } |
761 | $x->babs(); |
58cde26e |
762 | } |
763 | |
764 | sub bmod |
765 | { |
766 | # modulus |
767 | # (BINT or num_str, BINT or num_str) return BINT |
768 | my ($self,$x,$y) = objectify(2,@_); |
769 | |
770 | return $x if $x->modify('bmod'); |
771 | (&bdiv($self,$x,$y))[1]; |
772 | } |
773 | |
774 | sub bnot |
775 | { |
776 | # (num_str or BINT) return BINT |
777 | # represent ~x as twos-complement number |
778 | my ($self,$x) = objectify(1,@_); |
779 | return $x if $x->modify('bnot'); |
780 | $x->bneg(); $x->bdec(); # was: bsub(-1,$x);, time it someday |
781 | $x; |
782 | } |
783 | |
784 | sub is_zero |
785 | { |
786 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
787 | #my ($self,$x) = objectify(1,@_); |
58cde26e |
788 | my $x = shift; $x = $class->new($x) unless ref $x; |
0716bf9b |
789 | |
574bacfe |
790 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 |
791 | $CALC->_is_zero($x->{value}); |
792 | #return $CALC->_is_zero($x->{value}); |
58cde26e |
793 | } |
794 | |
795 | sub is_nan |
796 | { |
797 | # return true if arg (BINT or num_str) is NaN |
798 | #my ($self,$x) = objectify(1,@_); |
58cde26e |
799 | my $x = shift; $x = $class->new($x) unless ref $x; |
800 | return ($x->{sign} eq $nan); |
801 | } |
802 | |
803 | sub is_inf |
804 | { |
805 | # return true if arg (BINT or num_str) is +-inf |
806 | #my ($self,$x) = objectify(1,@_); |
58cde26e |
807 | my $x = shift; $x = $class->new($x) unless ref $x; |
808 | my $sign = shift || ''; |
809 | |
0716bf9b |
810 | return $x->{sign} =~ /^[+-]inf$/ if $sign eq ''; |
811 | return $x->{sign} =~ /^[$sign]inf$/; |
58cde26e |
812 | } |
813 | |
814 | sub is_one |
815 | { |
b22b3e31 |
816 | # return true if arg (BINT or num_str) is +1 |
817 | # or -1 if sign is given |
58cde26e |
818 | #my ($self,$x) = objectify(1,@_); |
819 | my $x = shift; $x = $class->new($x) unless ref $x; |
574bacfe |
820 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
0716bf9b |
821 | |
574bacfe |
822 | return 0 if $x->{sign} ne $sign; |
0716bf9b |
823 | return $CALC->_is_one($x->{value}); |
58cde26e |
824 | } |
825 | |
826 | sub is_odd |
827 | { |
828 | # return true when arg (BINT or num_str) is odd, false for even |
829 | my $x = shift; $x = $class->new($x) unless ref $x; |
830 | #my ($self,$x) = objectify(1,@_); |
0716bf9b |
831 | |
b22b3e31 |
832 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
0716bf9b |
833 | return $CALC->_is_odd($x->{value}); |
58cde26e |
834 | } |
835 | |
836 | sub is_even |
837 | { |
838 | # return true when arg (BINT or num_str) is even, false for odd |
839 | my $x = shift; $x = $class->new($x) unless ref $x; |
840 | #my ($self,$x) = objectify(1,@_); |
0716bf9b |
841 | |
b22b3e31 |
842 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
0716bf9b |
843 | return $CALC->_is_even($x->{value}); |
0716bf9b |
844 | } |
845 | |
846 | sub is_positive |
847 | { |
848 | # return true when arg (BINT or num_str) is positive (>= 0) |
849 | my $x = shift; $x = $class->new($x) unless ref $x; |
b22b3e31 |
850 | return ($x->{sign} =~ /^\+/); |
0716bf9b |
851 | } |
852 | |
853 | sub is_negative |
854 | { |
855 | # return true when arg (BINT or num_str) is negative (< 0) |
856 | my $x = shift; $x = $class->new($x) unless ref $x; |
b22b3e31 |
857 | return ($x->{sign} =~ /^-/); |
58cde26e |
858 | } |
859 | |
0716bf9b |
860 | ############################################################################### |
861 | |
58cde26e |
862 | sub bmul |
863 | { |
864 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
865 | # (BINT or num_str, BINT or num_str) return BINT |
866 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
0716bf9b |
867 | |
58cde26e |
868 | return $x if $x->modify('bmul'); |
574bacfe |
869 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
870 | # handle result = 0 |
871 | return $x if $x->is_zero(); |
872 | return $x->bzero() if $y->is_zero(); |
873 | # inf handling |
874 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
875 | { |
876 | # result will always be +-inf: |
877 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
878 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
879 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
880 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
881 | return $x->binf('-'); |
882 | } |
58cde26e |
883 | |
0716bf9b |
884 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
574bacfe |
885 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
58cde26e |
886 | return $x->round($a,$p,$r,$y); |
887 | } |
888 | |
889 | sub bdiv |
890 | { |
891 | # (dividend: BINT or num_str, divisor: BINT or num_str) return |
892 | # (BINT,BINT) (quo,rem) or BINT (only rem) |
58cde26e |
893 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
894 | |
895 | return $x if $x->modify('bdiv'); |
896 | |
574bacfe |
897 | # x / +-inf => 0, reminder x |
898 | return wantarray ? ($x->bzero(),$x->copy()) : $x->bzero() |
899 | if $y->{sign} =~ /^[+-]inf$/; |
0716bf9b |
900 | |
574bacfe |
901 | # NaN if x == NaN or y == NaN or x==y==0 |
58cde26e |
902 | return wantarray ? ($x->bnan(),bnan()) : $x->bnan() |
574bacfe |
903 | if (($x->is_nan() || $y->is_nan()) || |
904 | ($x->is_zero() && $y->is_zero())); |
905 | |
906 | # 5 / 0 => +inf, -6 / 0 => -inf |
907 | return wantarray |
908 | ? ($x->binf($x->{sign}),$self->bnan()) : $x->binf($x->{sign}) |
909 | if ($x->{sign} =~ /^[+-]$/ && $y->is_zero()); |
910 | |
911 | # old code: always NaN if /0 |
912 | #return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() |
913 | # if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || $y->is_zero()); |
58cde26e |
914 | |
915 | # 0 / something |
916 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
917 | |
918 | # Is $x in the interval [0, $y) ? |
0716bf9b |
919 | my $cmp = $CALC->_acmp($x->{value},$y->{value}); |
58cde26e |
920 | if (($cmp < 0) and ($x->{sign} eq $y->{sign})) |
921 | { |
922 | return $x->bzero() unless wantarray; |
923 | my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x |
924 | return ($x->bzero(),$t); |
925 | } |
926 | elsif ($cmp == 0) |
927 | { |
928 | # shortcut, both are the same, so set to +/- 1 |
574bacfe |
929 | $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') ); |
58cde26e |
930 | return $x unless wantarray; |
931 | return ($x,$self->bzero()); |
932 | } |
933 | |
934 | # calc new sign and in case $y == +/- 1, return $x |
935 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
936 | # check for / +-1 (cant use $y->is_one due to '-' |
0716bf9b |
937 | if (($y == 1) || ($y == -1)) # slow! |
938 | #if ((@{$y->{value}} == 1) && ($y->{value}->[0] == 1)) |
58cde26e |
939 | { |
940 | return wantarray ? ($x,$self->bzero()) : $x; |
941 | } |
942 | |
943 | # call div here |
944 | my $rem = $self->bzero(); |
945 | $rem->{sign} = $y->{sign}; |
0716bf9b |
946 | #($x->{value},$rem->{value}) = div($x->{value},$y->{value}); |
947 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); |
58cde26e |
948 | # do not leave rest "-0"; |
0716bf9b |
949 | # $rem->{sign} = '+' if (@{$rem->{value}} == 1) && ($rem->{value}->[0] == 0); |
950 | $rem->{sign} = '+' if $CALC->_is_zero($rem->{value}); |
58cde26e |
951 | if (($x->{sign} eq '-') and (!$rem->is_zero())) |
952 | { |
953 | $x->bdec(); |
954 | } |
955 | $x->round($a,$p,$r,$y); |
956 | if (wantarray) |
957 | { |
958 | $rem->round($a,$p,$r,$x,$y); |
959 | return ($x,$y-$rem) if $x->{sign} eq '-'; # was $x,$rem |
960 | return ($x,$rem); |
961 | } |
962 | return $x; |
963 | } |
964 | |
965 | sub bpow |
966 | { |
967 | # (BINT or num_str, BINT or num_str) return BINT |
968 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 |
969 | # modifies first argument |
58cde26e |
970 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
971 | |
972 | return $x if $x->modify('bpow'); |
973 | |
0716bf9b |
974 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
58cde26e |
975 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
574bacfe |
976 | return $x->__one() if $y->is_zero(); |
58cde26e |
977 | return $x if $x->is_one() || $y->is_one(); |
0716bf9b |
978 | #if ($x->{sign} eq '-' && @{$x->{value}} == 1 && $x->{value}->[0] == 1) |
979 | if ($x->{sign} eq '-' && $CALC->_is_one($x->{value})) |
58cde26e |
980 | { |
981 | # if $x == -1 and odd/even y => +1/-1 |
0716bf9b |
982 | return $y->is_odd() ? $x : $x->babs(); |
574bacfe |
983 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
58cde26e |
984 | } |
574bacfe |
985 | # 1 ** -y => 1 / (1 ** |y|) |
986 | # so do test for negative $y after above's clause |
58cde26e |
987 | return $x->bnan() if $y->{sign} eq '-'; |
988 | return $x if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
989 | |
0716bf9b |
990 | if ($CALC->can('_pow')) |
58cde26e |
991 | { |
574bacfe |
992 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
0716bf9b |
993 | return $x->round($a,$p,$r); |
58cde26e |
994 | } |
0716bf9b |
995 | # based on the assumption that shifting in base 10 is fast, and that mul |
996 | # works faster if numbers are small: we count trailing zeros (this step is |
997 | # O(1)..O(N), but in case of O(N) we save much more time due to this), |
998 | # stripping them out of the multiplication, and add $count * $y zeros |
999 | # afterwards like this: |
1000 | # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6 |
1001 | # creates deep recursion? |
574bacfe |
1002 | # my $zeros = $x->_trailing_zeros(); |
1003 | # if ($zeros > 0) |
1004 | # { |
1005 | # $x->brsft($zeros,10); # remove zeros |
1006 | # $x->bpow($y); # recursion (will not branch into here again) |
1007 | # $zeros = $y * $zeros; # real number of zeros to add |
1008 | # $x->blsft($zeros,10); |
1009 | # return $x->round($a,$p,$r); |
1010 | # } |
1011 | |
1012 | my $pow2 = $self->__one(); |
58cde26e |
1013 | my $y1 = $class->new($y); |
1014 | my ($res); |
1015 | while (!$y1->is_one()) |
1016 | { |
1017 | #print "bpow: p2: $pow2 x: $x y: $y1 r: $res\n"; |
1018 | #print "len ",$x->length(),"\n"; |
1019 | ($y1,$res)=&bdiv($y1,2); |
1020 | if (!$res->is_zero()) { &bmul($pow2,$x); } |
1021 | if (!$y1->is_zero()) { &bmul($x,$x); } |
0716bf9b |
1022 | #print "$x $y\n"; |
58cde26e |
1023 | } |
1024 | #print "bpow: e p2: $pow2 x: $x y: $y1 r: $res\n"; |
1025 | &bmul($x,$pow2) if (!$pow2->is_one()); |
1026 | #print "bpow: e p2: $pow2 x: $x y: $y1 r: $res\n"; |
1027 | return $x->round($a,$p,$r); |
1028 | } |
1029 | |
1030 | sub blsft |
1031 | { |
1032 | # (BINT or num_str, BINT or num_str) return BINT |
1033 | # compute x << y, base n, y >= 0 |
1034 | my ($self,$x,$y,$n) = objectify(2,@_); |
1035 | |
1036 | return $x if $x->modify('blsft'); |
1037 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1038 | |
574bacfe |
1039 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1040 | |
1041 | my $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft'); |
1042 | if (defined $t) |
1043 | { |
1044 | $x->{value} = $t; return $x; |
1045 | } |
1046 | # fallback |
1047 | return $x->bmul( $self->bpow($n, $y) ); |
58cde26e |
1048 | } |
1049 | |
1050 | sub brsft |
1051 | { |
1052 | # (BINT or num_str, BINT or num_str) return BINT |
1053 | # compute x >> y, base n, y >= 0 |
1054 | my ($self,$x,$y,$n) = objectify(2,@_); |
1055 | |
1056 | return $x if $x->modify('brsft'); |
1057 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1058 | |
1059 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
574bacfe |
1060 | |
1061 | my $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft'); |
1062 | if (defined $t) |
1063 | { |
1064 | $x->{value} = $t; return $x; |
1065 | } |
1066 | # fallback |
1067 | return scalar bdiv($x, $self->bpow($n, $y)); |
58cde26e |
1068 | } |
1069 | |
1070 | sub band |
1071 | { |
1072 | #(BINT or num_str, BINT or num_str) return BINT |
1073 | # compute x & y |
0716bf9b |
1074 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1075 | |
1076 | return $x if $x->modify('band'); |
1077 | |
1078 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1079 | return $x->bzero() if $y->is_zero(); |
0716bf9b |
1080 | |
574bacfe |
1081 | my $sign = 0; # sign of result |
1082 | $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-'); |
1083 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1084 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1085 | |
1086 | if ($CALC->can('_and') && $sx == 1 && $sy == 1) |
0716bf9b |
1087 | { |
574bacfe |
1088 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
0716bf9b |
1089 | return $x->round($a,$p,$r); |
1090 | } |
574bacfe |
1091 | |
0716bf9b |
1092 | my $m = new Math::BigInt 1; my ($xr,$yr); |
574bacfe |
1093 | my $x10000 = new Math::BigInt (0x1000); |
1094 | my $y1 = copy(ref($x),$y); # make copy |
1095 | $y1->babs(); # and positive |
1096 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1097 | use integer; # need this for negative bools |
0716bf9b |
1098 | while (!$x1->is_zero() && !$y1->is_zero()) |
58cde26e |
1099 | { |
0716bf9b |
1100 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e |
1101 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe |
1102 | # make both op's numbers! |
1103 | $x->badd( bmul( $class->new( |
1104 | abs($sx*int($xr->numify()) & $sy*int($yr->numify()))), |
1105 | $m)); |
58cde26e |
1106 | $m->bmul($x10000); |
1107 | } |
574bacfe |
1108 | $x->bneg() if $sign; |
0716bf9b |
1109 | return $x->round($a,$p,$r); |
58cde26e |
1110 | } |
1111 | |
1112 | sub bior |
1113 | { |
1114 | #(BINT or num_str, BINT or num_str) return BINT |
1115 | # compute x | y |
0716bf9b |
1116 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1117 | |
1118 | return $x if $x->modify('bior'); |
1119 | |
1120 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1121 | return $x if $y->is_zero(); |
574bacfe |
1122 | |
1123 | my $sign = 0; # sign of result |
1124 | $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-'); |
1125 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1126 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1127 | |
1128 | # don't use lib for negative values |
1129 | if ($CALC->can('_or') && $sx == 1 && $sy == 1) |
0716bf9b |
1130 | { |
574bacfe |
1131 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
0716bf9b |
1132 | return $x->round($a,$p,$r); |
1133 | } |
1134 | |
1135 | my $m = new Math::BigInt 1; my ($xr,$yr); |
58cde26e |
1136 | my $x10000 = new Math::BigInt (0x10000); |
574bacfe |
1137 | my $y1 = copy(ref($x),$y); # make copy |
1138 | $y1->babs(); # and positive |
1139 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1140 | use integer; # need this for negative bools |
0716bf9b |
1141 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e |
1142 | { |
0716bf9b |
1143 | ($x1, $xr) = bdiv($x1,$x10000); |
58cde26e |
1144 | ($y1, $yr) = bdiv($y1,$x10000); |
574bacfe |
1145 | # make both op's numbers! |
1146 | $x->badd( bmul( $class->new( |
1147 | abs($sx*int($xr->numify()) | $sy*int($yr->numify()))), |
1148 | $m)); |
1149 | # $x->badd( bmul( $class->new(int($xr->numify()) | int($yr->numify())), $m)); |
58cde26e |
1150 | $m->bmul($x10000); |
1151 | } |
574bacfe |
1152 | $x->bneg() if $sign; |
0716bf9b |
1153 | return $x->round($a,$p,$r); |
58cde26e |
1154 | } |
1155 | |
1156 | sub bxor |
1157 | { |
1158 | #(BINT or num_str, BINT or num_str) return BINT |
1159 | # compute x ^ y |
0716bf9b |
1160 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e |
1161 | |
1162 | return $x if $x->modify('bxor'); |
1163 | |
0716bf9b |
1164 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
58cde26e |
1165 | return $x if $y->is_zero(); |
1166 | return $x->bzero() if $x == $y; # shortcut |
0716bf9b |
1167 | |
574bacfe |
1168 | my $sign = 0; # sign of result |
1169 | $sign = 1 if $x->{sign} ne $y->{sign}; |
1170 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
1171 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
1172 | |
1173 | # don't use lib for negative values |
1174 | if ($CALC->can('_xor') && $sx == 1 && $sy == 1) |
0716bf9b |
1175 | { |
574bacfe |
1176 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
0716bf9b |
1177 | return $x->round($a,$p,$r); |
1178 | } |
1179 | |
1180 | my $m = new Math::BigInt 1; my ($xr,$yr); |
58cde26e |
1181 | my $x10000 = new Math::BigInt (0x10000); |
1182 | my $y1 = copy(ref($x),$y); # make copy |
574bacfe |
1183 | $y1->babs(); # and positive |
1184 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
1185 | use integer; # need this for negative bools |
0716bf9b |
1186 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e |
1187 | { |
0716bf9b |
1188 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e |
1189 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe |
1190 | # make both op's numbers! |
1191 | $x->badd( bmul( $class->new( |
1192 | abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))), |
1193 | $m)); |
1194 | # $x->badd( bmul( $class->new(int($xr->numify()) ^ int($yr->numify())), $m)); |
58cde26e |
1195 | $m->bmul($x10000); |
1196 | } |
574bacfe |
1197 | $x->bneg() if $sign; |
0716bf9b |
1198 | return $x->round($a,$p,$r); |
58cde26e |
1199 | } |
1200 | |
1201 | sub length |
1202 | { |
1203 | my ($self,$x) = objectify(1,@_); |
1204 | |
0716bf9b |
1205 | my $e = $CALC->_len($x->{value}); |
1206 | # # fallback, since we do not know the underlying representation |
1207 | #my $es = "$x"; my $c = 0; $c = 1 if $es =~ /^[+-]/; # if lib returns '+123' |
1208 | #my $e = CORE::length($es)-$c; |
1209 | return wantarray ? ($e,0) : $e; |
58cde26e |
1210 | } |
1211 | |
1212 | sub digit |
1213 | { |
0716bf9b |
1214 | # return the nth decimal digit, negative values count backward, 0 is right |
58cde26e |
1215 | my $x = shift; |
1216 | my $n = shift || 0; |
1217 | |
0716bf9b |
1218 | return $CALC->_digit($x->{value},$n); |
58cde26e |
1219 | } |
1220 | |
1221 | sub _trailing_zeros |
1222 | { |
1223 | # return the amount of trailing zeros in $x |
1224 | my $x = shift; |
1225 | $x = $class->new($x) unless ref $x; |
1226 | |
bd05a461 |
1227 | #return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/; |
574bacfe |
1228 | return 0 if $x->is_zero() || $x->{sign} !~ /^[+-]$/; |
0716bf9b |
1229 | |
1230 | return $CALC->_zeros($x->{value}) if $CALC->can('_zeros'); |
1231 | |
b22b3e31 |
1232 | # if not: since we do not know underlying internal representation: |
0716bf9b |
1233 | my $es = "$x"; $es =~ /([0]*)$/; |
1234 | |
1235 | return 0 if !defined $1; # no zeros |
1236 | return CORE::length("$1"); # as string, not as +0! |
58cde26e |
1237 | } |
1238 | |
1239 | sub bsqrt |
1240 | { |
1241 | my ($self,$x) = objectify(1,@_); |
1242 | |
1243 | return $x->bnan() if $x->{sign} =~ /\-|$nan/; # -x or NaN => NaN |
1244 | return $x->bzero() if $x->is_zero(); # 0 => 0 |
1245 | return $x if $x == 1; # 1 => 1 |
1246 | |
1247 | my $y = $x->copy(); # give us one more digit accur. |
1248 | my $l = int($x->length()/2); |
1249 | |
1250 | $x->bzero(); |
1251 | $x->binc(); # keep ref($x), but modify it |
1252 | $x *= 10 ** $l; |
1253 | |
1254 | # print "x: $y guess $x\n"; |
1255 | |
1256 | my $last = $self->bzero(); |
1257 | while ($last != $x) |
1258 | { |
1259 | $last = $x; |
1260 | $x += $y / $x; |
1261 | $x /= 2; |
1262 | } |
1263 | return $x; |
1264 | } |
1265 | |
1266 | sub exponent |
1267 | { |
1268 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) |
1269 | my ($self,$x) = objectify(1,@_); |
1270 | |
1271 | return bnan() if $x->is_nan(); |
1272 | my $e = $class->bzero(); |
1273 | return $e->binc() if $x->is_zero(); |
1274 | $e += $x->_trailing_zeros(); |
1275 | return $e; |
1276 | } |
1277 | |
1278 | sub mantissa |
1279 | { |
1280 | # return a copy of the mantissa (here always $self) |
1281 | my ($self,$x) = objectify(1,@_); |
1282 | |
1283 | return bnan() if $x->is_nan(); |
1284 | my $m = $x->copy(); |
1285 | # that's inefficient |
1286 | my $zeros = $m->_trailing_zeros(); |
1287 | $m /= 10 ** $zeros if $zeros != 0; |
1288 | return $m; |
1289 | } |
1290 | |
1291 | sub parts |
1292 | { |
1293 | # return a copy of both the exponent and the mantissa (here 0 and self) |
1294 | my $self = shift; |
1295 | $self = $class->new($self) unless ref $self; |
1296 | |
1297 | return ($self->mantissa(),$self->exponent()); |
1298 | } |
1299 | |
1300 | ############################################################################## |
1301 | # rounding functions |
1302 | |
1303 | sub bfround |
1304 | { |
1305 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
1306 | # $n == 0 => round to integer |
1307 | my $x = shift; $x = $class->new($x) unless ref $x; |
1308 | my ($scale,$mode) = $x->_scale_p($precision,$rnd_mode,@_); |
1309 | return $x if !defined $scale; # no-op |
1310 | |
1311 | # no-op for BigInts if $n <= 0 |
1312 | return $x if $scale <= 0; |
1313 | |
1314 | $x->bround( $x->length()-$scale, $mode); |
1315 | } |
1316 | |
1317 | sub _scan_for_nonzero |
1318 | { |
1319 | my $x = shift; |
1320 | my $pad = shift; |
0716bf9b |
1321 | my $xs = shift; |
58cde26e |
1322 | |
1323 | my $len = $x->length(); |
1324 | return 0 if $len == 1; # '5' is trailed by invisible zeros |
1325 | my $follow = $pad - 1; |
1326 | return 0 if $follow > $len || $follow < 1; |
1327 | #print "checking $x $r\n"; |
0716bf9b |
1328 | |
b22b3e31 |
1329 | # since we do not know underlying represention of $x, use decimal string |
0716bf9b |
1330 | #my $r = substr ($$xs,-$follow); |
58cde26e |
1331 | my $r = substr ("$x",-$follow); |
1332 | return 1 if $r =~ /[^0]/; return 0; |
58cde26e |
1333 | } |
1334 | |
1335 | sub fround |
1336 | { |
1337 | # to make life easier for switch between MBF and MBI (autoload fxxx() |
1338 | # like MBF does for bxxx()?) |
1339 | my $x = shift; |
1340 | return $x->bround(@_); |
1341 | } |
1342 | |
1343 | sub bround |
1344 | { |
1345 | # accuracy: +$n preserve $n digits from left, |
1346 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) |
1347 | # no-op for $n == 0 |
1348 | # and overwrite the rest with 0's, return normalized number |
1349 | # do not return $x->bnorm(), but $x |
1350 | my $x = shift; $x = $class->new($x) unless ref $x; |
1351 | my ($scale,$mode) = $x->_scale_a($accuracy,$rnd_mode,@_); |
1352 | return $x if !defined $scale; # no-op |
1353 | |
1354 | # print "MBI round: $x to $scale $mode\n"; |
1355 | # -scale means what? tom? hullo? -$scale needed by MBF round, but what for? |
574bacfe |
1356 | return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero() || $scale == 0; |
58cde26e |
1357 | |
1358 | # we have fewer digits than we want to scale to |
1359 | my $len = $x->length(); |
1360 | # print "$len $scale\n"; |
1361 | return $x if $len < abs($scale); |
1362 | |
1363 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 |
1364 | my ($pad,$digit_round,$digit_after); |
1365 | $pad = $len - $scale; |
1366 | $pad = abs($scale)+1 if $scale < 0; |
0716bf9b |
1367 | # do not use digit(), it is costly for binary => decimal |
1368 | #$digit_round = '0'; $digit_round = $x->digit($pad) if $pad < $len; |
1369 | #$digit_after = '0'; $digit_after = $x->digit($pad-1) if $pad > 0; |
1370 | my $xs = $CALC->_str($x->{value}); |
1371 | my $pl = -$pad-1; |
1372 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
1373 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 |
1374 | $digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len; |
1375 | $pl++; $pl ++ if $pad >= $len; |
1376 | $digit_after = '0'; $digit_after = substr($$xs,$pl,1) |
1377 | if $pad > 0; |
1378 | |
1379 | #my $d_round = '0'; $d_round = $x->digit($pad) if $pad < $len; |
1380 | #my $d_after = '0'; $d_after = $x->digit($pad-1) if $pad > 0; |
1381 | # print "$pad $pl $$xs $digit_round:$d_round $digit_after:$d_after\n"; |
58cde26e |
1382 | |
1383 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look |
1384 | # closer at the remaining digits of the original $x, remember decision |
1385 | my $round_up = 1; # default round up |
1386 | $round_up -- if |
1387 | ($mode eq 'trunc') || # trunc by round down |
1388 | ($digit_after =~ /[01234]/) || # round down anyway, |
1389 | # 6789 => round up |
1390 | ($digit_after eq '5') && # not 5000...0000 |
0716bf9b |
1391 | ($x->_scan_for_nonzero($pad,$xs) == 0) && |
58cde26e |
1392 | ( |
1393 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || |
1394 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || |
1395 | ($mode eq '+inf') && ($x->{sign} eq '-') || |
1396 | ($mode eq '-inf') && ($x->{sign} eq '+') || |
1397 | ($mode eq 'zero') # round down if zero, sign adjusted below |
1398 | ); |
1399 | # allow rounding one place left of mantissa |
1400 | #print "$pad $len $scale\n"; |
1401 | # this is triggering warnings, and buggy for $scale < 0 |
1402 | #if (-$scale != $len) |
1403 | { |
b22b3e31 |
1404 | # old code, depend on internal representation |
0716bf9b |
1405 | # split mantissa at $pad and then pad with zeros |
1406 | #my $s5 = int($pad / 5); |
1407 | #my $i = 0; |
1408 | #while ($i < $s5) |
1409 | # { |
1410 | # $x->{value}->[$i++] = 0; # replace with 5 x 0 |
1411 | # } |
1412 | #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0 |
1413 | #my $rem = $pad % 5; # so much left over |
1414 | #if ($rem > 0) |
1415 | # { |
1416 | # #print "remainder $rem\n"; |
1417 | ## #print "elem $x->{value}->[$s5]\n"; |
1418 | # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0' |
1419 | # } |
1420 | #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5' |
1421 | #print ${$CALC->_str($pad->{value})}," $len\n"; |
1422 | if (($pad > 0) && ($pad <= $len)) |
58cde26e |
1423 | { |
0716bf9b |
1424 | substr($$xs,-$pad,$pad) = '0' x $pad; |
1425 | $x->{value} = $CALC->_new($xs); # put back in |
58cde26e |
1426 | } |
0716bf9b |
1427 | elsif ($pad > $len) |
58cde26e |
1428 | { |
574bacfe |
1429 | $x->bzero(); # round to '0' |
58cde26e |
1430 | } |
574bacfe |
1431 | # print "res $pad $len $x $$xs\n"; |
58cde26e |
1432 | } |
0716bf9b |
1433 | # move this later on after the inc of the string |
1434 | #$x->{value} = $CALC->_new($xs); # put back in |
58cde26e |
1435 | if ($round_up) # what gave test above? |
1436 | { |
1437 | $pad = $len if $scale < 0; # tlr: whack 0.51=>1.0 |
1438 | # modify $x in place, undef, undef to avoid rounding |
58cde26e |
1439 | # str creation much faster than 10 ** something |
0716bf9b |
1440 | $x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad) ); |
1441 | # increment string in place, to avoid dec=>hex for the '1000...000' |
1442 | # $xs ...blah foo |
58cde26e |
1443 | } |
0716bf9b |
1444 | # to here: |
1445 | #$x->{value} = $CALC->_new($xs); # put back in |
58cde26e |
1446 | $x; |
1447 | } |
1448 | |
1449 | sub bfloor |
1450 | { |
1451 | # return integer less or equal then number, since it is already integer, |
1452 | # always returns $self |
1453 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
1454 | |
1455 | # not needed: return $x if $x->modify('bfloor'); |
1456 | |
1457 | return $x->round($a,$p,$r); |
1458 | } |
1459 | |
1460 | sub bceil |
1461 | { |
1462 | # return integer greater or equal then number, since it is already integer, |
1463 | # always returns $self |
1464 | my ($self,$x,$a,$p,$r) = objectify(1,@_); |
1465 | |
1466 | # not needed: return $x if $x->modify('bceil'); |
1467 | |
1468 | return $x->round($a,$p,$r); |
1469 | } |
1470 | |
1471 | ############################################################################## |
1472 | # private stuff (internal use only) |
1473 | |
574bacfe |
1474 | sub __one |
58cde26e |
1475 | { |
1476 | # internal speedup, set argument to 1, or create a +/- 1 |
1477 | my $self = shift; |
0716bf9b |
1478 | my $x = $self->bzero(); $x->{value} = $CALC->_one(); |
1479 | $x->{sign} = shift || '+'; |
1480 | return $x; |
58cde26e |
1481 | } |
1482 | |
1483 | sub _swap |
1484 | { |
1485 | # Overload will swap params if first one is no object ref so that the first |
1486 | # one is always an object ref. In this case, third param is true. |
1487 | # This routine is to overcome the effect of scalar,$object creating an object |
1488 | # of the class of this package, instead of the second param $object. This |
1489 | # happens inside overload, when the overload section of this package is |
1490 | # inherited by sub classes. |
1491 | # For overload cases (and this is used only there), we need to preserve the |
1492 | # args, hence the copy(). |
1493 | # You can override this method in a subclass, the overload section will call |
1494 | # $object->_swap() to make sure it arrives at the proper subclass, with some |
1495 | # exceptions like '+' and '-'. |
1496 | |
1497 | # object, (object|scalar) => preserve first and make copy |
1498 | # scalar, object => swapped, re-swap and create new from first |
1499 | # (using class of second object, not $class!!) |
1500 | my $self = shift; # for override in subclass |
1501 | #print "swap $self 0:$_[0] 1:$_[1] 2:$_[2]\n"; |
1502 | if ($_[2]) |
1503 | { |
1504 | my $c = ref ($_[0]) || $class; # fallback $class should not happen |
1505 | return ( $c->new($_[1]), $_[0] ); |
1506 | } |
17baacb7 |
1507 | return ( $_[0]->copy(), $_[1] ); |
58cde26e |
1508 | } |
1509 | |
1510 | sub objectify |
1511 | { |
1512 | # check for strings, if yes, return objects instead |
1513 | |
1514 | # the first argument is number of args objectify() should look at it will |
1515 | # return $count+1 elements, the first will be a classname. This is because |
1516 | # overloaded '""' calls bstr($object,undef,undef) and this would result in |
1517 | # useless objects beeing created and thrown away. So we cannot simple loop |
1518 | # over @_. If the given count is 0, all arguments will be used. |
1519 | |
1520 | # If the second arg is a ref, use it as class. |
1521 | # If not, try to use it as classname, unless undef, then use $class |
1522 | # (aka Math::BigInt). The latter shouldn't happen,though. |
1523 | |
1524 | # caller: gives us: |
1525 | # $x->badd(1); => ref x, scalar y |
1526 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y |
1527 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y |
1528 | # Math::BigInt::badd(1,2); => scalar x, scalar y |
1529 | # In the last case we check number of arguments to turn it silently into |
574bacfe |
1530 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e |
1531 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
1532 | # currently it tries 'Math::BigInt' + 1, which will not work. |
1533 | |
58cde26e |
1534 | my $count = abs(shift || 0); |
1535 | |
1536 | #print caller(),"\n"; |
1537 | |
1538 | my @a; # resulting array |
1539 | if (ref $_[0]) |
1540 | { |
1541 | # okay, got object as first |
1542 | $a[0] = ref $_[0]; |
1543 | } |
1544 | else |
1545 | { |
1546 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) |
1547 | $a[0] = $class; |
1548 | #print "@_\n"; sleep(1); |
1549 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
1550 | } |
1551 | #print caller(),"\n"; |
1552 | # print "Now in objectify, my class is today $a[0]\n"; |
1553 | my $k; |
1554 | if ($count == 0) |
1555 | { |
1556 | while (@_) |
1557 | { |
1558 | $k = shift; |
1559 | if (!ref($k)) |
1560 | { |
1561 | $k = $a[0]->new($k); |
1562 | } |
1563 | elsif (ref($k) ne $a[0]) |
1564 | { |
1565 | # foreign object, try to convert to integer |
1566 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 |
1567 | } |
58cde26e |
1568 | push @a,$k; |
1569 | } |
1570 | } |
1571 | else |
1572 | { |
1573 | while ($count > 0) |
1574 | { |
1575 | #print "$count\n"; |
1576 | $count--; |
1577 | $k = shift; |
1578 | if (!ref($k)) |
1579 | { |
1580 | $k = $a[0]->new($k); |
1581 | } |
1582 | elsif (ref($k) ne $a[0]) |
1583 | { |
1584 | # foreign object, try to convert to integer |
1585 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 |
1586 | } |
58cde26e |
1587 | push @a,$k; |
1588 | } |
1589 | push @a,@_; # return other params, too |
1590 | } |
1591 | #my $i = 0; |
1592 | #foreach (@a) |
1593 | # { |
1594 | # print "o $i $a[0]\n" if $i == 0; |
1595 | # print "o $i ",ref($_),"\n" if $i != 0; $i++; |
1596 | # } |
1597 | #print "objectify done: would return ",scalar @a," values\n"; |
1598 | #print caller(1),"\n" unless wantarray; |
1599 | die "$class objectify needs list context" unless wantarray; |
1600 | @a; |
1601 | } |
1602 | |
1603 | sub import |
1604 | { |
1605 | my $self = shift; |
1606 | #print "import $self @_\n"; |
0716bf9b |
1607 | my @a = @_; my $l = scalar @_; my $j = 0; |
1608 | for ( my $i = 0; $i < $l ; $i++,$j++ ) |
58cde26e |
1609 | { |
0716bf9b |
1610 | if ($_[$i] eq ':constant') |
58cde26e |
1611 | { |
0716bf9b |
1612 | # this causes overlord er load to step in |
58cde26e |
1613 | overload::constant integer => sub { $self->new(shift) }; |
0716bf9b |
1614 | splice @a, $j, 1; $j --; |
1615 | } |
1616 | elsif ($_[$i] =~ /^lib$/i) |
1617 | { |
1618 | # this causes a different low lib to take care... |
1619 | $CALC = $_[$i+1] || $CALC; |
574bacfe |
1620 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
0716bf9b |
1621 | splice @a, $j, $s; $j -= $s; |
58cde26e |
1622 | } |
1623 | } |
1624 | # any non :constant stuff is handled by our parent, Exporter |
1625 | # even if @_ is empty, to give it a chance |
0716bf9b |
1626 | #$self->SUPER::import(@a); # does not work |
1627 | $self->export_to_level(1,$self,@a); # need this instead |
58cde26e |
1628 | |
574bacfe |
1629 | # try to load core math lib |
1630 | my @c = split /\s*,\s*/,$CALC; |
1631 | push @c,'Calc'; # if all fail, try this |
1632 | foreach my $lib (@c) |
1633 | { |
1634 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
1635 | $lib =~ s/\.pm$//; |
1636 | if ($] < 5.6) |
1637 | { |
1638 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
1639 | # used in the same script, or eval inside import(). |
1640 | (my $mod = $lib . '.pm') =~ s!::!/!g; |
1641 | # require does not automatically :: => /, so portability problems arise |
bd05a461 |
1642 | eval { require $mod; $lib->import( @c ); } |
574bacfe |
1643 | } |
1644 | else |
1645 | { |
bd05a461 |
1646 | eval "use $lib @c;"; |
574bacfe |
1647 | } |
bd05a461 |
1648 | $CALC = $lib, last if $@ eq ''; # no error in loading lib? |
574bacfe |
1649 | } |
58cde26e |
1650 | } |
1651 | |
574bacfe |
1652 | sub __from_hex |
58cde26e |
1653 | { |
1654 | # convert a (ref to) big hex string to BigInt, return undef for error |
1655 | my $hs = shift; |
1656 | |
1657 | my $x = Math::BigInt->bzero(); |
1658 | return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
1659 | |
b22b3e31 |
1660 | my $sign = '+'; $sign = '-' if ($$hs =~ /^-/); |
58cde26e |
1661 | |
b22b3e31 |
1662 | $$hs =~ s/^[+-]//; # strip sign |
0716bf9b |
1663 | if ($CALC->can('_from_hex')) |
58cde26e |
1664 | { |
0716bf9b |
1665 | $x->{value} = $CALC->_from_hex($hs); |
58cde26e |
1666 | } |
0716bf9b |
1667 | else |
58cde26e |
1668 | { |
0716bf9b |
1669 | # fallback to pure perl |
1670 | my $mul = Math::BigInt->bzero(); $mul++; |
1671 | my $x65536 = Math::BigInt->new(65536); |
1672 | my $len = CORE::length($$hs)-2; |
1673 | $len = int($len/4); # 4-digit parts, w/o '0x' |
1674 | my $val; my $i = -4; |
1675 | while ($len >= 0) |
1676 | { |
1677 | $val = substr($$hs,$i,4); |
b22b3e31 |
1678 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because |
0716bf9b |
1679 | $val = hex($val); # hex does not like wrong chars |
1680 | # print "$val ",substr($$hs,$i,4),"\n"; |
1681 | $i -= 4; $len --; |
1682 | $x += $mul * $val if $val != 0; |
1683 | $mul *= $x65536 if $len >= 0; # skip last mul |
1684 | } |
58cde26e |
1685 | } |
0716bf9b |
1686 | $x->{sign} = $sign if !$x->is_zero(); # no '-0' |
58cde26e |
1687 | return $x; |
1688 | } |
1689 | |
574bacfe |
1690 | sub __from_bin |
58cde26e |
1691 | { |
1692 | # convert a (ref to) big binary string to BigInt, return undef for error |
1693 | my $bs = shift; |
1694 | |
1695 | my $x = Math::BigInt->bzero(); |
b22b3e31 |
1696 | return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/; |
58cde26e |
1697 | |
1698 | my $mul = Math::BigInt->bzero(); $mul++; |
1699 | my $x256 = Math::BigInt->new(256); |
1700 | |
0716bf9b |
1701 | my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/); |
b22b3e31 |
1702 | $$bs =~ s/^[+-]//; # strip sign |
0716bf9b |
1703 | if ($CALC->can('_from_bin')) |
58cde26e |
1704 | { |
0716bf9b |
1705 | $x->{value} = $CALC->_from_bin($bs); |
58cde26e |
1706 | } |
0716bf9b |
1707 | else |
58cde26e |
1708 | { |
0716bf9b |
1709 | my $len = CORE::length($$bs)-2; |
1710 | $len = int($len/8); # 8-digit parts, w/o '0b' |
1711 | my $val; my $i = -8; |
1712 | while ($len >= 0) |
1713 | { |
1714 | $val = substr($$bs,$i,8); |
b22b3e31 |
1715 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only |
1716 | #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0 |
0716bf9b |
1717 | $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8; |
1718 | $val = ord(pack('B8',$val)); |
1719 | # print "$val ",substr($$bs,$i,16),"\n"; |
1720 | $i -= 8; $len --; |
1721 | $x += $mul * $val if $val != 0; |
1722 | $mul *= $x256 if $len >= 0; # skip last mul |
1723 | } |
58cde26e |
1724 | } |
1725 | $x->{sign} = $sign if !$x->is_zero(); |
1726 | return $x; |
1727 | } |
1728 | |
1729 | sub _split |
1730 | { |
1731 | # (ref to num_str) return num_str |
1732 | # internal, take apart a string and return the pieces |
574bacfe |
1733 | # strip leading/trailing whitespace, leading zeros, underscore, reject |
1734 | # invalid input |
58cde26e |
1735 | my $x = shift; |
1736 | |
574bacfe |
1737 | # strip white space at front, also extranous leading zeros |
1738 | $$x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' |
1739 | $$x =~ s/^\s+//; # but this will |
58cde26e |
1740 | $$x =~ s/\s+$//g; # strip white space at end |
58cde26e |
1741 | |
574bacfe |
1742 | # shortcut, if nothing to split, return early |
1743 | if ($$x =~ /^[+-]?\d+$/) |
1744 | { |
1745 | $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; |
1746 | return (\$sign, $x, \'', \'', \0); |
1747 | } |
58cde26e |
1748 | |
574bacfe |
1749 | # invalid starting char? |
1750 | return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; |
58cde26e |
1751 | |
1752 | $$x =~ s/(\d)_(\d)/$1$2/g; # strip underscores between digits |
1753 | $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 |
1754 | |
574bacfe |
1755 | return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string |
1756 | return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string |
1757 | |
58cde26e |
1758 | # some possible inputs: |
1759 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 |
1760 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 |
1761 | |
1762 | #print "input: '$$x' "; |
1763 | my ($m,$e) = split /[Ee]/,$$x; |
1764 | $e = '0' if !defined $e || $e eq ""; |
1765 | # print "m '$m' e '$e'\n"; |
1766 | # sign,value for exponent,mantint,mantfrac |
1767 | my ($es,$ev,$mis,$miv,$mfv); |
1768 | # valid exponent? |
1769 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
1770 | { |
1771 | $es = $1; $ev = $2; |
1772 | #print "'$m' '$e' e: $es $ev "; |
1773 | # valid mantissa? |
1774 | return if $m eq '.' || $m eq ''; |
1775 | my ($mi,$mf) = split /\./,$m; |
1776 | $mi = '0' if !defined $mi; |
1777 | $mi .= '0' if $mi =~ /^[\-\+]?$/; |
1778 | $mf = '0' if !defined $mf || $mf eq ''; |
1779 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
1780 | { |
1781 | $mis = $1||'+'; $miv = $2; |
0716bf9b |
1782 | # print "$mis $miv"; |
58cde26e |
1783 | # valid, existing fraction part of mantissa? |
1784 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros |
1785 | $mfv = $1; |
1786 | #print " split: $mis $miv . $mfv E $es $ev\n"; |
1787 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
1788 | } |
1789 | } |
1790 | return; # NaN, not a number |
1791 | } |
1792 | |
58cde26e |
1793 | sub as_number |
1794 | { |
1795 | # an object might be asked to return itself as bigint on certain overloaded |
1796 | # operations, this does exactly this, so that sub classes can simple inherit |
1797 | # it or override with their own integer conversion routine |
1798 | my $self = shift; |
1799 | |
17baacb7 |
1800 | $self->copy(); |
58cde26e |
1801 | } |
1802 | |
bd05a461 |
1803 | sub as_hex |
1804 | { |
1805 | # return as hex string, with prefixed 0x |
1806 | my $x = shift; $x = $class->new($x) if !ref($x); |
1807 | |
1808 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
1809 | return '0x0' if $x->is_zero(); |
1810 | |
1811 | my $es = ''; my $s = ''; |
1812 | $s = $x->{sign} if $x->{sign} eq '-'; |
1813 | $s .= '0x'; |
1814 | if ($CALC->can('_as_hex')) |
1815 | { |
1816 | $es = $CALC->_as_hex($x->{value}); |
1817 | } |
1818 | else |
1819 | { |
1820 | my $x1 = $x->copy()->babs(); my $xr; |
1821 | my $x100 = Math::BigInt->new (0x100); |
1822 | while (!$x1->is_zero()) |
1823 | { |
1824 | ($x1, $xr) = bdiv($x1,$x100); |
1825 | $es .= unpack('h2',pack('C',$xr->numify())); |
1826 | } |
1827 | $es = reverse $es; |
1828 | $es =~ s/^[0]+//; # strip leading zeros |
1829 | } |
1830 | $s . $es; |
1831 | } |
1832 | |
1833 | sub as_bin |
1834 | { |
1835 | # return as binary string, with prefixed 0b |
1836 | my $x = shift; $x = $class->new($x) if !ref($x); |
1837 | |
1838 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
1839 | return '0b0' if $x->is_zero(); |
1840 | |
1841 | my $es = ''; my $s = ''; |
1842 | $s = $x->{sign} if $x->{sign} eq '-'; |
1843 | $s .= '0b'; |
1844 | if ($CALC->can('_as_bin')) |
1845 | { |
1846 | $es = $CALC->_as_bin($x->{value}); |
1847 | } |
1848 | else |
1849 | { |
1850 | my $x1 = $x->copy()->babs(); my $xr; |
1851 | my $x100 = Math::BigInt->new (0x100); |
1852 | while (!$x1->is_zero()) |
1853 | { |
1854 | ($x1, $xr) = bdiv($x1,$x100); |
1855 | $es .= unpack('b8',pack('C',$xr->numify())); |
1856 | } |
1857 | $es = reverse $es; |
1858 | $es =~ s/^[0]+//; # strip leading zeros |
1859 | } |
1860 | $s . $es; |
1861 | } |
1862 | |
58cde26e |
1863 | ############################################################################## |
0716bf9b |
1864 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e |
1865 | |
1866 | sub cmp |
1867 | { |
1868 | # post-normalized compare for internal use (honors signs) |
0716bf9b |
1869 | # input: ref to value, ref to value, sign, sign |
1870 | # output: <0, 0, >0 |
58cde26e |
1871 | my ($cx,$cy,$sx,$sy) = @_; |
1872 | |
58cde26e |
1873 | if ($sx eq '+') |
1874 | { |
1875 | return 1 if $sy eq '-'; # 0 check handled above |
0716bf9b |
1876 | return $CALC->_acmp($cx,$cy); |
58cde26e |
1877 | } |
1878 | else |
1879 | { |
1880 | # $sx eq '-' |
0716bf9b |
1881 | return -1 if $sy eq '+'; |
0716bf9b |
1882 | return $CALC->_acmp($cy,$cx); |
58cde26e |
1883 | } |
17baacb7 |
1884 | 0; # equal |
58cde26e |
1885 | } |
1886 | |
58cde26e |
1887 | sub _lcm |
1888 | { |
1889 | # (BINT or num_str, BINT or num_str) return BINT |
1890 | # does modify first argument |
1891 | # LCM |
1892 | |
1893 | my $x = shift; my $ty = shift; |
1894 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); |
1895 | return $x * $ty / bgcd($x,$ty); |
1896 | } |
1897 | |
574bacfe |
1898 | sub __gcd |
58cde26e |
1899 | { |
1900 | # (BINT or num_str, BINT or num_str) return BINT |
1901 | # does modify first arg |
1902 | # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296 |
58cde26e |
1903 | |
0716bf9b |
1904 | my $x = shift; my $ty = $class->new(shift); # preserve y, but make class |
1905 | return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/; |
58cde26e |
1906 | |
1907 | while (!$ty->is_zero()) |
1908 | { |
1909 | ($x, $ty) = ($ty,bmod($x,$ty)); |
1910 | } |
1911 | $x; |
1912 | } |
1913 | |
58cde26e |
1914 | ############################################################################### |
1915 | # this method return 0 if the object can be modified, or 1 for not |
1916 | # We use a fast use constant statement here, to avoid costly calls. Subclasses |
1917 | # may override it with special code (f.i. Math::BigInt::Constant does so) |
1918 | |
0716bf9b |
1919 | sub modify () { 0; } |
e16b8f49 |
1920 | |
a0d0e21e |
1921 | 1; |
a5f75d66 |
1922 | __END__ |
1923 | |
1924 | =head1 NAME |
1925 | |
1926 | Math::BigInt - Arbitrary size integer math package |
1927 | |
1928 | =head1 SYNOPSIS |
1929 | |
1930 | use Math::BigInt; |
58cde26e |
1931 | |
1932 | # Number creation |
574bacfe |
1933 | $x = Math::BigInt->new($str); # defaults to 0 |
1934 | $nan = Math::BigInt->bnan(); # create a NotANumber |
1935 | $zero = Math::BigInt->bzero(); # create a +0 |
1936 | $inf = Math::BigInt->binf(); # create a +inf |
1937 | $inf = Math::BigInt->binf('-'); # create a -inf |
1938 | $one = Math::BigInt->bone(); # create a +1 |
1939 | $one = Math::BigInt->bone('-'); # create a -1 |
58cde26e |
1940 | |
1941 | # Testing |
574bacfe |
1942 | $x->is_zero(); # true if arg is +0 |
1943 | $x->is_nan(); # true if arg is NaN |
0716bf9b |
1944 | $x->is_one(); # true if arg is +1 |
1945 | $x->is_one('-'); # true if arg is -1 |
1946 | $x->is_odd(); # true if odd, false for even |
1947 | $x->is_even(); # true if even, false for odd |
1948 | $x->is_positive(); # true if >= 0 |
1949 | $x->is_negative(); # true if < 0 |
1950 | $x->is_inf(sign); # true if +inf, or -inf (sign is default '+') |
1951 | |
58cde26e |
1952 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
1953 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
1954 | $x->sign(); # return the sign, either +,- or NaN |
1955 | $x->digit($n); # return the nth digit, counting from right |
1956 | $x->digit(-$n); # return the nth digit, counting from left |
1957 | |
1958 | # The following all modify their first argument: |
1959 | |
1960 | # set |
1961 | $x->bzero(); # set $x to 0 |
1962 | $x->bnan(); # set $x to NaN |
574bacfe |
1963 | $x->bone(); # set $x to +1 |
1964 | $x->bone('-'); # set $x to -1 |
58cde26e |
1965 | |
1966 | $x->bneg(); # negation |
1967 | $x->babs(); # absolute value |
1968 | $x->bnorm(); # normalize (no-op) |
1969 | $x->bnot(); # two's complement (bit wise not) |
1970 | $x->binc(); # increment x by 1 |
1971 | $x->bdec(); # decrement x by 1 |
1972 | |
1973 | $x->badd($y); # addition (add $y to $x) |
1974 | $x->bsub($y); # subtraction (subtract $y from $x) |
1975 | $x->bmul($y); # multiplication (multiply $x by $y) |
1976 | $x->bdiv($y); # divide, set $x to quotient |
1977 | # return (quo,rem) or quo if scalar |
1978 | |
1979 | $x->bmod($y); # modulus (x % y) |
1980 | $x->bpow($y); # power of arguments (x ** y) |
1981 | $x->blsft($y); # left shift |
1982 | $x->brsft($y); # right shift |
1983 | $x->blsft($y,$n); # left shift, by base $n (like 10) |
1984 | $x->brsft($y,$n); # right shift, by base $n (like 10) |
1985 | |
1986 | $x->band($y); # bitwise and |
1987 | $x->bior($y); # bitwise inclusive or |
1988 | $x->bxor($y); # bitwise exclusive or |
1989 | $x->bnot(); # bitwise not (two's complement) |
1990 | |
1991 | $x->bsqrt(); # calculate square-root |
1992 | |
1993 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r |
1994 | $x->bround($N); # accuracy: preserve $N digits |
1995 | $x->bfround($N); # round to $Nth digit, no-op for BigInts |
1996 | |
1997 | # The following do not modify their arguments in BigInt, but do in BigFloat: |
1998 | $x->bfloor(); # return integer less or equal than $x |
1999 | $x->bceil(); # return integer greater or equal than $x |
2000 | |
2001 | # The following do not modify their arguments: |
2002 | |
2003 | bgcd(@values); # greatest common divisor |
2004 | blcm(@values); # lowest common multiplicator |
bd05a461 |
2005 | |
58cde26e |
2006 | $x->length(); # return number of digits in number |
bd05a461 |
2007 | ($x,$f) = $x->length(); # length of number and length of fraction part, |
2008 | # latter is always 0 digits long for BigInt's |
58cde26e |
2009 | |
2010 | $x->exponent(); # return exponent as BigInt |
2011 | $x->mantissa(); # return mantissa as BigInt |
2012 | $x->parts(); # return (mantissa,exponent) as BigInt |
0716bf9b |
2013 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
2014 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) |
bd05a461 |
2015 | |
2016 | # conversation to string |
2017 | $x->bstr(); # normalized string |
2018 | $x->bsstr(); # normalized string in scientific notation |
2019 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
2020 | $x->as_bin(); # as signed binary string with prefixed 0b |
2021 | |
a5f75d66 |
2022 | |
2023 | =head1 DESCRIPTION |
2024 | |
58cde26e |
2025 | All operators (inlcuding basic math operations) are overloaded if you |
2026 | declare your big integers as |
a5f75d66 |
2027 | |
58cde26e |
2028 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 |
2029 | |
58cde26e |
2030 | Operations with overloaded operators preserve the arguments which is |
2031 | exactly what you expect. |
a5f75d66 |
2032 | |
2033 | =over 2 |
2034 | |
2035 | =item Canonical notation |
2036 | |
58cde26e |
2037 | Big integer values are strings of the form C</^[+-]\d+$/> with leading |
a5f75d66 |
2038 | zeros suppressed. |
2039 | |
58cde26e |
2040 | '-0' canonical value '-0', normalized '0' |
2041 | ' -123_123_123' canonical value '-123123123' |
2042 | '1_23_456_7890' canonical value '1234567890' |
2043 | |
a5f75d66 |
2044 | =item Input |
2045 | |
58cde26e |
2046 | Input values to these routines may be either Math::BigInt objects or |
2047 | strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>. |
2048 | |
2049 | You can include one underscore between any two digits. |
2050 | |
2051 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. |
2052 | Non integer values result in NaN. |
2053 | |
2054 | Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results |
2055 | in 'NaN'. |
2056 | |
2057 | bnorm() on a BigInt object is now effectively a no-op, since the numbers |
2058 | are always stored in normalized form. On a string, it creates a BigInt |
2059 | object. |
a5f75d66 |
2060 | |
2061 | =item Output |
2062 | |
58cde26e |
2063 | Output values are BigInt objects (normalized), except for bstr(), which |
2064 | returns a string in normalized form. |
2065 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
2066 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
2067 | return either undef, <0, 0 or >0 and are suited for sort. |
a5f75d66 |
2068 | |
2069 | =back |
2070 | |
0716bf9b |
2071 | =head1 ACCURACY and PRECISION |
2072 | |
b22b3e31 |
2073 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b |
2074 | accuracy and precision based rounding, both automatically after every |
b22b3e31 |
2075 | operation as well as manually. |
0716bf9b |
2076 | |
2077 | This section describes the accuracy/precision handling in Math::Big* as it |
b22b3e31 |
2078 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b |
2079 | abbreviations. |
2080 | |
2081 | Not yet implemented things (but with correct description) are marked with '!', |
2082 | things that need to be answered are marked with '?'. |
2083 | |
2084 | In the next paragraph follows a short description of terms used here (because |
574bacfe |
2085 | these may differ from terms used by others people or documentation). |
0716bf9b |
2086 | |
b22b3e31 |
2087 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b |
2088 | precision), F (fallback) and R (rounding mode) will be used. |
2089 | |
2090 | =head2 Precision P |
2091 | |
2092 | A fixed number of digits before (positive) or after (negative) |
b22b3e31 |
2093 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
2094 | integer like 123 (or 120). A precision of 2 means two digits to the left |
2095 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that |
2096 | numbers with zeros before the decimal point may have different precisions, |
2097 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value |
2098 | was). It could also have p < 0, when the digits after the decimal point |
2099 | are zero. |
0716bf9b |
2100 | |
574bacfe |
2101 | The string output (of floating point numbers) will be padded with zeros: |
2102 | |
2103 | Initial value P A Result String |
2104 | ------------------------------------------------------------ |
2105 | 1234.01 -3 1000 1000 |
2106 | 1234 -2 1200 1200 |
2107 | 1234.5 -1 1230 1230 |
2108 | 1234.001 1 1234 1234.0 |
2109 | 1234.01 0 1234 1234 |
2110 | 1234.01 2 1234.01 1234.01 |
2111 | 1234.01 5 1234.01 1234.01000 |
2112 | |
2113 | For BigInts, no padding occurs. |
0716bf9b |
2114 | |
2115 | =head2 Accuracy A |
2116 | |
2117 | Number of significant digits. Leading zeros are not counted. A |
2118 | number may have an accuracy greater than the non-zero digits |
b22b3e31 |
2119 | when there are zeros in it or trailing zeros. For example, 123.456 has |
2120 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. |
0716bf9b |
2121 | |
574bacfe |
2122 | The string output (of floating point numbers) will be padded with zeros: |
2123 | |
2124 | Initial value P A Result String |
2125 | ------------------------------------------------------------ |
2126 | 1234.01 3 1230 1230 |
2127 | 1234.01 6 1234.01 1234.01 |
2128 | 1234.1 8 1234.1 1234.1000 |
2129 | |
2130 | For BigInts, no padding occurs. |
2131 | |
0716bf9b |
2132 | =head2 Fallback F |
a5f75d66 |
2133 | |
574bacfe |
2134 | When both A and P are undefined, this is used as a fallback accuracy when |
2135 | dividing numbers. |
0716bf9b |
2136 | |
2137 | =head2 Rounding mode R |
2138 | |
2139 | When rounding a number, different 'styles' or 'kinds' |
2140 | of rounding are possible. (Note that random rounding, as in |
2141 | Math::Round, is not implemented.) |
58cde26e |
2142 | |
2143 | =over 2 |
a5f75d66 |
2144 | |
0716bf9b |
2145 | =item 'trunc' |
2146 | |
2147 | truncation invariably removes all digits following the |
2148 | rounding place, replacing them with zeros. Thus, 987.65 rounded |
b22b3e31 |
2149 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b |
2150 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 |
2151 | decimal point (P=-2) becomes 123.46. |
0716bf9b |
2152 | |
2153 | All other implemented styles of rounding attempt to round to the |
2154 | "nearest digit." If the digit D immediately to the right of the |
2155 | rounding place (skipping the decimal point) is greater than 5, the |
2156 | number is incremented at the rounding place (possibly causing a |
2157 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds |
2158 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly |
2159 | truncated at the rounding place: e.g. when rounding to units, 0.4 |
2160 | rounds to 0, and -19.4 rounds to -19. |
2161 | |
2162 | However the results of other styles of rounding differ if the |
2163 | digit immediately to the right of the rounding place (skipping the |
2164 | decimal point) is 5 and if there are no digits, or no digits other |
2165 | than 0, after that 5. In such cases: |
2166 | |
2167 | =item 'even' |
2168 | |
2169 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 |
2170 | if it is not already. E.g., when rounding to the first sigdig, 0.45 |
2171 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. |
2172 | |
2173 | =item 'odd' |
2174 | |
2175 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if |
2176 | it is not already. E.g., when rounding to the first sigdig, 0.45 |
2177 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. |
2178 | |
2179 | =item '+inf' |
2180 | |
2181 | round to plus infinity, i.e. always round up. E.g., when |
2182 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, |
b22b3e31 |
2183 | and 0.4501 also becomes 0.5. |
0716bf9b |
2184 | |
2185 | =item '-inf' |
2186 | |
2187 | round to minus infinity, i.e. always round down. E.g., when |
2188 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, |
2189 | but 0.4501 becomes 0.5. |
2190 | |
2191 | =item 'zero' |
2192 | |
2193 | round to zero, i.e. positive numbers down, negative ones up. |
2194 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 |
2195 | becomes -0.5, but 0.4501 becomes 0.5. |
2196 | |
2197 | =back |
2198 | |
2199 | The handling of A & P in MBI/MBF (the old core code shipped with Perl |
2200 | versions <= 5.7.2) is like this: |
2201 | |
2202 | =over 2 |
a5f75d66 |
2203 | |
0716bf9b |
2204 | =item Precision |
2205 | |
b22b3e31 |
2206 | * ffround($p) is able to round to $p number of digits after the decimal |
2207 | point |
0716bf9b |
2208 | * otherwise P is unused |
2209 | |
2210 | =item Accuracy (significant digits) |
2211 | |
2212 | * fround($a) rounds to $a significant digits |
2213 | * only fdiv() and fsqrt() take A as (optional) paramater |
b22b3e31 |
2214 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b |
2215 | of digits |
2216 | + rounding/truncating is only done when explicitly calling one of fround |
2217 | or ffround, and never for BigInt (not implemented) |
b22b3e31 |
2218 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b |
2219 | * the documentation and the comment in the code indicate two different ways |
2220 | on how fdiv() determines the maximum number of digits it should calculate, |
2221 | and the actual code does yet another thing |
2222 | POD: |
2223 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) |
2224 | Comment: |
2225 | result has at most max(scale, length(dividend), length(divisor)) digits |
2226 | Actual code: |
2227 | scale = max(scale, length(dividend)-1,length(divisor)-1); |
2228 | scale += length(divisior) - length(dividend); |
b22b3e31 |
2229 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b |
2230 | Actually, the 'difference' added to the scale is calculated from the |
2231 | number of "significant digits" in dividend and divisor, which is derived |
2232 | by looking at the length of the mantissa. Which is wrong, since it includes |
2233 | the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups |
2234 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange |
2235 | assumption that 124 has 3 significant digits, while 120/7 will get you |
2236 | '17', not '17.1' since 120 is thought to have 2 significant digits. |
2237 | The rounding after the division then uses the reminder and $y to determine |
2238 | wether it must round up or down. |
b22b3e31 |
2239 | ? I have no idea which is the right way. That's why I used a slightly more |
2240 | ? simple scheme and tweaked the few failing testcases to match it. |
58cde26e |
2241 | |
0716bf9b |
2242 | =back |
5dc6f178 |
2243 | |
0716bf9b |
2244 | This is how it works now: |
5dc6f178 |
2245 | |
0716bf9b |
2246 | =over 2 |
5dc6f178 |
2247 | |
0716bf9b |
2248 | =item Setting/Accessing |
2249 | |
2250 | * You can set the A global via $Math::BigInt::accuracy or |
2251 | $Math::BigFloat::accuracy or whatever class you are using. |
2252 | * You can also set P globally by using $Math::SomeClass::precision likewise. |
2253 | * Globals are classwide, and not inherited by subclasses. |
2254 | * to undefine A, use $Math::SomeCLass::accuracy = undef |
2255 | * to undefine P, use $Math::SomeClass::precision = undef |
2256 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 |
2257 | * If P is negative, this means round to the P'th place to the right of the |
2258 | decimal point; positive values mean to the left of the decimal point. |
2259 | P of 0 means round to integer. |
0716bf9b |
2260 | * to find out the current global A, take $Math::SomeClass::accuracy |
2261 | * use $x->accuracy() for the local setting of $x. |
2262 | * to find out the current global P, take $Math::SomeClass::precision |
2263 | * use $x->precision() for the local setting |
2264 | |
2265 | =item Creating numbers |
2266 | |
b22b3e31 |
2267 | !* When you create a number, there should be a way to define its A & P |
0716bf9b |
2268 | * When a number without specific A or P is created, but the globals are |
b22b3e31 |
2269 | defined, these should be used to round the number immediately and also |
2270 | stored locally with the number. Thus changing the global defaults later on |
2271 | will not change the A or P of previously created numbers (i.e., A and P of |
0716bf9b |
2272 | $x will be what was in effect when $x was created) |
2273 | |
2274 | =item Usage |
2275 | |
b22b3e31 |
2276 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b |
2277 | operation according to the rules below |
b22b3e31 |
2278 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
2279 | after the decimal point |
574bacfe |
2280 | * Math::BigFloat uses Math::BigInts internally, but setting A or P inside |
2281 | Math::BigInt as globals should not tamper with the parts of a BigFloat. |
2282 | Thus a flag is used to mark all Math::BigFloat numbers as 'never round' |
0716bf9b |
2283 | |
2284 | =item Precedence |
2285 | |
b22b3e31 |
2286 | * It only makes sense that a number has only one of A or P at a time. |
2287 | Since you can set/get both A and P, there is a rule that will practically |
2288 | enforce only A or P to be in effect at a time, even if both are set. |
2289 | This is called precedence. |
2290 | !* If two objects are involved in an operation, and one of them has A in |
0716bf9b |
2291 | ! effect, and the other P, this should result in a warning or an error, |
2292 | ! probably in NaN. |
2293 | * A takes precendence over P (Hint: A comes before P). If A is defined, it |
b22b3e31 |
2294 | is used, otherwise P is used. If neither of them is defined, nothing is |
2295 | used, i.e. the result will have as many digits as it can (with an |
2296 | exception for fdiv/fsqrt) and will not be rounded. |
2297 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of |
2298 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. |
2299 | If either the dividend's or the divisor's mantissa has more digits than |
2300 | the value of F, the higher value will be used instead of F. |
2301 | This is to limit the digits (A) of the result (just consider what would |
2302 | happen with unlimited A and P in the case of 1/3 :-) |
2303 | * fdiv will calculate 1 more digit than required (determined by |
0716bf9b |
2304 | A, P or F), and, if F is not used, round the result |
b22b3e31 |
2305 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe |
2306 | or P of 5, but this can not be helped - or can it?) |
b22b3e31 |
2307 | * Thus you can have the math done by on Math::Big* class in three modes: |
0716bf9b |
2308 | + never round (this is the default): |
2309 | This is done by setting A and P to undef. No math operation |
b22b3e31 |
2310 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
0716bf9b |
2311 | against overflows. You must explicitely call bround(), bfround() or |
b22b3e31 |
2312 | round() (the latter with parameters). |
2313 | Note: Once you have rounded a number, the settings will 'stick' on it |
2314 | and 'infect' all other numbers engaged in math operations with it, since |
0716bf9b |
2315 | local settings have the highest precedence. So, to get SaferRound[tm], |
2316 | use a copy() before rounding like this: |
2317 | |
2318 | $x = Math::BigFloat->new(12.34); |
2319 | $y = Math::BigFloat->new(98.76); |
2320 | $z = $x * $y; # 1218.6984 |
2321 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) |
2322 | $z = $x * $y; # still 1218.6984, without |
2323 | # copy would have been 1210! |
2324 | |
2325 | + round after each op: |
b22b3e31 |
2326 | After each single operation (except for testing like is_zero()), the |
2327 | method round() is called and the result is rounded appropriately. By |
0716bf9b |
2328 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 |
2329 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
2330 | and P to -2, globally. |
0716bf9b |
2331 | |
b22b3e31 |
2332 | ?Maybe an extra option that forbids local A & P settings would be in order, |
2333 | ?so that intermediate rounding does not 'poison' further math? |
0716bf9b |
2334 | |
2335 | =item Overriding globals |
2336 | |
2337 | * you will be able to give A, P and R as an argument to all the calculation |
b22b3e31 |
2338 | routines; the second parameter is A, the third one is P, and the fourth is |
0716bf9b |
2339 | R (shift place by one for binary operations like add). P is used only if |
b22b3e31 |
2340 | the first parameter (A) is undefined. These three parameters override the |
2341 | globals in the order detailed as follows, i.e. the first defined value |
0716bf9b |
2342 | wins: |
b22b3e31 |
2343 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b |
2344 | + parameter A |
2345 | + parameter P |
2346 | + local A (if defined on both of the operands: smaller one is taken) |
2347 | + local P (if defined on both of the operands: smaller one is taken) |
2348 | + global A |
2349 | + global P |
2350 | + global F |
b22b3e31 |
2351 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b |
2352 | arguments (A and P) instead of one |
2353 | |
2354 | =item Local settings |
2355 | |
2356 | * You can set A and P locally by using $x->accuracy() and $x->precision() |
2357 | and thus force different A and P for different objects/numbers. |
b22b3e31 |
2358 | * Setting A or P this way immediately rounds $x to the new value. |
0716bf9b |
2359 | |
2360 | =item Rounding |
2361 | |
b22b3e31 |
2362 | * the rounding routines will use the respective global or local settings. |
0716bf9b |
2363 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
2364 | is for precision |
2365 | * the two rounding functions take as the second parameter one of the |
2366 | following rounding modes (R): |
2367 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' |
2368 | * you can set and get the global R by using Math::SomeClass->round_mode() |
2369 | or by setting $Math::SomeClass::rnd_mode |
2370 | * after each operation, $result->round() is called, and the result may |
b22b3e31 |
2371 | eventually be rounded (that is, if A or P were set either locally, |
2372 | globally or as parameter to the operation) |
0716bf9b |
2373 | * to manually round a number, call $x->round($A,$P,$rnd_mode); |
b22b3e31 |
2374 | this will round the number by using the appropriate rounding function |
0716bf9b |
2375 | and then normalize it. |
b22b3e31 |
2376 | * rounding modifies the local settings of the number: |
0716bf9b |
2377 | |
2378 | $x = Math::BigFloat->new(123.456); |
2379 | $x->accuracy(5); |
2380 | $x->bround(4); |
2381 | |
2382 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() |
2383 | will be 4 from now on. |
2384 | |
2385 | =item Default values |
2386 | |
2387 | * R: 'even' |
2388 | * F: 40 |
2389 | * A: undef |
2390 | * P: undef |
2391 | |
2392 | =item Remarks |
2393 | |
2394 | * The defaults are set up so that the new code gives the same results as |
2395 | the old code (except in a few cases on fdiv): |
2396 | + Both A and P are undefined and thus will not be used for rounding |
2397 | after each operation. |
2398 | + round() is thus a no-op, unless given extra parameters A and P |
58cde26e |
2399 | |
2400 | =back |
2401 | |
0716bf9b |
2402 | =head1 INTERNALS |
2403 | |
574bacfe |
2404 | The actual numbers are stored as unsigned big integers (with seperate sign). |
2405 | You should neither care about nor depend on the internal representation; it |
2406 | might change without notice. Use only method calls like C<< $x->sign(); >> |
2407 | instead relying on the internal hash keys like in C<< $x->{sign}; >>. |
2408 | |
2409 | =head2 MATH LIBRARY |
58cde26e |
2410 | |
574bacfe |
2411 | Math with the numbers is done (by default) by a module called |
2412 | Math::BigInt::Calc. This is equivalent to saying: |
2413 | |
2414 | use Math::BigInt lib => 'Calc'; |
58cde26e |
2415 | |
0716bf9b |
2416 | You can change this by using: |
58cde26e |
2417 | |
0716bf9b |
2418 | use Math::BigInt lib => 'BitVect'; |
58cde26e |
2419 | |
574bacfe |
2420 | The following would first try to find Math::BigInt::Foo, then |
2421 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
0716bf9b |
2422 | |
574bacfe |
2423 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
58cde26e |
2424 | |
574bacfe |
2425 | Calc.pm uses as internal format an array of elements of some decimal base |
2426 | (usually 1e5, but this might change to 1e7) with the least significant digit |
2427 | first, while BitVect.pm uses a bit vector of base 2, most significant bit |
2428 | first. Other modules might use even different means of representing the |
2429 | numbers. See the respective module documentation for further details. |
58cde26e |
2430 | |
574bacfe |
2431 | =head2 SIGN |
2432 | |
2433 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. |
2434 | |
2435 | A sign of 'NaN' is used to represent the result when input arguments are not |
2436 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively |
2437 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
2438 | '-inf' when dividing any negative number by 0. |
58cde26e |
2439 | |
2440 | =head2 mantissa(), exponent() and parts() |
2441 | |
2442 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such |
2443 | that: |
2444 | |
2445 | $m = $x->mantissa(); |
2446 | $e = $x->exponent(); |
2447 | $y = $m * ( 10 ** $e ); |
2448 | print "ok\n" if $x == $y; |
2449 | |
b22b3e31 |
2450 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
2451 | in one go. Both the returned mantissa and exponent have a sign. |
58cde26e |
2452 | |
574bacfe |
2453 | Currently, for BigInts C<$e> will be always 0, except for NaN, +inf and -inf, |
2454 | where it will be NaN; and for $x == 0, where it will be 1 |
2455 | (to be compatible with Math::BigFloat's internal representation of a zero as |
2456 | C<0E1>). |
58cde26e |
2457 | |
2458 | C<$m> will always be a copy of the original number. The relation between $e |
b22b3e31 |
2459 | and $m might change in the future, but will always be equivalent in a |
0716bf9b |
2460 | numerical sense, e.g. $m might get minimized. |
2461 | |
58cde26e |
2462 | =head1 EXAMPLES |
2463 | |
574bacfe |
2464 | use Math::BigInt qw(bstr); |
2465 | |
2466 | sub bint { Math::BigInt->new(shift); } |
2467 | |
58cde26e |
2468 | $x = bstr("1234") # string "1234" |
2469 | $x = "$x"; # same as bstr() |
2470 | $x = bneg("1234") # Bigint "-1234" |
2471 | $x = Math::BigInt->bneg("1234"); # Bigint "-1234" |
2472 | $x = Math::BigInt->babs("-12345"); # Bigint "12345" |
2473 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" |
2474 | $x = bint(1) + bint(2); # BigInt "3" |
2475 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") |
2476 | $x = bint(1); # BigInt "1" |
2477 | $x = $x + 5 / 2; # BigInt "3" |
2478 | $x = $x ** 3; # BigInt "27" |
2479 | $x *= 2; # BigInt "54" |
2480 | $x = new Math::BigInt; # BigInt "0" |
2481 | $x--; # BigInt "-1" |
2482 | $x = Math::BigInt->badd(4,5) # BigInt "9" |
2483 | $x = Math::BigInt::badd(4,5) # BigInt "9" |
2484 | print $x->bsstr(); # 9e+0 |
a5f75d66 |
2485 | |
0716bf9b |
2486 | Examples for rounding: |
2487 | |
2488 | use Math::BigFloat; |
2489 | use Test; |
2490 | |
2491 | $x = Math::BigFloat->new(123.4567); |
2492 | $y = Math::BigFloat->new(123.456789); |
2493 | $Math::BigFloat::accuracy = 4; # no more A than 4 |
2494 | |
2495 | ok ($x->copy()->fround(),123.4); # even rounding |
2496 | print $x->copy()->fround(),"\n"; # 123.4 |
2497 | Math::BigFloat->round_mode('odd'); # round to odd |
2498 | print $x->copy()->fround(),"\n"; # 123.5 |
2499 | $Math::BigFloat::accuracy = 5; # no more A than 5 |
2500 | Math::BigFloat->round_mode('odd'); # round to odd |
2501 | print $x->copy()->fround(),"\n"; # 123.46 |
2502 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 |
2503 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 |
2504 | |
2505 | $Math::BigFloat::accuracy = undef; # A not important |
2506 | $Math::BigFloat::precision = 2; # P important |
2507 | print $x->copy()->bnorm(),"\n"; # 123.46 |
2508 | print $x->copy()->fround(),"\n"; # 123.46 |
2509 | |
bd05a461 |
2510 | Examples for converting: |
2511 | |
2512 | my $x = Math::BigInt->new('0b1'.'01' x 123); |
2513 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; |
2514 | |
b3ac6de7 |
2515 | =head1 Autocreating constants |
2516 | |
58cde26e |
2517 | After C<use Math::BigInt ':constant'> all the B<integer> decimal constants |
2518 | in the given scope are converted to C<Math::BigInt>. This conversion |
b3ac6de7 |
2519 | happens at compile time. |
2520 | |
b22b3e31 |
2521 | In particular, |
b3ac6de7 |
2522 | |
58cde26e |
2523 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
2524 | |
2525 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b |
2526 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e |
2527 | |
2528 | Please note that strings and floating point constants are not affected, |
2529 | so that |
2530 | |
2531 | use Math::BigInt qw/:constant/; |
2532 | |
2533 | $x = 1234567890123456789012345678901234567890 |
2534 | + 123456789123456789; |
b22b3e31 |
2535 | $y = '1234567890123456789012345678901234567890' |
58cde26e |
2536 | + '123456789123456789'; |
b3ac6de7 |
2537 | |
b22b3e31 |
2538 | do not work. You need an explicit Math::BigInt->new() around one of the |
2539 | operands. |
58cde26e |
2540 | |
2541 | =head1 PERFORMANCE |
2542 | |
2543 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x |
2544 | must be made in the second case. For long numbers, the copy can eat up to 20% |
b22b3e31 |
2545 | of the work (in the case of addition/subtraction, less for |
58cde26e |
2546 | multiplication/division). If $y is very small compared to $x, the form |
2547 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes |
2548 | more time then the actual addition. |
2549 | |
b22b3e31 |
2550 | With a technique called copy-on-write, the cost of copying with overload could |
58cde26e |
2551 | be minimized or even completely avoided. This is currently not implemented. |
2552 | |
2553 | The new version of this module is slower on new(), bstr() and numify(). Some |
2554 | operations may be slower for small numbers, but are significantly faster for |
2555 | big numbers. Other operations are now constant (O(1), like bneg(), babs() |
2556 | etc), instead of O(N) and thus nearly always take much less time. |
2557 | |
574bacfe |
2558 | If you find the Calc module to slow, try to install any of the replacement |
2559 | modules and see if they help you. |
b3ac6de7 |
2560 | |
574bacfe |
2561 | =head2 Alternative math libraries |
0716bf9b |
2562 | |
2563 | You can use an alternative library to drive Math::BigInt via: |
2564 | |
2565 | use Math::BigInt lib => 'Module'; |
2566 | |
574bacfe |
2567 | The default is called Math::BigInt::Calc and is a pure-perl implementation |
2568 | that consists mainly of the standard routine present in earlier versions of |
2569 | Math::BigInt. |
0716bf9b |
2570 | |
2571 | There are also Math::BigInt::Scalar (primarily for testing) and |
574bacfe |
2572 | Math::BigInt::BitVect; as well as Math::BigInt::Pari and likely others. |
2573 | All these can be found via L<http://search.cpan.org/>: |
0716bf9b |
2574 | |
2575 | use Math::BigInt lib => 'BitVect'; |
2576 | |
2577 | my $x = Math::BigInt->new(2); |
2578 | print $x ** (1024*1024); |
2579 | |
574bacfe |
2580 | For more benchmark results see http://bloodgate.com/perl/benchmarks.html |
2581 | |
a5f75d66 |
2582 | =head1 BUGS |
2583 | |
58cde26e |
2584 | =over 2 |
2585 | |
574bacfe |
2586 | =item Out of Memory! |
58cde26e |
2587 | |
2588 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and |
2589 | C<eval()> in your code will crash with "Out of memory". This is probably an |
2590 | overload/exporter bug. You can workaround by not having C<eval()> |
574bacfe |
2591 | and ':constant' at the same time or upgrade your Perl to a newer version. |
2592 | |
2593 | =item Fails to load Calc on Perl prior 5.6.0 |
2594 | |
2595 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt |
2596 | will fall back to eval { require ... } when loading the math lib on Perls |
2597 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on |
2598 | filesystems using a different seperator. |
58cde26e |
2599 | |
2600 | =back |
2601 | |
2602 | =head1 CAVEATS |
2603 | |
2604 | Some things might not work as you expect them. Below is documented what is |
2605 | known to be troublesome: |
2606 | |
2607 | =over 1 |
2608 | |
2609 | =item stringify, bstr(), bsstr() and 'cmp' |
2610 | |
2611 | Both stringify and bstr() now drop the leading '+'. The old code would return |
2612 | '+3', the new returns '3'. This is to be consistent with Perl and to make |
2613 | cmp (especially with overloading) to work as you expect. It also solves |
2614 | problems with Test.pm, it's ok() uses 'eq' internally. |
2615 | |
2616 | Mark said, when asked about to drop the '+' altogether, or make only cmp work: |
2617 | |
2618 | I agree (with the first alternative), don't add the '+' on positive |
2619 | numbers. It's not as important anymore with the new internal |
2620 | form for numbers. It made doing things like abs and neg easier, |
2621 | but those have to be done differently now anyway. |
2622 | |
2623 | So, the following examples will now work all as expected: |
2624 | |
2625 | use Test; |
2626 | BEGIN { plan tests => 1 } |
2627 | use Math::BigInt; |
2628 | |
2629 | my $x = new Math::BigInt 3*3; |
2630 | my $y = new Math::BigInt 3*3; |
2631 | |
2632 | ok ($x,3*3); |
2633 | print "$x eq 9" if $x eq $y; |
2634 | print "$x eq 9" if $x eq '9'; |
2635 | print "$x eq 9" if $x eq 3*3; |
2636 | |
2637 | Additionally, the following still works: |
2638 | |
2639 | print "$x == 9" if $x == $y; |
2640 | print "$x == 9" if $x == 9; |
2641 | print "$x == 9" if $x == 3*3; |
2642 | |
2643 | There is now a C<bsstr()> method to get the string in scientific notation aka |
2644 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() |
2645 | for comparisation, but Perl will represent some numbers as 100 and others |
2646 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before doing eq: |
2647 | |
2648 | use Test; |
2649 | BEGIN { plan tests => 3 } |
2650 | use Math::BigInt; |
2651 | |
2652 | $x = Math::BigInt->new('1e56'); $y = 1e56; |
2653 | ok ($x,$y); # will fail |
2654 | ok ($x->bsstr(),$y); # okay |
2655 | $y = Math::BigInt->new($y); |
2656 | ok ($x,$y); # okay |
2657 | |
574bacfe |
2658 | There is not yet a way to get a number automatically represented in exactly |
2659 | the way Perl represents it. |
2660 | |
58cde26e |
2661 | =item int() |
2662 | |
2663 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a |
2664 | Perl scalar: |
2665 | |
2666 | $x = Math::BigInt->new(123); |
2667 | $y = int($x); # BigInt 123 |
2668 | $x = Math::BigFloat->new(123.45); |
2669 | $y = int($x); # BigInt 123 |
2670 | |
2671 | In all Perl versions you can use C<as_number()> for the same effect: |
2672 | |
2673 | $x = Math::BigFloat->new(123.45); |
2674 | $y = $x->as_number(); # BigInt 123 |
2675 | |
2676 | This also works for other subclasses, like Math::String. |
2677 | |
574bacfe |
2678 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. |
2679 | |
58cde26e |
2680 | =item bdiv |
2681 | |
2682 | The following will probably not do what you expect: |
2683 | |
bd05a461 |
2684 | $c = Math::BigInt->new(123); |
2685 | print $c->length(),"\n"; # prints 30 |
2686 | |
2687 | It prints both the number of digits in the number and in the fraction part |
2688 | since print calls C<length()> in list context. Use something like: |
2689 | |
2690 | print scalar $c->length(),"\n"; # prints 3 |
2691 | |
2692 | =item bdiv |
2693 | |
2694 | The following will probably not do what you expect: |
2695 | |
58cde26e |
2696 | print $c->bdiv(10000),"\n"; |
2697 | |
2698 | It prints both quotient and reminder since print calls C<bdiv()> in list |
2699 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want |
2700 | to use |
2701 | |
2702 | print $c / 10000,"\n"; |
2703 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c |
2704 | |
2705 | instead. |
2706 | |
2707 | The quotient is always the greatest integer less than or equal to the |
2708 | real-valued quotient of the two operands, and the remainder (when it is |
2709 | nonzero) always has the same sign as the second operand; so, for |
2710 | example, |
2711 | |
574bacfe |
2712 | 1 / 4 => ( 0, 1) |
2713 | 1 / -4 => (-1,-3) |
58cde26e |
2714 | -3 / 4 => (-1, 1) |
2715 | -3 / -4 => ( 0,-3) |
2716 | |
2717 | As a consequence, the behavior of the operator % agrees with the |
2718 | behavior of Perl's built-in % operator (as documented in the perlop |
2719 | manpage), and the equation |
2720 | |
2721 | $x == ($x / $y) * $y + ($x % $y) |
2722 | |
2723 | holds true for any $x and $y, which justifies calling the two return |
2724 | values of bdiv() the quotient and remainder. |
2725 | |
2726 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will |
2727 | not change BigInt's way to do things. This is because under 'use integer' Perl |
2728 | will do what the underlying C thinks is right and this is different for each |
2729 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug |
2730 | the author to implement it ;) |
2731 | |
2732 | =item Modifying and = |
2733 | |
2734 | Beware of: |
2735 | |
2736 | $x = Math::BigFloat->new(5); |
2737 | $y = $x; |
2738 | |
2739 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
2740 | a second reference to the B<same> object and stores it in $y. Thus anything |
17baacb7 |
2741 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
2742 | Or in other words, C<=> is only safe if you modify your BigInts only via |
2743 | overloaded math. As soon as you use a method call it breaks: |
58cde26e |
2744 | |
2745 | $x->bmul(2); |
2746 | print "$x, $y\n"; # prints '10, 10' |
2747 | |
2748 | If you want a true copy of $x, use: |
2749 | |
2750 | $y = $x->copy(); |
2751 | |
17baacb7 |
2752 | You can also chain the calls like this, this will make first a copy and then |
2753 | multiply it by 2: |
2754 | |
2755 | $y = $x->copy()->bmul(2); |
2756 | |
b22b3e31 |
2757 | See also the documentation for overload.pm regarding C<=>. |
58cde26e |
2758 | |
2759 | =item bpow |
2760 | |
2761 | C<bpow()> (and the rounding functions) now modifies the first argument and |
574bacfe |
2762 | returns it, unlike the old code which left it alone and only returned the |
58cde26e |
2763 | result. This is to be consistent with C<badd()> etc. The first three will |
2764 | modify $x, the last one won't: |
2765 | |
2766 | print bpow($x,$i),"\n"; # modify $x |
2767 | print $x->bpow($i),"\n"; # ditto |
2768 | print $x **= $i,"\n"; # the same |
2769 | print $x ** $i,"\n"; # leave $x alone |
2770 | |
2771 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. |
2772 | |
2773 | =item Overloading -$x |
2774 | |
2775 | The following: |
2776 | |
2777 | $x = -$x; |
2778 | |
2779 | is slower than |
2780 | |
2781 | $x->bneg(); |
2782 | |
2783 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant |
2784 | needs to preserve $x since it does not know that it later will get overwritten. |
0716bf9b |
2785 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e |
2786 | |
2787 | With Copy-On-Write, this issue will be gone. Stay tuned... |
2788 | |
2789 | =item Mixing different object types |
2790 | |
2791 | In Perl you will get a floating point value if you do one of the following: |
2792 | |
2793 | $float = 5.0 + 2; |
2794 | $float = 2 + 5.0; |
2795 | $float = 5 / 2; |
2796 | |
2797 | With overloaded math, only the first two variants will result in a BigFloat: |
2798 | |
2799 | use Math::BigInt; |
2800 | use Math::BigFloat; |
2801 | |
2802 | $mbf = Math::BigFloat->new(5); |
2803 | $mbi2 = Math::BigInteger->new(5); |
2804 | $mbi = Math::BigInteger->new(2); |
2805 | |
2806 | # what actually gets called: |
2807 | $float = $mbf + $mbi; # $mbf->badd() |
2808 | $float = $mbf / $mbi; # $mbf->bdiv() |
2809 | $integer = $mbi + $mbf; # $mbi->badd() |
2810 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() |
2811 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() |
2812 | |
2813 | This is because math with overloaded operators follows the first (dominating) |
2814 | operand, this one's operation is called and returns thus the result. So, |
2815 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
2816 | the result should be a Math::BigFloat or the second operant is one. |
2817 | |
2818 | To get a Math::BigFloat you either need to call the operation manually, |
2819 | make sure the operands are already of the proper type or casted to that type |
2820 | via Math::BigFloat->new(): |
2821 | |
2822 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 |
2823 | |
2824 | Beware of simple "casting" the entire expression, this would only convert |
2825 | the already computed result: |
2826 | |
2827 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! |
2828 | |
0716bf9b |
2829 | Beware also of the order of more complicated expressions like: |
58cde26e |
2830 | |
2831 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int |
2832 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto |
2833 | |
2834 | If in doubt, break the expression into simpler terms, or cast all operands |
2835 | to the desired resulting type. |
2836 | |
2837 | Scalar values are a bit different, since: |
2838 | |
2839 | $float = 2 + $mbf; |
2840 | $float = $mbf + 2; |
2841 | |
2842 | will both result in the proper type due to the way the overloaded math works. |
2843 | |
2844 | This section also applies to other overloaded math packages, like Math::String. |
2845 | |
2846 | =item bsqrt() |
2847 | |
2848 | C<bsqrt()> works only good if the result is an big integer, e.g. the square |
2849 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
2850 | mode. |
2851 | |
2852 | If you want a better approximation of the square root, then use: |
2853 | |
2854 | $x = Math::BigFloat->new(12); |
2855 | $Math::BigFloat::precision = 0; |
2856 | Math::BigFloat->round_mode('even'); |
2857 | print $x->copy->bsqrt(),"\n"; # 4 |
2858 | |
2859 | $Math::BigFloat::precision = 2; |
2860 | print $x->bsqrt(),"\n"; # 3.46 |
2861 | print $x->bsqrt(3),"\n"; # 3.464 |
2862 | |
2863 | =back |
2864 | |
2865 | =head1 LICENSE |
2866 | |
2867 | This program is free software; you may redistribute it and/or modify it under |
2868 | the same terms as Perl itself. |
a5f75d66 |
2869 | |
0716bf9b |
2870 | =head1 SEE ALSO |
2871 | |
2872 | L<Math::BigFloat> and L<Math::Big>. |
2873 | |
574bacfe |
2874 | L<Math::BigInt::BitVect> and L<Math::BigInt::Pari>. |
2875 | |
58cde26e |
2876 | =head1 AUTHORS |
a5f75d66 |
2877 | |
58cde26e |
2878 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
2879 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001. |
a5f75d66 |
2880 | |
2881 | =cut |