Commit | Line | Data |
---|---|---|
13a12e00 JH |
1 | package Math::BigInt; |
2 | ||
3 | # | |
4 | # "Mike had an infinite amount to do and a negative amount of time in which | |
5 | # to do it." - Before and After | |
6 | # | |
7 | ||
58cde26e | 8 | # The following hash values are used: |
0716bf9b | 9 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) |
58cde26e JH |
10 | # sign : +,-,NaN,+inf,-inf |
11 | # _a : accuracy | |
12 | # _p : precision | |
0716bf9b | 13 | # _f : flags, used by MBF to flag parts of a float as untouchable |
b4f14daa | 14 | |
574bacfe JH |
15 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since |
16 | # underlying lib might change the reference! | |
17 | ||
58cde26e | 18 | my $class = "Math::BigInt"; |
0716bf9b | 19 | require 5.005; |
58cde26e | 20 | |
07d34614 | 21 | $VERSION = '1.58'; |
58cde26e JH |
22 | use Exporter; |
23 | @ISA = qw( Exporter ); | |
61f5c3f5 | 24 | @EXPORT_OK = qw( objectify _swap bgcd blcm); |
027dc388 | 25 | use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/; |
b3abae2a | 26 | use vars qw/$upgrade $downgrade/; |
58cde26e JH |
27 | use strict; |
28 | ||
29 | # Inside overload, the first arg is always an object. If the original code had | |
30 | # it reversed (like $x = 2 * $y), then the third paramater indicates this | |
31 | # swapping. To make it work, we use a helper routine which not only reswaps the | |
32 | # params, but also makes a new object in this case. See _swap() for details, | |
33 | # especially the cases of operators with different classes. | |
34 | ||
35 | # For overloaded ops with only one argument we simple use $_[0]->copy() to | |
36 | # preserve the argument. | |
37 | ||
38 | # Thus inheritance of overload operators becomes possible and transparent for | |
39 | # our subclasses without the need to repeat the entire overload section there. | |
a0d0e21e | 40 | |
a5f75d66 | 41 | use overload |
58cde26e JH |
42 | '=' => sub { $_[0]->copy(); }, |
43 | ||
44 | # '+' and '-' do not use _swap, since it is a triffle slower. If you want to | |
45 | # override _swap (if ever), then override overload of '+' and '-', too! | |
46 | # for sub it is a bit tricky to keep b: b-a => -a+b | |
47 | '-' => sub { my $c = $_[0]->copy; $_[2] ? | |
48 | $c->bneg()->badd($_[1]) : | |
49 | $c->bsub( $_[1]) }, | |
50 | '+' => sub { $_[0]->copy()->badd($_[1]); }, | |
51 | ||
52 | # some shortcuts for speed (assumes that reversed order of arguments is routed | |
53 | # to normal '+' and we thus can always modify first arg. If this is changed, | |
54 | # this breaks and must be adjusted.) | |
55 | '+=' => sub { $_[0]->badd($_[1]); }, | |
56 | '-=' => sub { $_[0]->bsub($_[1]); }, | |
57 | '*=' => sub { $_[0]->bmul($_[1]); }, | |
58 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, | |
027dc388 JH |
59 | '%=' => sub { $_[0]->bmod($_[1]); }, |
60 | '^=' => sub { $_[0]->bxor($_[1]); }, | |
61 | '&=' => sub { $_[0]->band($_[1]); }, | |
62 | '|=' => sub { $_[0]->bior($_[1]); }, | |
58cde26e JH |
63 | '**=' => sub { $_[0]->bpow($_[1]); }, |
64 | ||
b3abae2a | 65 | # not supported by Perl yet |
027dc388 JH |
66 | '..' => \&_pointpoint, |
67 | ||
58cde26e | 68 | '<=>' => sub { $_[2] ? |
bd05a461 JH |
69 | ref($_[0])->bcmp($_[1],$_[0]) : |
70 | ref($_[0])->bcmp($_[0],$_[1])}, | |
027dc388 | 71 | 'cmp' => sub { |
58cde26e | 72 | $_[2] ? |
b3abae2a JH |
73 | "$_[1]" cmp $_[0]->bstr() : |
74 | $_[0]->bstr() cmp "$_[1]" }, | |
58cde26e | 75 | |
61f5c3f5 | 76 | 'log' => sub { $_[0]->copy()->blog(); }, |
58cde26e JH |
77 | 'int' => sub { $_[0]->copy(); }, |
78 | 'neg' => sub { $_[0]->copy()->bneg(); }, | |
79 | 'abs' => sub { $_[0]->copy()->babs(); }, | |
b3abae2a | 80 | 'sqrt' => sub { $_[0]->copy()->bsqrt(); }, |
58cde26e JH |
81 | '~' => sub { $_[0]->copy()->bnot(); }, |
82 | ||
83 | '*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); }, | |
84 | '/' => sub { my @a = ref($_[0])->_swap(@_);scalar $a[0]->bdiv($a[1]);}, | |
85 | '%' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmod($a[1]); }, | |
86 | '**' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bpow($a[1]); }, | |
87 | '<<' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->blsft($a[1]); }, | |
88 | '>>' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->brsft($a[1]); }, | |
89 | ||
90 | '&' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->band($a[1]); }, | |
91 | '|' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bior($a[1]); }, | |
92 | '^' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bxor($a[1]); }, | |
93 | ||
94 | # can modify arg of ++ and --, so avoid a new-copy for speed, but don't | |
574bacfe | 95 | # use $_[0]->__one(), it modifies $_[0] to be 1! |
58cde26e JH |
96 | '++' => sub { $_[0]->binc() }, |
97 | '--' => sub { $_[0]->bdec() }, | |
98 | ||
99 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers | |
100 | 'bool' => sub { | |
101 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ | |
102 | # v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-( | |
103 | my $t = !$_[0]->is_zero(); | |
104 | undef $t if $t == 0; | |
b3abae2a | 105 | $t; |
58cde26e | 106 | }, |
a0d0e21e | 107 | |
027dc388 JH |
108 | # the original qw() does not work with the TIESCALAR below, why? |
109 | # Order of arguments unsignificant | |
110 | '""' => sub { $_[0]->bstr(); }, | |
111 | '0+' => sub { $_[0]->numify(); } | |
a5f75d66 | 112 | ; |
a0d0e21e | 113 | |
58cde26e JH |
114 | ############################################################################## |
115 | # global constants, flags and accessory | |
116 | ||
0716bf9b JH |
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 | |
61f5c3f5 | 123 | my $IMPORT = 0; # did import() yet? |
0716bf9b | 124 | |
ee15d750 JH |
125 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
126 | $accuracy = undef; | |
127 | $precision = undef; | |
128 | $div_scale = 40; | |
58cde26e | 129 | |
b3abae2a JH |
130 | $upgrade = undef; # default is no upgrade |
131 | $downgrade = undef; # default is no downgrade | |
132 | ||
027dc388 JH |
133 | ############################################################################## |
134 | # the old code had $rnd_mode, so we need to support it, too | |
135 | ||
136 | $rnd_mode = 'even'; | |
137 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } | |
138 | sub FETCH { return $round_mode; } | |
139 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } | |
140 | ||
141 | BEGIN { tie $rnd_mode, 'Math::BigInt'; } | |
142 | ||
143 | ############################################################################## | |
144 | ||
58cde26e JH |
145 | sub round_mode |
146 | { | |
ee15d750 | 147 | no strict 'refs'; |
58cde26e | 148 | # make Class->round_mode() work |
ee15d750 JH |
149 | my $self = shift; |
150 | my $class = ref($self) || $self || __PACKAGE__; | |
58cde26e JH |
151 | if (defined $_[0]) |
152 | { | |
153 | my $m = shift; | |
154 | die "Unknown round mode $m" | |
155 | if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; | |
b3abae2a | 156 | return ${"${class}::round_mode"} = $m; |
58cde26e | 157 | } |
ee15d750 JH |
158 | return ${"${class}::round_mode"}; |
159 | } | |
160 | ||
b3abae2a JH |
161 | sub upgrade |
162 | { | |
163 | no strict 'refs'; | |
28df3e88 | 164 | # make Class->upgrade() work |
b3abae2a JH |
165 | my $self = shift; |
166 | my $class = ref($self) || $self || __PACKAGE__; | |
9393ace2 JH |
167 | # need to set new value? |
168 | if (@_ > 0) | |
b3abae2a JH |
169 | { |
170 | my $u = shift; | |
171 | return ${"${class}::upgrade"} = $u; | |
172 | } | |
173 | return ${"${class}::upgrade"}; | |
174 | } | |
175 | ||
28df3e88 JH |
176 | sub downgrade |
177 | { | |
178 | no strict 'refs'; | |
179 | # make Class->downgrade() work | |
180 | my $self = shift; | |
181 | my $class = ref($self) || $self || __PACKAGE__; | |
9393ace2 JH |
182 | # need to set new value? |
183 | if (@_ > 0) | |
28df3e88 JH |
184 | { |
185 | my $u = shift; | |
186 | return ${"${class}::downgrade"} = $u; | |
187 | } | |
188 | return ${"${class}::downgrade"}; | |
189 | } | |
190 | ||
ee15d750 JH |
191 | sub div_scale |
192 | { | |
193 | no strict 'refs'; | |
194 | # make Class->round_mode() work | |
195 | my $self = shift; | |
196 | my $class = ref($self) || $self || __PACKAGE__; | |
197 | if (defined $_[0]) | |
198 | { | |
199 | die ('div_scale must be greater than zero') if $_[0] < 0; | |
200 | ${"${class}::div_scale"} = shift; | |
201 | } | |
202 | return ${"${class}::div_scale"}; | |
58cde26e JH |
203 | } |
204 | ||
205 | sub accuracy | |
206 | { | |
ee15d750 JH |
207 | # $x->accuracy($a); ref($x) $a |
208 | # $x->accuracy(); ref($x) | |
209 | # Class->accuracy(); class | |
210 | # Class->accuracy($a); class $a | |
58cde26e | 211 | |
ee15d750 JH |
212 | my $x = shift; |
213 | my $class = ref($x) || $x || __PACKAGE__; | |
58cde26e | 214 | |
ee15d750 JH |
215 | no strict 'refs'; |
216 | # need to set new value? | |
58cde26e JH |
217 | if (@_ > 0) |
218 | { | |
ee15d750 JH |
219 | my $a = shift; |
220 | die ('accuracy must not be zero') if defined $a && $a == 0; | |
221 | if (ref($x)) | |
222 | { | |
223 | # $object->accuracy() or fallback to global | |
224 | $x->bround($a) if defined $a; | |
225 | $x->{_a} = $a; # set/overwrite, even if not rounded | |
226 | $x->{_p} = undef; # clear P | |
227 | } | |
228 | else | |
229 | { | |
230 | # set global | |
231 | ${"${class}::accuracy"} = $a; | |
b3abae2a | 232 | ${"${class}::precision"} = undef; # clear P |
ee15d750 JH |
233 | } |
234 | return $a; # shortcut | |
235 | } | |
236 | ||
237 | if (ref($x)) | |
238 | { | |
239 | # $object->accuracy() or fallback to global | |
240 | return $x->{_a} || ${"${class}::accuracy"}; | |
58cde26e | 241 | } |
ee15d750 | 242 | return ${"${class}::accuracy"}; |
58cde26e JH |
243 | } |
244 | ||
245 | sub precision | |
246 | { | |
ee15d750 JH |
247 | # $x->precision($p); ref($x) $p |
248 | # $x->precision(); ref($x) | |
249 | # Class->precision(); class | |
250 | # Class->precision($p); class $p | |
58cde26e | 251 | |
ee15d750 JH |
252 | my $x = shift; |
253 | my $class = ref($x) || $x || __PACKAGE__; | |
58cde26e | 254 | |
ee15d750 JH |
255 | no strict 'refs'; |
256 | # need to set new value? | |
58cde26e JH |
257 | if (@_ > 0) |
258 | { | |
ee15d750 JH |
259 | my $p = shift; |
260 | if (ref($x)) | |
261 | { | |
262 | # $object->precision() or fallback to global | |
263 | $x->bfround($p) if defined $p; | |
264 | $x->{_p} = $p; # set/overwrite, even if not rounded | |
b3abae2a | 265 | $x->{_a} = undef; # clear A |
ee15d750 JH |
266 | } |
267 | else | |
268 | { | |
269 | # set global | |
270 | ${"${class}::precision"} = $p; | |
b3abae2a | 271 | ${"${class}::accuracy"} = undef; # clear A |
ee15d750 JH |
272 | } |
273 | return $p; # shortcut | |
58cde26e | 274 | } |
ee15d750 JH |
275 | |
276 | if (ref($x)) | |
277 | { | |
278 | # $object->precision() or fallback to global | |
279 | return $x->{_p} || ${"${class}::precision"}; | |
280 | } | |
281 | return ${"${class}::precision"}; | |
58cde26e JH |
282 | } |
283 | ||
b3abae2a JH |
284 | sub config |
285 | { | |
286 | # return (later set?) configuration data as hash ref | |
287 | my $class = shift || 'Math::BigInt'; | |
288 | ||
289 | no strict 'refs'; | |
290 | my $lib = $CALC; | |
291 | my $cfg = { | |
292 | lib => $lib, | |
293 | lib_version => ${"${lib}::VERSION"}, | |
294 | class => $class, | |
295 | }; | |
296 | foreach ( | |
28df3e88 | 297 | qw/upgrade downgrade precision accuracy round_mode VERSION div_scale/) |
b3abae2a JH |
298 | { |
299 | $cfg->{lc($_)} = ${"${class}::$_"}; | |
300 | }; | |
301 | $cfg; | |
302 | } | |
303 | ||
58cde26e JH |
304 | sub _scale_a |
305 | { | |
306 | # select accuracy parameter based on precedence, | |
307 | # used by bround() and bfround(), may return undef for scale (means no op) | |
308 | my ($x,$s,$m,$scale,$mode) = @_; | |
309 | $scale = $x->{_a} if !defined $scale; | |
310 | $scale = $s if (!defined $scale); | |
311 | $mode = $m if !defined $mode; | |
312 | return ($scale,$mode); | |
313 | } | |
314 | ||
315 | sub _scale_p | |
316 | { | |
317 | # select precision parameter based on precedence, | |
318 | # used by bround() and bfround(), may return undef for scale (means no op) | |
319 | my ($x,$s,$m,$scale,$mode) = @_; | |
320 | $scale = $x->{_p} if !defined $scale; | |
321 | $scale = $s if (!defined $scale); | |
322 | $mode = $m if !defined $mode; | |
323 | return ($scale,$mode); | |
324 | } | |
325 | ||
326 | ############################################################################## | |
327 | # constructors | |
328 | ||
329 | sub copy | |
330 | { | |
331 | my ($c,$x); | |
332 | if (@_ > 1) | |
333 | { | |
334 | # if two arguments, the first one is the class to "swallow" subclasses | |
335 | ($c,$x) = @_; | |
336 | } | |
337 | else | |
338 | { | |
339 | $x = shift; | |
340 | $c = ref($x); | |
341 | } | |
342 | return unless ref($x); # only for objects | |
343 | ||
344 | my $self = {}; bless $self,$c; | |
394e6ffb | 345 | my $r; |
58cde26e JH |
346 | foreach my $k (keys %$x) |
347 | { | |
0716bf9b JH |
348 | if ($k eq 'value') |
349 | { | |
394e6ffb JH |
350 | $self->{value} = $CALC->_copy($x->{value}); next; |
351 | } | |
352 | if (!($r = ref($x->{$k}))) | |
353 | { | |
354 | $self->{$k} = $x->{$k}; next; | |
0716bf9b | 355 | } |
394e6ffb | 356 | if ($r eq 'SCALAR') |
0716bf9b JH |
357 | { |
358 | $self->{$k} = \${$x->{$k}}; | |
359 | } | |
394e6ffb | 360 | elsif ($r eq 'ARRAY') |
58cde26e JH |
361 | { |
362 | $self->{$k} = [ @{$x->{$k}} ]; | |
363 | } | |
394e6ffb | 364 | elsif ($r eq 'HASH') |
58cde26e JH |
365 | { |
366 | # only one level deep! | |
367 | foreach my $h (keys %{$x->{$k}}) | |
368 | { | |
369 | $self->{$k}->{$h} = $x->{$k}->{$h}; | |
370 | } | |
371 | } | |
394e6ffb | 372 | else # normal ref |
58cde26e | 373 | { |
61f5c3f5 | 374 | my $xk = $x->{$k}; |
394e6ffb JH |
375 | if ($xk->can('copy')) |
376 | { | |
377 | $self->{$k} = $xk->copy(); | |
378 | } | |
379 | else | |
380 | { | |
381 | $self->{$k} = $xk->new($xk); | |
382 | } | |
58cde26e JH |
383 | } |
384 | } | |
385 | $self; | |
386 | } | |
387 | ||
388 | sub new | |
389 | { | |
b22b3e31 | 390 | # create a new BigInt object from a string or another BigInt object. |
0716bf9b | 391 | # see hash keys documented at top |
58cde26e JH |
392 | |
393 | # the argument could be an object, so avoid ||, && etc on it, this would | |
b22b3e31 PN |
394 | # cause costly overloaded code to be called. The only allowed ops are |
395 | # ref() and defined. | |
58cde26e | 396 | |
61f5c3f5 | 397 | my ($class,$wanted,$a,$p,$r) = @_; |
58cde26e | 398 | |
61f5c3f5 T |
399 | # avoid numify-calls by not using || on $wanted! |
400 | return $class->bzero($a,$p) if !defined $wanted; # default to 0 | |
9393ace2 JH |
401 | return $class->copy($wanted,$a,$p,$r) |
402 | if ref($wanted) && $wanted->isa($class); # MBI or subclass | |
58cde26e | 403 | |
61f5c3f5 T |
404 | $class->import() if $IMPORT == 0; # make require work |
405 | ||
9393ace2 JH |
406 | my $self = bless {}, $class; |
407 | ||
408 | # shortcut for "normal" numbers | |
409 | if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*$/)) | |
410 | { | |
411 | $self->{sign} = $1 || '+'; | |
412 | my $ref = \$wanted; | |
413 | if ($wanted =~ /^[+-]/) | |
414 | { | |
415 | # remove sign without touching wanted | |
416 | my $t = $wanted; $t =~ s/^[+-]//; $ref = \$t; | |
417 | } | |
418 | $self->{value} = $CALC->_new($ref); | |
419 | no strict 'refs'; | |
420 | if ( (defined $a) || (defined $p) | |
421 | || (defined ${"${class}::precision"}) | |
422 | || (defined ${"${class}::accuracy"}) | |
423 | ) | |
424 | { | |
425 | $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p); | |
426 | } | |
427 | return $self; | |
428 | } | |
429 | ||
58cde26e | 430 | # handle '+inf', '-inf' first |
ee15d750 | 431 | if ($wanted =~ /^[+-]?inf$/) |
58cde26e | 432 | { |
0716bf9b | 433 | $self->{value} = $CALC->_zero(); |
ee15d750 | 434 | $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
58cde26e JH |
435 | return $self; |
436 | } | |
437 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign | |
438 | my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted); | |
58cde26e JH |
439 | if (!ref $mis) |
440 | { | |
441 | die "$wanted is not a number initialized to $class" if !$NaNOK; | |
442 | #print "NaN 1\n"; | |
0716bf9b | 443 | $self->{value} = $CALC->_zero(); |
58cde26e JH |
444 | $self->{sign} = $nan; |
445 | return $self; | |
446 | } | |
574bacfe JH |
447 | if (!ref $miv) |
448 | { | |
449 | # _from_hex or _from_bin | |
450 | $self->{value} = $mis->{value}; | |
451 | $self->{sign} = $mis->{sign}; | |
452 | return $self; # throw away $mis | |
453 | } | |
58cde26e JH |
454 | # make integer from mantissa by adjusting exp, then convert to bigint |
455 | $self->{sign} = $$mis; # store sign | |
0716bf9b | 456 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
58cde26e JH |
457 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
458 | if ($e > 0) | |
459 | { | |
460 | my $diff = $e - CORE::length($$mfv); | |
461 | if ($diff < 0) # Not integer | |
462 | { | |
463 | #print "NOI 1\n"; | |
b3abae2a | 464 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
465 | $self->{sign} = $nan; |
466 | } | |
467 | else # diff >= 0 | |
468 | { | |
469 | # adjust fraction and add it to value | |
470 | # print "diff > 0 $$miv\n"; | |
471 | $$miv = $$miv . ($$mfv . '0' x $diff); | |
472 | } | |
473 | } | |
474 | else | |
475 | { | |
476 | if ($$mfv ne '') # e <= 0 | |
477 | { | |
478 | # fraction and negative/zero E => NOI | |
479 | #print "NOI 2 \$\$mfv '$$mfv'\n"; | |
b3abae2a | 480 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
481 | $self->{sign} = $nan; |
482 | } | |
483 | elsif ($e < 0) | |
484 | { | |
485 | # xE-y, and empty mfv | |
486 | #print "xE-y\n"; | |
487 | $e = abs($e); | |
488 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? | |
489 | { | |
490 | #print "NOI 3\n"; | |
b3abae2a | 491 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
492 | $self->{sign} = $nan; |
493 | } | |
494 | } | |
495 | } | |
496 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 | |
0716bf9b | 497 | $self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/; |
0716bf9b | 498 | # if any of the globals is set, use them to round and store them inside $self |
61f5c3f5 T |
499 | # do not round for new($x,undef,undef) since that is used by MBF to signal |
500 | # no rounding | |
501 | $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p; | |
9393ace2 | 502 | $self; |
58cde26e JH |
503 | } |
504 | ||
58cde26e JH |
505 | sub bnan |
506 | { | |
507 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' | |
b4f14daa | 508 | my $self = shift; |
58cde26e JH |
509 | $self = $class if !defined $self; |
510 | if (!ref($self)) | |
511 | { | |
512 | my $c = $self; $self = {}; bless $self, $c; | |
513 | } | |
61f5c3f5 | 514 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 515 | return if $self->modify('bnan'); |
13a12e00 JH |
516 | my $c = ref($self); |
517 | if ($self->can('_bnan')) | |
518 | { | |
519 | # use subclass to initialize | |
520 | $self->_bnan(); | |
521 | } | |
522 | else | |
523 | { | |
524 | # otherwise do our own thing | |
525 | $self->{value} = $CALC->_zero(); | |
526 | } | |
58cde26e | 527 | $self->{sign} = $nan; |
394e6ffb | 528 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly |
58cde26e | 529 | return $self; |
b4f14daa | 530 | } |
58cde26e JH |
531 | |
532 | sub binf | |
533 | { | |
534 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' | |
535 | # the sign is either '+', or if given, used from there | |
536 | my $self = shift; | |
56b9c951 | 537 | my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/; |
58cde26e JH |
538 | $self = $class if !defined $self; |
539 | if (!ref($self)) | |
540 | { | |
541 | my $c = $self; $self = {}; bless $self, $c; | |
542 | } | |
61f5c3f5 | 543 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 544 | return if $self->modify('binf'); |
13a12e00 JH |
545 | my $c = ref($self); |
546 | if ($self->can('_binf')) | |
547 | { | |
548 | # use subclass to initialize | |
549 | $self->_binf(); | |
550 | } | |
551 | else | |
552 | { | |
553 | # otherwise do our own thing | |
554 | $self->{value} = $CALC->_zero(); | |
555 | } | |
56b9c951 JH |
556 | $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf |
557 | $self->{sign} = $sign; | |
394e6ffb | 558 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
58cde26e JH |
559 | return $self; |
560 | } | |
561 | ||
562 | sub bzero | |
563 | { | |
564 | # create a bigint '+0', if given a BigInt, set it to 0 | |
565 | my $self = shift; | |
566 | $self = $class if !defined $self; | |
0716bf9b | 567 | |
58cde26e JH |
568 | if (!ref($self)) |
569 | { | |
570 | my $c = $self; $self = {}; bless $self, $c; | |
571 | } | |
61f5c3f5 | 572 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 573 | return if $self->modify('bzero'); |
13a12e00 JH |
574 | |
575 | if ($self->can('_bzero')) | |
576 | { | |
577 | # use subclass to initialize | |
578 | $self->_bzero(); | |
579 | } | |
580 | else | |
581 | { | |
582 | # otherwise do our own thing | |
583 | $self->{value} = $CALC->_zero(); | |
584 | } | |
58cde26e | 585 | $self->{sign} = '+'; |
61f5c3f5 T |
586 | if (@_ > 0) |
587 | { | |
588 | $self->{_a} = $_[0] | |
589 | if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a}); | |
590 | $self->{_p} = $_[1] | |
591 | if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p}); | |
592 | } | |
58cde26e JH |
593 | return $self; |
594 | } | |
595 | ||
574bacfe JH |
596 | sub bone |
597 | { | |
598 | # create a bigint '+1' (or -1 if given sign '-'), | |
599 | # if given a BigInt, set it to +1 or -1, respecively | |
600 | my $self = shift; | |
601 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; | |
602 | $self = $class if !defined $self; | |
394e6ffb | 603 | |
574bacfe JH |
604 | if (!ref($self)) |
605 | { | |
606 | my $c = $self; $self = {}; bless $self, $c; | |
607 | } | |
61f5c3f5 | 608 | $self->import() if $IMPORT == 0; # make require work |
574bacfe | 609 | return if $self->modify('bone'); |
13a12e00 JH |
610 | |
611 | if ($self->can('_bone')) | |
612 | { | |
613 | # use subclass to initialize | |
614 | $self->_bone(); | |
615 | } | |
616 | else | |
617 | { | |
618 | # otherwise do our own thing | |
619 | $self->{value} = $CALC->_one(); | |
620 | } | |
574bacfe | 621 | $self->{sign} = $sign; |
61f5c3f5 T |
622 | if (@_ > 0) |
623 | { | |
624 | $self->{_a} = $_[0] | |
625 | if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a}); | |
626 | $self->{_p} = $_[1] | |
627 | if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p}); | |
628 | } | |
574bacfe JH |
629 | return $self; |
630 | } | |
631 | ||
58cde26e JH |
632 | ############################################################################## |
633 | # string conversation | |
634 | ||
635 | sub bsstr | |
636 | { | |
637 | # (ref to BFLOAT or num_str ) return num_str | |
638 | # Convert number from internal format to scientific string format. | |
639 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") | |
dccbb853 JH |
640 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
641 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 642 | |
574bacfe JH |
643 | if ($x->{sign} !~ /^[+-]$/) |
644 | { | |
645 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
646 | return 'inf'; # +inf | |
647 | } | |
58cde26e | 648 | my ($m,$e) = $x->parts(); |
574bacfe | 649 | # e can only be positive |
58cde26e JH |
650 | my $sign = 'e+'; |
651 | # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s; | |
652 | return $m->bstr().$sign.$e->bstr(); | |
653 | } | |
654 | ||
655 | sub bstr | |
656 | { | |
0716bf9b | 657 | # make a string from bigint object |
ee15d750 JH |
658 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
659 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
56b9c951 | 660 | |
574bacfe JH |
661 | if ($x->{sign} !~ /^[+-]$/) |
662 | { | |
663 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
664 | return 'inf'; # +inf | |
665 | } | |
0716bf9b JH |
666 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
667 | return $es.${$CALC->_str($x->{value})}; | |
58cde26e JH |
668 | } |
669 | ||
670 | sub numify | |
671 | { | |
394e6ffb | 672 | # Make a "normal" scalar from a BigInt object |
58cde26e | 673 | my $x = shift; $x = $class->new($x) unless ref $x; |
0716bf9b JH |
674 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
675 | my $num = $CALC->_num($x->{value}); | |
676 | return -$num if $x->{sign} eq '-'; | |
9393ace2 | 677 | $num; |
58cde26e JH |
678 | } |
679 | ||
680 | ############################################################################## | |
681 | # public stuff (usually prefixed with "b") | |
682 | ||
683 | sub sign | |
684 | { | |
9393ace2 | 685 | # return the sign of the number: +/-/-inf/+inf/NaN |
ee15d750 JH |
686 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
687 | ||
9393ace2 | 688 | $x->{sign}; |
58cde26e JH |
689 | } |
690 | ||
ee15d750 | 691 | sub _find_round_parameters |
58cde26e JH |
692 | { |
693 | # After any operation or when calling round(), the result is rounded by | |
694 | # regarding the A & P from arguments, local parameters, or globals. | |
61f5c3f5 T |
695 | |
696 | # This procedure finds the round parameters, but it is for speed reasons | |
697 | # duplicated in round. Otherwise, it is tested by the testsuite and used | |
698 | # by fdiv(). | |
699 | ||
394e6ffb JH |
700 | my ($self,$a,$p,$r,@args) = @_; |
701 | # $a accuracy, if given by caller | |
702 | # $p precision, if given by caller | |
703 | # $r round_mode, if given by caller | |
704 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
58cde26e | 705 | |
17baacb7 | 706 | # leave bigfloat parts alone |
ee15d750 | 707 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
17baacb7 | 708 | |
394e6ffb | 709 | my $c = ref($self); # find out class of argument(s) |
574bacfe | 710 | no strict 'refs'; |
574bacfe | 711 | |
58cde26e | 712 | # now pick $a or $p, but only if we have got "arguments" |
61f5c3f5 | 713 | if (!defined $a) |
58cde26e | 714 | { |
61f5c3f5 | 715 | foreach ($self,@args) |
58cde26e JH |
716 | { |
717 | # take the defined one, or if both defined, the one that is smaller | |
718 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
719 | } | |
61f5c3f5 T |
720 | } |
721 | if (!defined $p) | |
ee15d750 | 722 | { |
61f5c3f5 T |
723 | # even if $a is defined, take $p, to signal error for both defined |
724 | foreach ($self,@args) | |
725 | { | |
726 | # take the defined one, or if both defined, the one that is bigger | |
727 | # -2 > -3, and 3 > 2 | |
728 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
729 | } | |
ee15d750 | 730 | } |
61f5c3f5 T |
731 | # if still none defined, use globals (#2) |
732 | $a = ${"$c\::accuracy"} unless defined $a; | |
733 | $p = ${"$c\::precision"} unless defined $p; | |
734 | ||
735 | # no rounding today? | |
736 | return ($self) unless defined $a || defined $p; # early out | |
737 | ||
738 | # set A and set P is an fatal error | |
739 | return ($self->bnan()) if defined $a && defined $p; | |
740 | ||
741 | $r = ${"$c\::round_mode"} unless defined $r; | |
742 | die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; | |
743 | ||
744 | return ($self,$a,$p,$r); | |
ee15d750 JH |
745 | } |
746 | ||
747 | sub round | |
748 | { | |
61f5c3f5 | 749 | # Round $self according to given parameters, or given second argument's |
ee15d750 | 750 | # parameters or global defaults |
ee15d750 | 751 | |
61f5c3f5 T |
752 | # for speed reasons, _find_round_parameters is embeded here: |
753 | ||
754 | my ($self,$a,$p,$r,@args) = @_; | |
755 | # $a accuracy, if given by caller | |
756 | # $p precision, if given by caller | |
757 | # $r round_mode, if given by caller | |
758 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
759 | ||
760 | # leave bigfloat parts alone | |
761 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; | |
762 | ||
763 | my $c = ref($self); # find out class of argument(s) | |
764 | no strict 'refs'; | |
765 | ||
766 | # now pick $a or $p, but only if we have got "arguments" | |
767 | if (!defined $a) | |
58cde26e | 768 | { |
61f5c3f5 T |
769 | foreach ($self,@args) |
770 | { | |
771 | # take the defined one, or if both defined, the one that is smaller | |
772 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
773 | } | |
58cde26e | 774 | } |
61f5c3f5 T |
775 | if (!defined $p) |
776 | { | |
777 | # even if $a is defined, take $p, to signal error for both defined | |
778 | foreach ($self,@args) | |
779 | { | |
780 | # take the defined one, or if both defined, the one that is bigger | |
781 | # -2 > -3, and 3 > 2 | |
782 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
783 | } | |
784 | } | |
785 | # if still none defined, use globals (#2) | |
786 | $a = ${"$c\::accuracy"} unless defined $a; | |
787 | $p = ${"$c\::precision"} unless defined $p; | |
788 | ||
789 | # no rounding today? | |
790 | return $self unless defined $a || defined $p; # early out | |
791 | ||
792 | # set A and set P is an fatal error | |
793 | return $self->bnan() if defined $a && defined $p; | |
794 | ||
795 | $r = ${"$c\::round_mode"} unless defined $r; | |
796 | die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; | |
797 | ||
798 | # now round, by calling either fround or ffround: | |
799 | if (defined $a) | |
800 | { | |
801 | $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a; | |
802 | } | |
803 | else # both can't be undefined due to early out | |
58cde26e | 804 | { |
61f5c3f5 | 805 | $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p; |
58cde26e | 806 | } |
61f5c3f5 | 807 | $self->bnorm(); # after round, normalize |
58cde26e JH |
808 | } |
809 | ||
17baacb7 | 810 | sub bnorm |
58cde26e | 811 | { |
027dc388 | 812 | # (numstr or BINT) return BINT |
58cde26e | 813 | # Normalize number -- no-op here |
dccbb853 | 814 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
b3abae2a | 815 | $x; |
58cde26e JH |
816 | } |
817 | ||
818 | sub babs | |
819 | { | |
820 | # (BINT or num_str) return BINT | |
821 | # make number absolute, or return absolute BINT from string | |
ee15d750 JH |
822 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
823 | ||
58cde26e JH |
824 | return $x if $x->modify('babs'); |
825 | # post-normalized abs for internal use (does nothing for NaN) | |
826 | $x->{sign} =~ s/^-/+/; | |
827 | $x; | |
828 | } | |
829 | ||
830 | sub bneg | |
831 | { | |
832 | # (BINT or num_str) return BINT | |
833 | # negate number or make a negated number from string | |
ee15d750 JH |
834 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
835 | ||
58cde26e | 836 | return $x if $x->modify('bneg'); |
b3abae2a | 837 | |
58cde26e | 838 | # for +0 dont negate (to have always normalized) |
b3abae2a | 839 | $x->{sign} =~ tr/+-/-+/ if !$x->is_zero(); # does nothing for NaN |
58cde26e JH |
840 | $x; |
841 | } | |
842 | ||
843 | sub bcmp | |
844 | { | |
845 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
846 | # (BINT or num_str, BINT or num_str) return cond_code | |
847 | my ($self,$x,$y) = objectify(2,@_); | |
0716bf9b JH |
848 | |
849 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
850 | { | |
851 | # handle +-inf and NaN | |
852 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
574bacfe | 853 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b JH |
854 | return +1 if $x->{sign} eq '+inf'; |
855 | return -1 if $x->{sign} eq '-inf'; | |
856 | return -1 if $y->{sign} eq '+inf'; | |
b3abae2a | 857 | return +1; |
0716bf9b | 858 | } |
574bacfe JH |
859 | # check sign for speed first |
860 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
861 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
862 | ||
863 | # shortcut | |
864 | my $xz = $x->is_zero(); | |
865 | my $yz = $y->is_zero(); | |
866 | return 0 if $xz && $yz; # 0 <=> 0 | |
867 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y | |
868 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 | |
dccbb853 JH |
869 | |
870 | # post-normalized compare for internal use (honors signs) | |
871 | if ($x->{sign} eq '+') | |
872 | { | |
56b9c951 | 873 | # $x and $y both > 0 |
dccbb853 JH |
874 | return $CALC->_acmp($x->{value},$y->{value}); |
875 | } | |
876 | ||
56b9c951 | 877 | # $x && $y both < 0 |
b3abae2a | 878 | $CALC->_acmp($y->{value},$x->{value}); # swaped (lib does only 0,1,-1) |
58cde26e JH |
879 | } |
880 | ||
881 | sub bacmp | |
882 | { | |
883 | # Compares 2 values, ignoring their signs. | |
884 | # Returns one of undef, <0, =0, >0. (suitable for sort) | |
885 | # (BINT, BINT) return cond_code | |
886 | my ($self,$x,$y) = objectify(2,@_); | |
574bacfe JH |
887 | |
888 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
889 | { | |
890 | # handle +-inf and NaN | |
891 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
892 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
893 | return +1; # inf is always bigger | |
894 | } | |
b3abae2a | 895 | $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1 |
58cde26e JH |
896 | } |
897 | ||
898 | sub badd | |
899 | { | |
900 | # add second arg (BINT or string) to first (BINT) (modifies first) | |
901 | # return result as BINT | |
61f5c3f5 | 902 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e JH |
903 | |
904 | return $x if $x->modify('badd'); | |
56b9c951 | 905 | return $upgrade->badd($x,$y,@r) if defined $upgrade && |
8f675a64 | 906 | ((!$x->isa($self)) || (!$y->isa($self))); |
58cde26e | 907 | |
61f5c3f5 | 908 | $r[3] = $y; # no push! |
574bacfe JH |
909 | # inf and NaN handling |
910 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
911 | { | |
912 | # NaN first | |
913 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
13a12e00 JH |
914 | # inf handling |
915 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
574bacfe | 916 | { |
b3abae2a JH |
917 | # +inf++inf or -inf+-inf => same, rest is NaN |
918 | return $x if $x->{sign} eq $y->{sign}; | |
919 | return $x->bnan(); | |
574bacfe JH |
920 | } |
921 | # +-inf + something => +inf | |
922 | # something +-inf => +-inf | |
923 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; | |
924 | return $x; | |
925 | } | |
926 | ||
58cde26e JH |
927 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
928 | ||
929 | if ($sx eq $sy) | |
930 | { | |
574bacfe | 931 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e JH |
932 | $x->{sign} = $sx; |
933 | } | |
934 | else | |
935 | { | |
574bacfe | 936 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e JH |
937 | if ($a > 0) |
938 | { | |
939 | #print "swapped sub (a=$a)\n"; | |
574bacfe | 940 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e JH |
941 | $x->{sign} = $sy; |
942 | } | |
943 | elsif ($a == 0) | |
944 | { | |
945 | # speedup, if equal, set result to 0 | |
0716bf9b JH |
946 | #print "equal sub, result = 0\n"; |
947 | $x->{value} = $CALC->_zero(); | |
58cde26e JH |
948 | $x->{sign} = '+'; |
949 | } | |
950 | else # a < 0 | |
951 | { | |
952 | #print "unswapped sub (a=$a)\n"; | |
574bacfe | 953 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
58cde26e | 954 | $x->{sign} = $sx; |
a0d0e21e | 955 | } |
a0d0e21e | 956 | } |
61f5c3f5 | 957 | $x->round(@r); |
58cde26e JH |
958 | } |
959 | ||
960 | sub bsub | |
961 | { | |
962 | # (BINT or num_str, BINT or num_str) return num_str | |
963 | # subtract second arg from first, modify first | |
b3abae2a | 964 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e | 965 | |
58cde26e | 966 | return $x if $x->modify('bsub'); |
8f675a64 JH |
967 | |
968 | # upgrade done by badd(): | |
b3abae2a | 969 | # return $upgrade->badd($x,$y,@r) if defined $upgrade && |
8f675a64 | 970 | # ((!$x->isa($self)) || (!$y->isa($self))); |
b3abae2a JH |
971 | |
972 | if ($y->is_zero()) | |
973 | { | |
974 | return $x->round(@r); | |
e745a66c | 975 | } |
b3abae2a JH |
976 | |
977 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN | |
978 | $x->badd($y,@r); # badd does not leave internal zeros | |
979 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) | |
61f5c3f5 | 980 | $x; # already rounded by badd() or no round necc. |
58cde26e JH |
981 | } |
982 | ||
983 | sub binc | |
984 | { | |
985 | # increment arg by one | |
ee15d750 | 986 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 987 | return $x if $x->modify('binc'); |
e745a66c JH |
988 | |
989 | if ($x->{sign} eq '+') | |
990 | { | |
991 | $x->{value} = $CALC->_inc($x->{value}); | |
992 | return $x->round($a,$p,$r); | |
993 | } | |
994 | elsif ($x->{sign} eq '-') | |
995 | { | |
996 | $x->{value} = $CALC->_dec($x->{value}); | |
997 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 | |
998 | return $x->round($a,$p,$r); | |
999 | } | |
1000 | # inf, nan handling etc | |
61f5c3f5 | 1001 | $x->badd($self->__one(),$a,$p,$r); # badd does round |
58cde26e JH |
1002 | } |
1003 | ||
1004 | sub bdec | |
1005 | { | |
1006 | # decrement arg by one | |
ee15d750 | 1007 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1008 | return $x if $x->modify('bdec'); |
e745a66c JH |
1009 | |
1010 | my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+'; | |
1011 | # <= 0 | |
1012 | if (($x->{sign} eq '-') || $zero) | |
1013 | { | |
1014 | $x->{value} = $CALC->_inc($x->{value}); | |
1015 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 | |
1016 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 | |
1017 | return $x->round($a,$p,$r); | |
1018 | } | |
1019 | # > 0 | |
1020 | elsif ($x->{sign} eq '+') | |
1021 | { | |
1022 | $x->{value} = $CALC->_dec($x->{value}); | |
1023 | return $x->round($a,$p,$r); | |
1024 | } | |
1025 | # inf, nan handling etc | |
61f5c3f5 | 1026 | $x->badd($self->__one('-'),$a,$p,$r); # badd does round |
58cde26e JH |
1027 | } |
1028 | ||
61f5c3f5 T |
1029 | sub blog |
1030 | { | |
1031 | # not implemented yet | |
b3abae2a | 1032 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
61f5c3f5 | 1033 | |
b3abae2a JH |
1034 | return $upgrade->blog($x,$base,$a,$p,$r) if defined $upgrade; |
1035 | ||
61f5c3f5 T |
1036 | return $x->bnan(); |
1037 | } | |
1038 | ||
58cde26e JH |
1039 | sub blcm |
1040 | { | |
1041 | # (BINT or num_str, BINT or num_str) return BINT | |
1042 | # does not modify arguments, but returns new object | |
1043 | # Lowest Common Multiplicator | |
58cde26e | 1044 | |
0716bf9b JH |
1045 | my $y = shift; my ($x); |
1046 | if (ref($y)) | |
1047 | { | |
1048 | $x = $y->copy(); | |
1049 | } | |
1050 | else | |
1051 | { | |
1052 | $x = $class->new($y); | |
1053 | } | |
dccbb853 | 1054 | while (@_) { $x = __lcm($x,shift); } |
58cde26e JH |
1055 | $x; |
1056 | } | |
1057 | ||
1058 | sub bgcd | |
1059 | { | |
1060 | # (BINT or num_str, BINT or num_str) return BINT | |
1061 | # does not modify arguments, but returns new object | |
1062 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) | |
0716bf9b | 1063 | |
dccbb853 JH |
1064 | my $y = shift; |
1065 | $y = __PACKAGE__->new($y) if !ref($y); | |
1066 | my $self = ref($y); | |
1067 | my $x = $y->copy(); # keep arguments | |
0716bf9b JH |
1068 | if ($CALC->can('_gcd')) |
1069 | { | |
1070 | while (@_) | |
1071 | { | |
dccbb853 | 1072 | $y = shift; $y = $self->new($y) if !ref($y); |
0716bf9b JH |
1073 | next if $y->is_zero(); |
1074 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? | |
1075 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one(); | |
1076 | } | |
1077 | } | |
1078 | else | |
1079 | { | |
1080 | while (@_) | |
1081 | { | |
dccbb853 JH |
1082 | $y = shift; $y = $self->new($y) if !ref($y); |
1083 | $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN | |
0716bf9b JH |
1084 | } |
1085 | } | |
1086 | $x->babs(); | |
58cde26e JH |
1087 | } |
1088 | ||
58cde26e JH |
1089 | sub bnot |
1090 | { | |
1091 | # (num_str or BINT) return BINT | |
1092 | # represent ~x as twos-complement number | |
ee15d750 JH |
1093 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1094 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1095 | ||
58cde26e | 1096 | return $x if $x->modify('bnot'); |
61f5c3f5 | 1097 | $x->bneg()->bdec(); # bdec already does round |
58cde26e JH |
1098 | } |
1099 | ||
b3abae2a JH |
1100 | # is_foo test routines |
1101 | ||
58cde26e JH |
1102 | sub is_zero |
1103 | { | |
1104 | # return true if arg (BINT or num_str) is zero (array '+', '0') | |
ee15d750 JH |
1105 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1106 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
0716bf9b | 1107 | |
574bacfe | 1108 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 | 1109 | $CALC->_is_zero($x->{value}); |
58cde26e JH |
1110 | } |
1111 | ||
1112 | sub is_nan | |
1113 | { | |
1114 | # return true if arg (BINT or num_str) is NaN | |
ee15d750 JH |
1115 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
1116 | ||
1117 | return 1 if $x->{sign} eq $nan; | |
28df3e88 | 1118 | 0; |
58cde26e JH |
1119 | } |
1120 | ||
1121 | sub is_inf | |
1122 | { | |
1123 | # return true if arg (BINT or num_str) is +-inf | |
ee15d750 JH |
1124 | my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1125 | ||
1126 | $sign = '' if !defined $sign; | |
9393ace2 | 1127 | return 1 if $sign eq $x->{sign}; # match ("+inf" eq "+inf") |
ee15d750 | 1128 | return 0 if $sign !~ /^([+-]|)$/; |
58cde26e | 1129 | |
ee15d750 JH |
1130 | if ($sign eq '') |
1131 | { | |
1132 | return 1 if ($x->{sign} =~ /^[+-]inf$/); | |
1133 | return 0; | |
1134 | } | |
1135 | $sign = quotemeta($sign.'inf'); | |
1136 | return 1 if ($x->{sign} =~ /^$sign$/); | |
28df3e88 | 1137 | 0; |
58cde26e JH |
1138 | } |
1139 | ||
1140 | sub is_one | |
1141 | { | |
b22b3e31 PN |
1142 | # return true if arg (BINT or num_str) is +1 |
1143 | # or -1 if sign is given | |
ee15d750 JH |
1144 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1145 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1146 | ||
1147 | $sign = '' if !defined $sign; $sign = '+' if $sign ne '-'; | |
0716bf9b | 1148 | |
ee15d750 | 1149 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
394e6ffb | 1150 | $CALC->_is_one($x->{value}); |
58cde26e JH |
1151 | } |
1152 | ||
1153 | sub is_odd | |
1154 | { | |
1155 | # return true when arg (BINT or num_str) is odd, false for even | |
ee15d750 JH |
1156 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1157 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
0716bf9b | 1158 | |
b22b3e31 | 1159 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1160 | $CALC->_is_odd($x->{value}); |
58cde26e JH |
1161 | } |
1162 | ||
1163 | sub is_even | |
1164 | { | |
1165 | # return true when arg (BINT or num_str) is even, false for odd | |
ee15d750 JH |
1166 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1167 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
0716bf9b | 1168 | |
b22b3e31 | 1169 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1170 | $CALC->_is_even($x->{value}); |
0716bf9b JH |
1171 | } |
1172 | ||
1173 | sub is_positive | |
1174 | { | |
1175 | # return true when arg (BINT or num_str) is positive (>= 0) | |
ee15d750 JH |
1176 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1177 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1178 | ||
1179 | return 1 if $x->{sign} =~ /^\+/; | |
394e6ffb | 1180 | 0; |
0716bf9b JH |
1181 | } |
1182 | ||
1183 | sub is_negative | |
1184 | { | |
1185 | # return true when arg (BINT or num_str) is negative (< 0) | |
ee15d750 JH |
1186 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1187 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1188 | ||
1189 | return 1 if ($x->{sign} =~ /^-/); | |
394e6ffb | 1190 | 0; |
58cde26e JH |
1191 | } |
1192 | ||
b3abae2a JH |
1193 | sub is_int |
1194 | { | |
1195 | # return true when arg (BINT or num_str) is an integer | |
1196 | # always true for BigInt, but different for Floats | |
1197 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster | |
1198 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1199 | ||
1200 | $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't | |
1201 | } | |
1202 | ||
0716bf9b JH |
1203 | ############################################################################### |
1204 | ||
58cde26e JH |
1205 | sub bmul |
1206 | { | |
1207 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 | |
1208 | # (BINT or num_str, BINT or num_str) return BINT | |
61f5c3f5 | 1209 | my ($self,$x,$y,@r) = objectify(2,@_); |
0716bf9b | 1210 | |
58cde26e | 1211 | return $x if $x->modify('bmul'); |
61f5c3f5 | 1212 | |
574bacfe | 1213 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
b3abae2a | 1214 | |
574bacfe JH |
1215 | # inf handling |
1216 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1217 | { | |
b3abae2a | 1218 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe JH |
1219 | # result will always be +-inf: |
1220 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
1221 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
1222 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
1223 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
1224 | return $x->binf('-'); | |
1225 | } | |
9393ace2 JH |
1226 | |
1227 | return $upgrade->bmul($x,$y,@r) | |
1228 | if defined $upgrade && $y->isa($upgrade); | |
1229 | ||
1230 | $r[3] = $y; # no push here | |
58cde26e | 1231 | |
0716bf9b | 1232 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
dccbb853 | 1233 | |
b3abae2a JH |
1234 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
1235 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 | |
1236 | $x->round(@r); | |
dccbb853 JH |
1237 | } |
1238 | ||
1239 | sub _div_inf | |
1240 | { | |
1241 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code | |
1242 | my ($self,$x,$y) = @_; | |
1243 | ||
1244 | # NaN if x == NaN or y == NaN or x==y==0 | |
1245 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() | |
1246 | if (($x->is_nan() || $y->is_nan()) || | |
1247 | ($x->is_zero() && $y->is_zero())); | |
1248 | ||
b3abae2a JH |
1249 | # +-inf / +-inf == NaN, reminder also NaN |
1250 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
dccbb853 | 1251 | { |
b3abae2a | 1252 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan(); |
dccbb853 JH |
1253 | } |
1254 | # x / +-inf => 0, remainder x (works even if x == 0) | |
1255 | if ($y->{sign} =~ /^[+-]inf$/) | |
1256 | { | |
1257 | my $t = $x->copy(); # binf clobbers up $x | |
1258 | return wantarray ? ($x->bzero(),$t) : $x->bzero() | |
1259 | } | |
1260 | ||
1261 | # 5 / 0 => +inf, -6 / 0 => -inf | |
1262 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf | |
1263 | # exception: -8 / 0 has remainder -8, not 8 | |
1264 | # exception: -inf / 0 has remainder -inf, not inf | |
1265 | if ($y->is_zero()) | |
1266 | { | |
1267 | # +-inf / 0 => special case for -inf | |
1268 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); | |
1269 | if (!$x->is_zero() && !$x->is_inf()) | |
1270 | { | |
1271 | my $t = $x->copy(); # binf clobbers up $x | |
1272 | return wantarray ? | |
1273 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) | |
1274 | } | |
1275 | } | |
1276 | ||
1277 | # last case: +-inf / ordinary number | |
1278 | my $sign = '+inf'; | |
1279 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; | |
1280 | $x->{sign} = $sign; | |
1281 | return wantarray ? ($x,$self->bzero()) : $x; | |
58cde26e JH |
1282 | } |
1283 | ||
1284 | sub bdiv | |
1285 | { | |
1286 | # (dividend: BINT or num_str, divisor: BINT or num_str) return | |
1287 | # (BINT,BINT) (quo,rem) or BINT (only rem) | |
61f5c3f5 | 1288 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e JH |
1289 | |
1290 | return $x if $x->modify('bdiv'); | |
1291 | ||
dccbb853 JH |
1292 | return $self->_div_inf($x,$y) |
1293 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
58cde26e | 1294 | |
d614cd8b | 1295 | #print "mbi bdiv $x $y\n"; |
9393ace2 | 1296 | return $upgrade->bdiv($upgrade->new($x),$y,@r) |
8f675a64 | 1297 | if defined $upgrade && !$y->isa($self); |
9393ace2 | 1298 | |
61f5c3f5 T |
1299 | $r[3] = $y; # no push! |
1300 | ||
58cde26e | 1301 | # 0 / something |
61f5c3f5 T |
1302 | return |
1303 | wantarray ? ($x->round(@r),$self->bzero(@r)):$x->round(@r) if $x->is_zero(); | |
58cde26e | 1304 | |
b3abae2a | 1305 | # Is $x in the interval [0, $y) (aka $x <= $y) ? |
0716bf9b | 1306 | my $cmp = $CALC->_acmp($x->{value},$y->{value}); |
b3abae2a | 1307 | if (($cmp < 0) and (($x->{sign} eq $y->{sign}) or !wantarray)) |
58cde26e | 1308 | { |
9393ace2 JH |
1309 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
1310 | if defined $upgrade; | |
b3abae2a | 1311 | |
61f5c3f5 | 1312 | return $x->bzero()->round(@r) unless wantarray; |
58cde26e | 1313 | my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x |
61f5c3f5 | 1314 | return ($x->bzero()->round(@r),$t); |
58cde26e JH |
1315 | } |
1316 | elsif ($cmp == 0) | |
1317 | { | |
1318 | # shortcut, both are the same, so set to +/- 1 | |
574bacfe | 1319 | $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') ); |
58cde26e | 1320 | return $x unless wantarray; |
61f5c3f5 | 1321 | return ($x->round(@r),$self->bzero(@r)); |
58cde26e | 1322 | } |
9393ace2 JH |
1323 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
1324 | if defined $upgrade; | |
58cde26e JH |
1325 | |
1326 | # calc new sign and in case $y == +/- 1, return $x | |
dccbb853 | 1327 | my $xsign = $x->{sign}; # keep |
58cde26e JH |
1328 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
1329 | # check for / +-1 (cant use $y->is_one due to '-' | |
394e6ffb | 1330 | if ($CALC->_is_one($y->{value})) |
58cde26e | 1331 | { |
61f5c3f5 | 1332 | return wantarray ? ($x->round(@r),$self->bzero(@r)) : $x->round(@r); |
58cde26e JH |
1333 | } |
1334 | ||
58cde26e JH |
1335 | if (wantarray) |
1336 | { | |
394e6ffb JH |
1337 | my $rem = $self->bzero(); |
1338 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); | |
1339 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
61f5c3f5 | 1340 | $x->round(@r); |
dccbb853 JH |
1341 | if (! $CALC->_is_zero($rem->{value})) |
1342 | { | |
1343 | $rem->{sign} = $y->{sign}; | |
1344 | $rem = $y-$rem if $xsign ne $y->{sign}; # one of them '-' | |
1345 | } | |
1346 | else | |
1347 | { | |
1348 | $rem->{sign} = '+'; # dont leave -0 | |
1349 | } | |
61f5c3f5 | 1350 | $rem->round(@r); |
58cde26e JH |
1351 | return ($x,$rem); |
1352 | } | |
394e6ffb JH |
1353 | |
1354 | $x->{value} = $CALC->_div($x->{value},$y->{value}); | |
1355 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
61f5c3f5 | 1356 | $x->round(@r); |
58cde26e JH |
1357 | } |
1358 | ||
d614cd8b JH |
1359 | ############################################################################### |
1360 | # modulus functions | |
1361 | ||
dccbb853 JH |
1362 | sub bmod |
1363 | { | |
1364 | # modulus (or remainder) | |
1365 | # (BINT or num_str, BINT or num_str) return BINT | |
61f5c3f5 | 1366 | my ($self,$x,$y,@r) = objectify(2,@_); |
28df3e88 | 1367 | |
dccbb853 | 1368 | return $x if $x->modify('bmod'); |
61f5c3f5 | 1369 | $r[3] = $y; # no push! |
dccbb853 JH |
1370 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) |
1371 | { | |
1372 | my ($d,$r) = $self->_div_inf($x,$y); | |
61f5c3f5 | 1373 | return $r->round(@r); |
dccbb853 JH |
1374 | } |
1375 | ||
1376 | if ($CALC->can('_mod')) | |
1377 | { | |
1378 | # calc new sign and in case $y == +/- 1, return $x | |
1379 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); | |
dccbb853 JH |
1380 | if (!$CALC->_is_zero($x->{value})) |
1381 | { | |
b3abae2a | 1382 | my $xsign = $x->{sign}; |
dccbb853 | 1383 | $x->{sign} = $y->{sign}; |
07d34614 T |
1384 | if ($xsign ne $y->{sign}) |
1385 | { | |
1386 | my $t = [ @{$x->{value}} ]; # copy $x | |
1387 | $x->{value} = [ @{$y->{value}} ]; # copy $y to $x | |
1388 | $x->{value} = $CALC->_sub($y->{value},$t,1); # $y-$x | |
1389 | } | |
dccbb853 JH |
1390 | } |
1391 | else | |
1392 | { | |
1393 | $x->{sign} = '+'; # dont leave -0 | |
1394 | } | |
61f5c3f5 | 1395 | return $x->round(@r); |
dccbb853 | 1396 | } |
b3abae2a JH |
1397 | my ($t,$rem) = $self->bdiv($x->copy(),$y,@r); # slow way (also rounds) |
1398 | # modify in place | |
1399 | foreach (qw/value sign _a _p/) | |
1400 | { | |
1401 | $x->{$_} = $rem->{$_}; | |
1402 | } | |
1403 | $x; | |
dccbb853 JH |
1404 | } |
1405 | ||
07d34614 | 1406 | sub bmodinv |
d614cd8b JH |
1407 | { |
1408 | # modular inverse. given a number which is (hopefully) relatively | |
1409 | # prime to the modulus, calculate its inverse using Euclid's | |
1410 | # alogrithm. if the number is not relatively prime to the modulus | |
1411 | # (i.e. their gcd is not one) then NaN is returned. | |
1412 | ||
1413 | my ($self,$num,$mod,@r) = objectify(2,@_); | |
1414 | ||
1415 | return $num if $num->modify('bmodinv'); | |
1416 | ||
1417 | return $num->bnan() | |
1418 | if ($mod->{sign} ne '+' # -, NaN, +inf, -inf | |
1419 | || $num->is_zero() # or num == 0 | |
1420 | || $num->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf | |
1421 | ); | |
07d34614 T |
1422 | return $num # i.e., NaN or some kind of infinity, |
1423 | if ($num->{sign} !~ /^[+-]$/); | |
1424 | ||
1425 | if ($CALC->can('_modinv')) | |
1426 | { | |
1427 | $num->{value} = $CALC->_modinv($mod->{value}); | |
1428 | return $num; | |
1429 | } | |
d614cd8b JH |
1430 | |
1431 | # the remaining case, nonpositive case, $num < 0, is addressed below. | |
1432 | ||
1433 | my ($u, $u1) = ($self->bzero(), $self->bone()); | |
1434 | my ($a, $b) = ($mod->copy(), $num->copy()); | |
1435 | ||
1436 | # put least residue into $b if $num was negative | |
07d34614 | 1437 | $b->bmod($mod) if $b->{sign} eq '-'; |
d614cd8b | 1438 | |
07d34614 T |
1439 | # Euclid's Algorithm |
1440 | while (!$b->is_zero()) | |
1441 | { | |
1442 | ($a, my $q, $b) = ($b, $a->copy()->bdiv($b)); | |
1443 | ($u, $u1) = ($u1, $u - $u1 * $q); | |
d614cd8b JH |
1444 | } |
1445 | ||
07d34614 T |
1446 | # if the gcd is not 1, then return NaN! It would be pointless to |
1447 | # have called bgcd first, because we would then be performing the | |
1448 | # same Euclidean Algorithm *twice* | |
1449 | return $num->bnan() unless $a->is_one(); | |
d614cd8b | 1450 | |
07d34614 T |
1451 | $u->bmod($mod); |
1452 | $num->{value} = $u->{value}; | |
1453 | $num->{sign} = $u->{sign}; | |
1454 | $num; | |
d614cd8b JH |
1455 | } |
1456 | ||
07d34614 | 1457 | sub bmodpow |
d614cd8b JH |
1458 | { |
1459 | # takes a very large number to a very large exponent in a given very | |
1460 | # large modulus, quickly, thanks to binary exponentation. supports | |
1461 | # negative exponents. | |
1462 | my ($self,$num,$exp,$mod,@r) = objectify(3,@_); | |
1463 | ||
1464 | return $num if $num->modify('bmodpow'); | |
1465 | ||
1466 | # check modulus for valid values | |
1467 | return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf | |
1468 | || $mod->is_zero()); | |
1469 | ||
1470 | # check exponent for valid values | |
1471 | if ($exp->{sign} =~ /\w/) | |
1472 | { | |
1473 | # i.e., if it's NaN, +inf, or -inf... | |
1474 | return $num->bnan(); | |
1475 | } | |
07d34614 T |
1476 | |
1477 | my $exp1 = $exp->copy(); | |
1478 | if ($exp->{sign} eq '-') | |
d614cd8b | 1479 | { |
07d34614 | 1480 | $exp1->babs(); |
d614cd8b | 1481 | $num->bmodinv ($mod); |
07d34614 | 1482 | # return $num if $num->{sign} !~ /^[+-]/; # see next check |
d614cd8b JH |
1483 | } |
1484 | ||
07d34614 T |
1485 | # check num for valid values (also NaN if there was no inverse) |
1486 | return $num->bnan() if $num->{sign} !~ /^[+-]$/; | |
d614cd8b | 1487 | |
07d34614 T |
1488 | if ($CALC->can('_modpow')) |
1489 | { | |
1490 | # $exp and $mod are positive, result is also positive | |
1491 | $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value}); | |
1492 | return $num; | |
1493 | } | |
d614cd8b | 1494 | |
07d34614 T |
1495 | # in the trivial case, |
1496 | return $num->bzero() if $mod->is_one(); | |
1497 | return $num->bone() if $num->is_zero() or $num->is_one(); | |
d614cd8b | 1498 | |
07d34614 T |
1499 | $num->bmod($mod); # if $x is large, make it smaller first |
1500 | my $acc = $num->copy(); $num->bone(); # keep ref to $num | |
1501 | ||
1502 | while( !$exp1->is_zero() ) | |
1503 | { | |
1504 | if( $exp1->is_odd() ) | |
1505 | { | |
1506 | $num->bmul($acc)->bmod($mod); | |
d614cd8b | 1507 | } |
07d34614 T |
1508 | $acc->bmul($acc)->bmod($mod); |
1509 | $exp1->brsft( 1, 2); # remove last (binary) digit | |
d614cd8b | 1510 | } |
07d34614 | 1511 | $num; |
d614cd8b JH |
1512 | } |
1513 | ||
1514 | ############################################################################### | |
1515 | ||
b3abae2a JH |
1516 | sub bfac |
1517 | { | |
1518 | # (BINT or num_str, BINT or num_str) return BINT | |
1519 | # compute factorial numbers | |
1520 | # modifies first argument | |
1521 | my ($self,$x,@r) = objectify(1,@_); | |
1522 | ||
1523 | return $x if $x->modify('bfac'); | |
1524 | ||
1525 | return $x->bnan() if $x->{sign} ne '+'; # inf, NnN, <0 etc => NaN | |
1526 | return $x->bone(@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 | |
1527 | ||
1528 | if ($CALC->can('_fac')) | |
1529 | { | |
1530 | $x->{value} = $CALC->_fac($x->{value}); | |
1531 | return $x->round(@r); | |
1532 | } | |
1533 | ||
1534 | my $n = $x->copy(); | |
1535 | $x->bone(); | |
1536 | my $f = $self->new(2); | |
1537 | while ($f->bacmp($n) < 0) | |
1538 | { | |
1539 | $x->bmul($f); $f->binc(); | |
1540 | } | |
1541 | $x->bmul($f); # last step | |
1542 | $x->round(@r); # round | |
1543 | } | |
1544 | ||
58cde26e JH |
1545 | sub bpow |
1546 | { | |
1547 | # (BINT or num_str, BINT or num_str) return BINT | |
1548 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 | |
1549 | # modifies first argument | |
61f5c3f5 | 1550 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e JH |
1551 | |
1552 | return $x if $x->modify('bpow'); | |
9393ace2 JH |
1553 | |
1554 | return $upgrade->bpow($upgrade->new($x),$y,@r) | |
8f675a64 | 1555 | if defined $upgrade && !$y->isa($self); |
9393ace2 | 1556 | |
61f5c3f5 | 1557 | $r[3] = $y; # no push! |
0716bf9b | 1558 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
58cde26e | 1559 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
61f5c3f5 T |
1560 | return $x->bone(@r) if $y->is_zero(); |
1561 | return $x->round(@r) if $x->is_one() || $y->is_one(); | |
0716bf9b | 1562 | if ($x->{sign} eq '-' && $CALC->_is_one($x->{value})) |
58cde26e JH |
1563 | { |
1564 | # if $x == -1 and odd/even y => +1/-1 | |
61f5c3f5 | 1565 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
574bacfe | 1566 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
58cde26e | 1567 | } |
574bacfe JH |
1568 | # 1 ** -y => 1 / (1 ** |y|) |
1569 | # so do test for negative $y after above's clause | |
58cde26e | 1570 | return $x->bnan() if $y->{sign} eq '-'; |
61f5c3f5 | 1571 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
58cde26e | 1572 | |
0716bf9b | 1573 | if ($CALC->can('_pow')) |
58cde26e | 1574 | { |
574bacfe | 1575 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
61f5c3f5 | 1576 | return $x->round(@r); |
58cde26e | 1577 | } |
027dc388 JH |
1578 | |
1579 | # based on the assumption that shifting in base 10 is fast, and that mul | |
1580 | # works faster if numbers are small: we count trailing zeros (this step is | |
1581 | # O(1)..O(N), but in case of O(N) we save much more time due to this), | |
1582 | # stripping them out of the multiplication, and add $count * $y zeros | |
1583 | # afterwards like this: | |
1584 | # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6 | |
1585 | # creates deep recursion? | |
574bacfe JH |
1586 | # my $zeros = $x->_trailing_zeros(); |
1587 | # if ($zeros > 0) | |
1588 | # { | |
1589 | # $x->brsft($zeros,10); # remove zeros | |
1590 | # $x->bpow($y); # recursion (will not branch into here again) | |
1591 | # $zeros = $y * $zeros; # real number of zeros to add | |
1592 | # $x->blsft($zeros,10); | |
1593 | # return $x->round($a,$p,$r); | |
1594 | # } | |
1595 | ||
1596 | my $pow2 = $self->__one(); | |
58cde26e | 1597 | my $y1 = $class->new($y); |
dccbb853 | 1598 | my $two = $self->new(2); |
58cde26e JH |
1599 | while (!$y1->is_one()) |
1600 | { | |
dccbb853 JH |
1601 | $pow2->bmul($x) if $y1->is_odd(); |
1602 | $y1->bdiv($two); | |
027dc388 | 1603 | $x->bmul($x); |
58cde26e | 1604 | } |
dccbb853 | 1605 | $x->bmul($pow2) unless $pow2->is_one(); |
56b9c951 | 1606 | $x->round(@r); |
58cde26e JH |
1607 | } |
1608 | ||
1609 | sub blsft | |
1610 | { | |
1611 | # (BINT or num_str, BINT or num_str) return BINT | |
1612 | # compute x << y, base n, y >= 0 | |
b3abae2a | 1613 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1614 | |
1615 | return $x if $x->modify('blsft'); | |
1616 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
b3abae2a | 1617 | return $x->round($a,$p,$r) if $y->is_zero(); |
58cde26e | 1618 | |
574bacfe JH |
1619 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1620 | ||
027dc388 | 1621 | my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft'); |
574bacfe JH |
1622 | if (defined $t) |
1623 | { | |
b3abae2a | 1624 | $x->{value} = $t; return $x->round($a,$p,$r); |
574bacfe JH |
1625 | } |
1626 | # fallback | |
b3abae2a | 1627 | return $x->bmul( $self->bpow($n, $y, $a, $p, $r), $a, $p, $r ); |
58cde26e JH |
1628 | } |
1629 | ||
1630 | sub brsft | |
1631 | { | |
1632 | # (BINT or num_str, BINT or num_str) return BINT | |
1633 | # compute x >> y, base n, y >= 0 | |
b3abae2a | 1634 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1635 | |
1636 | return $x if $x->modify('brsft'); | |
1637 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
b3abae2a JH |
1638 | return $x->round($a,$p,$r) if $y->is_zero(); |
1639 | return $x->bzero($a,$p,$r) if $x->is_zero(); # 0 => 0 | |
58cde26e JH |
1640 | |
1641 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; | |
574bacfe | 1642 | |
b3abae2a JH |
1643 | # this only works for negative numbers when shifting in base 2 |
1644 | if (($x->{sign} eq '-') && ($n == 2)) | |
1645 | { | |
1646 | return $x->round($a,$p,$r) if $x->is_one('-'); # -1 => -1 | |
1647 | if (!$y->is_one()) | |
1648 | { | |
1649 | # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al | |
1650 | # but perhaps there is a better emulation for two's complement shift... | |
1651 | # if $y != 1, we must simulate it by doing: | |
1652 | # convert to bin, flip all bits, shift, and be done | |
1653 | $x->binc(); # -3 => -2 | |
1654 | my $bin = $x->as_bin(); | |
1655 | $bin =~ s/^-0b//; # strip '-0b' prefix | |
1656 | $bin =~ tr/10/01/; # flip bits | |
1657 | # now shift | |
8f675a64 | 1658 | if (CORE::length($bin) <= $y) |
b3abae2a JH |
1659 | { |
1660 | $bin = '0'; # shifting to far right creates -1 | |
1661 | # 0, because later increment makes | |
1662 | # that 1, attached '-' makes it '-1' | |
1663 | # because -1 >> x == -1 ! | |
1664 | } | |
1665 | else | |
1666 | { | |
1667 | $bin =~ s/.{$y}$//; # cut off at the right side | |
1668 | $bin = '1' . $bin; # extend left side by one dummy '1' | |
1669 | $bin =~ tr/10/01/; # flip bits back | |
1670 | } | |
1671 | my $res = $self->new('0b'.$bin); # add prefix and convert back | |
1672 | $res->binc(); # remember to increment | |
1673 | $x->{value} = $res->{value}; # take over value | |
1674 | return $x->round($a,$p,$r); # we are done now, magic, isn't? | |
1675 | } | |
1676 | $x->bdec(); # n == 2, but $y == 1: this fixes it | |
1677 | } | |
1678 | ||
027dc388 | 1679 | my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft'); |
574bacfe JH |
1680 | if (defined $t) |
1681 | { | |
b3abae2a JH |
1682 | $x->{value} = $t; |
1683 | return $x->round($a,$p,$r); | |
574bacfe JH |
1684 | } |
1685 | # fallback | |
b3abae2a JH |
1686 | $x->bdiv($self->bpow($n,$y, $a,$p,$r), $a,$p,$r); |
1687 | $x; | |
58cde26e JH |
1688 | } |
1689 | ||
1690 | sub band | |
1691 | { | |
1692 | #(BINT or num_str, BINT or num_str) return BINT | |
1693 | # compute x & y | |
0716bf9b | 1694 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1695 | |
1696 | return $x if $x->modify('band'); | |
1697 | ||
b3abae2a JH |
1698 | local $Math::BigInt::upgrade = undef; |
1699 | ||
58cde26e | 1700 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
394e6ffb | 1701 | return $x->bzero() if $y->is_zero() || $x->is_zero(); |
0716bf9b | 1702 | |
574bacfe JH |
1703 | my $sign = 0; # sign of result |
1704 | $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-'); | |
1705 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; | |
1706 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; | |
1707 | ||
1708 | if ($CALC->can('_and') && $sx == 1 && $sy == 1) | |
0716bf9b | 1709 | { |
574bacfe | 1710 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
0716bf9b JH |
1711 | return $x->round($a,$p,$r); |
1712 | } | |
574bacfe | 1713 | |
b3abae2a JH |
1714 | my $m = $self->bone(); my ($xr,$yr); |
1715 | my $x10000 = $self->new (0x1000); | |
574bacfe JH |
1716 | my $y1 = copy(ref($x),$y); # make copy |
1717 | $y1->babs(); # and positive | |
1718 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! | |
1719 | use integer; # need this for negative bools | |
0716bf9b | 1720 | while (!$x1->is_zero() && !$y1->is_zero()) |
58cde26e | 1721 | { |
0716bf9b | 1722 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e | 1723 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe JH |
1724 | # make both op's numbers! |
1725 | $x->badd( bmul( $class->new( | |
1726 | abs($sx*int($xr->numify()) & $sy*int($yr->numify()))), | |
1727 | $m)); | |
58cde26e JH |
1728 | $m->bmul($x10000); |
1729 | } | |
574bacfe | 1730 | $x->bneg() if $sign; |
0716bf9b | 1731 | return $x->round($a,$p,$r); |
58cde26e JH |
1732 | } |
1733 | ||
1734 | sub bior | |
1735 | { | |
1736 | #(BINT or num_str, BINT or num_str) return BINT | |
1737 | # compute x | y | |
0716bf9b | 1738 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1739 | |
1740 | return $x if $x->modify('bior'); | |
1741 | ||
b3abae2a JH |
1742 | local $Math::BigInt::upgrade = undef; |
1743 | ||
58cde26e JH |
1744 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1745 | return $x if $y->is_zero(); | |
574bacfe JH |
1746 | |
1747 | my $sign = 0; # sign of result | |
1748 | $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-'); | |
1749 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; | |
1750 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; | |
1751 | ||
1752 | # don't use lib for negative values | |
1753 | if ($CALC->can('_or') && $sx == 1 && $sy == 1) | |
0716bf9b | 1754 | { |
574bacfe | 1755 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
0716bf9b JH |
1756 | return $x->round($a,$p,$r); |
1757 | } | |
1758 | ||
b3abae2a JH |
1759 | my $m = $self->bone(); my ($xr,$yr); |
1760 | my $x10000 = $self->new(0x10000); | |
574bacfe JH |
1761 | my $y1 = copy(ref($x),$y); # make copy |
1762 | $y1->babs(); # and positive | |
1763 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! | |
1764 | use integer; # need this for negative bools | |
0716bf9b | 1765 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e | 1766 | { |
0716bf9b | 1767 | ($x1, $xr) = bdiv($x1,$x10000); |
58cde26e | 1768 | ($y1, $yr) = bdiv($y1,$x10000); |
574bacfe JH |
1769 | # make both op's numbers! |
1770 | $x->badd( bmul( $class->new( | |
1771 | abs($sx*int($xr->numify()) | $sy*int($yr->numify()))), | |
1772 | $m)); | |
58cde26e JH |
1773 | $m->bmul($x10000); |
1774 | } | |
574bacfe | 1775 | $x->bneg() if $sign; |
0716bf9b | 1776 | return $x->round($a,$p,$r); |
58cde26e JH |
1777 | } |
1778 | ||
1779 | sub bxor | |
1780 | { | |
1781 | #(BINT or num_str, BINT or num_str) return BINT | |
1782 | # compute x ^ y | |
0716bf9b | 1783 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1784 | |
1785 | return $x if $x->modify('bxor'); | |
1786 | ||
b3abae2a JH |
1787 | local $Math::BigInt::upgrade = undef; |
1788 | ||
0716bf9b | 1789 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
58cde26e | 1790 | return $x if $y->is_zero(); |
0716bf9b | 1791 | |
574bacfe JH |
1792 | my $sign = 0; # sign of result |
1793 | $sign = 1 if $x->{sign} ne $y->{sign}; | |
1794 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; | |
1795 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; | |
1796 | ||
1797 | # don't use lib for negative values | |
1798 | if ($CALC->can('_xor') && $sx == 1 && $sy == 1) | |
0716bf9b | 1799 | { |
574bacfe | 1800 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
0716bf9b JH |
1801 | return $x->round($a,$p,$r); |
1802 | } | |
1803 | ||
394e6ffb | 1804 | my $m = $self->bone(); my ($xr,$yr); |
b3abae2a | 1805 | my $x10000 = $self->new(0x10000); |
58cde26e | 1806 | my $y1 = copy(ref($x),$y); # make copy |
574bacfe JH |
1807 | $y1->babs(); # and positive |
1808 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! | |
1809 | use integer; # need this for negative bools | |
0716bf9b | 1810 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e | 1811 | { |
0716bf9b | 1812 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e | 1813 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe JH |
1814 | # make both op's numbers! |
1815 | $x->badd( bmul( $class->new( | |
1816 | abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))), | |
1817 | $m)); | |
58cde26e JH |
1818 | $m->bmul($x10000); |
1819 | } | |
574bacfe | 1820 | $x->bneg() if $sign; |
0716bf9b | 1821 | return $x->round($a,$p,$r); |
58cde26e JH |
1822 | } |
1823 | ||
1824 | sub length | |
1825 | { | |
ee15d750 | 1826 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1827 | |
0716bf9b | 1828 | my $e = $CALC->_len($x->{value}); |
0716bf9b | 1829 | return wantarray ? ($e,0) : $e; |
58cde26e JH |
1830 | } |
1831 | ||
1832 | sub digit | |
1833 | { | |
0716bf9b | 1834 | # return the nth decimal digit, negative values count backward, 0 is right |
56b9c951 JH |
1835 | my ($self,$x,$n) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1836 | $n = 0 if !defined $n; | |
58cde26e | 1837 | |
56b9c951 | 1838 | $CALC->_digit($x->{value},$n); |
58cde26e JH |
1839 | } |
1840 | ||
1841 | sub _trailing_zeros | |
1842 | { | |
1843 | # return the amount of trailing zeros in $x | |
1844 | my $x = shift; | |
1845 | $x = $class->new($x) unless ref $x; | |
1846 | ||
dccbb853 | 1847 | return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/; |
0716bf9b JH |
1848 | |
1849 | return $CALC->_zeros($x->{value}) if $CALC->can('_zeros'); | |
1850 | ||
b22b3e31 | 1851 | # if not: since we do not know underlying internal representation: |
0716bf9b | 1852 | my $es = "$x"; $es =~ /([0]*)$/; |
0716bf9b JH |
1853 | return 0 if !defined $1; # no zeros |
1854 | return CORE::length("$1"); # as string, not as +0! | |
58cde26e JH |
1855 | } |
1856 | ||
1857 | sub bsqrt | |
1858 | { | |
394e6ffb | 1859 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1860 | |
b3abae2a JH |
1861 | return $x if $x->modify('bsqrt'); |
1862 | ||
394e6ffb JH |
1863 | return $x->bnan() if $x->{sign} ne '+'; # -x or inf or NaN => NaN |
1864 | return $x->bzero($a,$p) if $x->is_zero(); # 0 => 0 | |
1865 | return $x->round($a,$p,$r) if $x->is_one(); # 1 => 1 | |
b3abae2a JH |
1866 | |
1867 | return $upgrade->bsqrt($x,$a,$p,$r) if defined $upgrade; | |
58cde26e | 1868 | |
394e6ffb JH |
1869 | if ($CALC->can('_sqrt')) |
1870 | { | |
1871 | $x->{value} = $CALC->_sqrt($x->{value}); | |
1872 | return $x->round($a,$p,$r); | |
1873 | } | |
1874 | ||
b3abae2a | 1875 | return $x->bone($a,$p) if $x < 4; # 2,3 => 1 |
394e6ffb | 1876 | my $y = $x->copy(); |
58cde26e JH |
1877 | my $l = int($x->length()/2); |
1878 | ||
394e6ffb JH |
1879 | $x->bone(); # keep ref($x), but modify it |
1880 | $x->blsft($l,10); | |
58cde26e JH |
1881 | |
1882 | my $last = $self->bzero(); | |
394e6ffb JH |
1883 | my $two = $self->new(2); |
1884 | my $lastlast = $x+$two; | |
1885 | while ($last != $x && $lastlast != $x) | |
58cde26e | 1886 | { |
394e6ffb | 1887 | $lastlast = $last; $last = $x; |
58cde26e | 1888 | $x += $y / $x; |
394e6ffb | 1889 | $x /= $two; |
58cde26e | 1890 | } |
394e6ffb | 1891 | $x-- if $x * $x > $y; # overshot? |
b3abae2a | 1892 | $x->round($a,$p,$r); |
58cde26e JH |
1893 | } |
1894 | ||
1895 | sub exponent | |
1896 | { | |
1897 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) | |
ee15d750 | 1898 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1899 | |
ee15d750 JH |
1900 | if ($x->{sign} !~ /^[+-]$/) |
1901 | { | |
1902 | my $s = $x->{sign}; $s =~ s/^[+-]//; | |
1903 | return $self->new($s); # -inf,+inf => inf | |
1904 | } | |
58cde26e JH |
1905 | my $e = $class->bzero(); |
1906 | return $e->binc() if $x->is_zero(); | |
1907 | $e += $x->_trailing_zeros(); | |
56b9c951 | 1908 | $e; |
58cde26e JH |
1909 | } |
1910 | ||
1911 | sub mantissa | |
1912 | { | |
ee15d750 JH |
1913 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
1914 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 1915 | |
ee15d750 JH |
1916 | if ($x->{sign} !~ /^[+-]$/) |
1917 | { | |
28df3e88 | 1918 | return $self->new($x->{sign}); # keep + or - sign |
ee15d750 | 1919 | } |
58cde26e JH |
1920 | my $m = $x->copy(); |
1921 | # that's inefficient | |
1922 | my $zeros = $m->_trailing_zeros(); | |
56b9c951 JH |
1923 | $m->brsft($zeros,10) if $zeros != 0; |
1924 | # $m /= 10 ** $zeros if $zeros != 0; | |
1925 | $m; | |
58cde26e JH |
1926 | } |
1927 | ||
1928 | sub parts | |
1929 | { | |
ee15d750 JH |
1930 | # return a copy of both the exponent and the mantissa |
1931 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 1932 | |
ee15d750 | 1933 | return ($x->mantissa(),$x->exponent()); |
58cde26e JH |
1934 | } |
1935 | ||
1936 | ############################################################################## | |
1937 | # rounding functions | |
1938 | ||
1939 | sub bfround | |
1940 | { | |
1941 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' | |
ee15d750 | 1942 | # $n == 0 || $n == 1 => round to integer |
58cde26e | 1943 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 | 1944 | my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_); |
58cde26e | 1945 | return $x if !defined $scale; # no-op |
b3abae2a | 1946 | return $x if $x->modify('bfround'); |
58cde26e JH |
1947 | |
1948 | # no-op for BigInts if $n <= 0 | |
ee15d750 JH |
1949 | if ($scale <= 0) |
1950 | { | |
61f5c3f5 | 1951 | $x->{_a} = undef; # clear an eventual set A |
ee15d750 JH |
1952 | $x->{_p} = $scale; return $x; |
1953 | } | |
58cde26e JH |
1954 | |
1955 | $x->bround( $x->length()-$scale, $mode); | |
ee15d750 JH |
1956 | $x->{_a} = undef; # bround sets {_a} |
1957 | $x->{_p} = $scale; # so correct it | |
1958 | $x; | |
58cde26e JH |
1959 | } |
1960 | ||
1961 | sub _scan_for_nonzero | |
1962 | { | |
1963 | my $x = shift; | |
1964 | my $pad = shift; | |
0716bf9b | 1965 | my $xs = shift; |
58cde26e JH |
1966 | |
1967 | my $len = $x->length(); | |
1968 | return 0 if $len == 1; # '5' is trailed by invisible zeros | |
1969 | my $follow = $pad - 1; | |
1970 | return 0 if $follow > $len || $follow < 1; | |
0716bf9b | 1971 | |
b22b3e31 | 1972 | # since we do not know underlying represention of $x, use decimal string |
0716bf9b | 1973 | #my $r = substr ($$xs,-$follow); |
58cde26e JH |
1974 | my $r = substr ("$x",-$follow); |
1975 | return 1 if $r =~ /[^0]/; return 0; | |
58cde26e JH |
1976 | } |
1977 | ||
1978 | sub fround | |
1979 | { | |
1980 | # to make life easier for switch between MBF and MBI (autoload fxxx() | |
1981 | # like MBF does for bxxx()?) | |
1982 | my $x = shift; | |
1983 | return $x->bround(@_); | |
1984 | } | |
1985 | ||
1986 | sub bround | |
1987 | { | |
1988 | # accuracy: +$n preserve $n digits from left, | |
1989 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) | |
1990 | # no-op for $n == 0 | |
1991 | # and overwrite the rest with 0's, return normalized number | |
1992 | # do not return $x->bnorm(), but $x | |
61f5c3f5 | 1993 | |
58cde26e | 1994 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 | 1995 | my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_); |
61f5c3f5 | 1996 | return $x if !defined $scale; # no-op |
b3abae2a | 1997 | return $x if $x->modify('bround'); |
58cde26e | 1998 | |
61f5c3f5 T |
1999 | if ($x->is_zero() || $scale == 0) |
2000 | { | |
2001 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 | |
2002 | return $x; | |
2003 | } | |
2004 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN | |
58cde26e JH |
2005 | |
2006 | # we have fewer digits than we want to scale to | |
2007 | my $len = $x->length(); | |
ee15d750 JH |
2008 | # scale < 0, but > -len (not >=!) |
2009 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) | |
2010 | { | |
61f5c3f5 | 2011 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
ee15d750 JH |
2012 | return $x; |
2013 | } | |
58cde26e JH |
2014 | |
2015 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 | |
2016 | my ($pad,$digit_round,$digit_after); | |
2017 | $pad = $len - $scale; | |
ee15d750 JH |
2018 | $pad = abs($scale-1) if $scale < 0; |
2019 | ||
0716bf9b | 2020 | # do not use digit(), it is costly for binary => decimal |
ee15d750 | 2021 | |
0716bf9b JH |
2022 | my $xs = $CALC->_str($x->{value}); |
2023 | my $pl = -$pad-1; | |
ee15d750 | 2024 | |
0716bf9b JH |
2025 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
2026 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 | |
2027 | $digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len; | |
2028 | $pl++; $pl ++ if $pad >= $len; | |
61f5c3f5 | 2029 | $digit_after = '0'; $digit_after = substr($$xs,$pl,1) if $pad > 0; |
ee15d750 JH |
2030 | |
2031 | # print "$pad $pl $$xs dr $digit_round da $digit_after\n"; | |
58cde26e JH |
2032 | |
2033 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look | |
2034 | # closer at the remaining digits of the original $x, remember decision | |
2035 | my $round_up = 1; # default round up | |
2036 | $round_up -- if | |
2037 | ($mode eq 'trunc') || # trunc by round down | |
2038 | ($digit_after =~ /[01234]/) || # round down anyway, | |
2039 | # 6789 => round up | |
2040 | ($digit_after eq '5') && # not 5000...0000 | |
0716bf9b | 2041 | ($x->_scan_for_nonzero($pad,$xs) == 0) && |
58cde26e JH |
2042 | ( |
2043 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || | |
2044 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || | |
2045 | ($mode eq '+inf') && ($x->{sign} eq '-') || | |
2046 | ($mode eq '-inf') && ($x->{sign} eq '+') || | |
2047 | ($mode eq 'zero') # round down if zero, sign adjusted below | |
2048 | ); | |
61f5c3f5 T |
2049 | my $put_back = 0; # not yet modified |
2050 | ||
2051 | # old code, depend on internal representation | |
2052 | # split mantissa at $pad and then pad with zeros | |
2053 | #my $s5 = int($pad / 5); | |
2054 | #my $i = 0; | |
2055 | #while ($i < $s5) | |
2056 | # { | |
2057 | # $x->{value}->[$i++] = 0; # replace with 5 x 0 | |
2058 | # } | |
2059 | #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0 | |
2060 | #my $rem = $pad % 5; # so much left over | |
2061 | #if ($rem > 0) | |
2062 | # { | |
2063 | # #print "remainder $rem\n"; | |
2064 | ## #print "elem $x->{value}->[$s5]\n"; | |
2065 | # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0' | |
2066 | # } | |
2067 | #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5' | |
2068 | #print ${$CALC->_str($pad->{value})}," $len\n"; | |
2069 | ||
2070 | if (($pad > 0) && ($pad <= $len)) | |
2071 | { | |
2072 | substr($$xs,-$pad,$pad) = '0' x $pad; | |
2073 | $put_back = 1; | |
58cde26e | 2074 | } |
61f5c3f5 T |
2075 | elsif ($pad > $len) |
2076 | { | |
2077 | $x->bzero(); # round to '0' | |
2078 | } | |
2079 | ||
58cde26e JH |
2080 | if ($round_up) # what gave test above? |
2081 | { | |
61f5c3f5 T |
2082 | $put_back = 1; |
2083 | $pad = $len, $$xs = '0'x$pad if $scale < 0; # tlr: whack 0.51=>1.0 | |
2084 | ||
2085 | # we modify directly the string variant instead of creating a number and | |
2086 | # adding it | |
2087 | my $c = 0; $pad ++; # for $pad == $len case | |
2088 | while ($pad <= $len) | |
2089 | { | |
2090 | $c = substr($$xs,-$pad,1) + 1; $c = '0' if $c eq '10'; | |
2091 | substr($$xs,-$pad,1) = $c; $pad++; | |
2092 | last if $c != 0; # no overflow => early out | |
2093 | } | |
2094 | $$xs = '1'.$$xs if $c == 0; | |
2095 | ||
2096 | # $x->badd( Math::BigInt->new($x->{sign}.'1'. '0' x $pad) ); | |
58cde26e | 2097 | } |
61f5c3f5 | 2098 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back in |
ee15d750 JH |
2099 | |
2100 | $x->{_a} = $scale if $scale >= 0; | |
2101 | if ($scale < 0) | |
2102 | { | |
2103 | $x->{_a} = $len+$scale; | |
2104 | $x->{_a} = 0 if $scale < -$len; | |
2105 | } | |
58cde26e JH |
2106 | $x; |
2107 | } | |
2108 | ||
2109 | sub bfloor | |
2110 | { | |
2111 | # return integer less or equal then number, since it is already integer, | |
2112 | # always returns $self | |
ee15d750 | 2113 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e JH |
2114 | |
2115 | # not needed: return $x if $x->modify('bfloor'); | |
58cde26e JH |
2116 | return $x->round($a,$p,$r); |
2117 | } | |
2118 | ||
2119 | sub bceil | |
2120 | { | |
2121 | # return integer greater or equal then number, since it is already integer, | |
2122 | # always returns $self | |
ee15d750 | 2123 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e JH |
2124 | |
2125 | # not needed: return $x if $x->modify('bceil'); | |
58cde26e JH |
2126 | return $x->round($a,$p,$r); |
2127 | } | |
2128 | ||
2129 | ############################################################################## | |
2130 | # private stuff (internal use only) | |
2131 | ||
574bacfe | 2132 | sub __one |
58cde26e JH |
2133 | { |
2134 | # internal speedup, set argument to 1, or create a +/- 1 | |
2135 | my $self = shift; | |
dccbb853 | 2136 | my $x = $self->bone(); # $x->{value} = $CALC->_one(); |
0716bf9b JH |
2137 | $x->{sign} = shift || '+'; |
2138 | return $x; | |
58cde26e JH |
2139 | } |
2140 | ||
2141 | sub _swap | |
2142 | { | |
2143 | # Overload will swap params if first one is no object ref so that the first | |
2144 | # one is always an object ref. In this case, third param is true. | |
2145 | # This routine is to overcome the effect of scalar,$object creating an object | |
2146 | # of the class of this package, instead of the second param $object. This | |
2147 | # happens inside overload, when the overload section of this package is | |
2148 | # inherited by sub classes. | |
2149 | # For overload cases (and this is used only there), we need to preserve the | |
2150 | # args, hence the copy(). | |
2151 | # You can override this method in a subclass, the overload section will call | |
2152 | # $object->_swap() to make sure it arrives at the proper subclass, with some | |
394e6ffb JH |
2153 | # exceptions like '+' and '-'. To make '+' and '-' work, you also need to |
2154 | # specify your own overload for them. | |
58cde26e JH |
2155 | |
2156 | # object, (object|scalar) => preserve first and make copy | |
2157 | # scalar, object => swapped, re-swap and create new from first | |
2158 | # (using class of second object, not $class!!) | |
2159 | my $self = shift; # for override in subclass | |
58cde26e JH |
2160 | if ($_[2]) |
2161 | { | |
2162 | my $c = ref ($_[0]) || $class; # fallback $class should not happen | |
2163 | return ( $c->new($_[1]), $_[0] ); | |
2164 | } | |
17baacb7 | 2165 | return ( $_[0]->copy(), $_[1] ); |
58cde26e JH |
2166 | } |
2167 | ||
2168 | sub objectify | |
2169 | { | |
2170 | # check for strings, if yes, return objects instead | |
2171 | ||
2172 | # the first argument is number of args objectify() should look at it will | |
2173 | # return $count+1 elements, the first will be a classname. This is because | |
2174 | # overloaded '""' calls bstr($object,undef,undef) and this would result in | |
2175 | # useless objects beeing created and thrown away. So we cannot simple loop | |
2176 | # over @_. If the given count is 0, all arguments will be used. | |
2177 | ||
2178 | # If the second arg is a ref, use it as class. | |
2179 | # If not, try to use it as classname, unless undef, then use $class | |
2180 | # (aka Math::BigInt). The latter shouldn't happen,though. | |
2181 | ||
2182 | # caller: gives us: | |
2183 | # $x->badd(1); => ref x, scalar y | |
2184 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y | |
2185 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y | |
2186 | # Math::BigInt::badd(1,2); => scalar x, scalar y | |
2187 | # In the last case we check number of arguments to turn it silently into | |
574bacfe | 2188 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e JH |
2189 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
2190 | # currently it tries 'Math::BigInt' + 1, which will not work. | |
ee15d750 JH |
2191 | |
2192 | # some shortcut for the common cases | |
ee15d750 JH |
2193 | # $x->unary_op(); |
2194 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); | |
ee15d750 | 2195 | |
58cde26e JH |
2196 | my $count = abs(shift || 0); |
2197 | ||
9393ace2 | 2198 | my (@a,$k,$d); # resulting array, temp, and downgrade |
58cde26e JH |
2199 | if (ref $_[0]) |
2200 | { | |
2201 | # okay, got object as first | |
2202 | $a[0] = ref $_[0]; | |
2203 | } | |
2204 | else | |
2205 | { | |
2206 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) | |
2207 | $a[0] = $class; | |
58cde26e JH |
2208 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
2209 | } | |
8f675a64 | 2210 | |
9393ace2 JH |
2211 | no strict 'refs'; |
2212 | # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats | |
2213 | if (defined ${"$a[0]::downgrade"}) | |
2214 | { | |
2215 | $d = ${"$a[0]::downgrade"}; | |
2216 | ${"$a[0]::downgrade"} = undef; | |
2217 | } | |
2218 | ||
d614cd8b | 2219 | my $up = ${"$a[0]::upgrade"}; |
58cde26e | 2220 | # print "Now in objectify, my class is today $a[0]\n"; |
58cde26e JH |
2221 | if ($count == 0) |
2222 | { | |
2223 | while (@_) | |
2224 | { | |
2225 | $k = shift; | |
2226 | if (!ref($k)) | |
2227 | { | |
2228 | $k = $a[0]->new($k); | |
2229 | } | |
d614cd8b | 2230 | elsif (!defined $up && ref($k) ne $a[0]) |
58cde26e JH |
2231 | { |
2232 | # foreign object, try to convert to integer | |
2233 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
e16b8f49 | 2234 | } |
58cde26e JH |
2235 | push @a,$k; |
2236 | } | |
2237 | } | |
2238 | else | |
2239 | { | |
2240 | while ($count > 0) | |
2241 | { | |
58cde26e JH |
2242 | $count--; |
2243 | $k = shift; | |
2244 | if (!ref($k)) | |
2245 | { | |
2246 | $k = $a[0]->new($k); | |
2247 | } | |
d614cd8b | 2248 | elsif (!defined $up && ref($k) ne $a[0]) |
58cde26e JH |
2249 | { |
2250 | # foreign object, try to convert to integer | |
2251 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
e16b8f49 | 2252 | } |
58cde26e JH |
2253 | push @a,$k; |
2254 | } | |
2255 | push @a,@_; # return other params, too | |
2256 | } | |
58cde26e | 2257 | die "$class objectify needs list context" unless wantarray; |
9393ace2 | 2258 | ${"$a[0]::downgrade"} = $d; |
58cde26e JH |
2259 | @a; |
2260 | } | |
2261 | ||
2262 | sub import | |
2263 | { | |
2264 | my $self = shift; | |
61f5c3f5 T |
2265 | |
2266 | $IMPORT++; | |
8f675a64 JH |
2267 | my @a; my $l = scalar @_; |
2268 | for ( my $i = 0; $i < $l ; $i++ ) | |
58cde26e | 2269 | { |
0716bf9b | 2270 | if ($_[$i] eq ':constant') |
58cde26e | 2271 | { |
0716bf9b | 2272 | # this causes overlord er load to step in |
58cde26e | 2273 | overload::constant integer => sub { $self->new(shift) }; |
56b9c951 | 2274 | overload::constant binary => sub { $self->new(shift) }; |
0716bf9b | 2275 | } |
b3abae2a JH |
2276 | elsif ($_[$i] eq 'upgrade') |
2277 | { | |
2278 | # this causes upgrading | |
2279 | $upgrade = $_[$i+1]; # or undef to disable | |
8f675a64 | 2280 | $i++; |
b3abae2a | 2281 | } |
0716bf9b JH |
2282 | elsif ($_[$i] =~ /^lib$/i) |
2283 | { | |
2284 | # this causes a different low lib to take care... | |
61f5c3f5 | 2285 | $CALC = $_[$i+1] || ''; |
8f675a64 JH |
2286 | $i++; |
2287 | } | |
2288 | else | |
2289 | { | |
2290 | push @a, $_[$i]; | |
58cde26e JH |
2291 | } |
2292 | } | |
2293 | # any non :constant stuff is handled by our parent, Exporter | |
2294 | # even if @_ is empty, to give it a chance | |
dccbb853 JH |
2295 | $self->SUPER::import(@a); # need it for subclasses |
2296 | $self->export_to_level(1,$self,@a); # need it for MBF | |
58cde26e | 2297 | |
574bacfe JH |
2298 | # try to load core math lib |
2299 | my @c = split /\s*,\s*/,$CALC; | |
2300 | push @c,'Calc'; # if all fail, try this | |
61f5c3f5 | 2301 | $CALC = ''; # signal error |
574bacfe JH |
2302 | foreach my $lib (@c) |
2303 | { | |
07d34614 | 2304 | next if ($lib || '') eq ''; |
574bacfe JH |
2305 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
2306 | $lib =~ s/\.pm$//; | |
61f5c3f5 | 2307 | if ($] < 5.006) |
574bacfe JH |
2308 | { |
2309 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is | |
2310 | # used in the same script, or eval inside import(). | |
07d34614 T |
2311 | my @parts = split /::/, $lib; # Math::BigInt => Math BigInt |
2312 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm | |
2313 | require File::Spec; | |
2314 | $file = File::Spec->catfile (@parts, $file); | |
2315 | eval { require "$file"; $lib->import( @c ); } | |
574bacfe JH |
2316 | } |
2317 | else | |
2318 | { | |
61f5c3f5 | 2319 | eval "use $lib qw/@c/;"; |
574bacfe | 2320 | } |
bd05a461 | 2321 | $CALC = $lib, last if $@ eq ''; # no error in loading lib? |
574bacfe | 2322 | } |
61f5c3f5 | 2323 | die "Couldn't load any math lib, not even the default" if $CALC eq ''; |
58cde26e JH |
2324 | } |
2325 | ||
574bacfe | 2326 | sub __from_hex |
58cde26e JH |
2327 | { |
2328 | # convert a (ref to) big hex string to BigInt, return undef for error | |
2329 | my $hs = shift; | |
2330 | ||
2331 | my $x = Math::BigInt->bzero(); | |
394e6ffb JH |
2332 | |
2333 | # strip underscores | |
2334 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
2335 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
2336 | ||
58cde26e JH |
2337 | return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
2338 | ||
b22b3e31 | 2339 | my $sign = '+'; $sign = '-' if ($$hs =~ /^-/); |
58cde26e | 2340 | |
b22b3e31 | 2341 | $$hs =~ s/^[+-]//; # strip sign |
0716bf9b | 2342 | if ($CALC->can('_from_hex')) |
58cde26e | 2343 | { |
0716bf9b | 2344 | $x->{value} = $CALC->_from_hex($hs); |
58cde26e | 2345 | } |
0716bf9b | 2346 | else |
58cde26e | 2347 | { |
0716bf9b JH |
2348 | # fallback to pure perl |
2349 | my $mul = Math::BigInt->bzero(); $mul++; | |
2350 | my $x65536 = Math::BigInt->new(65536); | |
2351 | my $len = CORE::length($$hs)-2; | |
2352 | $len = int($len/4); # 4-digit parts, w/o '0x' | |
2353 | my $val; my $i = -4; | |
2354 | while ($len >= 0) | |
2355 | { | |
2356 | $val = substr($$hs,$i,4); | |
b22b3e31 | 2357 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because |
0716bf9b | 2358 | $val = hex($val); # hex does not like wrong chars |
0716bf9b JH |
2359 | $i -= 4; $len --; |
2360 | $x += $mul * $val if $val != 0; | |
2361 | $mul *= $x65536 if $len >= 0; # skip last mul | |
2362 | } | |
58cde26e | 2363 | } |
13a12e00 JH |
2364 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2365 | $x; | |
58cde26e JH |
2366 | } |
2367 | ||
574bacfe | 2368 | sub __from_bin |
58cde26e JH |
2369 | { |
2370 | # convert a (ref to) big binary string to BigInt, return undef for error | |
2371 | my $bs = shift; | |
2372 | ||
2373 | my $x = Math::BigInt->bzero(); | |
394e6ffb JH |
2374 | # strip underscores |
2375 | $$bs =~ s/([01])_([01])/$1$2/g; | |
2376 | $$bs =~ s/([01])_([01])/$1$2/g; | |
b22b3e31 | 2377 | return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/; |
58cde26e | 2378 | |
0716bf9b | 2379 | my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/); |
b22b3e31 | 2380 | $$bs =~ s/^[+-]//; # strip sign |
0716bf9b | 2381 | if ($CALC->can('_from_bin')) |
58cde26e | 2382 | { |
0716bf9b | 2383 | $x->{value} = $CALC->_from_bin($bs); |
58cde26e | 2384 | } |
0716bf9b | 2385 | else |
58cde26e | 2386 | { |
13a12e00 JH |
2387 | my $mul = Math::BigInt->bzero(); $mul++; |
2388 | my $x256 = Math::BigInt->new(256); | |
0716bf9b JH |
2389 | my $len = CORE::length($$bs)-2; |
2390 | $len = int($len/8); # 8-digit parts, w/o '0b' | |
2391 | my $val; my $i = -8; | |
2392 | while ($len >= 0) | |
2393 | { | |
2394 | $val = substr($$bs,$i,8); | |
b22b3e31 PN |
2395 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only |
2396 | #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0 | |
394e6ffb JH |
2397 | # slower: |
2398 | # $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8; | |
2399 | $val = ord(pack('B8',substr('00000000'.$val,-8,8))); | |
0716bf9b JH |
2400 | $i -= 8; $len --; |
2401 | $x += $mul * $val if $val != 0; | |
2402 | $mul *= $x256 if $len >= 0; # skip last mul | |
2403 | } | |
58cde26e | 2404 | } |
13a12e00 JH |
2405 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2406 | $x; | |
58cde26e JH |
2407 | } |
2408 | ||
2409 | sub _split | |
2410 | { | |
2411 | # (ref to num_str) return num_str | |
2412 | # internal, take apart a string and return the pieces | |
dccbb853 | 2413 | # strip leading/trailing whitespace, leading zeros, underscore and reject |
574bacfe | 2414 | # invalid input |
58cde26e JH |
2415 | my $x = shift; |
2416 | ||
574bacfe JH |
2417 | # strip white space at front, also extranous leading zeros |
2418 | $$x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' | |
2419 | $$x =~ s/^\s+//; # but this will | |
58cde26e | 2420 | $$x =~ s/\s+$//g; # strip white space at end |
58cde26e | 2421 | |
574bacfe JH |
2422 | # shortcut, if nothing to split, return early |
2423 | if ($$x =~ /^[+-]?\d+$/) | |
2424 | { | |
2425 | $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; | |
2426 | return (\$sign, $x, \'', \'', \0); | |
2427 | } | |
58cde26e | 2428 | |
574bacfe JH |
2429 | # invalid starting char? |
2430 | return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; | |
58cde26e | 2431 | |
574bacfe JH |
2432 | return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string |
2433 | return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string | |
394e6ffb JH |
2434 | |
2435 | # strip underscores between digits | |
2436 | $$x =~ s/(\d)_(\d)/$1$2/g; | |
2437 | $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 | |
574bacfe | 2438 | |
58cde26e JH |
2439 | # some possible inputs: |
2440 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 | |
2441 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 | |
2442 | ||
027dc388 JH |
2443 | return if $$x =~ /[Ee].*[Ee]/; # more than one E => error |
2444 | ||
58cde26e JH |
2445 | my ($m,$e) = split /[Ee]/,$$x; |
2446 | $e = '0' if !defined $e || $e eq ""; | |
58cde26e JH |
2447 | # sign,value for exponent,mantint,mantfrac |
2448 | my ($es,$ev,$mis,$miv,$mfv); | |
2449 | # valid exponent? | |
2450 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros | |
2451 | { | |
2452 | $es = $1; $ev = $2; | |
58cde26e JH |
2453 | # valid mantissa? |
2454 | return if $m eq '.' || $m eq ''; | |
07d34614 T |
2455 | my ($mi,$mf,$last) = split /\./,$m; |
2456 | return if defined $last; # last defined => 1.2.3 or others | |
58cde26e JH |
2457 | $mi = '0' if !defined $mi; |
2458 | $mi .= '0' if $mi =~ /^[\-\+]?$/; | |
2459 | $mf = '0' if !defined $mf || $mf eq ''; | |
2460 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros | |
2461 | { | |
2462 | $mis = $1||'+'; $miv = $2; | |
58cde26e JH |
2463 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros |
2464 | $mfv = $1; | |
58cde26e JH |
2465 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
2466 | } | |
2467 | } | |
2468 | return; # NaN, not a number | |
2469 | } | |
2470 | ||
58cde26e JH |
2471 | sub as_number |
2472 | { | |
2473 | # an object might be asked to return itself as bigint on certain overloaded | |
2474 | # operations, this does exactly this, so that sub classes can simple inherit | |
2475 | # it or override with their own integer conversion routine | |
2476 | my $self = shift; | |
2477 | ||
17baacb7 | 2478 | $self->copy(); |
58cde26e JH |
2479 | } |
2480 | ||
bd05a461 JH |
2481 | sub as_hex |
2482 | { | |
2483 | # return as hex string, with prefixed 0x | |
2484 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2485 | ||
2486 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2487 | return '0x0' if $x->is_zero(); | |
2488 | ||
2489 | my $es = ''; my $s = ''; | |
2490 | $s = $x->{sign} if $x->{sign} eq '-'; | |
bd05a461 JH |
2491 | if ($CALC->can('_as_hex')) |
2492 | { | |
ee15d750 | 2493 | $es = ${$CALC->_as_hex($x->{value})}; |
bd05a461 JH |
2494 | } |
2495 | else | |
2496 | { | |
2497 | my $x1 = $x->copy()->babs(); my $xr; | |
61f5c3f5 | 2498 | my $x10000 = Math::BigInt->new (0x10000); |
bd05a461 JH |
2499 | while (!$x1->is_zero()) |
2500 | { | |
61f5c3f5 T |
2501 | ($x1, $xr) = bdiv($x1,$x10000); |
2502 | $es .= unpack('h4',pack('v',$xr->numify())); | |
bd05a461 JH |
2503 | } |
2504 | $es = reverse $es; | |
2505 | $es =~ s/^[0]+//; # strip leading zeros | |
ee15d750 | 2506 | $s .= '0x'; |
bd05a461 JH |
2507 | } |
2508 | $s . $es; | |
2509 | } | |
2510 | ||
2511 | sub as_bin | |
2512 | { | |
2513 | # return as binary string, with prefixed 0b | |
2514 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2515 | ||
2516 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2517 | return '0b0' if $x->is_zero(); | |
2518 | ||
2519 | my $es = ''; my $s = ''; | |
2520 | $s = $x->{sign} if $x->{sign} eq '-'; | |
bd05a461 JH |
2521 | if ($CALC->can('_as_bin')) |
2522 | { | |
ee15d750 | 2523 | $es = ${$CALC->_as_bin($x->{value})}; |
bd05a461 JH |
2524 | } |
2525 | else | |
2526 | { | |
2527 | my $x1 = $x->copy()->babs(); my $xr; | |
61f5c3f5 | 2528 | my $x10000 = Math::BigInt->new (0x10000); |
bd05a461 JH |
2529 | while (!$x1->is_zero()) |
2530 | { | |
61f5c3f5 T |
2531 | ($x1, $xr) = bdiv($x1,$x10000); |
2532 | $es .= unpack('b16',pack('v',$xr->numify())); | |
bd05a461 JH |
2533 | } |
2534 | $es = reverse $es; | |
2535 | $es =~ s/^[0]+//; # strip leading zeros | |
ee15d750 | 2536 | $s .= '0b'; |
bd05a461 JH |
2537 | } |
2538 | $s . $es; | |
2539 | } | |
2540 | ||
58cde26e | 2541 | ############################################################################## |
0716bf9b | 2542 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e | 2543 | |
dccbb853 | 2544 | sub __lcm |
58cde26e JH |
2545 | { |
2546 | # (BINT or num_str, BINT or num_str) return BINT | |
2547 | # does modify first argument | |
2548 | # LCM | |
2549 | ||
2550 | my $x = shift; my $ty = shift; | |
2551 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); | |
2552 | return $x * $ty / bgcd($x,$ty); | |
2553 | } | |
2554 | ||
574bacfe | 2555 | sub __gcd |
58cde26e JH |
2556 | { |
2557 | # (BINT or num_str, BINT or num_str) return BINT | |
dccbb853 | 2558 | # does modify both arguments |
58cde26e | 2559 | # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296 |
dccbb853 JH |
2560 | my ($x,$ty) = @_; |
2561 | ||
0716bf9b | 2562 | return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/; |
58cde26e JH |
2563 | |
2564 | while (!$ty->is_zero()) | |
2565 | { | |
2566 | ($x, $ty) = ($ty,bmod($x,$ty)); | |
2567 | } | |
2568 | $x; | |
2569 | } | |
2570 | ||
58cde26e JH |
2571 | ############################################################################### |
2572 | # this method return 0 if the object can be modified, or 1 for not | |
2573 | # We use a fast use constant statement here, to avoid costly calls. Subclasses | |
2574 | # may override it with special code (f.i. Math::BigInt::Constant does so) | |
2575 | ||
0716bf9b | 2576 | sub modify () { 0; } |
e16b8f49 | 2577 | |
a0d0e21e | 2578 | 1; |
a5f75d66 AD |
2579 | __END__ |
2580 | ||
2581 | =head1 NAME | |
2582 | ||
2583 | Math::BigInt - Arbitrary size integer math package | |
2584 | ||
2585 | =head1 SYNOPSIS | |
2586 | ||
2587 | use Math::BigInt; | |
58cde26e JH |
2588 | |
2589 | # Number creation | |
574bacfe JH |
2590 | $x = Math::BigInt->new($str); # defaults to 0 |
2591 | $nan = Math::BigInt->bnan(); # create a NotANumber | |
2592 | $zero = Math::BigInt->bzero(); # create a +0 | |
2593 | $inf = Math::BigInt->binf(); # create a +inf | |
2594 | $inf = Math::BigInt->binf('-'); # create a -inf | |
2595 | $one = Math::BigInt->bone(); # create a +1 | |
2596 | $one = Math::BigInt->bone('-'); # create a -1 | |
58cde26e JH |
2597 | |
2598 | # Testing | |
574bacfe JH |
2599 | $x->is_zero(); # true if arg is +0 |
2600 | $x->is_nan(); # true if arg is NaN | |
0716bf9b JH |
2601 | $x->is_one(); # true if arg is +1 |
2602 | $x->is_one('-'); # true if arg is -1 | |
2603 | $x->is_odd(); # true if odd, false for even | |
2604 | $x->is_even(); # true if even, false for odd | |
2605 | $x->is_positive(); # true if >= 0 | |
2606 | $x->is_negative(); # true if < 0 | |
2607 | $x->is_inf(sign); # true if +inf, or -inf (sign is default '+') | |
b3abae2a | 2608 | $x->is_int(); # true if $x is an integer (not a float) |
0716bf9b | 2609 | |
58cde26e JH |
2610 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
2611 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
2612 | $x->sign(); # return the sign, either +,- or NaN | |
2613 | $x->digit($n); # return the nth digit, counting from right | |
2614 | $x->digit(-$n); # return the nth digit, counting from left | |
2615 | ||
2616 | # The following all modify their first argument: | |
2617 | ||
2618 | # set | |
2619 | $x->bzero(); # set $x to 0 | |
2620 | $x->bnan(); # set $x to NaN | |
574bacfe JH |
2621 | $x->bone(); # set $x to +1 |
2622 | $x->bone('-'); # set $x to -1 | |
b3abae2a JH |
2623 | $x->binf(); # set $x to inf |
2624 | $x->binf('-'); # set $x to -inf | |
58cde26e JH |
2625 | |
2626 | $x->bneg(); # negation | |
2627 | $x->babs(); # absolute value | |
2628 | $x->bnorm(); # normalize (no-op) | |
2629 | $x->bnot(); # two's complement (bit wise not) | |
2630 | $x->binc(); # increment x by 1 | |
2631 | $x->bdec(); # decrement x by 1 | |
2632 | ||
2633 | $x->badd($y); # addition (add $y to $x) | |
2634 | $x->bsub($y); # subtraction (subtract $y from $x) | |
2635 | $x->bmul($y); # multiplication (multiply $x by $y) | |
2636 | $x->bdiv($y); # divide, set $x to quotient | |
2637 | # return (quo,rem) or quo if scalar | |
2638 | ||
2639 | $x->bmod($y); # modulus (x % y) | |
07d34614 T |
2640 | $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod)) |
2641 | $x->bmodinv($mod); # the inverse of $x in the given modulus $mod | |
d614cd8b | 2642 | |
58cde26e JH |
2643 | $x->bpow($y); # power of arguments (x ** y) |
2644 | $x->blsft($y); # left shift | |
2645 | $x->brsft($y); # right shift | |
2646 | $x->blsft($y,$n); # left shift, by base $n (like 10) | |
2647 | $x->brsft($y,$n); # right shift, by base $n (like 10) | |
2648 | ||
2649 | $x->band($y); # bitwise and | |
2650 | $x->bior($y); # bitwise inclusive or | |
2651 | $x->bxor($y); # bitwise exclusive or | |
2652 | $x->bnot(); # bitwise not (two's complement) | |
2653 | ||
2654 | $x->bsqrt(); # calculate square-root | |
b3abae2a | 2655 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
58cde26e JH |
2656 | |
2657 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r | |
2658 | $x->bround($N); # accuracy: preserve $N digits | |
2659 | $x->bfround($N); # round to $Nth digit, no-op for BigInts | |
2660 | ||
2661 | # The following do not modify their arguments in BigInt, but do in BigFloat: | |
2662 | $x->bfloor(); # return integer less or equal than $x | |
2663 | $x->bceil(); # return integer greater or equal than $x | |
2664 | ||
2665 | # The following do not modify their arguments: | |
2666 | ||
dccbb853 JH |
2667 | bgcd(@values); # greatest common divisor (no OO style) |
2668 | blcm(@values); # lowest common multiplicator (no OO style) | |
bd05a461 | 2669 | |
58cde26e | 2670 | $x->length(); # return number of digits in number |
bd05a461 JH |
2671 | ($x,$f) = $x->length(); # length of number and length of fraction part, |
2672 | # latter is always 0 digits long for BigInt's | |
58cde26e JH |
2673 | |
2674 | $x->exponent(); # return exponent as BigInt | |
ee15d750 | 2675 | $x->mantissa(); # return (signed) mantissa as BigInt |
58cde26e | 2676 | $x->parts(); # return (mantissa,exponent) as BigInt |
0716bf9b JH |
2677 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
2678 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) | |
bd05a461 JH |
2679 | |
2680 | # conversation to string | |
2681 | $x->bstr(); # normalized string | |
2682 | $x->bsstr(); # normalized string in scientific notation | |
2683 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x | |
2684 | $x->as_bin(); # as signed binary string with prefixed 0b | |
8f675a64 JH |
2685 | |
2686 | Math::BigInt->config(); # return hash containing configuration/version | |
bd05a461 | 2687 | |
a5f75d66 AD |
2688 | =head1 DESCRIPTION |
2689 | ||
58cde26e JH |
2690 | All operators (inlcuding basic math operations) are overloaded if you |
2691 | declare your big integers as | |
a5f75d66 | 2692 | |
58cde26e | 2693 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 | 2694 | |
58cde26e JH |
2695 | Operations with overloaded operators preserve the arguments which is |
2696 | exactly what you expect. | |
a5f75d66 AD |
2697 | |
2698 | =over 2 | |
2699 | ||
2700 | =item Canonical notation | |
2701 | ||
58cde26e | 2702 | Big integer values are strings of the form C</^[+-]\d+$/> with leading |
a5f75d66 AD |
2703 | zeros suppressed. |
2704 | ||
58cde26e JH |
2705 | '-0' canonical value '-0', normalized '0' |
2706 | ' -123_123_123' canonical value '-123123123' | |
2707 | '1_23_456_7890' canonical value '1234567890' | |
2708 | ||
a5f75d66 AD |
2709 | =item Input |
2710 | ||
58cde26e JH |
2711 | Input values to these routines may be either Math::BigInt objects or |
2712 | strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>. | |
2713 | ||
2714 | You can include one underscore between any two digits. | |
2715 | ||
2716 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. | |
2717 | Non integer values result in NaN. | |
2718 | ||
2719 | Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results | |
2720 | in 'NaN'. | |
2721 | ||
2722 | bnorm() on a BigInt object is now effectively a no-op, since the numbers | |
2723 | are always stored in normalized form. On a string, it creates a BigInt | |
2724 | object. | |
a5f75d66 AD |
2725 | |
2726 | =item Output | |
2727 | ||
58cde26e JH |
2728 | Output values are BigInt objects (normalized), except for bstr(), which |
2729 | returns a string in normalized form. | |
2730 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, | |
2731 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) | |
2732 | return either undef, <0, 0 or >0 and are suited for sort. | |
a5f75d66 AD |
2733 | |
2734 | =back | |
2735 | ||
b3abae2a JH |
2736 | =head1 METHODS |
2737 | ||
2738 | Each of the methods below accepts three additional parameters. These arguments | |
2739 | $A, $P and $R are accuracy, precision and round_mode. Please see more in the | |
2740 | section about ACCURACY and ROUNDIND. | |
2741 | ||
8f675a64 JH |
2742 | =head2 config |
2743 | ||
2744 | use Data::Dumper; | |
2745 | ||
2746 | print Dumper ( Math::BigInt->config() ); | |
2747 | ||
2748 | Returns a hash containing the configuration, e.g. the version number, lib | |
2749 | loaded etc. | |
2750 | ||
13a12e00 JH |
2751 | =head2 accuracy |
2752 | ||
2753 | $x->accuracy(5); # local for $x | |
2754 | $class->accuracy(5); # global for all members of $class | |
2755 | ||
2756 | Set or get the global or local accuracy, aka how many significant digits the | |
2757 | results have. Please see the section about L<ACCURACY AND PRECISION> for | |
2758 | further details. | |
2759 | ||
2760 | Value must be greater than zero. Pass an undef value to disable it: | |
2761 | ||
2762 | $x->accuracy(undef); | |
2763 | Math::BigInt->accuracy(undef); | |
2764 | ||
2765 | Returns the current accuracy. For C<$x->accuracy()> it will return either the | |
2766 | local accuracy, or if not defined, the global. This means the return value | |
2767 | represents the accuracy that will be in effect for $x: | |
2768 | ||
2769 | $y = Math::BigInt->new(1234567); # unrounded | |
2770 | print Math::BigInt->accuracy(4),"\n"; # set 4, print 4 | |
2771 | $x = Math::BigInt->new(123456); # will be automatically rounded | |
2772 | print "$x $y\n"; # '123500 1234567' | |
2773 | print $x->accuracy(),"\n"; # will be 4 | |
2774 | print $y->accuracy(),"\n"; # also 4, since global is 4 | |
2775 | print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5 | |
2776 | print $x->accuracy(),"\n"; # still 4 | |
2777 | print $y->accuracy(),"\n"; # 5, since global is 5 | |
2778 | ||
b3abae2a JH |
2779 | =head2 brsft |
2780 | ||
2781 | $x->brsft($y,$n); | |
2782 | ||
2783 | Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and | |
2784 | 2, but others work, too. | |
2785 | ||
2786 | Right shifting usually amounts to dividing $x by $n ** $y and truncating the | |
2787 | result: | |
2788 | ||
2789 | ||
2790 | $x = Math::BigInt->new(10); | |
2791 | $x->brsft(1); # same as $x >> 1: 5 | |
2792 | $x = Math::BigInt->new(1234); | |
2793 | $x->brsft(2,10); # result 12 | |
2794 | ||
2795 | There is one exception, and that is base 2 with negative $x: | |
2796 | ||
2797 | ||
2798 | $x = Math::BigInt->new(-5); | |
2799 | print $x->brsft(1); | |
2800 | ||
2801 | This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the | |
2802 | result). | |
2803 | ||
2804 | =head2 new | |
2805 | ||
2806 | $x = Math::BigInt->new($str,$A,$P,$R); | |
2807 | ||
2808 | Creates a new BigInt object from a string or another BigInt object. The | |
2809 | input is accepted as decimal, hex (with leading '0x') or binary (with leading | |
2810 | '0b'). | |
2811 | ||
2812 | =head2 bnan | |
2813 | ||
2814 | $x = Math::BigInt->bnan(); | |
2815 | ||
2816 | Creates a new BigInt object representing NaN (Not A Number). | |
2817 | If used on an object, it will set it to NaN: | |
2818 | ||
2819 | $x->bnan(); | |
2820 | ||
2821 | =head2 bzero | |
2822 | ||
2823 | $x = Math::BigInt->bzero(); | |
2824 | ||
2825 | Creates a new BigInt object representing zero. | |
2826 | If used on an object, it will set it to zero: | |
2827 | ||
2828 | $x->bzero(); | |
2829 | ||
2830 | =head2 binf | |
2831 | ||
2832 | $x = Math::BigInt->binf($sign); | |
2833 | ||
2834 | Creates a new BigInt object representing infinity. The optional argument is | |
2835 | either '-' or '+', indicating whether you want infinity or minus infinity. | |
2836 | If used on an object, it will set it to infinity: | |
2837 | ||
2838 | $x->binf(); | |
2839 | $x->binf('-'); | |
2840 | ||
2841 | =head2 bone | |
2842 | ||
2843 | $x = Math::BigInt->binf($sign); | |
2844 | ||
2845 | Creates a new BigInt object representing one. The optional argument is | |
2846 | either '-' or '+', indicating whether you want one or minus one. | |
2847 | If used on an object, it will set it to one: | |
2848 | ||
2849 | $x->bone(); # +1 | |
2850 | $x->bone('-'); # -1 | |
2851 | ||
56b9c951 JH |
2852 | =head2 is_one()/is_zero()/is_nan()/is_inf() |
2853 | ||
b3abae2a JH |
2854 | |
2855 | $x->is_zero(); # true if arg is +0 | |
2856 | $x->is_nan(); # true if arg is NaN | |
2857 | $x->is_one(); # true if arg is +1 | |
2858 | $x->is_one('-'); # true if arg is -1 | |
b3abae2a JH |
2859 | $x->is_inf(); # true if +inf |
2860 | $x->is_inf('-'); # true if -inf (sign is default '+') | |
56b9c951 JH |
2861 | |
2862 | These methods all test the BigInt for beeing one specific value and return | |
2863 | true or false depending on the input. These are faster than doing something | |
2864 | like: | |
2865 | ||
2866 | if ($x == 0) | |
2867 | ||
2868 | =head2 is_positive()/is_negative() | |
2869 | ||
2870 | $x->is_positive(); # true if >= 0 | |
2871 | $x->is_negative(); # true if < 0 | |
2872 | ||
2873 | The methods return true if the argument is positive or negative, respectively. | |
2874 | C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and | |
2875 | C<-inf> is negative. A C<zero> is positive. | |
2876 | ||
2877 | These methods are only testing the sign, and not the value. | |
2878 | ||
2879 | =head2 is_odd()/is_even()/is_int() | |
2880 | ||
2881 | $x->is_odd(); # true if odd, false for even | |
2882 | $x->is_even(); # true if even, false for odd | |
b3abae2a JH |
2883 | $x->is_int(); # true if $x is an integer |
2884 | ||
56b9c951 JH |
2885 | The return true when the argument satisfies the condition. C<NaN>, C<+inf>, |
2886 | C<-inf> are not integers and are neither odd nor even. | |
b3abae2a JH |
2887 | |
2888 | =head2 bcmp | |
2889 | ||
56b9c951 JH |
2890 | $x->bcmp($y); |
2891 | ||
2892 | Compares $x with $y and takes the sign into account. | |
2893 | Returns -1, 0, 1 or undef. | |
b3abae2a JH |
2894 | |
2895 | =head2 bacmp | |
2896 | ||
56b9c951 JH |
2897 | $x->bacmp($y); |
2898 | ||
2899 | Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef. | |
b3abae2a JH |
2900 | |
2901 | =head2 sign | |
2902 | ||
56b9c951 JH |
2903 | $x->sign(); |
2904 | ||
2905 | Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN. | |
b3abae2a JH |
2906 | |
2907 | =head2 bcmp | |
2908 | ||
2909 | $x->digit($n); # return the nth digit, counting from right | |
2910 | ||
2911 | =head2 bneg | |
2912 | ||
2913 | $x->bneg(); | |
2914 | ||
2915 | Negate the number, e.g. change the sign between '+' and '-', or between '+inf' | |
2916 | and '-inf', respectively. Does nothing for NaN or zero. | |
2917 | ||
2918 | =head2 babs | |
2919 | ||
2920 | $x->babs(); | |
2921 | ||
2922 | Set the number to it's absolute value, e.g. change the sign from '-' to '+' | |
2923 | and from '-inf' to '+inf', respectively. Does nothing for NaN or positive | |
2924 | numbers. | |
2925 | ||
2926 | =head2 bnorm | |
2927 | ||
2928 | $x->bnorm(); # normalize (no-op) | |
2929 | ||
2930 | =head2 bnot | |
2931 | ||
2932 | $x->bnot(); # two's complement (bit wise not) | |
2933 | ||
2934 | =head2 binc | |
2935 | ||
2936 | $x->binc(); # increment x by 1 | |
2937 | ||
2938 | =head2 bdec | |
2939 | ||
2940 | $x->bdec(); # decrement x by 1 | |
2941 | ||
2942 | =head2 badd | |
2943 | ||
2944 | $x->badd($y); # addition (add $y to $x) | |
2945 | ||
2946 | =head2 bsub | |
2947 | ||
2948 | $x->bsub($y); # subtraction (subtract $y from $x) | |
2949 | ||
2950 | =head2 bmul | |
2951 | ||
2952 | $x->bmul($y); # multiplication (multiply $x by $y) | |
2953 | ||
2954 | =head2 bdiv | |
2955 | ||
2956 | $x->bdiv($y); # divide, set $x to quotient | |
2957 | # return (quo,rem) or quo if scalar | |
2958 | ||
2959 | =head2 bmod | |
2960 | ||
2961 | $x->bmod($y); # modulus (x % y) | |
2962 | ||
d614cd8b JH |
2963 | =head2 bmodinv |
2964 | ||
d614cd8b JH |
2965 | bmodinv($num,$mod); # modular inverse (no OO style) |
2966 | ||
2967 | Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is | |
2968 | returned unless C<$num> is relatively prime to C<$mod>, i.e. unless | |
2969 | C<bgcd($num, $mod)==1>. | |
2970 | ||
2971 | =head2 bmodpow | |
2972 | ||
d614cd8b JH |
2973 | bmodpow($num,$exp,$mod); # modular exponentation ($num**$exp % $mod) |
2974 | ||
2975 | Returns the value of C<$num> taken to the power C<$exp> in the modulus | |
2976 | C<$mod> using binary exponentation. C<bmodpow> is far superior to | |
2977 | writing | |
2978 | ||
2979 | $num ** $exp % $mod | |
2980 | ||
2981 | because C<bmodpow> is much faster--it reduces internal variables into | |
2982 | the modulus whenever possible, so it operates on smaller numbers. | |
2983 | ||
2984 | C<bmodpow> also supports negative exponents. | |
2985 | ||
2986 | bmodpow($num, -1, $mod) | |
2987 | ||
2988 | is exactly equivalent to | |
2989 | ||
2990 | bmodinv($num, $mod) | |
2991 | ||
b3abae2a JH |
2992 | =head2 bpow |
2993 | ||
2994 | $x->bpow($y); # power of arguments (x ** y) | |
2995 | ||
2996 | =head2 blsft | |
2997 | ||
2998 | $x->blsft($y); # left shift | |
2999 | $x->blsft($y,$n); # left shift, by base $n (like 10) | |
3000 | ||
3001 | =head2 brsft | |
3002 | ||
3003 | $x->brsft($y); # right shift | |
3004 | $x->brsft($y,$n); # right shift, by base $n (like 10) | |
3005 | ||
3006 | =head2 band | |
3007 | ||
3008 | $x->band($y); # bitwise and | |
3009 | ||
3010 | =head2 bior | |
3011 | ||
3012 | $x->bior($y); # bitwise inclusive or | |
3013 | ||
3014 | =head2 bxor | |
3015 | ||
3016 | $x->bxor($y); # bitwise exclusive or | |
3017 | ||
3018 | =head2 bnot | |
3019 | ||
3020 | $x->bnot(); # bitwise not (two's complement) | |
3021 | ||
3022 | =head2 bsqrt | |
3023 | ||
3024 | $x->bsqrt(); # calculate square-root | |
3025 | ||
3026 | =head2 bfac | |
3027 | ||
3028 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) | |
3029 | ||
3030 | =head2 round | |
3031 | ||
3032 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r | |
3033 | ||
3034 | =head2 bround | |
3035 | ||
3036 | $x->bround($N); # accuracy: preserve $N digits | |
3037 | ||
3038 | =head2 bfround | |
3039 | ||
3040 | $x->bfround($N); # round to $Nth digit, no-op for BigInts | |
3041 | ||
3042 | =head2 bfloor | |
3043 | ||
3044 | $x->bfloor(); | |
3045 | ||
3046 | Set $x to the integer less or equal than $x. This is a no-op in BigInt, but | |
3047 | does change $x in BigFloat. | |
3048 | ||
3049 | =head2 bceil | |
3050 | ||
3051 | $x->bceil(); | |
3052 | ||
3053 | Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but | |
3054 | does change $x in BigFloat. | |
3055 | ||
3056 | =head2 bgcd | |
3057 | ||
3058 | bgcd(@values); # greatest common divisor (no OO style) | |
3059 | ||
3060 | =head2 blcm | |
3061 | ||
3062 | blcm(@values); # lowest common multiplicator (no OO style) | |
3063 | ||
3064 | head2 length | |
3065 | ||
3066 | $x->length(); | |
3067 | ($xl,$fl) = $x->length(); | |
3068 | ||
3069 | Returns the number of digits in the decimal representation of the number. | |
3070 | In list context, returns the length of the integer and fraction part. For | |
3071 | BigInt's, the length of the fraction part will always be 0. | |
3072 | ||
3073 | =head2 exponent | |
3074 | ||
3075 | $x->exponent(); | |
3076 | ||
3077 | Return the exponent of $x as BigInt. | |
3078 | ||
3079 | =head2 mantissa | |
3080 | ||
3081 | $x->mantissa(); | |
3082 | ||
3083 | Return the signed mantissa of $x as BigInt. | |
3084 | ||
3085 | =head2 parts | |
3086 | ||
3087 | $x->parts(); # return (mantissa,exponent) as BigInt | |
3088 | ||
3089 | =head2 copy | |
3090 | ||
3091 | $x->copy(); # make a true copy of $x (unlike $y = $x;) | |
3092 | ||
3093 | =head2 as_number | |
3094 | ||
3095 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) | |
3096 | ||
3097 | =head2 bsrt | |
3098 | ||
3099 | $x->bstr(); # normalized string | |
3100 | ||
3101 | =head2 bsstr | |
3102 | ||
3103 | $x->bsstr(); # normalized string in scientific notation | |
3104 | ||
3105 | =head2 as_hex | |
3106 | ||
3107 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x | |
3108 | ||
3109 | =head2 as_bin | |
3110 | ||
3111 | $x->as_bin(); # as signed binary string with prefixed 0b | |
3112 | ||
0716bf9b JH |
3113 | =head1 ACCURACY and PRECISION |
3114 | ||
b22b3e31 | 3115 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b | 3116 | accuracy and precision based rounding, both automatically after every |
b22b3e31 | 3117 | operation as well as manually. |
0716bf9b JH |
3118 | |
3119 | This section describes the accuracy/precision handling in Math::Big* as it | |
b22b3e31 | 3120 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b JH |
3121 | abbreviations. |
3122 | ||
3123 | Not yet implemented things (but with correct description) are marked with '!', | |
3124 | things that need to be answered are marked with '?'. | |
3125 | ||
3126 | In the next paragraph follows a short description of terms used here (because | |
574bacfe | 3127 | these may differ from terms used by others people or documentation). |
0716bf9b | 3128 | |
b22b3e31 | 3129 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b JH |
3130 | precision), F (fallback) and R (rounding mode) will be used. |
3131 | ||
3132 | =head2 Precision P | |
3133 | ||
3134 | A fixed number of digits before (positive) or after (negative) | |
b22b3e31 PN |
3135 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
3136 | integer like 123 (or 120). A precision of 2 means two digits to the left | |
3137 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that | |
3138 | numbers with zeros before the decimal point may have different precisions, | |
3139 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value | |
3140 | was). It could also have p < 0, when the digits after the decimal point | |
3141 | are zero. | |
0716bf9b | 3142 | |
574bacfe JH |
3143 | The string output (of floating point numbers) will be padded with zeros: |
3144 | ||
3145 | Initial value P A Result String | |
3146 | ------------------------------------------------------------ | |
3147 | 1234.01 -3 1000 1000 | |
3148 | 1234 -2 1200 1200 | |
3149 | 1234.5 -1 1230 1230 | |
3150 | 1234.001 1 1234 1234.0 | |
3151 | 1234.01 0 1234 1234 | |
3152 | 1234.01 2 1234.01 1234.01 | |
3153 | 1234.01 5 1234.01 1234.01000 | |
3154 | ||
3155 | For BigInts, no padding occurs. | |
0716bf9b JH |
3156 | |
3157 | =head2 Accuracy A | |
3158 | ||
3159 | Number of significant digits. Leading zeros are not counted. A | |
3160 | number may have an accuracy greater than the non-zero digits | |
b22b3e31 PN |
3161 | when there are zeros in it or trailing zeros. For example, 123.456 has |
3162 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. | |
0716bf9b | 3163 | |
574bacfe JH |
3164 | The string output (of floating point numbers) will be padded with zeros: |
3165 | ||
3166 | Initial value P A Result String | |
3167 | ------------------------------------------------------------ | |
3168 | 1234.01 3 1230 1230 | |
3169 | 1234.01 6 1234.01 1234.01 | |
3170 | 1234.1 8 1234.1 1234.1000 | |
3171 | ||
3172 | For BigInts, no padding occurs. | |
3173 | ||
0716bf9b | 3174 | =head2 Fallback F |
a5f75d66 | 3175 | |
574bacfe JH |
3176 | When both A and P are undefined, this is used as a fallback accuracy when |
3177 | dividing numbers. | |
0716bf9b JH |
3178 | |
3179 | =head2 Rounding mode R | |
3180 | ||
3181 | When rounding a number, different 'styles' or 'kinds' | |
3182 | of rounding are possible. (Note that random rounding, as in | |
3183 | Math::Round, is not implemented.) | |
58cde26e JH |
3184 | |
3185 | =over 2 | |
a5f75d66 | 3186 | |
0716bf9b JH |
3187 | =item 'trunc' |
3188 | ||
3189 | truncation invariably removes all digits following the | |
3190 | rounding place, replacing them with zeros. Thus, 987.65 rounded | |
b22b3e31 | 3191 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b | 3192 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 | 3193 | decimal point (P=-2) becomes 123.46. |
0716bf9b JH |
3194 | |
3195 | All other implemented styles of rounding attempt to round to the | |
3196 | "nearest digit." If the digit D immediately to the right of the | |
3197 | rounding place (skipping the decimal point) is greater than 5, the | |
3198 | number is incremented at the rounding place (possibly causing a | |
3199 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds | |
3200 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly | |
3201 | truncated at the rounding place: e.g. when rounding to units, 0.4 | |
3202 | rounds to 0, and -19.4 rounds to -19. | |
3203 | ||
3204 | However the results of other styles of rounding differ if the | |
3205 | digit immediately to the right of the rounding place (skipping the | |
3206 | decimal point) is 5 and if there are no digits, or no digits other | |
3207 | than 0, after that 5. In such cases: | |
3208 | ||
3209 | =item 'even' | |
3210 | ||
3211 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 | |
3212 | if it is not already. E.g., when rounding to the first sigdig, 0.45 | |
3213 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. | |
3214 | ||
3215 | =item 'odd' | |
3216 | ||
3217 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if | |
3218 | it is not already. E.g., when rounding to the first sigdig, 0.45 | |
3219 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. | |
3220 | ||
3221 | =item '+inf' | |
3222 | ||
3223 | round to plus infinity, i.e. always round up. E.g., when | |
3224 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, | |
b22b3e31 | 3225 | and 0.4501 also becomes 0.5. |
0716bf9b JH |
3226 | |
3227 | =item '-inf' | |
3228 | ||
3229 | round to minus infinity, i.e. always round down. E.g., when | |
3230 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, | |
3231 | but 0.4501 becomes 0.5. | |
3232 | ||
3233 | =item 'zero' | |
3234 | ||
3235 | round to zero, i.e. positive numbers down, negative ones up. | |
3236 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 | |
3237 | becomes -0.5, but 0.4501 becomes 0.5. | |
3238 | ||
3239 | =back | |
3240 | ||
3241 | The handling of A & P in MBI/MBF (the old core code shipped with Perl | |
3242 | versions <= 5.7.2) is like this: | |
3243 | ||
3244 | =over 2 | |
a5f75d66 | 3245 | |
0716bf9b JH |
3246 | =item Precision |
3247 | ||
b22b3e31 PN |
3248 | * ffround($p) is able to round to $p number of digits after the decimal |
3249 | point | |
0716bf9b JH |
3250 | * otherwise P is unused |
3251 | ||
3252 | =item Accuracy (significant digits) | |
3253 | ||
3254 | * fround($a) rounds to $a significant digits | |
3255 | * only fdiv() and fsqrt() take A as (optional) paramater | |
b22b3e31 | 3256 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b JH |
3257 | of digits |
3258 | + rounding/truncating is only done when explicitly calling one of fround | |
3259 | or ffround, and never for BigInt (not implemented) | |
b22b3e31 | 3260 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b JH |
3261 | * the documentation and the comment in the code indicate two different ways |
3262 | on how fdiv() determines the maximum number of digits it should calculate, | |
3263 | and the actual code does yet another thing | |
3264 | POD: | |
3265 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) | |
3266 | Comment: | |
3267 | result has at most max(scale, length(dividend), length(divisor)) digits | |
3268 | Actual code: | |
3269 | scale = max(scale, length(dividend)-1,length(divisor)-1); | |
3270 | scale += length(divisior) - length(dividend); | |
b22b3e31 | 3271 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b JH |
3272 | Actually, the 'difference' added to the scale is calculated from the |
3273 | number of "significant digits" in dividend and divisor, which is derived | |
3274 | by looking at the length of the mantissa. Which is wrong, since it includes | |
3275 | the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups | |
3276 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange | |
3277 | assumption that 124 has 3 significant digits, while 120/7 will get you | |
3278 | '17', not '17.1' since 120 is thought to have 2 significant digits. | |
dccbb853 | 3279 | The rounding after the division then uses the remainder and $y to determine |
0716bf9b | 3280 | wether it must round up or down. |
b22b3e31 PN |
3281 | ? I have no idea which is the right way. That's why I used a slightly more |
3282 | ? simple scheme and tweaked the few failing testcases to match it. | |
58cde26e | 3283 | |
0716bf9b | 3284 | =back |
5dc6f178 | 3285 | |
0716bf9b | 3286 | This is how it works now: |
5dc6f178 | 3287 | |
0716bf9b | 3288 | =over 2 |
5dc6f178 | 3289 | |
0716bf9b JH |
3290 | =item Setting/Accessing |
3291 | ||
b3abae2a JH |
3292 | * You can set the A global via Math::BigInt->accuracy() or |
3293 | Math::BigFloat->accuracy() or whatever class you are using. | |
3294 | * You can also set P globally by using Math::SomeClass->precision() likewise. | |
0716bf9b | 3295 | * Globals are classwide, and not inherited by subclasses. |
b3abae2a JH |
3296 | * to undefine A, use Math::SomeCLass->accuracy(undef); |
3297 | * to undefine P, use Math::SomeClass->precision(undef); | |
3298 | * Setting Math::SomeClass->accuracy() clears automatically | |
3299 | Math::SomeClass->precision(), and vice versa. | |
0716bf9b | 3300 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 PN |
3301 | * If P is negative, this means round to the P'th place to the right of the |
3302 | decimal point; positive values mean to the left of the decimal point. | |
3303 | P of 0 means round to integer. | |
b3abae2a JH |
3304 | * to find out the current global A, take Math::SomeClass->accuracy() |
3305 | * to find out the current global P, take Math::SomeClass->precision() | |
3306 | * use $x->accuracy() respective $x->precision() for the local setting of $x. | |
3307 | * Please note that $x->accuracy() respecive $x->precision() fall back to the | |
3308 | defined globals, when $x's A or P is not set. | |
0716bf9b JH |
3309 | |
3310 | =item Creating numbers | |
3311 | ||
b3abae2a JH |
3312 | * When you create a number, you can give it's desired A or P via: |
3313 | $x = Math::BigInt->new($number,$A,$P); | |
3314 | * Only one of A or P can be defined, otherwise the result is NaN | |
3315 | * If no A or P is give ($x = Math::BigInt->new($number) form), then the | |
3316 | globals (if set) will be used. Thus changing the global defaults later on | |
b22b3e31 | 3317 | will not change the A or P of previously created numbers (i.e., A and P of |
b3abae2a JH |
3318 | $x will be what was in effect when $x was created) |
3319 | * If given undef for A and P, B<no> rounding will occur, and the globals will | |
3320 | B<not> be used. This is used by subclasses to create numbers without | |
3321 | suffering rounding in the parent. Thus a subclass is able to have it's own | |
3322 | globals enforced upon creation of a number by using | |
3323 | $x = Math::BigInt->new($number,undef,undef): | |
3324 | ||
3325 | use Math::Bigint::SomeSubclass; | |
3326 | use Math::BigInt; | |
3327 | ||
3328 | Math::BigInt->accuracy(2); | |
3329 | Math::BigInt::SomeSubClass->accuracy(3); | |
3330 | $x = Math::BigInt::SomeSubClass->new(1234); | |
3331 | ||
3332 | $x is now 1230, and not 1200. A subclass might choose to implement | |
3333 | this otherwise, e.g. falling back to the parent's A and P. | |
0716bf9b JH |
3334 | |
3335 | =item Usage | |
3336 | ||
b22b3e31 | 3337 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b | 3338 | operation according to the rules below |
b22b3e31 PN |
3339 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
3340 | after the decimal point | |
574bacfe JH |
3341 | * Math::BigFloat uses Math::BigInts internally, but setting A or P inside |
3342 | Math::BigInt as globals should not tamper with the parts of a BigFloat. | |
3343 | Thus a flag is used to mark all Math::BigFloat numbers as 'never round' | |
0716bf9b JH |
3344 | |
3345 | =item Precedence | |
3346 | ||
b22b3e31 PN |
3347 | * It only makes sense that a number has only one of A or P at a time. |
3348 | Since you can set/get both A and P, there is a rule that will practically | |
3349 | enforce only A or P to be in effect at a time, even if both are set. | |
3350 | This is called precedence. | |
b3abae2a JH |
3351 | * If two objects are involved in an operation, and one of them has A in |
3352 | effect, and the other P, this results in an error (NaN). | |
0716bf9b | 3353 | * A takes precendence over P (Hint: A comes before P). If A is defined, it |
b22b3e31 PN |
3354 | is used, otherwise P is used. If neither of them is defined, nothing is |
3355 | used, i.e. the result will have as many digits as it can (with an | |
3356 | exception for fdiv/fsqrt) and will not be rounded. | |
3357 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of | |
3358 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. | |
3359 | If either the dividend's or the divisor's mantissa has more digits than | |
3360 | the value of F, the higher value will be used instead of F. | |
3361 | This is to limit the digits (A) of the result (just consider what would | |
3362 | happen with unlimited A and P in the case of 1/3 :-) | |
b3abae2a | 3363 | * fdiv will calculate (at least) 4 more digits than required (determined by |
0716bf9b | 3364 | A, P or F), and, if F is not used, round the result |
b22b3e31 | 3365 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe | 3366 | or P of 5, but this can not be helped - or can it?) |
b22b3e31 | 3367 | * Thus you can have the math done by on Math::Big* class in three modes: |
0716bf9b JH |
3368 | + never round (this is the default): |
3369 | This is done by setting A and P to undef. No math operation | |
b22b3e31 | 3370 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
0716bf9b | 3371 | against overflows. You must explicitely call bround(), bfround() or |
b22b3e31 PN |
3372 | round() (the latter with parameters). |
3373 | Note: Once you have rounded a number, the settings will 'stick' on it | |
3374 | and 'infect' all other numbers engaged in math operations with it, since | |
0716bf9b JH |
3375 | local settings have the highest precedence. So, to get SaferRound[tm], |
3376 | use a copy() before rounding like this: | |
3377 | ||
3378 | $x = Math::BigFloat->new(12.34); | |
3379 | $y = Math::BigFloat->new(98.76); | |
3380 | $z = $x * $y; # 1218.6984 | |
3381 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) | |
3382 | $z = $x * $y; # still 1218.6984, without | |
3383 | # copy would have been 1210! | |
3384 | ||
3385 | + round after each op: | |
b22b3e31 PN |
3386 | After each single operation (except for testing like is_zero()), the |
3387 | method round() is called and the result is rounded appropriately. By | |
0716bf9b | 3388 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 PN |
3389 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
3390 | and P to -2, globally. | |
0716bf9b | 3391 | |
b22b3e31 PN |
3392 | ?Maybe an extra option that forbids local A & P settings would be in order, |
3393 | ?so that intermediate rounding does not 'poison' further math? | |
0716bf9b JH |
3394 | |
3395 | =item Overriding globals | |
3396 | ||
3397 | * you will be able to give A, P and R as an argument to all the calculation | |
b22b3e31 | 3398 | routines; the second parameter is A, the third one is P, and the fourth is |
b3abae2a | 3399 | R (shift right by one for binary operations like badd). P is used only if |
b22b3e31 PN |
3400 | the first parameter (A) is undefined. These three parameters override the |
3401 | globals in the order detailed as follows, i.e. the first defined value | |
0716bf9b | 3402 | wins: |
b22b3e31 | 3403 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b JH |
3404 | + parameter A |
3405 | + parameter P | |
3406 | + local A (if defined on both of the operands: smaller one is taken) | |
b3abae2a | 3407 | + local P (if defined on both of the operands: bigger one is taken) |
0716bf9b JH |
3408 | + global A |
3409 | + global P | |
3410 | + global F | |
b22b3e31 | 3411 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b JH |
3412 | arguments (A and P) instead of one |
3413 | ||
3414 | =item Local settings | |
3415 | ||
3416 | * You can set A and P locally by using $x->accuracy() and $x->precision() | |
3417 | and thus force different A and P for different objects/numbers. | |
b22b3e31 | 3418 | * Setting A or P this way immediately rounds $x to the new value. |
b3abae2a | 3419 | * $x->accuracy() clears $x->precision(), and vice versa. |
0716bf9b JH |
3420 | |
3421 | =item Rounding | |
3422 | ||
b22b3e31 | 3423 | * the rounding routines will use the respective global or local settings. |
0716bf9b JH |
3424 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
3425 | is for precision | |
3426 | * the two rounding functions take as the second parameter one of the | |
3427 | following rounding modes (R): | |
3428 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' | |
3429 | * you can set and get the global R by using Math::SomeClass->round_mode() | |
ee15d750 | 3430 | or by setting $Math::SomeClass::round_mode |
0716bf9b | 3431 | * after each operation, $result->round() is called, and the result may |
b22b3e31 PN |
3432 | eventually be rounded (that is, if A or P were set either locally, |
3433 | globally or as parameter to the operation) | |
ee15d750 | 3434 | * to manually round a number, call $x->round($A,$P,$round_mode); |
b22b3e31 | 3435 | this will round the number by using the appropriate rounding function |
0716bf9b | 3436 | and then normalize it. |
b22b3e31 | 3437 | * rounding modifies the local settings of the number: |
0716bf9b JH |
3438 | |
3439 | $x = Math::BigFloat->new(123.456); | |
3440 | $x->accuracy(5); | |
3441 | $x->bround(4); | |
3442 | ||
3443 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() | |
3444 | will be 4 from now on. | |
3445 | ||
3446 | =item Default values | |
3447 | ||
3448 | * R: 'even' | |
3449 | * F: 40 | |
3450 | * A: undef | |
3451 | * P: undef | |
3452 | ||
3453 | =item Remarks | |
3454 | ||
3455 | * The defaults are set up so that the new code gives the same results as | |
3456 | the old code (except in a few cases on fdiv): | |
3457 | + Both A and P are undefined and thus will not be used for rounding | |
3458 | after each operation. | |
3459 | + round() is thus a no-op, unless given extra parameters A and P | |
58cde26e JH |
3460 | |
3461 | =back | |
3462 | ||
0716bf9b JH |
3463 | =head1 INTERNALS |
3464 | ||
574bacfe JH |
3465 | The actual numbers are stored as unsigned big integers (with seperate sign). |
3466 | You should neither care about nor depend on the internal representation; it | |
3467 | might change without notice. Use only method calls like C<< $x->sign(); >> | |
3468 | instead relying on the internal hash keys like in C<< $x->{sign}; >>. | |
3469 | ||
3470 | =head2 MATH LIBRARY | |
58cde26e | 3471 | |
574bacfe JH |
3472 | Math with the numbers is done (by default) by a module called |
3473 | Math::BigInt::Calc. This is equivalent to saying: | |
3474 | ||
3475 | use Math::BigInt lib => 'Calc'; | |
58cde26e | 3476 | |
0716bf9b | 3477 | You can change this by using: |
58cde26e | 3478 | |
0716bf9b | 3479 | use Math::BigInt lib => 'BitVect'; |
58cde26e | 3480 | |
574bacfe JH |
3481 | The following would first try to find Math::BigInt::Foo, then |
3482 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
0716bf9b | 3483 | |
574bacfe | 3484 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
58cde26e | 3485 | |
574bacfe | 3486 | Calc.pm uses as internal format an array of elements of some decimal base |
b3abae2a JH |
3487 | (usually 1e5 or 1e7) with the least significant digit first, while BitVect.pm |
3488 | uses a bit vector of base 2, most significant bit first. Other modules might | |
3489 | use even different means of representing the numbers. See the respective | |
3490 | module documentation for further details. | |
58cde26e | 3491 | |
574bacfe JH |
3492 | =head2 SIGN |
3493 | ||
3494 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. | |
3495 | ||
3496 | A sign of 'NaN' is used to represent the result when input arguments are not | |
3497 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively | |
3498 | minus infinity. You will get '+inf' when dividing a positive number by 0, and | |
3499 | '-inf' when dividing any negative number by 0. | |
58cde26e JH |
3500 | |
3501 | =head2 mantissa(), exponent() and parts() | |
3502 | ||
3503 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such | |
3504 | that: | |
3505 | ||
3506 | $m = $x->mantissa(); | |
3507 | $e = $x->exponent(); | |
3508 | $y = $m * ( 10 ** $e ); | |
3509 | print "ok\n" if $x == $y; | |
3510 | ||
b22b3e31 PN |
3511 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
3512 | in one go. Both the returned mantissa and exponent have a sign. | |
58cde26e | 3513 | |
574bacfe JH |
3514 | Currently, for BigInts C<$e> will be always 0, except for NaN, +inf and -inf, |
3515 | where it will be NaN; and for $x == 0, where it will be 1 | |
3516 | (to be compatible with Math::BigFloat's internal representation of a zero as | |
3517 | C<0E1>). | |
58cde26e JH |
3518 | |
3519 | C<$m> will always be a copy of the original number. The relation between $e | |
b22b3e31 | 3520 | and $m might change in the future, but will always be equivalent in a |
0716bf9b JH |
3521 | numerical sense, e.g. $m might get minimized. |
3522 | ||
58cde26e JH |
3523 | =head1 EXAMPLES |
3524 | ||
394e6ffb | 3525 | use Math::BigInt; |
574bacfe JH |
3526 | |
3527 | sub bint { Math::BigInt->new(shift); } | |
3528 | ||
394e6ffb | 3529 | $x = Math::BigInt->bstr("1234") # string "1234" |
58cde26e | 3530 | $x = "$x"; # same as bstr() |
58cde26e JH |
3531 | $x = Math::BigInt->bneg("1234"); # Bigint "-1234" |
3532 | $x = Math::BigInt->babs("-12345"); # Bigint "12345" | |
3533 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" | |
3534 | $x = bint(1) + bint(2); # BigInt "3" | |
3535 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") | |
3536 | $x = bint(1); # BigInt "1" | |
3537 | $x = $x + 5 / 2; # BigInt "3" | |
3538 | $x = $x ** 3; # BigInt "27" | |
3539 | $x *= 2; # BigInt "54" | |
394e6ffb | 3540 | $x = Math::BigInt->new(0); # BigInt "0" |
58cde26e JH |
3541 | $x--; # BigInt "-1" |
3542 | $x = Math::BigInt->badd(4,5) # BigInt "9" | |
58cde26e | 3543 | print $x->bsstr(); # 9e+0 |
a5f75d66 | 3544 | |
0716bf9b JH |
3545 | Examples for rounding: |
3546 | ||
3547 | use Math::BigFloat; | |
3548 | use Test; | |
3549 | ||
3550 | $x = Math::BigFloat->new(123.4567); | |
3551 | $y = Math::BigFloat->new(123.456789); | |
394e6ffb | 3552 | Math::BigFloat->accuracy(4); # no more A than 4 |
0716bf9b JH |
3553 | |
3554 | ok ($x->copy()->fround(),123.4); # even rounding | |
3555 | print $x->copy()->fround(),"\n"; # 123.4 | |
3556 | Math::BigFloat->round_mode('odd'); # round to odd | |
3557 | print $x->copy()->fround(),"\n"; # 123.5 | |
394e6ffb | 3558 | Math::BigFloat->accuracy(5); # no more A than 5 |
0716bf9b JH |
3559 | Math::BigFloat->round_mode('odd'); # round to odd |
3560 | print $x->copy()->fround(),"\n"; # 123.46 | |
3561 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 | |
3562 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 | |
3563 | ||
394e6ffb JH |
3564 | Math::BigFloat->accuracy(undef); # A not important now |
3565 | Math::BigFloat->precision(2); # P important | |
3566 | print $x->copy()->bnorm(),"\n"; # 123.46 | |
3567 | print $x->copy()->fround(),"\n"; # 123.46 | |
0716bf9b | 3568 | |
bd05a461 JH |
3569 | Examples for converting: |
3570 | ||
3571 | my $x = Math::BigInt->new('0b1'.'01' x 123); | |
3572 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; | |
3573 | ||
b3ac6de7 IZ |
3574 | =head1 Autocreating constants |
3575 | ||
56b9c951 JH |
3576 | After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal |
3577 | and binary constants in the given scope are converted to C<Math::BigInt>. | |
3578 | This conversion happens at compile time. | |
b3ac6de7 | 3579 | |
b22b3e31 | 3580 | In particular, |
b3ac6de7 | 3581 | |
58cde26e JH |
3582 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
3583 | ||
56b9c951 | 3584 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b | 3585 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e JH |
3586 | |
3587 | Please note that strings and floating point constants are not affected, | |
3588 | so that | |
3589 | ||
3590 | use Math::BigInt qw/:constant/; | |
3591 | ||
3592 | $x = 1234567890123456789012345678901234567890 | |
3593 | + 123456789123456789; | |
b22b3e31 | 3594 | $y = '1234567890123456789012345678901234567890' |
58cde26e | 3595 | + '123456789123456789'; |
b3ac6de7 | 3596 | |
b22b3e31 | 3597 | do not work. You need an explicit Math::BigInt->new() around one of the |
394e6ffb JH |
3598 | operands. You should also quote large constants to protect loss of precision: |
3599 | ||
3600 | use Math::Bigint; | |
3601 | ||
3602 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); | |
3603 | ||
3604 | Without the quotes Perl would convert the large number to a floating point | |
3605 | constant at compile time and then hand the result to BigInt, which results in | |
3606 | an truncated result or a NaN. | |
58cde26e | 3607 | |
56b9c951 JH |
3608 | This also applies to integers that look like floating point constants: |
3609 | ||
3610 | use Math::BigInt ':constant'; | |
3611 | ||
3612 | print ref(123e2),"\n"; | |
3613 | print ref(123.2e2),"\n"; | |
3614 | ||
3615 | will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat> | |
3616 | to get this to work. | |
3617 | ||
58cde26e JH |
3618 | =head1 PERFORMANCE |
3619 | ||
3620 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x | |
3621 | must be made in the second case. For long numbers, the copy can eat up to 20% | |
b22b3e31 | 3622 | of the work (in the case of addition/subtraction, less for |
58cde26e JH |
3623 | multiplication/division). If $y is very small compared to $x, the form |
3624 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes | |
3625 | more time then the actual addition. | |
3626 | ||
b22b3e31 | 3627 | With a technique called copy-on-write, the cost of copying with overload could |
394e6ffb JH |
3628 | be minimized or even completely avoided. A test implementation of COW did show |
3629 | performance gains for overloaded math, but introduced a performance loss due | |
3630 | to a constant overhead for all other operatons. | |
3631 | ||
3632 | The rewritten version of this module is slower on certain operations, like | |
3633 | new(), bstr() and numify(). The reason are that it does now more work and | |
3634 | handles more cases. The time spent in these operations is usually gained in | |
3635 | the other operations so that programs on the average should get faster. If | |
3636 | they don't, please contect the author. | |
58cde26e | 3637 | |
394e6ffb JH |
3638 | Some operations may be slower for small numbers, but are significantly faster |
3639 | for big numbers. Other operations are now constant (O(1), like bneg(), babs() | |
3640 | etc), instead of O(N) and thus nearly always take much less time. These | |
3641 | optimizations were done on purpose. | |
58cde26e | 3642 | |
574bacfe JH |
3643 | If you find the Calc module to slow, try to install any of the replacement |
3644 | modules and see if they help you. | |
b3ac6de7 | 3645 | |
574bacfe | 3646 | =head2 Alternative math libraries |
0716bf9b JH |
3647 | |
3648 | You can use an alternative library to drive Math::BigInt via: | |
3649 | ||
3650 | use Math::BigInt lib => 'Module'; | |
3651 | ||
394e6ffb | 3652 | See L<MATH LIBRARY> for more information. |
0716bf9b | 3653 | |
394e6ffb | 3654 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. |
574bacfe | 3655 | |
b3abae2a JH |
3656 | =head2 SUBCLASSING |
3657 | ||
3658 | =head1 Subclassing Math::BigInt | |
3659 | ||
3660 | The basic design of Math::BigInt allows simple subclasses with very little | |
3661 | work, as long as a few simple rules are followed: | |
3662 | ||
3663 | =over 2 | |
3664 | ||
3665 | =item * | |
3666 | ||
3667 | The public API must remain consistent, i.e. if a sub-class is overloading | |
3668 | addition, the sub-class must use the same name, in this case badd(). The | |
3669 | reason for this is that Math::BigInt is optimized to call the object methods | |
3670 | directly. | |
3671 | ||
3672 | =item * | |
3673 | ||
3674 | The private object hash keys like C<$x->{sign}> may not be changed, but | |
3675 | additional keys can be added, like C<$x->{_custom}>. | |
3676 | ||
3677 | =item * | |
3678 | ||
3679 | Accessor functions are available for all existing object hash keys and should | |
3680 | be used instead of directly accessing the internal hash keys. The reason for | |
3681 | this is that Math::BigInt itself has a pluggable interface which permits it | |
3682 | to support different storage methods. | |
3683 | ||
3684 | =back | |
3685 | ||
3686 | More complex sub-classes may have to replicate more of the logic internal of | |
3687 | Math::BigInt if they need to change more basic behaviors. A subclass that | |
3688 | needs to merely change the output only needs to overload C<bstr()>. | |
3689 | ||
3690 | All other object methods and overloaded functions can be directly inherited | |
3691 | from the parent class. | |
3692 | ||
3693 | At the very minimum, any subclass will need to provide it's own C<new()> and can | |
3694 | store additional hash keys in the object. There are also some package globals | |
3695 | that must be defined, e.g.: | |
3696 | ||
3697 | # Globals | |
3698 | $accuracy = undef; | |
3699 | $precision = -2; # round to 2 decimal places | |
3700 | $round_mode = 'even'; | |
3701 | $div_scale = 40; | |
3702 | ||
3703 | Additionally, you might want to provide the following two globals to allow | |
3704 | auto-upgrading and auto-downgrading to work correctly: | |
3705 | ||
3706 | $upgrade = undef; | |
3707 | $downgrade = undef; | |
3708 | ||
3709 | This allows Math::BigInt to correctly retrieve package globals from the | |
3710 | subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or | |
3711 | t/Math/BigFloat/SubClass.pm completely functional subclass examples. | |
3712 | ||
3713 | Don't forget to | |
3714 | ||
3715 | use overload; | |
3716 | ||
3717 | in your subclass to automatically inherit the overloading from the parent. If | |
3718 | you like, you can change part of the overloading, look at Math::String for an | |
3719 | example. | |
3720 | ||
3721 | =head1 UPGRADING | |
3722 | ||
3723 | When used like this: | |
3724 | ||
3725 | use Math::BigInt upgrade => 'Foo::Bar'; | |
3726 | ||
3727 | certain operations will 'upgrade' their calculation and thus the result to | |
3728 | the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat: | |
3729 | ||
3730 | use Math::BigInt upgrade => 'Math::BigFloat'; | |
3731 | ||
3732 | As a shortcut, you can use the module C<bignum>: | |
3733 | ||
3734 | use bignum; | |
3735 | ||
3736 | Also good for oneliners: | |
3737 | ||
3738 | perl -Mbignum -le 'print 2 ** 255' | |
3739 | ||
3740 | This makes it possible to mix arguments of different classes (as in 2.5 + 2) | |
3741 | as well es preserve accuracy (as in sqrt(3)). | |
3742 | ||
3743 | Beware: This feature is not fully implemented yet. | |
3744 | ||
3745 | =head2 Auto-upgrade | |
3746 | ||
3747 | The following methods upgrade themselves unconditionally; that is if upgrade | |
3748 | is in effect, they will always hand up their work: | |
3749 | ||
3750 | =over 2 | |
3751 | ||
3752 | =item bsqrt() | |
3753 | ||
3754 | =item div() | |
3755 | ||
3756 | =item blog() | |
3757 | ||
3758 | =back | |
3759 | ||
3760 | Beware: This list is not complete. | |
3761 | ||
3762 | All other methods upgrade themselves only when one (or all) of their | |
3763 | arguments are of the class mentioned in $upgrade (This might change in later | |
3764 | versions to a more sophisticated scheme): | |
3765 | ||
a5f75d66 AD |
3766 | =head1 BUGS |
3767 | ||
58cde26e JH |
3768 | =over 2 |
3769 | ||
574bacfe | 3770 | =item Out of Memory! |
58cde26e JH |
3771 | |
3772 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and | |
3773 | C<eval()> in your code will crash with "Out of memory". This is probably an | |
3774 | overload/exporter bug. You can workaround by not having C<eval()> | |
574bacfe JH |
3775 | and ':constant' at the same time or upgrade your Perl to a newer version. |
3776 | ||
3777 | =item Fails to load Calc on Perl prior 5.6.0 | |
3778 | ||
3779 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt | |
3780 | will fall back to eval { require ... } when loading the math lib on Perls | |
3781 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on | |
3782 | filesystems using a different seperator. | |
58cde26e JH |
3783 | |
3784 | =back | |
3785 | ||
3786 | =head1 CAVEATS | |
3787 | ||
3788 | Some things might not work as you expect them. Below is documented what is | |
3789 | known to be troublesome: | |
3790 | ||
3791 | =over 1 | |
3792 | ||
3793 | =item stringify, bstr(), bsstr() and 'cmp' | |
3794 | ||
3795 | Both stringify and bstr() now drop the leading '+'. The old code would return | |
3796 | '+3', the new returns '3'. This is to be consistent with Perl and to make | |
3797 | cmp (especially with overloading) to work as you expect. It also solves | |
3798 | problems with Test.pm, it's ok() uses 'eq' internally. | |
3799 | ||
3800 | Mark said, when asked about to drop the '+' altogether, or make only cmp work: | |
3801 | ||
3802 | I agree (with the first alternative), don't add the '+' on positive | |
3803 | numbers. It's not as important anymore with the new internal | |
3804 | form for numbers. It made doing things like abs and neg easier, | |
3805 | but those have to be done differently now anyway. | |
3806 | ||
3807 | So, the following examples will now work all as expected: | |
3808 | ||
3809 | use Test; | |
3810 | BEGIN { plan tests => 1 } | |
3811 | use Math::BigInt; | |
3812 | ||
3813 | my $x = new Math::BigInt 3*3; | |
3814 | my $y = new Math::BigInt 3*3; | |
3815 | ||
3816 | ok ($x,3*3); | |
3817 | print "$x eq 9" if $x eq $y; | |
3818 | print "$x eq 9" if $x eq '9'; | |
3819 | print "$x eq 9" if $x eq 3*3; | |
3820 | ||
3821 | Additionally, the following still works: | |
3822 | ||
3823 | print "$x == 9" if $x == $y; | |
3824 | print "$x == 9" if $x == 9; | |
3825 | print "$x == 9" if $x == 3*3; | |
3826 | ||
3827 | There is now a C<bsstr()> method to get the string in scientific notation aka | |
3828 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() | |
3829 | for comparisation, but Perl will represent some numbers as 100 and others | |
3830 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before doing eq: | |
3831 | ||
3832 | use Test; | |
3833 | BEGIN { plan tests => 3 } | |
3834 | use Math::BigInt; | |
3835 | ||
3836 | $x = Math::BigInt->new('1e56'); $y = 1e56; | |
3837 | ok ($x,$y); # will fail | |
3838 | ok ($x->bsstr(),$y); # okay | |
3839 | $y = Math::BigInt->new($y); | |
3840 | ok ($x,$y); # okay | |
3841 | ||
394e6ffb JH |
3842 | Alternatively, simple use <=> for comparisations, that will get it always |
3843 | right. There is not yet a way to get a number automatically represented as | |
3844 | a string that matches exactly the way Perl represents it. | |
574bacfe | 3845 | |
58cde26e JH |
3846 | =item int() |
3847 | ||
3848 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a | |
3849 | Perl scalar: | |
3850 | ||
3851 | $x = Math::BigInt->new(123); | |
3852 | $y = int($x); # BigInt 123 | |
3853 | $x = Math::BigFloat->new(123.45); | |
3854 | $y = int($x); # BigInt 123 | |
3855 | ||
3856 | In all Perl versions you can use C<as_number()> for the same effect: | |
3857 | ||
3858 | $x = Math::BigFloat->new(123.45); | |
3859 | $y = $x->as_number(); # BigInt 123 | |
3860 | ||
3861 | This also works for other subclasses, like Math::String. | |
3862 | ||
574bacfe JH |
3863 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. |
3864 | ||
dccbb853 | 3865 | =item length |
58cde26e JH |
3866 | |
3867 | The following will probably not do what you expect: | |
3868 | ||
bd05a461 JH |
3869 | $c = Math::BigInt->new(123); |
3870 | print $c->length(),"\n"; # prints 30 | |
3871 | ||
3872 | It prints both the number of digits in the number and in the fraction part | |
3873 | since print calls C<length()> in list context. Use something like: | |
3874 | ||
3875 | print scalar $c->length(),"\n"; # prints 3 | |
3876 | ||
3877 | =item bdiv | |
3878 | ||
3879 | The following will probably not do what you expect: | |
3880 | ||
58cde26e JH |
3881 | print $c->bdiv(10000),"\n"; |
3882 | ||
dccbb853 | 3883 | It prints both quotient and remainder since print calls C<bdiv()> in list |
58cde26e JH |
3884 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want |
3885 | to use | |
3886 | ||
3887 | print $c / 10000,"\n"; | |
3888 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c | |
3889 | ||
3890 | instead. | |
3891 | ||
3892 | The quotient is always the greatest integer less than or equal to the | |
3893 | real-valued quotient of the two operands, and the remainder (when it is | |
3894 | nonzero) always has the same sign as the second operand; so, for | |
3895 | example, | |
3896 | ||
dccbb853 JH |
3897 | 1 / 4 => ( 0, 1) |
3898 | 1 / -4 => (-1,-3) | |
3899 | -3 / 4 => (-1, 1) | |
3900 | -3 / -4 => ( 0,-3) | |
3901 | -11 / 2 => (-5,1) | |
3902 | 11 /-2 => (-5,-1) | |
58cde26e JH |
3903 | |
3904 | As a consequence, the behavior of the operator % agrees with the | |
3905 | behavior of Perl's built-in % operator (as documented in the perlop | |
3906 | manpage), and the equation | |
3907 | ||
3908 | $x == ($x / $y) * $y + ($x % $y) | |
3909 | ||
3910 | holds true for any $x and $y, which justifies calling the two return | |
dccbb853 JH |
3911 | values of bdiv() the quotient and remainder. The only exception to this rule |
3912 | are when $y == 0 and $x is negative, then the remainder will also be | |
3913 | negative. See below under "infinity handling" for the reasoning behing this. | |
58cde26e JH |
3914 | |
3915 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will | |
3916 | not change BigInt's way to do things. This is because under 'use integer' Perl | |
3917 | will do what the underlying C thinks is right and this is different for each | |
3918 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug | |
3919 | the author to implement it ;) | |
3920 | ||
dccbb853 JH |
3921 | =item infinity handling |
3922 | ||
3923 | Here are some examples that explain the reasons why certain results occur while | |
3924 | handling infinity: | |
3925 | ||
3926 | The following table shows the result of the division and the remainder, so that | |
3927 | the equation above holds true. Some "ordinary" cases are strewn in to show more | |
3928 | clearly the reasoning: | |
3929 | ||
3930 | A / B = C, R so that C * B + R = A | |
3931 | ========================================================= | |
3932 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 | |
3933 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 | |
3934 | 0 / inf = 0, 0 0 * inf + 0 = 0 | |
3935 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 | |
3936 | 5 / inf = 0, 5 0 * inf + 5 = 5 | |
3937 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 | |
3938 | -5/ inf = 0, -5 0 * inf + -5 = -5 | |
3939 | -5/-inf = 0, -5 0 * -inf + -5 = -5 | |
3940 | inf/ 5 = inf, 0 inf * 5 + 0 = inf | |
3941 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf | |
3942 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf | |
3943 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf | |
3944 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 | |
3945 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 | |
3946 | inf/ inf = 1, 0 1 * inf + 0 = inf | |
3947 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf | |
3948 | inf/-inf = -1, 0 -1 * -inf + 0 = inf | |
3949 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf | |
3950 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 | |
3951 | inf/ 0 = inf, inf inf * 0 + inf = inf | |
3952 | 0/ 0 = NaN | |
3953 | ||
3954 | These cases below violate the "remainder has the sign of the second of the two | |
3955 | arguments", since they wouldn't match up otherwise. | |
3956 | ||
3957 | A / B = C, R so that C * B + R = A | |
3958 | ======================================================== | |
3959 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf | |
3960 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 | |
3961 | ||
58cde26e JH |
3962 | =item Modifying and = |
3963 | ||
3964 | Beware of: | |
3965 | ||
3966 | $x = Math::BigFloat->new(5); | |
3967 | $y = $x; | |
3968 | ||
3969 | It will not do what you think, e.g. making a copy of $x. Instead it just makes | |
3970 | a second reference to the B<same> object and stores it in $y. Thus anything | |
17baacb7 JH |
3971 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
3972 | Or in other words, C<=> is only safe if you modify your BigInts only via | |
3973 | overloaded math. As soon as you use a method call it breaks: | |
58cde26e JH |
3974 | |
3975 | $x->bmul(2); | |
3976 | print "$x, $y\n"; # prints '10, 10' | |
3977 | ||
3978 | If you want a true copy of $x, use: | |
3979 | ||
3980 | $y = $x->copy(); | |
3981 | ||
17baacb7 JH |
3982 | You can also chain the calls like this, this will make first a copy and then |
3983 | multiply it by 2: | |
3984 | ||
3985 | $y = $x->copy()->bmul(2); | |
3986 | ||
b22b3e31 | 3987 | See also the documentation for overload.pm regarding C<=>. |
58cde26e JH |
3988 | |
3989 | =item bpow | |
3990 | ||
3991 | C<bpow()> (and the rounding functions) now modifies the first argument and | |
574bacfe | 3992 | returns it, unlike the old code which left it alone and only returned the |
58cde26e JH |
3993 | result. This is to be consistent with C<badd()> etc. The first three will |
3994 | modify $x, the last one won't: | |
3995 | ||
3996 | print bpow($x,$i),"\n"; # modify $x | |
3997 | print $x->bpow($i),"\n"; # ditto | |
3998 | print $x **= $i,"\n"; # the same | |
3999 | print $x ** $i,"\n"; # leave $x alone | |
4000 | ||
4001 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. | |
4002 | ||
4003 | =item Overloading -$x | |
4004 | ||
4005 | The following: | |
4006 | ||
4007 | $x = -$x; | |
4008 | ||
4009 | is slower than | |
4010 | ||
4011 | $x->bneg(); | |
4012 | ||
4013 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant | |
4014 | needs to preserve $x since it does not know that it later will get overwritten. | |
0716bf9b | 4015 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e | 4016 | |
394e6ffb JH |
4017 | With Copy-On-Write, this issue would be gone, but C-o-W is not implemented |
4018 | since it is slower for all other things. | |
58cde26e JH |
4019 | |
4020 | =item Mixing different object types | |
4021 | ||
4022 | In Perl you will get a floating point value if you do one of the following: | |
4023 | ||
4024 | $float = 5.0 + 2; | |
4025 | $float = 2 + 5.0; | |
4026 | $float = 5 / 2; | |
4027 | ||
4028 | With overloaded math, only the first two variants will result in a BigFloat: | |
4029 | ||
4030 | use Math::BigInt; | |
4031 | use Math::BigFloat; | |
4032 | ||
4033 | $mbf = Math::BigFloat->new(5); | |
4034 | $mbi2 = Math::BigInteger->new(5); | |
4035 | $mbi = Math::BigInteger->new(2); | |
4036 | ||
4037 | # what actually gets called: | |
4038 | $float = $mbf + $mbi; # $mbf->badd() | |
4039 | $float = $mbf / $mbi; # $mbf->bdiv() | |
4040 | $integer = $mbi + $mbf; # $mbi->badd() | |
4041 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() | |
4042 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() | |
4043 | ||
4044 | This is because math with overloaded operators follows the first (dominating) | |
394e6ffb | 4045 | operand, and the operation of that is called and returns thus the result. So, |
58cde26e JH |
4046 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
4047 | the result should be a Math::BigFloat or the second operant is one. | |
4048 | ||
4049 | To get a Math::BigFloat you either need to call the operation manually, | |
4050 | make sure the operands are already of the proper type or casted to that type | |
4051 | via Math::BigFloat->new(): | |
4052 | ||
4053 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 | |
4054 | ||
4055 | Beware of simple "casting" the entire expression, this would only convert | |
4056 | the already computed result: | |
4057 | ||
4058 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! | |
4059 | ||
0716bf9b | 4060 | Beware also of the order of more complicated expressions like: |
58cde26e JH |
4061 | |
4062 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int | |
4063 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto | |
4064 | ||
4065 | If in doubt, break the expression into simpler terms, or cast all operands | |
4066 | to the desired resulting type. | |
4067 | ||
4068 | Scalar values are a bit different, since: | |
4069 | ||
4070 | $float = 2 + $mbf; | |
4071 | $float = $mbf + 2; | |
4072 | ||
4073 | will both result in the proper type due to the way the overloaded math works. | |
4074 | ||
4075 | This section also applies to other overloaded math packages, like Math::String. | |
4076 | ||
b3abae2a JH |
4077 | One solution to you problem might be L<autoupgrading|upgrading>. |
4078 | ||
58cde26e JH |
4079 | =item bsqrt() |
4080 | ||
394e6ffb | 4081 | C<bsqrt()> works only good if the result is a big integer, e.g. the square |
58cde26e JH |
4082 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
4083 | mode. | |
4084 | ||
4085 | If you want a better approximation of the square root, then use: | |
4086 | ||
4087 | $x = Math::BigFloat->new(12); | |
394e6ffb | 4088 | Math::BigFloat->precision(0); |
58cde26e JH |
4089 | Math::BigFloat->round_mode('even'); |
4090 | print $x->copy->bsqrt(),"\n"; # 4 | |
4091 | ||
394e6ffb | 4092 | Math::BigFloat->precision(2); |
58cde26e JH |
4093 | print $x->bsqrt(),"\n"; # 3.46 |
4094 | print $x->bsqrt(3),"\n"; # 3.464 | |
4095 | ||
b3abae2a JH |
4096 | =item brsft() |
4097 | ||
4098 | For negative numbers in base see also L<brsft|brsft>. | |
4099 | ||
58cde26e JH |
4100 | =back |
4101 | ||
4102 | =head1 LICENSE | |
4103 | ||
4104 | This program is free software; you may redistribute it and/or modify it under | |
4105 | the same terms as Perl itself. | |
a5f75d66 | 4106 | |
0716bf9b JH |
4107 | =head1 SEE ALSO |
4108 | ||
027dc388 JH |
4109 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
4110 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
0716bf9b | 4111 | |
027dc388 JH |
4112 | The package at |
4113 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains | |
4114 | more documentation including a full version history, testcases, empty | |
4115 | subclass files and benchmarks. | |
574bacfe | 4116 | |
58cde26e | 4117 | =head1 AUTHORS |
a5f75d66 | 4118 | |
58cde26e JH |
4119 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
4120 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001. | |
a5f75d66 AD |
4121 | |
4122 | =cut |