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 | |
56b9c951 | 21 | $VERSION = '1.55'; |
58cde26e JH |
22 | use Exporter; |
23 | @ISA = qw( Exporter ); | |
61f5c3f5 | 24 | @EXPORT_OK = qw( objectify _swap bgcd blcm); |
027dc388 | 25 | use vars qw/$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 | } | |
0716bf9b | 527 | $self->{value} = $CALC->_zero(); |
58cde26e | 528 | $self->{sign} = $nan; |
394e6ffb | 529 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly |
58cde26e | 530 | return $self; |
b4f14daa | 531 | } |
58cde26e JH |
532 | |
533 | sub binf | |
534 | { | |
535 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' | |
536 | # the sign is either '+', or if given, used from there | |
537 | my $self = shift; | |
56b9c951 | 538 | my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/; |
58cde26e JH |
539 | $self = $class if !defined $self; |
540 | if (!ref($self)) | |
541 | { | |
542 | my $c = $self; $self = {}; bless $self, $c; | |
543 | } | |
61f5c3f5 | 544 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 545 | return if $self->modify('binf'); |
13a12e00 JH |
546 | my $c = ref($self); |
547 | if ($self->can('_binf')) | |
548 | { | |
549 | # use subclass to initialize | |
550 | $self->_binf(); | |
551 | } | |
552 | else | |
553 | { | |
554 | # otherwise do our own thing | |
555 | $self->{value} = $CALC->_zero(); | |
556 | } | |
56b9c951 JH |
557 | $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf |
558 | $self->{sign} = $sign; | |
394e6ffb | 559 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
58cde26e JH |
560 | return $self; |
561 | } | |
562 | ||
563 | sub bzero | |
564 | { | |
565 | # create a bigint '+0', if given a BigInt, set it to 0 | |
566 | my $self = shift; | |
567 | $self = $class if !defined $self; | |
0716bf9b | 568 | |
58cde26e JH |
569 | if (!ref($self)) |
570 | { | |
571 | my $c = $self; $self = {}; bless $self, $c; | |
572 | } | |
61f5c3f5 | 573 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 574 | return if $self->modify('bzero'); |
13a12e00 JH |
575 | |
576 | if ($self->can('_bzero')) | |
577 | { | |
578 | # use subclass to initialize | |
579 | $self->_bzero(); | |
580 | } | |
581 | else | |
582 | { | |
583 | # otherwise do our own thing | |
584 | $self->{value} = $CALC->_zero(); | |
585 | } | |
58cde26e | 586 | $self->{sign} = '+'; |
61f5c3f5 T |
587 | if (@_ > 0) |
588 | { | |
589 | $self->{_a} = $_[0] | |
590 | if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a}); | |
591 | $self->{_p} = $_[1] | |
592 | if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p}); | |
593 | } | |
58cde26e JH |
594 | return $self; |
595 | } | |
596 | ||
574bacfe JH |
597 | sub bone |
598 | { | |
599 | # create a bigint '+1' (or -1 if given sign '-'), | |
600 | # if given a BigInt, set it to +1 or -1, respecively | |
601 | my $self = shift; | |
602 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; | |
603 | $self = $class if !defined $self; | |
394e6ffb | 604 | |
574bacfe JH |
605 | if (!ref($self)) |
606 | { | |
607 | my $c = $self; $self = {}; bless $self, $c; | |
608 | } | |
61f5c3f5 | 609 | $self->import() if $IMPORT == 0; # make require work |
574bacfe | 610 | return if $self->modify('bone'); |
13a12e00 JH |
611 | |
612 | if ($self->can('_bone')) | |
613 | { | |
614 | # use subclass to initialize | |
615 | $self->_bone(); | |
616 | } | |
617 | else | |
618 | { | |
619 | # otherwise do our own thing | |
620 | $self->{value} = $CALC->_one(); | |
621 | } | |
574bacfe | 622 | $self->{sign} = $sign; |
61f5c3f5 T |
623 | if (@_ > 0) |
624 | { | |
625 | $self->{_a} = $_[0] | |
626 | if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a}); | |
627 | $self->{_p} = $_[1] | |
628 | if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p}); | |
629 | } | |
574bacfe JH |
630 | return $self; |
631 | } | |
632 | ||
58cde26e JH |
633 | ############################################################################## |
634 | # string conversation | |
635 | ||
636 | sub bsstr | |
637 | { | |
638 | # (ref to BFLOAT or num_str ) return num_str | |
639 | # Convert number from internal format to scientific string format. | |
640 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") | |
dccbb853 JH |
641 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
642 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 643 | |
574bacfe JH |
644 | if ($x->{sign} !~ /^[+-]$/) |
645 | { | |
646 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
647 | return 'inf'; # +inf | |
648 | } | |
58cde26e | 649 | my ($m,$e) = $x->parts(); |
574bacfe | 650 | # e can only be positive |
58cde26e JH |
651 | my $sign = 'e+'; |
652 | # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s; | |
653 | return $m->bstr().$sign.$e->bstr(); | |
654 | } | |
655 | ||
656 | sub bstr | |
657 | { | |
0716bf9b | 658 | # make a string from bigint object |
ee15d750 JH |
659 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
660 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
56b9c951 | 661 | |
574bacfe JH |
662 | if ($x->{sign} !~ /^[+-]$/) |
663 | { | |
664 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
665 | return 'inf'; # +inf | |
666 | } | |
0716bf9b JH |
667 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
668 | return $es.${$CALC->_str($x->{value})}; | |
58cde26e JH |
669 | } |
670 | ||
671 | sub numify | |
672 | { | |
394e6ffb | 673 | # Make a "normal" scalar from a BigInt object |
58cde26e | 674 | my $x = shift; $x = $class->new($x) unless ref $x; |
0716bf9b JH |
675 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
676 | my $num = $CALC->_num($x->{value}); | |
677 | return -$num if $x->{sign} eq '-'; | |
9393ace2 | 678 | $num; |
58cde26e JH |
679 | } |
680 | ||
681 | ############################################################################## | |
682 | # public stuff (usually prefixed with "b") | |
683 | ||
684 | sub sign | |
685 | { | |
9393ace2 | 686 | # return the sign of the number: +/-/-inf/+inf/NaN |
ee15d750 JH |
687 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
688 | ||
9393ace2 | 689 | $x->{sign}; |
58cde26e JH |
690 | } |
691 | ||
ee15d750 | 692 | sub _find_round_parameters |
58cde26e JH |
693 | { |
694 | # After any operation or when calling round(), the result is rounded by | |
695 | # regarding the A & P from arguments, local parameters, or globals. | |
61f5c3f5 T |
696 | |
697 | # This procedure finds the round parameters, but it is for speed reasons | |
698 | # duplicated in round. Otherwise, it is tested by the testsuite and used | |
699 | # by fdiv(). | |
700 | ||
394e6ffb JH |
701 | my ($self,$a,$p,$r,@args) = @_; |
702 | # $a accuracy, if given by caller | |
703 | # $p precision, if given by caller | |
704 | # $r round_mode, if given by caller | |
705 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
58cde26e | 706 | |
17baacb7 | 707 | # leave bigfloat parts alone |
ee15d750 | 708 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
17baacb7 | 709 | |
394e6ffb | 710 | my $c = ref($self); # find out class of argument(s) |
574bacfe | 711 | no strict 'refs'; |
574bacfe | 712 | |
58cde26e | 713 | # now pick $a or $p, but only if we have got "arguments" |
61f5c3f5 | 714 | if (!defined $a) |
58cde26e | 715 | { |
61f5c3f5 | 716 | foreach ($self,@args) |
58cde26e JH |
717 | { |
718 | # take the defined one, or if both defined, the one that is smaller | |
719 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
720 | } | |
61f5c3f5 T |
721 | } |
722 | if (!defined $p) | |
ee15d750 | 723 | { |
61f5c3f5 T |
724 | # even if $a is defined, take $p, to signal error for both defined |
725 | foreach ($self,@args) | |
726 | { | |
727 | # take the defined one, or if both defined, the one that is bigger | |
728 | # -2 > -3, and 3 > 2 | |
729 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
730 | } | |
ee15d750 | 731 | } |
61f5c3f5 T |
732 | # if still none defined, use globals (#2) |
733 | $a = ${"$c\::accuracy"} unless defined $a; | |
734 | $p = ${"$c\::precision"} unless defined $p; | |
735 | ||
736 | # no rounding today? | |
737 | return ($self) unless defined $a || defined $p; # early out | |
738 | ||
739 | # set A and set P is an fatal error | |
740 | return ($self->bnan()) if defined $a && defined $p; | |
741 | ||
742 | $r = ${"$c\::round_mode"} unless defined $r; | |
743 | die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; | |
744 | ||
745 | return ($self,$a,$p,$r); | |
ee15d750 JH |
746 | } |
747 | ||
748 | sub round | |
749 | { | |
61f5c3f5 | 750 | # Round $self according to given parameters, or given second argument's |
ee15d750 | 751 | # parameters or global defaults |
ee15d750 | 752 | |
61f5c3f5 T |
753 | # for speed reasons, _find_round_parameters is embeded here: |
754 | ||
755 | my ($self,$a,$p,$r,@args) = @_; | |
756 | # $a accuracy, if given by caller | |
757 | # $p precision, if given by caller | |
758 | # $r round_mode, if given by caller | |
759 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
760 | ||
761 | # leave bigfloat parts alone | |
762 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; | |
763 | ||
764 | my $c = ref($self); # find out class of argument(s) | |
765 | no strict 'refs'; | |
766 | ||
767 | # now pick $a or $p, but only if we have got "arguments" | |
768 | if (!defined $a) | |
58cde26e | 769 | { |
61f5c3f5 T |
770 | foreach ($self,@args) |
771 | { | |
772 | # take the defined one, or if both defined, the one that is smaller | |
773 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
774 | } | |
58cde26e | 775 | } |
61f5c3f5 T |
776 | if (!defined $p) |
777 | { | |
778 | # even if $a is defined, take $p, to signal error for both defined | |
779 | foreach ($self,@args) | |
780 | { | |
781 | # take the defined one, or if both defined, the one that is bigger | |
782 | # -2 > -3, and 3 > 2 | |
783 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
784 | } | |
785 | } | |
786 | # if still none defined, use globals (#2) | |
787 | $a = ${"$c\::accuracy"} unless defined $a; | |
788 | $p = ${"$c\::precision"} unless defined $p; | |
789 | ||
790 | # no rounding today? | |
791 | return $self unless defined $a || defined $p; # early out | |
792 | ||
793 | # set A and set P is an fatal error | |
794 | return $self->bnan() if defined $a && defined $p; | |
795 | ||
796 | $r = ${"$c\::round_mode"} unless defined $r; | |
797 | die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; | |
798 | ||
799 | # now round, by calling either fround or ffround: | |
800 | if (defined $a) | |
801 | { | |
802 | $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a; | |
803 | } | |
804 | else # both can't be undefined due to early out | |
58cde26e | 805 | { |
61f5c3f5 | 806 | $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p; |
58cde26e | 807 | } |
61f5c3f5 | 808 | $self->bnorm(); # after round, normalize |
58cde26e JH |
809 | } |
810 | ||
17baacb7 | 811 | sub bnorm |
58cde26e | 812 | { |
027dc388 | 813 | # (numstr or BINT) return BINT |
58cde26e | 814 | # Normalize number -- no-op here |
dccbb853 | 815 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
b3abae2a | 816 | $x; |
58cde26e JH |
817 | } |
818 | ||
819 | sub babs | |
820 | { | |
821 | # (BINT or num_str) return BINT | |
822 | # make number absolute, or return absolute BINT from string | |
ee15d750 JH |
823 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
824 | ||
58cde26e JH |
825 | return $x if $x->modify('babs'); |
826 | # post-normalized abs for internal use (does nothing for NaN) | |
827 | $x->{sign} =~ s/^-/+/; | |
828 | $x; | |
829 | } | |
830 | ||
831 | sub bneg | |
832 | { | |
833 | # (BINT or num_str) return BINT | |
834 | # negate number or make a negated number from string | |
ee15d750 JH |
835 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
836 | ||
58cde26e | 837 | return $x if $x->modify('bneg'); |
b3abae2a | 838 | |
58cde26e | 839 | # for +0 dont negate (to have always normalized) |
b3abae2a | 840 | $x->{sign} =~ tr/+-/-+/ if !$x->is_zero(); # does nothing for NaN |
58cde26e JH |
841 | $x; |
842 | } | |
843 | ||
844 | sub bcmp | |
845 | { | |
846 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
847 | # (BINT or num_str, BINT or num_str) return cond_code | |
848 | my ($self,$x,$y) = objectify(2,@_); | |
0716bf9b JH |
849 | |
850 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
851 | { | |
852 | # handle +-inf and NaN | |
853 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
574bacfe | 854 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b JH |
855 | return +1 if $x->{sign} eq '+inf'; |
856 | return -1 if $x->{sign} eq '-inf'; | |
857 | return -1 if $y->{sign} eq '+inf'; | |
b3abae2a | 858 | return +1; |
0716bf9b | 859 | } |
574bacfe JH |
860 | # check sign for speed first |
861 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
862 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
863 | ||
864 | # shortcut | |
865 | my $xz = $x->is_zero(); | |
866 | my $yz = $y->is_zero(); | |
867 | return 0 if $xz && $yz; # 0 <=> 0 | |
868 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y | |
869 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 | |
dccbb853 JH |
870 | |
871 | # post-normalized compare for internal use (honors signs) | |
872 | if ($x->{sign} eq '+') | |
873 | { | |
56b9c951 | 874 | # $x and $y both > 0 |
dccbb853 JH |
875 | return $CALC->_acmp($x->{value},$y->{value}); |
876 | } | |
877 | ||
56b9c951 | 878 | # $x && $y both < 0 |
b3abae2a | 879 | $CALC->_acmp($y->{value},$x->{value}); # swaped (lib does only 0,1,-1) |
58cde26e JH |
880 | } |
881 | ||
882 | sub bacmp | |
883 | { | |
884 | # Compares 2 values, ignoring their signs. | |
885 | # Returns one of undef, <0, =0, >0. (suitable for sort) | |
886 | # (BINT, BINT) return cond_code | |
887 | my ($self,$x,$y) = objectify(2,@_); | |
574bacfe JH |
888 | |
889 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
890 | { | |
891 | # handle +-inf and NaN | |
892 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
893 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
894 | return +1; # inf is always bigger | |
895 | } | |
b3abae2a | 896 | $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1 |
58cde26e JH |
897 | } |
898 | ||
899 | sub badd | |
900 | { | |
901 | # add second arg (BINT or string) to first (BINT) (modifies first) | |
902 | # return result as BINT | |
61f5c3f5 | 903 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e JH |
904 | |
905 | return $x if $x->modify('badd'); | |
b3abae2a JH |
906 | # print "mbi badd ",join(' ',caller()),"\n"; |
907 | # print "upgrade => ",$upgrade||'undef', | |
908 | # " \$x (",ref($x),") \$y (",ref($y),")\n"; | |
56b9c951 JH |
909 | return $upgrade->badd($x,$y,@r) if defined $upgrade && |
910 | ((ref($x) eq $upgrade) || (ref($y) eq $upgrade)); | |
b3abae2a | 911 | # print "still badd\n"; |
58cde26e | 912 | |
61f5c3f5 | 913 | $r[3] = $y; # no push! |
574bacfe JH |
914 | # inf and NaN handling |
915 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
916 | { | |
917 | # NaN first | |
918 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
13a12e00 JH |
919 | # inf handling |
920 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
574bacfe | 921 | { |
b3abae2a JH |
922 | # +inf++inf or -inf+-inf => same, rest is NaN |
923 | return $x if $x->{sign} eq $y->{sign}; | |
924 | return $x->bnan(); | |
574bacfe JH |
925 | } |
926 | # +-inf + something => +inf | |
927 | # something +-inf => +-inf | |
928 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; | |
929 | return $x; | |
930 | } | |
931 | ||
58cde26e JH |
932 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
933 | ||
934 | if ($sx eq $sy) | |
935 | { | |
574bacfe | 936 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e JH |
937 | $x->{sign} = $sx; |
938 | } | |
939 | else | |
940 | { | |
574bacfe | 941 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e JH |
942 | if ($a > 0) |
943 | { | |
944 | #print "swapped sub (a=$a)\n"; | |
574bacfe | 945 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e JH |
946 | $x->{sign} = $sy; |
947 | } | |
948 | elsif ($a == 0) | |
949 | { | |
950 | # speedup, if equal, set result to 0 | |
0716bf9b JH |
951 | #print "equal sub, result = 0\n"; |
952 | $x->{value} = $CALC->_zero(); | |
58cde26e JH |
953 | $x->{sign} = '+'; |
954 | } | |
955 | else # a < 0 | |
956 | { | |
957 | #print "unswapped sub (a=$a)\n"; | |
574bacfe | 958 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
58cde26e | 959 | $x->{sign} = $sx; |
a0d0e21e | 960 | } |
a0d0e21e | 961 | } |
61f5c3f5 | 962 | $x->round(@r); |
58cde26e JH |
963 | } |
964 | ||
965 | sub bsub | |
966 | { | |
967 | # (BINT or num_str, BINT or num_str) return num_str | |
968 | # subtract second arg from first, modify first | |
b3abae2a | 969 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e | 970 | |
58cde26e | 971 | return $x if $x->modify('bsub'); |
b3abae2a JH |
972 | # return $upgrade->badd($x,$y,@r) if defined $upgrade && |
973 | # ((ref($x) eq $upgrade) || (ref($y) eq $upgrade)); | |
974 | ||
975 | if ($y->is_zero()) | |
976 | { | |
977 | return $x->round(@r); | |
e745a66c | 978 | } |
b3abae2a JH |
979 | |
980 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN | |
981 | $x->badd($y,@r); # badd does not leave internal zeros | |
982 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) | |
61f5c3f5 | 983 | $x; # already rounded by badd() or no round necc. |
58cde26e JH |
984 | } |
985 | ||
986 | sub binc | |
987 | { | |
988 | # increment arg by one | |
ee15d750 | 989 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 990 | return $x if $x->modify('binc'); |
e745a66c JH |
991 | |
992 | if ($x->{sign} eq '+') | |
993 | { | |
994 | $x->{value} = $CALC->_inc($x->{value}); | |
995 | return $x->round($a,$p,$r); | |
996 | } | |
997 | elsif ($x->{sign} eq '-') | |
998 | { | |
999 | $x->{value} = $CALC->_dec($x->{value}); | |
1000 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 | |
1001 | return $x->round($a,$p,$r); | |
1002 | } | |
1003 | # inf, nan handling etc | |
61f5c3f5 | 1004 | $x->badd($self->__one(),$a,$p,$r); # badd does round |
58cde26e JH |
1005 | } |
1006 | ||
1007 | sub bdec | |
1008 | { | |
1009 | # decrement arg by one | |
ee15d750 | 1010 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1011 | return $x if $x->modify('bdec'); |
e745a66c JH |
1012 | |
1013 | my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+'; | |
1014 | # <= 0 | |
1015 | if (($x->{sign} eq '-') || $zero) | |
1016 | { | |
1017 | $x->{value} = $CALC->_inc($x->{value}); | |
1018 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 | |
1019 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 | |
1020 | return $x->round($a,$p,$r); | |
1021 | } | |
1022 | # > 0 | |
1023 | elsif ($x->{sign} eq '+') | |
1024 | { | |
1025 | $x->{value} = $CALC->_dec($x->{value}); | |
1026 | return $x->round($a,$p,$r); | |
1027 | } | |
1028 | # inf, nan handling etc | |
61f5c3f5 | 1029 | $x->badd($self->__one('-'),$a,$p,$r); # badd does round |
58cde26e JH |
1030 | } |
1031 | ||
61f5c3f5 T |
1032 | sub blog |
1033 | { | |
1034 | # not implemented yet | |
b3abae2a | 1035 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
61f5c3f5 | 1036 | |
b3abae2a JH |
1037 | return $upgrade->blog($x,$base,$a,$p,$r) if defined $upgrade; |
1038 | ||
61f5c3f5 T |
1039 | return $x->bnan(); |
1040 | } | |
1041 | ||
58cde26e JH |
1042 | sub blcm |
1043 | { | |
1044 | # (BINT or num_str, BINT or num_str) return BINT | |
1045 | # does not modify arguments, but returns new object | |
1046 | # Lowest Common Multiplicator | |
58cde26e | 1047 | |
0716bf9b JH |
1048 | my $y = shift; my ($x); |
1049 | if (ref($y)) | |
1050 | { | |
1051 | $x = $y->copy(); | |
1052 | } | |
1053 | else | |
1054 | { | |
1055 | $x = $class->new($y); | |
1056 | } | |
dccbb853 | 1057 | while (@_) { $x = __lcm($x,shift); } |
58cde26e JH |
1058 | $x; |
1059 | } | |
1060 | ||
1061 | sub bgcd | |
1062 | { | |
1063 | # (BINT or num_str, BINT or num_str) return BINT | |
1064 | # does not modify arguments, but returns new object | |
1065 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) | |
0716bf9b | 1066 | |
dccbb853 JH |
1067 | my $y = shift; |
1068 | $y = __PACKAGE__->new($y) if !ref($y); | |
1069 | my $self = ref($y); | |
1070 | my $x = $y->copy(); # keep arguments | |
0716bf9b JH |
1071 | if ($CALC->can('_gcd')) |
1072 | { | |
1073 | while (@_) | |
1074 | { | |
dccbb853 | 1075 | $y = shift; $y = $self->new($y) if !ref($y); |
0716bf9b JH |
1076 | next if $y->is_zero(); |
1077 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? | |
1078 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one(); | |
1079 | } | |
1080 | } | |
1081 | else | |
1082 | { | |
1083 | while (@_) | |
1084 | { | |
dccbb853 JH |
1085 | $y = shift; $y = $self->new($y) if !ref($y); |
1086 | $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN | |
0716bf9b JH |
1087 | } |
1088 | } | |
1089 | $x->babs(); | |
58cde26e JH |
1090 | } |
1091 | ||
58cde26e JH |
1092 | sub bnot |
1093 | { | |
1094 | # (num_str or BINT) return BINT | |
1095 | # represent ~x as twos-complement number | |
ee15d750 JH |
1096 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1097 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1098 | ||
58cde26e | 1099 | return $x if $x->modify('bnot'); |
61f5c3f5 | 1100 | $x->bneg()->bdec(); # bdec already does round |
58cde26e JH |
1101 | } |
1102 | ||
b3abae2a JH |
1103 | # is_foo test routines |
1104 | ||
58cde26e JH |
1105 | sub is_zero |
1106 | { | |
1107 | # return true if arg (BINT or num_str) is zero (array '+', '0') | |
ee15d750 JH |
1108 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1109 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
0716bf9b | 1110 | |
574bacfe | 1111 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 | 1112 | $CALC->_is_zero($x->{value}); |
58cde26e JH |
1113 | } |
1114 | ||
1115 | sub is_nan | |
1116 | { | |
1117 | # return true if arg (BINT or num_str) is NaN | |
ee15d750 JH |
1118 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
1119 | ||
1120 | return 1 if $x->{sign} eq $nan; | |
28df3e88 | 1121 | 0; |
58cde26e JH |
1122 | } |
1123 | ||
1124 | sub is_inf | |
1125 | { | |
1126 | # return true if arg (BINT or num_str) is +-inf | |
ee15d750 JH |
1127 | my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1128 | ||
1129 | $sign = '' if !defined $sign; | |
9393ace2 | 1130 | return 1 if $sign eq $x->{sign}; # match ("+inf" eq "+inf") |
ee15d750 | 1131 | return 0 if $sign !~ /^([+-]|)$/; |
58cde26e | 1132 | |
ee15d750 JH |
1133 | if ($sign eq '') |
1134 | { | |
1135 | return 1 if ($x->{sign} =~ /^[+-]inf$/); | |
1136 | return 0; | |
1137 | } | |
1138 | $sign = quotemeta($sign.'inf'); | |
1139 | return 1 if ($x->{sign} =~ /^$sign$/); | |
28df3e88 | 1140 | 0; |
58cde26e JH |
1141 | } |
1142 | ||
1143 | sub is_one | |
1144 | { | |
b22b3e31 PN |
1145 | # return true if arg (BINT or num_str) is +1 |
1146 | # or -1 if sign is given | |
ee15d750 JH |
1147 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1148 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1149 | ||
1150 | $sign = '' if !defined $sign; $sign = '+' if $sign ne '-'; | |
0716bf9b | 1151 | |
ee15d750 | 1152 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
394e6ffb | 1153 | $CALC->_is_one($x->{value}); |
58cde26e JH |
1154 | } |
1155 | ||
1156 | sub is_odd | |
1157 | { | |
1158 | # return true when arg (BINT or num_str) is odd, false for even | |
ee15d750 JH |
1159 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1160 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
0716bf9b | 1161 | |
b22b3e31 | 1162 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1163 | $CALC->_is_odd($x->{value}); |
58cde26e JH |
1164 | } |
1165 | ||
1166 | sub is_even | |
1167 | { | |
1168 | # return true when arg (BINT or num_str) is even, false for odd | |
ee15d750 JH |
1169 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1170 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
0716bf9b | 1171 | |
b22b3e31 | 1172 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1173 | $CALC->_is_even($x->{value}); |
0716bf9b JH |
1174 | } |
1175 | ||
1176 | sub is_positive | |
1177 | { | |
1178 | # return true when arg (BINT or num_str) is positive (>= 0) | |
ee15d750 JH |
1179 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1180 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1181 | ||
1182 | return 1 if $x->{sign} =~ /^\+/; | |
394e6ffb | 1183 | 0; |
0716bf9b JH |
1184 | } |
1185 | ||
1186 | sub is_negative | |
1187 | { | |
1188 | # return true when arg (BINT or num_str) is negative (< 0) | |
ee15d750 JH |
1189 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1190 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1191 | ||
1192 | return 1 if ($x->{sign} =~ /^-/); | |
394e6ffb | 1193 | 0; |
58cde26e JH |
1194 | } |
1195 | ||
b3abae2a JH |
1196 | sub is_int |
1197 | { | |
1198 | # return true when arg (BINT or num_str) is an integer | |
1199 | # always true for BigInt, but different for Floats | |
1200 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster | |
1201 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1202 | ||
1203 | $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't | |
1204 | } | |
1205 | ||
0716bf9b JH |
1206 | ############################################################################### |
1207 | ||
58cde26e JH |
1208 | sub bmul |
1209 | { | |
1210 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 | |
1211 | # (BINT or num_str, BINT or num_str) return BINT | |
61f5c3f5 | 1212 | my ($self,$x,$y,@r) = objectify(2,@_); |
0716bf9b | 1213 | |
58cde26e | 1214 | return $x if $x->modify('bmul'); |
61f5c3f5 | 1215 | |
574bacfe | 1216 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
b3abae2a | 1217 | |
574bacfe JH |
1218 | # inf handling |
1219 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1220 | { | |
b3abae2a | 1221 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe JH |
1222 | # result will always be +-inf: |
1223 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
1224 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
1225 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
1226 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
1227 | return $x->binf('-'); | |
1228 | } | |
9393ace2 JH |
1229 | |
1230 | return $upgrade->bmul($x,$y,@r) | |
1231 | if defined $upgrade && $y->isa($upgrade); | |
1232 | ||
1233 | $r[3] = $y; # no push here | |
58cde26e | 1234 | |
0716bf9b | 1235 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
dccbb853 | 1236 | |
b3abae2a JH |
1237 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
1238 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 | |
1239 | $x->round(@r); | |
dccbb853 JH |
1240 | } |
1241 | ||
1242 | sub _div_inf | |
1243 | { | |
1244 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code | |
1245 | my ($self,$x,$y) = @_; | |
1246 | ||
1247 | # NaN if x == NaN or y == NaN or x==y==0 | |
1248 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() | |
1249 | if (($x->is_nan() || $y->is_nan()) || | |
1250 | ($x->is_zero() && $y->is_zero())); | |
1251 | ||
b3abae2a JH |
1252 | # +-inf / +-inf == NaN, reminder also NaN |
1253 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
dccbb853 | 1254 | { |
b3abae2a | 1255 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan(); |
dccbb853 JH |
1256 | } |
1257 | # x / +-inf => 0, remainder x (works even if x == 0) | |
1258 | if ($y->{sign} =~ /^[+-]inf$/) | |
1259 | { | |
1260 | my $t = $x->copy(); # binf clobbers up $x | |
1261 | return wantarray ? ($x->bzero(),$t) : $x->bzero() | |
1262 | } | |
1263 | ||
1264 | # 5 / 0 => +inf, -6 / 0 => -inf | |
1265 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf | |
1266 | # exception: -8 / 0 has remainder -8, not 8 | |
1267 | # exception: -inf / 0 has remainder -inf, not inf | |
1268 | if ($y->is_zero()) | |
1269 | { | |
1270 | # +-inf / 0 => special case for -inf | |
1271 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); | |
1272 | if (!$x->is_zero() && !$x->is_inf()) | |
1273 | { | |
1274 | my $t = $x->copy(); # binf clobbers up $x | |
1275 | return wantarray ? | |
1276 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) | |
1277 | } | |
1278 | } | |
1279 | ||
1280 | # last case: +-inf / ordinary number | |
1281 | my $sign = '+inf'; | |
1282 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; | |
1283 | $x->{sign} = $sign; | |
1284 | return wantarray ? ($x,$self->bzero()) : $x; | |
58cde26e JH |
1285 | } |
1286 | ||
1287 | sub bdiv | |
1288 | { | |
1289 | # (dividend: BINT or num_str, divisor: BINT or num_str) return | |
1290 | # (BINT,BINT) (quo,rem) or BINT (only rem) | |
61f5c3f5 | 1291 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e JH |
1292 | |
1293 | return $x if $x->modify('bdiv'); | |
1294 | ||
dccbb853 JH |
1295 | return $self->_div_inf($x,$y) |
1296 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
58cde26e | 1297 | |
9393ace2 JH |
1298 | return $upgrade->bdiv($upgrade->new($x),$y,@r) |
1299 | if defined $upgrade && $y->isa($upgrade); | |
1300 | ||
61f5c3f5 T |
1301 | $r[3] = $y; # no push! |
1302 | ||
58cde26e | 1303 | # 0 / something |
61f5c3f5 T |
1304 | return |
1305 | wantarray ? ($x->round(@r),$self->bzero(@r)):$x->round(@r) if $x->is_zero(); | |
58cde26e | 1306 | |
b3abae2a | 1307 | # Is $x in the interval [0, $y) (aka $x <= $y) ? |
0716bf9b | 1308 | my $cmp = $CALC->_acmp($x->{value},$y->{value}); |
b3abae2a | 1309 | if (($cmp < 0) and (($x->{sign} eq $y->{sign}) or !wantarray)) |
58cde26e | 1310 | { |
9393ace2 JH |
1311 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
1312 | if defined $upgrade; | |
b3abae2a | 1313 | |
61f5c3f5 | 1314 | return $x->bzero()->round(@r) unless wantarray; |
58cde26e | 1315 | my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x |
61f5c3f5 | 1316 | return ($x->bzero()->round(@r),$t); |
58cde26e JH |
1317 | } |
1318 | elsif ($cmp == 0) | |
1319 | { | |
1320 | # shortcut, both are the same, so set to +/- 1 | |
574bacfe | 1321 | $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') ); |
58cde26e | 1322 | return $x unless wantarray; |
61f5c3f5 | 1323 | return ($x->round(@r),$self->bzero(@r)); |
58cde26e | 1324 | } |
9393ace2 JH |
1325 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
1326 | if defined $upgrade; | |
58cde26e JH |
1327 | |
1328 | # calc new sign and in case $y == +/- 1, return $x | |
dccbb853 | 1329 | my $xsign = $x->{sign}; # keep |
58cde26e JH |
1330 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
1331 | # check for / +-1 (cant use $y->is_one due to '-' | |
394e6ffb | 1332 | if ($CALC->_is_one($y->{value})) |
58cde26e | 1333 | { |
61f5c3f5 | 1334 | return wantarray ? ($x->round(@r),$self->bzero(@r)) : $x->round(@r); |
58cde26e JH |
1335 | } |
1336 | ||
58cde26e JH |
1337 | if (wantarray) |
1338 | { | |
394e6ffb JH |
1339 | my $rem = $self->bzero(); |
1340 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); | |
1341 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
61f5c3f5 | 1342 | $x->round(@r); |
dccbb853 JH |
1343 | if (! $CALC->_is_zero($rem->{value})) |
1344 | { | |
1345 | $rem->{sign} = $y->{sign}; | |
1346 | $rem = $y-$rem if $xsign ne $y->{sign}; # one of them '-' | |
1347 | } | |
1348 | else | |
1349 | { | |
1350 | $rem->{sign} = '+'; # dont leave -0 | |
1351 | } | |
61f5c3f5 | 1352 | $rem->round(@r); |
58cde26e JH |
1353 | return ($x,$rem); |
1354 | } | |
394e6ffb JH |
1355 | |
1356 | $x->{value} = $CALC->_div($x->{value},$y->{value}); | |
1357 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
61f5c3f5 | 1358 | $x->round(@r); |
58cde26e JH |
1359 | } |
1360 | ||
dccbb853 JH |
1361 | sub bmod |
1362 | { | |
1363 | # modulus (or remainder) | |
1364 | # (BINT or num_str, BINT or num_str) return BINT | |
61f5c3f5 | 1365 | my ($self,$x,$y,@r) = objectify(2,@_); |
28df3e88 | 1366 | |
dccbb853 | 1367 | return $x if $x->modify('bmod'); |
61f5c3f5 | 1368 | $r[3] = $y; # no push! |
dccbb853 JH |
1369 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) |
1370 | { | |
1371 | my ($d,$r) = $self->_div_inf($x,$y); | |
61f5c3f5 | 1372 | return $r->round(@r); |
dccbb853 JH |
1373 | } |
1374 | ||
1375 | if ($CALC->can('_mod')) | |
1376 | { | |
1377 | # calc new sign and in case $y == +/- 1, return $x | |
1378 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); | |
dccbb853 JH |
1379 | if (!$CALC->_is_zero($x->{value})) |
1380 | { | |
b3abae2a | 1381 | my $xsign = $x->{sign}; |
dccbb853 JH |
1382 | $x->{sign} = $y->{sign}; |
1383 | $x = $y-$x if $xsign ne $y->{sign}; # one of them '-' | |
1384 | } | |
1385 | else | |
1386 | { | |
1387 | $x->{sign} = '+'; # dont leave -0 | |
1388 | } | |
61f5c3f5 | 1389 | return $x->round(@r); |
dccbb853 | 1390 | } |
b3abae2a JH |
1391 | my ($t,$rem) = $self->bdiv($x->copy(),$y,@r); # slow way (also rounds) |
1392 | # modify in place | |
1393 | foreach (qw/value sign _a _p/) | |
1394 | { | |
1395 | $x->{$_} = $rem->{$_}; | |
1396 | } | |
1397 | $x; | |
dccbb853 JH |
1398 | } |
1399 | ||
b3abae2a JH |
1400 | sub bfac |
1401 | { | |
1402 | # (BINT or num_str, BINT or num_str) return BINT | |
1403 | # compute factorial numbers | |
1404 | # modifies first argument | |
1405 | my ($self,$x,@r) = objectify(1,@_); | |
1406 | ||
1407 | return $x if $x->modify('bfac'); | |
1408 | ||
1409 | return $x->bnan() if $x->{sign} ne '+'; # inf, NnN, <0 etc => NaN | |
1410 | return $x->bone(@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 | |
1411 | ||
1412 | if ($CALC->can('_fac')) | |
1413 | { | |
1414 | $x->{value} = $CALC->_fac($x->{value}); | |
1415 | return $x->round(@r); | |
1416 | } | |
1417 | ||
1418 | my $n = $x->copy(); | |
1419 | $x->bone(); | |
1420 | my $f = $self->new(2); | |
1421 | while ($f->bacmp($n) < 0) | |
1422 | { | |
1423 | $x->bmul($f); $f->binc(); | |
1424 | } | |
1425 | $x->bmul($f); # last step | |
1426 | $x->round(@r); # round | |
1427 | } | |
1428 | ||
58cde26e JH |
1429 | sub bpow |
1430 | { | |
1431 | # (BINT or num_str, BINT or num_str) return BINT | |
1432 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 | |
1433 | # modifies first argument | |
61f5c3f5 | 1434 | my ($self,$x,$y,@r) = objectify(2,@_); |
58cde26e JH |
1435 | |
1436 | return $x if $x->modify('bpow'); | |
9393ace2 JH |
1437 | |
1438 | return $upgrade->bpow($upgrade->new($x),$y,@r) | |
1439 | if defined $upgrade && $y->isa($upgrade); | |
1440 | ||
61f5c3f5 | 1441 | $r[3] = $y; # no push! |
0716bf9b | 1442 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
58cde26e | 1443 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
61f5c3f5 T |
1444 | return $x->bone(@r) if $y->is_zero(); |
1445 | return $x->round(@r) if $x->is_one() || $y->is_one(); | |
0716bf9b | 1446 | if ($x->{sign} eq '-' && $CALC->_is_one($x->{value})) |
58cde26e JH |
1447 | { |
1448 | # if $x == -1 and odd/even y => +1/-1 | |
61f5c3f5 | 1449 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
574bacfe | 1450 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
58cde26e | 1451 | } |
574bacfe JH |
1452 | # 1 ** -y => 1 / (1 ** |y|) |
1453 | # so do test for negative $y after above's clause | |
58cde26e | 1454 | return $x->bnan() if $y->{sign} eq '-'; |
61f5c3f5 | 1455 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
58cde26e | 1456 | |
0716bf9b | 1457 | if ($CALC->can('_pow')) |
58cde26e | 1458 | { |
574bacfe | 1459 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
61f5c3f5 | 1460 | return $x->round(@r); |
58cde26e | 1461 | } |
027dc388 JH |
1462 | |
1463 | # based on the assumption that shifting in base 10 is fast, and that mul | |
1464 | # works faster if numbers are small: we count trailing zeros (this step is | |
1465 | # O(1)..O(N), but in case of O(N) we save much more time due to this), | |
1466 | # stripping them out of the multiplication, and add $count * $y zeros | |
1467 | # afterwards like this: | |
1468 | # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6 | |
1469 | # creates deep recursion? | |
574bacfe JH |
1470 | # my $zeros = $x->_trailing_zeros(); |
1471 | # if ($zeros > 0) | |
1472 | # { | |
1473 | # $x->brsft($zeros,10); # remove zeros | |
1474 | # $x->bpow($y); # recursion (will not branch into here again) | |
1475 | # $zeros = $y * $zeros; # real number of zeros to add | |
1476 | # $x->blsft($zeros,10); | |
1477 | # return $x->round($a,$p,$r); | |
1478 | # } | |
1479 | ||
1480 | my $pow2 = $self->__one(); | |
58cde26e | 1481 | my $y1 = $class->new($y); |
dccbb853 | 1482 | my $two = $self->new(2); |
58cde26e JH |
1483 | while (!$y1->is_one()) |
1484 | { | |
dccbb853 JH |
1485 | $pow2->bmul($x) if $y1->is_odd(); |
1486 | $y1->bdiv($two); | |
027dc388 | 1487 | $x->bmul($x); |
58cde26e | 1488 | } |
dccbb853 | 1489 | $x->bmul($pow2) unless $pow2->is_one(); |
56b9c951 | 1490 | $x->round(@r); |
58cde26e JH |
1491 | } |
1492 | ||
1493 | sub blsft | |
1494 | { | |
1495 | # (BINT or num_str, BINT or num_str) return BINT | |
1496 | # compute x << y, base n, y >= 0 | |
b3abae2a | 1497 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1498 | |
1499 | return $x if $x->modify('blsft'); | |
1500 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
b3abae2a | 1501 | return $x->round($a,$p,$r) if $y->is_zero(); |
58cde26e | 1502 | |
574bacfe JH |
1503 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1504 | ||
027dc388 | 1505 | my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft'); |
574bacfe JH |
1506 | if (defined $t) |
1507 | { | |
b3abae2a | 1508 | $x->{value} = $t; return $x->round($a,$p,$r); |
574bacfe JH |
1509 | } |
1510 | # fallback | |
b3abae2a | 1511 | return $x->bmul( $self->bpow($n, $y, $a, $p, $r), $a, $p, $r ); |
58cde26e JH |
1512 | } |
1513 | ||
1514 | sub brsft | |
1515 | { | |
1516 | # (BINT or num_str, BINT or num_str) return BINT | |
1517 | # compute x >> y, base n, y >= 0 | |
b3abae2a | 1518 | my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1519 | |
1520 | return $x if $x->modify('brsft'); | |
1521 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
b3abae2a JH |
1522 | return $x->round($a,$p,$r) if $y->is_zero(); |
1523 | return $x->bzero($a,$p,$r) if $x->is_zero(); # 0 => 0 | |
58cde26e JH |
1524 | |
1525 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; | |
574bacfe | 1526 | |
b3abae2a JH |
1527 | # this only works for negative numbers when shifting in base 2 |
1528 | if (($x->{sign} eq '-') && ($n == 2)) | |
1529 | { | |
1530 | return $x->round($a,$p,$r) if $x->is_one('-'); # -1 => -1 | |
1531 | if (!$y->is_one()) | |
1532 | { | |
1533 | # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al | |
1534 | # but perhaps there is a better emulation for two's complement shift... | |
1535 | # if $y != 1, we must simulate it by doing: | |
1536 | # convert to bin, flip all bits, shift, and be done | |
1537 | $x->binc(); # -3 => -2 | |
1538 | my $bin = $x->as_bin(); | |
1539 | $bin =~ s/^-0b//; # strip '-0b' prefix | |
1540 | $bin =~ tr/10/01/; # flip bits | |
1541 | # now shift | |
1542 | if (length($bin) <= $y) | |
1543 | { | |
1544 | $bin = '0'; # shifting to far right creates -1 | |
1545 | # 0, because later increment makes | |
1546 | # that 1, attached '-' makes it '-1' | |
1547 | # because -1 >> x == -1 ! | |
1548 | } | |
1549 | else | |
1550 | { | |
1551 | $bin =~ s/.{$y}$//; # cut off at the right side | |
1552 | $bin = '1' . $bin; # extend left side by one dummy '1' | |
1553 | $bin =~ tr/10/01/; # flip bits back | |
1554 | } | |
1555 | my $res = $self->new('0b'.$bin); # add prefix and convert back | |
1556 | $res->binc(); # remember to increment | |
1557 | $x->{value} = $res->{value}; # take over value | |
1558 | return $x->round($a,$p,$r); # we are done now, magic, isn't? | |
1559 | } | |
1560 | $x->bdec(); # n == 2, but $y == 1: this fixes it | |
1561 | } | |
1562 | ||
027dc388 | 1563 | my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft'); |
574bacfe JH |
1564 | if (defined $t) |
1565 | { | |
b3abae2a JH |
1566 | $x->{value} = $t; |
1567 | return $x->round($a,$p,$r); | |
574bacfe JH |
1568 | } |
1569 | # fallback | |
b3abae2a JH |
1570 | $x->bdiv($self->bpow($n,$y, $a,$p,$r), $a,$p,$r); |
1571 | $x; | |
58cde26e JH |
1572 | } |
1573 | ||
1574 | sub band | |
1575 | { | |
1576 | #(BINT or num_str, BINT or num_str) return BINT | |
1577 | # compute x & y | |
0716bf9b | 1578 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1579 | |
1580 | return $x if $x->modify('band'); | |
1581 | ||
b3abae2a JH |
1582 | local $Math::BigInt::upgrade = undef; |
1583 | ||
58cde26e | 1584 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
394e6ffb | 1585 | return $x->bzero() if $y->is_zero() || $x->is_zero(); |
0716bf9b | 1586 | |
574bacfe JH |
1587 | my $sign = 0; # sign of result |
1588 | $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-'); | |
1589 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; | |
1590 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; | |
1591 | ||
1592 | if ($CALC->can('_and') && $sx == 1 && $sy == 1) | |
0716bf9b | 1593 | { |
574bacfe | 1594 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
0716bf9b JH |
1595 | return $x->round($a,$p,$r); |
1596 | } | |
574bacfe | 1597 | |
b3abae2a JH |
1598 | my $m = $self->bone(); my ($xr,$yr); |
1599 | my $x10000 = $self->new (0x1000); | |
574bacfe JH |
1600 | my $y1 = copy(ref($x),$y); # make copy |
1601 | $y1->babs(); # and positive | |
1602 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! | |
1603 | use integer; # need this for negative bools | |
0716bf9b | 1604 | while (!$x1->is_zero() && !$y1->is_zero()) |
58cde26e | 1605 | { |
0716bf9b | 1606 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e | 1607 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe JH |
1608 | # make both op's numbers! |
1609 | $x->badd( bmul( $class->new( | |
1610 | abs($sx*int($xr->numify()) & $sy*int($yr->numify()))), | |
1611 | $m)); | |
58cde26e JH |
1612 | $m->bmul($x10000); |
1613 | } | |
574bacfe | 1614 | $x->bneg() if $sign; |
0716bf9b | 1615 | return $x->round($a,$p,$r); |
58cde26e JH |
1616 | } |
1617 | ||
1618 | sub bior | |
1619 | { | |
1620 | #(BINT or num_str, BINT or num_str) return BINT | |
1621 | # compute x | y | |
0716bf9b | 1622 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1623 | |
1624 | return $x if $x->modify('bior'); | |
1625 | ||
b3abae2a JH |
1626 | local $Math::BigInt::upgrade = undef; |
1627 | ||
58cde26e JH |
1628 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
1629 | return $x if $y->is_zero(); | |
574bacfe JH |
1630 | |
1631 | my $sign = 0; # sign of result | |
1632 | $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-'); | |
1633 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; | |
1634 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; | |
1635 | ||
1636 | # don't use lib for negative values | |
1637 | if ($CALC->can('_or') && $sx == 1 && $sy == 1) | |
0716bf9b | 1638 | { |
574bacfe | 1639 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
0716bf9b JH |
1640 | return $x->round($a,$p,$r); |
1641 | } | |
1642 | ||
b3abae2a JH |
1643 | my $m = $self->bone(); my ($xr,$yr); |
1644 | my $x10000 = $self->new(0x10000); | |
574bacfe JH |
1645 | my $y1 = copy(ref($x),$y); # make copy |
1646 | $y1->babs(); # and positive | |
1647 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! | |
1648 | use integer; # need this for negative bools | |
0716bf9b | 1649 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e | 1650 | { |
0716bf9b | 1651 | ($x1, $xr) = bdiv($x1,$x10000); |
58cde26e | 1652 | ($y1, $yr) = bdiv($y1,$x10000); |
574bacfe JH |
1653 | # make both op's numbers! |
1654 | $x->badd( bmul( $class->new( | |
1655 | abs($sx*int($xr->numify()) | $sy*int($yr->numify()))), | |
1656 | $m)); | |
58cde26e JH |
1657 | $m->bmul($x10000); |
1658 | } | |
574bacfe | 1659 | $x->bneg() if $sign; |
0716bf9b | 1660 | return $x->round($a,$p,$r); |
58cde26e JH |
1661 | } |
1662 | ||
1663 | sub bxor | |
1664 | { | |
1665 | #(BINT or num_str, BINT or num_str) return BINT | |
1666 | # compute x ^ y | |
0716bf9b | 1667 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
58cde26e JH |
1668 | |
1669 | return $x if $x->modify('bxor'); | |
1670 | ||
b3abae2a JH |
1671 | local $Math::BigInt::upgrade = undef; |
1672 | ||
0716bf9b | 1673 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
58cde26e | 1674 | return $x if $y->is_zero(); |
0716bf9b | 1675 | |
574bacfe JH |
1676 | my $sign = 0; # sign of result |
1677 | $sign = 1 if $x->{sign} ne $y->{sign}; | |
1678 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; | |
1679 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; | |
1680 | ||
1681 | # don't use lib for negative values | |
1682 | if ($CALC->can('_xor') && $sx == 1 && $sy == 1) | |
0716bf9b | 1683 | { |
574bacfe | 1684 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
0716bf9b JH |
1685 | return $x->round($a,$p,$r); |
1686 | } | |
1687 | ||
394e6ffb | 1688 | my $m = $self->bone(); my ($xr,$yr); |
b3abae2a | 1689 | my $x10000 = $self->new(0x10000); |
58cde26e | 1690 | my $y1 = copy(ref($x),$y); # make copy |
574bacfe JH |
1691 | $y1->babs(); # and positive |
1692 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! | |
1693 | use integer; # need this for negative bools | |
0716bf9b | 1694 | while (!$x1->is_zero() || !$y1->is_zero()) |
58cde26e | 1695 | { |
0716bf9b | 1696 | ($x1, $xr) = bdiv($x1, $x10000); |
58cde26e | 1697 | ($y1, $yr) = bdiv($y1, $x10000); |
574bacfe JH |
1698 | # make both op's numbers! |
1699 | $x->badd( bmul( $class->new( | |
1700 | abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))), | |
1701 | $m)); | |
58cde26e JH |
1702 | $m->bmul($x10000); |
1703 | } | |
574bacfe | 1704 | $x->bneg() if $sign; |
0716bf9b | 1705 | return $x->round($a,$p,$r); |
58cde26e JH |
1706 | } |
1707 | ||
1708 | sub length | |
1709 | { | |
ee15d750 | 1710 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1711 | |
0716bf9b | 1712 | my $e = $CALC->_len($x->{value}); |
0716bf9b | 1713 | return wantarray ? ($e,0) : $e; |
58cde26e JH |
1714 | } |
1715 | ||
1716 | sub digit | |
1717 | { | |
0716bf9b | 1718 | # return the nth decimal digit, negative values count backward, 0 is right |
56b9c951 JH |
1719 | my ($self,$x,$n) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1720 | $n = 0 if !defined $n; | |
58cde26e | 1721 | |
56b9c951 | 1722 | $CALC->_digit($x->{value},$n); |
58cde26e JH |
1723 | } |
1724 | ||
1725 | sub _trailing_zeros | |
1726 | { | |
1727 | # return the amount of trailing zeros in $x | |
1728 | my $x = shift; | |
1729 | $x = $class->new($x) unless ref $x; | |
1730 | ||
dccbb853 | 1731 | return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/; |
0716bf9b JH |
1732 | |
1733 | return $CALC->_zeros($x->{value}) if $CALC->can('_zeros'); | |
1734 | ||
b22b3e31 | 1735 | # if not: since we do not know underlying internal representation: |
0716bf9b | 1736 | my $es = "$x"; $es =~ /([0]*)$/; |
0716bf9b JH |
1737 | return 0 if !defined $1; # no zeros |
1738 | return CORE::length("$1"); # as string, not as +0! | |
58cde26e JH |
1739 | } |
1740 | ||
1741 | sub bsqrt | |
1742 | { | |
394e6ffb | 1743 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1744 | |
b3abae2a JH |
1745 | return $x if $x->modify('bsqrt'); |
1746 | ||
394e6ffb JH |
1747 | return $x->bnan() if $x->{sign} ne '+'; # -x or inf or NaN => NaN |
1748 | return $x->bzero($a,$p) if $x->is_zero(); # 0 => 0 | |
1749 | return $x->round($a,$p,$r) if $x->is_one(); # 1 => 1 | |
b3abae2a JH |
1750 | |
1751 | return $upgrade->bsqrt($x,$a,$p,$r) if defined $upgrade; | |
58cde26e | 1752 | |
394e6ffb JH |
1753 | if ($CALC->can('_sqrt')) |
1754 | { | |
1755 | $x->{value} = $CALC->_sqrt($x->{value}); | |
1756 | return $x->round($a,$p,$r); | |
1757 | } | |
1758 | ||
b3abae2a | 1759 | return $x->bone($a,$p) if $x < 4; # 2,3 => 1 |
394e6ffb | 1760 | my $y = $x->copy(); |
58cde26e JH |
1761 | my $l = int($x->length()/2); |
1762 | ||
394e6ffb JH |
1763 | $x->bone(); # keep ref($x), but modify it |
1764 | $x->blsft($l,10); | |
58cde26e JH |
1765 | |
1766 | my $last = $self->bzero(); | |
394e6ffb JH |
1767 | my $two = $self->new(2); |
1768 | my $lastlast = $x+$two; | |
1769 | while ($last != $x && $lastlast != $x) | |
58cde26e | 1770 | { |
394e6ffb | 1771 | $lastlast = $last; $last = $x; |
58cde26e | 1772 | $x += $y / $x; |
394e6ffb | 1773 | $x /= $two; |
58cde26e | 1774 | } |
394e6ffb | 1775 | $x-- if $x * $x > $y; # overshot? |
b3abae2a | 1776 | $x->round($a,$p,$r); |
58cde26e JH |
1777 | } |
1778 | ||
1779 | sub exponent | |
1780 | { | |
1781 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) | |
ee15d750 | 1782 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 1783 | |
ee15d750 JH |
1784 | if ($x->{sign} !~ /^[+-]$/) |
1785 | { | |
1786 | my $s = $x->{sign}; $s =~ s/^[+-]//; | |
1787 | return $self->new($s); # -inf,+inf => inf | |
1788 | } | |
58cde26e JH |
1789 | my $e = $class->bzero(); |
1790 | return $e->binc() if $x->is_zero(); | |
1791 | $e += $x->_trailing_zeros(); | |
56b9c951 | 1792 | $e; |
58cde26e JH |
1793 | } |
1794 | ||
1795 | sub mantissa | |
1796 | { | |
ee15d750 JH |
1797 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
1798 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 1799 | |
ee15d750 JH |
1800 | if ($x->{sign} !~ /^[+-]$/) |
1801 | { | |
28df3e88 | 1802 | return $self->new($x->{sign}); # keep + or - sign |
ee15d750 | 1803 | } |
58cde26e JH |
1804 | my $m = $x->copy(); |
1805 | # that's inefficient | |
1806 | my $zeros = $m->_trailing_zeros(); | |
56b9c951 JH |
1807 | $m->brsft($zeros,10) if $zeros != 0; |
1808 | # $m /= 10 ** $zeros if $zeros != 0; | |
1809 | $m; | |
58cde26e JH |
1810 | } |
1811 | ||
1812 | sub parts | |
1813 | { | |
ee15d750 JH |
1814 | # return a copy of both the exponent and the mantissa |
1815 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 1816 | |
ee15d750 | 1817 | return ($x->mantissa(),$x->exponent()); |
58cde26e JH |
1818 | } |
1819 | ||
1820 | ############################################################################## | |
1821 | # rounding functions | |
1822 | ||
1823 | sub bfround | |
1824 | { | |
1825 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' | |
ee15d750 | 1826 | # $n == 0 || $n == 1 => round to integer |
58cde26e | 1827 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 | 1828 | my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_); |
58cde26e | 1829 | return $x if !defined $scale; # no-op |
b3abae2a | 1830 | return $x if $x->modify('bfround'); |
58cde26e JH |
1831 | |
1832 | # no-op for BigInts if $n <= 0 | |
ee15d750 JH |
1833 | if ($scale <= 0) |
1834 | { | |
61f5c3f5 | 1835 | $x->{_a} = undef; # clear an eventual set A |
ee15d750 JH |
1836 | $x->{_p} = $scale; return $x; |
1837 | } | |
58cde26e JH |
1838 | |
1839 | $x->bround( $x->length()-$scale, $mode); | |
ee15d750 JH |
1840 | $x->{_a} = undef; # bround sets {_a} |
1841 | $x->{_p} = $scale; # so correct it | |
1842 | $x; | |
58cde26e JH |
1843 | } |
1844 | ||
1845 | sub _scan_for_nonzero | |
1846 | { | |
1847 | my $x = shift; | |
1848 | my $pad = shift; | |
0716bf9b | 1849 | my $xs = shift; |
58cde26e JH |
1850 | |
1851 | my $len = $x->length(); | |
1852 | return 0 if $len == 1; # '5' is trailed by invisible zeros | |
1853 | my $follow = $pad - 1; | |
1854 | return 0 if $follow > $len || $follow < 1; | |
0716bf9b | 1855 | |
b22b3e31 | 1856 | # since we do not know underlying represention of $x, use decimal string |
0716bf9b | 1857 | #my $r = substr ($$xs,-$follow); |
58cde26e JH |
1858 | my $r = substr ("$x",-$follow); |
1859 | return 1 if $r =~ /[^0]/; return 0; | |
58cde26e JH |
1860 | } |
1861 | ||
1862 | sub fround | |
1863 | { | |
1864 | # to make life easier for switch between MBF and MBI (autoload fxxx() | |
1865 | # like MBF does for bxxx()?) | |
1866 | my $x = shift; | |
1867 | return $x->bround(@_); | |
1868 | } | |
1869 | ||
1870 | sub bround | |
1871 | { | |
1872 | # accuracy: +$n preserve $n digits from left, | |
1873 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) | |
1874 | # no-op for $n == 0 | |
1875 | # and overwrite the rest with 0's, return normalized number | |
1876 | # do not return $x->bnorm(), but $x | |
61f5c3f5 | 1877 | |
58cde26e | 1878 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 | 1879 | my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_); |
61f5c3f5 | 1880 | return $x if !defined $scale; # no-op |
b3abae2a | 1881 | return $x if $x->modify('bround'); |
58cde26e | 1882 | |
61f5c3f5 T |
1883 | if ($x->is_zero() || $scale == 0) |
1884 | { | |
1885 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 | |
1886 | return $x; | |
1887 | } | |
1888 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN | |
58cde26e JH |
1889 | |
1890 | # we have fewer digits than we want to scale to | |
1891 | my $len = $x->length(); | |
ee15d750 JH |
1892 | # scale < 0, but > -len (not >=!) |
1893 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) | |
1894 | { | |
61f5c3f5 | 1895 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
ee15d750 JH |
1896 | return $x; |
1897 | } | |
58cde26e JH |
1898 | |
1899 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 | |
1900 | my ($pad,$digit_round,$digit_after); | |
1901 | $pad = $len - $scale; | |
ee15d750 JH |
1902 | $pad = abs($scale-1) if $scale < 0; |
1903 | ||
0716bf9b | 1904 | # do not use digit(), it is costly for binary => decimal |
ee15d750 | 1905 | |
0716bf9b JH |
1906 | my $xs = $CALC->_str($x->{value}); |
1907 | my $pl = -$pad-1; | |
ee15d750 | 1908 | |
0716bf9b JH |
1909 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
1910 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 | |
1911 | $digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len; | |
1912 | $pl++; $pl ++ if $pad >= $len; | |
61f5c3f5 | 1913 | $digit_after = '0'; $digit_after = substr($$xs,$pl,1) if $pad > 0; |
ee15d750 JH |
1914 | |
1915 | # print "$pad $pl $$xs dr $digit_round da $digit_after\n"; | |
58cde26e JH |
1916 | |
1917 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look | |
1918 | # closer at the remaining digits of the original $x, remember decision | |
1919 | my $round_up = 1; # default round up | |
1920 | $round_up -- if | |
1921 | ($mode eq 'trunc') || # trunc by round down | |
1922 | ($digit_after =~ /[01234]/) || # round down anyway, | |
1923 | # 6789 => round up | |
1924 | ($digit_after eq '5') && # not 5000...0000 | |
0716bf9b | 1925 | ($x->_scan_for_nonzero($pad,$xs) == 0) && |
58cde26e JH |
1926 | ( |
1927 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || | |
1928 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || | |
1929 | ($mode eq '+inf') && ($x->{sign} eq '-') || | |
1930 | ($mode eq '-inf') && ($x->{sign} eq '+') || | |
1931 | ($mode eq 'zero') # round down if zero, sign adjusted below | |
1932 | ); | |
61f5c3f5 T |
1933 | my $put_back = 0; # not yet modified |
1934 | ||
1935 | # old code, depend on internal representation | |
1936 | # split mantissa at $pad and then pad with zeros | |
1937 | #my $s5 = int($pad / 5); | |
1938 | #my $i = 0; | |
1939 | #while ($i < $s5) | |
1940 | # { | |
1941 | # $x->{value}->[$i++] = 0; # replace with 5 x 0 | |
1942 | # } | |
1943 | #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0 | |
1944 | #my $rem = $pad % 5; # so much left over | |
1945 | #if ($rem > 0) | |
1946 | # { | |
1947 | # #print "remainder $rem\n"; | |
1948 | ## #print "elem $x->{value}->[$s5]\n"; | |
1949 | # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0' | |
1950 | # } | |
1951 | #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5' | |
1952 | #print ${$CALC->_str($pad->{value})}," $len\n"; | |
1953 | ||
1954 | if (($pad > 0) && ($pad <= $len)) | |
1955 | { | |
1956 | substr($$xs,-$pad,$pad) = '0' x $pad; | |
1957 | $put_back = 1; | |
58cde26e | 1958 | } |
61f5c3f5 T |
1959 | elsif ($pad > $len) |
1960 | { | |
1961 | $x->bzero(); # round to '0' | |
1962 | } | |
1963 | ||
58cde26e JH |
1964 | if ($round_up) # what gave test above? |
1965 | { | |
61f5c3f5 T |
1966 | $put_back = 1; |
1967 | $pad = $len, $$xs = '0'x$pad if $scale < 0; # tlr: whack 0.51=>1.0 | |
1968 | ||
1969 | # we modify directly the string variant instead of creating a number and | |
1970 | # adding it | |
1971 | my $c = 0; $pad ++; # for $pad == $len case | |
1972 | while ($pad <= $len) | |
1973 | { | |
1974 | $c = substr($$xs,-$pad,1) + 1; $c = '0' if $c eq '10'; | |
1975 | substr($$xs,-$pad,1) = $c; $pad++; | |
1976 | last if $c != 0; # no overflow => early out | |
1977 | } | |
1978 | $$xs = '1'.$$xs if $c == 0; | |
1979 | ||
1980 | # $x->badd( Math::BigInt->new($x->{sign}.'1'. '0' x $pad) ); | |
58cde26e | 1981 | } |
61f5c3f5 | 1982 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back in |
ee15d750 JH |
1983 | |
1984 | $x->{_a} = $scale if $scale >= 0; | |
1985 | if ($scale < 0) | |
1986 | { | |
1987 | $x->{_a} = $len+$scale; | |
1988 | $x->{_a} = 0 if $scale < -$len; | |
1989 | } | |
58cde26e JH |
1990 | $x; |
1991 | } | |
1992 | ||
1993 | sub bfloor | |
1994 | { | |
1995 | # return integer less or equal then number, since it is already integer, | |
1996 | # always returns $self | |
ee15d750 | 1997 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e JH |
1998 | |
1999 | # not needed: return $x if $x->modify('bfloor'); | |
58cde26e JH |
2000 | return $x->round($a,$p,$r); |
2001 | } | |
2002 | ||
2003 | sub bceil | |
2004 | { | |
2005 | # return integer greater or equal then number, since it is already integer, | |
2006 | # always returns $self | |
ee15d750 | 2007 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e JH |
2008 | |
2009 | # not needed: return $x if $x->modify('bceil'); | |
58cde26e JH |
2010 | return $x->round($a,$p,$r); |
2011 | } | |
2012 | ||
2013 | ############################################################################## | |
2014 | # private stuff (internal use only) | |
2015 | ||
574bacfe | 2016 | sub __one |
58cde26e JH |
2017 | { |
2018 | # internal speedup, set argument to 1, or create a +/- 1 | |
2019 | my $self = shift; | |
dccbb853 | 2020 | my $x = $self->bone(); # $x->{value} = $CALC->_one(); |
0716bf9b JH |
2021 | $x->{sign} = shift || '+'; |
2022 | return $x; | |
58cde26e JH |
2023 | } |
2024 | ||
2025 | sub _swap | |
2026 | { | |
2027 | # Overload will swap params if first one is no object ref so that the first | |
2028 | # one is always an object ref. In this case, third param is true. | |
2029 | # This routine is to overcome the effect of scalar,$object creating an object | |
2030 | # of the class of this package, instead of the second param $object. This | |
2031 | # happens inside overload, when the overload section of this package is | |
2032 | # inherited by sub classes. | |
2033 | # For overload cases (and this is used only there), we need to preserve the | |
2034 | # args, hence the copy(). | |
2035 | # You can override this method in a subclass, the overload section will call | |
2036 | # $object->_swap() to make sure it arrives at the proper subclass, with some | |
394e6ffb JH |
2037 | # exceptions like '+' and '-'. To make '+' and '-' work, you also need to |
2038 | # specify your own overload for them. | |
58cde26e JH |
2039 | |
2040 | # object, (object|scalar) => preserve first and make copy | |
2041 | # scalar, object => swapped, re-swap and create new from first | |
2042 | # (using class of second object, not $class!!) | |
2043 | my $self = shift; # for override in subclass | |
58cde26e JH |
2044 | if ($_[2]) |
2045 | { | |
2046 | my $c = ref ($_[0]) || $class; # fallback $class should not happen | |
2047 | return ( $c->new($_[1]), $_[0] ); | |
2048 | } | |
17baacb7 | 2049 | return ( $_[0]->copy(), $_[1] ); |
58cde26e JH |
2050 | } |
2051 | ||
2052 | sub objectify | |
2053 | { | |
2054 | # check for strings, if yes, return objects instead | |
2055 | ||
2056 | # the first argument is number of args objectify() should look at it will | |
2057 | # return $count+1 elements, the first will be a classname. This is because | |
2058 | # overloaded '""' calls bstr($object,undef,undef) and this would result in | |
2059 | # useless objects beeing created and thrown away. So we cannot simple loop | |
2060 | # over @_. If the given count is 0, all arguments will be used. | |
2061 | ||
2062 | # If the second arg is a ref, use it as class. | |
2063 | # If not, try to use it as classname, unless undef, then use $class | |
2064 | # (aka Math::BigInt). The latter shouldn't happen,though. | |
2065 | ||
2066 | # caller: gives us: | |
2067 | # $x->badd(1); => ref x, scalar y | |
2068 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y | |
2069 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y | |
2070 | # Math::BigInt::badd(1,2); => scalar x, scalar y | |
2071 | # In the last case we check number of arguments to turn it silently into | |
574bacfe | 2072 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e JH |
2073 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
2074 | # currently it tries 'Math::BigInt' + 1, which will not work. | |
ee15d750 JH |
2075 | |
2076 | # some shortcut for the common cases | |
2077 | ||
2078 | # $x->unary_op(); | |
2079 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); | |
ee15d750 | 2080 | |
58cde26e JH |
2081 | my $count = abs(shift || 0); |
2082 | ||
9393ace2 | 2083 | my (@a,$k,$d); # resulting array, temp, and downgrade |
58cde26e JH |
2084 | if (ref $_[0]) |
2085 | { | |
2086 | # okay, got object as first | |
2087 | $a[0] = ref $_[0]; | |
2088 | } | |
2089 | else | |
2090 | { | |
2091 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) | |
2092 | $a[0] = $class; | |
58cde26e JH |
2093 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
2094 | } | |
9393ace2 JH |
2095 | no strict 'refs'; |
2096 | # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats | |
2097 | if (defined ${"$a[0]::downgrade"}) | |
2098 | { | |
2099 | $d = ${"$a[0]::downgrade"}; | |
2100 | ${"$a[0]::downgrade"} = undef; | |
2101 | } | |
2102 | ||
58cde26e | 2103 | # print "Now in objectify, my class is today $a[0]\n"; |
58cde26e JH |
2104 | if ($count == 0) |
2105 | { | |
2106 | while (@_) | |
2107 | { | |
2108 | $k = shift; | |
2109 | if (!ref($k)) | |
2110 | { | |
2111 | $k = $a[0]->new($k); | |
2112 | } | |
2113 | elsif (ref($k) ne $a[0]) | |
2114 | { | |
2115 | # foreign object, try to convert to integer | |
2116 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
e16b8f49 | 2117 | } |
58cde26e JH |
2118 | push @a,$k; |
2119 | } | |
2120 | } | |
2121 | else | |
2122 | { | |
2123 | while ($count > 0) | |
2124 | { | |
58cde26e JH |
2125 | $count--; |
2126 | $k = shift; | |
2127 | if (!ref($k)) | |
2128 | { | |
2129 | $k = $a[0]->new($k); | |
2130 | } | |
2131 | elsif (ref($k) ne $a[0]) | |
2132 | { | |
2133 | # foreign object, try to convert to integer | |
2134 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
e16b8f49 | 2135 | } |
58cde26e JH |
2136 | push @a,$k; |
2137 | } | |
2138 | push @a,@_; # return other params, too | |
2139 | } | |
58cde26e | 2140 | die "$class objectify needs list context" unless wantarray; |
9393ace2 | 2141 | ${"$a[0]::downgrade"} = $d; |
58cde26e JH |
2142 | @a; |
2143 | } | |
2144 | ||
2145 | sub import | |
2146 | { | |
2147 | my $self = shift; | |
61f5c3f5 T |
2148 | |
2149 | $IMPORT++; | |
0716bf9b JH |
2150 | my @a = @_; my $l = scalar @_; my $j = 0; |
2151 | for ( my $i = 0; $i < $l ; $i++,$j++ ) | |
58cde26e | 2152 | { |
0716bf9b | 2153 | if ($_[$i] eq ':constant') |
58cde26e | 2154 | { |
0716bf9b | 2155 | # this causes overlord er load to step in |
58cde26e | 2156 | overload::constant integer => sub { $self->new(shift) }; |
56b9c951 | 2157 | overload::constant binary => sub { $self->new(shift) }; |
0716bf9b JH |
2158 | splice @a, $j, 1; $j --; |
2159 | } | |
b3abae2a JH |
2160 | elsif ($_[$i] eq 'upgrade') |
2161 | { | |
2162 | # this causes upgrading | |
2163 | $upgrade = $_[$i+1]; # or undef to disable | |
2164 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." | |
2165 | splice @a, $j, $s; $j -= $s; | |
2166 | } | |
0716bf9b JH |
2167 | elsif ($_[$i] =~ /^lib$/i) |
2168 | { | |
2169 | # this causes a different low lib to take care... | |
61f5c3f5 | 2170 | $CALC = $_[$i+1] || ''; |
b3abae2a | 2171 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
0716bf9b | 2172 | splice @a, $j, $s; $j -= $s; |
58cde26e JH |
2173 | } |
2174 | } | |
2175 | # any non :constant stuff is handled by our parent, Exporter | |
2176 | # even if @_ is empty, to give it a chance | |
dccbb853 JH |
2177 | $self->SUPER::import(@a); # need it for subclasses |
2178 | $self->export_to_level(1,$self,@a); # need it for MBF | |
58cde26e | 2179 | |
574bacfe JH |
2180 | # try to load core math lib |
2181 | my @c = split /\s*,\s*/,$CALC; | |
2182 | push @c,'Calc'; # if all fail, try this | |
61f5c3f5 | 2183 | $CALC = ''; # signal error |
574bacfe JH |
2184 | foreach my $lib (@c) |
2185 | { | |
2186 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; | |
2187 | $lib =~ s/\.pm$//; | |
61f5c3f5 | 2188 | if ($] < 5.006) |
574bacfe JH |
2189 | { |
2190 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is | |
2191 | # used in the same script, or eval inside import(). | |
2192 | (my $mod = $lib . '.pm') =~ s!::!/!g; | |
2193 | # require does not automatically :: => /, so portability problems arise | |
bd05a461 | 2194 | eval { require $mod; $lib->import( @c ); } |
574bacfe JH |
2195 | } |
2196 | else | |
2197 | { | |
61f5c3f5 | 2198 | eval "use $lib qw/@c/;"; |
574bacfe | 2199 | } |
bd05a461 | 2200 | $CALC = $lib, last if $@ eq ''; # no error in loading lib? |
574bacfe | 2201 | } |
61f5c3f5 | 2202 | die "Couldn't load any math lib, not even the default" if $CALC eq ''; |
58cde26e JH |
2203 | } |
2204 | ||
574bacfe | 2205 | sub __from_hex |
58cde26e JH |
2206 | { |
2207 | # convert a (ref to) big hex string to BigInt, return undef for error | |
2208 | my $hs = shift; | |
2209 | ||
2210 | my $x = Math::BigInt->bzero(); | |
394e6ffb JH |
2211 | |
2212 | # strip underscores | |
2213 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
2214 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
2215 | ||
58cde26e JH |
2216 | return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
2217 | ||
b22b3e31 | 2218 | my $sign = '+'; $sign = '-' if ($$hs =~ /^-/); |
58cde26e | 2219 | |
b22b3e31 | 2220 | $$hs =~ s/^[+-]//; # strip sign |
0716bf9b | 2221 | if ($CALC->can('_from_hex')) |
58cde26e | 2222 | { |
0716bf9b | 2223 | $x->{value} = $CALC->_from_hex($hs); |
58cde26e | 2224 | } |
0716bf9b | 2225 | else |
58cde26e | 2226 | { |
0716bf9b JH |
2227 | # fallback to pure perl |
2228 | my $mul = Math::BigInt->bzero(); $mul++; | |
2229 | my $x65536 = Math::BigInt->new(65536); | |
2230 | my $len = CORE::length($$hs)-2; | |
2231 | $len = int($len/4); # 4-digit parts, w/o '0x' | |
2232 | my $val; my $i = -4; | |
2233 | while ($len >= 0) | |
2234 | { | |
2235 | $val = substr($$hs,$i,4); | |
b22b3e31 | 2236 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because |
0716bf9b | 2237 | $val = hex($val); # hex does not like wrong chars |
0716bf9b JH |
2238 | $i -= 4; $len --; |
2239 | $x += $mul * $val if $val != 0; | |
2240 | $mul *= $x65536 if $len >= 0; # skip last mul | |
2241 | } | |
58cde26e | 2242 | } |
13a12e00 JH |
2243 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2244 | $x; | |
58cde26e JH |
2245 | } |
2246 | ||
574bacfe | 2247 | sub __from_bin |
58cde26e JH |
2248 | { |
2249 | # convert a (ref to) big binary string to BigInt, return undef for error | |
2250 | my $bs = shift; | |
2251 | ||
2252 | my $x = Math::BigInt->bzero(); | |
394e6ffb JH |
2253 | # strip underscores |
2254 | $$bs =~ s/([01])_([01])/$1$2/g; | |
2255 | $$bs =~ s/([01])_([01])/$1$2/g; | |
b22b3e31 | 2256 | return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/; |
58cde26e | 2257 | |
0716bf9b | 2258 | my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/); |
b22b3e31 | 2259 | $$bs =~ s/^[+-]//; # strip sign |
0716bf9b | 2260 | if ($CALC->can('_from_bin')) |
58cde26e | 2261 | { |
0716bf9b | 2262 | $x->{value} = $CALC->_from_bin($bs); |
58cde26e | 2263 | } |
0716bf9b | 2264 | else |
58cde26e | 2265 | { |
13a12e00 JH |
2266 | my $mul = Math::BigInt->bzero(); $mul++; |
2267 | my $x256 = Math::BigInt->new(256); | |
0716bf9b JH |
2268 | my $len = CORE::length($$bs)-2; |
2269 | $len = int($len/8); # 8-digit parts, w/o '0b' | |
2270 | my $val; my $i = -8; | |
2271 | while ($len >= 0) | |
2272 | { | |
2273 | $val = substr($$bs,$i,8); | |
b22b3e31 PN |
2274 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only |
2275 | #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0 | |
394e6ffb JH |
2276 | # slower: |
2277 | # $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8; | |
2278 | $val = ord(pack('B8',substr('00000000'.$val,-8,8))); | |
0716bf9b JH |
2279 | $i -= 8; $len --; |
2280 | $x += $mul * $val if $val != 0; | |
2281 | $mul *= $x256 if $len >= 0; # skip last mul | |
2282 | } | |
58cde26e | 2283 | } |
13a12e00 JH |
2284 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2285 | $x; | |
58cde26e JH |
2286 | } |
2287 | ||
2288 | sub _split | |
2289 | { | |
2290 | # (ref to num_str) return num_str | |
2291 | # internal, take apart a string and return the pieces | |
dccbb853 | 2292 | # strip leading/trailing whitespace, leading zeros, underscore and reject |
574bacfe | 2293 | # invalid input |
58cde26e JH |
2294 | my $x = shift; |
2295 | ||
574bacfe JH |
2296 | # strip white space at front, also extranous leading zeros |
2297 | $$x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' | |
2298 | $$x =~ s/^\s+//; # but this will | |
58cde26e | 2299 | $$x =~ s/\s+$//g; # strip white space at end |
58cde26e | 2300 | |
574bacfe JH |
2301 | # shortcut, if nothing to split, return early |
2302 | if ($$x =~ /^[+-]?\d+$/) | |
2303 | { | |
2304 | $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; | |
2305 | return (\$sign, $x, \'', \'', \0); | |
2306 | } | |
58cde26e | 2307 | |
574bacfe JH |
2308 | # invalid starting char? |
2309 | return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; | |
58cde26e | 2310 | |
574bacfe JH |
2311 | return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string |
2312 | return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string | |
394e6ffb JH |
2313 | |
2314 | # strip underscores between digits | |
2315 | $$x =~ s/(\d)_(\d)/$1$2/g; | |
2316 | $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 | |
574bacfe | 2317 | |
58cde26e JH |
2318 | # some possible inputs: |
2319 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 | |
2320 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 | |
2321 | ||
027dc388 JH |
2322 | return if $$x =~ /[Ee].*[Ee]/; # more than one E => error |
2323 | ||
58cde26e JH |
2324 | my ($m,$e) = split /[Ee]/,$$x; |
2325 | $e = '0' if !defined $e || $e eq ""; | |
58cde26e JH |
2326 | # sign,value for exponent,mantint,mantfrac |
2327 | my ($es,$ev,$mis,$miv,$mfv); | |
2328 | # valid exponent? | |
2329 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros | |
2330 | { | |
2331 | $es = $1; $ev = $2; | |
58cde26e JH |
2332 | # valid mantissa? |
2333 | return if $m eq '.' || $m eq ''; | |
2334 | my ($mi,$mf) = split /\./,$m; | |
2335 | $mi = '0' if !defined $mi; | |
2336 | $mi .= '0' if $mi =~ /^[\-\+]?$/; | |
2337 | $mf = '0' if !defined $mf || $mf eq ''; | |
2338 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros | |
2339 | { | |
2340 | $mis = $1||'+'; $miv = $2; | |
58cde26e JH |
2341 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros |
2342 | $mfv = $1; | |
58cde26e JH |
2343 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
2344 | } | |
2345 | } | |
2346 | return; # NaN, not a number | |
2347 | } | |
2348 | ||
58cde26e JH |
2349 | sub as_number |
2350 | { | |
2351 | # an object might be asked to return itself as bigint on certain overloaded | |
2352 | # operations, this does exactly this, so that sub classes can simple inherit | |
2353 | # it or override with their own integer conversion routine | |
2354 | my $self = shift; | |
2355 | ||
17baacb7 | 2356 | $self->copy(); |
58cde26e JH |
2357 | } |
2358 | ||
bd05a461 JH |
2359 | sub as_hex |
2360 | { | |
2361 | # return as hex string, with prefixed 0x | |
2362 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2363 | ||
2364 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2365 | return '0x0' if $x->is_zero(); | |
2366 | ||
2367 | my $es = ''; my $s = ''; | |
2368 | $s = $x->{sign} if $x->{sign} eq '-'; | |
bd05a461 JH |
2369 | if ($CALC->can('_as_hex')) |
2370 | { | |
ee15d750 | 2371 | $es = ${$CALC->_as_hex($x->{value})}; |
bd05a461 JH |
2372 | } |
2373 | else | |
2374 | { | |
2375 | my $x1 = $x->copy()->babs(); my $xr; | |
61f5c3f5 | 2376 | my $x10000 = Math::BigInt->new (0x10000); |
bd05a461 JH |
2377 | while (!$x1->is_zero()) |
2378 | { | |
61f5c3f5 T |
2379 | ($x1, $xr) = bdiv($x1,$x10000); |
2380 | $es .= unpack('h4',pack('v',$xr->numify())); | |
bd05a461 JH |
2381 | } |
2382 | $es = reverse $es; | |
2383 | $es =~ s/^[0]+//; # strip leading zeros | |
ee15d750 | 2384 | $s .= '0x'; |
bd05a461 JH |
2385 | } |
2386 | $s . $es; | |
2387 | } | |
2388 | ||
2389 | sub as_bin | |
2390 | { | |
2391 | # return as binary string, with prefixed 0b | |
2392 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2393 | ||
2394 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2395 | return '0b0' if $x->is_zero(); | |
2396 | ||
2397 | my $es = ''; my $s = ''; | |
2398 | $s = $x->{sign} if $x->{sign} eq '-'; | |
bd05a461 JH |
2399 | if ($CALC->can('_as_bin')) |
2400 | { | |
ee15d750 | 2401 | $es = ${$CALC->_as_bin($x->{value})}; |
bd05a461 JH |
2402 | } |
2403 | else | |
2404 | { | |
2405 | my $x1 = $x->copy()->babs(); my $xr; | |
61f5c3f5 | 2406 | my $x10000 = Math::BigInt->new (0x10000); |
bd05a461 JH |
2407 | while (!$x1->is_zero()) |
2408 | { | |
61f5c3f5 T |
2409 | ($x1, $xr) = bdiv($x1,$x10000); |
2410 | $es .= unpack('b16',pack('v',$xr->numify())); | |
bd05a461 JH |
2411 | } |
2412 | $es = reverse $es; | |
2413 | $es =~ s/^[0]+//; # strip leading zeros | |
ee15d750 | 2414 | $s .= '0b'; |
bd05a461 JH |
2415 | } |
2416 | $s . $es; | |
2417 | } | |
2418 | ||
58cde26e | 2419 | ############################################################################## |
0716bf9b | 2420 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e | 2421 | |
dccbb853 | 2422 | sub __lcm |
58cde26e JH |
2423 | { |
2424 | # (BINT or num_str, BINT or num_str) return BINT | |
2425 | # does modify first argument | |
2426 | # LCM | |
2427 | ||
2428 | my $x = shift; my $ty = shift; | |
2429 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); | |
2430 | return $x * $ty / bgcd($x,$ty); | |
2431 | } | |
2432 | ||
574bacfe | 2433 | sub __gcd |
58cde26e JH |
2434 | { |
2435 | # (BINT or num_str, BINT or num_str) return BINT | |
dccbb853 | 2436 | # does modify both arguments |
58cde26e | 2437 | # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296 |
dccbb853 JH |
2438 | my ($x,$ty) = @_; |
2439 | ||
0716bf9b | 2440 | return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/; |
58cde26e JH |
2441 | |
2442 | while (!$ty->is_zero()) | |
2443 | { | |
2444 | ($x, $ty) = ($ty,bmod($x,$ty)); | |
2445 | } | |
2446 | $x; | |
2447 | } | |
2448 | ||
58cde26e JH |
2449 | ############################################################################### |
2450 | # this method return 0 if the object can be modified, or 1 for not | |
2451 | # We use a fast use constant statement here, to avoid costly calls. Subclasses | |
2452 | # may override it with special code (f.i. Math::BigInt::Constant does so) | |
2453 | ||
0716bf9b | 2454 | sub modify () { 0; } |
e16b8f49 | 2455 | |
a0d0e21e | 2456 | 1; |
a5f75d66 AD |
2457 | __END__ |
2458 | ||
2459 | =head1 NAME | |
2460 | ||
2461 | Math::BigInt - Arbitrary size integer math package | |
2462 | ||
2463 | =head1 SYNOPSIS | |
2464 | ||
2465 | use Math::BigInt; | |
58cde26e JH |
2466 | |
2467 | # Number creation | |
574bacfe JH |
2468 | $x = Math::BigInt->new($str); # defaults to 0 |
2469 | $nan = Math::BigInt->bnan(); # create a NotANumber | |
2470 | $zero = Math::BigInt->bzero(); # create a +0 | |
2471 | $inf = Math::BigInt->binf(); # create a +inf | |
2472 | $inf = Math::BigInt->binf('-'); # create a -inf | |
2473 | $one = Math::BigInt->bone(); # create a +1 | |
2474 | $one = Math::BigInt->bone('-'); # create a -1 | |
58cde26e JH |
2475 | |
2476 | # Testing | |
574bacfe JH |
2477 | $x->is_zero(); # true if arg is +0 |
2478 | $x->is_nan(); # true if arg is NaN | |
0716bf9b JH |
2479 | $x->is_one(); # true if arg is +1 |
2480 | $x->is_one('-'); # true if arg is -1 | |
2481 | $x->is_odd(); # true if odd, false for even | |
2482 | $x->is_even(); # true if even, false for odd | |
2483 | $x->is_positive(); # true if >= 0 | |
2484 | $x->is_negative(); # true if < 0 | |
2485 | $x->is_inf(sign); # true if +inf, or -inf (sign is default '+') | |
b3abae2a | 2486 | $x->is_int(); # true if $x is an integer (not a float) |
0716bf9b | 2487 | |
58cde26e JH |
2488 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
2489 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
2490 | $x->sign(); # return the sign, either +,- or NaN | |
2491 | $x->digit($n); # return the nth digit, counting from right | |
2492 | $x->digit(-$n); # return the nth digit, counting from left | |
2493 | ||
2494 | # The following all modify their first argument: | |
2495 | ||
2496 | # set | |
2497 | $x->bzero(); # set $x to 0 | |
2498 | $x->bnan(); # set $x to NaN | |
574bacfe JH |
2499 | $x->bone(); # set $x to +1 |
2500 | $x->bone('-'); # set $x to -1 | |
b3abae2a JH |
2501 | $x->binf(); # set $x to inf |
2502 | $x->binf('-'); # set $x to -inf | |
58cde26e JH |
2503 | |
2504 | $x->bneg(); # negation | |
2505 | $x->babs(); # absolute value | |
2506 | $x->bnorm(); # normalize (no-op) | |
2507 | $x->bnot(); # two's complement (bit wise not) | |
2508 | $x->binc(); # increment x by 1 | |
2509 | $x->bdec(); # decrement x by 1 | |
2510 | ||
2511 | $x->badd($y); # addition (add $y to $x) | |
2512 | $x->bsub($y); # subtraction (subtract $y from $x) | |
2513 | $x->bmul($y); # multiplication (multiply $x by $y) | |
2514 | $x->bdiv($y); # divide, set $x to quotient | |
2515 | # return (quo,rem) or quo if scalar | |
2516 | ||
2517 | $x->bmod($y); # modulus (x % y) | |
2518 | $x->bpow($y); # power of arguments (x ** y) | |
2519 | $x->blsft($y); # left shift | |
2520 | $x->brsft($y); # right shift | |
2521 | $x->blsft($y,$n); # left shift, by base $n (like 10) | |
2522 | $x->brsft($y,$n); # right shift, by base $n (like 10) | |
2523 | ||
2524 | $x->band($y); # bitwise and | |
2525 | $x->bior($y); # bitwise inclusive or | |
2526 | $x->bxor($y); # bitwise exclusive or | |
2527 | $x->bnot(); # bitwise not (two's complement) | |
2528 | ||
2529 | $x->bsqrt(); # calculate square-root | |
b3abae2a | 2530 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
58cde26e JH |
2531 | |
2532 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r | |
2533 | $x->bround($N); # accuracy: preserve $N digits | |
2534 | $x->bfround($N); # round to $Nth digit, no-op for BigInts | |
2535 | ||
2536 | # The following do not modify their arguments in BigInt, but do in BigFloat: | |
2537 | $x->bfloor(); # return integer less or equal than $x | |
2538 | $x->bceil(); # return integer greater or equal than $x | |
2539 | ||
2540 | # The following do not modify their arguments: | |
2541 | ||
dccbb853 JH |
2542 | bgcd(@values); # greatest common divisor (no OO style) |
2543 | blcm(@values); # lowest common multiplicator (no OO style) | |
bd05a461 | 2544 | |
58cde26e | 2545 | $x->length(); # return number of digits in number |
bd05a461 JH |
2546 | ($x,$f) = $x->length(); # length of number and length of fraction part, |
2547 | # latter is always 0 digits long for BigInt's | |
58cde26e JH |
2548 | |
2549 | $x->exponent(); # return exponent as BigInt | |
ee15d750 | 2550 | $x->mantissa(); # return (signed) mantissa as BigInt |
58cde26e | 2551 | $x->parts(); # return (mantissa,exponent) as BigInt |
0716bf9b JH |
2552 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
2553 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) | |
bd05a461 JH |
2554 | |
2555 | # conversation to string | |
2556 | $x->bstr(); # normalized string | |
2557 | $x->bsstr(); # normalized string in scientific notation | |
2558 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x | |
2559 | $x->as_bin(); # as signed binary string with prefixed 0b | |
2560 | ||
a5f75d66 AD |
2561 | =head1 DESCRIPTION |
2562 | ||
58cde26e JH |
2563 | All operators (inlcuding basic math operations) are overloaded if you |
2564 | declare your big integers as | |
a5f75d66 | 2565 | |
58cde26e | 2566 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 | 2567 | |
58cde26e JH |
2568 | Operations with overloaded operators preserve the arguments which is |
2569 | exactly what you expect. | |
a5f75d66 AD |
2570 | |
2571 | =over 2 | |
2572 | ||
2573 | =item Canonical notation | |
2574 | ||
58cde26e | 2575 | Big integer values are strings of the form C</^[+-]\d+$/> with leading |
a5f75d66 AD |
2576 | zeros suppressed. |
2577 | ||
58cde26e JH |
2578 | '-0' canonical value '-0', normalized '0' |
2579 | ' -123_123_123' canonical value '-123123123' | |
2580 | '1_23_456_7890' canonical value '1234567890' | |
2581 | ||
a5f75d66 AD |
2582 | =item Input |
2583 | ||
58cde26e JH |
2584 | Input values to these routines may be either Math::BigInt objects or |
2585 | strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>. | |
2586 | ||
2587 | You can include one underscore between any two digits. | |
2588 | ||
2589 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. | |
2590 | Non integer values result in NaN. | |
2591 | ||
2592 | Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results | |
2593 | in 'NaN'. | |
2594 | ||
2595 | bnorm() on a BigInt object is now effectively a no-op, since the numbers | |
2596 | are always stored in normalized form. On a string, it creates a BigInt | |
2597 | object. | |
a5f75d66 AD |
2598 | |
2599 | =item Output | |
2600 | ||
58cde26e JH |
2601 | Output values are BigInt objects (normalized), except for bstr(), which |
2602 | returns a string in normalized form. | |
2603 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, | |
2604 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) | |
2605 | return either undef, <0, 0 or >0 and are suited for sort. | |
a5f75d66 AD |
2606 | |
2607 | =back | |
2608 | ||
b3abae2a JH |
2609 | =head1 METHODS |
2610 | ||
2611 | Each of the methods below accepts three additional parameters. These arguments | |
2612 | $A, $P and $R are accuracy, precision and round_mode. Please see more in the | |
2613 | section about ACCURACY and ROUNDIND. | |
2614 | ||
13a12e00 JH |
2615 | =head2 accuracy |
2616 | ||
2617 | $x->accuracy(5); # local for $x | |
2618 | $class->accuracy(5); # global for all members of $class | |
2619 | ||
2620 | Set or get the global or local accuracy, aka how many significant digits the | |
2621 | results have. Please see the section about L<ACCURACY AND PRECISION> for | |
2622 | further details. | |
2623 | ||
2624 | Value must be greater than zero. Pass an undef value to disable it: | |
2625 | ||
2626 | $x->accuracy(undef); | |
2627 | Math::BigInt->accuracy(undef); | |
2628 | ||
2629 | Returns the current accuracy. For C<$x->accuracy()> it will return either the | |
2630 | local accuracy, or if not defined, the global. This means the return value | |
2631 | represents the accuracy that will be in effect for $x: | |
2632 | ||
2633 | $y = Math::BigInt->new(1234567); # unrounded | |
2634 | print Math::BigInt->accuracy(4),"\n"; # set 4, print 4 | |
2635 | $x = Math::BigInt->new(123456); # will be automatically rounded | |
2636 | print "$x $y\n"; # '123500 1234567' | |
2637 | print $x->accuracy(),"\n"; # will be 4 | |
2638 | print $y->accuracy(),"\n"; # also 4, since global is 4 | |
2639 | print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5 | |
2640 | print $x->accuracy(),"\n"; # still 4 | |
2641 | print $y->accuracy(),"\n"; # 5, since global is 5 | |
2642 | ||
b3abae2a JH |
2643 | =head2 brsft |
2644 | ||
2645 | $x->brsft($y,$n); | |
2646 | ||
2647 | Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and | |
2648 | 2, but others work, too. | |
2649 | ||
2650 | Right shifting usually amounts to dividing $x by $n ** $y and truncating the | |
2651 | result: | |
2652 | ||
2653 | ||
2654 | $x = Math::BigInt->new(10); | |
2655 | $x->brsft(1); # same as $x >> 1: 5 | |
2656 | $x = Math::BigInt->new(1234); | |
2657 | $x->brsft(2,10); # result 12 | |
2658 | ||
2659 | There is one exception, and that is base 2 with negative $x: | |
2660 | ||
2661 | ||
2662 | $x = Math::BigInt->new(-5); | |
2663 | print $x->brsft(1); | |
2664 | ||
2665 | This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the | |
2666 | result). | |
2667 | ||
2668 | =head2 new | |
2669 | ||
2670 | $x = Math::BigInt->new($str,$A,$P,$R); | |
2671 | ||
2672 | Creates a new BigInt object from a string or another BigInt object. The | |
2673 | input is accepted as decimal, hex (with leading '0x') or binary (with leading | |
2674 | '0b'). | |
2675 | ||
2676 | =head2 bnan | |
2677 | ||
2678 | $x = Math::BigInt->bnan(); | |
2679 | ||
2680 | Creates a new BigInt object representing NaN (Not A Number). | |
2681 | If used on an object, it will set it to NaN: | |
2682 | ||
2683 | $x->bnan(); | |
2684 | ||
2685 | =head2 bzero | |
2686 | ||
2687 | $x = Math::BigInt->bzero(); | |
2688 | ||
2689 | Creates a new BigInt object representing zero. | |
2690 | If used on an object, it will set it to zero: | |
2691 | ||
2692 | $x->bzero(); | |
2693 | ||
2694 | =head2 binf | |
2695 | ||
2696 | $x = Math::BigInt->binf($sign); | |
2697 | ||
2698 | Creates a new BigInt object representing infinity. The optional argument is | |
2699 | either '-' or '+', indicating whether you want infinity or minus infinity. | |
2700 | If used on an object, it will set it to infinity: | |
2701 | ||
2702 | $x->binf(); | |
2703 | $x->binf('-'); | |
2704 | ||
2705 | =head2 bone | |
2706 | ||
2707 | $x = Math::BigInt->binf($sign); | |
2708 | ||
2709 | Creates a new BigInt object representing one. The optional argument is | |
2710 | either '-' or '+', indicating whether you want one or minus one. | |
2711 | If used on an object, it will set it to one: | |
2712 | ||
2713 | $x->bone(); # +1 | |
2714 | $x->bone('-'); # -1 | |
2715 | ||
56b9c951 JH |
2716 | =head2 is_one()/is_zero()/is_nan()/is_inf() |
2717 | ||
b3abae2a JH |
2718 | |
2719 | $x->is_zero(); # true if arg is +0 | |
2720 | $x->is_nan(); # true if arg is NaN | |
2721 | $x->is_one(); # true if arg is +1 | |
2722 | $x->is_one('-'); # true if arg is -1 | |
b3abae2a JH |
2723 | $x->is_inf(); # true if +inf |
2724 | $x->is_inf('-'); # true if -inf (sign is default '+') | |
56b9c951 JH |
2725 | |
2726 | These methods all test the BigInt for beeing one specific value and return | |
2727 | true or false depending on the input. These are faster than doing something | |
2728 | like: | |
2729 | ||
2730 | if ($x == 0) | |
2731 | ||
2732 | =head2 is_positive()/is_negative() | |
2733 | ||
2734 | $x->is_positive(); # true if >= 0 | |
2735 | $x->is_negative(); # true if < 0 | |
2736 | ||
2737 | The methods return true if the argument is positive or negative, respectively. | |
2738 | C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and | |
2739 | C<-inf> is negative. A C<zero> is positive. | |
2740 | ||
2741 | These methods are only testing the sign, and not the value. | |
2742 | ||
2743 | =head2 is_odd()/is_even()/is_int() | |
2744 | ||
2745 | $x->is_odd(); # true if odd, false for even | |
2746 | $x->is_even(); # true if even, false for odd | |
b3abae2a JH |
2747 | $x->is_int(); # true if $x is an integer |
2748 | ||
56b9c951 JH |
2749 | The return true when the argument satisfies the condition. C<NaN>, C<+inf>, |
2750 | C<-inf> are not integers and are neither odd nor even. | |
b3abae2a JH |
2751 | |
2752 | =head2 bcmp | |
2753 | ||
56b9c951 JH |
2754 | $x->bcmp($y); |
2755 | ||
2756 | Compares $x with $y and takes the sign into account. | |
2757 | Returns -1, 0, 1 or undef. | |
b3abae2a JH |
2758 | |
2759 | =head2 bacmp | |
2760 | ||
56b9c951 JH |
2761 | $x->bacmp($y); |
2762 | ||
2763 | Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef. | |
b3abae2a JH |
2764 | |
2765 | =head2 sign | |
2766 | ||
56b9c951 JH |
2767 | $x->sign(); |
2768 | ||
2769 | Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN. | |
b3abae2a JH |
2770 | |
2771 | =head2 bcmp | |
2772 | ||
2773 | $x->digit($n); # return the nth digit, counting from right | |
2774 | ||
2775 | =head2 bneg | |
2776 | ||
2777 | $x->bneg(); | |
2778 | ||
2779 | Negate the number, e.g. change the sign between '+' and '-', or between '+inf' | |
2780 | and '-inf', respectively. Does nothing for NaN or zero. | |
2781 | ||
2782 | =head2 babs | |
2783 | ||
2784 | $x->babs(); | |
2785 | ||
2786 | Set the number to it's absolute value, e.g. change the sign from '-' to '+' | |
2787 | and from '-inf' to '+inf', respectively. Does nothing for NaN or positive | |
2788 | numbers. | |
2789 | ||
2790 | =head2 bnorm | |
2791 | ||
2792 | $x->bnorm(); # normalize (no-op) | |
2793 | ||
2794 | =head2 bnot | |
2795 | ||
2796 | $x->bnot(); # two's complement (bit wise not) | |
2797 | ||
2798 | =head2 binc | |
2799 | ||
2800 | $x->binc(); # increment x by 1 | |
2801 | ||
2802 | =head2 bdec | |
2803 | ||
2804 | $x->bdec(); # decrement x by 1 | |
2805 | ||
2806 | =head2 badd | |
2807 | ||
2808 | $x->badd($y); # addition (add $y to $x) | |
2809 | ||
2810 | =head2 bsub | |
2811 | ||
2812 | $x->bsub($y); # subtraction (subtract $y from $x) | |
2813 | ||
2814 | =head2 bmul | |
2815 | ||
2816 | $x->bmul($y); # multiplication (multiply $x by $y) | |
2817 | ||
2818 | =head2 bdiv | |
2819 | ||
2820 | $x->bdiv($y); # divide, set $x to quotient | |
2821 | # return (quo,rem) or quo if scalar | |
2822 | ||
2823 | =head2 bmod | |
2824 | ||
2825 | $x->bmod($y); # modulus (x % y) | |
2826 | ||
2827 | =head2 bpow | |
2828 | ||
2829 | $x->bpow($y); # power of arguments (x ** y) | |
2830 | ||
2831 | =head2 blsft | |
2832 | ||
2833 | $x->blsft($y); # left shift | |
2834 | $x->blsft($y,$n); # left shift, by base $n (like 10) | |
2835 | ||
2836 | =head2 brsft | |
2837 | ||
2838 | $x->brsft($y); # right shift | |
2839 | $x->brsft($y,$n); # right shift, by base $n (like 10) | |
2840 | ||
2841 | =head2 band | |
2842 | ||
2843 | $x->band($y); # bitwise and | |
2844 | ||
2845 | =head2 bior | |
2846 | ||
2847 | $x->bior($y); # bitwise inclusive or | |
2848 | ||
2849 | =head2 bxor | |
2850 | ||
2851 | $x->bxor($y); # bitwise exclusive or | |
2852 | ||
2853 | =head2 bnot | |
2854 | ||
2855 | $x->bnot(); # bitwise not (two's complement) | |
2856 | ||
2857 | =head2 bsqrt | |
2858 | ||
2859 | $x->bsqrt(); # calculate square-root | |
2860 | ||
2861 | =head2 bfac | |
2862 | ||
2863 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) | |
2864 | ||
2865 | =head2 round | |
2866 | ||
2867 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r | |
2868 | ||
2869 | =head2 bround | |
2870 | ||
2871 | $x->bround($N); # accuracy: preserve $N digits | |
2872 | ||
2873 | =head2 bfround | |
2874 | ||
2875 | $x->bfround($N); # round to $Nth digit, no-op for BigInts | |
2876 | ||
2877 | =head2 bfloor | |
2878 | ||
2879 | $x->bfloor(); | |
2880 | ||
2881 | Set $x to the integer less or equal than $x. This is a no-op in BigInt, but | |
2882 | does change $x in BigFloat. | |
2883 | ||
2884 | =head2 bceil | |
2885 | ||
2886 | $x->bceil(); | |
2887 | ||
2888 | Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but | |
2889 | does change $x in BigFloat. | |
2890 | ||
2891 | =head2 bgcd | |
2892 | ||
2893 | bgcd(@values); # greatest common divisor (no OO style) | |
2894 | ||
2895 | =head2 blcm | |
2896 | ||
2897 | blcm(@values); # lowest common multiplicator (no OO style) | |
2898 | ||
2899 | head2 length | |
2900 | ||
2901 | $x->length(); | |
2902 | ($xl,$fl) = $x->length(); | |
2903 | ||
2904 | Returns the number of digits in the decimal representation of the number. | |
2905 | In list context, returns the length of the integer and fraction part. For | |
2906 | BigInt's, the length of the fraction part will always be 0. | |
2907 | ||
2908 | =head2 exponent | |
2909 | ||
2910 | $x->exponent(); | |
2911 | ||
2912 | Return the exponent of $x as BigInt. | |
2913 | ||
2914 | =head2 mantissa | |
2915 | ||
2916 | $x->mantissa(); | |
2917 | ||
2918 | Return the signed mantissa of $x as BigInt. | |
2919 | ||
2920 | =head2 parts | |
2921 | ||
2922 | $x->parts(); # return (mantissa,exponent) as BigInt | |
2923 | ||
2924 | =head2 copy | |
2925 | ||
2926 | $x->copy(); # make a true copy of $x (unlike $y = $x;) | |
2927 | ||
2928 | =head2 as_number | |
2929 | ||
2930 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) | |
2931 | ||
2932 | =head2 bsrt | |
2933 | ||
2934 | $x->bstr(); # normalized string | |
2935 | ||
2936 | =head2 bsstr | |
2937 | ||
2938 | $x->bsstr(); # normalized string in scientific notation | |
2939 | ||
2940 | =head2 as_hex | |
2941 | ||
2942 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x | |
2943 | ||
2944 | =head2 as_bin | |
2945 | ||
2946 | $x->as_bin(); # as signed binary string with prefixed 0b | |
2947 | ||
0716bf9b JH |
2948 | =head1 ACCURACY and PRECISION |
2949 | ||
b22b3e31 | 2950 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b | 2951 | accuracy and precision based rounding, both automatically after every |
b22b3e31 | 2952 | operation as well as manually. |
0716bf9b JH |
2953 | |
2954 | This section describes the accuracy/precision handling in Math::Big* as it | |
b22b3e31 | 2955 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b JH |
2956 | abbreviations. |
2957 | ||
2958 | Not yet implemented things (but with correct description) are marked with '!', | |
2959 | things that need to be answered are marked with '?'. | |
2960 | ||
2961 | In the next paragraph follows a short description of terms used here (because | |
574bacfe | 2962 | these may differ from terms used by others people or documentation). |
0716bf9b | 2963 | |
b22b3e31 | 2964 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b JH |
2965 | precision), F (fallback) and R (rounding mode) will be used. |
2966 | ||
2967 | =head2 Precision P | |
2968 | ||
2969 | A fixed number of digits before (positive) or after (negative) | |
b22b3e31 PN |
2970 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
2971 | integer like 123 (or 120). A precision of 2 means two digits to the left | |
2972 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that | |
2973 | numbers with zeros before the decimal point may have different precisions, | |
2974 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value | |
2975 | was). It could also have p < 0, when the digits after the decimal point | |
2976 | are zero. | |
0716bf9b | 2977 | |
574bacfe JH |
2978 | The string output (of floating point numbers) will be padded with zeros: |
2979 | ||
2980 | Initial value P A Result String | |
2981 | ------------------------------------------------------------ | |
2982 | 1234.01 -3 1000 1000 | |
2983 | 1234 -2 1200 1200 | |
2984 | 1234.5 -1 1230 1230 | |
2985 | 1234.001 1 1234 1234.0 | |
2986 | 1234.01 0 1234 1234 | |
2987 | 1234.01 2 1234.01 1234.01 | |
2988 | 1234.01 5 1234.01 1234.01000 | |
2989 | ||
2990 | For BigInts, no padding occurs. | |
0716bf9b JH |
2991 | |
2992 | =head2 Accuracy A | |
2993 | ||
2994 | Number of significant digits. Leading zeros are not counted. A | |
2995 | number may have an accuracy greater than the non-zero digits | |
b22b3e31 PN |
2996 | when there are zeros in it or trailing zeros. For example, 123.456 has |
2997 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. | |
0716bf9b | 2998 | |
574bacfe JH |
2999 | The string output (of floating point numbers) will be padded with zeros: |
3000 | ||
3001 | Initial value P A Result String | |
3002 | ------------------------------------------------------------ | |
3003 | 1234.01 3 1230 1230 | |
3004 | 1234.01 6 1234.01 1234.01 | |
3005 | 1234.1 8 1234.1 1234.1000 | |
3006 | ||
3007 | For BigInts, no padding occurs. | |
3008 | ||
0716bf9b | 3009 | =head2 Fallback F |
a5f75d66 | 3010 | |
574bacfe JH |
3011 | When both A and P are undefined, this is used as a fallback accuracy when |
3012 | dividing numbers. | |
0716bf9b JH |
3013 | |
3014 | =head2 Rounding mode R | |
3015 | ||
3016 | When rounding a number, different 'styles' or 'kinds' | |
3017 | of rounding are possible. (Note that random rounding, as in | |
3018 | Math::Round, is not implemented.) | |
58cde26e JH |
3019 | |
3020 | =over 2 | |
a5f75d66 | 3021 | |
0716bf9b JH |
3022 | =item 'trunc' |
3023 | ||
3024 | truncation invariably removes all digits following the | |
3025 | rounding place, replacing them with zeros. Thus, 987.65 rounded | |
b22b3e31 | 3026 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b | 3027 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 | 3028 | decimal point (P=-2) becomes 123.46. |
0716bf9b JH |
3029 | |
3030 | All other implemented styles of rounding attempt to round to the | |
3031 | "nearest digit." If the digit D immediately to the right of the | |
3032 | rounding place (skipping the decimal point) is greater than 5, the | |
3033 | number is incremented at the rounding place (possibly causing a | |
3034 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds | |
3035 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly | |
3036 | truncated at the rounding place: e.g. when rounding to units, 0.4 | |
3037 | rounds to 0, and -19.4 rounds to -19. | |
3038 | ||
3039 | However the results of other styles of rounding differ if the | |
3040 | digit immediately to the right of the rounding place (skipping the | |
3041 | decimal point) is 5 and if there are no digits, or no digits other | |
3042 | than 0, after that 5. In such cases: | |
3043 | ||
3044 | =item 'even' | |
3045 | ||
3046 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 | |
3047 | if it is not already. E.g., when rounding to the first sigdig, 0.45 | |
3048 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. | |
3049 | ||
3050 | =item 'odd' | |
3051 | ||
3052 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if | |
3053 | it is not already. E.g., when rounding to the first sigdig, 0.45 | |
3054 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. | |
3055 | ||
3056 | =item '+inf' | |
3057 | ||
3058 | round to plus infinity, i.e. always round up. E.g., when | |
3059 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, | |
b22b3e31 | 3060 | and 0.4501 also becomes 0.5. |
0716bf9b JH |
3061 | |
3062 | =item '-inf' | |
3063 | ||
3064 | round to minus infinity, i.e. always round down. E.g., when | |
3065 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, | |
3066 | but 0.4501 becomes 0.5. | |
3067 | ||
3068 | =item 'zero' | |
3069 | ||
3070 | round to zero, i.e. positive numbers down, negative ones up. | |
3071 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 | |
3072 | becomes -0.5, but 0.4501 becomes 0.5. | |
3073 | ||
3074 | =back | |
3075 | ||
3076 | The handling of A & P in MBI/MBF (the old core code shipped with Perl | |
3077 | versions <= 5.7.2) is like this: | |
3078 | ||
3079 | =over 2 | |
a5f75d66 | 3080 | |
0716bf9b JH |
3081 | =item Precision |
3082 | ||
b22b3e31 PN |
3083 | * ffround($p) is able to round to $p number of digits after the decimal |
3084 | point | |
0716bf9b JH |
3085 | * otherwise P is unused |
3086 | ||
3087 | =item Accuracy (significant digits) | |
3088 | ||
3089 | * fround($a) rounds to $a significant digits | |
3090 | * only fdiv() and fsqrt() take A as (optional) paramater | |
b22b3e31 | 3091 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b JH |
3092 | of digits |
3093 | + rounding/truncating is only done when explicitly calling one of fround | |
3094 | or ffround, and never for BigInt (not implemented) | |
b22b3e31 | 3095 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b JH |
3096 | * the documentation and the comment in the code indicate two different ways |
3097 | on how fdiv() determines the maximum number of digits it should calculate, | |
3098 | and the actual code does yet another thing | |
3099 | POD: | |
3100 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) | |
3101 | Comment: | |
3102 | result has at most max(scale, length(dividend), length(divisor)) digits | |
3103 | Actual code: | |
3104 | scale = max(scale, length(dividend)-1,length(divisor)-1); | |
3105 | scale += length(divisior) - length(dividend); | |
b22b3e31 | 3106 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b JH |
3107 | Actually, the 'difference' added to the scale is calculated from the |
3108 | number of "significant digits" in dividend and divisor, which is derived | |
3109 | by looking at the length of the mantissa. Which is wrong, since it includes | |
3110 | the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups | |
3111 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange | |
3112 | assumption that 124 has 3 significant digits, while 120/7 will get you | |
3113 | '17', not '17.1' since 120 is thought to have 2 significant digits. | |
dccbb853 | 3114 | The rounding after the division then uses the remainder and $y to determine |
0716bf9b | 3115 | wether it must round up or down. |
b22b3e31 PN |
3116 | ? I have no idea which is the right way. That's why I used a slightly more |
3117 | ? simple scheme and tweaked the few failing testcases to match it. | |
58cde26e | 3118 | |
0716bf9b | 3119 | =back |
5dc6f178 | 3120 | |
0716bf9b | 3121 | This is how it works now: |
5dc6f178 | 3122 | |
0716bf9b | 3123 | =over 2 |
5dc6f178 | 3124 | |
0716bf9b JH |
3125 | =item Setting/Accessing |
3126 | ||
b3abae2a JH |
3127 | * You can set the A global via Math::BigInt->accuracy() or |
3128 | Math::BigFloat->accuracy() or whatever class you are using. | |
3129 | * You can also set P globally by using Math::SomeClass->precision() likewise. | |
0716bf9b | 3130 | * Globals are classwide, and not inherited by subclasses. |
b3abae2a JH |
3131 | * to undefine A, use Math::SomeCLass->accuracy(undef); |
3132 | * to undefine P, use Math::SomeClass->precision(undef); | |
3133 | * Setting Math::SomeClass->accuracy() clears automatically | |
3134 | Math::SomeClass->precision(), and vice versa. | |
0716bf9b | 3135 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 PN |
3136 | * If P is negative, this means round to the P'th place to the right of the |
3137 | decimal point; positive values mean to the left of the decimal point. | |
3138 | P of 0 means round to integer. | |
b3abae2a JH |
3139 | * to find out the current global A, take Math::SomeClass->accuracy() |
3140 | * to find out the current global P, take Math::SomeClass->precision() | |
3141 | * use $x->accuracy() respective $x->precision() for the local setting of $x. | |
3142 | * Please note that $x->accuracy() respecive $x->precision() fall back to the | |
3143 | defined globals, when $x's A or P is not set. | |
0716bf9b JH |
3144 | |
3145 | =item Creating numbers | |
3146 | ||
b3abae2a JH |
3147 | * When you create a number, you can give it's desired A or P via: |
3148 | $x = Math::BigInt->new($number,$A,$P); | |
3149 | * Only one of A or P can be defined, otherwise the result is NaN | |
3150 | * If no A or P is give ($x = Math::BigInt->new($number) form), then the | |
3151 | globals (if set) will be used. Thus changing the global defaults later on | |
b22b3e31 | 3152 | will not change the A or P of previously created numbers (i.e., A and P of |
b3abae2a JH |
3153 | $x will be what was in effect when $x was created) |
3154 | * If given undef for A and P, B<no> rounding will occur, and the globals will | |
3155 | B<not> be used. This is used by subclasses to create numbers without | |
3156 | suffering rounding in the parent. Thus a subclass is able to have it's own | |
3157 | globals enforced upon creation of a number by using | |
3158 | $x = Math::BigInt->new($number,undef,undef): | |
3159 | ||
3160 | use Math::Bigint::SomeSubclass; | |
3161 | use Math::BigInt; | |
3162 | ||
3163 | Math::BigInt->accuracy(2); | |
3164 | Math::BigInt::SomeSubClass->accuracy(3); | |
3165 | $x = Math::BigInt::SomeSubClass->new(1234); | |
3166 | ||
3167 | $x is now 1230, and not 1200. A subclass might choose to implement | |
3168 | this otherwise, e.g. falling back to the parent's A and P. | |
0716bf9b JH |
3169 | |
3170 | =item Usage | |
3171 | ||
b22b3e31 | 3172 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b | 3173 | operation according to the rules below |
b22b3e31 PN |
3174 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
3175 | after the decimal point | |
574bacfe JH |
3176 | * Math::BigFloat uses Math::BigInts internally, but setting A or P inside |
3177 | Math::BigInt as globals should not tamper with the parts of a BigFloat. | |
3178 | Thus a flag is used to mark all Math::BigFloat numbers as 'never round' | |
0716bf9b JH |
3179 | |
3180 | =item Precedence | |
3181 | ||
b22b3e31 PN |
3182 | * It only makes sense that a number has only one of A or P at a time. |
3183 | Since you can set/get both A and P, there is a rule that will practically | |
3184 | enforce only A or P to be in effect at a time, even if both are set. | |
3185 | This is called precedence. | |
b3abae2a JH |
3186 | * If two objects are involved in an operation, and one of them has A in |
3187 | effect, and the other P, this results in an error (NaN). | |
0716bf9b | 3188 | * A takes precendence over P (Hint: A comes before P). If A is defined, it |
b22b3e31 PN |
3189 | is used, otherwise P is used. If neither of them is defined, nothing is |
3190 | used, i.e. the result will have as many digits as it can (with an | |
3191 | exception for fdiv/fsqrt) and will not be rounded. | |
3192 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of | |
3193 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. | |
3194 | If either the dividend's or the divisor's mantissa has more digits than | |
3195 | the value of F, the higher value will be used instead of F. | |
3196 | This is to limit the digits (A) of the result (just consider what would | |
3197 | happen with unlimited A and P in the case of 1/3 :-) | |
b3abae2a | 3198 | * fdiv will calculate (at least) 4 more digits than required (determined by |
0716bf9b | 3199 | A, P or F), and, if F is not used, round the result |
b22b3e31 | 3200 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe | 3201 | or P of 5, but this can not be helped - or can it?) |
b22b3e31 | 3202 | * Thus you can have the math done by on Math::Big* class in three modes: |
0716bf9b JH |
3203 | + never round (this is the default): |
3204 | This is done by setting A and P to undef. No math operation | |
b22b3e31 | 3205 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
0716bf9b | 3206 | against overflows. You must explicitely call bround(), bfround() or |
b22b3e31 PN |
3207 | round() (the latter with parameters). |
3208 | Note: Once you have rounded a number, the settings will 'stick' on it | |
3209 | and 'infect' all other numbers engaged in math operations with it, since | |
0716bf9b JH |
3210 | local settings have the highest precedence. So, to get SaferRound[tm], |
3211 | use a copy() before rounding like this: | |
3212 | ||
3213 | $x = Math::BigFloat->new(12.34); | |
3214 | $y = Math::BigFloat->new(98.76); | |
3215 | $z = $x * $y; # 1218.6984 | |
3216 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) | |
3217 | $z = $x * $y; # still 1218.6984, without | |
3218 | # copy would have been 1210! | |
3219 | ||
3220 | + round after each op: | |
b22b3e31 PN |
3221 | After each single operation (except for testing like is_zero()), the |
3222 | method round() is called and the result is rounded appropriately. By | |
0716bf9b | 3223 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 PN |
3224 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
3225 | and P to -2, globally. | |
0716bf9b | 3226 | |
b22b3e31 PN |
3227 | ?Maybe an extra option that forbids local A & P settings would be in order, |
3228 | ?so that intermediate rounding does not 'poison' further math? | |
0716bf9b JH |
3229 | |
3230 | =item Overriding globals | |
3231 | ||
3232 | * you will be able to give A, P and R as an argument to all the calculation | |
b22b3e31 | 3233 | routines; the second parameter is A, the third one is P, and the fourth is |
b3abae2a | 3234 | R (shift right by one for binary operations like badd). P is used only if |
b22b3e31 PN |
3235 | the first parameter (A) is undefined. These three parameters override the |
3236 | globals in the order detailed as follows, i.e. the first defined value | |
0716bf9b | 3237 | wins: |
b22b3e31 | 3238 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b JH |
3239 | + parameter A |
3240 | + parameter P | |
3241 | + local A (if defined on both of the operands: smaller one is taken) | |
b3abae2a | 3242 | + local P (if defined on both of the operands: bigger one is taken) |
0716bf9b JH |
3243 | + global A |
3244 | + global P | |
3245 | + global F | |
b22b3e31 | 3246 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b JH |
3247 | arguments (A and P) instead of one |
3248 | ||
3249 | =item Local settings | |
3250 | ||
3251 | * You can set A and P locally by using $x->accuracy() and $x->precision() | |
3252 | and thus force different A and P for different objects/numbers. | |
b22b3e31 | 3253 | * Setting A or P this way immediately rounds $x to the new value. |
b3abae2a | 3254 | * $x->accuracy() clears $x->precision(), and vice versa. |
0716bf9b JH |
3255 | |
3256 | =item Rounding | |
3257 | ||
b22b3e31 | 3258 | * the rounding routines will use the respective global or local settings. |
0716bf9b JH |
3259 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
3260 | is for precision | |
3261 | * the two rounding functions take as the second parameter one of the | |
3262 | following rounding modes (R): | |
3263 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' | |
3264 | * you can set and get the global R by using Math::SomeClass->round_mode() | |
ee15d750 | 3265 | or by setting $Math::SomeClass::round_mode |
0716bf9b | 3266 | * after each operation, $result->round() is called, and the result may |
b22b3e31 PN |
3267 | eventually be rounded (that is, if A or P were set either locally, |
3268 | globally or as parameter to the operation) | |
ee15d750 | 3269 | * to manually round a number, call $x->round($A,$P,$round_mode); |
b22b3e31 | 3270 | this will round the number by using the appropriate rounding function |
0716bf9b | 3271 | and then normalize it. |
b22b3e31 | 3272 | * rounding modifies the local settings of the number: |
0716bf9b JH |
3273 | |
3274 | $x = Math::BigFloat->new(123.456); | |
3275 | $x->accuracy(5); | |
3276 | $x->bround(4); | |
3277 | ||
3278 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() | |
3279 | will be 4 from now on. | |
3280 | ||
3281 | =item Default values | |
3282 | ||
3283 | * R: 'even' | |
3284 | * F: 40 | |
3285 | * A: undef | |
3286 | * P: undef | |
3287 | ||
3288 | =item Remarks | |
3289 | ||
3290 | * The defaults are set up so that the new code gives the same results as | |
3291 | the old code (except in a few cases on fdiv): | |
3292 | + Both A and P are undefined and thus will not be used for rounding | |
3293 | after each operation. | |
3294 | + round() is thus a no-op, unless given extra parameters A and P | |
58cde26e JH |
3295 | |
3296 | =back | |
3297 | ||
0716bf9b JH |
3298 | =head1 INTERNALS |
3299 | ||
574bacfe JH |
3300 | The actual numbers are stored as unsigned big integers (with seperate sign). |
3301 | You should neither care about nor depend on the internal representation; it | |
3302 | might change without notice. Use only method calls like C<< $x->sign(); >> | |
3303 | instead relying on the internal hash keys like in C<< $x->{sign}; >>. | |
3304 | ||
3305 | =head2 MATH LIBRARY | |
58cde26e | 3306 | |
574bacfe JH |
3307 | Math with the numbers is done (by default) by a module called |
3308 | Math::BigInt::Calc. This is equivalent to saying: | |
3309 | ||
3310 | use Math::BigInt lib => 'Calc'; | |
58cde26e | 3311 | |
0716bf9b | 3312 | You can change this by using: |
58cde26e | 3313 | |
0716bf9b | 3314 | use Math::BigInt lib => 'BitVect'; |
58cde26e | 3315 | |
574bacfe JH |
3316 | The following would first try to find Math::BigInt::Foo, then |
3317 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
0716bf9b | 3318 | |
574bacfe | 3319 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
58cde26e | 3320 | |
574bacfe | 3321 | Calc.pm uses as internal format an array of elements of some decimal base |
b3abae2a JH |
3322 | (usually 1e5 or 1e7) with the least significant digit first, while BitVect.pm |
3323 | uses a bit vector of base 2, most significant bit first. Other modules might | |
3324 | use even different means of representing the numbers. See the respective | |
3325 | module documentation for further details. | |
58cde26e | 3326 | |
574bacfe JH |
3327 | =head2 SIGN |
3328 | ||
3329 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. | |
3330 | ||
3331 | A sign of 'NaN' is used to represent the result when input arguments are not | |
3332 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively | |
3333 | minus infinity. You will get '+inf' when dividing a positive number by 0, and | |
3334 | '-inf' when dividing any negative number by 0. | |
58cde26e JH |
3335 | |
3336 | =head2 mantissa(), exponent() and parts() | |
3337 | ||
3338 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such | |
3339 | that: | |
3340 | ||
3341 | $m = $x->mantissa(); | |
3342 | $e = $x->exponent(); | |
3343 | $y = $m * ( 10 ** $e ); | |
3344 | print "ok\n" if $x == $y; | |
3345 | ||
b22b3e31 PN |
3346 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
3347 | in one go. Both the returned mantissa and exponent have a sign. | |
58cde26e | 3348 | |
574bacfe JH |
3349 | Currently, for BigInts C<$e> will be always 0, except for NaN, +inf and -inf, |
3350 | where it will be NaN; and for $x == 0, where it will be 1 | |
3351 | (to be compatible with Math::BigFloat's internal representation of a zero as | |
3352 | C<0E1>). | |
58cde26e JH |
3353 | |
3354 | C<$m> will always be a copy of the original number. The relation between $e | |
b22b3e31 | 3355 | and $m might change in the future, but will always be equivalent in a |
0716bf9b JH |
3356 | numerical sense, e.g. $m might get minimized. |
3357 | ||
58cde26e JH |
3358 | =head1 EXAMPLES |
3359 | ||
394e6ffb | 3360 | use Math::BigInt; |
574bacfe JH |
3361 | |
3362 | sub bint { Math::BigInt->new(shift); } | |
3363 | ||
394e6ffb | 3364 | $x = Math::BigInt->bstr("1234") # string "1234" |
58cde26e | 3365 | $x = "$x"; # same as bstr() |
58cde26e JH |
3366 | $x = Math::BigInt->bneg("1234"); # Bigint "-1234" |
3367 | $x = Math::BigInt->babs("-12345"); # Bigint "12345" | |
3368 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" | |
3369 | $x = bint(1) + bint(2); # BigInt "3" | |
3370 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") | |
3371 | $x = bint(1); # BigInt "1" | |
3372 | $x = $x + 5 / 2; # BigInt "3" | |
3373 | $x = $x ** 3; # BigInt "27" | |
3374 | $x *= 2; # BigInt "54" | |
394e6ffb | 3375 | $x = Math::BigInt->new(0); # BigInt "0" |
58cde26e JH |
3376 | $x--; # BigInt "-1" |
3377 | $x = Math::BigInt->badd(4,5) # BigInt "9" | |
58cde26e | 3378 | print $x->bsstr(); # 9e+0 |
a5f75d66 | 3379 | |
0716bf9b JH |
3380 | Examples for rounding: |
3381 | ||
3382 | use Math::BigFloat; | |
3383 | use Test; | |
3384 | ||
3385 | $x = Math::BigFloat->new(123.4567); | |
3386 | $y = Math::BigFloat->new(123.456789); | |
394e6ffb | 3387 | Math::BigFloat->accuracy(4); # no more A than 4 |
0716bf9b JH |
3388 | |
3389 | ok ($x->copy()->fround(),123.4); # even rounding | |
3390 | print $x->copy()->fround(),"\n"; # 123.4 | |
3391 | Math::BigFloat->round_mode('odd'); # round to odd | |
3392 | print $x->copy()->fround(),"\n"; # 123.5 | |
394e6ffb | 3393 | Math::BigFloat->accuracy(5); # no more A than 5 |
0716bf9b JH |
3394 | Math::BigFloat->round_mode('odd'); # round to odd |
3395 | print $x->copy()->fround(),"\n"; # 123.46 | |
3396 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 | |
3397 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 | |
3398 | ||
394e6ffb JH |
3399 | Math::BigFloat->accuracy(undef); # A not important now |
3400 | Math::BigFloat->precision(2); # P important | |
3401 | print $x->copy()->bnorm(),"\n"; # 123.46 | |
3402 | print $x->copy()->fround(),"\n"; # 123.46 | |
0716bf9b | 3403 | |
bd05a461 JH |
3404 | Examples for converting: |
3405 | ||
3406 | my $x = Math::BigInt->new('0b1'.'01' x 123); | |
3407 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; | |
3408 | ||
b3ac6de7 IZ |
3409 | =head1 Autocreating constants |
3410 | ||
56b9c951 JH |
3411 | After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal |
3412 | and binary constants in the given scope are converted to C<Math::BigInt>. | |
3413 | This conversion happens at compile time. | |
b3ac6de7 | 3414 | |
b22b3e31 | 3415 | In particular, |
b3ac6de7 | 3416 | |
58cde26e JH |
3417 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
3418 | ||
56b9c951 | 3419 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b | 3420 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e JH |
3421 | |
3422 | Please note that strings and floating point constants are not affected, | |
3423 | so that | |
3424 | ||
3425 | use Math::BigInt qw/:constant/; | |
3426 | ||
3427 | $x = 1234567890123456789012345678901234567890 | |
3428 | + 123456789123456789; | |
b22b3e31 | 3429 | $y = '1234567890123456789012345678901234567890' |
58cde26e | 3430 | + '123456789123456789'; |
b3ac6de7 | 3431 | |
b22b3e31 | 3432 | do not work. You need an explicit Math::BigInt->new() around one of the |
394e6ffb JH |
3433 | operands. You should also quote large constants to protect loss of precision: |
3434 | ||
3435 | use Math::Bigint; | |
3436 | ||
3437 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); | |
3438 | ||
3439 | Without the quotes Perl would convert the large number to a floating point | |
3440 | constant at compile time and then hand the result to BigInt, which results in | |
3441 | an truncated result or a NaN. | |
58cde26e | 3442 | |
56b9c951 JH |
3443 | This also applies to integers that look like floating point constants: |
3444 | ||
3445 | use Math::BigInt ':constant'; | |
3446 | ||
3447 | print ref(123e2),"\n"; | |
3448 | print ref(123.2e2),"\n"; | |
3449 | ||
3450 | will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat> | |
3451 | to get this to work. | |
3452 | ||
58cde26e JH |
3453 | =head1 PERFORMANCE |
3454 | ||
3455 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x | |
3456 | must be made in the second case. For long numbers, the copy can eat up to 20% | |
b22b3e31 | 3457 | of the work (in the case of addition/subtraction, less for |
58cde26e JH |
3458 | multiplication/division). If $y is very small compared to $x, the form |
3459 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes | |
3460 | more time then the actual addition. | |
3461 | ||
b22b3e31 | 3462 | With a technique called copy-on-write, the cost of copying with overload could |
394e6ffb JH |
3463 | be minimized or even completely avoided. A test implementation of COW did show |
3464 | performance gains for overloaded math, but introduced a performance loss due | |
3465 | to a constant overhead for all other operatons. | |
3466 | ||
3467 | The rewritten version of this module is slower on certain operations, like | |
3468 | new(), bstr() and numify(). The reason are that it does now more work and | |
3469 | handles more cases. The time spent in these operations is usually gained in | |
3470 | the other operations so that programs on the average should get faster. If | |
3471 | they don't, please contect the author. | |
58cde26e | 3472 | |
394e6ffb JH |
3473 | Some operations may be slower for small numbers, but are significantly faster |
3474 | for big numbers. Other operations are now constant (O(1), like bneg(), babs() | |
3475 | etc), instead of O(N) and thus nearly always take much less time. These | |
3476 | optimizations were done on purpose. | |
58cde26e | 3477 | |
574bacfe JH |
3478 | If you find the Calc module to slow, try to install any of the replacement |
3479 | modules and see if they help you. | |
b3ac6de7 | 3480 | |
574bacfe | 3481 | =head2 Alternative math libraries |
0716bf9b JH |
3482 | |
3483 | You can use an alternative library to drive Math::BigInt via: | |
3484 | ||
3485 | use Math::BigInt lib => 'Module'; | |
3486 | ||
394e6ffb | 3487 | See L<MATH LIBRARY> for more information. |
0716bf9b | 3488 | |
394e6ffb | 3489 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. |
574bacfe | 3490 | |
b3abae2a JH |
3491 | =head2 SUBCLASSING |
3492 | ||
3493 | =head1 Subclassing Math::BigInt | |
3494 | ||
3495 | The basic design of Math::BigInt allows simple subclasses with very little | |
3496 | work, as long as a few simple rules are followed: | |
3497 | ||
3498 | =over 2 | |
3499 | ||
3500 | =item * | |
3501 | ||
3502 | The public API must remain consistent, i.e. if a sub-class is overloading | |
3503 | addition, the sub-class must use the same name, in this case badd(). The | |
3504 | reason for this is that Math::BigInt is optimized to call the object methods | |
3505 | directly. | |
3506 | ||
3507 | =item * | |
3508 | ||
3509 | The private object hash keys like C<$x->{sign}> may not be changed, but | |
3510 | additional keys can be added, like C<$x->{_custom}>. | |
3511 | ||
3512 | =item * | |
3513 | ||
3514 | Accessor functions are available for all existing object hash keys and should | |
3515 | be used instead of directly accessing the internal hash keys. The reason for | |
3516 | this is that Math::BigInt itself has a pluggable interface which permits it | |
3517 | to support different storage methods. | |
3518 | ||
3519 | =back | |
3520 | ||
3521 | More complex sub-classes may have to replicate more of the logic internal of | |
3522 | Math::BigInt if they need to change more basic behaviors. A subclass that | |
3523 | needs to merely change the output only needs to overload C<bstr()>. | |
3524 | ||
3525 | All other object methods and overloaded functions can be directly inherited | |
3526 | from the parent class. | |
3527 | ||
3528 | At the very minimum, any subclass will need to provide it's own C<new()> and can | |
3529 | store additional hash keys in the object. There are also some package globals | |
3530 | that must be defined, e.g.: | |
3531 | ||
3532 | # Globals | |
3533 | $accuracy = undef; | |
3534 | $precision = -2; # round to 2 decimal places | |
3535 | $round_mode = 'even'; | |
3536 | $div_scale = 40; | |
3537 | ||
3538 | Additionally, you might want to provide the following two globals to allow | |
3539 | auto-upgrading and auto-downgrading to work correctly: | |
3540 | ||
3541 | $upgrade = undef; | |
3542 | $downgrade = undef; | |
3543 | ||
3544 | This allows Math::BigInt to correctly retrieve package globals from the | |
3545 | subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or | |
3546 | t/Math/BigFloat/SubClass.pm completely functional subclass examples. | |
3547 | ||
3548 | Don't forget to | |
3549 | ||
3550 | use overload; | |
3551 | ||
3552 | in your subclass to automatically inherit the overloading from the parent. If | |
3553 | you like, you can change part of the overloading, look at Math::String for an | |
3554 | example. | |
3555 | ||
3556 | =head1 UPGRADING | |
3557 | ||
3558 | When used like this: | |
3559 | ||
3560 | use Math::BigInt upgrade => 'Foo::Bar'; | |
3561 | ||
3562 | certain operations will 'upgrade' their calculation and thus the result to | |
3563 | the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat: | |
3564 | ||
3565 | use Math::BigInt upgrade => 'Math::BigFloat'; | |
3566 | ||
3567 | As a shortcut, you can use the module C<bignum>: | |
3568 | ||
3569 | use bignum; | |
3570 | ||
3571 | Also good for oneliners: | |
3572 | ||
3573 | perl -Mbignum -le 'print 2 ** 255' | |
3574 | ||
3575 | This makes it possible to mix arguments of different classes (as in 2.5 + 2) | |
3576 | as well es preserve accuracy (as in sqrt(3)). | |
3577 | ||
3578 | Beware: This feature is not fully implemented yet. | |
3579 | ||
3580 | =head2 Auto-upgrade | |
3581 | ||
3582 | The following methods upgrade themselves unconditionally; that is if upgrade | |
3583 | is in effect, they will always hand up their work: | |
3584 | ||
3585 | =over 2 | |
3586 | ||
3587 | =item bsqrt() | |
3588 | ||
3589 | =item div() | |
3590 | ||
3591 | =item blog() | |
3592 | ||
3593 | =back | |
3594 | ||
3595 | Beware: This list is not complete. | |
3596 | ||
3597 | All other methods upgrade themselves only when one (or all) of their | |
3598 | arguments are of the class mentioned in $upgrade (This might change in later | |
3599 | versions to a more sophisticated scheme): | |
3600 | ||
a5f75d66 AD |
3601 | =head1 BUGS |
3602 | ||
58cde26e JH |
3603 | =over 2 |
3604 | ||
574bacfe | 3605 | =item Out of Memory! |
58cde26e JH |
3606 | |
3607 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and | |
3608 | C<eval()> in your code will crash with "Out of memory". This is probably an | |
3609 | overload/exporter bug. You can workaround by not having C<eval()> | |
574bacfe JH |
3610 | and ':constant' at the same time or upgrade your Perl to a newer version. |
3611 | ||
3612 | =item Fails to load Calc on Perl prior 5.6.0 | |
3613 | ||
3614 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt | |
3615 | will fall back to eval { require ... } when loading the math lib on Perls | |
3616 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on | |
3617 | filesystems using a different seperator. | |
58cde26e JH |
3618 | |
3619 | =back | |
3620 | ||
3621 | =head1 CAVEATS | |
3622 | ||
3623 | Some things might not work as you expect them. Below is documented what is | |
3624 | known to be troublesome: | |
3625 | ||
3626 | =over 1 | |
3627 | ||
3628 | =item stringify, bstr(), bsstr() and 'cmp' | |
3629 | ||
3630 | Both stringify and bstr() now drop the leading '+'. The old code would return | |
3631 | '+3', the new returns '3'. This is to be consistent with Perl and to make | |
3632 | cmp (especially with overloading) to work as you expect. It also solves | |
3633 | problems with Test.pm, it's ok() uses 'eq' internally. | |
3634 | ||
3635 | Mark said, when asked about to drop the '+' altogether, or make only cmp work: | |
3636 | ||
3637 | I agree (with the first alternative), don't add the '+' on positive | |
3638 | numbers. It's not as important anymore with the new internal | |
3639 | form for numbers. It made doing things like abs and neg easier, | |
3640 | but those have to be done differently now anyway. | |
3641 | ||
3642 | So, the following examples will now work all as expected: | |
3643 | ||
3644 | use Test; | |
3645 | BEGIN { plan tests => 1 } | |
3646 | use Math::BigInt; | |
3647 | ||
3648 | my $x = new Math::BigInt 3*3; | |
3649 | my $y = new Math::BigInt 3*3; | |
3650 | ||
3651 | ok ($x,3*3); | |
3652 | print "$x eq 9" if $x eq $y; | |
3653 | print "$x eq 9" if $x eq '9'; | |
3654 | print "$x eq 9" if $x eq 3*3; | |
3655 | ||
3656 | Additionally, the following still works: | |
3657 | ||
3658 | print "$x == 9" if $x == $y; | |
3659 | print "$x == 9" if $x == 9; | |
3660 | print "$x == 9" if $x == 3*3; | |
3661 | ||
3662 | There is now a C<bsstr()> method to get the string in scientific notation aka | |
3663 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() | |
3664 | for comparisation, but Perl will represent some numbers as 100 and others | |
3665 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before doing eq: | |
3666 | ||
3667 | use Test; | |
3668 | BEGIN { plan tests => 3 } | |
3669 | use Math::BigInt; | |
3670 | ||
3671 | $x = Math::BigInt->new('1e56'); $y = 1e56; | |
3672 | ok ($x,$y); # will fail | |
3673 | ok ($x->bsstr(),$y); # okay | |
3674 | $y = Math::BigInt->new($y); | |
3675 | ok ($x,$y); # okay | |
3676 | ||
394e6ffb JH |
3677 | Alternatively, simple use <=> for comparisations, that will get it always |
3678 | right. There is not yet a way to get a number automatically represented as | |
3679 | a string that matches exactly the way Perl represents it. | |
574bacfe | 3680 | |
58cde26e JH |
3681 | =item int() |
3682 | ||
3683 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a | |
3684 | Perl scalar: | |
3685 | ||
3686 | $x = Math::BigInt->new(123); | |
3687 | $y = int($x); # BigInt 123 | |
3688 | $x = Math::BigFloat->new(123.45); | |
3689 | $y = int($x); # BigInt 123 | |
3690 | ||
3691 | In all Perl versions you can use C<as_number()> for the same effect: | |
3692 | ||
3693 | $x = Math::BigFloat->new(123.45); | |
3694 | $y = $x->as_number(); # BigInt 123 | |
3695 | ||
3696 | This also works for other subclasses, like Math::String. | |
3697 | ||
574bacfe JH |
3698 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. |
3699 | ||
dccbb853 | 3700 | =item length |
58cde26e JH |
3701 | |
3702 | The following will probably not do what you expect: | |
3703 | ||
bd05a461 JH |
3704 | $c = Math::BigInt->new(123); |
3705 | print $c->length(),"\n"; # prints 30 | |
3706 | ||
3707 | It prints both the number of digits in the number and in the fraction part | |
3708 | since print calls C<length()> in list context. Use something like: | |
3709 | ||
3710 | print scalar $c->length(),"\n"; # prints 3 | |
3711 | ||
3712 | =item bdiv | |
3713 | ||
3714 | The following will probably not do what you expect: | |
3715 | ||
58cde26e JH |
3716 | print $c->bdiv(10000),"\n"; |
3717 | ||
dccbb853 | 3718 | It prints both quotient and remainder since print calls C<bdiv()> in list |
58cde26e JH |
3719 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want |
3720 | to use | |
3721 | ||
3722 | print $c / 10000,"\n"; | |
3723 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c | |
3724 | ||
3725 | instead. | |
3726 | ||
3727 | The quotient is always the greatest integer less than or equal to the | |
3728 | real-valued quotient of the two operands, and the remainder (when it is | |
3729 | nonzero) always has the same sign as the second operand; so, for | |
3730 | example, | |
3731 | ||
dccbb853 JH |
3732 | 1 / 4 => ( 0, 1) |
3733 | 1 / -4 => (-1,-3) | |
3734 | -3 / 4 => (-1, 1) | |
3735 | -3 / -4 => ( 0,-3) | |
3736 | -11 / 2 => (-5,1) | |
3737 | 11 /-2 => (-5,-1) | |
58cde26e JH |
3738 | |
3739 | As a consequence, the behavior of the operator % agrees with the | |
3740 | behavior of Perl's built-in % operator (as documented in the perlop | |
3741 | manpage), and the equation | |
3742 | ||
3743 | $x == ($x / $y) * $y + ($x % $y) | |
3744 | ||
3745 | holds true for any $x and $y, which justifies calling the two return | |
dccbb853 JH |
3746 | values of bdiv() the quotient and remainder. The only exception to this rule |
3747 | are when $y == 0 and $x is negative, then the remainder will also be | |
3748 | negative. See below under "infinity handling" for the reasoning behing this. | |
58cde26e JH |
3749 | |
3750 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will | |
3751 | not change BigInt's way to do things. This is because under 'use integer' Perl | |
3752 | will do what the underlying C thinks is right and this is different for each | |
3753 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug | |
3754 | the author to implement it ;) | |
3755 | ||
dccbb853 JH |
3756 | =item infinity handling |
3757 | ||
3758 | Here are some examples that explain the reasons why certain results occur while | |
3759 | handling infinity: | |
3760 | ||
3761 | The following table shows the result of the division and the remainder, so that | |
3762 | the equation above holds true. Some "ordinary" cases are strewn in to show more | |
3763 | clearly the reasoning: | |
3764 | ||
3765 | A / B = C, R so that C * B + R = A | |
3766 | ========================================================= | |
3767 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 | |
3768 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 | |
3769 | 0 / inf = 0, 0 0 * inf + 0 = 0 | |
3770 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 | |
3771 | 5 / inf = 0, 5 0 * inf + 5 = 5 | |
3772 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 | |
3773 | -5/ inf = 0, -5 0 * inf + -5 = -5 | |
3774 | -5/-inf = 0, -5 0 * -inf + -5 = -5 | |
3775 | inf/ 5 = inf, 0 inf * 5 + 0 = inf | |
3776 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf | |
3777 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf | |
3778 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf | |
3779 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 | |
3780 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 | |
3781 | inf/ inf = 1, 0 1 * inf + 0 = inf | |
3782 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf | |
3783 | inf/-inf = -1, 0 -1 * -inf + 0 = inf | |
3784 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf | |
3785 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 | |
3786 | inf/ 0 = inf, inf inf * 0 + inf = inf | |
3787 | 0/ 0 = NaN | |
3788 | ||
3789 | These cases below violate the "remainder has the sign of the second of the two | |
3790 | arguments", since they wouldn't match up otherwise. | |
3791 | ||
3792 | A / B = C, R so that C * B + R = A | |
3793 | ======================================================== | |
3794 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf | |
3795 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 | |
3796 | ||
58cde26e JH |
3797 | =item Modifying and = |
3798 | ||
3799 | Beware of: | |
3800 | ||
3801 | $x = Math::BigFloat->new(5); | |
3802 | $y = $x; | |
3803 | ||
3804 | It will not do what you think, e.g. making a copy of $x. Instead it just makes | |
3805 | a second reference to the B<same> object and stores it in $y. Thus anything | |
17baacb7 JH |
3806 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
3807 | Or in other words, C<=> is only safe if you modify your BigInts only via | |
3808 | overloaded math. As soon as you use a method call it breaks: | |
58cde26e JH |
3809 | |
3810 | $x->bmul(2); | |
3811 | print "$x, $y\n"; # prints '10, 10' | |
3812 | ||
3813 | If you want a true copy of $x, use: | |
3814 | ||
3815 | $y = $x->copy(); | |
3816 | ||
17baacb7 JH |
3817 | You can also chain the calls like this, this will make first a copy and then |
3818 | multiply it by 2: | |
3819 | ||
3820 | $y = $x->copy()->bmul(2); | |
3821 | ||
b22b3e31 | 3822 | See also the documentation for overload.pm regarding C<=>. |
58cde26e JH |
3823 | |
3824 | =item bpow | |
3825 | ||
3826 | C<bpow()> (and the rounding functions) now modifies the first argument and | |
574bacfe | 3827 | returns it, unlike the old code which left it alone and only returned the |
58cde26e JH |
3828 | result. This is to be consistent with C<badd()> etc. The first three will |
3829 | modify $x, the last one won't: | |
3830 | ||
3831 | print bpow($x,$i),"\n"; # modify $x | |
3832 | print $x->bpow($i),"\n"; # ditto | |
3833 | print $x **= $i,"\n"; # the same | |
3834 | print $x ** $i,"\n"; # leave $x alone | |
3835 | ||
3836 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. | |
3837 | ||
3838 | =item Overloading -$x | |
3839 | ||
3840 | The following: | |
3841 | ||
3842 | $x = -$x; | |
3843 | ||
3844 | is slower than | |
3845 | ||
3846 | $x->bneg(); | |
3847 | ||
3848 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant | |
3849 | needs to preserve $x since it does not know that it later will get overwritten. | |
0716bf9b | 3850 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e | 3851 | |
394e6ffb JH |
3852 | With Copy-On-Write, this issue would be gone, but C-o-W is not implemented |
3853 | since it is slower for all other things. | |
58cde26e JH |
3854 | |
3855 | =item Mixing different object types | |
3856 | ||
3857 | In Perl you will get a floating point value if you do one of the following: | |
3858 | ||
3859 | $float = 5.0 + 2; | |
3860 | $float = 2 + 5.0; | |
3861 | $float = 5 / 2; | |
3862 | ||
3863 | With overloaded math, only the first two variants will result in a BigFloat: | |
3864 | ||
3865 | use Math::BigInt; | |
3866 | use Math::BigFloat; | |
3867 | ||
3868 | $mbf = Math::BigFloat->new(5); | |
3869 | $mbi2 = Math::BigInteger->new(5); | |
3870 | $mbi = Math::BigInteger->new(2); | |
3871 | ||
3872 | # what actually gets called: | |
3873 | $float = $mbf + $mbi; # $mbf->badd() | |
3874 | $float = $mbf / $mbi; # $mbf->bdiv() | |
3875 | $integer = $mbi + $mbf; # $mbi->badd() | |
3876 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() | |
3877 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() | |
3878 | ||
3879 | This is because math with overloaded operators follows the first (dominating) | |
394e6ffb | 3880 | operand, and the operation of that is called and returns thus the result. So, |
58cde26e JH |
3881 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
3882 | the result should be a Math::BigFloat or the second operant is one. | |
3883 | ||
3884 | To get a Math::BigFloat you either need to call the operation manually, | |
3885 | make sure the operands are already of the proper type or casted to that type | |
3886 | via Math::BigFloat->new(): | |
3887 | ||
3888 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 | |
3889 | ||
3890 | Beware of simple "casting" the entire expression, this would only convert | |
3891 | the already computed result: | |
3892 | ||
3893 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! | |
3894 | ||
0716bf9b | 3895 | Beware also of the order of more complicated expressions like: |
58cde26e JH |
3896 | |
3897 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int | |
3898 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto | |
3899 | ||
3900 | If in doubt, break the expression into simpler terms, or cast all operands | |
3901 | to the desired resulting type. | |
3902 | ||
3903 | Scalar values are a bit different, since: | |
3904 | ||
3905 | $float = 2 + $mbf; | |
3906 | $float = $mbf + 2; | |
3907 | ||
3908 | will both result in the proper type due to the way the overloaded math works. | |
3909 | ||
3910 | This section also applies to other overloaded math packages, like Math::String. | |
3911 | ||
b3abae2a JH |
3912 | One solution to you problem might be L<autoupgrading|upgrading>. |
3913 | ||
58cde26e JH |
3914 | =item bsqrt() |
3915 | ||
394e6ffb | 3916 | C<bsqrt()> works only good if the result is a big integer, e.g. the square |
58cde26e JH |
3917 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
3918 | mode. | |
3919 | ||
3920 | If you want a better approximation of the square root, then use: | |
3921 | ||
3922 | $x = Math::BigFloat->new(12); | |
394e6ffb | 3923 | Math::BigFloat->precision(0); |
58cde26e JH |
3924 | Math::BigFloat->round_mode('even'); |
3925 | print $x->copy->bsqrt(),"\n"; # 4 | |
3926 | ||
394e6ffb | 3927 | Math::BigFloat->precision(2); |
58cde26e JH |
3928 | print $x->bsqrt(),"\n"; # 3.46 |
3929 | print $x->bsqrt(3),"\n"; # 3.464 | |
3930 | ||
b3abae2a JH |
3931 | =item brsft() |
3932 | ||
3933 | For negative numbers in base see also L<brsft|brsft>. | |
3934 | ||
58cde26e JH |
3935 | =back |
3936 | ||
3937 | =head1 LICENSE | |
3938 | ||
3939 | This program is free software; you may redistribute it and/or modify it under | |
3940 | the same terms as Perl itself. | |
a5f75d66 | 3941 | |
0716bf9b JH |
3942 | =head1 SEE ALSO |
3943 | ||
027dc388 JH |
3944 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
3945 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
0716bf9b | 3946 | |
027dc388 JH |
3947 | The package at |
3948 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains | |
3949 | more documentation including a full version history, testcases, empty | |
3950 | subclass files and benchmarks. | |
574bacfe | 3951 | |
58cde26e | 3952 | =head1 AUTHORS |
a5f75d66 | 3953 | |
58cde26e JH |
3954 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
3955 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001. | |
a5f75d66 AD |
3956 | |
3957 | =cut |