Commit | Line | Data |
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920dae64 AT |
1 | |
2 | # | |
3 | # "Tax the rat farms." - Lord Vetinari | |
4 | # | |
5 | ||
6 | # The following hash values are used: | |
7 | # sign : +,-,NaN,+inf,-inf | |
8 | # _d : denominator | |
9 | # _n : numeraotr (value = _n/_d) | |
10 | # _a : accuracy | |
11 | # _p : precision | |
12 | # You should not look at the innards of a BigRat - use the methods for this. | |
13 | ||
14 | package Math::BigRat; | |
15 | ||
16 | require 5.005_03; | |
17 | use strict; | |
18 | ||
19 | use Math::BigFloat; | |
20 | use vars qw($VERSION @ISA $upgrade $downgrade | |
21 | $accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf); | |
22 | ||
23 | @ISA = qw(Math::BigFloat); | |
24 | ||
25 | $VERSION = '0.15'; | |
26 | ||
27 | use overload; # inherit overload from Math::BigFloat | |
28 | ||
29 | BEGIN | |
30 | { | |
31 | *objectify = \&Math::BigInt::objectify; # inherit this from BigInt | |
32 | *AUTOLOAD = \&Math::BigFloat::AUTOLOAD; # can't inherit AUTOLOAD | |
33 | # we inherit these from BigFloat because currently it is not possible | |
34 | # that MBF has a different $MBI variable than we, because MBF also uses | |
35 | # Math::BigInt::config->('lib'); (there is always only one library loaded) | |
36 | *_e_add = \&Math::BigFloat::_e_add; | |
37 | *_e_sub = \&Math::BigFloat::_e_sub; | |
38 | *as_int = \&as_number; | |
39 | *is_pos = \&is_positive; | |
40 | *is_neg = \&is_negative; | |
41 | } | |
42 | ||
43 | ############################################################################## | |
44 | # Global constants and flags. Access these only via the accessor methods! | |
45 | ||
46 | $accuracy = $precision = undef; | |
47 | $round_mode = 'even'; | |
48 | $div_scale = 40; | |
49 | $upgrade = undef; | |
50 | $downgrade = undef; | |
51 | ||
52 | # These are internally, and not to be used from the outside at all! | |
53 | ||
54 | $_trap_nan = 0; # are NaNs ok? set w/ config() | |
55 | $_trap_inf = 0; # are infs ok? set w/ config() | |
56 | ||
57 | # the package we are using for our private parts, defaults to: | |
58 | # Math::BigInt->config()->{lib} | |
59 | my $MBI = 'Math::BigInt::Calc'; | |
60 | ||
61 | my $nan = 'NaN'; | |
62 | my $class = 'Math::BigRat'; | |
63 | ||
64 | sub isa | |
65 | { | |
66 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't | |
67 | UNIVERSAL::isa(@_); | |
68 | } | |
69 | ||
70 | ############################################################################## | |
71 | ||
72 | sub _new_from_float | |
73 | { | |
74 | # turn a single float input into a rational number (like '0.1') | |
75 | my ($self,$f) = @_; | |
76 | ||
77 | return $self->bnan() if $f->is_nan(); | |
78 | return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/; | |
79 | ||
80 | $self->{_n} = $MBI->_copy( $f->{_m} ); # mantissa | |
81 | $self->{_d} = $MBI->_one(); | |
82 | $self->{sign} = $f->{sign} || '+'; | |
83 | if ($f->{_es} eq '-') | |
84 | { | |
85 | # something like Math::BigRat->new('0.1'); | |
86 | # 1 / 1 => 1/10 | |
87 | $MBI->_lsft ( $self->{_d}, $f->{_e} ,10); | |
88 | } | |
89 | else | |
90 | { | |
91 | # something like Math::BigRat->new('10'); | |
92 | # 1 / 1 => 10/1 | |
93 | $MBI->_lsft ( $self->{_n}, $f->{_e} ,10) unless | |
94 | $MBI->_is_zero($f->{_e}); | |
95 | } | |
96 | $self; | |
97 | } | |
98 | ||
99 | sub new | |
100 | { | |
101 | # create a Math::BigRat | |
102 | my $class = shift; | |
103 | ||
104 | my ($n,$d) = @_; | |
105 | ||
106 | my $self = { }; bless $self,$class; | |
107 | ||
108 | # input like (BigInt) or (BigFloat): | |
109 | if ((!defined $d) && (ref $n) && (!$n->isa('Math::BigRat'))) | |
110 | { | |
111 | if ($n->isa('Math::BigFloat')) | |
112 | { | |
113 | $self->_new_from_float($n); | |
114 | } | |
115 | if ($n->isa('Math::BigInt')) | |
116 | { | |
117 | # TODO: trap NaN, inf | |
118 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N | |
119 | $self->{_d} = $MBI->_one(); # d => 1 | |
120 | $self->{sign} = $n->{sign}; | |
121 | } | |
122 | if ($n->isa('Math::BigInt::Lite')) | |
123 | { | |
124 | # TODO: trap NaN, inf | |
125 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; | |
126 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = N | |
127 | $self->{_d} = $MBI->_one(); # d => 1 | |
128 | } | |
129 | return $self->bnorm(); # normalize (120/1 => 12/10) | |
130 | } | |
131 | ||
132 | # input like (BigInt,BigInt) or (BigLite,BigLite): | |
133 | if (ref($d) && ref($n)) | |
134 | { | |
135 | # do N first (for $self->{sign}): | |
136 | if ($n->isa('Math::BigInt')) | |
137 | { | |
138 | # TODO: trap NaN, inf | |
139 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N | |
140 | $self->{sign} = $n->{sign}; | |
141 | } | |
142 | elsif ($n->isa('Math::BigInt::Lite')) | |
143 | { | |
144 | # TODO: trap NaN, inf | |
145 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; | |
146 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = $n | |
147 | } | |
148 | else | |
149 | { | |
150 | require Carp; | |
151 | Carp::croak(ref($n) . " is not a recognized object format for Math::BigRat->new"); | |
152 | } | |
153 | # now D: | |
154 | if ($d->isa('Math::BigInt')) | |
155 | { | |
156 | # TODO: trap NaN, inf | |
157 | $self->{_d} = $MBI->_copy($d->{value}); # "mantissa" = D | |
158 | # +/+ or -/- => +, +/- or -/+ => - | |
159 | $self->{sign} = $d->{sign} ne $self->{sign} ? '-' : '+'; | |
160 | } | |
161 | elsif ($d->isa('Math::BigInt::Lite')) | |
162 | { | |
163 | # TODO: trap NaN, inf | |
164 | $self->{_d} = $MBI->_new(abs($$d)); # "mantissa" = D | |
165 | my $ds = '+'; $ds = '-' if $$d < 0; | |
166 | # +/+ or -/- => +, +/- or -/+ => - | |
167 | $self->{sign} = $ds ne $self->{sign} ? '-' : '+'; | |
168 | } | |
169 | else | |
170 | { | |
171 | require Carp; | |
172 | Carp::croak(ref($d) . " is not a recognized object format for Math::BigRat->new"); | |
173 | } | |
174 | return $self->bnorm(); # normalize (120/1 => 12/10) | |
175 | } | |
176 | return $n->copy() if ref $n; # already a BigRat | |
177 | ||
178 | if (!defined $n) | |
179 | { | |
180 | $self->{_n} = $MBI->_zero(); # undef => 0 | |
181 | $self->{_d} = $MBI->_one(); | |
182 | $self->{sign} = '+'; | |
183 | return $self; | |
184 | } | |
185 | ||
186 | # string input with / delimiter | |
187 | if ($n =~ /\s*\/\s*/) | |
188 | { | |
189 | return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid | |
190 | return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid | |
191 | ($n,$d) = split (/\//,$n); | |
192 | # try as BigFloats first | |
193 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) | |
194 | { | |
195 | local $Math::BigFloat::accuracy = undef; | |
196 | local $Math::BigFloat::precision = undef; | |
197 | ||
198 | # one of them looks like a float | |
199 | my $nf = Math::BigFloat->new($n,undef,undef); | |
200 | $self->{sign} = '+'; | |
201 | return $self->bnan() if $nf->is_nan(); | |
202 | ||
203 | $self->{_n} = $MBI->_copy( $nf->{_m} ); # get mantissa | |
204 | ||
205 | # now correct $self->{_n} due to $n | |
206 | my $f = Math::BigFloat->new($d,undef,undef); | |
207 | return $self->bnan() if $f->is_nan(); | |
208 | $self->{_d} = $MBI->_copy( $f->{_m} ); | |
209 | ||
210 | # calculate the difference between nE and dE | |
211 | # XXX TODO: check that exponent() makes a copy to avoid copy() | |
212 | my $diff_e = $nf->exponent()->copy()->bsub( $f->exponent); | |
213 | if ($diff_e->is_negative()) | |
214 | { | |
215 | # < 0: mul d with it | |
216 | $MBI->_lsft( $self->{_d}, $MBI->_new( $diff_e->babs()), 10); | |
217 | } | |
218 | elsif (!$diff_e->is_zero()) | |
219 | { | |
220 | # > 0: mul n with it | |
221 | $MBI->_lsft( $self->{_n}, $MBI->_new( $diff_e), 10); | |
222 | } | |
223 | } | |
224 | else | |
225 | { | |
226 | # both d and n look like (big)ints | |
227 | ||
228 | $self->{sign} = '+'; # no sign => '+' | |
229 | $self->{_n} = undef; | |
230 | $self->{_d} = undef; | |
231 | if ($n =~ /^([+-]?)0*(\d+)\z/) # first part ok? | |
232 | { | |
233 | $self->{sign} = $1 || '+'; # no sign => '+' | |
234 | $self->{_n} = $MBI->_new($2 || 0); | |
235 | } | |
236 | ||
237 | if ($d =~ /^([+-]?)0*(\d+)\z/) # second part ok? | |
238 | { | |
239 | $self->{sign} =~ tr/+-/-+/ if ($1 || '') eq '-'; # negate if second part neg. | |
240 | $self->{_d} = $MBI->_new($2 || 0); | |
241 | } | |
242 | ||
243 | if (!defined $self->{_n} || !defined $self->{_d}) | |
244 | { | |
245 | $d = Math::BigInt->new($d,undef,undef) unless ref $d; | |
246 | $n = Math::BigInt->new($n,undef,undef) unless ref $n; | |
247 | ||
248 | if ($n->{sign} =~ /^[+-]$/ && $d->{sign} =~ /^[+-]$/) | |
249 | { | |
250 | # both parts are ok as integers (wierd things like ' 1e0' | |
251 | $self->{_n} = $MBI->_copy($n->{value}); | |
252 | $self->{_d} = $MBI->_copy($d->{value}); | |
253 | $self->{sign} = $n->{sign}; | |
254 | $self->{sign} =~ tr/+-/-+/ if $d->{sign} eq '-'; # -1/-2 => 1/2 | |
255 | return $self->bnorm(); | |
256 | } | |
257 | ||
258 | $self->{sign} = '+'; # a default sign | |
259 | return $self->bnan() if $n->is_nan() || $d->is_nan(); | |
260 | ||
261 | # handle inf cases: | |
262 | if ($n->is_inf() || $d->is_inf()) | |
263 | { | |
264 | if ($n->is_inf()) | |
265 | { | |
266 | return $self->bnan() if $d->is_inf(); # both are inf => NaN | |
267 | my $s = '+'; # '+inf/+123' or '-inf/-123' | |
268 | $s = '-' if substr($n->{sign},0,1) ne $d->{sign}; | |
269 | # +-inf/123 => +-inf | |
270 | return $self->binf($s); | |
271 | } | |
272 | # 123/inf => 0 | |
273 | return $self->bzero(); | |
274 | } | |
275 | } | |
276 | } | |
277 | ||
278 | return $self->bnorm(); | |
279 | } | |
280 | ||
281 | # simple string input | |
282 | if (($n =~ /[\.eE]/)) | |
283 | { | |
284 | # looks like a float, quacks like a float, so probably is a float | |
285 | $self->{sign} = 'NaN'; | |
286 | local $Math::BigFloat::accuracy = undef; | |
287 | local $Math::BigFloat::precision = undef; | |
288 | $self->_new_from_float(Math::BigFloat->new($n,undef,undef)); | |
289 | } | |
290 | else | |
291 | { | |
292 | # for simple forms, use $MBI directly | |
293 | if ($n =~ /^([+-]?)0*(\d+)\z/) | |
294 | { | |
295 | $self->{sign} = $1 || '+'; | |
296 | $self->{_n} = $MBI->_new($2 || 0); | |
297 | $self->{_d} = $MBI->_one(); | |
298 | } | |
299 | else | |
300 | { | |
301 | my $n = Math::BigInt->new($n,undef,undef); | |
302 | $self->{_n} = $MBI->_copy($n->{value}); | |
303 | $self->{_d} = $MBI->_one(); | |
304 | $self->{sign} = $n->{sign}; | |
305 | return $self->bnan() if $self->{sign} eq 'NaN'; | |
306 | return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/; | |
307 | } | |
308 | } | |
309 | $self->bnorm(); | |
310 | } | |
311 | ||
312 | sub copy | |
313 | { | |
314 | # if two arguments, the first one is the class to "swallow" subclasses | |
315 | my ($c,$x) = @_; | |
316 | ||
317 | if (scalar @_ == 1) | |
318 | { | |
319 | $x = $_[0]; | |
320 | $c = ref($x); | |
321 | } | |
322 | return unless ref($x); # only for objects | |
323 | ||
324 | my $self = bless {}, $c; | |
325 | ||
326 | $self->{sign} = $x->{sign}; | |
327 | $self->{_d} = $MBI->_copy($x->{_d}); | |
328 | $self->{_n} = $MBI->_copy($x->{_n}); | |
329 | $self->{_a} = $x->{_a} if defined $x->{_a}; | |
330 | $self->{_p} = $x->{_p} if defined $x->{_p}; | |
331 | $self; | |
332 | } | |
333 | ||
334 | ############################################################################## | |
335 | ||
336 | sub config | |
337 | { | |
338 | # return (later set?) configuration data as hash ref | |
339 | my $class = shift || 'Math::BigRat'; | |
340 | ||
341 | my $cfg = $class->SUPER::config(@_); | |
342 | ||
343 | # now we need only to override the ones that are different from our parent | |
344 | $cfg->{class} = $class; | |
345 | $cfg->{with} = $MBI; | |
346 | $cfg; | |
347 | } | |
348 | ||
349 | ############################################################################## | |
350 | ||
351 | sub bstr | |
352 | { | |
353 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
354 | ||
355 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc | |
356 | { | |
357 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf | |
358 | return $s; | |
359 | } | |
360 | ||
361 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2' | |
362 | ||
363 | return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d}); | |
364 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); | |
365 | } | |
366 | ||
367 | sub bsstr | |
368 | { | |
369 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
370 | ||
371 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc | |
372 | { | |
373 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf | |
374 | return $s; | |
375 | } | |
376 | ||
377 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 | |
378 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); | |
379 | } | |
380 | ||
381 | sub bnorm | |
382 | { | |
383 | # reduce the number to the shortest form | |
384 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
385 | ||
386 | # Both parts must be objects of whatever we are using today. | |
387 | # Second check because Calc.pm has ARRAY res as unblessed objects. | |
388 | if (ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY') | |
389 | { | |
390 | require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).') in bnorm()'); | |
391 | } | |
392 | if (ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY') | |
393 | { | |
394 | require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).') in bnorm()'); | |
395 | } | |
396 | ||
397 | # no normalize for NaN, inf etc. | |
398 | return $x if $x->{sign} !~ /^[+-]$/; | |
399 | ||
400 | # normalize zeros to 0/1 | |
401 | if ($MBI->_is_zero($x->{_n})) | |
402 | { | |
403 | $x->{sign} = '+'; # never leave a -0 | |
404 | $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d}); | |
405 | return $x; | |
406 | } | |
407 | ||
408 | return $x if $MBI->_is_one($x->{_d}); # no need to reduce | |
409 | ||
410 | # reduce other numbers | |
411 | my $gcd = $MBI->_copy($x->{_n}); | |
412 | $gcd = $MBI->_gcd($gcd,$x->{_d}); | |
413 | ||
414 | if (!$MBI->_is_one($gcd)) | |
415 | { | |
416 | $x->{_n} = $MBI->_div($x->{_n},$gcd); | |
417 | $x->{_d} = $MBI->_div($x->{_d},$gcd); | |
418 | } | |
419 | $x; | |
420 | } | |
421 | ||
422 | ############################################################################## | |
423 | # sign manipulation | |
424 | ||
425 | sub bneg | |
426 | { | |
427 | # (BRAT or num_str) return BRAT | |
428 | # negate number or make a negated number from string | |
429 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
430 | ||
431 | return $x if $x->modify('bneg'); | |
432 | ||
433 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN' | |
434 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $MBI->_is_zero($x->{_n})); | |
435 | $x; | |
436 | } | |
437 | ||
438 | ############################################################################## | |
439 | # special values | |
440 | ||
441 | sub _bnan | |
442 | { | |
443 | # used by parent class bnan() to initialize number to NaN | |
444 | my $self = shift; | |
445 | ||
446 | if ($_trap_nan) | |
447 | { | |
448 | require Carp; | |
449 | my $class = ref($self); | |
450 | # "$self" below will stringify the object, this blows up if $self is a | |
451 | # partial object (happens under trap_nan), so fix it beforehand | |
452 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; | |
453 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; | |
454 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); | |
455 | } | |
456 | $self->{_n} = $MBI->_zero(); | |
457 | $self->{_d} = $MBI->_zero(); | |
458 | } | |
459 | ||
460 | sub _binf | |
461 | { | |
462 | # used by parent class bone() to initialize number to +inf/-inf | |
463 | my $self = shift; | |
464 | ||
465 | if ($_trap_inf) | |
466 | { | |
467 | require Carp; | |
468 | my $class = ref($self); | |
469 | # "$self" below will stringify the object, this blows up if $self is a | |
470 | # partial object (happens under trap_nan), so fix it beforehand | |
471 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; | |
472 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; | |
473 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); | |
474 | } | |
475 | $self->{_n} = $MBI->_zero(); | |
476 | $self->{_d} = $MBI->_zero(); | |
477 | } | |
478 | ||
479 | sub _bone | |
480 | { | |
481 | # used by parent class bone() to initialize number to +1/-1 | |
482 | my $self = shift; | |
483 | $self->{_n} = $MBI->_one(); | |
484 | $self->{_d} = $MBI->_one(); | |
485 | } | |
486 | ||
487 | sub _bzero | |
488 | { | |
489 | # used by parent class bzero() to initialize number to 0 | |
490 | my $self = shift; | |
491 | $self->{_n} = $MBI->_zero(); | |
492 | $self->{_d} = $MBI->_one(); | |
493 | } | |
494 | ||
495 | ############################################################################## | |
496 | # mul/add/div etc | |
497 | ||
498 | sub badd | |
499 | { | |
500 | # add two rational numbers | |
501 | ||
502 | # set up parameters | |
503 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
504 | # objectify is costly, so avoid it | |
505 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
506 | { | |
507 | ($self,$x,$y,@r) = objectify(2,@_); | |
508 | } | |
509 | ||
510 | # +inf + +inf => +inf, -inf + -inf => -inf | |
511 | return $x->binf(substr($x->{sign},0,1)) | |
512 | if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; | |
513 | ||
514 | # +inf + -inf or -inf + +inf => NaN | |
515 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
516 | ||
517 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 | |
518 | # - + - = --------- = -- | |
519 | # 4 3 4*3 12 | |
520 | ||
521 | # we do not compute the gcd() here, but simple do: | |
522 | # 5 7 5*3 + 7*4 43 | |
523 | # - + - = --------- = -- | |
524 | # 4 3 4*3 12 | |
525 | ||
526 | # and bnorm() will then take care of the rest | |
527 | ||
528 | # 5 * 3 | |
529 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); | |
530 | ||
531 | # 7 * 4 | |
532 | my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} ); | |
533 | ||
534 | # 5 * 3 + 7 * 4 | |
535 | ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign}); | |
536 | ||
537 | # 4 * 3 | |
538 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); | |
539 | ||
540 | # normalize result, and possible round | |
541 | $x->bnorm()->round(@r); | |
542 | } | |
543 | ||
544 | sub bsub | |
545 | { | |
546 | # subtract two rational numbers | |
547 | ||
548 | # set up parameters | |
549 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
550 | # objectify is costly, so avoid it | |
551 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
552 | { | |
553 | ($self,$x,$y,@r) = objectify(2,@_); | |
554 | } | |
555 | ||
556 | # flip sign of $x, call badd(), then flip sign of result | |
557 | $x->{sign} =~ tr/+-/-+/ | |
558 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 | |
559 | $x->badd($y,@r); # does norm and round | |
560 | $x->{sign} =~ tr/+-/-+/ | |
561 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 | |
562 | $x; | |
563 | } | |
564 | ||
565 | sub bmul | |
566 | { | |
567 | # multiply two rational numbers | |
568 | ||
569 | # set up parameters | |
570 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
571 | # objectify is costly, so avoid it | |
572 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
573 | { | |
574 | ($self,$x,$y,@r) = objectify(2,@_); | |
575 | } | |
576 | ||
577 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); | |
578 | ||
579 | # inf handling | |
580 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
581 | { | |
582 | return $x->bnan() if $x->is_zero() || $y->is_zero(); | |
583 | # result will always be +-inf: | |
584 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
585 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
586 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
587 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
588 | return $x->binf('-'); | |
589 | } | |
590 | ||
591 | # x== 0 # also: or y == 1 or y == -1 | |
592 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); | |
593 | ||
594 | # XXX TODO: | |
595 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) | |
596 | # and reducing in one step. This would save us the bnorm() at the end. | |
597 | ||
598 | # 1 2 1 * 2 2 1 | |
599 | # - * - = ----- = - = - | |
600 | # 4 3 4 * 3 12 6 | |
601 | ||
602 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); | |
603 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); | |
604 | ||
605 | # compute new sign | |
606 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; | |
607 | ||
608 | $x->bnorm()->round(@r); | |
609 | } | |
610 | ||
611 | sub bdiv | |
612 | { | |
613 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return | |
614 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) | |
615 | ||
616 | # set up parameters | |
617 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
618 | # objectify is costly, so avoid it | |
619 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
620 | { | |
621 | ($self,$x,$y,@r) = objectify(2,@_); | |
622 | } | |
623 | ||
624 | return $self->_div_inf($x,$y) | |
625 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
626 | ||
627 | # x== 0 # also: or y == 1 or y == -1 | |
628 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); | |
629 | ||
630 | # XXX TODO: list context, upgrade | |
631 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) | |
632 | # and reducing in one step. This would save us the bnorm() at the end. | |
633 | ||
634 | # 1 1 1 3 | |
635 | # - / - == - * - | |
636 | # 4 3 4 1 | |
637 | ||
638 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); | |
639 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); | |
640 | ||
641 | # compute new sign | |
642 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; | |
643 | ||
644 | $x->bnorm()->round(@r); | |
645 | $x; | |
646 | } | |
647 | ||
648 | sub bmod | |
649 | { | |
650 | # compute "remainder" (in Perl way) of $x / $y | |
651 | ||
652 | # set up parameters | |
653 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
654 | # objectify is costly, so avoid it | |
655 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
656 | { | |
657 | ($self,$x,$y,@r) = objectify(2,@_); | |
658 | } | |
659 | ||
660 | return $self->_div_inf($x,$y) | |
661 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
662 | ||
663 | return $x if $x->is_zero(); # 0 / 7 = 0, mod 0 | |
664 | ||
665 | # compute $x - $y * floor($x/$y), keeping the sign of $x | |
666 | ||
667 | # copy x to u, make it positive and then do a normal division ($u/$y) | |
668 | my $u = bless { sign => '+' }, $self; | |
669 | $u->{_n} = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d} ); | |
670 | $u->{_d} = $MBI->_mul( $MBI->_copy($x->{_d}), $y->{_n} ); | |
671 | ||
672 | # compute floor(u) | |
673 | if (! $MBI->_is_one($u->{_d})) | |
674 | { | |
675 | $u->{_n} = $MBI->_div($u->{_n},$u->{_d}); # 22/7 => 3/1 w/ truncate | |
676 | # no need to set $u->{_d} to 1, since below we set it to $y->{_d} anyway | |
677 | } | |
678 | ||
679 | # now compute $y * $u | |
680 | $u->{_d} = $MBI->_copy($y->{_d}); # 1 * $y->{_d}, see floor above | |
681 | $u->{_n} = $MBI->_mul($u->{_n},$y->{_n}); | |
682 | ||
683 | my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive | |
684 | # compute $x - $u | |
685 | $x->bsub($u); | |
686 | $x->{sign} = $xsign; # put sign back | |
687 | ||
688 | $x->bnorm()->round(@r); | |
689 | } | |
690 | ||
691 | ############################################################################## | |
692 | # bdec/binc | |
693 | ||
694 | sub bdec | |
695 | { | |
696 | # decrement value (subtract 1) | |
697 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
698 | ||
699 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf | |
700 | ||
701 | if ($x->{sign} eq '-') | |
702 | { | |
703 | $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2 | |
704 | } | |
705 | else | |
706 | { | |
707 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? | |
708 | { | |
709 | # 1/3 -- => -2/3 | |
710 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); | |
711 | $x->{sign} = '-'; | |
712 | } | |
713 | else | |
714 | { | |
715 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 | |
716 | } | |
717 | } | |
718 | $x->bnorm()->round(@r); | |
719 | } | |
720 | ||
721 | sub binc | |
722 | { | |
723 | # increment value (add 1) | |
724 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
725 | ||
726 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf | |
727 | ||
728 | if ($x->{sign} eq '-') | |
729 | { | |
730 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) | |
731 | { | |
732 | # -1/3 ++ => 2/3 (overflow at 0) | |
733 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); | |
734 | $x->{sign} = '+'; | |
735 | } | |
736 | else | |
737 | { | |
738 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 | |
739 | } | |
740 | } | |
741 | else | |
742 | { | |
743 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 | |
744 | } | |
745 | $x->bnorm()->round(@r); | |
746 | } | |
747 | ||
748 | ############################################################################## | |
749 | # is_foo methods (the rest is inherited) | |
750 | ||
751 | sub is_int | |
752 | { | |
753 | # return true if arg (BRAT or num_str) is an integer | |
754 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
755 | ||
756 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't | |
757 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer | |
758 | 0; | |
759 | } | |
760 | ||
761 | sub is_zero | |
762 | { | |
763 | # return true if arg (BRAT or num_str) is zero | |
764 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
765 | ||
766 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); | |
767 | 0; | |
768 | } | |
769 | ||
770 | sub is_one | |
771 | { | |
772 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given | |
773 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
774 | ||
775 | my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; | |
776 | return 1 | |
777 | if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})); | |
778 | 0; | |
779 | } | |
780 | ||
781 | sub is_odd | |
782 | { | |
783 | # return true if arg (BFLOAT or num_str) is odd or false if even | |
784 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
785 | ||
786 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't | |
787 | ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1 | |
788 | 0; | |
789 | } | |
790 | ||
791 | sub is_even | |
792 | { | |
793 | # return true if arg (BINT or num_str) is even or false if odd | |
794 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
795 | ||
796 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't | |
797 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never | |
798 | && $MBI->_is_even($x->{_n})); # but 4/1 is | |
799 | 0; | |
800 | } | |
801 | ||
802 | ############################################################################## | |
803 | # parts() and friends | |
804 | ||
805 | sub numerator | |
806 | { | |
807 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
808 | ||
809 | # NaN, inf, -inf | |
810 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); | |
811 | ||
812 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; | |
813 | $n; | |
814 | } | |
815 | ||
816 | sub denominator | |
817 | { | |
818 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
819 | ||
820 | # NaN | |
821 | return Math::BigInt->new($x->{sign}) if $x->{sign} eq 'NaN'; | |
822 | # inf, -inf | |
823 | return Math::BigInt->bone() if $x->{sign} !~ /^[+-]$/; | |
824 | ||
825 | Math::BigInt->new($MBI->_str($x->{_d})); | |
826 | } | |
827 | ||
828 | sub parts | |
829 | { | |
830 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
831 | ||
832 | my $c = 'Math::BigInt'; | |
833 | ||
834 | return ($c->bnan(),$c->bnan()) if $x->{sign} eq 'NaN'; | |
835 | return ($c->binf(),$c->binf()) if $x->{sign} eq '+inf'; | |
836 | return ($c->binf('-'),$c->binf()) if $x->{sign} eq '-inf'; | |
837 | ||
838 | my $n = $c->new( $MBI->_str($x->{_n})); | |
839 | $n->{sign} = $x->{sign}; | |
840 | my $d = $c->new( $MBI->_str($x->{_d})); | |
841 | ($n,$d); | |
842 | } | |
843 | ||
844 | sub length | |
845 | { | |
846 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
847 | ||
848 | return $nan unless $x->is_int(); | |
849 | $MBI->_len($x->{_n}); # length(-123/1) => length(123) | |
850 | } | |
851 | ||
852 | sub digit | |
853 | { | |
854 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); | |
855 | ||
856 | return $nan unless $x->is_int(); | |
857 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) | |
858 | } | |
859 | ||
860 | ############################################################################## | |
861 | # special calc routines | |
862 | ||
863 | sub bceil | |
864 | { | |
865 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
866 | ||
867 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf | |
868 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 | |
869 | ||
870 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate | |
871 | $x->{_d} = $MBI->_one(); # d => 1 | |
872 | $x->{_n} = $MBI->_inc($x->{_n}) | |
873 | if $x->{sign} eq '+'; # +22/7 => 4/1 | |
874 | $x->{sign} = '+' if $MBI->_is_zero($x->{_n}); # -0 => 0 | |
875 | $x; | |
876 | } | |
877 | ||
878 | sub bfloor | |
879 | { | |
880 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
881 | ||
882 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf | |
883 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 | |
884 | ||
885 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate | |
886 | $x->{_d} = $MBI->_one(); # d => 1 | |
887 | $x->{_n} = $MBI->_inc($x->{_n}) | |
888 | if $x->{sign} eq '-'; # -22/7 => -4/1 | |
889 | $x; | |
890 | } | |
891 | ||
892 | sub bfac | |
893 | { | |
894 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
895 | ||
896 | # if $x is not an integer | |
897 | if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d}))) | |
898 | { | |
899 | return $x->bnan(); | |
900 | } | |
901 | ||
902 | $x->{_n} = $MBI->_fac($x->{_n}); | |
903 | # since _d is 1, we don't need to reduce/norm the result | |
904 | $x->round(@r); | |
905 | } | |
906 | ||
907 | sub bpow | |
908 | { | |
909 | # power ($x ** $y) | |
910 | ||
911 | # set up parameters | |
912 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
913 | # objectify is costly, so avoid it | |
914 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
915 | { | |
916 | ($self,$x,$y,@r) = objectify(2,@_); | |
917 | } | |
918 | ||
919 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x | |
920 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; | |
921 | return $x->bone(@r) if $y->is_zero(); | |
922 | return $x->round(@r) if $x->is_one() || $y->is_one(); | |
923 | ||
924 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) | |
925 | { | |
926 | # if $x == -1 and odd/even y => +1/-1 | |
927 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); | |
928 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; | |
929 | } | |
930 | # 1 ** -y => 1 / (1 ** |y|) | |
931 | # so do test for negative $y after above's clause | |
932 | ||
933 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) | |
934 | ||
935 | # shortcut y/1 (and/or x/1) | |
936 | if ($MBI->_is_one($y->{_d})) | |
937 | { | |
938 | # shortcut for x/1 and y/1 | |
939 | if ($MBI->_is_one($x->{_d})) | |
940 | { | |
941 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 | |
942 | if ($y->{sign} eq '-') | |
943 | { | |
944 | # 0.2 ** -3 => 1/(0.2 ** 3) | |
945 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap | |
946 | } | |
947 | # correct sign; + ** + => + | |
948 | if ($x->{sign} eq '-') | |
949 | { | |
950 | # - * - => +, - * - * - => - | |
951 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); | |
952 | } | |
953 | return $x->round(@r); | |
954 | } | |
955 | # x/z ** y/1 | |
956 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y | |
957 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); | |
958 | if ($y->{sign} eq '-') | |
959 | { | |
960 | # 0.2 ** -3 => 1/(0.2 ** 3) | |
961 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap | |
962 | } | |
963 | # correct sign; + ** + => + | |
964 | if ($x->{sign} eq '-') | |
965 | { | |
966 | # - * - => +, - * - * - => - | |
967 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); | |
968 | } | |
969 | return $x->round(@r); | |
970 | } | |
971 | ||
972 | # regular calculation (this is wrong for d/e ** f/g) | |
973 | my $pow2 = $self->bone(); | |
974 | my $y1 = $MBI->_div ( $MBI->_copy($y->{_n}), $y->{_d}); | |
975 | my $two = $MBI->_two(); | |
976 | ||
977 | while (!$MBI->_is_one($y1)) | |
978 | { | |
979 | $pow2->bmul($x) if $MBI->_is_odd($y1); | |
980 | $MBI->_div($y1, $two); | |
981 | $x->bmul($x); | |
982 | } | |
983 | $x->bmul($pow2) unless $pow2->is_one(); | |
984 | # n ** -x => 1/n ** x | |
985 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; | |
986 | $x->bnorm()->round(@r); | |
987 | } | |
988 | ||
989 | sub blog | |
990 | { | |
991 | # set up parameters | |
992 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
993 | ||
994 | # objectify is costly, so avoid it | |
995 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
996 | { | |
997 | ($self,$x,$y,@r) = objectify(2,$class,@_); | |
998 | } | |
999 | ||
1000 | # blog(1,Y) => 0 | |
1001 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; | |
1002 | ||
1003 | # $x <= 0 => NaN | |
1004 | return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; | |
1005 | ||
1006 | if ($x->is_int() && $y->is_int()) | |
1007 | { | |
1008 | return $self->new($x->as_number()->blog($y->as_number(),@r)); | |
1009 | } | |
1010 | ||
1011 | # do it with floats | |
1012 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); | |
1013 | } | |
1014 | ||
1015 | sub _float_from_part | |
1016 | { | |
1017 | my $x = shift; | |
1018 | ||
1019 | my $f = Math::BigFloat->bzero(); | |
1020 | $f->{_m} = $MBI->_copy($x); | |
1021 | $f->{_e} = $MBI->_zero(); | |
1022 | ||
1023 | $f; | |
1024 | } | |
1025 | ||
1026 | sub _as_float | |
1027 | { | |
1028 | my $x = shift; | |
1029 | ||
1030 | local $Math::BigFloat::upgrade = undef; | |
1031 | local $Math::BigFloat::accuracy = undef; | |
1032 | local $Math::BigFloat::precision = undef; | |
1033 | # 22/7 => 3.142857143.. | |
1034 | ||
1035 | my $a = $x->accuracy() || 0; | |
1036 | if ($a != 0 || !$MBI->_is_one($x->{_d})) | |
1037 | { | |
1038 | # n/d | |
1039 | return Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy()); | |
1040 | } | |
1041 | # just n | |
1042 | Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n})); | |
1043 | } | |
1044 | ||
1045 | sub broot | |
1046 | { | |
1047 | # set up parameters | |
1048 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1049 | # objectify is costly, so avoid it | |
1050 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1051 | { | |
1052 | ($self,$x,$y,@r) = objectify(2,@_); | |
1053 | } | |
1054 | ||
1055 | if ($x->is_int() && $y->is_int()) | |
1056 | { | |
1057 | return $self->new($x->as_number()->broot($y->as_number(),@r)); | |
1058 | } | |
1059 | ||
1060 | # do it with floats | |
1061 | $x->_new_from_float( $x->_as_float()->broot($y,@r) ); | |
1062 | } | |
1063 | ||
1064 | sub bmodpow | |
1065 | { | |
1066 | # set up parameters | |
1067 | my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); | |
1068 | # objectify is costly, so avoid it | |
1069 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1070 | { | |
1071 | ($self,$x,$y,$m,@r) = objectify(3,@_); | |
1072 | } | |
1073 | ||
1074 | # $x or $y or $m are NaN or +-inf => NaN | |
1075 | return $x->bnan() | |
1076 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || | |
1077 | $m->{sign} !~ /^[+-]$/; | |
1078 | ||
1079 | if ($x->is_int() && $y->is_int() && $m->is_int()) | |
1080 | { | |
1081 | return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); | |
1082 | } | |
1083 | ||
1084 | warn ("bmodpow() not fully implemented"); | |
1085 | $x->bnan(); | |
1086 | } | |
1087 | ||
1088 | sub bmodinv | |
1089 | { | |
1090 | # set up parameters | |
1091 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1092 | # objectify is costly, so avoid it | |
1093 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1094 | { | |
1095 | ($self,$x,$y,@r) = objectify(2,@_); | |
1096 | } | |
1097 | ||
1098 | # $x or $y are NaN or +-inf => NaN | |
1099 | return $x->bnan() | |
1100 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; | |
1101 | ||
1102 | if ($x->is_int() && $y->is_int()) | |
1103 | { | |
1104 | return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); | |
1105 | } | |
1106 | ||
1107 | warn ("bmodinv() not fully implemented"); | |
1108 | $x->bnan(); | |
1109 | } | |
1110 | ||
1111 | sub bsqrt | |
1112 | { | |
1113 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
1114 | ||
1115 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 | |
1116 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf | |
1117 | return $x->round(@r) if $x->is_zero() || $x->is_one(); | |
1118 | ||
1119 | local $Math::BigFloat::upgrade = undef; | |
1120 | local $Math::BigFloat::downgrade = undef; | |
1121 | local $Math::BigFloat::precision = undef; | |
1122 | local $Math::BigFloat::accuracy = undef; | |
1123 | local $Math::BigInt::upgrade = undef; | |
1124 | local $Math::BigInt::precision = undef; | |
1125 | local $Math::BigInt::accuracy = undef; | |
1126 | ||
1127 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); | |
1128 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); | |
1129 | ||
1130 | # XXX TODO: we probably can optimze this: | |
1131 | ||
1132 | # if sqrt(D) was not integer | |
1133 | if ($x->{_d}->{_es} ne '+') | |
1134 | { | |
1135 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 | |
1136 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 | |
1137 | } | |
1138 | # if sqrt(N) was not integer | |
1139 | if ($x->{_n}->{_es} ne '+') | |
1140 | { | |
1141 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 | |
1142 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 | |
1143 | } | |
1144 | ||
1145 | # convert parts to $MBI again | |
1146 | $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10) | |
1147 | if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY'; | |
1148 | $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10) | |
1149 | if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY'; | |
1150 | ||
1151 | $x->bnorm()->round(@r); | |
1152 | } | |
1153 | ||
1154 | sub blsft | |
1155 | { | |
1156 | my ($self,$x,$y,$b,@r) = objectify(3,@_); | |
1157 | ||
1158 | $b = 2 unless defined $b; | |
1159 | $b = $self->new($b) unless ref ($b); | |
1160 | $x->bmul( $b->copy()->bpow($y), @r); | |
1161 | $x; | |
1162 | } | |
1163 | ||
1164 | sub brsft | |
1165 | { | |
1166 | my ($self,$x,$y,$b,@r) = objectify(3,@_); | |
1167 | ||
1168 | $b = 2 unless defined $b; | |
1169 | $b = $self->new($b) unless ref ($b); | |
1170 | $x->bdiv( $b->copy()->bpow($y), @r); | |
1171 | $x; | |
1172 | } | |
1173 | ||
1174 | ############################################################################## | |
1175 | # round | |
1176 | ||
1177 | sub round | |
1178 | { | |
1179 | $_[0]; | |
1180 | } | |
1181 | ||
1182 | sub bround | |
1183 | { | |
1184 | $_[0]; | |
1185 | } | |
1186 | ||
1187 | sub bfround | |
1188 | { | |
1189 | $_[0]; | |
1190 | } | |
1191 | ||
1192 | ############################################################################## | |
1193 | # comparing | |
1194 | ||
1195 | sub bcmp | |
1196 | { | |
1197 | # compare two signed numbers | |
1198 | ||
1199 | # set up parameters | |
1200 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1201 | # objectify is costly, so avoid it | |
1202 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1203 | { | |
1204 | ($self,$x,$y) = objectify(2,@_); | |
1205 | } | |
1206 | ||
1207 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1208 | { | |
1209 | # handle +-inf and NaN | |
1210 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1211 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; | |
1212 | return +1 if $x->{sign} eq '+inf'; | |
1213 | return -1 if $x->{sign} eq '-inf'; | |
1214 | return -1 if $y->{sign} eq '+inf'; | |
1215 | return +1; | |
1216 | } | |
1217 | # check sign for speed first | |
1218 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
1219 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
1220 | ||
1221 | # shortcut | |
1222 | my $xz = $MBI->_is_zero($x->{_n}); | |
1223 | my $yz = $MBI->_is_zero($y->{_n}); | |
1224 | return 0 if $xz && $yz; # 0 <=> 0 | |
1225 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y | |
1226 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 | |
1227 | ||
1228 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); | |
1229 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); | |
1230 | ||
1231 | my $cmp = $MBI->_acmp($t,$u); # signs are equal | |
1232 | $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse | |
1233 | $cmp; | |
1234 | } | |
1235 | ||
1236 | sub bacmp | |
1237 | { | |
1238 | # compare two numbers (as unsigned) | |
1239 | ||
1240 | # set up parameters | |
1241 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1242 | # objectify is costly, so avoid it | |
1243 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1244 | { | |
1245 | ($self,$x,$y) = objectify(2,$class,@_); | |
1246 | } | |
1247 | ||
1248 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1249 | { | |
1250 | # handle +-inf and NaN | |
1251 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1252 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
1253 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; | |
1254 | return -1; | |
1255 | } | |
1256 | ||
1257 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); | |
1258 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); | |
1259 | $MBI->_acmp($t,$u); # ignore signs | |
1260 | } | |
1261 | ||
1262 | ############################################################################## | |
1263 | # output conversation | |
1264 | ||
1265 | sub numify | |
1266 | { | |
1267 | # convert 17/8 => float (aka 2.125) | |
1268 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1269 | ||
1270 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc | |
1271 | ||
1272 | # N/1 => N | |
1273 | my $neg = ''; $neg = '-' if $x->{sign} eq '-'; | |
1274 | return $neg . $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); | |
1275 | ||
1276 | $x->_as_float()->numify() + 0.0; | |
1277 | } | |
1278 | ||
1279 | sub as_number | |
1280 | { | |
1281 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1282 | ||
1283 | return Math::BigInt->new($x) if $x->{sign} !~ /^[+-]$/; # NaN, inf etc | |
1284 | ||
1285 | my $u = Math::BigInt->bzero(); | |
1286 | $u->{sign} = $x->{sign}; | |
1287 | $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3 | |
1288 | $u; | |
1289 | } | |
1290 | ||
1291 | sub as_bin | |
1292 | { | |
1293 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1294 | ||
1295 | return $x unless $x->is_int(); | |
1296 | ||
1297 | my $s = $x->{sign}; $s = '' if $s eq '+'; | |
1298 | $s . $MBI->_as_bin($x->{_n}); | |
1299 | } | |
1300 | ||
1301 | sub as_hex | |
1302 | { | |
1303 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1304 | ||
1305 | return $x unless $x->is_int(); | |
1306 | ||
1307 | my $s = $x->{sign}; $s = '' if $s eq '+'; | |
1308 | $s . $MBI->_as_hex($x->{_n}); | |
1309 | } | |
1310 | ||
1311 | ############################################################################## | |
1312 | # import | |
1313 | ||
1314 | sub import | |
1315 | { | |
1316 | my $self = shift; | |
1317 | my $l = scalar @_; | |
1318 | my $lib = ''; my @a; | |
1319 | ||
1320 | for ( my $i = 0; $i < $l ; $i++) | |
1321 | { | |
1322 | if ( $_[$i] eq ':constant' ) | |
1323 | { | |
1324 | # this rest causes overlord er load to step in | |
1325 | overload::constant float => sub { $self->new(shift); }; | |
1326 | } | |
1327 | # elsif ($_[$i] eq 'upgrade') | |
1328 | # { | |
1329 | # # this causes upgrading | |
1330 | # $upgrade = $_[$i+1]; # or undef to disable | |
1331 | # $i++; | |
1332 | # } | |
1333 | elsif ($_[$i] eq 'downgrade') | |
1334 | { | |
1335 | # this causes downgrading | |
1336 | $downgrade = $_[$i+1]; # or undef to disable | |
1337 | $i++; | |
1338 | } | |
1339 | elsif ($_[$i] eq 'lib') | |
1340 | { | |
1341 | $lib = $_[$i+1] || ''; # default Calc | |
1342 | $i++; | |
1343 | } | |
1344 | elsif ($_[$i] eq 'with') | |
1345 | { | |
1346 | # this argument is no longer used | |
1347 | #$MBI = $_[$i+1] || 'Math::BigInt::Calc'; # default Math::BigInt::Calc | |
1348 | $i++; | |
1349 | } | |
1350 | else | |
1351 | { | |
1352 | push @a, $_[$i]; | |
1353 | } | |
1354 | } | |
1355 | require Math::BigInt; | |
1356 | ||
1357 | # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still have GMP | |
1358 | if ($lib ne '') | |
1359 | { | |
1360 | my @c = split /\s*,\s*/, $lib; | |
1361 | foreach (@c) | |
1362 | { | |
1363 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters | |
1364 | } | |
1365 | $lib = join(",", @c); | |
1366 | } | |
1367 | my @import = ('objectify'); | |
1368 | push @import, lib => $lib if $lib ne ''; | |
1369 | ||
1370 | # MBI already loaded, so feed it our lib arguments | |
1371 | Math::BigInt->import( @import ); | |
1372 | ||
1373 | $MBI = Math::BigFloat->config()->{lib}; | |
1374 | ||
1375 | # register us with MBI to get notified of future lib changes | |
1376 | Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } ); | |
1377 | ||
1378 | # any non :constant stuff is handled by our parent, Exporter (loaded | |
1379 | # by Math::BigFloat, even if @_ is empty, to give it a chance | |
1380 | $self->SUPER::import(@a); # for subclasses | |
1381 | $self->export_to_level(1,$self,@a); # need this, too | |
1382 | } | |
1383 | ||
1384 | 1; | |
1385 | ||
1386 | __END__ | |
1387 | ||
1388 | =head1 NAME | |
1389 | ||
1390 | Math::BigRat - Arbitrary big rational numbers | |
1391 | ||
1392 | =head1 SYNOPSIS | |
1393 | ||
1394 | use Math::BigRat; | |
1395 | ||
1396 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; | |
1397 | ||
1398 | print $x->bstr(),"\n"; | |
1399 | print $x ** 2,"\n"; | |
1400 | ||
1401 | my $y = Math::BigRat->new('inf'); | |
1402 | print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; | |
1403 | ||
1404 | my $z = Math::BigRat->new(144); $z->bsqrt(); | |
1405 | ||
1406 | =head1 DESCRIPTION | |
1407 | ||
1408 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support | |
1409 | for arbitrary big rational numbers. | |
1410 | ||
1411 | =head2 MATH LIBRARY | |
1412 | ||
1413 | Math with the numbers is done (by default) by a module called | |
1414 | Math::BigInt::Calc. This is equivalent to saying: | |
1415 | ||
1416 | use Math::BigRat lib => 'Calc'; | |
1417 | ||
1418 | You can change this by using: | |
1419 | ||
1420 | use Math::BigRat lib => 'BitVect'; | |
1421 | ||
1422 | The following would first try to find Math::BigInt::Foo, then | |
1423 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
1424 | ||
1425 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; | |
1426 | ||
1427 | Calc.pm uses as internal format an array of elements of some decimal base | |
1428 | (usually 1e7, but this might be different for some systems) with the least | |
1429 | significant digit first, while BitVect.pm uses a bit vector of base 2, most | |
1430 | significant bit first. Other modules might use even different means of | |
1431 | representing the numbers. See the respective module documentation for further | |
1432 | details. | |
1433 | ||
1434 | Currently the following replacement libraries exist, search for them at CPAN: | |
1435 | ||
1436 | Math::BigInt::BitVect | |
1437 | Math::BigInt::GMP | |
1438 | Math::BigInt::Pari | |
1439 | Math::BigInt::FastCalc | |
1440 | ||
1441 | =head1 METHODS | |
1442 | ||
1443 | Any methods not listed here are dervied from Math::BigFloat (or | |
1444 | Math::BigInt), so make sure you check these two modules for further | |
1445 | information. | |
1446 | ||
1447 | =head2 new() | |
1448 | ||
1449 | $x = Math::BigRat->new('1/3'); | |
1450 | ||
1451 | Create a new Math::BigRat object. Input can come in various forms: | |
1452 | ||
1453 | $x = Math::BigRat->new(123); # scalars | |
1454 | $x = Math::BigRat->new('inf'); # infinity | |
1455 | $x = Math::BigRat->new('123.3'); # float | |
1456 | $x = Math::BigRat->new('1/3'); # simple string | |
1457 | $x = Math::BigRat->new('1 / 3'); # spaced | |
1458 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats | |
1459 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt | |
1460 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat | |
1461 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite | |
1462 | ||
1463 | # You can also give D and N as different objects: | |
1464 | $x = Math::BigRat->new( | |
1465 | Math::BigInt->new(-123), | |
1466 | Math::BigInt->new(7), | |
1467 | ); # => -123/7 | |
1468 | ||
1469 | =head2 numerator() | |
1470 | ||
1471 | $n = $x->numerator(); | |
1472 | ||
1473 | Returns a copy of the numerator (the part above the line) as signed BigInt. | |
1474 | ||
1475 | =head2 denominator() | |
1476 | ||
1477 | $d = $x->denominator(); | |
1478 | ||
1479 | Returns a copy of the denominator (the part under the line) as positive BigInt. | |
1480 | ||
1481 | =head2 parts() | |
1482 | ||
1483 | ($n,$d) = $x->parts(); | |
1484 | ||
1485 | Return a list consisting of (signed) numerator and (unsigned) denominator as | |
1486 | BigInts. | |
1487 | ||
1488 | =head2 as_int() | |
1489 | ||
1490 | $x = Math::BigRat->new('13/7'); | |
1491 | print $x->as_int(),"\n"; # '1' | |
1492 | ||
1493 | Returns a copy of the object as BigInt, truncated to an integer. | |
1494 | ||
1495 | C<as_number()> is an alias for C<as_int()>. | |
1496 | ||
1497 | =head2 as_hex() | |
1498 | ||
1499 | $x = Math::BigRat->new('13'); | |
1500 | print $x->as_hex(),"\n"; # '0xd' | |
1501 | ||
1502 | Returns the BigRat as hexadecimal string. Works only for integers. | |
1503 | ||
1504 | =head2 as_bin() | |
1505 | ||
1506 | $x = Math::BigRat->new('13'); | |
1507 | print $x->as_bin(),"\n"; # '0x1101' | |
1508 | ||
1509 | Returns the BigRat as binary string. Works only for integers. | |
1510 | ||
1511 | =head2 bfac() | |
1512 | ||
1513 | $x->bfac(); | |
1514 | ||
1515 | Calculates the factorial of $x. For instance: | |
1516 | ||
1517 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 | |
1518 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 | |
1519 | ||
1520 | Works currently only for integers. | |
1521 | ||
1522 | =head2 blog() | |
1523 | ||
1524 | Is not yet implemented. | |
1525 | ||
1526 | =head2 bround()/round()/bfround() | |
1527 | ||
1528 | Are not yet implemented. | |
1529 | ||
1530 | =head2 bmod() | |
1531 | ||
1532 | use Math::BigRat; | |
1533 | my $x = Math::BigRat->new('7/4'); | |
1534 | my $y = Math::BigRat->new('4/3'); | |
1535 | print $x->bmod($y); | |
1536 | ||
1537 | Set $x to the remainder of the division of $x by $y. | |
1538 | ||
1539 | =head2 is_one() | |
1540 | ||
1541 | print "$x is 1\n" if $x->is_one(); | |
1542 | ||
1543 | Return true if $x is exactly one, otherwise false. | |
1544 | ||
1545 | =head2 is_zero() | |
1546 | ||
1547 | print "$x is 0\n" if $x->is_zero(); | |
1548 | ||
1549 | Return true if $x is exactly zero, otherwise false. | |
1550 | ||
1551 | =head2 is_pos() | |
1552 | ||
1553 | print "$x is >= 0\n" if $x->is_positive(); | |
1554 | ||
1555 | Return true if $x is positive (greater than or equal to zero), otherwise | |
1556 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. | |
1557 | ||
1558 | C<is_positive()> is an alias for C<is_pos()>. | |
1559 | ||
1560 | =head2 is_neg() | |
1561 | ||
1562 | print "$x is < 0\n" if $x->is_negative(); | |
1563 | ||
1564 | Return true if $x is negative (smaller than zero), otherwise false. Please | |
1565 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. | |
1566 | ||
1567 | C<is_negative()> is an alias for C<is_neg()>. | |
1568 | ||
1569 | =head2 is_int() | |
1570 | ||
1571 | print "$x is an integer\n" if $x->is_int(); | |
1572 | ||
1573 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise | |
1574 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. | |
1575 | ||
1576 | =head2 is_odd() | |
1577 | ||
1578 | print "$x is odd\n" if $x->is_odd(); | |
1579 | ||
1580 | Return true if $x is odd, otherwise false. | |
1581 | ||
1582 | =head2 is_even() | |
1583 | ||
1584 | print "$x is even\n" if $x->is_even(); | |
1585 | ||
1586 | Return true if $x is even, otherwise false. | |
1587 | ||
1588 | =head2 bceil() | |
1589 | ||
1590 | $x->bceil(); | |
1591 | ||
1592 | Set $x to the next bigger integer value (e.g. truncate the number to integer | |
1593 | and then increment it by one). | |
1594 | ||
1595 | =head2 bfloor() | |
1596 | ||
1597 | $x->bfloor(); | |
1598 | ||
1599 | Truncate $x to an integer value. | |
1600 | ||
1601 | =head2 bsqrt() | |
1602 | ||
1603 | $x->bsqrt(); | |
1604 | ||
1605 | Calculate the square root of $x. | |
1606 | ||
1607 | =head2 config | |
1608 | ||
1609 | use Data::Dumper; | |
1610 | ||
1611 | print Dumper ( Math::BigRat->config() ); | |
1612 | print Math::BigRat->config()->{lib},"\n"; | |
1613 | ||
1614 | Returns a hash containing the configuration, e.g. the version number, lib | |
1615 | loaded etc. The following hash keys are currently filled in with the | |
1616 | appropriate information. | |
1617 | ||
1618 | key RO/RW Description | |
1619 | Example | |
1620 | ============================================================ | |
1621 | lib RO Name of the Math library | |
1622 | Math::BigInt::Calc | |
1623 | lib_version RO Version of 'lib' | |
1624 | 0.30 | |
1625 | class RO The class of config you just called | |
1626 | Math::BigRat | |
1627 | version RO version number of the class you used | |
1628 | 0.10 | |
1629 | upgrade RW To which class numbers are upgraded | |
1630 | undef | |
1631 | downgrade RW To which class numbers are downgraded | |
1632 | undef | |
1633 | precision RW Global precision | |
1634 | undef | |
1635 | accuracy RW Global accuracy | |
1636 | undef | |
1637 | round_mode RW Global round mode | |
1638 | even | |
1639 | div_scale RW Fallback acccuracy for div | |
1640 | 40 | |
1641 | trap_nan RW Trap creation of NaN (undef = no) | |
1642 | undef | |
1643 | trap_inf RW Trap creation of +inf/-inf (undef = no) | |
1644 | undef | |
1645 | ||
1646 | By passing a reference to a hash you may set the configuration values. This | |
1647 | works only for values that a marked with a C<RW> above, anything else is | |
1648 | read-only. | |
1649 | ||
1650 | =head1 BUGS | |
1651 | ||
1652 | Some things are not yet implemented, or only implemented half-way: | |
1653 | ||
1654 | =over 2 | |
1655 | ||
1656 | =item inf handling (partial) | |
1657 | ||
1658 | =item NaN handling (partial) | |
1659 | ||
1660 | =item rounding (not implemented except for bceil/bfloor) | |
1661 | ||
1662 | =item $x ** $y where $y is not an integer | |
1663 | ||
1664 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) | |
1665 | ||
1666 | =back | |
1667 | ||
1668 | =head1 LICENSE | |
1669 | ||
1670 | This program is free software; you may redistribute it and/or modify it under | |
1671 | the same terms as Perl itself. | |
1672 | ||
1673 | =head1 SEE ALSO | |
1674 | ||
1675 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, | |
1676 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
1677 | ||
1678 | See L<http://search.cpan.org/search?dist=bignum> for a way to use | |
1679 | Math::BigRat. | |
1680 | ||
1681 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> | |
1682 | may contain more documentation and examples as well as testcases. | |
1683 | ||
1684 | =head1 AUTHORS | |
1685 | ||
1686 | (C) by Tels L<http://bloodgate.com/> 2001 - 2005. | |
1687 | ||
1688 | =cut |