Commit | Line | Data |
a4e2b1c6 |
1 | |
2 | # |
7d341013 |
3 | # "Tax the rat farms." - Lord Vetinari |
a4e2b1c6 |
4 | # |
184f15d5 |
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 |
7afd7a91 |
12 | # You should not look at the innards of a BigRat - use the methods for this. |
184f15d5 |
13 | |
14 | package Math::BigRat; |
15 | |
a4e2b1c6 |
16 | require 5.005_03; |
184f15d5 |
17 | use strict; |
18 | |
184f15d5 |
19 | use Math::BigFloat; |
12fc2493 |
20 | use vars qw($VERSION @ISA $upgrade $downgrade |
990fb837 |
21 | $accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf); |
184f15d5 |
22 | |
233f7bc0 |
23 | @ISA = qw(Math::BigFloat); |
184f15d5 |
24 | |
233f7bc0 |
25 | $VERSION = '0.15'; |
184f15d5 |
26 | |
12fc2493 |
27 | use overload; # inherit overload from Math::BigFloat |
184f15d5 |
28 | |
12fc2493 |
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; |
b68b7ab1 |
38 | *as_int = \&as_number; |
39 | *is_pos = \&is_positive; |
40 | *is_neg = \&is_negative; |
12fc2493 |
41 | } |
9b924220 |
42 | |
184f15d5 |
43 | ############################################################################## |
12fc2493 |
44 | # Global constants and flags. Access these only via the accessor methods! |
184f15d5 |
45 | |
184f15d5 |
46 | $accuracy = $precision = undef; |
47 | $round_mode = 'even'; |
48 | $div_scale = 40; |
49 | $upgrade = undef; |
50 | $downgrade = undef; |
51 | |
12fc2493 |
52 | # These are internally, and not to be used from the outside at all! |
990fb837 |
53 | |
54 | $_trap_nan = 0; # are NaNs ok? set w/ config() |
55 | $_trap_inf = 0; # are infs ok? set w/ config() |
56 | |
12fc2493 |
57 | # the package we are using for our private parts, defaults to: |
58 | # Math::BigInt->config()->{lib} |
59 | my $MBI = 'Math::BigInt::Calc'; |
60 | |
184f15d5 |
61 | my $nan = 'NaN'; |
9b924220 |
62 | my $class = 'Math::BigRat'; |
184f15d5 |
63 | |
8f675a64 |
64 | sub isa |
65 | { |
66 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't |
67 | UNIVERSAL::isa(@_); |
68 | } |
69 | |
12fc2493 |
70 | ############################################################################## |
9b924220 |
71 | |
184f15d5 |
72 | sub _new_from_float |
73 | { |
7afd7a91 |
74 | # turn a single float input into a rational number (like '0.1') |
184f15d5 |
75 | my ($self,$f) = @_; |
76 | |
77 | return $self->bnan() if $f->is_nan(); |
9b924220 |
78 | return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/; |
184f15d5 |
79 | |
12fc2493 |
80 | $self->{_n} = $MBI->_copy( $f->{_m} ); # mantissa |
81 | $self->{_d} = $MBI->_one(); |
9b924220 |
82 | $self->{sign} = $f->{sign} || '+'; |
83 | if ($f->{_es} eq '-') |
184f15d5 |
84 | { |
85 | # something like Math::BigRat->new('0.1'); |
9b924220 |
86 | # 1 / 1 => 1/10 |
12fc2493 |
87 | $MBI->_lsft ( $self->{_d}, $f->{_e} ,10); |
184f15d5 |
88 | } |
89 | else |
90 | { |
91 | # something like Math::BigRat->new('10'); |
92 | # 1 / 1 => 10/1 |
12fc2493 |
93 | $MBI->_lsft ( $self->{_n}, $f->{_e} ,10) unless |
94 | $MBI->_is_zero($f->{_e}); |
184f15d5 |
95 | } |
184f15d5 |
96 | $self; |
97 | } |
98 | |
99 | sub new |
100 | { |
101 | # create a Math::BigRat |
102 | my $class = shift; |
103 | |
b68b7ab1 |
104 | my ($n,$d) = @_; |
184f15d5 |
105 | |
106 | my $self = { }; bless $self,$class; |
107 | |
b68b7ab1 |
108 | # input like (BigInt) or (BigFloat): |
6de7f0cc |
109 | if ((!defined $d) && (ref $n) && (!$n->isa('Math::BigRat'))) |
184f15d5 |
110 | { |
184f15d5 |
111 | if ($n->isa('Math::BigFloat')) |
112 | { |
7afd7a91 |
113 | $self->_new_from_float($n); |
184f15d5 |
114 | } |
115 | if ($n->isa('Math::BigInt')) |
116 | { |
990fb837 |
117 | # TODO: trap NaN, inf |
b68b7ab1 |
118 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N |
12fc2493 |
119 | $self->{_d} = $MBI->_one(); # d => 1 |
120 | $self->{sign} = $n->{sign}; |
8f675a64 |
121 | } |
122 | if ($n->isa('Math::BigInt::Lite')) |
123 | { |
990fb837 |
124 | # TODO: trap NaN, inf |
125 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; |
b68b7ab1 |
126 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = N |
12fc2493 |
127 | $self->{_d} = $MBI->_one(); # d => 1 |
184f15d5 |
128 | } |
12fc2493 |
129 | return $self->bnorm(); # normalize (120/1 => 12/10) |
184f15d5 |
130 | } |
b68b7ab1 |
131 | |
132 | # input like (BigInt,BigInt) or (BigLite,BigLite): |
133 | if (ref($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 | } |
12fc2493 |
176 | return $n->copy() if ref $n; # already a BigRat |
184f15d5 |
177 | |
178 | if (!defined $n) |
179 | { |
12fc2493 |
180 | $self->{_n} = $MBI->_zero(); # undef => 0 |
181 | $self->{_d} = $MBI->_one(); |
184f15d5 |
182 | $self->{sign} = '+'; |
12fc2493 |
183 | return $self; |
184f15d5 |
184 | } |
12fc2493 |
185 | |
184f15d5 |
186 | # string input with / delimiter |
187 | if ($n =~ /\s*\/\s*/) |
188 | { |
990fb837 |
189 | return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
190 | return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid |
184f15d5 |
191 | ($n,$d) = split (/\//,$n); |
192 | # try as BigFloats first |
193 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) |
194 | { |
7d341013 |
195 | local $Math::BigFloat::accuracy = undef; |
196 | local $Math::BigFloat::precision = undef; |
9b924220 |
197 | |
12fc2493 |
198 | # one of them looks like a float |
9b924220 |
199 | my $nf = Math::BigFloat->new($n,undef,undef); |
990fb837 |
200 | $self->{sign} = '+'; |
201 | return $self->bnan() if $nf->is_nan(); |
233f7bc0 |
202 | |
12fc2493 |
203 | $self->{_n} = $MBI->_copy( $nf->{_m} ); # get mantissa |
9b924220 |
204 | |
184f15d5 |
205 | # now correct $self->{_n} due to $n |
7d341013 |
206 | my $f = Math::BigFloat->new($d,undef,undef); |
990fb837 |
207 | return $self->bnan() if $f->is_nan(); |
12fc2493 |
208 | $self->{_d} = $MBI->_copy( $f->{_m} ); |
9b924220 |
209 | |
990fb837 |
210 | # calculate the difference between nE and dE |
12fc2493 |
211 | # XXX TODO: check that exponent() makes a copy to avoid copy() |
212 | my $diff_e = $nf->exponent()->copy()->bsub( $f->exponent); |
990fb837 |
213 | if ($diff_e->is_negative()) |
214 | { |
215 | # < 0: mul d with it |
12fc2493 |
216 | $MBI->_lsft( $self->{_d}, $MBI->_new( $diff_e->babs()), 10); |
990fb837 |
217 | } |
218 | elsif (!$diff_e->is_zero()) |
184f15d5 |
219 | { |
990fb837 |
220 | # > 0: mul n with it |
12fc2493 |
221 | $MBI->_lsft( $self->{_n}, $MBI->_new( $diff_e), 10); |
184f15d5 |
222 | } |
184f15d5 |
223 | } |
224 | else |
225 | { |
12fc2493 |
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 $n; |
233f7bc0 |
247 | |
12fc2493 |
248 | if ($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() || $d->is_inf()) |
7afd7a91 |
263 | { |
12fc2493 |
264 | if ($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(); |
7afd7a91 |
274 | } |
12fc2493 |
275 | } |
184f15d5 |
276 | } |
990fb837 |
277 | |
184f15d5 |
278 | return $self->bnorm(); |
279 | } |
280 | |
281 | # simple string input |
282 | if (($n =~ /[\.eE]/)) |
283 | { |
7d341013 |
284 | # looks like a float, quacks like a float, so probably is a float |
12fc2493 |
285 | $self->{sign} = 'NaN'; |
7d341013 |
286 | local $Math::BigFloat::accuracy = undef; |
287 | local $Math::BigFloat::precision = undef; |
7d341013 |
288 | $self->_new_from_float(Math::BigFloat->new($n,undef,undef)); |
184f15d5 |
289 | } |
290 | else |
291 | { |
12fc2493 |
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 | } |
184f15d5 |
308 | } |
309 | $self->bnorm(); |
310 | } |
311 | |
9b924220 |
312 | sub copy |
313 | { |
b68b7ab1 |
314 | # if two arguments, the first one is the class to "swallow" subclasses |
315 | my ($c,$x) = @_; |
316 | |
317 | if (scalar @_ == 1) |
9b924220 |
318 | { |
b68b7ab1 |
319 | $x = $_[0]; |
9b924220 |
320 | $c = ref($x); |
321 | } |
322 | return unless ref($x); # only for objects |
323 | |
12fc2493 |
324 | my $self = bless {}, $c; |
9b924220 |
325 | |
326 | $self->{sign} = $x->{sign}; |
12fc2493 |
327 | $self->{_d} = $MBI->_copy($x->{_d}); |
328 | $self->{_n} = $MBI->_copy($x->{_n}); |
9b924220 |
329 | $self->{_a} = $x->{_a} if defined $x->{_a}; |
330 | $self->{_p} = $x->{_p} if defined $x->{_p}; |
331 | $self; |
332 | } |
333 | |
990fb837 |
334 | ############################################################################## |
335 | |
336 | sub config |
337 | { |
338 | # return (later set?) configuration data as hash ref |
b68b7ab1 |
339 | my $class = shift || 'Math::BigRat'; |
990fb837 |
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 | $cfg; |
347 | } |
348 | |
349 | ############################################################################## |
8f675a64 |
350 | |
184f15d5 |
351 | sub bstr |
352 | { |
7afd7a91 |
353 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
354 | |
355 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
356 | { |
357 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
358 | return $s; |
359 | } |
360 | |
7afd7a91 |
361 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2' |
184f15d5 |
362 | |
12fc2493 |
363 | return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d}); |
364 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
365 | } |
366 | |
367 | sub bsstr |
368 | { |
b68b7ab1 |
369 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
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 |
12fc2493 |
378 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
379 | } |
380 | |
381 | sub bnorm |
382 | { |
12fc2493 |
383 | # reduce the number to the shortest form |
b68b7ab1 |
384 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
385 | |
12fc2493 |
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') |
990fb837 |
389 | { |
12fc2493 |
390 | require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).') in bnorm()'); |
990fb837 |
391 | } |
12fc2493 |
392 | if (ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY') |
990fb837 |
393 | { |
12fc2493 |
394 | require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).') in bnorm()'); |
990fb837 |
395 | } |
6de7f0cc |
396 | |
6de7f0cc |
397 | # no normalize for NaN, inf etc. |
398 | return $x if $x->{sign} !~ /^[+-]$/; |
399 | |
184f15d5 |
400 | # normalize zeros to 0/1 |
12fc2493 |
401 | if ($MBI->_is_zero($x->{_n})) |
184f15d5 |
402 | { |
12fc2493 |
403 | $x->{sign} = '+'; # never leave a -0 |
404 | $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d}); |
184f15d5 |
405 | return $x; |
406 | } |
407 | |
12fc2493 |
408 | return $x if $MBI->_is_one($x->{_d}); # no need to reduce |
6de7f0cc |
409 | |
184f15d5 |
410 | # reduce other numbers |
12fc2493 |
411 | my $gcd = $MBI->_copy($x->{_n}); |
412 | $gcd = $MBI->_gcd($gcd,$x->{_d}); |
413 | |
414 | if (!$MBI->_is_one($gcd)) |
184f15d5 |
415 | { |
12fc2493 |
416 | $x->{_n} = $MBI->_div($x->{_n},$gcd); |
417 | $x->{_d} = $MBI->_div($x->{_d},$gcd); |
184f15d5 |
418 | } |
184f15d5 |
419 | $x; |
420 | } |
421 | |
422 | ############################################################################## |
b68b7ab1 |
423 | # sign manipulation |
424 | |
425 | sub bneg |
426 | { |
427 | # (BRAT or num_str) return BRAT |
428 | # negate number or make a negated number from string |
429 | my ($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 | ############################################################################## |
184f15d5 |
439 | # special values |
440 | |
441 | sub _bnan |
442 | { |
990fb837 |
443 | # used by parent class bnan() to initialize number to NaN |
184f15d5 |
444 | my $self = shift; |
990fb837 |
445 | |
446 | if ($_trap_nan) |
447 | { |
448 | require Carp; |
449 | my $class = ref($self); |
233f7bc0 |
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}; |
990fb837 |
454 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
455 | } |
12fc2493 |
456 | $self->{_n} = $MBI->_zero(); |
457 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
458 | } |
459 | |
460 | sub _binf |
461 | { |
7d341013 |
462 | # used by parent class bone() to initialize number to +inf/-inf |
184f15d5 |
463 | my $self = shift; |
990fb837 |
464 | |
465 | if ($_trap_inf) |
466 | { |
467 | require Carp; |
468 | my $class = ref($self); |
233f7bc0 |
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}; |
990fb837 |
473 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); |
474 | } |
12fc2493 |
475 | $self->{_n} = $MBI->_zero(); |
476 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
477 | } |
478 | |
479 | sub _bone |
480 | { |
7d341013 |
481 | # used by parent class bone() to initialize number to +1/-1 |
184f15d5 |
482 | my $self = shift; |
12fc2493 |
483 | $self->{_n} = $MBI->_one(); |
484 | $self->{_d} = $MBI->_one(); |
184f15d5 |
485 | } |
486 | |
487 | sub _bzero |
488 | { |
990fb837 |
489 | # used by parent class bzero() to initialize number to 0 |
184f15d5 |
490 | my $self = shift; |
12fc2493 |
491 | $self->{_n} = $MBI->_zero(); |
492 | $self->{_d} = $MBI->_one(); |
184f15d5 |
493 | } |
494 | |
495 | ############################################################################## |
496 | # mul/add/div etc |
497 | |
498 | sub badd |
499 | { |
7afd7a91 |
500 | # add two rational numbers |
7d341013 |
501 | |
502 | # set up parameters |
503 | my ($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 | } |
184f15d5 |
509 | |
12fc2493 |
510 | # +inf + +inf => +inf, -inf + -inf => -inf |
511 | return $x->binf(substr($x->{sign},0,1)) |
512 | if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
184f15d5 |
513 | |
12fc2493 |
514 | # +inf + -inf or -inf + +inf => NaN |
515 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
184f15d5 |
516 | |
517 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
518 | # - + - = --------- = -- |
519 | # 4 3 4*3 12 |
520 | |
7d341013 |
521 | # we do not compute the gcd() here, but simple do: |
233f7bc0 |
522 | # 5 7 5*3 + 7*4 43 |
7d341013 |
523 | # - + - = --------- = -- |
524 | # 4 3 4*3 12 |
525 | |
12fc2493 |
526 | # and bnorm() will then take care of the rest |
184f15d5 |
527 | |
233f7bc0 |
528 | # 5 * 3 |
12fc2493 |
529 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
7d341013 |
530 | |
233f7bc0 |
531 | # 7 * 4 |
12fc2493 |
532 | my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} ); |
184f15d5 |
533 | |
233f7bc0 |
534 | # 5 * 3 + 7 * 4 |
12fc2493 |
535 | ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign}); |
184f15d5 |
536 | |
233f7bc0 |
537 | # 4 * 3 |
12fc2493 |
538 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
539 | |
233f7bc0 |
540 | # normalize result, and possible round |
7d341013 |
541 | $x->bnorm()->round(@r); |
184f15d5 |
542 | } |
543 | |
544 | sub bsub |
545 | { |
7afd7a91 |
546 | # subtract two rational numbers |
7d341013 |
547 | |
548 | # set up parameters |
549 | my ($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 | } |
184f15d5 |
555 | |
7afd7a91 |
556 | # flip sign of $x, call badd(), then flip sign of result |
557 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
558 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
559 | $x->badd($y,@r); # does norm and round |
7afd7a91 |
560 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
561 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
7afd7a91 |
562 | $x; |
184f15d5 |
563 | } |
564 | |
565 | sub bmul |
566 | { |
7afd7a91 |
567 | # multiply two rational numbers |
7d341013 |
568 | |
569 | # set up parameters |
570 | my ($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 | } |
184f15d5 |
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 | |
12fc2493 |
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. |
184f15d5 |
597 | |
12fc2493 |
598 | # 1 2 1 * 2 2 1 |
599 | # - * - = ----- = - = - |
600 | # 4 3 4 * 3 12 6 |
7d341013 |
601 | |
12fc2493 |
602 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); |
603 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
604 | |
605 | # compute new sign |
606 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
607 | |
7d341013 |
608 | $x->bnorm()->round(@r); |
184f15d5 |
609 | } |
610 | |
611 | sub bdiv |
612 | { |
613 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
614 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
7d341013 |
615 | |
616 | # set up parameters |
617 | my ($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 | } |
184f15d5 |
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 | |
12fc2493 |
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. |
184f15d5 |
633 | |
184f15d5 |
634 | # 1 1 1 3 |
635 | # - / - == - * - |
636 | # 4 3 4 1 |
7d341013 |
637 | |
12fc2493 |
638 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
639 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); |
184f15d5 |
640 | |
641 | # compute new sign |
642 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
643 | |
7d341013 |
644 | $x->bnorm()->round(@r); |
6de7f0cc |
645 | $x; |
184f15d5 |
646 | } |
647 | |
990fb837 |
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 | |
990fb837 |
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 $x |
666 | |
12fc2493 |
667 | # copy x to u, make it positive and then do a normal division ($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})) |
990fb837 |
674 | { |
12fc2493 |
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 |
990fb837 |
677 | } |
678 | |
12fc2493 |
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}); |
990fb837 |
682 | |
12fc2493 |
683 | my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive |
990fb837 |
684 | # compute $x - $u |
685 | $x->bsub($u); |
686 | $x->{sign} = $xsign; # put sign back |
687 | |
688 | $x->bnorm()->round(@r); |
990fb837 |
689 | } |
690 | |
184f15d5 |
691 | ############################################################################## |
a4e2b1c6 |
692 | # bdec/binc |
693 | |
694 | sub bdec |
695 | { |
696 | # decrement value (subtract 1) |
697 | my ($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 | { |
12fc2493 |
703 | $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2 |
a4e2b1c6 |
704 | } |
705 | else |
706 | { |
12fc2493 |
707 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? |
a4e2b1c6 |
708 | { |
709 | # 1/3 -- => -2/3 |
12fc2493 |
710 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
711 | $x->{sign} = '-'; |
712 | } |
713 | else |
714 | { |
12fc2493 |
715 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 |
a4e2b1c6 |
716 | } |
717 | } |
718 | $x->bnorm()->round(@r); |
a4e2b1c6 |
719 | } |
720 | |
721 | sub binc |
722 | { |
723 | # increment value (add 1) |
724 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
725 | |
726 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
727 | |
728 | if ($x->{sign} eq '-') |
729 | { |
12fc2493 |
730 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) |
a4e2b1c6 |
731 | { |
732 | # -1/3 ++ => 2/3 (overflow at 0) |
12fc2493 |
733 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
734 | $x->{sign} = '+'; |
735 | } |
736 | else |
737 | { |
12fc2493 |
738 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 |
a4e2b1c6 |
739 | } |
740 | } |
741 | else |
742 | { |
12fc2493 |
743 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 |
a4e2b1c6 |
744 | } |
745 | $x->bnorm()->round(@r); |
a4e2b1c6 |
746 | } |
747 | |
748 | ############################################################################## |
184f15d5 |
749 | # is_foo methods (the rest is inherited) |
750 | |
751 | sub is_int |
752 | { |
753 | # return true if arg (BRAT or num_str) is an integer |
9b924220 |
754 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
755 | |
756 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
12fc2493 |
757 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer |
184f15d5 |
758 | 0; |
759 | } |
760 | |
761 | sub is_zero |
762 | { |
763 | # return true if arg (BRAT or num_str) is zero |
9b924220 |
764 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
765 | |
12fc2493 |
766 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); |
184f15d5 |
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 |
9b924220 |
773 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
774 | |
9b924220 |
775 | my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; |
184f15d5 |
776 | return 1 |
12fc2493 |
777 | if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})); |
184f15d5 |
778 | 0; |
779 | } |
780 | |
781 | sub is_odd |
782 | { |
783 | # return true if arg (BFLOAT or num_str) is odd or false if even |
9b924220 |
784 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
785 | |
786 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
12fc2493 |
787 | ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1 |
184f15d5 |
788 | 0; |
789 | } |
790 | |
791 | sub is_even |
792 | { |
793 | # return true if arg (BINT or num_str) is even or false if odd |
9b924220 |
794 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
795 | |
796 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
12fc2493 |
797 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never |
798 | && $MBI->_is_even($x->{_n})); # but 4/1 is |
184f15d5 |
799 | 0; |
800 | } |
801 | |
184f15d5 |
802 | ############################################################################## |
803 | # parts() and friends |
804 | |
805 | sub numerator |
806 | { |
807 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
a4e2b1c6 |
808 | |
12fc2493 |
809 | # NaN, inf, -inf |
810 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
a4e2b1c6 |
811 | |
12fc2493 |
812 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; |
184f15d5 |
813 | $n; |
814 | } |
815 | |
816 | sub denominator |
817 | { |
818 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
819 | |
12fc2493 |
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})); |
184f15d5 |
826 | } |
827 | |
828 | sub parts |
829 | { |
830 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
831 | |
12fc2493 |
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'; |
a4e2b1c6 |
837 | |
12fc2493 |
838 | my $n = $c->new( $MBI->_str($x->{_n})); |
184f15d5 |
839 | $n->{sign} = $x->{sign}; |
12fc2493 |
840 | my $d = $c->new( $MBI->_str($x->{_d})); |
841 | ($n,$d); |
184f15d5 |
842 | } |
843 | |
844 | sub length |
845 | { |
9b924220 |
846 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
847 | |
848 | return $nan unless $x->is_int(); |
12fc2493 |
849 | $MBI->_len($x->{_n}); # length(-123/1) => length(123) |
184f15d5 |
850 | } |
851 | |
852 | sub digit |
853 | { |
12fc2493 |
854 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); |
9b924220 |
855 | |
856 | return $nan unless $x->is_int(); |
12fc2493 |
857 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) |
184f15d5 |
858 | } |
859 | |
860 | ############################################################################## |
861 | # special calc routines |
862 | |
863 | sub bceil |
864 | { |
865 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
866 | |
12fc2493 |
867 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
868 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
869 | |
12fc2493 |
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 |
184f15d5 |
875 | $x; |
876 | } |
877 | |
878 | sub bfloor |
879 | { |
880 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
881 | |
12fc2493 |
882 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
883 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
884 | |
12fc2493 |
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 |
184f15d5 |
889 | $x; |
890 | } |
891 | |
892 | sub bfac |
893 | { |
a4e2b1c6 |
894 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
895 | |
12fc2493 |
896 | # if $x is not an integer |
897 | if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d}))) |
a4e2b1c6 |
898 | { |
12fc2493 |
899 | return $x->bnan(); |
a4e2b1c6 |
900 | } |
12fc2493 |
901 | |
902 | $x->{_n} = $MBI->_fac($x->{_n}); |
903 | # since _d is 1, we don't need to reduce/norm the result |
904 | $x->round(@r); |
184f15d5 |
905 | } |
906 | |
907 | sub bpow |
908 | { |
7d341013 |
909 | # power ($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 | } |
184f15d5 |
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() || $y->is_one(); |
12fc2493 |
923 | |
924 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) |
184f15d5 |
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 |
12fc2493 |
932 | |
184f15d5 |
933 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
934 | |
a4e2b1c6 |
935 | # shortcut y/1 (and/or x/1) |
12fc2493 |
936 | if ($MBI->_is_one($y->{_d})) |
a4e2b1c6 |
937 | { |
938 | # shortcut for x/1 and y/1 |
12fc2493 |
939 | if ($MBI->_is_one($x->{_d})) |
a4e2b1c6 |
940 | { |
12fc2493 |
941 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
a4e2b1c6 |
942 | if ($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 | # - * - => +, - * - * - => - |
12fc2493 |
951 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
952 | } |
953 | return $x->round(@r); |
954 | } |
955 | # x/z ** y/1 |
12fc2493 |
956 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
957 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); |
a4e2b1c6 |
958 | if ($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 | # - * - => +, - * - * - => - |
12fc2493 |
967 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
968 | } |
969 | return $x->round(@r); |
970 | } |
971 | |
972 | # regular calculation (this is wrong for d/e ** f/g) |
12fc2493 |
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)) |
184f15d5 |
978 | { |
12fc2493 |
979 | $pow2->bmul($x) if $MBI->_is_odd($y1); |
980 | $MBI->_div($y1, $two); |
184f15d5 |
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 '-'; |
7d341013 |
986 | $x->bnorm()->round(@r); |
184f15d5 |
987 | } |
988 | |
989 | sub blog |
990 | { |
7afd7a91 |
991 | # set up parameters |
992 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
993 | |
994 | # objectify is costly, so avoid it |
995 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
996 | { |
9b924220 |
997 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
7afd7a91 |
998 | } |
999 | |
9b924220 |
1000 | # blog(1,Y) => 0 |
1001 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; |
1002 | |
7afd7a91 |
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 | |
9b924220 |
1011 | # do it with floats |
1012 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); |
1013 | } |
1014 | |
12fc2493 |
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 | |
9b924220 |
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.. |
12fc2493 |
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})); |
7afd7a91 |
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 | } |
9b924220 |
1059 | |
1060 | # do it with floats |
1061 | $x->_new_from_float( $x->_as_float()->broot($y,@r) ); |
7afd7a91 |
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 | $x->bnan(); |
184f15d5 |
1109 | } |
1110 | |
1111 | sub bsqrt |
1112 | { |
990fb837 |
1113 | my ($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; |
9b924220 |
1126 | |
12fc2493 |
1127 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); |
1128 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); |
1129 | |
1130 | # XXX TODO: we probably can optimze this: |
184f15d5 |
1131 | |
990fb837 |
1132 | # if sqrt(D) was not integer |
9b924220 |
1133 | if ($x->{_d}->{_es} ne '+') |
990fb837 |
1134 | { |
9b924220 |
1135 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 |
12fc2493 |
1136 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 |
990fb837 |
1137 | } |
1138 | # if sqrt(N) was not integer |
9b924220 |
1139 | if ($x->{_n}->{_es} ne '+') |
990fb837 |
1140 | { |
9b924220 |
1141 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 |
12fc2493 |
1142 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 |
990fb837 |
1143 | } |
12fc2493 |
1144 | |
990fb837 |
1145 | # convert parts to $MBI again |
12fc2493 |
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 | |
990fb837 |
1151 | $x->bnorm()->round(@r); |
184f15d5 |
1152 | } |
1153 | |
1154 | sub blsft |
1155 | { |
9b924220 |
1156 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1157 | |
9b924220 |
1158 | $b = 2 unless defined $b; |
1159 | $b = $self->new($b) unless ref ($b); |
1160 | $x->bmul( $b->copy()->bpow($y), @r); |
184f15d5 |
1161 | $x; |
1162 | } |
1163 | |
1164 | sub brsft |
1165 | { |
12fc2493 |
1166 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1167 | |
9b924220 |
1168 | $b = 2 unless defined $b; |
1169 | $b = $self->new($b) unless ref ($b); |
1170 | $x->bdiv( $b->copy()->bpow($y), @r); |
184f15d5 |
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 | $_[0]; |
1190 | } |
1191 | |
1192 | ############################################################################## |
1193 | # comparing |
1194 | |
1195 | sub bcmp |
1196 | { |
7afd7a91 |
1197 | # compare two signed numbers |
1198 | |
1199 | # set up parameters |
1200 | my ($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,$y) = objectify(2,@_); |
1205 | } |
184f15d5 |
1206 | |
1207 | if (($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 |
12fc2493 |
1222 | my $xz = $MBI->_is_zero($x->{_n}); |
1223 | my $yz = $MBI->_is_zero($y->{_n}); |
184f15d5 |
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 | |
12fc2493 |
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 | $cmp; |
184f15d5 |
1234 | } |
1235 | |
1236 | sub bacmp |
1237 | { |
7afd7a91 |
1238 | # compare two numbers (as unsigned) |
9b924220 |
1239 | |
7afd7a91 |
1240 | # set up parameters |
1241 | my ($self,$x,$y) = (ref($_[0]),@_); |
1242 | # objectify is costly, so avoid it |
1243 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1244 | { |
9b924220 |
1245 | ($self,$x,$y) = objectify(2,$class,@_); |
7afd7a91 |
1246 | } |
184f15d5 |
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 $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
7afd7a91 |
1253 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1254 | return -1; |
184f15d5 |
1255 | } |
1256 | |
12fc2493 |
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,$u); # ignore signs |
184f15d5 |
1260 | } |
1261 | |
1262 | ############################################################################## |
1263 | # output conversation |
1264 | |
7d341013 |
1265 | sub numify |
1266 | { |
1267 | # convert 17/8 => float (aka 2.125) |
b68b7ab1 |
1268 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
7d341013 |
1269 | |
1270 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc |
1271 | |
93c87d9d |
1272 | # N/1 => N |
b68b7ab1 |
1273 | my $neg = ''; $neg = '-' if $x->{sign} eq '-'; |
1274 | return $neg . $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); |
93c87d9d |
1275 | |
b68b7ab1 |
1276 | $x->_as_float()->numify() + 0.0; |
7d341013 |
1277 | } |
1278 | |
184f15d5 |
1279 | sub as_number |
1280 | { |
9b924220 |
1281 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
1282 | |
12fc2493 |
1283 | return Math::BigInt->new($x) if $x->{sign} !~ /^[+-]$/; # NaN, inf etc |
990fb837 |
1284 | |
12fc2493 |
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 | $u; |
184f15d5 |
1289 | } |
1290 | |
9b924220 |
1291 | sub as_bin |
1292 | { |
1293 | my ($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 '+'; |
12fc2493 |
1298 | $s . $MBI->_as_bin($x->{_n}); |
9b924220 |
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 '+'; |
12fc2493 |
1308 | $s . $MBI->_as_hex($x->{_n}); |
9b924220 |
1309 | } |
1310 | |
b68b7ab1 |
1311 | ############################################################################## |
1312 | # import |
1313 | |
6de7f0cc |
1314 | sub import |
1315 | { |
1316 | my $self = shift; |
1317 | my $l = scalar @_; |
1318 | my $lib = ''; my @a; |
9b924220 |
1319 | |
6de7f0cc |
1320 | for ( my $i = 0; $i < $l ; $i++) |
1321 | { |
6de7f0cc |
1322 | if ( $_[$i] eq ':constant' ) |
1323 | { |
1324 | # this rest causes overlord er load to step in |
6de7f0cc |
1325 | overload::constant float => sub { $self->new(shift); }; |
1326 | } |
1327 | # elsif ($_[$i] eq 'upgrade') |
1328 | # { |
1329 | # # this causes upgrading |
b68b7ab1 |
1330 | # $upgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1331 | # $i++; |
1332 | # } |
1333 | elsif ($_[$i] eq 'downgrade') |
1334 | { |
1335 | # this causes downgrading |
b68b7ab1 |
1336 | $downgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1337 | $i++; |
1338 | } |
1339 | elsif ($_[$i] eq 'lib') |
1340 | { |
b68b7ab1 |
1341 | $lib = $_[$i+1] || ''; # default Calc |
6de7f0cc |
1342 | $i++; |
1343 | } |
1344 | elsif ($_[$i] eq 'with') |
1345 | { |
233f7bc0 |
1346 | # this argument is no longer used |
1347 | #$MBI = $_[$i+1] || 'Math::BigInt::Calc'; # default Math::BigInt::Calc |
6de7f0cc |
1348 | $i++; |
1349 | } |
1350 | else |
1351 | { |
1352 | push @a, $_[$i]; |
1353 | } |
1354 | } |
b68b7ab1 |
1355 | require Math::BigInt; |
6de7f0cc |
1356 | |
b68b7ab1 |
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) |
6de7f0cc |
1362 | { |
b68b7ab1 |
1363 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters |
6de7f0cc |
1364 | } |
233f7bc0 |
1365 | $lib = join(",", @c); |
93c87d9d |
1366 | } |
233f7bc0 |
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 ); |
6de7f0cc |
1372 | |
12fc2493 |
1373 | $MBI = Math::BigFloat->config()->{lib}; |
b68b7ab1 |
1374 | |
1375 | # register us with MBI to get notified of future lib changes |
1376 | Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } ); |
9b924220 |
1377 | |
233f7bc0 |
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 |
6de7f0cc |
1380 | $self->SUPER::import(@a); # for subclasses |
1381 | $self->export_to_level(1,$self,@a); # need this, too |
1382 | } |
184f15d5 |
1383 | |
1384 | 1; |
1385 | |
1386 | __END__ |
1387 | |
1388 | =head1 NAME |
1389 | |
b68b7ab1 |
1390 | Math::BigRat - Arbitrary big rational numbers |
184f15d5 |
1391 | |
1392 | =head1 SYNOPSIS |
1393 | |
7d341013 |
1394 | use Math::BigRat; |
184f15d5 |
1395 | |
7afd7a91 |
1396 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
184f15d5 |
1397 | |
7d341013 |
1398 | print $x->bstr(),"\n"; |
1399 | print $x ** 2,"\n"; |
184f15d5 |
1400 | |
7afd7a91 |
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 | |
184f15d5 |
1406 | =head1 DESCRIPTION |
1407 | |
7d341013 |
1408 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
b68b7ab1 |
1409 | for arbitrary big rational numbers. |
184f15d5 |
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 |
7d341013 |
1428 | (usually 1e7, but this might be different for some systems) with the least |
184f15d5 |
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 | |
7d341013 |
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 | |
184f15d5 |
1441 | =head1 METHODS |
1442 | |
7d341013 |
1443 | Any methods not listed here are dervied from Math::BigFloat (or |
6de7f0cc |
1444 | Math::BigInt), so make sure you check these two modules for further |
1445 | information. |
1446 | |
1447 | =head2 new() |
184f15d5 |
1448 | |
1449 | $x = Math::BigRat->new('1/3'); |
1450 | |
1451 | Create a new Math::BigRat object. Input can come in various forms: |
1452 | |
7d341013 |
1453 | $x = Math::BigRat->new(123); # scalars |
7afd7a91 |
1454 | $x = Math::BigRat->new('inf'); # infinity |
7d341013 |
1455 | $x = Math::BigRat->new('123.3'); # float |
184f15d5 |
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 |
6de7f0cc |
1461 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
184f15d5 |
1462 | |
b68b7ab1 |
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 | |
6de7f0cc |
1469 | =head2 numerator() |
184f15d5 |
1470 | |
1471 | $n = $x->numerator(); |
1472 | |
1473 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
1474 | |
6de7f0cc |
1475 | =head2 denominator() |
184f15d5 |
1476 | |
1477 | $d = $x->denominator(); |
1478 | |
1479 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
1480 | |
6de7f0cc |
1481 | =head2 parts() |
184f15d5 |
1482 | |
1483 | ($n,$d) = $x->parts(); |
1484 | |
1485 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
1486 | BigInts. |
1487 | |
b68b7ab1 |
1488 | =head2 as_int() |
6de7f0cc |
1489 | |
7d341013 |
1490 | $x = Math::BigRat->new('13/7'); |
b68b7ab1 |
1491 | print $x->as_int(),"\n"; # '1' |
1492 | |
1493 | Returns a copy of the object as BigInt, truncated to an integer. |
7d341013 |
1494 | |
b68b7ab1 |
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. |
6de7f0cc |
1510 | |
a4e2b1c6 |
1511 | =head2 bfac() |
6de7f0cc |
1512 | |
a4e2b1c6 |
1513 | $x->bfac(); |
6de7f0cc |
1514 | |
a4e2b1c6 |
1515 | Calculates the factorial of $x. For instance: |
6de7f0cc |
1516 | |
a4e2b1c6 |
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 |
184f15d5 |
1519 | |
7d341013 |
1520 | Works currently only for integers. |
6de7f0cc |
1521 | |
a4e2b1c6 |
1522 | =head2 blog() |
6de7f0cc |
1523 | |
a4e2b1c6 |
1524 | Is not yet implemented. |
6de7f0cc |
1525 | |
a4e2b1c6 |
1526 | =head2 bround()/round()/bfround() |
6de7f0cc |
1527 | |
a4e2b1c6 |
1528 | Are not yet implemented. |
6de7f0cc |
1529 | |
990fb837 |
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 $y. |
1538 | |
7d341013 |
1539 | =head2 is_one() |
1540 | |
1541 | print "$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 $x is exactly zero, otherwise false. |
1550 | |
b68b7ab1 |
1551 | =head2 is_pos() |
7d341013 |
1552 | |
1553 | print "$x is >= 0\n" if $x->is_positive(); |
1554 | |
1555 | Return true if $x is positive (greater than or equal to zero), otherwise |
1556 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. |
1557 | |
b68b7ab1 |
1558 | C<is_positive()> is an alias for C<is_pos()>. |
1559 | |
1560 | =head2 is_neg() |
7d341013 |
1561 | |
1562 | print "$x is < 0\n" if $x->is_negative(); |
1563 | |
1564 | Return true if $x is negative (smaller than zero), otherwise false. Please |
1565 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. |
1566 | |
b68b7ab1 |
1567 | C<is_negative()> is an alias for C<is_neg()>. |
1568 | |
7d341013 |
1569 | =head2 is_int() |
1570 | |
1571 | print "$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. |
6de7f0cc |
1600 | |
7afd7a91 |
1601 | =head2 bsqrt() |
1602 | |
1603 | $x->bsqrt(); |
1604 | |
1605 | Calculate the square root of $x. |
1606 | |
990fb837 |
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 | |
a4e2b1c6 |
1650 | =head1 BUGS |
6de7f0cc |
1651 | |
7d341013 |
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 | |
7afd7a91 |
1664 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) |
1665 | |
7d341013 |
1666 | =back |
184f15d5 |
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 | |
7d341013 |
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. |
184f15d5 |
1683 | |
1684 | =head1 AUTHORS |
1685 | |
b68b7ab1 |
1686 | (C) by Tels L<http://bloodgate.com/> 2001 - 2005. |
184f15d5 |
1687 | |
1688 | =cut |