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 |
7d341013 |
12 | # _f : flags, used by MBR to flag parts of a rationale as untouchable |
184f15d5 |
13 | |
14 | package Math::BigRat; |
15 | |
a4e2b1c6 |
16 | require 5.005_03; |
184f15d5 |
17 | use strict; |
18 | |
19 | use Exporter; |
20 | use Math::BigFloat; |
21 | use vars qw($VERSION @ISA $PACKAGE @EXPORT_OK $upgrade $downgrade |
22 | $accuracy $precision $round_mode $div_scale); |
23 | |
24 | @ISA = qw(Exporter Math::BigFloat); |
25 | @EXPORT_OK = qw(); |
26 | |
7d341013 |
27 | $VERSION = '0.09'; |
184f15d5 |
28 | |
29 | use overload; # inherit from Math::BigFloat |
30 | |
31 | ############################################################################## |
32 | # global constants, flags and accessory |
33 | |
34 | use constant MB_NEVER_ROUND => 0x0001; |
35 | |
36 | $accuracy = $precision = undef; |
37 | $round_mode = 'even'; |
38 | $div_scale = 40; |
39 | $upgrade = undef; |
40 | $downgrade = undef; |
41 | |
42 | my $nan = 'NaN'; |
43 | my $class = 'Math::BigRat'; |
6de7f0cc |
44 | my $MBI = 'Math::BigInt'; |
184f15d5 |
45 | |
8f675a64 |
46 | sub isa |
47 | { |
48 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't |
49 | UNIVERSAL::isa(@_); |
50 | } |
51 | |
184f15d5 |
52 | sub _new_from_float |
53 | { |
7d341013 |
54 | # turn a single float input into a rationale (like '0.1') |
184f15d5 |
55 | my ($self,$f) = @_; |
56 | |
57 | return $self->bnan() if $f->is_nan(); |
58 | return $self->binf('-inf') if $f->{sign} eq '-inf'; |
59 | return $self->binf('+inf') if $f->{sign} eq '+inf'; |
60 | |
184f15d5 |
61 | $self->{_n} = $f->{_m}->copy(); # mantissa |
6de7f0cc |
62 | $self->{_d} = $MBI->bone(); |
184f15d5 |
63 | $self->{sign} = $f->{sign}; $self->{_n}->{sign} = '+'; |
64 | if ($f->{_e}->{sign} eq '-') |
65 | { |
66 | # something like Math::BigRat->new('0.1'); |
67 | $self->{_d}->blsft($f->{_e}->copy()->babs(),10); # 1 / 1 => 1/10 |
68 | } |
69 | else |
70 | { |
71 | # something like Math::BigRat->new('10'); |
72 | # 1 / 1 => 10/1 |
73 | $self->{_n}->blsft($f->{_e},10) unless $f->{_e}->is_zero(); |
74 | } |
184f15d5 |
75 | $self; |
76 | } |
77 | |
78 | sub new |
79 | { |
80 | # create a Math::BigRat |
81 | my $class = shift; |
82 | |
83 | my ($n,$d) = shift; |
84 | |
85 | my $self = { }; bless $self,$class; |
86 | |
184f15d5 |
87 | # input like (BigInt,BigInt) or (BigFloat,BigFloat) not handled yet |
88 | |
6de7f0cc |
89 | if ((!defined $d) && (ref $n) && (!$n->isa('Math::BigRat'))) |
184f15d5 |
90 | { |
184f15d5 |
91 | if ($n->isa('Math::BigFloat')) |
92 | { |
184f15d5 |
93 | return $self->_new_from_float($n)->bnorm(); |
94 | } |
95 | if ($n->isa('Math::BigInt')) |
96 | { |
8f675a64 |
97 | $self->{_n} = $n->copy(); # "mantissa" = $n |
6de7f0cc |
98 | $self->{_d} = $MBI->bone(); |
8f675a64 |
99 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
100 | return $self->bnorm(); |
101 | } |
102 | if ($n->isa('Math::BigInt::Lite')) |
103 | { |
7d341013 |
104 | $self->{_n} = $MBI->new($$n,undef,undef); # "mantissa" = $n |
6de7f0cc |
105 | $self->{_d} = $MBI->bone(); |
184f15d5 |
106 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
107 | return $self->bnorm(); |
108 | } |
109 | } |
110 | return $n->copy() if ref $n; |
184f15d5 |
111 | |
112 | if (!defined $n) |
113 | { |
7d341013 |
114 | $self->{_n} = $MBI->bzero(); # undef => 0 |
6de7f0cc |
115 | $self->{_d} = $MBI->bone(); |
184f15d5 |
116 | $self->{sign} = '+'; |
117 | return $self->bnorm(); |
118 | } |
119 | # string input with / delimiter |
120 | if ($n =~ /\s*\/\s*/) |
121 | { |
122 | return Math::BigRat->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
123 | return Math::BigRat->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid |
124 | ($n,$d) = split (/\//,$n); |
125 | # try as BigFloats first |
126 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) |
127 | { |
128 | # one of them looks like a float |
7d341013 |
129 | # Math::BigFloat($n,undef,undef) does not what it is supposed to do, so: |
130 | local $Math::BigFloat::accuracy = undef; |
131 | local $Math::BigFloat::precision = undef; |
132 | local $Math::BigInt::accuracy = undef; |
133 | local $Math::BigInt::precision = undef; |
184f15d5 |
134 | $self->_new_from_float(Math::BigFloat->new($n)); |
135 | # now correct $self->{_n} due to $n |
7d341013 |
136 | my $f = Math::BigFloat->new($d,undef,undef); |
184f15d5 |
137 | if ($f->{_e}->{sign} eq '-') |
138 | { |
139 | # 10 / 0.1 => 100/1 |
140 | $self->{_n}->blsft($f->{_e}->copy()->babs(),10); |
141 | } |
142 | else |
143 | { |
144 | $self->{_d}->blsft($f->{_e},10); # 1 / 1 => 10/1 |
145 | } |
146 | } |
147 | else |
148 | { |
7d341013 |
149 | # both d and n are (big)ints |
150 | $self->{_n} = $MBI->new($n,undef,undef); |
151 | $self->{_d} = $MBI->new($d,undef,undef); |
184f15d5 |
152 | return $self->bnan() if $self->{_n}->is_nan() || $self->{_d}->is_nan(); |
153 | # inf handling is missing here |
154 | |
155 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
156 | # if $d is negative, flip sign |
157 | $self->{sign} =~ tr/+-/-+/ if $self->{_d}->{sign} eq '-'; |
158 | $self->{_d}->{sign} = '+'; # normalize |
159 | } |
160 | return $self->bnorm(); |
161 | } |
162 | |
163 | # simple string input |
164 | if (($n =~ /[\.eE]/)) |
165 | { |
7d341013 |
166 | # looks like a float, quacks like a float, so probably is a float |
167 | # Math::BigFloat($n,undef,undef) does not what it is supposed to do, so: |
168 | local $Math::BigFloat::accuracy = undef; |
169 | local $Math::BigFloat::precision = undef; |
170 | local $Math::BigInt::accuracy = undef; |
171 | local $Math::BigInt::precision = undef; |
172 | $self->_new_from_float(Math::BigFloat->new($n,undef,undef)); |
184f15d5 |
173 | } |
174 | else |
175 | { |
7d341013 |
176 | $self->{_n} = $MBI->new($n,undef,undef); |
6de7f0cc |
177 | $self->{_d} = $MBI->bone(); |
184f15d5 |
178 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
a4e2b1c6 |
179 | return $self->bnan() if $self->{sign} eq 'NaN'; |
180 | return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/; |
184f15d5 |
181 | } |
182 | $self->bnorm(); |
183 | } |
184 | |
8f675a64 |
185 | ############################################################################### |
186 | |
184f15d5 |
187 | sub bstr |
188 | { |
189 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
190 | |
191 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
192 | { |
193 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
194 | return $s; |
195 | } |
196 | |
184f15d5 |
197 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
198 | |
199 | return $s.$x->{_n}->bstr() if $x->{_d}->is_one(); |
200 | return $s.$x->{_n}->bstr() . '/' . $x->{_d}->bstr(); |
201 | } |
202 | |
203 | sub bsstr |
204 | { |
205 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
206 | |
207 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
208 | { |
209 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
210 | return $s; |
211 | } |
212 | |
213 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
7d341013 |
214 | return $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr(); |
184f15d5 |
215 | } |
216 | |
217 | sub bnorm |
218 | { |
219 | # reduce the number to the shortest form and remember this (so that we |
220 | # don't reduce again) |
221 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
222 | |
6de7f0cc |
223 | # both parts must be BigInt's |
224 | die ("n is not $MBI but (".ref($x->{_n}).')') |
225 | if ref($x->{_n}) ne $MBI; |
226 | die ("d is not $MBI but (".ref($x->{_d}).')') |
227 | if ref($x->{_d}) ne $MBI; |
228 | |
184f15d5 |
229 | # this is to prevent automatically rounding when MBI's globals are set |
230 | $x->{_d}->{_f} = MB_NEVER_ROUND; |
231 | $x->{_n}->{_f} = MB_NEVER_ROUND; |
232 | # 'forget' that parts were rounded via MBI::bround() in MBF's bfround() |
233 | $x->{_d}->{_a} = undef; $x->{_n}->{_a} = undef; |
234 | $x->{_d}->{_p} = undef; $x->{_n}->{_p} = undef; |
235 | |
6de7f0cc |
236 | # no normalize for NaN, inf etc. |
237 | return $x if $x->{sign} !~ /^[+-]$/; |
238 | |
184f15d5 |
239 | # normalize zeros to 0/1 |
240 | if (($x->{sign} =~ /^[+-]$/) && |
241 | ($x->{_n}->is_zero())) |
242 | { |
a4e2b1c6 |
243 | $x->{sign} = '+'; # never -0 |
6de7f0cc |
244 | $x->{_d} = $MBI->bone() unless $x->{_d}->is_one(); |
184f15d5 |
245 | return $x; |
246 | } |
247 | |
a4e2b1c6 |
248 | return $x if $x->{_d}->is_one(); # no need to reduce |
6de7f0cc |
249 | |
184f15d5 |
250 | # reduce other numbers |
8f675a64 |
251 | # disable upgrade in BigInt, otherwise deep recursion |
252 | local $Math::BigInt::upgrade = undef; |
7d341013 |
253 | local $Math::BigInt::accuracy = undef; |
254 | local $Math::BigInt::precision = undef; |
184f15d5 |
255 | my $gcd = $x->{_n}->bgcd($x->{_d}); |
256 | |
257 | if (!$gcd->is_one()) |
258 | { |
259 | $x->{_n}->bdiv($gcd); |
260 | $x->{_d}->bdiv($gcd); |
261 | } |
184f15d5 |
262 | $x; |
263 | } |
264 | |
265 | ############################################################################## |
266 | # special values |
267 | |
268 | sub _bnan |
269 | { |
270 | # used by parent class bone() to initialize number to 1 |
271 | my $self = shift; |
a4e2b1c6 |
272 | $self->{_n} = $MBI->bzero(); |
273 | $self->{_d} = $MBI->bzero(); |
184f15d5 |
274 | } |
275 | |
276 | sub _binf |
277 | { |
7d341013 |
278 | # used by parent class bone() to initialize number to +inf/-inf |
184f15d5 |
279 | my $self = shift; |
a4e2b1c6 |
280 | $self->{_n} = $MBI->bzero(); |
281 | $self->{_d} = $MBI->bzero(); |
184f15d5 |
282 | } |
283 | |
284 | sub _bone |
285 | { |
7d341013 |
286 | # used by parent class bone() to initialize number to +1/-1 |
184f15d5 |
287 | my $self = shift; |
a4e2b1c6 |
288 | $self->{_n} = $MBI->bone(); |
289 | $self->{_d} = $MBI->bone(); |
184f15d5 |
290 | } |
291 | |
292 | sub _bzero |
293 | { |
7d341013 |
294 | # used by parent class bone() to initialize number to 0 |
184f15d5 |
295 | my $self = shift; |
a4e2b1c6 |
296 | $self->{_n} = $MBI->bzero(); |
297 | $self->{_d} = $MBI->bone(); |
184f15d5 |
298 | } |
299 | |
300 | ############################################################################## |
301 | # mul/add/div etc |
302 | |
303 | sub badd |
304 | { |
7d341013 |
305 | # add two rationales |
306 | |
307 | # set up parameters |
308 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
309 | # objectify is costly, so avoid it |
310 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
311 | { |
312 | ($self,$x,$y,@r) = objectify(2,@_); |
313 | } |
184f15d5 |
314 | |
6de7f0cc |
315 | $x = $self->new($x) unless $x->isa($self); |
316 | $y = $self->new($y) unless $y->isa($self); |
184f15d5 |
317 | |
8f675a64 |
318 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
7d341013 |
319 | # TODO: inf handling |
184f15d5 |
320 | |
321 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
322 | # - + - = --------- = -- |
323 | # 4 3 4*3 12 |
324 | |
7d341013 |
325 | # we do not compute the gcd() here, but simple do: |
326 | # 5 7 5*3 + 7*4 41 |
327 | # - + - = --------- = -- |
328 | # 4 3 4*3 12 |
329 | |
330 | # the gcd() calculation and reducing is then done in bnorm() |
184f15d5 |
331 | |
7d341013 |
332 | local $Math::BigInt::accuracy = undef; |
333 | local $Math::BigInt::precision = undef; |
334 | |
335 | $x->{_n}->bmul($y->{_d}); $x->{_n}->{sign} = $x->{sign}; |
336 | my $m = $y->{_n}->copy()->bmul($x->{_d}); |
184f15d5 |
337 | $m->{sign} = $y->{sign}; # 2/1 - 2/1 |
338 | $x->{_n}->badd($m); |
339 | |
340 | $x->{_d}->bmul($y->{_d}); |
341 | |
342 | # calculate new sign |
343 | $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; |
344 | |
7d341013 |
345 | $x->bnorm()->round(@r); |
184f15d5 |
346 | } |
347 | |
348 | sub bsub |
349 | { |
7d341013 |
350 | # subtract two rationales |
351 | |
352 | # set up parameters |
353 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
354 | # objectify is costly, so avoid it |
355 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
356 | { |
357 | ($self,$x,$y,@r) = objectify(2,@_); |
358 | } |
184f15d5 |
359 | |
8f675a64 |
360 | $x = $class->new($x) unless $x->isa($class); |
361 | $y = $class->new($y) unless $y->isa($class); |
362 | |
184f15d5 |
363 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
364 | # TODO: inf handling |
365 | |
7d341013 |
366 | # 1 1 gcd(3,4) = 1 1*3 - 1*4 7 |
367 | # - - - = --------- = -- |
184f15d5 |
368 | # 4 3 4*3 12 |
7d341013 |
369 | |
370 | # we do not compute the gcd() here, but simple do: |
371 | # 5 7 5*3 - 7*4 13 |
372 | # - - - = --------- = - -- |
373 | # 4 3 4*3 12 |
184f15d5 |
374 | |
7d341013 |
375 | local $Math::BigInt::accuracy = undef; |
376 | local $Math::BigInt::precision = undef; |
184f15d5 |
377 | |
7d341013 |
378 | $x->{_n}->bmul($y->{_d}); $x->{_n}->{sign} = $x->{sign}; |
379 | my $m = $y->{_n}->copy()->bmul($x->{_d}); |
184f15d5 |
380 | $m->{sign} = $y->{sign}; # 2/1 - 2/1 |
381 | $x->{_n}->bsub($m); |
382 | |
383 | $x->{_d}->bmul($y->{_d}); |
384 | |
385 | # calculate new sign |
386 | $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; |
387 | |
7d341013 |
388 | $x->bnorm()->round(@r); |
184f15d5 |
389 | } |
390 | |
391 | sub bmul |
392 | { |
7d341013 |
393 | # multiply two rationales |
394 | |
395 | # set up parameters |
396 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
397 | # objectify is costly, so avoid it |
398 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
399 | { |
400 | ($self,$x,$y,@r) = objectify(2,@_); |
401 | } |
184f15d5 |
402 | |
8f675a64 |
403 | $x = $class->new($x) unless $x->isa($class); |
404 | $y = $class->new($y) unless $y->isa($class); |
405 | |
184f15d5 |
406 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
407 | |
408 | # inf handling |
409 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
410 | { |
411 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
412 | # result will always be +-inf: |
413 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
414 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
415 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
416 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
417 | return $x->binf('-'); |
418 | } |
419 | |
420 | # x== 0 # also: or y == 1 or y == -1 |
421 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
422 | |
184f15d5 |
423 | # According to Knuth, this can be optimized by doingtwice gcd (for d and n) |
424 | # and reducing in one step) |
425 | |
426 | # 1 1 2 1 |
427 | # - * - = - = - |
428 | # 4 3 12 6 |
7d341013 |
429 | |
430 | local $Math::BigInt::accuracy = undef; |
431 | local $Math::BigInt::precision = undef; |
184f15d5 |
432 | $x->{_n}->bmul($y->{_n}); |
433 | $x->{_d}->bmul($y->{_d}); |
434 | |
435 | # compute new sign |
436 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
437 | |
7d341013 |
438 | $x->bnorm()->round(@r); |
184f15d5 |
439 | } |
440 | |
441 | sub bdiv |
442 | { |
443 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
444 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
7d341013 |
445 | |
446 | # set up parameters |
447 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
448 | # objectify is costly, so avoid it |
449 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
450 | { |
451 | ($self,$x,$y,@r) = objectify(2,@_); |
452 | } |
184f15d5 |
453 | |
8f675a64 |
454 | $x = $class->new($x) unless $x->isa($class); |
455 | $y = $class->new($y) unless $y->isa($class); |
456 | |
184f15d5 |
457 | return $self->_div_inf($x,$y) |
458 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
459 | |
460 | # x== 0 # also: or y == 1 or y == -1 |
461 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
462 | |
463 | # TODO: list context, upgrade |
464 | |
184f15d5 |
465 | # 1 1 1 3 |
466 | # - / - == - * - |
467 | # 4 3 4 1 |
7d341013 |
468 | |
469 | # local $Math::BigInt::accuracy = undef; |
470 | # local $Math::BigInt::precision = undef; |
184f15d5 |
471 | $x->{_n}->bmul($y->{_d}); |
472 | $x->{_d}->bmul($y->{_n}); |
473 | |
474 | # compute new sign |
475 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
476 | |
7d341013 |
477 | $x->bnorm()->round(@r); |
6de7f0cc |
478 | $x; |
184f15d5 |
479 | } |
480 | |
481 | ############################################################################## |
a4e2b1c6 |
482 | # bdec/binc |
483 | |
484 | sub bdec |
485 | { |
486 | # decrement value (subtract 1) |
487 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
488 | |
489 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
490 | |
491 | if ($x->{sign} eq '-') |
492 | { |
493 | $x->{_n}->badd($x->{_d}); # -5/2 => -7/2 |
494 | } |
495 | else |
496 | { |
497 | if ($x->{_n}->bacmp($x->{_d}) < 0) |
498 | { |
499 | # 1/3 -- => -2/3 |
500 | $x->{_n} = $x->{_d} - $x->{_n}; |
501 | $x->{sign} = '-'; |
502 | } |
503 | else |
504 | { |
505 | $x->{_n}->bsub($x->{_d}); # 5/2 => 3/2 |
506 | } |
507 | } |
508 | $x->bnorm()->round(@r); |
a4e2b1c6 |
509 | } |
510 | |
511 | sub binc |
512 | { |
513 | # increment value (add 1) |
514 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
515 | |
516 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
517 | |
518 | if ($x->{sign} eq '-') |
519 | { |
520 | if ($x->{_n}->bacmp($x->{_d}) < 0) |
521 | { |
522 | # -1/3 ++ => 2/3 (overflow at 0) |
523 | $x->{_n} = $x->{_d} - $x->{_n}; |
524 | $x->{sign} = '+'; |
525 | } |
526 | else |
527 | { |
528 | $x->{_n}->bsub($x->{_d}); # -5/2 => -3/2 |
529 | } |
530 | } |
531 | else |
532 | { |
533 | $x->{_n}->badd($x->{_d}); # 5/2 => 7/2 |
534 | } |
535 | $x->bnorm()->round(@r); |
a4e2b1c6 |
536 | } |
537 | |
538 | ############################################################################## |
184f15d5 |
539 | # is_foo methods (the rest is inherited) |
540 | |
541 | sub is_int |
542 | { |
543 | # return true if arg (BRAT or num_str) is an integer |
544 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
545 | |
546 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
7d341013 |
547 | $x->{_d}->is_one(); # x/y && y != 1 => no integer |
184f15d5 |
548 | 0; |
549 | } |
550 | |
551 | sub is_zero |
552 | { |
553 | # return true if arg (BRAT or num_str) is zero |
554 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
555 | |
556 | return 1 if $x->{sign} eq '+' && $x->{_n}->is_zero(); |
557 | 0; |
558 | } |
559 | |
560 | sub is_one |
561 | { |
562 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
563 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
564 | |
565 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
566 | return 1 |
567 | if ($x->{sign} eq $sign && $x->{_n}->is_one() && $x->{_d}->is_one()); |
568 | 0; |
569 | } |
570 | |
571 | sub is_odd |
572 | { |
573 | # return true if arg (BFLOAT or num_str) is odd or false if even |
574 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
575 | |
576 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
577 | ($x->{_d}->is_one() && $x->{_n}->is_odd()); # x/2 is not, but 3/1 |
578 | 0; |
579 | } |
580 | |
581 | sub is_even |
582 | { |
583 | # return true if arg (BINT or num_str) is even or false if odd |
584 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
585 | |
586 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
587 | return 1 if ($x->{_d}->is_one() # x/3 is never |
588 | && $x->{_n}->is_even()); # but 4/1 is |
589 | 0; |
590 | } |
591 | |
592 | BEGIN |
593 | { |
594 | *objectify = \&Math::BigInt::objectify; |
595 | } |
596 | |
597 | ############################################################################## |
598 | # parts() and friends |
599 | |
600 | sub numerator |
601 | { |
602 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
a4e2b1c6 |
603 | |
604 | return $MBI->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
605 | |
184f15d5 |
606 | my $n = $x->{_n}->copy(); $n->{sign} = $x->{sign}; |
607 | $n; |
608 | } |
609 | |
610 | sub denominator |
611 | { |
612 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
613 | |
a4e2b1c6 |
614 | return $MBI->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
184f15d5 |
615 | $x->{_d}->copy(); |
616 | } |
617 | |
618 | sub parts |
619 | { |
620 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
621 | |
a4e2b1c6 |
622 | return ($self->bnan(),$self->bnan()) if $x->{sign} eq 'NaN'; |
623 | return ($self->binf(),$self->binf()) if $x->{sign} eq '+inf'; |
624 | return ($self->binf('-'),$self->binf()) if $x->{sign} eq '-inf'; |
625 | |
184f15d5 |
626 | my $n = $x->{_n}->copy(); |
627 | $n->{sign} = $x->{sign}; |
a4e2b1c6 |
628 | return ($n,$x->{_d}->copy()); |
184f15d5 |
629 | } |
630 | |
631 | sub length |
632 | { |
633 | return 0; |
634 | } |
635 | |
636 | sub digit |
637 | { |
638 | return 0; |
639 | } |
640 | |
641 | ############################################################################## |
642 | # special calc routines |
643 | |
644 | sub bceil |
645 | { |
646 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
647 | |
648 | return $x unless $x->{sign} =~ /^[+-]$/; |
649 | return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 |
650 | |
a4e2b1c6 |
651 | $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 w/ truncate |
184f15d5 |
652 | $x->{_d}->bone(); |
653 | $x->{_n}->binc() if $x->{sign} eq '+'; # +22/7 => 4/1 |
a4e2b1c6 |
654 | $x->{sign} = '+' if $x->{_n}->is_zero(); # -0 => 0 |
184f15d5 |
655 | $x; |
656 | } |
657 | |
658 | sub bfloor |
659 | { |
660 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
661 | |
662 | return $x unless $x->{sign} =~ /^[+-]$/; |
663 | return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 |
664 | |
a4e2b1c6 |
665 | $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 w/ truncate |
184f15d5 |
666 | $x->{_d}->bone(); |
667 | $x->{_n}->binc() if $x->{sign} eq '-'; # -22/7 => -4/1 |
668 | $x; |
669 | } |
670 | |
671 | sub bfac |
672 | { |
a4e2b1c6 |
673 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
674 | |
675 | if (($x->{sign} eq '+') && ($x->{_d}->is_one())) |
676 | { |
677 | $x->{_n}->bfac(); |
678 | return $x->round(@r); |
679 | } |
680 | $x->bnan(); |
184f15d5 |
681 | } |
682 | |
683 | sub bpow |
684 | { |
7d341013 |
685 | # power ($x ** $y) |
686 | |
687 | # set up parameters |
688 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
689 | # objectify is costly, so avoid it |
690 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
691 | { |
692 | ($self,$x,$y,@r) = objectify(2,@_); |
693 | } |
184f15d5 |
694 | |
695 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
696 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
697 | return $x->bone(@r) if $y->is_zero(); |
698 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
699 | if ($x->{sign} eq '-' && $x->{_n}->is_one() && $x->{_d}->is_one()) |
700 | { |
701 | # if $x == -1 and odd/even y => +1/-1 |
702 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
703 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
704 | } |
705 | # 1 ** -y => 1 / (1 ** |y|) |
706 | # so do test for negative $y after above's clause |
707 | # return $x->bnan() if $y->{sign} eq '-'; |
708 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
709 | |
a4e2b1c6 |
710 | # shortcut y/1 (and/or x/1) |
711 | if ($y->{_d}->is_one()) |
712 | { |
713 | # shortcut for x/1 and y/1 |
714 | if ($x->{_d}->is_one()) |
715 | { |
716 | $x->{_n}->bpow($y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
717 | if ($y->{sign} eq '-') |
718 | { |
719 | # 0.2 ** -3 => 1/(0.2 ** 3) |
720 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
721 | } |
722 | # correct sign; + ** + => + |
723 | if ($x->{sign} eq '-') |
724 | { |
725 | # - * - => +, - * - * - => - |
726 | $x->{sign} = '+' if $y->{_n}->is_even(); |
727 | } |
728 | return $x->round(@r); |
729 | } |
730 | # x/z ** y/1 |
731 | $x->{_n}->bpow($y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
732 | $x->{_d}->bpow($y->{_n}); |
733 | if ($y->{sign} eq '-') |
734 | { |
735 | # 0.2 ** -3 => 1/(0.2 ** 3) |
736 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
737 | } |
738 | # correct sign; + ** + => + |
739 | if ($x->{sign} eq '-') |
740 | { |
741 | # - * - => +, - * - * - => - |
742 | $x->{sign} = '+' if $y->{_n}->is_even(); |
743 | } |
744 | return $x->round(@r); |
745 | } |
746 | |
747 | # regular calculation (this is wrong for d/e ** f/g) |
184f15d5 |
748 | my $pow2 = $self->__one(); |
a4e2b1c6 |
749 | my $y1 = $MBI->new($y->{_n}/$y->{_d})->babs(); |
750 | my $two = $MBI->new(2); |
184f15d5 |
751 | while (!$y1->is_one()) |
752 | { |
184f15d5 |
753 | $pow2->bmul($x) if $y1->is_odd(); |
754 | $y1->bdiv($two); |
755 | $x->bmul($x); |
756 | } |
757 | $x->bmul($pow2) unless $pow2->is_one(); |
758 | # n ** -x => 1/n ** x |
759 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; |
7d341013 |
760 | $x->bnorm()->round(@r); |
184f15d5 |
761 | } |
762 | |
763 | sub blog |
764 | { |
765 | return Math::BigRat->bnan(); |
766 | } |
767 | |
768 | sub bsqrt |
769 | { |
770 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
771 | |
772 | return $x->bnan() if $x->{sign} ne '+'; # inf, NaN, -1 etc |
773 | $x->{_d}->bsqrt($a,$p,$r); |
774 | $x->{_n}->bsqrt($a,$p,$r); |
775 | $x->bnorm(); |
776 | } |
777 | |
778 | sub blsft |
779 | { |
780 | my ($self,$x,$y,$b,$a,$p,$r) = objectify(3,@_); |
781 | |
782 | $x->bmul( $b->copy()->bpow($y), $a,$p,$r); |
783 | $x; |
784 | } |
785 | |
786 | sub brsft |
787 | { |
788 | my ($self,$x,$y,$b,$a,$p,$r) = objectify(2,@_); |
789 | |
790 | $x->bdiv( $b->copy()->bpow($y), $a,$p,$r); |
791 | $x; |
792 | } |
793 | |
794 | ############################################################################## |
795 | # round |
796 | |
797 | sub round |
798 | { |
799 | $_[0]; |
800 | } |
801 | |
802 | sub bround |
803 | { |
804 | $_[0]; |
805 | } |
806 | |
807 | sub bfround |
808 | { |
809 | $_[0]; |
810 | } |
811 | |
812 | ############################################################################## |
813 | # comparing |
814 | |
815 | sub bcmp |
816 | { |
817 | my ($self,$x,$y) = objectify(2,@_); |
818 | |
819 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
820 | { |
821 | # handle +-inf and NaN |
822 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
823 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
824 | return +1 if $x->{sign} eq '+inf'; |
825 | return -1 if $x->{sign} eq '-inf'; |
826 | return -1 if $y->{sign} eq '+inf'; |
827 | return +1; |
828 | } |
829 | # check sign for speed first |
830 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
831 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
832 | |
833 | # shortcut |
834 | my $xz = $x->{_n}->is_zero(); |
835 | my $yz = $y->{_n}->is_zero(); |
836 | return 0 if $xz && $yz; # 0 <=> 0 |
837 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
838 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
839 | |
840 | my $t = $x->{_n} * $y->{_d}; $t->{sign} = $x->{sign}; |
841 | my $u = $y->{_n} * $x->{_d}; $u->{sign} = $y->{sign}; |
842 | $t->bcmp($u); |
843 | } |
844 | |
845 | sub bacmp |
846 | { |
847 | my ($self,$x,$y) = objectify(2,@_); |
848 | |
849 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
850 | { |
851 | # handle +-inf and NaN |
852 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
853 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
854 | return +1; # inf is always bigger |
855 | } |
856 | |
857 | my $t = $x->{_n} * $y->{_d}; |
858 | my $u = $y->{_n} * $x->{_d}; |
859 | $t->bacmp($u); |
860 | } |
861 | |
862 | ############################################################################## |
863 | # output conversation |
864 | |
7d341013 |
865 | sub numify |
866 | { |
867 | # convert 17/8 => float (aka 2.125) |
868 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
869 | |
870 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc |
871 | |
872 | my $t = Math::BigFloat->new($x->{_n}); |
873 | $t->bneg() if $x->is_negative(); |
874 | $t->bdiv($x->{_d}); |
875 | $t->numify(); |
876 | } |
877 | |
184f15d5 |
878 | sub as_number |
879 | { |
880 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
881 | |
882 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf etc |
883 | my $t = $x->{_n}->copy()->bdiv($x->{_d}); # 22/7 => 3 |
884 | $t->{sign} = $x->{sign}; |
885 | $t; |
886 | } |
887 | |
6de7f0cc |
888 | sub import |
889 | { |
890 | my $self = shift; |
891 | my $l = scalar @_; |
892 | my $lib = ''; my @a; |
893 | for ( my $i = 0; $i < $l ; $i++) |
894 | { |
895 | # print "at $_[$i] (",$_[$i+1]||'undef',")\n"; |
896 | if ( $_[$i] eq ':constant' ) |
897 | { |
898 | # this rest causes overlord er load to step in |
899 | # print "overload @_\n"; |
900 | overload::constant float => sub { $self->new(shift); }; |
901 | } |
902 | # elsif ($_[$i] eq 'upgrade') |
903 | # { |
904 | # # this causes upgrading |
905 | # $upgrade = $_[$i+1]; # or undef to disable |
906 | # $i++; |
907 | # } |
908 | elsif ($_[$i] eq 'downgrade') |
909 | { |
910 | # this causes downgrading |
911 | $downgrade = $_[$i+1]; # or undef to disable |
912 | $i++; |
913 | } |
914 | elsif ($_[$i] eq 'lib') |
915 | { |
916 | $lib = $_[$i+1] || ''; # default Calc |
917 | $i++; |
918 | } |
919 | elsif ($_[$i] eq 'with') |
920 | { |
921 | $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt |
922 | $i++; |
923 | } |
924 | else |
925 | { |
926 | push @a, $_[$i]; |
927 | } |
928 | } |
929 | # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work |
930 | my $mbilib = eval { Math::BigInt->config()->{lib} }; |
931 | if ((defined $mbilib) && ($MBI eq 'Math::BigInt')) |
932 | { |
933 | # MBI already loaded |
934 | $MBI->import('lib',"$lib,$mbilib", 'objectify'); |
935 | } |
936 | else |
937 | { |
a4e2b1c6 |
938 | # MBI not loaded, or not with "Math::BigInt" |
6de7f0cc |
939 | $lib .= ",$mbilib" if defined $mbilib; |
940 | |
6de7f0cc |
941 | if ($] < 5.006) |
942 | { |
943 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
944 | # used in the same script, or eval inside import(). |
945 | my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt |
946 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm |
947 | $file = File::Spec->catfile (@parts, $file); |
948 | eval { require $file; $MBI->import( lib => '$lib', 'objectify' ); } |
949 | } |
950 | else |
951 | { |
952 | my $rc = "use $MBI lib => '$lib', 'objectify';"; |
953 | eval $rc; |
954 | } |
955 | } |
956 | die ("Couldn't load $MBI: $! $@") if $@; |
957 | |
958 | # any non :constant stuff is handled by our parent, Exporter |
959 | # even if @_ is empty, to give it a chance |
960 | $self->SUPER::import(@a); # for subclasses |
961 | $self->export_to_level(1,$self,@a); # need this, too |
962 | } |
184f15d5 |
963 | |
964 | 1; |
965 | |
966 | __END__ |
967 | |
968 | =head1 NAME |
969 | |
7d341013 |
970 | Math::BigRat - arbitrarily big rationales |
184f15d5 |
971 | |
972 | =head1 SYNOPSIS |
973 | |
7d341013 |
974 | use Math::BigRat; |
184f15d5 |
975 | |
7d341013 |
976 | $x = Math::BigRat->new('3/7'); $x += '5/9'; |
184f15d5 |
977 | |
7d341013 |
978 | print $x->bstr(),"\n"; |
979 | print $x ** 2,"\n"; |
184f15d5 |
980 | |
981 | =head1 DESCRIPTION |
982 | |
7d341013 |
983 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
984 | for arbitrarily big rationales. |
184f15d5 |
985 | |
986 | =head2 MATH LIBRARY |
987 | |
988 | Math with the numbers is done (by default) by a module called |
989 | Math::BigInt::Calc. This is equivalent to saying: |
990 | |
991 | use Math::BigRat lib => 'Calc'; |
992 | |
993 | You can change this by using: |
994 | |
995 | use Math::BigRat lib => 'BitVect'; |
996 | |
997 | The following would first try to find Math::BigInt::Foo, then |
998 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
999 | |
1000 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
1001 | |
1002 | Calc.pm uses as internal format an array of elements of some decimal base |
7d341013 |
1003 | (usually 1e7, but this might be different for some systems) with the least |
184f15d5 |
1004 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
1005 | significant bit first. Other modules might use even different means of |
1006 | representing the numbers. See the respective module documentation for further |
1007 | details. |
1008 | |
7d341013 |
1009 | Currently the following replacement libraries exist, search for them at CPAN: |
1010 | |
1011 | Math::BigInt::BitVect |
1012 | Math::BigInt::GMP |
1013 | Math::BigInt::Pari |
1014 | Math::BigInt::FastCalc |
1015 | |
184f15d5 |
1016 | =head1 METHODS |
1017 | |
7d341013 |
1018 | Any methods not listed here are dervied from Math::BigFloat (or |
6de7f0cc |
1019 | Math::BigInt), so make sure you check these two modules for further |
1020 | information. |
1021 | |
1022 | =head2 new() |
184f15d5 |
1023 | |
1024 | $x = Math::BigRat->new('1/3'); |
1025 | |
1026 | Create a new Math::BigRat object. Input can come in various forms: |
1027 | |
7d341013 |
1028 | $x = Math::BigRat->new(123); # scalars |
1029 | $x = Math::BigRat->new('123.3'); # float |
184f15d5 |
1030 | $x = Math::BigRat->new('1/3'); # simple string |
1031 | $x = Math::BigRat->new('1 / 3'); # spaced |
1032 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
1033 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
1034 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
6de7f0cc |
1035 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
184f15d5 |
1036 | |
6de7f0cc |
1037 | =head2 numerator() |
184f15d5 |
1038 | |
1039 | $n = $x->numerator(); |
1040 | |
1041 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
1042 | |
6de7f0cc |
1043 | =head2 denominator() |
184f15d5 |
1044 | |
1045 | $d = $x->denominator(); |
1046 | |
1047 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
1048 | |
6de7f0cc |
1049 | =head2 parts() |
184f15d5 |
1050 | |
1051 | ($n,$d) = $x->parts(); |
1052 | |
1053 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
1054 | BigInts. |
1055 | |
6de7f0cc |
1056 | =head2 as_number() |
1057 | |
7d341013 |
1058 | $x = Math::BigRat->new('13/7'); |
1059 | print $x->as_number(),"\n"; # '1' |
1060 | |
6de7f0cc |
1061 | Returns a copy of the object as BigInt by truncating it to integer. |
1062 | |
a4e2b1c6 |
1063 | =head2 bfac() |
6de7f0cc |
1064 | |
a4e2b1c6 |
1065 | $x->bfac(); |
6de7f0cc |
1066 | |
a4e2b1c6 |
1067 | Calculates the factorial of $x. For instance: |
6de7f0cc |
1068 | |
a4e2b1c6 |
1069 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 |
1070 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 |
184f15d5 |
1071 | |
7d341013 |
1072 | Works currently only for integers. |
6de7f0cc |
1073 | |
a4e2b1c6 |
1074 | =head2 blog() |
6de7f0cc |
1075 | |
a4e2b1c6 |
1076 | Is not yet implemented. |
6de7f0cc |
1077 | |
a4e2b1c6 |
1078 | =head2 bround()/round()/bfround() |
6de7f0cc |
1079 | |
a4e2b1c6 |
1080 | Are not yet implemented. |
6de7f0cc |
1081 | |
7d341013 |
1082 | =head2 is_one() |
1083 | |
1084 | print "$x is 1\n" if $x->is_one(); |
1085 | |
1086 | Return true if $x is exactly one, otherwise false. |
1087 | |
1088 | =head2 is_zero() |
1089 | |
1090 | print "$x is 0\n" if $x->is_zero(); |
1091 | |
1092 | Return true if $x is exactly zero, otherwise false. |
1093 | |
1094 | =head2 is_positive() |
1095 | |
1096 | print "$x is >= 0\n" if $x->is_positive(); |
1097 | |
1098 | Return true if $x is positive (greater than or equal to zero), otherwise |
1099 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. |
1100 | |
1101 | =head2 is_negative() |
1102 | |
1103 | print "$x is < 0\n" if $x->is_negative(); |
1104 | |
1105 | Return true if $x is negative (smaller than zero), otherwise false. Please |
1106 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. |
1107 | |
1108 | =head2 is_int() |
1109 | |
1110 | print "$x is an integer\n" if $x->is_int(); |
1111 | |
1112 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise |
1113 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. |
1114 | |
1115 | =head2 is_odd() |
1116 | |
1117 | print "$x is odd\n" if $x->is_odd(); |
1118 | |
1119 | Return true if $x is odd, otherwise false. |
1120 | |
1121 | =head2 is_even() |
1122 | |
1123 | print "$x is even\n" if $x->is_even(); |
1124 | |
1125 | Return true if $x is even, otherwise false. |
1126 | |
1127 | =head2 bceil() |
1128 | |
1129 | $x->bceil(); |
1130 | |
1131 | Set $x to the next bigger integer value (e.g. truncate the number to integer |
1132 | and then increment it by one). |
1133 | |
1134 | =head2 bfloor() |
1135 | |
1136 | $x->bfloor(); |
1137 | |
1138 | Truncate $x to an integer value. |
6de7f0cc |
1139 | |
a4e2b1c6 |
1140 | =head1 BUGS |
6de7f0cc |
1141 | |
7d341013 |
1142 | Some things are not yet implemented, or only implemented half-way: |
1143 | |
1144 | =over 2 |
1145 | |
1146 | =item inf handling (partial) |
1147 | |
1148 | =item NaN handling (partial) |
1149 | |
1150 | =item rounding (not implemented except for bceil/bfloor) |
1151 | |
1152 | =item $x ** $y where $y is not an integer |
1153 | |
1154 | =back |
184f15d5 |
1155 | |
1156 | =head1 LICENSE |
1157 | |
1158 | This program is free software; you may redistribute it and/or modify it under |
1159 | the same terms as Perl itself. |
1160 | |
1161 | =head1 SEE ALSO |
1162 | |
1163 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
1164 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
1165 | |
7d341013 |
1166 | See L<http://search.cpan.org/search?dist=bignum> for a way to use |
1167 | Math::BigRat. |
1168 | |
1169 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> |
1170 | may contain more documentation and examples as well as testcases. |
184f15d5 |
1171 | |
1172 | =head1 AUTHORS |
1173 | |
1174 | (C) by Tels L<http://bloodgate.com/> 2001-2002. |
1175 | |
1176 | =cut |