Commit | Line | Data |
184f15d5 |
1 | #!/usr/bin/perl -w |
2 | |
3 | # The following hash values are used: |
4 | # sign : +,-,NaN,+inf,-inf |
5 | # _d : denominator |
6 | # _n : numeraotr (value = _n/_d) |
7 | # _a : accuracy |
8 | # _p : precision |
9 | # _f : flags, used by MBR to flag parts of a rationale as untouchable |
10 | |
11 | package Math::BigRat; |
12 | |
13 | require 5.005_02; |
14 | use strict; |
15 | |
16 | use Exporter; |
17 | use Math::BigFloat; |
18 | use vars qw($VERSION @ISA $PACKAGE @EXPORT_OK $upgrade $downgrade |
19 | $accuracy $precision $round_mode $div_scale); |
20 | |
21 | @ISA = qw(Exporter Math::BigFloat); |
22 | @EXPORT_OK = qw(); |
23 | |
24 | $VERSION = '0.04'; |
25 | |
26 | use overload; # inherit from Math::BigFloat |
27 | |
28 | ############################################################################## |
29 | # global constants, flags and accessory |
30 | |
31 | use constant MB_NEVER_ROUND => 0x0001; |
32 | |
33 | $accuracy = $precision = undef; |
34 | $round_mode = 'even'; |
35 | $div_scale = 40; |
36 | $upgrade = undef; |
37 | $downgrade = undef; |
38 | |
39 | my $nan = 'NaN'; |
40 | my $class = 'Math::BigRat'; |
41 | |
42 | sub _new_from_float |
43 | { |
44 | # turn a single float input into a rationale (like '0.1') |
45 | my ($self,$f) = @_; |
46 | |
47 | return $self->bnan() if $f->is_nan(); |
48 | return $self->binf('-inf') if $f->{sign} eq '-inf'; |
49 | return $self->binf('+inf') if $f->{sign} eq '+inf'; |
50 | |
51 | #print "f $f caller", join(' ',caller()),"\n"; |
52 | $self->{_n} = $f->{_m}->copy(); # mantissa |
53 | $self->{_d} = Math::BigInt->bone(); |
54 | $self->{sign} = $f->{sign}; $self->{_n}->{sign} = '+'; |
55 | if ($f->{_e}->{sign} eq '-') |
56 | { |
57 | # something like Math::BigRat->new('0.1'); |
58 | $self->{_d}->blsft($f->{_e}->copy()->babs(),10); # 1 / 1 => 1/10 |
59 | } |
60 | else |
61 | { |
62 | # something like Math::BigRat->new('10'); |
63 | # 1 / 1 => 10/1 |
64 | $self->{_n}->blsft($f->{_e},10) unless $f->{_e}->is_zero(); |
65 | } |
66 | # print "float new $self->{_n} / $self->{_d}\n"; |
67 | $self; |
68 | } |
69 | |
70 | sub new |
71 | { |
72 | # create a Math::BigRat |
73 | my $class = shift; |
74 | |
75 | my ($n,$d) = shift; |
76 | |
77 | my $self = { }; bless $self,$class; |
78 | |
79 | # print "ref ",ref($d),"\n"; |
80 | # if (ref($d)) |
81 | # { |
82 | # print "isa float ",$d->isa('Math::BigFloat'),"\n"; |
83 | # print "isa int ",$d->isa('Math::BigInt'),"\n"; |
84 | # print "isa rat ",$d->isa('Math::BigRat'),"\n"; |
85 | # } |
86 | |
87 | # input like (BigInt,BigInt) or (BigFloat,BigFloat) not handled yet |
88 | |
89 | if ((ref $n) && (!$n->isa('Math::BigRat'))) |
90 | { |
91 | # print "is ref, but not rat\n"; |
92 | if ($n->isa('Math::BigFloat')) |
93 | { |
94 | # print "is ref, and float\n"; |
95 | return $self->_new_from_float($n)->bnorm(); |
96 | } |
97 | if ($n->isa('Math::BigInt')) |
98 | { |
99 | # print "is ref, and int\n"; |
100 | $self->{_n} = $n->copy(); # "mantissa" = $d |
101 | $self->{_d} = Math::BigInt->bone(); |
102 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
103 | return $self->bnorm(); |
104 | } |
105 | } |
106 | return $n->copy() if ref $n; |
107 | |
108 | # print "is string\n"; |
109 | |
110 | if (!defined $n) |
111 | { |
112 | $self->{_n} = Math::BigInt->bzero(); # undef => 0 |
113 | $self->{_d} = Math::BigInt->bone(); |
114 | $self->{sign} = '+'; |
115 | return $self->bnorm(); |
116 | } |
117 | # string input with / delimiter |
118 | if ($n =~ /\s*\/\s*/) |
119 | { |
120 | return Math::BigRat->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
121 | return Math::BigRat->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid |
122 | ($n,$d) = split (/\//,$n); |
123 | # try as BigFloats first |
124 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) |
125 | { |
126 | # one of them looks like a float |
127 | $self->_new_from_float(Math::BigFloat->new($n)); |
128 | # now correct $self->{_n} due to $n |
129 | my $f = Math::BigFloat->new($d); |
130 | if ($f->{_e}->{sign} eq '-') |
131 | { |
132 | # 10 / 0.1 => 100/1 |
133 | $self->{_n}->blsft($f->{_e}->copy()->babs(),10); |
134 | } |
135 | else |
136 | { |
137 | $self->{_d}->blsft($f->{_e},10); # 1 / 1 => 10/1 |
138 | } |
139 | } |
140 | else |
141 | { |
142 | $self->{_n} = Math::BigInt->new($n); |
143 | $self->{_d} = Math::BigInt->new($d); |
144 | return $self->bnan() if $self->{_n}->is_nan() || $self->{_d}->is_nan(); |
145 | # inf handling is missing here |
146 | |
147 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
148 | # if $d is negative, flip sign |
149 | $self->{sign} =~ tr/+-/-+/ if $self->{_d}->{sign} eq '-'; |
150 | $self->{_d}->{sign} = '+'; # normalize |
151 | } |
152 | return $self->bnorm(); |
153 | } |
154 | |
155 | # simple string input |
156 | if (($n =~ /[\.eE]/)) |
157 | { |
158 | # looks like a float |
159 | # print "float-like string $d\n"; |
160 | $self->_new_from_float(Math::BigFloat->new($n)); |
161 | } |
162 | else |
163 | { |
164 | $self->{_n} = Math::BigInt->new($n); |
165 | $self->{_d} = Math::BigInt->bone(); |
166 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
167 | } |
168 | $self->bnorm(); |
169 | } |
170 | |
171 | sub bstr |
172 | { |
173 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
174 | |
175 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
176 | { |
177 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
178 | return $s; |
179 | } |
180 | |
181 | # print "bstr $x->{sign} $x->{_n} $x->{_d}\n"; |
182 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
183 | |
184 | return $s.$x->{_n}->bstr() if $x->{_d}->is_one(); |
185 | return $s.$x->{_n}->bstr() . '/' . $x->{_d}->bstr(); |
186 | } |
187 | |
188 | sub bsstr |
189 | { |
190 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
191 | |
192 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
193 | { |
194 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
195 | return $s; |
196 | } |
197 | |
198 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
199 | return $x->{_n}->bstr() . '/' . $x->{_d}->bstr(); |
200 | } |
201 | |
202 | sub bnorm |
203 | { |
204 | # reduce the number to the shortest form and remember this (so that we |
205 | # don't reduce again) |
206 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
207 | |
208 | # this is to prevent automatically rounding when MBI's globals are set |
209 | $x->{_d}->{_f} = MB_NEVER_ROUND; |
210 | $x->{_n}->{_f} = MB_NEVER_ROUND; |
211 | # 'forget' that parts were rounded via MBI::bround() in MBF's bfround() |
212 | $x->{_d}->{_a} = undef; $x->{_n}->{_a} = undef; |
213 | $x->{_d}->{_p} = undef; $x->{_n}->{_p} = undef; |
214 | |
215 | # normalize zeros to 0/1 |
216 | if (($x->{sign} =~ /^[+-]$/) && |
217 | ($x->{_n}->is_zero())) |
218 | { |
219 | $x->{sign} = '+'; # never -0 |
220 | $x->{_d} = Math::BigInt->bone() unless $x->{_d}->is_one(); |
221 | return $x; |
222 | } |
223 | |
224 | # print "$x->{_n} / $x->{_d} => "; |
225 | # reduce other numbers |
226 | my $gcd = $x->{_n}->bgcd($x->{_d}); |
227 | |
228 | if (!$gcd->is_one()) |
229 | { |
230 | $x->{_n}->bdiv($gcd); |
231 | $x->{_d}->bdiv($gcd); |
232 | } |
233 | # print "$x->{_n} / $x->{_d}\n"; |
234 | $x; |
235 | } |
236 | |
237 | ############################################################################## |
238 | # special values |
239 | |
240 | sub _bnan |
241 | { |
242 | # used by parent class bone() to initialize number to 1 |
243 | my $self = shift; |
244 | $self->{_n} = Math::BigInt->bzero(); |
245 | $self->{_d} = Math::BigInt->bzero(); |
246 | } |
247 | |
248 | sub _binf |
249 | { |
250 | # used by parent class bone() to initialize number to 1 |
251 | my $self = shift; |
252 | $self->{_n} = Math::BigInt->bzero(); |
253 | $self->{_d} = Math::BigInt->bzero(); |
254 | } |
255 | |
256 | sub _bone |
257 | { |
258 | # used by parent class bone() to initialize number to 1 |
259 | my $self = shift; |
260 | $self->{_n} = Math::BigInt->bone(); |
261 | $self->{_d} = Math::BigInt->bone(); |
262 | } |
263 | |
264 | sub _bzero |
265 | { |
266 | # used by parent class bone() to initialize number to 1 |
267 | my $self = shift; |
268 | $self->{_n} = Math::BigInt->bzero(); |
269 | $self->{_d} = Math::BigInt->bone(); |
270 | } |
271 | |
272 | ############################################################################## |
273 | # mul/add/div etc |
274 | |
275 | sub badd |
276 | { |
277 | # add two rationales |
278 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
279 | |
280 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
281 | |
282 | # TODO: upgrade |
283 | |
284 | # # upgrade |
285 | # return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
286 | |
287 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
288 | # - + - = --------- = -- |
289 | # 4 3 4*3 12 |
290 | |
291 | my $gcd = $x->{_d}->bgcd($y->{_d}); |
292 | |
293 | my $aa = $x->{_d}->copy(); |
294 | my $bb = $y->{_d}->copy(); |
295 | if ($gcd->is_one()) |
296 | { |
297 | $bb->bdiv($gcd); $aa->bdiv($gcd); |
298 | } |
299 | $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign}; |
300 | my $m = $y->{_n}->copy()->bmul($aa); |
301 | $m->{sign} = $y->{sign}; # 2/1 - 2/1 |
302 | $x->{_n}->badd($m); |
303 | |
304 | $x->{_d}->bmul($y->{_d}); |
305 | |
306 | # calculate new sign |
307 | $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; |
308 | |
309 | $x->bnorm()->round($a,$p,$r); |
310 | } |
311 | |
312 | sub bsub |
313 | { |
314 | # subtract two rationales |
315 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
316 | |
317 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
318 | # TODO: inf handling |
319 | |
320 | # TODO: upgrade |
321 | |
322 | # # upgrade |
323 | # return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
324 | |
325 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
326 | # - + - = --------- = -- |
327 | # 4 3 4*3 12 |
328 | |
329 | my $gcd = $x->{_d}->bgcd($y->{_d}); |
330 | |
331 | my $aa = $x->{_d}->copy(); |
332 | my $bb = $y->{_d}->copy(); |
333 | if ($gcd->is_one()) |
334 | { |
335 | $bb->bdiv($gcd); $aa->bdiv($gcd); |
336 | } |
337 | $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign}; |
338 | my $m = $y->{_n}->copy()->bmul($aa); |
339 | $m->{sign} = $y->{sign}; # 2/1 - 2/1 |
340 | $x->{_n}->bsub($m); |
341 | |
342 | $x->{_d}->bmul($y->{_d}); |
343 | |
344 | # calculate new sign |
345 | $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; |
346 | |
347 | $x->bnorm()->round($a,$p,$r); |
348 | } |
349 | |
350 | sub bmul |
351 | { |
352 | # multiply two rationales |
353 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
354 | |
355 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
356 | |
357 | # inf handling |
358 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
359 | { |
360 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
361 | # result will always be +-inf: |
362 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
363 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
364 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
365 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
366 | return $x->binf('-'); |
367 | } |
368 | |
369 | # x== 0 # also: or y == 1 or y == -1 |
370 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
371 | |
372 | # TODO: upgrade |
373 | |
374 | # # upgrade |
375 | # return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
376 | |
377 | # According to Knuth, this can be optimized by doingtwice gcd (for d and n) |
378 | # and reducing in one step) |
379 | |
380 | # 1 1 2 1 |
381 | # - * - = - = - |
382 | # 4 3 12 6 |
383 | $x->{_n}->bmul($y->{_n}); |
384 | $x->{_d}->bmul($y->{_d}); |
385 | |
386 | # compute new sign |
387 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
388 | |
389 | $x->bnorm()->round($a,$p,$r); |
390 | } |
391 | |
392 | sub bdiv |
393 | { |
394 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
395 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
396 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
397 | |
398 | return $self->_div_inf($x,$y) |
399 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
400 | |
401 | # x== 0 # also: or y == 1 or y == -1 |
402 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
403 | |
404 | # TODO: list context, upgrade |
405 | |
406 | # # upgrade |
407 | # return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
408 | |
409 | # 1 1 1 3 |
410 | # - / - == - * - |
411 | # 4 3 4 1 |
412 | $x->{_n}->bmul($y->{_d}); |
413 | $x->{_d}->bmul($y->{_n}); |
414 | |
415 | # compute new sign |
416 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
417 | |
418 | $x->bnorm()->round($a,$p,$r); |
419 | } |
420 | |
421 | ############################################################################## |
422 | # is_foo methods (the rest is inherited) |
423 | |
424 | sub is_int |
425 | { |
426 | # return true if arg (BRAT or num_str) is an integer |
427 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
428 | |
429 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
430 | $x->{_d}->is_one(); # 1e-1 => no integer |
431 | 0; |
432 | } |
433 | |
434 | sub is_zero |
435 | { |
436 | # return true if arg (BRAT or num_str) is zero |
437 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
438 | |
439 | return 1 if $x->{sign} eq '+' && $x->{_n}->is_zero(); |
440 | 0; |
441 | } |
442 | |
443 | sub is_one |
444 | { |
445 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
446 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
447 | |
448 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
449 | return 1 |
450 | if ($x->{sign} eq $sign && $x->{_n}->is_one() && $x->{_d}->is_one()); |
451 | 0; |
452 | } |
453 | |
454 | sub is_odd |
455 | { |
456 | # return true if arg (BFLOAT or num_str) is odd or false if even |
457 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
458 | |
459 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
460 | ($x->{_d}->is_one() && $x->{_n}->is_odd()); # x/2 is not, but 3/1 |
461 | 0; |
462 | } |
463 | |
464 | sub is_even |
465 | { |
466 | # return true if arg (BINT or num_str) is even or false if odd |
467 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
468 | |
469 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
470 | return 1 if ($x->{_d}->is_one() # x/3 is never |
471 | && $x->{_n}->is_even()); # but 4/1 is |
472 | 0; |
473 | } |
474 | |
475 | BEGIN |
476 | { |
477 | *objectify = \&Math::BigInt::objectify; |
478 | } |
479 | |
480 | ############################################################################## |
481 | # parts() and friends |
482 | |
483 | sub numerator |
484 | { |
485 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
486 | |
487 | my $n = $x->{_n}->copy(); $n->{sign} = $x->{sign}; |
488 | $n; |
489 | } |
490 | |
491 | sub denominator |
492 | { |
493 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
494 | |
495 | $x->{_d}->copy(); |
496 | } |
497 | |
498 | sub parts |
499 | { |
500 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
501 | |
502 | my $n = $x->{_n}->copy(); |
503 | $n->{sign} = $x->{sign}; |
504 | return ($x->{_n}->copy(),$x->{_d}->copy()); |
505 | } |
506 | |
507 | sub length |
508 | { |
509 | return 0; |
510 | } |
511 | |
512 | sub digit |
513 | { |
514 | return 0; |
515 | } |
516 | |
517 | ############################################################################## |
518 | # special calc routines |
519 | |
520 | sub bceil |
521 | { |
522 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
523 | |
524 | return $x unless $x->{sign} =~ /^[+-]$/; |
525 | return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 |
526 | |
527 | $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 |
528 | $x->{_d}->bone(); |
529 | $x->{_n}->binc() if $x->{sign} eq '+'; # +22/7 => 4/1 |
530 | $x; |
531 | } |
532 | |
533 | sub bfloor |
534 | { |
535 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
536 | |
537 | return $x unless $x->{sign} =~ /^[+-]$/; |
538 | return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 |
539 | |
540 | $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 |
541 | $x->{_d}->bone(); |
542 | $x->{_n}->binc() if $x->{sign} eq '-'; # -22/7 => -4/1 |
543 | $x; |
544 | } |
545 | |
546 | sub bfac |
547 | { |
548 | return Math::BigRat->bnan(); |
549 | } |
550 | |
551 | sub bpow |
552 | { |
553 | my ($self,$x,$y,@r) = objectify(2,@_); |
554 | |
555 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
556 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
557 | return $x->bone(@r) if $y->is_zero(); |
558 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
559 | if ($x->{sign} eq '-' && $x->{_n}->is_one() && $x->{_d}->is_one()) |
560 | { |
561 | # if $x == -1 and odd/even y => +1/-1 |
562 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
563 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
564 | } |
565 | # 1 ** -y => 1 / (1 ** |y|) |
566 | # so do test for negative $y after above's clause |
567 | # return $x->bnan() if $y->{sign} eq '-'; |
568 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
569 | |
570 | my $pow2 = $self->__one(); |
571 | my $y1 = Math::BigInt->new($y->{_n}/$y->{_d})->babs(); |
572 | my $two = Math::BigInt->new(2); |
573 | while (!$y1->is_one()) |
574 | { |
575 | print "at $y1 (= $x)\n"; |
576 | $pow2->bmul($x) if $y1->is_odd(); |
577 | $y1->bdiv($two); |
578 | $x->bmul($x); |
579 | } |
580 | $x->bmul($pow2) unless $pow2->is_one(); |
581 | # n ** -x => 1/n ** x |
582 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; |
583 | $x; |
584 | #$x->round(@r); |
585 | } |
586 | |
587 | sub blog |
588 | { |
589 | return Math::BigRat->bnan(); |
590 | } |
591 | |
592 | sub bsqrt |
593 | { |
594 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
595 | |
596 | return $x->bnan() if $x->{sign} ne '+'; # inf, NaN, -1 etc |
597 | $x->{_d}->bsqrt($a,$p,$r); |
598 | $x->{_n}->bsqrt($a,$p,$r); |
599 | $x->bnorm(); |
600 | } |
601 | |
602 | sub blsft |
603 | { |
604 | my ($self,$x,$y,$b,$a,$p,$r) = objectify(3,@_); |
605 | |
606 | $x->bmul( $b->copy()->bpow($y), $a,$p,$r); |
607 | $x; |
608 | } |
609 | |
610 | sub brsft |
611 | { |
612 | my ($self,$x,$y,$b,$a,$p,$r) = objectify(2,@_); |
613 | |
614 | $x->bdiv( $b->copy()->bpow($y), $a,$p,$r); |
615 | $x; |
616 | } |
617 | |
618 | ############################################################################## |
619 | # round |
620 | |
621 | sub round |
622 | { |
623 | $_[0]; |
624 | } |
625 | |
626 | sub bround |
627 | { |
628 | $_[0]; |
629 | } |
630 | |
631 | sub bfround |
632 | { |
633 | $_[0]; |
634 | } |
635 | |
636 | ############################################################################## |
637 | # comparing |
638 | |
639 | sub bcmp |
640 | { |
641 | my ($self,$x,$y) = objectify(2,@_); |
642 | |
643 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
644 | { |
645 | # handle +-inf and NaN |
646 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
647 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
648 | return +1 if $x->{sign} eq '+inf'; |
649 | return -1 if $x->{sign} eq '-inf'; |
650 | return -1 if $y->{sign} eq '+inf'; |
651 | return +1; |
652 | } |
653 | # check sign for speed first |
654 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
655 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
656 | |
657 | # shortcut |
658 | my $xz = $x->{_n}->is_zero(); |
659 | my $yz = $y->{_n}->is_zero(); |
660 | return 0 if $xz && $yz; # 0 <=> 0 |
661 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
662 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
663 | |
664 | my $t = $x->{_n} * $y->{_d}; $t->{sign} = $x->{sign}; |
665 | my $u = $y->{_n} * $x->{_d}; $u->{sign} = $y->{sign}; |
666 | $t->bcmp($u); |
667 | } |
668 | |
669 | sub bacmp |
670 | { |
671 | my ($self,$x,$y) = objectify(2,@_); |
672 | |
673 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
674 | { |
675 | # handle +-inf and NaN |
676 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
677 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
678 | return +1; # inf is always bigger |
679 | } |
680 | |
681 | my $t = $x->{_n} * $y->{_d}; |
682 | my $u = $y->{_n} * $x->{_d}; |
683 | $t->bacmp($u); |
684 | } |
685 | |
686 | ############################################################################## |
687 | # output conversation |
688 | |
689 | sub as_number |
690 | { |
691 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
692 | |
693 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf etc |
694 | my $t = $x->{_n}->copy()->bdiv($x->{_d}); # 22/7 => 3 |
695 | $t->{sign} = $x->{sign}; |
696 | $t; |
697 | } |
698 | |
699 | #sub import |
700 | # { |
701 | # my $self = shift; |
702 | # Math::BigInt->import(@_); |
703 | # $self->SUPER::import(@_); # need it for subclasses |
704 | # #$self->export_to_level(1,$self,@_); # need this ? |
705 | # } |
706 | |
707 | 1; |
708 | |
709 | __END__ |
710 | |
711 | =head1 NAME |
712 | |
713 | Math::BigRat - arbitrarily big rationales |
714 | |
715 | =head1 SYNOPSIS |
716 | |
717 | use Math::BigRat; |
718 | |
719 | $x = Math::BigRat->new('3/7'); |
720 | |
721 | print $x->bstr(),"\n"; |
722 | |
723 | =head1 DESCRIPTION |
724 | |
725 | This is just a placeholder until the real thing is up and running. Watch this |
726 | space... |
727 | |
728 | =head2 MATH LIBRARY |
729 | |
730 | Math with the numbers is done (by default) by a module called |
731 | Math::BigInt::Calc. This is equivalent to saying: |
732 | |
733 | use Math::BigRat lib => 'Calc'; |
734 | |
735 | You can change this by using: |
736 | |
737 | use Math::BigRat lib => 'BitVect'; |
738 | |
739 | The following would first try to find Math::BigInt::Foo, then |
740 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
741 | |
742 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
743 | |
744 | Calc.pm uses as internal format an array of elements of some decimal base |
745 | (usually 1e7, but this might be differen for some systems) with the least |
746 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
747 | significant bit first. Other modules might use even different means of |
748 | representing the numbers. See the respective module documentation for further |
749 | details. |
750 | |
751 | =head1 METHODS |
752 | |
753 | =head2 new |
754 | |
755 | $x = Math::BigRat->new('1/3'); |
756 | |
757 | Create a new Math::BigRat object. Input can come in various forms: |
758 | |
759 | $x = Math::BigRat->new('1/3'); # simple string |
760 | $x = Math::BigRat->new('1 / 3'); # spaced |
761 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
762 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
763 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
764 | |
765 | =head2 numerator |
766 | |
767 | $n = $x->numerator(); |
768 | |
769 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
770 | |
771 | =head2 denominator |
772 | |
773 | $d = $x->denominator(); |
774 | |
775 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
776 | |
777 | =head2 parts |
778 | |
779 | ($n,$d) = $x->parts(); |
780 | |
781 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
782 | BigInts. |
783 | |
784 | =head1 BUGS |
785 | |
786 | None know yet. Please see also L<Math::BigInt>. |
787 | |
788 | =head1 LICENSE |
789 | |
790 | This program is free software; you may redistribute it and/or modify it under |
791 | the same terms as Perl itself. |
792 | |
793 | =head1 SEE ALSO |
794 | |
795 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
796 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
797 | |
798 | The package at |
799 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigRat> may |
800 | contain more documentation and examples as well as testcases. |
801 | |
802 | =head1 AUTHORS |
803 | |
804 | (C) by Tels L<http://bloodgate.com/> 2001-2002. |
805 | |
806 | =cut |