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184f15d5 JH |
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 | |
bce7c187 | 9 | # _f : flags, used by MBR to flag parts of a rational as untouchable |
184f15d5 JH |
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 | ||
8f675a64 | 24 | $VERSION = '0.05'; |
184f15d5 JH |
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 | ||
8f675a64 JH |
42 | sub isa |
43 | { | |
44 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't | |
45 | UNIVERSAL::isa(@_); | |
46 | } | |
47 | ||
184f15d5 JH |
48 | sub _new_from_float |
49 | { | |
bce7c187 | 50 | # turn a single float input into a rational (like '0.1') |
184f15d5 JH |
51 | my ($self,$f) = @_; |
52 | ||
53 | return $self->bnan() if $f->is_nan(); | |
54 | return $self->binf('-inf') if $f->{sign} eq '-inf'; | |
55 | return $self->binf('+inf') if $f->{sign} eq '+inf'; | |
56 | ||
57 | #print "f $f caller", join(' ',caller()),"\n"; | |
58 | $self->{_n} = $f->{_m}->copy(); # mantissa | |
59 | $self->{_d} = Math::BigInt->bone(); | |
60 | $self->{sign} = $f->{sign}; $self->{_n}->{sign} = '+'; | |
61 | if ($f->{_e}->{sign} eq '-') | |
62 | { | |
63 | # something like Math::BigRat->new('0.1'); | |
64 | $self->{_d}->blsft($f->{_e}->copy()->babs(),10); # 1 / 1 => 1/10 | |
65 | } | |
66 | else | |
67 | { | |
68 | # something like Math::BigRat->new('10'); | |
69 | # 1 / 1 => 10/1 | |
70 | $self->{_n}->blsft($f->{_e},10) unless $f->{_e}->is_zero(); | |
71 | } | |
72 | # print "float new $self->{_n} / $self->{_d}\n"; | |
73 | $self; | |
74 | } | |
75 | ||
76 | sub new | |
77 | { | |
78 | # create a Math::BigRat | |
79 | my $class = shift; | |
80 | ||
81 | my ($n,$d) = shift; | |
82 | ||
83 | my $self = { }; bless $self,$class; | |
84 | ||
85 | # print "ref ",ref($d),"\n"; | |
86 | # if (ref($d)) | |
87 | # { | |
88 | # print "isa float ",$d->isa('Math::BigFloat'),"\n"; | |
89 | # print "isa int ",$d->isa('Math::BigInt'),"\n"; | |
90 | # print "isa rat ",$d->isa('Math::BigRat'),"\n"; | |
91 | # } | |
92 | ||
93 | # input like (BigInt,BigInt) or (BigFloat,BigFloat) not handled yet | |
94 | ||
95 | if ((ref $n) && (!$n->isa('Math::BigRat'))) | |
96 | { | |
97 | # print "is ref, but not rat\n"; | |
98 | if ($n->isa('Math::BigFloat')) | |
99 | { | |
8f675a64 | 100 | # print "is ref, and float\n"; |
184f15d5 JH |
101 | return $self->_new_from_float($n)->bnorm(); |
102 | } | |
103 | if ($n->isa('Math::BigInt')) | |
104 | { | |
105 | # print "is ref, and int\n"; | |
8f675a64 JH |
106 | $self->{_n} = $n->copy(); # "mantissa" = $n |
107 | $self->{_d} = Math::BigInt->bone(); | |
108 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; | |
109 | return $self->bnorm(); | |
110 | } | |
111 | if ($n->isa('Math::BigInt::Lite')) | |
112 | { | |
113 | # print "is ref, and lite\n"; | |
114 | $self->{_n} = Math::BigInt->new($$n); # "mantissa" = $n | |
184f15d5 JH |
115 | $self->{_d} = Math::BigInt->bone(); |
116 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; | |
117 | return $self->bnorm(); | |
118 | } | |
119 | } | |
120 | return $n->copy() if ref $n; | |
121 | ||
122 | # print "is string\n"; | |
123 | ||
124 | if (!defined $n) | |
125 | { | |
126 | $self->{_n} = Math::BigInt->bzero(); # undef => 0 | |
127 | $self->{_d} = Math::BigInt->bone(); | |
128 | $self->{sign} = '+'; | |
129 | return $self->bnorm(); | |
130 | } | |
131 | # string input with / delimiter | |
132 | if ($n =~ /\s*\/\s*/) | |
133 | { | |
134 | return Math::BigRat->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid | |
135 | return Math::BigRat->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid | |
136 | ($n,$d) = split (/\//,$n); | |
137 | # try as BigFloats first | |
138 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) | |
139 | { | |
140 | # one of them looks like a float | |
141 | $self->_new_from_float(Math::BigFloat->new($n)); | |
142 | # now correct $self->{_n} due to $n | |
143 | my $f = Math::BigFloat->new($d); | |
144 | if ($f->{_e}->{sign} eq '-') | |
145 | { | |
146 | # 10 / 0.1 => 100/1 | |
147 | $self->{_n}->blsft($f->{_e}->copy()->babs(),10); | |
148 | } | |
149 | else | |
150 | { | |
151 | $self->{_d}->blsft($f->{_e},10); # 1 / 1 => 10/1 | |
152 | } | |
153 | } | |
154 | else | |
155 | { | |
156 | $self->{_n} = Math::BigInt->new($n); | |
157 | $self->{_d} = Math::BigInt->new($d); | |
158 | return $self->bnan() if $self->{_n}->is_nan() || $self->{_d}->is_nan(); | |
159 | # inf handling is missing here | |
160 | ||
161 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; | |
162 | # if $d is negative, flip sign | |
163 | $self->{sign} =~ tr/+-/-+/ if $self->{_d}->{sign} eq '-'; | |
164 | $self->{_d}->{sign} = '+'; # normalize | |
165 | } | |
166 | return $self->bnorm(); | |
167 | } | |
168 | ||
169 | # simple string input | |
170 | if (($n =~ /[\.eE]/)) | |
171 | { | |
172 | # looks like a float | |
173 | # print "float-like string $d\n"; | |
174 | $self->_new_from_float(Math::BigFloat->new($n)); | |
175 | } | |
176 | else | |
177 | { | |
178 | $self->{_n} = Math::BigInt->new($n); | |
179 | $self->{_d} = Math::BigInt->bone(); | |
180 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; | |
181 | } | |
182 | $self->bnorm(); | |
183 | } | |
184 | ||
8f675a64 JH |
185 | ############################################################################### |
186 | ||
184f15d5 JH |
187 | sub bstr |
188 | { | |
189 | my ($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 | ||
197 | # print "bstr $x->{sign} $x->{_n} $x->{_d}\n"; | |
198 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 | |
199 | ||
200 | return $s.$x->{_n}->bstr() if $x->{_d}->is_one(); | |
201 | return $s.$x->{_n}->bstr() . '/' . $x->{_d}->bstr(); | |
202 | } | |
203 | ||
204 | sub bsstr | |
205 | { | |
206 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
207 | ||
208 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc | |
209 | { | |
210 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf | |
211 | return $s; | |
212 | } | |
213 | ||
214 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 | |
215 | return $x->{_n}->bstr() . '/' . $x->{_d}->bstr(); | |
216 | } | |
217 | ||
218 | sub bnorm | |
219 | { | |
220 | # reduce the number to the shortest form and remember this (so that we | |
221 | # don't reduce again) | |
222 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
223 | ||
224 | # this is to prevent automatically rounding when MBI's globals are set | |
225 | $x->{_d}->{_f} = MB_NEVER_ROUND; | |
226 | $x->{_n}->{_f} = MB_NEVER_ROUND; | |
227 | # 'forget' that parts were rounded via MBI::bround() in MBF's bfround() | |
228 | $x->{_d}->{_a} = undef; $x->{_n}->{_a} = undef; | |
229 | $x->{_d}->{_p} = undef; $x->{_n}->{_p} = undef; | |
230 | ||
231 | # normalize zeros to 0/1 | |
232 | if (($x->{sign} =~ /^[+-]$/) && | |
233 | ($x->{_n}->is_zero())) | |
234 | { | |
235 | $x->{sign} = '+'; # never -0 | |
236 | $x->{_d} = Math::BigInt->bone() unless $x->{_d}->is_one(); | |
237 | return $x; | |
238 | } | |
239 | ||
240 | # print "$x->{_n} / $x->{_d} => "; | |
241 | # reduce other numbers | |
8f675a64 JH |
242 | # print "bgcd $x->{_n} (",ref($x->{_n}),") $x->{_d} (",ref($x->{_d}),")\n"; |
243 | # disable upgrade in BigInt, otherwise deep recursion | |
244 | local $Math::BigInt::upgrade = undef; | |
184f15d5 JH |
245 | my $gcd = $x->{_n}->bgcd($x->{_d}); |
246 | ||
247 | if (!$gcd->is_one()) | |
248 | { | |
249 | $x->{_n}->bdiv($gcd); | |
250 | $x->{_d}->bdiv($gcd); | |
251 | } | |
252 | # print "$x->{_n} / $x->{_d}\n"; | |
253 | $x; | |
254 | } | |
255 | ||
256 | ############################################################################## | |
257 | # special values | |
258 | ||
259 | sub _bnan | |
260 | { | |
261 | # used by parent class bone() to initialize number to 1 | |
262 | my $self = shift; | |
263 | $self->{_n} = Math::BigInt->bzero(); | |
264 | $self->{_d} = Math::BigInt->bzero(); | |
265 | } | |
266 | ||
267 | sub _binf | |
268 | { | |
269 | # used by parent class bone() to initialize number to 1 | |
270 | my $self = shift; | |
271 | $self->{_n} = Math::BigInt->bzero(); | |
272 | $self->{_d} = Math::BigInt->bzero(); | |
273 | } | |
274 | ||
275 | sub _bone | |
276 | { | |
277 | # used by parent class bone() to initialize number to 1 | |
278 | my $self = shift; | |
279 | $self->{_n} = Math::BigInt->bone(); | |
280 | $self->{_d} = Math::BigInt->bone(); | |
281 | } | |
282 | ||
283 | sub _bzero | |
284 | { | |
285 | # used by parent class bone() to initialize number to 1 | |
286 | my $self = shift; | |
287 | $self->{_n} = Math::BigInt->bzero(); | |
288 | $self->{_d} = Math::BigInt->bone(); | |
289 | } | |
290 | ||
291 | ############################################################################## | |
292 | # mul/add/div etc | |
293 | ||
294 | sub badd | |
295 | { | |
bce7c187 | 296 | # add two rationals |
184f15d5 JH |
297 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
298 | ||
8f675a64 JH |
299 | $x = $class->new($x) unless $x->isa($class); |
300 | $y = $class->new($y) unless $y->isa($class); | |
184f15d5 | 301 | |
8f675a64 | 302 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
184f15d5 JH |
303 | |
304 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 | |
305 | # - + - = --------- = -- | |
306 | # 4 3 4*3 12 | |
307 | ||
308 | my $gcd = $x->{_d}->bgcd($y->{_d}); | |
309 | ||
310 | my $aa = $x->{_d}->copy(); | |
311 | my $bb = $y->{_d}->copy(); | |
312 | if ($gcd->is_one()) | |
313 | { | |
314 | $bb->bdiv($gcd); $aa->bdiv($gcd); | |
315 | } | |
316 | $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign}; | |
317 | my $m = $y->{_n}->copy()->bmul($aa); | |
318 | $m->{sign} = $y->{sign}; # 2/1 - 2/1 | |
319 | $x->{_n}->badd($m); | |
320 | ||
321 | $x->{_d}->bmul($y->{_d}); | |
322 | ||
323 | # calculate new sign | |
324 | $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; | |
325 | ||
326 | $x->bnorm()->round($a,$p,$r); | |
327 | } | |
328 | ||
329 | sub bsub | |
330 | { | |
bce7c187 | 331 | # subtract two rationals |
184f15d5 JH |
332 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
333 | ||
8f675a64 JH |
334 | $x = $class->new($x) unless $x->isa($class); |
335 | $y = $class->new($y) unless $y->isa($class); | |
336 | ||
184f15d5 JH |
337 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
338 | # TODO: inf handling | |
339 | ||
184f15d5 JH |
340 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
341 | # - + - = --------- = -- | |
342 | # 4 3 4*3 12 | |
343 | ||
344 | my $gcd = $x->{_d}->bgcd($y->{_d}); | |
345 | ||
346 | my $aa = $x->{_d}->copy(); | |
347 | my $bb = $y->{_d}->copy(); | |
348 | if ($gcd->is_one()) | |
349 | { | |
350 | $bb->bdiv($gcd); $aa->bdiv($gcd); | |
351 | } | |
352 | $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign}; | |
353 | my $m = $y->{_n}->copy()->bmul($aa); | |
354 | $m->{sign} = $y->{sign}; # 2/1 - 2/1 | |
355 | $x->{_n}->bsub($m); | |
356 | ||
357 | $x->{_d}->bmul($y->{_d}); | |
358 | ||
359 | # calculate new sign | |
360 | $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; | |
361 | ||
362 | $x->bnorm()->round($a,$p,$r); | |
363 | } | |
364 | ||
365 | sub bmul | |
366 | { | |
bce7c187 | 367 | # multiply two rationals |
184f15d5 JH |
368 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
369 | ||
8f675a64 JH |
370 | $x = $class->new($x) unless $x->isa($class); |
371 | $y = $class->new($y) unless $y->isa($class); | |
372 | ||
184f15d5 JH |
373 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
374 | ||
375 | # inf handling | |
376 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
377 | { | |
378 | return $x->bnan() if $x->is_zero() || $y->is_zero(); | |
379 | # result will always be +-inf: | |
380 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
381 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
382 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
383 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
384 | return $x->binf('-'); | |
385 | } | |
386 | ||
387 | # x== 0 # also: or y == 1 or y == -1 | |
388 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); | |
389 | ||
184f15d5 JH |
390 | # According to Knuth, this can be optimized by doingtwice gcd (for d and n) |
391 | # and reducing in one step) | |
392 | ||
393 | # 1 1 2 1 | |
394 | # - * - = - = - | |
395 | # 4 3 12 6 | |
396 | $x->{_n}->bmul($y->{_n}); | |
397 | $x->{_d}->bmul($y->{_d}); | |
398 | ||
399 | # compute new sign | |
400 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; | |
401 | ||
402 | $x->bnorm()->round($a,$p,$r); | |
403 | } | |
404 | ||
405 | sub bdiv | |
406 | { | |
407 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return | |
408 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) | |
409 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); | |
410 | ||
8f675a64 JH |
411 | $x = $class->new($x) unless $x->isa($class); |
412 | $y = $class->new($y) unless $y->isa($class); | |
413 | ||
184f15d5 JH |
414 | return $self->_div_inf($x,$y) |
415 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
416 | ||
417 | # x== 0 # also: or y == 1 or y == -1 | |
418 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); | |
419 | ||
420 | # TODO: list context, upgrade | |
421 | ||
184f15d5 JH |
422 | # 1 1 1 3 |
423 | # - / - == - * - | |
424 | # 4 3 4 1 | |
425 | $x->{_n}->bmul($y->{_d}); | |
426 | $x->{_d}->bmul($y->{_n}); | |
427 | ||
428 | # compute new sign | |
429 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; | |
430 | ||
431 | $x->bnorm()->round($a,$p,$r); | |
432 | } | |
433 | ||
434 | ############################################################################## | |
435 | # is_foo methods (the rest is inherited) | |
436 | ||
437 | sub is_int | |
438 | { | |
439 | # return true if arg (BRAT or num_str) is an integer | |
440 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
441 | ||
442 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't | |
443 | $x->{_d}->is_one(); # 1e-1 => no integer | |
444 | 0; | |
445 | } | |
446 | ||
447 | sub is_zero | |
448 | { | |
449 | # return true if arg (BRAT or num_str) is zero | |
450 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
451 | ||
452 | return 1 if $x->{sign} eq '+' && $x->{_n}->is_zero(); | |
453 | 0; | |
454 | } | |
455 | ||
456 | sub is_one | |
457 | { | |
458 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given | |
459 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
460 | ||
461 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; | |
462 | return 1 | |
463 | if ($x->{sign} eq $sign && $x->{_n}->is_one() && $x->{_d}->is_one()); | |
464 | 0; | |
465 | } | |
466 | ||
467 | sub is_odd | |
468 | { | |
469 | # return true if arg (BFLOAT or num_str) is odd or false if even | |
470 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
471 | ||
472 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't | |
473 | ($x->{_d}->is_one() && $x->{_n}->is_odd()); # x/2 is not, but 3/1 | |
474 | 0; | |
475 | } | |
476 | ||
477 | sub is_even | |
478 | { | |
479 | # return true if arg (BINT or num_str) is even or false if odd | |
480 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
481 | ||
482 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't | |
483 | return 1 if ($x->{_d}->is_one() # x/3 is never | |
484 | && $x->{_n}->is_even()); # but 4/1 is | |
485 | 0; | |
486 | } | |
487 | ||
488 | BEGIN | |
489 | { | |
490 | *objectify = \&Math::BigInt::objectify; | |
491 | } | |
492 | ||
493 | ############################################################################## | |
494 | # parts() and friends | |
495 | ||
496 | sub numerator | |
497 | { | |
498 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
499 | ||
500 | my $n = $x->{_n}->copy(); $n->{sign} = $x->{sign}; | |
501 | $n; | |
502 | } | |
503 | ||
504 | sub denominator | |
505 | { | |
506 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
507 | ||
508 | $x->{_d}->copy(); | |
509 | } | |
510 | ||
511 | sub parts | |
512 | { | |
513 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
514 | ||
515 | my $n = $x->{_n}->copy(); | |
516 | $n->{sign} = $x->{sign}; | |
517 | return ($x->{_n}->copy(),$x->{_d}->copy()); | |
518 | } | |
519 | ||
520 | sub length | |
521 | { | |
522 | return 0; | |
523 | } | |
524 | ||
525 | sub digit | |
526 | { | |
527 | return 0; | |
528 | } | |
529 | ||
530 | ############################################################################## | |
531 | # special calc routines | |
532 | ||
533 | sub bceil | |
534 | { | |
535 | my ($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 | $x; | |
544 | } | |
545 | ||
546 | sub bfloor | |
547 | { | |
548 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
549 | ||
550 | return $x unless $x->{sign} =~ /^[+-]$/; | |
551 | return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 | |
552 | ||
553 | $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 | |
554 | $x->{_d}->bone(); | |
555 | $x->{_n}->binc() if $x->{sign} eq '-'; # -22/7 => -4/1 | |
556 | $x; | |
557 | } | |
558 | ||
559 | sub bfac | |
560 | { | |
561 | return Math::BigRat->bnan(); | |
562 | } | |
563 | ||
564 | sub bpow | |
565 | { | |
566 | my ($self,$x,$y,@r) = objectify(2,@_); | |
567 | ||
568 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x | |
569 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; | |
570 | return $x->bone(@r) if $y->is_zero(); | |
571 | return $x->round(@r) if $x->is_one() || $y->is_one(); | |
572 | if ($x->{sign} eq '-' && $x->{_n}->is_one() && $x->{_d}->is_one()) | |
573 | { | |
574 | # if $x == -1 and odd/even y => +1/-1 | |
575 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); | |
576 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; | |
577 | } | |
578 | # 1 ** -y => 1 / (1 ** |y|) | |
579 | # so do test for negative $y after above's clause | |
580 | # return $x->bnan() if $y->{sign} eq '-'; | |
581 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) | |
582 | ||
583 | my $pow2 = $self->__one(); | |
584 | my $y1 = Math::BigInt->new($y->{_n}/$y->{_d})->babs(); | |
585 | my $two = Math::BigInt->new(2); | |
586 | while (!$y1->is_one()) | |
587 | { | |
588 | print "at $y1 (= $x)\n"; | |
589 | $pow2->bmul($x) if $y1->is_odd(); | |
590 | $y1->bdiv($two); | |
591 | $x->bmul($x); | |
592 | } | |
593 | $x->bmul($pow2) unless $pow2->is_one(); | |
594 | # n ** -x => 1/n ** x | |
595 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; | |
596 | $x; | |
597 | #$x->round(@r); | |
598 | } | |
599 | ||
600 | sub blog | |
601 | { | |
602 | return Math::BigRat->bnan(); | |
603 | } | |
604 | ||
605 | sub bsqrt | |
606 | { | |
607 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
608 | ||
609 | return $x->bnan() if $x->{sign} ne '+'; # inf, NaN, -1 etc | |
610 | $x->{_d}->bsqrt($a,$p,$r); | |
611 | $x->{_n}->bsqrt($a,$p,$r); | |
612 | $x->bnorm(); | |
613 | } | |
614 | ||
615 | sub blsft | |
616 | { | |
617 | my ($self,$x,$y,$b,$a,$p,$r) = objectify(3,@_); | |
618 | ||
619 | $x->bmul( $b->copy()->bpow($y), $a,$p,$r); | |
620 | $x; | |
621 | } | |
622 | ||
623 | sub brsft | |
624 | { | |
625 | my ($self,$x,$y,$b,$a,$p,$r) = objectify(2,@_); | |
626 | ||
627 | $x->bdiv( $b->copy()->bpow($y), $a,$p,$r); | |
628 | $x; | |
629 | } | |
630 | ||
631 | ############################################################################## | |
632 | # round | |
633 | ||
634 | sub round | |
635 | { | |
636 | $_[0]; | |
637 | } | |
638 | ||
639 | sub bround | |
640 | { | |
641 | $_[0]; | |
642 | } | |
643 | ||
644 | sub bfround | |
645 | { | |
646 | $_[0]; | |
647 | } | |
648 | ||
649 | ############################################################################## | |
650 | # comparing | |
651 | ||
652 | sub bcmp | |
653 | { | |
654 | my ($self,$x,$y) = objectify(2,@_); | |
655 | ||
656 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
657 | { | |
658 | # handle +-inf and NaN | |
659 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
660 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; | |
661 | return +1 if $x->{sign} eq '+inf'; | |
662 | return -1 if $x->{sign} eq '-inf'; | |
663 | return -1 if $y->{sign} eq '+inf'; | |
664 | return +1; | |
665 | } | |
666 | # check sign for speed first | |
667 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
668 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
669 | ||
670 | # shortcut | |
671 | my $xz = $x->{_n}->is_zero(); | |
672 | my $yz = $y->{_n}->is_zero(); | |
673 | return 0 if $xz && $yz; # 0 <=> 0 | |
674 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y | |
675 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 | |
676 | ||
677 | my $t = $x->{_n} * $y->{_d}; $t->{sign} = $x->{sign}; | |
678 | my $u = $y->{_n} * $x->{_d}; $u->{sign} = $y->{sign}; | |
679 | $t->bcmp($u); | |
680 | } | |
681 | ||
682 | sub bacmp | |
683 | { | |
684 | my ($self,$x,$y) = objectify(2,@_); | |
685 | ||
686 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
687 | { | |
688 | # handle +-inf and NaN | |
689 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
690 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
691 | return +1; # inf is always bigger | |
692 | } | |
693 | ||
694 | my $t = $x->{_n} * $y->{_d}; | |
695 | my $u = $y->{_n} * $x->{_d}; | |
696 | $t->bacmp($u); | |
697 | } | |
698 | ||
699 | ############################################################################## | |
700 | # output conversation | |
701 | ||
702 | sub as_number | |
703 | { | |
704 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
705 | ||
706 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf etc | |
707 | my $t = $x->{_n}->copy()->bdiv($x->{_d}); # 22/7 => 3 | |
708 | $t->{sign} = $x->{sign}; | |
709 | $t; | |
710 | } | |
711 | ||
712 | #sub import | |
713 | # { | |
714 | # my $self = shift; | |
715 | # Math::BigInt->import(@_); | |
716 | # $self->SUPER::import(@_); # need it for subclasses | |
717 | # #$self->export_to_level(1,$self,@_); # need this ? | |
718 | # } | |
719 | ||
720 | 1; | |
721 | ||
722 | __END__ | |
723 | ||
724 | =head1 NAME | |
725 | ||
bce7c187 | 726 | Math::BigRat - arbitrarily big rationals |
184f15d5 JH |
727 | |
728 | =head1 SYNOPSIS | |
729 | ||
730 | use Math::BigRat; | |
731 | ||
732 | $x = Math::BigRat->new('3/7'); | |
733 | ||
734 | print $x->bstr(),"\n"; | |
735 | ||
736 | =head1 DESCRIPTION | |
737 | ||
738 | This is just a placeholder until the real thing is up and running. Watch this | |
739 | space... | |
740 | ||
741 | =head2 MATH LIBRARY | |
742 | ||
743 | Math with the numbers is done (by default) by a module called | |
744 | Math::BigInt::Calc. This is equivalent to saying: | |
745 | ||
746 | use Math::BigRat lib => 'Calc'; | |
747 | ||
748 | You can change this by using: | |
749 | ||
750 | use Math::BigRat lib => 'BitVect'; | |
751 | ||
752 | The following would first try to find Math::BigInt::Foo, then | |
753 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
754 | ||
755 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; | |
756 | ||
757 | Calc.pm uses as internal format an array of elements of some decimal base | |
758 | (usually 1e7, but this might be differen for some systems) with the least | |
759 | significant digit first, while BitVect.pm uses a bit vector of base 2, most | |
760 | significant bit first. Other modules might use even different means of | |
761 | representing the numbers. See the respective module documentation for further | |
762 | details. | |
763 | ||
764 | =head1 METHODS | |
765 | ||
766 | =head2 new | |
767 | ||
768 | $x = Math::BigRat->new('1/3'); | |
769 | ||
770 | Create a new Math::BigRat object. Input can come in various forms: | |
771 | ||
772 | $x = Math::BigRat->new('1/3'); # simple string | |
773 | $x = Math::BigRat->new('1 / 3'); # spaced | |
774 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats | |
775 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt | |
776 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat | |
777 | ||
778 | =head2 numerator | |
779 | ||
780 | $n = $x->numerator(); | |
781 | ||
782 | Returns a copy of the numerator (the part above the line) as signed BigInt. | |
783 | ||
784 | =head2 denominator | |
785 | ||
786 | $d = $x->denominator(); | |
787 | ||
788 | Returns a copy of the denominator (the part under the line) as positive BigInt. | |
789 | ||
790 | =head2 parts | |
791 | ||
792 | ($n,$d) = $x->parts(); | |
793 | ||
794 | Return a list consisting of (signed) numerator and (unsigned) denominator as | |
795 | BigInts. | |
796 | ||
797 | =head1 BUGS | |
798 | ||
799 | None know yet. Please see also L<Math::BigInt>. | |
800 | ||
801 | =head1 LICENSE | |
802 | ||
803 | This program is free software; you may redistribute it and/or modify it under | |
804 | the same terms as Perl itself. | |
805 | ||
806 | =head1 SEE ALSO | |
807 | ||
808 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, | |
809 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
810 | ||
811 | The package at | |
812 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigRat> may | |
813 | contain more documentation and examples as well as testcases. | |
814 | ||
815 | =head1 AUTHORS | |
816 | ||
817 | (C) by Tels L<http://bloodgate.com/> 2001-2002. | |
818 | ||
819 | =cut |