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 | |
7afd7a91 |
19 | require Exporter; |
184f15d5 |
20 | use Math::BigFloat; |
12fc2493 |
21 | use vars qw($VERSION @ISA $upgrade $downgrade |
990fb837 |
22 | $accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf); |
184f15d5 |
23 | |
24 | @ISA = qw(Exporter Math::BigFloat); |
184f15d5 |
25 | |
b68b7ab1 |
26 | $VERSION = '0.14'; |
184f15d5 |
27 | |
12fc2493 |
28 | use overload; # inherit overload from Math::BigFloat |
184f15d5 |
29 | |
12fc2493 |
30 | BEGIN |
31 | { |
32 | *objectify = \&Math::BigInt::objectify; # inherit this from BigInt |
33 | *AUTOLOAD = \&Math::BigFloat::AUTOLOAD; # can't inherit AUTOLOAD |
34 | # we inherit these from BigFloat because currently it is not possible |
35 | # that MBF has a different $MBI variable than we, because MBF also uses |
36 | # Math::BigInt::config->('lib'); (there is always only one library loaded) |
37 | *_e_add = \&Math::BigFloat::_e_add; |
38 | *_e_sub = \&Math::BigFloat::_e_sub; |
b68b7ab1 |
39 | *as_int = \&as_number; |
40 | *is_pos = \&is_positive; |
41 | *is_neg = \&is_negative; |
12fc2493 |
42 | } |
9b924220 |
43 | |
184f15d5 |
44 | ############################################################################## |
12fc2493 |
45 | # Global constants and flags. Access these only via the accessor methods! |
184f15d5 |
46 | |
184f15d5 |
47 | $accuracy = $precision = undef; |
48 | $round_mode = 'even'; |
49 | $div_scale = 40; |
50 | $upgrade = undef; |
51 | $downgrade = undef; |
52 | |
12fc2493 |
53 | # These are internally, and not to be used from the outside at all! |
990fb837 |
54 | |
55 | $_trap_nan = 0; # are NaNs ok? set w/ config() |
56 | $_trap_inf = 0; # are infs ok? set w/ config() |
57 | |
12fc2493 |
58 | # the package we are using for our private parts, defaults to: |
59 | # Math::BigInt->config()->{lib} |
60 | my $MBI = 'Math::BigInt::Calc'; |
61 | |
184f15d5 |
62 | my $nan = 'NaN'; |
9b924220 |
63 | my $class = 'Math::BigRat'; |
64 | my $IMPORT = 0; |
184f15d5 |
65 | |
8f675a64 |
66 | sub isa |
67 | { |
68 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't |
69 | UNIVERSAL::isa(@_); |
70 | } |
71 | |
12fc2493 |
72 | ############################################################################## |
9b924220 |
73 | |
184f15d5 |
74 | sub _new_from_float |
75 | { |
7afd7a91 |
76 | # turn a single float input into a rational number (like '0.1') |
184f15d5 |
77 | my ($self,$f) = @_; |
78 | |
79 | return $self->bnan() if $f->is_nan(); |
9b924220 |
80 | return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/; |
184f15d5 |
81 | |
12fc2493 |
82 | $self->{_n} = $MBI->_copy( $f->{_m} ); # mantissa |
83 | $self->{_d} = $MBI->_one(); |
9b924220 |
84 | $self->{sign} = $f->{sign} || '+'; |
85 | if ($f->{_es} eq '-') |
184f15d5 |
86 | { |
87 | # something like Math::BigRat->new('0.1'); |
9b924220 |
88 | # 1 / 1 => 1/10 |
12fc2493 |
89 | $MBI->_lsft ( $self->{_d}, $f->{_e} ,10); |
184f15d5 |
90 | } |
91 | else |
92 | { |
93 | # something like Math::BigRat->new('10'); |
94 | # 1 / 1 => 10/1 |
12fc2493 |
95 | $MBI->_lsft ( $self->{_n}, $f->{_e} ,10) unless |
96 | $MBI->_is_zero($f->{_e}); |
184f15d5 |
97 | } |
184f15d5 |
98 | $self; |
99 | } |
100 | |
101 | sub new |
102 | { |
103 | # create a Math::BigRat |
104 | my $class = shift; |
105 | |
b68b7ab1 |
106 | my ($n,$d) = @_; |
184f15d5 |
107 | |
108 | my $self = { }; bless $self,$class; |
109 | |
b68b7ab1 |
110 | # input like (BigInt) or (BigFloat): |
6de7f0cc |
111 | if ((!defined $d) && (ref $n) && (!$n->isa('Math::BigRat'))) |
184f15d5 |
112 | { |
184f15d5 |
113 | if ($n->isa('Math::BigFloat')) |
114 | { |
7afd7a91 |
115 | $self->_new_from_float($n); |
184f15d5 |
116 | } |
117 | if ($n->isa('Math::BigInt')) |
118 | { |
990fb837 |
119 | # TODO: trap NaN, inf |
b68b7ab1 |
120 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N |
12fc2493 |
121 | $self->{_d} = $MBI->_one(); # d => 1 |
122 | $self->{sign} = $n->{sign}; |
8f675a64 |
123 | } |
124 | if ($n->isa('Math::BigInt::Lite')) |
125 | { |
990fb837 |
126 | # TODO: trap NaN, inf |
127 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; |
b68b7ab1 |
128 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = N |
12fc2493 |
129 | $self->{_d} = $MBI->_one(); # d => 1 |
184f15d5 |
130 | } |
12fc2493 |
131 | return $self->bnorm(); # normalize (120/1 => 12/10) |
184f15d5 |
132 | } |
b68b7ab1 |
133 | |
134 | # input like (BigInt,BigInt) or (BigLite,BigLite): |
135 | if (ref($d) && ref($n)) |
136 | { |
137 | # do N first (for $self->{sign}): |
138 | if ($n->isa('Math::BigInt')) |
139 | { |
140 | # TODO: trap NaN, inf |
141 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N |
142 | $self->{sign} = $n->{sign}; |
143 | } |
144 | elsif ($n->isa('Math::BigInt::Lite')) |
145 | { |
146 | # TODO: trap NaN, inf |
147 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; |
148 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = $n |
149 | } |
150 | else |
151 | { |
152 | require Carp; |
153 | Carp::croak(ref($n) . " is not a recognized object format for Math::BigRat->new"); |
154 | } |
155 | # now D: |
156 | if ($d->isa('Math::BigInt')) |
157 | { |
158 | # TODO: trap NaN, inf |
159 | $self->{_d} = $MBI->_copy($d->{value}); # "mantissa" = D |
160 | # +/+ or -/- => +, +/- or -/+ => - |
161 | $self->{sign} = $d->{sign} ne $self->{sign} ? '-' : '+'; |
162 | } |
163 | elsif ($d->isa('Math::BigInt::Lite')) |
164 | { |
165 | # TODO: trap NaN, inf |
166 | $self->{_d} = $MBI->_new(abs($$d)); # "mantissa" = D |
167 | my $ds = '+'; $ds = '-' if $$d < 0; |
168 | # +/+ or -/- => +, +/- or -/+ => - |
169 | $self->{sign} = $ds ne $self->{sign} ? '-' : '+'; |
170 | } |
171 | else |
172 | { |
173 | require Carp; |
174 | Carp::croak(ref($d) . " is not a recognized object format for Math::BigRat->new"); |
175 | } |
176 | return $self->bnorm(); # normalize (120/1 => 12/10) |
177 | } |
12fc2493 |
178 | return $n->copy() if ref $n; # already a BigRat |
184f15d5 |
179 | |
180 | if (!defined $n) |
181 | { |
12fc2493 |
182 | $self->{_n} = $MBI->_zero(); # undef => 0 |
183 | $self->{_d} = $MBI->_one(); |
184f15d5 |
184 | $self->{sign} = '+'; |
12fc2493 |
185 | return $self; |
184f15d5 |
186 | } |
12fc2493 |
187 | |
184f15d5 |
188 | # string input with / delimiter |
189 | if ($n =~ /\s*\/\s*/) |
190 | { |
990fb837 |
191 | return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
192 | return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid |
184f15d5 |
193 | ($n,$d) = split (/\//,$n); |
194 | # try as BigFloats first |
195 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) |
196 | { |
7d341013 |
197 | local $Math::BigFloat::accuracy = undef; |
198 | local $Math::BigFloat::precision = undef; |
9b924220 |
199 | |
12fc2493 |
200 | # one of them looks like a float |
9b924220 |
201 | my $nf = Math::BigFloat->new($n,undef,undef); |
990fb837 |
202 | $self->{sign} = '+'; |
203 | return $self->bnan() if $nf->is_nan(); |
12fc2493 |
204 | $self->{_n} = $MBI->_copy( $nf->{_m} ); # get mantissa |
9b924220 |
205 | |
184f15d5 |
206 | # now correct $self->{_n} due to $n |
7d341013 |
207 | my $f = Math::BigFloat->new($d,undef,undef); |
990fb837 |
208 | return $self->bnan() if $f->is_nan(); |
12fc2493 |
209 | $self->{_d} = $MBI->_copy( $f->{_m} ); |
9b924220 |
210 | |
990fb837 |
211 | # calculate the difference between nE and dE |
12fc2493 |
212 | # XXX TODO: check that exponent() makes a copy to avoid copy() |
213 | my $diff_e = $nf->exponent()->copy()->bsub( $f->exponent); |
990fb837 |
214 | if ($diff_e->is_negative()) |
215 | { |
216 | # < 0: mul d with it |
12fc2493 |
217 | $MBI->_lsft( $self->{_d}, $MBI->_new( $diff_e->babs()), 10); |
990fb837 |
218 | } |
219 | elsif (!$diff_e->is_zero()) |
184f15d5 |
220 | { |
990fb837 |
221 | # > 0: mul n with it |
12fc2493 |
222 | $MBI->_lsft( $self->{_n}, $MBI->_new( $diff_e), 10); |
184f15d5 |
223 | } |
184f15d5 |
224 | } |
225 | else |
226 | { |
12fc2493 |
227 | # both d and n look like (big)ints |
228 | |
229 | $self->{sign} = '+'; # no sign => '+' |
230 | $self->{_n} = undef; |
231 | $self->{_d} = undef; |
232 | if ($n =~ /^([+-]?)0*(\d+)\z/) # first part ok? |
233 | { |
234 | $self->{sign} = $1 || '+'; # no sign => '+' |
235 | $self->{_n} = $MBI->_new($2 || 0); |
236 | } |
237 | |
238 | if ($d =~ /^([+-]?)0*(\d+)\z/) # second part ok? |
239 | { |
240 | $self->{sign} =~ tr/+-/-+/ if ($1 || '') eq '-'; # negate if second part neg. |
241 | $self->{_d} = $MBI->_new($2 || 0); |
242 | } |
243 | |
244 | if (!defined $self->{_n} || !defined $self->{_d}) |
245 | { |
246 | $d = Math::BigInt->new($d,undef,undef) unless ref $d; |
247 | $n = Math::BigInt->new($n,undef,undef) unless ref $n; |
248 | |
249 | if ($n->{sign} =~ /^[+-]$/ && $d->{sign} =~ /^[+-]$/) |
250 | { |
251 | # both parts are ok as integers (wierd things like ' 1e0' |
252 | $self->{_n} = $MBI->_copy($n->{value}); |
253 | $self->{_d} = $MBI->_copy($d->{value}); |
254 | $self->{sign} = $n->{sign}; |
255 | $self->{sign} =~ tr/+-/-+/ if $d->{sign} eq '-'; # -1/-2 => 1/2 |
256 | return $self->bnorm(); |
257 | } |
258 | |
259 | $self->{sign} = '+'; # a default sign |
260 | return $self->bnan() if $n->is_nan() || $d->is_nan(); |
261 | |
262 | # handle inf cases: |
263 | if ($n->is_inf() || $d->is_inf()) |
7afd7a91 |
264 | { |
12fc2493 |
265 | if ($n->is_inf()) |
266 | { |
267 | return $self->bnan() if $d->is_inf(); # both are inf => NaN |
268 | my $s = '+'; # '+inf/+123' or '-inf/-123' |
269 | $s = '-' if substr($n->{sign},0,1) ne $d->{sign}; |
270 | # +-inf/123 => +-inf |
271 | return $self->binf($s); |
272 | } |
273 | # 123/inf => 0 |
274 | return $self->bzero(); |
7afd7a91 |
275 | } |
12fc2493 |
276 | } |
184f15d5 |
277 | } |
990fb837 |
278 | |
184f15d5 |
279 | return $self->bnorm(); |
280 | } |
281 | |
282 | # simple string input |
283 | if (($n =~ /[\.eE]/)) |
284 | { |
7d341013 |
285 | # looks like a float, quacks like a float, so probably is a float |
12fc2493 |
286 | $self->{sign} = 'NaN'; |
7d341013 |
287 | local $Math::BigFloat::accuracy = undef; |
288 | local $Math::BigFloat::precision = undef; |
7d341013 |
289 | $self->_new_from_float(Math::BigFloat->new($n,undef,undef)); |
184f15d5 |
290 | } |
291 | else |
292 | { |
12fc2493 |
293 | # for simple forms, use $MBI directly |
294 | if ($n =~ /^([+-]?)0*(\d+)\z/) |
295 | { |
296 | $self->{sign} = $1 || '+'; |
297 | $self->{_n} = $MBI->_new($2 || 0); |
298 | $self->{_d} = $MBI->_one(); |
299 | } |
300 | else |
301 | { |
302 | my $n = Math::BigInt->new($n,undef,undef); |
303 | $self->{_n} = $MBI->_copy($n->{value}); |
304 | $self->{_d} = $MBI->_one(); |
305 | $self->{sign} = $n->{sign}; |
306 | return $self->bnan() if $self->{sign} eq 'NaN'; |
307 | return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/; |
308 | } |
184f15d5 |
309 | } |
310 | $self->bnorm(); |
311 | } |
312 | |
9b924220 |
313 | sub copy |
314 | { |
b68b7ab1 |
315 | # if two arguments, the first one is the class to "swallow" subclasses |
316 | my ($c,$x) = @_; |
317 | |
318 | if (scalar @_ == 1) |
9b924220 |
319 | { |
b68b7ab1 |
320 | $x = $_[0]; |
9b924220 |
321 | $c = ref($x); |
322 | } |
323 | return unless ref($x); # only for objects |
324 | |
12fc2493 |
325 | my $self = bless {}, $c; |
9b924220 |
326 | |
327 | $self->{sign} = $x->{sign}; |
12fc2493 |
328 | $self->{_d} = $MBI->_copy($x->{_d}); |
329 | $self->{_n} = $MBI->_copy($x->{_n}); |
9b924220 |
330 | $self->{_a} = $x->{_a} if defined $x->{_a}; |
331 | $self->{_p} = $x->{_p} if defined $x->{_p}; |
332 | $self; |
333 | } |
334 | |
990fb837 |
335 | ############################################################################## |
336 | |
337 | sub config |
338 | { |
339 | # return (later set?) configuration data as hash ref |
b68b7ab1 |
340 | my $class = shift || 'Math::BigRat'; |
990fb837 |
341 | |
342 | my $cfg = $class->SUPER::config(@_); |
343 | |
344 | # now we need only to override the ones that are different from our parent |
345 | $cfg->{class} = $class; |
346 | $cfg->{with} = $MBI; |
347 | $cfg; |
348 | } |
349 | |
350 | ############################################################################## |
8f675a64 |
351 | |
184f15d5 |
352 | sub bstr |
353 | { |
7afd7a91 |
354 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
355 | |
356 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
357 | { |
358 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
359 | return $s; |
360 | } |
361 | |
7afd7a91 |
362 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2' |
184f15d5 |
363 | |
12fc2493 |
364 | return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d}); |
365 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
366 | } |
367 | |
368 | sub bsstr |
369 | { |
b68b7ab1 |
370 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
371 | |
372 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
373 | { |
374 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
375 | return $s; |
376 | } |
377 | |
378 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
12fc2493 |
379 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
380 | } |
381 | |
382 | sub bnorm |
383 | { |
12fc2493 |
384 | # reduce the number to the shortest form |
b68b7ab1 |
385 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
386 | |
12fc2493 |
387 | # Both parts must be objects of whatever we are using today. |
388 | # Second check because Calc.pm has ARRAY res as unblessed objects. |
389 | if (ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY') |
990fb837 |
390 | { |
12fc2493 |
391 | require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).') in bnorm()'); |
990fb837 |
392 | } |
12fc2493 |
393 | if (ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY') |
990fb837 |
394 | { |
12fc2493 |
395 | require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).') in bnorm()'); |
990fb837 |
396 | } |
6de7f0cc |
397 | |
6de7f0cc |
398 | # no normalize for NaN, inf etc. |
399 | return $x if $x->{sign} !~ /^[+-]$/; |
400 | |
184f15d5 |
401 | # normalize zeros to 0/1 |
12fc2493 |
402 | if ($MBI->_is_zero($x->{_n})) |
184f15d5 |
403 | { |
12fc2493 |
404 | $x->{sign} = '+'; # never leave a -0 |
405 | $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d}); |
184f15d5 |
406 | return $x; |
407 | } |
408 | |
12fc2493 |
409 | return $x if $MBI->_is_one($x->{_d}); # no need to reduce |
6de7f0cc |
410 | |
184f15d5 |
411 | # reduce other numbers |
12fc2493 |
412 | my $gcd = $MBI->_copy($x->{_n}); |
413 | $gcd = $MBI->_gcd($gcd,$x->{_d}); |
414 | |
415 | if (!$MBI->_is_one($gcd)) |
184f15d5 |
416 | { |
12fc2493 |
417 | $x->{_n} = $MBI->_div($x->{_n},$gcd); |
418 | $x->{_d} = $MBI->_div($x->{_d},$gcd); |
184f15d5 |
419 | } |
184f15d5 |
420 | $x; |
421 | } |
422 | |
423 | ############################################################################## |
b68b7ab1 |
424 | # sign manipulation |
425 | |
426 | sub bneg |
427 | { |
428 | # (BRAT or num_str) return BRAT |
429 | # negate number or make a negated number from string |
430 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
431 | |
432 | return $x if $x->modify('bneg'); |
433 | |
434 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN' |
435 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $MBI->_is_zero($x->{_n})); |
436 | $x; |
437 | } |
438 | |
439 | ############################################################################## |
184f15d5 |
440 | # special values |
441 | |
442 | sub _bnan |
443 | { |
990fb837 |
444 | # used by parent class bnan() to initialize number to NaN |
184f15d5 |
445 | my $self = shift; |
990fb837 |
446 | |
447 | if ($_trap_nan) |
448 | { |
449 | require Carp; |
450 | my $class = ref($self); |
451 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
452 | } |
12fc2493 |
453 | $self->{_n} = $MBI->_zero(); |
454 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
455 | } |
456 | |
457 | sub _binf |
458 | { |
7d341013 |
459 | # used by parent class bone() to initialize number to +inf/-inf |
184f15d5 |
460 | my $self = shift; |
990fb837 |
461 | |
462 | if ($_trap_inf) |
463 | { |
464 | require Carp; |
465 | my $class = ref($self); |
466 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); |
467 | } |
12fc2493 |
468 | $self->{_n} = $MBI->_zero(); |
469 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
470 | } |
471 | |
472 | sub _bone |
473 | { |
7d341013 |
474 | # used by parent class bone() to initialize number to +1/-1 |
184f15d5 |
475 | my $self = shift; |
12fc2493 |
476 | $self->{_n} = $MBI->_one(); |
477 | $self->{_d} = $MBI->_one(); |
184f15d5 |
478 | } |
479 | |
480 | sub _bzero |
481 | { |
990fb837 |
482 | # used by parent class bzero() to initialize number to 0 |
184f15d5 |
483 | my $self = shift; |
12fc2493 |
484 | $self->{_n} = $MBI->_zero(); |
485 | $self->{_d} = $MBI->_one(); |
184f15d5 |
486 | } |
487 | |
488 | ############################################################################## |
489 | # mul/add/div etc |
490 | |
491 | sub badd |
492 | { |
7afd7a91 |
493 | # add two rational numbers |
7d341013 |
494 | |
495 | # set up parameters |
496 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
497 | # objectify is costly, so avoid it |
498 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
499 | { |
500 | ($self,$x,$y,@r) = objectify(2,@_); |
501 | } |
184f15d5 |
502 | |
12fc2493 |
503 | # +inf + +inf => +inf, -inf + -inf => -inf |
504 | return $x->binf(substr($x->{sign},0,1)) |
505 | if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
184f15d5 |
506 | |
12fc2493 |
507 | # +inf + -inf or -inf + +inf => NaN |
508 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
184f15d5 |
509 | |
510 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
511 | # - + - = --------- = -- |
512 | # 4 3 4*3 12 |
513 | |
7d341013 |
514 | # we do not compute the gcd() here, but simple do: |
515 | # 5 7 5*3 + 7*4 41 |
516 | # - + - = --------- = -- |
517 | # 4 3 4*3 12 |
518 | |
12fc2493 |
519 | # and bnorm() will then take care of the rest |
184f15d5 |
520 | |
12fc2493 |
521 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
7d341013 |
522 | |
12fc2493 |
523 | my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} ); |
184f15d5 |
524 | |
12fc2493 |
525 | ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign}); |
184f15d5 |
526 | |
12fc2493 |
527 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
528 | |
12fc2493 |
529 | # normalize and round |
7d341013 |
530 | $x->bnorm()->round(@r); |
184f15d5 |
531 | } |
532 | |
533 | sub bsub |
534 | { |
7afd7a91 |
535 | # subtract two rational numbers |
7d341013 |
536 | |
537 | # set up parameters |
538 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
539 | # objectify is costly, so avoid it |
540 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
541 | { |
542 | ($self,$x,$y,@r) = objectify(2,@_); |
543 | } |
184f15d5 |
544 | |
7afd7a91 |
545 | # flip sign of $x, call badd(), then flip sign of result |
546 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
547 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
548 | $x->badd($y,@r); # does norm and round |
7afd7a91 |
549 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
550 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
7afd7a91 |
551 | $x; |
184f15d5 |
552 | } |
553 | |
554 | sub bmul |
555 | { |
7afd7a91 |
556 | # multiply two rational numbers |
7d341013 |
557 | |
558 | # set up parameters |
559 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
560 | # objectify is costly, so avoid it |
561 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
562 | { |
563 | ($self,$x,$y,@r) = objectify(2,@_); |
564 | } |
184f15d5 |
565 | |
566 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
567 | |
568 | # inf handling |
569 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
570 | { |
571 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
572 | # result will always be +-inf: |
573 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
574 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
575 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
576 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
577 | return $x->binf('-'); |
578 | } |
579 | |
580 | # x== 0 # also: or y == 1 or y == -1 |
581 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
582 | |
12fc2493 |
583 | # XXX TODO: |
584 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
585 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
586 | |
12fc2493 |
587 | # 1 2 1 * 2 2 1 |
588 | # - * - = ----- = - = - |
589 | # 4 3 4 * 3 12 6 |
7d341013 |
590 | |
12fc2493 |
591 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); |
592 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
593 | |
594 | # compute new sign |
595 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
596 | |
7d341013 |
597 | $x->bnorm()->round(@r); |
184f15d5 |
598 | } |
599 | |
600 | sub bdiv |
601 | { |
602 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
603 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
7d341013 |
604 | |
605 | # set up parameters |
606 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
607 | # objectify is costly, so avoid it |
608 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
609 | { |
610 | ($self,$x,$y,@r) = objectify(2,@_); |
611 | } |
184f15d5 |
612 | |
613 | return $self->_div_inf($x,$y) |
614 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
615 | |
616 | # x== 0 # also: or y == 1 or y == -1 |
617 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
618 | |
12fc2493 |
619 | # XXX TODO: list context, upgrade |
620 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
621 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
622 | |
184f15d5 |
623 | # 1 1 1 3 |
624 | # - / - == - * - |
625 | # 4 3 4 1 |
7d341013 |
626 | |
12fc2493 |
627 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
628 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); |
184f15d5 |
629 | |
630 | # compute new sign |
631 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
632 | |
7d341013 |
633 | $x->bnorm()->round(@r); |
6de7f0cc |
634 | $x; |
184f15d5 |
635 | } |
636 | |
990fb837 |
637 | sub bmod |
638 | { |
639 | # compute "remainder" (in Perl way) of $x / $y |
640 | |
641 | # set up parameters |
642 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
643 | # objectify is costly, so avoid it |
644 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
645 | { |
646 | ($self,$x,$y,@r) = objectify(2,@_); |
647 | } |
648 | |
990fb837 |
649 | return $self->_div_inf($x,$y) |
650 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
651 | |
652 | return $x if $x->is_zero(); # 0 / 7 = 0, mod 0 |
653 | |
654 | # compute $x - $y * floor($x/$y), keeping the sign of $x |
655 | |
12fc2493 |
656 | # copy x to u, make it positive and then do a normal division ($u/$y) |
657 | my $u = bless { sign => '+' }, $self; |
658 | $u->{_n} = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d} ); |
659 | $u->{_d} = $MBI->_mul( $MBI->_copy($x->{_d}), $y->{_n} ); |
660 | |
661 | # compute floor(u) |
662 | if (! $MBI->_is_one($u->{_d})) |
990fb837 |
663 | { |
12fc2493 |
664 | $u->{_n} = $MBI->_div($u->{_n},$u->{_d}); # 22/7 => 3/1 w/ truncate |
665 | # no need to set $u->{_d} to 1, since below we set it to $y->{_d} anyway |
990fb837 |
666 | } |
667 | |
12fc2493 |
668 | # now compute $y * $u |
669 | $u->{_d} = $MBI->_copy($y->{_d}); # 1 * $y->{_d}, see floor above |
670 | $u->{_n} = $MBI->_mul($u->{_n},$y->{_n}); |
990fb837 |
671 | |
12fc2493 |
672 | my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive |
990fb837 |
673 | # compute $x - $u |
674 | $x->bsub($u); |
675 | $x->{sign} = $xsign; # put sign back |
676 | |
677 | $x->bnorm()->round(@r); |
990fb837 |
678 | } |
679 | |
184f15d5 |
680 | ############################################################################## |
a4e2b1c6 |
681 | # bdec/binc |
682 | |
683 | sub bdec |
684 | { |
685 | # decrement value (subtract 1) |
686 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
687 | |
688 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
689 | |
690 | if ($x->{sign} eq '-') |
691 | { |
12fc2493 |
692 | $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2 |
a4e2b1c6 |
693 | } |
694 | else |
695 | { |
12fc2493 |
696 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? |
a4e2b1c6 |
697 | { |
698 | # 1/3 -- => -2/3 |
12fc2493 |
699 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
700 | $x->{sign} = '-'; |
701 | } |
702 | else |
703 | { |
12fc2493 |
704 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 |
a4e2b1c6 |
705 | } |
706 | } |
707 | $x->bnorm()->round(@r); |
a4e2b1c6 |
708 | } |
709 | |
710 | sub binc |
711 | { |
712 | # increment value (add 1) |
713 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
714 | |
715 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
716 | |
717 | if ($x->{sign} eq '-') |
718 | { |
12fc2493 |
719 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) |
a4e2b1c6 |
720 | { |
721 | # -1/3 ++ => 2/3 (overflow at 0) |
12fc2493 |
722 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
723 | $x->{sign} = '+'; |
724 | } |
725 | else |
726 | { |
12fc2493 |
727 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 |
a4e2b1c6 |
728 | } |
729 | } |
730 | else |
731 | { |
12fc2493 |
732 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 |
a4e2b1c6 |
733 | } |
734 | $x->bnorm()->round(@r); |
a4e2b1c6 |
735 | } |
736 | |
737 | ############################################################################## |
184f15d5 |
738 | # is_foo methods (the rest is inherited) |
739 | |
740 | sub is_int |
741 | { |
742 | # return true if arg (BRAT or num_str) is an integer |
9b924220 |
743 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
744 | |
745 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
12fc2493 |
746 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer |
184f15d5 |
747 | 0; |
748 | } |
749 | |
750 | sub is_zero |
751 | { |
752 | # return true if arg (BRAT or num_str) is zero |
9b924220 |
753 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
754 | |
12fc2493 |
755 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); |
184f15d5 |
756 | 0; |
757 | } |
758 | |
759 | sub is_one |
760 | { |
761 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
9b924220 |
762 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
763 | |
9b924220 |
764 | my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; |
184f15d5 |
765 | return 1 |
12fc2493 |
766 | if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})); |
184f15d5 |
767 | 0; |
768 | } |
769 | |
770 | sub is_odd |
771 | { |
772 | # return true if arg (BFLOAT or num_str) is odd or false if even |
9b924220 |
773 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
774 | |
775 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
12fc2493 |
776 | ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1 |
184f15d5 |
777 | 0; |
778 | } |
779 | |
780 | sub is_even |
781 | { |
782 | # return true if arg (BINT or num_str) is even or false if odd |
9b924220 |
783 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
784 | |
785 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
12fc2493 |
786 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never |
787 | && $MBI->_is_even($x->{_n})); # but 4/1 is |
184f15d5 |
788 | 0; |
789 | } |
790 | |
184f15d5 |
791 | ############################################################################## |
792 | # parts() and friends |
793 | |
794 | sub numerator |
795 | { |
796 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
a4e2b1c6 |
797 | |
12fc2493 |
798 | # NaN, inf, -inf |
799 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
a4e2b1c6 |
800 | |
12fc2493 |
801 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; |
184f15d5 |
802 | $n; |
803 | } |
804 | |
805 | sub denominator |
806 | { |
807 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
808 | |
12fc2493 |
809 | # NaN |
810 | return Math::BigInt->new($x->{sign}) if $x->{sign} eq 'NaN'; |
811 | # inf, -inf |
812 | return Math::BigInt->bone() if $x->{sign} !~ /^[+-]$/; |
813 | |
814 | Math::BigInt->new($MBI->_str($x->{_d})); |
184f15d5 |
815 | } |
816 | |
817 | sub parts |
818 | { |
819 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
820 | |
12fc2493 |
821 | my $c = 'Math::BigInt'; |
822 | |
823 | return ($c->bnan(),$c->bnan()) if $x->{sign} eq 'NaN'; |
824 | return ($c->binf(),$c->binf()) if $x->{sign} eq '+inf'; |
825 | return ($c->binf('-'),$c->binf()) if $x->{sign} eq '-inf'; |
a4e2b1c6 |
826 | |
12fc2493 |
827 | my $n = $c->new( $MBI->_str($x->{_n})); |
184f15d5 |
828 | $n->{sign} = $x->{sign}; |
12fc2493 |
829 | my $d = $c->new( $MBI->_str($x->{_d})); |
830 | ($n,$d); |
184f15d5 |
831 | } |
832 | |
833 | sub length |
834 | { |
9b924220 |
835 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
836 | |
837 | return $nan unless $x->is_int(); |
12fc2493 |
838 | $MBI->_len($x->{_n}); # length(-123/1) => length(123) |
184f15d5 |
839 | } |
840 | |
841 | sub digit |
842 | { |
12fc2493 |
843 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); |
9b924220 |
844 | |
845 | return $nan unless $x->is_int(); |
12fc2493 |
846 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) |
184f15d5 |
847 | } |
848 | |
849 | ############################################################################## |
850 | # special calc routines |
851 | |
852 | sub bceil |
853 | { |
854 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
855 | |
12fc2493 |
856 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
857 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
858 | |
12fc2493 |
859 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
860 | $x->{_d} = $MBI->_one(); # d => 1 |
861 | $x->{_n} = $MBI->_inc($x->{_n}) |
862 | if $x->{sign} eq '+'; # +22/7 => 4/1 |
863 | $x->{sign} = '+' if $MBI->_is_zero($x->{_n}); # -0 => 0 |
184f15d5 |
864 | $x; |
865 | } |
866 | |
867 | sub bfloor |
868 | { |
869 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
870 | |
12fc2493 |
871 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
872 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
873 | |
12fc2493 |
874 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
875 | $x->{_d} = $MBI->_one(); # d => 1 |
876 | $x->{_n} = $MBI->_inc($x->{_n}) |
877 | if $x->{sign} eq '-'; # -22/7 => -4/1 |
184f15d5 |
878 | $x; |
879 | } |
880 | |
881 | sub bfac |
882 | { |
a4e2b1c6 |
883 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
884 | |
12fc2493 |
885 | # if $x is not an integer |
886 | if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d}))) |
a4e2b1c6 |
887 | { |
12fc2493 |
888 | return $x->bnan(); |
a4e2b1c6 |
889 | } |
12fc2493 |
890 | |
891 | $x->{_n} = $MBI->_fac($x->{_n}); |
892 | # since _d is 1, we don't need to reduce/norm the result |
893 | $x->round(@r); |
184f15d5 |
894 | } |
895 | |
896 | sub bpow |
897 | { |
7d341013 |
898 | # power ($x ** $y) |
899 | |
900 | # set up parameters |
901 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
902 | # objectify is costly, so avoid it |
903 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
904 | { |
905 | ($self,$x,$y,@r) = objectify(2,@_); |
906 | } |
184f15d5 |
907 | |
908 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
909 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
910 | return $x->bone(@r) if $y->is_zero(); |
911 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
12fc2493 |
912 | |
913 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) |
184f15d5 |
914 | { |
915 | # if $x == -1 and odd/even y => +1/-1 |
916 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
917 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
918 | } |
919 | # 1 ** -y => 1 / (1 ** |y|) |
920 | # so do test for negative $y after above's clause |
12fc2493 |
921 | |
184f15d5 |
922 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
923 | |
a4e2b1c6 |
924 | # shortcut y/1 (and/or x/1) |
12fc2493 |
925 | if ($MBI->_is_one($y->{_d})) |
a4e2b1c6 |
926 | { |
927 | # shortcut for x/1 and y/1 |
12fc2493 |
928 | if ($MBI->_is_one($x->{_d})) |
a4e2b1c6 |
929 | { |
12fc2493 |
930 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
a4e2b1c6 |
931 | if ($y->{sign} eq '-') |
932 | { |
933 | # 0.2 ** -3 => 1/(0.2 ** 3) |
934 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
935 | } |
936 | # correct sign; + ** + => + |
937 | if ($x->{sign} eq '-') |
938 | { |
939 | # - * - => +, - * - * - => - |
12fc2493 |
940 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
941 | } |
942 | return $x->round(@r); |
943 | } |
944 | # x/z ** y/1 |
12fc2493 |
945 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
946 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); |
a4e2b1c6 |
947 | if ($y->{sign} eq '-') |
948 | { |
949 | # 0.2 ** -3 => 1/(0.2 ** 3) |
950 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
951 | } |
952 | # correct sign; + ** + => + |
953 | if ($x->{sign} eq '-') |
954 | { |
955 | # - * - => +, - * - * - => - |
12fc2493 |
956 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
957 | } |
958 | return $x->round(@r); |
959 | } |
960 | |
961 | # regular calculation (this is wrong for d/e ** f/g) |
12fc2493 |
962 | my $pow2 = $self->bone(); |
963 | my $y1 = $MBI->_div ( $MBI->_copy($y->{_n}), $y->{_d}); |
964 | my $two = $MBI->_two(); |
965 | |
966 | while (!$MBI->_is_one($y1)) |
184f15d5 |
967 | { |
12fc2493 |
968 | $pow2->bmul($x) if $MBI->_is_odd($y1); |
969 | $MBI->_div($y1, $two); |
184f15d5 |
970 | $x->bmul($x); |
971 | } |
972 | $x->bmul($pow2) unless $pow2->is_one(); |
973 | # n ** -x => 1/n ** x |
974 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; |
7d341013 |
975 | $x->bnorm()->round(@r); |
184f15d5 |
976 | } |
977 | |
978 | sub blog |
979 | { |
7afd7a91 |
980 | # set up parameters |
981 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
982 | |
983 | # objectify is costly, so avoid it |
984 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
985 | { |
9b924220 |
986 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
7afd7a91 |
987 | } |
988 | |
9b924220 |
989 | # blog(1,Y) => 0 |
990 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; |
991 | |
7afd7a91 |
992 | # $x <= 0 => NaN |
993 | return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; |
994 | |
995 | if ($x->is_int() && $y->is_int()) |
996 | { |
997 | return $self->new($x->as_number()->blog($y->as_number(),@r)); |
998 | } |
999 | |
9b924220 |
1000 | # do it with floats |
1001 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); |
1002 | } |
1003 | |
12fc2493 |
1004 | sub _float_from_part |
1005 | { |
1006 | my $x = shift; |
1007 | |
1008 | my $f = Math::BigFloat->bzero(); |
1009 | $f->{_m} = $MBI->_copy($x); |
1010 | $f->{_e} = $MBI->_zero(); |
1011 | |
1012 | $f; |
1013 | } |
1014 | |
9b924220 |
1015 | sub _as_float |
1016 | { |
1017 | my $x = shift; |
1018 | |
1019 | local $Math::BigFloat::upgrade = undef; |
1020 | local $Math::BigFloat::accuracy = undef; |
1021 | local $Math::BigFloat::precision = undef; |
1022 | # 22/7 => 3.142857143.. |
12fc2493 |
1023 | |
1024 | my $a = $x->accuracy() || 0; |
1025 | if ($a != 0 || !$MBI->_is_one($x->{_d})) |
1026 | { |
1027 | # n/d |
1028 | return Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy()); |
1029 | } |
1030 | # just n |
1031 | Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n})); |
7afd7a91 |
1032 | } |
1033 | |
1034 | sub broot |
1035 | { |
1036 | # set up parameters |
1037 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1038 | # objectify is costly, so avoid it |
1039 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1040 | { |
1041 | ($self,$x,$y,@r) = objectify(2,@_); |
1042 | } |
1043 | |
1044 | if ($x->is_int() && $y->is_int()) |
1045 | { |
1046 | return $self->new($x->as_number()->broot($y->as_number(),@r)); |
1047 | } |
9b924220 |
1048 | |
1049 | # do it with floats |
1050 | $x->_new_from_float( $x->_as_float()->broot($y,@r) ); |
7afd7a91 |
1051 | } |
1052 | |
1053 | sub bmodpow |
1054 | { |
1055 | # set up parameters |
1056 | my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); |
1057 | # objectify is costly, so avoid it |
1058 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1059 | { |
1060 | ($self,$x,$y,$m,@r) = objectify(3,@_); |
1061 | } |
1062 | |
1063 | # $x or $y or $m are NaN or +-inf => NaN |
1064 | return $x->bnan() |
1065 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || |
1066 | $m->{sign} !~ /^[+-]$/; |
1067 | |
1068 | if ($x->is_int() && $y->is_int() && $m->is_int()) |
1069 | { |
1070 | return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); |
1071 | } |
1072 | |
1073 | warn ("bmodpow() not fully implemented"); |
1074 | $x->bnan(); |
1075 | } |
1076 | |
1077 | sub bmodinv |
1078 | { |
1079 | # set up parameters |
1080 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1081 | # objectify is costly, so avoid it |
1082 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1083 | { |
1084 | ($self,$x,$y,@r) = objectify(2,@_); |
1085 | } |
1086 | |
1087 | # $x or $y are NaN or +-inf => NaN |
1088 | return $x->bnan() |
1089 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; |
1090 | |
1091 | if ($x->is_int() && $y->is_int()) |
1092 | { |
1093 | return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); |
1094 | } |
1095 | |
1096 | warn ("bmodinv() not fully implemented"); |
1097 | $x->bnan(); |
184f15d5 |
1098 | } |
1099 | |
1100 | sub bsqrt |
1101 | { |
990fb837 |
1102 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1103 | |
1104 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 |
1105 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf |
1106 | return $x->round(@r) if $x->is_zero() || $x->is_one(); |
1107 | |
1108 | local $Math::BigFloat::upgrade = undef; |
1109 | local $Math::BigFloat::downgrade = undef; |
1110 | local $Math::BigFloat::precision = undef; |
1111 | local $Math::BigFloat::accuracy = undef; |
1112 | local $Math::BigInt::upgrade = undef; |
1113 | local $Math::BigInt::precision = undef; |
1114 | local $Math::BigInt::accuracy = undef; |
9b924220 |
1115 | |
12fc2493 |
1116 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); |
1117 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); |
1118 | |
1119 | # XXX TODO: we probably can optimze this: |
184f15d5 |
1120 | |
990fb837 |
1121 | # if sqrt(D) was not integer |
9b924220 |
1122 | if ($x->{_d}->{_es} ne '+') |
990fb837 |
1123 | { |
9b924220 |
1124 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 |
12fc2493 |
1125 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 |
990fb837 |
1126 | } |
1127 | # if sqrt(N) was not integer |
9b924220 |
1128 | if ($x->{_n}->{_es} ne '+') |
990fb837 |
1129 | { |
9b924220 |
1130 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 |
12fc2493 |
1131 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 |
990fb837 |
1132 | } |
12fc2493 |
1133 | |
990fb837 |
1134 | # convert parts to $MBI again |
12fc2493 |
1135 | $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10) |
1136 | if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY'; |
1137 | $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10) |
1138 | if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY'; |
1139 | |
990fb837 |
1140 | $x->bnorm()->round(@r); |
184f15d5 |
1141 | } |
1142 | |
1143 | sub blsft |
1144 | { |
9b924220 |
1145 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1146 | |
9b924220 |
1147 | $b = 2 unless defined $b; |
1148 | $b = $self->new($b) unless ref ($b); |
1149 | $x->bmul( $b->copy()->bpow($y), @r); |
184f15d5 |
1150 | $x; |
1151 | } |
1152 | |
1153 | sub brsft |
1154 | { |
12fc2493 |
1155 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1156 | |
9b924220 |
1157 | $b = 2 unless defined $b; |
1158 | $b = $self->new($b) unless ref ($b); |
1159 | $x->bdiv( $b->copy()->bpow($y), @r); |
184f15d5 |
1160 | $x; |
1161 | } |
1162 | |
1163 | ############################################################################## |
1164 | # round |
1165 | |
1166 | sub round |
1167 | { |
1168 | $_[0]; |
1169 | } |
1170 | |
1171 | sub bround |
1172 | { |
1173 | $_[0]; |
1174 | } |
1175 | |
1176 | sub bfround |
1177 | { |
1178 | $_[0]; |
1179 | } |
1180 | |
1181 | ############################################################################## |
1182 | # comparing |
1183 | |
1184 | sub bcmp |
1185 | { |
7afd7a91 |
1186 | # compare two signed numbers |
1187 | |
1188 | # set up parameters |
1189 | my ($self,$x,$y) = (ref($_[0]),@_); |
1190 | # objectify is costly, so avoid it |
1191 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1192 | { |
1193 | ($self,$x,$y) = objectify(2,@_); |
1194 | } |
184f15d5 |
1195 | |
1196 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1197 | { |
1198 | # handle +-inf and NaN |
1199 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1200 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
1201 | return +1 if $x->{sign} eq '+inf'; |
1202 | return -1 if $x->{sign} eq '-inf'; |
1203 | return -1 if $y->{sign} eq '+inf'; |
1204 | return +1; |
1205 | } |
1206 | # check sign for speed first |
1207 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
1208 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
1209 | |
1210 | # shortcut |
12fc2493 |
1211 | my $xz = $MBI->_is_zero($x->{_n}); |
1212 | my $yz = $MBI->_is_zero($y->{_n}); |
184f15d5 |
1213 | return 0 if $xz && $yz; # 0 <=> 0 |
1214 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
1215 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
1216 | |
12fc2493 |
1217 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1218 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1219 | |
1220 | my $cmp = $MBI->_acmp($t,$u); # signs are equal |
1221 | $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse |
1222 | $cmp; |
184f15d5 |
1223 | } |
1224 | |
1225 | sub bacmp |
1226 | { |
7afd7a91 |
1227 | # compare two numbers (as unsigned) |
9b924220 |
1228 | |
7afd7a91 |
1229 | # set up parameters |
1230 | my ($self,$x,$y) = (ref($_[0]),@_); |
1231 | # objectify is costly, so avoid it |
1232 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1233 | { |
9b924220 |
1234 | ($self,$x,$y) = objectify(2,$class,@_); |
7afd7a91 |
1235 | } |
184f15d5 |
1236 | |
1237 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1238 | { |
1239 | # handle +-inf and NaN |
1240 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1241 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
7afd7a91 |
1242 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1243 | return -1; |
184f15d5 |
1244 | } |
1245 | |
12fc2493 |
1246 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1247 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1248 | $MBI->_acmp($t,$u); # ignore signs |
184f15d5 |
1249 | } |
1250 | |
1251 | ############################################################################## |
1252 | # output conversation |
1253 | |
7d341013 |
1254 | sub numify |
1255 | { |
1256 | # convert 17/8 => float (aka 2.125) |
b68b7ab1 |
1257 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
7d341013 |
1258 | |
1259 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc |
1260 | |
93c87d9d |
1261 | # N/1 => N |
b68b7ab1 |
1262 | my $neg = ''; $neg = '-' if $x->{sign} eq '-'; |
1263 | return $neg . $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); |
93c87d9d |
1264 | |
b68b7ab1 |
1265 | $x->_as_float()->numify() + 0.0; |
7d341013 |
1266 | } |
1267 | |
184f15d5 |
1268 | sub as_number |
1269 | { |
9b924220 |
1270 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
1271 | |
12fc2493 |
1272 | return Math::BigInt->new($x) if $x->{sign} !~ /^[+-]$/; # NaN, inf etc |
990fb837 |
1273 | |
12fc2493 |
1274 | my $u = Math::BigInt->bzero(); |
1275 | $u->{sign} = $x->{sign}; |
1276 | $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3 |
1277 | $u; |
184f15d5 |
1278 | } |
1279 | |
9b924220 |
1280 | sub as_bin |
1281 | { |
1282 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1283 | |
1284 | return $x unless $x->is_int(); |
1285 | |
1286 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1287 | $s . $MBI->_as_bin($x->{_n}); |
9b924220 |
1288 | } |
1289 | |
1290 | sub as_hex |
1291 | { |
1292 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1293 | |
1294 | return $x unless $x->is_int(); |
1295 | |
1296 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1297 | $s . $MBI->_as_hex($x->{_n}); |
9b924220 |
1298 | } |
1299 | |
b68b7ab1 |
1300 | ############################################################################## |
1301 | # import |
1302 | |
6de7f0cc |
1303 | sub import |
1304 | { |
1305 | my $self = shift; |
1306 | my $l = scalar @_; |
1307 | my $lib = ''; my @a; |
9b924220 |
1308 | $IMPORT++; |
1309 | |
6de7f0cc |
1310 | for ( my $i = 0; $i < $l ; $i++) |
1311 | { |
6de7f0cc |
1312 | if ( $_[$i] eq ':constant' ) |
1313 | { |
1314 | # this rest causes overlord er load to step in |
6de7f0cc |
1315 | overload::constant float => sub { $self->new(shift); }; |
1316 | } |
1317 | # elsif ($_[$i] eq 'upgrade') |
1318 | # { |
1319 | # # this causes upgrading |
b68b7ab1 |
1320 | # $upgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1321 | # $i++; |
1322 | # } |
1323 | elsif ($_[$i] eq 'downgrade') |
1324 | { |
1325 | # this causes downgrading |
b68b7ab1 |
1326 | $downgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1327 | $i++; |
1328 | } |
1329 | elsif ($_[$i] eq 'lib') |
1330 | { |
b68b7ab1 |
1331 | $lib = $_[$i+1] || ''; # default Calc |
6de7f0cc |
1332 | $i++; |
1333 | } |
1334 | elsif ($_[$i] eq 'with') |
1335 | { |
b68b7ab1 |
1336 | $MBI = $_[$i+1] || 'Math::BigInt::Calc'; # default Math::BigInt::Calc |
6de7f0cc |
1337 | $i++; |
1338 | } |
1339 | else |
1340 | { |
1341 | push @a, $_[$i]; |
1342 | } |
1343 | } |
b68b7ab1 |
1344 | require Math::BigInt; |
6de7f0cc |
1345 | |
b68b7ab1 |
1346 | # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still have GMP |
1347 | if ($lib ne '') |
1348 | { |
1349 | my @c = split /\s*,\s*/, $lib; |
1350 | foreach (@c) |
6de7f0cc |
1351 | { |
b68b7ab1 |
1352 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters |
6de7f0cc |
1353 | } |
b68b7ab1 |
1354 | # MBI already loaded, so feed it our lib arguments |
1355 | $MBI->import('lib' => $lib . join(",",@c), 'objectify'); |
93c87d9d |
1356 | } |
6de7f0cc |
1357 | |
12fc2493 |
1358 | $MBI = Math::BigFloat->config()->{lib}; |
b68b7ab1 |
1359 | |
1360 | # register us with MBI to get notified of future lib changes |
1361 | Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } ); |
9b924220 |
1362 | |
6de7f0cc |
1363 | # any non :constant stuff is handled by our parent, Exporter |
1364 | # even if @_ is empty, to give it a chance |
1365 | $self->SUPER::import(@a); # for subclasses |
1366 | $self->export_to_level(1,$self,@a); # need this, too |
1367 | } |
184f15d5 |
1368 | |
1369 | 1; |
1370 | |
1371 | __END__ |
1372 | |
1373 | =head1 NAME |
1374 | |
b68b7ab1 |
1375 | Math::BigRat - Arbitrary big rational numbers |
184f15d5 |
1376 | |
1377 | =head1 SYNOPSIS |
1378 | |
7d341013 |
1379 | use Math::BigRat; |
184f15d5 |
1380 | |
7afd7a91 |
1381 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
184f15d5 |
1382 | |
7d341013 |
1383 | print $x->bstr(),"\n"; |
1384 | print $x ** 2,"\n"; |
184f15d5 |
1385 | |
7afd7a91 |
1386 | my $y = Math::BigRat->new('inf'); |
1387 | print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; |
1388 | |
1389 | my $z = Math::BigRat->new(144); $z->bsqrt(); |
1390 | |
184f15d5 |
1391 | =head1 DESCRIPTION |
1392 | |
7d341013 |
1393 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
b68b7ab1 |
1394 | for arbitrary big rational numbers. |
184f15d5 |
1395 | |
1396 | =head2 MATH LIBRARY |
1397 | |
1398 | Math with the numbers is done (by default) by a module called |
1399 | Math::BigInt::Calc. This is equivalent to saying: |
1400 | |
1401 | use Math::BigRat lib => 'Calc'; |
1402 | |
1403 | You can change this by using: |
1404 | |
1405 | use Math::BigRat lib => 'BitVect'; |
1406 | |
1407 | The following would first try to find Math::BigInt::Foo, then |
1408 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
1409 | |
1410 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
1411 | |
1412 | Calc.pm uses as internal format an array of elements of some decimal base |
7d341013 |
1413 | (usually 1e7, but this might be different for some systems) with the least |
184f15d5 |
1414 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
1415 | significant bit first. Other modules might use even different means of |
1416 | representing the numbers. See the respective module documentation for further |
1417 | details. |
1418 | |
7d341013 |
1419 | Currently the following replacement libraries exist, search for them at CPAN: |
1420 | |
1421 | Math::BigInt::BitVect |
1422 | Math::BigInt::GMP |
1423 | Math::BigInt::Pari |
1424 | Math::BigInt::FastCalc |
1425 | |
184f15d5 |
1426 | =head1 METHODS |
1427 | |
7d341013 |
1428 | Any methods not listed here are dervied from Math::BigFloat (or |
6de7f0cc |
1429 | Math::BigInt), so make sure you check these two modules for further |
1430 | information. |
1431 | |
1432 | =head2 new() |
184f15d5 |
1433 | |
1434 | $x = Math::BigRat->new('1/3'); |
1435 | |
1436 | Create a new Math::BigRat object. Input can come in various forms: |
1437 | |
7d341013 |
1438 | $x = Math::BigRat->new(123); # scalars |
7afd7a91 |
1439 | $x = Math::BigRat->new('inf'); # infinity |
7d341013 |
1440 | $x = Math::BigRat->new('123.3'); # float |
184f15d5 |
1441 | $x = Math::BigRat->new('1/3'); # simple string |
1442 | $x = Math::BigRat->new('1 / 3'); # spaced |
1443 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
1444 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
1445 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
6de7f0cc |
1446 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
184f15d5 |
1447 | |
b68b7ab1 |
1448 | # You can also give D and N as different objects: |
1449 | $x = Math::BigRat->new( |
1450 | Math::BigInt->new(-123), |
1451 | Math::BigInt->new(7), |
1452 | ); # => -123/7 |
1453 | |
6de7f0cc |
1454 | =head2 numerator() |
184f15d5 |
1455 | |
1456 | $n = $x->numerator(); |
1457 | |
1458 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
1459 | |
6de7f0cc |
1460 | =head2 denominator() |
184f15d5 |
1461 | |
1462 | $d = $x->denominator(); |
1463 | |
1464 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
1465 | |
6de7f0cc |
1466 | =head2 parts() |
184f15d5 |
1467 | |
1468 | ($n,$d) = $x->parts(); |
1469 | |
1470 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
1471 | BigInts. |
1472 | |
b68b7ab1 |
1473 | =head2 as_int() |
6de7f0cc |
1474 | |
7d341013 |
1475 | $x = Math::BigRat->new('13/7'); |
b68b7ab1 |
1476 | print $x->as_int(),"\n"; # '1' |
1477 | |
1478 | Returns a copy of the object as BigInt, truncated to an integer. |
7d341013 |
1479 | |
b68b7ab1 |
1480 | C<as_number()> is an alias for C<as_int()>. |
1481 | |
1482 | =head2 as_hex() |
1483 | |
1484 | $x = Math::BigRat->new('13'); |
1485 | print $x->as_hex(),"\n"; # '0xd' |
1486 | |
1487 | Returns the BigRat as hexadecimal string. Works only for integers. |
1488 | |
1489 | =head2 as_bin() |
1490 | |
1491 | $x = Math::BigRat->new('13'); |
1492 | print $x->as_bin(),"\n"; # '0x1101' |
1493 | |
1494 | Returns the BigRat as binary string. Works only for integers. |
6de7f0cc |
1495 | |
a4e2b1c6 |
1496 | =head2 bfac() |
6de7f0cc |
1497 | |
a4e2b1c6 |
1498 | $x->bfac(); |
6de7f0cc |
1499 | |
a4e2b1c6 |
1500 | Calculates the factorial of $x. For instance: |
6de7f0cc |
1501 | |
a4e2b1c6 |
1502 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 |
1503 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 |
184f15d5 |
1504 | |
7d341013 |
1505 | Works currently only for integers. |
6de7f0cc |
1506 | |
a4e2b1c6 |
1507 | =head2 blog() |
6de7f0cc |
1508 | |
a4e2b1c6 |
1509 | Is not yet implemented. |
6de7f0cc |
1510 | |
a4e2b1c6 |
1511 | =head2 bround()/round()/bfround() |
6de7f0cc |
1512 | |
a4e2b1c6 |
1513 | Are not yet implemented. |
6de7f0cc |
1514 | |
990fb837 |
1515 | =head2 bmod() |
1516 | |
1517 | use Math::BigRat; |
1518 | my $x = Math::BigRat->new('7/4'); |
1519 | my $y = Math::BigRat->new('4/3'); |
1520 | print $x->bmod($y); |
1521 | |
1522 | Set $x to the remainder of the division of $x by $y. |
1523 | |
7d341013 |
1524 | =head2 is_one() |
1525 | |
1526 | print "$x is 1\n" if $x->is_one(); |
1527 | |
1528 | Return true if $x is exactly one, otherwise false. |
1529 | |
1530 | =head2 is_zero() |
1531 | |
1532 | print "$x is 0\n" if $x->is_zero(); |
1533 | |
1534 | Return true if $x is exactly zero, otherwise false. |
1535 | |
b68b7ab1 |
1536 | =head2 is_pos() |
7d341013 |
1537 | |
1538 | print "$x is >= 0\n" if $x->is_positive(); |
1539 | |
1540 | Return true if $x is positive (greater than or equal to zero), otherwise |
1541 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. |
1542 | |
b68b7ab1 |
1543 | C<is_positive()> is an alias for C<is_pos()>. |
1544 | |
1545 | =head2 is_neg() |
7d341013 |
1546 | |
1547 | print "$x is < 0\n" if $x->is_negative(); |
1548 | |
1549 | Return true if $x is negative (smaller than zero), otherwise false. Please |
1550 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. |
1551 | |
b68b7ab1 |
1552 | C<is_negative()> is an alias for C<is_neg()>. |
1553 | |
7d341013 |
1554 | =head2 is_int() |
1555 | |
1556 | print "$x is an integer\n" if $x->is_int(); |
1557 | |
1558 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise |
1559 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. |
1560 | |
1561 | =head2 is_odd() |
1562 | |
1563 | print "$x is odd\n" if $x->is_odd(); |
1564 | |
1565 | Return true if $x is odd, otherwise false. |
1566 | |
1567 | =head2 is_even() |
1568 | |
1569 | print "$x is even\n" if $x->is_even(); |
1570 | |
1571 | Return true if $x is even, otherwise false. |
1572 | |
1573 | =head2 bceil() |
1574 | |
1575 | $x->bceil(); |
1576 | |
1577 | Set $x to the next bigger integer value (e.g. truncate the number to integer |
1578 | and then increment it by one). |
1579 | |
1580 | =head2 bfloor() |
1581 | |
1582 | $x->bfloor(); |
1583 | |
1584 | Truncate $x to an integer value. |
6de7f0cc |
1585 | |
7afd7a91 |
1586 | =head2 bsqrt() |
1587 | |
1588 | $x->bsqrt(); |
1589 | |
1590 | Calculate the square root of $x. |
1591 | |
990fb837 |
1592 | =head2 config |
1593 | |
1594 | use Data::Dumper; |
1595 | |
1596 | print Dumper ( Math::BigRat->config() ); |
1597 | print Math::BigRat->config()->{lib},"\n"; |
1598 | |
1599 | Returns a hash containing the configuration, e.g. the version number, lib |
1600 | loaded etc. The following hash keys are currently filled in with the |
1601 | appropriate information. |
1602 | |
1603 | key RO/RW Description |
1604 | Example |
1605 | ============================================================ |
1606 | lib RO Name of the Math library |
1607 | Math::BigInt::Calc |
1608 | lib_version RO Version of 'lib' |
1609 | 0.30 |
1610 | class RO The class of config you just called |
1611 | Math::BigRat |
1612 | version RO version number of the class you used |
1613 | 0.10 |
1614 | upgrade RW To which class numbers are upgraded |
1615 | undef |
1616 | downgrade RW To which class numbers are downgraded |
1617 | undef |
1618 | precision RW Global precision |
1619 | undef |
1620 | accuracy RW Global accuracy |
1621 | undef |
1622 | round_mode RW Global round mode |
1623 | even |
1624 | div_scale RW Fallback acccuracy for div |
1625 | 40 |
1626 | trap_nan RW Trap creation of NaN (undef = no) |
1627 | undef |
1628 | trap_inf RW Trap creation of +inf/-inf (undef = no) |
1629 | undef |
1630 | |
1631 | By passing a reference to a hash you may set the configuration values. This |
1632 | works only for values that a marked with a C<RW> above, anything else is |
1633 | read-only. |
1634 | |
a4e2b1c6 |
1635 | =head1 BUGS |
6de7f0cc |
1636 | |
7d341013 |
1637 | Some things are not yet implemented, or only implemented half-way: |
1638 | |
1639 | =over 2 |
1640 | |
1641 | =item inf handling (partial) |
1642 | |
1643 | =item NaN handling (partial) |
1644 | |
1645 | =item rounding (not implemented except for bceil/bfloor) |
1646 | |
1647 | =item $x ** $y where $y is not an integer |
1648 | |
7afd7a91 |
1649 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) |
1650 | |
7d341013 |
1651 | =back |
184f15d5 |
1652 | |
1653 | =head1 LICENSE |
1654 | |
1655 | This program is free software; you may redistribute it and/or modify it under |
1656 | the same terms as Perl itself. |
1657 | |
1658 | =head1 SEE ALSO |
1659 | |
1660 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
1661 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
1662 | |
7d341013 |
1663 | See L<http://search.cpan.org/search?dist=bignum> for a way to use |
1664 | Math::BigRat. |
1665 | |
1666 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> |
1667 | may contain more documentation and examples as well as testcases. |
184f15d5 |
1668 | |
1669 | =head1 AUTHORS |
1670 | |
b68b7ab1 |
1671 | (C) by Tels L<http://bloodgate.com/> 2001 - 2005. |
184f15d5 |
1672 | |
1673 | =cut |