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 | |
b8884ce4 |
16 | # anythig older is untested, and unlikely to work |
17 | use 5.006002; |
184f15d5 |
18 | use strict; |
19 | |
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 | |
233f7bc0 |
24 | @ISA = qw(Math::BigFloat); |
184f15d5 |
25 | |
bce28014 |
26 | $VERSION = '0.18'; |
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'; |
184f15d5 |
64 | |
8f675a64 |
65 | sub isa |
66 | { |
67 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't |
68 | UNIVERSAL::isa(@_); |
69 | } |
70 | |
12fc2493 |
71 | ############################################################################## |
9b924220 |
72 | |
184f15d5 |
73 | sub _new_from_float |
74 | { |
7afd7a91 |
75 | # turn a single float input into a rational number (like '0.1') |
184f15d5 |
76 | my ($self,$f) = @_; |
77 | |
78 | return $self->bnan() if $f->is_nan(); |
9b924220 |
79 | return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/; |
184f15d5 |
80 | |
12fc2493 |
81 | $self->{_n} = $MBI->_copy( $f->{_m} ); # mantissa |
82 | $self->{_d} = $MBI->_one(); |
9b924220 |
83 | $self->{sign} = $f->{sign} || '+'; |
84 | if ($f->{_es} eq '-') |
184f15d5 |
85 | { |
86 | # something like Math::BigRat->new('0.1'); |
9b924220 |
87 | # 1 / 1 => 1/10 |
12fc2493 |
88 | $MBI->_lsft ( $self->{_d}, $f->{_e} ,10); |
184f15d5 |
89 | } |
90 | else |
91 | { |
92 | # something like Math::BigRat->new('10'); |
93 | # 1 / 1 => 10/1 |
12fc2493 |
94 | $MBI->_lsft ( $self->{_n}, $f->{_e} ,10) unless |
95 | $MBI->_is_zero($f->{_e}); |
184f15d5 |
96 | } |
184f15d5 |
97 | $self; |
98 | } |
99 | |
100 | sub new |
101 | { |
102 | # create a Math::BigRat |
103 | my $class = shift; |
104 | |
b68b7ab1 |
105 | my ($n,$d) = @_; |
184f15d5 |
106 | |
107 | my $self = { }; bless $self,$class; |
108 | |
b68b7ab1 |
109 | # input like (BigInt) or (BigFloat): |
6de7f0cc |
110 | if ((!defined $d) && (ref $n) && (!$n->isa('Math::BigRat'))) |
184f15d5 |
111 | { |
184f15d5 |
112 | if ($n->isa('Math::BigFloat')) |
113 | { |
7afd7a91 |
114 | $self->_new_from_float($n); |
184f15d5 |
115 | } |
116 | if ($n->isa('Math::BigInt')) |
117 | { |
990fb837 |
118 | # TODO: trap NaN, inf |
b68b7ab1 |
119 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N |
12fc2493 |
120 | $self->{_d} = $MBI->_one(); # d => 1 |
121 | $self->{sign} = $n->{sign}; |
8f675a64 |
122 | } |
123 | if ($n->isa('Math::BigInt::Lite')) |
124 | { |
990fb837 |
125 | # TODO: trap NaN, inf |
126 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; |
b68b7ab1 |
127 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = N |
12fc2493 |
128 | $self->{_d} = $MBI->_one(); # d => 1 |
184f15d5 |
129 | } |
12fc2493 |
130 | return $self->bnorm(); # normalize (120/1 => 12/10) |
184f15d5 |
131 | } |
b68b7ab1 |
132 | |
133 | # input like (BigInt,BigInt) or (BigLite,BigLite): |
134 | if (ref($d) && ref($n)) |
135 | { |
136 | # do N first (for $self->{sign}): |
137 | if ($n->isa('Math::BigInt')) |
138 | { |
139 | # TODO: trap NaN, inf |
140 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N |
141 | $self->{sign} = $n->{sign}; |
142 | } |
143 | elsif ($n->isa('Math::BigInt::Lite')) |
144 | { |
145 | # TODO: trap NaN, inf |
146 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; |
147 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = $n |
148 | } |
149 | else |
150 | { |
151 | require Carp; |
152 | Carp::croak(ref($n) . " is not a recognized object format for Math::BigRat->new"); |
153 | } |
154 | # now D: |
155 | if ($d->isa('Math::BigInt')) |
156 | { |
157 | # TODO: trap NaN, inf |
158 | $self->{_d} = $MBI->_copy($d->{value}); # "mantissa" = D |
159 | # +/+ or -/- => +, +/- or -/+ => - |
160 | $self->{sign} = $d->{sign} ne $self->{sign} ? '-' : '+'; |
161 | } |
162 | elsif ($d->isa('Math::BigInt::Lite')) |
163 | { |
164 | # TODO: trap NaN, inf |
165 | $self->{_d} = $MBI->_new(abs($$d)); # "mantissa" = D |
166 | my $ds = '+'; $ds = '-' if $$d < 0; |
167 | # +/+ or -/- => +, +/- or -/+ => - |
168 | $self->{sign} = $ds ne $self->{sign} ? '-' : '+'; |
169 | } |
170 | else |
171 | { |
172 | require Carp; |
173 | Carp::croak(ref($d) . " is not a recognized object format for Math::BigRat->new"); |
174 | } |
175 | return $self->bnorm(); # normalize (120/1 => 12/10) |
176 | } |
12fc2493 |
177 | return $n->copy() if ref $n; # already a BigRat |
184f15d5 |
178 | |
179 | if (!defined $n) |
180 | { |
12fc2493 |
181 | $self->{_n} = $MBI->_zero(); # undef => 0 |
182 | $self->{_d} = $MBI->_one(); |
184f15d5 |
183 | $self->{sign} = '+'; |
12fc2493 |
184 | return $self; |
184f15d5 |
185 | } |
12fc2493 |
186 | |
184f15d5 |
187 | # string input with / delimiter |
188 | if ($n =~ /\s*\/\s*/) |
189 | { |
990fb837 |
190 | return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
191 | return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid |
184f15d5 |
192 | ($n,$d) = split (/\//,$n); |
193 | # try as BigFloats first |
194 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) |
195 | { |
7d341013 |
196 | local $Math::BigFloat::accuracy = undef; |
197 | local $Math::BigFloat::precision = undef; |
9b924220 |
198 | |
12fc2493 |
199 | # one of them looks like a float |
9b924220 |
200 | my $nf = Math::BigFloat->new($n,undef,undef); |
990fb837 |
201 | $self->{sign} = '+'; |
202 | return $self->bnan() if $nf->is_nan(); |
233f7bc0 |
203 | |
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 | $self->{_d} = undef; |
b8884ce4 |
232 | if ($n =~ /^([+-]?)0*([0-9]+)\z/) # first part ok? |
12fc2493 |
233 | { |
234 | $self->{sign} = $1 || '+'; # no sign => '+' |
235 | $self->{_n} = $MBI->_new($2 || 0); |
236 | } |
237 | |
b8884ce4 |
238 | if ($d =~ /^([+-]?)0*([0-9]+)\z/) # second part ok? |
12fc2493 |
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 $n; |
233f7bc0 |
248 | |
12fc2493 |
249 | if ($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 $MBI directly |
b8884ce4 |
294 | if ($n =~ /^([+-]?)0*([0-9]+)\z/) |
12fc2493 |
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); |
233f7bc0 |
451 | # "$self" below will stringify the object, this blows up if $self is a |
452 | # partial object (happens under trap_nan), so fix it beforehand |
453 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; |
454 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; |
990fb837 |
455 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
456 | } |
12fc2493 |
457 | $self->{_n} = $MBI->_zero(); |
458 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
459 | } |
460 | |
461 | sub _binf |
462 | { |
7d341013 |
463 | # used by parent class bone() to initialize number to +inf/-inf |
184f15d5 |
464 | my $self = shift; |
990fb837 |
465 | |
466 | if ($_trap_inf) |
467 | { |
468 | require Carp; |
469 | my $class = ref($self); |
233f7bc0 |
470 | # "$self" below will stringify the object, this blows up if $self is a |
471 | # partial object (happens under trap_nan), so fix it beforehand |
472 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; |
473 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; |
990fb837 |
474 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); |
475 | } |
12fc2493 |
476 | $self->{_n} = $MBI->_zero(); |
477 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
478 | } |
479 | |
480 | sub _bone |
481 | { |
7d341013 |
482 | # used by parent class bone() to initialize number to +1/-1 |
184f15d5 |
483 | my $self = shift; |
12fc2493 |
484 | $self->{_n} = $MBI->_one(); |
485 | $self->{_d} = $MBI->_one(); |
184f15d5 |
486 | } |
487 | |
488 | sub _bzero |
489 | { |
990fb837 |
490 | # used by parent class bzero() to initialize number to 0 |
184f15d5 |
491 | my $self = shift; |
12fc2493 |
492 | $self->{_n} = $MBI->_zero(); |
493 | $self->{_d} = $MBI->_one(); |
184f15d5 |
494 | } |
495 | |
496 | ############################################################################## |
497 | # mul/add/div etc |
498 | |
499 | sub badd |
500 | { |
7afd7a91 |
501 | # add two rational numbers |
7d341013 |
502 | |
503 | # set up parameters |
504 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
505 | # objectify is costly, so avoid it |
506 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
507 | { |
508 | ($self,$x,$y,@r) = objectify(2,@_); |
509 | } |
184f15d5 |
510 | |
12fc2493 |
511 | # +inf + +inf => +inf, -inf + -inf => -inf |
512 | return $x->binf(substr($x->{sign},0,1)) |
513 | if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
184f15d5 |
514 | |
12fc2493 |
515 | # +inf + -inf or -inf + +inf => NaN |
516 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
184f15d5 |
517 | |
518 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
519 | # - + - = --------- = -- |
520 | # 4 3 4*3 12 |
521 | |
7d341013 |
522 | # we do not compute the gcd() here, but simple do: |
233f7bc0 |
523 | # 5 7 5*3 + 7*4 43 |
7d341013 |
524 | # - + - = --------- = -- |
525 | # 4 3 4*3 12 |
526 | |
12fc2493 |
527 | # and bnorm() will then take care of the rest |
184f15d5 |
528 | |
233f7bc0 |
529 | # 5 * 3 |
12fc2493 |
530 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
7d341013 |
531 | |
233f7bc0 |
532 | # 7 * 4 |
12fc2493 |
533 | my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} ); |
184f15d5 |
534 | |
233f7bc0 |
535 | # 5 * 3 + 7 * 4 |
12fc2493 |
536 | ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign}); |
184f15d5 |
537 | |
233f7bc0 |
538 | # 4 * 3 |
12fc2493 |
539 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
540 | |
233f7bc0 |
541 | # normalize result, and possible round |
7d341013 |
542 | $x->bnorm()->round(@r); |
184f15d5 |
543 | } |
544 | |
545 | sub bsub |
546 | { |
7afd7a91 |
547 | # subtract two rational numbers |
7d341013 |
548 | |
549 | # set up parameters |
550 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
551 | # objectify is costly, so avoid it |
552 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
553 | { |
554 | ($self,$x,$y,@r) = objectify(2,@_); |
555 | } |
184f15d5 |
556 | |
7afd7a91 |
557 | # flip sign of $x, call badd(), then flip sign of result |
558 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
559 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
560 | $x->badd($y,@r); # does norm and round |
7afd7a91 |
561 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
562 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
7afd7a91 |
563 | $x; |
184f15d5 |
564 | } |
565 | |
566 | sub bmul |
567 | { |
7afd7a91 |
568 | # multiply two rational numbers |
7d341013 |
569 | |
570 | # set up parameters |
571 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
572 | # objectify is costly, so avoid it |
573 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
574 | { |
575 | ($self,$x,$y,@r) = objectify(2,@_); |
576 | } |
184f15d5 |
577 | |
578 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
579 | |
580 | # inf handling |
581 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
582 | { |
583 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
584 | # result will always be +-inf: |
585 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
586 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
587 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
588 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
589 | return $x->binf('-'); |
590 | } |
591 | |
592 | # x== 0 # also: or y == 1 or y == -1 |
593 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
594 | |
12fc2493 |
595 | # XXX TODO: |
596 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
597 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
598 | |
12fc2493 |
599 | # 1 2 1 * 2 2 1 |
600 | # - * - = ----- = - = - |
601 | # 4 3 4 * 3 12 6 |
7d341013 |
602 | |
12fc2493 |
603 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); |
604 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
605 | |
606 | # compute new sign |
607 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
608 | |
7d341013 |
609 | $x->bnorm()->round(@r); |
184f15d5 |
610 | } |
611 | |
612 | sub bdiv |
613 | { |
614 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
615 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
7d341013 |
616 | |
617 | # set up parameters |
618 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
619 | # objectify is costly, so avoid it |
620 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
621 | { |
622 | ($self,$x,$y,@r) = objectify(2,@_); |
623 | } |
184f15d5 |
624 | |
625 | return $self->_div_inf($x,$y) |
626 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
627 | |
628 | # x== 0 # also: or y == 1 or y == -1 |
629 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
630 | |
12fc2493 |
631 | # XXX TODO: list context, upgrade |
632 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
633 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
634 | |
184f15d5 |
635 | # 1 1 1 3 |
636 | # - / - == - * - |
637 | # 4 3 4 1 |
7d341013 |
638 | |
12fc2493 |
639 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
640 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); |
184f15d5 |
641 | |
642 | # compute new sign |
643 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
644 | |
7d341013 |
645 | $x->bnorm()->round(@r); |
6de7f0cc |
646 | $x; |
184f15d5 |
647 | } |
648 | |
990fb837 |
649 | sub bmod |
650 | { |
651 | # compute "remainder" (in Perl way) of $x / $y |
652 | |
653 | # set up parameters |
654 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
655 | # objectify is costly, so avoid it |
656 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
657 | { |
658 | ($self,$x,$y,@r) = objectify(2,@_); |
659 | } |
660 | |
990fb837 |
661 | return $self->_div_inf($x,$y) |
662 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
663 | |
664 | return $x if $x->is_zero(); # 0 / 7 = 0, mod 0 |
665 | |
666 | # compute $x - $y * floor($x/$y), keeping the sign of $x |
667 | |
12fc2493 |
668 | # copy x to u, make it positive and then do a normal division ($u/$y) |
669 | my $u = bless { sign => '+' }, $self; |
670 | $u->{_n} = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d} ); |
671 | $u->{_d} = $MBI->_mul( $MBI->_copy($x->{_d}), $y->{_n} ); |
672 | |
673 | # compute floor(u) |
674 | if (! $MBI->_is_one($u->{_d})) |
990fb837 |
675 | { |
12fc2493 |
676 | $u->{_n} = $MBI->_div($u->{_n},$u->{_d}); # 22/7 => 3/1 w/ truncate |
677 | # no need to set $u->{_d} to 1, since below we set it to $y->{_d} anyway |
990fb837 |
678 | } |
679 | |
12fc2493 |
680 | # now compute $y * $u |
681 | $u->{_d} = $MBI->_copy($y->{_d}); # 1 * $y->{_d}, see floor above |
682 | $u->{_n} = $MBI->_mul($u->{_n},$y->{_n}); |
990fb837 |
683 | |
12fc2493 |
684 | my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive |
990fb837 |
685 | # compute $x - $u |
686 | $x->bsub($u); |
687 | $x->{sign} = $xsign; # put sign back |
688 | |
689 | $x->bnorm()->round(@r); |
990fb837 |
690 | } |
691 | |
184f15d5 |
692 | ############################################################################## |
a4e2b1c6 |
693 | # bdec/binc |
694 | |
695 | sub bdec |
696 | { |
697 | # decrement value (subtract 1) |
698 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
699 | |
700 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
701 | |
702 | if ($x->{sign} eq '-') |
703 | { |
12fc2493 |
704 | $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2 |
a4e2b1c6 |
705 | } |
706 | else |
707 | { |
12fc2493 |
708 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? |
a4e2b1c6 |
709 | { |
710 | # 1/3 -- => -2/3 |
12fc2493 |
711 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
712 | $x->{sign} = '-'; |
713 | } |
714 | else |
715 | { |
12fc2493 |
716 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 |
a4e2b1c6 |
717 | } |
718 | } |
719 | $x->bnorm()->round(@r); |
a4e2b1c6 |
720 | } |
721 | |
722 | sub binc |
723 | { |
724 | # increment value (add 1) |
725 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
726 | |
727 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
728 | |
729 | if ($x->{sign} eq '-') |
730 | { |
12fc2493 |
731 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) |
a4e2b1c6 |
732 | { |
733 | # -1/3 ++ => 2/3 (overflow at 0) |
12fc2493 |
734 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
735 | $x->{sign} = '+'; |
736 | } |
737 | else |
738 | { |
12fc2493 |
739 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 |
a4e2b1c6 |
740 | } |
741 | } |
742 | else |
743 | { |
12fc2493 |
744 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 |
a4e2b1c6 |
745 | } |
746 | $x->bnorm()->round(@r); |
a4e2b1c6 |
747 | } |
748 | |
749 | ############################################################################## |
184f15d5 |
750 | # is_foo methods (the rest is inherited) |
751 | |
752 | sub is_int |
753 | { |
754 | # return true if arg (BRAT or num_str) is an integer |
9b924220 |
755 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
756 | |
757 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
12fc2493 |
758 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer |
184f15d5 |
759 | 0; |
760 | } |
761 | |
762 | sub is_zero |
763 | { |
764 | # return true if arg (BRAT or num_str) is zero |
9b924220 |
765 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
766 | |
12fc2493 |
767 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); |
184f15d5 |
768 | 0; |
769 | } |
770 | |
771 | sub is_one |
772 | { |
773 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
9b924220 |
774 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
775 | |
9b924220 |
776 | my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; |
184f15d5 |
777 | return 1 |
12fc2493 |
778 | if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})); |
184f15d5 |
779 | 0; |
780 | } |
781 | |
782 | sub is_odd |
783 | { |
784 | # return true if arg (BFLOAT or num_str) is odd or false if even |
9b924220 |
785 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
786 | |
787 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
12fc2493 |
788 | ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1 |
184f15d5 |
789 | 0; |
790 | } |
791 | |
792 | sub is_even |
793 | { |
794 | # return true if arg (BINT or num_str) is even or false if odd |
9b924220 |
795 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
796 | |
797 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
12fc2493 |
798 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never |
799 | && $MBI->_is_even($x->{_n})); # but 4/1 is |
184f15d5 |
800 | 0; |
801 | } |
802 | |
184f15d5 |
803 | ############################################################################## |
804 | # parts() and friends |
805 | |
806 | sub numerator |
807 | { |
808 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
a4e2b1c6 |
809 | |
12fc2493 |
810 | # NaN, inf, -inf |
811 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
a4e2b1c6 |
812 | |
12fc2493 |
813 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; |
184f15d5 |
814 | $n; |
815 | } |
816 | |
817 | sub denominator |
818 | { |
819 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
820 | |
12fc2493 |
821 | # NaN |
822 | return Math::BigInt->new($x->{sign}) if $x->{sign} eq 'NaN'; |
823 | # inf, -inf |
824 | return Math::BigInt->bone() if $x->{sign} !~ /^[+-]$/; |
825 | |
826 | Math::BigInt->new($MBI->_str($x->{_d})); |
184f15d5 |
827 | } |
828 | |
829 | sub parts |
830 | { |
831 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
832 | |
12fc2493 |
833 | my $c = 'Math::BigInt'; |
834 | |
835 | return ($c->bnan(),$c->bnan()) if $x->{sign} eq 'NaN'; |
836 | return ($c->binf(),$c->binf()) if $x->{sign} eq '+inf'; |
837 | return ($c->binf('-'),$c->binf()) if $x->{sign} eq '-inf'; |
a4e2b1c6 |
838 | |
12fc2493 |
839 | my $n = $c->new( $MBI->_str($x->{_n})); |
184f15d5 |
840 | $n->{sign} = $x->{sign}; |
12fc2493 |
841 | my $d = $c->new( $MBI->_str($x->{_d})); |
842 | ($n,$d); |
184f15d5 |
843 | } |
844 | |
845 | sub length |
846 | { |
9b924220 |
847 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
848 | |
849 | return $nan unless $x->is_int(); |
12fc2493 |
850 | $MBI->_len($x->{_n}); # length(-123/1) => length(123) |
184f15d5 |
851 | } |
852 | |
853 | sub digit |
854 | { |
12fc2493 |
855 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); |
9b924220 |
856 | |
857 | return $nan unless $x->is_int(); |
12fc2493 |
858 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) |
184f15d5 |
859 | } |
860 | |
861 | ############################################################################## |
862 | # special calc routines |
863 | |
864 | sub bceil |
865 | { |
866 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
867 | |
12fc2493 |
868 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
869 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
870 | |
12fc2493 |
871 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
872 | $x->{_d} = $MBI->_one(); # d => 1 |
873 | $x->{_n} = $MBI->_inc($x->{_n}) |
874 | if $x->{sign} eq '+'; # +22/7 => 4/1 |
875 | $x->{sign} = '+' if $MBI->_is_zero($x->{_n}); # -0 => 0 |
184f15d5 |
876 | $x; |
877 | } |
878 | |
879 | sub bfloor |
880 | { |
881 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
882 | |
12fc2493 |
883 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
884 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
885 | |
12fc2493 |
886 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
887 | $x->{_d} = $MBI->_one(); # d => 1 |
888 | $x->{_n} = $MBI->_inc($x->{_n}) |
889 | if $x->{sign} eq '-'; # -22/7 => -4/1 |
184f15d5 |
890 | $x; |
891 | } |
892 | |
893 | sub bfac |
894 | { |
a4e2b1c6 |
895 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
896 | |
12fc2493 |
897 | # if $x is not an integer |
898 | if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d}))) |
a4e2b1c6 |
899 | { |
12fc2493 |
900 | return $x->bnan(); |
a4e2b1c6 |
901 | } |
12fc2493 |
902 | |
903 | $x->{_n} = $MBI->_fac($x->{_n}); |
904 | # since _d is 1, we don't need to reduce/norm the result |
905 | $x->round(@r); |
184f15d5 |
906 | } |
907 | |
908 | sub bpow |
909 | { |
7d341013 |
910 | # power ($x ** $y) |
911 | |
912 | # set up parameters |
913 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
914 | # objectify is costly, so avoid it |
915 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
916 | { |
917 | ($self,$x,$y,@r) = objectify(2,@_); |
918 | } |
184f15d5 |
919 | |
920 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
921 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
922 | return $x->bone(@r) if $y->is_zero(); |
923 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
12fc2493 |
924 | |
925 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) |
184f15d5 |
926 | { |
927 | # if $x == -1 and odd/even y => +1/-1 |
928 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
929 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
930 | } |
931 | # 1 ** -y => 1 / (1 ** |y|) |
932 | # so do test for negative $y after above's clause |
12fc2493 |
933 | |
184f15d5 |
934 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
935 | |
a4e2b1c6 |
936 | # shortcut y/1 (and/or x/1) |
12fc2493 |
937 | if ($MBI->_is_one($y->{_d})) |
a4e2b1c6 |
938 | { |
939 | # shortcut for x/1 and y/1 |
12fc2493 |
940 | if ($MBI->_is_one($x->{_d})) |
a4e2b1c6 |
941 | { |
12fc2493 |
942 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
a4e2b1c6 |
943 | if ($y->{sign} eq '-') |
944 | { |
945 | # 0.2 ** -3 => 1/(0.2 ** 3) |
946 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
947 | } |
948 | # correct sign; + ** + => + |
949 | if ($x->{sign} eq '-') |
950 | { |
951 | # - * - => +, - * - * - => - |
12fc2493 |
952 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
953 | } |
954 | return $x->round(@r); |
955 | } |
956 | # x/z ** y/1 |
12fc2493 |
957 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
958 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); |
a4e2b1c6 |
959 | if ($y->{sign} eq '-') |
960 | { |
961 | # 0.2 ** -3 => 1/(0.2 ** 3) |
962 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
963 | } |
964 | # correct sign; + ** + => + |
965 | if ($x->{sign} eq '-') |
966 | { |
967 | # - * - => +, - * - * - => - |
12fc2493 |
968 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
969 | } |
970 | return $x->round(@r); |
971 | } |
972 | |
973 | # regular calculation (this is wrong for d/e ** f/g) |
12fc2493 |
974 | my $pow2 = $self->bone(); |
975 | my $y1 = $MBI->_div ( $MBI->_copy($y->{_n}), $y->{_d}); |
976 | my $two = $MBI->_two(); |
977 | |
978 | while (!$MBI->_is_one($y1)) |
184f15d5 |
979 | { |
12fc2493 |
980 | $pow2->bmul($x) if $MBI->_is_odd($y1); |
981 | $MBI->_div($y1, $two); |
184f15d5 |
982 | $x->bmul($x); |
983 | } |
984 | $x->bmul($pow2) unless $pow2->is_one(); |
985 | # n ** -x => 1/n ** x |
986 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; |
7d341013 |
987 | $x->bnorm()->round(@r); |
184f15d5 |
988 | } |
989 | |
990 | sub blog |
991 | { |
7afd7a91 |
992 | # set up parameters |
993 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
994 | |
995 | # objectify is costly, so avoid it |
996 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
997 | { |
9b924220 |
998 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
7afd7a91 |
999 | } |
1000 | |
9b924220 |
1001 | # blog(1,Y) => 0 |
1002 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; |
1003 | |
7afd7a91 |
1004 | # $x <= 0 => NaN |
1005 | return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; |
1006 | |
1007 | if ($x->is_int() && $y->is_int()) |
1008 | { |
1009 | return $self->new($x->as_number()->blog($y->as_number(),@r)); |
1010 | } |
1011 | |
9b924220 |
1012 | # do it with floats |
1013 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); |
1014 | } |
1015 | |
12fc2493 |
1016 | sub _float_from_part |
1017 | { |
1018 | my $x = shift; |
1019 | |
1020 | my $f = Math::BigFloat->bzero(); |
1021 | $f->{_m} = $MBI->_copy($x); |
1022 | $f->{_e} = $MBI->_zero(); |
1023 | |
1024 | $f; |
1025 | } |
1026 | |
9b924220 |
1027 | sub _as_float |
1028 | { |
1029 | my $x = shift; |
1030 | |
1031 | local $Math::BigFloat::upgrade = undef; |
1032 | local $Math::BigFloat::accuracy = undef; |
1033 | local $Math::BigFloat::precision = undef; |
1034 | # 22/7 => 3.142857143.. |
12fc2493 |
1035 | |
1036 | my $a = $x->accuracy() || 0; |
1037 | if ($a != 0 || !$MBI->_is_one($x->{_d})) |
1038 | { |
1039 | # n/d |
1040 | return Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy()); |
1041 | } |
1042 | # just n |
1043 | Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n})); |
7afd7a91 |
1044 | } |
1045 | |
1046 | sub broot |
1047 | { |
1048 | # set up parameters |
1049 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1050 | # objectify is costly, so avoid it |
1051 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1052 | { |
1053 | ($self,$x,$y,@r) = objectify(2,@_); |
1054 | } |
1055 | |
1056 | if ($x->is_int() && $y->is_int()) |
1057 | { |
1058 | return $self->new($x->as_number()->broot($y->as_number(),@r)); |
1059 | } |
9b924220 |
1060 | |
1061 | # do it with floats |
1062 | $x->_new_from_float( $x->_as_float()->broot($y,@r) ); |
7afd7a91 |
1063 | } |
1064 | |
1065 | sub bmodpow |
1066 | { |
1067 | # set up parameters |
1068 | my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); |
1069 | # objectify is costly, so avoid it |
1070 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1071 | { |
1072 | ($self,$x,$y,$m,@r) = objectify(3,@_); |
1073 | } |
1074 | |
1075 | # $x or $y or $m are NaN or +-inf => NaN |
1076 | return $x->bnan() |
1077 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || |
1078 | $m->{sign} !~ /^[+-]$/; |
1079 | |
1080 | if ($x->is_int() && $y->is_int() && $m->is_int()) |
1081 | { |
1082 | return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); |
1083 | } |
1084 | |
1085 | warn ("bmodpow() not fully implemented"); |
1086 | $x->bnan(); |
1087 | } |
1088 | |
1089 | sub bmodinv |
1090 | { |
1091 | # set up parameters |
1092 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1093 | # objectify is costly, so avoid it |
1094 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1095 | { |
1096 | ($self,$x,$y,@r) = objectify(2,@_); |
1097 | } |
1098 | |
1099 | # $x or $y are NaN or +-inf => NaN |
1100 | return $x->bnan() |
1101 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; |
1102 | |
1103 | if ($x->is_int() && $y->is_int()) |
1104 | { |
1105 | return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); |
1106 | } |
1107 | |
1108 | warn ("bmodinv() not fully implemented"); |
1109 | $x->bnan(); |
184f15d5 |
1110 | } |
1111 | |
1112 | sub bsqrt |
1113 | { |
990fb837 |
1114 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1115 | |
1116 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 |
1117 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf |
1118 | return $x->round(@r) if $x->is_zero() || $x->is_one(); |
1119 | |
1120 | local $Math::BigFloat::upgrade = undef; |
1121 | local $Math::BigFloat::downgrade = undef; |
1122 | local $Math::BigFloat::precision = undef; |
1123 | local $Math::BigFloat::accuracy = undef; |
1124 | local $Math::BigInt::upgrade = undef; |
1125 | local $Math::BigInt::precision = undef; |
1126 | local $Math::BigInt::accuracy = undef; |
9b924220 |
1127 | |
12fc2493 |
1128 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); |
1129 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); |
1130 | |
1131 | # XXX TODO: we probably can optimze this: |
184f15d5 |
1132 | |
990fb837 |
1133 | # if sqrt(D) was not integer |
9b924220 |
1134 | if ($x->{_d}->{_es} ne '+') |
990fb837 |
1135 | { |
9b924220 |
1136 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 |
12fc2493 |
1137 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 |
990fb837 |
1138 | } |
1139 | # if sqrt(N) was not integer |
9b924220 |
1140 | if ($x->{_n}->{_es} ne '+') |
990fb837 |
1141 | { |
9b924220 |
1142 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 |
12fc2493 |
1143 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 |
990fb837 |
1144 | } |
12fc2493 |
1145 | |
990fb837 |
1146 | # convert parts to $MBI again |
12fc2493 |
1147 | $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10) |
1148 | if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY'; |
1149 | $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10) |
1150 | if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY'; |
1151 | |
990fb837 |
1152 | $x->bnorm()->round(@r); |
184f15d5 |
1153 | } |
1154 | |
1155 | sub blsft |
1156 | { |
9b924220 |
1157 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1158 | |
9b924220 |
1159 | $b = 2 unless defined $b; |
1160 | $b = $self->new($b) unless ref ($b); |
1161 | $x->bmul( $b->copy()->bpow($y), @r); |
184f15d5 |
1162 | $x; |
1163 | } |
1164 | |
1165 | sub brsft |
1166 | { |
12fc2493 |
1167 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1168 | |
9b924220 |
1169 | $b = 2 unless defined $b; |
1170 | $b = $self->new($b) unless ref ($b); |
1171 | $x->bdiv( $b->copy()->bpow($y), @r); |
184f15d5 |
1172 | $x; |
1173 | } |
1174 | |
1175 | ############################################################################## |
1176 | # round |
1177 | |
1178 | sub round |
1179 | { |
1180 | $_[0]; |
1181 | } |
1182 | |
1183 | sub bround |
1184 | { |
1185 | $_[0]; |
1186 | } |
1187 | |
1188 | sub bfround |
1189 | { |
1190 | $_[0]; |
1191 | } |
1192 | |
1193 | ############################################################################## |
1194 | # comparing |
1195 | |
1196 | sub bcmp |
1197 | { |
7afd7a91 |
1198 | # compare two signed numbers |
1199 | |
1200 | # set up parameters |
1201 | my ($self,$x,$y) = (ref($_[0]),@_); |
1202 | # objectify is costly, so avoid it |
1203 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1204 | { |
1205 | ($self,$x,$y) = objectify(2,@_); |
1206 | } |
184f15d5 |
1207 | |
1208 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1209 | { |
1210 | # handle +-inf and NaN |
1211 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1212 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
1213 | return +1 if $x->{sign} eq '+inf'; |
1214 | return -1 if $x->{sign} eq '-inf'; |
1215 | return -1 if $y->{sign} eq '+inf'; |
1216 | return +1; |
1217 | } |
1218 | # check sign for speed first |
1219 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
1220 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
1221 | |
1222 | # shortcut |
12fc2493 |
1223 | my $xz = $MBI->_is_zero($x->{_n}); |
1224 | my $yz = $MBI->_is_zero($y->{_n}); |
184f15d5 |
1225 | return 0 if $xz && $yz; # 0 <=> 0 |
1226 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
1227 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
1228 | |
12fc2493 |
1229 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1230 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1231 | |
1232 | my $cmp = $MBI->_acmp($t,$u); # signs are equal |
1233 | $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse |
1234 | $cmp; |
184f15d5 |
1235 | } |
1236 | |
1237 | sub bacmp |
1238 | { |
7afd7a91 |
1239 | # compare two numbers (as unsigned) |
9b924220 |
1240 | |
7afd7a91 |
1241 | # set up parameters |
1242 | my ($self,$x,$y) = (ref($_[0]),@_); |
1243 | # objectify is costly, so avoid it |
1244 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1245 | { |
9b924220 |
1246 | ($self,$x,$y) = objectify(2,$class,@_); |
7afd7a91 |
1247 | } |
184f15d5 |
1248 | |
1249 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1250 | { |
1251 | # handle +-inf and NaN |
1252 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1253 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
7afd7a91 |
1254 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1255 | return -1; |
184f15d5 |
1256 | } |
1257 | |
12fc2493 |
1258 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1259 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1260 | $MBI->_acmp($t,$u); # ignore signs |
184f15d5 |
1261 | } |
1262 | |
1263 | ############################################################################## |
1264 | # output conversation |
1265 | |
7d341013 |
1266 | sub numify |
1267 | { |
1268 | # convert 17/8 => float (aka 2.125) |
b68b7ab1 |
1269 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
7d341013 |
1270 | |
1271 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc |
1272 | |
93c87d9d |
1273 | # N/1 => N |
b68b7ab1 |
1274 | my $neg = ''; $neg = '-' if $x->{sign} eq '-'; |
1275 | return $neg . $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); |
93c87d9d |
1276 | |
b68b7ab1 |
1277 | $x->_as_float()->numify() + 0.0; |
7d341013 |
1278 | } |
1279 | |
184f15d5 |
1280 | sub as_number |
1281 | { |
9b924220 |
1282 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
1283 | |
12fc2493 |
1284 | return Math::BigInt->new($x) if $x->{sign} !~ /^[+-]$/; # NaN, inf etc |
990fb837 |
1285 | |
12fc2493 |
1286 | my $u = Math::BigInt->bzero(); |
1287 | $u->{sign} = $x->{sign}; |
1288 | $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3 |
1289 | $u; |
184f15d5 |
1290 | } |
1291 | |
9b924220 |
1292 | sub as_bin |
1293 | { |
1294 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1295 | |
1296 | return $x unless $x->is_int(); |
1297 | |
1298 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1299 | $s . $MBI->_as_bin($x->{_n}); |
9b924220 |
1300 | } |
1301 | |
1302 | sub as_hex |
1303 | { |
1304 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1305 | |
1306 | return $x unless $x->is_int(); |
1307 | |
1308 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1309 | $s . $MBI->_as_hex($x->{_n}); |
9b924220 |
1310 | } |
1311 | |
b8884ce4 |
1312 | sub as_oct |
1313 | { |
1314 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1315 | |
1316 | return $x unless $x->is_int(); |
1317 | |
1318 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
1319 | $s . $MBI->_as_oct($x->{_n}); |
1320 | } |
1321 | |
1322 | ############################################################################## |
1323 | |
1324 | sub from_hex |
1325 | { |
1326 | my $class = shift; |
1327 | |
1328 | $class->new(@_); |
1329 | } |
1330 | |
1331 | sub from_bin |
1332 | { |
1333 | my $class = shift; |
1334 | |
1335 | $class->new(@_); |
1336 | } |
1337 | |
1338 | sub from_oct |
1339 | { |
1340 | my $class = shift; |
1341 | |
1342 | my @parts; |
1343 | for my $c (@_) |
1344 | { |
1345 | push @parts, Math::BigInt->from_oct($c); |
1346 | } |
1347 | $class->new ( @parts ); |
1348 | } |
1349 | |
b68b7ab1 |
1350 | ############################################################################## |
1351 | # import |
1352 | |
6de7f0cc |
1353 | sub import |
1354 | { |
1355 | my $self = shift; |
1356 | my $l = scalar @_; |
1357 | my $lib = ''; my @a; |
b8884ce4 |
1358 | my $try = 'try'; |
9b924220 |
1359 | |
6de7f0cc |
1360 | for ( my $i = 0; $i < $l ; $i++) |
1361 | { |
6de7f0cc |
1362 | if ( $_[$i] eq ':constant' ) |
1363 | { |
1364 | # this rest causes overlord er load to step in |
6de7f0cc |
1365 | overload::constant float => sub { $self->new(shift); }; |
1366 | } |
1367 | # elsif ($_[$i] eq 'upgrade') |
1368 | # { |
1369 | # # this causes upgrading |
b68b7ab1 |
1370 | # $upgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1371 | # $i++; |
1372 | # } |
1373 | elsif ($_[$i] eq 'downgrade') |
1374 | { |
1375 | # this causes downgrading |
b68b7ab1 |
1376 | $downgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1377 | $i++; |
1378 | } |
b8884ce4 |
1379 | elsif ($_[$i] =~ /^(lib|try|only)\z/) |
6de7f0cc |
1380 | { |
b68b7ab1 |
1381 | $lib = $_[$i+1] || ''; # default Calc |
b8884ce4 |
1382 | $try = $1; # lib, try or only |
6de7f0cc |
1383 | $i++; |
1384 | } |
1385 | elsif ($_[$i] eq 'with') |
1386 | { |
233f7bc0 |
1387 | # this argument is no longer used |
1388 | #$MBI = $_[$i+1] || 'Math::BigInt::Calc'; # default Math::BigInt::Calc |
6de7f0cc |
1389 | $i++; |
1390 | } |
1391 | else |
1392 | { |
1393 | push @a, $_[$i]; |
1394 | } |
1395 | } |
b68b7ab1 |
1396 | require Math::BigInt; |
6de7f0cc |
1397 | |
b68b7ab1 |
1398 | # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still have GMP |
1399 | if ($lib ne '') |
1400 | { |
1401 | my @c = split /\s*,\s*/, $lib; |
1402 | foreach (@c) |
6de7f0cc |
1403 | { |
b68b7ab1 |
1404 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters |
6de7f0cc |
1405 | } |
233f7bc0 |
1406 | $lib = join(",", @c); |
93c87d9d |
1407 | } |
233f7bc0 |
1408 | my @import = ('objectify'); |
b8884ce4 |
1409 | push @import, $try => $lib if $lib ne ''; |
233f7bc0 |
1410 | |
1411 | # MBI already loaded, so feed it our lib arguments |
1412 | Math::BigInt->import( @import ); |
6de7f0cc |
1413 | |
12fc2493 |
1414 | $MBI = Math::BigFloat->config()->{lib}; |
b68b7ab1 |
1415 | |
1416 | # register us with MBI to get notified of future lib changes |
1417 | Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } ); |
9b924220 |
1418 | |
233f7bc0 |
1419 | # any non :constant stuff is handled by our parent, Exporter (loaded |
1420 | # by Math::BigFloat, even if @_ is empty, to give it a chance |
6de7f0cc |
1421 | $self->SUPER::import(@a); # for subclasses |
1422 | $self->export_to_level(1,$self,@a); # need this, too |
1423 | } |
184f15d5 |
1424 | |
1425 | 1; |
1426 | |
1427 | __END__ |
1428 | |
1429 | =head1 NAME |
1430 | |
b68b7ab1 |
1431 | Math::BigRat - Arbitrary big rational numbers |
184f15d5 |
1432 | |
1433 | =head1 SYNOPSIS |
1434 | |
7d341013 |
1435 | use Math::BigRat; |
184f15d5 |
1436 | |
7afd7a91 |
1437 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
184f15d5 |
1438 | |
7d341013 |
1439 | print $x->bstr(),"\n"; |
1440 | print $x ** 2,"\n"; |
184f15d5 |
1441 | |
7afd7a91 |
1442 | my $y = Math::BigRat->new('inf'); |
1443 | print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; |
1444 | |
1445 | my $z = Math::BigRat->new(144); $z->bsqrt(); |
1446 | |
184f15d5 |
1447 | =head1 DESCRIPTION |
1448 | |
7d341013 |
1449 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
b68b7ab1 |
1450 | for arbitrary big rational numbers. |
184f15d5 |
1451 | |
1452 | =head2 MATH LIBRARY |
1453 | |
b8884ce4 |
1454 | You can change the underlying module that does the low-level |
1455 | math operations by using: |
184f15d5 |
1456 | |
b8884ce4 |
1457 | use Math::BigRat try => 'GMP'; |
184f15d5 |
1458 | |
b8884ce4 |
1459 | Note: This needs Math::BigInt::GMP installed. |
184f15d5 |
1460 | |
1461 | The following would first try to find Math::BigInt::Foo, then |
1462 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
1463 | |
b8884ce4 |
1464 | use Math::BigRat try => 'Foo,Math::BigInt::Bar'; |
184f15d5 |
1465 | |
b8884ce4 |
1466 | If you want to get warned when the fallback occurs, replace "try" with |
1467 | "lib": |
184f15d5 |
1468 | |
b8884ce4 |
1469 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
7d341013 |
1470 | |
b8884ce4 |
1471 | If you want the code to die instead, replace "try" with |
1472 | "only": |
1473 | |
1474 | use Math::BigRat only => 'Foo,Math::BigInt::Bar'; |
7d341013 |
1475 | |
184f15d5 |
1476 | =head1 METHODS |
1477 | |
3c4b39be |
1478 | Any methods not listed here are derived from Math::BigFloat (or |
6de7f0cc |
1479 | Math::BigInt), so make sure you check these two modules for further |
1480 | information. |
1481 | |
1482 | =head2 new() |
184f15d5 |
1483 | |
1484 | $x = Math::BigRat->new('1/3'); |
1485 | |
1486 | Create a new Math::BigRat object. Input can come in various forms: |
1487 | |
7d341013 |
1488 | $x = Math::BigRat->new(123); # scalars |
7afd7a91 |
1489 | $x = Math::BigRat->new('inf'); # infinity |
7d341013 |
1490 | $x = Math::BigRat->new('123.3'); # float |
184f15d5 |
1491 | $x = Math::BigRat->new('1/3'); # simple string |
1492 | $x = Math::BigRat->new('1 / 3'); # spaced |
1493 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
1494 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
1495 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
6de7f0cc |
1496 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
184f15d5 |
1497 | |
b68b7ab1 |
1498 | # You can also give D and N as different objects: |
1499 | $x = Math::BigRat->new( |
1500 | Math::BigInt->new(-123), |
1501 | Math::BigInt->new(7), |
1502 | ); # => -123/7 |
1503 | |
6de7f0cc |
1504 | =head2 numerator() |
184f15d5 |
1505 | |
1506 | $n = $x->numerator(); |
1507 | |
1508 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
1509 | |
6de7f0cc |
1510 | =head2 denominator() |
184f15d5 |
1511 | |
1512 | $d = $x->denominator(); |
1513 | |
1514 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
1515 | |
6de7f0cc |
1516 | =head2 parts() |
184f15d5 |
1517 | |
1518 | ($n,$d) = $x->parts(); |
1519 | |
1520 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
1521 | BigInts. |
1522 | |
b8884ce4 |
1523 | =head2 numify() |
1524 | |
1525 | my $y = $x->numify(); |
1526 | |
1527 | Returns the object as a scalar. This will lose some data if the object |
1528 | cannot be represented by a normal Perl scalar (integer or float), so |
1529 | use as_int() instead. |
1530 | |
1531 | This routine is automatically used whenever a scalar is required: |
1532 | |
1533 | my $x = Math::BigRat->new('3/1'); |
1534 | @array = (1,2,3); |
1535 | $y = $array[$x]; # set $y to 3 |
1536 | |
1537 | =head2 as_int()/as_number() |
6de7f0cc |
1538 | |
7d341013 |
1539 | $x = Math::BigRat->new('13/7'); |
b68b7ab1 |
1540 | print $x->as_int(),"\n"; # '1' |
1541 | |
1542 | Returns a copy of the object as BigInt, truncated to an integer. |
7d341013 |
1543 | |
b68b7ab1 |
1544 | C<as_number()> is an alias for C<as_int()>. |
1545 | |
1546 | =head2 as_hex() |
1547 | |
1548 | $x = Math::BigRat->new('13'); |
1549 | print $x->as_hex(),"\n"; # '0xd' |
1550 | |
1551 | Returns the BigRat as hexadecimal string. Works only for integers. |
1552 | |
1553 | =head2 as_bin() |
1554 | |
1555 | $x = Math::BigRat->new('13'); |
1556 | print $x->as_bin(),"\n"; # '0x1101' |
1557 | |
1558 | Returns the BigRat as binary string. Works only for integers. |
6de7f0cc |
1559 | |
b8884ce4 |
1560 | =head2 as_oct() |
1561 | |
1562 | $x = Math::BigRat->new('13'); |
1563 | print $x->as_oct(),"\n"; # '015' |
1564 | |
1565 | Returns the BigRat as octal string. Works only for integers. |
1566 | |
1567 | =head2 from_hex()/from_bin()/from_oct() |
1568 | |
1569 | my $h = Math::BigRat->from_hex('0x10'); |
1570 | my $b = Math::BigRat->from_bin('0b10000000'); |
1571 | my $o = Math::BigRat->from_oct('020'); |
1572 | |
1573 | Create a BigRat from an hexadecimal, binary or octal number |
1574 | in string form. |
1575 | |
1576 | =head2 length() |
1577 | |
1578 | $len = $x->length(); |
1579 | |
1580 | Return the length of $x in digitis for integer values. |
1581 | |
1582 | =head2 digit() |
1583 | |
1584 | print Math::BigRat->new('123/1')->digit(1); # 1 |
1585 | print Math::BigRat->new('123/1')->digit(-1); # 3 |
1586 | |
1587 | Return the N'ths digit from X when X is an integer value. |
1588 | |
1589 | =head2 bnorm() |
1590 | |
1591 | $x->bnorm(); |
1592 | |
1593 | Reduce the number to the shortest form. This routine is called |
1594 | automatically whenever it is needed. |
1595 | |
a4e2b1c6 |
1596 | =head2 bfac() |
6de7f0cc |
1597 | |
a4e2b1c6 |
1598 | $x->bfac(); |
6de7f0cc |
1599 | |
a4e2b1c6 |
1600 | Calculates the factorial of $x. For instance: |
6de7f0cc |
1601 | |
a4e2b1c6 |
1602 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 |
1603 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 |
184f15d5 |
1604 | |
7d341013 |
1605 | Works currently only for integers. |
6de7f0cc |
1606 | |
a4e2b1c6 |
1607 | =head2 blog() |
6de7f0cc |
1608 | |
a4e2b1c6 |
1609 | Is not yet implemented. |
6de7f0cc |
1610 | |
a4e2b1c6 |
1611 | =head2 bround()/round()/bfround() |
6de7f0cc |
1612 | |
a4e2b1c6 |
1613 | Are not yet implemented. |
6de7f0cc |
1614 | |
990fb837 |
1615 | =head2 bmod() |
1616 | |
1617 | use Math::BigRat; |
1618 | my $x = Math::BigRat->new('7/4'); |
1619 | my $y = Math::BigRat->new('4/3'); |
1620 | print $x->bmod($y); |
1621 | |
1622 | Set $x to the remainder of the division of $x by $y. |
1623 | |
b8884ce4 |
1624 | =head2 bneg() |
1625 | |
1626 | $x->bneg(); |
1627 | |
1628 | Used to negate the object in-place. |
1629 | |
7d341013 |
1630 | =head2 is_one() |
1631 | |
1632 | print "$x is 1\n" if $x->is_one(); |
1633 | |
1634 | Return true if $x is exactly one, otherwise false. |
1635 | |
1636 | =head2 is_zero() |
1637 | |
1638 | print "$x is 0\n" if $x->is_zero(); |
1639 | |
1640 | Return true if $x is exactly zero, otherwise false. |
1641 | |
b8884ce4 |
1642 | =head2 is_pos()/is_positive() |
7d341013 |
1643 | |
1644 | print "$x is >= 0\n" if $x->is_positive(); |
1645 | |
1646 | Return true if $x is positive (greater than or equal to zero), otherwise |
1647 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. |
1648 | |
b68b7ab1 |
1649 | C<is_positive()> is an alias for C<is_pos()>. |
1650 | |
b8884ce4 |
1651 | =head2 is_neg()/is_negative() |
7d341013 |
1652 | |
1653 | print "$x is < 0\n" if $x->is_negative(); |
1654 | |
1655 | Return true if $x is negative (smaller than zero), otherwise false. Please |
1656 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. |
1657 | |
b68b7ab1 |
1658 | C<is_negative()> is an alias for C<is_neg()>. |
1659 | |
7d341013 |
1660 | =head2 is_int() |
1661 | |
1662 | print "$x is an integer\n" if $x->is_int(); |
1663 | |
1664 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise |
1665 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. |
1666 | |
1667 | =head2 is_odd() |
1668 | |
1669 | print "$x is odd\n" if $x->is_odd(); |
1670 | |
1671 | Return true if $x is odd, otherwise false. |
1672 | |
1673 | =head2 is_even() |
1674 | |
1675 | print "$x is even\n" if $x->is_even(); |
1676 | |
1677 | Return true if $x is even, otherwise false. |
1678 | |
1679 | =head2 bceil() |
1680 | |
1681 | $x->bceil(); |
1682 | |
1683 | Set $x to the next bigger integer value (e.g. truncate the number to integer |
1684 | and then increment it by one). |
1685 | |
1686 | =head2 bfloor() |
1687 | |
1688 | $x->bfloor(); |
1689 | |
1690 | Truncate $x to an integer value. |
6de7f0cc |
1691 | |
7afd7a91 |
1692 | =head2 bsqrt() |
1693 | |
1694 | $x->bsqrt(); |
1695 | |
1696 | Calculate the square root of $x. |
1697 | |
b8884ce4 |
1698 | =head2 broot() |
1699 | |
1700 | $x->broot($n); |
1701 | |
1702 | Calculate the N'th root of $x. |
1703 | |
1704 | =head2 badd()/bmul()/bsub()/bdiv()/bdec()/binc() |
1705 | |
1706 | Please see the documentation in L<Math::BigInt>. |
1707 | |
1708 | =head2 copy() |
1709 | |
1710 | my $z = $x->copy(); |
1711 | |
1712 | Makes a deep copy of the object. |
1713 | |
1714 | Please see the documentation in L<Math::BigInt> for further details. |
1715 | |
1716 | =head2 bstr()/bsstr() |
1717 | |
1718 | my $x = Math::BigInt->new('8/4'); |
1719 | print $x->bstr(),"\n"; # prints 1/2 |
1720 | print $x->bsstr(),"\n"; # prints 1/2 |
1721 | |
1722 | Return a string representating this object. |
1723 | |
1724 | =head2 bacmp()/bcmp() |
1725 | |
1726 | Used to compare numbers. |
1727 | |
1728 | Please see the documentation in L<Math::BigInt> for further details. |
1729 | |
1730 | =head2 blsft()/brsft() |
1731 | |
1732 | Used to shift numbers left/right. |
1733 | |
1734 | Please see the documentation in L<Math::BigInt> for further details. |
1735 | |
1736 | =head2 bpow() |
1737 | |
1738 | $x->bpow($y); |
1739 | |
1740 | Compute $x ** $y. |
1741 | |
1742 | Please see the documentation in L<Math::BigInt> for further details. |
1743 | |
1744 | =head2 config() |
990fb837 |
1745 | |
1746 | use Data::Dumper; |
1747 | |
1748 | print Dumper ( Math::BigRat->config() ); |
1749 | print Math::BigRat->config()->{lib},"\n"; |
1750 | |
1751 | Returns a hash containing the configuration, e.g. the version number, lib |
1752 | loaded etc. The following hash keys are currently filled in with the |
1753 | appropriate information. |
1754 | |
1755 | key RO/RW Description |
1756 | Example |
1757 | ============================================================ |
1758 | lib RO Name of the Math library |
1759 | Math::BigInt::Calc |
1760 | lib_version RO Version of 'lib' |
1761 | 0.30 |
1762 | class RO The class of config you just called |
1763 | Math::BigRat |
1764 | version RO version number of the class you used |
1765 | 0.10 |
1766 | upgrade RW To which class numbers are upgraded |
1767 | undef |
1768 | downgrade RW To which class numbers are downgraded |
1769 | undef |
1770 | precision RW Global precision |
1771 | undef |
1772 | accuracy RW Global accuracy |
1773 | undef |
1774 | round_mode RW Global round mode |
1775 | even |
3c4b39be |
1776 | div_scale RW Fallback accuracy for div |
990fb837 |
1777 | 40 |
1778 | trap_nan RW Trap creation of NaN (undef = no) |
1779 | undef |
1780 | trap_inf RW Trap creation of +inf/-inf (undef = no) |
1781 | undef |
1782 | |
1783 | By passing a reference to a hash you may set the configuration values. This |
1784 | works only for values that a marked with a C<RW> above, anything else is |
1785 | read-only. |
1786 | |
a4e2b1c6 |
1787 | =head1 BUGS |
6de7f0cc |
1788 | |
7d341013 |
1789 | Some things are not yet implemented, or only implemented half-way: |
1790 | |
1791 | =over 2 |
1792 | |
1793 | =item inf handling (partial) |
1794 | |
1795 | =item NaN handling (partial) |
1796 | |
1797 | =item rounding (not implemented except for bceil/bfloor) |
1798 | |
1799 | =item $x ** $y where $y is not an integer |
1800 | |
7afd7a91 |
1801 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) |
1802 | |
7d341013 |
1803 | =back |
184f15d5 |
1804 | |
1805 | =head1 LICENSE |
1806 | |
1807 | This program is free software; you may redistribute it and/or modify it under |
1808 | the same terms as Perl itself. |
1809 | |
1810 | =head1 SEE ALSO |
1811 | |
1812 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
1813 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
1814 | |
7d341013 |
1815 | See L<http://search.cpan.org/search?dist=bignum> for a way to use |
1816 | Math::BigRat. |
1817 | |
1818 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> |
1819 | may contain more documentation and examples as well as testcases. |
184f15d5 |
1820 | |
1821 | =head1 AUTHORS |
1822 | |
b8884ce4 |
1823 | (C) by Tels L<http://bloodgate.com/> 2001 - 2007. |
184f15d5 |
1824 | |
1825 | =cut |