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 |
08a3f4a9 |
17 | use 5.006; |
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 | |
c6c613ed |
26 | $VERSION = '0.24'; |
27 | $VERSION = eval $VERSION; |
184f15d5 |
28 | |
12fc2493 |
29 | use overload; # inherit overload from Math::BigFloat |
184f15d5 |
30 | |
12fc2493 |
31 | BEGIN |
32 | { |
33 | *objectify = \&Math::BigInt::objectify; # inherit this from BigInt |
34 | *AUTOLOAD = \&Math::BigFloat::AUTOLOAD; # can't inherit AUTOLOAD |
35 | # we inherit these from BigFloat because currently it is not possible |
36 | # that MBF has a different $MBI variable than we, because MBF also uses |
37 | # Math::BigInt::config->('lib'); (there is always only one library loaded) |
38 | *_e_add = \&Math::BigFloat::_e_add; |
39 | *_e_sub = \&Math::BigFloat::_e_sub; |
b68b7ab1 |
40 | *as_int = \&as_number; |
41 | *is_pos = \&is_positive; |
42 | *is_neg = \&is_negative; |
12fc2493 |
43 | } |
9b924220 |
44 | |
184f15d5 |
45 | ############################################################################## |
12fc2493 |
46 | # Global constants and flags. Access these only via the accessor methods! |
184f15d5 |
47 | |
184f15d5 |
48 | $accuracy = $precision = undef; |
49 | $round_mode = 'even'; |
50 | $div_scale = 40; |
51 | $upgrade = undef; |
52 | $downgrade = undef; |
53 | |
12fc2493 |
54 | # These are internally, and not to be used from the outside at all! |
990fb837 |
55 | |
56 | $_trap_nan = 0; # are NaNs ok? set w/ config() |
57 | $_trap_inf = 0; # are infs ok? set w/ config() |
58 | |
12fc2493 |
59 | # the package we are using for our private parts, defaults to: |
60 | # Math::BigInt->config()->{lib} |
61 | my $MBI = 'Math::BigInt::Calc'; |
62 | |
184f15d5 |
63 | my $nan = 'NaN'; |
9b924220 |
64 | my $class = 'Math::BigRat'; |
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(); |
233f7bc0 |
204 | |
12fc2493 |
205 | $self->{_n} = $MBI->_copy( $nf->{_m} ); # get mantissa |
9b924220 |
206 | |
184f15d5 |
207 | # now correct $self->{_n} due to $n |
7d341013 |
208 | my $f = Math::BigFloat->new($d,undef,undef); |
990fb837 |
209 | return $self->bnan() if $f->is_nan(); |
12fc2493 |
210 | $self->{_d} = $MBI->_copy( $f->{_m} ); |
9b924220 |
211 | |
990fb837 |
212 | # calculate the difference between nE and dE |
bd49aa09 |
213 | my $diff_e = $nf->exponent()->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 $self->bnorm(); |
280 | } |
281 | |
282 | # simple string input |
c6c613ed |
283 | if (($n =~ /[\.eE]/) && $n !~ /^0x/) |
184f15d5 |
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 $class = shift || 'Math::BigRat'; |
990fb837 |
341 | |
116a1b2f |
342 | if (@_ == 1 && ref($_[0]) ne 'HASH') |
343 | { |
344 | my $cfg = $class->SUPER::config(); |
345 | return $cfg->{$_[0]}; |
346 | } |
347 | |
990fb837 |
348 | my $cfg = $class->SUPER::config(@_); |
349 | |
350 | # now we need only to override the ones that are different from our parent |
351 | $cfg->{class} = $class; |
352 | $cfg->{with} = $MBI; |
353 | $cfg; |
354 | } |
355 | |
356 | ############################################################################## |
8f675a64 |
357 | |
184f15d5 |
358 | sub bstr |
359 | { |
7afd7a91 |
360 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
361 | |
362 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
363 | { |
364 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
365 | return $s; |
366 | } |
367 | |
7afd7a91 |
368 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2' |
184f15d5 |
369 | |
12fc2493 |
370 | return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d}); |
371 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
372 | } |
373 | |
374 | sub bsstr |
375 | { |
b68b7ab1 |
376 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
377 | |
378 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
379 | { |
380 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
381 | return $s; |
382 | } |
383 | |
384 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
12fc2493 |
385 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
386 | } |
387 | |
388 | sub bnorm |
389 | { |
12fc2493 |
390 | # reduce the number to the shortest form |
b68b7ab1 |
391 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
392 | |
12fc2493 |
393 | # Both parts must be objects of whatever we are using today. |
bd49aa09 |
394 | if ( my $c = $MBI->_check($x->{_n}) ) |
990fb837 |
395 | { |
bd49aa09 |
396 | require Carp; Carp::croak ("n did not pass the self-check ($c) in bnorm()"); |
990fb837 |
397 | } |
bd49aa09 |
398 | if ( my $c = $MBI->_check($x->{_d}) ) |
990fb837 |
399 | { |
bd49aa09 |
400 | require Carp; Carp::croak ("d did not pass the self-check ($c) in bnorm()"); |
990fb837 |
401 | } |
6de7f0cc |
402 | |
6de7f0cc |
403 | # no normalize for NaN, inf etc. |
404 | return $x if $x->{sign} !~ /^[+-]$/; |
405 | |
184f15d5 |
406 | # normalize zeros to 0/1 |
12fc2493 |
407 | if ($MBI->_is_zero($x->{_n})) |
184f15d5 |
408 | { |
12fc2493 |
409 | $x->{sign} = '+'; # never leave a -0 |
410 | $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d}); |
184f15d5 |
411 | return $x; |
412 | } |
413 | |
12fc2493 |
414 | return $x if $MBI->_is_one($x->{_d}); # no need to reduce |
6de7f0cc |
415 | |
184f15d5 |
416 | # reduce other numbers |
12fc2493 |
417 | my $gcd = $MBI->_copy($x->{_n}); |
418 | $gcd = $MBI->_gcd($gcd,$x->{_d}); |
419 | |
420 | if (!$MBI->_is_one($gcd)) |
184f15d5 |
421 | { |
12fc2493 |
422 | $x->{_n} = $MBI->_div($x->{_n},$gcd); |
423 | $x->{_d} = $MBI->_div($x->{_d},$gcd); |
184f15d5 |
424 | } |
184f15d5 |
425 | $x; |
426 | } |
427 | |
428 | ############################################################################## |
b68b7ab1 |
429 | # sign manipulation |
430 | |
431 | sub bneg |
432 | { |
433 | # (BRAT or num_str) return BRAT |
434 | # negate number or make a negated number from string |
435 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
436 | |
437 | return $x if $x->modify('bneg'); |
438 | |
439 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN' |
440 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $MBI->_is_zero($x->{_n})); |
441 | $x; |
442 | } |
443 | |
444 | ############################################################################## |
184f15d5 |
445 | # special values |
446 | |
447 | sub _bnan |
448 | { |
990fb837 |
449 | # used by parent class bnan() to initialize number to NaN |
184f15d5 |
450 | my $self = shift; |
990fb837 |
451 | |
452 | if ($_trap_nan) |
453 | { |
454 | require Carp; |
455 | my $class = ref($self); |
233f7bc0 |
456 | # "$self" below will stringify the object, this blows up if $self is a |
457 | # partial object (happens under trap_nan), so fix it beforehand |
458 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; |
459 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; |
990fb837 |
460 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
461 | } |
12fc2493 |
462 | $self->{_n} = $MBI->_zero(); |
463 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
464 | } |
465 | |
466 | sub _binf |
467 | { |
7d341013 |
468 | # used by parent class bone() to initialize number to +inf/-inf |
184f15d5 |
469 | my $self = shift; |
990fb837 |
470 | |
471 | if ($_trap_inf) |
472 | { |
473 | require Carp; |
474 | my $class = ref($self); |
233f7bc0 |
475 | # "$self" below will stringify the object, this blows up if $self is a |
476 | # partial object (happens under trap_nan), so fix it beforehand |
477 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; |
478 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; |
990fb837 |
479 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); |
480 | } |
12fc2493 |
481 | $self->{_n} = $MBI->_zero(); |
482 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
483 | } |
484 | |
485 | sub _bone |
486 | { |
7d341013 |
487 | # used by parent class bone() to initialize number to +1/-1 |
184f15d5 |
488 | my $self = shift; |
12fc2493 |
489 | $self->{_n} = $MBI->_one(); |
490 | $self->{_d} = $MBI->_one(); |
184f15d5 |
491 | } |
492 | |
493 | sub _bzero |
494 | { |
990fb837 |
495 | # used by parent class bzero() to initialize number to 0 |
184f15d5 |
496 | my $self = shift; |
12fc2493 |
497 | $self->{_n} = $MBI->_zero(); |
498 | $self->{_d} = $MBI->_one(); |
184f15d5 |
499 | } |
500 | |
501 | ############################################################################## |
502 | # mul/add/div etc |
503 | |
504 | sub badd |
505 | { |
7afd7a91 |
506 | # add two rational numbers |
7d341013 |
507 | |
508 | # set up parameters |
509 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
510 | # objectify is costly, so avoid it |
511 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
512 | { |
513 | ($self,$x,$y,@r) = objectify(2,@_); |
514 | } |
184f15d5 |
515 | |
12fc2493 |
516 | # +inf + +inf => +inf, -inf + -inf => -inf |
517 | return $x->binf(substr($x->{sign},0,1)) |
518 | if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
184f15d5 |
519 | |
12fc2493 |
520 | # +inf + -inf or -inf + +inf => NaN |
521 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
184f15d5 |
522 | |
523 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
524 | # - + - = --------- = -- |
525 | # 4 3 4*3 12 |
526 | |
7d341013 |
527 | # we do not compute the gcd() here, but simple do: |
233f7bc0 |
528 | # 5 7 5*3 + 7*4 43 |
7d341013 |
529 | # - + - = --------- = -- |
530 | # 4 3 4*3 12 |
531 | |
12fc2493 |
532 | # and bnorm() will then take care of the rest |
184f15d5 |
533 | |
233f7bc0 |
534 | # 5 * 3 |
12fc2493 |
535 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
7d341013 |
536 | |
233f7bc0 |
537 | # 7 * 4 |
12fc2493 |
538 | my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} ); |
184f15d5 |
539 | |
233f7bc0 |
540 | # 5 * 3 + 7 * 4 |
12fc2493 |
541 | ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign}); |
184f15d5 |
542 | |
233f7bc0 |
543 | # 4 * 3 |
12fc2493 |
544 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
545 | |
233f7bc0 |
546 | # normalize result, and possible round |
7d341013 |
547 | $x->bnorm()->round(@r); |
184f15d5 |
548 | } |
549 | |
550 | sub bsub |
551 | { |
7afd7a91 |
552 | # subtract two rational numbers |
7d341013 |
553 | |
554 | # set up parameters |
555 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
556 | # objectify is costly, so avoid it |
557 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
558 | { |
559 | ($self,$x,$y,@r) = objectify(2,@_); |
560 | } |
184f15d5 |
561 | |
7afd7a91 |
562 | # flip sign of $x, call badd(), then flip sign of result |
563 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
564 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
565 | $x->badd($y,@r); # does norm and round |
7afd7a91 |
566 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
567 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
7afd7a91 |
568 | $x; |
184f15d5 |
569 | } |
570 | |
571 | sub bmul |
572 | { |
7afd7a91 |
573 | # multiply two rational numbers |
7d341013 |
574 | |
575 | # set up parameters |
576 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
577 | # objectify is costly, so avoid it |
578 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
579 | { |
580 | ($self,$x,$y,@r) = objectify(2,@_); |
581 | } |
184f15d5 |
582 | |
583 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
584 | |
585 | # inf handling |
586 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
587 | { |
588 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
589 | # result will always be +-inf: |
590 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
591 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
592 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
593 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
594 | return $x->binf('-'); |
595 | } |
596 | |
597 | # x== 0 # also: or y == 1 or y == -1 |
598 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
599 | |
12fc2493 |
600 | # XXX TODO: |
601 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
602 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
603 | |
12fc2493 |
604 | # 1 2 1 * 2 2 1 |
605 | # - * - = ----- = - = - |
606 | # 4 3 4 * 3 12 6 |
7d341013 |
607 | |
12fc2493 |
608 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); |
609 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
610 | |
611 | # compute new sign |
612 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
613 | |
7d341013 |
614 | $x->bnorm()->round(@r); |
184f15d5 |
615 | } |
616 | |
617 | sub bdiv |
618 | { |
619 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
620 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
7d341013 |
621 | |
622 | # set up parameters |
623 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
624 | # objectify is costly, so avoid it |
625 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
626 | { |
627 | ($self,$x,$y,@r) = objectify(2,@_); |
628 | } |
184f15d5 |
629 | |
630 | return $self->_div_inf($x,$y) |
631 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
632 | |
633 | # x== 0 # also: or y == 1 or y == -1 |
634 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
635 | |
12fc2493 |
636 | # XXX TODO: list context, upgrade |
637 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
638 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
639 | |
184f15d5 |
640 | # 1 1 1 3 |
641 | # - / - == - * - |
642 | # 4 3 4 1 |
7d341013 |
643 | |
12fc2493 |
644 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
645 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); |
184f15d5 |
646 | |
647 | # compute new sign |
648 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
649 | |
7d341013 |
650 | $x->bnorm()->round(@r); |
6de7f0cc |
651 | $x; |
184f15d5 |
652 | } |
653 | |
990fb837 |
654 | sub bmod |
655 | { |
656 | # compute "remainder" (in Perl way) of $x / $y |
657 | |
658 | # set up parameters |
659 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
660 | # objectify is costly, so avoid it |
661 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
662 | { |
663 | ($self,$x,$y,@r) = objectify(2,@_); |
664 | } |
665 | |
990fb837 |
666 | return $self->_div_inf($x,$y) |
667 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
668 | |
669 | return $x if $x->is_zero(); # 0 / 7 = 0, mod 0 |
670 | |
671 | # compute $x - $y * floor($x/$y), keeping the sign of $x |
672 | |
12fc2493 |
673 | # copy x to u, make it positive and then do a normal division ($u/$y) |
674 | my $u = bless { sign => '+' }, $self; |
675 | $u->{_n} = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d} ); |
676 | $u->{_d} = $MBI->_mul( $MBI->_copy($x->{_d}), $y->{_n} ); |
677 | |
678 | # compute floor(u) |
679 | if (! $MBI->_is_one($u->{_d})) |
990fb837 |
680 | { |
12fc2493 |
681 | $u->{_n} = $MBI->_div($u->{_n},$u->{_d}); # 22/7 => 3/1 w/ truncate |
682 | # no need to set $u->{_d} to 1, since below we set it to $y->{_d} anyway |
990fb837 |
683 | } |
684 | |
12fc2493 |
685 | # now compute $y * $u |
686 | $u->{_d} = $MBI->_copy($y->{_d}); # 1 * $y->{_d}, see floor above |
687 | $u->{_n} = $MBI->_mul($u->{_n},$y->{_n}); |
990fb837 |
688 | |
12fc2493 |
689 | my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive |
990fb837 |
690 | # compute $x - $u |
691 | $x->bsub($u); |
692 | $x->{sign} = $xsign; # put sign back |
693 | |
694 | $x->bnorm()->round(@r); |
990fb837 |
695 | } |
696 | |
184f15d5 |
697 | ############################################################################## |
a4e2b1c6 |
698 | # bdec/binc |
699 | |
700 | sub bdec |
701 | { |
702 | # decrement value (subtract 1) |
703 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
704 | |
705 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
706 | |
707 | if ($x->{sign} eq '-') |
708 | { |
12fc2493 |
709 | $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2 |
a4e2b1c6 |
710 | } |
711 | else |
712 | { |
12fc2493 |
713 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? |
a4e2b1c6 |
714 | { |
715 | # 1/3 -- => -2/3 |
12fc2493 |
716 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
717 | $x->{sign} = '-'; |
718 | } |
719 | else |
720 | { |
12fc2493 |
721 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 |
a4e2b1c6 |
722 | } |
723 | } |
724 | $x->bnorm()->round(@r); |
a4e2b1c6 |
725 | } |
726 | |
727 | sub binc |
728 | { |
729 | # increment value (add 1) |
730 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
731 | |
732 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
733 | |
734 | if ($x->{sign} eq '-') |
735 | { |
12fc2493 |
736 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) |
a4e2b1c6 |
737 | { |
738 | # -1/3 ++ => 2/3 (overflow at 0) |
12fc2493 |
739 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
740 | $x->{sign} = '+'; |
741 | } |
742 | else |
743 | { |
12fc2493 |
744 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 |
a4e2b1c6 |
745 | } |
746 | } |
747 | else |
748 | { |
12fc2493 |
749 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 |
a4e2b1c6 |
750 | } |
751 | $x->bnorm()->round(@r); |
a4e2b1c6 |
752 | } |
753 | |
754 | ############################################################################## |
184f15d5 |
755 | # is_foo methods (the rest is inherited) |
756 | |
757 | sub is_int |
758 | { |
759 | # return true if arg (BRAT or num_str) is an integer |
9b924220 |
760 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
761 | |
762 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
12fc2493 |
763 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer |
184f15d5 |
764 | 0; |
765 | } |
766 | |
767 | sub is_zero |
768 | { |
769 | # return true if arg (BRAT or num_str) is zero |
9b924220 |
770 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
771 | |
12fc2493 |
772 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); |
184f15d5 |
773 | 0; |
774 | } |
775 | |
776 | sub is_one |
777 | { |
778 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
9b924220 |
779 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
780 | |
9b924220 |
781 | my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; |
184f15d5 |
782 | return 1 |
12fc2493 |
783 | if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})); |
184f15d5 |
784 | 0; |
785 | } |
786 | |
787 | sub is_odd |
788 | { |
789 | # return true if arg (BFLOAT or num_str) is odd or false if even |
9b924220 |
790 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
791 | |
792 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
12fc2493 |
793 | ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1 |
184f15d5 |
794 | 0; |
795 | } |
796 | |
797 | sub is_even |
798 | { |
799 | # return true if arg (BINT or num_str) is even or false if odd |
9b924220 |
800 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
801 | |
802 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
12fc2493 |
803 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never |
804 | && $MBI->_is_even($x->{_n})); # but 4/1 is |
184f15d5 |
805 | 0; |
806 | } |
807 | |
184f15d5 |
808 | ############################################################################## |
809 | # parts() and friends |
810 | |
811 | sub numerator |
812 | { |
813 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
a4e2b1c6 |
814 | |
12fc2493 |
815 | # NaN, inf, -inf |
816 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
a4e2b1c6 |
817 | |
12fc2493 |
818 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; |
184f15d5 |
819 | $n; |
820 | } |
821 | |
822 | sub denominator |
823 | { |
824 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
825 | |
12fc2493 |
826 | # NaN |
827 | return Math::BigInt->new($x->{sign}) if $x->{sign} eq 'NaN'; |
828 | # inf, -inf |
829 | return Math::BigInt->bone() if $x->{sign} !~ /^[+-]$/; |
830 | |
831 | Math::BigInt->new($MBI->_str($x->{_d})); |
184f15d5 |
832 | } |
833 | |
834 | sub parts |
835 | { |
836 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
837 | |
12fc2493 |
838 | my $c = 'Math::BigInt'; |
839 | |
840 | return ($c->bnan(),$c->bnan()) if $x->{sign} eq 'NaN'; |
841 | return ($c->binf(),$c->binf()) if $x->{sign} eq '+inf'; |
842 | return ($c->binf('-'),$c->binf()) if $x->{sign} eq '-inf'; |
a4e2b1c6 |
843 | |
12fc2493 |
844 | my $n = $c->new( $MBI->_str($x->{_n})); |
184f15d5 |
845 | $n->{sign} = $x->{sign}; |
12fc2493 |
846 | my $d = $c->new( $MBI->_str($x->{_d})); |
847 | ($n,$d); |
184f15d5 |
848 | } |
849 | |
850 | sub length |
851 | { |
9b924220 |
852 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
853 | |
854 | return $nan unless $x->is_int(); |
12fc2493 |
855 | $MBI->_len($x->{_n}); # length(-123/1) => length(123) |
184f15d5 |
856 | } |
857 | |
858 | sub digit |
859 | { |
12fc2493 |
860 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); |
9b924220 |
861 | |
862 | return $nan unless $x->is_int(); |
12fc2493 |
863 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) |
184f15d5 |
864 | } |
865 | |
866 | ############################################################################## |
867 | # special calc routines |
868 | |
869 | sub bceil |
870 | { |
871 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
872 | |
12fc2493 |
873 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
874 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
875 | |
12fc2493 |
876 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
877 | $x->{_d} = $MBI->_one(); # d => 1 |
878 | $x->{_n} = $MBI->_inc($x->{_n}) |
879 | if $x->{sign} eq '+'; # +22/7 => 4/1 |
880 | $x->{sign} = '+' if $MBI->_is_zero($x->{_n}); # -0 => 0 |
184f15d5 |
881 | $x; |
882 | } |
883 | |
884 | sub bfloor |
885 | { |
886 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
887 | |
12fc2493 |
888 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
889 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
890 | |
12fc2493 |
891 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
892 | $x->{_d} = $MBI->_one(); # d => 1 |
893 | $x->{_n} = $MBI->_inc($x->{_n}) |
894 | if $x->{sign} eq '-'; # -22/7 => -4/1 |
184f15d5 |
895 | $x; |
896 | } |
897 | |
898 | sub bfac |
899 | { |
a4e2b1c6 |
900 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
901 | |
12fc2493 |
902 | # if $x is not an integer |
903 | if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d}))) |
a4e2b1c6 |
904 | { |
12fc2493 |
905 | return $x->bnan(); |
a4e2b1c6 |
906 | } |
12fc2493 |
907 | |
908 | $x->{_n} = $MBI->_fac($x->{_n}); |
909 | # since _d is 1, we don't need to reduce/norm the result |
910 | $x->round(@r); |
184f15d5 |
911 | } |
912 | |
913 | sub bpow |
914 | { |
7d341013 |
915 | # power ($x ** $y) |
916 | |
917 | # set up parameters |
918 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
919 | # objectify is costly, so avoid it |
920 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
921 | { |
922 | ($self,$x,$y,@r) = objectify(2,@_); |
923 | } |
184f15d5 |
924 | |
925 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
926 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
927 | return $x->bone(@r) if $y->is_zero(); |
928 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
12fc2493 |
929 | |
930 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) |
184f15d5 |
931 | { |
932 | # if $x == -1 and odd/even y => +1/-1 |
933 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
934 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
935 | } |
936 | # 1 ** -y => 1 / (1 ** |y|) |
937 | # so do test for negative $y after above's clause |
12fc2493 |
938 | |
184f15d5 |
939 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
940 | |
4de3d162 |
941 | # shortcut if y == 1/N (is then sqrt() respective broot()) |
942 | if ($MBI->_is_one($y->{_n})) |
943 | { |
944 | return $x->bsqrt(@r) if $MBI->_is_two($y->{_d}); # 1/2 => sqrt |
945 | return $x->broot($MBI->_str($y->{_d}),@r); # 1/N => root(N) |
946 | } |
947 | |
a4e2b1c6 |
948 | # shortcut y/1 (and/or x/1) |
12fc2493 |
949 | if ($MBI->_is_one($y->{_d})) |
a4e2b1c6 |
950 | { |
951 | # shortcut for x/1 and y/1 |
12fc2493 |
952 | if ($MBI->_is_one($x->{_d})) |
a4e2b1c6 |
953 | { |
12fc2493 |
954 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
a4e2b1c6 |
955 | if ($y->{sign} eq '-') |
956 | { |
957 | # 0.2 ** -3 => 1/(0.2 ** 3) |
958 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
959 | } |
960 | # correct sign; + ** + => + |
961 | if ($x->{sign} eq '-') |
962 | { |
963 | # - * - => +, - * - * - => - |
12fc2493 |
964 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
965 | } |
966 | return $x->round(@r); |
967 | } |
968 | # x/z ** y/1 |
12fc2493 |
969 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
970 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); |
a4e2b1c6 |
971 | if ($y->{sign} eq '-') |
972 | { |
973 | # 0.2 ** -3 => 1/(0.2 ** 3) |
974 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
975 | } |
976 | # correct sign; + ** + => + |
977 | if ($x->{sign} eq '-') |
978 | { |
979 | # - * - => +, - * - * - => - |
12fc2493 |
980 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
981 | } |
982 | return $x->round(@r); |
983 | } |
984 | |
4de3d162 |
985 | # print STDERR "# $x $y\n"; |
12fc2493 |
986 | |
4de3d162 |
987 | # otherwise: |
988 | |
989 | # n/d n ______________ |
990 | # a/b = -\/ (a/b) ** d |
991 | |
992 | # (a/b) ** n == (a ** n) / (b ** n) |
993 | $MBI->_pow($x->{_n}, $y->{_n} ); |
994 | $MBI->_pow($x->{_d}, $y->{_n} ); |
995 | |
996 | return $x->broot($MBI->_str($y->{_d}),@r); # n/d => root(n) |
184f15d5 |
997 | } |
998 | |
999 | sub blog |
1000 | { |
7afd7a91 |
1001 | # set up parameters |
1002 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1003 | |
1004 | # objectify is costly, so avoid it |
1005 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1006 | { |
9b924220 |
1007 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
7afd7a91 |
1008 | } |
1009 | |
9b924220 |
1010 | # blog(1,Y) => 0 |
1011 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; |
1012 | |
7afd7a91 |
1013 | # $x <= 0 => NaN |
1014 | return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; |
1015 | |
1016 | if ($x->is_int() && $y->is_int()) |
1017 | { |
1018 | return $self->new($x->as_number()->blog($y->as_number(),@r)); |
1019 | } |
1020 | |
9b924220 |
1021 | # do it with floats |
1022 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); |
1023 | } |
1024 | |
116a1b2f |
1025 | sub bexp |
1026 | { |
1027 | # set up parameters |
4de3d162 |
1028 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
116a1b2f |
1029 | |
1030 | # objectify is costly, so avoid it |
1031 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1032 | { |
4de3d162 |
1033 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
116a1b2f |
1034 | } |
1035 | |
4de3d162 |
1036 | return $x->binf(@r) if $x->{sign} eq '+inf'; |
1037 | return $x->bzero(@r) if $x->{sign} eq '-inf'; |
116a1b2f |
1038 | |
1039 | # we need to limit the accuracy to protect against overflow |
1040 | my $fallback = 0; |
1041 | my ($scale,@params); |
4de3d162 |
1042 | ($x,@params) = $x->_find_round_parameters(@r); |
116a1b2f |
1043 | |
1044 | # also takes care of the "error in _find_round_parameters?" case |
1045 | return $x if $x->{sign} eq 'NaN'; |
1046 | |
1047 | # no rounding at all, so must use fallback |
1048 | if (scalar @params == 0) |
1049 | { |
1050 | # simulate old behaviour |
4de3d162 |
1051 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1052 | $params[1] = undef; # P = undef |
1053 | $scale = $params[0]+4; # at least four more for proper round |
1054 | $params[2] = $r[2]; # round mode by caller or undef |
1055 | $fallback = 1; # to clear a/p afterwards |
116a1b2f |
1056 | } |
1057 | else |
1058 | { |
1059 | # the 4 below is empirical, and there might be cases where it's not enough... |
1060 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
1061 | } |
1062 | |
1063 | return $x->bone(@params) if $x->is_zero(); |
1064 | |
1065 | # See the comments in Math::BigFloat on how this algorithm works. |
1066 | # Basically we calculate A and B (where B is faculty(N)) so that A/B = e |
1067 | |
1068 | my $x_org = $x->copy(); |
1069 | if ($scale <= 75) |
1070 | { |
1071 | # set $x directly from a cached string form |
1072 | $x->{_n} = $MBI->_new("90933395208605785401971970164779391644753259799242"); |
1073 | $x->{_d} = $MBI->_new("33452526613163807108170062053440751665152000000000"); |
1074 | $x->{sign} = '+'; |
1075 | } |
1076 | else |
1077 | { |
1078 | # compute A and B so that e = A / B. |
1079 | |
1080 | # After some terms we end up with this, so we use it as a starting point: |
1081 | my $A = $MBI->_new("90933395208605785401971970164779391644753259799242"); |
1082 | my $F = $MBI->_new(42); my $step = 42; |
1083 | |
1084 | # Compute how many steps we need to take to get $A and $B sufficiently big |
1085 | my $steps = Math::BigFloat::_len_to_steps($scale - 4); |
1086 | # print STDERR "# Doing $steps steps for ", $scale-4, " digits\n"; |
1087 | while ($step++ <= $steps) |
1088 | { |
1089 | # calculate $a * $f + 1 |
1090 | $A = $MBI->_mul($A, $F); |
1091 | $A = $MBI->_inc($A); |
1092 | # increment f |
1093 | $F = $MBI->_inc($F); |
1094 | } |
1095 | # compute $B as factorial of $steps (this is faster than doing it manually) |
1096 | my $B = $MBI->_fac($MBI->_new($steps)); |
1097 | |
1098 | # print "A ", $MBI->_str($A), "\nB ", $MBI->_str($B), "\n"; |
1099 | |
1100 | $x->{_n} = $A; |
1101 | $x->{_d} = $B; |
1102 | $x->{sign} = '+'; |
1103 | } |
1104 | |
1105 | # $x contains now an estimate of e, with some surplus digits, so we can round |
1106 | if (!$x_org->is_one()) |
1107 | { |
1108 | # raise $x to the wanted power and round it in one step: |
1109 | $x->bpow($x_org, @params); |
1110 | } |
1111 | else |
1112 | { |
1113 | # else just round the already computed result |
1114 | delete $x->{_a}; delete $x->{_p}; |
1115 | # shortcut to not run through _find_round_parameters again |
1116 | if (defined $params[0]) |
1117 | { |
1118 | $x->bround($params[0],$params[2]); # then round accordingly |
1119 | } |
1120 | else |
1121 | { |
1122 | $x->bfround($params[1],$params[2]); # then round accordingly |
1123 | } |
1124 | } |
1125 | if ($fallback) |
1126 | { |
1127 | # clear a/p after round, since user did not request it |
1128 | delete $x->{_a}; delete $x->{_p}; |
1129 | } |
1130 | |
1131 | $x; |
1132 | } |
1133 | |
1134 | sub bnok |
1135 | { |
1136 | # set up parameters |
1137 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1138 | |
1139 | # objectify is costly, so avoid it |
1140 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1141 | { |
1142 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
1143 | } |
1144 | |
1145 | # do it with floats |
1146 | $x->_new_from_float( $x->_as_float()->bnok(Math::BigFloat->new("$y"),@r) ); |
1147 | } |
1148 | |
12fc2493 |
1149 | sub _float_from_part |
1150 | { |
1151 | my $x = shift; |
1152 | |
1153 | my $f = Math::BigFloat->bzero(); |
1154 | $f->{_m} = $MBI->_copy($x); |
1155 | $f->{_e} = $MBI->_zero(); |
1156 | |
1157 | $f; |
1158 | } |
1159 | |
9b924220 |
1160 | sub _as_float |
1161 | { |
1162 | my $x = shift; |
1163 | |
1164 | local $Math::BigFloat::upgrade = undef; |
1165 | local $Math::BigFloat::accuracy = undef; |
1166 | local $Math::BigFloat::precision = undef; |
1167 | # 22/7 => 3.142857143.. |
12fc2493 |
1168 | |
1169 | my $a = $x->accuracy() || 0; |
1170 | if ($a != 0 || !$MBI->_is_one($x->{_d})) |
1171 | { |
1172 | # n/d |
4de3d162 |
1173 | return scalar Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy()); |
12fc2493 |
1174 | } |
1175 | # just n |
1176 | Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n})); |
7afd7a91 |
1177 | } |
1178 | |
1179 | sub broot |
1180 | { |
1181 | # set up parameters |
1182 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1183 | # objectify is costly, so avoid it |
1184 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1185 | { |
1186 | ($self,$x,$y,@r) = objectify(2,@_); |
1187 | } |
1188 | |
1189 | if ($x->is_int() && $y->is_int()) |
1190 | { |
1191 | return $self->new($x->as_number()->broot($y->as_number(),@r)); |
1192 | } |
9b924220 |
1193 | |
1194 | # do it with floats |
4de3d162 |
1195 | $x->_new_from_float( $x->_as_float()->broot($y->_as_float(),@r) )->bnorm()->bround(@r); |
7afd7a91 |
1196 | } |
1197 | |
1198 | sub bmodpow |
1199 | { |
1200 | # set up parameters |
1201 | my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); |
1202 | # objectify is costly, so avoid it |
1203 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1204 | { |
1205 | ($self,$x,$y,$m,@r) = objectify(3,@_); |
1206 | } |
1207 | |
1208 | # $x or $y or $m are NaN or +-inf => NaN |
1209 | return $x->bnan() |
1210 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || |
1211 | $m->{sign} !~ /^[+-]$/; |
1212 | |
1213 | if ($x->is_int() && $y->is_int() && $m->is_int()) |
1214 | { |
1215 | return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); |
1216 | } |
1217 | |
1218 | warn ("bmodpow() not fully implemented"); |
1219 | $x->bnan(); |
1220 | } |
1221 | |
1222 | sub bmodinv |
1223 | { |
1224 | # set up parameters |
1225 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1226 | # objectify is costly, so avoid it |
1227 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1228 | { |
1229 | ($self,$x,$y,@r) = objectify(2,@_); |
1230 | } |
1231 | |
1232 | # $x or $y are NaN or +-inf => NaN |
1233 | return $x->bnan() |
1234 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; |
1235 | |
1236 | if ($x->is_int() && $y->is_int()) |
1237 | { |
1238 | return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); |
1239 | } |
1240 | |
1241 | warn ("bmodinv() not fully implemented"); |
1242 | $x->bnan(); |
184f15d5 |
1243 | } |
1244 | |
1245 | sub bsqrt |
1246 | { |
990fb837 |
1247 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1248 | |
1249 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 |
1250 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf |
1251 | return $x->round(@r) if $x->is_zero() || $x->is_one(); |
1252 | |
1253 | local $Math::BigFloat::upgrade = undef; |
1254 | local $Math::BigFloat::downgrade = undef; |
1255 | local $Math::BigFloat::precision = undef; |
1256 | local $Math::BigFloat::accuracy = undef; |
1257 | local $Math::BigInt::upgrade = undef; |
1258 | local $Math::BigInt::precision = undef; |
1259 | local $Math::BigInt::accuracy = undef; |
9b924220 |
1260 | |
12fc2493 |
1261 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); |
1262 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); |
1263 | |
1264 | # XXX TODO: we probably can optimze this: |
184f15d5 |
1265 | |
990fb837 |
1266 | # if sqrt(D) was not integer |
9b924220 |
1267 | if ($x->{_d}->{_es} ne '+') |
990fb837 |
1268 | { |
9b924220 |
1269 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 |
12fc2493 |
1270 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 |
990fb837 |
1271 | } |
1272 | # if sqrt(N) was not integer |
9b924220 |
1273 | if ($x->{_n}->{_es} ne '+') |
990fb837 |
1274 | { |
9b924220 |
1275 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 |
12fc2493 |
1276 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 |
990fb837 |
1277 | } |
12fc2493 |
1278 | |
990fb837 |
1279 | # convert parts to $MBI again |
12fc2493 |
1280 | $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10) |
1281 | if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY'; |
1282 | $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10) |
1283 | if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY'; |
1284 | |
990fb837 |
1285 | $x->bnorm()->round(@r); |
184f15d5 |
1286 | } |
1287 | |
1288 | sub blsft |
1289 | { |
9b924220 |
1290 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1291 | |
9b924220 |
1292 | $b = 2 unless defined $b; |
1293 | $b = $self->new($b) unless ref ($b); |
1294 | $x->bmul( $b->copy()->bpow($y), @r); |
184f15d5 |
1295 | $x; |
1296 | } |
1297 | |
1298 | sub brsft |
1299 | { |
12fc2493 |
1300 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1301 | |
9b924220 |
1302 | $b = 2 unless defined $b; |
1303 | $b = $self->new($b) unless ref ($b); |
1304 | $x->bdiv( $b->copy()->bpow($y), @r); |
184f15d5 |
1305 | $x; |
1306 | } |
1307 | |
1308 | ############################################################################## |
1309 | # round |
1310 | |
1311 | sub round |
1312 | { |
1313 | $_[0]; |
1314 | } |
1315 | |
1316 | sub bround |
1317 | { |
1318 | $_[0]; |
1319 | } |
1320 | |
1321 | sub bfround |
1322 | { |
1323 | $_[0]; |
1324 | } |
1325 | |
1326 | ############################################################################## |
1327 | # comparing |
1328 | |
1329 | sub bcmp |
1330 | { |
7afd7a91 |
1331 | # compare two signed numbers |
1332 | |
1333 | # set up parameters |
1334 | my ($self,$x,$y) = (ref($_[0]),@_); |
1335 | # objectify is costly, so avoid it |
1336 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1337 | { |
1338 | ($self,$x,$y) = objectify(2,@_); |
1339 | } |
184f15d5 |
1340 | |
1341 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1342 | { |
1343 | # handle +-inf and NaN |
1344 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1345 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
1346 | return +1 if $x->{sign} eq '+inf'; |
1347 | return -1 if $x->{sign} eq '-inf'; |
1348 | return -1 if $y->{sign} eq '+inf'; |
1349 | return +1; |
1350 | } |
1351 | # check sign for speed first |
1352 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
1353 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
1354 | |
1355 | # shortcut |
12fc2493 |
1356 | my $xz = $MBI->_is_zero($x->{_n}); |
1357 | my $yz = $MBI->_is_zero($y->{_n}); |
184f15d5 |
1358 | return 0 if $xz && $yz; # 0 <=> 0 |
1359 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
1360 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
1361 | |
12fc2493 |
1362 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1363 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1364 | |
1365 | my $cmp = $MBI->_acmp($t,$u); # signs are equal |
1366 | $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse |
1367 | $cmp; |
184f15d5 |
1368 | } |
1369 | |
1370 | sub bacmp |
1371 | { |
7afd7a91 |
1372 | # compare two numbers (as unsigned) |
9b924220 |
1373 | |
7afd7a91 |
1374 | # set up parameters |
1375 | my ($self,$x,$y) = (ref($_[0]),@_); |
1376 | # objectify is costly, so avoid it |
1377 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1378 | { |
9b924220 |
1379 | ($self,$x,$y) = objectify(2,$class,@_); |
7afd7a91 |
1380 | } |
184f15d5 |
1381 | |
1382 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1383 | { |
1384 | # handle +-inf and NaN |
1385 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1386 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
7afd7a91 |
1387 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1388 | return -1; |
184f15d5 |
1389 | } |
1390 | |
12fc2493 |
1391 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1392 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1393 | $MBI->_acmp($t,$u); # ignore signs |
184f15d5 |
1394 | } |
1395 | |
1396 | ############################################################################## |
1397 | # output conversation |
1398 | |
7d341013 |
1399 | sub numify |
1400 | { |
1401 | # convert 17/8 => float (aka 2.125) |
b68b7ab1 |
1402 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
7d341013 |
1403 | |
1404 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc |
1405 | |
93c87d9d |
1406 | # N/1 => N |
b68b7ab1 |
1407 | my $neg = ''; $neg = '-' if $x->{sign} eq '-'; |
1408 | return $neg . $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); |
93c87d9d |
1409 | |
b68b7ab1 |
1410 | $x->_as_float()->numify() + 0.0; |
7d341013 |
1411 | } |
1412 | |
184f15d5 |
1413 | sub as_number |
1414 | { |
9b924220 |
1415 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
1416 | |
08a3f4a9 |
1417 | # NaN, inf etc |
1418 | return Math::BigInt->new($x->{sign}) if $x->{sign} !~ /^[+-]$/; |
990fb837 |
1419 | |
12fc2493 |
1420 | my $u = Math::BigInt->bzero(); |
1421 | $u->{sign} = $x->{sign}; |
1422 | $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3 |
1423 | $u; |
184f15d5 |
1424 | } |
1425 | |
4de3d162 |
1426 | sub as_float |
1427 | { |
1428 | # return N/D as Math::BigFloat |
1429 | |
1430 | # set up parameters |
1431 | my ($self,$x,@r) = (ref($_[0]),@_); |
1432 | # objectify is costly, so avoid it |
1433 | ($self,$x,@r) = objectify(1,$class,@_) unless ref $_[0]; |
1434 | |
1435 | # NaN, inf etc |
1436 | return Math::BigFloat->new($x->{sign}) if $x->{sign} !~ /^[+-]$/; |
1437 | |
1438 | my $u = Math::BigFloat->bzero(); |
1439 | $u->{sign} = $x->{sign}; |
1440 | # n |
1441 | $u->{_m} = $MBI->_copy($x->{_n}); |
1442 | $u->{_e} = $MBI->_zero(); |
1443 | $u->bdiv( $MBI->_str($x->{_d}), @r); |
1444 | # return $u |
1445 | $u; |
1446 | } |
1447 | |
9b924220 |
1448 | sub as_bin |
1449 | { |
1450 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1451 | |
1452 | return $x unless $x->is_int(); |
1453 | |
1454 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1455 | $s . $MBI->_as_bin($x->{_n}); |
9b924220 |
1456 | } |
1457 | |
1458 | sub as_hex |
1459 | { |
1460 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1461 | |
1462 | return $x unless $x->is_int(); |
1463 | |
1464 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1465 | $s . $MBI->_as_hex($x->{_n}); |
9b924220 |
1466 | } |
1467 | |
b8884ce4 |
1468 | sub as_oct |
1469 | { |
1470 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1471 | |
1472 | return $x unless $x->is_int(); |
1473 | |
1474 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
1475 | $s . $MBI->_as_oct($x->{_n}); |
1476 | } |
1477 | |
1478 | ############################################################################## |
1479 | |
1480 | sub from_hex |
1481 | { |
1482 | my $class = shift; |
1483 | |
1484 | $class->new(@_); |
1485 | } |
1486 | |
1487 | sub from_bin |
1488 | { |
1489 | my $class = shift; |
1490 | |
1491 | $class->new(@_); |
1492 | } |
1493 | |
1494 | sub from_oct |
1495 | { |
1496 | my $class = shift; |
1497 | |
1498 | my @parts; |
1499 | for my $c (@_) |
1500 | { |
1501 | push @parts, Math::BigInt->from_oct($c); |
1502 | } |
1503 | $class->new ( @parts ); |
1504 | } |
1505 | |
b68b7ab1 |
1506 | ############################################################################## |
1507 | # import |
1508 | |
6de7f0cc |
1509 | sub import |
1510 | { |
1511 | my $self = shift; |
1512 | my $l = scalar @_; |
1513 | my $lib = ''; my @a; |
b8884ce4 |
1514 | my $try = 'try'; |
9b924220 |
1515 | |
6de7f0cc |
1516 | for ( my $i = 0; $i < $l ; $i++) |
1517 | { |
6de7f0cc |
1518 | if ( $_[$i] eq ':constant' ) |
1519 | { |
1520 | # this rest causes overlord er load to step in |
6de7f0cc |
1521 | overload::constant float => sub { $self->new(shift); }; |
1522 | } |
1523 | # elsif ($_[$i] eq 'upgrade') |
1524 | # { |
1525 | # # this causes upgrading |
b68b7ab1 |
1526 | # $upgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1527 | # $i++; |
1528 | # } |
1529 | elsif ($_[$i] eq 'downgrade') |
1530 | { |
1531 | # this causes downgrading |
b68b7ab1 |
1532 | $downgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1533 | $i++; |
1534 | } |
b8884ce4 |
1535 | elsif ($_[$i] =~ /^(lib|try|only)\z/) |
6de7f0cc |
1536 | { |
b68b7ab1 |
1537 | $lib = $_[$i+1] || ''; # default Calc |
b8884ce4 |
1538 | $try = $1; # lib, try or only |
6de7f0cc |
1539 | $i++; |
1540 | } |
1541 | elsif ($_[$i] eq 'with') |
1542 | { |
233f7bc0 |
1543 | # this argument is no longer used |
1544 | #$MBI = $_[$i+1] || 'Math::BigInt::Calc'; # default Math::BigInt::Calc |
6de7f0cc |
1545 | $i++; |
1546 | } |
1547 | else |
1548 | { |
1549 | push @a, $_[$i]; |
1550 | } |
1551 | } |
b68b7ab1 |
1552 | require Math::BigInt; |
6de7f0cc |
1553 | |
b68b7ab1 |
1554 | # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still have GMP |
1555 | if ($lib ne '') |
1556 | { |
1557 | my @c = split /\s*,\s*/, $lib; |
1558 | foreach (@c) |
6de7f0cc |
1559 | { |
b68b7ab1 |
1560 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters |
6de7f0cc |
1561 | } |
233f7bc0 |
1562 | $lib = join(",", @c); |
93c87d9d |
1563 | } |
233f7bc0 |
1564 | my @import = ('objectify'); |
b8884ce4 |
1565 | push @import, $try => $lib if $lib ne ''; |
233f7bc0 |
1566 | |
1567 | # MBI already loaded, so feed it our lib arguments |
1568 | Math::BigInt->import( @import ); |
6de7f0cc |
1569 | |
12fc2493 |
1570 | $MBI = Math::BigFloat->config()->{lib}; |
b68b7ab1 |
1571 | |
1572 | # register us with MBI to get notified of future lib changes |
1573 | Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } ); |
9b924220 |
1574 | |
233f7bc0 |
1575 | # any non :constant stuff is handled by our parent, Exporter (loaded |
1576 | # by Math::BigFloat, even if @_ is empty, to give it a chance |
6de7f0cc |
1577 | $self->SUPER::import(@a); # for subclasses |
1578 | $self->export_to_level(1,$self,@a); # need this, too |
1579 | } |
184f15d5 |
1580 | |
1581 | 1; |
1582 | |
1583 | __END__ |
1584 | |
1585 | =head1 NAME |
1586 | |
b68b7ab1 |
1587 | Math::BigRat - Arbitrary big rational numbers |
184f15d5 |
1588 | |
1589 | =head1 SYNOPSIS |
1590 | |
7d341013 |
1591 | use Math::BigRat; |
184f15d5 |
1592 | |
7afd7a91 |
1593 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
184f15d5 |
1594 | |
7d341013 |
1595 | print $x->bstr(),"\n"; |
1596 | print $x ** 2,"\n"; |
184f15d5 |
1597 | |
7afd7a91 |
1598 | my $y = Math::BigRat->new('inf'); |
1599 | print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; |
1600 | |
1601 | my $z = Math::BigRat->new(144); $z->bsqrt(); |
1602 | |
184f15d5 |
1603 | =head1 DESCRIPTION |
1604 | |
7d341013 |
1605 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
b68b7ab1 |
1606 | for arbitrary big rational numbers. |
184f15d5 |
1607 | |
1608 | =head2 MATH LIBRARY |
1609 | |
b8884ce4 |
1610 | You can change the underlying module that does the low-level |
1611 | math operations by using: |
184f15d5 |
1612 | |
b8884ce4 |
1613 | use Math::BigRat try => 'GMP'; |
184f15d5 |
1614 | |
b8884ce4 |
1615 | Note: This needs Math::BigInt::GMP installed. |
184f15d5 |
1616 | |
1617 | The following would first try to find Math::BigInt::Foo, then |
1618 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
1619 | |
b8884ce4 |
1620 | use Math::BigRat try => 'Foo,Math::BigInt::Bar'; |
184f15d5 |
1621 | |
b8884ce4 |
1622 | If you want to get warned when the fallback occurs, replace "try" with |
1623 | "lib": |
184f15d5 |
1624 | |
b8884ce4 |
1625 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
7d341013 |
1626 | |
b8884ce4 |
1627 | If you want the code to die instead, replace "try" with |
1628 | "only": |
1629 | |
1630 | use Math::BigRat only => 'Foo,Math::BigInt::Bar'; |
7d341013 |
1631 | |
184f15d5 |
1632 | =head1 METHODS |
1633 | |
3c4b39be |
1634 | Any methods not listed here are derived from Math::BigFloat (or |
6de7f0cc |
1635 | Math::BigInt), so make sure you check these two modules for further |
1636 | information. |
1637 | |
1638 | =head2 new() |
184f15d5 |
1639 | |
1640 | $x = Math::BigRat->new('1/3'); |
1641 | |
1642 | Create a new Math::BigRat object. Input can come in various forms: |
1643 | |
7d341013 |
1644 | $x = Math::BigRat->new(123); # scalars |
7afd7a91 |
1645 | $x = Math::BigRat->new('inf'); # infinity |
7d341013 |
1646 | $x = Math::BigRat->new('123.3'); # float |
184f15d5 |
1647 | $x = Math::BigRat->new('1/3'); # simple string |
1648 | $x = Math::BigRat->new('1 / 3'); # spaced |
1649 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
1650 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
1651 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
6de7f0cc |
1652 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
184f15d5 |
1653 | |
b68b7ab1 |
1654 | # You can also give D and N as different objects: |
1655 | $x = Math::BigRat->new( |
1656 | Math::BigInt->new(-123), |
1657 | Math::BigInt->new(7), |
1658 | ); # => -123/7 |
1659 | |
6de7f0cc |
1660 | =head2 numerator() |
184f15d5 |
1661 | |
1662 | $n = $x->numerator(); |
1663 | |
1664 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
1665 | |
6de7f0cc |
1666 | =head2 denominator() |
184f15d5 |
1667 | |
1668 | $d = $x->denominator(); |
1669 | |
1670 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
1671 | |
6de7f0cc |
1672 | =head2 parts() |
184f15d5 |
1673 | |
1674 | ($n,$d) = $x->parts(); |
1675 | |
1676 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
1677 | BigInts. |
1678 | |
b8884ce4 |
1679 | =head2 numify() |
1680 | |
1681 | my $y = $x->numify(); |
1682 | |
1683 | Returns the object as a scalar. This will lose some data if the object |
1684 | cannot be represented by a normal Perl scalar (integer or float), so |
4de3d162 |
1685 | use L<as_int()> or L<as_float()> instead. |
b8884ce4 |
1686 | |
1687 | This routine is automatically used whenever a scalar is required: |
1688 | |
1689 | my $x = Math::BigRat->new('3/1'); |
c6c613ed |
1690 | @array = (0,1,2,3); |
b8884ce4 |
1691 | $y = $array[$x]; # set $y to 3 |
1692 | |
1693 | =head2 as_int()/as_number() |
6de7f0cc |
1694 | |
7d341013 |
1695 | $x = Math::BigRat->new('13/7'); |
b68b7ab1 |
1696 | print $x->as_int(),"\n"; # '1' |
1697 | |
1698 | Returns a copy of the object as BigInt, truncated to an integer. |
7d341013 |
1699 | |
b68b7ab1 |
1700 | C<as_number()> is an alias for C<as_int()>. |
1701 | |
4de3d162 |
1702 | =head2 as_float() |
1703 | |
1704 | $x = Math::BigRat->new('13/7'); |
1705 | print $x->as_float(),"\n"; # '1' |
1706 | |
1707 | $x = Math::BigRat->new('2/3'); |
1708 | print $x->as_float(5),"\n"; # '0.66667' |
1709 | |
1710 | Returns a copy of the object as BigFloat, preserving the |
1711 | accuracy as wanted, or the default of 40 digits. |
1712 | |
1713 | This method was added in v0.22 of Math::BigRat (April 2008). |
1714 | |
b68b7ab1 |
1715 | =head2 as_hex() |
1716 | |
1717 | $x = Math::BigRat->new('13'); |
1718 | print $x->as_hex(),"\n"; # '0xd' |
1719 | |
1720 | Returns the BigRat as hexadecimal string. Works only for integers. |
1721 | |
1722 | =head2 as_bin() |
1723 | |
1724 | $x = Math::BigRat->new('13'); |
1725 | print $x->as_bin(),"\n"; # '0x1101' |
1726 | |
1727 | Returns the BigRat as binary string. Works only for integers. |
6de7f0cc |
1728 | |
b8884ce4 |
1729 | =head2 as_oct() |
1730 | |
1731 | $x = Math::BigRat->new('13'); |
1732 | print $x->as_oct(),"\n"; # '015' |
1733 | |
1734 | Returns the BigRat as octal string. Works only for integers. |
1735 | |
1736 | =head2 from_hex()/from_bin()/from_oct() |
1737 | |
1738 | my $h = Math::BigRat->from_hex('0x10'); |
1739 | my $b = Math::BigRat->from_bin('0b10000000'); |
1740 | my $o = Math::BigRat->from_oct('020'); |
1741 | |
1742 | Create a BigRat from an hexadecimal, binary or octal number |
1743 | in string form. |
1744 | |
1745 | =head2 length() |
1746 | |
1747 | $len = $x->length(); |
1748 | |
1749 | Return the length of $x in digitis for integer values. |
1750 | |
1751 | =head2 digit() |
1752 | |
1753 | print Math::BigRat->new('123/1')->digit(1); # 1 |
1754 | print Math::BigRat->new('123/1')->digit(-1); # 3 |
1755 | |
1756 | Return the N'ths digit from X when X is an integer value. |
1757 | |
1758 | =head2 bnorm() |
1759 | |
1760 | $x->bnorm(); |
1761 | |
1762 | Reduce the number to the shortest form. This routine is called |
1763 | automatically whenever it is needed. |
1764 | |
a4e2b1c6 |
1765 | =head2 bfac() |
6de7f0cc |
1766 | |
a4e2b1c6 |
1767 | $x->bfac(); |
6de7f0cc |
1768 | |
a4e2b1c6 |
1769 | Calculates the factorial of $x. For instance: |
6de7f0cc |
1770 | |
a4e2b1c6 |
1771 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 |
1772 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 |
184f15d5 |
1773 | |
7d341013 |
1774 | Works currently only for integers. |
6de7f0cc |
1775 | |
a4e2b1c6 |
1776 | =head2 bround()/round()/bfround() |
6de7f0cc |
1777 | |
a4e2b1c6 |
1778 | Are not yet implemented. |
6de7f0cc |
1779 | |
990fb837 |
1780 | =head2 bmod() |
1781 | |
1782 | use Math::BigRat; |
1783 | my $x = Math::BigRat->new('7/4'); |
1784 | my $y = Math::BigRat->new('4/3'); |
1785 | print $x->bmod($y); |
1786 | |
1787 | Set $x to the remainder of the division of $x by $y. |
1788 | |
b8884ce4 |
1789 | =head2 bneg() |
1790 | |
1791 | $x->bneg(); |
1792 | |
1793 | Used to negate the object in-place. |
1794 | |
7d341013 |
1795 | =head2 is_one() |
1796 | |
1797 | print "$x is 1\n" if $x->is_one(); |
1798 | |
1799 | Return true if $x is exactly one, otherwise false. |
1800 | |
1801 | =head2 is_zero() |
1802 | |
1803 | print "$x is 0\n" if $x->is_zero(); |
1804 | |
1805 | Return true if $x is exactly zero, otherwise false. |
1806 | |
b8884ce4 |
1807 | =head2 is_pos()/is_positive() |
7d341013 |
1808 | |
1809 | print "$x is >= 0\n" if $x->is_positive(); |
1810 | |
1811 | Return true if $x is positive (greater than or equal to zero), otherwise |
1812 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. |
1813 | |
b68b7ab1 |
1814 | C<is_positive()> is an alias for C<is_pos()>. |
1815 | |
b8884ce4 |
1816 | =head2 is_neg()/is_negative() |
7d341013 |
1817 | |
1818 | print "$x is < 0\n" if $x->is_negative(); |
1819 | |
1820 | Return true if $x is negative (smaller than zero), otherwise false. Please |
1821 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. |
1822 | |
b68b7ab1 |
1823 | C<is_negative()> is an alias for C<is_neg()>. |
1824 | |
7d341013 |
1825 | =head2 is_int() |
1826 | |
1827 | print "$x is an integer\n" if $x->is_int(); |
1828 | |
1829 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise |
1830 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. |
1831 | |
1832 | =head2 is_odd() |
1833 | |
1834 | print "$x is odd\n" if $x->is_odd(); |
1835 | |
1836 | Return true if $x is odd, otherwise false. |
1837 | |
1838 | =head2 is_even() |
1839 | |
1840 | print "$x is even\n" if $x->is_even(); |
1841 | |
1842 | Return true if $x is even, otherwise false. |
1843 | |
1844 | =head2 bceil() |
1845 | |
1846 | $x->bceil(); |
1847 | |
1848 | Set $x to the next bigger integer value (e.g. truncate the number to integer |
1849 | and then increment it by one). |
1850 | |
1851 | =head2 bfloor() |
1852 | |
1853 | $x->bfloor(); |
1854 | |
1855 | Truncate $x to an integer value. |
6de7f0cc |
1856 | |
7afd7a91 |
1857 | =head2 bsqrt() |
1858 | |
1859 | $x->bsqrt(); |
1860 | |
1861 | Calculate the square root of $x. |
1862 | |
b8884ce4 |
1863 | =head2 broot() |
1864 | |
1865 | $x->broot($n); |
1866 | |
1867 | Calculate the N'th root of $x. |
1868 | |
1869 | =head2 badd()/bmul()/bsub()/bdiv()/bdec()/binc() |
1870 | |
1871 | Please see the documentation in L<Math::BigInt>. |
1872 | |
1873 | =head2 copy() |
1874 | |
1875 | my $z = $x->copy(); |
1876 | |
1877 | Makes a deep copy of the object. |
1878 | |
1879 | Please see the documentation in L<Math::BigInt> for further details. |
1880 | |
1881 | =head2 bstr()/bsstr() |
1882 | |
1883 | my $x = Math::BigInt->new('8/4'); |
1884 | print $x->bstr(),"\n"; # prints 1/2 |
1885 | print $x->bsstr(),"\n"; # prints 1/2 |
1886 | |
1887 | Return a string representating this object. |
1888 | |
1889 | =head2 bacmp()/bcmp() |
1890 | |
1891 | Used to compare numbers. |
1892 | |
1893 | Please see the documentation in L<Math::BigInt> for further details. |
1894 | |
1895 | =head2 blsft()/brsft() |
1896 | |
1897 | Used to shift numbers left/right. |
1898 | |
1899 | Please see the documentation in L<Math::BigInt> for further details. |
1900 | |
1901 | =head2 bpow() |
1902 | |
1903 | $x->bpow($y); |
1904 | |
1905 | Compute $x ** $y. |
1906 | |
1907 | Please see the documentation in L<Math::BigInt> for further details. |
1908 | |
116a1b2f |
1909 | =head2 bexp() |
1910 | |
1911 | $x->bexp($accuracy); # calculate e ** X |
1912 | |
1913 | Calculates two integers A and B so that A/B is equal to C<e ** $x>, where C<e> is |
1914 | Euler's number. |
1915 | |
1916 | This method was added in v0.20 of Math::BigRat (May 2007). |
1917 | |
1918 | See also L<blog()>. |
1919 | |
1920 | =head2 bnok() |
1921 | |
1922 | $x->bnok($y); # x over y (binomial coefficient n over k) |
1923 | |
1924 | Calculates the binomial coefficient n over k, also called the "choose" |
1925 | function. The result is equivalent to: |
1926 | |
1927 | ( n ) n! |
1928 | | - | = ------- |
1929 | ( k ) k!(n-k)! |
1930 | |
1931 | This method was added in v0.20 of Math::BigRat (May 2007). |
1932 | |
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1933 | =head2 config() |
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1934 | |
1935 | use Data::Dumper; |
1936 | |
1937 | print Dumper ( Math::BigRat->config() ); |
1938 | print Math::BigRat->config()->{lib},"\n"; |
1939 | |
1940 | Returns a hash containing the configuration, e.g. the version number, lib |
1941 | loaded etc. The following hash keys are currently filled in with the |
1942 | appropriate information. |
1943 | |
1944 | key RO/RW Description |
1945 | Example |
1946 | ============================================================ |
1947 | lib RO Name of the Math library |
1948 | Math::BigInt::Calc |
1949 | lib_version RO Version of 'lib' |
1950 | 0.30 |
1951 | class RO The class of config you just called |
1952 | Math::BigRat |
1953 | version RO version number of the class you used |
1954 | 0.10 |
1955 | upgrade RW To which class numbers are upgraded |
1956 | undef |
1957 | downgrade RW To which class numbers are downgraded |
1958 | undef |
1959 | precision RW Global precision |
1960 | undef |
1961 | accuracy RW Global accuracy |
1962 | undef |
1963 | round_mode RW Global round mode |
1964 | even |
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1965 | div_scale RW Fallback accuracy for div |
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1966 | 40 |
1967 | trap_nan RW Trap creation of NaN (undef = no) |
1968 | undef |
1969 | trap_inf RW Trap creation of +inf/-inf (undef = no) |
1970 | undef |
1971 | |
1972 | By passing a reference to a hash you may set the configuration values. This |
1973 | works only for values that a marked with a C<RW> above, anything else is |
1974 | read-only. |
1975 | |
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1976 | =head2 objectify() |
1977 | |
1978 | This is an internal routine that turns scalars into objects. |
1979 | |
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1980 | =head1 BUGS |
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1981 | |
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1982 | Some things are not yet implemented, or only implemented half-way: |
1983 | |
1984 | =over 2 |
1985 | |
1986 | =item inf handling (partial) |
1987 | |
1988 | =item NaN handling (partial) |
1989 | |
1990 | =item rounding (not implemented except for bceil/bfloor) |
1991 | |
1992 | =item $x ** $y where $y is not an integer |
1993 | |
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1994 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) |
1995 | |
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1996 | =back |
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1997 | |
1998 | =head1 LICENSE |
1999 | |
2000 | This program is free software; you may redistribute it and/or modify it under |
2001 | the same terms as Perl itself. |
2002 | |
2003 | =head1 SEE ALSO |
2004 | |
2005 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
2006 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
2007 | |
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2008 | See L<http://search.cpan.org/search?dist=bignum> for a way to use |
2009 | Math::BigRat. |
2010 | |
2011 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> |
2012 | may contain more documentation and examples as well as testcases. |
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2013 | |
2014 | =head1 AUTHORS |
2015 | |
c6c613ed |
2016 | (C) by Tels L<http://bloodgate.com/> 2001 - 2009. |
2017 | |
2018 | Currently maintained by Jonathan "Duke" Leto <jonathan@leto.net> L<http://leto.net> |
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2019 | |
2020 | =cut |