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 | |
08a3f4a9 |
26 | $VERSION = '0.21'; |
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 |
bd49aa09 |
212 | my $diff_e = $nf->exponent()->bsub( $f->exponent); |
990fb837 |
213 | if ($diff_e->is_negative()) |
214 | { |
215 | # < 0: mul d with it |
12fc2493 |
216 | $MBI->_lsft( $self->{_d}, $MBI->_new( $diff_e->babs()), 10); |
990fb837 |
217 | } |
218 | elsif (!$diff_e->is_zero()) |
184f15d5 |
219 | { |
990fb837 |
220 | # > 0: mul n with it |
12fc2493 |
221 | $MBI->_lsft( $self->{_n}, $MBI->_new( $diff_e), 10); |
184f15d5 |
222 | } |
184f15d5 |
223 | } |
224 | else |
225 | { |
12fc2493 |
226 | # both d and n look like (big)ints |
227 | |
228 | $self->{sign} = '+'; # no sign => '+' |
229 | $self->{_n} = undef; |
230 | $self->{_d} = undef; |
b8884ce4 |
231 | if ($n =~ /^([+-]?)0*([0-9]+)\z/) # first part ok? |
12fc2493 |
232 | { |
233 | $self->{sign} = $1 || '+'; # no sign => '+' |
234 | $self->{_n} = $MBI->_new($2 || 0); |
235 | } |
236 | |
b8884ce4 |
237 | if ($d =~ /^([+-]?)0*([0-9]+)\z/) # second part ok? |
12fc2493 |
238 | { |
239 | $self->{sign} =~ tr/+-/-+/ if ($1 || '') eq '-'; # negate if second part neg. |
240 | $self->{_d} = $MBI->_new($2 || 0); |
241 | } |
242 | |
243 | if (!defined $self->{_n} || !defined $self->{_d}) |
244 | { |
245 | $d = Math::BigInt->new($d,undef,undef) unless ref $d; |
246 | $n = Math::BigInt->new($n,undef,undef) unless ref $n; |
233f7bc0 |
247 | |
12fc2493 |
248 | if ($n->{sign} =~ /^[+-]$/ && $d->{sign} =~ /^[+-]$/) |
249 | { |
250 | # both parts are ok as integers (wierd things like ' 1e0' |
251 | $self->{_n} = $MBI->_copy($n->{value}); |
252 | $self->{_d} = $MBI->_copy($d->{value}); |
253 | $self->{sign} = $n->{sign}; |
254 | $self->{sign} =~ tr/+-/-+/ if $d->{sign} eq '-'; # -1/-2 => 1/2 |
255 | return $self->bnorm(); |
256 | } |
257 | |
258 | $self->{sign} = '+'; # a default sign |
259 | return $self->bnan() if $n->is_nan() || $d->is_nan(); |
260 | |
261 | # handle inf cases: |
262 | if ($n->is_inf() || $d->is_inf()) |
7afd7a91 |
263 | { |
12fc2493 |
264 | if ($n->is_inf()) |
265 | { |
266 | return $self->bnan() if $d->is_inf(); # both are inf => NaN |
267 | my $s = '+'; # '+inf/+123' or '-inf/-123' |
268 | $s = '-' if substr($n->{sign},0,1) ne $d->{sign}; |
269 | # +-inf/123 => +-inf |
270 | return $self->binf($s); |
271 | } |
272 | # 123/inf => 0 |
273 | return $self->bzero(); |
7afd7a91 |
274 | } |
12fc2493 |
275 | } |
184f15d5 |
276 | } |
990fb837 |
277 | |
184f15d5 |
278 | return $self->bnorm(); |
279 | } |
280 | |
281 | # simple string input |
282 | if (($n =~ /[\.eE]/)) |
283 | { |
7d341013 |
284 | # looks like a float, quacks like a float, so probably is a float |
12fc2493 |
285 | $self->{sign} = 'NaN'; |
7d341013 |
286 | local $Math::BigFloat::accuracy = undef; |
287 | local $Math::BigFloat::precision = undef; |
7d341013 |
288 | $self->_new_from_float(Math::BigFloat->new($n,undef,undef)); |
184f15d5 |
289 | } |
290 | else |
291 | { |
12fc2493 |
292 | # for simple forms, use $MBI directly |
b8884ce4 |
293 | if ($n =~ /^([+-]?)0*([0-9]+)\z/) |
12fc2493 |
294 | { |
295 | $self->{sign} = $1 || '+'; |
296 | $self->{_n} = $MBI->_new($2 || 0); |
297 | $self->{_d} = $MBI->_one(); |
298 | } |
299 | else |
300 | { |
301 | my $n = Math::BigInt->new($n,undef,undef); |
302 | $self->{_n} = $MBI->_copy($n->{value}); |
303 | $self->{_d} = $MBI->_one(); |
304 | $self->{sign} = $n->{sign}; |
305 | return $self->bnan() if $self->{sign} eq 'NaN'; |
306 | return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/; |
307 | } |
184f15d5 |
308 | } |
309 | $self->bnorm(); |
310 | } |
311 | |
9b924220 |
312 | sub copy |
313 | { |
b68b7ab1 |
314 | # if two arguments, the first one is the class to "swallow" subclasses |
315 | my ($c,$x) = @_; |
316 | |
317 | if (scalar @_ == 1) |
9b924220 |
318 | { |
b68b7ab1 |
319 | $x = $_[0]; |
9b924220 |
320 | $c = ref($x); |
321 | } |
322 | return unless ref($x); # only for objects |
323 | |
12fc2493 |
324 | my $self = bless {}, $c; |
9b924220 |
325 | |
326 | $self->{sign} = $x->{sign}; |
12fc2493 |
327 | $self->{_d} = $MBI->_copy($x->{_d}); |
328 | $self->{_n} = $MBI->_copy($x->{_n}); |
9b924220 |
329 | $self->{_a} = $x->{_a} if defined $x->{_a}; |
330 | $self->{_p} = $x->{_p} if defined $x->{_p}; |
331 | $self; |
332 | } |
333 | |
990fb837 |
334 | ############################################################################## |
335 | |
336 | sub config |
337 | { |
338 | # return (later set?) configuration data as hash ref |
b68b7ab1 |
339 | my $class = shift || 'Math::BigRat'; |
990fb837 |
340 | |
116a1b2f |
341 | if (@_ == 1 && ref($_[0]) ne 'HASH') |
342 | { |
343 | my $cfg = $class->SUPER::config(); |
344 | return $cfg->{$_[0]}; |
345 | } |
346 | |
990fb837 |
347 | my $cfg = $class->SUPER::config(@_); |
348 | |
349 | # now we need only to override the ones that are different from our parent |
350 | $cfg->{class} = $class; |
351 | $cfg->{with} = $MBI; |
352 | $cfg; |
353 | } |
354 | |
355 | ############################################################################## |
8f675a64 |
356 | |
184f15d5 |
357 | sub bstr |
358 | { |
7afd7a91 |
359 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
360 | |
361 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
362 | { |
363 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
364 | return $s; |
365 | } |
366 | |
7afd7a91 |
367 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2' |
184f15d5 |
368 | |
12fc2493 |
369 | return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d}); |
370 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
371 | } |
372 | |
373 | sub bsstr |
374 | { |
b68b7ab1 |
375 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
376 | |
377 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
378 | { |
379 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
380 | return $s; |
381 | } |
382 | |
383 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
12fc2493 |
384 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
385 | } |
386 | |
387 | sub bnorm |
388 | { |
12fc2493 |
389 | # reduce the number to the shortest form |
b68b7ab1 |
390 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
391 | |
12fc2493 |
392 | # Both parts must be objects of whatever we are using today. |
bd49aa09 |
393 | if ( my $c = $MBI->_check($x->{_n}) ) |
990fb837 |
394 | { |
bd49aa09 |
395 | require Carp; Carp::croak ("n did not pass the self-check ($c) in bnorm()"); |
990fb837 |
396 | } |
bd49aa09 |
397 | if ( my $c = $MBI->_check($x->{_d}) ) |
990fb837 |
398 | { |
bd49aa09 |
399 | require Carp; Carp::croak ("d did not pass the self-check ($c) in bnorm()"); |
990fb837 |
400 | } |
6de7f0cc |
401 | |
6de7f0cc |
402 | # no normalize for NaN, inf etc. |
403 | return $x if $x->{sign} !~ /^[+-]$/; |
404 | |
184f15d5 |
405 | # normalize zeros to 0/1 |
12fc2493 |
406 | if ($MBI->_is_zero($x->{_n})) |
184f15d5 |
407 | { |
12fc2493 |
408 | $x->{sign} = '+'; # never leave a -0 |
409 | $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d}); |
184f15d5 |
410 | return $x; |
411 | } |
412 | |
12fc2493 |
413 | return $x if $MBI->_is_one($x->{_d}); # no need to reduce |
6de7f0cc |
414 | |
184f15d5 |
415 | # reduce other numbers |
12fc2493 |
416 | my $gcd = $MBI->_copy($x->{_n}); |
417 | $gcd = $MBI->_gcd($gcd,$x->{_d}); |
418 | |
419 | if (!$MBI->_is_one($gcd)) |
184f15d5 |
420 | { |
12fc2493 |
421 | $x->{_n} = $MBI->_div($x->{_n},$gcd); |
422 | $x->{_d} = $MBI->_div($x->{_d},$gcd); |
184f15d5 |
423 | } |
184f15d5 |
424 | $x; |
425 | } |
426 | |
427 | ############################################################################## |
b68b7ab1 |
428 | # sign manipulation |
429 | |
430 | sub bneg |
431 | { |
432 | # (BRAT or num_str) return BRAT |
433 | # negate number or make a negated number from string |
434 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
435 | |
436 | return $x if $x->modify('bneg'); |
437 | |
438 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN' |
439 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $MBI->_is_zero($x->{_n})); |
440 | $x; |
441 | } |
442 | |
443 | ############################################################################## |
184f15d5 |
444 | # special values |
445 | |
446 | sub _bnan |
447 | { |
990fb837 |
448 | # used by parent class bnan() to initialize number to NaN |
184f15d5 |
449 | my $self = shift; |
990fb837 |
450 | |
451 | if ($_trap_nan) |
452 | { |
453 | require Carp; |
454 | my $class = ref($self); |
233f7bc0 |
455 | # "$self" below will stringify the object, this blows up if $self is a |
456 | # partial object (happens under trap_nan), so fix it beforehand |
457 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; |
458 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; |
990fb837 |
459 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
460 | } |
12fc2493 |
461 | $self->{_n} = $MBI->_zero(); |
462 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
463 | } |
464 | |
465 | sub _binf |
466 | { |
7d341013 |
467 | # used by parent class bone() to initialize number to +inf/-inf |
184f15d5 |
468 | my $self = shift; |
990fb837 |
469 | |
470 | if ($_trap_inf) |
471 | { |
472 | require Carp; |
473 | my $class = ref($self); |
233f7bc0 |
474 | # "$self" below will stringify the object, this blows up if $self is a |
475 | # partial object (happens under trap_nan), so fix it beforehand |
476 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; |
477 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; |
990fb837 |
478 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); |
479 | } |
12fc2493 |
480 | $self->{_n} = $MBI->_zero(); |
481 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
482 | } |
483 | |
484 | sub _bone |
485 | { |
7d341013 |
486 | # used by parent class bone() to initialize number to +1/-1 |
184f15d5 |
487 | my $self = shift; |
12fc2493 |
488 | $self->{_n} = $MBI->_one(); |
489 | $self->{_d} = $MBI->_one(); |
184f15d5 |
490 | } |
491 | |
492 | sub _bzero |
493 | { |
990fb837 |
494 | # used by parent class bzero() to initialize number to 0 |
184f15d5 |
495 | my $self = shift; |
12fc2493 |
496 | $self->{_n} = $MBI->_zero(); |
497 | $self->{_d} = $MBI->_one(); |
184f15d5 |
498 | } |
499 | |
500 | ############################################################################## |
501 | # mul/add/div etc |
502 | |
503 | sub badd |
504 | { |
7afd7a91 |
505 | # add two rational numbers |
7d341013 |
506 | |
507 | # set up parameters |
508 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
509 | # objectify is costly, so avoid it |
510 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
511 | { |
512 | ($self,$x,$y,@r) = objectify(2,@_); |
513 | } |
184f15d5 |
514 | |
12fc2493 |
515 | # +inf + +inf => +inf, -inf + -inf => -inf |
516 | return $x->binf(substr($x->{sign},0,1)) |
517 | if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
184f15d5 |
518 | |
12fc2493 |
519 | # +inf + -inf or -inf + +inf => NaN |
520 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
184f15d5 |
521 | |
522 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
523 | # - + - = --------- = -- |
524 | # 4 3 4*3 12 |
525 | |
7d341013 |
526 | # we do not compute the gcd() here, but simple do: |
233f7bc0 |
527 | # 5 7 5*3 + 7*4 43 |
7d341013 |
528 | # - + - = --------- = -- |
529 | # 4 3 4*3 12 |
530 | |
12fc2493 |
531 | # and bnorm() will then take care of the rest |
184f15d5 |
532 | |
233f7bc0 |
533 | # 5 * 3 |
12fc2493 |
534 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
7d341013 |
535 | |
233f7bc0 |
536 | # 7 * 4 |
12fc2493 |
537 | my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} ); |
184f15d5 |
538 | |
233f7bc0 |
539 | # 5 * 3 + 7 * 4 |
12fc2493 |
540 | ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign}); |
184f15d5 |
541 | |
233f7bc0 |
542 | # 4 * 3 |
12fc2493 |
543 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
544 | |
233f7bc0 |
545 | # normalize result, and possible round |
7d341013 |
546 | $x->bnorm()->round(@r); |
184f15d5 |
547 | } |
548 | |
549 | sub bsub |
550 | { |
7afd7a91 |
551 | # subtract two rational numbers |
7d341013 |
552 | |
553 | # set up parameters |
554 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
555 | # objectify is costly, so avoid it |
556 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
557 | { |
558 | ($self,$x,$y,@r) = objectify(2,@_); |
559 | } |
184f15d5 |
560 | |
7afd7a91 |
561 | # flip sign of $x, call badd(), then flip sign of result |
562 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
563 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
564 | $x->badd($y,@r); # does norm and round |
7afd7a91 |
565 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
566 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
7afd7a91 |
567 | $x; |
184f15d5 |
568 | } |
569 | |
570 | sub bmul |
571 | { |
7afd7a91 |
572 | # multiply two rational numbers |
7d341013 |
573 | |
574 | # set up parameters |
575 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
576 | # objectify is costly, so avoid it |
577 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
578 | { |
579 | ($self,$x,$y,@r) = objectify(2,@_); |
580 | } |
184f15d5 |
581 | |
582 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
583 | |
584 | # inf handling |
585 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
586 | { |
587 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
588 | # result will always be +-inf: |
589 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
590 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
591 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
592 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
593 | return $x->binf('-'); |
594 | } |
595 | |
596 | # x== 0 # also: or y == 1 or y == -1 |
597 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
598 | |
12fc2493 |
599 | # XXX TODO: |
600 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
601 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
602 | |
12fc2493 |
603 | # 1 2 1 * 2 2 1 |
604 | # - * - = ----- = - = - |
605 | # 4 3 4 * 3 12 6 |
7d341013 |
606 | |
12fc2493 |
607 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); |
608 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
609 | |
610 | # compute new sign |
611 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
612 | |
7d341013 |
613 | $x->bnorm()->round(@r); |
184f15d5 |
614 | } |
615 | |
616 | sub bdiv |
617 | { |
618 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
619 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
7d341013 |
620 | |
621 | # set up parameters |
622 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
623 | # objectify is costly, so avoid it |
624 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
625 | { |
626 | ($self,$x,$y,@r) = objectify(2,@_); |
627 | } |
184f15d5 |
628 | |
629 | return $self->_div_inf($x,$y) |
630 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
631 | |
632 | # x== 0 # also: or y == 1 or y == -1 |
633 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
634 | |
12fc2493 |
635 | # XXX TODO: list context, upgrade |
636 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
637 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
638 | |
184f15d5 |
639 | # 1 1 1 3 |
640 | # - / - == - * - |
641 | # 4 3 4 1 |
7d341013 |
642 | |
12fc2493 |
643 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
644 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); |
184f15d5 |
645 | |
646 | # compute new sign |
647 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
648 | |
7d341013 |
649 | $x->bnorm()->round(@r); |
6de7f0cc |
650 | $x; |
184f15d5 |
651 | } |
652 | |
990fb837 |
653 | sub bmod |
654 | { |
655 | # compute "remainder" (in Perl way) of $x / $y |
656 | |
657 | # set up parameters |
658 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
659 | # objectify is costly, so avoid it |
660 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
661 | { |
662 | ($self,$x,$y,@r) = objectify(2,@_); |
663 | } |
664 | |
990fb837 |
665 | return $self->_div_inf($x,$y) |
666 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
667 | |
668 | return $x if $x->is_zero(); # 0 / 7 = 0, mod 0 |
669 | |
670 | # compute $x - $y * floor($x/$y), keeping the sign of $x |
671 | |
12fc2493 |
672 | # copy x to u, make it positive and then do a normal division ($u/$y) |
673 | my $u = bless { sign => '+' }, $self; |
674 | $u->{_n} = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d} ); |
675 | $u->{_d} = $MBI->_mul( $MBI->_copy($x->{_d}), $y->{_n} ); |
676 | |
677 | # compute floor(u) |
678 | if (! $MBI->_is_one($u->{_d})) |
990fb837 |
679 | { |
12fc2493 |
680 | $u->{_n} = $MBI->_div($u->{_n},$u->{_d}); # 22/7 => 3/1 w/ truncate |
681 | # no need to set $u->{_d} to 1, since below we set it to $y->{_d} anyway |
990fb837 |
682 | } |
683 | |
12fc2493 |
684 | # now compute $y * $u |
685 | $u->{_d} = $MBI->_copy($y->{_d}); # 1 * $y->{_d}, see floor above |
686 | $u->{_n} = $MBI->_mul($u->{_n},$y->{_n}); |
990fb837 |
687 | |
12fc2493 |
688 | my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive |
990fb837 |
689 | # compute $x - $u |
690 | $x->bsub($u); |
691 | $x->{sign} = $xsign; # put sign back |
692 | |
693 | $x->bnorm()->round(@r); |
990fb837 |
694 | } |
695 | |
184f15d5 |
696 | ############################################################################## |
a4e2b1c6 |
697 | # bdec/binc |
698 | |
699 | sub bdec |
700 | { |
701 | # decrement value (subtract 1) |
702 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
703 | |
704 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
705 | |
706 | if ($x->{sign} eq '-') |
707 | { |
12fc2493 |
708 | $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2 |
a4e2b1c6 |
709 | } |
710 | else |
711 | { |
12fc2493 |
712 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? |
a4e2b1c6 |
713 | { |
714 | # 1/3 -- => -2/3 |
12fc2493 |
715 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
716 | $x->{sign} = '-'; |
717 | } |
718 | else |
719 | { |
12fc2493 |
720 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 |
a4e2b1c6 |
721 | } |
722 | } |
723 | $x->bnorm()->round(@r); |
a4e2b1c6 |
724 | } |
725 | |
726 | sub binc |
727 | { |
728 | # increment value (add 1) |
729 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
730 | |
731 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
732 | |
733 | if ($x->{sign} eq '-') |
734 | { |
12fc2493 |
735 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) |
a4e2b1c6 |
736 | { |
737 | # -1/3 ++ => 2/3 (overflow at 0) |
12fc2493 |
738 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
739 | $x->{sign} = '+'; |
740 | } |
741 | else |
742 | { |
12fc2493 |
743 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 |
a4e2b1c6 |
744 | } |
745 | } |
746 | else |
747 | { |
12fc2493 |
748 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 |
a4e2b1c6 |
749 | } |
750 | $x->bnorm()->round(@r); |
a4e2b1c6 |
751 | } |
752 | |
753 | ############################################################################## |
184f15d5 |
754 | # is_foo methods (the rest is inherited) |
755 | |
756 | sub is_int |
757 | { |
758 | # return true if arg (BRAT or num_str) is an integer |
9b924220 |
759 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
760 | |
761 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
12fc2493 |
762 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer |
184f15d5 |
763 | 0; |
764 | } |
765 | |
766 | sub is_zero |
767 | { |
768 | # return true if arg (BRAT or num_str) is zero |
9b924220 |
769 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
770 | |
12fc2493 |
771 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); |
184f15d5 |
772 | 0; |
773 | } |
774 | |
775 | sub is_one |
776 | { |
777 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
9b924220 |
778 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
779 | |
9b924220 |
780 | my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; |
184f15d5 |
781 | return 1 |
12fc2493 |
782 | if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})); |
184f15d5 |
783 | 0; |
784 | } |
785 | |
786 | sub is_odd |
787 | { |
788 | # return true if arg (BFLOAT or num_str) is odd or false if even |
9b924220 |
789 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
790 | |
791 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
12fc2493 |
792 | ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1 |
184f15d5 |
793 | 0; |
794 | } |
795 | |
796 | sub is_even |
797 | { |
798 | # return true if arg (BINT or num_str) is even or false if odd |
9b924220 |
799 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
800 | |
801 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
12fc2493 |
802 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never |
803 | && $MBI->_is_even($x->{_n})); # but 4/1 is |
184f15d5 |
804 | 0; |
805 | } |
806 | |
184f15d5 |
807 | ############################################################################## |
808 | # parts() and friends |
809 | |
810 | sub numerator |
811 | { |
812 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
a4e2b1c6 |
813 | |
12fc2493 |
814 | # NaN, inf, -inf |
815 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
a4e2b1c6 |
816 | |
12fc2493 |
817 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; |
184f15d5 |
818 | $n; |
819 | } |
820 | |
821 | sub denominator |
822 | { |
823 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
824 | |
12fc2493 |
825 | # NaN |
826 | return Math::BigInt->new($x->{sign}) if $x->{sign} eq 'NaN'; |
827 | # inf, -inf |
828 | return Math::BigInt->bone() if $x->{sign} !~ /^[+-]$/; |
829 | |
830 | Math::BigInt->new($MBI->_str($x->{_d})); |
184f15d5 |
831 | } |
832 | |
833 | sub parts |
834 | { |
835 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
836 | |
12fc2493 |
837 | my $c = 'Math::BigInt'; |
838 | |
839 | return ($c->bnan(),$c->bnan()) if $x->{sign} eq 'NaN'; |
840 | return ($c->binf(),$c->binf()) if $x->{sign} eq '+inf'; |
841 | return ($c->binf('-'),$c->binf()) if $x->{sign} eq '-inf'; |
a4e2b1c6 |
842 | |
12fc2493 |
843 | my $n = $c->new( $MBI->_str($x->{_n})); |
184f15d5 |
844 | $n->{sign} = $x->{sign}; |
12fc2493 |
845 | my $d = $c->new( $MBI->_str($x->{_d})); |
846 | ($n,$d); |
184f15d5 |
847 | } |
848 | |
849 | sub length |
850 | { |
9b924220 |
851 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
852 | |
853 | return $nan unless $x->is_int(); |
12fc2493 |
854 | $MBI->_len($x->{_n}); # length(-123/1) => length(123) |
184f15d5 |
855 | } |
856 | |
857 | sub digit |
858 | { |
12fc2493 |
859 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); |
9b924220 |
860 | |
861 | return $nan unless $x->is_int(); |
12fc2493 |
862 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) |
184f15d5 |
863 | } |
864 | |
865 | ############################################################################## |
866 | # special calc routines |
867 | |
868 | sub bceil |
869 | { |
870 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
871 | |
12fc2493 |
872 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
873 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
874 | |
12fc2493 |
875 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
876 | $x->{_d} = $MBI->_one(); # d => 1 |
877 | $x->{_n} = $MBI->_inc($x->{_n}) |
878 | if $x->{sign} eq '+'; # +22/7 => 4/1 |
879 | $x->{sign} = '+' if $MBI->_is_zero($x->{_n}); # -0 => 0 |
184f15d5 |
880 | $x; |
881 | } |
882 | |
883 | sub bfloor |
884 | { |
885 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
886 | |
12fc2493 |
887 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
888 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
889 | |
12fc2493 |
890 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
891 | $x->{_d} = $MBI->_one(); # d => 1 |
892 | $x->{_n} = $MBI->_inc($x->{_n}) |
893 | if $x->{sign} eq '-'; # -22/7 => -4/1 |
184f15d5 |
894 | $x; |
895 | } |
896 | |
897 | sub bfac |
898 | { |
a4e2b1c6 |
899 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
900 | |
12fc2493 |
901 | # if $x is not an integer |
902 | if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d}))) |
a4e2b1c6 |
903 | { |
12fc2493 |
904 | return $x->bnan(); |
a4e2b1c6 |
905 | } |
12fc2493 |
906 | |
907 | $x->{_n} = $MBI->_fac($x->{_n}); |
908 | # since _d is 1, we don't need to reduce/norm the result |
909 | $x->round(@r); |
184f15d5 |
910 | } |
911 | |
912 | sub bpow |
913 | { |
7d341013 |
914 | # power ($x ** $y) |
915 | |
916 | # set up parameters |
917 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
918 | # objectify is costly, so avoid it |
919 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
920 | { |
921 | ($self,$x,$y,@r) = objectify(2,@_); |
922 | } |
184f15d5 |
923 | |
924 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
925 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
926 | return $x->bone(@r) if $y->is_zero(); |
927 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
12fc2493 |
928 | |
929 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) |
184f15d5 |
930 | { |
931 | # if $x == -1 and odd/even y => +1/-1 |
932 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
933 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
934 | } |
935 | # 1 ** -y => 1 / (1 ** |y|) |
936 | # so do test for negative $y after above's clause |
12fc2493 |
937 | |
184f15d5 |
938 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
939 | |
a4e2b1c6 |
940 | # shortcut y/1 (and/or x/1) |
12fc2493 |
941 | if ($MBI->_is_one($y->{_d})) |
a4e2b1c6 |
942 | { |
943 | # shortcut for x/1 and y/1 |
12fc2493 |
944 | if ($MBI->_is_one($x->{_d})) |
a4e2b1c6 |
945 | { |
12fc2493 |
946 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
a4e2b1c6 |
947 | if ($y->{sign} eq '-') |
948 | { |
949 | # 0.2 ** -3 => 1/(0.2 ** 3) |
950 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
951 | } |
952 | # correct sign; + ** + => + |
953 | if ($x->{sign} eq '-') |
954 | { |
955 | # - * - => +, - * - * - => - |
12fc2493 |
956 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
957 | } |
958 | return $x->round(@r); |
959 | } |
960 | # x/z ** y/1 |
12fc2493 |
961 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
962 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); |
a4e2b1c6 |
963 | if ($y->{sign} eq '-') |
964 | { |
965 | # 0.2 ** -3 => 1/(0.2 ** 3) |
966 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
967 | } |
968 | # correct sign; + ** + => + |
969 | if ($x->{sign} eq '-') |
970 | { |
971 | # - * - => +, - * - * - => - |
12fc2493 |
972 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
973 | } |
974 | return $x->round(@r); |
975 | } |
976 | |
977 | # regular calculation (this is wrong for d/e ** f/g) |
12fc2493 |
978 | my $pow2 = $self->bone(); |
979 | my $y1 = $MBI->_div ( $MBI->_copy($y->{_n}), $y->{_d}); |
980 | my $two = $MBI->_two(); |
981 | |
982 | while (!$MBI->_is_one($y1)) |
184f15d5 |
983 | { |
12fc2493 |
984 | $pow2->bmul($x) if $MBI->_is_odd($y1); |
985 | $MBI->_div($y1, $two); |
184f15d5 |
986 | $x->bmul($x); |
987 | } |
988 | $x->bmul($pow2) unless $pow2->is_one(); |
989 | # n ** -x => 1/n ** x |
990 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; |
7d341013 |
991 | $x->bnorm()->round(@r); |
184f15d5 |
992 | } |
993 | |
994 | sub blog |
995 | { |
7afd7a91 |
996 | # set up parameters |
997 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
998 | |
999 | # objectify is costly, so avoid it |
1000 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1001 | { |
9b924220 |
1002 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
7afd7a91 |
1003 | } |
1004 | |
9b924220 |
1005 | # blog(1,Y) => 0 |
1006 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; |
1007 | |
7afd7a91 |
1008 | # $x <= 0 => NaN |
1009 | return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; |
1010 | |
1011 | if ($x->is_int() && $y->is_int()) |
1012 | { |
1013 | return $self->new($x->as_number()->blog($y->as_number(),@r)); |
1014 | } |
1015 | |
9b924220 |
1016 | # do it with floats |
1017 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); |
1018 | } |
1019 | |
116a1b2f |
1020 | sub bexp |
1021 | { |
1022 | # set up parameters |
1023 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
1024 | |
1025 | # objectify is costly, so avoid it |
1026 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1027 | { |
1028 | ($self,$x,$y,$a,$p,$r) = objectify(2,$class,@_); |
1029 | } |
1030 | |
1031 | return $x->binf() if $x->{sign} eq '+inf'; |
1032 | return $x->bzero() if $x->{sign} eq '-inf'; |
1033 | |
1034 | # we need to limit the accuracy to protect against overflow |
1035 | my $fallback = 0; |
1036 | my ($scale,@params); |
1037 | ($x,@params) = $x->_find_round_parameters($a,$p,$r); |
1038 | |
1039 | # also takes care of the "error in _find_round_parameters?" case |
1040 | return $x if $x->{sign} eq 'NaN'; |
1041 | |
1042 | # no rounding at all, so must use fallback |
1043 | if (scalar @params == 0) |
1044 | { |
1045 | # simulate old behaviour |
1046 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1047 | $params[1] = undef; # P = undef |
1048 | $scale = $params[0]+4; # at least four more for proper round |
1049 | $params[2] = $r; # round mode by caller or undef |
1050 | $fallback = 1; # to clear a/p afterwards |
1051 | } |
1052 | else |
1053 | { |
1054 | # the 4 below is empirical, and there might be cases where it's not enough... |
1055 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined |
1056 | } |
1057 | |
1058 | return $x->bone(@params) if $x->is_zero(); |
1059 | |
1060 | # See the comments in Math::BigFloat on how this algorithm works. |
1061 | # Basically we calculate A and B (where B is faculty(N)) so that A/B = e |
1062 | |
1063 | my $x_org = $x->copy(); |
1064 | if ($scale <= 75) |
1065 | { |
1066 | # set $x directly from a cached string form |
1067 | $x->{_n} = $MBI->_new("90933395208605785401971970164779391644753259799242"); |
1068 | $x->{_d} = $MBI->_new("33452526613163807108170062053440751665152000000000"); |
1069 | $x->{sign} = '+'; |
1070 | } |
1071 | else |
1072 | { |
1073 | # compute A and B so that e = A / B. |
1074 | |
1075 | # After some terms we end up with this, so we use it as a starting point: |
1076 | my $A = $MBI->_new("90933395208605785401971970164779391644753259799242"); |
1077 | my $F = $MBI->_new(42); my $step = 42; |
1078 | |
1079 | # Compute how many steps we need to take to get $A and $B sufficiently big |
1080 | my $steps = Math::BigFloat::_len_to_steps($scale - 4); |
1081 | # print STDERR "# Doing $steps steps for ", $scale-4, " digits\n"; |
1082 | while ($step++ <= $steps) |
1083 | { |
1084 | # calculate $a * $f + 1 |
1085 | $A = $MBI->_mul($A, $F); |
1086 | $A = $MBI->_inc($A); |
1087 | # increment f |
1088 | $F = $MBI->_inc($F); |
1089 | } |
1090 | # compute $B as factorial of $steps (this is faster than doing it manually) |
1091 | my $B = $MBI->_fac($MBI->_new($steps)); |
1092 | |
1093 | # print "A ", $MBI->_str($A), "\nB ", $MBI->_str($B), "\n"; |
1094 | |
1095 | $x->{_n} = $A; |
1096 | $x->{_d} = $B; |
1097 | $x->{sign} = '+'; |
1098 | } |
1099 | |
1100 | # $x contains now an estimate of e, with some surplus digits, so we can round |
1101 | if (!$x_org->is_one()) |
1102 | { |
1103 | # raise $x to the wanted power and round it in one step: |
1104 | $x->bpow($x_org, @params); |
1105 | } |
1106 | else |
1107 | { |
1108 | # else just round the already computed result |
1109 | delete $x->{_a}; delete $x->{_p}; |
1110 | # shortcut to not run through _find_round_parameters again |
1111 | if (defined $params[0]) |
1112 | { |
1113 | $x->bround($params[0],$params[2]); # then round accordingly |
1114 | } |
1115 | else |
1116 | { |
1117 | $x->bfround($params[1],$params[2]); # then round accordingly |
1118 | } |
1119 | } |
1120 | if ($fallback) |
1121 | { |
1122 | # clear a/p after round, since user did not request it |
1123 | delete $x->{_a}; delete $x->{_p}; |
1124 | } |
1125 | |
1126 | $x; |
1127 | } |
1128 | |
1129 | sub bnok |
1130 | { |
1131 | # set up parameters |
1132 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1133 | |
1134 | # objectify is costly, so avoid it |
1135 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1136 | { |
1137 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
1138 | } |
1139 | |
1140 | # do it with floats |
1141 | $x->_new_from_float( $x->_as_float()->bnok(Math::BigFloat->new("$y"),@r) ); |
1142 | } |
1143 | |
12fc2493 |
1144 | sub _float_from_part |
1145 | { |
1146 | my $x = shift; |
1147 | |
1148 | my $f = Math::BigFloat->bzero(); |
1149 | $f->{_m} = $MBI->_copy($x); |
1150 | $f->{_e} = $MBI->_zero(); |
1151 | |
1152 | $f; |
1153 | } |
1154 | |
9b924220 |
1155 | sub _as_float |
1156 | { |
1157 | my $x = shift; |
1158 | |
1159 | local $Math::BigFloat::upgrade = undef; |
1160 | local $Math::BigFloat::accuracy = undef; |
1161 | local $Math::BigFloat::precision = undef; |
1162 | # 22/7 => 3.142857143.. |
12fc2493 |
1163 | |
1164 | my $a = $x->accuracy() || 0; |
1165 | if ($a != 0 || !$MBI->_is_one($x->{_d})) |
1166 | { |
1167 | # n/d |
1168 | return Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy()); |
1169 | } |
1170 | # just n |
1171 | Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n})); |
7afd7a91 |
1172 | } |
1173 | |
1174 | sub broot |
1175 | { |
1176 | # set up parameters |
1177 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1178 | # objectify is costly, so avoid it |
1179 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1180 | { |
1181 | ($self,$x,$y,@r) = objectify(2,@_); |
1182 | } |
1183 | |
1184 | if ($x->is_int() && $y->is_int()) |
1185 | { |
1186 | return $self->new($x->as_number()->broot($y->as_number(),@r)); |
1187 | } |
9b924220 |
1188 | |
1189 | # do it with floats |
1190 | $x->_new_from_float( $x->_as_float()->broot($y,@r) ); |
7afd7a91 |
1191 | } |
1192 | |
1193 | sub bmodpow |
1194 | { |
1195 | # set up parameters |
1196 | my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); |
1197 | # objectify is costly, so avoid it |
1198 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1199 | { |
1200 | ($self,$x,$y,$m,@r) = objectify(3,@_); |
1201 | } |
1202 | |
1203 | # $x or $y or $m are NaN or +-inf => NaN |
1204 | return $x->bnan() |
1205 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || |
1206 | $m->{sign} !~ /^[+-]$/; |
1207 | |
1208 | if ($x->is_int() && $y->is_int() && $m->is_int()) |
1209 | { |
1210 | return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); |
1211 | } |
1212 | |
1213 | warn ("bmodpow() not fully implemented"); |
1214 | $x->bnan(); |
1215 | } |
1216 | |
1217 | sub bmodinv |
1218 | { |
1219 | # set up parameters |
1220 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1221 | # objectify is costly, so avoid it |
1222 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1223 | { |
1224 | ($self,$x,$y,@r) = objectify(2,@_); |
1225 | } |
1226 | |
1227 | # $x or $y are NaN or +-inf => NaN |
1228 | return $x->bnan() |
1229 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; |
1230 | |
1231 | if ($x->is_int() && $y->is_int()) |
1232 | { |
1233 | return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); |
1234 | } |
1235 | |
1236 | warn ("bmodinv() not fully implemented"); |
1237 | $x->bnan(); |
184f15d5 |
1238 | } |
1239 | |
1240 | sub bsqrt |
1241 | { |
990fb837 |
1242 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1243 | |
1244 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 |
1245 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf |
1246 | return $x->round(@r) if $x->is_zero() || $x->is_one(); |
1247 | |
1248 | local $Math::BigFloat::upgrade = undef; |
1249 | local $Math::BigFloat::downgrade = undef; |
1250 | local $Math::BigFloat::precision = undef; |
1251 | local $Math::BigFloat::accuracy = undef; |
1252 | local $Math::BigInt::upgrade = undef; |
1253 | local $Math::BigInt::precision = undef; |
1254 | local $Math::BigInt::accuracy = undef; |
9b924220 |
1255 | |
12fc2493 |
1256 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); |
1257 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); |
1258 | |
1259 | # XXX TODO: we probably can optimze this: |
184f15d5 |
1260 | |
990fb837 |
1261 | # if sqrt(D) was not integer |
9b924220 |
1262 | if ($x->{_d}->{_es} ne '+') |
990fb837 |
1263 | { |
9b924220 |
1264 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 |
12fc2493 |
1265 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 |
990fb837 |
1266 | } |
1267 | # if sqrt(N) was not integer |
9b924220 |
1268 | if ($x->{_n}->{_es} ne '+') |
990fb837 |
1269 | { |
9b924220 |
1270 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 |
12fc2493 |
1271 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 |
990fb837 |
1272 | } |
12fc2493 |
1273 | |
990fb837 |
1274 | # convert parts to $MBI again |
12fc2493 |
1275 | $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10) |
1276 | if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY'; |
1277 | $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10) |
1278 | if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY'; |
1279 | |
990fb837 |
1280 | $x->bnorm()->round(@r); |
184f15d5 |
1281 | } |
1282 | |
1283 | sub blsft |
1284 | { |
9b924220 |
1285 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1286 | |
9b924220 |
1287 | $b = 2 unless defined $b; |
1288 | $b = $self->new($b) unless ref ($b); |
1289 | $x->bmul( $b->copy()->bpow($y), @r); |
184f15d5 |
1290 | $x; |
1291 | } |
1292 | |
1293 | sub brsft |
1294 | { |
12fc2493 |
1295 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1296 | |
9b924220 |
1297 | $b = 2 unless defined $b; |
1298 | $b = $self->new($b) unless ref ($b); |
1299 | $x->bdiv( $b->copy()->bpow($y), @r); |
184f15d5 |
1300 | $x; |
1301 | } |
1302 | |
1303 | ############################################################################## |
1304 | # round |
1305 | |
1306 | sub round |
1307 | { |
1308 | $_[0]; |
1309 | } |
1310 | |
1311 | sub bround |
1312 | { |
1313 | $_[0]; |
1314 | } |
1315 | |
1316 | sub bfround |
1317 | { |
1318 | $_[0]; |
1319 | } |
1320 | |
1321 | ############################################################################## |
1322 | # comparing |
1323 | |
1324 | sub bcmp |
1325 | { |
7afd7a91 |
1326 | # compare two signed numbers |
1327 | |
1328 | # set up parameters |
1329 | my ($self,$x,$y) = (ref($_[0]),@_); |
1330 | # objectify is costly, so avoid it |
1331 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1332 | { |
1333 | ($self,$x,$y) = objectify(2,@_); |
1334 | } |
184f15d5 |
1335 | |
1336 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1337 | { |
1338 | # handle +-inf and NaN |
1339 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1340 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
1341 | return +1 if $x->{sign} eq '+inf'; |
1342 | return -1 if $x->{sign} eq '-inf'; |
1343 | return -1 if $y->{sign} eq '+inf'; |
1344 | return +1; |
1345 | } |
1346 | # check sign for speed first |
1347 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
1348 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
1349 | |
1350 | # shortcut |
12fc2493 |
1351 | my $xz = $MBI->_is_zero($x->{_n}); |
1352 | my $yz = $MBI->_is_zero($y->{_n}); |
184f15d5 |
1353 | return 0 if $xz && $yz; # 0 <=> 0 |
1354 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
1355 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
1356 | |
12fc2493 |
1357 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1358 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1359 | |
1360 | my $cmp = $MBI->_acmp($t,$u); # signs are equal |
1361 | $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse |
1362 | $cmp; |
184f15d5 |
1363 | } |
1364 | |
1365 | sub bacmp |
1366 | { |
7afd7a91 |
1367 | # compare two numbers (as unsigned) |
9b924220 |
1368 | |
7afd7a91 |
1369 | # set up parameters |
1370 | my ($self,$x,$y) = (ref($_[0]),@_); |
1371 | # objectify is costly, so avoid it |
1372 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1373 | { |
9b924220 |
1374 | ($self,$x,$y) = objectify(2,$class,@_); |
7afd7a91 |
1375 | } |
184f15d5 |
1376 | |
1377 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1378 | { |
1379 | # handle +-inf and NaN |
1380 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1381 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
7afd7a91 |
1382 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1383 | return -1; |
184f15d5 |
1384 | } |
1385 | |
12fc2493 |
1386 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1387 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1388 | $MBI->_acmp($t,$u); # ignore signs |
184f15d5 |
1389 | } |
1390 | |
1391 | ############################################################################## |
1392 | # output conversation |
1393 | |
7d341013 |
1394 | sub numify |
1395 | { |
1396 | # convert 17/8 => float (aka 2.125) |
b68b7ab1 |
1397 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
7d341013 |
1398 | |
1399 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc |
1400 | |
93c87d9d |
1401 | # N/1 => N |
b68b7ab1 |
1402 | my $neg = ''; $neg = '-' if $x->{sign} eq '-'; |
1403 | return $neg . $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); |
93c87d9d |
1404 | |
b68b7ab1 |
1405 | $x->_as_float()->numify() + 0.0; |
7d341013 |
1406 | } |
1407 | |
184f15d5 |
1408 | sub as_number |
1409 | { |
9b924220 |
1410 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
1411 | |
08a3f4a9 |
1412 | # NaN, inf etc |
1413 | return Math::BigInt->new($x->{sign}) if $x->{sign} !~ /^[+-]$/; |
990fb837 |
1414 | |
12fc2493 |
1415 | my $u = Math::BigInt->bzero(); |
1416 | $u->{sign} = $x->{sign}; |
1417 | $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3 |
1418 | $u; |
184f15d5 |
1419 | } |
1420 | |
9b924220 |
1421 | sub as_bin |
1422 | { |
1423 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1424 | |
1425 | return $x unless $x->is_int(); |
1426 | |
1427 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1428 | $s . $MBI->_as_bin($x->{_n}); |
9b924220 |
1429 | } |
1430 | |
1431 | sub as_hex |
1432 | { |
1433 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1434 | |
1435 | return $x unless $x->is_int(); |
1436 | |
1437 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1438 | $s . $MBI->_as_hex($x->{_n}); |
9b924220 |
1439 | } |
1440 | |
b8884ce4 |
1441 | sub as_oct |
1442 | { |
1443 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1444 | |
1445 | return $x unless $x->is_int(); |
1446 | |
1447 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
1448 | $s . $MBI->_as_oct($x->{_n}); |
1449 | } |
1450 | |
1451 | ############################################################################## |
1452 | |
1453 | sub from_hex |
1454 | { |
1455 | my $class = shift; |
1456 | |
1457 | $class->new(@_); |
1458 | } |
1459 | |
1460 | sub from_bin |
1461 | { |
1462 | my $class = shift; |
1463 | |
1464 | $class->new(@_); |
1465 | } |
1466 | |
1467 | sub from_oct |
1468 | { |
1469 | my $class = shift; |
1470 | |
1471 | my @parts; |
1472 | for my $c (@_) |
1473 | { |
1474 | push @parts, Math::BigInt->from_oct($c); |
1475 | } |
1476 | $class->new ( @parts ); |
1477 | } |
1478 | |
b68b7ab1 |
1479 | ############################################################################## |
1480 | # import |
1481 | |
6de7f0cc |
1482 | sub import |
1483 | { |
1484 | my $self = shift; |
1485 | my $l = scalar @_; |
1486 | my $lib = ''; my @a; |
b8884ce4 |
1487 | my $try = 'try'; |
9b924220 |
1488 | |
6de7f0cc |
1489 | for ( my $i = 0; $i < $l ; $i++) |
1490 | { |
6de7f0cc |
1491 | if ( $_[$i] eq ':constant' ) |
1492 | { |
1493 | # this rest causes overlord er load to step in |
6de7f0cc |
1494 | overload::constant float => sub { $self->new(shift); }; |
1495 | } |
1496 | # elsif ($_[$i] eq 'upgrade') |
1497 | # { |
1498 | # # this causes upgrading |
b68b7ab1 |
1499 | # $upgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1500 | # $i++; |
1501 | # } |
1502 | elsif ($_[$i] eq 'downgrade') |
1503 | { |
1504 | # this causes downgrading |
b68b7ab1 |
1505 | $downgrade = $_[$i+1]; # or undef to disable |
6de7f0cc |
1506 | $i++; |
1507 | } |
b8884ce4 |
1508 | elsif ($_[$i] =~ /^(lib|try|only)\z/) |
6de7f0cc |
1509 | { |
b68b7ab1 |
1510 | $lib = $_[$i+1] || ''; # default Calc |
b8884ce4 |
1511 | $try = $1; # lib, try or only |
6de7f0cc |
1512 | $i++; |
1513 | } |
1514 | elsif ($_[$i] eq 'with') |
1515 | { |
233f7bc0 |
1516 | # this argument is no longer used |
1517 | #$MBI = $_[$i+1] || 'Math::BigInt::Calc'; # default Math::BigInt::Calc |
6de7f0cc |
1518 | $i++; |
1519 | } |
1520 | else |
1521 | { |
1522 | push @a, $_[$i]; |
1523 | } |
1524 | } |
b68b7ab1 |
1525 | require Math::BigInt; |
6de7f0cc |
1526 | |
b68b7ab1 |
1527 | # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still have GMP |
1528 | if ($lib ne '') |
1529 | { |
1530 | my @c = split /\s*,\s*/, $lib; |
1531 | foreach (@c) |
6de7f0cc |
1532 | { |
b68b7ab1 |
1533 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters |
6de7f0cc |
1534 | } |
233f7bc0 |
1535 | $lib = join(",", @c); |
93c87d9d |
1536 | } |
233f7bc0 |
1537 | my @import = ('objectify'); |
b8884ce4 |
1538 | push @import, $try => $lib if $lib ne ''; |
233f7bc0 |
1539 | |
1540 | # MBI already loaded, so feed it our lib arguments |
1541 | Math::BigInt->import( @import ); |
6de7f0cc |
1542 | |
12fc2493 |
1543 | $MBI = Math::BigFloat->config()->{lib}; |
b68b7ab1 |
1544 | |
1545 | # register us with MBI to get notified of future lib changes |
1546 | Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } ); |
9b924220 |
1547 | |
233f7bc0 |
1548 | # any non :constant stuff is handled by our parent, Exporter (loaded |
1549 | # by Math::BigFloat, even if @_ is empty, to give it a chance |
6de7f0cc |
1550 | $self->SUPER::import(@a); # for subclasses |
1551 | $self->export_to_level(1,$self,@a); # need this, too |
1552 | } |
184f15d5 |
1553 | |
1554 | 1; |
1555 | |
1556 | __END__ |
1557 | |
1558 | =head1 NAME |
1559 | |
b68b7ab1 |
1560 | Math::BigRat - Arbitrary big rational numbers |
184f15d5 |
1561 | |
1562 | =head1 SYNOPSIS |
1563 | |
7d341013 |
1564 | use Math::BigRat; |
184f15d5 |
1565 | |
7afd7a91 |
1566 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
184f15d5 |
1567 | |
7d341013 |
1568 | print $x->bstr(),"\n"; |
1569 | print $x ** 2,"\n"; |
184f15d5 |
1570 | |
7afd7a91 |
1571 | my $y = Math::BigRat->new('inf'); |
1572 | print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; |
1573 | |
1574 | my $z = Math::BigRat->new(144); $z->bsqrt(); |
1575 | |
184f15d5 |
1576 | =head1 DESCRIPTION |
1577 | |
7d341013 |
1578 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
b68b7ab1 |
1579 | for arbitrary big rational numbers. |
184f15d5 |
1580 | |
1581 | =head2 MATH LIBRARY |
1582 | |
b8884ce4 |
1583 | You can change the underlying module that does the low-level |
1584 | math operations by using: |
184f15d5 |
1585 | |
b8884ce4 |
1586 | use Math::BigRat try => 'GMP'; |
184f15d5 |
1587 | |
b8884ce4 |
1588 | Note: This needs Math::BigInt::GMP installed. |
184f15d5 |
1589 | |
1590 | The following would first try to find Math::BigInt::Foo, then |
1591 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
1592 | |
b8884ce4 |
1593 | use Math::BigRat try => 'Foo,Math::BigInt::Bar'; |
184f15d5 |
1594 | |
b8884ce4 |
1595 | If you want to get warned when the fallback occurs, replace "try" with |
1596 | "lib": |
184f15d5 |
1597 | |
b8884ce4 |
1598 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
7d341013 |
1599 | |
b8884ce4 |
1600 | If you want the code to die instead, replace "try" with |
1601 | "only": |
1602 | |
1603 | use Math::BigRat only => 'Foo,Math::BigInt::Bar'; |
7d341013 |
1604 | |
184f15d5 |
1605 | =head1 METHODS |
1606 | |
3c4b39be |
1607 | Any methods not listed here are derived from Math::BigFloat (or |
6de7f0cc |
1608 | Math::BigInt), so make sure you check these two modules for further |
1609 | information. |
1610 | |
1611 | =head2 new() |
184f15d5 |
1612 | |
1613 | $x = Math::BigRat->new('1/3'); |
1614 | |
1615 | Create a new Math::BigRat object. Input can come in various forms: |
1616 | |
7d341013 |
1617 | $x = Math::BigRat->new(123); # scalars |
7afd7a91 |
1618 | $x = Math::BigRat->new('inf'); # infinity |
7d341013 |
1619 | $x = Math::BigRat->new('123.3'); # float |
184f15d5 |
1620 | $x = Math::BigRat->new('1/3'); # simple string |
1621 | $x = Math::BigRat->new('1 / 3'); # spaced |
1622 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
1623 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
1624 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
6de7f0cc |
1625 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
184f15d5 |
1626 | |
b68b7ab1 |
1627 | # You can also give D and N as different objects: |
1628 | $x = Math::BigRat->new( |
1629 | Math::BigInt->new(-123), |
1630 | Math::BigInt->new(7), |
1631 | ); # => -123/7 |
1632 | |
6de7f0cc |
1633 | =head2 numerator() |
184f15d5 |
1634 | |
1635 | $n = $x->numerator(); |
1636 | |
1637 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
1638 | |
6de7f0cc |
1639 | =head2 denominator() |
184f15d5 |
1640 | |
1641 | $d = $x->denominator(); |
1642 | |
1643 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
1644 | |
6de7f0cc |
1645 | =head2 parts() |
184f15d5 |
1646 | |
1647 | ($n,$d) = $x->parts(); |
1648 | |
1649 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
1650 | BigInts. |
1651 | |
b8884ce4 |
1652 | =head2 numify() |
1653 | |
1654 | my $y = $x->numify(); |
1655 | |
1656 | Returns the object as a scalar. This will lose some data if the object |
1657 | cannot be represented by a normal Perl scalar (integer or float), so |
1658 | use as_int() instead. |
1659 | |
1660 | This routine is automatically used whenever a scalar is required: |
1661 | |
1662 | my $x = Math::BigRat->new('3/1'); |
1663 | @array = (1,2,3); |
1664 | $y = $array[$x]; # set $y to 3 |
1665 | |
1666 | =head2 as_int()/as_number() |
6de7f0cc |
1667 | |
7d341013 |
1668 | $x = Math::BigRat->new('13/7'); |
b68b7ab1 |
1669 | print $x->as_int(),"\n"; # '1' |
1670 | |
1671 | Returns a copy of the object as BigInt, truncated to an integer. |
7d341013 |
1672 | |
b68b7ab1 |
1673 | C<as_number()> is an alias for C<as_int()>. |
1674 | |
1675 | =head2 as_hex() |
1676 | |
1677 | $x = Math::BigRat->new('13'); |
1678 | print $x->as_hex(),"\n"; # '0xd' |
1679 | |
1680 | Returns the BigRat as hexadecimal string. Works only for integers. |
1681 | |
1682 | =head2 as_bin() |
1683 | |
1684 | $x = Math::BigRat->new('13'); |
1685 | print $x->as_bin(),"\n"; # '0x1101' |
1686 | |
1687 | Returns the BigRat as binary string. Works only for integers. |
6de7f0cc |
1688 | |
b8884ce4 |
1689 | =head2 as_oct() |
1690 | |
1691 | $x = Math::BigRat->new('13'); |
1692 | print $x->as_oct(),"\n"; # '015' |
1693 | |
1694 | Returns the BigRat as octal string. Works only for integers. |
1695 | |
1696 | =head2 from_hex()/from_bin()/from_oct() |
1697 | |
1698 | my $h = Math::BigRat->from_hex('0x10'); |
1699 | my $b = Math::BigRat->from_bin('0b10000000'); |
1700 | my $o = Math::BigRat->from_oct('020'); |
1701 | |
1702 | Create a BigRat from an hexadecimal, binary or octal number |
1703 | in string form. |
1704 | |
1705 | =head2 length() |
1706 | |
1707 | $len = $x->length(); |
1708 | |
1709 | Return the length of $x in digitis for integer values. |
1710 | |
1711 | =head2 digit() |
1712 | |
1713 | print Math::BigRat->new('123/1')->digit(1); # 1 |
1714 | print Math::BigRat->new('123/1')->digit(-1); # 3 |
1715 | |
1716 | Return the N'ths digit from X when X is an integer value. |
1717 | |
1718 | =head2 bnorm() |
1719 | |
1720 | $x->bnorm(); |
1721 | |
1722 | Reduce the number to the shortest form. This routine is called |
1723 | automatically whenever it is needed. |
1724 | |
a4e2b1c6 |
1725 | =head2 bfac() |
6de7f0cc |
1726 | |
a4e2b1c6 |
1727 | $x->bfac(); |
6de7f0cc |
1728 | |
a4e2b1c6 |
1729 | Calculates the factorial of $x. For instance: |
6de7f0cc |
1730 | |
a4e2b1c6 |
1731 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 |
1732 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 |
184f15d5 |
1733 | |
7d341013 |
1734 | Works currently only for integers. |
6de7f0cc |
1735 | |
a4e2b1c6 |
1736 | =head2 bround()/round()/bfround() |
6de7f0cc |
1737 | |
a4e2b1c6 |
1738 | Are not yet implemented. |
6de7f0cc |
1739 | |
990fb837 |
1740 | =head2 bmod() |
1741 | |
1742 | use Math::BigRat; |
1743 | my $x = Math::BigRat->new('7/4'); |
1744 | my $y = Math::BigRat->new('4/3'); |
1745 | print $x->bmod($y); |
1746 | |
1747 | Set $x to the remainder of the division of $x by $y. |
1748 | |
b8884ce4 |
1749 | =head2 bneg() |
1750 | |
1751 | $x->bneg(); |
1752 | |
1753 | Used to negate the object in-place. |
1754 | |
7d341013 |
1755 | =head2 is_one() |
1756 | |
1757 | print "$x is 1\n" if $x->is_one(); |
1758 | |
1759 | Return true if $x is exactly one, otherwise false. |
1760 | |
1761 | =head2 is_zero() |
1762 | |
1763 | print "$x is 0\n" if $x->is_zero(); |
1764 | |
1765 | Return true if $x is exactly zero, otherwise false. |
1766 | |
b8884ce4 |
1767 | =head2 is_pos()/is_positive() |
7d341013 |
1768 | |
1769 | print "$x is >= 0\n" if $x->is_positive(); |
1770 | |
1771 | Return true if $x is positive (greater than or equal to zero), otherwise |
1772 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. |
1773 | |
b68b7ab1 |
1774 | C<is_positive()> is an alias for C<is_pos()>. |
1775 | |
b8884ce4 |
1776 | =head2 is_neg()/is_negative() |
7d341013 |
1777 | |
1778 | print "$x is < 0\n" if $x->is_negative(); |
1779 | |
1780 | Return true if $x is negative (smaller than zero), otherwise false. Please |
1781 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. |
1782 | |
b68b7ab1 |
1783 | C<is_negative()> is an alias for C<is_neg()>. |
1784 | |
7d341013 |
1785 | =head2 is_int() |
1786 | |
1787 | print "$x is an integer\n" if $x->is_int(); |
1788 | |
1789 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise |
1790 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. |
1791 | |
1792 | =head2 is_odd() |
1793 | |
1794 | print "$x is odd\n" if $x->is_odd(); |
1795 | |
1796 | Return true if $x is odd, otherwise false. |
1797 | |
1798 | =head2 is_even() |
1799 | |
1800 | print "$x is even\n" if $x->is_even(); |
1801 | |
1802 | Return true if $x is even, otherwise false. |
1803 | |
1804 | =head2 bceil() |
1805 | |
1806 | $x->bceil(); |
1807 | |
1808 | Set $x to the next bigger integer value (e.g. truncate the number to integer |
1809 | and then increment it by one). |
1810 | |
1811 | =head2 bfloor() |
1812 | |
1813 | $x->bfloor(); |
1814 | |
1815 | Truncate $x to an integer value. |
6de7f0cc |
1816 | |
7afd7a91 |
1817 | =head2 bsqrt() |
1818 | |
1819 | $x->bsqrt(); |
1820 | |
1821 | Calculate the square root of $x. |
1822 | |
b8884ce4 |
1823 | =head2 broot() |
1824 | |
1825 | $x->broot($n); |
1826 | |
1827 | Calculate the N'th root of $x. |
1828 | |
1829 | =head2 badd()/bmul()/bsub()/bdiv()/bdec()/binc() |
1830 | |
1831 | Please see the documentation in L<Math::BigInt>. |
1832 | |
1833 | =head2 copy() |
1834 | |
1835 | my $z = $x->copy(); |
1836 | |
1837 | Makes a deep copy of the object. |
1838 | |
1839 | Please see the documentation in L<Math::BigInt> for further details. |
1840 | |
1841 | =head2 bstr()/bsstr() |
1842 | |
1843 | my $x = Math::BigInt->new('8/4'); |
1844 | print $x->bstr(),"\n"; # prints 1/2 |
1845 | print $x->bsstr(),"\n"; # prints 1/2 |
1846 | |
1847 | Return a string representating this object. |
1848 | |
1849 | =head2 bacmp()/bcmp() |
1850 | |
1851 | Used to compare numbers. |
1852 | |
1853 | Please see the documentation in L<Math::BigInt> for further details. |
1854 | |
1855 | =head2 blsft()/brsft() |
1856 | |
1857 | Used to shift numbers left/right. |
1858 | |
1859 | Please see the documentation in L<Math::BigInt> for further details. |
1860 | |
1861 | =head2 bpow() |
1862 | |
1863 | $x->bpow($y); |
1864 | |
1865 | Compute $x ** $y. |
1866 | |
1867 | Please see the documentation in L<Math::BigInt> for further details. |
1868 | |
116a1b2f |
1869 | =head2 bexp() |
1870 | |
1871 | $x->bexp($accuracy); # calculate e ** X |
1872 | |
1873 | Calculates two integers A and B so that A/B is equal to C<e ** $x>, where C<e> is |
1874 | Euler's number. |
1875 | |
1876 | This method was added in v0.20 of Math::BigRat (May 2007). |
1877 | |
1878 | See also L<blog()>. |
1879 | |
1880 | =head2 bnok() |
1881 | |
1882 | $x->bnok($y); # x over y (binomial coefficient n over k) |
1883 | |
1884 | Calculates the binomial coefficient n over k, also called the "choose" |
1885 | function. The result is equivalent to: |
1886 | |
1887 | ( n ) n! |
1888 | | - | = ------- |
1889 | ( k ) k!(n-k)! |
1890 | |
1891 | This method was added in v0.20 of Math::BigRat (May 2007). |
1892 | |
b8884ce4 |
1893 | =head2 config() |
990fb837 |
1894 | |
1895 | use Data::Dumper; |
1896 | |
1897 | print Dumper ( Math::BigRat->config() ); |
1898 | print Math::BigRat->config()->{lib},"\n"; |
1899 | |
1900 | Returns a hash containing the configuration, e.g. the version number, lib |
1901 | loaded etc. The following hash keys are currently filled in with the |
1902 | appropriate information. |
1903 | |
1904 | key RO/RW Description |
1905 | Example |
1906 | ============================================================ |
1907 | lib RO Name of the Math library |
1908 | Math::BigInt::Calc |
1909 | lib_version RO Version of 'lib' |
1910 | 0.30 |
1911 | class RO The class of config you just called |
1912 | Math::BigRat |
1913 | version RO version number of the class you used |
1914 | 0.10 |
1915 | upgrade RW To which class numbers are upgraded |
1916 | undef |
1917 | downgrade RW To which class numbers are downgraded |
1918 | undef |
1919 | precision RW Global precision |
1920 | undef |
1921 | accuracy RW Global accuracy |
1922 | undef |
1923 | round_mode RW Global round mode |
1924 | even |
3c4b39be |
1925 | div_scale RW Fallback accuracy for div |
990fb837 |
1926 | 40 |
1927 | trap_nan RW Trap creation of NaN (undef = no) |
1928 | undef |
1929 | trap_inf RW Trap creation of +inf/-inf (undef = no) |
1930 | undef |
1931 | |
1932 | By passing a reference to a hash you may set the configuration values. This |
1933 | works only for values that a marked with a C<RW> above, anything else is |
1934 | read-only. |
1935 | |
a4e2b1c6 |
1936 | =head1 BUGS |
6de7f0cc |
1937 | |
7d341013 |
1938 | Some things are not yet implemented, or only implemented half-way: |
1939 | |
1940 | =over 2 |
1941 | |
1942 | =item inf handling (partial) |
1943 | |
1944 | =item NaN handling (partial) |
1945 | |
1946 | =item rounding (not implemented except for bceil/bfloor) |
1947 | |
1948 | =item $x ** $y where $y is not an integer |
1949 | |
7afd7a91 |
1950 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) |
1951 | |
7d341013 |
1952 | =back |
184f15d5 |
1953 | |
1954 | =head1 LICENSE |
1955 | |
1956 | This program is free software; you may redistribute it and/or modify it under |
1957 | the same terms as Perl itself. |
1958 | |
1959 | =head1 SEE ALSO |
1960 | |
1961 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
1962 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
1963 | |
7d341013 |
1964 | See L<http://search.cpan.org/search?dist=bignum> for a way to use |
1965 | Math::BigRat. |
1966 | |
1967 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> |
1968 | may contain more documentation and examples as well as testcases. |
184f15d5 |
1969 | |
1970 | =head1 AUTHORS |
1971 | |
b8884ce4 |
1972 | (C) by Tels L<http://bloodgate.com/> 2001 - 2007. |
184f15d5 |
1973 | |
1974 | =cut |