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 |
b1f79218 |
12 | # _f : flags, used by MBR to flag parts of a rational as untouchable |
7afd7a91 |
13 | # You should not look at the innards of a BigRat - use the methods for this. |
184f15d5 |
14 | |
15 | package Math::BigRat; |
16 | |
a4e2b1c6 |
17 | require 5.005_03; |
184f15d5 |
18 | use strict; |
19 | |
7afd7a91 |
20 | require Exporter; |
184f15d5 |
21 | use Math::BigFloat; |
12fc2493 |
22 | use vars qw($VERSION @ISA $upgrade $downgrade |
990fb837 |
23 | $accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf); |
184f15d5 |
24 | |
25 | @ISA = qw(Exporter Math::BigFloat); |
184f15d5 |
26 | |
12fc2493 |
27 | $VERSION = '0.13'; |
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; |
40 | } |
9b924220 |
41 | |
184f15d5 |
42 | ############################################################################## |
12fc2493 |
43 | # Global constants and flags. Access these only via the accessor methods! |
184f15d5 |
44 | |
184f15d5 |
45 | $accuracy = $precision = undef; |
46 | $round_mode = 'even'; |
47 | $div_scale = 40; |
48 | $upgrade = undef; |
49 | $downgrade = undef; |
50 | |
12fc2493 |
51 | # These are internally, and not to be used from the outside at all! |
990fb837 |
52 | |
53 | $_trap_nan = 0; # are NaNs ok? set w/ config() |
54 | $_trap_inf = 0; # are infs ok? set w/ config() |
55 | |
12fc2493 |
56 | # the package we are using for our private parts, defaults to: |
57 | # Math::BigInt->config()->{lib} |
58 | my $MBI = 'Math::BigInt::Calc'; |
59 | |
184f15d5 |
60 | my $nan = 'NaN'; |
9b924220 |
61 | my $class = 'Math::BigRat'; |
62 | my $IMPORT = 0; |
184f15d5 |
63 | |
8f675a64 |
64 | sub isa |
65 | { |
66 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't |
67 | UNIVERSAL::isa(@_); |
68 | } |
69 | |
12fc2493 |
70 | ############################################################################## |
9b924220 |
71 | |
184f15d5 |
72 | sub _new_from_float |
73 | { |
7afd7a91 |
74 | # turn a single float input into a rational number (like '0.1') |
184f15d5 |
75 | my ($self,$f) = @_; |
76 | |
77 | return $self->bnan() if $f->is_nan(); |
9b924220 |
78 | return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/; |
184f15d5 |
79 | |
12fc2493 |
80 | $self->{_n} = $MBI->_copy( $f->{_m} ); # mantissa |
81 | $self->{_d} = $MBI->_one(); |
9b924220 |
82 | $self->{sign} = $f->{sign} || '+'; |
83 | if ($f->{_es} eq '-') |
184f15d5 |
84 | { |
85 | # something like Math::BigRat->new('0.1'); |
9b924220 |
86 | # 1 / 1 => 1/10 |
12fc2493 |
87 | $MBI->_lsft ( $self->{_d}, $f->{_e} ,10); |
184f15d5 |
88 | } |
89 | else |
90 | { |
91 | # something like Math::BigRat->new('10'); |
92 | # 1 / 1 => 10/1 |
12fc2493 |
93 | $MBI->_lsft ( $self->{_n}, $f->{_e} ,10) unless |
94 | $MBI->_is_zero($f->{_e}); |
184f15d5 |
95 | } |
184f15d5 |
96 | $self; |
97 | } |
98 | |
99 | sub new |
100 | { |
101 | # create a Math::BigRat |
102 | my $class = shift; |
103 | |
104 | my ($n,$d) = shift; |
105 | |
106 | my $self = { }; bless $self,$class; |
107 | |
184f15d5 |
108 | # input like (BigInt,BigInt) or (BigFloat,BigFloat) not handled yet |
109 | |
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 |
12fc2493 |
119 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = $n |
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 $$n < 0; |
12fc2493 |
127 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = $n |
128 | $self->{_d} = $MBI->_one(); # d => 1 |
184f15d5 |
129 | } |
12fc2493 |
130 | return $self->bnorm(); # normalize (120/1 => 12/10) |
184f15d5 |
131 | } |
12fc2493 |
132 | return $n->copy() if ref $n; # already a BigRat |
184f15d5 |
133 | |
134 | if (!defined $n) |
135 | { |
12fc2493 |
136 | $self->{_n} = $MBI->_zero(); # undef => 0 |
137 | $self->{_d} = $MBI->_one(); |
184f15d5 |
138 | $self->{sign} = '+'; |
12fc2493 |
139 | return $self; |
184f15d5 |
140 | } |
12fc2493 |
141 | |
184f15d5 |
142 | # string input with / delimiter |
143 | if ($n =~ /\s*\/\s*/) |
144 | { |
990fb837 |
145 | return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
146 | return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid |
184f15d5 |
147 | ($n,$d) = split (/\//,$n); |
148 | # try as BigFloats first |
149 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) |
150 | { |
7d341013 |
151 | local $Math::BigFloat::accuracy = undef; |
152 | local $Math::BigFloat::precision = undef; |
9b924220 |
153 | |
12fc2493 |
154 | # one of them looks like a float |
9b924220 |
155 | my $nf = Math::BigFloat->new($n,undef,undef); |
990fb837 |
156 | $self->{sign} = '+'; |
157 | return $self->bnan() if $nf->is_nan(); |
12fc2493 |
158 | $self->{_n} = $MBI->_copy( $nf->{_m} ); # get mantissa |
9b924220 |
159 | |
184f15d5 |
160 | # now correct $self->{_n} due to $n |
7d341013 |
161 | my $f = Math::BigFloat->new($d,undef,undef); |
990fb837 |
162 | return $self->bnan() if $f->is_nan(); |
12fc2493 |
163 | $self->{_d} = $MBI->_copy( $f->{_m} ); |
9b924220 |
164 | |
990fb837 |
165 | # calculate the difference between nE and dE |
12fc2493 |
166 | # XXX TODO: check that exponent() makes a copy to avoid copy() |
167 | my $diff_e = $nf->exponent()->copy()->bsub( $f->exponent); |
990fb837 |
168 | if ($diff_e->is_negative()) |
169 | { |
170 | # < 0: mul d with it |
12fc2493 |
171 | $MBI->_lsft( $self->{_d}, $MBI->_new( $diff_e->babs()), 10); |
990fb837 |
172 | } |
173 | elsif (!$diff_e->is_zero()) |
184f15d5 |
174 | { |
990fb837 |
175 | # > 0: mul n with it |
12fc2493 |
176 | $MBI->_lsft( $self->{_n}, $MBI->_new( $diff_e), 10); |
184f15d5 |
177 | } |
184f15d5 |
178 | } |
179 | else |
180 | { |
12fc2493 |
181 | # both d and n look like (big)ints |
182 | |
183 | $self->{sign} = '+'; # no sign => '+' |
184 | $self->{_n} = undef; |
185 | $self->{_d} = undef; |
186 | if ($n =~ /^([+-]?)0*(\d+)\z/) # first part ok? |
187 | { |
188 | $self->{sign} = $1 || '+'; # no sign => '+' |
189 | $self->{_n} = $MBI->_new($2 || 0); |
190 | } |
191 | |
192 | if ($d =~ /^([+-]?)0*(\d+)\z/) # second part ok? |
193 | { |
194 | $self->{sign} =~ tr/+-/-+/ if ($1 || '') eq '-'; # negate if second part neg. |
195 | $self->{_d} = $MBI->_new($2 || 0); |
196 | } |
197 | |
198 | if (!defined $self->{_n} || !defined $self->{_d}) |
199 | { |
200 | $d = Math::BigInt->new($d,undef,undef) unless ref $d; |
201 | $n = Math::BigInt->new($n,undef,undef) unless ref $n; |
202 | |
203 | if ($n->{sign} =~ /^[+-]$/ && $d->{sign} =~ /^[+-]$/) |
204 | { |
205 | # both parts are ok as integers (wierd things like ' 1e0' |
206 | $self->{_n} = $MBI->_copy($n->{value}); |
207 | $self->{_d} = $MBI->_copy($d->{value}); |
208 | $self->{sign} = $n->{sign}; |
209 | $self->{sign} =~ tr/+-/-+/ if $d->{sign} eq '-'; # -1/-2 => 1/2 |
210 | return $self->bnorm(); |
211 | } |
212 | |
213 | $self->{sign} = '+'; # a default sign |
214 | return $self->bnan() if $n->is_nan() || $d->is_nan(); |
215 | |
216 | # handle inf cases: |
217 | if ($n->is_inf() || $d->is_inf()) |
7afd7a91 |
218 | { |
12fc2493 |
219 | if ($n->is_inf()) |
220 | { |
221 | return $self->bnan() if $d->is_inf(); # both are inf => NaN |
222 | my $s = '+'; # '+inf/+123' or '-inf/-123' |
223 | $s = '-' if substr($n->{sign},0,1) ne $d->{sign}; |
224 | # +-inf/123 => +-inf |
225 | return $self->binf($s); |
226 | } |
227 | # 123/inf => 0 |
228 | return $self->bzero(); |
7afd7a91 |
229 | } |
12fc2493 |
230 | } |
184f15d5 |
231 | } |
990fb837 |
232 | |
184f15d5 |
233 | return $self->bnorm(); |
234 | } |
235 | |
236 | # simple string input |
237 | if (($n =~ /[\.eE]/)) |
238 | { |
7d341013 |
239 | # looks like a float, quacks like a float, so probably is a float |
12fc2493 |
240 | $self->{sign} = 'NaN'; |
7d341013 |
241 | local $Math::BigFloat::accuracy = undef; |
242 | local $Math::BigFloat::precision = undef; |
7d341013 |
243 | $self->_new_from_float(Math::BigFloat->new($n,undef,undef)); |
184f15d5 |
244 | } |
245 | else |
246 | { |
12fc2493 |
247 | # for simple forms, use $MBI directly |
248 | if ($n =~ /^([+-]?)0*(\d+)\z/) |
249 | { |
250 | $self->{sign} = $1 || '+'; |
251 | $self->{_n} = $MBI->_new($2 || 0); |
252 | $self->{_d} = $MBI->_one(); |
253 | } |
254 | else |
255 | { |
256 | my $n = Math::BigInt->new($n,undef,undef); |
257 | $self->{_n} = $MBI->_copy($n->{value}); |
258 | $self->{_d} = $MBI->_one(); |
259 | $self->{sign} = $n->{sign}; |
260 | return $self->bnan() if $self->{sign} eq 'NaN'; |
261 | return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/; |
262 | } |
184f15d5 |
263 | } |
264 | $self->bnorm(); |
265 | } |
266 | |
9b924220 |
267 | sub copy |
268 | { |
269 | my ($c,$x); |
270 | if (@_ > 1) |
271 | { |
272 | # if two arguments, the first one is the class to "swallow" subclasses |
273 | ($c,$x) = @_; |
274 | } |
275 | else |
276 | { |
277 | $x = shift; |
278 | $c = ref($x); |
279 | } |
280 | return unless ref($x); # only for objects |
281 | |
12fc2493 |
282 | my $self = bless {}, $c; |
9b924220 |
283 | |
284 | $self->{sign} = $x->{sign}; |
12fc2493 |
285 | $self->{_d} = $MBI->_copy($x->{_d}); |
286 | $self->{_n} = $MBI->_copy($x->{_n}); |
9b924220 |
287 | $self->{_a} = $x->{_a} if defined $x->{_a}; |
288 | $self->{_p} = $x->{_p} if defined $x->{_p}; |
289 | $self; |
290 | } |
291 | |
990fb837 |
292 | ############################################################################## |
293 | |
294 | sub config |
295 | { |
296 | # return (later set?) configuration data as hash ref |
297 | my $class = shift || 'Math::BigFloat'; |
298 | |
299 | my $cfg = $class->SUPER::config(@_); |
300 | |
301 | # now we need only to override the ones that are different from our parent |
302 | $cfg->{class} = $class; |
303 | $cfg->{with} = $MBI; |
304 | $cfg; |
305 | } |
306 | |
307 | ############################################################################## |
8f675a64 |
308 | |
184f15d5 |
309 | sub bstr |
310 | { |
7afd7a91 |
311 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
312 | |
313 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
314 | { |
315 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
316 | return $s; |
317 | } |
318 | |
7afd7a91 |
319 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2' |
184f15d5 |
320 | |
12fc2493 |
321 | return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d}); |
322 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
323 | } |
324 | |
325 | sub bsstr |
326 | { |
327 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
328 | |
329 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
330 | { |
331 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
332 | return $s; |
333 | } |
334 | |
335 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
12fc2493 |
336 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
184f15d5 |
337 | } |
338 | |
339 | sub bnorm |
340 | { |
12fc2493 |
341 | # reduce the number to the shortest form |
184f15d5 |
342 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
343 | |
12fc2493 |
344 | # Both parts must be objects of whatever we are using today. |
345 | # Second check because Calc.pm has ARRAY res as unblessed objects. |
346 | if (ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY') |
990fb837 |
347 | { |
12fc2493 |
348 | require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).') in bnorm()'); |
990fb837 |
349 | } |
12fc2493 |
350 | if (ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY') |
990fb837 |
351 | { |
12fc2493 |
352 | require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).') in bnorm()'); |
990fb837 |
353 | } |
6de7f0cc |
354 | |
6de7f0cc |
355 | # no normalize for NaN, inf etc. |
356 | return $x if $x->{sign} !~ /^[+-]$/; |
357 | |
184f15d5 |
358 | # normalize zeros to 0/1 |
12fc2493 |
359 | if ($MBI->_is_zero($x->{_n})) |
184f15d5 |
360 | { |
12fc2493 |
361 | $x->{sign} = '+'; # never leave a -0 |
362 | $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d}); |
184f15d5 |
363 | return $x; |
364 | } |
365 | |
12fc2493 |
366 | return $x if $MBI->_is_one($x->{_d}); # no need to reduce |
6de7f0cc |
367 | |
184f15d5 |
368 | # reduce other numbers |
12fc2493 |
369 | my $gcd = $MBI->_copy($x->{_n}); |
370 | $gcd = $MBI->_gcd($gcd,$x->{_d}); |
371 | |
372 | if (!$MBI->_is_one($gcd)) |
184f15d5 |
373 | { |
12fc2493 |
374 | $x->{_n} = $MBI->_div($x->{_n},$gcd); |
375 | $x->{_d} = $MBI->_div($x->{_d},$gcd); |
184f15d5 |
376 | } |
184f15d5 |
377 | $x; |
378 | } |
379 | |
380 | ############################################################################## |
381 | # special values |
382 | |
383 | sub _bnan |
384 | { |
990fb837 |
385 | # used by parent class bnan() to initialize number to NaN |
184f15d5 |
386 | my $self = shift; |
990fb837 |
387 | |
388 | if ($_trap_nan) |
389 | { |
390 | require Carp; |
391 | my $class = ref($self); |
392 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
393 | } |
12fc2493 |
394 | $self->{_n} = $MBI->_zero(); |
395 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
396 | } |
397 | |
398 | sub _binf |
399 | { |
7d341013 |
400 | # used by parent class bone() to initialize number to +inf/-inf |
184f15d5 |
401 | my $self = shift; |
990fb837 |
402 | |
403 | if ($_trap_inf) |
404 | { |
405 | require Carp; |
406 | my $class = ref($self); |
407 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); |
408 | } |
12fc2493 |
409 | $self->{_n} = $MBI->_zero(); |
410 | $self->{_d} = $MBI->_zero(); |
184f15d5 |
411 | } |
412 | |
413 | sub _bone |
414 | { |
7d341013 |
415 | # used by parent class bone() to initialize number to +1/-1 |
184f15d5 |
416 | my $self = shift; |
12fc2493 |
417 | $self->{_n} = $MBI->_one(); |
418 | $self->{_d} = $MBI->_one(); |
184f15d5 |
419 | } |
420 | |
421 | sub _bzero |
422 | { |
990fb837 |
423 | # used by parent class bzero() to initialize number to 0 |
184f15d5 |
424 | my $self = shift; |
12fc2493 |
425 | $self->{_n} = $MBI->_zero(); |
426 | $self->{_d} = $MBI->_one(); |
184f15d5 |
427 | } |
428 | |
429 | ############################################################################## |
430 | # mul/add/div etc |
431 | |
432 | sub badd |
433 | { |
7afd7a91 |
434 | # add two rational numbers |
7d341013 |
435 | |
436 | # set up parameters |
437 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
438 | # objectify is costly, so avoid it |
439 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
440 | { |
441 | ($self,$x,$y,@r) = objectify(2,@_); |
442 | } |
184f15d5 |
443 | |
12fc2493 |
444 | # +inf + +inf => +inf, -inf + -inf => -inf |
445 | return $x->binf(substr($x->{sign},0,1)) |
446 | if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
184f15d5 |
447 | |
12fc2493 |
448 | # +inf + -inf or -inf + +inf => NaN |
449 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
184f15d5 |
450 | |
451 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
452 | # - + - = --------- = -- |
453 | # 4 3 4*3 12 |
454 | |
7d341013 |
455 | # we do not compute the gcd() here, but simple do: |
456 | # 5 7 5*3 + 7*4 41 |
457 | # - + - = --------- = -- |
458 | # 4 3 4*3 12 |
459 | |
12fc2493 |
460 | # and bnorm() will then take care of the rest |
184f15d5 |
461 | |
12fc2493 |
462 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
7d341013 |
463 | |
12fc2493 |
464 | my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} ); |
184f15d5 |
465 | |
12fc2493 |
466 | ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign}); |
184f15d5 |
467 | |
12fc2493 |
468 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
469 | |
12fc2493 |
470 | # normalize and round |
7d341013 |
471 | $x->bnorm()->round(@r); |
184f15d5 |
472 | } |
473 | |
474 | sub bsub |
475 | { |
7afd7a91 |
476 | # subtract two rational numbers |
7d341013 |
477 | |
478 | # set up parameters |
479 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
480 | # objectify is costly, so avoid it |
481 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
482 | { |
483 | ($self,$x,$y,@r) = objectify(2,@_); |
484 | } |
184f15d5 |
485 | |
7afd7a91 |
486 | # flip sign of $x, call badd(), then flip sign of result |
487 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
488 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
489 | $x->badd($y,@r); # does norm and round |
7afd7a91 |
490 | $x->{sign} =~ tr/+-/-+/ |
12fc2493 |
491 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
7afd7a91 |
492 | $x; |
184f15d5 |
493 | } |
494 | |
495 | sub bmul |
496 | { |
7afd7a91 |
497 | # multiply two rational numbers |
7d341013 |
498 | |
499 | # set up parameters |
500 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
501 | # objectify is costly, so avoid it |
502 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
503 | { |
504 | ($self,$x,$y,@r) = objectify(2,@_); |
505 | } |
184f15d5 |
506 | |
507 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
508 | |
509 | # inf handling |
510 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
511 | { |
512 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
513 | # result will always be +-inf: |
514 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
515 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
516 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
517 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
518 | return $x->binf('-'); |
519 | } |
520 | |
521 | # x== 0 # also: or y == 1 or y == -1 |
522 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
523 | |
12fc2493 |
524 | # XXX TODO: |
525 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
526 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
527 | |
12fc2493 |
528 | # 1 2 1 * 2 2 1 |
529 | # - * - = ----- = - = - |
530 | # 4 3 4 * 3 12 6 |
7d341013 |
531 | |
12fc2493 |
532 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); |
533 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
184f15d5 |
534 | |
535 | # compute new sign |
536 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
537 | |
7d341013 |
538 | $x->bnorm()->round(@r); |
184f15d5 |
539 | } |
540 | |
541 | sub bdiv |
542 | { |
543 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
544 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
7d341013 |
545 | |
546 | # set up parameters |
547 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
548 | # objectify is costly, so avoid it |
549 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
550 | { |
551 | ($self,$x,$y,@r) = objectify(2,@_); |
552 | } |
184f15d5 |
553 | |
554 | return $self->_div_inf($x,$y) |
555 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
556 | |
557 | # x== 0 # also: or y == 1 or y == -1 |
558 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
559 | |
12fc2493 |
560 | # XXX TODO: list context, upgrade |
561 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
562 | # and reducing in one step. This would save us the bnorm() at the end. |
184f15d5 |
563 | |
184f15d5 |
564 | # 1 1 1 3 |
565 | # - / - == - * - |
566 | # 4 3 4 1 |
7d341013 |
567 | |
12fc2493 |
568 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
569 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); |
184f15d5 |
570 | |
571 | # compute new sign |
572 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
573 | |
7d341013 |
574 | $x->bnorm()->round(@r); |
6de7f0cc |
575 | $x; |
184f15d5 |
576 | } |
577 | |
990fb837 |
578 | sub bmod |
579 | { |
580 | # compute "remainder" (in Perl way) of $x / $y |
581 | |
582 | # set up parameters |
583 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
584 | # objectify is costly, so avoid it |
585 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
586 | { |
587 | ($self,$x,$y,@r) = objectify(2,@_); |
588 | } |
589 | |
990fb837 |
590 | return $self->_div_inf($x,$y) |
591 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
592 | |
593 | return $x if $x->is_zero(); # 0 / 7 = 0, mod 0 |
594 | |
595 | # compute $x - $y * floor($x/$y), keeping the sign of $x |
596 | |
12fc2493 |
597 | # copy x to u, make it positive and then do a normal division ($u/$y) |
598 | my $u = bless { sign => '+' }, $self; |
599 | $u->{_n} = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d} ); |
600 | $u->{_d} = $MBI->_mul( $MBI->_copy($x->{_d}), $y->{_n} ); |
601 | |
602 | # compute floor(u) |
603 | if (! $MBI->_is_one($u->{_d})) |
990fb837 |
604 | { |
12fc2493 |
605 | $u->{_n} = $MBI->_div($u->{_n},$u->{_d}); # 22/7 => 3/1 w/ truncate |
606 | # no need to set $u->{_d} to 1, since below we set it to $y->{_d} anyway |
990fb837 |
607 | } |
608 | |
12fc2493 |
609 | # now compute $y * $u |
610 | $u->{_d} = $MBI->_copy($y->{_d}); # 1 * $y->{_d}, see floor above |
611 | $u->{_n} = $MBI->_mul($u->{_n},$y->{_n}); |
990fb837 |
612 | |
12fc2493 |
613 | my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive |
990fb837 |
614 | # compute $x - $u |
615 | $x->bsub($u); |
616 | $x->{sign} = $xsign; # put sign back |
617 | |
618 | $x->bnorm()->round(@r); |
990fb837 |
619 | } |
620 | |
184f15d5 |
621 | ############################################################################## |
a4e2b1c6 |
622 | # bdec/binc |
623 | |
624 | sub bdec |
625 | { |
626 | # decrement value (subtract 1) |
627 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
628 | |
629 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
630 | |
631 | if ($x->{sign} eq '-') |
632 | { |
12fc2493 |
633 | $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2 |
a4e2b1c6 |
634 | } |
635 | else |
636 | { |
12fc2493 |
637 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? |
a4e2b1c6 |
638 | { |
639 | # 1/3 -- => -2/3 |
12fc2493 |
640 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
641 | $x->{sign} = '-'; |
642 | } |
643 | else |
644 | { |
12fc2493 |
645 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 |
a4e2b1c6 |
646 | } |
647 | } |
648 | $x->bnorm()->round(@r); |
a4e2b1c6 |
649 | } |
650 | |
651 | sub binc |
652 | { |
653 | # increment value (add 1) |
654 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
655 | |
656 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
657 | |
658 | if ($x->{sign} eq '-') |
659 | { |
12fc2493 |
660 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) |
a4e2b1c6 |
661 | { |
662 | # -1/3 ++ => 2/3 (overflow at 0) |
12fc2493 |
663 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 |
664 | $x->{sign} = '+'; |
665 | } |
666 | else |
667 | { |
12fc2493 |
668 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 |
a4e2b1c6 |
669 | } |
670 | } |
671 | else |
672 | { |
12fc2493 |
673 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 |
a4e2b1c6 |
674 | } |
675 | $x->bnorm()->round(@r); |
a4e2b1c6 |
676 | } |
677 | |
678 | ############################################################################## |
184f15d5 |
679 | # is_foo methods (the rest is inherited) |
680 | |
681 | sub is_int |
682 | { |
683 | # return true if arg (BRAT or num_str) is an integer |
9b924220 |
684 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
685 | |
686 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
12fc2493 |
687 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer |
184f15d5 |
688 | 0; |
689 | } |
690 | |
691 | sub is_zero |
692 | { |
693 | # return true if arg (BRAT or num_str) is zero |
9b924220 |
694 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
695 | |
12fc2493 |
696 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); |
184f15d5 |
697 | 0; |
698 | } |
699 | |
700 | sub is_one |
701 | { |
702 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
9b924220 |
703 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
704 | |
9b924220 |
705 | my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; |
184f15d5 |
706 | return 1 |
12fc2493 |
707 | if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})); |
184f15d5 |
708 | 0; |
709 | } |
710 | |
711 | sub is_odd |
712 | { |
713 | # return true if arg (BFLOAT or num_str) is odd or false if even |
9b924220 |
714 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
715 | |
716 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
12fc2493 |
717 | ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1 |
184f15d5 |
718 | 0; |
719 | } |
720 | |
721 | sub is_even |
722 | { |
723 | # return true if arg (BINT or num_str) is even or false if odd |
9b924220 |
724 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
725 | |
726 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
12fc2493 |
727 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never |
728 | && $MBI->_is_even($x->{_n})); # but 4/1 is |
184f15d5 |
729 | 0; |
730 | } |
731 | |
184f15d5 |
732 | ############################################################################## |
733 | # parts() and friends |
734 | |
735 | sub numerator |
736 | { |
737 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
a4e2b1c6 |
738 | |
12fc2493 |
739 | # NaN, inf, -inf |
740 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
a4e2b1c6 |
741 | |
12fc2493 |
742 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; |
184f15d5 |
743 | $n; |
744 | } |
745 | |
746 | sub denominator |
747 | { |
748 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
749 | |
12fc2493 |
750 | # NaN |
751 | return Math::BigInt->new($x->{sign}) if $x->{sign} eq 'NaN'; |
752 | # inf, -inf |
753 | return Math::BigInt->bone() if $x->{sign} !~ /^[+-]$/; |
754 | |
755 | Math::BigInt->new($MBI->_str($x->{_d})); |
184f15d5 |
756 | } |
757 | |
758 | sub parts |
759 | { |
760 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
761 | |
12fc2493 |
762 | my $c = 'Math::BigInt'; |
763 | |
764 | return ($c->bnan(),$c->bnan()) if $x->{sign} eq 'NaN'; |
765 | return ($c->binf(),$c->binf()) if $x->{sign} eq '+inf'; |
766 | return ($c->binf('-'),$c->binf()) if $x->{sign} eq '-inf'; |
a4e2b1c6 |
767 | |
12fc2493 |
768 | my $n = $c->new( $MBI->_str($x->{_n})); |
184f15d5 |
769 | $n->{sign} = $x->{sign}; |
12fc2493 |
770 | my $d = $c->new( $MBI->_str($x->{_d})); |
771 | ($n,$d); |
184f15d5 |
772 | } |
773 | |
774 | sub length |
775 | { |
9b924220 |
776 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
777 | |
778 | return $nan unless $x->is_int(); |
12fc2493 |
779 | $MBI->_len($x->{_n}); # length(-123/1) => length(123) |
184f15d5 |
780 | } |
781 | |
782 | sub digit |
783 | { |
12fc2493 |
784 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); |
9b924220 |
785 | |
786 | return $nan unless $x->is_int(); |
12fc2493 |
787 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) |
184f15d5 |
788 | } |
789 | |
790 | ############################################################################## |
791 | # special calc routines |
792 | |
793 | sub bceil |
794 | { |
795 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
796 | |
12fc2493 |
797 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
798 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
799 | |
12fc2493 |
800 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
801 | $x->{_d} = $MBI->_one(); # d => 1 |
802 | $x->{_n} = $MBI->_inc($x->{_n}) |
803 | if $x->{sign} eq '+'; # +22/7 => 4/1 |
804 | $x->{sign} = '+' if $MBI->_is_zero($x->{_n}); # -0 => 0 |
184f15d5 |
805 | $x; |
806 | } |
807 | |
808 | sub bfloor |
809 | { |
810 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
811 | |
12fc2493 |
812 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
813 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
184f15d5 |
814 | |
12fc2493 |
815 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
816 | $x->{_d} = $MBI->_one(); # d => 1 |
817 | $x->{_n} = $MBI->_inc($x->{_n}) |
818 | if $x->{sign} eq '-'; # -22/7 => -4/1 |
184f15d5 |
819 | $x; |
820 | } |
821 | |
822 | sub bfac |
823 | { |
a4e2b1c6 |
824 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
825 | |
12fc2493 |
826 | # if $x is not an integer |
827 | if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d}))) |
a4e2b1c6 |
828 | { |
12fc2493 |
829 | return $x->bnan(); |
a4e2b1c6 |
830 | } |
12fc2493 |
831 | |
832 | $x->{_n} = $MBI->_fac($x->{_n}); |
833 | # since _d is 1, we don't need to reduce/norm the result |
834 | $x->round(@r); |
184f15d5 |
835 | } |
836 | |
837 | sub bpow |
838 | { |
7d341013 |
839 | # power ($x ** $y) |
840 | |
841 | # set up parameters |
842 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
843 | # objectify is costly, so avoid it |
844 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
845 | { |
846 | ($self,$x,$y,@r) = objectify(2,@_); |
847 | } |
184f15d5 |
848 | |
849 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
850 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
851 | return $x->bone(@r) if $y->is_zero(); |
852 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
12fc2493 |
853 | |
854 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) |
184f15d5 |
855 | { |
856 | # if $x == -1 and odd/even y => +1/-1 |
857 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
858 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
859 | } |
860 | # 1 ** -y => 1 / (1 ** |y|) |
861 | # so do test for negative $y after above's clause |
12fc2493 |
862 | |
184f15d5 |
863 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
864 | |
a4e2b1c6 |
865 | # shortcut y/1 (and/or x/1) |
12fc2493 |
866 | if ($MBI->_is_one($y->{_d})) |
a4e2b1c6 |
867 | { |
868 | # shortcut for x/1 and y/1 |
12fc2493 |
869 | if ($MBI->_is_one($x->{_d})) |
a4e2b1c6 |
870 | { |
12fc2493 |
871 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
a4e2b1c6 |
872 | if ($y->{sign} eq '-') |
873 | { |
874 | # 0.2 ** -3 => 1/(0.2 ** 3) |
875 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
876 | } |
877 | # correct sign; + ** + => + |
878 | if ($x->{sign} eq '-') |
879 | { |
880 | # - * - => +, - * - * - => - |
12fc2493 |
881 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
882 | } |
883 | return $x->round(@r); |
884 | } |
885 | # x/z ** y/1 |
12fc2493 |
886 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
887 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); |
a4e2b1c6 |
888 | if ($y->{sign} eq '-') |
889 | { |
890 | # 0.2 ** -3 => 1/(0.2 ** 3) |
891 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
892 | } |
893 | # correct sign; + ** + => + |
894 | if ($x->{sign} eq '-') |
895 | { |
896 | # - * - => +, - * - * - => - |
12fc2493 |
897 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 |
898 | } |
899 | return $x->round(@r); |
900 | } |
901 | |
902 | # regular calculation (this is wrong for d/e ** f/g) |
12fc2493 |
903 | my $pow2 = $self->bone(); |
904 | my $y1 = $MBI->_div ( $MBI->_copy($y->{_n}), $y->{_d}); |
905 | my $two = $MBI->_two(); |
906 | |
907 | while (!$MBI->_is_one($y1)) |
184f15d5 |
908 | { |
12fc2493 |
909 | $pow2->bmul($x) if $MBI->_is_odd($y1); |
910 | $MBI->_div($y1, $two); |
184f15d5 |
911 | $x->bmul($x); |
912 | } |
913 | $x->bmul($pow2) unless $pow2->is_one(); |
914 | # n ** -x => 1/n ** x |
915 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; |
7d341013 |
916 | $x->bnorm()->round(@r); |
184f15d5 |
917 | } |
918 | |
919 | sub blog |
920 | { |
7afd7a91 |
921 | # set up parameters |
922 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
923 | |
924 | # objectify is costly, so avoid it |
925 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
926 | { |
9b924220 |
927 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
7afd7a91 |
928 | } |
929 | |
9b924220 |
930 | # blog(1,Y) => 0 |
931 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; |
932 | |
7afd7a91 |
933 | # $x <= 0 => NaN |
934 | return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; |
935 | |
936 | if ($x->is_int() && $y->is_int()) |
937 | { |
938 | return $self->new($x->as_number()->blog($y->as_number(),@r)); |
939 | } |
940 | |
9b924220 |
941 | # do it with floats |
942 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); |
943 | } |
944 | |
12fc2493 |
945 | sub _float_from_part |
946 | { |
947 | my $x = shift; |
948 | |
949 | my $f = Math::BigFloat->bzero(); |
950 | $f->{_m} = $MBI->_copy($x); |
951 | $f->{_e} = $MBI->_zero(); |
952 | |
953 | $f; |
954 | } |
955 | |
9b924220 |
956 | sub _as_float |
957 | { |
958 | my $x = shift; |
959 | |
960 | local $Math::BigFloat::upgrade = undef; |
961 | local $Math::BigFloat::accuracy = undef; |
962 | local $Math::BigFloat::precision = undef; |
963 | # 22/7 => 3.142857143.. |
12fc2493 |
964 | |
965 | my $a = $x->accuracy() || 0; |
966 | if ($a != 0 || !$MBI->_is_one($x->{_d})) |
967 | { |
968 | # n/d |
969 | return Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy()); |
970 | } |
971 | # just n |
972 | Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n})); |
7afd7a91 |
973 | } |
974 | |
975 | sub broot |
976 | { |
977 | # set up parameters |
978 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
979 | # objectify is costly, so avoid it |
980 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
981 | { |
982 | ($self,$x,$y,@r) = objectify(2,@_); |
983 | } |
984 | |
985 | if ($x->is_int() && $y->is_int()) |
986 | { |
987 | return $self->new($x->as_number()->broot($y->as_number(),@r)); |
988 | } |
9b924220 |
989 | |
990 | # do it with floats |
991 | $x->_new_from_float( $x->_as_float()->broot($y,@r) ); |
7afd7a91 |
992 | } |
993 | |
994 | sub bmodpow |
995 | { |
996 | # set up parameters |
997 | my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); |
998 | # objectify is costly, so avoid it |
999 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1000 | { |
1001 | ($self,$x,$y,$m,@r) = objectify(3,@_); |
1002 | } |
1003 | |
1004 | # $x or $y or $m are NaN or +-inf => NaN |
1005 | return $x->bnan() |
1006 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || |
1007 | $m->{sign} !~ /^[+-]$/; |
1008 | |
1009 | if ($x->is_int() && $y->is_int() && $m->is_int()) |
1010 | { |
1011 | return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); |
1012 | } |
1013 | |
1014 | warn ("bmodpow() not fully implemented"); |
1015 | $x->bnan(); |
1016 | } |
1017 | |
1018 | sub bmodinv |
1019 | { |
1020 | # set up parameters |
1021 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
1022 | # objectify is costly, so avoid it |
1023 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1024 | { |
1025 | ($self,$x,$y,@r) = objectify(2,@_); |
1026 | } |
1027 | |
1028 | # $x or $y are NaN or +-inf => NaN |
1029 | return $x->bnan() |
1030 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; |
1031 | |
1032 | if ($x->is_int() && $y->is_int()) |
1033 | { |
1034 | return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); |
1035 | } |
1036 | |
1037 | warn ("bmodinv() not fully implemented"); |
1038 | $x->bnan(); |
184f15d5 |
1039 | } |
1040 | |
1041 | sub bsqrt |
1042 | { |
990fb837 |
1043 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1044 | |
1045 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 |
1046 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf |
1047 | return $x->round(@r) if $x->is_zero() || $x->is_one(); |
1048 | |
1049 | local $Math::BigFloat::upgrade = undef; |
1050 | local $Math::BigFloat::downgrade = undef; |
1051 | local $Math::BigFloat::precision = undef; |
1052 | local $Math::BigFloat::accuracy = undef; |
1053 | local $Math::BigInt::upgrade = undef; |
1054 | local $Math::BigInt::precision = undef; |
1055 | local $Math::BigInt::accuracy = undef; |
9b924220 |
1056 | |
12fc2493 |
1057 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); |
1058 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); |
1059 | |
1060 | # XXX TODO: we probably can optimze this: |
184f15d5 |
1061 | |
990fb837 |
1062 | # if sqrt(D) was not integer |
9b924220 |
1063 | if ($x->{_d}->{_es} ne '+') |
990fb837 |
1064 | { |
9b924220 |
1065 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 |
12fc2493 |
1066 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 |
990fb837 |
1067 | } |
1068 | # if sqrt(N) was not integer |
9b924220 |
1069 | if ($x->{_n}->{_es} ne '+') |
990fb837 |
1070 | { |
9b924220 |
1071 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 |
12fc2493 |
1072 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 |
990fb837 |
1073 | } |
12fc2493 |
1074 | |
990fb837 |
1075 | # convert parts to $MBI again |
12fc2493 |
1076 | $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10) |
1077 | if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY'; |
1078 | $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10) |
1079 | if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY'; |
1080 | |
990fb837 |
1081 | $x->bnorm()->round(@r); |
184f15d5 |
1082 | } |
1083 | |
1084 | sub blsft |
1085 | { |
9b924220 |
1086 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1087 | |
9b924220 |
1088 | $b = 2 unless defined $b; |
1089 | $b = $self->new($b) unless ref ($b); |
1090 | $x->bmul( $b->copy()->bpow($y), @r); |
184f15d5 |
1091 | $x; |
1092 | } |
1093 | |
1094 | sub brsft |
1095 | { |
12fc2493 |
1096 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 |
1097 | |
9b924220 |
1098 | $b = 2 unless defined $b; |
1099 | $b = $self->new($b) unless ref ($b); |
1100 | $x->bdiv( $b->copy()->bpow($y), @r); |
184f15d5 |
1101 | $x; |
1102 | } |
1103 | |
1104 | ############################################################################## |
1105 | # round |
1106 | |
1107 | sub round |
1108 | { |
1109 | $_[0]; |
1110 | } |
1111 | |
1112 | sub bround |
1113 | { |
1114 | $_[0]; |
1115 | } |
1116 | |
1117 | sub bfround |
1118 | { |
1119 | $_[0]; |
1120 | } |
1121 | |
1122 | ############################################################################## |
1123 | # comparing |
1124 | |
1125 | sub bcmp |
1126 | { |
7afd7a91 |
1127 | # compare two signed numbers |
1128 | |
1129 | # set up parameters |
1130 | my ($self,$x,$y) = (ref($_[0]),@_); |
1131 | # objectify is costly, so avoid it |
1132 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1133 | { |
1134 | ($self,$x,$y) = objectify(2,@_); |
1135 | } |
184f15d5 |
1136 | |
1137 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1138 | { |
1139 | # handle +-inf and NaN |
1140 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1141 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
1142 | return +1 if $x->{sign} eq '+inf'; |
1143 | return -1 if $x->{sign} eq '-inf'; |
1144 | return -1 if $y->{sign} eq '+inf'; |
1145 | return +1; |
1146 | } |
1147 | # check sign for speed first |
1148 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
1149 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
1150 | |
1151 | # shortcut |
12fc2493 |
1152 | my $xz = $MBI->_is_zero($x->{_n}); |
1153 | my $yz = $MBI->_is_zero($y->{_n}); |
184f15d5 |
1154 | return 0 if $xz && $yz; # 0 <=> 0 |
1155 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
1156 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
1157 | |
12fc2493 |
1158 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1159 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1160 | |
1161 | my $cmp = $MBI->_acmp($t,$u); # signs are equal |
1162 | $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse |
1163 | $cmp; |
184f15d5 |
1164 | } |
1165 | |
1166 | sub bacmp |
1167 | { |
7afd7a91 |
1168 | # compare two numbers (as unsigned) |
9b924220 |
1169 | |
7afd7a91 |
1170 | # set up parameters |
1171 | my ($self,$x,$y) = (ref($_[0]),@_); |
1172 | # objectify is costly, so avoid it |
1173 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1174 | { |
9b924220 |
1175 | ($self,$x,$y) = objectify(2,$class,@_); |
7afd7a91 |
1176 | } |
184f15d5 |
1177 | |
1178 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1179 | { |
1180 | # handle +-inf and NaN |
1181 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
1182 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
7afd7a91 |
1183 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1184 | return -1; |
184f15d5 |
1185 | } |
1186 | |
12fc2493 |
1187 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1188 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
1189 | $MBI->_acmp($t,$u); # ignore signs |
184f15d5 |
1190 | } |
1191 | |
1192 | ############################################################################## |
1193 | # output conversation |
1194 | |
7d341013 |
1195 | sub numify |
1196 | { |
1197 | # convert 17/8 => float (aka 2.125) |
1198 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
1199 | |
1200 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc |
1201 | |
93c87d9d |
1202 | # N/1 => N |
12fc2493 |
1203 | return $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); |
93c87d9d |
1204 | |
1205 | # N/D |
1206 | my $neg = 1; $neg = -1 if $x->{sign} ne '+'; |
12fc2493 |
1207 | $neg * $MBI->_num($x->{_n}) / $MBI->_num($x->{_d}); # return sign * N/D |
7d341013 |
1208 | } |
1209 | |
184f15d5 |
1210 | sub as_number |
1211 | { |
9b924220 |
1212 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 |
1213 | |
12fc2493 |
1214 | return Math::BigInt->new($x) if $x->{sign} !~ /^[+-]$/; # NaN, inf etc |
990fb837 |
1215 | |
12fc2493 |
1216 | my $u = Math::BigInt->bzero(); |
1217 | $u->{sign} = $x->{sign}; |
1218 | $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3 |
1219 | $u; |
184f15d5 |
1220 | } |
1221 | |
9b924220 |
1222 | sub as_bin |
1223 | { |
1224 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1225 | |
1226 | return $x unless $x->is_int(); |
1227 | |
1228 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1229 | $s . $MBI->_as_bin($x->{_n}); |
9b924220 |
1230 | } |
1231 | |
1232 | sub as_hex |
1233 | { |
1234 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1235 | |
1236 | return $x unless $x->is_int(); |
1237 | |
1238 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
12fc2493 |
1239 | $s . $MBI->_as_hex($x->{_n}); |
9b924220 |
1240 | } |
1241 | |
6de7f0cc |
1242 | sub import |
1243 | { |
1244 | my $self = shift; |
1245 | my $l = scalar @_; |
1246 | my $lib = ''; my @a; |
9b924220 |
1247 | $IMPORT++; |
1248 | |
6de7f0cc |
1249 | for ( my $i = 0; $i < $l ; $i++) |
1250 | { |
1251 | # print "at $_[$i] (",$_[$i+1]||'undef',")\n"; |
1252 | if ( $_[$i] eq ':constant' ) |
1253 | { |
1254 | # this rest causes overlord er load to step in |
1255 | # print "overload @_\n"; |
1256 | overload::constant float => sub { $self->new(shift); }; |
1257 | } |
1258 | # elsif ($_[$i] eq 'upgrade') |
1259 | # { |
1260 | # # this causes upgrading |
1261 | # $upgrade = $_[$i+1]; # or undef to disable |
1262 | # $i++; |
1263 | # } |
1264 | elsif ($_[$i] eq 'downgrade') |
1265 | { |
1266 | # this causes downgrading |
1267 | $downgrade = $_[$i+1]; # or undef to disable |
1268 | $i++; |
1269 | } |
1270 | elsif ($_[$i] eq 'lib') |
1271 | { |
1272 | $lib = $_[$i+1] || ''; # default Calc |
1273 | $i++; |
1274 | } |
1275 | elsif ($_[$i] eq 'with') |
1276 | { |
1277 | $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt |
1278 | $i++; |
1279 | } |
1280 | else |
1281 | { |
1282 | push @a, $_[$i]; |
1283 | } |
1284 | } |
9b924220 |
1285 | # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still work |
6de7f0cc |
1286 | my $mbilib = eval { Math::BigInt->config()->{lib} }; |
1287 | if ((defined $mbilib) && ($MBI eq 'Math::BigInt')) |
1288 | { |
1289 | # MBI already loaded |
1290 | $MBI->import('lib',"$lib,$mbilib", 'objectify'); |
1291 | } |
1292 | else |
1293 | { |
a4e2b1c6 |
1294 | # MBI not loaded, or not with "Math::BigInt" |
6de7f0cc |
1295 | $lib .= ",$mbilib" if defined $mbilib; |
1296 | |
6de7f0cc |
1297 | if ($] < 5.006) |
1298 | { |
1299 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
1300 | # used in the same script, or eval inside import(). |
1301 | my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt |
1302 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm |
1303 | $file = File::Spec->catfile (@parts, $file); |
1304 | eval { require $file; $MBI->import( lib => '$lib', 'objectify' ); } |
1305 | } |
1306 | else |
1307 | { |
1308 | my $rc = "use $MBI lib => '$lib', 'objectify';"; |
1309 | eval $rc; |
1310 | } |
1311 | } |
93c87d9d |
1312 | if ($@) |
1313 | { |
1314 | require Carp; Carp::croak ("Couldn't load $MBI: $! $@"); |
1315 | } |
6de7f0cc |
1316 | |
12fc2493 |
1317 | $MBI = Math::BigFloat->config()->{lib}; |
9b924220 |
1318 | |
6de7f0cc |
1319 | # any non :constant stuff is handled by our parent, Exporter |
1320 | # even if @_ is empty, to give it a chance |
1321 | $self->SUPER::import(@a); # for subclasses |
1322 | $self->export_to_level(1,$self,@a); # need this, too |
1323 | } |
184f15d5 |
1324 | |
1325 | 1; |
1326 | |
1327 | __END__ |
1328 | |
1329 | =head1 NAME |
1330 | |
7afd7a91 |
1331 | Math::BigRat - arbitrarily big rational numbers |
184f15d5 |
1332 | |
1333 | =head1 SYNOPSIS |
1334 | |
7d341013 |
1335 | use Math::BigRat; |
184f15d5 |
1336 | |
7afd7a91 |
1337 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
184f15d5 |
1338 | |
7d341013 |
1339 | print $x->bstr(),"\n"; |
1340 | print $x ** 2,"\n"; |
184f15d5 |
1341 | |
7afd7a91 |
1342 | my $y = Math::BigRat->new('inf'); |
1343 | print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; |
1344 | |
1345 | my $z = Math::BigRat->new(144); $z->bsqrt(); |
1346 | |
184f15d5 |
1347 | =head1 DESCRIPTION |
1348 | |
7d341013 |
1349 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
7afd7a91 |
1350 | for arbitrarily big rational numbers. |
184f15d5 |
1351 | |
1352 | =head2 MATH LIBRARY |
1353 | |
1354 | Math with the numbers is done (by default) by a module called |
1355 | Math::BigInt::Calc. This is equivalent to saying: |
1356 | |
1357 | use Math::BigRat lib => 'Calc'; |
1358 | |
1359 | You can change this by using: |
1360 | |
1361 | use Math::BigRat lib => 'BitVect'; |
1362 | |
1363 | The following would first try to find Math::BigInt::Foo, then |
1364 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
1365 | |
1366 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
1367 | |
1368 | Calc.pm uses as internal format an array of elements of some decimal base |
7d341013 |
1369 | (usually 1e7, but this might be different for some systems) with the least |
184f15d5 |
1370 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
1371 | significant bit first. Other modules might use even different means of |
1372 | representing the numbers. See the respective module documentation for further |
1373 | details. |
1374 | |
7d341013 |
1375 | Currently the following replacement libraries exist, search for them at CPAN: |
1376 | |
1377 | Math::BigInt::BitVect |
1378 | Math::BigInt::GMP |
1379 | Math::BigInt::Pari |
1380 | Math::BigInt::FastCalc |
1381 | |
184f15d5 |
1382 | =head1 METHODS |
1383 | |
7d341013 |
1384 | Any methods not listed here are dervied from Math::BigFloat (or |
6de7f0cc |
1385 | Math::BigInt), so make sure you check these two modules for further |
1386 | information. |
1387 | |
1388 | =head2 new() |
184f15d5 |
1389 | |
1390 | $x = Math::BigRat->new('1/3'); |
1391 | |
1392 | Create a new Math::BigRat object. Input can come in various forms: |
1393 | |
7d341013 |
1394 | $x = Math::BigRat->new(123); # scalars |
7afd7a91 |
1395 | $x = Math::BigRat->new('inf'); # infinity |
7d341013 |
1396 | $x = Math::BigRat->new('123.3'); # float |
184f15d5 |
1397 | $x = Math::BigRat->new('1/3'); # simple string |
1398 | $x = Math::BigRat->new('1 / 3'); # spaced |
1399 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
1400 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
1401 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
6de7f0cc |
1402 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
184f15d5 |
1403 | |
6de7f0cc |
1404 | =head2 numerator() |
184f15d5 |
1405 | |
1406 | $n = $x->numerator(); |
1407 | |
1408 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
1409 | |
6de7f0cc |
1410 | =head2 denominator() |
184f15d5 |
1411 | |
1412 | $d = $x->denominator(); |
1413 | |
1414 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
1415 | |
6de7f0cc |
1416 | =head2 parts() |
184f15d5 |
1417 | |
1418 | ($n,$d) = $x->parts(); |
1419 | |
1420 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
1421 | BigInts. |
1422 | |
6de7f0cc |
1423 | =head2 as_number() |
1424 | |
7d341013 |
1425 | $x = Math::BigRat->new('13/7'); |
1426 | print $x->as_number(),"\n"; # '1' |
1427 | |
990fb837 |
1428 | Returns a copy of the object as BigInt trunced it to integer. |
6de7f0cc |
1429 | |
a4e2b1c6 |
1430 | =head2 bfac() |
6de7f0cc |
1431 | |
a4e2b1c6 |
1432 | $x->bfac(); |
6de7f0cc |
1433 | |
a4e2b1c6 |
1434 | Calculates the factorial of $x. For instance: |
6de7f0cc |
1435 | |
a4e2b1c6 |
1436 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 |
1437 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 |
184f15d5 |
1438 | |
7d341013 |
1439 | Works currently only for integers. |
6de7f0cc |
1440 | |
a4e2b1c6 |
1441 | =head2 blog() |
6de7f0cc |
1442 | |
a4e2b1c6 |
1443 | Is not yet implemented. |
6de7f0cc |
1444 | |
a4e2b1c6 |
1445 | =head2 bround()/round()/bfround() |
6de7f0cc |
1446 | |
a4e2b1c6 |
1447 | Are not yet implemented. |
6de7f0cc |
1448 | |
990fb837 |
1449 | =head2 bmod() |
1450 | |
1451 | use Math::BigRat; |
1452 | my $x = Math::BigRat->new('7/4'); |
1453 | my $y = Math::BigRat->new('4/3'); |
1454 | print $x->bmod($y); |
1455 | |
1456 | Set $x to the remainder of the division of $x by $y. |
1457 | |
7d341013 |
1458 | =head2 is_one() |
1459 | |
1460 | print "$x is 1\n" if $x->is_one(); |
1461 | |
1462 | Return true if $x is exactly one, otherwise false. |
1463 | |
1464 | =head2 is_zero() |
1465 | |
1466 | print "$x is 0\n" if $x->is_zero(); |
1467 | |
1468 | Return true if $x is exactly zero, otherwise false. |
1469 | |
1470 | =head2 is_positive() |
1471 | |
1472 | print "$x is >= 0\n" if $x->is_positive(); |
1473 | |
1474 | Return true if $x is positive (greater than or equal to zero), otherwise |
1475 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. |
1476 | |
1477 | =head2 is_negative() |
1478 | |
1479 | print "$x is < 0\n" if $x->is_negative(); |
1480 | |
1481 | Return true if $x is negative (smaller than zero), otherwise false. Please |
1482 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. |
1483 | |
1484 | =head2 is_int() |
1485 | |
1486 | print "$x is an integer\n" if $x->is_int(); |
1487 | |
1488 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise |
1489 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. |
1490 | |
1491 | =head2 is_odd() |
1492 | |
1493 | print "$x is odd\n" if $x->is_odd(); |
1494 | |
1495 | Return true if $x is odd, otherwise false. |
1496 | |
1497 | =head2 is_even() |
1498 | |
1499 | print "$x is even\n" if $x->is_even(); |
1500 | |
1501 | Return true if $x is even, otherwise false. |
1502 | |
1503 | =head2 bceil() |
1504 | |
1505 | $x->bceil(); |
1506 | |
1507 | Set $x to the next bigger integer value (e.g. truncate the number to integer |
1508 | and then increment it by one). |
1509 | |
1510 | =head2 bfloor() |
1511 | |
1512 | $x->bfloor(); |
1513 | |
1514 | Truncate $x to an integer value. |
6de7f0cc |
1515 | |
7afd7a91 |
1516 | =head2 bsqrt() |
1517 | |
1518 | $x->bsqrt(); |
1519 | |
1520 | Calculate the square root of $x. |
1521 | |
990fb837 |
1522 | =head2 config |
1523 | |
1524 | use Data::Dumper; |
1525 | |
1526 | print Dumper ( Math::BigRat->config() ); |
1527 | print Math::BigRat->config()->{lib},"\n"; |
1528 | |
1529 | Returns a hash containing the configuration, e.g. the version number, lib |
1530 | loaded etc. The following hash keys are currently filled in with the |
1531 | appropriate information. |
1532 | |
1533 | key RO/RW Description |
1534 | Example |
1535 | ============================================================ |
1536 | lib RO Name of the Math library |
1537 | Math::BigInt::Calc |
1538 | lib_version RO Version of 'lib' |
1539 | 0.30 |
1540 | class RO The class of config you just called |
1541 | Math::BigRat |
1542 | version RO version number of the class you used |
1543 | 0.10 |
1544 | upgrade RW To which class numbers are upgraded |
1545 | undef |
1546 | downgrade RW To which class numbers are downgraded |
1547 | undef |
1548 | precision RW Global precision |
1549 | undef |
1550 | accuracy RW Global accuracy |
1551 | undef |
1552 | round_mode RW Global round mode |
1553 | even |
1554 | div_scale RW Fallback acccuracy for div |
1555 | 40 |
1556 | trap_nan RW Trap creation of NaN (undef = no) |
1557 | undef |
1558 | trap_inf RW Trap creation of +inf/-inf (undef = no) |
1559 | undef |
1560 | |
1561 | By passing a reference to a hash you may set the configuration values. This |
1562 | works only for values that a marked with a C<RW> above, anything else is |
1563 | read-only. |
1564 | |
a4e2b1c6 |
1565 | =head1 BUGS |
6de7f0cc |
1566 | |
7d341013 |
1567 | Some things are not yet implemented, or only implemented half-way: |
1568 | |
1569 | =over 2 |
1570 | |
1571 | =item inf handling (partial) |
1572 | |
1573 | =item NaN handling (partial) |
1574 | |
1575 | =item rounding (not implemented except for bceil/bfloor) |
1576 | |
1577 | =item $x ** $y where $y is not an integer |
1578 | |
7afd7a91 |
1579 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) |
1580 | |
7d341013 |
1581 | =back |
184f15d5 |
1582 | |
1583 | =head1 LICENSE |
1584 | |
1585 | This program is free software; you may redistribute it and/or modify it under |
1586 | the same terms as Perl itself. |
1587 | |
1588 | =head1 SEE ALSO |
1589 | |
1590 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
1591 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
1592 | |
7d341013 |
1593 | See L<http://search.cpan.org/search?dist=bignum> for a way to use |
1594 | Math::BigRat. |
1595 | |
1596 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> |
1597 | may contain more documentation and examples as well as testcases. |
184f15d5 |
1598 | |
1599 | =head1 AUTHORS |
1600 | |
7afd7a91 |
1601 | (C) by Tels L<http://bloodgate.com/> 2001, 2002, 2003, 2004. |
184f15d5 |
1602 | |
1603 | =cut |