Commit | Line | Data |
---|---|---|
a4e2b1c6 JH |
1 | |
2 | # | |
7d341013 | 3 | # "Tax the rat farms." - Lord Vetinari |
a4e2b1c6 | 4 | # |
184f15d5 JH |
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 JH |
13 | |
14 | package Math::BigRat; | |
15 | ||
b8884ce4 | 16 | # anythig older is untested, and unlikely to work |
08a3f4a9 | 17 | use 5.006; |
184f15d5 JH |
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 | |
4de3d162 | 26 | $VERSION = '0.22'; |
184f15d5 | 27 | |
12fc2493 | 28 | use overload; # inherit overload from Math::BigFloat |
184f15d5 | 29 | |
12fc2493 AMS |
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 T |
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 JH |
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 RGS |
54 | |
55 | $_trap_nan = 0; # are NaNs ok? set w/ config() | |
56 | $_trap_inf = 0; # are infs ok? set w/ config() | |
57 | ||
12fc2493 AMS |
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 JH |
65 | sub isa |
66 | { | |
67 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't | |
68 | UNIVERSAL::isa(@_); | |
69 | } | |
70 | ||
12fc2493 | 71 | ############################################################################## |
9b924220 | 72 | |
184f15d5 JH |
73 | sub _new_from_float |
74 | { | |
7afd7a91 | 75 | # turn a single float input into a rational number (like '0.1') |
184f15d5 JH |
76 | my ($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 AMS |
81 | $self->{_n} = $MBI->_copy( $f->{_m} ); # mantissa |
82 | $self->{_d} = $MBI->_one(); | |
9b924220 RGS |
83 | $self->{sign} = $f->{sign} || '+'; |
84 | if ($f->{_es} eq '-') | |
184f15d5 JH |
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 JH |
89 | } |
90 | else | |
91 | { | |
92 | # something like Math::BigRat->new('10'); | |
93 | # 1 / 1 => 10/1 | |
12fc2493 AMS |
94 | $MBI->_lsft ( $self->{_n}, $f->{_e} ,10) unless |
95 | $MBI->_is_zero($f->{_e}); | |
184f15d5 | 96 | } |
184f15d5 JH |
97 | $self; |
98 | } | |
99 | ||
100 | sub new | |
101 | { | |
102 | # create a Math::BigRat | |
103 | my $class = shift; | |
104 | ||
b68b7ab1 | 105 | my ($n,$d) = @_; |
184f15d5 JH |
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 JH |
112 | if ($n->isa('Math::BigFloat')) |
113 | { | |
7afd7a91 | 114 | $self->_new_from_float($n); |
184f15d5 JH |
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 AMS |
120 | $self->{_d} = $MBI->_one(); # d => 1 |
121 | $self->{sign} = $n->{sign}; | |
8f675a64 JH |
122 | } |
123 | if ($n->isa('Math::BigInt::Lite')) | |
124 | { | |
990fb837 RGS |
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 $self->bnorm(); # normalize (120/1 => 12/10) |
184f15d5 | 131 | } |
b68b7ab1 T |
132 | |
133 | # input like (BigInt,BigInt) or (BigLite,BigLite): | |
134 | if (ref($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 JH |
178 | |
179 | if (!defined $n) | |
180 | { | |
12fc2493 AMS |
181 | $self->{_n} = $MBI->_zero(); # undef => 0 |
182 | $self->{_d} = $MBI->_one(); | |
184f15d5 | 183 | $self->{sign} = '+'; |
12fc2493 | 184 | return $self; |
184f15d5 | 185 | } |
12fc2493 | 186 | |
184f15d5 JH |
187 | # string input with / delimiter |
188 | if ($n =~ /\s*\/\s*/) | |
189 | { | |
990fb837 RGS |
190 | return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
191 | return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid | |
184f15d5 JH |
192 | ($n,$d) = split (/\//,$n); |
193 | # try as BigFloats first | |
194 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) | |
195 | { | |
7d341013 T |
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 RGS |
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( $f->exponent); |
990fb837 RGS |
213 | if ($diff_e->is_negative()) |
214 | { | |
215 | # < 0: mul d with it | |
12fc2493 | 216 | $MBI->_lsft( $self->{_d}, $MBI->_new( $diff_e->babs()), 10); |
990fb837 RGS |
217 | } |
218 | elsif (!$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 JH |
223 | } |
224 | else | |
225 | { | |
12fc2493 AMS |
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 AMS |
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 AMS |
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 $n; | |
233f7bc0 | 247 | |
12fc2493 AMS |
248 | if ($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() || $d->is_inf()) | |
7afd7a91 | 263 | { |
12fc2493 AMS |
264 | if ($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 JH |
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 T |
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 JH |
289 | } |
290 | else | |
291 | { | |
12fc2493 | 292 | # for simple forms, use $MBI directly |
b8884ce4 | 293 | if ($n =~ /^([+-]?)0*([0-9]+)\z/) |
12fc2493 AMS |
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 JH |
308 | } |
309 | $self->bnorm(); | |
310 | } | |
311 | ||
9b924220 RGS |
312 | sub copy |
313 | { | |
b68b7ab1 T |
314 | # if two arguments, the first one is the class to "swallow" subclasses |
315 | my ($c,$x) = @_; | |
316 | ||
317 | if (scalar @_ == 1) | |
9b924220 | 318 | { |
b68b7ab1 | 319 | $x = $_[0]; |
9b924220 RGS |
320 | $c = ref($x); |
321 | } | |
322 | return unless ref($x); # only for objects | |
323 | ||
12fc2493 | 324 | my $self = bless {}, $c; |
9b924220 RGS |
325 | |
326 | $self->{sign} = $x->{sign}; | |
12fc2493 AMS |
327 | $self->{_d} = $MBI->_copy($x->{_d}); |
328 | $self->{_n} = $MBI->_copy($x->{_n}); | |
9b924220 RGS |
329 | $self->{_a} = $x->{_a} if defined $x->{_a}; |
330 | $self->{_p} = $x->{_p} if defined $x->{_p}; | |
331 | $self; | |
332 | } | |
333 | ||
990fb837 RGS |
334 | ############################################################################## |
335 | ||
336 | sub config | |
337 | { | |
338 | # return (later set?) configuration data as hash ref | |
b68b7ab1 | 339 | my $class = shift || 'Math::BigRat'; |
990fb837 | 340 | |
116a1b2f SP |
341 | if (@_ == 1 && ref($_[0]) ne 'HASH') |
342 | { | |
343 | my $cfg = $class->SUPER::config(); | |
344 | return $cfg->{$_[0]}; | |
345 | } | |
346 | ||
990fb837 RGS |
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 | $cfg; | |
353 | } | |
354 | ||
355 | ############################################################################## | |
8f675a64 | 356 | |
184f15d5 JH |
357 | sub bstr |
358 | { | |
7afd7a91 | 359 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 JH |
360 | |
361 | if ($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 AMS |
369 | return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d}); |
370 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); | |
184f15d5 JH |
371 | } |
372 | ||
373 | sub bsstr | |
374 | { | |
b68b7ab1 | 375 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 JH |
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 JH |
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 JH |
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 AMS |
408 | $x->{sign} = '+'; # never leave a -0 |
409 | $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d}); | |
184f15d5 JH |
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 AMS |
416 | my $gcd = $MBI->_copy($x->{_n}); |
417 | $gcd = $MBI->_gcd($gcd,$x->{_d}); | |
418 | ||
419 | if (!$MBI->_is_one($gcd)) | |
184f15d5 | 420 | { |
12fc2493 AMS |
421 | $x->{_n} = $MBI->_div($x->{_n},$gcd); |
422 | $x->{_d} = $MBI->_div($x->{_d},$gcd); | |
184f15d5 | 423 | } |
184f15d5 JH |
424 | $x; |
425 | } | |
426 | ||
427 | ############################################################################## | |
b68b7ab1 T |
428 | # sign manipulation |
429 | ||
430 | sub bneg | |
431 | { | |
432 | # (BRAT or num_str) return BRAT | |
433 | # negate number or make a negated number from string | |
434 | my ($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 JH |
444 | # special values |
445 | ||
446 | sub _bnan | |
447 | { | |
990fb837 | 448 | # used by parent class bnan() to initialize number to NaN |
184f15d5 | 449 | my $self = shift; |
990fb837 RGS |
450 | |
451 | if ($_trap_nan) | |
452 | { | |
453 | require Carp; | |
454 | my $class = ref($self); | |
233f7bc0 T |
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 RGS |
459 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
460 | } | |
12fc2493 AMS |
461 | $self->{_n} = $MBI->_zero(); |
462 | $self->{_d} = $MBI->_zero(); | |
184f15d5 JH |
463 | } |
464 | ||
465 | sub _binf | |
466 | { | |
7d341013 | 467 | # used by parent class bone() to initialize number to +inf/-inf |
184f15d5 | 468 | my $self = shift; |
990fb837 RGS |
469 | |
470 | if ($_trap_inf) | |
471 | { | |
472 | require Carp; | |
473 | my $class = ref($self); | |
233f7bc0 T |
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 RGS |
478 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); |
479 | } | |
12fc2493 AMS |
480 | $self->{_n} = $MBI->_zero(); |
481 | $self->{_d} = $MBI->_zero(); | |
184f15d5 JH |
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 AMS |
488 | $self->{_n} = $MBI->_one(); |
489 | $self->{_d} = $MBI->_one(); | |
184f15d5 JH |
490 | } |
491 | ||
492 | sub _bzero | |
493 | { | |
990fb837 | 494 | # used by parent class bzero() to initialize number to 0 |
184f15d5 | 495 | my $self = shift; |
12fc2493 AMS |
496 | $self->{_n} = $MBI->_zero(); |
497 | $self->{_d} = $MBI->_one(); | |
184f15d5 JH |
498 | } |
499 | ||
500 | ############################################################################## | |
501 | # mul/add/div etc | |
502 | ||
503 | sub badd | |
504 | { | |
7afd7a91 | 505 | # add two rational numbers |
7d341013 T |
506 | |
507 | # set up parameters | |
508 | my ($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 AMS |
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 AMS |
519 | # +inf + -inf or -inf + +inf => NaN |
520 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
184f15d5 JH |
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 T |
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 | $x->bnorm()->round(@r); |
184f15d5 JH |
547 | } |
548 | ||
549 | sub bsub | |
550 | { | |
7afd7a91 | 551 | # subtract two rational numbers |
7d341013 T |
552 | |
553 | # set up parameters | |
554 | my ($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 T |
561 | # flip sign of $x, call badd(), then flip sign of result |
562 | $x->{sign} =~ tr/+-/-+/ | |
12fc2493 AMS |
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 | $x; |
184f15d5 JH |
568 | } |
569 | ||
570 | sub bmul | |
571 | { | |
7afd7a91 | 572 | # multiply two rational numbers |
7d341013 T |
573 | |
574 | # set up parameters | |
575 | my ($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 JH |
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 AMS |
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 AMS |
603 | # 1 2 1 * 2 2 1 |
604 | # - * - = ----- = - = - | |
605 | # 4 3 4 * 3 12 6 | |
7d341013 | 606 | |
12fc2493 AMS |
607 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); |
608 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); | |
184f15d5 JH |
609 | |
610 | # compute new sign | |
611 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; | |
612 | ||
7d341013 | 613 | $x->bnorm()->round(@r); |
184f15d5 JH |
614 | } |
615 | ||
616 | sub bdiv | |
617 | { | |
618 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return | |
619 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) | |
7d341013 T |
620 | |
621 | # set up parameters | |
622 | my ($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 JH |
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 AMS |
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 JH |
639 | # 1 1 1 3 |
640 | # - / - == - * - | |
641 | # 4 3 4 1 | |
7d341013 | 642 | |
12fc2493 AMS |
643 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
644 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); | |
184f15d5 JH |
645 | |
646 | # compute new sign | |
647 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; | |
648 | ||
7d341013 | 649 | $x->bnorm()->round(@r); |
6de7f0cc | 650 | $x; |
184f15d5 JH |
651 | } |
652 | ||
990fb837 RGS |
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 RGS |
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 $x | |
671 | ||
12fc2493 AMS |
672 | # copy x to u, make it positive and then do a normal division ($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 AMS |
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 RGS |
682 | } |
683 | ||
12fc2493 AMS |
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 RGS |
689 | # compute $x - $u |
690 | $x->bsub($u); | |
691 | $x->{sign} = $xsign; # put sign back | |
692 | ||
693 | $x->bnorm()->round(@r); | |
990fb837 RGS |
694 | } |
695 | ||
184f15d5 | 696 | ############################################################################## |
a4e2b1c6 JH |
697 | # bdec/binc |
698 | ||
699 | sub bdec | |
700 | { | |
701 | # decrement value (subtract 1) | |
702 | my ($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}, $x->{_d}); # -5/2 => -7/2 |
a4e2b1c6 JH |
709 | } |
710 | else | |
711 | { | |
12fc2493 | 712 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? |
a4e2b1c6 JH |
713 | { |
714 | # 1/3 -- => -2/3 | |
12fc2493 | 715 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 JH |
716 | $x->{sign} = '-'; |
717 | } | |
718 | else | |
719 | { | |
12fc2493 | 720 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 |
a4e2b1c6 JH |
721 | } |
722 | } | |
723 | $x->bnorm()->round(@r); | |
a4e2b1c6 JH |
724 | } |
725 | ||
726 | sub binc | |
727 | { | |
728 | # increment value (add 1) | |
729 | my ($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 JH |
736 | { |
737 | # -1/3 ++ => 2/3 (overflow at 0) | |
12fc2493 | 738 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
a4e2b1c6 JH |
739 | $x->{sign} = '+'; |
740 | } | |
741 | else | |
742 | { | |
12fc2493 | 743 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 |
a4e2b1c6 JH |
744 | } |
745 | } | |
746 | else | |
747 | { | |
12fc2493 | 748 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 |
a4e2b1c6 JH |
749 | } |
750 | $x->bnorm()->round(@r); | |
a4e2b1c6 JH |
751 | } |
752 | ||
753 | ############################################################################## | |
184f15d5 JH |
754 | # is_foo methods (the rest is inherited) |
755 | ||
756 | sub is_int | |
757 | { | |
758 | # return true if arg (BRAT or num_str) is an integer | |
9b924220 | 759 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 JH |
760 | |
761 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't | |
12fc2493 | 762 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer |
184f15d5 JH |
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 JH |
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 JH |
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 JH |
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 JH |
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 JH |
800 | |
801 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't | |
12fc2493 AMS |
802 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never |
803 | && $MBI->_is_even($x->{_n})); # but 4/1 is | |
184f15d5 JH |
804 | 0; |
805 | } | |
806 | ||
184f15d5 JH |
807 | ############################################################################## |
808 | # parts() and friends | |
809 | ||
810 | sub numerator | |
811 | { | |
812 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
a4e2b1c6 | 813 | |
12fc2493 AMS |
814 | # NaN, inf, -inf |
815 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); | |
a4e2b1c6 | 816 | |
12fc2493 | 817 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; |
184f15d5 JH |
818 | $n; |
819 | } | |
820 | ||
821 | sub denominator | |
822 | { | |
823 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
824 | ||
12fc2493 AMS |
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 JH |
831 | } |
832 | ||
833 | sub parts | |
834 | { | |
835 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
836 | ||
12fc2493 AMS |
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 AMS |
845 | my $d = $c->new( $MBI->_str($x->{_d})); |
846 | ($n,$d); | |
184f15d5 JH |
847 | } |
848 | ||
849 | sub length | |
850 | { | |
9b924220 RGS |
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 JH |
855 | } |
856 | ||
857 | sub digit | |
858 | { | |
12fc2493 | 859 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); |
9b924220 RGS |
860 | |
861 | return $nan unless $x->is_int(); | |
12fc2493 | 862 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) |
184f15d5 JH |
863 | } |
864 | ||
865 | ############################################################################## | |
866 | # special calc routines | |
867 | ||
868 | sub bceil | |
869 | { | |
870 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
871 | ||
12fc2493 AMS |
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 AMS |
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 JH |
880 | $x; |
881 | } | |
882 | ||
883 | sub bfloor | |
884 | { | |
885 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
886 | ||
12fc2493 AMS |
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 AMS |
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 JH |
894 | $x; |
895 | } | |
896 | ||
897 | sub bfac | |
898 | { | |
a4e2b1c6 JH |
899 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
900 | ||
12fc2493 AMS |
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 AMS |
906 | |
907 | $x->{_n} = $MBI->_fac($x->{_n}); | |
908 | # since _d is 1, we don't need to reduce/norm the result | |
909 | $x->round(@r); | |
184f15d5 JH |
910 | } |
911 | ||
912 | sub bpow | |
913 | { | |
7d341013 T |
914 | # power ($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 JH |
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() || $y->is_one(); | |
12fc2493 AMS |
928 | |
929 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) | |
184f15d5 JH |
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 JH |
938 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
939 | ||
4de3d162 T |
940 | # shortcut if y == 1/N (is then sqrt() respective broot()) |
941 | if ($MBI->_is_one($y->{_n})) | |
942 | { | |
943 | return $x->bsqrt(@r) if $MBI->_is_two($y->{_d}); # 1/2 => sqrt | |
944 | return $x->broot($MBI->_str($y->{_d}),@r); # 1/N => root(N) | |
945 | } | |
946 | ||
a4e2b1c6 | 947 | # shortcut y/1 (and/or x/1) |
12fc2493 | 948 | if ($MBI->_is_one($y->{_d})) |
a4e2b1c6 JH |
949 | { |
950 | # shortcut for x/1 and y/1 | |
12fc2493 | 951 | if ($MBI->_is_one($x->{_d})) |
a4e2b1c6 | 952 | { |
12fc2493 | 953 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
a4e2b1c6 JH |
954 | if ($y->{sign} eq '-') |
955 | { | |
956 | # 0.2 ** -3 => 1/(0.2 ** 3) | |
957 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap | |
958 | } | |
959 | # correct sign; + ** + => + | |
960 | if ($x->{sign} eq '-') | |
961 | { | |
962 | # - * - => +, - * - * - => - | |
12fc2493 | 963 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 JH |
964 | } |
965 | return $x->round(@r); | |
966 | } | |
967 | # x/z ** y/1 | |
12fc2493 AMS |
968 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
969 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); | |
a4e2b1c6 JH |
970 | if ($y->{sign} eq '-') |
971 | { | |
972 | # 0.2 ** -3 => 1/(0.2 ** 3) | |
973 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap | |
974 | } | |
975 | # correct sign; + ** + => + | |
976 | if ($x->{sign} eq '-') | |
977 | { | |
978 | # - * - => +, - * - * - => - | |
12fc2493 | 979 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
a4e2b1c6 JH |
980 | } |
981 | return $x->round(@r); | |
982 | } | |
983 | ||
4de3d162 | 984 | # print STDERR "# $x $y\n"; |
12fc2493 | 985 | |
4de3d162 T |
986 | # otherwise: |
987 | ||
988 | # n/d n ______________ | |
989 | # a/b = -\/ (a/b) ** d | |
990 | ||
991 | # (a/b) ** n == (a ** n) / (b ** n) | |
992 | $MBI->_pow($x->{_n}, $y->{_n} ); | |
993 | $MBI->_pow($x->{_d}, $y->{_n} ); | |
994 | ||
995 | return $x->broot($MBI->_str($y->{_d}),@r); # n/d => root(n) | |
184f15d5 JH |
996 | } |
997 | ||
998 | sub blog | |
999 | { | |
7afd7a91 T |
1000 | # set up parameters |
1001 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1002 | ||
1003 | # objectify is costly, so avoid it | |
1004 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1005 | { | |
9b924220 | 1006 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
7afd7a91 T |
1007 | } |
1008 | ||
9b924220 RGS |
1009 | # blog(1,Y) => 0 |
1010 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; | |
1011 | ||
7afd7a91 T |
1012 | # $x <= 0 => NaN |
1013 | return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; | |
1014 | ||
1015 | if ($x->is_int() && $y->is_int()) | |
1016 | { | |
1017 | return $self->new($x->as_number()->blog($y->as_number(),@r)); | |
1018 | } | |
1019 | ||
9b924220 RGS |
1020 | # do it with floats |
1021 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); | |
1022 | } | |
1023 | ||
116a1b2f SP |
1024 | sub bexp |
1025 | { | |
1026 | # set up parameters | |
4de3d162 | 1027 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
116a1b2f SP |
1028 | |
1029 | # objectify is costly, so avoid it | |
1030 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1031 | { | |
4de3d162 | 1032 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
116a1b2f SP |
1033 | } |
1034 | ||
4de3d162 T |
1035 | return $x->binf(@r) if $x->{sign} eq '+inf'; |
1036 | return $x->bzero(@r) if $x->{sign} eq '-inf'; | |
116a1b2f SP |
1037 | |
1038 | # we need to limit the accuracy to protect against overflow | |
1039 | my $fallback = 0; | |
1040 | my ($scale,@params); | |
4de3d162 | 1041 | ($x,@params) = $x->_find_round_parameters(@r); |
116a1b2f SP |
1042 | |
1043 | # also takes care of the "error in _find_round_parameters?" case | |
1044 | return $x if $x->{sign} eq 'NaN'; | |
1045 | ||
1046 | # no rounding at all, so must use fallback | |
1047 | if (scalar @params == 0) | |
1048 | { | |
1049 | # simulate old behaviour | |
4de3d162 T |
1050 | $params[0] = $self->div_scale(); # and round to it as accuracy |
1051 | $params[1] = undef; # P = undef | |
1052 | $scale = $params[0]+4; # at least four more for proper round | |
1053 | $params[2] = $r[2]; # round mode by caller or undef | |
1054 | $fallback = 1; # to clear a/p afterwards | |
116a1b2f SP |
1055 | } |
1056 | else | |
1057 | { | |
1058 | # the 4 below is empirical, and there might be cases where it's not enough... | |
1059 | $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined | |
1060 | } | |
1061 | ||
1062 | return $x->bone(@params) if $x->is_zero(); | |
1063 | ||
1064 | # See the comments in Math::BigFloat on how this algorithm works. | |
1065 | # Basically we calculate A and B (where B is faculty(N)) so that A/B = e | |
1066 | ||
1067 | my $x_org = $x->copy(); | |
1068 | if ($scale <= 75) | |
1069 | { | |
1070 | # set $x directly from a cached string form | |
1071 | $x->{_n} = $MBI->_new("90933395208605785401971970164779391644753259799242"); | |
1072 | $x->{_d} = $MBI->_new("33452526613163807108170062053440751665152000000000"); | |
1073 | $x->{sign} = '+'; | |
1074 | } | |
1075 | else | |
1076 | { | |
1077 | # compute A and B so that e = A / B. | |
1078 | ||
1079 | # After some terms we end up with this, so we use it as a starting point: | |
1080 | my $A = $MBI->_new("90933395208605785401971970164779391644753259799242"); | |
1081 | my $F = $MBI->_new(42); my $step = 42; | |
1082 | ||
1083 | # Compute how many steps we need to take to get $A and $B sufficiently big | |
1084 | my $steps = Math::BigFloat::_len_to_steps($scale - 4); | |
1085 | # print STDERR "# Doing $steps steps for ", $scale-4, " digits\n"; | |
1086 | while ($step++ <= $steps) | |
1087 | { | |
1088 | # calculate $a * $f + 1 | |
1089 | $A = $MBI->_mul($A, $F); | |
1090 | $A = $MBI->_inc($A); | |
1091 | # increment f | |
1092 | $F = $MBI->_inc($F); | |
1093 | } | |
1094 | # compute $B as factorial of $steps (this is faster than doing it manually) | |
1095 | my $B = $MBI->_fac($MBI->_new($steps)); | |
1096 | ||
1097 | # print "A ", $MBI->_str($A), "\nB ", $MBI->_str($B), "\n"; | |
1098 | ||
1099 | $x->{_n} = $A; | |
1100 | $x->{_d} = $B; | |
1101 | $x->{sign} = '+'; | |
1102 | } | |
1103 | ||
1104 | # $x contains now an estimate of e, with some surplus digits, so we can round | |
1105 | if (!$x_org->is_one()) | |
1106 | { | |
1107 | # raise $x to the wanted power and round it in one step: | |
1108 | $x->bpow($x_org, @params); | |
1109 | } | |
1110 | else | |
1111 | { | |
1112 | # else just round the already computed result | |
1113 | delete $x->{_a}; delete $x->{_p}; | |
1114 | # shortcut to not run through _find_round_parameters again | |
1115 | if (defined $params[0]) | |
1116 | { | |
1117 | $x->bround($params[0],$params[2]); # then round accordingly | |
1118 | } | |
1119 | else | |
1120 | { | |
1121 | $x->bfround($params[1],$params[2]); # then round accordingly | |
1122 | } | |
1123 | } | |
1124 | if ($fallback) | |
1125 | { | |
1126 | # clear a/p after round, since user did not request it | |
1127 | delete $x->{_a}; delete $x->{_p}; | |
1128 | } | |
1129 | ||
1130 | $x; | |
1131 | } | |
1132 | ||
1133 | sub bnok | |
1134 | { | |
1135 | # set up parameters | |
1136 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1137 | ||
1138 | # objectify is costly, so avoid it | |
1139 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1140 | { | |
1141 | ($self,$x,$y,@r) = objectify(2,$class,@_); | |
1142 | } | |
1143 | ||
1144 | # do it with floats | |
1145 | $x->_new_from_float( $x->_as_float()->bnok(Math::BigFloat->new("$y"),@r) ); | |
1146 | } | |
1147 | ||
12fc2493 AMS |
1148 | sub _float_from_part |
1149 | { | |
1150 | my $x = shift; | |
1151 | ||
1152 | my $f = Math::BigFloat->bzero(); | |
1153 | $f->{_m} = $MBI->_copy($x); | |
1154 | $f->{_e} = $MBI->_zero(); | |
1155 | ||
1156 | $f; | |
1157 | } | |
1158 | ||
9b924220 RGS |
1159 | sub _as_float |
1160 | { | |
1161 | my $x = shift; | |
1162 | ||
1163 | local $Math::BigFloat::upgrade = undef; | |
1164 | local $Math::BigFloat::accuracy = undef; | |
1165 | local $Math::BigFloat::precision = undef; | |
1166 | # 22/7 => 3.142857143.. | |
12fc2493 AMS |
1167 | |
1168 | my $a = $x->accuracy() || 0; | |
1169 | if ($a != 0 || !$MBI->_is_one($x->{_d})) | |
1170 | { | |
1171 | # n/d | |
4de3d162 | 1172 | return scalar Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy()); |
12fc2493 AMS |
1173 | } |
1174 | # just n | |
1175 | Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n})); | |
7afd7a91 T |
1176 | } |
1177 | ||
1178 | sub broot | |
1179 | { | |
1180 | # set up parameters | |
1181 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1182 | # objectify is costly, so avoid it | |
1183 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1184 | { | |
1185 | ($self,$x,$y,@r) = objectify(2,@_); | |
1186 | } | |
1187 | ||
1188 | if ($x->is_int() && $y->is_int()) | |
1189 | { | |
1190 | return $self->new($x->as_number()->broot($y->as_number(),@r)); | |
1191 | } | |
9b924220 RGS |
1192 | |
1193 | # do it with floats | |
4de3d162 | 1194 | $x->_new_from_float( $x->_as_float()->broot($y->_as_float(),@r) )->bnorm()->bround(@r); |
7afd7a91 T |
1195 | } |
1196 | ||
1197 | sub bmodpow | |
1198 | { | |
1199 | # set up parameters | |
1200 | my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); | |
1201 | # objectify is costly, so avoid it | |
1202 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1203 | { | |
1204 | ($self,$x,$y,$m,@r) = objectify(3,@_); | |
1205 | } | |
1206 | ||
1207 | # $x or $y or $m are NaN or +-inf => NaN | |
1208 | return $x->bnan() | |
1209 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || | |
1210 | $m->{sign} !~ /^[+-]$/; | |
1211 | ||
1212 | if ($x->is_int() && $y->is_int() && $m->is_int()) | |
1213 | { | |
1214 | return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); | |
1215 | } | |
1216 | ||
1217 | warn ("bmodpow() not fully implemented"); | |
1218 | $x->bnan(); | |
1219 | } | |
1220 | ||
1221 | sub bmodinv | |
1222 | { | |
1223 | # set up parameters | |
1224 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1225 | # objectify is costly, so avoid it | |
1226 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1227 | { | |
1228 | ($self,$x,$y,@r) = objectify(2,@_); | |
1229 | } | |
1230 | ||
1231 | # $x or $y are NaN or +-inf => NaN | |
1232 | return $x->bnan() | |
1233 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; | |
1234 | ||
1235 | if ($x->is_int() && $y->is_int()) | |
1236 | { | |
1237 | return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); | |
1238 | } | |
1239 | ||
1240 | warn ("bmodinv() not fully implemented"); | |
1241 | $x->bnan(); | |
184f15d5 JH |
1242 | } |
1243 | ||
1244 | sub bsqrt | |
1245 | { | |
990fb837 RGS |
1246 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
1247 | ||
1248 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 | |
1249 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf | |
1250 | return $x->round(@r) if $x->is_zero() || $x->is_one(); | |
1251 | ||
1252 | local $Math::BigFloat::upgrade = undef; | |
1253 | local $Math::BigFloat::downgrade = undef; | |
1254 | local $Math::BigFloat::precision = undef; | |
1255 | local $Math::BigFloat::accuracy = undef; | |
1256 | local $Math::BigInt::upgrade = undef; | |
1257 | local $Math::BigInt::precision = undef; | |
1258 | local $Math::BigInt::accuracy = undef; | |
9b924220 | 1259 | |
12fc2493 AMS |
1260 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); |
1261 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); | |
1262 | ||
1263 | # XXX TODO: we probably can optimze this: | |
184f15d5 | 1264 | |
990fb837 | 1265 | # if sqrt(D) was not integer |
9b924220 | 1266 | if ($x->{_d}->{_es} ne '+') |
990fb837 | 1267 | { |
9b924220 | 1268 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 |
12fc2493 | 1269 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 |
990fb837 RGS |
1270 | } |
1271 | # if sqrt(N) was not integer | |
9b924220 | 1272 | if ($x->{_n}->{_es} ne '+') |
990fb837 | 1273 | { |
9b924220 | 1274 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 |
12fc2493 | 1275 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 |
990fb837 | 1276 | } |
12fc2493 | 1277 | |
990fb837 | 1278 | # convert parts to $MBI again |
12fc2493 AMS |
1279 | $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10) |
1280 | if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY'; | |
1281 | $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10) | |
1282 | if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY'; | |
1283 | ||
990fb837 | 1284 | $x->bnorm()->round(@r); |
184f15d5 JH |
1285 | } |
1286 | ||
1287 | sub blsft | |
1288 | { | |
9b924220 | 1289 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 | 1290 | |
9b924220 RGS |
1291 | $b = 2 unless defined $b; |
1292 | $b = $self->new($b) unless ref ($b); | |
1293 | $x->bmul( $b->copy()->bpow($y), @r); | |
184f15d5 JH |
1294 | $x; |
1295 | } | |
1296 | ||
1297 | sub brsft | |
1298 | { | |
12fc2493 | 1299 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
184f15d5 | 1300 | |
9b924220 RGS |
1301 | $b = 2 unless defined $b; |
1302 | $b = $self->new($b) unless ref ($b); | |
1303 | $x->bdiv( $b->copy()->bpow($y), @r); | |
184f15d5 JH |
1304 | $x; |
1305 | } | |
1306 | ||
1307 | ############################################################################## | |
1308 | # round | |
1309 | ||
1310 | sub round | |
1311 | { | |
1312 | $_[0]; | |
1313 | } | |
1314 | ||
1315 | sub bround | |
1316 | { | |
1317 | $_[0]; | |
1318 | } | |
1319 | ||
1320 | sub bfround | |
1321 | { | |
1322 | $_[0]; | |
1323 | } | |
1324 | ||
1325 | ############################################################################## | |
1326 | # comparing | |
1327 | ||
1328 | sub bcmp | |
1329 | { | |
7afd7a91 T |
1330 | # compare two signed numbers |
1331 | ||
1332 | # set up parameters | |
1333 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1334 | # objectify is costly, so avoid it | |
1335 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1336 | { | |
1337 | ($self,$x,$y) = objectify(2,@_); | |
1338 | } | |
184f15d5 JH |
1339 | |
1340 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1341 | { | |
1342 | # handle +-inf and NaN | |
1343 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1344 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; | |
1345 | return +1 if $x->{sign} eq '+inf'; | |
1346 | return -1 if $x->{sign} eq '-inf'; | |
1347 | return -1 if $y->{sign} eq '+inf'; | |
1348 | return +1; | |
1349 | } | |
1350 | # check sign for speed first | |
1351 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
1352 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
1353 | ||
1354 | # shortcut | |
12fc2493 AMS |
1355 | my $xz = $MBI->_is_zero($x->{_n}); |
1356 | my $yz = $MBI->_is_zero($y->{_n}); | |
184f15d5 JH |
1357 | return 0 if $xz && $yz; # 0 <=> 0 |
1358 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y | |
1359 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 | |
1360 | ||
12fc2493 AMS |
1361 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1362 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); | |
1363 | ||
1364 | my $cmp = $MBI->_acmp($t,$u); # signs are equal | |
1365 | $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse | |
1366 | $cmp; | |
184f15d5 JH |
1367 | } |
1368 | ||
1369 | sub bacmp | |
1370 | { | |
7afd7a91 | 1371 | # compare two numbers (as unsigned) |
9b924220 | 1372 | |
7afd7a91 T |
1373 | # set up parameters |
1374 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1375 | # objectify is costly, so avoid it | |
1376 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1377 | { | |
9b924220 | 1378 | ($self,$x,$y) = objectify(2,$class,@_); |
7afd7a91 | 1379 | } |
184f15d5 JH |
1380 | |
1381 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1382 | { | |
1383 | # handle +-inf and NaN | |
1384 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1385 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
7afd7a91 T |
1386 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1387 | return -1; | |
184f15d5 JH |
1388 | } |
1389 | ||
12fc2493 AMS |
1390 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
1391 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); | |
1392 | $MBI->_acmp($t,$u); # ignore signs | |
184f15d5 JH |
1393 | } |
1394 | ||
1395 | ############################################################################## | |
1396 | # output conversation | |
1397 | ||
7d341013 T |
1398 | sub numify |
1399 | { | |
1400 | # convert 17/8 => float (aka 2.125) | |
b68b7ab1 | 1401 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
7d341013 T |
1402 | |
1403 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc | |
1404 | ||
93c87d9d | 1405 | # N/1 => N |
b68b7ab1 T |
1406 | my $neg = ''; $neg = '-' if $x->{sign} eq '-'; |
1407 | return $neg . $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); | |
93c87d9d | 1408 | |
b68b7ab1 | 1409 | $x->_as_float()->numify() + 0.0; |
7d341013 T |
1410 | } |
1411 | ||
184f15d5 JH |
1412 | sub as_number |
1413 | { | |
9b924220 | 1414 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
184f15d5 | 1415 | |
08a3f4a9 T |
1416 | # NaN, inf etc |
1417 | return Math::BigInt->new($x->{sign}) if $x->{sign} !~ /^[+-]$/; | |
990fb837 | 1418 | |
12fc2493 AMS |
1419 | my $u = Math::BigInt->bzero(); |
1420 | $u->{sign} = $x->{sign}; | |
1421 | $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3 | |
1422 | $u; | |
184f15d5 JH |
1423 | } |
1424 | ||
4de3d162 T |
1425 | sub as_float |
1426 | { | |
1427 | # return N/D as Math::BigFloat | |
1428 | ||
1429 | # set up parameters | |
1430 | my ($self,$x,@r) = (ref($_[0]),@_); | |
1431 | # objectify is costly, so avoid it | |
1432 | ($self,$x,@r) = objectify(1,$class,@_) unless ref $_[0]; | |
1433 | ||
1434 | # NaN, inf etc | |
1435 | return Math::BigFloat->new($x->{sign}) if $x->{sign} !~ /^[+-]$/; | |
1436 | ||
1437 | my $u = Math::BigFloat->bzero(); | |
1438 | $u->{sign} = $x->{sign}; | |
1439 | # n | |
1440 | $u->{_m} = $MBI->_copy($x->{_n}); | |
1441 | $u->{_e} = $MBI->_zero(); | |
1442 | $u->bdiv( $MBI->_str($x->{_d}), @r); | |
1443 | # return $u | |
1444 | $u; | |
1445 | } | |
1446 | ||
9b924220 RGS |
1447 | sub as_bin |
1448 | { | |
1449 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1450 | ||
1451 | return $x unless $x->is_int(); | |
1452 | ||
1453 | my $s = $x->{sign}; $s = '' if $s eq '+'; | |
12fc2493 | 1454 | $s . $MBI->_as_bin($x->{_n}); |
9b924220 RGS |
1455 | } |
1456 | ||
1457 | sub as_hex | |
1458 | { | |
1459 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1460 | ||
1461 | return $x unless $x->is_int(); | |
1462 | ||
1463 | my $s = $x->{sign}; $s = '' if $s eq '+'; | |
12fc2493 | 1464 | $s . $MBI->_as_hex($x->{_n}); |
9b924220 RGS |
1465 | } |
1466 | ||
b8884ce4 T |
1467 | sub as_oct |
1468 | { | |
1469 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); | |
1470 | ||
1471 | return $x unless $x->is_int(); | |
1472 | ||
1473 | my $s = $x->{sign}; $s = '' if $s eq '+'; | |
1474 | $s . $MBI->_as_oct($x->{_n}); | |
1475 | } | |
1476 | ||
1477 | ############################################################################## | |
1478 | ||
1479 | sub from_hex | |
1480 | { | |
1481 | my $class = shift; | |
1482 | ||
1483 | $class->new(@_); | |
1484 | } | |
1485 | ||
1486 | sub from_bin | |
1487 | { | |
1488 | my $class = shift; | |
1489 | ||
1490 | $class->new(@_); | |
1491 | } | |
1492 | ||
1493 | sub from_oct | |
1494 | { | |
1495 | my $class = shift; | |
1496 | ||
1497 | my @parts; | |
1498 | for my $c (@_) | |
1499 | { | |
1500 | push @parts, Math::BigInt->from_oct($c); | |
1501 | } | |
1502 | $class->new ( @parts ); | |
1503 | } | |
1504 | ||
b68b7ab1 T |
1505 | ############################################################################## |
1506 | # import | |
1507 | ||
6de7f0cc JH |
1508 | sub import |
1509 | { | |
1510 | my $self = shift; | |
1511 | my $l = scalar @_; | |
1512 | my $lib = ''; my @a; | |
b8884ce4 | 1513 | my $try = 'try'; |
9b924220 | 1514 | |
6de7f0cc JH |
1515 | for ( my $i = 0; $i < $l ; $i++) |
1516 | { | |
6de7f0cc JH |
1517 | if ( $_[$i] eq ':constant' ) |
1518 | { | |
1519 | # this rest causes overlord er load to step in | |
6de7f0cc JH |
1520 | overload::constant float => sub { $self->new(shift); }; |
1521 | } | |
1522 | # elsif ($_[$i] eq 'upgrade') | |
1523 | # { | |
1524 | # # this causes upgrading | |
b68b7ab1 | 1525 | # $upgrade = $_[$i+1]; # or undef to disable |
6de7f0cc JH |
1526 | # $i++; |
1527 | # } | |
1528 | elsif ($_[$i] eq 'downgrade') | |
1529 | { | |
1530 | # this causes downgrading | |
b68b7ab1 | 1531 | $downgrade = $_[$i+1]; # or undef to disable |
6de7f0cc JH |
1532 | $i++; |
1533 | } | |
b8884ce4 | 1534 | elsif ($_[$i] =~ /^(lib|try|only)\z/) |
6de7f0cc | 1535 | { |
b68b7ab1 | 1536 | $lib = $_[$i+1] || ''; # default Calc |
b8884ce4 | 1537 | $try = $1; # lib, try or only |
6de7f0cc JH |
1538 | $i++; |
1539 | } | |
1540 | elsif ($_[$i] eq 'with') | |
1541 | { | |
233f7bc0 T |
1542 | # this argument is no longer used |
1543 | #$MBI = $_[$i+1] || 'Math::BigInt::Calc'; # default Math::BigInt::Calc | |
6de7f0cc JH |
1544 | $i++; |
1545 | } | |
1546 | else | |
1547 | { | |
1548 | push @a, $_[$i]; | |
1549 | } | |
1550 | } | |
b68b7ab1 | 1551 | require Math::BigInt; |
6de7f0cc | 1552 | |
b68b7ab1 T |
1553 | # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still have GMP |
1554 | if ($lib ne '') | |
1555 | { | |
1556 | my @c = split /\s*,\s*/, $lib; | |
1557 | foreach (@c) | |
6de7f0cc | 1558 | { |
b68b7ab1 | 1559 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters |
6de7f0cc | 1560 | } |
233f7bc0 | 1561 | $lib = join(",", @c); |
93c87d9d | 1562 | } |
233f7bc0 | 1563 | my @import = ('objectify'); |
b8884ce4 | 1564 | push @import, $try => $lib if $lib ne ''; |
233f7bc0 T |
1565 | |
1566 | # MBI already loaded, so feed it our lib arguments | |
1567 | Math::BigInt->import( @import ); | |
6de7f0cc | 1568 | |
12fc2493 | 1569 | $MBI = Math::BigFloat->config()->{lib}; |
b68b7ab1 T |
1570 | |
1571 | # register us with MBI to get notified of future lib changes | |
1572 | Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } ); | |
9b924220 | 1573 | |
233f7bc0 T |
1574 | # any non :constant stuff is handled by our parent, Exporter (loaded |
1575 | # by Math::BigFloat, even if @_ is empty, to give it a chance | |
6de7f0cc JH |
1576 | $self->SUPER::import(@a); # for subclasses |
1577 | $self->export_to_level(1,$self,@a); # need this, too | |
1578 | } | |
184f15d5 JH |
1579 | |
1580 | 1; | |
1581 | ||
1582 | __END__ | |
1583 | ||
1584 | =head1 NAME | |
1585 | ||
b68b7ab1 | 1586 | Math::BigRat - Arbitrary big rational numbers |
184f15d5 JH |
1587 | |
1588 | =head1 SYNOPSIS | |
1589 | ||
7d341013 | 1590 | use Math::BigRat; |
184f15d5 | 1591 | |
7afd7a91 | 1592 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
184f15d5 | 1593 | |
7d341013 T |
1594 | print $x->bstr(),"\n"; |
1595 | print $x ** 2,"\n"; | |
184f15d5 | 1596 | |
7afd7a91 T |
1597 | my $y = Math::BigRat->new('inf'); |
1598 | print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; | |
1599 | ||
1600 | my $z = Math::BigRat->new(144); $z->bsqrt(); | |
1601 | ||
184f15d5 JH |
1602 | =head1 DESCRIPTION |
1603 | ||
7d341013 | 1604 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
b68b7ab1 | 1605 | for arbitrary big rational numbers. |
184f15d5 JH |
1606 | |
1607 | =head2 MATH LIBRARY | |
1608 | ||
b8884ce4 T |
1609 | You can change the underlying module that does the low-level |
1610 | math operations by using: | |
184f15d5 | 1611 | |
b8884ce4 | 1612 | use Math::BigRat try => 'GMP'; |
184f15d5 | 1613 | |
b8884ce4 | 1614 | Note: This needs Math::BigInt::GMP installed. |
184f15d5 JH |
1615 | |
1616 | The following would first try to find Math::BigInt::Foo, then | |
1617 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
1618 | ||
b8884ce4 | 1619 | use Math::BigRat try => 'Foo,Math::BigInt::Bar'; |
184f15d5 | 1620 | |
b8884ce4 T |
1621 | If you want to get warned when the fallback occurs, replace "try" with |
1622 | "lib": | |
184f15d5 | 1623 | |
b8884ce4 | 1624 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
7d341013 | 1625 | |
b8884ce4 T |
1626 | If you want the code to die instead, replace "try" with |
1627 | "only": | |
1628 | ||
1629 | use Math::BigRat only => 'Foo,Math::BigInt::Bar'; | |
7d341013 | 1630 | |
184f15d5 JH |
1631 | =head1 METHODS |
1632 | ||
3c4b39be | 1633 | Any methods not listed here are derived from Math::BigFloat (or |
6de7f0cc JH |
1634 | Math::BigInt), so make sure you check these two modules for further |
1635 | information. | |
1636 | ||
1637 | =head2 new() | |
184f15d5 JH |
1638 | |
1639 | $x = Math::BigRat->new('1/3'); | |
1640 | ||
1641 | Create a new Math::BigRat object. Input can come in various forms: | |
1642 | ||
7d341013 | 1643 | $x = Math::BigRat->new(123); # scalars |
7afd7a91 | 1644 | $x = Math::BigRat->new('inf'); # infinity |
7d341013 | 1645 | $x = Math::BigRat->new('123.3'); # float |
184f15d5 JH |
1646 | $x = Math::BigRat->new('1/3'); # simple string |
1647 | $x = Math::BigRat->new('1 / 3'); # spaced | |
1648 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats | |
1649 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt | |
1650 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat | |
6de7f0cc | 1651 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
184f15d5 | 1652 | |
b68b7ab1 T |
1653 | # You can also give D and N as different objects: |
1654 | $x = Math::BigRat->new( | |
1655 | Math::BigInt->new(-123), | |
1656 | Math::BigInt->new(7), | |
1657 | ); # => -123/7 | |
1658 | ||
6de7f0cc | 1659 | =head2 numerator() |
184f15d5 JH |
1660 | |
1661 | $n = $x->numerator(); | |
1662 | ||
1663 | Returns a copy of the numerator (the part above the line) as signed BigInt. | |
1664 | ||
6de7f0cc | 1665 | =head2 denominator() |
184f15d5 JH |
1666 | |
1667 | $d = $x->denominator(); | |
1668 | ||
1669 | Returns a copy of the denominator (the part under the line) as positive BigInt. | |
1670 | ||
6de7f0cc | 1671 | =head2 parts() |
184f15d5 JH |
1672 | |
1673 | ($n,$d) = $x->parts(); | |
1674 | ||
1675 | Return a list consisting of (signed) numerator and (unsigned) denominator as | |
1676 | BigInts. | |
1677 | ||
b8884ce4 T |
1678 | =head2 numify() |
1679 | ||
1680 | my $y = $x->numify(); | |
1681 | ||
1682 | Returns the object as a scalar. This will lose some data if the object | |
1683 | cannot be represented by a normal Perl scalar (integer or float), so | |
4de3d162 | 1684 | use L<as_int()> or L<as_float()> instead. |
b8884ce4 T |
1685 | |
1686 | This routine is automatically used whenever a scalar is required: | |
1687 | ||
1688 | my $x = Math::BigRat->new('3/1'); | |
1689 | @array = (1,2,3); | |
1690 | $y = $array[$x]; # set $y to 3 | |
1691 | ||
1692 | =head2 as_int()/as_number() | |
6de7f0cc | 1693 | |
7d341013 | 1694 | $x = Math::BigRat->new('13/7'); |
b68b7ab1 T |
1695 | print $x->as_int(),"\n"; # '1' |
1696 | ||
1697 | Returns a copy of the object as BigInt, truncated to an integer. | |
7d341013 | 1698 | |
b68b7ab1 T |
1699 | C<as_number()> is an alias for C<as_int()>. |
1700 | ||
4de3d162 T |
1701 | =head2 as_float() |
1702 | ||
1703 | $x = Math::BigRat->new('13/7'); | |
1704 | print $x->as_float(),"\n"; # '1' | |
1705 | ||
1706 | $x = Math::BigRat->new('2/3'); | |
1707 | print $x->as_float(5),"\n"; # '0.66667' | |
1708 | ||
1709 | Returns a copy of the object as BigFloat, preserving the | |
1710 | accuracy as wanted, or the default of 40 digits. | |
1711 | ||
1712 | This method was added in v0.22 of Math::BigRat (April 2008). | |
1713 | ||
b68b7ab1 T |
1714 | =head2 as_hex() |
1715 | ||
1716 | $x = Math::BigRat->new('13'); | |
1717 | print $x->as_hex(),"\n"; # '0xd' | |
1718 | ||
1719 | Returns the BigRat as hexadecimal string. Works only for integers. | |
1720 | ||
1721 | =head2 as_bin() | |
1722 | ||
1723 | $x = Math::BigRat->new('13'); | |
1724 | print $x->as_bin(),"\n"; # '0x1101' | |
1725 | ||
1726 | Returns the BigRat as binary string. Works only for integers. | |
6de7f0cc | 1727 | |
b8884ce4 T |
1728 | =head2 as_oct() |
1729 | ||
1730 | $x = Math::BigRat->new('13'); | |
1731 | print $x->as_oct(),"\n"; # '015' | |
1732 | ||
1733 | Returns the BigRat as octal string. Works only for integers. | |
1734 | ||
1735 | =head2 from_hex()/from_bin()/from_oct() | |
1736 | ||
1737 | my $h = Math::BigRat->from_hex('0x10'); | |
1738 | my $b = Math::BigRat->from_bin('0b10000000'); | |
1739 | my $o = Math::BigRat->from_oct('020'); | |
1740 | ||
1741 | Create a BigRat from an hexadecimal, binary or octal number | |
1742 | in string form. | |
1743 | ||
1744 | =head2 length() | |
1745 | ||
1746 | $len = $x->length(); | |
1747 | ||
1748 | Return the length of $x in digitis for integer values. | |
1749 | ||
1750 | =head2 digit() | |
1751 | ||
1752 | print Math::BigRat->new('123/1')->digit(1); # 1 | |
1753 | print Math::BigRat->new('123/1')->digit(-1); # 3 | |
1754 | ||
1755 | Return the N'ths digit from X when X is an integer value. | |
1756 | ||
1757 | =head2 bnorm() | |
1758 | ||
1759 | $x->bnorm(); | |
1760 | ||
1761 | Reduce the number to the shortest form. This routine is called | |
1762 | automatically whenever it is needed. | |
1763 | ||
a4e2b1c6 | 1764 | =head2 bfac() |
6de7f0cc | 1765 | |
a4e2b1c6 | 1766 | $x->bfac(); |
6de7f0cc | 1767 | |
a4e2b1c6 | 1768 | Calculates the factorial of $x. For instance: |
6de7f0cc | 1769 | |
a4e2b1c6 JH |
1770 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 |
1771 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 | |
184f15d5 | 1772 | |
7d341013 | 1773 | Works currently only for integers. |
6de7f0cc | 1774 | |
a4e2b1c6 | 1775 | =head2 bround()/round()/bfround() |
6de7f0cc | 1776 | |
a4e2b1c6 | 1777 | Are not yet implemented. |
6de7f0cc | 1778 | |
990fb837 RGS |
1779 | =head2 bmod() |
1780 | ||
1781 | use Math::BigRat; | |
1782 | my $x = Math::BigRat->new('7/4'); | |
1783 | my $y = Math::BigRat->new('4/3'); | |
1784 | print $x->bmod($y); | |
1785 | ||
1786 | Set $x to the remainder of the division of $x by $y. | |
1787 | ||
b8884ce4 T |
1788 | =head2 bneg() |
1789 | ||
1790 | $x->bneg(); | |
1791 | ||
1792 | Used to negate the object in-place. | |
1793 | ||
7d341013 T |
1794 | =head2 is_one() |
1795 | ||
1796 | print "$x is 1\n" if $x->is_one(); | |
1797 | ||
1798 | Return true if $x is exactly one, otherwise false. | |
1799 | ||
1800 | =head2 is_zero() | |
1801 | ||
1802 | print "$x is 0\n" if $x->is_zero(); | |
1803 | ||
1804 | Return true if $x is exactly zero, otherwise false. | |
1805 | ||
b8884ce4 | 1806 | =head2 is_pos()/is_positive() |
7d341013 T |
1807 | |
1808 | print "$x is >= 0\n" if $x->is_positive(); | |
1809 | ||
1810 | Return true if $x is positive (greater than or equal to zero), otherwise | |
1811 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. | |
1812 | ||
b68b7ab1 T |
1813 | C<is_positive()> is an alias for C<is_pos()>. |
1814 | ||
b8884ce4 | 1815 | =head2 is_neg()/is_negative() |
7d341013 T |
1816 | |
1817 | print "$x is < 0\n" if $x->is_negative(); | |
1818 | ||
1819 | Return true if $x is negative (smaller than zero), otherwise false. Please | |
1820 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. | |
1821 | ||
b68b7ab1 T |
1822 | C<is_negative()> is an alias for C<is_neg()>. |
1823 | ||
7d341013 T |
1824 | =head2 is_int() |
1825 | ||
1826 | print "$x is an integer\n" if $x->is_int(); | |
1827 | ||
1828 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise | |
1829 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. | |
1830 | ||
1831 | =head2 is_odd() | |
1832 | ||
1833 | print "$x is odd\n" if $x->is_odd(); | |
1834 | ||
1835 | Return true if $x is odd, otherwise false. | |
1836 | ||
1837 | =head2 is_even() | |
1838 | ||
1839 | print "$x is even\n" if $x->is_even(); | |
1840 | ||
1841 | Return true if $x is even, otherwise false. | |
1842 | ||
1843 | =head2 bceil() | |
1844 | ||
1845 | $x->bceil(); | |
1846 | ||
1847 | Set $x to the next bigger integer value (e.g. truncate the number to integer | |
1848 | and then increment it by one). | |
1849 | ||
1850 | =head2 bfloor() | |
1851 | ||
1852 | $x->bfloor(); | |
1853 | ||
1854 | Truncate $x to an integer value. | |
6de7f0cc | 1855 | |
7afd7a91 T |
1856 | =head2 bsqrt() |
1857 | ||
1858 | $x->bsqrt(); | |
1859 | ||
1860 | Calculate the square root of $x. | |
1861 | ||
b8884ce4 T |
1862 | =head2 broot() |
1863 | ||
1864 | $x->broot($n); | |
1865 | ||
1866 | Calculate the N'th root of $x. | |
1867 | ||
1868 | =head2 badd()/bmul()/bsub()/bdiv()/bdec()/binc() | |
1869 | ||
1870 | Please see the documentation in L<Math::BigInt>. | |
1871 | ||
1872 | =head2 copy() | |
1873 | ||
1874 | my $z = $x->copy(); | |
1875 | ||
1876 | Makes a deep copy of the object. | |
1877 | ||
1878 | Please see the documentation in L<Math::BigInt> for further details. | |
1879 | ||
1880 | =head2 bstr()/bsstr() | |
1881 | ||
1882 | my $x = Math::BigInt->new('8/4'); | |
1883 | print $x->bstr(),"\n"; # prints 1/2 | |
1884 | print $x->bsstr(),"\n"; # prints 1/2 | |
1885 | ||
1886 | Return a string representating this object. | |
1887 | ||
1888 | =head2 bacmp()/bcmp() | |
1889 | ||
1890 | Used to compare numbers. | |
1891 | ||
1892 | Please see the documentation in L<Math::BigInt> for further details. | |
1893 | ||
1894 | =head2 blsft()/brsft() | |
1895 | ||
1896 | Used to shift numbers left/right. | |
1897 | ||
1898 | Please see the documentation in L<Math::BigInt> for further details. | |
1899 | ||
1900 | =head2 bpow() | |
1901 | ||
1902 | $x->bpow($y); | |
1903 | ||
1904 | Compute $x ** $y. | |
1905 | ||
1906 | Please see the documentation in L<Math::BigInt> for further details. | |
1907 | ||
116a1b2f SP |
1908 | =head2 bexp() |
1909 | ||
1910 | $x->bexp($accuracy); # calculate e ** X | |
1911 | ||
1912 | Calculates two integers A and B so that A/B is equal to C<e ** $x>, where C<e> is | |
1913 | Euler's number. | |
1914 | ||
1915 | This method was added in v0.20 of Math::BigRat (May 2007). | |
1916 | ||
1917 | See also L<blog()>. | |
1918 | ||
1919 | =head2 bnok() | |
1920 | ||
1921 | $x->bnok($y); # x over y (binomial coefficient n over k) | |
1922 | ||
1923 | Calculates the binomial coefficient n over k, also called the "choose" | |
1924 | function. The result is equivalent to: | |
1925 | ||
1926 | ( n ) n! | |
1927 | | - | = ------- | |
1928 | ( k ) k!(n-k)! | |
1929 | ||
1930 | This method was added in v0.20 of Math::BigRat (May 2007). | |
1931 | ||
b8884ce4 | 1932 | =head2 config() |
990fb837 RGS |
1933 | |
1934 | use Data::Dumper; | |
1935 | ||
1936 | print Dumper ( Math::BigRat->config() ); | |
1937 | print Math::BigRat->config()->{lib},"\n"; | |
1938 | ||
1939 | Returns a hash containing the configuration, e.g. the version number, lib | |
1940 | loaded etc. The following hash keys are currently filled in with the | |
1941 | appropriate information. | |
1942 | ||
1943 | key RO/RW Description | |
1944 | Example | |
1945 | ============================================================ | |
1946 | lib RO Name of the Math library | |
1947 | Math::BigInt::Calc | |
1948 | lib_version RO Version of 'lib' | |
1949 | 0.30 | |
1950 | class RO The class of config you just called | |
1951 | Math::BigRat | |
1952 | version RO version number of the class you used | |
1953 | 0.10 | |
1954 | upgrade RW To which class numbers are upgraded | |
1955 | undef | |
1956 | downgrade RW To which class numbers are downgraded | |
1957 | undef | |
1958 | precision RW Global precision | |
1959 | undef | |
1960 | accuracy RW Global accuracy | |
1961 | undef | |
1962 | round_mode RW Global round mode | |
1963 | even | |
3c4b39be | 1964 | div_scale RW Fallback accuracy for div |
990fb837 RGS |
1965 | 40 |
1966 | trap_nan RW Trap creation of NaN (undef = no) | |
1967 | undef | |
1968 | trap_inf RW Trap creation of +inf/-inf (undef = no) | |
1969 | undef | |
1970 | ||
1971 | By passing a reference to a hash you may set the configuration values. This | |
1972 | works only for values that a marked with a C<RW> above, anything else is | |
1973 | read-only. | |
1974 | ||
4de3d162 T |
1975 | =head2 objectify() |
1976 | ||
1977 | This is an internal routine that turns scalars into objects. | |
1978 | ||
a4e2b1c6 | 1979 | =head1 BUGS |
6de7f0cc | 1980 | |
7d341013 T |
1981 | Some things are not yet implemented, or only implemented half-way: |
1982 | ||
1983 | =over 2 | |
1984 | ||
1985 | =item inf handling (partial) | |
1986 | ||
1987 | =item NaN handling (partial) | |
1988 | ||
1989 | =item rounding (not implemented except for bceil/bfloor) | |
1990 | ||
1991 | =item $x ** $y where $y is not an integer | |
1992 | ||
7afd7a91 T |
1993 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) |
1994 | ||
7d341013 | 1995 | =back |
184f15d5 JH |
1996 | |
1997 | =head1 LICENSE | |
1998 | ||
1999 | This program is free software; you may redistribute it and/or modify it under | |
2000 | the same terms as Perl itself. | |
2001 | ||
2002 | =head1 SEE ALSO | |
2003 | ||
2004 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, | |
2005 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
2006 | ||
7d341013 T |
2007 | See L<http://search.cpan.org/search?dist=bignum> for a way to use |
2008 | Math::BigRat. | |
2009 | ||
2010 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> | |
2011 | may contain more documentation and examples as well as testcases. | |
184f15d5 JH |
2012 | |
2013 | =head1 AUTHORS | |
2014 | ||
4de3d162 | 2015 | (C) by Tels L<http://bloodgate.com/> 2001 - 2008. |
184f15d5 JH |
2016 | |
2017 | =cut |