Commit | Line | Data |
---|---|---|
13a12e00 JH |
1 | package Math::BigInt; |
2 | ||
3 | # | |
4 | # "Mike had an infinite amount to do and a negative amount of time in which | |
5 | # to do it." - Before and After | |
6 | # | |
7 | ||
58cde26e | 8 | # The following hash values are used: |
0716bf9b | 9 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) |
58cde26e JH |
10 | # sign : +,-,NaN,+inf,-inf |
11 | # _a : accuracy | |
12 | # _p : precision | |
0716bf9b | 13 | # _f : flags, used by MBF to flag parts of a float as untouchable |
b4f14daa | 14 | |
574bacfe JH |
15 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since |
16 | # underlying lib might change the reference! | |
17 | ||
58cde26e | 18 | my $class = "Math::BigInt"; |
08a3f4a9 | 19 | use 5.006; |
58cde26e | 20 | |
7aa7e0ae | 21 | $VERSION = '1.88'; |
b68b7ab1 | 22 | |
233f7bc0 T |
23 | @ISA = qw(Exporter); |
24 | @EXPORT_OK = qw(objectify bgcd blcm); | |
b68b7ab1 | 25 | |
b282a552 T |
26 | # _trap_inf and _trap_nan are internal and should never be accessed from the |
27 | # outside | |
28 | use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode | |
29 | $upgrade $downgrade $_trap_nan $_trap_inf/; | |
58cde26e JH |
30 | use strict; |
31 | ||
32 | # Inside overload, the first arg is always an object. If the original code had | |
091c87b1 T |
33 | # it reversed (like $x = 2 * $y), then the third paramater is true. |
34 | # In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes | |
35 | # no difference, but in some cases it does. | |
58cde26e JH |
36 | |
37 | # For overloaded ops with only one argument we simple use $_[0]->copy() to | |
38 | # preserve the argument. | |
39 | ||
40 | # Thus inheritance of overload operators becomes possible and transparent for | |
41 | # our subclasses without the need to repeat the entire overload section there. | |
a0d0e21e | 42 | |
a5f75d66 | 43 | use overload |
58cde26e JH |
44 | '=' => sub { $_[0]->copy(); }, |
45 | ||
58cde26e JH |
46 | # some shortcuts for speed (assumes that reversed order of arguments is routed |
47 | # to normal '+' and we thus can always modify first arg. If this is changed, | |
48 | # this breaks and must be adjusted.) | |
49 | '+=' => sub { $_[0]->badd($_[1]); }, | |
50 | '-=' => sub { $_[0]->bsub($_[1]); }, | |
51 | '*=' => sub { $_[0]->bmul($_[1]); }, | |
52 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, | |
027dc388 JH |
53 | '%=' => sub { $_[0]->bmod($_[1]); }, |
54 | '^=' => sub { $_[0]->bxor($_[1]); }, | |
55 | '&=' => sub { $_[0]->band($_[1]); }, | |
56 | '|=' => sub { $_[0]->bior($_[1]); }, | |
58cde26e | 57 | |
b68b7ab1 | 58 | '**=' => sub { $_[0]->bpow($_[1]); }, |
2d2b2744 T |
59 | '<<=' => sub { $_[0]->blsft($_[1]); }, |
60 | '>>=' => sub { $_[0]->brsft($_[1]); }, | |
61 | ||
b3abae2a | 62 | # not supported by Perl yet |
027dc388 JH |
63 | '..' => \&_pointpoint, |
64 | ||
a0ac753d | 65 | '<=>' => sub { my $rc = $_[2] ? |
bd05a461 | 66 | ref($_[0])->bcmp($_[1],$_[0]) : |
a0ac753d T |
67 | $_[0]->bcmp($_[1]); |
68 | $rc = 1 unless defined $rc; | |
69 | $rc <=> 0; | |
70 | }, | |
71 | # we need '>=' to get things like "1 >= NaN" right: | |
72 | '>=' => sub { my $rc = $_[2] ? | |
73 | ref($_[0])->bcmp($_[1],$_[0]) : | |
74 | $_[0]->bcmp($_[1]); | |
75 | # if there was a NaN involved, return false | |
76 | return '' unless defined $rc; | |
77 | $rc >= 0; | |
78 | }, | |
027dc388 | 79 | 'cmp' => sub { |
58cde26e | 80 | $_[2] ? |
b3abae2a JH |
81 | "$_[1]" cmp $_[0]->bstr() : |
82 | $_[0]->bstr() cmp "$_[1]" }, | |
58cde26e | 83 | |
60a1aa19 T |
84 | 'cos' => sub { $_[0]->copy->bcos(); }, |
85 | 'sin' => sub { $_[0]->copy->bsin(); }, | |
a87115f0 | 86 | 'atan2' => sub { $_[2] ? |
20e2035c T |
87 | ref($_[0])->new($_[1])->batan2($_[0]) : |
88 | $_[0]->copy()->batan2($_[1]) }, | |
091c87b1 | 89 | |
b68b7ab1 T |
90 | # are not yet overloadable |
91 | #'hex' => sub { print "hex"; $_[0]; }, | |
92 | #'oct' => sub { print "oct"; $_[0]; }, | |
93 | ||
a0ac753d T |
94 | # log(N) is log(N, e), where e is Euler's number |
95 | 'log' => sub { $_[0]->copy()->blog($_[1], undef); }, | |
7d193e39 | 96 | 'exp' => sub { $_[0]->copy()->bexp($_[1]); }, |
58cde26e JH |
97 | 'int' => sub { $_[0]->copy(); }, |
98 | 'neg' => sub { $_[0]->copy()->bneg(); }, | |
99 | 'abs' => sub { $_[0]->copy()->babs(); }, | |
b3abae2a | 100 | 'sqrt' => sub { $_[0]->copy()->bsqrt(); }, |
58cde26e JH |
101 | '~' => sub { $_[0]->copy()->bnot(); }, |
102 | ||
12fc2493 | 103 | # for subtract it's a bit tricky to not modify b: b-a => -a+b |
091c87b1 | 104 | '-' => sub { my $c = $_[0]->copy; $_[2] ? |
a87115f0 RGS |
105 | $c->bneg()->badd( $_[1]) : |
106 | $c->bsub( $_[1]) }, | |
091c87b1 T |
107 | '+' => sub { $_[0]->copy()->badd($_[1]); }, |
108 | '*' => sub { $_[0]->copy()->bmul($_[1]); }, | |
109 | ||
110 | '/' => sub { | |
111 | $_[2] ? ref($_[0])->new($_[1])->bdiv($_[0]) : $_[0]->copy->bdiv($_[1]); | |
112 | }, | |
113 | '%' => sub { | |
114 | $_[2] ? ref($_[0])->new($_[1])->bmod($_[0]) : $_[0]->copy->bmod($_[1]); | |
115 | }, | |
116 | '**' => sub { | |
117 | $_[2] ? ref($_[0])->new($_[1])->bpow($_[0]) : $_[0]->copy->bpow($_[1]); | |
118 | }, | |
119 | '<<' => sub { | |
120 | $_[2] ? ref($_[0])->new($_[1])->blsft($_[0]) : $_[0]->copy->blsft($_[1]); | |
121 | }, | |
122 | '>>' => sub { | |
123 | $_[2] ? ref($_[0])->new($_[1])->brsft($_[0]) : $_[0]->copy->brsft($_[1]); | |
124 | }, | |
125 | '&' => sub { | |
126 | $_[2] ? ref($_[0])->new($_[1])->band($_[0]) : $_[0]->copy->band($_[1]); | |
127 | }, | |
128 | '|' => sub { | |
129 | $_[2] ? ref($_[0])->new($_[1])->bior($_[0]) : $_[0]->copy->bior($_[1]); | |
130 | }, | |
131 | '^' => sub { | |
132 | $_[2] ? ref($_[0])->new($_[1])->bxor($_[0]) : $_[0]->copy->bxor($_[1]); | |
133 | }, | |
134 | ||
135 | # can modify arg of ++ and --, so avoid a copy() for speed, but don't | |
136 | # use $_[0]->bone(), it would modify $_[0] to be 1! | |
58cde26e JH |
137 | '++' => sub { $_[0]->binc() }, |
138 | '--' => sub { $_[0]->bdec() }, | |
139 | ||
140 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers | |
141 | 'bool' => sub { | |
142 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ | |
091c87b1 | 143 | # v5.6.1 dumps on this: return !$_[0]->is_zero() || undef; :-( |
3a427a11 RGS |
144 | my $t = undef; |
145 | $t = 1 if !$_[0]->is_zero(); | |
b3abae2a | 146 | $t; |
58cde26e | 147 | }, |
a0d0e21e | 148 | |
027dc388 JH |
149 | # the original qw() does not work with the TIESCALAR below, why? |
150 | # Order of arguments unsignificant | |
151 | '""' => sub { $_[0]->bstr(); }, | |
152 | '0+' => sub { $_[0]->numify(); } | |
a5f75d66 | 153 | ; |
a0d0e21e | 154 | |
58cde26e JH |
155 | ############################################################################## |
156 | # global constants, flags and accessory | |
157 | ||
b68b7ab1 T |
158 | # These vars are public, but their direct usage is not recommended, use the |
159 | # accessor methods instead | |
0716bf9b | 160 | |
7b29e1e6 | 161 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common' |
ee15d750 JH |
162 | $accuracy = undef; |
163 | $precision = undef; | |
164 | $div_scale = 40; | |
58cde26e | 165 | |
b3abae2a JH |
166 | $upgrade = undef; # default is no upgrade |
167 | $downgrade = undef; # default is no downgrade | |
168 | ||
b68b7ab1 | 169 | # These are internally, and not to be used from the outside at all |
990fb837 RGS |
170 | |
171 | $_trap_nan = 0; # are NaNs ok? set w/ config() | |
172 | $_trap_inf = 0; # are infs ok? set w/ config() | |
173 | my $nan = 'NaN'; # constants for easier life | |
174 | ||
233f7bc0 T |
175 | my $CALC = 'Math::BigInt::FastCalc'; # module to do the low level math |
176 | # default is FastCalc.pm | |
990fb837 RGS |
177 | my $IMPORT = 0; # was import() called yet? |
178 | # used to make require work | |
9b924220 RGS |
179 | my %WARN; # warn only once for low-level libs |
180 | my %CAN; # cache for $CALC->can(...) | |
b68b7ab1 | 181 | my %CALLBACKS; # callbacks to notify on lib loads |
b282a552 | 182 | my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math |
b282a552 | 183 | |
027dc388 JH |
184 | ############################################################################## |
185 | # the old code had $rnd_mode, so we need to support it, too | |
186 | ||
187 | $rnd_mode = 'even'; | |
188 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } | |
189 | sub FETCH { return $round_mode; } | |
190 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } | |
191 | ||
b282a552 T |
192 | BEGIN |
193 | { | |
194 | # tie to enable $rnd_mode to work transparently | |
195 | tie $rnd_mode, 'Math::BigInt'; | |
196 | ||
197 | # set up some handy alias names | |
198 | *as_int = \&as_number; | |
199 | *is_pos = \&is_positive; | |
200 | *is_neg = \&is_negative; | |
201 | } | |
027dc388 JH |
202 | |
203 | ############################################################################## | |
204 | ||
58cde26e JH |
205 | sub round_mode |
206 | { | |
ee15d750 | 207 | no strict 'refs'; |
58cde26e | 208 | # make Class->round_mode() work |
ee15d750 JH |
209 | my $self = shift; |
210 | my $class = ref($self) || $self || __PACKAGE__; | |
58cde26e JH |
211 | if (defined $_[0]) |
212 | { | |
213 | my $m = shift; | |
7b29e1e6 | 214 | if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/) |
990fb837 RGS |
215 | { |
216 | require Carp; Carp::croak ("Unknown round mode '$m'"); | |
217 | } | |
b3abae2a | 218 | return ${"${class}::round_mode"} = $m; |
58cde26e | 219 | } |
990fb837 | 220 | ${"${class}::round_mode"}; |
ee15d750 JH |
221 | } |
222 | ||
b3abae2a JH |
223 | sub upgrade |
224 | { | |
225 | no strict 'refs'; | |
28df3e88 | 226 | # make Class->upgrade() work |
b3abae2a JH |
227 | my $self = shift; |
228 | my $class = ref($self) || $self || __PACKAGE__; | |
9393ace2 JH |
229 | # need to set new value? |
230 | if (@_ > 0) | |
b3abae2a | 231 | { |
b68b7ab1 | 232 | return ${"${class}::upgrade"} = $_[0]; |
b3abae2a | 233 | } |
990fb837 | 234 | ${"${class}::upgrade"}; |
b3abae2a JH |
235 | } |
236 | ||
28df3e88 JH |
237 | sub downgrade |
238 | { | |
239 | no strict 'refs'; | |
240 | # make Class->downgrade() work | |
241 | my $self = shift; | |
242 | my $class = ref($self) || $self || __PACKAGE__; | |
9393ace2 JH |
243 | # need to set new value? |
244 | if (@_ > 0) | |
28df3e88 | 245 | { |
b68b7ab1 | 246 | return ${"${class}::downgrade"} = $_[0]; |
28df3e88 | 247 | } |
990fb837 | 248 | ${"${class}::downgrade"}; |
28df3e88 JH |
249 | } |
250 | ||
ee15d750 JH |
251 | sub div_scale |
252 | { | |
253 | no strict 'refs'; | |
990fb837 | 254 | # make Class->div_scale() work |
ee15d750 JH |
255 | my $self = shift; |
256 | my $class = ref($self) || $self || __PACKAGE__; | |
257 | if (defined $_[0]) | |
258 | { | |
990fb837 RGS |
259 | if ($_[0] < 0) |
260 | { | |
261 | require Carp; Carp::croak ('div_scale must be greater than zero'); | |
262 | } | |
b68b7ab1 | 263 | ${"${class}::div_scale"} = $_[0]; |
ee15d750 | 264 | } |
990fb837 | 265 | ${"${class}::div_scale"}; |
58cde26e JH |
266 | } |
267 | ||
268 | sub accuracy | |
269 | { | |
ee15d750 JH |
270 | # $x->accuracy($a); ref($x) $a |
271 | # $x->accuracy(); ref($x) | |
272 | # Class->accuracy(); class | |
273 | # Class->accuracy($a); class $a | |
58cde26e | 274 | |
ee15d750 JH |
275 | my $x = shift; |
276 | my $class = ref($x) || $x || __PACKAGE__; | |
58cde26e | 277 | |
ee15d750 JH |
278 | no strict 'refs'; |
279 | # need to set new value? | |
58cde26e JH |
280 | if (@_ > 0) |
281 | { | |
ee15d750 | 282 | my $a = shift; |
990fb837 RGS |
283 | # convert objects to scalars to avoid deep recursion. If object doesn't |
284 | # have numify(), then hopefully it will have overloading for int() and | |
285 | # boolean test without wandering into a deep recursion path... | |
286 | $a = $a->numify() if ref($a) && $a->can('numify'); | |
287 | ||
288 | if (defined $a) | |
289 | { | |
290 | # also croak on non-numerical | |
291 | if (!$a || $a <= 0) | |
292 | { | |
293 | require Carp; | |
294 | Carp::croak ('Argument to accuracy must be greater than zero'); | |
295 | } | |
296 | if (int($a) != $a) | |
297 | { | |
298 | require Carp; Carp::croak ('Argument to accuracy must be an integer'); | |
299 | } | |
300 | } | |
ee15d750 JH |
301 | if (ref($x)) |
302 | { | |
303 | # $object->accuracy() or fallback to global | |
ef9466ea T |
304 | $x->bround($a) if $a; # not for undef, 0 |
305 | $x->{_a} = $a; # set/overwrite, even if not rounded | |
306 | delete $x->{_p}; # clear P | |
990fb837 | 307 | $a = ${"${class}::accuracy"} unless defined $a; # proper return value |
ee15d750 JH |
308 | } |
309 | else | |
310 | { | |
ef9466ea T |
311 | ${"${class}::accuracy"} = $a; # set global A |
312 | ${"${class}::precision"} = undef; # clear global P | |
ee15d750 | 313 | } |
ef9466ea | 314 | return $a; # shortcut |
ee15d750 JH |
315 | } |
316 | ||
b68b7ab1 | 317 | my $a; |
f9a08e12 | 318 | # $object->accuracy() or fallback to global |
b68b7ab1 | 319 | $a = $x->{_a} if ref($x); |
f9a08e12 | 320 | # but don't return global undef, when $x's accuracy is 0! |
b68b7ab1 T |
321 | $a = ${"${class}::accuracy"} if !defined $a; |
322 | $a; | |
990fb837 | 323 | } |
58cde26e JH |
324 | |
325 | sub precision | |
326 | { | |
ee15d750 JH |
327 | # $x->precision($p); ref($x) $p |
328 | # $x->precision(); ref($x) | |
329 | # Class->precision(); class | |
330 | # Class->precision($p); class $p | |
58cde26e | 331 | |
ee15d750 JH |
332 | my $x = shift; |
333 | my $class = ref($x) || $x || __PACKAGE__; | |
58cde26e | 334 | |
ee15d750 | 335 | no strict 'refs'; |
58cde26e JH |
336 | if (@_ > 0) |
337 | { | |
ee15d750 | 338 | my $p = shift; |
990fb837 RGS |
339 | # convert objects to scalars to avoid deep recursion. If object doesn't |
340 | # have numify(), then hopefully it will have overloading for int() and | |
341 | # boolean test without wandering into a deep recursion path... | |
342 | $p = $p->numify() if ref($p) && $p->can('numify'); | |
343 | if ((defined $p) && (int($p) != $p)) | |
344 | { | |
345 | require Carp; Carp::croak ('Argument to precision must be an integer'); | |
346 | } | |
ee15d750 JH |
347 | if (ref($x)) |
348 | { | |
349 | # $object->precision() or fallback to global | |
ef9466ea T |
350 | $x->bfround($p) if $p; # not for undef, 0 |
351 | $x->{_p} = $p; # set/overwrite, even if not rounded | |
352 | delete $x->{_a}; # clear A | |
990fb837 | 353 | $p = ${"${class}::precision"} unless defined $p; # proper return value |
ee15d750 JH |
354 | } |
355 | else | |
356 | { | |
ef9466ea T |
357 | ${"${class}::precision"} = $p; # set global P |
358 | ${"${class}::accuracy"} = undef; # clear global A | |
ee15d750 | 359 | } |
ef9466ea | 360 | return $p; # shortcut |
58cde26e | 361 | } |
ee15d750 | 362 | |
b68b7ab1 | 363 | my $p; |
f9a08e12 | 364 | # $object->precision() or fallback to global |
b68b7ab1 | 365 | $p = $x->{_p} if ref($x); |
f9a08e12 | 366 | # but don't return global undef, when $x's precision is 0! |
b68b7ab1 T |
367 | $p = ${"${class}::precision"} if !defined $p; |
368 | $p; | |
990fb837 | 369 | } |
58cde26e | 370 | |
b3abae2a JH |
371 | sub config |
372 | { | |
990fb837 | 373 | # return (or set) configuration data as hash ref |
b3abae2a JH |
374 | my $class = shift || 'Math::BigInt'; |
375 | ||
376 | no strict 'refs'; | |
2ebb273f | 377 | if (@_ > 1 || (@_ == 1 && (ref($_[0]) eq 'HASH'))) |
990fb837 RGS |
378 | { |
379 | # try to set given options as arguments from hash | |
380 | ||
381 | my $args = $_[0]; | |
382 | if (ref($args) ne 'HASH') | |
383 | { | |
384 | $args = { @_ }; | |
385 | } | |
386 | # these values can be "set" | |
387 | my $set_args = {}; | |
388 | foreach my $key ( | |
389 | qw/trap_inf trap_nan | |
390 | upgrade downgrade precision accuracy round_mode div_scale/ | |
391 | ) | |
392 | { | |
393 | $set_args->{$key} = $args->{$key} if exists $args->{$key}; | |
394 | delete $args->{$key}; | |
395 | } | |
396 | if (keys %$args > 0) | |
397 | { | |
398 | require Carp; | |
399 | Carp::croak ("Illegal key(s) '", | |
400 | join("','",keys %$args),"' passed to $class\->config()"); | |
401 | } | |
402 | foreach my $key (keys %$set_args) | |
403 | { | |
404 | if ($key =~ /^trap_(inf|nan)\z/) | |
405 | { | |
406 | ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0); | |
407 | next; | |
408 | } | |
409 | # use a call instead of just setting the $variable to check argument | |
410 | $class->$key($set_args->{$key}); | |
411 | } | |
412 | } | |
413 | ||
414 | # now return actual configuration | |
415 | ||
b3abae2a | 416 | my $cfg = { |
990fb837 RGS |
417 | lib => $CALC, |
418 | lib_version => ${"${CALC}::VERSION"}, | |
b3abae2a | 419 | class => $class, |
990fb837 RGS |
420 | trap_nan => ${"${class}::_trap_nan"}, |
421 | trap_inf => ${"${class}::_trap_inf"}, | |
422 | version => ${"${class}::VERSION"}, | |
b3abae2a | 423 | }; |
990fb837 RGS |
424 | foreach my $key (qw/ |
425 | upgrade downgrade precision accuracy round_mode div_scale | |
426 | /) | |
b3abae2a | 427 | { |
990fb837 | 428 | $cfg->{$key} = ${"${class}::$key"}; |
b3abae2a | 429 | }; |
2ebb273f T |
430 | if (@_ == 1 && (ref($_[0]) ne 'HASH')) |
431 | { | |
432 | # calls of the style config('lib') return just this value | |
433 | return $cfg->{$_[0]}; | |
434 | } | |
b3abae2a JH |
435 | $cfg; |
436 | } | |
437 | ||
58cde26e JH |
438 | sub _scale_a |
439 | { | |
440 | # select accuracy parameter based on precedence, | |
441 | # used by bround() and bfround(), may return undef for scale (means no op) | |
b68b7ab1 T |
442 | my ($x,$scale,$mode) = @_; |
443 | ||
444 | $scale = $x->{_a} unless defined $scale; | |
445 | ||
446 | no strict 'refs'; | |
447 | my $class = ref($x); | |
448 | ||
449 | $scale = ${ $class . '::accuracy' } unless defined $scale; | |
450 | $mode = ${ $class . '::round_mode' } unless defined $mode; | |
451 | ||
452 | ($scale,$mode); | |
58cde26e JH |
453 | } |
454 | ||
455 | sub _scale_p | |
456 | { | |
457 | # select precision parameter based on precedence, | |
458 | # used by bround() and bfround(), may return undef for scale (means no op) | |
b68b7ab1 T |
459 | my ($x,$scale,$mode) = @_; |
460 | ||
461 | $scale = $x->{_p} unless defined $scale; | |
462 | ||
463 | no strict 'refs'; | |
464 | my $class = ref($x); | |
465 | ||
466 | $scale = ${ $class . '::precision' } unless defined $scale; | |
467 | $mode = ${ $class . '::round_mode' } unless defined $mode; | |
468 | ||
469 | ($scale,$mode); | |
58cde26e JH |
470 | } |
471 | ||
472 | ############################################################################## | |
473 | # constructors | |
474 | ||
475 | sub copy | |
476 | { | |
86f0d17a | 477 | # if two arguments, the first one is the class to "swallow" subclasses |
58cde26e JH |
478 | if (@_ > 1) |
479 | { | |
86f0d17a T |
480 | my $self = bless { |
481 | sign => $_[1]->{sign}, | |
482 | value => $CALC->_copy($_[1]->{value}), | |
483 | }, $_[0] if @_ > 1; | |
484 | ||
485 | $self->{_a} = $_[1]->{_a} if defined $_[1]->{_a}; | |
486 | $self->{_p} = $_[1]->{_p} if defined $_[1]->{_p}; | |
487 | return $self; | |
58cde26e | 488 | } |
58cde26e | 489 | |
86f0d17a T |
490 | my $self = bless { |
491 | sign => $_[0]->{sign}, | |
492 | value => $CALC->_copy($_[0]->{value}), | |
493 | }, ref($_[0]); | |
9b924220 | 494 | |
86f0d17a T |
495 | $self->{_a} = $_[0]->{_a} if defined $_[0]->{_a}; |
496 | $self->{_p} = $_[0]->{_p} if defined $_[0]->{_p}; | |
58cde26e JH |
497 | $self; |
498 | } | |
499 | ||
500 | sub new | |
501 | { | |
b22b3e31 | 502 | # create a new BigInt object from a string or another BigInt object. |
0716bf9b | 503 | # see hash keys documented at top |
58cde26e JH |
504 | |
505 | # the argument could be an object, so avoid ||, && etc on it, this would | |
b22b3e31 PN |
506 | # cause costly overloaded code to be called. The only allowed ops are |
507 | # ref() and defined. | |
58cde26e | 508 | |
61f5c3f5 | 509 | my ($class,$wanted,$a,$p,$r) = @_; |
58cde26e | 510 | |
61f5c3f5 T |
511 | # avoid numify-calls by not using || on $wanted! |
512 | return $class->bzero($a,$p) if !defined $wanted; # default to 0 | |
9393ace2 JH |
513 | return $class->copy($wanted,$a,$p,$r) |
514 | if ref($wanted) && $wanted->isa($class); # MBI or subclass | |
58cde26e | 515 | |
61f5c3f5 T |
516 | $class->import() if $IMPORT == 0; # make require work |
517 | ||
9393ace2 JH |
518 | my $self = bless {}, $class; |
519 | ||
520 | # shortcut for "normal" numbers | |
739c8b3a | 521 | if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/)) |
9393ace2 JH |
522 | { |
523 | $self->{sign} = $1 || '+'; | |
9b924220 | 524 | |
9393ace2 JH |
525 | if ($wanted =~ /^[+-]/) |
526 | { | |
56d9de68 | 527 | # remove sign without touching wanted to make it work with constants |
9b924220 RGS |
528 | my $t = $wanted; $t =~ s/^[+-]//; |
529 | $self->{value} = $CALC->_new($t); | |
530 | } | |
531 | else | |
532 | { | |
533 | $self->{value} = $CALC->_new($wanted); | |
9393ace2 | 534 | } |
9393ace2 JH |
535 | no strict 'refs'; |
536 | if ( (defined $a) || (defined $p) | |
537 | || (defined ${"${class}::precision"}) | |
538 | || (defined ${"${class}::accuracy"}) | |
539 | ) | |
540 | { | |
541 | $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p); | |
542 | } | |
543 | return $self; | |
544 | } | |
545 | ||
58cde26e | 546 | # handle '+inf', '-inf' first |
233f7bc0 | 547 | if ($wanted =~ /^[+-]?inf\z/) |
58cde26e | 548 | { |
233f7bc0 T |
549 | $self->{sign} = $wanted; # set a default sign for bstr() |
550 | return $self->binf($wanted); | |
58cde26e JH |
551 | } |
552 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign | |
9b924220 | 553 | my ($mis,$miv,$mfv,$es,$ev) = _split($wanted); |
58cde26e JH |
554 | if (!ref $mis) |
555 | { | |
990fb837 RGS |
556 | if ($_trap_nan) |
557 | { | |
558 | require Carp; Carp::croak("$wanted is not a number in $class"); | |
559 | } | |
0716bf9b | 560 | $self->{value} = $CALC->_zero(); |
58cde26e JH |
561 | $self->{sign} = $nan; |
562 | return $self; | |
563 | } | |
574bacfe JH |
564 | if (!ref $miv) |
565 | { | |
566 | # _from_hex or _from_bin | |
567 | $self->{value} = $mis->{value}; | |
568 | $self->{sign} = $mis->{sign}; | |
569 | return $self; # throw away $mis | |
570 | } | |
58cde26e JH |
571 | # make integer from mantissa by adjusting exp, then convert to bigint |
572 | $self->{sign} = $$mis; # store sign | |
0716bf9b | 573 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
58cde26e JH |
574 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
575 | if ($e > 0) | |
576 | { | |
577 | my $diff = $e - CORE::length($$mfv); | |
578 | if ($diff < 0) # Not integer | |
579 | { | |
990fb837 RGS |
580 | if ($_trap_nan) |
581 | { | |
582 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
583 | } | |
58cde26e | 584 | #print "NOI 1\n"; |
b3abae2a | 585 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
586 | $self->{sign} = $nan; |
587 | } | |
588 | else # diff >= 0 | |
589 | { | |
590 | # adjust fraction and add it to value | |
990fb837 | 591 | #print "diff > 0 $$miv\n"; |
58cde26e JH |
592 | $$miv = $$miv . ($$mfv . '0' x $diff); |
593 | } | |
594 | } | |
595 | else | |
596 | { | |
597 | if ($$mfv ne '') # e <= 0 | |
598 | { | |
599 | # fraction and negative/zero E => NOI | |
990fb837 RGS |
600 | if ($_trap_nan) |
601 | { | |
602 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
603 | } | |
58cde26e | 604 | #print "NOI 2 \$\$mfv '$$mfv'\n"; |
b3abae2a | 605 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
606 | $self->{sign} = $nan; |
607 | } | |
608 | elsif ($e < 0) | |
609 | { | |
610 | # xE-y, and empty mfv | |
611 | #print "xE-y\n"; | |
612 | $e = abs($e); | |
613 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? | |
614 | { | |
990fb837 RGS |
615 | if ($_trap_nan) |
616 | { | |
617 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
618 | } | |
58cde26e | 619 | #print "NOI 3\n"; |
b3abae2a | 620 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
621 | $self->{sign} = $nan; |
622 | } | |
623 | } | |
624 | } | |
625 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 | |
9b924220 | 626 | $self->{value} = $CALC->_new($$miv) if $self->{sign} =~ /^[+-]$/; |
0716bf9b | 627 | # if any of the globals is set, use them to round and store them inside $self |
61f5c3f5 T |
628 | # do not round for new($x,undef,undef) since that is used by MBF to signal |
629 | # no rounding | |
630 | $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p; | |
9393ace2 | 631 | $self; |
58cde26e JH |
632 | } |
633 | ||
58cde26e JH |
634 | sub bnan |
635 | { | |
636 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' | |
b4f14daa | 637 | my $self = shift; |
58cde26e JH |
638 | $self = $class if !defined $self; |
639 | if (!ref($self)) | |
640 | { | |
641 | my $c = $self; $self = {}; bless $self, $c; | |
642 | } | |
990fb837 RGS |
643 | no strict 'refs'; |
644 | if (${"${class}::_trap_nan"}) | |
645 | { | |
646 | require Carp; | |
647 | Carp::croak ("Tried to set $self to NaN in $class\::bnan()"); | |
648 | } | |
61f5c3f5 | 649 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 650 | return if $self->modify('bnan'); |
13a12e00 JH |
651 | if ($self->can('_bnan')) |
652 | { | |
653 | # use subclass to initialize | |
654 | $self->_bnan(); | |
655 | } | |
656 | else | |
657 | { | |
658 | # otherwise do our own thing | |
659 | $self->{value} = $CALC->_zero(); | |
660 | } | |
58cde26e | 661 | $self->{sign} = $nan; |
394e6ffb | 662 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly |
ef9466ea | 663 | $self; |
b4f14daa | 664 | } |
58cde26e JH |
665 | |
666 | sub binf | |
667 | { | |
668 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' | |
669 | # the sign is either '+', or if given, used from there | |
670 | my $self = shift; | |
56b9c951 | 671 | my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/; |
58cde26e JH |
672 | $self = $class if !defined $self; |
673 | if (!ref($self)) | |
674 | { | |
675 | my $c = $self; $self = {}; bless $self, $c; | |
676 | } | |
990fb837 RGS |
677 | no strict 'refs'; |
678 | if (${"${class}::_trap_inf"}) | |
679 | { | |
680 | require Carp; | |
233f7bc0 | 681 | Carp::croak ("Tried to set $self to +-inf in $class\::binf()"); |
990fb837 | 682 | } |
61f5c3f5 | 683 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 684 | return if $self->modify('binf'); |
13a12e00 JH |
685 | if ($self->can('_binf')) |
686 | { | |
687 | # use subclass to initialize | |
688 | $self->_binf(); | |
689 | } | |
690 | else | |
691 | { | |
692 | # otherwise do our own thing | |
693 | $self->{value} = $CALC->_zero(); | |
694 | } | |
56b9c951 JH |
695 | $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf |
696 | $self->{sign} = $sign; | |
394e6ffb | 697 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
ef9466ea | 698 | $self; |
58cde26e JH |
699 | } |
700 | ||
701 | sub bzero | |
702 | { | |
703 | # create a bigint '+0', if given a BigInt, set it to 0 | |
704 | my $self = shift; | |
12fc2493 | 705 | $self = __PACKAGE__ if !defined $self; |
0716bf9b | 706 | |
58cde26e JH |
707 | if (!ref($self)) |
708 | { | |
709 | my $c = $self; $self = {}; bless $self, $c; | |
710 | } | |
61f5c3f5 | 711 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 712 | return if $self->modify('bzero'); |
990fb837 | 713 | |
13a12e00 JH |
714 | if ($self->can('_bzero')) |
715 | { | |
716 | # use subclass to initialize | |
717 | $self->_bzero(); | |
718 | } | |
719 | else | |
720 | { | |
721 | # otherwise do our own thing | |
722 | $self->{value} = $CALC->_zero(); | |
723 | } | |
58cde26e | 724 | $self->{sign} = '+'; |
61f5c3f5 T |
725 | if (@_ > 0) |
726 | { | |
f9a08e12 JH |
727 | if (@_ > 3) |
728 | { | |
729 | # call like: $x->bzero($a,$p,$r,$y); | |
730 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); | |
731 | } | |
732 | else | |
733 | { | |
734 | $self->{_a} = $_[0] | |
735 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); | |
736 | $self->{_p} = $_[1] | |
737 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); | |
738 | } | |
61f5c3f5 | 739 | } |
f9a08e12 | 740 | $self; |
58cde26e JH |
741 | } |
742 | ||
574bacfe JH |
743 | sub bone |
744 | { | |
745 | # create a bigint '+1' (or -1 if given sign '-'), | |
3c4b39be | 746 | # if given a BigInt, set it to +1 or -1, respectively |
574bacfe JH |
747 | my $self = shift; |
748 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; | |
749 | $self = $class if !defined $self; | |
990fb837 | 750 | |
574bacfe JH |
751 | if (!ref($self)) |
752 | { | |
753 | my $c = $self; $self = {}; bless $self, $c; | |
754 | } | |
61f5c3f5 | 755 | $self->import() if $IMPORT == 0; # make require work |
574bacfe | 756 | return if $self->modify('bone'); |
13a12e00 JH |
757 | |
758 | if ($self->can('_bone')) | |
759 | { | |
760 | # use subclass to initialize | |
761 | $self->_bone(); | |
762 | } | |
763 | else | |
764 | { | |
765 | # otherwise do our own thing | |
766 | $self->{value} = $CALC->_one(); | |
767 | } | |
574bacfe | 768 | $self->{sign} = $sign; |
61f5c3f5 T |
769 | if (@_ > 0) |
770 | { | |
f9a08e12 JH |
771 | if (@_ > 3) |
772 | { | |
773 | # call like: $x->bone($sign,$a,$p,$r,$y); | |
774 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); | |
775 | } | |
776 | else | |
777 | { | |
091c87b1 | 778 | # call like: $x->bone($sign,$a,$p,$r); |
f9a08e12 JH |
779 | $self->{_a} = $_[0] |
780 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); | |
781 | $self->{_p} = $_[1] | |
782 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); | |
783 | } | |
61f5c3f5 | 784 | } |
f9a08e12 | 785 | $self; |
574bacfe JH |
786 | } |
787 | ||
58cde26e JH |
788 | ############################################################################## |
789 | # string conversation | |
790 | ||
791 | sub bsstr | |
792 | { | |
793 | # (ref to BFLOAT or num_str ) return num_str | |
794 | # Convert number from internal format to scientific string format. | |
795 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") | |
b68b7ab1 | 796 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e | 797 | |
574bacfe JH |
798 | if ($x->{sign} !~ /^[+-]$/) |
799 | { | |
800 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
801 | return 'inf'; # +inf | |
802 | } | |
58cde26e | 803 | my ($m,$e) = $x->parts(); |
b282a552 T |
804 | #$m->bstr() . 'e+' . $e->bstr(); # e can only be positive in BigInt |
805 | # 'e+' because E can only be positive in BigInt | |
9b924220 | 806 | $m->bstr() . 'e+' . $CALC->_str($e->{value}); |
58cde26e JH |
807 | } |
808 | ||
809 | sub bstr | |
810 | { | |
0716bf9b | 811 | # make a string from bigint object |
b68b7ab1 | 812 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
56b9c951 | 813 | |
574bacfe JH |
814 | if ($x->{sign} !~ /^[+-]$/) |
815 | { | |
816 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
817 | return 'inf'; # +inf | |
818 | } | |
0716bf9b | 819 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 820 | $es.$CALC->_str($x->{value}); |
58cde26e JH |
821 | } |
822 | ||
823 | sub numify | |
824 | { | |
394e6ffb | 825 | # Make a "normal" scalar from a BigInt object |
58cde26e | 826 | my $x = shift; $x = $class->new($x) unless ref $x; |
56d9de68 T |
827 | |
828 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; | |
0716bf9b JH |
829 | my $num = $CALC->_num($x->{value}); |
830 | return -$num if $x->{sign} eq '-'; | |
9393ace2 | 831 | $num; |
58cde26e JH |
832 | } |
833 | ||
834 | ############################################################################## | |
835 | # public stuff (usually prefixed with "b") | |
836 | ||
837 | sub sign | |
838 | { | |
9393ace2 | 839 | # return the sign of the number: +/-/-inf/+inf/NaN |
b282a552 | 840 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 841 | |
9393ace2 | 842 | $x->{sign}; |
58cde26e JH |
843 | } |
844 | ||
ee15d750 | 845 | sub _find_round_parameters |
58cde26e JH |
846 | { |
847 | # After any operation or when calling round(), the result is rounded by | |
848 | # regarding the A & P from arguments, local parameters, or globals. | |
61f5c3f5 | 849 | |
990fb837 RGS |
850 | # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!! |
851 | ||
61f5c3f5 T |
852 | # This procedure finds the round parameters, but it is for speed reasons |
853 | # duplicated in round. Otherwise, it is tested by the testsuite and used | |
854 | # by fdiv(). | |
990fb837 RGS |
855 | |
856 | # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P | |
857 | # were requested/defined (locally or globally or both) | |
61f5c3f5 | 858 | |
394e6ffb JH |
859 | my ($self,$a,$p,$r,@args) = @_; |
860 | # $a accuracy, if given by caller | |
861 | # $p precision, if given by caller | |
862 | # $r round_mode, if given by caller | |
863 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
58cde26e | 864 | |
394e6ffb | 865 | my $c = ref($self); # find out class of argument(s) |
574bacfe | 866 | no strict 'refs'; |
574bacfe | 867 | |
86b76201 | 868 | # convert to normal scalar for speed and correctness in inner parts |
86f0d17a T |
869 | $a = $a->can('numify') ? $a->numify() : "$a" if defined $a && ref($a); |
870 | $p = $p->can('numify') ? $p->numify() : "$p" if defined $p && ref($p); | |
86b76201 | 871 | |
58cde26e | 872 | # now pick $a or $p, but only if we have got "arguments" |
61f5c3f5 | 873 | if (!defined $a) |
58cde26e | 874 | { |
61f5c3f5 | 875 | foreach ($self,@args) |
58cde26e JH |
876 | { |
877 | # take the defined one, or if both defined, the one that is smaller | |
878 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
879 | } | |
61f5c3f5 T |
880 | } |
881 | if (!defined $p) | |
ee15d750 | 882 | { |
61f5c3f5 T |
883 | # even if $a is defined, take $p, to signal error for both defined |
884 | foreach ($self,@args) | |
885 | { | |
886 | # take the defined one, or if both defined, the one that is bigger | |
887 | # -2 > -3, and 3 > 2 | |
888 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
889 | } | |
ee15d750 | 890 | } |
61f5c3f5 T |
891 | # if still none defined, use globals (#2) |
892 | $a = ${"$c\::accuracy"} unless defined $a; | |
893 | $p = ${"$c\::precision"} unless defined $p; | |
990fb837 RGS |
894 | |
895 | # A == 0 is useless, so undef it to signal no rounding | |
896 | $a = undef if defined $a && $a == 0; | |
61f5c3f5 T |
897 | |
898 | # no rounding today? | |
899 | return ($self) unless defined $a || defined $p; # early out | |
900 | ||
901 | # set A and set P is an fatal error | |
990fb837 | 902 | return ($self->bnan()) if defined $a && defined $p; # error |
61f5c3f5 T |
903 | |
904 | $r = ${"$c\::round_mode"} unless defined $r; | |
7b29e1e6 | 905 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/) |
990fb837 RGS |
906 | { |
907 | require Carp; Carp::croak ("Unknown round mode '$r'"); | |
908 | } | |
909 | ||
910 | ($self,$a,$p,$r); | |
ee15d750 JH |
911 | } |
912 | ||
913 | sub round | |
914 | { | |
61f5c3f5 | 915 | # Round $self according to given parameters, or given second argument's |
ee15d750 | 916 | # parameters or global defaults |
ee15d750 | 917 | |
61f5c3f5 T |
918 | # for speed reasons, _find_round_parameters is embeded here: |
919 | ||
920 | my ($self,$a,$p,$r,@args) = @_; | |
921 | # $a accuracy, if given by caller | |
922 | # $p precision, if given by caller | |
923 | # $r round_mode, if given by caller | |
924 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
925 | ||
61f5c3f5 T |
926 | my $c = ref($self); # find out class of argument(s) |
927 | no strict 'refs'; | |
928 | ||
929 | # now pick $a or $p, but only if we have got "arguments" | |
930 | if (!defined $a) | |
58cde26e | 931 | { |
61f5c3f5 T |
932 | foreach ($self,@args) |
933 | { | |
934 | # take the defined one, or if both defined, the one that is smaller | |
935 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
936 | } | |
58cde26e | 937 | } |
61f5c3f5 T |
938 | if (!defined $p) |
939 | { | |
940 | # even if $a is defined, take $p, to signal error for both defined | |
941 | foreach ($self,@args) | |
942 | { | |
943 | # take the defined one, or if both defined, the one that is bigger | |
944 | # -2 > -3, and 3 > 2 | |
945 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
946 | } | |
947 | } | |
948 | # if still none defined, use globals (#2) | |
949 | $a = ${"$c\::accuracy"} unless defined $a; | |
950 | $p = ${"$c\::precision"} unless defined $p; | |
951 | ||
990fb837 RGS |
952 | # A == 0 is useless, so undef it to signal no rounding |
953 | $a = undef if defined $a && $a == 0; | |
954 | ||
61f5c3f5 T |
955 | # no rounding today? |
956 | return $self unless defined $a || defined $p; # early out | |
957 | ||
958 | # set A and set P is an fatal error | |
959 | return $self->bnan() if defined $a && defined $p; | |
960 | ||
961 | $r = ${"$c\::round_mode"} unless defined $r; | |
7b29e1e6 | 962 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/) |
990fb837 | 963 | { |
b282a552 | 964 | require Carp; Carp::croak ("Unknown round mode '$r'"); |
990fb837 | 965 | } |
61f5c3f5 T |
966 | |
967 | # now round, by calling either fround or ffround: | |
968 | if (defined $a) | |
969 | { | |
970 | $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a; | |
971 | } | |
972 | else # both can't be undefined due to early out | |
58cde26e | 973 | { |
61f5c3f5 | 974 | $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p; |
58cde26e | 975 | } |
7b29e1e6 | 976 | # bround() or bfround() already callled bnorm() if nec. |
12fc2493 | 977 | $self; |
58cde26e JH |
978 | } |
979 | ||
17baacb7 | 980 | sub bnorm |
58cde26e | 981 | { |
027dc388 | 982 | # (numstr or BINT) return BINT |
58cde26e | 983 | # Normalize number -- no-op here |
b282a552 | 984 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
b3abae2a | 985 | $x; |
58cde26e JH |
986 | } |
987 | ||
988 | sub babs | |
989 | { | |
990 | # (BINT or num_str) return BINT | |
991 | # make number absolute, or return absolute BINT from string | |
b68b7ab1 | 992 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 993 | |
58cde26e JH |
994 | return $x if $x->modify('babs'); |
995 | # post-normalized abs for internal use (does nothing for NaN) | |
996 | $x->{sign} =~ s/^-/+/; | |
997 | $x; | |
998 | } | |
999 | ||
1000 | sub bneg | |
1001 | { | |
1002 | # (BINT or num_str) return BINT | |
1003 | # negate number or make a negated number from string | |
b68b7ab1 | 1004 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 1005 | |
58cde26e | 1006 | return $x if $x->modify('bneg'); |
b3abae2a | 1007 | |
b68b7ab1 T |
1008 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN' |
1009 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value})); | |
58cde26e JH |
1010 | $x; |
1011 | } | |
1012 | ||
1013 | sub bcmp | |
1014 | { | |
1015 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
1016 | # (BINT or num_str, BINT or num_str) return cond_code | |
f9a08e12 JH |
1017 | |
1018 | # set up parameters | |
1019 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1020 | ||
1021 | # objectify is costly, so avoid it | |
1022 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1023 | { | |
1024 | ($self,$x,$y) = objectify(2,@_); | |
1025 | } | |
0716bf9b | 1026 | |
56d9de68 T |
1027 | return $upgrade->bcmp($x,$y) if defined $upgrade && |
1028 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1029 | ||
0716bf9b JH |
1030 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1031 | { | |
1032 | # handle +-inf and NaN | |
1033 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
574bacfe | 1034 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b JH |
1035 | return +1 if $x->{sign} eq '+inf'; |
1036 | return -1 if $x->{sign} eq '-inf'; | |
1037 | return -1 if $y->{sign} eq '+inf'; | |
b3abae2a | 1038 | return +1; |
0716bf9b | 1039 | } |
574bacfe JH |
1040 | # check sign for speed first |
1041 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
1042 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
1043 | ||
f9a08e12 JH |
1044 | # have same sign, so compare absolute values. Don't make tests for zero here |
1045 | # because it's actually slower than testin in Calc (especially w/ Pari et al) | |
1046 | ||
dccbb853 JH |
1047 | # post-normalized compare for internal use (honors signs) |
1048 | if ($x->{sign} eq '+') | |
1049 | { | |
56b9c951 | 1050 | # $x and $y both > 0 |
dccbb853 JH |
1051 | return $CALC->_acmp($x->{value},$y->{value}); |
1052 | } | |
1053 | ||
56b9c951 | 1054 | # $x && $y both < 0 |
b282a552 | 1055 | $CALC->_acmp($y->{value},$x->{value}); # swaped acmp (lib returns 0,1,-1) |
58cde26e JH |
1056 | } |
1057 | ||
1058 | sub bacmp | |
1059 | { | |
1060 | # Compares 2 values, ignoring their signs. | |
1061 | # Returns one of undef, <0, =0, >0. (suitable for sort) | |
1062 | # (BINT, BINT) return cond_code | |
574bacfe | 1063 | |
f9a08e12 JH |
1064 | # set up parameters |
1065 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1066 | # objectify is costly, so avoid it | |
1067 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1068 | { | |
1069 | ($self,$x,$y) = objectify(2,@_); | |
1070 | } | |
1071 | ||
56d9de68 T |
1072 | return $upgrade->bacmp($x,$y) if defined $upgrade && |
1073 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1074 | ||
574bacfe JH |
1075 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1076 | { | |
1077 | # handle +-inf and NaN | |
1078 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1079 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
ef9466ea T |
1080 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1081 | return -1; | |
574bacfe | 1082 | } |
b3abae2a | 1083 | $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1 |
58cde26e JH |
1084 | } |
1085 | ||
1086 | sub badd | |
1087 | { | |
1088 | # add second arg (BINT or string) to first (BINT) (modifies first) | |
1089 | # return result as BINT | |
f9a08e12 JH |
1090 | |
1091 | # set up parameters | |
1092 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1093 | # objectify is costly, so avoid it | |
1094 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1095 | { | |
1096 | ($self,$x,$y,@r) = objectify(2,@_); | |
1097 | } | |
58cde26e JH |
1098 | |
1099 | return $x if $x->modify('badd'); | |
091c87b1 | 1100 | return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade && |
8f675a64 | 1101 | ((!$x->isa($self)) || (!$y->isa($self))); |
58cde26e | 1102 | |
61f5c3f5 | 1103 | $r[3] = $y; # no push! |
574bacfe JH |
1104 | # inf and NaN handling |
1105 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1106 | { | |
1107 | # NaN first | |
1108 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
13a12e00 JH |
1109 | # inf handling |
1110 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
574bacfe | 1111 | { |
b3abae2a JH |
1112 | # +inf++inf or -inf+-inf => same, rest is NaN |
1113 | return $x if $x->{sign} eq $y->{sign}; | |
1114 | return $x->bnan(); | |
574bacfe JH |
1115 | } |
1116 | # +-inf + something => +inf | |
1117 | # something +-inf => +-inf | |
1118 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; | |
1119 | return $x; | |
1120 | } | |
1121 | ||
b282a552 | 1122 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
58cde26e JH |
1123 | |
1124 | if ($sx eq $sy) | |
1125 | { | |
574bacfe | 1126 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e JH |
1127 | } |
1128 | else | |
1129 | { | |
574bacfe | 1130 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e JH |
1131 | if ($a > 0) |
1132 | { | |
574bacfe | 1133 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e JH |
1134 | $x->{sign} = $sy; |
1135 | } | |
1136 | elsif ($a == 0) | |
1137 | { | |
1138 | # speedup, if equal, set result to 0 | |
0716bf9b | 1139 | $x->{value} = $CALC->_zero(); |
58cde26e JH |
1140 | $x->{sign} = '+'; |
1141 | } | |
1142 | else # a < 0 | |
1143 | { | |
574bacfe | 1144 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
a0d0e21e | 1145 | } |
a0d0e21e | 1146 | } |
b68b7ab1 | 1147 | $x->round(@r); |
58cde26e JH |
1148 | } |
1149 | ||
1150 | sub bsub | |
1151 | { | |
091c87b1 | 1152 | # (BINT or num_str, BINT or num_str) return BINT |
58cde26e | 1153 | # subtract second arg from first, modify first |
f9a08e12 JH |
1154 | |
1155 | # set up parameters | |
1156 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
7d193e39 | 1157 | |
f9a08e12 JH |
1158 | # objectify is costly, so avoid it |
1159 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1160 | { | |
1161 | ($self,$x,$y,@r) = objectify(2,@_); | |
1162 | } | |
58cde26e | 1163 | |
58cde26e | 1164 | return $x if $x->modify('bsub'); |
8f675a64 | 1165 | |
9b924220 RGS |
1166 | return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade && |
1167 | ((!$x->isa($self)) || (!$y->isa($self))); | |
b3abae2a | 1168 | |
b68b7ab1 | 1169 | return $x->round(@r) if $y->is_zero(); |
b3abae2a | 1170 | |
a87115f0 RGS |
1171 | # To correctly handle the lone special case $x->bsub($x), we note the sign |
1172 | # of $x, then flip the sign from $y, and if the sign of $x did change, too, | |
1173 | # then we caught the special case: | |
1174 | my $xsign = $x->{sign}; | |
1175 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN | |
1176 | if ($xsign ne $x->{sign}) | |
03874afe | 1177 | { |
a87115f0 RGS |
1178 | # special case of $x->bsub($x) results in 0 |
1179 | return $x->bzero(@r) if $xsign =~ /^[+-]$/; | |
03874afe T |
1180 | return $x->bnan(); # NaN, -inf, +inf |
1181 | } | |
b3abae2a JH |
1182 | $x->badd($y,@r); # badd does not leave internal zeros |
1183 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) | |
7b29e1e6 | 1184 | $x; # already rounded by badd() or no round nec. |
58cde26e JH |
1185 | } |
1186 | ||
1187 | sub binc | |
1188 | { | |
1189 | # increment arg by one | |
ee15d750 | 1190 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1191 | return $x if $x->modify('binc'); |
e745a66c JH |
1192 | |
1193 | if ($x->{sign} eq '+') | |
1194 | { | |
1195 | $x->{value} = $CALC->_inc($x->{value}); | |
b68b7ab1 | 1196 | return $x->round($a,$p,$r); |
e745a66c JH |
1197 | } |
1198 | elsif ($x->{sign} eq '-') | |
1199 | { | |
1200 | $x->{value} = $CALC->_dec($x->{value}); | |
1201 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 | |
b68b7ab1 | 1202 | return $x->round($a,$p,$r); |
e745a66c JH |
1203 | } |
1204 | # inf, nan handling etc | |
091c87b1 | 1205 | $x->badd($self->bone(),$a,$p,$r); # badd does round |
58cde26e JH |
1206 | } |
1207 | ||
1208 | sub bdec | |
1209 | { | |
1210 | # decrement arg by one | |
b282a552 | 1211 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1212 | return $x if $x->modify('bdec'); |
e745a66c | 1213 | |
b282a552 | 1214 | if ($x->{sign} eq '-') |
e745a66c | 1215 | { |
b68b7ab1 | 1216 | # x already < 0 |
e745a66c | 1217 | $x->{value} = $CALC->_inc($x->{value}); |
b282a552 T |
1218 | } |
1219 | else | |
e745a66c | 1220 | { |
b68b7ab1 | 1221 | return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf or NaN |
b282a552 T |
1222 | # >= 0 |
1223 | if ($CALC->_is_zero($x->{value})) | |
1224 | { | |
1225 | # == 0 | |
1226 | $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1 | |
1227 | } | |
1228 | else | |
1229 | { | |
1230 | # > 0 | |
1231 | $x->{value} = $CALC->_dec($x->{value}); | |
1232 | } | |
e745a66c | 1233 | } |
b68b7ab1 | 1234 | $x->round(@r); |
b282a552 | 1235 | } |
58cde26e | 1236 | |
61f5c3f5 T |
1237 | sub blog |
1238 | { | |
091c87b1 T |
1239 | # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base |
1240 | # $base of $x) | |
1241 | ||
1242 | # set up parameters | |
b68b7ab1 | 1243 | my ($self,$x,$base,@r) = (undef,@_); |
091c87b1 T |
1244 | # objectify is costly, so avoid it |
1245 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1246 | { | |
b68b7ab1 | 1247 | ($self,$x,$base,@r) = objectify(1,ref($x),@_); |
091c87b1 | 1248 | } |
a0ac753d | 1249 | |
ef9466ea T |
1250 | return $x if $x->modify('blog'); |
1251 | ||
2ebb273f T |
1252 | $base = $self->new($base) if defined $base && !ref $base; |
1253 | ||
091c87b1 T |
1254 | # inf, -inf, NaN, <0 => NaN |
1255 | return $x->bnan() | |
9b924220 | 1256 | if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+'); |
091c87b1 | 1257 | |
9b924220 RGS |
1258 | return $upgrade->blog($upgrade->new($x),$base,@r) if |
1259 | defined $upgrade; | |
091c87b1 | 1260 | |
a0ac753d T |
1261 | # fix for bug #24969: |
1262 | # the default base is e (Euler's number) which is not an integer | |
1263 | if (!defined $base) | |
1264 | { | |
1265 | require Math::BigFloat; | |
1266 | my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int(); | |
1267 | # modify $x in place | |
1268 | $x->{value} = $u->{value}; | |
1269 | $x->{sign} = $u->{sign}; | |
1270 | return $x; | |
1271 | } | |
1272 | ||
9b924220 RGS |
1273 | my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value}); |
1274 | return $x->bnan() unless defined $rc; # not possible to take log? | |
1275 | $x->{value} = $rc; | |
1276 | $x->round(@r); | |
61f5c3f5 | 1277 | } |
091c87b1 | 1278 | |
50109ad0 RGS |
1279 | sub bnok |
1280 | { | |
1281 | # Calculate n over k (binomial coefficient or "choose" function) as integer. | |
1282 | # set up parameters | |
1283 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1284 | ||
1285 | # objectify is costly, so avoid it | |
1286 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1287 | { | |
1288 | ($self,$x,$y,@r) = objectify(2,@_); | |
1289 | } | |
1290 | ||
1291 | return $x if $x->modify('bnok'); | |
1292 | return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'; | |
1293 | return $x->binf() if $x->{sign} eq '+inf'; | |
1294 | ||
1295 | # k > n or k < 0 => 0 | |
1296 | my $cmp = $x->bacmp($y); | |
1297 | return $x->bzero() if $cmp < 0 || $y->{sign} =~ /^-/; | |
1298 | # k == n => 1 | |
1299 | return $x->bone(@r) if $cmp == 0; | |
1300 | ||
1301 | if ($CALC->can('_nok')) | |
1302 | { | |
1303 | $x->{value} = $CALC->_nok($x->{value},$y->{value}); | |
1304 | } | |
1305 | else | |
1306 | { | |
1307 | # ( 7 ) 7! 7*6*5 * 4*3*2*1 7 * 6 * 5 | |
1308 | # ( - ) = --------- = --------------- = --------- | |
1309 | # ( 3 ) 3! (7-3)! 3*2*1 * 4*3*2*1 3 * 2 * 1 | |
1310 | ||
1311 | # compute n - k + 2 (so we start with 5 in the example above) | |
1312 | my $z = $x - $y; | |
1313 | if (!$z->is_one()) | |
1314 | { | |
1315 | $z->binc(); | |
1316 | my $r = $z->copy(); $z->binc(); | |
1317 | my $d = $self->new(2); | |
1318 | while ($z->bacmp($x) <= 0) # f < x ? | |
1319 | { | |
1320 | $r->bmul($z); $r->bdiv($d); | |
1321 | $z->binc(); $d->binc(); | |
1322 | } | |
1323 | $x->{value} = $r->{value}; $x->{sign} = '+'; | |
1324 | } | |
1325 | else { $x->bone(); } | |
1326 | } | |
1327 | $x->round(@r); | |
1328 | } | |
1329 | ||
7d193e39 T |
1330 | sub bexp |
1331 | { | |
1332 | # Calculate e ** $x (Euler's number to the power of X), truncated to | |
1333 | # an integer value. | |
1334 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
1335 | return $x if $x->modify('bexp'); | |
1336 | ||
1337 | # inf, -inf, NaN, <0 => NaN | |
1338 | return $x->bnan() if $x->{sign} eq 'NaN'; | |
1339 | return $x->bone() if $x->is_zero(); | |
1340 | return $x if $x->{sign} eq '+inf'; | |
1341 | return $x->bzero() if $x->{sign} eq '-inf'; | |
1342 | ||
1343 | my $u; | |
1344 | { | |
1345 | # run through Math::BigFloat unless told otherwise | |
50109ad0 | 1346 | require Math::BigFloat unless defined $upgrade; |
7d193e39 T |
1347 | local $upgrade = 'Math::BigFloat' unless defined $upgrade; |
1348 | # calculate result, truncate it to integer | |
1349 | $u = $upgrade->bexp($upgrade->new($x),@r); | |
1350 | } | |
1351 | ||
1352 | if (!defined $upgrade) | |
1353 | { | |
1354 | $u = $u->as_int(); | |
1355 | # modify $x in place | |
1356 | $x->{value} = $u->{value}; | |
1357 | $x->round(@r); | |
1358 | } | |
1359 | else { $x = $u; } | |
1360 | } | |
1361 | ||
58cde26e JH |
1362 | sub blcm |
1363 | { | |
1364 | # (BINT or num_str, BINT or num_str) return BINT | |
1365 | # does not modify arguments, but returns new object | |
1366 | # Lowest Common Multiplicator | |
58cde26e | 1367 | |
0716bf9b JH |
1368 | my $y = shift; my ($x); |
1369 | if (ref($y)) | |
1370 | { | |
1371 | $x = $y->copy(); | |
1372 | } | |
1373 | else | |
1374 | { | |
12fc2493 | 1375 | $x = $class->new($y); |
0716bf9b | 1376 | } |
9b924220 RGS |
1377 | my $self = ref($x); |
1378 | while (@_) | |
1379 | { | |
1380 | my $y = shift; $y = $self->new($y) if !ref ($y); | |
1381 | $x = __lcm($x,$y); | |
1382 | } | |
58cde26e JH |
1383 | $x; |
1384 | } | |
1385 | ||
1386 | sub bgcd | |
1387 | { | |
1388 | # (BINT or num_str, BINT or num_str) return BINT | |
1389 | # does not modify arguments, but returns new object | |
1390 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) | |
0716bf9b | 1391 | |
dccbb853 | 1392 | my $y = shift; |
12fc2493 | 1393 | $y = $class->new($y) if !ref($y); |
dccbb853 | 1394 | my $self = ref($y); |
9b924220 RGS |
1395 | my $x = $y->copy()->babs(); # keep arguments |
1396 | return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN? | |
1397 | ||
1398 | while (@_) | |
0716bf9b | 1399 | { |
9b924220 | 1400 | $y = shift; $y = $self->new($y) if !ref($y); |
9b924220 | 1401 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? |
b68b7ab1 T |
1402 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); |
1403 | last if $CALC->_is_one($x->{value}); | |
0716bf9b | 1404 | } |
9b924220 | 1405 | $x; |
58cde26e JH |
1406 | } |
1407 | ||
58cde26e JH |
1408 | sub bnot |
1409 | { | |
1410 | # (num_str or BINT) return BINT | |
1411 | # represent ~x as twos-complement number | |
ee15d750 JH |
1412 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1413 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1414 | ||
58cde26e | 1415 | return $x if $x->modify('bnot'); |
091c87b1 | 1416 | $x->binc()->bneg(); # binc already does round |
58cde26e JH |
1417 | } |
1418 | ||
091c87b1 | 1419 | ############################################################################## |
b3abae2a | 1420 | # is_foo test routines |
091c87b1 | 1421 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
b3abae2a | 1422 | |
58cde26e JH |
1423 | sub is_zero |
1424 | { | |
1425 | # return true if arg (BINT or num_str) is zero (array '+', '0') | |
ee15d750 | 1426 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1427 | |
574bacfe | 1428 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 | 1429 | $CALC->_is_zero($x->{value}); |
58cde26e JH |
1430 | } |
1431 | ||
1432 | sub is_nan | |
1433 | { | |
1434 | # return true if arg (BINT or num_str) is NaN | |
091c87b1 | 1435 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 1436 | |
091c87b1 | 1437 | $x->{sign} eq $nan ? 1 : 0; |
58cde26e JH |
1438 | } |
1439 | ||
1440 | sub is_inf | |
1441 | { | |
1442 | # return true if arg (BINT or num_str) is +-inf | |
091c87b1 | 1443 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
58cde26e | 1444 | |
091c87b1 | 1445 | if (defined $sign) |
ee15d750 | 1446 | { |
091c87b1 T |
1447 | $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf |
1448 | $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-' | |
1449 | return $x->{sign} =~ /^$sign$/ ? 1 : 0; | |
ee15d750 | 1450 | } |
091c87b1 | 1451 | $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity |
58cde26e JH |
1452 | } |
1453 | ||
1454 | sub is_one | |
1455 | { | |
091c87b1 | 1456 | # return true if arg (BINT or num_str) is +1, or -1 if sign is given |
ee15d750 JH |
1457 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
1458 | ||
990fb837 | 1459 | $sign = '+' if !defined $sign || $sign ne '-'; |
0716bf9b | 1460 | |
ee15d750 | 1461 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
394e6ffb | 1462 | $CALC->_is_one($x->{value}); |
58cde26e JH |
1463 | } |
1464 | ||
1465 | sub is_odd | |
1466 | { | |
1467 | # return true when arg (BINT or num_str) is odd, false for even | |
ee15d750 | 1468 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1469 | |
b22b3e31 | 1470 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1471 | $CALC->_is_odd($x->{value}); |
58cde26e JH |
1472 | } |
1473 | ||
1474 | sub is_even | |
1475 | { | |
1476 | # return true when arg (BINT or num_str) is even, false for odd | |
ee15d750 | 1477 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1478 | |
b22b3e31 | 1479 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1480 | $CALC->_is_even($x->{value}); |
0716bf9b JH |
1481 | } |
1482 | ||
1483 | sub is_positive | |
1484 | { | |
1485 | # return true when arg (BINT or num_str) is positive (>= 0) | |
ee15d750 | 1486 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
b68b7ab1 T |
1487 | |
1488 | return 1 if $x->{sign} eq '+inf'; # +inf is positive | |
1489 | ||
1490 | # 0+ is neither positive nor negative | |
1491 | ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0; | |
0716bf9b JH |
1492 | } |
1493 | ||
1494 | sub is_negative | |
1495 | { | |
1496 | # return true when arg (BINT or num_str) is negative (< 0) | |
ee15d750 JH |
1497 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1498 | ||
b68b7ab1 | 1499 | $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not |
58cde26e JH |
1500 | } |
1501 | ||
b3abae2a JH |
1502 | sub is_int |
1503 | { | |
1504 | # return true when arg (BINT or num_str) is an integer | |
091c87b1 | 1505 | # always true for BigInt, but different for BigFloats |
b3abae2a JH |
1506 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1507 | ||
1508 | $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't | |
1509 | } | |
1510 | ||
0716bf9b JH |
1511 | ############################################################################### |
1512 | ||
58cde26e JH |
1513 | sub bmul |
1514 | { | |
c97ef841 | 1515 | # multiply the first number by the second number |
58cde26e | 1516 | # (BINT or num_str, BINT or num_str) return BINT |
f9a08e12 JH |
1517 | |
1518 | # set up parameters | |
1519 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1520 | # objectify is costly, so avoid it | |
1521 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1522 | { | |
1523 | ($self,$x,$y,@r) = objectify(2,@_); | |
1524 | } | |
a0ac753d | 1525 | |
58cde26e | 1526 | return $x if $x->modify('bmul'); |
61f5c3f5 | 1527 | |
574bacfe | 1528 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
b3abae2a | 1529 | |
574bacfe JH |
1530 | # inf handling |
1531 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1532 | { | |
b3abae2a | 1533 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe JH |
1534 | # result will always be +-inf: |
1535 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
1536 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
1537 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
1538 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
1539 | return $x->binf('-'); | |
1540 | } | |
9b924220 RGS |
1541 | |
1542 | return $upgrade->bmul($x,$upgrade->new($y),@r) | |
1543 | if defined $upgrade && !$y->isa($self); | |
9393ace2 JH |
1544 | |
1545 | $r[3] = $y; # no push here | |
58cde26e | 1546 | |
0716bf9b | 1547 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
dccbb853 | 1548 | |
b3abae2a JH |
1549 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
1550 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 | |
f9a08e12 | 1551 | |
b68b7ab1 | 1552 | $x->round(@r); |
dccbb853 JH |
1553 | } |
1554 | ||
80365507 T |
1555 | sub bmuladd |
1556 | { | |
1557 | # multiply two numbers and then add the third to the result | |
1558 | # (BINT or num_str, BINT or num_str, BINT or num_str) return BINT | |
1559 | ||
1560 | # set up parameters | |
1561 | my ($self,$x,$y,$z,@r) = (ref($_[0]),@_); | |
1562 | # objectify is costly, so avoid it | |
1563 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1564 | { | |
1565 | ($self,$x,$y,$z,@r) = objectify(3,@_); | |
1566 | } | |
1567 | ||
1568 | return $x if $x->modify('bmuladd'); | |
1569 | ||
1570 | return $x->bnan() if ($x->{sign} eq $nan) || | |
1571 | ($y->{sign} eq $nan) || | |
1572 | ($z->{sign} eq $nan); | |
1573 | ||
1574 | # inf handling of x and y | |
1575 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1576 | { | |
1577 | return $x->bnan() if $x->is_zero() || $y->is_zero(); | |
1578 | # result will always be +-inf: | |
1579 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
1580 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
1581 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
1582 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
1583 | return $x->binf('-'); | |
1584 | } | |
1585 | # inf handling x*y and z | |
1586 | if (($z->{sign} =~ /^[+-]inf$/)) | |
1587 | { | |
1588 | # something +-inf => +-inf | |
1589 | $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/; | |
1590 | } | |
1591 | ||
1592 | return $upgrade->bmuladd($x,$upgrade->new($y),$upgrade->new($z),@r) | |
1593 | if defined $upgrade && (!$y->isa($self) || !$z->isa($self) || !$x->isa($self)); | |
1594 | ||
c97ef841 | 1595 | # TODO: what if $y and $z have A or P set? |
80365507 T |
1596 | $r[3] = $z; # no push here |
1597 | ||
1598 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + | |
1599 | ||
1600 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math | |
1601 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 | |
1602 | ||
1603 | my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); # get signs | |
1604 | ||
1605 | if ($sx eq $sz) | |
1606 | { | |
1607 | $x->{value} = $CALC->_add($x->{value},$z->{value}); # same sign, abs add | |
1608 | } | |
1609 | else | |
1610 | { | |
1611 | my $a = $CALC->_acmp ($z->{value},$x->{value}); # absolute compare | |
1612 | if ($a > 0) | |
1613 | { | |
1614 | $x->{value} = $CALC->_sub($z->{value},$x->{value},1); # abs sub w/ swap | |
1615 | $x->{sign} = $sz; | |
1616 | } | |
1617 | elsif ($a == 0) | |
1618 | { | |
1619 | # speedup, if equal, set result to 0 | |
1620 | $x->{value} = $CALC->_zero(); | |
1621 | $x->{sign} = '+'; | |
1622 | } | |
1623 | else # a < 0 | |
1624 | { | |
1625 | $x->{value} = $CALC->_sub($x->{value}, $z->{value}); # abs sub | |
1626 | } | |
1627 | } | |
1628 | $x->round(@r); | |
1629 | } | |
1630 | ||
dccbb853 JH |
1631 | sub _div_inf |
1632 | { | |
1633 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code | |
1634 | my ($self,$x,$y) = @_; | |
1635 | ||
1636 | # NaN if x == NaN or y == NaN or x==y==0 | |
1637 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() | |
1638 | if (($x->is_nan() || $y->is_nan()) || | |
1639 | ($x->is_zero() && $y->is_zero())); | |
1640 | ||
b3abae2a JH |
1641 | # +-inf / +-inf == NaN, reminder also NaN |
1642 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
dccbb853 | 1643 | { |
b3abae2a | 1644 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan(); |
dccbb853 JH |
1645 | } |
1646 | # x / +-inf => 0, remainder x (works even if x == 0) | |
1647 | if ($y->{sign} =~ /^[+-]inf$/) | |
1648 | { | |
f9a08e12 | 1649 | my $t = $x->copy(); # bzero clobbers up $x |
dccbb853 JH |
1650 | return wantarray ? ($x->bzero(),$t) : $x->bzero() |
1651 | } | |
1652 | ||
1653 | # 5 / 0 => +inf, -6 / 0 => -inf | |
1654 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf | |
1655 | # exception: -8 / 0 has remainder -8, not 8 | |
1656 | # exception: -inf / 0 has remainder -inf, not inf | |
1657 | if ($y->is_zero()) | |
1658 | { | |
1659 | # +-inf / 0 => special case for -inf | |
1660 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); | |
1661 | if (!$x->is_zero() && !$x->is_inf()) | |
1662 | { | |
1663 | my $t = $x->copy(); # binf clobbers up $x | |
1664 | return wantarray ? | |
1665 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) | |
1666 | } | |
1667 | } | |
1668 | ||
1669 | # last case: +-inf / ordinary number | |
1670 | my $sign = '+inf'; | |
1671 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; | |
1672 | $x->{sign} = $sign; | |
1673 | return wantarray ? ($x,$self->bzero()) : $x; | |
58cde26e JH |
1674 | } |
1675 | ||
1676 | sub bdiv | |
1677 | { | |
1678 | # (dividend: BINT or num_str, divisor: BINT or num_str) return | |
1679 | # (BINT,BINT) (quo,rem) or BINT (only rem) | |
f9a08e12 JH |
1680 | |
1681 | # set up parameters | |
1682 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1683 | # objectify is costly, so avoid it | |
1684 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1685 | { | |
1686 | ($self,$x,$y,@r) = objectify(2,@_); | |
1687 | } | |
58cde26e JH |
1688 | |
1689 | return $x if $x->modify('bdiv'); | |
1690 | ||
dccbb853 JH |
1691 | return $self->_div_inf($x,$y) |
1692 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
58cde26e | 1693 | |
9393ace2 JH |
1694 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
1695 | if defined $upgrade; | |
58cde26e | 1696 | |
990fb837 RGS |
1697 | $r[3] = $y; # no push! |
1698 | ||
58cde26e | 1699 | # calc new sign and in case $y == +/- 1, return $x |
dccbb853 | 1700 | my $xsign = $x->{sign}; # keep |
58cde26e | 1701 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
58cde26e | 1702 | |
58cde26e JH |
1703 | if (wantarray) |
1704 | { | |
394e6ffb JH |
1705 | my $rem = $self->bzero(); |
1706 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); | |
1707 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
f9a08e12 JH |
1708 | $rem->{_a} = $x->{_a}; |
1709 | $rem->{_p} = $x->{_p}; | |
b68b7ab1 | 1710 | $x->round(@r); |
dccbb853 JH |
1711 | if (! $CALC->_is_zero($rem->{value})) |
1712 | { | |
1713 | $rem->{sign} = $y->{sign}; | |
990fb837 | 1714 | $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-' |
dccbb853 JH |
1715 | } |
1716 | else | |
1717 | { | |
1718 | $rem->{sign} = '+'; # dont leave -0 | |
1719 | } | |
b68b7ab1 | 1720 | $rem->round(@r); |
990fb837 | 1721 | return ($x,$rem); |
58cde26e | 1722 | } |
394e6ffb JH |
1723 | |
1724 | $x->{value} = $CALC->_div($x->{value},$y->{value}); | |
1725 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
f9a08e12 | 1726 | |
b68b7ab1 | 1727 | $x->round(@r); |
58cde26e JH |
1728 | } |
1729 | ||
d614cd8b JH |
1730 | ############################################################################### |
1731 | # modulus functions | |
1732 | ||
dccbb853 JH |
1733 | sub bmod |
1734 | { | |
1735 | # modulus (or remainder) | |
1736 | # (BINT or num_str, BINT or num_str) return BINT | |
f9a08e12 JH |
1737 | |
1738 | # set up parameters | |
1739 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1740 | # objectify is costly, so avoid it | |
1741 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1742 | { | |
1743 | ($self,$x,$y,@r) = objectify(2,@_); | |
1744 | } | |
28df3e88 | 1745 | |
dccbb853 | 1746 | return $x if $x->modify('bmod'); |
61f5c3f5 | 1747 | $r[3] = $y; # no push! |
dccbb853 JH |
1748 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) |
1749 | { | |
1750 | my ($d,$r) = $self->_div_inf($x,$y); | |
f9a08e12 JH |
1751 | $x->{sign} = $r->{sign}; |
1752 | $x->{value} = $r->{value}; | |
1753 | return $x->round(@r); | |
dccbb853 JH |
1754 | } |
1755 | ||
9b924220 RGS |
1756 | # calc new sign and in case $y == +/- 1, return $x |
1757 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); | |
1758 | if (!$CALC->_is_zero($x->{value})) | |
dccbb853 | 1759 | { |
b68b7ab1 T |
1760 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1) # $y-$x |
1761 | if ($x->{sign} ne $y->{sign}); | |
9b924220 | 1762 | $x->{sign} = $y->{sign}; |
dccbb853 | 1763 | } |
9b924220 | 1764 | else |
b3abae2a | 1765 | { |
9b924220 | 1766 | $x->{sign} = '+'; # dont leave -0 |
b3abae2a | 1767 | } |
b68b7ab1 | 1768 | $x->round(@r); |
dccbb853 JH |
1769 | } |
1770 | ||
07d34614 | 1771 | sub bmodinv |
d614cd8b | 1772 | { |
56d9de68 | 1773 | # Modular inverse. given a number which is (hopefully) relatively |
d614cd8b | 1774 | # prime to the modulus, calculate its inverse using Euclid's |
56d9de68 | 1775 | # alogrithm. If the number is not relatively prime to the modulus |
d614cd8b JH |
1776 | # (i.e. their gcd is not one) then NaN is returned. |
1777 | ||
f9a08e12 | 1778 | # set up parameters |
b68b7ab1 | 1779 | my ($self,$x,$y,@r) = (undef,@_); |
56d9de68 | 1780 | # objectify is costly, so avoid it |
f9a08e12 JH |
1781 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1782 | { | |
1783 | ($self,$x,$y,@r) = objectify(2,@_); | |
56d9de68 | 1784 | } |
d614cd8b | 1785 | |
f9a08e12 | 1786 | return $x if $x->modify('bmodinv'); |
d614cd8b | 1787 | |
f9a08e12 | 1788 | return $x->bnan() |
56d9de68 T |
1789 | if ($y->{sign} ne '+' # -, NaN, +inf, -inf |
1790 | || $x->is_zero() # or num == 0 | |
1791 | || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf | |
d614cd8b | 1792 | ); |
1ddff52a | 1793 | |
f9a08e12 JH |
1794 | # put least residue into $x if $x was negative, and thus make it positive |
1795 | $x->bmod($y) if $x->{sign} eq '-'; | |
07d34614 | 1796 | |
9b924220 RGS |
1797 | my $sign; |
1798 | ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value}); | |
1799 | return $x->bnan() if !defined $x->{value}; # in case no GCD found | |
1800 | return $x if !defined $sign; # already real result | |
1801 | $x->{sign} = $sign; # flip/flop see below | |
1802 | $x->bmod($y); # calc real result | |
1803 | $x; | |
d614cd8b JH |
1804 | } |
1805 | ||
07d34614 | 1806 | sub bmodpow |
d614cd8b JH |
1807 | { |
1808 | # takes a very large number to a very large exponent in a given very | |
80365507 | 1809 | # large modulus, quickly, thanks to binary exponentation. Supports |
d614cd8b JH |
1810 | # negative exponents. |
1811 | my ($self,$num,$exp,$mod,@r) = objectify(3,@_); | |
1812 | ||
1813 | return $num if $num->modify('bmodpow'); | |
1814 | ||
1815 | # check modulus for valid values | |
1816 | return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf | |
1817 | || $mod->is_zero()); | |
1818 | ||
1819 | # check exponent for valid values | |
1820 | if ($exp->{sign} =~ /\w/) | |
1821 | { | |
1822 | # i.e., if it's NaN, +inf, or -inf... | |
1823 | return $num->bnan(); | |
1824 | } | |
07d34614 | 1825 | |
1ddff52a | 1826 | $num->bmodinv ($mod) if ($exp->{sign} eq '-'); |
d614cd8b | 1827 | |
1ddff52a | 1828 | # check num for valid values (also NaN if there was no inverse but $exp < 0) |
07d34614 | 1829 | return $num->bnan() if $num->{sign} !~ /^[+-]$/; |
d614cd8b | 1830 | |
9b924220 RGS |
1831 | # $mod is positive, sign on $exp is ignored, result also positive |
1832 | $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value}); | |
1833 | $num; | |
d614cd8b JH |
1834 | } |
1835 | ||
1836 | ############################################################################### | |
1837 | ||
b3abae2a JH |
1838 | sub bfac |
1839 | { | |
1840 | # (BINT or num_str, BINT or num_str) return BINT | |
091c87b1 | 1841 | # compute factorial number from $x, modify $x in place |
b68b7ab1 | 1842 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
b3abae2a | 1843 | |
b68b7ab1 T |
1844 | return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf |
1845 | return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN | |
b3abae2a | 1846 | |
9b924220 RGS |
1847 | $x->{value} = $CALC->_fac($x->{value}); |
1848 | $x->round(@r); | |
b3abae2a JH |
1849 | } |
1850 | ||
58cde26e JH |
1851 | sub bpow |
1852 | { | |
1853 | # (BINT or num_str, BINT or num_str) return BINT | |
1854 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 | |
1855 | # modifies first argument | |
aef458a0 | 1856 | |
f9a08e12 JH |
1857 | # set up parameters |
1858 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1859 | # objectify is costly, so avoid it | |
1860 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1861 | { | |
1862 | ($self,$x,$y,@r) = objectify(2,@_); | |
1863 | } | |
58cde26e JH |
1864 | |
1865 | return $x if $x->modify('bpow'); | |
9393ace2 | 1866 | |
2d2b2744 T |
1867 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
1868 | ||
1869 | # inf handling | |
1870 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1871 | { | |
1872 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
1873 | { | |
1874 | # +-inf ** +-inf | |
1875 | return $x->bnan(); | |
1876 | } | |
1877 | # +-inf ** Y | |
1878 | if ($x->{sign} =~ /^[+-]inf/) | |
1879 | { | |
1880 | # +inf ** 0 => NaN | |
1881 | return $x->bnan() if $y->is_zero(); | |
1882 | # -inf ** -1 => 1/inf => 0 | |
1883 | return $x->bzero() if $y->is_one('-') && $x->is_negative(); | |
1884 | ||
1885 | # +inf ** Y => inf | |
1886 | return $x if $x->{sign} eq '+inf'; | |
1887 | ||
1888 | # -inf ** Y => -inf if Y is odd | |
1889 | return $x if $y->is_odd(); | |
1890 | return $x->babs(); | |
1891 | } | |
1892 | # X ** +-inf | |
1893 | ||
1894 | # 1 ** +inf => 1 | |
1895 | return $x if $x->is_one(); | |
1896 | ||
1897 | # 0 ** inf => 0 | |
1898 | return $x if $x->is_zero() && $y->{sign} =~ /^[+]/; | |
1899 | ||
1900 | # 0 ** -inf => inf | |
1901 | return $x->binf() if $x->is_zero(); | |
1902 | ||
1903 | # -1 ** -inf => NaN | |
1904 | return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/; | |
1905 | ||
1906 | # -X ** -inf => 0 | |
1907 | return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/; | |
1908 | ||
1909 | # -1 ** inf => NaN | |
1910 | return $x->bnan() if $x->{sign} eq '-'; | |
1911 | ||
1912 | # X ** inf => inf | |
1913 | return $x->binf() if $y->{sign} =~ /^[+]/; | |
1914 | # X ** -inf => 0 | |
1915 | return $x->bzero(); | |
1916 | } | |
1917 | ||
9393ace2 | 1918 | return $upgrade->bpow($upgrade->new($x),$y,@r) |
7b29e1e6 | 1919 | if defined $upgrade && (!$y->isa($self) || $y->{sign} eq '-'); |
9393ace2 | 1920 | |
61f5c3f5 | 1921 | $r[3] = $y; # no push! |
b282a552 T |
1922 | |
1923 | # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu | |
1924 | ||
9b924220 RGS |
1925 | my $new_sign = '+'; |
1926 | $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+'); | |
1927 | ||
1928 | # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf | |
1929 | return $x->binf() | |
1930 | if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value}); | |
574bacfe JH |
1931 | # 1 ** -y => 1 / (1 ** |y|) |
1932 | # so do test for negative $y after above's clause | |
9b924220 | 1933 | return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value}); |
027dc388 | 1934 | |
9b924220 RGS |
1935 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
1936 | $x->{sign} = $new_sign; | |
1937 | $x->{sign} = '+' if $CALC->_is_zero($y->{value}); | |
b68b7ab1 | 1938 | $x->round(@r); |
58cde26e JH |
1939 | } |
1940 | ||
1941 | sub blsft | |
1942 | { | |
1943 | # (BINT or num_str, BINT or num_str) return BINT | |
1944 | # compute x << y, base n, y >= 0 | |
f9a08e12 JH |
1945 | |
1946 | # set up parameters | |
1947 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); | |
1948 | # objectify is costly, so avoid it | |
1949 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1950 | { | |
1951 | ($self,$x,$y,$n,@r) = objectify(2,@_); | |
1952 | } | |
1953 | ||
58cde26e JH |
1954 | return $x if $x->modify('blsft'); |
1955 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
f9a08e12 | 1956 | return $x->round(@r) if $y->is_zero(); |
58cde26e | 1957 | |
574bacfe JH |
1958 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1959 | ||
9b924220 RGS |
1960 | $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n); |
1961 | $x->round(@r); | |
58cde26e JH |
1962 | } |
1963 | ||
1964 | sub brsft | |
1965 | { | |
1966 | # (BINT or num_str, BINT or num_str) return BINT | |
1967 | # compute x >> y, base n, y >= 0 | |
f9a08e12 JH |
1968 | |
1969 | # set up parameters | |
1970 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); | |
1971 | # objectify is costly, so avoid it | |
1972 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1973 | { | |
1974 | ($self,$x,$y,$n,@r) = objectify(2,@_); | |
1975 | } | |
58cde26e JH |
1976 | |
1977 | return $x if $x->modify('brsft'); | |
1978 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
f9a08e12 JH |
1979 | return $x->round(@r) if $y->is_zero(); |
1980 | return $x->bzero(@r) if $x->is_zero(); # 0 => 0 | |
58cde26e JH |
1981 | |
1982 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; | |
574bacfe | 1983 | |
b3abae2a JH |
1984 | # this only works for negative numbers when shifting in base 2 |
1985 | if (($x->{sign} eq '-') && ($n == 2)) | |
1986 | { | |
f9a08e12 | 1987 | return $x->round(@r) if $x->is_one('-'); # -1 => -1 |
b3abae2a JH |
1988 | if (!$y->is_one()) |
1989 | { | |
1990 | # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al | |
1991 | # but perhaps there is a better emulation for two's complement shift... | |
1992 | # if $y != 1, we must simulate it by doing: | |
1993 | # convert to bin, flip all bits, shift, and be done | |
1994 | $x->binc(); # -3 => -2 | |
1995 | my $bin = $x->as_bin(); | |
1996 | $bin =~ s/^-0b//; # strip '-0b' prefix | |
1997 | $bin =~ tr/10/01/; # flip bits | |
1998 | # now shift | |
a0ac753d | 1999 | if ($y >= CORE::length($bin)) |
b3abae2a JH |
2000 | { |
2001 | $bin = '0'; # shifting to far right creates -1 | |
2002 | # 0, because later increment makes | |
2003 | # that 1, attached '-' makes it '-1' | |
2004 | # because -1 >> x == -1 ! | |
2005 | } | |
2006 | else | |
2007 | { | |
2008 | $bin =~ s/.{$y}$//; # cut off at the right side | |
2009 | $bin = '1' . $bin; # extend left side by one dummy '1' | |
2010 | $bin =~ tr/10/01/; # flip bits back | |
2011 | } | |
2012 | my $res = $self->new('0b'.$bin); # add prefix and convert back | |
2013 | $res->binc(); # remember to increment | |
2014 | $x->{value} = $res->{value}; # take over value | |
f9a08e12 | 2015 | return $x->round(@r); # we are done now, magic, isn't? |
b3abae2a | 2016 | } |
b282a552 | 2017 | # x < 0, n == 2, y == 1 |
b3abae2a JH |
2018 | $x->bdec(); # n == 2, but $y == 1: this fixes it |
2019 | } | |
2020 | ||
9b924220 RGS |
2021 | $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n); |
2022 | $x->round(@r); | |
58cde26e JH |
2023 | } |
2024 | ||
2025 | sub band | |
2026 | { | |
2027 | #(BINT or num_str, BINT or num_str) return BINT | |
2028 | # compute x & y | |
f9a08e12 JH |
2029 | |
2030 | # set up parameters | |
2031 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
2032 | # objectify is costly, so avoid it | |
2033 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
2034 | { | |
2035 | ($self,$x,$y,@r) = objectify(2,@_); | |
2036 | } | |
58cde26e JH |
2037 | |
2038 | return $x if $x->modify('band'); | |
2039 | ||
f9a08e12 | 2040 | $r[3] = $y; # no push! |
b3abae2a | 2041 | |
58cde26e | 2042 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
0716bf9b | 2043 | |
b282a552 T |
2044 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
2045 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe | 2046 | |
9b924220 | 2047 | if ($sx == 1 && $sy == 1) |
0716bf9b | 2048 | { |
574bacfe | 2049 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
f9a08e12 | 2050 | return $x->round(@r); |
0716bf9b | 2051 | } |
091c87b1 T |
2052 | |
2053 | if ($CAN{signed_and}) | |
2054 | { | |
2055 | $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy); | |
2056 | return $x->round(@r); | |
2057 | } | |
b282a552 T |
2058 | |
2059 | require $EMU_LIB; | |
2060 | __emu_band($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
2061 | } |
2062 | ||
2063 | sub bior | |
2064 | { | |
2065 | #(BINT or num_str, BINT or num_str) return BINT | |
2066 | # compute x | y | |
f9a08e12 JH |
2067 | |
2068 | # set up parameters | |
2069 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
2070 | # objectify is costly, so avoid it | |
2071 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
2072 | { | |
2073 | ($self,$x,$y,@r) = objectify(2,@_); | |
2074 | } | |
58cde26e JH |
2075 | |
2076 | return $x if $x->modify('bior'); | |
f9a08e12 | 2077 | $r[3] = $y; # no push! |
58cde26e JH |
2078 | |
2079 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
574bacfe | 2080 | |
b282a552 T |
2081 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
2082 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe | 2083 | |
091c87b1 T |
2084 | # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior() |
2085 | ||
574bacfe | 2086 | # don't use lib for negative values |
9b924220 | 2087 | if ($sx == 1 && $sy == 1) |
0716bf9b | 2088 | { |
574bacfe | 2089 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
f9a08e12 | 2090 | return $x->round(@r); |
0716bf9b JH |
2091 | } |
2092 | ||
b282a552 | 2093 | # if lib can do negative values, let it handle this |
091c87b1 T |
2094 | if ($CAN{signed_or}) |
2095 | { | |
2096 | $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy); | |
2097 | return $x->round(@r); | |
2098 | } | |
2099 | ||
b282a552 T |
2100 | require $EMU_LIB; |
2101 | __emu_bior($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
2102 | } |
2103 | ||
2104 | sub bxor | |
2105 | { | |
2106 | #(BINT or num_str, BINT or num_str) return BINT | |
2107 | # compute x ^ y | |
f9a08e12 JH |
2108 | |
2109 | # set up parameters | |
2110 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
2111 | # objectify is costly, so avoid it | |
2112 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
2113 | { | |
2114 | ($self,$x,$y,@r) = objectify(2,@_); | |
2115 | } | |
58cde26e JH |
2116 | |
2117 | return $x if $x->modify('bxor'); | |
f9a08e12 | 2118 | $r[3] = $y; # no push! |
58cde26e | 2119 | |
0716bf9b | 2120 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
0716bf9b | 2121 | |
b282a552 T |
2122 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
2123 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe JH |
2124 | |
2125 | # don't use lib for negative values | |
9b924220 | 2126 | if ($sx == 1 && $sy == 1) |
0716bf9b | 2127 | { |
574bacfe | 2128 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
f9a08e12 | 2129 | return $x->round(@r); |
0716bf9b | 2130 | } |
091c87b1 | 2131 | |
b282a552 | 2132 | # if lib can do negative values, let it handle this |
091c87b1 T |
2133 | if ($CAN{signed_xor}) |
2134 | { | |
2135 | $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy); | |
2136 | return $x->round(@r); | |
2137 | } | |
0716bf9b | 2138 | |
b282a552 T |
2139 | require $EMU_LIB; |
2140 | __emu_bxor($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
2141 | } |
2142 | ||
2143 | sub length | |
2144 | { | |
b282a552 | 2145 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e | 2146 | |
0716bf9b | 2147 | my $e = $CALC->_len($x->{value}); |
091c87b1 | 2148 | wantarray ? ($e,0) : $e; |
58cde26e JH |
2149 | } |
2150 | ||
2151 | sub digit | |
2152 | { | |
0716bf9b | 2153 | # return the nth decimal digit, negative values count backward, 0 is right |
ef9466ea | 2154 | my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
58cde26e | 2155 | |
ef9466ea | 2156 | $n = $n->numify() if ref($n); |
f9a08e12 | 2157 | $CALC->_digit($x->{value},$n||0); |
58cde26e JH |
2158 | } |
2159 | ||
2160 | sub _trailing_zeros | |
2161 | { | |
b282a552 | 2162 | # return the amount of trailing zeros in $x (as scalar) |
58cde26e JH |
2163 | my $x = shift; |
2164 | $x = $class->new($x) unless ref $x; | |
2165 | ||
9b924220 | 2166 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc |
0716bf9b | 2167 | |
9b924220 | 2168 | $CALC->_zeros($x->{value}); # must handle odd values, 0 etc |
58cde26e JH |
2169 | } |
2170 | ||
2171 | sub bsqrt | |
2172 | { | |
990fb837 | 2173 | # calculate square root of $x |
b68b7ab1 | 2174 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
58cde26e | 2175 | |
b3abae2a JH |
2176 | return $x if $x->modify('bsqrt'); |
2177 | ||
990fb837 RGS |
2178 | return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN |
2179 | return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf | |
b3abae2a | 2180 | |
f9a08e12 | 2181 | return $upgrade->bsqrt($x,@r) if defined $upgrade; |
58cde26e | 2182 | |
9b924220 RGS |
2183 | $x->{value} = $CALC->_sqrt($x->{value}); |
2184 | $x->round(@r); | |
58cde26e JH |
2185 | } |
2186 | ||
990fb837 RGS |
2187 | sub broot |
2188 | { | |
2189 | # calculate $y'th root of $x | |
c38b2de2 | 2190 | |
990fb837 RGS |
2191 | # set up parameters |
2192 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
c38b2de2 JH |
2193 | |
2194 | $y = $self->new(2) unless defined $y; | |
2195 | ||
990fb837 | 2196 | # objectify is costly, so avoid it |
c38b2de2 | 2197 | if ((!ref($x)) || (ref($x) ne ref($y))) |
990fb837 | 2198 | { |
3a427a11 | 2199 | ($self,$x,$y,@r) = objectify(2,$self || $class,@_); |
990fb837 RGS |
2200 | } |
2201 | ||
2202 | return $x if $x->modify('broot'); | |
2203 | ||
2204 | # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0 | |
2205 | return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() || | |
2206 | $y->{sign} !~ /^\+$/; | |
2207 | ||
2208 | return $x->round(@r) | |
2209 | if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one(); | |
2210 | ||
c38b2de2 | 2211 | return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade; |
990fb837 | 2212 | |
9b924220 RGS |
2213 | $x->{value} = $CALC->_root($x->{value},$y->{value}); |
2214 | $x->round(@r); | |
990fb837 RGS |
2215 | } |
2216 | ||
58cde26e JH |
2217 | sub exponent |
2218 | { | |
2219 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) | |
ee15d750 | 2220 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 2221 | |
ee15d750 JH |
2222 | if ($x->{sign} !~ /^[+-]$/) |
2223 | { | |
b282a552 T |
2224 | my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf |
2225 | return $self->new($s); | |
ee15d750 | 2226 | } |
b282a552 T |
2227 | return $self->bone() if $x->is_zero(); |
2228 | ||
7d193e39 T |
2229 | # 12300 => 2 trailing zeros => exponent is 2 |
2230 | $self->new( $CALC->_zeros($x->{value}) ); | |
58cde26e JH |
2231 | } |
2232 | ||
2233 | sub mantissa | |
2234 | { | |
ee15d750 JH |
2235 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
2236 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 2237 | |
ee15d750 JH |
2238 | if ($x->{sign} !~ /^[+-]$/) |
2239 | { | |
b282a552 T |
2240 | # for NaN, +inf, -inf: keep the sign |
2241 | return $self->new($x->{sign}); | |
ee15d750 | 2242 | } |
b282a552 | 2243 | my $m = $x->copy(); delete $m->{_p}; delete $m->{_a}; |
7d193e39 | 2244 | |
b282a552 | 2245 | # that's a bit inefficient: |
7d193e39 | 2246 | my $zeros = $CALC->_zeros($m->{value}); |
56b9c951 | 2247 | $m->brsft($zeros,10) if $zeros != 0; |
56b9c951 | 2248 | $m; |
58cde26e JH |
2249 | } |
2250 | ||
2251 | sub parts | |
2252 | { | |
ee15d750 | 2253 | # return a copy of both the exponent and the mantissa |
091c87b1 | 2254 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e | 2255 | |
091c87b1 | 2256 | ($x->mantissa(),$x->exponent()); |
58cde26e JH |
2257 | } |
2258 | ||
2259 | ############################################################################## | |
2260 | # rounding functions | |
2261 | ||
2262 | sub bfround | |
2263 | { | |
2264 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' | |
ee15d750 | 2265 | # $n == 0 || $n == 1 => round to integer |
ef9466ea | 2266 | my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x; |
b282a552 | 2267 | |
b68b7ab1 | 2268 | my ($scale,$mode) = $x->_scale_p(@_); |
b282a552 T |
2269 | |
2270 | return $x if !defined $scale || $x->modify('bfround'); # no-op | |
58cde26e JH |
2271 | |
2272 | # no-op for BigInts if $n <= 0 | |
b282a552 | 2273 | $x->bround( $x->length()-$scale, $mode) if $scale > 0; |
58cde26e | 2274 | |
ef9466ea T |
2275 | delete $x->{_a}; # delete to save memory |
2276 | $x->{_p} = $scale; # store new _p | |
ee15d750 | 2277 | $x; |
58cde26e JH |
2278 | } |
2279 | ||
2280 | sub _scan_for_nonzero | |
2281 | { | |
ae161977 RGS |
2282 | # internal, used by bround() to scan for non-zeros after a '5' |
2283 | my ($x,$pad,$xs,$len) = @_; | |
58cde26e | 2284 | |
ae161977 | 2285 | return 0 if $len == 1; # "5" is trailed by invisible zeros |
58cde26e JH |
2286 | my $follow = $pad - 1; |
2287 | return 0 if $follow > $len || $follow < 1; | |
0716bf9b | 2288 | |
ae161977 RGS |
2289 | # use the string form to check whether only '0's follow or not |
2290 | substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0; | |
58cde26e JH |
2291 | } |
2292 | ||
2293 | sub fround | |
2294 | { | |
091c87b1 T |
2295 | # Exists to make life easier for switch between MBF and MBI (should we |
2296 | # autoload fxxx() like MBF does for bxxx()?) | |
b68b7ab1 | 2297 | my $x = shift; $x = $class->new($x) unless ref $x; |
091c87b1 | 2298 | $x->bround(@_); |
58cde26e JH |
2299 | } |
2300 | ||
2301 | sub bround | |
2302 | { | |
2303 | # accuracy: +$n preserve $n digits from left, | |
2304 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) | |
2305 | # no-op for $n == 0 | |
2306 | # and overwrite the rest with 0's, return normalized number | |
2307 | # do not return $x->bnorm(), but $x | |
61f5c3f5 | 2308 | |
58cde26e | 2309 | my $x = shift; $x = $class->new($x) unless ref $x; |
b68b7ab1 T |
2310 | my ($scale,$mode) = $x->_scale_a(@_); |
2311 | return $x if !defined $scale || $x->modify('bround'); # no-op | |
58cde26e | 2312 | |
61f5c3f5 T |
2313 | if ($x->is_zero() || $scale == 0) |
2314 | { | |
2315 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 | |
2316 | return $x; | |
2317 | } | |
2318 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN | |
58cde26e JH |
2319 | |
2320 | # we have fewer digits than we want to scale to | |
2321 | my $len = $x->length(); | |
56d9de68 T |
2322 | # convert $scale to a scalar in case it is an object (put's a limit on the |
2323 | # number length, but this would already limited by memory constraints), makes | |
2324 | # it faster | |
2325 | $scale = $scale->numify() if ref ($scale); | |
2326 | ||
ee15d750 JH |
2327 | # scale < 0, but > -len (not >=!) |
2328 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) | |
2329 | { | |
61f5c3f5 | 2330 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
ee15d750 JH |
2331 | return $x; |
2332 | } | |
58cde26e JH |
2333 | |
2334 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 | |
2335 | my ($pad,$digit_round,$digit_after); | |
2336 | $pad = $len - $scale; | |
ee15d750 JH |
2337 | $pad = abs($scale-1) if $scale < 0; |
2338 | ||
ae161977 RGS |
2339 | # do not use digit(), it is very costly for binary => decimal |
2340 | # getting the entire string is also costly, but we need to do it only once | |
0716bf9b JH |
2341 | my $xs = $CALC->_str($x->{value}); |
2342 | my $pl = -$pad-1; | |
56d9de68 | 2343 | |
0716bf9b JH |
2344 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
2345 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 | |
9b924220 | 2346 | $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len; |
0716bf9b | 2347 | $pl++; $pl ++ if $pad >= $len; |
9b924220 | 2348 | $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0; |
ee15d750 | 2349 | |
58cde26e JH |
2350 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look |
2351 | # closer at the remaining digits of the original $x, remember decision | |
2352 | my $round_up = 1; # default round up | |
2353 | $round_up -- if | |
2354 | ($mode eq 'trunc') || # trunc by round down | |
2355 | ($digit_after =~ /[01234]/) || # round down anyway, | |
2356 | # 6789 => round up | |
2357 | ($digit_after eq '5') && # not 5000...0000 | |
ae161977 | 2358 | ($x->_scan_for_nonzero($pad,$xs,$len) == 0) && |
58cde26e JH |
2359 | ( |
2360 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || | |
2361 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || | |
2362 | ($mode eq '+inf') && ($x->{sign} eq '-') || | |
2363 | ($mode eq '-inf') && ($x->{sign} eq '+') || | |
2364 | ($mode eq 'zero') # round down if zero, sign adjusted below | |
2365 | ); | |
61f5c3f5 T |
2366 | my $put_back = 0; # not yet modified |
2367 | ||
61f5c3f5 T |
2368 | if (($pad > 0) && ($pad <= $len)) |
2369 | { | |
ae161977 RGS |
2370 | substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...' |
2371 | $put_back = 1; # need to put back | |
58cde26e | 2372 | } |
61f5c3f5 T |
2373 | elsif ($pad > $len) |
2374 | { | |
2375 | $x->bzero(); # round to '0' | |
2376 | } | |
2377 | ||
58cde26e JH |
2378 | if ($round_up) # what gave test above? |
2379 | { | |
ae161977 | 2380 | $put_back = 1; # need to put back |
9b924220 | 2381 | $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0 |
61f5c3f5 T |
2382 | |
2383 | # we modify directly the string variant instead of creating a number and | |
f9a08e12 | 2384 | # adding it, since that is faster (we already have the string) |
61f5c3f5 T |
2385 | my $c = 0; $pad ++; # for $pad == $len case |
2386 | while ($pad <= $len) | |
2387 | { | |
9b924220 RGS |
2388 | $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10'; |
2389 | substr($xs,-$pad,1) = $c; $pad++; | |
61f5c3f5 T |
2390 | last if $c != 0; # no overflow => early out |
2391 | } | |
9b924220 | 2392 | $xs = '1'.$xs if $c == 0; |
61f5c3f5 | 2393 | |
58cde26e | 2394 | } |
ae161977 | 2395 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed |
ee15d750 JH |
2396 | |
2397 | $x->{_a} = $scale if $scale >= 0; | |
2398 | if ($scale < 0) | |
2399 | { | |
2400 | $x->{_a} = $len+$scale; | |
2401 | $x->{_a} = 0 if $scale < -$len; | |
2402 | } | |
58cde26e JH |
2403 | $x; |
2404 | } | |
2405 | ||
2406 | sub bfloor | |
2407 | { | |
091c87b1 T |
2408 | # return integer less or equal then number; no-op since it's already integer |
2409 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
58cde26e | 2410 | |
f9a08e12 | 2411 | $x->round(@r); |
58cde26e JH |
2412 | } |
2413 | ||
2414 | sub bceil | |
2415 | { | |
091c87b1 T |
2416 | # return integer greater or equal then number; no-op since it's already int |
2417 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
58cde26e | 2418 | |
f9a08e12 | 2419 | $x->round(@r); |
58cde26e JH |
2420 | } |
2421 | ||
091c87b1 T |
2422 | sub as_number |
2423 | { | |
2424 | # An object might be asked to return itself as bigint on certain overloaded | |
7b29e1e6 | 2425 | # operations. This does exactly this, so that sub classes can simple inherit |
091c87b1 T |
2426 | # it or override with their own integer conversion routine. |
2427 | $_[0]->copy(); | |
2428 | } | |
58cde26e | 2429 | |
091c87b1 | 2430 | sub as_hex |
58cde26e | 2431 | { |
091c87b1 T |
2432 | # return as hex string, with prefixed 0x |
2433 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2434 | ||
2435 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2436 | ||
b282a552 | 2437 | my $s = ''; |
091c87b1 | 2438 | $s = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 2439 | $s . $CALC->_as_hex($x->{value}); |
58cde26e JH |
2440 | } |
2441 | ||
091c87b1 | 2442 | sub as_bin |
58cde26e | 2443 | { |
091c87b1 T |
2444 | # return as binary string, with prefixed 0b |
2445 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2446 | ||
2447 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2448 | ||
b282a552 | 2449 | my $s = ''; $s = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 2450 | return $s . $CALC->_as_bin($x->{value}); |
58cde26e JH |
2451 | } |
2452 | ||
7b29e1e6 T |
2453 | sub as_oct |
2454 | { | |
2455 | # return as octal string, with prefixed 0 | |
2456 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2457 | ||
2458 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2459 | ||
2460 | my $s = ''; $s = $x->{sign} if $x->{sign} eq '-'; | |
2461 | return $s . $CALC->_as_oct($x->{value}); | |
2462 | } | |
2463 | ||
091c87b1 T |
2464 | ############################################################################## |
2465 | # private stuff (internal use only) | |
2466 | ||
58cde26e JH |
2467 | sub objectify |
2468 | { | |
2469 | # check for strings, if yes, return objects instead | |
2470 | ||
2471 | # the first argument is number of args objectify() should look at it will | |
2472 | # return $count+1 elements, the first will be a classname. This is because | |
2473 | # overloaded '""' calls bstr($object,undef,undef) and this would result in | |
3c4b39be | 2474 | # useless objects being created and thrown away. So we cannot simple loop |
58cde26e JH |
2475 | # over @_. If the given count is 0, all arguments will be used. |
2476 | ||
2477 | # If the second arg is a ref, use it as class. | |
2478 | # If not, try to use it as classname, unless undef, then use $class | |
2479 | # (aka Math::BigInt). The latter shouldn't happen,though. | |
2480 | ||
2481 | # caller: gives us: | |
2482 | # $x->badd(1); => ref x, scalar y | |
2483 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y | |
2484 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y | |
2485 | # Math::BigInt::badd(1,2); => scalar x, scalar y | |
2486 | # In the last case we check number of arguments to turn it silently into | |
574bacfe | 2487 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e JH |
2488 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
2489 | # currently it tries 'Math::BigInt' + 1, which will not work. | |
ee15d750 JH |
2490 | |
2491 | # some shortcut for the common cases | |
ee15d750 JH |
2492 | # $x->unary_op(); |
2493 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); | |
ee15d750 | 2494 | |
58cde26e JH |
2495 | my $count = abs(shift || 0); |
2496 | ||
9393ace2 | 2497 | my (@a,$k,$d); # resulting array, temp, and downgrade |
58cde26e JH |
2498 | if (ref $_[0]) |
2499 | { | |
2500 | # okay, got object as first | |
2501 | $a[0] = ref $_[0]; | |
2502 | } | |
2503 | else | |
2504 | { | |
2505 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) | |
2506 | $a[0] = $class; | |
58cde26e JH |
2507 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
2508 | } | |
8f675a64 | 2509 | |
9393ace2 JH |
2510 | no strict 'refs'; |
2511 | # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats | |
2512 | if (defined ${"$a[0]::downgrade"}) | |
2513 | { | |
2514 | $d = ${"$a[0]::downgrade"}; | |
2515 | ${"$a[0]::downgrade"} = undef; | |
2516 | } | |
2517 | ||
d614cd8b | 2518 | my $up = ${"$a[0]::upgrade"}; |
7d193e39 | 2519 | # print STDERR "# Now in objectify, my class is today $a[0], count = $count\n"; |
58cde26e JH |
2520 | if ($count == 0) |
2521 | { | |
2522 | while (@_) | |
2523 | { | |
2524 | $k = shift; | |
2525 | if (!ref($k)) | |
2526 | { | |
2527 | $k = $a[0]->new($k); | |
2528 | } | |
d614cd8b | 2529 | elsif (!defined $up && ref($k) ne $a[0]) |
58cde26e JH |
2530 | { |
2531 | # foreign object, try to convert to integer | |
2532 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
e16b8f49 | 2533 | } |
58cde26e JH |
2534 | push @a,$k; |
2535 | } | |
2536 | } | |
2537 | else | |
2538 | { | |
2539 | while ($count > 0) | |
2540 | { | |
58cde26e | 2541 | $count--; |
7d193e39 | 2542 | $k = shift; |
58cde26e JH |
2543 | if (!ref($k)) |
2544 | { | |
2545 | $k = $a[0]->new($k); | |
2546 | } | |
d614cd8b | 2547 | elsif (!defined $up && ref($k) ne $a[0]) |
58cde26e JH |
2548 | { |
2549 | # foreign object, try to convert to integer | |
a0ac753d | 2550 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 | 2551 | } |
58cde26e JH |
2552 | push @a,$k; |
2553 | } | |
2554 | push @a,@_; # return other params, too | |
2555 | } | |
990fb837 RGS |
2556 | if (! wantarray) |
2557 | { | |
2558 | require Carp; Carp::croak ("$class objectify needs list context"); | |
2559 | } | |
9393ace2 | 2560 | ${"$a[0]::downgrade"} = $d; |
58cde26e JH |
2561 | @a; |
2562 | } | |
2563 | ||
b68b7ab1 T |
2564 | sub _register_callback |
2565 | { | |
2566 | my ($class,$callback) = @_; | |
2567 | ||
2568 | if (ref($callback) ne 'CODE') | |
2569 | { | |
2570 | require Carp; | |
2571 | Carp::croak ("$callback is not a coderef"); | |
2572 | } | |
2573 | $CALLBACKS{$class} = $callback; | |
2574 | } | |
2575 | ||
58cde26e JH |
2576 | sub import |
2577 | { | |
2578 | my $self = shift; | |
61f5c3f5 | 2579 | |
091c87b1 | 2580 | $IMPORT++; # remember we did import() |
8f675a64 | 2581 | my @a; my $l = scalar @_; |
7b29e1e6 | 2582 | my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die |
8f675a64 | 2583 | for ( my $i = 0; $i < $l ; $i++ ) |
58cde26e | 2584 | { |
0716bf9b | 2585 | if ($_[$i] eq ':constant') |
58cde26e | 2586 | { |
0716bf9b | 2587 | # this causes overlord er load to step in |
091c87b1 T |
2588 | overload::constant |
2589 | integer => sub { $self->new(shift) }, | |
2590 | binary => sub { $self->new(shift) }; | |
0716bf9b | 2591 | } |
b3abae2a JH |
2592 | elsif ($_[$i] eq 'upgrade') |
2593 | { | |
2594 | # this causes upgrading | |
2595 | $upgrade = $_[$i+1]; # or undef to disable | |
8f675a64 | 2596 | $i++; |
b3abae2a | 2597 | } |
7b29e1e6 | 2598 | elsif ($_[$i] =~ /^(lib|try|only)\z/) |
0716bf9b JH |
2599 | { |
2600 | # this causes a different low lib to take care... | |
61f5c3f5 | 2601 | $CALC = $_[$i+1] || ''; |
7b29e1e6 T |
2602 | # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback) |
2603 | $warn_or_die = 1 if $_[$i] eq 'lib'; | |
2604 | $warn_or_die = 2 if $_[$i] eq 'only'; | |
8f675a64 JH |
2605 | $i++; |
2606 | } | |
2607 | else | |
2608 | { | |
2609 | push @a, $_[$i]; | |
58cde26e JH |
2610 | } |
2611 | } | |
2612 | # any non :constant stuff is handled by our parent, Exporter | |
b68b7ab1 T |
2613 | if (@a > 0) |
2614 | { | |
2615 | require Exporter; | |
2616 | ||
2617 | $self->SUPER::import(@a); # need it for subclasses | |
2618 | $self->export_to_level(1,$self,@a); # need it for MBF | |
2619 | } | |
58cde26e | 2620 | |
574bacfe JH |
2621 | # try to load core math lib |
2622 | my @c = split /\s*,\s*/,$CALC; | |
b68b7ab1 T |
2623 | foreach (@c) |
2624 | { | |
2625 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters | |
2626 | } | |
7b29e1e6 T |
2627 | push @c, \'FastCalc', \'Calc' # if all fail, try these |
2628 | if $warn_or_die < 2; # but not for "only" | |
61f5c3f5 | 2629 | $CALC = ''; # signal error |
7b29e1e6 | 2630 | foreach my $l (@c) |
574bacfe | 2631 | { |
7b29e1e6 T |
2632 | # fallback libraries are "marked" as \'string', extract string if nec. |
2633 | my $lib = $l; $lib = $$l if ref($l); | |
2634 | ||
07d34614 | 2635 | next if ($lib || '') eq ''; |
574bacfe JH |
2636 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
2637 | $lib =~ s/\.pm$//; | |
61f5c3f5 | 2638 | if ($] < 5.006) |
574bacfe | 2639 | { |
b68b7ab1 T |
2640 | # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is |
2641 | # used in the same script, or eval("") inside import(). | |
07d34614 T |
2642 | my @parts = split /::/, $lib; # Math::BigInt => Math BigInt |
2643 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm | |
2644 | require File::Spec; | |
2645 | $file = File::Spec->catfile (@parts, $file); | |
2646 | eval { require "$file"; $lib->import( @c ); } | |
574bacfe JH |
2647 | } |
2648 | else | |
2649 | { | |
61f5c3f5 | 2650 | eval "use $lib qw/@c/;"; |
574bacfe | 2651 | } |
9b924220 RGS |
2652 | if ($@ eq '') |
2653 | { | |
2654 | my $ok = 1; | |
2655 | # loaded it ok, see if the api_version() is high enough | |
2656 | if ($lib->can('api_version') && $lib->api_version() >= 1.0) | |
2657 | { | |
2658 | $ok = 0; | |
2659 | # api_version matches, check if it really provides anything we need | |
2660 | for my $method (qw/ | |
2661 | one two ten | |
2662 | str num | |
2663 | add mul div sub dec inc | |
2664 | acmp len digit is_one is_zero is_even is_odd | |
2665 | is_two is_ten | |
7b29e1e6 T |
2666 | zeros new copy check |
2667 | from_hex from_oct from_bin as_hex as_bin as_oct | |
9b924220 RGS |
2668 | rsft lsft xor and or |
2669 | mod sqrt root fac pow modinv modpow log_int gcd | |
2670 | /) | |
2671 | { | |
2672 | if (!$lib->can("_$method")) | |
2673 | { | |
2674 | if (($WARN{$lib}||0) < 2) | |
2675 | { | |
2676 | require Carp; | |
2677 | Carp::carp ("$lib is missing method '_$method'"); | |
2678 | $WARN{$lib} = 1; # still warn about the lib | |
2679 | } | |
2680 | $ok++; last; | |
2681 | } | |
2682 | } | |
2683 | } | |
2684 | if ($ok == 0) | |
2685 | { | |
2686 | $CALC = $lib; | |
7b29e1e6 T |
2687 | if ($warn_or_die > 0 && ref($l)) |
2688 | { | |
2689 | require Carp; | |
2690 | my $msg = "Math::BigInt: couldn't load specified math lib(s), fallback to $lib"; | |
2691 | Carp::carp ($msg) if $warn_or_die == 1; | |
2692 | Carp::croak ($msg) if $warn_or_die == 2; | |
2693 | } | |
9b924220 RGS |
2694 | last; # found a usable one, break |
2695 | } | |
2696 | else | |
2697 | { | |
2698 | if (($WARN{$lib}||0) < 2) | |
2699 | { | |
a87115f0 | 2700 | my $ver = eval "\$$lib\::VERSION" || 'unknown'; |
9b924220 RGS |
2701 | require Carp; |
2702 | Carp::carp ("Cannot load outdated $lib v$ver, please upgrade"); | |
2703 | $WARN{$lib} = 2; # never warn again | |
2704 | } | |
2705 | } | |
2706 | } | |
574bacfe | 2707 | } |
990fb837 RGS |
2708 | if ($CALC eq '') |
2709 | { | |
2710 | require Carp; | |
7b29e1e6 T |
2711 | if ($warn_or_die == 2) |
2712 | { | |
2713 | Carp::croak ("Couldn't load specified math lib(s) and fallback disallowed"); | |
2714 | } | |
2715 | else | |
2716 | { | |
2717 | Carp::croak ("Couldn't load any math lib(s), not even fallback to Calc.pm"); | |
2718 | } | |
091c87b1 | 2719 | } |
091c87b1 | 2720 | |
b68b7ab1 T |
2721 | # notify callbacks |
2722 | foreach my $class (keys %CALLBACKS) | |
2723 | { | |
2724 | &{$CALLBACKS{$class}}($CALC); | |
2725 | } | |
2726 | ||
2727 | # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib | |
2728 | # functions | |
091c87b1 T |
2729 | |
2730 | %CAN = (); | |
b68b7ab1 | 2731 | for my $method (qw/ signed_and signed_or signed_xor /) |
091c87b1 T |
2732 | { |
2733 | $CAN{$method} = $CALC->can("_$method") ? 1 : 0; | |
990fb837 | 2734 | } |
b68b7ab1 T |
2735 | |
2736 | # import done | |
58cde26e JH |
2737 | } |
2738 | ||
7b29e1e6 T |
2739 | sub from_hex |
2740 | { | |
2741 | # create a bigint from a hexadecimal string | |
2742 | my ($self, $hs) = @_; | |
2743 | ||
7aa7e0ae | 2744 | my $rc = __from_hex($hs); |
7b29e1e6 T |
2745 | |
2746 | return $self->bnan() unless defined $rc; | |
2747 | ||
2748 | $rc; | |
2749 | } | |
2750 | ||
2751 | sub from_bin | |
2752 | { | |
2753 | # create a bigint from a hexadecimal string | |
2754 | my ($self, $bs) = @_; | |
2755 | ||
7aa7e0ae | 2756 | my $rc = __from_bin($bs); |
7b29e1e6 T |
2757 | |
2758 | return $self->bnan() unless defined $rc; | |
2759 | ||
2760 | $rc; | |
2761 | } | |
2762 | ||
2763 | sub from_oct | |
2764 | { | |
2765 | # create a bigint from a hexadecimal string | |
2766 | my ($self, $os) = @_; | |
2767 | ||
2768 | my $x = $self->bzero(); | |
2769 | ||
2770 | # strip underscores | |
7aa7e0ae T |
2771 | $os =~ s/([0-7])_([0-7])/$1$2/g; |
2772 | $os =~ s/([0-7])_([0-7])/$1$2/g; | |
7b29e1e6 | 2773 | |
7aa7e0ae | 2774 | return $x->bnan() if $os !~ /^[\-\+]?0[0-7]+\z/; |
7b29e1e6 T |
2775 | |
2776 | my $sign = '+'; $sign = '-' if $os =~ /^-/; | |
2777 | ||
2778 | $os =~ s/^[+-]//; # strip sign | |
2779 | $x->{value} = $CALC->_from_oct($os); | |
2780 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' | |
2781 | $x; | |
2782 | } | |
2783 | ||
574bacfe | 2784 | sub __from_hex |
58cde26e | 2785 | { |
b68b7ab1 | 2786 | # internal |
58cde26e JH |
2787 | # convert a (ref to) big hex string to BigInt, return undef for error |
2788 | my $hs = shift; | |
2789 | ||
2790 | my $x = Math::BigInt->bzero(); | |
394e6ffb JH |
2791 | |
2792 | # strip underscores | |
9b924220 RGS |
2793 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
2794 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
394e6ffb | 2795 | |
9b924220 | 2796 | return $x->bnan() if $hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
58cde26e | 2797 | |
9b924220 | 2798 | my $sign = '+'; $sign = '-' if $hs =~ /^-/; |
58cde26e | 2799 | |
9b924220 RGS |
2800 | $hs =~ s/^[+-]//; # strip sign |
2801 | $x->{value} = $CALC->_from_hex($hs); | |
13a12e00 JH |
2802 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2803 | $x; | |
58cde26e JH |
2804 | } |
2805 | ||
574bacfe | 2806 | sub __from_bin |
58cde26e | 2807 | { |
b68b7ab1 | 2808 | # internal |
58cde26e JH |
2809 | # convert a (ref to) big binary string to BigInt, return undef for error |
2810 | my $bs = shift; | |
2811 | ||
2812 | my $x = Math::BigInt->bzero(); | |
7b29e1e6 | 2813 | |
394e6ffb | 2814 | # strip underscores |
9b924220 RGS |
2815 | $bs =~ s/([01])_([01])/$1$2/g; |
2816 | $bs =~ s/([01])_([01])/$1$2/g; | |
2817 | return $x->bnan() if $bs !~ /^[+-]?0b[01]+$/; | |
58cde26e | 2818 | |
9b924220 RGS |
2819 | my $sign = '+'; $sign = '-' if $bs =~ /^\-/; |
2820 | $bs =~ s/^[+-]//; # strip sign | |
2821 | ||
2822 | $x->{value} = $CALC->_from_bin($bs); | |
13a12e00 JH |
2823 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2824 | $x; | |
58cde26e JH |
2825 | } |
2826 | ||
2827 | sub _split | |
2828 | { | |
b68b7ab1 T |
2829 | # input: num_str; output: undef for invalid or |
2830 | # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,\$exp_sign,\$exp_value) | |
2831 | # Internal, take apart a string and return the pieces. | |
2832 | # Strip leading/trailing whitespace, leading zeros, underscore and reject | |
2833 | # invalid input. | |
58cde26e JH |
2834 | my $x = shift; |
2835 | ||
574bacfe | 2836 | # strip white space at front, also extranous leading zeros |
7b29e1e6 T |
2837 | $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' |
2838 | $x =~ s/^\s+//; # but this will | |
2839 | $x =~ s/\s+$//g; # strip white space at end | |
58cde26e | 2840 | |
574bacfe | 2841 | # shortcut, if nothing to split, return early |
7b29e1e6 | 2842 | if ($x =~ /^[+-]?[0-9]+\z/) |
574bacfe | 2843 | { |
9b924220 RGS |
2844 | $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; |
2845 | return (\$sign, \$x, \'', \'', \0); | |
574bacfe | 2846 | } |
58cde26e | 2847 | |
574bacfe | 2848 | # invalid starting char? |
9b924220 | 2849 | return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; |
58cde26e | 2850 | |
7b29e1e6 T |
2851 | return __from_hex($x) if $x =~ /^[\-\+]?0x/; # hex string |
2852 | return __from_bin($x) if $x =~ /^[\-\+]?0b/; # binary string | |
394e6ffb JH |
2853 | |
2854 | # strip underscores between digits | |
7b29e1e6 T |
2855 | $x =~ s/([0-9])_([0-9])/$1$2/g; |
2856 | $x =~ s/([0-9])_([0-9])/$1$2/g; # do twice for 1_2_3 | |
574bacfe | 2857 | |
58cde26e JH |
2858 | # some possible inputs: |
2859 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 | |
aef458a0 | 2860 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999 |
58cde26e | 2861 | |
9b924220 | 2862 | my ($m,$e,$last) = split /[Ee]/,$x; |
56d9de68 | 2863 | return if defined $last; # last defined => 1e2E3 or others |
58cde26e | 2864 | $e = '0' if !defined $e || $e eq ""; |
56d9de68 | 2865 | |
58cde26e JH |
2866 | # sign,value for exponent,mantint,mantfrac |
2867 | my ($es,$ev,$mis,$miv,$mfv); | |
2868 | # valid exponent? | |
7b29e1e6 | 2869 | if ($e =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros |
58cde26e JH |
2870 | { |
2871 | $es = $1; $ev = $2; | |
58cde26e JH |
2872 | # valid mantissa? |
2873 | return if $m eq '.' || $m eq ''; | |
56d9de68 | 2874 | my ($mi,$mf,$lastf) = split /\./,$m; |
8df1e0a2 | 2875 | return if defined $lastf; # lastf defined => 1.2.3 or others |
58cde26e JH |
2876 | $mi = '0' if !defined $mi; |
2877 | $mi .= '0' if $mi =~ /^[\-\+]?$/; | |
2878 | $mf = '0' if !defined $mf || $mf eq ''; | |
7b29e1e6 | 2879 | if ($mi =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros |
58cde26e JH |
2880 | { |
2881 | $mis = $1||'+'; $miv = $2; | |
7b29e1e6 | 2882 | return unless ($mf =~ /^([0-9]*?)0*$/); # strip trailing zeros |
58cde26e | 2883 | $mfv = $1; |
aef458a0 JH |
2884 | # handle the 0e999 case here |
2885 | $ev = 0 if $miv eq '0' && $mfv eq ''; | |
58cde26e JH |
2886 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
2887 | } | |
2888 | } | |
2889 | return; # NaN, not a number | |
2890 | } | |
2891 | ||
58cde26e | 2892 | ############################################################################## |
0716bf9b | 2893 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e | 2894 | |
dccbb853 | 2895 | sub __lcm |
58cde26e JH |
2896 | { |
2897 | # (BINT or num_str, BINT or num_str) return BINT | |
2898 | # does modify first argument | |
2899 | # LCM | |
2900 | ||
b68b7ab1 | 2901 | my ($x,$ty) = @_; |
58cde26e | 2902 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); |
b68b7ab1 T |
2903 | my $method = ref($x) . '::bgcd'; |
2904 | no strict 'refs'; | |
2905 | $x * $ty / &$method($x,$ty); | |
58cde26e JH |
2906 | } |
2907 | ||
58cde26e | 2908 | ############################################################################### |
fdb4b05f T |
2909 | # trigonometric functions |
2910 | ||
2911 | sub bpi | |
2912 | { | |
2913 | # Calculate PI to N digits. Unless upgrading is in effect, returns the | |
2914 | # result truncated to an integer, that is, always returns '3'. | |
2915 | my ($self,$n) = @_; | |
2916 | if (@_ == 1) | |
2917 | { | |
2918 | # called like Math::BigInt::bpi(10); | |
2919 | $n = $self; $self = $class; | |
2920 | } | |
2921 | $self = ref($self) if ref($self); | |
2922 | ||
2923 | return $upgrade->new($n) if defined $upgrade; | |
2924 | ||
2925 | # hard-wired to "3" | |
2926 | $self->new(3); | |
2927 | } | |
2928 | ||
60a1aa19 T |
2929 | sub bcos |
2930 | { | |
2931 | # Calculate cosinus(x) to N digits. Unless upgrading is in effect, returns the | |
2932 | # result truncated to an integer. | |
2933 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
2934 | ||
2935 | return $x if $x->modify('bcos'); | |
2936 | ||
2937 | return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN | |
2938 | ||
2939 | return $upgrade->new($x)->bcos(@r) if defined $upgrade; | |
2940 | ||
20e2035c | 2941 | require Math::BigFloat; |
60a1aa19 T |
2942 | # calculate the result and truncate it to integer |
2943 | my $t = Math::BigFloat->new($x)->bcos(@r)->as_int(); | |
2944 | ||
2945 | $x->bone() if $t->is_one(); | |
2946 | $x->bzero() if $t->is_zero(); | |
2947 | $x->round(@r); | |
2948 | } | |
2949 | ||
2950 | sub bsin | |
2951 | { | |
2952 | # Calculate sinus(x) to N digits. Unless upgrading is in effect, returns the | |
2953 | # result truncated to an integer. | |
2954 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
2955 | ||
2956 | return $x if $x->modify('bsin'); | |
2957 | ||
2958 | return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN | |
2959 | ||
2960 | return $upgrade->new($x)->bsin(@r) if defined $upgrade; | |
2961 | ||
20e2035c | 2962 | require Math::BigFloat; |
60a1aa19 T |
2963 | # calculate the result and truncate it to integer |
2964 | my $t = Math::BigFloat->new($x)->bsin(@r)->as_int(); | |
2965 | ||
2966 | $x->bone() if $t->is_one(); | |
2967 | $x->bzero() if $t->is_zero(); | |
2968 | $x->round(@r); | |
2969 | } | |
2970 | ||
20e2035c T |
2971 | sub batan2 |
2972 | { | |
30afc38d | 2973 | # calculate arcus tangens of ($y/$x) |
20e2035c T |
2974 | |
2975 | # set up parameters | |
30afc38d | 2976 | my ($self,$y,$x,@r) = (ref($_[0]),@_); |
20e2035c T |
2977 | # objectify is costly, so avoid it |
2978 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
2979 | { | |
30afc38d | 2980 | ($self,$y,$x,@r) = objectify(2,@_); |
20e2035c T |
2981 | } |
2982 | ||
30afc38d | 2983 | return $y if $y->modify('batan2'); |
20e2035c | 2984 | |
30afc38d T |
2985 | return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan); |
2986 | ||
2987 | return $y->bzero() if $y->is_zero() && $x->{sign} eq '+'; # x >= 0 | |
20e2035c T |
2988 | |
2989 | # inf handling | |
30afc38d T |
2990 | # +-inf => --PI/2 => +-1 |
2991 | return $y->bone( substr($y->{sign},0,1) ) if $y->{sign} =~ /^[+-]inf$/; | |
20e2035c | 2992 | |
30afc38d | 2993 | return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade; |
20e2035c T |
2994 | |
2995 | require Math::BigFloat; | |
30afc38d | 2996 | my $r = Math::BigFloat->new($y)->batan2(Math::BigFloat->new($x),@r)->as_int(); |
20e2035c T |
2997 | |
2998 | $x->{value} = $r->{value}; | |
2999 | $x->{sign} = $r->{sign}; | |
3000 | ||
3001 | $x; | |
3002 | } | |
3003 | ||
60a1aa19 T |
3004 | sub batan |
3005 | { | |
3006 | # Calculate arcus tangens of x to N digits. Unless upgrading is in effect, returns the | |
3007 | # result truncated to an integer. | |
3008 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
3009 | ||
3010 | return $x if $x->modify('batan'); | |
3011 | ||
3012 | return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN | |
3013 | ||
3014 | return $upgrade->new($x)->batan(@r) if defined $upgrade; | |
3015 | ||
3016 | # calculate the result and truncate it to integer | |
3017 | my $t = Math::BigFloat->new($x)->batan(@r); | |
3018 | ||
3019 | $x->{value} = $CALC->_new( $x->as_int()->bstr() ); | |
3020 | $x->round(@r); | |
3021 | } | |
3022 | ||
fdb4b05f | 3023 | ############################################################################### |
b68b7ab1 | 3024 | # this method returns 0 if the object can be modified, or 1 if not. |
b282a552 | 3025 | # We use a fast constant sub() here, to avoid costly calls. Subclasses |
58cde26e JH |
3026 | # may override it with special code (f.i. Math::BigInt::Constant does so) |
3027 | ||
0716bf9b | 3028 | sub modify () { 0; } |
e16b8f49 | 3029 | |
a0d0e21e | 3030 | 1; |
a5f75d66 AD |
3031 | __END__ |
3032 | ||
233f7bc0 T |
3033 | =pod |
3034 | ||
a5f75d66 AD |
3035 | =head1 NAME |
3036 | ||
233f7bc0 | 3037 | Math::BigInt - Arbitrary size integer/float math package |
a5f75d66 AD |
3038 | |
3039 | =head1 SYNOPSIS | |
3040 | ||
3041 | use Math::BigInt; | |
58cde26e | 3042 | |
990fb837 RGS |
3043 | # or make it faster: install (optional) Math::BigInt::GMP |
3044 | # and always use (it will fall back to pure Perl if the | |
3045 | # GMP library is not installed): | |
3046 | ||
7b29e1e6 | 3047 | # will warn if Math::BigInt::GMP cannot be found |
990fb837 RGS |
3048 | use Math::BigInt lib => 'GMP'; |
3049 | ||
7b29e1e6 T |
3050 | # to supress the warning use this: |
3051 | # use Math::BigInt try => 'GMP'; | |
3052 | ||
9b924220 RGS |
3053 | my $str = '1234567890'; |
3054 | my @values = (64,74,18); | |
3055 | my $n = 1; my $sign = '-'; | |
3056 | ||
58cde26e | 3057 | # Number creation |
fdb4b05f T |
3058 | my $x = Math::BigInt->new($str); # defaults to 0 |
3059 | my $y = $x->copy(); # make a true copy | |
3060 | my $nan = Math::BigInt->bnan(); # create a NotANumber | |
3061 | my $zero = Math::BigInt->bzero(); # create a +0 | |
3062 | my $inf = Math::BigInt->binf(); # create a +inf | |
3063 | my $inf = Math::BigInt->binf('-'); # create a -inf | |
3064 | my $one = Math::BigInt->bone(); # create a +1 | |
3065 | my $mone = Math::BigInt->bone('-'); # create a -1 | |
3066 | ||
3067 | my $pi = Math::BigInt->bpi(); # returns '3' | |
3068 | # see Math::BigFloat::bpi() | |
58cde26e | 3069 | |
7b29e1e6 T |
3070 | $h = Math::BigInt->new('0x123'); # from hexadecimal |
3071 | $b = Math::BigInt->new('0b101'); # from binary | |
3072 | $o = Math::BigInt->from_oct('0101'); # from octal | |
3073 | ||
56d9de68 T |
3074 | # Testing (don't modify their arguments) |
3075 | # (return true if the condition is met, otherwise false) | |
3076 | ||
3077 | $x->is_zero(); # if $x is +0 | |
3078 | $x->is_nan(); # if $x is NaN | |
3079 | $x->is_one(); # if $x is +1 | |
3080 | $x->is_one('-'); # if $x is -1 | |
3081 | $x->is_odd(); # if $x is odd | |
3082 | $x->is_even(); # if $x is even | |
b282a552 T |
3083 | $x->is_pos(); # if $x >= 0 |
3084 | $x->is_neg(); # if $x < 0 | |
9b924220 | 3085 | $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+') |
56d9de68 T |
3086 | $x->is_int(); # if $x is an integer (not a float) |
3087 | ||
3c4b39be | 3088 | # comparing and digit/sign extraction |
56d9de68 T |
3089 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
3090 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
3091 | $x->sign(); # return the sign, either +,- or NaN | |
3092 | $x->digit($n); # return the nth digit, counting from right | |
3093 | $x->digit(-$n); # return the nth digit, counting from left | |
58cde26e | 3094 | |
990fb837 RGS |
3095 | # The following all modify their first argument. If you want to preserve |
3096 | # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is | |
3c4b39be | 3097 | # necessary when mixing $a = $b assignments with non-overloaded math. |
58cde26e | 3098 | |
56d9de68 T |
3099 | $x->bzero(); # set $x to 0 |
3100 | $x->bnan(); # set $x to NaN | |
3101 | $x->bone(); # set $x to +1 | |
3102 | $x->bone('-'); # set $x to -1 | |
3103 | $x->binf(); # set $x to inf | |
3104 | $x->binf('-'); # set $x to -inf | |
3105 | ||
3106 | $x->bneg(); # negation | |
3107 | $x->babs(); # absolute value | |
3108 | $x->bnorm(); # normalize (no-op in BigInt) | |
3109 | $x->bnot(); # two's complement (bit wise not) | |
3110 | $x->binc(); # increment $x by 1 | |
3111 | $x->bdec(); # decrement $x by 1 | |
58cde26e | 3112 | |
56d9de68 T |
3113 | $x->badd($y); # addition (add $y to $x) |
3114 | $x->bsub($y); # subtraction (subtract $y from $x) | |
3115 | $x->bmul($y); # multiplication (multiply $x by $y) | |
3116 | $x->bdiv($y); # divide, set $x to quotient | |
3117 | # return (quo,rem) or quo if scalar | |
3118 | ||
80365507 T |
3119 | $x->bmuladd($y,$z); # $x = $x * $y + $z |
3120 | ||
56d9de68 T |
3121 | $x->bmod($y); # modulus (x % y) |
3122 | $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod)) | |
3123 | $x->bmodinv($mod); # the inverse of $x in the given modulus $mod | |
3124 | ||
3125 | $x->bpow($y); # power of arguments (x ** y) | |
7d193e39 T |
3126 | $x->blsft($y); # left shift in base 2 |
3127 | $x->brsft($y); # right shift in base 2 | |
7b29e1e6 T |
3128 | # returns (quo,rem) or quo if in scalar context |
3129 | $x->blsft($y,$n); # left shift by $y places in base $n | |
3130 | $x->brsft($y,$n); # right shift by $y places in base $n | |
3131 | # returns (quo,rem) or quo if in scalar context | |
58cde26e | 3132 | |
56d9de68 T |
3133 | $x->band($y); # bitwise and |
3134 | $x->bior($y); # bitwise inclusive or | |
3135 | $x->bxor($y); # bitwise exclusive or | |
3136 | $x->bnot(); # bitwise not (two's complement) | |
3137 | ||
3138 | $x->bsqrt(); # calculate square-root | |
990fb837 | 3139 | $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) |
56d9de68 | 3140 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
58cde26e | 3141 | |
50109ad0 RGS |
3142 | $x->bnok($y); # x over y (binomial coefficient n over k) |
3143 | ||
7d193e39 T |
3144 | $x->blog(); # logarithm of $x to base e (Euler's number) |
3145 | $x->blog($base); # logarithm of $x to base $base (f.i. 2) | |
3146 | $x->bexp(); # calculate e ** $x where e is Euler's number | |
3147 | ||
990fb837 | 3148 | $x->round($A,$P,$mode); # round to accuracy or precision using mode $mode |
9b924220 RGS |
3149 | $x->bround($n); # accuracy: preserve $n digits |
3150 | $x->bfround($n); # round to $nth digit, no-op for BigInts | |
58cde26e | 3151 | |
990fb837 | 3152 | # The following do not modify their arguments in BigInt (are no-ops), |
56d9de68 | 3153 | # but do so in BigFloat: |
58cde26e | 3154 | |
56d9de68 T |
3155 | $x->bfloor(); # return integer less or equal than $x |
3156 | $x->bceil(); # return integer greater or equal than $x | |
58cde26e JH |
3157 | |
3158 | # The following do not modify their arguments: | |
3159 | ||
9b924220 RGS |
3160 | # greatest common divisor (no OO style) |
3161 | my $gcd = Math::BigInt::bgcd(@values); | |
3162 | # lowest common multiplicator (no OO style) | |
3163 | my $lcm = Math::BigInt::blcm(@values); | |
bd05a461 | 3164 | |
56d9de68 | 3165 | $x->length(); # return number of digits in number |
9b924220 | 3166 | ($xl,$f) = $x->length(); # length of number and length of fraction part, |
b68b7ab1 | 3167 | # latter is always 0 digits long for BigInts |
56d9de68 T |
3168 | |
3169 | $x->exponent(); # return exponent as BigInt | |
3170 | $x->mantissa(); # return (signed) mantissa as BigInt | |
3171 | $x->parts(); # return (mantissa,exponent) as BigInt | |
3172 | $x->copy(); # make a true copy of $x (unlike $y = $x;) | |
b282a552 T |
3173 | $x->as_int(); # return as BigInt (in BigInt: same as copy()) |
3174 | $x->numify(); # return as scalar (might overflow!) | |
bd05a461 | 3175 | |
56d9de68 | 3176 | # conversation to string (do not modify their argument) |
b68b7ab1 T |
3177 | $x->bstr(); # normalized string (e.g. '3') |
3178 | $x->bsstr(); # norm. string in scientific notation (e.g. '3E0') | |
56d9de68 T |
3179 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
3180 | $x->as_bin(); # as signed binary string with prefixed 0b | |
7b29e1e6 | 3181 | $x->as_oct(); # as signed octal string with prefixed 0 |
b282a552 | 3182 | |
bd05a461 | 3183 | |
f9a08e12 | 3184 | # precision and accuracy (see section about rounding for more) |
56d9de68 T |
3185 | $x->precision(); # return P of $x (or global, if P of $x undef) |
3186 | $x->precision($n); # set P of $x to $n | |
3187 | $x->accuracy(); # return A of $x (or global, if A of $x undef) | |
3188 | $x->accuracy($n); # set A $x to $n | |
f9a08e12 | 3189 | |
56d9de68 | 3190 | # Global methods |
b68b7ab1 T |
3191 | Math::BigInt->precision(); # get/set global P for all BigInt objects |
3192 | Math::BigInt->accuracy(); # get/set global A for all BigInt objects | |
3193 | Math::BigInt->round_mode(); # get/set global round mode, one of | |
7b29e1e6 | 3194 | # 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common' |
b68b7ab1 | 3195 | Math::BigInt->config(); # return hash containing configuration |
f9a08e12 | 3196 | |
a5f75d66 AD |
3197 | =head1 DESCRIPTION |
3198 | ||
3c4b39be | 3199 | All operators (including basic math operations) are overloaded if you |
58cde26e | 3200 | declare your big integers as |
a5f75d66 | 3201 | |
58cde26e | 3202 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 | 3203 | |
58cde26e JH |
3204 | Operations with overloaded operators preserve the arguments which is |
3205 | exactly what you expect. | |
a5f75d66 AD |
3206 | |
3207 | =over 2 | |
3208 | ||
aef458a0 | 3209 | =item Input |
a5f75d66 | 3210 | |
aef458a0 JH |
3211 | Input values to these routines may be any string, that looks like a number |
3212 | and results in an integer, including hexadecimal and binary numbers. | |
58cde26e | 3213 | |
aef458a0 JH |
3214 | Scalars holding numbers may also be passed, but note that non-integer numbers |
3215 | may already have lost precision due to the conversation to float. Quote | |
091c87b1 | 3216 | your input if you want BigInt to see all the digits: |
a5f75d66 | 3217 | |
aef458a0 JH |
3218 | $x = Math::BigInt->new(12345678890123456789); # bad |
3219 | $x = Math::BigInt->new('12345678901234567890'); # good | |
58cde26e | 3220 | |
56d9de68 | 3221 | You can include one underscore between any two digits. |
58cde26e JH |
3222 | |
3223 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. | |
aef458a0 | 3224 | Non-integer values result in NaN. |
58cde26e | 3225 | |
7b29e1e6 T |
3226 | Hexadecimal (prefixed with "0x") and binary numbers (prefixed with "0b") |
3227 | are accepted, too. Please note that octal numbers are not recognized | |
3228 | by new(), so the following will print "123": | |
3229 | ||
3230 | perl -MMath::BigInt -le 'print Math::BigInt->new("0123")' | |
3231 | ||
3232 | To convert an octal number, use from_oct(); | |
3233 | ||
3234 | perl -MMath::BigInt -le 'print Math::BigInt->from_oct("0123")' | |
3235 | ||
aef458a0 | 3236 | Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('') |
091c87b1 T |
3237 | results in 'NaN'. This might change in the future, so use always the following |
3238 | explicit forms to get a zero or NaN: | |
3239 | ||
3240 | $zero = Math::BigInt->bzero(); | |
3241 | $nan = Math::BigInt->bnan(); | |
58cde26e | 3242 | |
aef458a0 | 3243 | C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers |
091c87b1 | 3244 | are always stored in normalized form. If passed a string, creates a BigInt |
aef458a0 | 3245 | object from the input. |
a5f75d66 AD |
3246 | |
3247 | =item Output | |
3248 | ||
b68b7ab1 T |
3249 | Output values are BigInt objects (normalized), except for the methods which |
3250 | return a string (see L<SYNOPSIS>). | |
3251 | ||
58cde26e | 3252 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
b68b7ab1 T |
3253 | C<is_nan()>, etc.) return true or false, while others (C<bcmp()>, C<bacmp()>) |
3254 | return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort. | |
a5f75d66 AD |
3255 | |
3256 | =back | |
3257 | ||
b3abae2a JH |
3258 | =head1 METHODS |
3259 | ||
56d9de68 | 3260 | Each of the methods below (except config(), accuracy() and precision()) |
b68b7ab1 T |
3261 | accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R> |
3262 | are C<accuracy>, C<precision> and C<round_mode>. Please see the section about | |
56d9de68 | 3263 | L<ACCURACY and PRECISION> for more information. |
b3abae2a | 3264 | |
7b29e1e6 | 3265 | =head2 config() |
8f675a64 JH |
3266 | |
3267 | use Data::Dumper; | |
3268 | ||
3269 | print Dumper ( Math::BigInt->config() ); | |
56d9de68 | 3270 | print Math::BigInt->config()->{lib},"\n"; |
8f675a64 JH |
3271 | |
3272 | Returns a hash containing the configuration, e.g. the version number, lib | |
56d9de68 T |
3273 | loaded etc. The following hash keys are currently filled in with the |
3274 | appropriate information. | |
3275 | ||
3276 | key Description | |
3277 | Example | |
3278 | ============================================================ | |
091c87b1 | 3279 | lib Name of the low-level math library |
56d9de68 | 3280 | Math::BigInt::Calc |
091c87b1 | 3281 | lib_version Version of low-level math library (see 'lib') |
56d9de68 | 3282 | 0.30 |
091c87b1 | 3283 | class The class name of config() you just called |
56d9de68 | 3284 | Math::BigInt |
091c87b1 | 3285 | upgrade To which class math operations might be upgraded |
56d9de68 | 3286 | Math::BigFloat |
091c87b1 | 3287 | downgrade To which class math operations might be downgraded |
56d9de68 T |
3288 | undef |
3289 | precision Global precision | |
3290 | undef | |
3291 | accuracy Global accuracy | |
3292 | undef | |
3293 | round_mode Global round mode | |
3294 | even | |
3295 | version version number of the class you used | |
3296 | 1.61 | |
3c4b39be | 3297 | div_scale Fallback accuracy for div |
56d9de68 | 3298 | 40 |
091c87b1 T |
3299 | trap_nan If true, traps creation of NaN via croak() |
3300 | 1 | |
3301 | trap_inf If true, traps creation of +inf/-inf via croak() | |
3302 | 1 | |
56d9de68 | 3303 | |
c38b2de2 | 3304 | The following values can be set by passing C<config()> a reference to a hash: |
93c87d9d T |
3305 | |
3306 | trap_inf trap_nan | |
3307 | upgrade downgrade precision accuracy round_mode div_scale | |
3308 | ||
3309 | Example: | |
3310 | ||
3311 | $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } ); | |
8f675a64 | 3312 | |
7b29e1e6 | 3313 | =head2 accuracy() |
13a12e00 JH |
3314 | |
3315 | $x->accuracy(5); # local for $x | |
56d9de68 | 3316 | CLASS->accuracy(5); # global for all members of CLASS |
233f7bc0 T |
3317 | # Note: This also applies to new()! |
3318 | ||
3319 | $A = $x->accuracy(); # read out accuracy that affects $x | |
3320 | $A = CLASS->accuracy(); # read out global accuracy | |
13a12e00 JH |
3321 | |
3322 | Set or get the global or local accuracy, aka how many significant digits the | |
233f7bc0 T |
3323 | results have. If you set a global accuracy, then this also applies to new()! |
3324 | ||
3325 | Warning! The accuracy I<sticks>, e.g. once you created a number under the | |
3326 | influence of C<< CLASS->accuracy($A) >>, all results from math operations with | |
3327 | that number will also be rounded. | |
3328 | ||
3c4b39be | 3329 | In most cases, you should probably round the results explicitly using one of |
233f7bc0 T |
3330 | L<round()>, L<bround()> or L<bfround()> or by passing the desired accuracy |
3331 | to the math operation as additional parameter: | |
3332 | ||
3333 | my $x = Math::BigInt->new(30000); | |
3334 | my $y = Math::BigInt->new(7); | |
3335 | print scalar $x->copy()->bdiv($y, 2); # print 4300 | |
3336 | print scalar $x->copy()->bdiv($y)->bround(2); # print 4300 | |
56d9de68 T |
3337 | |
3338 | Please see the section about L<ACCURACY AND PRECISION> for further details. | |
13a12e00 JH |
3339 | |
3340 | Value must be greater than zero. Pass an undef value to disable it: | |
3341 | ||
3342 | $x->accuracy(undef); | |
3343 | Math::BigInt->accuracy(undef); | |
3344 | ||
3345 | Returns the current accuracy. For C<$x->accuracy()> it will return either the | |
3346 | local accuracy, or if not defined, the global. This means the return value | |
3347 | represents the accuracy that will be in effect for $x: | |
3348 | ||
3349 | $y = Math::BigInt->new(1234567); # unrounded | |
3350 | print Math::BigInt->accuracy(4),"\n"; # set 4, print 4 | |
233f7bc0 | 3351 | $x = Math::BigInt->new(123456); # $x will be automatically rounded! |
13a12e00 JH |
3352 | print "$x $y\n"; # '123500 1234567' |
3353 | print $x->accuracy(),"\n"; # will be 4 | |
3354 | print $y->accuracy(),"\n"; # also 4, since global is 4 | |
3355 | print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5 | |
3356 | print $x->accuracy(),"\n"; # still 4 | |
3357 | print $y->accuracy(),"\n"; # 5, since global is 5 | |
3358 | ||
56d9de68 T |
3359 | Note: Works also for subclasses like Math::BigFloat. Each class has it's own |
3360 | globals separated from Math::BigInt, but it is possible to subclass | |
3361 | Math::BigInt and make the globals of the subclass aliases to the ones from | |
3362 | Math::BigInt. | |
3363 | ||
7b29e1e6 | 3364 | =head2 precision() |
56d9de68 | 3365 | |
233f7bc0 T |
3366 | $x->precision(-2); # local for $x, round at the second digit right of the dot |
3367 | $x->precision(2); # ditto, round at the second digit left of the dot | |
3368 | ||
3369 | CLASS->precision(5); # Global for all members of CLASS | |
3370 | # This also applies to new()! | |
3371 | CLASS->precision(-5); # ditto | |
3372 | ||
3373 | $P = CLASS->precision(); # read out global precision | |
3374 | $P = $x->precision(); # read out precision that affects $x | |
3375 | ||
3376 | Note: You probably want to use L<accuracy()> instead. With L<accuracy> you | |
3377 | set the number of digits each result should have, with L<precision> you | |
3378 | set the place where to round! | |
56d9de68 | 3379 | |
233f7bc0 T |
3380 | C<precision()> sets or gets the global or local precision, aka at which digit |
3381 | before or after the dot to round all results. A set global precision also | |
3382 | applies to all newly created numbers! | |
3383 | ||
3384 | In Math::BigInt, passing a negative number precision has no effect since no | |
3385 | numbers have digits after the dot. In L<Math::BigFloat>, it will round all | |
3386 | results to P digits after the dot. | |
56d9de68 T |
3387 | |
3388 | Please see the section about L<ACCURACY AND PRECISION> for further details. | |
3389 | ||
233f7bc0 | 3390 | Pass an undef value to disable it: |
56d9de68 T |
3391 | |
3392 | $x->precision(undef); | |
3393 | Math::BigInt->precision(undef); | |
3394 | ||
3395 | Returns the current precision. For C<$x->precision()> it will return either the | |
3396 | local precision of $x, or if not defined, the global. This means the return | |
233f7bc0 | 3397 | value represents the prevision that will be in effect for $x: |
56d9de68 T |
3398 | |
3399 | $y = Math::BigInt->new(1234567); # unrounded | |
3400 | print Math::BigInt->precision(4),"\n"; # set 4, print 4 | |
3401 | $x = Math::BigInt->new(123456); # will be automatically rounded | |
233f7bc0 | 3402 | print $x; # print "120000"! |
56d9de68 | 3403 | |
233f7bc0 T |
3404 | Note: Works also for subclasses like L<Math::BigFloat>. Each class has its |
3405 | own globals separated from Math::BigInt, but it is possible to subclass | |
56d9de68 T |
3406 | Math::BigInt and make the globals of the subclass aliases to the ones from |
3407 | Math::BigInt. | |
3408 | ||
7b29e1e6 | 3409 | =head2 brsft() |
b3abae2a JH |
3410 | |
3411 | $x->brsft($y,$n); | |
3412 | ||
3413 | Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and | |
3414 | 2, but others work, too. | |
3415 | ||
3416 | Right shifting usually amounts to dividing $x by $n ** $y and truncating the | |
3417 | result: | |
3418 | ||
3419 | ||
3420 | $x = Math::BigInt->new(10); | |
3421 | $x->brsft(1); # same as $x >> 1: 5 | |
3422 | $x = Math::BigInt->new(1234); | |
3423 | $x->brsft(2,10); # result 12 | |
3424 | ||
3425 | There is one exception, and that is base 2 with negative $x: | |
3426 | ||
3427 | ||
3428 | $x = Math::BigInt->new(-5); | |
3429 | print $x->brsft(1); | |
3430 | ||
3431 | This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the | |
3432 | result). | |
3433 | ||
7b29e1e6 | 3434 | =head2 new() |
b3abae2a JH |
3435 | |
3436 | $x = Math::BigInt->new($str,$A,$P,$R); | |
3437 | ||
aef458a0 | 3438 | Creates a new BigInt object from a scalar or another BigInt object. The |
b3abae2a JH |
3439 | input is accepted as decimal, hex (with leading '0x') or binary (with leading |
3440 | '0b'). | |
3441 | ||
aef458a0 JH |
3442 | See L<Input> for more info on accepted input formats. |
3443 | ||
7b29e1e6 T |
3444 | =head2 from_oct() |
3445 | ||
7aa7e0ae | 3446 | $x = Math::BigInt->from_oct("0775"); # input is octal |
7b29e1e6 T |
3447 | |
3448 | =head2 from_hex() | |
3449 | ||
7aa7e0ae | 3450 | $x = Math::BigInt->from_hex("0xcafe"); # input is hexadecimal |
7b29e1e6 T |
3451 | |
3452 | =head2 from_bin() | |
3453 | ||
7aa7e0ae | 3454 | $x = Math::BigInt->from_oct("0x10011"); # input is binary |
7b29e1e6 T |
3455 | |
3456 | =head2 bnan() | |
b3abae2a JH |
3457 | |
3458 | $x = Math::BigInt->bnan(); | |
3459 | ||
3460 | Creates a new BigInt object representing NaN (Not A Number). | |
3461 | If used on an object, it will set it to NaN: | |
3462 | ||
3463 | $x->bnan(); | |
3464 | ||
7b29e1e6 | 3465 | =head2 bzero() |
b3abae2a JH |
3466 | |
3467 | $x = Math::BigInt->bzero(); | |
3468 | ||
3469 | Creates a new BigInt object representing zero. | |
3470 | If used on an object, it will set it to zero: | |
3471 | ||
3472 | $x->bzero(); | |
3473 | ||
7b29e1e6 | 3474 | =head2 binf() |
b3abae2a JH |
3475 | |
3476 | $x = Math::BigInt->binf($sign); | |
3477 | ||
3478 | Creates a new BigInt object representing infinity. The optional argument is | |
3479 | either '-' or '+', indicating whether you want infinity or minus infinity. | |
3480 | If used on an object, it will set it to infinity: | |
3481 | ||
3482 | $x->binf(); | |
3483 | $x->binf('-'); | |
3484 | ||
7b29e1e6 | 3485 | =head2 bone() |
b3abae2a JH |
3486 | |
3487 | $x = Math::BigInt->binf($sign); | |
3488 | ||
3489 | Creates a new BigInt object representing one. The optional argument is | |
3490 | either '-' or '+', indicating whether you want one or minus one. | |
3491 | If used on an object, it will set it to one: | |
3492 | ||
3493 | $x->bone(); # +1 | |
3494 | $x->bone('-'); # -1 | |
3495 | ||
56b9c951 JH |
3496 | =head2 is_one()/is_zero()/is_nan()/is_inf() |
3497 | ||
b3abae2a JH |
3498 | |
3499 | $x->is_zero(); # true if arg is +0 | |
3500 | $x->is_nan(); # true if arg is NaN | |
3501 | $x->is_one(); # true if arg is +1 | |
3502 | $x->is_one('-'); # true if arg is -1 | |
b3abae2a JH |
3503 | $x->is_inf(); # true if +inf |
3504 | $x->is_inf('-'); # true if -inf (sign is default '+') | |
56b9c951 | 3505 | |
3c4b39be | 3506 | These methods all test the BigInt for being one specific value and return |
56b9c951 JH |
3507 | true or false depending on the input. These are faster than doing something |
3508 | like: | |
3509 | ||
3510 | if ($x == 0) | |
3511 | ||
7b29e1e6 | 3512 | =head2 is_pos()/is_neg()/is_positive()/is_negative() |
56b9c951 | 3513 | |
b68b7ab1 T |
3514 | $x->is_pos(); # true if > 0 |
3515 | $x->is_neg(); # true if < 0 | |
56b9c951 JH |
3516 | |
3517 | The methods return true if the argument is positive or negative, respectively. | |
3518 | C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and | |
b68b7ab1 | 3519 | C<-inf> is negative. A C<zero> is neither positive nor negative. |
56b9c951 JH |
3520 | |
3521 | These methods are only testing the sign, and not the value. | |
3522 | ||
3c4b39be | 3523 | C<is_positive()> and C<is_negative()> are aliases to C<is_pos()> and |
b282a552 T |
3524 | C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were |
3525 | introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced | |
3526 | in v1.68. | |
3527 | ||
56b9c951 JH |
3528 | =head2 is_odd()/is_even()/is_int() |
3529 | ||
3530 | $x->is_odd(); # true if odd, false for even | |
3531 | $x->is_even(); # true if even, false for odd | |
b3abae2a JH |
3532 | $x->is_int(); # true if $x is an integer |
3533 | ||
56b9c951 JH |
3534 | The return true when the argument satisfies the condition. C<NaN>, C<+inf>, |
3535 | C<-inf> are not integers and are neither odd nor even. | |
b3abae2a | 3536 | |
c38b2de2 JH |
3537 | In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers. |
3538 | ||
7b29e1e6 | 3539 | =head2 bcmp() |
b3abae2a | 3540 | |
56b9c951 JH |
3541 | $x->bcmp($y); |
3542 | ||
3543 | Compares $x with $y and takes the sign into account. | |
3544 | Returns -1, 0, 1 or undef. | |
b3abae2a | 3545 | |
7b29e1e6 | 3546 | =head2 bacmp() |
b3abae2a | 3547 | |
56b9c951 JH |
3548 | $x->bacmp($y); |
3549 | ||
3550 | Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef. | |
b3abae2a | 3551 | |
7b29e1e6 | 3552 | =head2 sign() |
b3abae2a | 3553 | |
56b9c951 JH |
3554 | $x->sign(); |
3555 | ||
3556 | Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN. | |
b3abae2a | 3557 | |
b68b7ab1 T |
3558 | If you want $x to have a certain sign, use one of the following methods: |
3559 | ||
3560 | $x->babs(); # '+' | |
3561 | $x->babs()->bneg(); # '-' | |
3562 | $x->bnan(); # 'NaN' | |
3563 | $x->binf(); # '+inf' | |
3564 | $x->binf('-'); # '-inf' | |
3565 | ||
7b29e1e6 | 3566 | =head2 digit() |
091c87b1 T |
3567 | |
3568 | $x->digit($n); # return the nth digit, counting from right | |
b3abae2a | 3569 | |
091c87b1 | 3570 | If C<$n> is negative, returns the digit counting from left. |
b3abae2a | 3571 | |
7b29e1e6 | 3572 | =head2 bneg() |
b3abae2a JH |
3573 | |
3574 | $x->bneg(); | |
3575 | ||
3576 | Negate the number, e.g. change the sign between '+' and '-', or between '+inf' | |
3577 | and '-inf', respectively. Does nothing for NaN or zero. | |
3578 | ||
7b29e1e6 | 3579 | =head2 babs() |
b3abae2a JH |
3580 | |
3581 | $x->babs(); | |
3582 | ||
86b76201 | 3583 | Set the number to its absolute value, e.g. change the sign from '-' to '+' |
b3abae2a JH |
3584 | and from '-inf' to '+inf', respectively. Does nothing for NaN or positive |
3585 | numbers. | |
3586 | ||
7b29e1e6 | 3587 | =head2 bnorm() |
b3abae2a | 3588 | |
56d9de68 | 3589 | $x->bnorm(); # normalize (no-op) |
b3abae2a | 3590 | |
7b29e1e6 | 3591 | =head2 bnot() |
b3abae2a | 3592 | |
091c87b1 T |
3593 | $x->bnot(); |
3594 | ||
86b76201 | 3595 | Two's complement (bitwise not). This is equivalent to |
091c87b1 T |
3596 | |
3597 | $x->binc()->bneg(); | |
3598 | ||
3599 | but faster. | |
b3abae2a | 3600 | |
7b29e1e6 | 3601 | =head2 binc() |
b3abae2a | 3602 | |
56d9de68 | 3603 | $x->binc(); # increment x by 1 |
b3abae2a | 3604 | |
7b29e1e6 | 3605 | =head2 bdec() |
b3abae2a | 3606 | |
56d9de68 | 3607 | $x->bdec(); # decrement x by 1 |
b3abae2a | 3608 | |
7b29e1e6 | 3609 | =head2 badd() |
b3abae2a | 3610 | |
56d9de68 | 3611 | $x->badd($y); # addition (add $y to $x) |
b3abae2a | 3612 | |
7b29e1e6 | 3613 | =head2 bsub() |
b3abae2a | 3614 | |
56d9de68 | 3615 | $x->bsub($y); # subtraction (subtract $y from $x) |
b3abae2a | 3616 | |
7b29e1e6 | 3617 | =head2 bmul() |
b3abae2a | 3618 | |
56d9de68 | 3619 | $x->bmul($y); # multiplication (multiply $x by $y) |
b3abae2a | 3620 | |
80365507 T |
3621 | =head2 bmuladd() |
3622 | ||
3623 | $x->bmuladd($y,$z); | |
3624 | ||
3625 | Multiply $x by $y, and then add $z to the result, | |
3626 | ||
3627 | This method was added in v1.87 of Math::BigInt (June 2007). | |
3628 | ||
7b29e1e6 | 3629 | =head2 bdiv() |
b3abae2a | 3630 | |
56d9de68 T |
3631 | $x->bdiv($y); # divide, set $x to quotient |
3632 | # return (quo,rem) or quo if scalar | |
b3abae2a | 3633 | |
7b29e1e6 | 3634 | =head2 bmod() |
b3abae2a | 3635 | |
56d9de68 | 3636 | $x->bmod($y); # modulus (x % y) |
b3abae2a | 3637 | |
7b29e1e6 | 3638 | =head2 bmodinv() |
d614cd8b | 3639 | |
56d9de68 | 3640 | num->bmodinv($mod); # modular inverse |
d614cd8b JH |
3641 | |
3642 | Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is | |
3643 | returned unless C<$num> is relatively prime to C<$mod>, i.e. unless | |
3644 | C<bgcd($num, $mod)==1>. | |
3645 | ||
7b29e1e6 | 3646 | =head2 bmodpow() |
d614cd8b | 3647 | |
56d9de68 T |
3648 | $num->bmodpow($exp,$mod); # modular exponentation |
3649 | # ($num**$exp % $mod) | |
d614cd8b JH |
3650 | |
3651 | Returns the value of C<$num> taken to the power C<$exp> in the modulus | |
3652 | C<$mod> using binary exponentation. C<bmodpow> is far superior to | |
3653 | writing | |
3654 | ||
56d9de68 | 3655 | $num ** $exp % $mod |
d614cd8b | 3656 | |
091c87b1 | 3657 | because it is much faster - it reduces internal variables into |
d614cd8b JH |
3658 | the modulus whenever possible, so it operates on smaller numbers. |
3659 | ||
3660 | C<bmodpow> also supports negative exponents. | |
3661 | ||
56d9de68 | 3662 | bmodpow($num, -1, $mod) |
d614cd8b JH |
3663 | |
3664 | is exactly equivalent to | |
3665 | ||
56d9de68 | 3666 | bmodinv($num, $mod) |
d614cd8b | 3667 | |
7b29e1e6 | 3668 | =head2 bpow() |
b3abae2a | 3669 | |
56d9de68 | 3670 | $x->bpow($y); # power of arguments (x ** y) |
b3abae2a | 3671 | |
7d193e39 T |
3672 | =head2 blog() |
3673 | ||
3674 | $x->blog($base, $accuracy); # logarithm of x to the base $base | |
3675 | ||
3676 | If C<$base> is not defined, Euler's number (e) is used: | |
3677 | ||
3678 | print $x->blog(undef, 100); # log(x) to 100 digits | |
3679 | ||
3680 | =head2 bexp() | |
3681 | ||
3682 | $x->bexp($accuracy); # calculate e ** X | |
3683 | ||
3684 | Calculates the expression C<e ** $x> where C<e> is Euler's number. | |
3685 | ||
3686 | This method was added in v1.82 of Math::BigInt (April 2007). | |
3687 | ||
3688 | See also L<blog()>. | |
3689 | ||
50109ad0 RGS |
3690 | =head2 bnok() |
3691 | ||
3692 | $x->bnok($y); # x over y (binomial coefficient n over k) | |
3693 | ||
3694 | Calculates the binomial coefficient n over k, also called the "choose" | |
3695 | function. The result is equivalent to: | |
3696 | ||
3697 | ( n ) n! | |
3698 | | - | = ------- | |
3699 | ( k ) k!(n-k)! | |
3700 | ||
3701 | This method was added in v1.84 of Math::BigInt (April 2007). | |
3702 | ||
fdb4b05f T |
3703 | =head2 bpi() |
3704 | ||
3705 | print Math::BigInt->bpi(100), "\n"; # 3 | |
3706 | ||
20e2035c T |
3707 | Returns PI truncated to an integer, with the argument being ignored. This means |
3708 | under BigInt this always returns C<3>. | |
fdb4b05f | 3709 | |
20e2035c T |
3710 | If upgrading is in effect, returns PI, rounded to N digits with the |
3711 | current rounding mode: | |
fdb4b05f T |
3712 | |
3713 | use Math::BigFloat; | |
3714 | use Math::BigInt upgrade => Math::BigFloat; | |
3715 | print Math::BigInt->bpi(3), "\n"; # 3.14 | |
3716 | print Math::BigInt->bpi(100), "\n"; # 3.1415.... | |
3717 | ||
3718 | This method was added in v1.87 of Math::BigInt (June 2007). | |
3719 | ||
60a1aa19 T |
3720 | =head2 bcos() |
3721 | ||
20e2035c | 3722 | my $x = Math::BigInt->new(1); |
60a1aa19 T |
3723 | print $x->bcos(100), "\n"; |
3724 | ||
3725 | Calculate the cosinus of $x, modifying $x in place. | |
3726 | ||
20e2035c T |
3727 | In BigInt, unless upgrading is in effect, the result is truncated to an |
3728 | integer. | |
3729 | ||
60a1aa19 T |
3730 | This method was added in v1.87 of Math::BigInt (June 2007). |
3731 | ||
3732 | =head2 bsin() | |
3733 | ||
20e2035c | 3734 | my $x = Math::BigInt->new(1); |
60a1aa19 T |
3735 | print $x->bsin(100), "\n"; |
3736 | ||
3737 | Calculate the sinus of $x, modifying $x in place. | |
3738 | ||
20e2035c T |
3739 | In BigInt, unless upgrading is in effect, the result is truncated to an |
3740 | integer. | |
3741 | ||
60a1aa19 T |
3742 | This method was added in v1.87 of Math::BigInt (June 2007). |
3743 | ||
30afc38d | 3744 | =head2 batan2() |
60a1aa19 | 3745 | |
20e2035c | 3746 | my $x = Math::BigInt->new(1); |
30afc38d T |
3747 | my $y = Math::BigInt->new(1); |
3748 | print $y->batan2($x), "\n"; | |
60a1aa19 | 3749 | |
30afc38d | 3750 | Calculate the arcus tangens of C<$y> divided by C<$x>, modifying $y in place. |
60a1aa19 | 3751 | |
20e2035c T |
3752 | In BigInt, unless upgrading is in effect, the result is truncated to an |
3753 | integer. | |
3754 | ||
3755 | This method was added in v1.87 of Math::BigInt (June 2007). | |
3756 | ||
30afc38d | 3757 | =head2 batan() |
20e2035c | 3758 | |
30afc38d T |
3759 | my $x = Math::BigFloat->new(0.5); |
3760 | print $x->batan(100), "\n"; | |
20e2035c | 3761 | |
30afc38d | 3762 | Calculate the arcus tangens of $x, modifying $x in place. |
20e2035c T |
3763 | |
3764 | In BigInt, unless upgrading is in effect, the result is truncated to an | |
3765 | integer. | |
3766 | ||
60a1aa19 T |
3767 | This method was added in v1.87 of Math::BigInt (June 2007). |
3768 | ||
7b29e1e6 | 3769 | =head2 blsft() |
b3abae2a | 3770 | |
7d193e39 | 3771 | $x->blsft($y); # left shift in base 2 |
56d9de68 | 3772 | $x->blsft($y,$n); # left shift, in base $n (like 10) |
b3abae2a | 3773 | |
7b29e1e6 | 3774 | =head2 brsft() |
b3abae2a | 3775 | |
7d193e39 | 3776 | $x->brsft($y); # right shift in base 2 |
56d9de68 | 3777 | $x->brsft($y,$n); # right shift, in base $n (like 10) |
b3abae2a | 3778 | |
7b29e1e6 | 3779 | =head2 band() |
b3abae2a | 3780 | |
56d9de68 | 3781 | $x->band($y); # bitwise and |
b3abae2a | 3782 | |
7b29e1e6 | 3783 | =head2 bior() |
b3abae2a | 3784 | |
56d9de68 | 3785 | $x->bior($y); # bitwise inclusive or |
b3abae2a | 3786 | |
7b29e1e6 | 3787 | =head2 bxor() |
b3abae2a | 3788 | |
56d9de68 | 3789 | $x->bxor($y); # bitwise exclusive or |
b3abae2a | 3790 | |
7b29e1e6 | 3791 | =head2 bnot() |
b3abae2a | 3792 | |
56d9de68 | 3793 | $x->bnot(); # bitwise not (two's complement) |
b3abae2a | 3794 | |
7b29e1e6 | 3795 | =head2 bsqrt() |
b3abae2a | 3796 | |
56d9de68 | 3797 | $x->bsqrt(); # calculate square-root |
b3abae2a | 3798 | |
f7f86b73 T |
3799 | =head2 broot() |
3800 | ||
3801 | $x->broot($N); | |
3802 | ||
3803 | Calculates the N'th root of C<$x>. | |
3804 | ||
7b29e1e6 | 3805 | =head2 bfac() |
b3abae2a | 3806 | |
56d9de68 | 3807 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
b3abae2a | 3808 | |
7b29e1e6 | 3809 | =head2 round() |
b3abae2a | 3810 | |
56d9de68 T |
3811 | $x->round($A,$P,$round_mode); |
3812 | ||
3813 | Round $x to accuracy C<$A> or precision C<$P> using the round mode | |
3814 | C<$round_mode>. | |
b3abae2a | 3815 | |
7b29e1e6 | 3816 | =head2 bround() |
b3abae2a | 3817 | |
56d9de68 | 3818 | $x->bround($N); # accuracy: preserve $N digits |
b3abae2a | 3819 | |
7b29e1e6 | 3820 | =head2 bfround() |
b3abae2a | 3821 | |
56d9de68 | 3822 | $x->bfround($N); # round to $Nth digit, no-op for BigInts |
b3abae2a | 3823 | |
7b29e1e6 | 3824 | =head2 bfloor() |
b3abae2a JH |
3825 | |
3826 | $x->bfloor(); | |
3827 | ||
3828 | Set $x to the integer less or equal than $x. This is a no-op in BigInt, but | |
3829 | does change $x in BigFloat. | |
3830 | ||
7b29e1e6 | 3831 | =head2 bceil() |
b3abae2a JH |
3832 | |
3833 | $x->bceil(); | |
3834 | ||
3835 | Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but | |
3836 | does change $x in BigFloat. | |
3837 | ||
7b29e1e6 | 3838 | =head2 bgcd() |
b3abae2a | 3839 | |
56d9de68 | 3840 | bgcd(@values); # greatest common divisor (no OO style) |
b3abae2a | 3841 | |
7b29e1e6 | 3842 | =head2 blcm() |
b3abae2a | 3843 | |
56d9de68 | 3844 | blcm(@values); # lowest common multiplicator (no OO style) |
b3abae2a | 3845 | |
7b29e1e6 | 3846 | head2 length() |
b3abae2a JH |
3847 | |
3848 | $x->length(); | |
3849 | ($xl,$fl) = $x->length(); | |
3850 | ||
3851 | Returns the number of digits in the decimal representation of the number. | |
3852 | In list context, returns the length of the integer and fraction part. For | |
3853 | BigInt's, the length of the fraction part will always be 0. | |
3854 | ||
7b29e1e6 | 3855 | =head2 exponent() |
b3abae2a JH |
3856 | |
3857 | $x->exponent(); | |
3858 | ||
3859 | Return the exponent of $x as BigInt. | |
3860 | ||
7b29e1e6 | 3861 | =head2 mantissa() |
b3abae2a JH |
3862 | |
3863 | $x->mantissa(); | |
3864 | ||
3865 | Return the signed mantissa of $x as BigInt. | |
3866 | ||
7b29e1e6 | 3867 | =head2 parts() |
b3abae2a | 3868 | |
56d9de68 | 3869 | $x->parts(); # return (mantissa,exponent) as BigInt |
b3abae2a | 3870 | |
7b29e1e6 | 3871 | =head2 copy() |
b3abae2a | 3872 | |
56d9de68 | 3873 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
b3abae2a | 3874 | |
7b29e1e6 | 3875 | =head2 as_int()/as_number() |
b3abae2a | 3876 | |
b282a552 T |
3877 | $x->as_int(); |
3878 | ||
3879 | Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as | |
3880 | C<copy()>. | |
3881 | ||
3882 | C<as_number()> is an alias to this method. C<as_number> was introduced in | |
3883 | v1.22, while C<as_int()> was only introduced in v1.68. | |
b3abae2a | 3884 | |
7b29e1e6 | 3885 | =head2 bstr() |
b282a552 T |
3886 | |
3887 | $x->bstr(); | |
b3abae2a | 3888 | |
3c4b39be | 3889 | Returns a normalized string representation of C<$x>. |
b3abae2a | 3890 | |
7b29e1e6 | 3891 | =head2 bsstr() |
b3abae2a | 3892 | |
56d9de68 | 3893 | $x->bsstr(); # normalized string in scientific notation |
b3abae2a | 3894 | |
7b29e1e6 | 3895 | =head2 as_hex() |
b3abae2a | 3896 | |
56d9de68 | 3897 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
b3abae2a | 3898 | |
7b29e1e6 | 3899 | =head2 as_bin() |
b3abae2a | 3900 | |
56d9de68 | 3901 | $x->as_bin(); # as signed binary string with prefixed 0b |
b3abae2a | 3902 | |
7b29e1e6 T |
3903 | =head2 as_oct() |
3904 | ||
3905 | $x->as_oct(); # as signed octal string with prefixed 0 | |
3906 | ||
3907 | =head2 numify() | |
3908 | ||
3909 | print $x->numify(); | |
3910 | ||
3911 | This returns a normal Perl scalar from $x. It is used automatically | |
3912 | whenever a scalar is needed, for instance in array index operations. | |
3913 | ||
3914 | This loses precision, to avoid this use L<as_int()> instead. | |
3915 | ||
3916 | =head2 modify() | |
3917 | ||
3918 | $x->modify('bpowd'); | |
3919 | ||
3920 | This method returns 0 if the object can be modified with the given | |
3921 | peration, or 1 if not. | |
3922 | ||
3923 | This is used for instance by L<Math::BigInt::Constant>. | |
3924 | ||
3925 | =head2 upgrade()/downgrade() | |
3926 | ||
3927 | Set/get the class for downgrade/upgrade operations. Thuis is used | |
3928 | for instance by L<bignum>. The defaults are '', thus the following | |
3929 | operation will create a BigInt, not a BigFloat: | |
3930 | ||
3931 | my $i = Math::BigInt->new(123); | |
3932 | my $f = Math::BigFloat->new('123.1'); | |
3933 | ||
3934 | print $i + $f,"\n"; # print 246 | |
3935 | ||
3936 | =head2 div_scale() | |
3937 | ||
3938 | Set/get the number of digits for the default precision in divide | |
3939 | operations. | |
3940 | ||
3941 | =head2 round_mode() | |
3942 | ||
3943 | Set/get the current round mode. | |
3944 | ||
0716bf9b JH |
3945 | =head1 ACCURACY and PRECISION |
3946 | ||
b22b3e31 | 3947 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b | 3948 | accuracy and precision based rounding, both automatically after every |
091c87b1 | 3949 | operation, as well as manually. |
0716bf9b JH |
3950 | |
3951 | This section describes the accuracy/precision handling in Math::Big* as it | |
b22b3e31 | 3952 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b JH |
3953 | abbreviations. |
3954 | ||
3955 | Not yet implemented things (but with correct description) are marked with '!', | |
3956 | things that need to be answered are marked with '?'. | |
3957 | ||
3958 | In the next paragraph follows a short description of terms used here (because | |
574bacfe | 3959 | these may differ from terms used by others people or documentation). |
0716bf9b | 3960 | |
b22b3e31 | 3961 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b JH |
3962 | precision), F (fallback) and R (rounding mode) will be used. |
3963 | ||
3964 | =head2 Precision P | |
3965 | ||
3966 | A fixed number of digits before (positive) or after (negative) | |
b22b3e31 PN |
3967 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
3968 | integer like 123 (or 120). A precision of 2 means two digits to the left | |
3969 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that | |
3970 | numbers with zeros before the decimal point may have different precisions, | |
3971 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value | |
3972 | was). It could also have p < 0, when the digits after the decimal point | |
3973 | are zero. | |
0716bf9b | 3974 | |
574bacfe JH |
3975 | The string output (of floating point numbers) will be padded with zeros: |
3976 | ||
3977 | Initial value P A Result String | |
3978 | ------------------------------------------------------------ | |
3979 | 1234.01 -3 1000 1000 | |
3980 | 1234 -2 1200 1200 | |
3981 | 1234.5 -1 1230 1230 | |
3982 | 1234.001 1 1234 1234.0 | |
3983 | 1234.01 0 1234 1234 | |
3984 | 1234.01 2 1234.01 1234.01 | |
3985 | 1234.01 5 1234.01 1234.01000 | |
3986 | ||
3987 | For BigInts, no padding occurs. | |
0716bf9b JH |
3988 | |
3989 | =head2 Accuracy A | |
3990 | ||
3991 | Number of significant digits. Leading zeros are not counted. A | |
3992 | number may have an accuracy greater than the non-zero digits | |
b22b3e31 PN |
3993 | when there are zeros in it or trailing zeros. For example, 123.456 has |
3994 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. | |
0716bf9b | 3995 | |
574bacfe JH |
3996 | The string output (of floating point numbers) will be padded with zeros: |
3997 | ||
3998 | Initial value P A Result String | |
3999 | ------------------------------------------------------------ | |
4000 | 1234.01 3 1230 1230 | |
4001 | 1234.01 6 1234.01 1234.01 | |
4002 | 1234.1 8 1234.1 1234.1000 | |
4003 | ||
4004 | For BigInts, no padding occurs. | |
4005 | ||
0716bf9b | 4006 | =head2 Fallback F |
a5f75d66 | 4007 | |
574bacfe JH |
4008 | When both A and P are undefined, this is used as a fallback accuracy when |
4009 | dividing numbers. | |
0716bf9b JH |
4010 | |
4011 | =head2 Rounding mode R | |
4012 | ||
4013 | When rounding a number, different 'styles' or 'kinds' | |
4014 | of rounding are possible. (Note that random rounding, as in | |
4015 | Math::Round, is not implemented.) | |
58cde26e JH |
4016 | |
4017 | =over 2 | |
a5f75d66 | 4018 | |
0716bf9b JH |
4019 | =item 'trunc' |
4020 | ||
4021 | truncation invariably removes all digits following the | |
4022 | rounding place, replacing them with zeros. Thus, 987.65 rounded | |
b22b3e31 | 4023 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b | 4024 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 | 4025 | decimal point (P=-2) becomes 123.46. |
0716bf9b JH |
4026 | |
4027 | All other implemented styles of rounding attempt to round to the | |
4028 | "nearest digit." If the digit D immediately to the right of the | |
4029 | rounding place (skipping the decimal point) is greater than 5, the | |
4030 | number is incremented at the rounding place (possibly causing a | |
4031 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds | |
4032 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly | |
4033 | truncated at the rounding place: e.g. when rounding to units, 0.4 | |
4034 | rounds to 0, and -19.4 rounds to -19. | |
4035 | ||
4036 | However the results of other styles of rounding differ if the | |
4037 | digit immediately to the right of the rounding place (skipping the | |
4038 | decimal point) is 5 and if there are no digits, or no digits other | |
4039 | than 0, after that 5. In such cases: | |
4040 | ||
4041 | =item 'even' | |
4042 | ||
4043 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 | |
4044 | if it is not already. E.g., when rounding to the first sigdig, 0.45 | |
4045 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. | |
4046 | ||
4047 | =item 'odd' | |
4048 | ||
4049 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if | |
4050 | it is not already. E.g., when rounding to the first sigdig, 0.45 | |
4051 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. | |
4052 | ||
4053 | =item '+inf' | |
4054 | ||
4055 | round to plus infinity, i.e. always round up. E.g., when | |
4056 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, | |
b22b3e31 | 4057 | and 0.4501 also becomes 0.5. |
0716bf9b JH |
4058 | |
4059 | =item '-inf' | |
4060 | ||
4061 | round to minus infinity, i.e. always round down. E.g., when | |
4062 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, | |
4063 | but 0.4501 becomes 0.5. | |
4064 | ||
4065 | =item 'zero' | |
4066 | ||
4067 | round to zero, i.e. positive numbers down, negative ones up. | |
4068 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 | |
4069 | becomes -0.5, but 0.4501 becomes 0.5. | |
4070 | ||
7b29e1e6 T |
4071 | =item 'common' |
4072 | ||
4073 | round up if the digit immediately to the right of the rounding place | |
4074 | is 5 or greater, otherwise round down. E.g., 0.15 becomes 0.2 and | |
4075 | 0.149 becomes 0.1. | |
4076 | ||
0716bf9b JH |
4077 | =back |
4078 | ||
4079 | The handling of A & P in MBI/MBF (the old core code shipped with Perl | |
4080 | versions <= 5.7.2) is like this: | |
4081 | ||
4082 | =over 2 | |
a5f75d66 | 4083 | |
0716bf9b JH |
4084 | =item Precision |
4085 | ||
b22b3e31 PN |
4086 | * ffround($p) is able to round to $p number of digits after the decimal |
4087 | point | |
0716bf9b JH |
4088 | * otherwise P is unused |
4089 | ||
4090 | =item Accuracy (significant digits) | |
4091 | ||
4092 | * fround($a) rounds to $a significant digits | |
4093 | * only fdiv() and fsqrt() take A as (optional) paramater | |
b22b3e31 | 4094 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b JH |
4095 | of digits |
4096 | + rounding/truncating is only done when explicitly calling one of fround | |
4097 | or ffround, and never for BigInt (not implemented) | |
b22b3e31 | 4098 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b JH |
4099 | * the documentation and the comment in the code indicate two different ways |
4100 | on how fdiv() determines the maximum number of digits it should calculate, | |
4101 | and the actual code does yet another thing | |
4102 | POD: | |
4103 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) | |
4104 | Comment: | |
4105 | result has at most max(scale, length(dividend), length(divisor)) digits | |
4106 | Actual code: | |
4107 | scale = max(scale, length(dividend)-1,length(divisor)-1); | |
3c4b39be | 4108 | scale += length(divisor) - length(dividend); |
b22b3e31 | 4109 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b JH |
4110 | Actually, the 'difference' added to the scale is calculated from the |
4111 | number of "significant digits" in dividend and divisor, which is derived | |
4112 | by looking at the length of the mantissa. Which is wrong, since it includes | |
091c87b1 | 4113 | the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops |
0716bf9b JH |
4114 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange |
4115 | assumption that 124 has 3 significant digits, while 120/7 will get you | |
4116 | '17', not '17.1' since 120 is thought to have 2 significant digits. | |
dccbb853 | 4117 | The rounding after the division then uses the remainder and $y to determine |
0716bf9b | 4118 | wether it must round up or down. |
b22b3e31 PN |
4119 | ? I have no idea which is the right way. That's why I used a slightly more |
4120 | ? simple scheme and tweaked the few failing testcases to match it. | |
58cde26e | 4121 | |
0716bf9b | 4122 | =back |
5dc6f178 | 4123 | |
0716bf9b | 4124 | This is how it works now: |
5dc6f178 | 4125 | |
0716bf9b | 4126 | =over 2 |
5dc6f178 | 4127 | |
0716bf9b JH |
4128 | =item Setting/Accessing |
4129 | ||
091c87b1 T |
4130 | * You can set the A global via C<< Math::BigInt->accuracy() >> or |
4131 | C<< Math::BigFloat->accuracy() >> or whatever class you are using. | |
4132 | * You can also set P globally by using C<< Math::SomeClass->precision() >> | |
4133 | likewise. | |
0716bf9b | 4134 | * Globals are classwide, and not inherited by subclasses. |
091c87b1 T |
4135 | * to undefine A, use C<< Math::SomeCLass->accuracy(undef); >> |
4136 | * to undefine P, use C<< Math::SomeClass->precision(undef); >> | |
4137 | * Setting C<< Math::SomeClass->accuracy() >> clears automatically | |
4138 | C<< Math::SomeClass->precision() >>, and vice versa. | |
0716bf9b | 4139 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 PN |
4140 | * If P is negative, this means round to the P'th place to the right of the |
4141 | decimal point; positive values mean to the left of the decimal point. | |
4142 | P of 0 means round to integer. | |
091c87b1 T |
4143 | * to find out the current global A, use C<< Math::SomeClass->accuracy() >> |
4144 | * to find out the current global P, use C<< Math::SomeClass->precision() >> | |
4145 | * use C<< $x->accuracy() >> respective C<< $x->precision() >> for the local | |
4146 | setting of C<< $x >>. | |
3c4b39be | 4147 | * Please note that C<< $x->accuracy() >> respective C<< $x->precision() >> |
091c87b1 T |
4148 | return eventually defined global A or P, when C<< $x >>'s A or P is not |
4149 | set. | |
0716bf9b JH |
4150 | |
4151 | =item Creating numbers | |
4152 | ||
86b76201 | 4153 | * When you create a number, you can give the desired A or P via: |
b3abae2a JH |
4154 | $x = Math::BigInt->new($number,$A,$P); |
4155 | * Only one of A or P can be defined, otherwise the result is NaN | |
4156 | * If no A or P is give ($x = Math::BigInt->new($number) form), then the | |
4157 | globals (if set) will be used. Thus changing the global defaults later on | |
b22b3e31 | 4158 | will not change the A or P of previously created numbers (i.e., A and P of |
b3abae2a JH |
4159 | $x will be what was in effect when $x was created) |
4160 | * If given undef for A and P, B<no> rounding will occur, and the globals will | |
4161 | B<not> be used. This is used by subclasses to create numbers without | |
86b76201 | 4162 | suffering rounding in the parent. Thus a subclass is able to have its own |
b3abae2a | 4163 | globals enforced upon creation of a number by using |
091c87b1 | 4164 | C<< $x = Math::BigInt->new($number,undef,undef) >>: |
b3abae2a | 4165 | |
990fb837 | 4166 | use Math::BigInt::SomeSubclass; |
b3abae2a JH |
4167 | use Math::BigInt; |
4168 | ||
4169 | Math::BigInt->accuracy(2); | |
4170 | Math::BigInt::SomeSubClass->accuracy(3); | |
4171 | $x = Math::BigInt::SomeSubClass->new(1234); | |
4172 | ||
4173 | $x is now 1230, and not 1200. A subclass might choose to implement | |
4174 | this otherwise, e.g. falling back to the parent's A and P. | |
0716bf9b JH |
4175 | |
4176 | =item Usage | |
4177 | ||
b22b3e31 | 4178 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b | 4179 | operation according to the rules below |
b22b3e31 PN |
4180 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
4181 | after the decimal point | |
091c87b1 T |
4182 | * Math::BigFloat uses Math::BigInt internally, but setting A or P inside |
4183 | Math::BigInt as globals does not tamper with the parts of a BigFloat. | |
4184 | A flag is used to mark all Math::BigFloat numbers as 'never round'. | |
0716bf9b JH |
4185 | |
4186 | =item Precedence | |
4187 | ||
b22b3e31 | 4188 | * It only makes sense that a number has only one of A or P at a time. |
091c87b1 T |
4189 | If you set either A or P on one object, or globally, the other one will |
4190 | be automatically cleared. | |
b3abae2a JH |
4191 | * If two objects are involved in an operation, and one of them has A in |
4192 | effect, and the other P, this results in an error (NaN). | |
3c4b39be | 4193 | * A takes precedence over P (Hint: A comes before P). |
091c87b1 T |
4194 | If neither of them is defined, nothing is used, i.e. the result will have |
4195 | as many digits as it can (with an exception for fdiv/fsqrt) and will not | |
4196 | be rounded. | |
b22b3e31 PN |
4197 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of |
4198 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. | |
4199 | If either the dividend's or the divisor's mantissa has more digits than | |
4200 | the value of F, the higher value will be used instead of F. | |
4201 | This is to limit the digits (A) of the result (just consider what would | |
4202 | happen with unlimited A and P in the case of 1/3 :-) | |
b3abae2a | 4203 | * fdiv will calculate (at least) 4 more digits than required (determined by |
0716bf9b | 4204 | A, P or F), and, if F is not used, round the result |
b22b3e31 | 4205 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe | 4206 | or P of 5, but this can not be helped - or can it?) |
091c87b1 | 4207 | * Thus you can have the math done by on Math::Big* class in two modi: |
0716bf9b JH |
4208 | + never round (this is the default): |
4209 | This is done by setting A and P to undef. No math operation | |
b22b3e31 | 4210 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
3c4b39be | 4211 | against overflows. You must explicitly call bround(), bfround() or |
b22b3e31 PN |
4212 | round() (the latter with parameters). |
4213 | Note: Once you have rounded a number, the settings will 'stick' on it | |
4214 | and 'infect' all other numbers engaged in math operations with it, since | |
0716bf9b JH |
4215 | local settings have the highest precedence. So, to get SaferRound[tm], |
4216 | use a copy() before rounding like this: | |
4217 | ||
4218 | $x = Math::BigFloat->new(12.34); | |
4219 | $y = Math::BigFloat->new(98.76); | |
4220 | $z = $x * $y; # 1218.6984 | |
4221 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) | |
4222 | $z = $x * $y; # still 1218.6984, without | |
4223 | # copy would have been 1210! | |
4224 | ||
4225 | + round after each op: | |
b22b3e31 PN |
4226 | After each single operation (except for testing like is_zero()), the |
4227 | method round() is called and the result is rounded appropriately. By | |
0716bf9b | 4228 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 PN |
4229 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
4230 | and P to -2, globally. | |
0716bf9b | 4231 | |
b22b3e31 PN |
4232 | ?Maybe an extra option that forbids local A & P settings would be in order, |
4233 | ?so that intermediate rounding does not 'poison' further math? | |
0716bf9b JH |
4234 | |
4235 | =item Overriding globals | |
4236 | ||
4237 | * you will be able to give A, P and R as an argument to all the calculation | |
b22b3e31 | 4238 | routines; the second parameter is A, the third one is P, and the fourth is |
b3abae2a | 4239 | R (shift right by one for binary operations like badd). P is used only if |
b22b3e31 PN |
4240 | the first parameter (A) is undefined. These three parameters override the |
4241 | globals in the order detailed as follows, i.e. the first defined value | |
0716bf9b | 4242 | wins: |
b22b3e31 | 4243 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b JH |
4244 | + parameter A |
4245 | + parameter P | |
4246 | + local A (if defined on both of the operands: smaller one is taken) | |
b3abae2a | 4247 | + local P (if defined on both of the operands: bigger one is taken) |
0716bf9b JH |
4248 | + global A |
4249 | + global P | |
4250 | + global F | |
b22b3e31 | 4251 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b JH |
4252 | arguments (A and P) instead of one |
4253 | ||
4254 | =item Local settings | |
4255 | ||
091c87b1 T |
4256 | * You can set A or P locally by using C<< $x->accuracy() >> or |
4257 | C<< $x->precision() >> | |
0716bf9b | 4258 | and thus force different A and P for different objects/numbers. |
b22b3e31 | 4259 | * Setting A or P this way immediately rounds $x to the new value. |
091c87b1 | 4260 | * C<< $x->accuracy() >> clears C<< $x->precision() >>, and vice versa. |
0716bf9b JH |
4261 | |
4262 | =item Rounding | |
4263 | ||
b22b3e31 | 4264 | * the rounding routines will use the respective global or local settings. |
0716bf9b JH |
4265 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
4266 | is for precision | |
4267 | * the two rounding functions take as the second parameter one of the | |
4268 | following rounding modes (R): | |
7b29e1e6 | 4269 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc', 'common' |
091c87b1 T |
4270 | * you can set/get the global R by using C<< Math::SomeClass->round_mode() >> |
4271 | or by setting C<< $Math::SomeClass::round_mode >> | |
4272 | * after each operation, C<< $result->round() >> is called, and the result may | |
b22b3e31 PN |
4273 | eventually be rounded (that is, if A or P were set either locally, |
4274 | globally or as parameter to the operation) | |
091c87b1 | 4275 | * to manually round a number, call C<< $x->round($A,$P,$round_mode); >> |
b22b3e31 | 4276 | this will round the number by using the appropriate rounding function |
0716bf9b | 4277 | and then normalize it. |
b22b3e31 | 4278 | * rounding modifies the local settings of the number: |
0716bf9b JH |
4279 | |
4280 | $x = Math::BigFloat->new(123.456); | |
4281 | $x->accuracy(5); | |
4282 | $x->bround(4); | |
4283 | ||
4284 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() | |
4285 | will be 4 from now on. | |
4286 | ||
4287 | =item Default values | |
4288 | ||
4289 | * R: 'even' | |
4290 | * F: 40 | |
4291 | * A: undef | |
4292 | * P: undef | |
4293 | ||
4294 | =item Remarks | |
4295 | ||
4296 | * The defaults are set up so that the new code gives the same results as | |
4297 | the old code (except in a few cases on fdiv): | |
4298 | + Both A and P are undefined and thus will not be used for rounding | |
4299 | after each operation. | |
4300 | + round() is thus a no-op, unless given extra parameters A and P | |
58cde26e JH |
4301 | |
4302 | =back | |
4303 | ||
b68b7ab1 T |
4304 | =head1 Infinity and Not a Number |
4305 | ||
4306 | While BigInt has extensive handling of inf and NaN, certain quirks remain. | |
4307 | ||
4308 | =over 2 | |
4309 | ||
4310 | =item oct()/hex() | |
4311 | ||
4312 | These perl routines currently (as of Perl v.5.8.6) cannot handle passed | |
4313 | inf. | |
4314 | ||
4315 | te@linux:~> perl -wle 'print 2 ** 3333' | |
4316 | inf | |
4317 | te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333' | |
4318 | 1 | |
4319 | te@linux:~> perl -wle 'print oct(2 ** 3333)' | |
4320 | 0 | |
4321 | te@linux:~> perl -wle 'print hex(2 ** 3333)' | |
4322 | Illegal hexadecimal digit 'i' ignored at -e line 1. | |
4323 | 0 | |
4324 | ||
4325 | The same problems occur if you pass them Math::BigInt->binf() objects. Since | |
4326 | overloading these routines is not possible, this cannot be fixed from BigInt. | |
4327 | ||
4328 | =item ==, !=, <, >, <=, >= with NaNs | |
4329 | ||
4330 | BigInt's bcmp() routine currently returns undef to signal that a NaN was | |
3c4b39be | 4331 | involved in a comparison. However, the overload code turns that into |
b68b7ab1 T |
4332 | either 1 or '' and thus operations like C<< NaN != NaN >> might return |
4333 | wrong values. | |
4334 | ||
4335 | =item log(-inf) | |
4336 | ||
4337 | C<< log(-inf) >> is highly weird. Since log(-x)=pi*i+log(x), then | |
4338 | log(-inf)=pi*i+inf. However, since the imaginary part is finite, the real | |
4339 | infinity "overshadows" it, so the number might as well just be infinity. | |
4340 | However, the result is a complex number, and since BigInt/BigFloat can only | |
4341 | have real numbers as results, the result is NaN. | |
4342 | ||
4343 | =item exp(), cos(), sin(), atan2() | |
4344 | ||
4345 | These all might have problems handling infinity right. | |
4346 | ||
4347 | =back | |
4348 | ||
0716bf9b JH |
4349 | =head1 INTERNALS |
4350 | ||
574bacfe | 4351 | The actual numbers are stored as unsigned big integers (with seperate sign). |
b68b7ab1 | 4352 | |
574bacfe | 4353 | You should neither care about nor depend on the internal representation; it |
b68b7ab1 T |
4354 | might change without notice. Use B<ONLY> method calls like C<< $x->sign(); >> |
4355 | instead relying on the internal representation. | |
574bacfe JH |
4356 | |
4357 | =head2 MATH LIBRARY | |
58cde26e | 4358 | |
574bacfe | 4359 | Math with the numbers is done (by default) by a module called |
091c87b1 | 4360 | C<Math::BigInt::Calc>. This is equivalent to saying: |
574bacfe JH |
4361 | |
4362 | use Math::BigInt lib => 'Calc'; | |
58cde26e | 4363 | |
0716bf9b | 4364 | You can change this by using: |
58cde26e | 4365 | |
0716bf9b | 4366 | use Math::BigInt lib => 'BitVect'; |
58cde26e | 4367 | |
574bacfe JH |
4368 | The following would first try to find Math::BigInt::Foo, then |
4369 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
0716bf9b | 4370 | |
574bacfe | 4371 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
58cde26e | 4372 | |
091c87b1 | 4373 | Since Math::BigInt::GMP is in almost all cases faster than Calc (especially in |
b68b7ab1 | 4374 | math involving really big numbers, where it is B<much> faster), and there is |
091c87b1 T |
4375 | no penalty if Math::BigInt::GMP is not installed, it is a good idea to always |
4376 | use the following: | |
4377 | ||
4378 | use Math::BigInt lib => 'GMP'; | |
4379 | ||
4380 | Different low-level libraries use different formats to store the | |
b68b7ab1 T |
4381 | numbers. You should B<NOT> depend on the number having a specific format |
4382 | internally. | |
091c87b1 T |
4383 | |
4384 | See the respective math library module documentation for further details. | |
58cde26e | 4385 | |
574bacfe JH |
4386 | =head2 SIGN |
4387 | ||
b68b7ab1 | 4388 | The sign is either '+', '-', 'NaN', '+inf' or '-inf'. |
574bacfe JH |
4389 | |
4390 | A sign of 'NaN' is used to represent the result when input arguments are not | |
4391 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively | |
4392 | minus infinity. You will get '+inf' when dividing a positive number by 0, and | |
4393 | '-inf' when dividing any negative number by 0. | |
58cde26e JH |
4394 | |
4395 | =head2 mantissa(), exponent() and parts() | |
4396 | ||
4397 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such | |
4398 | that: | |
4399 | ||
4400 | $m = $x->mantissa(); | |
4401 | $e = $x->exponent(); | |
4402 | $y = $m * ( 10 ** $e ); | |
4403 | print "ok\n" if $x == $y; | |
4404 | ||
b22b3e31 PN |
4405 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
4406 | in one go. Both the returned mantissa and exponent have a sign. | |
58cde26e | 4407 | |
7b29e1e6 T |
4408 | Currently, for BigInts C<$e> is always 0, except +inf and -inf, where it is |
4409 | C<+inf>; and for NaN, where it is C<NaN>; and for C<$x == 0>, where it is C<1> | |
4410 | (to be compatible with Math::BigFloat's internal representation of a zero as | |
4411 | C<0E1>). | |
58cde26e | 4412 | |
091c87b1 T |
4413 | C<$m> is currently just a copy of the original number. The relation between |
4414 | C<$e> and C<$m> will stay always the same, though their real values might | |
4415 | change. | |
0716bf9b | 4416 | |
58cde26e JH |
4417 | =head1 EXAMPLES |
4418 | ||
394e6ffb | 4419 | use Math::BigInt; |
574bacfe JH |
4420 | |
4421 | sub bint { Math::BigInt->new(shift); } | |
4422 | ||
394e6ffb | 4423 | $x = Math::BigInt->bstr("1234") # string "1234" |
58cde26e | 4424 | $x = "$x"; # same as bstr() |
990fb837 RGS |
4425 | $x = Math::BigInt->bneg("1234"); # BigInt "-1234" |
4426 | $x = Math::BigInt->babs("-12345"); # BigInt "12345" | |
7b29e1e6 | 4427 | $x = Math::BigInt->bnorm("-0.00"); # BigInt "0" |
58cde26e JH |
4428 | $x = bint(1) + bint(2); # BigInt "3" |
4429 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") | |
4430 | $x = bint(1); # BigInt "1" | |
4431 | $x = $x + 5 / 2; # BigInt "3" | |
4432 | $x = $x ** 3; # BigInt "27" | |
4433 | $x *= 2; # BigInt "54" | |
394e6ffb | 4434 | $x = Math::BigInt->new(0); # BigInt "0" |
58cde26e JH |
4435 | $x--; # BigInt "-1" |
4436 | $x = Math::BigInt->badd(4,5) # BigInt "9" | |
58cde26e | 4437 | print $x->bsstr(); # 9e+0 |
a5f75d66 | 4438 | |
0716bf9b JH |
4439 | Examples for rounding: |
4440 | ||
4441 | use Math::BigFloat; | |
4442 | use Test; | |
4443 | ||
4444 | $x = Math::BigFloat->new(123.4567); | |
4445 | $y = Math::BigFloat->new(123.456789); | |
394e6ffb | 4446 | Math::BigFloat->accuracy(4); # no more A than 4 |
0716bf9b JH |
4447 | |
4448 | ok ($x->copy()->fround(),123.4); # even rounding | |
4449 | print $x->copy()->fround(),"\n"; # 123.4 | |
4450 | Math::BigFloat->round_mode('odd'); # round to odd | |
4451 | print $x->copy()->fround(),"\n"; # 123.5 | |
394e6ffb | 4452 | Math::BigFloat->accuracy(5); # no more A than 5 |
0716bf9b JH |
4453 | Math::BigFloat->round_mode('odd'); # round to odd |
4454 | print $x->copy()->fround(),"\n"; # 123.46 | |
4455 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 | |
4456 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 | |
4457 | ||
394e6ffb JH |
4458 | Math::BigFloat->accuracy(undef); # A not important now |
4459 | Math::BigFloat->precision(2); # P important | |
4460 | print $x->copy()->bnorm(),"\n"; # 123.46 | |
4461 | print $x->copy()->fround(),"\n"; # 123.46 | |
0716bf9b | 4462 | |
bd05a461 JH |
4463 | Examples for converting: |
4464 | ||
4465 | my $x = Math::BigInt->new('0b1'.'01' x 123); | |
4466 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; | |
4467 | ||
b3ac6de7 IZ |
4468 | =head1 Autocreating constants |
4469 | ||
56b9c951 JH |
4470 | After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal |
4471 | and binary constants in the given scope are converted to C<Math::BigInt>. | |
4472 | This conversion happens at compile time. | |
b3ac6de7 | 4473 | |
b22b3e31 | 4474 | In particular, |
b3ac6de7 | 4475 | |
58cde26e JH |
4476 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
4477 | ||
56b9c951 | 4478 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b | 4479 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e JH |
4480 | |
4481 | Please note that strings and floating point constants are not affected, | |
4482 | so that | |
4483 | ||
4484 | use Math::BigInt qw/:constant/; | |
4485 | ||
4486 | $x = 1234567890123456789012345678901234567890 | |
4487 | + 123456789123456789; | |
b22b3e31 | 4488 | $y = '1234567890123456789012345678901234567890' |
58cde26e | 4489 | + '123456789123456789'; |
b3ac6de7 | 4490 | |
b22b3e31 | 4491 | do not work. You need an explicit Math::BigInt->new() around one of the |
394e6ffb JH |
4492 | operands. You should also quote large constants to protect loss of precision: |
4493 | ||
990fb837 | 4494 | use Math::BigInt; |
394e6ffb JH |
4495 | |
4496 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); | |
4497 | ||
4498 | Without the quotes Perl would convert the large number to a floating point | |
4499 | constant at compile time and then hand the result to BigInt, which results in | |
4500 | an truncated result or a NaN. | |
58cde26e | 4501 | |
56b9c951 JH |
4502 | This also applies to integers that look like floating point constants: |
4503 | ||
4504 | use Math::BigInt ':constant'; | |
4505 | ||
4506 | print ref(123e2),"\n"; | |
4507 | print ref(123.2e2),"\n"; | |
4508 | ||
4509 | will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat> | |
4510 | to get this to work. | |
4511 | ||
58cde26e JH |
4512 | =head1 PERFORMANCE |
4513 | ||
4514 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x | |
4515 | must be made in the second case. For long numbers, the copy can eat up to 20% | |
b22b3e31 | 4516 | of the work (in the case of addition/subtraction, less for |
58cde26e JH |
4517 | multiplication/division). If $y is very small compared to $x, the form |
4518 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes | |
4519 | more time then the actual addition. | |
4520 | ||
b22b3e31 | 4521 | With a technique called copy-on-write, the cost of copying with overload could |
394e6ffb JH |
4522 | be minimized or even completely avoided. A test implementation of COW did show |
4523 | performance gains for overloaded math, but introduced a performance loss due | |
3c4b39be | 4524 | to a constant overhead for all other operations. So Math::BigInt does currently |
091c87b1 | 4525 | not COW. |
394e6ffb | 4526 | |
091c87b1 T |
4527 | The rewritten version of this module (vs. v0.01) is slower on certain |
4528 | operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it | |
4529 | does now more work and handles much more cases. The time spent in these | |
4530 | operations is usually gained in the other math operations so that code on | |
4531 | the average should get (much) faster. If they don't, please contact the author. | |
58cde26e | 4532 | |
394e6ffb | 4533 | Some operations may be slower for small numbers, but are significantly faster |
091c87b1 T |
4534 | for big numbers. Other operations are now constant (O(1), like C<bneg()>, |
4535 | C<babs()> etc), instead of O(N) and thus nearly always take much less time. | |
4536 | These optimizations were done on purpose. | |
58cde26e | 4537 | |
574bacfe JH |
4538 | If you find the Calc module to slow, try to install any of the replacement |
4539 | modules and see if they help you. | |
b3ac6de7 | 4540 | |
574bacfe | 4541 | =head2 Alternative math libraries |
0716bf9b JH |
4542 | |
4543 | You can use an alternative library to drive Math::BigInt via: | |
4544 | ||
4545 | use Math::BigInt lib => 'Module'; | |
4546 | ||
394e6ffb | 4547 | See L<MATH LIBRARY> for more information. |
0716bf9b | 4548 | |
394e6ffb | 4549 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. |
574bacfe | 4550 | |
b3abae2a JH |
4551 | =head2 SUBCLASSING |
4552 | ||
4553 | =head1 Subclassing Math::BigInt | |
4554 | ||
4555 | The basic design of Math::BigInt allows simple subclasses with very little | |
4556 | work, as long as a few simple rules are followed: | |
4557 | ||
4558 | =over 2 | |
4559 | ||
4560 | =item * | |
4561 | ||
4562 | The public API must remain consistent, i.e. if a sub-class is overloading | |
4563 | addition, the sub-class must use the same name, in this case badd(). The | |
4564 | reason for this is that Math::BigInt is optimized to call the object methods | |
4565 | directly. | |
4566 | ||
4567 | =item * | |
4568 | ||
4569 | The private object hash keys like C<$x->{sign}> may not be changed, but | |
4570 | additional keys can be added, like C<$x->{_custom}>. | |
4571 | ||
4572 | =item * | |
4573 | ||
4574 | Accessor functions are available for all existing object hash keys and should | |
4575 | be used instead of directly accessing the internal hash keys. The reason for | |
4576 | this is that Math::BigInt itself has a pluggable interface which permits it | |
4577 | to support different storage methods. | |
4578 | ||
4579 | =back | |
4580 | ||
4581 | More complex sub-classes may have to replicate more of the logic internal of | |
4582 | Math::BigInt if they need to change more basic behaviors. A subclass that | |
4583 | needs to merely change the output only needs to overload C<bstr()>. | |
4584 | ||
4585 | All other object methods and overloaded functions can be directly inherited | |
4586 | from the parent class. | |
4587 | ||
86b76201 | 4588 | At the very minimum, any subclass will need to provide its own C<new()> and can |
b3abae2a JH |
4589 | store additional hash keys in the object. There are also some package globals |
4590 | that must be defined, e.g.: | |
4591 | ||
4592 | # Globals | |
4593 | $accuracy = undef; | |
4594 | $precision = -2; # round to 2 decimal places | |
4595 | $round_mode = 'even'; | |
4596 | $div_scale = 40; | |
4597 | ||
4598 | Additionally, you might want to provide the following two globals to allow | |
4599 | auto-upgrading and auto-downgrading to work correctly: | |
4600 | ||
4601 | $upgrade = undef; | |
4602 | $downgrade = undef; | |
4603 | ||
4604 | This allows Math::BigInt to correctly retrieve package globals from the | |
4605 | subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or | |
4606 | t/Math/BigFloat/SubClass.pm completely functional subclass examples. | |
4607 | ||
4608 | Don't forget to | |
4609 | ||
4610 | use overload; | |
4611 | ||
4612 | in your subclass to automatically inherit the overloading from the parent. If | |
4613 | you like, you can change part of the overloading, look at Math::String for an | |
4614 | example. | |
4615 | ||
4616 | =head1 UPGRADING | |
4617 | ||
4618 | When used like this: | |
4619 | ||
4620 | use Math::BigInt upgrade => 'Foo::Bar'; | |
4621 | ||
4622 | certain operations will 'upgrade' their calculation and thus the result to | |
4623 | the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat: | |
4624 | ||
4625 | use Math::BigInt upgrade => 'Math::BigFloat'; | |
4626 | ||
4627 | As a shortcut, you can use the module C<bignum>: | |
4628 | ||
4629 | use bignum; | |
4630 | ||
4631 | Also good for oneliners: | |
4632 | ||
4633 | perl -Mbignum -le 'print 2 ** 255' | |
4634 | ||
4635 | This makes it possible to mix arguments of different classes (as in 2.5 + 2) | |
4636 | as well es preserve accuracy (as in sqrt(3)). | |
4637 | ||
4638 | Beware: This feature is not fully implemented yet. | |
4639 | ||
4640 | =head2 Auto-upgrade | |
4641 | ||
4642 | The following methods upgrade themselves unconditionally; that is if upgrade | |
4643 | is in effect, they will always hand up their work: | |
4644 | ||
4645 | =over 2 | |
4646 | ||
4647 | =item bsqrt() | |
4648 | ||
4649 | =item div() | |
4650 | ||
4651 | =item blog() | |
4652 | ||
7d193e39 T |
4653 | =item bexp() |
4654 | ||
b3abae2a JH |
4655 | =back |
4656 | ||
4657 | Beware: This list is not complete. | |
4658 | ||
4659 | All other methods upgrade themselves only when one (or all) of their | |
4660 | arguments are of the class mentioned in $upgrade (This might change in later | |
4661 | versions to a more sophisticated scheme): | |
4662 | ||
fdb4b05f T |
4663 | =head1 EXPORTS |
4664 | ||
4665 | C<Math::BigInt> exports nothing by default, but can export the following methods: | |
4666 | ||
4667 | bgcd | |
4668 | blcm | |
4669 | ||
58cde26e JH |
4670 | =head1 CAVEATS |
4671 | ||
4672 | Some things might not work as you expect them. Below is documented what is | |
4673 | known to be troublesome: | |
4674 | ||
4675 | =over 1 | |
4676 | ||
091c87b1 | 4677 | =item bstr(), bsstr() and 'cmp' |
58cde26e | 4678 | |
091c87b1 T |
4679 | Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now |
4680 | drop the leading '+'. The old code would return '+3', the new returns '3'. | |
4681 | This is to be consistent with Perl and to make C<cmp> (especially with | |
4682 | overloading) to work as you expect. It also solves problems with C<Test.pm>, | |
86b76201 | 4683 | because its C<ok()> uses 'eq' internally. |
58cde26e | 4684 | |
091c87b1 T |
4685 | Mark Biggar said, when asked about to drop the '+' altogether, or make only |
4686 | C<cmp> work: | |
58cde26e JH |
4687 | |
4688 | I agree (with the first alternative), don't add the '+' on positive | |
4689 | numbers. It's not as important anymore with the new internal | |
4690 | form for numbers. It made doing things like abs and neg easier, | |
4691 | but those have to be done differently now anyway. | |
4692 | ||
4693 | So, the following examples will now work all as expected: | |
4694 | ||
4695 | use Test; | |
4696 | BEGIN { plan tests => 1 } | |
4697 | use Math::BigInt; | |
4698 | ||
4699 | my $x = new Math::BigInt 3*3; | |
4700 | my $y = new Math::BigInt 3*3; | |
4701 | ||
4702 | ok ($x,3*3); | |
4703 | print "$x eq 9" if $x eq $y; | |
4704 | print "$x eq 9" if $x eq '9'; | |
4705 | print "$x eq 9" if $x eq 3*3; | |
4706 | ||
4707 | Additionally, the following still works: | |
4708 | ||
4709 | print "$x == 9" if $x == $y; | |
4710 | print "$x == 9" if $x == 9; | |
4711 | print "$x == 9" if $x == 3*3; | |
4712 | ||
4713 | There is now a C<bsstr()> method to get the string in scientific notation aka | |
4714 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() | |
3c4b39be | 4715 | for comparison, but Perl will represent some numbers as 100 and others |
091c87b1 T |
4716 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before |
4717 | comparing them as strings: | |
58cde26e JH |
4718 | |
4719 | use Test; | |
4720 | BEGIN { plan tests => 3 } | |
4721 | use Math::BigInt; | |
4722 | ||
4723 | $x = Math::BigInt->new('1e56'); $y = 1e56; | |
4724 | ok ($x,$y); # will fail | |
4725 | ok ($x->bsstr(),$y); # okay | |
4726 | $y = Math::BigInt->new($y); | |
4727 | ok ($x,$y); # okay | |
4728 | ||
3c4b39be | 4729 | Alternatively, simple use C<< <=> >> for comparisons, this will get it |
091c87b1 T |
4730 | always right. There is not yet a way to get a number automatically represented |
4731 | as a string that matches exactly the way Perl represents it. | |
574bacfe | 4732 | |
b68b7ab1 T |
4733 | See also the section about L<Infinity and Not a Number> for problems in |
4734 | comparing NaNs. | |
4735 | ||
58cde26e JH |
4736 | =item int() |
4737 | ||
4738 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a | |
4739 | Perl scalar: | |
4740 | ||
4741 | $x = Math::BigInt->new(123); | |
4742 | $y = int($x); # BigInt 123 | |
4743 | $x = Math::BigFloat->new(123.45); | |
4744 | $y = int($x); # BigInt 123 | |
4745 | ||
b68b7ab1 T |
4746 | In all Perl versions you can use C<as_number()> or C<as_int> for the same |
4747 | effect: | |
58cde26e JH |
4748 | |
4749 | $x = Math::BigFloat->new(123.45); | |
4750 | $y = $x->as_number(); # BigInt 123 | |
b68b7ab1 | 4751 | $y = $x->as_int(); # ditto |
58cde26e JH |
4752 | |
4753 | This also works for other subclasses, like Math::String. | |
4754 | ||
b68b7ab1 T |
4755 | If you want a real Perl scalar, use C<numify()>: |
4756 | ||
4757 | $y = $x->numify(); # 123 as scalar | |
4758 | ||
4759 | This is seldom necessary, though, because this is done automatically, like | |
4760 | when you access an array: | |
4761 | ||
4762 | $z = $array[$x]; # does work automatically | |
4763 | ||
dccbb853 | 4764 | =item length |
58cde26e JH |
4765 | |
4766 | The following will probably not do what you expect: | |
4767 | ||
bd05a461 JH |
4768 | $c = Math::BigInt->new(123); |
4769 | print $c->length(),"\n"; # prints 30 | |
4770 | ||
4771 | It prints both the number of digits in the number and in the fraction part | |
4772 | since print calls C<length()> in list context. Use something like: | |
4773 | ||
4774 | print scalar $c->length(),"\n"; # prints 3 | |
4775 | ||
4776 | =item bdiv | |
4777 | ||
4778 | The following will probably not do what you expect: | |
4779 | ||
58cde26e JH |
4780 | print $c->bdiv(10000),"\n"; |
4781 | ||
dccbb853 | 4782 | It prints both quotient and remainder since print calls C<bdiv()> in list |
3c4b39be | 4783 | context. Also, C<bdiv()> will modify $c, so be careful. You probably want |
58cde26e JH |
4784 | to use |
4785 | ||
4786 | print $c / 10000,"\n"; | |
4787 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c | |
4788 | ||
4789 | instead. | |
4790 | ||
4791 | The quotient is always the greatest integer less than or equal to the | |
4792 | real-valued quotient of the two operands, and the remainder (when it is | |
4793 | nonzero) always has the same sign as the second operand; so, for | |
4794 | example, | |
4795 | ||
dccbb853 JH |
4796 | 1 / 4 => ( 0, 1) |
4797 | 1 / -4 => (-1,-3) | |
4798 | -3 / 4 => (-1, 1) | |
4799 | -3 / -4 => ( 0,-3) | |
4800 | -11 / 2 => (-5,1) | |
4801 | 11 /-2 => (-5,-1) | |
58cde26e JH |
4802 | |
4803 | As a consequence, the behavior of the operator % agrees with the | |
4804 | behavior of Perl's built-in % operator (as documented in the perlop | |
4805 | manpage), and the equation | |
4806 | ||
4807 | $x == ($x / $y) * $y + ($x % $y) | |
4808 | ||
4809 | holds true for any $x and $y, which justifies calling the two return | |
dccbb853 JH |
4810 | values of bdiv() the quotient and remainder. The only exception to this rule |
4811 | are when $y == 0 and $x is negative, then the remainder will also be | |
3c4b39be | 4812 | negative. See below under "infinity handling" for the reasoning behind this. |
58cde26e JH |
4813 | |
4814 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will | |
4815 | not change BigInt's way to do things. This is because under 'use integer' Perl | |
4816 | will do what the underlying C thinks is right and this is different for each | |
4817 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug | |
4818 | the author to implement it ;) | |
4819 | ||
dccbb853 JH |
4820 | =item infinity handling |
4821 | ||
4822 | Here are some examples that explain the reasons why certain results occur while | |
4823 | handling infinity: | |
4824 | ||
4825 | The following table shows the result of the division and the remainder, so that | |
4826 | the equation above holds true. Some "ordinary" cases are strewn in to show more | |
4827 | clearly the reasoning: | |
4828 | ||
4829 | A / B = C, R so that C * B + R = A | |
4830 | ========================================================= | |
4831 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 | |
4832 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 | |
4833 | 0 / inf = 0, 0 0 * inf + 0 = 0 | |
4834 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 | |
4835 | 5 / inf = 0, 5 0 * inf + 5 = 5 | |
4836 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 | |
4837 | -5/ inf = 0, -5 0 * inf + -5 = -5 | |
4838 | -5/-inf = 0, -5 0 * -inf + -5 = -5 | |
4839 | inf/ 5 = inf, 0 inf * 5 + 0 = inf | |
4840 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf | |
4841 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf | |
4842 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf | |
4843 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 | |
4844 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 | |
4845 | inf/ inf = 1, 0 1 * inf + 0 = inf | |
4846 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf | |
4847 | inf/-inf = -1, 0 -1 * -inf + 0 = inf | |
4848 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf | |
4849 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 | |
4850 | inf/ 0 = inf, inf inf * 0 + inf = inf | |
4851 | 0/ 0 = NaN | |
4852 | ||
4853 | These cases below violate the "remainder has the sign of the second of the two | |
4854 | arguments", since they wouldn't match up otherwise. | |
4855 | ||
4856 | A / B = C, R so that C * B + R = A | |
4857 | ======================================================== | |
4858 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf | |
4859 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 | |
4860 | ||
58cde26e JH |
4861 | =item Modifying and = |
4862 | ||
4863 | Beware of: | |
4864 | ||
4865 | $x = Math::BigFloat->new(5); | |
4866 | $y = $x; | |
4867 | ||
4868 | It will not do what you think, e.g. making a copy of $x. Instead it just makes | |
4869 | a second reference to the B<same> object and stores it in $y. Thus anything | |
17baacb7 JH |
4870 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
4871 | Or in other words, C<=> is only safe if you modify your BigInts only via | |
4872 | overloaded math. As soon as you use a method call it breaks: | |
58cde26e JH |
4873 | |
4874 | $x->bmul(2); | |
4875 | print "$x, $y\n"; # prints '10, 10' | |
4876 | ||
4877 | If you want a true copy of $x, use: | |
4878 | ||
4879 | $y = $x->copy(); | |
4880 | ||
17baacb7 JH |
4881 | You can also chain the calls like this, this will make first a copy and then |
4882 | multiply it by 2: | |
4883 | ||
4884 | $y = $x->copy()->bmul(2); | |
4885 | ||
b22b3e31 | 4886 | See also the documentation for overload.pm regarding C<=>. |
58cde26e JH |
4887 | |
4888 | =item bpow | |
4889 | ||
4890 | C<bpow()> (and the rounding functions) now modifies the first argument and | |
574bacfe | 4891 | returns it, unlike the old code which left it alone and only returned the |
58cde26e JH |
4892 | result. This is to be consistent with C<badd()> etc. The first three will |
4893 | modify $x, the last one won't: | |
4894 | ||
4895 | print bpow($x,$i),"\n"; # modify $x | |
4896 | print $x->bpow($i),"\n"; # ditto | |
4897 | print $x **= $i,"\n"; # the same | |
4898 | print $x ** $i,"\n"; # leave $x alone | |
4899 | ||
4900 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. | |
4901 | ||
4902 | =item Overloading -$x | |
4903 | ||
4904 | The following: | |
4905 | ||
4906 | $x = -$x; | |
4907 | ||
4908 | is slower than | |
4909 | ||
4910 | $x->bneg(); | |
4911 | ||
4912 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant | |
4913 | needs to preserve $x since it does not know that it later will get overwritten. | |
0716bf9b | 4914 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e | 4915 | |
58cde26e JH |
4916 | =item Mixing different object types |
4917 | ||
4918 | In Perl you will get a floating point value if you do one of the following: | |
4919 | ||
4920 | $float = 5.0 + 2; | |
4921 | $float = 2 + 5.0; | |
4922 | $float = 5 / 2; | |
4923 | ||
4924 | With overloaded math, only the first two variants will result in a BigFloat: | |
4925 | ||
4926 | use Math::BigInt; | |
4927 | use Math::BigFloat; | |
4928 | ||
4929 | $mbf = Math::BigFloat->new(5); | |
4930 | $mbi2 = Math::BigInteger->new(5); | |
4931 | $mbi = Math::BigInteger->new(2); | |
4932 | ||
4933 | # what actually gets called: | |
4934 | $float = $mbf + $mbi; # $mbf->badd() | |
4935 | $float = $mbf / $mbi; # $mbf->bdiv() | |
4936 | $integer = $mbi + $mbf; # $mbi->badd() | |
4937 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() | |
4938 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() | |
4939 | ||
4940 | This is because math with overloaded operators follows the first (dominating) | |
394e6ffb | 4941 | operand, and the operation of that is called and returns thus the result. So, |
58cde26e JH |
4942 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
4943 | the result should be a Math::BigFloat or the second operant is one. | |
4944 | ||
4945 | To get a Math::BigFloat you either need to call the operation manually, | |
4946 | make sure the operands are already of the proper type or casted to that type | |
4947 | via Math::BigFloat->new(): | |
4948 | ||
4949 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 | |
4950 | ||
4951 | Beware of simple "casting" the entire expression, this would only convert | |
4952 | the already computed result: | |
4953 | ||
4954 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! | |
4955 | ||
0716bf9b | 4956 | Beware also of the order of more complicated expressions like: |
58cde26e JH |
4957 | |
4958 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int | |
4959 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto | |
4960 | ||
4961 | If in doubt, break the expression into simpler terms, or cast all operands | |
4962 | to the desired resulting type. | |
4963 | ||
4964 | Scalar values are a bit different, since: | |
4965 | ||
4966 | $float = 2 + $mbf; | |
4967 | $float = $mbf + 2; | |
4968 | ||
4969 | will both result in the proper type due to the way the overloaded math works. | |
4970 | ||
4971 | This section also applies to other overloaded math packages, like Math::String. | |
4972 | ||
990fb837 RGS |
4973 | One solution to you problem might be autoupgrading|upgrading. See the |
4974 | pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this. | |
b3abae2a | 4975 | |
58cde26e JH |
4976 | =item bsqrt() |
4977 | ||
394e6ffb | 4978 | C<bsqrt()> works only good if the result is a big integer, e.g. the square |
58cde26e | 4979 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
990fb837 | 4980 | mode. The reason is that the result is always truncated to an integer. |
58cde26e JH |
4981 | |
4982 | If you want a better approximation of the square root, then use: | |
4983 | ||
4984 | $x = Math::BigFloat->new(12); | |
394e6ffb | 4985 | Math::BigFloat->precision(0); |
58cde26e JH |
4986 | Math::BigFloat->round_mode('even'); |
4987 | print $x->copy->bsqrt(),"\n"; # 4 | |
4988 | ||
394e6ffb | 4989 | Math::BigFloat->precision(2); |
58cde26e JH |
4990 | print $x->bsqrt(),"\n"; # 3.46 |
4991 | print $x->bsqrt(3),"\n"; # 3.464 | |
4992 | ||
b3abae2a JH |
4993 | =item brsft() |
4994 | ||
4995 | For negative numbers in base see also L<brsft|brsft>. | |
4996 | ||
58cde26e JH |
4997 | =back |
4998 | ||
4999 | =head1 LICENSE | |
5000 | ||
5001 | This program is free software; you may redistribute it and/or modify it under | |
5002 | the same terms as Perl itself. | |
a5f75d66 | 5003 | |
0716bf9b JH |
5004 | =head1 SEE ALSO |
5005 | ||
990fb837 RGS |
5006 | L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as |
5007 | L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
5008 | ||
5009 | The pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest | |
5010 | because they solve the autoupgrading/downgrading issue, at least partly. | |
0716bf9b | 5011 | |
027dc388 JH |
5012 | The package at |
5013 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains | |
5014 | more documentation including a full version history, testcases, empty | |
5015 | subclass files and benchmarks. | |
574bacfe | 5016 | |
58cde26e | 5017 | =head1 AUTHORS |
a5f75d66 | 5018 | |
58cde26e | 5019 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
7b29e1e6 T |
5020 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2006 |
5021 | and still at it in 2007. | |
990fb837 RGS |
5022 | |
5023 | Many people contributed in one or more ways to the final beast, see the file | |
3c4b39be | 5024 | CREDITS for an (incomplete) list. If you miss your name, please drop me a |
990fb837 | 5025 | mail. Thank you! |
a5f75d66 AD |
5026 | |
5027 | =cut |