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 | |
0dceeee6 | 21 | $VERSION = '1.89'; |
b68b7ab1 | 22 | |
233f7bc0 T |
23 | @ISA = qw(Exporter); |
24 | @EXPORT_OK = qw(objectify bgcd blcm); | |
b68b7ab1 | 25 | |
b282a552 T |
26 | # _trap_inf and _trap_nan are internal and should never be accessed from the |
27 | # outside | |
28 | use vars qw/$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 || $a <= 0) | |
292 | { | |
293 | require Carp; | |
d5351619 | 294 | Carp::croak ('Argument to accuracy must be greater than zero'); |
990fb837 RGS |
295 | } |
296 | if (int($a) != $a) | |
297 | { | |
d5351619 T |
298 | require Carp; |
299 | Carp::croak ('Argument to accuracy must be an integer'); | |
990fb837 RGS |
300 | } |
301 | } | |
ee15d750 JH |
302 | if (ref($x)) |
303 | { | |
304 | # $object->accuracy() or fallback to global | |
ef9466ea T |
305 | $x->bround($a) if $a; # not for undef, 0 |
306 | $x->{_a} = $a; # set/overwrite, even if not rounded | |
307 | delete $x->{_p}; # clear P | |
990fb837 | 308 | $a = ${"${class}::accuracy"} unless defined $a; # proper return value |
ee15d750 JH |
309 | } |
310 | else | |
311 | { | |
ef9466ea T |
312 | ${"${class}::accuracy"} = $a; # set global A |
313 | ${"${class}::precision"} = undef; # clear global P | |
ee15d750 | 314 | } |
ef9466ea | 315 | return $a; # shortcut |
ee15d750 JH |
316 | } |
317 | ||
b68b7ab1 | 318 | my $a; |
f9a08e12 | 319 | # $object->accuracy() or fallback to global |
b68b7ab1 | 320 | $a = $x->{_a} if ref($x); |
f9a08e12 | 321 | # but don't return global undef, when $x's accuracy is 0! |
b68b7ab1 T |
322 | $a = ${"${class}::accuracy"} if !defined $a; |
323 | $a; | |
990fb837 | 324 | } |
58cde26e JH |
325 | |
326 | sub precision | |
327 | { | |
ee15d750 JH |
328 | # $x->precision($p); ref($x) $p |
329 | # $x->precision(); ref($x) | |
330 | # Class->precision(); class | |
331 | # Class->precision($p); class $p | |
58cde26e | 332 | |
ee15d750 JH |
333 | my $x = shift; |
334 | my $class = ref($x) || $x || __PACKAGE__; | |
58cde26e | 335 | |
ee15d750 | 336 | no strict 'refs'; |
58cde26e JH |
337 | if (@_ > 0) |
338 | { | |
ee15d750 | 339 | my $p = shift; |
990fb837 RGS |
340 | # convert objects to scalars to avoid deep recursion. If object doesn't |
341 | # have numify(), then hopefully it will have overloading for int() and | |
342 | # boolean test without wandering into a deep recursion path... | |
343 | $p = $p->numify() if ref($p) && $p->can('numify'); | |
344 | if ((defined $p) && (int($p) != $p)) | |
345 | { | |
346 | require Carp; Carp::croak ('Argument to precision must be an integer'); | |
347 | } | |
ee15d750 JH |
348 | if (ref($x)) |
349 | { | |
350 | # $object->precision() or fallback to global | |
ef9466ea T |
351 | $x->bfround($p) if $p; # not for undef, 0 |
352 | $x->{_p} = $p; # set/overwrite, even if not rounded | |
353 | delete $x->{_a}; # clear A | |
990fb837 | 354 | $p = ${"${class}::precision"} unless defined $p; # proper return value |
ee15d750 JH |
355 | } |
356 | else | |
357 | { | |
ef9466ea T |
358 | ${"${class}::precision"} = $p; # set global P |
359 | ${"${class}::accuracy"} = undef; # clear global A | |
ee15d750 | 360 | } |
ef9466ea | 361 | return $p; # shortcut |
58cde26e | 362 | } |
ee15d750 | 363 | |
b68b7ab1 | 364 | my $p; |
f9a08e12 | 365 | # $object->precision() or fallback to global |
b68b7ab1 | 366 | $p = $x->{_p} if ref($x); |
f9a08e12 | 367 | # but don't return global undef, when $x's precision is 0! |
b68b7ab1 T |
368 | $p = ${"${class}::precision"} if !defined $p; |
369 | $p; | |
990fb837 | 370 | } |
58cde26e | 371 | |
b3abae2a JH |
372 | sub config |
373 | { | |
990fb837 | 374 | # return (or set) configuration data as hash ref |
b3abae2a JH |
375 | my $class = shift || 'Math::BigInt'; |
376 | ||
377 | no strict 'refs'; | |
2ebb273f | 378 | if (@_ > 1 || (@_ == 1 && (ref($_[0]) eq 'HASH'))) |
990fb837 RGS |
379 | { |
380 | # try to set given options as arguments from hash | |
381 | ||
382 | my $args = $_[0]; | |
383 | if (ref($args) ne 'HASH') | |
384 | { | |
385 | $args = { @_ }; | |
386 | } | |
387 | # these values can be "set" | |
388 | my $set_args = {}; | |
389 | foreach my $key ( | |
390 | qw/trap_inf trap_nan | |
391 | upgrade downgrade precision accuracy round_mode div_scale/ | |
392 | ) | |
393 | { | |
394 | $set_args->{$key} = $args->{$key} if exists $args->{$key}; | |
395 | delete $args->{$key}; | |
396 | } | |
397 | if (keys %$args > 0) | |
398 | { | |
399 | require Carp; | |
400 | Carp::croak ("Illegal key(s) '", | |
401 | join("','",keys %$args),"' passed to $class\->config()"); | |
402 | } | |
403 | foreach my $key (keys %$set_args) | |
404 | { | |
405 | if ($key =~ /^trap_(inf|nan)\z/) | |
406 | { | |
407 | ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0); | |
408 | next; | |
409 | } | |
410 | # use a call instead of just setting the $variable to check argument | |
411 | $class->$key($set_args->{$key}); | |
412 | } | |
413 | } | |
414 | ||
415 | # now return actual configuration | |
416 | ||
b3abae2a | 417 | my $cfg = { |
990fb837 RGS |
418 | lib => $CALC, |
419 | lib_version => ${"${CALC}::VERSION"}, | |
b3abae2a | 420 | class => $class, |
990fb837 RGS |
421 | trap_nan => ${"${class}::_trap_nan"}, |
422 | trap_inf => ${"${class}::_trap_inf"}, | |
423 | version => ${"${class}::VERSION"}, | |
b3abae2a | 424 | }; |
990fb837 RGS |
425 | foreach my $key (qw/ |
426 | upgrade downgrade precision accuracy round_mode div_scale | |
427 | /) | |
b3abae2a | 428 | { |
990fb837 | 429 | $cfg->{$key} = ${"${class}::$key"}; |
b3abae2a | 430 | }; |
2ebb273f T |
431 | if (@_ == 1 && (ref($_[0]) ne 'HASH')) |
432 | { | |
433 | # calls of the style config('lib') return just this value | |
434 | return $cfg->{$_[0]}; | |
435 | } | |
b3abae2a JH |
436 | $cfg; |
437 | } | |
438 | ||
58cde26e JH |
439 | sub _scale_a |
440 | { | |
441 | # select accuracy parameter based on precedence, | |
442 | # used by bround() and bfround(), may return undef for scale (means no op) | |
b68b7ab1 T |
443 | my ($x,$scale,$mode) = @_; |
444 | ||
445 | $scale = $x->{_a} unless defined $scale; | |
446 | ||
447 | no strict 'refs'; | |
448 | my $class = ref($x); | |
449 | ||
450 | $scale = ${ $class . '::accuracy' } unless defined $scale; | |
451 | $mode = ${ $class . '::round_mode' } unless defined $mode; | |
452 | ||
d5351619 T |
453 | if (defined $scale) |
454 | { | |
455 | $scale = $scale->can('numify') ? $scale->numify() : "$scale" if ref($scale); | |
456 | $scale = int($scale); | |
457 | } | |
458 | ||
b68b7ab1 | 459 | ($scale,$mode); |
58cde26e JH |
460 | } |
461 | ||
462 | sub _scale_p | |
463 | { | |
464 | # select precision parameter based on precedence, | |
465 | # used by bround() and bfround(), may return undef for scale (means no op) | |
b68b7ab1 T |
466 | my ($x,$scale,$mode) = @_; |
467 | ||
468 | $scale = $x->{_p} unless defined $scale; | |
469 | ||
470 | no strict 'refs'; | |
471 | my $class = ref($x); | |
472 | ||
473 | $scale = ${ $class . '::precision' } unless defined $scale; | |
474 | $mode = ${ $class . '::round_mode' } unless defined $mode; | |
475 | ||
d5351619 T |
476 | if (defined $scale) |
477 | { | |
478 | $scale = $scale->can('numify') ? $scale->numify() : "$scale" if ref($scale); | |
479 | $scale = int($scale); | |
480 | } | |
481 | ||
b68b7ab1 | 482 | ($scale,$mode); |
58cde26e JH |
483 | } |
484 | ||
485 | ############################################################################## | |
486 | # constructors | |
487 | ||
488 | sub copy | |
489 | { | |
86f0d17a | 490 | # if two arguments, the first one is the class to "swallow" subclasses |
58cde26e JH |
491 | if (@_ > 1) |
492 | { | |
86f0d17a T |
493 | my $self = bless { |
494 | sign => $_[1]->{sign}, | |
495 | value => $CALC->_copy($_[1]->{value}), | |
496 | }, $_[0] if @_ > 1; | |
497 | ||
498 | $self->{_a} = $_[1]->{_a} if defined $_[1]->{_a}; | |
499 | $self->{_p} = $_[1]->{_p} if defined $_[1]->{_p}; | |
500 | return $self; | |
58cde26e | 501 | } |
58cde26e | 502 | |
86f0d17a T |
503 | my $self = bless { |
504 | sign => $_[0]->{sign}, | |
505 | value => $CALC->_copy($_[0]->{value}), | |
506 | }, ref($_[0]); | |
9b924220 | 507 | |
86f0d17a T |
508 | $self->{_a} = $_[0]->{_a} if defined $_[0]->{_a}; |
509 | $self->{_p} = $_[0]->{_p} if defined $_[0]->{_p}; | |
58cde26e JH |
510 | $self; |
511 | } | |
512 | ||
513 | sub new | |
514 | { | |
b22b3e31 | 515 | # create a new BigInt object from a string or another BigInt object. |
0716bf9b | 516 | # see hash keys documented at top |
58cde26e JH |
517 | |
518 | # the argument could be an object, so avoid ||, && etc on it, this would | |
b22b3e31 PN |
519 | # cause costly overloaded code to be called. The only allowed ops are |
520 | # ref() and defined. | |
58cde26e | 521 | |
61f5c3f5 | 522 | my ($class,$wanted,$a,$p,$r) = @_; |
58cde26e | 523 | |
61f5c3f5 T |
524 | # avoid numify-calls by not using || on $wanted! |
525 | return $class->bzero($a,$p) if !defined $wanted; # default to 0 | |
9393ace2 JH |
526 | return $class->copy($wanted,$a,$p,$r) |
527 | if ref($wanted) && $wanted->isa($class); # MBI or subclass | |
58cde26e | 528 | |
61f5c3f5 T |
529 | $class->import() if $IMPORT == 0; # make require work |
530 | ||
9393ace2 JH |
531 | my $self = bless {}, $class; |
532 | ||
533 | # shortcut for "normal" numbers | |
739c8b3a | 534 | if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/)) |
9393ace2 JH |
535 | { |
536 | $self->{sign} = $1 || '+'; | |
9b924220 | 537 | |
9393ace2 JH |
538 | if ($wanted =~ /^[+-]/) |
539 | { | |
56d9de68 | 540 | # remove sign without touching wanted to make it work with constants |
9b924220 RGS |
541 | my $t = $wanted; $t =~ s/^[+-]//; |
542 | $self->{value} = $CALC->_new($t); | |
543 | } | |
544 | else | |
545 | { | |
546 | $self->{value} = $CALC->_new($wanted); | |
9393ace2 | 547 | } |
9393ace2 JH |
548 | no strict 'refs'; |
549 | if ( (defined $a) || (defined $p) | |
550 | || (defined ${"${class}::precision"}) | |
551 | || (defined ${"${class}::accuracy"}) | |
552 | ) | |
553 | { | |
554 | $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p); | |
555 | } | |
556 | return $self; | |
557 | } | |
558 | ||
58cde26e | 559 | # handle '+inf', '-inf' first |
233f7bc0 | 560 | if ($wanted =~ /^[+-]?inf\z/) |
58cde26e | 561 | { |
233f7bc0 T |
562 | $self->{sign} = $wanted; # set a default sign for bstr() |
563 | return $self->binf($wanted); | |
58cde26e JH |
564 | } |
565 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign | |
9b924220 | 566 | my ($mis,$miv,$mfv,$es,$ev) = _split($wanted); |
58cde26e JH |
567 | if (!ref $mis) |
568 | { | |
990fb837 RGS |
569 | if ($_trap_nan) |
570 | { | |
571 | require Carp; Carp::croak("$wanted is not a number in $class"); | |
572 | } | |
0716bf9b | 573 | $self->{value} = $CALC->_zero(); |
58cde26e JH |
574 | $self->{sign} = $nan; |
575 | return $self; | |
576 | } | |
574bacfe JH |
577 | if (!ref $miv) |
578 | { | |
579 | # _from_hex or _from_bin | |
580 | $self->{value} = $mis->{value}; | |
581 | $self->{sign} = $mis->{sign}; | |
582 | return $self; # throw away $mis | |
583 | } | |
58cde26e JH |
584 | # make integer from mantissa by adjusting exp, then convert to bigint |
585 | $self->{sign} = $$mis; # store sign | |
0716bf9b | 586 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
58cde26e JH |
587 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
588 | if ($e > 0) | |
589 | { | |
590 | my $diff = $e - CORE::length($$mfv); | |
591 | if ($diff < 0) # Not integer | |
592 | { | |
990fb837 RGS |
593 | if ($_trap_nan) |
594 | { | |
595 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
596 | } | |
58cde26e | 597 | #print "NOI 1\n"; |
b3abae2a | 598 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
599 | $self->{sign} = $nan; |
600 | } | |
601 | else # diff >= 0 | |
602 | { | |
603 | # adjust fraction and add it to value | |
990fb837 | 604 | #print "diff > 0 $$miv\n"; |
58cde26e JH |
605 | $$miv = $$miv . ($$mfv . '0' x $diff); |
606 | } | |
607 | } | |
608 | else | |
609 | { | |
610 | if ($$mfv ne '') # e <= 0 | |
611 | { | |
612 | # fraction and negative/zero E => NOI | |
990fb837 RGS |
613 | if ($_trap_nan) |
614 | { | |
615 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
616 | } | |
58cde26e | 617 | #print "NOI 2 \$\$mfv '$$mfv'\n"; |
b3abae2a | 618 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
619 | $self->{sign} = $nan; |
620 | } | |
621 | elsif ($e < 0) | |
622 | { | |
623 | # xE-y, and empty mfv | |
624 | #print "xE-y\n"; | |
625 | $e = abs($e); | |
626 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? | |
627 | { | |
990fb837 RGS |
628 | if ($_trap_nan) |
629 | { | |
630 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
631 | } | |
58cde26e | 632 | #print "NOI 3\n"; |
b3abae2a | 633 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
634 | $self->{sign} = $nan; |
635 | } | |
636 | } | |
637 | } | |
638 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 | |
9b924220 | 639 | $self->{value} = $CALC->_new($$miv) if $self->{sign} =~ /^[+-]$/; |
0716bf9b | 640 | # if any of the globals is set, use them to round and store them inside $self |
61f5c3f5 T |
641 | # do not round for new($x,undef,undef) since that is used by MBF to signal |
642 | # no rounding | |
643 | $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p; | |
9393ace2 | 644 | $self; |
58cde26e JH |
645 | } |
646 | ||
58cde26e JH |
647 | sub bnan |
648 | { | |
649 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' | |
b4f14daa | 650 | my $self = shift; |
58cde26e JH |
651 | $self = $class if !defined $self; |
652 | if (!ref($self)) | |
653 | { | |
654 | my $c = $self; $self = {}; bless $self, $c; | |
655 | } | |
990fb837 RGS |
656 | no strict 'refs'; |
657 | if (${"${class}::_trap_nan"}) | |
658 | { | |
659 | require Carp; | |
660 | Carp::croak ("Tried to set $self to NaN in $class\::bnan()"); | |
661 | } | |
61f5c3f5 | 662 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 663 | return if $self->modify('bnan'); |
13a12e00 JH |
664 | if ($self->can('_bnan')) |
665 | { | |
666 | # use subclass to initialize | |
667 | $self->_bnan(); | |
668 | } | |
669 | else | |
670 | { | |
671 | # otherwise do our own thing | |
672 | $self->{value} = $CALC->_zero(); | |
673 | } | |
58cde26e | 674 | $self->{sign} = $nan; |
394e6ffb | 675 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly |
ef9466ea | 676 | $self; |
b4f14daa | 677 | } |
58cde26e JH |
678 | |
679 | sub binf | |
680 | { | |
681 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' | |
682 | # the sign is either '+', or if given, used from there | |
683 | my $self = shift; | |
56b9c951 | 684 | my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/; |
58cde26e JH |
685 | $self = $class if !defined $self; |
686 | if (!ref($self)) | |
687 | { | |
688 | my $c = $self; $self = {}; bless $self, $c; | |
689 | } | |
990fb837 RGS |
690 | no strict 'refs'; |
691 | if (${"${class}::_trap_inf"}) | |
692 | { | |
693 | require Carp; | |
233f7bc0 | 694 | Carp::croak ("Tried to set $self to +-inf in $class\::binf()"); |
990fb837 | 695 | } |
61f5c3f5 | 696 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 697 | return if $self->modify('binf'); |
13a12e00 JH |
698 | if ($self->can('_binf')) |
699 | { | |
700 | # use subclass to initialize | |
701 | $self->_binf(); | |
702 | } | |
703 | else | |
704 | { | |
705 | # otherwise do our own thing | |
706 | $self->{value} = $CALC->_zero(); | |
707 | } | |
56b9c951 JH |
708 | $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf |
709 | $self->{sign} = $sign; | |
394e6ffb | 710 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
ef9466ea | 711 | $self; |
58cde26e JH |
712 | } |
713 | ||
714 | sub bzero | |
715 | { | |
716 | # create a bigint '+0', if given a BigInt, set it to 0 | |
717 | my $self = shift; | |
12fc2493 | 718 | $self = __PACKAGE__ if !defined $self; |
0716bf9b | 719 | |
58cde26e JH |
720 | if (!ref($self)) |
721 | { | |
722 | my $c = $self; $self = {}; bless $self, $c; | |
723 | } | |
61f5c3f5 | 724 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 725 | return if $self->modify('bzero'); |
990fb837 | 726 | |
13a12e00 JH |
727 | if ($self->can('_bzero')) |
728 | { | |
729 | # use subclass to initialize | |
730 | $self->_bzero(); | |
731 | } | |
732 | else | |
733 | { | |
734 | # otherwise do our own thing | |
735 | $self->{value} = $CALC->_zero(); | |
736 | } | |
58cde26e | 737 | $self->{sign} = '+'; |
61f5c3f5 T |
738 | if (@_ > 0) |
739 | { | |
f9a08e12 JH |
740 | if (@_ > 3) |
741 | { | |
742 | # call like: $x->bzero($a,$p,$r,$y); | |
743 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); | |
744 | } | |
745 | else | |
746 | { | |
747 | $self->{_a} = $_[0] | |
748 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); | |
749 | $self->{_p} = $_[1] | |
750 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); | |
751 | } | |
61f5c3f5 | 752 | } |
f9a08e12 | 753 | $self; |
58cde26e JH |
754 | } |
755 | ||
574bacfe JH |
756 | sub bone |
757 | { | |
758 | # create a bigint '+1' (or -1 if given sign '-'), | |
3c4b39be | 759 | # if given a BigInt, set it to +1 or -1, respectively |
574bacfe JH |
760 | my $self = shift; |
761 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; | |
762 | $self = $class if !defined $self; | |
990fb837 | 763 | |
574bacfe JH |
764 | if (!ref($self)) |
765 | { | |
766 | my $c = $self; $self = {}; bless $self, $c; | |
767 | } | |
61f5c3f5 | 768 | $self->import() if $IMPORT == 0; # make require work |
574bacfe | 769 | return if $self->modify('bone'); |
13a12e00 JH |
770 | |
771 | if ($self->can('_bone')) | |
772 | { | |
773 | # use subclass to initialize | |
774 | $self->_bone(); | |
775 | } | |
776 | else | |
777 | { | |
778 | # otherwise do our own thing | |
779 | $self->{value} = $CALC->_one(); | |
780 | } | |
574bacfe | 781 | $self->{sign} = $sign; |
61f5c3f5 T |
782 | if (@_ > 0) |
783 | { | |
f9a08e12 JH |
784 | if (@_ > 3) |
785 | { | |
786 | # call like: $x->bone($sign,$a,$p,$r,$y); | |
787 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); | |
788 | } | |
789 | else | |
790 | { | |
091c87b1 | 791 | # call like: $x->bone($sign,$a,$p,$r); |
f9a08e12 JH |
792 | $self->{_a} = $_[0] |
793 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); | |
794 | $self->{_p} = $_[1] | |
795 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); | |
796 | } | |
61f5c3f5 | 797 | } |
f9a08e12 | 798 | $self; |
574bacfe JH |
799 | } |
800 | ||
58cde26e JH |
801 | ############################################################################## |
802 | # string conversation | |
803 | ||
804 | sub bsstr | |
805 | { | |
806 | # (ref to BFLOAT or num_str ) return num_str | |
807 | # Convert number from internal format to scientific string format. | |
808 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") | |
b68b7ab1 | 809 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e | 810 | |
574bacfe JH |
811 | if ($x->{sign} !~ /^[+-]$/) |
812 | { | |
813 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
814 | return 'inf'; # +inf | |
815 | } | |
58cde26e | 816 | my ($m,$e) = $x->parts(); |
b282a552 T |
817 | #$m->bstr() . 'e+' . $e->bstr(); # e can only be positive in BigInt |
818 | # 'e+' because E can only be positive in BigInt | |
9b924220 | 819 | $m->bstr() . 'e+' . $CALC->_str($e->{value}); |
58cde26e JH |
820 | } |
821 | ||
822 | sub bstr | |
823 | { | |
0716bf9b | 824 | # make a string from bigint object |
b68b7ab1 | 825 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
56b9c951 | 826 | |
574bacfe JH |
827 | if ($x->{sign} !~ /^[+-]$/) |
828 | { | |
829 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
830 | return 'inf'; # +inf | |
831 | } | |
0716bf9b | 832 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 833 | $es.$CALC->_str($x->{value}); |
58cde26e JH |
834 | } |
835 | ||
836 | sub numify | |
837 | { | |
394e6ffb | 838 | # Make a "normal" scalar from a BigInt object |
58cde26e | 839 | my $x = shift; $x = $class->new($x) unless ref $x; |
56d9de68 T |
840 | |
841 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; | |
0716bf9b JH |
842 | my $num = $CALC->_num($x->{value}); |
843 | return -$num if $x->{sign} eq '-'; | |
9393ace2 | 844 | $num; |
58cde26e JH |
845 | } |
846 | ||
847 | ############################################################################## | |
848 | # public stuff (usually prefixed with "b") | |
849 | ||
850 | sub sign | |
851 | { | |
9393ace2 | 852 | # return the sign of the number: +/-/-inf/+inf/NaN |
b282a552 | 853 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 854 | |
9393ace2 | 855 | $x->{sign}; |
58cde26e JH |
856 | } |
857 | ||
ee15d750 | 858 | sub _find_round_parameters |
58cde26e JH |
859 | { |
860 | # After any operation or when calling round(), the result is rounded by | |
861 | # regarding the A & P from arguments, local parameters, or globals. | |
61f5c3f5 | 862 | |
990fb837 RGS |
863 | # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!! |
864 | ||
61f5c3f5 T |
865 | # This procedure finds the round parameters, but it is for speed reasons |
866 | # duplicated in round. Otherwise, it is tested by the testsuite and used | |
867 | # by fdiv(). | |
990fb837 RGS |
868 | |
869 | # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P | |
870 | # were requested/defined (locally or globally or both) | |
61f5c3f5 | 871 | |
394e6ffb JH |
872 | my ($self,$a,$p,$r,@args) = @_; |
873 | # $a accuracy, if given by caller | |
874 | # $p precision, if given by caller | |
875 | # $r round_mode, if given by caller | |
876 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
58cde26e | 877 | |
394e6ffb | 878 | my $c = ref($self); # find out class of argument(s) |
574bacfe | 879 | no strict 'refs'; |
574bacfe | 880 | |
86b76201 | 881 | # convert to normal scalar for speed and correctness in inner parts |
86f0d17a T |
882 | $a = $a->can('numify') ? $a->numify() : "$a" if defined $a && ref($a); |
883 | $p = $p->can('numify') ? $p->numify() : "$p" if defined $p && ref($p); | |
86b76201 | 884 | |
58cde26e | 885 | # now pick $a or $p, but only if we have got "arguments" |
61f5c3f5 | 886 | if (!defined $a) |
58cde26e | 887 | { |
61f5c3f5 | 888 | foreach ($self,@args) |
58cde26e JH |
889 | { |
890 | # take the defined one, or if both defined, the one that is smaller | |
891 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
892 | } | |
61f5c3f5 T |
893 | } |
894 | if (!defined $p) | |
ee15d750 | 895 | { |
61f5c3f5 T |
896 | # even if $a is defined, take $p, to signal error for both defined |
897 | foreach ($self,@args) | |
898 | { | |
899 | # take the defined one, or if both defined, the one that is bigger | |
900 | # -2 > -3, and 3 > 2 | |
901 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
902 | } | |
ee15d750 | 903 | } |
61f5c3f5 T |
904 | # if still none defined, use globals (#2) |
905 | $a = ${"$c\::accuracy"} unless defined $a; | |
906 | $p = ${"$c\::precision"} unless defined $p; | |
990fb837 RGS |
907 | |
908 | # A == 0 is useless, so undef it to signal no rounding | |
909 | $a = undef if defined $a && $a == 0; | |
61f5c3f5 T |
910 | |
911 | # no rounding today? | |
912 | return ($self) unless defined $a || defined $p; # early out | |
913 | ||
914 | # set A and set P is an fatal error | |
990fb837 | 915 | return ($self->bnan()) if defined $a && defined $p; # error |
61f5c3f5 T |
916 | |
917 | $r = ${"$c\::round_mode"} unless defined $r; | |
7b29e1e6 | 918 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/) |
990fb837 RGS |
919 | { |
920 | require Carp; Carp::croak ("Unknown round mode '$r'"); | |
921 | } | |
922 | ||
d5351619 T |
923 | $a = int($a) if defined $a; |
924 | $p = int($p) if defined $p; | |
925 | ||
990fb837 | 926 | ($self,$a,$p,$r); |
ee15d750 JH |
927 | } |
928 | ||
929 | sub round | |
930 | { | |
61f5c3f5 | 931 | # Round $self according to given parameters, or given second argument's |
ee15d750 | 932 | # parameters or global defaults |
ee15d750 | 933 | |
61f5c3f5 T |
934 | # for speed reasons, _find_round_parameters is embeded here: |
935 | ||
936 | my ($self,$a,$p,$r,@args) = @_; | |
937 | # $a accuracy, if given by caller | |
938 | # $p precision, if given by caller | |
939 | # $r round_mode, if given by caller | |
940 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
941 | ||
61f5c3f5 T |
942 | my $c = ref($self); # find out class of argument(s) |
943 | no strict 'refs'; | |
944 | ||
945 | # now pick $a or $p, but only if we have got "arguments" | |
946 | if (!defined $a) | |
58cde26e | 947 | { |
61f5c3f5 T |
948 | foreach ($self,@args) |
949 | { | |
950 | # take the defined one, or if both defined, the one that is smaller | |
951 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
952 | } | |
58cde26e | 953 | } |
61f5c3f5 T |
954 | if (!defined $p) |
955 | { | |
956 | # even if $a is defined, take $p, to signal error for both defined | |
957 | foreach ($self,@args) | |
958 | { | |
959 | # take the defined one, or if both defined, the one that is bigger | |
960 | # -2 > -3, and 3 > 2 | |
961 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
962 | } | |
963 | } | |
964 | # if still none defined, use globals (#2) | |
965 | $a = ${"$c\::accuracy"} unless defined $a; | |
966 | $p = ${"$c\::precision"} unless defined $p; | |
967 | ||
990fb837 RGS |
968 | # A == 0 is useless, so undef it to signal no rounding |
969 | $a = undef if defined $a && $a == 0; | |
970 | ||
61f5c3f5 T |
971 | # no rounding today? |
972 | return $self unless defined $a || defined $p; # early out | |
973 | ||
974 | # set A and set P is an fatal error | |
975 | return $self->bnan() if defined $a && defined $p; | |
976 | ||
977 | $r = ${"$c\::round_mode"} unless defined $r; | |
7b29e1e6 | 978 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/) |
990fb837 | 979 | { |
b282a552 | 980 | require Carp; Carp::croak ("Unknown round mode '$r'"); |
990fb837 | 981 | } |
61f5c3f5 T |
982 | |
983 | # now round, by calling either fround or ffround: | |
984 | if (defined $a) | |
985 | { | |
d5351619 | 986 | $self->bround(int($a),$r) if !defined $self->{_a} || $self->{_a} >= $a; |
61f5c3f5 T |
987 | } |
988 | else # both can't be undefined due to early out | |
58cde26e | 989 | { |
d5351619 | 990 | $self->bfround(int($p),$r) if !defined $self->{_p} || $self->{_p} <= $p; |
58cde26e | 991 | } |
7b29e1e6 | 992 | # bround() or bfround() already callled bnorm() if nec. |
12fc2493 | 993 | $self; |
58cde26e JH |
994 | } |
995 | ||
17baacb7 | 996 | sub bnorm |
58cde26e | 997 | { |
027dc388 | 998 | # (numstr or BINT) return BINT |
58cde26e | 999 | # Normalize number -- no-op here |
b282a552 | 1000 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
b3abae2a | 1001 | $x; |
58cde26e JH |
1002 | } |
1003 | ||
1004 | sub babs | |
1005 | { | |
1006 | # (BINT or num_str) return BINT | |
1007 | # make number absolute, or return absolute BINT from string | |
b68b7ab1 | 1008 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 1009 | |
58cde26e JH |
1010 | return $x if $x->modify('babs'); |
1011 | # post-normalized abs for internal use (does nothing for NaN) | |
1012 | $x->{sign} =~ s/^-/+/; | |
1013 | $x; | |
1014 | } | |
1015 | ||
1016 | sub bneg | |
1017 | { | |
1018 | # (BINT or num_str) return BINT | |
1019 | # negate number or make a negated number from string | |
b68b7ab1 | 1020 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 1021 | |
58cde26e | 1022 | return $x if $x->modify('bneg'); |
b3abae2a | 1023 | |
b68b7ab1 T |
1024 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN' |
1025 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value})); | |
58cde26e JH |
1026 | $x; |
1027 | } | |
1028 | ||
1029 | sub bcmp | |
1030 | { | |
1031 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
1032 | # (BINT or num_str, BINT or num_str) return cond_code | |
f9a08e12 JH |
1033 | |
1034 | # set up parameters | |
1035 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1036 | ||
1037 | # objectify is costly, so avoid it | |
1038 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1039 | { | |
1040 | ($self,$x,$y) = objectify(2,@_); | |
1041 | } | |
0716bf9b | 1042 | |
56d9de68 T |
1043 | return $upgrade->bcmp($x,$y) if defined $upgrade && |
1044 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1045 | ||
0716bf9b JH |
1046 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1047 | { | |
1048 | # handle +-inf and NaN | |
1049 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
574bacfe | 1050 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b JH |
1051 | return +1 if $x->{sign} eq '+inf'; |
1052 | return -1 if $x->{sign} eq '-inf'; | |
1053 | return -1 if $y->{sign} eq '+inf'; | |
b3abae2a | 1054 | return +1; |
0716bf9b | 1055 | } |
574bacfe JH |
1056 | # check sign for speed first |
1057 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
1058 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
1059 | ||
f9a08e12 JH |
1060 | # have same sign, so compare absolute values. Don't make tests for zero here |
1061 | # because it's actually slower than testin in Calc (especially w/ Pari et al) | |
1062 | ||
dccbb853 JH |
1063 | # post-normalized compare for internal use (honors signs) |
1064 | if ($x->{sign} eq '+') | |
1065 | { | |
56b9c951 | 1066 | # $x and $y both > 0 |
dccbb853 JH |
1067 | return $CALC->_acmp($x->{value},$y->{value}); |
1068 | } | |
1069 | ||
56b9c951 | 1070 | # $x && $y both < 0 |
b282a552 | 1071 | $CALC->_acmp($y->{value},$x->{value}); # swaped acmp (lib returns 0,1,-1) |
58cde26e JH |
1072 | } |
1073 | ||
1074 | sub bacmp | |
1075 | { | |
1076 | # Compares 2 values, ignoring their signs. | |
1077 | # Returns one of undef, <0, =0, >0. (suitable for sort) | |
1078 | # (BINT, BINT) return cond_code | |
574bacfe | 1079 | |
f9a08e12 JH |
1080 | # set up parameters |
1081 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1082 | # objectify is costly, so avoid it | |
1083 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1084 | { | |
1085 | ($self,$x,$y) = objectify(2,@_); | |
1086 | } | |
1087 | ||
56d9de68 T |
1088 | return $upgrade->bacmp($x,$y) if defined $upgrade && |
1089 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1090 | ||
574bacfe JH |
1091 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1092 | { | |
1093 | # handle +-inf and NaN | |
1094 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1095 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
ef9466ea T |
1096 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1097 | return -1; | |
574bacfe | 1098 | } |
b3abae2a | 1099 | $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1 |
58cde26e JH |
1100 | } |
1101 | ||
1102 | sub badd | |
1103 | { | |
1104 | # add second arg (BINT or string) to first (BINT) (modifies first) | |
1105 | # return result as BINT | |
f9a08e12 JH |
1106 | |
1107 | # set up parameters | |
1108 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1109 | # objectify is costly, so avoid it | |
1110 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1111 | { | |
1112 | ($self,$x,$y,@r) = objectify(2,@_); | |
1113 | } | |
58cde26e JH |
1114 | |
1115 | return $x if $x->modify('badd'); | |
091c87b1 | 1116 | return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade && |
8f675a64 | 1117 | ((!$x->isa($self)) || (!$y->isa($self))); |
58cde26e | 1118 | |
61f5c3f5 | 1119 | $r[3] = $y; # no push! |
574bacfe JH |
1120 | # inf and NaN handling |
1121 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1122 | { | |
1123 | # NaN first | |
1124 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
13a12e00 JH |
1125 | # inf handling |
1126 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
574bacfe | 1127 | { |
b3abae2a JH |
1128 | # +inf++inf or -inf+-inf => same, rest is NaN |
1129 | return $x if $x->{sign} eq $y->{sign}; | |
1130 | return $x->bnan(); | |
574bacfe JH |
1131 | } |
1132 | # +-inf + something => +inf | |
1133 | # something +-inf => +-inf | |
1134 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; | |
1135 | return $x; | |
1136 | } | |
1137 | ||
b282a552 | 1138 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
58cde26e JH |
1139 | |
1140 | if ($sx eq $sy) | |
1141 | { | |
574bacfe | 1142 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e JH |
1143 | } |
1144 | else | |
1145 | { | |
574bacfe | 1146 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e JH |
1147 | if ($a > 0) |
1148 | { | |
574bacfe | 1149 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e JH |
1150 | $x->{sign} = $sy; |
1151 | } | |
1152 | elsif ($a == 0) | |
1153 | { | |
1154 | # speedup, if equal, set result to 0 | |
0716bf9b | 1155 | $x->{value} = $CALC->_zero(); |
58cde26e JH |
1156 | $x->{sign} = '+'; |
1157 | } | |
1158 | else # a < 0 | |
1159 | { | |
574bacfe | 1160 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
a0d0e21e | 1161 | } |
a0d0e21e | 1162 | } |
b68b7ab1 | 1163 | $x->round(@r); |
58cde26e JH |
1164 | } |
1165 | ||
1166 | sub bsub | |
1167 | { | |
091c87b1 | 1168 | # (BINT or num_str, BINT or num_str) return BINT |
58cde26e | 1169 | # subtract second arg from first, modify first |
f9a08e12 JH |
1170 | |
1171 | # set up parameters | |
1172 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
7d193e39 | 1173 | |
f9a08e12 JH |
1174 | # objectify is costly, so avoid it |
1175 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1176 | { | |
1177 | ($self,$x,$y,@r) = objectify(2,@_); | |
1178 | } | |
58cde26e | 1179 | |
58cde26e | 1180 | return $x if $x->modify('bsub'); |
8f675a64 | 1181 | |
9b924220 RGS |
1182 | return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade && |
1183 | ((!$x->isa($self)) || (!$y->isa($self))); | |
b3abae2a | 1184 | |
b68b7ab1 | 1185 | return $x->round(@r) if $y->is_zero(); |
b3abae2a | 1186 | |
a87115f0 RGS |
1187 | # To correctly handle the lone special case $x->bsub($x), we note the sign |
1188 | # of $x, then flip the sign from $y, and if the sign of $x did change, too, | |
1189 | # then we caught the special case: | |
1190 | my $xsign = $x->{sign}; | |
1191 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN | |
1192 | if ($xsign ne $x->{sign}) | |
03874afe | 1193 | { |
a87115f0 RGS |
1194 | # special case of $x->bsub($x) results in 0 |
1195 | return $x->bzero(@r) if $xsign =~ /^[+-]$/; | |
03874afe T |
1196 | return $x->bnan(); # NaN, -inf, +inf |
1197 | } | |
b3abae2a JH |
1198 | $x->badd($y,@r); # badd does not leave internal zeros |
1199 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) | |
7b29e1e6 | 1200 | $x; # already rounded by badd() or no round nec. |
58cde26e JH |
1201 | } |
1202 | ||
1203 | sub binc | |
1204 | { | |
1205 | # increment arg by one | |
ee15d750 | 1206 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1207 | return $x if $x->modify('binc'); |
e745a66c JH |
1208 | |
1209 | if ($x->{sign} eq '+') | |
1210 | { | |
1211 | $x->{value} = $CALC->_inc($x->{value}); | |
b68b7ab1 | 1212 | return $x->round($a,$p,$r); |
e745a66c JH |
1213 | } |
1214 | elsif ($x->{sign} eq '-') | |
1215 | { | |
1216 | $x->{value} = $CALC->_dec($x->{value}); | |
1217 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 | |
b68b7ab1 | 1218 | return $x->round($a,$p,$r); |
e745a66c JH |
1219 | } |
1220 | # inf, nan handling etc | |
091c87b1 | 1221 | $x->badd($self->bone(),$a,$p,$r); # badd does round |
58cde26e JH |
1222 | } |
1223 | ||
1224 | sub bdec | |
1225 | { | |
1226 | # decrement arg by one | |
b282a552 | 1227 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1228 | return $x if $x->modify('bdec'); |
e745a66c | 1229 | |
b282a552 | 1230 | if ($x->{sign} eq '-') |
e745a66c | 1231 | { |
b68b7ab1 | 1232 | # x already < 0 |
e745a66c | 1233 | $x->{value} = $CALC->_inc($x->{value}); |
b282a552 T |
1234 | } |
1235 | else | |
e745a66c | 1236 | { |
b68b7ab1 | 1237 | return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf or NaN |
b282a552 T |
1238 | # >= 0 |
1239 | if ($CALC->_is_zero($x->{value})) | |
1240 | { | |
1241 | # == 0 | |
1242 | $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1 | |
1243 | } | |
1244 | else | |
1245 | { | |
1246 | # > 0 | |
1247 | $x->{value} = $CALC->_dec($x->{value}); | |
1248 | } | |
e745a66c | 1249 | } |
b68b7ab1 | 1250 | $x->round(@r); |
b282a552 | 1251 | } |
58cde26e | 1252 | |
61f5c3f5 T |
1253 | sub blog |
1254 | { | |
091c87b1 T |
1255 | # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base |
1256 | # $base of $x) | |
1257 | ||
1258 | # set up parameters | |
b68b7ab1 | 1259 | my ($self,$x,$base,@r) = (undef,@_); |
091c87b1 T |
1260 | # objectify is costly, so avoid it |
1261 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1262 | { | |
b68b7ab1 | 1263 | ($self,$x,$base,@r) = objectify(1,ref($x),@_); |
091c87b1 | 1264 | } |
a0ac753d | 1265 | |
ef9466ea T |
1266 | return $x if $x->modify('blog'); |
1267 | ||
2ebb273f T |
1268 | $base = $self->new($base) if defined $base && !ref $base; |
1269 | ||
091c87b1 T |
1270 | # inf, -inf, NaN, <0 => NaN |
1271 | return $x->bnan() | |
9b924220 | 1272 | if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+'); |
091c87b1 | 1273 | |
9b924220 RGS |
1274 | return $upgrade->blog($upgrade->new($x),$base,@r) if |
1275 | defined $upgrade; | |
091c87b1 | 1276 | |
a0ac753d T |
1277 | # fix for bug #24969: |
1278 | # the default base is e (Euler's number) which is not an integer | |
1279 | if (!defined $base) | |
1280 | { | |
1281 | require Math::BigFloat; | |
1282 | my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int(); | |
1283 | # modify $x in place | |
1284 | $x->{value} = $u->{value}; | |
1285 | $x->{sign} = $u->{sign}; | |
1286 | return $x; | |
1287 | } | |
1288 | ||
9b924220 RGS |
1289 | my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value}); |
1290 | return $x->bnan() unless defined $rc; # not possible to take log? | |
1291 | $x->{value} = $rc; | |
1292 | $x->round(@r); | |
61f5c3f5 | 1293 | } |
091c87b1 | 1294 | |
50109ad0 RGS |
1295 | sub bnok |
1296 | { | |
1297 | # Calculate n over k (binomial coefficient or "choose" function) as integer. | |
1298 | # set up parameters | |
1299 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1300 | ||
1301 | # objectify is costly, so avoid it | |
1302 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1303 | { | |
1304 | ($self,$x,$y,@r) = objectify(2,@_); | |
1305 | } | |
1306 | ||
1307 | return $x if $x->modify('bnok'); | |
1308 | return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'; | |
1309 | return $x->binf() if $x->{sign} eq '+inf'; | |
1310 | ||
1311 | # k > n or k < 0 => 0 | |
1312 | my $cmp = $x->bacmp($y); | |
1313 | return $x->bzero() if $cmp < 0 || $y->{sign} =~ /^-/; | |
1314 | # k == n => 1 | |
1315 | return $x->bone(@r) if $cmp == 0; | |
1316 | ||
1317 | if ($CALC->can('_nok')) | |
1318 | { | |
1319 | $x->{value} = $CALC->_nok($x->{value},$y->{value}); | |
1320 | } | |
1321 | else | |
1322 | { | |
1323 | # ( 7 ) 7! 7*6*5 * 4*3*2*1 7 * 6 * 5 | |
1324 | # ( - ) = --------- = --------------- = --------- | |
1325 | # ( 3 ) 3! (7-3)! 3*2*1 * 4*3*2*1 3 * 2 * 1 | |
1326 | ||
1327 | # compute n - k + 2 (so we start with 5 in the example above) | |
1328 | my $z = $x - $y; | |
1329 | if (!$z->is_one()) | |
1330 | { | |
1331 | $z->binc(); | |
1332 | my $r = $z->copy(); $z->binc(); | |
1333 | my $d = $self->new(2); | |
1334 | while ($z->bacmp($x) <= 0) # f < x ? | |
1335 | { | |
1336 | $r->bmul($z); $r->bdiv($d); | |
1337 | $z->binc(); $d->binc(); | |
1338 | } | |
1339 | $x->{value} = $r->{value}; $x->{sign} = '+'; | |
1340 | } | |
1341 | else { $x->bone(); } | |
1342 | } | |
1343 | $x->round(@r); | |
1344 | } | |
1345 | ||
7d193e39 T |
1346 | sub bexp |
1347 | { | |
1348 | # Calculate e ** $x (Euler's number to the power of X), truncated to | |
1349 | # an integer value. | |
1350 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); | |
1351 | return $x if $x->modify('bexp'); | |
1352 | ||
1353 | # inf, -inf, NaN, <0 => NaN | |
1354 | return $x->bnan() if $x->{sign} eq 'NaN'; | |
1355 | return $x->bone() if $x->is_zero(); | |
1356 | return $x if $x->{sign} eq '+inf'; | |
1357 | return $x->bzero() if $x->{sign} eq '-inf'; | |
1358 | ||
1359 | my $u; | |
1360 | { | |
1361 | # run through Math::BigFloat unless told otherwise | |
50109ad0 | 1362 | require Math::BigFloat unless defined $upgrade; |
7d193e39 T |
1363 | local $upgrade = 'Math::BigFloat' unless defined $upgrade; |
1364 | # calculate result, truncate it to integer | |
1365 | $u = $upgrade->bexp($upgrade->new($x),@r); | |
1366 | } | |
1367 | ||
1368 | if (!defined $upgrade) | |
1369 | { | |
1370 | $u = $u->as_int(); | |
1371 | # modify $x in place | |
1372 | $x->{value} = $u->{value}; | |
1373 | $x->round(@r); | |
1374 | } | |
1375 | else { $x = $u; } | |
1376 | } | |
1377 | ||
58cde26e JH |
1378 | sub blcm |
1379 | { | |
1380 | # (BINT or num_str, BINT or num_str) return BINT | |
1381 | # does not modify arguments, but returns new object | |
1382 | # Lowest Common Multiplicator | |
58cde26e | 1383 | |
0716bf9b JH |
1384 | my $y = shift; my ($x); |
1385 | if (ref($y)) | |
1386 | { | |
1387 | $x = $y->copy(); | |
1388 | } | |
1389 | else | |
1390 | { | |
12fc2493 | 1391 | $x = $class->new($y); |
0716bf9b | 1392 | } |
9b924220 RGS |
1393 | my $self = ref($x); |
1394 | while (@_) | |
1395 | { | |
1396 | my $y = shift; $y = $self->new($y) if !ref ($y); | |
1397 | $x = __lcm($x,$y); | |
1398 | } | |
58cde26e JH |
1399 | $x; |
1400 | } | |
1401 | ||
1402 | sub bgcd | |
1403 | { | |
1404 | # (BINT or num_str, BINT or num_str) return BINT | |
1405 | # does not modify arguments, but returns new object | |
1406 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) | |
0716bf9b | 1407 | |
dccbb853 | 1408 | my $y = shift; |
12fc2493 | 1409 | $y = $class->new($y) if !ref($y); |
dccbb853 | 1410 | my $self = ref($y); |
9b924220 RGS |
1411 | my $x = $y->copy()->babs(); # keep arguments |
1412 | return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN? | |
1413 | ||
1414 | while (@_) | |
0716bf9b | 1415 | { |
9b924220 | 1416 | $y = shift; $y = $self->new($y) if !ref($y); |
9b924220 | 1417 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? |
b68b7ab1 T |
1418 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); |
1419 | last if $CALC->_is_one($x->{value}); | |
0716bf9b | 1420 | } |
9b924220 | 1421 | $x; |
58cde26e JH |
1422 | } |
1423 | ||
58cde26e JH |
1424 | sub bnot |
1425 | { | |
1426 | # (num_str or BINT) return BINT | |
1427 | # represent ~x as twos-complement number | |
ee15d750 JH |
1428 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1429 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1430 | ||
58cde26e | 1431 | return $x if $x->modify('bnot'); |
091c87b1 | 1432 | $x->binc()->bneg(); # binc already does round |
58cde26e JH |
1433 | } |
1434 | ||
091c87b1 | 1435 | ############################################################################## |
b3abae2a | 1436 | # is_foo test routines |
091c87b1 | 1437 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
b3abae2a | 1438 | |
58cde26e JH |
1439 | sub is_zero |
1440 | { | |
1441 | # return true if arg (BINT or num_str) is zero (array '+', '0') | |
ee15d750 | 1442 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1443 | |
574bacfe | 1444 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 | 1445 | $CALC->_is_zero($x->{value}); |
58cde26e JH |
1446 | } |
1447 | ||
1448 | sub is_nan | |
1449 | { | |
1450 | # return true if arg (BINT or num_str) is NaN | |
091c87b1 | 1451 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 1452 | |
091c87b1 | 1453 | $x->{sign} eq $nan ? 1 : 0; |
58cde26e JH |
1454 | } |
1455 | ||
1456 | sub is_inf | |
1457 | { | |
1458 | # return true if arg (BINT or num_str) is +-inf | |
091c87b1 | 1459 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
58cde26e | 1460 | |
091c87b1 | 1461 | if (defined $sign) |
ee15d750 | 1462 | { |
091c87b1 T |
1463 | $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf |
1464 | $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-' | |
1465 | return $x->{sign} =~ /^$sign$/ ? 1 : 0; | |
ee15d750 | 1466 | } |
091c87b1 | 1467 | $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity |
58cde26e JH |
1468 | } |
1469 | ||
1470 | sub is_one | |
1471 | { | |
091c87b1 | 1472 | # return true if arg (BINT or num_str) is +1, or -1 if sign is given |
ee15d750 JH |
1473 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
1474 | ||
990fb837 | 1475 | $sign = '+' if !defined $sign || $sign ne '-'; |
0716bf9b | 1476 | |
ee15d750 | 1477 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
394e6ffb | 1478 | $CALC->_is_one($x->{value}); |
58cde26e JH |
1479 | } |
1480 | ||
1481 | sub is_odd | |
1482 | { | |
1483 | # return true when arg (BINT or num_str) is odd, false for even | |
ee15d750 | 1484 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1485 | |
b22b3e31 | 1486 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1487 | $CALC->_is_odd($x->{value}); |
58cde26e JH |
1488 | } |
1489 | ||
1490 | sub is_even | |
1491 | { | |
1492 | # return true when arg (BINT or num_str) is even, false for odd | |
ee15d750 | 1493 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1494 | |
b22b3e31 | 1495 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1496 | $CALC->_is_even($x->{value}); |
0716bf9b JH |
1497 | } |
1498 | ||
1499 | sub is_positive | |
1500 | { | |
1501 | # return true when arg (BINT or num_str) is positive (>= 0) | |
ee15d750 | 1502 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
b68b7ab1 T |
1503 | |
1504 | return 1 if $x->{sign} eq '+inf'; # +inf is positive | |
1505 | ||
1506 | # 0+ is neither positive nor negative | |
1507 | ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0; | |
0716bf9b JH |
1508 | } |
1509 | ||
1510 | sub is_negative | |
1511 | { | |
1512 | # return true when arg (BINT or num_str) is negative (< 0) | |
ee15d750 JH |
1513 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1514 | ||
b68b7ab1 | 1515 | $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not |
58cde26e JH |
1516 | } |
1517 | ||
b3abae2a JH |
1518 | sub is_int |
1519 | { | |
1520 | # return true when arg (BINT or num_str) is an integer | |
091c87b1 | 1521 | # always true for BigInt, but different for BigFloats |
b3abae2a JH |
1522 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1523 | ||
1524 | $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't | |
1525 | } | |
1526 | ||
0716bf9b JH |
1527 | ############################################################################### |
1528 | ||
58cde26e JH |
1529 | sub bmul |
1530 | { | |
c97ef841 | 1531 | # multiply the first number by the second number |
58cde26e | 1532 | # (BINT or num_str, BINT or num_str) return BINT |
f9a08e12 JH |
1533 | |
1534 | # set up parameters | |
1535 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1536 | # objectify is costly, so avoid it | |
1537 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1538 | { | |
1539 | ($self,$x,$y,@r) = objectify(2,@_); | |
1540 | } | |
a0ac753d | 1541 | |
58cde26e | 1542 | return $x if $x->modify('bmul'); |
61f5c3f5 | 1543 | |
574bacfe | 1544 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
b3abae2a | 1545 | |
574bacfe JH |
1546 | # inf handling |
1547 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1548 | { | |
b3abae2a | 1549 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe JH |
1550 | # result will always be +-inf: |
1551 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
1552 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
1553 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
1554 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
1555 | return $x->binf('-'); | |
1556 | } | |
9b924220 RGS |
1557 | |
1558 | return $upgrade->bmul($x,$upgrade->new($y),@r) | |
1559 | if defined $upgrade && !$y->isa($self); | |
9393ace2 JH |
1560 | |
1561 | $r[3] = $y; # no push here | |
58cde26e | 1562 | |
0716bf9b | 1563 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
dccbb853 | 1564 | |
b3abae2a JH |
1565 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
1566 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 | |
f9a08e12 | 1567 | |
b68b7ab1 | 1568 | $x->round(@r); |
dccbb853 JH |
1569 | } |
1570 | ||
80365507 T |
1571 | sub bmuladd |
1572 | { | |
1573 | # multiply two numbers and then add the third to the result | |
1574 | # (BINT or num_str, BINT or num_str, BINT or num_str) return BINT | |
1575 | ||
1576 | # set up parameters | |
1577 | my ($self,$x,$y,$z,@r) = (ref($_[0]),@_); | |
1578 | # objectify is costly, so avoid it | |
1579 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1580 | { | |
1581 | ($self,$x,$y,$z,@r) = objectify(3,@_); | |
1582 | } | |
1583 | ||
1584 | return $x if $x->modify('bmuladd'); | |
1585 | ||
1586 | return $x->bnan() if ($x->{sign} eq $nan) || | |
1587 | ($y->{sign} eq $nan) || | |
1588 | ($z->{sign} eq $nan); | |
1589 | ||
1590 | # inf handling of x and y | |
1591 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1592 | { | |
1593 | return $x->bnan() if $x->is_zero() || $y->is_zero(); | |
1594 | # result will always be +-inf: | |
1595 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
1596 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
1597 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
1598 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
1599 | return $x->binf('-'); | |
1600 | } | |
1601 | # inf handling x*y and z | |
1602 | if (($z->{sign} =~ /^[+-]inf$/)) | |
1603 | { | |
1604 | # something +-inf => +-inf | |
1605 | $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/; | |
1606 | } | |
1607 | ||
1608 | return $upgrade->bmuladd($x,$upgrade->new($y),$upgrade->new($z),@r) | |
1609 | if defined $upgrade && (!$y->isa($self) || !$z->isa($self) || !$x->isa($self)); | |
1610 | ||
c97ef841 | 1611 | # TODO: what if $y and $z have A or P set? |
80365507 T |
1612 | $r[3] = $z; # no push here |
1613 | ||
1614 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + | |
1615 | ||
1616 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math | |
1617 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 | |
1618 | ||
1619 | my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); # get signs | |
1620 | ||
1621 | if ($sx eq $sz) | |
1622 | { | |
1623 | $x->{value} = $CALC->_add($x->{value},$z->{value}); # same sign, abs add | |
1624 | } | |
1625 | else | |
1626 | { | |
1627 | my $a = $CALC->_acmp ($z->{value},$x->{value}); # absolute compare | |
1628 | if ($a > 0) | |
1629 | { | |
1630 | $x->{value} = $CALC->_sub($z->{value},$x->{value},1); # abs sub w/ swap | |
1631 | $x->{sign} = $sz; | |
1632 | } | |
1633 | elsif ($a == 0) | |
1634 | { | |
1635 | # speedup, if equal, set result to 0 | |
1636 | $x->{value} = $CALC->_zero(); | |
1637 | $x->{sign} = '+'; | |
1638 | } | |
1639 | else # a < 0 | |
1640 | { | |
1641 | $x->{value} = $CALC->_sub($x->{value}, $z->{value}); # abs sub | |
1642 | } | |
1643 | } | |
1644 | $x->round(@r); | |
1645 | } | |
1646 | ||
dccbb853 JH |
1647 | sub _div_inf |
1648 | { | |
1649 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code | |
1650 | my ($self,$x,$y) = @_; | |
1651 | ||
1652 | # NaN if x == NaN or y == NaN or x==y==0 | |
1653 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() | |
1654 | if (($x->is_nan() || $y->is_nan()) || | |
1655 | ($x->is_zero() && $y->is_zero())); | |
1656 | ||
b3abae2a JH |
1657 | # +-inf / +-inf == NaN, reminder also NaN |
1658 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
dccbb853 | 1659 | { |
b3abae2a | 1660 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan(); |
dccbb853 JH |
1661 | } |
1662 | # x / +-inf => 0, remainder x (works even if x == 0) | |
1663 | if ($y->{sign} =~ /^[+-]inf$/) | |
1664 | { | |
f9a08e12 | 1665 | my $t = $x->copy(); # bzero clobbers up $x |
dccbb853 JH |
1666 | return wantarray ? ($x->bzero(),$t) : $x->bzero() |
1667 | } | |
1668 | ||
1669 | # 5 / 0 => +inf, -6 / 0 => -inf | |
1670 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf | |
1671 | # exception: -8 / 0 has remainder -8, not 8 | |
1672 | # exception: -inf / 0 has remainder -inf, not inf | |
1673 | if ($y->is_zero()) | |
1674 | { | |
1675 | # +-inf / 0 => special case for -inf | |
1676 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); | |
1677 | if (!$x->is_zero() && !$x->is_inf()) | |
1678 | { | |
1679 | my $t = $x->copy(); # binf clobbers up $x | |
1680 | return wantarray ? | |
1681 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) | |
1682 | } | |
1683 | } | |
1684 | ||
1685 | # last case: +-inf / ordinary number | |
1686 | my $sign = '+inf'; | |
1687 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; | |
1688 | $x->{sign} = $sign; | |
1689 | return wantarray ? ($x,$self->bzero()) : $x; | |
58cde26e JH |
1690 | } |
1691 | ||
1692 | sub bdiv | |
1693 | { | |
1694 | # (dividend: BINT or num_str, divisor: BINT or num_str) return | |
1695 | # (BINT,BINT) (quo,rem) or BINT (only rem) | |
f9a08e12 JH |
1696 | |
1697 | # set up parameters | |
1698 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1699 | # objectify is costly, so avoid it | |
1700 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1701 | { | |
1702 | ($self,$x,$y,@r) = objectify(2,@_); | |
1703 | } | |
58cde26e JH |
1704 | |
1705 | return $x if $x->modify('bdiv'); | |
1706 | ||
dccbb853 JH |
1707 | return $self->_div_inf($x,$y) |
1708 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
58cde26e | 1709 | |
9393ace2 JH |
1710 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
1711 | if defined $upgrade; | |
58cde26e | 1712 | |
990fb837 RGS |
1713 | $r[3] = $y; # no push! |
1714 | ||
58cde26e | 1715 | # calc new sign and in case $y == +/- 1, return $x |
dccbb853 | 1716 | my $xsign = $x->{sign}; # keep |
58cde26e | 1717 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
58cde26e | 1718 | |
58cde26e JH |
1719 | if (wantarray) |
1720 | { | |
394e6ffb JH |
1721 | my $rem = $self->bzero(); |
1722 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); | |
1723 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
f9a08e12 JH |
1724 | $rem->{_a} = $x->{_a}; |
1725 | $rem->{_p} = $x->{_p}; | |
b68b7ab1 | 1726 | $x->round(@r); |
dccbb853 JH |
1727 | if (! $CALC->_is_zero($rem->{value})) |
1728 | { | |
1729 | $rem->{sign} = $y->{sign}; | |
990fb837 | 1730 | $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-' |
dccbb853 JH |
1731 | } |
1732 | else | |
1733 | { | |
1734 | $rem->{sign} = '+'; # dont leave -0 | |
1735 | } | |
b68b7ab1 | 1736 | $rem->round(@r); |
990fb837 | 1737 | return ($x,$rem); |
58cde26e | 1738 | } |
394e6ffb JH |
1739 | |
1740 | $x->{value} = $CALC->_div($x->{value},$y->{value}); | |
1741 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
f9a08e12 | 1742 | |
b68b7ab1 | 1743 | $x->round(@r); |
58cde26e JH |
1744 | } |
1745 | ||
d614cd8b JH |
1746 | ############################################################################### |
1747 | # modulus functions | |
1748 | ||
dccbb853 JH |
1749 | sub bmod |
1750 | { | |
1751 | # modulus (or remainder) | |
1752 | # (BINT or num_str, BINT or num_str) return BINT | |
f9a08e12 JH |
1753 | |
1754 | # set up parameters | |
1755 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1756 | # objectify is costly, so avoid it | |
1757 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1758 | { | |
1759 | ($self,$x,$y,@r) = objectify(2,@_); | |
1760 | } | |
28df3e88 | 1761 | |
dccbb853 | 1762 | return $x if $x->modify('bmod'); |
61f5c3f5 | 1763 | $r[3] = $y; # no push! |
dccbb853 JH |
1764 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) |
1765 | { | |
1766 | my ($d,$r) = $self->_div_inf($x,$y); | |
f9a08e12 JH |
1767 | $x->{sign} = $r->{sign}; |
1768 | $x->{value} = $r->{value}; | |
1769 | return $x->round(@r); | |
dccbb853 JH |
1770 | } |
1771 | ||
9b924220 RGS |
1772 | # calc new sign and in case $y == +/- 1, return $x |
1773 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); | |
1774 | if (!$CALC->_is_zero($x->{value})) | |
dccbb853 | 1775 | { |
b68b7ab1 T |
1776 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1) # $y-$x |
1777 | if ($x->{sign} ne $y->{sign}); | |
9b924220 | 1778 | $x->{sign} = $y->{sign}; |
dccbb853 | 1779 | } |
9b924220 | 1780 | else |
b3abae2a | 1781 | { |
9b924220 | 1782 | $x->{sign} = '+'; # dont leave -0 |
b3abae2a | 1783 | } |
b68b7ab1 | 1784 | $x->round(@r); |
dccbb853 JH |
1785 | } |
1786 | ||
07d34614 | 1787 | sub bmodinv |
d614cd8b | 1788 | { |
56d9de68 | 1789 | # Modular inverse. given a number which is (hopefully) relatively |
d614cd8b | 1790 | # prime to the modulus, calculate its inverse using Euclid's |
56d9de68 | 1791 | # alogrithm. If the number is not relatively prime to the modulus |
d614cd8b JH |
1792 | # (i.e. their gcd is not one) then NaN is returned. |
1793 | ||
f9a08e12 | 1794 | # set up parameters |
b68b7ab1 | 1795 | my ($self,$x,$y,@r) = (undef,@_); |
56d9de68 | 1796 | # objectify is costly, so avoid it |
f9a08e12 JH |
1797 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1798 | { | |
1799 | ($self,$x,$y,@r) = objectify(2,@_); | |
56d9de68 | 1800 | } |
d614cd8b | 1801 | |
f9a08e12 | 1802 | return $x if $x->modify('bmodinv'); |
d614cd8b | 1803 | |
f9a08e12 | 1804 | return $x->bnan() |
56d9de68 T |
1805 | if ($y->{sign} ne '+' # -, NaN, +inf, -inf |
1806 | || $x->is_zero() # or num == 0 | |
1807 | || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf | |
d614cd8b | 1808 | ); |
1ddff52a | 1809 | |
f9a08e12 JH |
1810 | # put least residue into $x if $x was negative, and thus make it positive |
1811 | $x->bmod($y) if $x->{sign} eq '-'; | |
07d34614 | 1812 | |
9b924220 RGS |
1813 | my $sign; |
1814 | ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value}); | |
1815 | return $x->bnan() if !defined $x->{value}; # in case no GCD found | |
1816 | return $x if !defined $sign; # already real result | |
1817 | $x->{sign} = $sign; # flip/flop see below | |
1818 | $x->bmod($y); # calc real result | |
1819 | $x; | |
d614cd8b JH |
1820 | } |
1821 | ||
07d34614 | 1822 | sub bmodpow |
d614cd8b JH |
1823 | { |
1824 | # takes a very large number to a very large exponent in a given very | |
80365507 | 1825 | # large modulus, quickly, thanks to binary exponentation. Supports |
d614cd8b JH |
1826 | # negative exponents. |
1827 | my ($self,$num,$exp,$mod,@r) = objectify(3,@_); | |
1828 | ||
1829 | return $num if $num->modify('bmodpow'); | |
1830 | ||
1831 | # check modulus for valid values | |
1832 | return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf | |
1833 | || $mod->is_zero()); | |
1834 | ||
1835 | # check exponent for valid values | |
1836 | if ($exp->{sign} =~ /\w/) | |
1837 | { | |
1838 | # i.e., if it's NaN, +inf, or -inf... | |
1839 | return $num->bnan(); | |
1840 | } | |
07d34614 | 1841 | |
1ddff52a | 1842 | $num->bmodinv ($mod) if ($exp->{sign} eq '-'); |
d614cd8b | 1843 | |
1ddff52a | 1844 | # check num for valid values (also NaN if there was no inverse but $exp < 0) |
07d34614 | 1845 | return $num->bnan() if $num->{sign} !~ /^[+-]$/; |
d614cd8b | 1846 | |
9b924220 RGS |
1847 | # $mod is positive, sign on $exp is ignored, result also positive |
1848 | $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value}); | |
1849 | $num; | |
d614cd8b JH |
1850 | } |
1851 | ||
1852 | ############################################################################### | |
1853 | ||
b3abae2a JH |
1854 | sub bfac |
1855 | { | |
1856 | # (BINT or num_str, BINT or num_str) return BINT | |
091c87b1 | 1857 | # compute factorial number from $x, modify $x in place |
b68b7ab1 | 1858 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
b3abae2a | 1859 | |
b68b7ab1 T |
1860 | return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf |
1861 | return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN | |
b3abae2a | 1862 | |
9b924220 RGS |
1863 | $x->{value} = $CALC->_fac($x->{value}); |
1864 | $x->round(@r); | |
b3abae2a JH |
1865 | } |
1866 | ||
58cde26e JH |
1867 | sub bpow |
1868 | { | |
1869 | # (BINT or num_str, BINT or num_str) return BINT | |
1870 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 | |
1871 | # modifies first argument | |
aef458a0 | 1872 | |
f9a08e12 JH |
1873 | # set up parameters |
1874 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1875 | # objectify is costly, so avoid it | |
1876 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1877 | { | |
1878 | ($self,$x,$y,@r) = objectify(2,@_); | |
1879 | } | |
58cde26e JH |
1880 | |
1881 | return $x if $x->modify('bpow'); | |
9393ace2 | 1882 | |
2d2b2744 T |
1883 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
1884 | ||
1885 | # inf handling | |
1886 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1887 | { | |
1888 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
1889 | { | |
1890 | # +-inf ** +-inf | |
1891 | return $x->bnan(); | |
1892 | } | |
1893 | # +-inf ** Y | |
1894 | if ($x->{sign} =~ /^[+-]inf/) | |
1895 | { | |
1896 | # +inf ** 0 => NaN | |
1897 | return $x->bnan() if $y->is_zero(); | |
1898 | # -inf ** -1 => 1/inf => 0 | |
1899 | return $x->bzero() if $y->is_one('-') && $x->is_negative(); | |
1900 | ||
1901 | # +inf ** Y => inf | |
1902 | return $x if $x->{sign} eq '+inf'; | |
1903 | ||
1904 | # -inf ** Y => -inf if Y is odd | |
1905 | return $x if $y->is_odd(); | |
1906 | return $x->babs(); | |
1907 | } | |
1908 | # X ** +-inf | |
1909 | ||
1910 | # 1 ** +inf => 1 | |
1911 | return $x if $x->is_one(); | |
1912 | ||
1913 | # 0 ** inf => 0 | |
1914 | return $x if $x->is_zero() && $y->{sign} =~ /^[+]/; | |
1915 | ||
1916 | # 0 ** -inf => inf | |
1917 | return $x->binf() if $x->is_zero(); | |
1918 | ||
1919 | # -1 ** -inf => NaN | |
1920 | return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/; | |
1921 | ||
1922 | # -X ** -inf => 0 | |
1923 | return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/; | |
1924 | ||
1925 | # -1 ** inf => NaN | |
1926 | return $x->bnan() if $x->{sign} eq '-'; | |
1927 | ||
1928 | # X ** inf => inf | |
1929 | return $x->binf() if $y->{sign} =~ /^[+]/; | |
1930 | # X ** -inf => 0 | |
1931 | return $x->bzero(); | |
1932 | } | |
1933 | ||
9393ace2 | 1934 | return $upgrade->bpow($upgrade->new($x),$y,@r) |
7b29e1e6 | 1935 | if defined $upgrade && (!$y->isa($self) || $y->{sign} eq '-'); |
9393ace2 | 1936 | |
61f5c3f5 | 1937 | $r[3] = $y; # no push! |
b282a552 T |
1938 | |
1939 | # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu | |
1940 | ||
9b924220 RGS |
1941 | my $new_sign = '+'; |
1942 | $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+'); | |
1943 | ||
1944 | # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf | |
1945 | return $x->binf() | |
1946 | if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value}); | |
574bacfe JH |
1947 | # 1 ** -y => 1 / (1 ** |y|) |
1948 | # so do test for negative $y after above's clause | |
9b924220 | 1949 | return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value}); |
027dc388 | 1950 | |
9b924220 RGS |
1951 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
1952 | $x->{sign} = $new_sign; | |
1953 | $x->{sign} = '+' if $CALC->_is_zero($y->{value}); | |
b68b7ab1 | 1954 | $x->round(@r); |
58cde26e JH |
1955 | } |
1956 | ||
1957 | sub blsft | |
1958 | { | |
1959 | # (BINT or num_str, BINT or num_str) return BINT | |
1960 | # compute x << y, base n, y >= 0 | |
f9a08e12 JH |
1961 | |
1962 | # set up parameters | |
1963 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); | |
1964 | # objectify is costly, so avoid it | |
1965 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1966 | { | |
1967 | ($self,$x,$y,$n,@r) = objectify(2,@_); | |
1968 | } | |
1969 | ||
58cde26e JH |
1970 | return $x if $x->modify('blsft'); |
1971 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
f9a08e12 | 1972 | return $x->round(@r) if $y->is_zero(); |
58cde26e | 1973 | |
574bacfe JH |
1974 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1975 | ||
9b924220 RGS |
1976 | $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n); |
1977 | $x->round(@r); | |
58cde26e JH |
1978 | } |
1979 | ||
1980 | sub brsft | |
1981 | { | |
1982 | # (BINT or num_str, BINT or num_str) return BINT | |
1983 | # compute x >> y, base n, y >= 0 | |
f9a08e12 JH |
1984 | |
1985 | # set up parameters | |
1986 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); | |
1987 | # objectify is costly, so avoid it | |
1988 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1989 | { | |
1990 | ($self,$x,$y,$n,@r) = objectify(2,@_); | |
1991 | } | |
58cde26e JH |
1992 | |
1993 | return $x if $x->modify('brsft'); | |
1994 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
f9a08e12 JH |
1995 | return $x->round(@r) if $y->is_zero(); |
1996 | return $x->bzero(@r) if $x->is_zero(); # 0 => 0 | |
58cde26e JH |
1997 | |
1998 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; | |
574bacfe | 1999 | |
b3abae2a JH |
2000 | # this only works for negative numbers when shifting in base 2 |
2001 | if (($x->{sign} eq '-') && ($n == 2)) | |
2002 | { | |
f9a08e12 | 2003 | return $x->round(@r) if $x->is_one('-'); # -1 => -1 |
b3abae2a JH |
2004 | if (!$y->is_one()) |
2005 | { | |
2006 | # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al | |
2007 | # but perhaps there is a better emulation for two's complement shift... | |
2008 | # if $y != 1, we must simulate it by doing: | |
2009 | # convert to bin, flip all bits, shift, and be done | |
2010 | $x->binc(); # -3 => -2 | |
2011 | my $bin = $x->as_bin(); | |
2012 | $bin =~ s/^-0b//; # strip '-0b' prefix | |
2013 | $bin =~ tr/10/01/; # flip bits | |
2014 | # now shift | |
a0ac753d | 2015 | if ($y >= CORE::length($bin)) |
b3abae2a JH |
2016 | { |
2017 | $bin = '0'; # shifting to far right creates -1 | |
2018 | # 0, because later increment makes | |
2019 | # that 1, attached '-' makes it '-1' | |
2020 | # because -1 >> x == -1 ! | |
2021 | } | |
2022 | else | |
2023 | { | |
2024 | $bin =~ s/.{$y}$//; # cut off at the right side | |
2025 | $bin = '1' . $bin; # extend left side by one dummy '1' | |
2026 | $bin =~ tr/10/01/; # flip bits back | |
2027 | } | |
2028 | my $res = $self->new('0b'.$bin); # add prefix and convert back | |
2029 | $res->binc(); # remember to increment | |
2030 | $x->{value} = $res->{value}; # take over value | |
f9a08e12 | 2031 | return $x->round(@r); # we are done now, magic, isn't? |
b3abae2a | 2032 | } |
b282a552 | 2033 | # x < 0, n == 2, y == 1 |
b3abae2a JH |
2034 | $x->bdec(); # n == 2, but $y == 1: this fixes it |
2035 | } | |
2036 | ||
9b924220 RGS |
2037 | $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n); |
2038 | $x->round(@r); | |
58cde26e JH |
2039 | } |
2040 | ||
2041 | sub band | |
2042 | { | |
2043 | #(BINT or num_str, BINT or num_str) return BINT | |
2044 | # compute x & y | |
f9a08e12 JH |
2045 | |
2046 | # set up parameters | |
2047 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
2048 | # objectify is costly, so avoid it | |
2049 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
2050 | { | |
2051 | ($self,$x,$y,@r) = objectify(2,@_); | |
2052 | } | |
58cde26e JH |
2053 | |
2054 | return $x if $x->modify('band'); | |
2055 | ||
f9a08e12 | 2056 | $r[3] = $y; # no push! |
b3abae2a | 2057 | |
58cde26e | 2058 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
0716bf9b | 2059 | |
b282a552 T |
2060 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
2061 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe | 2062 | |
9b924220 | 2063 | if ($sx == 1 && $sy == 1) |
0716bf9b | 2064 | { |
574bacfe | 2065 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
f9a08e12 | 2066 | return $x->round(@r); |
0716bf9b | 2067 | } |
091c87b1 T |
2068 | |
2069 | if ($CAN{signed_and}) | |
2070 | { | |
2071 | $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy); | |
2072 | return $x->round(@r); | |
2073 | } | |
b282a552 T |
2074 | |
2075 | require $EMU_LIB; | |
2076 | __emu_band($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
2077 | } |
2078 | ||
2079 | sub bior | |
2080 | { | |
2081 | #(BINT or num_str, BINT or num_str) return BINT | |
2082 | # compute x | y | |
f9a08e12 JH |
2083 | |
2084 | # set up parameters | |
2085 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
2086 | # objectify is costly, so avoid it | |
2087 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
2088 | { | |
2089 | ($self,$x,$y,@r) = objectify(2,@_); | |
2090 | } | |
58cde26e JH |
2091 | |
2092 | return $x if $x->modify('bior'); | |
f9a08e12 | 2093 | $r[3] = $y; # no push! |
58cde26e JH |
2094 | |
2095 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
574bacfe | 2096 | |
b282a552 T |
2097 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
2098 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe | 2099 | |
091c87b1 T |
2100 | # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior() |
2101 | ||
574bacfe | 2102 | # don't use lib for negative values |
9b924220 | 2103 | if ($sx == 1 && $sy == 1) |
0716bf9b | 2104 | { |
574bacfe | 2105 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
f9a08e12 | 2106 | return $x->round(@r); |
0716bf9b JH |
2107 | } |
2108 | ||
b282a552 | 2109 | # if lib can do negative values, let it handle this |
091c87b1 T |
2110 | if ($CAN{signed_or}) |
2111 | { | |
2112 | $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy); | |
2113 | return $x->round(@r); | |
2114 | } | |
2115 | ||
b282a552 T |
2116 | require $EMU_LIB; |
2117 | __emu_bior($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
2118 | } |
2119 | ||
2120 | sub bxor | |
2121 | { | |
2122 | #(BINT or num_str, BINT or num_str) return BINT | |
2123 | # compute x ^ y | |
f9a08e12 JH |
2124 | |
2125 | # set up parameters | |
2126 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
2127 | # objectify is costly, so avoid it | |
2128 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
2129 | { | |
2130 | ($self,$x,$y,@r) = objectify(2,@_); | |
2131 | } | |
58cde26e JH |
2132 | |
2133 | return $x if $x->modify('bxor'); | |
f9a08e12 | 2134 | $r[3] = $y; # no push! |
58cde26e | 2135 | |
0716bf9b | 2136 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
0716bf9b | 2137 | |
b282a552 T |
2138 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
2139 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe JH |
2140 | |
2141 | # don't use lib for negative values | |
9b924220 | 2142 | if ($sx == 1 && $sy == 1) |
0716bf9b | 2143 | { |
574bacfe | 2144 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
f9a08e12 | 2145 | return $x->round(@r); |
0716bf9b | 2146 | } |
091c87b1 | 2147 | |
b282a552 | 2148 | # if lib can do negative values, let it handle this |
091c87b1 T |
2149 | if ($CAN{signed_xor}) |
2150 | { | |
2151 | $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy); | |
2152 | return $x->round(@r); | |
2153 | } | |
0716bf9b | 2154 | |
b282a552 T |
2155 | require $EMU_LIB; |
2156 | __emu_bxor($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
2157 | } |
2158 | ||
2159 | sub length | |
2160 | { | |
b282a552 | 2161 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e | 2162 | |
0716bf9b | 2163 | my $e = $CALC->_len($x->{value}); |
091c87b1 | 2164 | wantarray ? ($e,0) : $e; |
58cde26e JH |
2165 | } |
2166 | ||
2167 | sub digit | |
2168 | { | |
0716bf9b | 2169 | # return the nth decimal digit, negative values count backward, 0 is right |
ef9466ea | 2170 | my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
58cde26e | 2171 | |
ef9466ea | 2172 | $n = $n->numify() if ref($n); |
f9a08e12 | 2173 | $CALC->_digit($x->{value},$n||0); |
58cde26e JH |
2174 | } |
2175 | ||
2176 | sub _trailing_zeros | |
2177 | { | |
b282a552 | 2178 | # return the amount of trailing zeros in $x (as scalar) |
58cde26e JH |
2179 | my $x = shift; |
2180 | $x = $class->new($x) unless ref $x; | |
2181 | ||
9b924220 | 2182 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc |
0716bf9b | 2183 | |
9b924220 | 2184 | $CALC->_zeros($x->{value}); # must handle odd values, 0 etc |
58cde26e JH |
2185 | } |
2186 | ||
2187 | sub bsqrt | |
2188 | { | |
990fb837 | 2189 | # calculate square root of $x |
b68b7ab1 | 2190 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
58cde26e | 2191 | |
b3abae2a JH |
2192 | return $x if $x->modify('bsqrt'); |
2193 | ||
990fb837 RGS |
2194 | return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN |
2195 | return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf | |
b3abae2a | 2196 | |
f9a08e12 | 2197 | return $upgrade->bsqrt($x,@r) if defined $upgrade; |
58cde26e | 2198 | |
9b924220 RGS |
2199 | $x->{value} = $CALC->_sqrt($x->{value}); |
2200 | $x->round(@r); | |
58cde26e JH |
2201 | } |
2202 | ||
990fb837 RGS |
2203 | sub broot |
2204 | { | |
2205 | # calculate $y'th root of $x | |
c38b2de2 | 2206 | |
990fb837 RGS |
2207 | # set up parameters |
2208 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
c38b2de2 JH |
2209 | |
2210 | $y = $self->new(2) unless defined $y; | |
2211 | ||
990fb837 | 2212 | # objectify is costly, so avoid it |
c38b2de2 | 2213 | if ((!ref($x)) || (ref($x) ne ref($y))) |
990fb837 | 2214 | { |
3a427a11 | 2215 | ($self,$x,$y,@r) = objectify(2,$self || $class,@_); |
990fb837 RGS |
2216 | } |
2217 | ||
2218 | return $x if $x->modify('broot'); | |
2219 | ||
2220 | # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0 | |
2221 | return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() || | |
2222 | $y->{sign} !~ /^\+$/; | |
2223 | ||
2224 | return $x->round(@r) | |
2225 | if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one(); | |
2226 | ||
c38b2de2 | 2227 | return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade; |
990fb837 | 2228 | |
9b924220 RGS |
2229 | $x->{value} = $CALC->_root($x->{value},$y->{value}); |
2230 | $x->round(@r); | |
990fb837 RGS |
2231 | } |
2232 | ||
58cde26e JH |
2233 | sub exponent |
2234 | { | |
2235 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) | |
ee15d750 | 2236 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 2237 | |
ee15d750 JH |
2238 | if ($x->{sign} !~ /^[+-]$/) |
2239 | { | |
b282a552 T |
2240 | my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf |
2241 | return $self->new($s); | |
ee15d750 | 2242 | } |
b282a552 T |
2243 | return $self->bone() if $x->is_zero(); |
2244 | ||
7d193e39 T |
2245 | # 12300 => 2 trailing zeros => exponent is 2 |
2246 | $self->new( $CALC->_zeros($x->{value}) ); | |
58cde26e JH |
2247 | } |
2248 | ||
2249 | sub mantissa | |
2250 | { | |
ee15d750 JH |
2251 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
2252 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 2253 | |
ee15d750 JH |
2254 | if ($x->{sign} !~ /^[+-]$/) |
2255 | { | |
b282a552 T |
2256 | # for NaN, +inf, -inf: keep the sign |
2257 | return $self->new($x->{sign}); | |
ee15d750 | 2258 | } |
b282a552 | 2259 | my $m = $x->copy(); delete $m->{_p}; delete $m->{_a}; |
7d193e39 | 2260 | |
b282a552 | 2261 | # that's a bit inefficient: |
7d193e39 | 2262 | my $zeros = $CALC->_zeros($m->{value}); |
56b9c951 | 2263 | $m->brsft($zeros,10) if $zeros != 0; |
56b9c951 | 2264 | $m; |
58cde26e JH |
2265 | } |
2266 | ||
2267 | sub parts | |
2268 | { | |
ee15d750 | 2269 | # return a copy of both the exponent and the mantissa |
091c87b1 | 2270 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e | 2271 | |
091c87b1 | 2272 | ($x->mantissa(),$x->exponent()); |
58cde26e JH |
2273 | } |
2274 | ||
2275 | ############################################################################## | |
2276 | # rounding functions | |
2277 | ||
2278 | sub bfround | |
2279 | { | |
2280 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' | |
ee15d750 | 2281 | # $n == 0 || $n == 1 => round to integer |
ef9466ea | 2282 | my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x; |
b282a552 | 2283 | |
b68b7ab1 | 2284 | my ($scale,$mode) = $x->_scale_p(@_); |
b282a552 T |
2285 | |
2286 | return $x if !defined $scale || $x->modify('bfround'); # no-op | |
58cde26e JH |
2287 | |
2288 | # no-op for BigInts if $n <= 0 | |
b282a552 | 2289 | $x->bround( $x->length()-$scale, $mode) if $scale > 0; |
58cde26e | 2290 | |
ef9466ea T |
2291 | delete $x->{_a}; # delete to save memory |
2292 | $x->{_p} = $scale; # store new _p | |
ee15d750 | 2293 | $x; |
58cde26e JH |
2294 | } |
2295 | ||
2296 | sub _scan_for_nonzero | |
2297 | { | |
ae161977 RGS |
2298 | # internal, used by bround() to scan for non-zeros after a '5' |
2299 | my ($x,$pad,$xs,$len) = @_; | |
58cde26e | 2300 | |
ae161977 | 2301 | return 0 if $len == 1; # "5" is trailed by invisible zeros |
58cde26e JH |
2302 | my $follow = $pad - 1; |
2303 | return 0 if $follow > $len || $follow < 1; | |
0716bf9b | 2304 | |
ae161977 RGS |
2305 | # use the string form to check whether only '0's follow or not |
2306 | substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0; | |
58cde26e JH |
2307 | } |
2308 | ||
2309 | sub fround | |
2310 | { | |
091c87b1 T |
2311 | # Exists to make life easier for switch between MBF and MBI (should we |
2312 | # autoload fxxx() like MBF does for bxxx()?) | |
b68b7ab1 | 2313 | my $x = shift; $x = $class->new($x) unless ref $x; |
091c87b1 | 2314 | $x->bround(@_); |
58cde26e JH |
2315 | } |
2316 | ||
2317 | sub bround | |
2318 | { | |
2319 | # accuracy: +$n preserve $n digits from left, | |
2320 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) | |
2321 | # no-op for $n == 0 | |
2322 | # and overwrite the rest with 0's, return normalized number | |
2323 | # do not return $x->bnorm(), but $x | |
61f5c3f5 | 2324 | |
58cde26e | 2325 | my $x = shift; $x = $class->new($x) unless ref $x; |
b68b7ab1 T |
2326 | my ($scale,$mode) = $x->_scale_a(@_); |
2327 | return $x if !defined $scale || $x->modify('bround'); # no-op | |
58cde26e | 2328 | |
61f5c3f5 T |
2329 | if ($x->is_zero() || $scale == 0) |
2330 | { | |
2331 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 | |
2332 | return $x; | |
2333 | } | |
2334 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN | |
58cde26e JH |
2335 | |
2336 | # we have fewer digits than we want to scale to | |
2337 | my $len = $x->length(); | |
56d9de68 T |
2338 | # convert $scale to a scalar in case it is an object (put's a limit on the |
2339 | # number length, but this would already limited by memory constraints), makes | |
2340 | # it faster | |
2341 | $scale = $scale->numify() if ref ($scale); | |
2342 | ||
ee15d750 JH |
2343 | # scale < 0, but > -len (not >=!) |
2344 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) | |
2345 | { | |
61f5c3f5 | 2346 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
ee15d750 JH |
2347 | return $x; |
2348 | } | |
58cde26e JH |
2349 | |
2350 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 | |
2351 | my ($pad,$digit_round,$digit_after); | |
2352 | $pad = $len - $scale; | |
ee15d750 JH |
2353 | $pad = abs($scale-1) if $scale < 0; |
2354 | ||
ae161977 RGS |
2355 | # do not use digit(), it is very costly for binary => decimal |
2356 | # getting the entire string is also costly, but we need to do it only once | |
0716bf9b JH |
2357 | my $xs = $CALC->_str($x->{value}); |
2358 | my $pl = -$pad-1; | |
56d9de68 | 2359 | |
0716bf9b JH |
2360 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
2361 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 | |
9b924220 | 2362 | $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len; |
0716bf9b | 2363 | $pl++; $pl ++ if $pad >= $len; |
9b924220 | 2364 | $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0; |
ee15d750 | 2365 | |
58cde26e JH |
2366 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look |
2367 | # closer at the remaining digits of the original $x, remember decision | |
2368 | my $round_up = 1; # default round up | |
2369 | $round_up -- if | |
2370 | ($mode eq 'trunc') || # trunc by round down | |
2371 | ($digit_after =~ /[01234]/) || # round down anyway, | |
2372 | # 6789 => round up | |
2373 | ($digit_after eq '5') && # not 5000...0000 | |
ae161977 | 2374 | ($x->_scan_for_nonzero($pad,$xs,$len) == 0) && |
58cde26e JH |
2375 | ( |
2376 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || | |
2377 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || | |
2378 | ($mode eq '+inf') && ($x->{sign} eq '-') || | |
2379 | ($mode eq '-inf') && ($x->{sign} eq '+') || | |
2380 | ($mode eq 'zero') # round down if zero, sign adjusted below | |
2381 | ); | |
61f5c3f5 T |
2382 | my $put_back = 0; # not yet modified |
2383 | ||
61f5c3f5 T |
2384 | if (($pad > 0) && ($pad <= $len)) |
2385 | { | |
ae161977 RGS |
2386 | substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...' |
2387 | $put_back = 1; # need to put back | |
58cde26e | 2388 | } |
61f5c3f5 T |
2389 | elsif ($pad > $len) |
2390 | { | |
2391 | $x->bzero(); # round to '0' | |
2392 | } | |
2393 | ||
58cde26e JH |
2394 | if ($round_up) # what gave test above? |
2395 | { | |
ae161977 | 2396 | $put_back = 1; # need to put back |
9b924220 | 2397 | $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0 |
61f5c3f5 T |
2398 | |
2399 | # we modify directly the string variant instead of creating a number and | |
f9a08e12 | 2400 | # adding it, since that is faster (we already have the string) |
61f5c3f5 T |
2401 | my $c = 0; $pad ++; # for $pad == $len case |
2402 | while ($pad <= $len) | |
2403 | { | |
9b924220 RGS |
2404 | $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10'; |
2405 | substr($xs,-$pad,1) = $c; $pad++; | |
61f5c3f5 T |
2406 | last if $c != 0; # no overflow => early out |
2407 | } | |
9b924220 | 2408 | $xs = '1'.$xs if $c == 0; |
61f5c3f5 | 2409 | |
58cde26e | 2410 | } |
ae161977 | 2411 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed |
ee15d750 JH |
2412 | |
2413 | $x->{_a} = $scale if $scale >= 0; | |
2414 | if ($scale < 0) | |
2415 | { | |
2416 | $x->{_a} = $len+$scale; | |
2417 | $x->{_a} = 0 if $scale < -$len; | |
2418 | } | |
58cde26e JH |
2419 | $x; |
2420 | } | |
2421 | ||
2422 | sub bfloor | |
2423 | { | |
091c87b1 T |
2424 | # return integer less or equal then number; no-op since it's already integer |
2425 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
58cde26e | 2426 | |
f9a08e12 | 2427 | $x->round(@r); |
58cde26e JH |
2428 | } |
2429 | ||
2430 | sub bceil | |
2431 | { | |
091c87b1 T |
2432 | # return integer greater or equal then number; no-op since it's already int |
2433 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
58cde26e | 2434 | |
f9a08e12 | 2435 | $x->round(@r); |
58cde26e JH |
2436 | } |
2437 | ||
091c87b1 T |
2438 | sub as_number |
2439 | { | |
2440 | # An object might be asked to return itself as bigint on certain overloaded | |
7b29e1e6 | 2441 | # operations. This does exactly this, so that sub classes can simple inherit |
091c87b1 T |
2442 | # it or override with their own integer conversion routine. |
2443 | $_[0]->copy(); | |
2444 | } | |
58cde26e | 2445 | |
091c87b1 | 2446 | sub as_hex |
58cde26e | 2447 | { |
091c87b1 T |
2448 | # return as hex string, with prefixed 0x |
2449 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2450 | ||
2451 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2452 | ||
b282a552 | 2453 | my $s = ''; |
091c87b1 | 2454 | $s = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 2455 | $s . $CALC->_as_hex($x->{value}); |
58cde26e JH |
2456 | } |
2457 | ||
091c87b1 | 2458 | sub as_bin |
58cde26e | 2459 | { |
091c87b1 T |
2460 | # return as binary string, with prefixed 0b |
2461 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2462 | ||
2463 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2464 | ||
b282a552 | 2465 | my $s = ''; $s = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 2466 | return $s . $CALC->_as_bin($x->{value}); |
58cde26e JH |
2467 | } |
2468 | ||
7b29e1e6 T |
2469 | sub as_oct |
2470 | { | |
2471 | # return as octal string, with prefixed 0 | |
2472 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2473 | ||
2474 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2475 | ||
2476 | my $s = ''; $s = $x->{sign} if $x->{sign} eq '-'; | |
2477 | return $s . $CALC->_as_oct($x->{value}); | |
2478 | } | |
2479 | ||
091c87b1 T |
2480 | ############################################################################## |
2481 | # private stuff (internal use only) | |
2482 | ||
58cde26e JH |
2483 | sub objectify |
2484 | { | |
2485 | # check for strings, if yes, return objects instead | |
2486 | ||
2487 | # the first argument is number of args objectify() should look at it will | |
2488 | # return $count+1 elements, the first will be a classname. This is because | |
2489 | # overloaded '""' calls bstr($object,undef,undef) and this would result in | |
3c4b39be | 2490 | # useless objects being created and thrown away. So we cannot simple loop |
58cde26e JH |
2491 | # over @_. If the given count is 0, all arguments will be used. |
2492 | ||
2493 | # If the second arg is a ref, use it as class. | |
2494 | # If not, try to use it as classname, unless undef, then use $class | |
2495 | # (aka Math::BigInt). The latter shouldn't happen,though. | |
2496 | ||
2497 | # caller: gives us: | |
2498 | # $x->badd(1); => ref x, scalar y | |
2499 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y | |
2500 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y | |
2501 | # Math::BigInt::badd(1,2); => scalar x, scalar y | |
2502 | # In the last case we check number of arguments to turn it silently into | |
574bacfe | 2503 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e JH |
2504 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
2505 | # currently it tries 'Math::BigInt' + 1, which will not work. | |
ee15d750 JH |
2506 | |
2507 | # some shortcut for the common cases | |
ee15d750 JH |
2508 | # $x->unary_op(); |
2509 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); | |
ee15d750 | 2510 | |
58cde26e JH |
2511 | my $count = abs(shift || 0); |
2512 | ||
9393ace2 | 2513 | my (@a,$k,$d); # resulting array, temp, and downgrade |
58cde26e JH |
2514 | if (ref $_[0]) |
2515 | { | |
2516 | # okay, got object as first | |
2517 | $a[0] = ref $_[0]; | |
2518 | } | |
2519 | else | |
2520 | { | |
2521 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) | |
2522 | $a[0] = $class; | |
58cde26e JH |
2523 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
2524 | } | |
8f675a64 | 2525 | |
9393ace2 JH |
2526 | no strict 'refs'; |
2527 | # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats | |
2528 | if (defined ${"$a[0]::downgrade"}) | |
2529 | { | |
2530 | $d = ${"$a[0]::downgrade"}; | |
2531 | ${"$a[0]::downgrade"} = undef; | |
2532 | } | |
2533 | ||
d614cd8b | 2534 | my $up = ${"$a[0]::upgrade"}; |
7d193e39 | 2535 | # print STDERR "# Now in objectify, my class is today $a[0], count = $count\n"; |
58cde26e JH |
2536 | if ($count == 0) |
2537 | { | |
2538 | while (@_) | |
2539 | { | |
2540 | $k = shift; | |
2541 | if (!ref($k)) | |
2542 | { | |
2543 | $k = $a[0]->new($k); | |
2544 | } | |
d614cd8b | 2545 | elsif (!defined $up && ref($k) ne $a[0]) |
58cde26e JH |
2546 | { |
2547 | # foreign object, try to convert to integer | |
2548 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
e16b8f49 | 2549 | } |
58cde26e JH |
2550 | push @a,$k; |
2551 | } | |
2552 | } | |
2553 | else | |
2554 | { | |
2555 | while ($count > 0) | |
2556 | { | |
58cde26e | 2557 | $count--; |
7d193e39 | 2558 | $k = shift; |
58cde26e JH |
2559 | if (!ref($k)) |
2560 | { | |
2561 | $k = $a[0]->new($k); | |
2562 | } | |
d614cd8b | 2563 | elsif (!defined $up && ref($k) ne $a[0]) |
58cde26e JH |
2564 | { |
2565 | # foreign object, try to convert to integer | |
a0ac753d | 2566 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
e16b8f49 | 2567 | } |
58cde26e JH |
2568 | push @a,$k; |
2569 | } | |
2570 | push @a,@_; # return other params, too | |
2571 | } | |
990fb837 RGS |
2572 | if (! wantarray) |
2573 | { | |
2574 | require Carp; Carp::croak ("$class objectify needs list context"); | |
2575 | } | |
9393ace2 | 2576 | ${"$a[0]::downgrade"} = $d; |
58cde26e JH |
2577 | @a; |
2578 | } | |
2579 | ||
b68b7ab1 T |
2580 | sub _register_callback |
2581 | { | |
2582 | my ($class,$callback) = @_; | |
2583 | ||
2584 | if (ref($callback) ne 'CODE') | |
2585 | { | |
2586 | require Carp; | |
2587 | Carp::croak ("$callback is not a coderef"); | |
2588 | } | |
2589 | $CALLBACKS{$class} = $callback; | |
2590 | } | |
2591 | ||
58cde26e JH |
2592 | sub import |
2593 | { | |
2594 | my $self = shift; | |
61f5c3f5 | 2595 | |
091c87b1 | 2596 | $IMPORT++; # remember we did import() |
8f675a64 | 2597 | my @a; my $l = scalar @_; |
7b29e1e6 | 2598 | my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die |
8f675a64 | 2599 | for ( my $i = 0; $i < $l ; $i++ ) |
58cde26e | 2600 | { |
0716bf9b | 2601 | if ($_[$i] eq ':constant') |
58cde26e | 2602 | { |
0716bf9b | 2603 | # this causes overlord er load to step in |
091c87b1 T |
2604 | overload::constant |
2605 | integer => sub { $self->new(shift) }, | |
2606 | binary => sub { $self->new(shift) }; | |
0716bf9b | 2607 | } |
b3abae2a JH |
2608 | elsif ($_[$i] eq 'upgrade') |
2609 | { | |
2610 | # this causes upgrading | |
2611 | $upgrade = $_[$i+1]; # or undef to disable | |
8f675a64 | 2612 | $i++; |
b3abae2a | 2613 | } |
7b29e1e6 | 2614 | elsif ($_[$i] =~ /^(lib|try|only)\z/) |
0716bf9b JH |
2615 | { |
2616 | # this causes a different low lib to take care... | |
61f5c3f5 | 2617 | $CALC = $_[$i+1] || ''; |
7b29e1e6 T |
2618 | # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback) |
2619 | $warn_or_die = 1 if $_[$i] eq 'lib'; | |
2620 | $warn_or_die = 2 if $_[$i] eq 'only'; | |
8f675a64 JH |
2621 | $i++; |
2622 | } | |
2623 | else | |
2624 | { | |
2625 | push @a, $_[$i]; | |
58cde26e JH |
2626 | } |
2627 | } | |
2628 | # any non :constant stuff is handled by our parent, Exporter | |
b68b7ab1 T |
2629 | if (@a > 0) |
2630 | { | |
2631 | require Exporter; | |
2632 | ||
2633 | $self->SUPER::import(@a); # need it for subclasses | |
2634 | $self->export_to_level(1,$self,@a); # need it for MBF | |
2635 | } | |
58cde26e | 2636 | |
574bacfe JH |
2637 | # try to load core math lib |
2638 | my @c = split /\s*,\s*/,$CALC; | |
b68b7ab1 T |
2639 | foreach (@c) |
2640 | { | |
2641 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters | |
2642 | } | |
7b29e1e6 T |
2643 | push @c, \'FastCalc', \'Calc' # if all fail, try these |
2644 | if $warn_or_die < 2; # but not for "only" | |
61f5c3f5 | 2645 | $CALC = ''; # signal error |
7b29e1e6 | 2646 | foreach my $l (@c) |
574bacfe | 2647 | { |
7b29e1e6 T |
2648 | # fallback libraries are "marked" as \'string', extract string if nec. |
2649 | my $lib = $l; $lib = $$l if ref($l); | |
2650 | ||
07d34614 | 2651 | next if ($lib || '') eq ''; |
574bacfe JH |
2652 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
2653 | $lib =~ s/\.pm$//; | |
61f5c3f5 | 2654 | if ($] < 5.006) |
574bacfe | 2655 | { |
b68b7ab1 T |
2656 | # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is |
2657 | # used in the same script, or eval("") inside import(). | |
07d34614 T |
2658 | my @parts = split /::/, $lib; # Math::BigInt => Math BigInt |
2659 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm | |
2660 | require File::Spec; | |
2661 | $file = File::Spec->catfile (@parts, $file); | |
2662 | eval { require "$file"; $lib->import( @c ); } | |
574bacfe JH |
2663 | } |
2664 | else | |
2665 | { | |
61f5c3f5 | 2666 | eval "use $lib qw/@c/;"; |
574bacfe | 2667 | } |
9b924220 RGS |
2668 | if ($@ eq '') |
2669 | { | |
2670 | my $ok = 1; | |
2671 | # loaded it ok, see if the api_version() is high enough | |
2672 | if ($lib->can('api_version') && $lib->api_version() >= 1.0) | |
2673 | { | |
2674 | $ok = 0; | |
2675 | # api_version matches, check if it really provides anything we need | |
2676 | for my $method (qw/ | |
2677 | one two ten | |
2678 | str num | |
2679 | add mul div sub dec inc | |
2680 | acmp len digit is_one is_zero is_even is_odd | |
2681 | is_two is_ten | |
7b29e1e6 T |
2682 | zeros new copy check |
2683 | from_hex from_oct from_bin as_hex as_bin as_oct | |
9b924220 RGS |
2684 | rsft lsft xor and or |
2685 | mod sqrt root fac pow modinv modpow log_int gcd | |
2686 | /) | |
2687 | { | |
2688 | if (!$lib->can("_$method")) | |
2689 | { | |
2690 | if (($WARN{$lib}||0) < 2) | |
2691 | { | |
2692 | require Carp; | |
2693 | Carp::carp ("$lib is missing method '_$method'"); | |
2694 | $WARN{$lib} = 1; # still warn about the lib | |
2695 | } | |
2696 | $ok++; last; | |
2697 | } | |
2698 | } | |
2699 | } | |
2700 | if ($ok == 0) | |
2701 | { | |
2702 | $CALC = $lib; | |
7b29e1e6 T |
2703 | if ($warn_or_die > 0 && ref($l)) |
2704 | { | |
2705 | require Carp; | |
2706 | my $msg = "Math::BigInt: couldn't load specified math lib(s), fallback to $lib"; | |
2707 | Carp::carp ($msg) if $warn_or_die == 1; | |
2708 | Carp::croak ($msg) if $warn_or_die == 2; | |
2709 | } | |
9b924220 RGS |
2710 | last; # found a usable one, break |
2711 | } | |
2712 | else | |
2713 | { | |
2714 | if (($WARN{$lib}||0) < 2) | |
2715 | { | |
a87115f0 | 2716 | my $ver = eval "\$$lib\::VERSION" || 'unknown'; |
9b924220 RGS |
2717 | require Carp; |
2718 | Carp::carp ("Cannot load outdated $lib v$ver, please upgrade"); | |
2719 | $WARN{$lib} = 2; # never warn again | |
2720 | } | |
2721 | } | |
2722 | } | |
574bacfe | 2723 | } |
990fb837 RGS |
2724 | if ($CALC eq '') |
2725 | { | |
2726 | require Carp; | |
7b29e1e6 T |
2727 | if ($warn_or_die == 2) |
2728 | { | |
2729 | Carp::croak ("Couldn't load specified math lib(s) and fallback disallowed"); | |
2730 | } | |
2731 | else | |
2732 | { | |
2733 | Carp::croak ("Couldn't load any math lib(s), not even fallback to Calc.pm"); | |
2734 | } | |
091c87b1 | 2735 | } |
091c87b1 | 2736 | |
b68b7ab1 T |
2737 | # notify callbacks |
2738 | foreach my $class (keys %CALLBACKS) | |
2739 | { | |
2740 | &{$CALLBACKS{$class}}($CALC); | |
2741 | } | |
2742 | ||
2743 | # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib | |
2744 | # functions | |
091c87b1 T |
2745 | |
2746 | %CAN = (); | |
b68b7ab1 | 2747 | for my $method (qw/ signed_and signed_or signed_xor /) |
091c87b1 T |
2748 | { |
2749 | $CAN{$method} = $CALC->can("_$method") ? 1 : 0; | |
990fb837 | 2750 | } |
b68b7ab1 T |
2751 | |
2752 | # import done | |
58cde26e JH |
2753 | } |
2754 | ||
7b29e1e6 T |
2755 | sub from_hex |
2756 | { | |
2757 | # create a bigint from a hexadecimal string | |
2758 | my ($self, $hs) = @_; | |
2759 | ||
7aa7e0ae | 2760 | my $rc = __from_hex($hs); |
7b29e1e6 T |
2761 | |
2762 | return $self->bnan() unless defined $rc; | |
2763 | ||
2764 | $rc; | |
2765 | } | |
2766 | ||
2767 | sub from_bin | |
2768 | { | |
2769 | # create a bigint from a hexadecimal string | |
2770 | my ($self, $bs) = @_; | |
2771 | ||
7aa7e0ae | 2772 | my $rc = __from_bin($bs); |
7b29e1e6 T |
2773 | |
2774 | return $self->bnan() unless defined $rc; | |
2775 | ||
2776 | $rc; | |
2777 | } | |
2778 | ||
2779 | sub from_oct | |
2780 | { | |
2781 | # create a bigint from a hexadecimal string | |
2782 | my ($self, $os) = @_; | |
2783 | ||
2784 | my $x = $self->bzero(); | |
2785 | ||
2786 | # strip underscores | |
7aa7e0ae T |
2787 | $os =~ s/([0-7])_([0-7])/$1$2/g; |
2788 | $os =~ s/([0-7])_([0-7])/$1$2/g; | |
7b29e1e6 | 2789 | |
7aa7e0ae | 2790 | return $x->bnan() if $os !~ /^[\-\+]?0[0-7]+\z/; |
7b29e1e6 T |
2791 | |
2792 | my $sign = '+'; $sign = '-' if $os =~ /^-/; | |
2793 | ||
2794 | $os =~ s/^[+-]//; # strip sign | |
2795 | $x->{value} = $CALC->_from_oct($os); | |
2796 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' | |
2797 | $x; | |
2798 | } | |
2799 | ||
574bacfe | 2800 | sub __from_hex |
58cde26e | 2801 | { |
b68b7ab1 | 2802 | # internal |
58cde26e JH |
2803 | # convert a (ref to) big hex string to BigInt, return undef for error |
2804 | my $hs = shift; | |
2805 | ||
2806 | my $x = Math::BigInt->bzero(); | |
394e6ffb JH |
2807 | |
2808 | # strip underscores | |
9b924220 RGS |
2809 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
2810 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
394e6ffb | 2811 | |
9b924220 | 2812 | return $x->bnan() if $hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
58cde26e | 2813 | |
9b924220 | 2814 | my $sign = '+'; $sign = '-' if $hs =~ /^-/; |
58cde26e | 2815 | |
9b924220 RGS |
2816 | $hs =~ s/^[+-]//; # strip sign |
2817 | $x->{value} = $CALC->_from_hex($hs); | |
13a12e00 JH |
2818 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2819 | $x; | |
58cde26e JH |
2820 | } |
2821 | ||
574bacfe | 2822 | sub __from_bin |
58cde26e | 2823 | { |
b68b7ab1 | 2824 | # internal |
58cde26e JH |
2825 | # convert a (ref to) big binary string to BigInt, return undef for error |
2826 | my $bs = shift; | |
2827 | ||
2828 | my $x = Math::BigInt->bzero(); | |
7b29e1e6 | 2829 | |
394e6ffb | 2830 | # strip underscores |
9b924220 RGS |
2831 | $bs =~ s/([01])_([01])/$1$2/g; |
2832 | $bs =~ s/([01])_([01])/$1$2/g; | |
2833 | return $x->bnan() if $bs !~ /^[+-]?0b[01]+$/; | |
58cde26e | 2834 | |
9b924220 RGS |
2835 | my $sign = '+'; $sign = '-' if $bs =~ /^\-/; |
2836 | $bs =~ s/^[+-]//; # strip sign | |
2837 | ||
2838 | $x->{value} = $CALC->_from_bin($bs); | |
13a12e00 JH |
2839 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2840 | $x; | |
58cde26e JH |
2841 | } |
2842 | ||
2843 | sub _split | |
2844 | { | |
b68b7ab1 T |
2845 | # input: num_str; output: undef for invalid or |
2846 | # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,\$exp_sign,\$exp_value) | |
2847 | # Internal, take apart a string and return the pieces. | |
2848 | # Strip leading/trailing whitespace, leading zeros, underscore and reject | |
2849 | # invalid input. | |
58cde26e JH |
2850 | my $x = shift; |
2851 | ||
574bacfe | 2852 | # strip white space at front, also extranous leading zeros |
7b29e1e6 T |
2853 | $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' |
2854 | $x =~ s/^\s+//; # but this will | |
2855 | $x =~ s/\s+$//g; # strip white space at end | |
58cde26e | 2856 | |
574bacfe | 2857 | # shortcut, if nothing to split, return early |
7b29e1e6 | 2858 | if ($x =~ /^[+-]?[0-9]+\z/) |
574bacfe | 2859 | { |
9b924220 RGS |
2860 | $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; |
2861 | return (\$sign, \$x, \'', \'', \0); | |
574bacfe | 2862 | } |
58cde26e | 2863 | |
574bacfe | 2864 | # invalid starting char? |
9b924220 | 2865 | return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; |
58cde26e | 2866 | |
7b29e1e6 T |
2867 | return __from_hex($x) if $x =~ /^[\-\+]?0x/; # hex string |
2868 | return __from_bin($x) if $x =~ /^[\-\+]?0b/; # binary string | |
394e6ffb JH |
2869 | |
2870 | # strip underscores between digits | |
7b29e1e6 T |
2871 | $x =~ s/([0-9])_([0-9])/$1$2/g; |
2872 | $x =~ s/([0-9])_([0-9])/$1$2/g; # do twice for 1_2_3 | |
574bacfe | 2873 | |
58cde26e JH |
2874 | # some possible inputs: |
2875 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 | |
aef458a0 | 2876 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999 |
58cde26e | 2877 | |
9b924220 | 2878 | my ($m,$e,$last) = split /[Ee]/,$x; |
56d9de68 | 2879 | return if defined $last; # last defined => 1e2E3 or others |
58cde26e | 2880 | $e = '0' if !defined $e || $e eq ""; |
56d9de68 | 2881 | |
58cde26e JH |
2882 | # sign,value for exponent,mantint,mantfrac |
2883 | my ($es,$ev,$mis,$miv,$mfv); | |
2884 | # valid exponent? | |
7b29e1e6 | 2885 | if ($e =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros |
58cde26e JH |
2886 | { |
2887 | $es = $1; $ev = $2; | |
58cde26e JH |
2888 | # valid mantissa? |
2889 | return if $m eq '.' || $m eq ''; | |
56d9de68 | 2890 | my ($mi,$mf,$lastf) = split /\./,$m; |
8df1e0a2 | 2891 | return if defined $lastf; # lastf defined => 1.2.3 or others |
58cde26e JH |
2892 | $mi = '0' if !defined $mi; |
2893 | $mi .= '0' if $mi =~ /^[\-\+]?$/; | |
2894 | $mf = '0' if !defined $mf || $mf eq ''; | |
7b29e1e6 | 2895 | if ($mi =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros |
58cde26e JH |
2896 | { |
2897 | $mis = $1||'+'; $miv = $2; | |
7b29e1e6 | 2898 | return unless ($mf =~ /^([0-9]*?)0*$/); # strip trailing zeros |
58cde26e | 2899 | $mfv = $1; |
aef458a0 JH |
2900 | # handle the 0e999 case here |
2901 | $ev = 0 if $miv eq '0' && $mfv eq ''; | |
58cde26e JH |
2902 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
2903 | } | |
2904 | } | |
2905 | return; # NaN, not a number | |
2906 | } | |
2907 | ||
58cde26e | 2908 | ############################################################################## |
0716bf9b | 2909 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e | 2910 | |
dccbb853 | 2911 | sub __lcm |
58cde26e JH |
2912 | { |
2913 | # (BINT or num_str, BINT or num_str) return BINT | |
2914 | # does modify first argument | |
2915 | # LCM | |
2916 | ||
b68b7ab1 | 2917 | my ($x,$ty) = @_; |
58cde26e | 2918 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); |
b68b7ab1 T |
2919 | my $method = ref($x) . '::bgcd'; |
2920 | no strict 'refs'; | |
2921 | $x * $ty / &$method($x,$ty); | |
58cde26e JH |
2922 | } |
2923 | ||
58cde26e | 2924 | ############################################################################### |
fdb4b05f T |
2925 | # trigonometric functions |
2926 | ||
2927 | sub bpi | |
2928 | { | |
2929 | # Calculate PI to N digits. Unless upgrading is in effect, returns the | |
2930 | # result truncated to an integer, that is, always returns '3'. | |
2931 | my ($self,$n) = @_; | |
2932 | if (@_ == 1) | |
2933 | { | |
2934 | # called like Math::BigInt::bpi(10); | |
2935 | $n = $self; $self = $class; | |
2936 | } | |
2937 | $self = ref($self) if ref($self); | |
2938 | ||
2939 | return $upgrade->new($n) if defined $upgrade; | |
2940 | ||
2941 | # hard-wired to "3" | |
2942 | $self->new(3); | |
2943 | } | |
2944 | ||
60a1aa19 T |
2945 | sub bcos |
2946 | { | |
2947 | # Calculate cosinus(x) to N digits. Unless upgrading is in effect, returns the | |
2948 | # result truncated to an integer. | |
2949 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
2950 | ||
2951 | return $x if $x->modify('bcos'); | |
2952 | ||
2953 | return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN | |
2954 | ||
2955 | return $upgrade->new($x)->bcos(@r) if defined $upgrade; | |
2956 | ||
20e2035c | 2957 | require Math::BigFloat; |
60a1aa19 T |
2958 | # calculate the result and truncate it to integer |
2959 | my $t = Math::BigFloat->new($x)->bcos(@r)->as_int(); | |
2960 | ||
2961 | $x->bone() if $t->is_one(); | |
2962 | $x->bzero() if $t->is_zero(); | |
2963 | $x->round(@r); | |
2964 | } | |
2965 | ||
2966 | sub bsin | |
2967 | { | |
2968 | # Calculate sinus(x) to N digits. Unless upgrading is in effect, returns the | |
2969 | # result truncated to an integer. | |
2970 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
2971 | ||
2972 | return $x if $x->modify('bsin'); | |
2973 | ||
2974 | return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN | |
2975 | ||
2976 | return $upgrade->new($x)->bsin(@r) if defined $upgrade; | |
2977 | ||
20e2035c | 2978 | require Math::BigFloat; |
60a1aa19 T |
2979 | # calculate the result and truncate it to integer |
2980 | my $t = Math::BigFloat->new($x)->bsin(@r)->as_int(); | |
2981 | ||
2982 | $x->bone() if $t->is_one(); | |
2983 | $x->bzero() if $t->is_zero(); | |
2984 | $x->round(@r); | |
2985 | } | |
2986 | ||
20e2035c T |
2987 | sub batan2 |
2988 | { | |
30afc38d | 2989 | # calculate arcus tangens of ($y/$x) |
20e2035c T |
2990 | |
2991 | # set up parameters | |
30afc38d | 2992 | my ($self,$y,$x,@r) = (ref($_[0]),@_); |
20e2035c T |
2993 | # objectify is costly, so avoid it |
2994 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
2995 | { | |
30afc38d | 2996 | ($self,$y,$x,@r) = objectify(2,@_); |
20e2035c T |
2997 | } |
2998 | ||
30afc38d | 2999 | return $y if $y->modify('batan2'); |
20e2035c | 3000 | |
30afc38d T |
3001 | return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan); |
3002 | ||
0dceeee6 RGS |
3003 | # Y X |
3004 | # != 0 -inf result is +- pi | |
3005 | if ($x->is_inf() || $y->is_inf()) | |
3006 | { | |
3007 | # upgrade to BigFloat etc. | |
3008 | return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade; | |
3009 | if ($y->is_inf()) | |
3010 | { | |
3011 | if ($x->{sign} eq '-inf') | |
3012 | { | |
3013 | # calculate 3 pi/4 => 2.3.. => 2 | |
3014 | $y->bone( substr($y->{sign},0,1) ); | |
3015 | $y->bmul($self->new(2)); | |
3016 | } | |
3017 | elsif ($x->{sign} eq '+inf') | |
3018 | { | |
3019 | # calculate pi/4 => 0.7 => 0 | |
3020 | $y->bzero(); | |
3021 | } | |
3022 | else | |
3023 | { | |
3024 | # calculate pi/2 => 1.5 => 1 | |
3025 | $y->bone( substr($y->{sign},0,1) ); | |
3026 | } | |
3027 | } | |
3028 | else | |
3029 | { | |
3030 | if ($x->{sign} eq '+inf') | |
3031 | { | |
3032 | # calculate pi/4 => 0.7 => 0 | |
3033 | $y->bzero(); | |
3034 | } | |
3035 | else | |
3036 | { | |
3037 | # PI => 3.1415.. => 3 | |
3038 | $y->bone( substr($y->{sign},0,1) ); | |
3039 | $y->bmul($self->new(3)); | |
3040 | } | |
3041 | } | |
3042 | return $y; | |
3043 | } | |
20e2035c | 3044 | |
30afc38d | 3045 | return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade; |
20e2035c T |
3046 | |
3047 | require Math::BigFloat; | |
30afc38d | 3048 | my $r = Math::BigFloat->new($y)->batan2(Math::BigFloat->new($x),@r)->as_int(); |
20e2035c T |
3049 | |
3050 | $x->{value} = $r->{value}; | |
3051 | $x->{sign} = $r->{sign}; | |
3052 | ||
3053 | $x; | |
3054 | } | |
3055 | ||
60a1aa19 T |
3056 | sub batan |
3057 | { | |
3058 | # Calculate arcus tangens of x to N digits. Unless upgrading is in effect, returns the | |
3059 | # result truncated to an integer. | |
3060 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
3061 | ||
3062 | return $x if $x->modify('batan'); | |
3063 | ||
3064 | return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN | |
3065 | ||
3066 | return $upgrade->new($x)->batan(@r) if defined $upgrade; | |
3067 | ||
3068 | # calculate the result and truncate it to integer | |
3069 | my $t = Math::BigFloat->new($x)->batan(@r); | |
3070 | ||
3071 | $x->{value} = $CALC->_new( $x->as_int()->bstr() ); | |
3072 | $x->round(@r); | |
3073 | } | |
3074 | ||
fdb4b05f | 3075 | ############################################################################### |
b68b7ab1 | 3076 | # this method returns 0 if the object can be modified, or 1 if not. |
b282a552 | 3077 | # We use a fast constant sub() here, to avoid costly calls. Subclasses |
58cde26e JH |
3078 | # may override it with special code (f.i. Math::BigInt::Constant does so) |
3079 | ||
0716bf9b | 3080 | sub modify () { 0; } |
e16b8f49 | 3081 | |
a0d0e21e | 3082 | 1; |
a5f75d66 AD |
3083 | __END__ |
3084 | ||
233f7bc0 T |
3085 | =pod |
3086 | ||
a5f75d66 AD |
3087 | =head1 NAME |
3088 | ||
233f7bc0 | 3089 | Math::BigInt - Arbitrary size integer/float math package |
a5f75d66 AD |
3090 | |
3091 | =head1 SYNOPSIS | |
3092 | ||
3093 | use Math::BigInt; | |
58cde26e | 3094 | |
0dceeee6 RGS |
3095 | # or make it faster with huge numbers: install (optional) |
3096 | # Math::BigInt::GMP and always use (it will fall back to | |
3097 | # pure Perl if the GMP library is not installed): | |
3098 | # (See also the L<MATH LIBRARY> section!) | |
990fb837 | 3099 | |
7b29e1e6 | 3100 | # will warn if Math::BigInt::GMP cannot be found |
990fb837 RGS |
3101 | use Math::BigInt lib => 'GMP'; |
3102 | ||
7b29e1e6 T |
3103 | # to supress the warning use this: |
3104 | # use Math::BigInt try => 'GMP'; | |
3105 | ||
0dceeee6 RGS |
3106 | # dies if GMP cannot be loaded: |
3107 | # use Math::BigInt only => 'GMP'; | |
3108 | ||
9b924220 RGS |
3109 | my $str = '1234567890'; |
3110 | my @values = (64,74,18); | |
3111 | my $n = 1; my $sign = '-'; | |
3112 | ||
58cde26e | 3113 | # Number creation |
fdb4b05f T |
3114 | my $x = Math::BigInt->new($str); # defaults to 0 |
3115 | my $y = $x->copy(); # make a true copy | |
3116 | my $nan = Math::BigInt->bnan(); # create a NotANumber | |
3117 | my $zero = Math::BigInt->bzero(); # create a +0 | |
3118 | my $inf = Math::BigInt->binf(); # create a +inf | |
3119 | my $inf = Math::BigInt->binf('-'); # create a -inf | |
3120 | my $one = Math::BigInt->bone(); # create a +1 | |
3121 | my $mone = Math::BigInt->bone('-'); # create a -1 | |
3122 | ||
3123 | my $pi = Math::BigInt->bpi(); # returns '3' | |
3124 | # see Math::BigFloat::bpi() | |
58cde26e | 3125 | |
7b29e1e6 T |
3126 | $h = Math::BigInt->new('0x123'); # from hexadecimal |
3127 | $b = Math::BigInt->new('0b101'); # from binary | |
3128 | $o = Math::BigInt->from_oct('0101'); # from octal | |
3129 | ||
56d9de68 T |
3130 | # Testing (don't modify their arguments) |
3131 | # (return true if the condition is met, otherwise false) | |
3132 | ||
3133 | $x->is_zero(); # if $x is +0 | |
3134 | $x->is_nan(); # if $x is NaN | |
3135 | $x->is_one(); # if $x is +1 | |
3136 | $x->is_one('-'); # if $x is -1 | |
3137 | $x->is_odd(); # if $x is odd | |
3138 | $x->is_even(); # if $x is even | |
b282a552 T |
3139 | $x->is_pos(); # if $x >= 0 |
3140 | $x->is_neg(); # if $x < 0 | |
9b924220 | 3141 | $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+') |
56d9de68 T |
3142 | $x->is_int(); # if $x is an integer (not a float) |
3143 | ||
3c4b39be | 3144 | # comparing and digit/sign extraction |
56d9de68 T |
3145 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
3146 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
3147 | $x->sign(); # return the sign, either +,- or NaN | |
3148 | $x->digit($n); # return the nth digit, counting from right | |
3149 | $x->digit(-$n); # return the nth digit, counting from left | |
58cde26e | 3150 | |
990fb837 RGS |
3151 | # The following all modify their first argument. If you want to preserve |
3152 | # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is | |
3c4b39be | 3153 | # necessary when mixing $a = $b assignments with non-overloaded math. |
58cde26e | 3154 | |
56d9de68 T |
3155 | $x->bzero(); # set $x to 0 |
3156 | $x->bnan(); # set $x to NaN | |
3157 | $x->bone(); # set $x to +1 | |
3158 | $x->bone('-'); # set $x to -1 | |
3159 | $x->binf(); # set $x to inf | |
3160 | $x->binf('-'); # set $x to -inf | |
3161 | ||
3162 | $x->bneg(); # negation | |
3163 | $x->babs(); # absolute value | |
3164 | $x->bnorm(); # normalize (no-op in BigInt) | |
3165 | $x->bnot(); # two's complement (bit wise not) | |
3166 | $x->binc(); # increment $x by 1 | |
3167 | $x->bdec(); # decrement $x by 1 | |
58cde26e | 3168 | |
56d9de68 T |
3169 | $x->badd($y); # addition (add $y to $x) |
3170 | $x->bsub($y); # subtraction (subtract $y from $x) | |
3171 | $x->bmul($y); # multiplication (multiply $x by $y) | |
3172 | $x->bdiv($y); # divide, set $x to quotient | |
3173 | # return (quo,rem) or quo if scalar | |
3174 | ||
80365507 T |
3175 | $x->bmuladd($y,$z); # $x = $x * $y + $z |
3176 | ||
56d9de68 T |
3177 | $x->bmod($y); # modulus (x % y) |
3178 | $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod)) | |
3179 | $x->bmodinv($mod); # the inverse of $x in the given modulus $mod | |
3180 | ||
3181 | $x->bpow($y); # power of arguments (x ** y) | |
7d193e39 T |
3182 | $x->blsft($y); # left shift in base 2 |
3183 | $x->brsft($y); # right shift in base 2 | |
7b29e1e6 T |
3184 | # returns (quo,rem) or quo if in scalar context |
3185 | $x->blsft($y,$n); # left shift by $y places in base $n | |
3186 | $x->brsft($y,$n); # right shift by $y places in base $n | |
3187 | # returns (quo,rem) or quo if in scalar context | |
58cde26e | 3188 | |
56d9de68 T |
3189 | $x->band($y); # bitwise and |
3190 | $x->bior($y); # bitwise inclusive or | |
3191 | $x->bxor($y); # bitwise exclusive or | |
3192 | $x->bnot(); # bitwise not (two's complement) | |
3193 | ||
3194 | $x->bsqrt(); # calculate square-root | |
990fb837 | 3195 | $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) |
56d9de68 | 3196 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
58cde26e | 3197 | |
50109ad0 RGS |
3198 | $x->bnok($y); # x over y (binomial coefficient n over k) |
3199 | ||
7d193e39 T |
3200 | $x->blog(); # logarithm of $x to base e (Euler's number) |
3201 | $x->blog($base); # logarithm of $x to base $base (f.i. 2) | |
3202 | $x->bexp(); # calculate e ** $x where e is Euler's number | |
3203 | ||
990fb837 | 3204 | $x->round($A,$P,$mode); # round to accuracy or precision using mode $mode |
9b924220 | 3205 | $x->bround($n); # accuracy: preserve $n digits |
d5351619 T |
3206 | $x->bfround($n); # $n > 0: round $nth digits, |
3207 | # $n < 0: round to the $nth digit after the | |
3208 | # dot, no-op for BigInts | |
58cde26e | 3209 | |
990fb837 | 3210 | # The following do not modify their arguments in BigInt (are no-ops), |
56d9de68 | 3211 | # but do so in BigFloat: |
58cde26e | 3212 | |
56d9de68 T |
3213 | $x->bfloor(); # return integer less or equal than $x |
3214 | $x->bceil(); # return integer greater or equal than $x | |
58cde26e JH |
3215 | |
3216 | # The following do not modify their arguments: | |
3217 | ||
9b924220 RGS |
3218 | # greatest common divisor (no OO style) |
3219 | my $gcd = Math::BigInt::bgcd(@values); | |
3220 | # lowest common multiplicator (no OO style) | |
3221 | my $lcm = Math::BigInt::blcm(@values); | |
bd05a461 | 3222 | |
56d9de68 | 3223 | $x->length(); # return number of digits in number |
9b924220 | 3224 | ($xl,$f) = $x->length(); # length of number and length of fraction part, |
b68b7ab1 | 3225 | # latter is always 0 digits long for BigInts |
56d9de68 T |
3226 | |
3227 | $x->exponent(); # return exponent as BigInt | |
3228 | $x->mantissa(); # return (signed) mantissa as BigInt | |
3229 | $x->parts(); # return (mantissa,exponent) as BigInt | |
3230 | $x->copy(); # make a true copy of $x (unlike $y = $x;) | |
b282a552 T |
3231 | $x->as_int(); # return as BigInt (in BigInt: same as copy()) |
3232 | $x->numify(); # return as scalar (might overflow!) | |
bd05a461 | 3233 | |
56d9de68 | 3234 | # conversation to string (do not modify their argument) |
b68b7ab1 T |
3235 | $x->bstr(); # normalized string (e.g. '3') |
3236 | $x->bsstr(); # norm. string in scientific notation (e.g. '3E0') | |
56d9de68 T |
3237 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
3238 | $x->as_bin(); # as signed binary string with prefixed 0b | |
7b29e1e6 | 3239 | $x->as_oct(); # as signed octal string with prefixed 0 |
b282a552 | 3240 | |
bd05a461 | 3241 | |
f9a08e12 | 3242 | # precision and accuracy (see section about rounding for more) |
56d9de68 T |
3243 | $x->precision(); # return P of $x (or global, if P of $x undef) |
3244 | $x->precision($n); # set P of $x to $n | |
3245 | $x->accuracy(); # return A of $x (or global, if A of $x undef) | |
3246 | $x->accuracy($n); # set A $x to $n | |
f9a08e12 | 3247 | |
56d9de68 | 3248 | # Global methods |
b68b7ab1 T |
3249 | Math::BigInt->precision(); # get/set global P for all BigInt objects |
3250 | Math::BigInt->accuracy(); # get/set global A for all BigInt objects | |
3251 | Math::BigInt->round_mode(); # get/set global round mode, one of | |
7b29e1e6 | 3252 | # 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common' |
b68b7ab1 | 3253 | Math::BigInt->config(); # return hash containing configuration |
f9a08e12 | 3254 | |
a5f75d66 AD |
3255 | =head1 DESCRIPTION |
3256 | ||
3c4b39be | 3257 | All operators (including basic math operations) are overloaded if you |
58cde26e | 3258 | declare your big integers as |
a5f75d66 | 3259 | |
58cde26e | 3260 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 | 3261 | |
58cde26e JH |
3262 | Operations with overloaded operators preserve the arguments which is |
3263 | exactly what you expect. | |
a5f75d66 AD |
3264 | |
3265 | =over 2 | |
3266 | ||
aef458a0 | 3267 | =item Input |
a5f75d66 | 3268 | |
aef458a0 JH |
3269 | Input values to these routines may be any string, that looks like a number |
3270 | and results in an integer, including hexadecimal and binary numbers. | |
58cde26e | 3271 | |
aef458a0 JH |
3272 | Scalars holding numbers may also be passed, but note that non-integer numbers |
3273 | may already have lost precision due to the conversation to float. Quote | |
091c87b1 | 3274 | your input if you want BigInt to see all the digits: |
a5f75d66 | 3275 | |
aef458a0 JH |
3276 | $x = Math::BigInt->new(12345678890123456789); # bad |
3277 | $x = Math::BigInt->new('12345678901234567890'); # good | |
58cde26e | 3278 | |
56d9de68 | 3279 | You can include one underscore between any two digits. |
58cde26e JH |
3280 | |
3281 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. | |
aef458a0 | 3282 | Non-integer values result in NaN. |
58cde26e | 3283 | |
7b29e1e6 T |
3284 | Hexadecimal (prefixed with "0x") and binary numbers (prefixed with "0b") |
3285 | are accepted, too. Please note that octal numbers are not recognized | |
3286 | by new(), so the following will print "123": | |
3287 | ||
3288 | perl -MMath::BigInt -le 'print Math::BigInt->new("0123")' | |
3289 | ||
3290 | To convert an octal number, use from_oct(); | |
3291 | ||
3292 | perl -MMath::BigInt -le 'print Math::BigInt->from_oct("0123")' | |
3293 | ||
aef458a0 | 3294 | Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('') |
091c87b1 T |
3295 | results in 'NaN'. This might change in the future, so use always the following |
3296 | explicit forms to get a zero or NaN: | |
3297 | ||
3298 | $zero = Math::BigInt->bzero(); | |
3299 | $nan = Math::BigInt->bnan(); | |
58cde26e | 3300 | |
aef458a0 | 3301 | C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers |
091c87b1 | 3302 | are always stored in normalized form. If passed a string, creates a BigInt |
aef458a0 | 3303 | object from the input. |
a5f75d66 AD |
3304 | |
3305 | =item Output | |
3306 | ||
b68b7ab1 T |
3307 | Output values are BigInt objects (normalized), except for the methods which |
3308 | return a string (see L<SYNOPSIS>). | |
3309 | ||
58cde26e | 3310 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
b68b7ab1 T |
3311 | C<is_nan()>, etc.) return true or false, while others (C<bcmp()>, C<bacmp()>) |
3312 | return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort. | |
a5f75d66 AD |
3313 | |
3314 | =back | |
3315 | ||
b3abae2a JH |
3316 | =head1 METHODS |
3317 | ||
56d9de68 | 3318 | Each of the methods below (except config(), accuracy() and precision()) |
b68b7ab1 T |
3319 | accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R> |
3320 | are C<accuracy>, C<precision> and C<round_mode>. Please see the section about | |
56d9de68 | 3321 | L<ACCURACY and PRECISION> for more information. |
b3abae2a | 3322 | |
7b29e1e6 | 3323 | =head2 config() |
8f675a64 JH |
3324 | |
3325 | use Data::Dumper; | |
3326 | ||
3327 | print Dumper ( Math::BigInt->config() ); | |
56d9de68 | 3328 | print Math::BigInt->config()->{lib},"\n"; |
8f675a64 JH |
3329 | |
3330 | Returns a hash containing the configuration, e.g. the version number, lib | |
56d9de68 T |
3331 | loaded etc. The following hash keys are currently filled in with the |
3332 | appropriate information. | |
3333 | ||
3334 | key Description | |
3335 | Example | |
3336 | ============================================================ | |
091c87b1 | 3337 | lib Name of the low-level math library |
56d9de68 | 3338 | Math::BigInt::Calc |
091c87b1 | 3339 | lib_version Version of low-level math library (see 'lib') |
56d9de68 | 3340 | 0.30 |
091c87b1 | 3341 | class The class name of config() you just called |
56d9de68 | 3342 | Math::BigInt |
091c87b1 | 3343 | upgrade To which class math operations might be upgraded |
56d9de68 | 3344 | Math::BigFloat |
091c87b1 | 3345 | downgrade To which class math operations might be downgraded |
56d9de68 T |
3346 | undef |
3347 | precision Global precision | |
3348 | undef | |
3349 | accuracy Global accuracy | |
3350 | undef | |
3351 | round_mode Global round mode | |
3352 | even | |
3353 | version version number of the class you used | |
3354 | 1.61 | |
3c4b39be | 3355 | div_scale Fallback accuracy for div |
56d9de68 | 3356 | 40 |
091c87b1 T |
3357 | trap_nan If true, traps creation of NaN via croak() |
3358 | 1 | |
3359 | trap_inf If true, traps creation of +inf/-inf via croak() | |
3360 | 1 | |
56d9de68 | 3361 | |
c38b2de2 | 3362 | The following values can be set by passing C<config()> a reference to a hash: |
93c87d9d T |
3363 | |
3364 | trap_inf trap_nan | |
3365 | upgrade downgrade precision accuracy round_mode div_scale | |
3366 | ||
3367 | Example: | |
3368 | ||
3369 | $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } ); | |
8f675a64 | 3370 | |
7b29e1e6 | 3371 | =head2 accuracy() |
13a12e00 JH |
3372 | |
3373 | $x->accuracy(5); # local for $x | |
56d9de68 | 3374 | CLASS->accuracy(5); # global for all members of CLASS |
233f7bc0 T |
3375 | # Note: This also applies to new()! |
3376 | ||
3377 | $A = $x->accuracy(); # read out accuracy that affects $x | |
3378 | $A = CLASS->accuracy(); # read out global accuracy | |
13a12e00 JH |
3379 | |
3380 | Set or get the global or local accuracy, aka how many significant digits the | |
233f7bc0 T |
3381 | results have. If you set a global accuracy, then this also applies to new()! |
3382 | ||
3383 | Warning! The accuracy I<sticks>, e.g. once you created a number under the | |
3384 | influence of C<< CLASS->accuracy($A) >>, all results from math operations with | |
3385 | that number will also be rounded. | |
3386 | ||
3c4b39be | 3387 | In most cases, you should probably round the results explicitly using one of |
233f7bc0 T |
3388 | L<round()>, L<bround()> or L<bfround()> or by passing the desired accuracy |
3389 | to the math operation as additional parameter: | |
3390 | ||
3391 | my $x = Math::BigInt->new(30000); | |
3392 | my $y = Math::BigInt->new(7); | |
3393 | print scalar $x->copy()->bdiv($y, 2); # print 4300 | |
3394 | print scalar $x->copy()->bdiv($y)->bround(2); # print 4300 | |
56d9de68 T |
3395 | |
3396 | Please see the section about L<ACCURACY AND PRECISION> for further details. | |
13a12e00 JH |
3397 | |
3398 | Value must be greater than zero. Pass an undef value to disable it: | |
3399 | ||
3400 | $x->accuracy(undef); | |
3401 | Math::BigInt->accuracy(undef); | |
3402 | ||
3403 | Returns the current accuracy. For C<$x->accuracy()> it will return either the | |
3404 | local accuracy, or if not defined, the global. This means the return value | |
3405 | represents the accuracy that will be in effect for $x: | |
3406 | ||
3407 | $y = Math::BigInt->new(1234567); # unrounded | |
3408 | print Math::BigInt->accuracy(4),"\n"; # set 4, print 4 | |
233f7bc0 | 3409 | $x = Math::BigInt->new(123456); # $x will be automatically rounded! |
13a12e00 JH |
3410 | print "$x $y\n"; # '123500 1234567' |
3411 | print $x->accuracy(),"\n"; # will be 4 | |
3412 | print $y->accuracy(),"\n"; # also 4, since global is 4 | |
3413 | print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5 | |
3414 | print $x->accuracy(),"\n"; # still 4 | |
3415 | print $y->accuracy(),"\n"; # 5, since global is 5 | |
3416 | ||
56d9de68 T |
3417 | Note: Works also for subclasses like Math::BigFloat. Each class has it's own |
3418 | globals separated from Math::BigInt, but it is possible to subclass | |
3419 | Math::BigInt and make the globals of the subclass aliases to the ones from | |
3420 | Math::BigInt. | |
3421 | ||
7b29e1e6 | 3422 | =head2 precision() |
56d9de68 | 3423 | |
233f7bc0 T |
3424 | $x->precision(-2); # local for $x, round at the second digit right of the dot |
3425 | $x->precision(2); # ditto, round at the second digit left of the dot | |
3426 | ||
3427 | CLASS->precision(5); # Global for all members of CLASS | |
3428 | # This also applies to new()! | |
3429 | CLASS->precision(-5); # ditto | |
3430 | ||
3431 | $P = CLASS->precision(); # read out global precision | |
3432 | $P = $x->precision(); # read out precision that affects $x | |
3433 | ||
3434 | Note: You probably want to use L<accuracy()> instead. With L<accuracy> you | |
3435 | set the number of digits each result should have, with L<precision> you | |
3436 | set the place where to round! | |
56d9de68 | 3437 | |
233f7bc0 T |
3438 | C<precision()> sets or gets the global or local precision, aka at which digit |
3439 | before or after the dot to round all results. A set global precision also | |
3440 | applies to all newly created numbers! | |
3441 | ||
3442 | In Math::BigInt, passing a negative number precision has no effect since no | |
3443 | numbers have digits after the dot. In L<Math::BigFloat>, it will round all | |
3444 | results to P digits after the dot. | |
56d9de68 T |
3445 | |
3446 | Please see the section about L<ACCURACY AND PRECISION> for further details. | |
3447 | ||
233f7bc0 | 3448 | Pass an undef value to disable it: |
56d9de68 T |
3449 | |
3450 | $x->precision(undef); | |
3451 | Math::BigInt->precision(undef); | |
3452 | ||
3453 | Returns the current precision. For C<$x->precision()> it will return either the | |
3454 | local precision of $x, or if not defined, the global. This means the return | |
233f7bc0 | 3455 | value represents the prevision that will be in effect for $x: |
56d9de68 T |
3456 | |
3457 | $y = Math::BigInt->new(1234567); # unrounded | |
3458 | print Math::BigInt->precision(4),"\n"; # set 4, print 4 | |
3459 | $x = Math::BigInt->new(123456); # will be automatically rounded | |
233f7bc0 | 3460 | print $x; # print "120000"! |
56d9de68 | 3461 | |
233f7bc0 T |
3462 | Note: Works also for subclasses like L<Math::BigFloat>. Each class has its |
3463 | own globals separated from Math::BigInt, but it is possible to subclass | |
56d9de68 T |
3464 | Math::BigInt and make the globals of the subclass aliases to the ones from |
3465 | Math::BigInt. | |
3466 | ||
7b29e1e6 | 3467 | =head2 brsft() |
b3abae2a JH |
3468 | |
3469 | $x->brsft($y,$n); | |
3470 | ||
3471 | Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and | |
3472 | 2, but others work, too. | |
3473 | ||
3474 | Right shifting usually amounts to dividing $x by $n ** $y and truncating the | |
3475 | result: | |
3476 | ||
3477 | ||
3478 | $x = Math::BigInt->new(10); | |
3479 | $x->brsft(1); # same as $x >> 1: 5 | |
3480 | $x = Math::BigInt->new(1234); | |
3481 | $x->brsft(2,10); # result 12 | |
3482 | ||
3483 | There is one exception, and that is base 2 with negative $x: | |
3484 | ||
3485 | ||
3486 | $x = Math::BigInt->new(-5); | |
3487 | print $x->brsft(1); | |
3488 | ||
3489 | This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the | |
3490 | result). | |
3491 | ||
7b29e1e6 | 3492 | =head2 new() |
b3abae2a JH |
3493 | |
3494 | $x = Math::BigInt->new($str,$A,$P,$R); | |
3495 | ||
aef458a0 | 3496 | Creates a new BigInt object from a scalar or another BigInt object. The |
b3abae2a JH |
3497 | input is accepted as decimal, hex (with leading '0x') or binary (with leading |
3498 | '0b'). | |
3499 | ||
aef458a0 JH |
3500 | See L<Input> for more info on accepted input formats. |
3501 | ||
7b29e1e6 T |
3502 | =head2 from_oct() |
3503 | ||
7aa7e0ae | 3504 | $x = Math::BigInt->from_oct("0775"); # input is octal |
7b29e1e6 T |
3505 | |
3506 | =head2 from_hex() | |
3507 | ||
7aa7e0ae | 3508 | $x = Math::BigInt->from_hex("0xcafe"); # input is hexadecimal |
7b29e1e6 T |
3509 | |
3510 | =head2 from_bin() | |
3511 | ||
7aa7e0ae | 3512 | $x = Math::BigInt->from_oct("0x10011"); # input is binary |
7b29e1e6 T |
3513 | |
3514 | =head2 bnan() | |
b3abae2a JH |
3515 | |
3516 | $x = Math::BigInt->bnan(); | |
3517 | ||
3518 | Creates a new BigInt object representing NaN (Not A Number). | |
3519 | If used on an object, it will set it to NaN: | |
3520 | ||
3521 | $x->bnan(); | |
3522 | ||
7b29e1e6 | 3523 | =head2 bzero() |
b3abae2a JH |
3524 | |
3525 | $x = Math::BigInt->bzero(); | |
3526 | ||
3527 | Creates a new BigInt object representing zero. | |
3528 | If used on an object, it will set it to zero: | |
3529 | ||
3530 | $x->bzero(); | |
3531 | ||
7b29e1e6 | 3532 | =head2 binf() |
b3abae2a JH |
3533 | |
3534 | $x = Math::BigInt->binf($sign); | |
3535 | ||
3536 | Creates a new BigInt object representing infinity. The optional argument is | |
3537 | either '-' or '+', indicating whether you want infinity or minus infinity. | |
3538 | If used on an object, it will set it to infinity: | |
3539 | ||
3540 | $x->binf(); | |
3541 | $x->binf('-'); | |
3542 | ||
7b29e1e6 | 3543 | =head2 bone() |
b3abae2a JH |
3544 | |
3545 | $x = Math::BigInt->binf($sign); | |
3546 | ||
3547 | Creates a new BigInt object representing one. The optional argument is | |
3548 | either '-' or '+', indicating whether you want one or minus one. | |
3549 | If used on an object, it will set it to one: | |
3550 | ||
3551 | $x->bone(); # +1 | |
3552 | $x->bone('-'); # -1 | |
3553 | ||
56b9c951 JH |
3554 | =head2 is_one()/is_zero()/is_nan()/is_inf() |
3555 | ||
b3abae2a JH |
3556 | |
3557 | $x->is_zero(); # true if arg is +0 | |
3558 | $x->is_nan(); # true if arg is NaN | |
3559 | $x->is_one(); # true if arg is +1 | |
3560 | $x->is_one('-'); # true if arg is -1 | |
b3abae2a JH |
3561 | $x->is_inf(); # true if +inf |
3562 | $x->is_inf('-'); # true if -inf (sign is default '+') | |
56b9c951 | 3563 | |
3c4b39be | 3564 | These methods all test the BigInt for being one specific value and return |
56b9c951 JH |
3565 | true or false depending on the input. These are faster than doing something |
3566 | like: | |
3567 | ||
3568 | if ($x == 0) | |
3569 | ||
7b29e1e6 | 3570 | =head2 is_pos()/is_neg()/is_positive()/is_negative() |
56b9c951 | 3571 | |
b68b7ab1 T |
3572 | $x->is_pos(); # true if > 0 |
3573 | $x->is_neg(); # true if < 0 | |
56b9c951 JH |
3574 | |
3575 | The methods return true if the argument is positive or negative, respectively. | |
3576 | C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and | |
b68b7ab1 | 3577 | C<-inf> is negative. A C<zero> is neither positive nor negative. |
56b9c951 JH |
3578 | |
3579 | These methods are only testing the sign, and not the value. | |
3580 | ||
3c4b39be | 3581 | C<is_positive()> and C<is_negative()> are aliases to C<is_pos()> and |
b282a552 T |
3582 | C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were |
3583 | introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced | |
3584 | in v1.68. | |
3585 | ||
56b9c951 JH |
3586 | =head2 is_odd()/is_even()/is_int() |
3587 | ||
3588 | $x->is_odd(); # true if odd, false for even | |
3589 | $x->is_even(); # true if even, false for odd | |
b3abae2a JH |
3590 | $x->is_int(); # true if $x is an integer |
3591 | ||
56b9c951 JH |
3592 | The return true when the argument satisfies the condition. C<NaN>, C<+inf>, |
3593 | C<-inf> are not integers and are neither odd nor even. | |
b3abae2a | 3594 | |
c38b2de2 JH |
3595 | In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers. |
3596 | ||
7b29e1e6 | 3597 | =head2 bcmp() |
b3abae2a | 3598 | |
56b9c951 JH |
3599 | $x->bcmp($y); |
3600 | ||
3601 | Compares $x with $y and takes the sign into account. | |
3602 | Returns -1, 0, 1 or undef. | |
b3abae2a | 3603 | |
7b29e1e6 | 3604 | =head2 bacmp() |
b3abae2a | 3605 | |
56b9c951 JH |
3606 | $x->bacmp($y); |
3607 | ||
3608 | Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef. | |
b3abae2a | 3609 | |
7b29e1e6 | 3610 | =head2 sign() |
b3abae2a | 3611 | |
56b9c951 JH |
3612 | $x->sign(); |
3613 | ||
3614 | Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN. | |
b3abae2a | 3615 | |
b68b7ab1 T |
3616 | If you want $x to have a certain sign, use one of the following methods: |
3617 | ||
3618 | $x->babs(); # '+' | |
3619 | $x->babs()->bneg(); # '-' | |
3620 | $x->bnan(); # 'NaN' | |
3621 | $x->binf(); # '+inf' | |
3622 | $x->binf('-'); # '-inf' | |
3623 | ||
7b29e1e6 | 3624 | =head2 digit() |
091c87b1 T |
3625 | |
3626 | $x->digit($n); # return the nth digit, counting from right | |
b3abae2a | 3627 | |
091c87b1 | 3628 | If C<$n> is negative, returns the digit counting from left. |
b3abae2a | 3629 | |
7b29e1e6 | 3630 | =head2 bneg() |
b3abae2a JH |
3631 | |
3632 | $x->bneg(); | |
3633 | ||
3634 | Negate the number, e.g. change the sign between '+' and '-', or between '+inf' | |
3635 | and '-inf', respectively. Does nothing for NaN or zero. | |
3636 | ||
7b29e1e6 | 3637 | =head2 babs() |
b3abae2a JH |
3638 | |
3639 | $x->babs(); | |
3640 | ||
86b76201 | 3641 | Set the number to its absolute value, e.g. change the sign from '-' to '+' |
b3abae2a JH |
3642 | and from '-inf' to '+inf', respectively. Does nothing for NaN or positive |
3643 | numbers. | |
3644 | ||
7b29e1e6 | 3645 | =head2 bnorm() |
b3abae2a | 3646 | |
56d9de68 | 3647 | $x->bnorm(); # normalize (no-op) |
b3abae2a | 3648 | |
7b29e1e6 | 3649 | =head2 bnot() |
b3abae2a | 3650 | |
091c87b1 T |
3651 | $x->bnot(); |
3652 | ||
86b76201 | 3653 | Two's complement (bitwise not). This is equivalent to |
091c87b1 T |
3654 | |
3655 | $x->binc()->bneg(); | |
3656 | ||
3657 | but faster. | |
b3abae2a | 3658 | |
7b29e1e6 | 3659 | =head2 binc() |
b3abae2a | 3660 | |
56d9de68 | 3661 | $x->binc(); # increment x by 1 |
b3abae2a | 3662 | |
7b29e1e6 | 3663 | =head2 bdec() |
b3abae2a | 3664 | |
56d9de68 | 3665 | $x->bdec(); # decrement x by 1 |
b3abae2a | 3666 | |
7b29e1e6 | 3667 | =head2 badd() |
b3abae2a | 3668 | |
56d9de68 | 3669 | $x->badd($y); # addition (add $y to $x) |
b3abae2a | 3670 | |
7b29e1e6 | 3671 | =head2 bsub() |
b3abae2a | 3672 | |
56d9de68 | 3673 | $x->bsub($y); # subtraction (subtract $y from $x) |
b3abae2a | 3674 | |
7b29e1e6 | 3675 | =head2 bmul() |
b3abae2a | 3676 | |
56d9de68 | 3677 | $x->bmul($y); # multiplication (multiply $x by $y) |
b3abae2a | 3678 | |
80365507 T |
3679 | =head2 bmuladd() |
3680 | ||
3681 | $x->bmuladd($y,$z); | |
3682 | ||
3683 | Multiply $x by $y, and then add $z to the result, | |
3684 | ||
3685 | This method was added in v1.87 of Math::BigInt (June 2007). | |
3686 | ||
7b29e1e6 | 3687 | =head2 bdiv() |
b3abae2a | 3688 | |
56d9de68 T |
3689 | $x->bdiv($y); # divide, set $x to quotient |
3690 | # return (quo,rem) or quo if scalar | |
b3abae2a | 3691 | |
7b29e1e6 | 3692 | =head2 bmod() |
b3abae2a | 3693 | |
56d9de68 | 3694 | $x->bmod($y); # modulus (x % y) |
b3abae2a | 3695 | |
7b29e1e6 | 3696 | =head2 bmodinv() |
d614cd8b | 3697 | |
56d9de68 | 3698 | num->bmodinv($mod); # modular inverse |
d614cd8b JH |
3699 | |
3700 | Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is | |
3701 | returned unless C<$num> is relatively prime to C<$mod>, i.e. unless | |
3702 | C<bgcd($num, $mod)==1>. | |
3703 | ||
7b29e1e6 | 3704 | =head2 bmodpow() |
d614cd8b | 3705 | |
56d9de68 T |
3706 | $num->bmodpow($exp,$mod); # modular exponentation |
3707 | # ($num**$exp % $mod) | |
d614cd8b JH |
3708 | |
3709 | Returns the value of C<$num> taken to the power C<$exp> in the modulus | |
3710 | C<$mod> using binary exponentation. C<bmodpow> is far superior to | |
3711 | writing | |
3712 | ||
56d9de68 | 3713 | $num ** $exp % $mod |
d614cd8b | 3714 | |
091c87b1 | 3715 | because it is much faster - it reduces internal variables into |
d614cd8b JH |
3716 | the modulus whenever possible, so it operates on smaller numbers. |
3717 | ||
3718 | C<bmodpow> also supports negative exponents. | |
3719 | ||
56d9de68 | 3720 | bmodpow($num, -1, $mod) |
d614cd8b JH |
3721 | |
3722 | is exactly equivalent to | |
3723 | ||
56d9de68 | 3724 | bmodinv($num, $mod) |
d614cd8b | 3725 | |
7b29e1e6 | 3726 | =head2 bpow() |
b3abae2a | 3727 | |
56d9de68 | 3728 | $x->bpow($y); # power of arguments (x ** y) |
b3abae2a | 3729 | |
7d193e39 T |
3730 | =head2 blog() |
3731 | ||
3732 | $x->blog($base, $accuracy); # logarithm of x to the base $base | |
3733 | ||
3734 | If C<$base> is not defined, Euler's number (e) is used: | |
3735 | ||
3736 | print $x->blog(undef, 100); # log(x) to 100 digits | |
3737 | ||
3738 | =head2 bexp() | |
3739 | ||
3740 | $x->bexp($accuracy); # calculate e ** X | |
3741 | ||
3742 | Calculates the expression C<e ** $x> where C<e> is Euler's number. | |
3743 | ||
3744 | This method was added in v1.82 of Math::BigInt (April 2007). | |
3745 | ||
3746 | See also L<blog()>. | |
3747 | ||
50109ad0 RGS |
3748 | =head2 bnok() |
3749 | ||
3750 | $x->bnok($y); # x over y (binomial coefficient n over k) | |
3751 | ||
3752 | Calculates the binomial coefficient n over k, also called the "choose" | |
3753 | function. The result is equivalent to: | |
3754 | ||
3755 | ( n ) n! | |
3756 | | - | = ------- | |
3757 | ( k ) k!(n-k)! | |
3758 | ||
3759 | This method was added in v1.84 of Math::BigInt (April 2007). | |
3760 | ||
fdb4b05f T |
3761 | =head2 bpi() |
3762 | ||
3763 | print Math::BigInt->bpi(100), "\n"; # 3 | |
3764 | ||
20e2035c T |
3765 | Returns PI truncated to an integer, with the argument being ignored. This means |
3766 | under BigInt this always returns C<3>. | |
fdb4b05f | 3767 | |
20e2035c T |
3768 | If upgrading is in effect, returns PI, rounded to N digits with the |
3769 | current rounding mode: | |
fdb4b05f T |
3770 | |
3771 | use Math::BigFloat; | |
3772 | use Math::BigInt upgrade => Math::BigFloat; | |
3773 | print Math::BigInt->bpi(3), "\n"; # 3.14 | |
3774 | print Math::BigInt->bpi(100), "\n"; # 3.1415.... | |
3775 | ||
3776 | This method was added in v1.87 of Math::BigInt (June 2007). | |
3777 | ||
60a1aa19 T |
3778 | =head2 bcos() |
3779 | ||
20e2035c | 3780 | my $x = Math::BigInt->new(1); |
60a1aa19 T |
3781 | print $x->bcos(100), "\n"; |
3782 | ||
3783 | Calculate the cosinus of $x, modifying $x in place. | |
3784 | ||
20e2035c T |
3785 | In BigInt, unless upgrading is in effect, the result is truncated to an |
3786 | integer. | |
3787 | ||
60a1aa19 T |
3788 | This method was added in v1.87 of Math::BigInt (June 2007). |
3789 | ||
3790 | =head2 bsin() | |
3791 | ||
20e2035c | 3792 | my $x = Math::BigInt->new(1); |
60a1aa19 T |
3793 | print $x->bsin(100), "\n"; |
3794 | ||
3795 | Calculate the sinus of $x, modifying $x in place. | |
3796 | ||
20e2035c T |
3797 | In BigInt, unless upgrading is in effect, the result is truncated to an |
3798 | integer. | |
3799 | ||
60a1aa19 T |
3800 | This method was added in v1.87 of Math::BigInt (June 2007). |
3801 | ||
30afc38d | 3802 | =head2 batan2() |
60a1aa19 | 3803 | |
20e2035c | 3804 | my $x = Math::BigInt->new(1); |
30afc38d T |
3805 | my $y = Math::BigInt->new(1); |
3806 | print $y->batan2($x), "\n"; | |
60a1aa19 | 3807 | |
30afc38d | 3808 | Calculate the arcus tangens of C<$y> divided by C<$x>, modifying $y in place. |
60a1aa19 | 3809 | |
20e2035c T |
3810 | In BigInt, unless upgrading is in effect, the result is truncated to an |
3811 | integer. | |
3812 | ||
3813 | This method was added in v1.87 of Math::BigInt (June 2007). | |
3814 | ||
30afc38d | 3815 | =head2 batan() |
20e2035c | 3816 | |
30afc38d T |
3817 | my $x = Math::BigFloat->new(0.5); |
3818 | print $x->batan(100), "\n"; | |
20e2035c | 3819 | |
30afc38d | 3820 | Calculate the arcus tangens of $x, modifying $x in place. |
20e2035c T |
3821 | |
3822 | In BigInt, unless upgrading is in effect, the result is truncated to an | |
3823 | integer. | |
3824 | ||
60a1aa19 T |
3825 | This method was added in v1.87 of Math::BigInt (June 2007). |
3826 | ||
7b29e1e6 | 3827 | =head2 blsft() |
b3abae2a | 3828 | |
7d193e39 | 3829 | $x->blsft($y); # left shift in base 2 |
56d9de68 | 3830 | $x->blsft($y,$n); # left shift, in base $n (like 10) |
b3abae2a | 3831 | |
7b29e1e6 | 3832 | =head2 brsft() |
b3abae2a | 3833 | |
7d193e39 | 3834 | $x->brsft($y); # right shift in base 2 |
56d9de68 | 3835 | $x->brsft($y,$n); # right shift, in base $n (like 10) |
b3abae2a | 3836 | |
7b29e1e6 | 3837 | =head2 band() |
b3abae2a | 3838 | |
56d9de68 | 3839 | $x->band($y); # bitwise and |
b3abae2a | 3840 | |
7b29e1e6 | 3841 | =head2 bior() |
b3abae2a | 3842 | |
56d9de68 | 3843 | $x->bior($y); # bitwise inclusive or |
b3abae2a | 3844 | |
7b29e1e6 | 3845 | =head2 bxor() |
b3abae2a | 3846 | |
56d9de68 | 3847 | $x->bxor($y); # bitwise exclusive or |
b3abae2a | 3848 | |
7b29e1e6 | 3849 | =head2 bnot() |
b3abae2a | 3850 | |
56d9de68 | 3851 | $x->bnot(); # bitwise not (two's complement) |
b3abae2a | 3852 | |
7b29e1e6 | 3853 | =head2 bsqrt() |
b3abae2a | 3854 | |
56d9de68 | 3855 | $x->bsqrt(); # calculate square-root |
b3abae2a | 3856 | |
f7f86b73 T |
3857 | =head2 broot() |
3858 | ||
3859 | $x->broot($N); | |
3860 | ||
3861 | Calculates the N'th root of C<$x>. | |
3862 | ||
7b29e1e6 | 3863 | =head2 bfac() |
b3abae2a | 3864 | |
56d9de68 | 3865 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
b3abae2a | 3866 | |
7b29e1e6 | 3867 | =head2 round() |
b3abae2a | 3868 | |
56d9de68 T |
3869 | $x->round($A,$P,$round_mode); |
3870 | ||
3871 | Round $x to accuracy C<$A> or precision C<$P> using the round mode | |
3872 | C<$round_mode>. | |
b3abae2a | 3873 | |
7b29e1e6 | 3874 | =head2 bround() |
b3abae2a | 3875 | |
56d9de68 | 3876 | $x->bround($N); # accuracy: preserve $N digits |
b3abae2a | 3877 | |
7b29e1e6 | 3878 | =head2 bfround() |
b3abae2a | 3879 | |
d5351619 T |
3880 | $x->bfround($N); |
3881 | ||
3882 | If N is > 0, rounds to the Nth digit from the left. If N < 0, rounds to | |
3883 | the Nth digit after the dot. Since BigInts are integers, the case N < 0 | |
3884 | is a no-op for them. | |
3885 | ||
3886 | Examples: | |
3887 | ||
3888 | Input N Result | |
3889 | =================================================== | |
3890 | 123456.123456 3 123500 | |
3891 | 123456.123456 2 123450 | |
3892 | 123456.123456 -2 123456.12 | |
3893 | 123456.123456 -3 123456.123 | |
b3abae2a | 3894 | |
7b29e1e6 | 3895 | =head2 bfloor() |
b3abae2a JH |
3896 | |
3897 | $x->bfloor(); | |
3898 | ||
3899 | Set $x to the integer less or equal than $x. This is a no-op in BigInt, but | |
3900 | does change $x in BigFloat. | |
3901 | ||
7b29e1e6 | 3902 | =head2 bceil() |
b3abae2a JH |
3903 | |
3904 | $x->bceil(); | |
3905 | ||
3906 | Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but | |
3907 | does change $x in BigFloat. | |
3908 | ||
7b29e1e6 | 3909 | =head2 bgcd() |
b3abae2a | 3910 | |
56d9de68 | 3911 | bgcd(@values); # greatest common divisor (no OO style) |
b3abae2a | 3912 | |
7b29e1e6 | 3913 | =head2 blcm() |
b3abae2a | 3914 | |
56d9de68 | 3915 | blcm(@values); # lowest common multiplicator (no OO style) |
b3abae2a | 3916 | |
7b29e1e6 | 3917 | head2 length() |
b3abae2a JH |
3918 | |
3919 | $x->length(); | |
3920 | ($xl,$fl) = $x->length(); | |
3921 | ||
3922 | Returns the number of digits in the decimal representation of the number. | |
3923 | In list context, returns the length of the integer and fraction part. For | |
3924 | BigInt's, the length of the fraction part will always be 0. | |
3925 | ||
7b29e1e6 | 3926 | =head2 exponent() |
b3abae2a JH |
3927 | |
3928 | $x->exponent(); | |
3929 | ||
3930 | Return the exponent of $x as BigInt. | |
3931 | ||
7b29e1e6 | 3932 | =head2 mantissa() |
b3abae2a JH |
3933 | |
3934 | $x->mantissa(); | |
3935 | ||
3936 | Return the signed mantissa of $x as BigInt. | |
3937 | ||
7b29e1e6 | 3938 | =head2 parts() |
b3abae2a | 3939 | |
56d9de68 | 3940 | $x->parts(); # return (mantissa,exponent) as BigInt |
b3abae2a | 3941 | |
7b29e1e6 | 3942 | =head2 copy() |
b3abae2a | 3943 | |
56d9de68 | 3944 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
b3abae2a | 3945 | |
7b29e1e6 | 3946 | =head2 as_int()/as_number() |
b3abae2a | 3947 | |
b282a552 T |
3948 | $x->as_int(); |
3949 | ||
3950 | Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as | |
3951 | C<copy()>. | |
3952 | ||
3953 | C<as_number()> is an alias to this method. C<as_number> was introduced in | |
3954 | v1.22, while C<as_int()> was only introduced in v1.68. | |
b3abae2a | 3955 | |
7b29e1e6 | 3956 | =head2 bstr() |
b282a552 T |
3957 | |
3958 | $x->bstr(); | |
b3abae2a | 3959 | |
3c4b39be | 3960 | Returns a normalized string representation of C<$x>. |
b3abae2a | 3961 | |
7b29e1e6 | 3962 | =head2 bsstr() |
b3abae2a | 3963 | |
56d9de68 | 3964 | $x->bsstr(); # normalized string in scientific notation |
b3abae2a | 3965 | |
7b29e1e6 | 3966 | =head2 as_hex() |
b3abae2a | 3967 | |
56d9de68 | 3968 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
b3abae2a | 3969 | |
7b29e1e6 | 3970 | =head2 as_bin() |
b3abae2a | 3971 | |
56d9de68 | 3972 | $x->as_bin(); # as signed binary string with prefixed 0b |
b3abae2a | 3973 | |
7b29e1e6 T |
3974 | =head2 as_oct() |
3975 | ||
3976 | $x->as_oct(); # as signed octal string with prefixed 0 | |
3977 | ||
3978 | =head2 numify() | |
3979 | ||
3980 | print $x->numify(); | |
3981 | ||
3982 | This returns a normal Perl scalar from $x. It is used automatically | |
3983 | whenever a scalar is needed, for instance in array index operations. | |
3984 | ||
3985 | This loses precision, to avoid this use L<as_int()> instead. | |
3986 | ||
3987 | =head2 modify() | |
3988 | ||
3989 | $x->modify('bpowd'); | |
3990 | ||
3991 | This method returns 0 if the object can be modified with the given | |
3992 | peration, or 1 if not. | |
3993 | ||
3994 | This is used for instance by L<Math::BigInt::Constant>. | |
3995 | ||
3996 | =head2 upgrade()/downgrade() | |
3997 | ||
3998 | Set/get the class for downgrade/upgrade operations. Thuis is used | |
3999 | for instance by L<bignum>. The defaults are '', thus the following | |
4000 | operation will create a BigInt, not a BigFloat: | |
4001 | ||
4002 | my $i = Math::BigInt->new(123); | |
4003 | my $f = Math::BigFloat->new('123.1'); | |
4004 | ||
4005 | print $i + $f,"\n"; # print 246 | |
4006 | ||
4007 | =head2 div_scale() | |
4008 | ||
4009 | Set/get the number of digits for the default precision in divide | |
4010 | operations. | |
4011 | ||
4012 | =head2 round_mode() | |
4013 | ||
4014 | Set/get the current round mode. | |
4015 | ||
0716bf9b JH |
4016 | =head1 ACCURACY and PRECISION |
4017 | ||
b22b3e31 | 4018 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b | 4019 | accuracy and precision based rounding, both automatically after every |
091c87b1 | 4020 | operation, as well as manually. |
0716bf9b JH |
4021 | |
4022 | This section describes the accuracy/precision handling in Math::Big* as it | |
b22b3e31 | 4023 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b JH |
4024 | abbreviations. |
4025 | ||
4026 | Not yet implemented things (but with correct description) are marked with '!', | |
4027 | things that need to be answered are marked with '?'. | |
4028 | ||
4029 | In the next paragraph follows a short description of terms used here (because | |
574bacfe | 4030 | these may differ from terms used by others people or documentation). |
0716bf9b | 4031 | |
b22b3e31 | 4032 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b JH |
4033 | precision), F (fallback) and R (rounding mode) will be used. |
4034 | ||
4035 | =head2 Precision P | |
4036 | ||
4037 | A fixed number of digits before (positive) or after (negative) | |
b22b3e31 PN |
4038 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
4039 | integer like 123 (or 120). A precision of 2 means two digits to the left | |
4040 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that | |
4041 | numbers with zeros before the decimal point may have different precisions, | |
4042 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value | |
4043 | was). It could also have p < 0, when the digits after the decimal point | |
4044 | are zero. | |
0716bf9b | 4045 | |
574bacfe JH |
4046 | The string output (of floating point numbers) will be padded with zeros: |
4047 | ||
4048 | Initial value P A Result String | |
4049 | ------------------------------------------------------------ | |
4050 | 1234.01 -3 1000 1000 | |
4051 | 1234 -2 1200 1200 | |
4052 | 1234.5 -1 1230 1230 | |
4053 | 1234.001 1 1234 1234.0 | |
4054 | 1234.01 0 1234 1234 | |
4055 | 1234.01 2 1234.01 1234.01 | |
4056 | 1234.01 5 1234.01 1234.01000 | |
4057 | ||
4058 | For BigInts, no padding occurs. | |
0716bf9b JH |
4059 | |
4060 | =head2 Accuracy A | |
4061 | ||
4062 | Number of significant digits. Leading zeros are not counted. A | |
4063 | number may have an accuracy greater than the non-zero digits | |
b22b3e31 PN |
4064 | when there are zeros in it or trailing zeros. For example, 123.456 has |
4065 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. | |
0716bf9b | 4066 | |
574bacfe JH |
4067 | The string output (of floating point numbers) will be padded with zeros: |
4068 | ||
4069 | Initial value P A Result String | |
4070 | ------------------------------------------------------------ | |
4071 | 1234.01 3 1230 1230 | |
4072 | 1234.01 6 1234.01 1234.01 | |
4073 | 1234.1 8 1234.1 1234.1000 | |
4074 | ||
4075 | For BigInts, no padding occurs. | |
4076 | ||
0716bf9b | 4077 | =head2 Fallback F |
a5f75d66 | 4078 | |
574bacfe JH |
4079 | When both A and P are undefined, this is used as a fallback accuracy when |
4080 | dividing numbers. | |
0716bf9b JH |
4081 | |
4082 | =head2 Rounding mode R | |
4083 | ||
4084 | When rounding a number, different 'styles' or 'kinds' | |
4085 | of rounding are possible. (Note that random rounding, as in | |
4086 | Math::Round, is not implemented.) | |
58cde26e JH |
4087 | |
4088 | =over 2 | |
a5f75d66 | 4089 | |
0716bf9b JH |
4090 | =item 'trunc' |
4091 | ||
4092 | truncation invariably removes all digits following the | |
4093 | rounding place, replacing them with zeros. Thus, 987.65 rounded | |
b22b3e31 | 4094 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b | 4095 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 | 4096 | decimal point (P=-2) becomes 123.46. |
0716bf9b JH |
4097 | |
4098 | All other implemented styles of rounding attempt to round to the | |
4099 | "nearest digit." If the digit D immediately to the right of the | |
4100 | rounding place (skipping the decimal point) is greater than 5, the | |
4101 | number is incremented at the rounding place (possibly causing a | |
4102 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds | |
4103 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly | |
4104 | truncated at the rounding place: e.g. when rounding to units, 0.4 | |
4105 | rounds to 0, and -19.4 rounds to -19. | |
4106 | ||
4107 | However the results of other styles of rounding differ if the | |
4108 | digit immediately to the right of the rounding place (skipping the | |
4109 | decimal point) is 5 and if there are no digits, or no digits other | |
4110 | than 0, after that 5. In such cases: | |
4111 | ||
4112 | =item 'even' | |
4113 | ||
4114 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 | |
4115 | if it is not already. E.g., when rounding to the first sigdig, 0.45 | |
4116 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. | |
4117 | ||
4118 | =item 'odd' | |
4119 | ||
4120 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if | |
4121 | it is not already. E.g., when rounding to the first sigdig, 0.45 | |
4122 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. | |
4123 | ||
4124 | =item '+inf' | |
4125 | ||
4126 | round to plus infinity, i.e. always round up. E.g., when | |
4127 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, | |
b22b3e31 | 4128 | and 0.4501 also becomes 0.5. |
0716bf9b JH |
4129 | |
4130 | =item '-inf' | |
4131 | ||
4132 | round to minus infinity, i.e. always round down. E.g., when | |
4133 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, | |
4134 | but 0.4501 becomes 0.5. | |
4135 | ||
4136 | =item 'zero' | |
4137 | ||
4138 | round to zero, i.e. positive numbers down, negative ones up. | |
4139 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 | |
4140 | becomes -0.5, but 0.4501 becomes 0.5. | |
4141 | ||
7b29e1e6 T |
4142 | =item 'common' |
4143 | ||
4144 | round up if the digit immediately to the right of the rounding place | |
4145 | is 5 or greater, otherwise round down. E.g., 0.15 becomes 0.2 and | |
4146 | 0.149 becomes 0.1. | |
4147 | ||
0716bf9b JH |
4148 | =back |
4149 | ||
4150 | The handling of A & P in MBI/MBF (the old core code shipped with Perl | |
4151 | versions <= 5.7.2) is like this: | |
4152 | ||
4153 | =over 2 | |
a5f75d66 | 4154 | |
0716bf9b JH |
4155 | =item Precision |
4156 | ||
b22b3e31 PN |
4157 | * ffround($p) is able to round to $p number of digits after the decimal |
4158 | point | |
0716bf9b JH |
4159 | * otherwise P is unused |
4160 | ||
4161 | =item Accuracy (significant digits) | |
4162 | ||
4163 | * fround($a) rounds to $a significant digits | |
4164 | * only fdiv() and fsqrt() take A as (optional) paramater | |
b22b3e31 | 4165 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b JH |
4166 | of digits |
4167 | + rounding/truncating is only done when explicitly calling one of fround | |
4168 | or ffround, and never for BigInt (not implemented) | |
b22b3e31 | 4169 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b JH |
4170 | * the documentation and the comment in the code indicate two different ways |
4171 | on how fdiv() determines the maximum number of digits it should calculate, | |
4172 | and the actual code does yet another thing | |
4173 | POD: | |
4174 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) | |
4175 | Comment: | |
4176 | result has at most max(scale, length(dividend), length(divisor)) digits | |
4177 | Actual code: | |
4178 | scale = max(scale, length(dividend)-1,length(divisor)-1); | |
3c4b39be | 4179 | scale += length(divisor) - length(dividend); |
b22b3e31 | 4180 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b JH |
4181 | Actually, the 'difference' added to the scale is calculated from the |
4182 | number of "significant digits" in dividend and divisor, which is derived | |
4183 | by looking at the length of the mantissa. Which is wrong, since it includes | |
091c87b1 | 4184 | the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops |
0716bf9b JH |
4185 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange |
4186 | assumption that 124 has 3 significant digits, while 120/7 will get you | |
4187 | '17', not '17.1' since 120 is thought to have 2 significant digits. | |
dccbb853 | 4188 | The rounding after the division then uses the remainder and $y to determine |
0716bf9b | 4189 | wether it must round up or down. |
b22b3e31 PN |
4190 | ? I have no idea which is the right way. That's why I used a slightly more |
4191 | ? simple scheme and tweaked the few failing testcases to match it. | |
58cde26e | 4192 | |
0716bf9b | 4193 | =back |
5dc6f178 | 4194 | |
0716bf9b | 4195 | This is how it works now: |
5dc6f178 | 4196 | |
0716bf9b | 4197 | =over 2 |
5dc6f178 | 4198 | |
0716bf9b JH |
4199 | =item Setting/Accessing |
4200 | ||
091c87b1 T |
4201 | * You can set the A global via C<< Math::BigInt->accuracy() >> or |
4202 | C<< Math::BigFloat->accuracy() >> or whatever class you are using. | |
4203 | * You can also set P globally by using C<< Math::SomeClass->precision() >> | |
4204 | likewise. | |
0716bf9b | 4205 | * Globals are classwide, and not inherited by subclasses. |
091c87b1 T |
4206 | * to undefine A, use C<< Math::SomeCLass->accuracy(undef); >> |
4207 | * to undefine P, use C<< Math::SomeClass->precision(undef); >> | |
4208 | * Setting C<< Math::SomeClass->accuracy() >> clears automatically | |
4209 | C<< Math::SomeClass->precision() >>, and vice versa. | |
0716bf9b | 4210 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 PN |
4211 | * If P is negative, this means round to the P'th place to the right of the |
4212 | decimal point; positive values mean to the left of the decimal point. | |
4213 | P of 0 means round to integer. | |
091c87b1 T |
4214 | * to find out the current global A, use C<< Math::SomeClass->accuracy() >> |
4215 | * to find out the current global P, use C<< Math::SomeClass->precision() >> | |
4216 | * use C<< $x->accuracy() >> respective C<< $x->precision() >> for the local | |
4217 | setting of C<< $x >>. | |
3c4b39be | 4218 | * Please note that C<< $x->accuracy() >> respective C<< $x->precision() >> |
091c87b1 T |
4219 | return eventually defined global A or P, when C<< $x >>'s A or P is not |
4220 | set. | |
0716bf9b JH |
4221 | |
4222 | =item Creating numbers | |
4223 | ||
86b76201 | 4224 | * When you create a number, you can give the desired A or P via: |
b3abae2a JH |
4225 | $x = Math::BigInt->new($number,$A,$P); |
4226 | * Only one of A or P can be defined, otherwise the result is NaN | |
4227 | * If no A or P is give ($x = Math::BigInt->new($number) form), then the | |
4228 | globals (if set) will be used. Thus changing the global defaults later on | |
b22b3e31 | 4229 | will not change the A or P of previously created numbers (i.e., A and P of |
b3abae2a JH |
4230 | $x will be what was in effect when $x was created) |
4231 | * If given undef for A and P, B<no> rounding will occur, and the globals will | |
4232 | B<not> be used. This is used by subclasses to create numbers without | |
86b76201 | 4233 | suffering rounding in the parent. Thus a subclass is able to have its own |
b3abae2a | 4234 | globals enforced upon creation of a number by using |
091c87b1 | 4235 | C<< $x = Math::BigInt->new($number,undef,undef) >>: |
b3abae2a | 4236 | |
990fb837 | 4237 | use Math::BigInt::SomeSubclass; |
b3abae2a JH |
4238 | use Math::BigInt; |
4239 | ||
4240 | Math::BigInt->accuracy(2); | |
4241 | Math::BigInt::SomeSubClass->accuracy(3); | |
4242 | $x = Math::BigInt::SomeSubClass->new(1234); | |
4243 | ||
4244 | $x is now 1230, and not 1200. A subclass might choose to implement | |
4245 | this otherwise, e.g. falling back to the parent's A and P. | |
0716bf9b JH |
4246 | |
4247 | =item Usage | |
4248 | ||
b22b3e31 | 4249 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b | 4250 | operation according to the rules below |
b22b3e31 PN |
4251 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
4252 | after the decimal point | |
091c87b1 T |
4253 | * Math::BigFloat uses Math::BigInt internally, but setting A or P inside |
4254 | Math::BigInt as globals does not tamper with the parts of a BigFloat. | |
4255 | A flag is used to mark all Math::BigFloat numbers as 'never round'. | |
0716bf9b JH |
4256 | |
4257 | =item Precedence | |
4258 | ||
b22b3e31 | 4259 | * It only makes sense that a number has only one of A or P at a time. |
091c87b1 T |
4260 | If you set either A or P on one object, or globally, the other one will |
4261 | be automatically cleared. | |
b3abae2a JH |
4262 | * If two objects are involved in an operation, and one of them has A in |
4263 | effect, and the other P, this results in an error (NaN). | |
3c4b39be | 4264 | * A takes precedence over P (Hint: A comes before P). |
091c87b1 T |
4265 | If neither of them is defined, nothing is used, i.e. the result will have |
4266 | as many digits as it can (with an exception for fdiv/fsqrt) and will not | |
4267 | be rounded. | |
b22b3e31 PN |
4268 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of |
4269 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. | |
4270 | If either the dividend's or the divisor's mantissa has more digits than | |
4271 | the value of F, the higher value will be used instead of F. | |
4272 | This is to limit the digits (A) of the result (just consider what would | |
4273 | happen with unlimited A and P in the case of 1/3 :-) | |
b3abae2a | 4274 | * fdiv will calculate (at least) 4 more digits than required (determined by |
0716bf9b | 4275 | A, P or F), and, if F is not used, round the result |
b22b3e31 | 4276 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe | 4277 | or P of 5, but this can not be helped - or can it?) |
091c87b1 | 4278 | * Thus you can have the math done by on Math::Big* class in two modi: |
0716bf9b JH |
4279 | + never round (this is the default): |
4280 | This is done by setting A and P to undef. No math operation | |
b22b3e31 | 4281 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
3c4b39be | 4282 | against overflows. You must explicitly call bround(), bfround() or |
b22b3e31 PN |
4283 | round() (the latter with parameters). |
4284 | Note: Once you have rounded a number, the settings will 'stick' on it | |
4285 | and 'infect' all other numbers engaged in math operations with it, since | |
0716bf9b JH |
4286 | local settings have the highest precedence. So, to get SaferRound[tm], |
4287 | use a copy() before rounding like this: | |
4288 | ||
4289 | $x = Math::BigFloat->new(12.34); | |
4290 | $y = Math::BigFloat->new(98.76); | |
4291 | $z = $x * $y; # 1218.6984 | |
4292 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) | |
4293 | $z = $x * $y; # still 1218.6984, without | |
4294 | # copy would have been 1210! | |
4295 | ||
4296 | + round after each op: | |
b22b3e31 PN |
4297 | After each single operation (except for testing like is_zero()), the |
4298 | method round() is called and the result is rounded appropriately. By | |
0716bf9b | 4299 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 PN |
4300 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
4301 | and P to -2, globally. | |
0716bf9b | 4302 | |
b22b3e31 PN |
4303 | ?Maybe an extra option that forbids local A & P settings would be in order, |
4304 | ?so that intermediate rounding does not 'poison' further math? | |
0716bf9b JH |
4305 | |
4306 | =item Overriding globals | |
4307 | ||
4308 | * you will be able to give A, P and R as an argument to all the calculation | |
b22b3e31 | 4309 | routines; the second parameter is A, the third one is P, and the fourth is |
b3abae2a | 4310 | R (shift right by one for binary operations like badd). P is used only if |
b22b3e31 PN |
4311 | the first parameter (A) is undefined. These three parameters override the |
4312 | globals in the order detailed as follows, i.e. the first defined value | |
0716bf9b | 4313 | wins: |
b22b3e31 | 4314 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b JH |
4315 | + parameter A |
4316 | + parameter P | |
4317 | + local A (if defined on both of the operands: smaller one is taken) | |
b3abae2a | 4318 | + local P (if defined on both of the operands: bigger one is taken) |
0716bf9b JH |
4319 | + global A |
4320 | + global P | |
4321 | + global F | |
b22b3e31 | 4322 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b JH |
4323 | arguments (A and P) instead of one |
4324 | ||
4325 | =item Local settings | |
4326 | ||
091c87b1 T |
4327 | * You can set A or P locally by using C<< $x->accuracy() >> or |
4328 | C<< $x->precision() >> | |
0716bf9b | 4329 | and thus force different A and P for different objects/numbers. |
b22b3e31 | 4330 | * Setting A or P this way immediately rounds $x to the new value. |
091c87b1 | 4331 | * C<< $x->accuracy() >> clears C<< $x->precision() >>, and vice versa. |
0716bf9b JH |
4332 | |
4333 | =item Rounding | |
4334 | ||
b22b3e31 | 4335 | * the rounding routines will use the respective global or local settings. |
0716bf9b JH |
4336 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
4337 | is for precision | |
4338 | * the two rounding functions take as the second parameter one of the | |
4339 | following rounding modes (R): | |
7b29e1e6 | 4340 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc', 'common' |
091c87b1 T |
4341 | * you can set/get the global R by using C<< Math::SomeClass->round_mode() >> |
4342 | or by setting C<< $Math::SomeClass::round_mode >> | |
4343 | * after each operation, C<< $result->round() >> is called, and the result may | |
b22b3e31 PN |
4344 | eventually be rounded (that is, if A or P were set either locally, |
4345 | globally or as parameter to the operation) | |
091c87b1 | 4346 | * to manually round a number, call C<< $x->round($A,$P,$round_mode); >> |
b22b3e31 | 4347 | this will round the number by using the appropriate rounding function |
0716bf9b | 4348 | and then normalize it. |
b22b3e31 | 4349 | * rounding modifies the local settings of the number: |
0716bf9b JH |
4350 | |
4351 | $x = Math::BigFloat->new(123.456); | |
4352 | $x->accuracy(5); | |
4353 | $x->bround(4); | |
4354 | ||
4355 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() | |
4356 | will be 4 from now on. | |
4357 | ||
4358 | =item Default values | |
4359 | ||
4360 | * R: 'even' | |
4361 | * F: 40 | |
4362 | * A: undef | |
4363 | * P: undef | |
4364 | ||
4365 | =item Remarks | |
4366 | ||
4367 | * The defaults are set up so that the new code gives the same results as | |
4368 | the old code (except in a few cases on fdiv): | |
4369 | + Both A and P are undefined and thus will not be used for rounding | |
4370 | after each operation. | |
4371 | + round() is thus a no-op, unless given extra parameters A and P | |
58cde26e JH |
4372 | |
4373 | =back | |
4374 | ||
b68b7ab1 T |
4375 | =head1 Infinity and Not a Number |
4376 | ||
4377 | While BigInt has extensive handling of inf and NaN, certain quirks remain. | |
4378 | ||
4379 | =over 2 | |
4380 | ||
4381 | =item oct()/hex() | |
4382 | ||
4383 | These perl routines currently (as of Perl v.5.8.6) cannot handle passed | |
4384 | inf. | |
4385 | ||
4386 | te@linux:~> perl -wle 'print 2 ** 3333' | |
4387 | inf | |
4388 | te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333' | |
4389 | 1 | |
4390 | te@linux:~> perl -wle 'print oct(2 ** 3333)' | |
4391 | 0 | |
4392 | te@linux:~> perl -wle 'print hex(2 ** 3333)' | |
4393 | Illegal hexadecimal digit 'i' ignored at -e line 1. | |
4394 | 0 | |
4395 | ||
4396 | The same problems occur if you pass them Math::BigInt->binf() objects. Since | |
4397 | overloading these routines is not possible, this cannot be fixed from BigInt. | |
4398 | ||
4399 | =item ==, !=, <, >, <=, >= with NaNs | |
4400 | ||
4401 | BigInt's bcmp() routine currently returns undef to signal that a NaN was | |
3c4b39be | 4402 | involved in a comparison. However, the overload code turns that into |
b68b7ab1 T |
4403 | either 1 or '' and thus operations like C<< NaN != NaN >> might return |
4404 | wrong values. | |
4405 | ||
4406 | =item log(-inf) | |
4407 | ||
4408 | C<< log(-inf) >> is highly weird. Since log(-x)=pi*i+log(x), then | |
4409 | log(-inf)=pi*i+inf. However, since the imaginary part is finite, the real | |
4410 | infinity "overshadows" it, so the number might as well just be infinity. | |
4411 | However, the result is a complex number, and since BigInt/BigFloat can only | |
4412 | have real numbers as results, the result is NaN. | |
4413 | ||
4414 | =item exp(), cos(), sin(), atan2() | |
4415 | ||
4416 | These all might have problems handling infinity right. | |
4417 | ||
4418 | =back | |
4419 | ||
0716bf9b JH |
4420 | =head1 INTERNALS |
4421 | ||
574bacfe | 4422 | The actual numbers are stored as unsigned big integers (with seperate sign). |
b68b7ab1 | 4423 | |
574bacfe | 4424 | You should neither care about nor depend on the internal representation; it |
b68b7ab1 T |
4425 | might change without notice. Use B<ONLY> method calls like C<< $x->sign(); >> |
4426 | instead relying on the internal representation. | |
574bacfe JH |
4427 | |
4428 | =head2 MATH LIBRARY | |
58cde26e | 4429 | |
574bacfe | 4430 | Math with the numbers is done (by default) by a module called |
091c87b1 | 4431 | C<Math::BigInt::Calc>. This is equivalent to saying: |
574bacfe | 4432 | |
0dceeee6 RGS |
4433 | use Math::BigInt try => 'Calc'; |
4434 | ||
4435 | You can change this backend library by using: | |
58cde26e | 4436 | |
0dceeee6 | 4437 | use Math::BigInt try => 'GMP'; |
58cde26e | 4438 | |
0dceeee6 RGS |
4439 | B<Note>: General purpose packages should not be explicit about the library |
4440 | to use; let the script author decide which is best. | |
4441 | ||
4442 | If your script works with huge numbers and Calc is too slow for them, | |
4443 | you can also for the loading of one of these libraries and if none | |
4444 | of them can be used, the code will die: | |
4445 | ||
4446 | use Math::BigInt only => 'GMP,Pari'; | |
58cde26e | 4447 | |
574bacfe JH |
4448 | The following would first try to find Math::BigInt::Foo, then |
4449 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
0716bf9b | 4450 | |
0dceeee6 RGS |
4451 | use Math::BigInt try => 'Foo,Math::BigInt::Bar'; |
4452 | ||
4453 | The library that is loaded last will be used. Note that this can be | |
4454 | overwritten at any time by loading a different library, and numbers | |
4455 | constructed with different libraries cannot be used in math operations | |
4456 | together. | |
4457 | ||
4458 | =head3 What library to use? | |
58cde26e | 4459 | |
0dceeee6 RGS |
4460 | B<Note>: General purpose packages should not be explicit about the library |
4461 | to use; let the script author decide which is best. | |
091c87b1 | 4462 | |
0dceeee6 RGS |
4463 | L<Math::BigInt::GMP> and L<Math::BigInt::Pari> are in cases involving big |
4464 | numbers much faster than Calc, however it is slower when dealing with very | |
4465 | small numbers (less than about 20 digits) and when converting very large | |
4466 | numbers to decimal (for instance for printing, rounding, calculating their | |
4467 | length in decimal etc). | |
091c87b1 | 4468 | |
0dceeee6 RGS |
4469 | So please select carefully what libary you want to use. |
4470 | ||
4471 | Different low-level libraries use different formats to store the numbers. | |
4472 | However, you should B<NOT> depend on the number having a specific format | |
b68b7ab1 | 4473 | internally. |
091c87b1 T |
4474 | |
4475 | See the respective math library module documentation for further details. | |
58cde26e | 4476 | |
574bacfe JH |
4477 | =head2 SIGN |
4478 | ||
b68b7ab1 | 4479 | The sign is either '+', '-', 'NaN', '+inf' or '-inf'. |
574bacfe JH |
4480 | |
4481 | A sign of 'NaN' is used to represent the result when input arguments are not | |
4482 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively | |
4483 | minus infinity. You will get '+inf' when dividing a positive number by 0, and | |
4484 | '-inf' when dividing any negative number by 0. | |
58cde26e JH |
4485 | |
4486 | =head2 mantissa(), exponent() and parts() | |
4487 | ||
4488 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such | |
4489 | that: | |
4490 | ||
4491 | $m = $x->mantissa(); | |
4492 | $e = $x->exponent(); | |
4493 | $y = $m * ( 10 ** $e ); | |
4494 | print "ok\n" if $x == $y; | |
4495 | ||
b22b3e31 PN |
4496 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
4497 | in one go. Both the returned mantissa and exponent have a sign. | |
58cde26e | 4498 | |
7b29e1e6 T |
4499 | Currently, for BigInts C<$e> is always 0, except +inf and -inf, where it is |
4500 | C<+inf>; and for NaN, where it is C<NaN>; and for C<$x == 0>, where it is C<1> | |
4501 | (to be compatible with Math::BigFloat's internal representation of a zero as | |
4502 | C<0E1>). | |
58cde26e | 4503 | |
091c87b1 T |
4504 | C<$m> is currently just a copy of the original number. The relation between |
4505 | C<$e> and C<$m> will stay always the same, though their real values might | |
4506 | change. | |
0716bf9b | 4507 | |
58cde26e JH |
4508 | =head1 EXAMPLES |
4509 | ||
394e6ffb | 4510 | use Math::BigInt; |
574bacfe JH |
4511 | |
4512 | sub bint { Math::BigInt->new(shift); } | |
4513 | ||
394e6ffb | 4514 | $x = Math::BigInt->bstr("1234") # string "1234" |
58cde26e | 4515 | $x = "$x"; # same as bstr() |
990fb837 RGS |
4516 | $x = Math::BigInt->bneg("1234"); # BigInt "-1234" |
4517 | $x = Math::BigInt->babs("-12345"); # BigInt "12345" | |
7b29e1e6 | 4518 | $x = Math::BigInt->bnorm("-0.00"); # BigInt "0" |
58cde26e JH |
4519 | $x = bint(1) + bint(2); # BigInt "3" |
4520 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") | |
4521 | $x = bint(1); # BigInt "1" | |
4522 | $x = $x + 5 / 2; # BigInt "3" | |
4523 | $x = $x ** 3; # BigInt "27" | |
4524 | $x *= 2; # BigInt "54" | |
394e6ffb | 4525 | $x = Math::BigInt->new(0); # BigInt "0" |
58cde26e JH |
4526 | $x--; # BigInt "-1" |
4527 | $x = Math::BigInt->badd(4,5) # BigInt "9" | |
58cde26e | 4528 | print $x->bsstr(); # 9e+0 |
a5f75d66 | 4529 | |
0716bf9b JH |
4530 | Examples for rounding: |
4531 | ||
4532 | use Math::BigFloat; | |
4533 | use Test; | |
4534 | ||
4535 | $x = Math::BigFloat->new(123.4567); | |
4536 | $y = Math::BigFloat->new(123.456789); | |
394e6ffb | 4537 | Math::BigFloat->accuracy(4); # no more A than 4 |
0716bf9b JH |
4538 | |
4539 | ok ($x->copy()->fround(),123.4); # even rounding | |
4540 | print $x->copy()->fround(),"\n"; # 123.4 | |
4541 | Math::BigFloat->round_mode('odd'); # round to odd | |
4542 | print $x->copy()->fround(),"\n"; # 123.5 | |
394e6ffb | 4543 | Math::BigFloat->accuracy(5); # no more A than 5 |
0716bf9b JH |
4544 | Math::BigFloat->round_mode('odd'); # round to odd |
4545 | print $x->copy()->fround(),"\n"; # 123.46 | |
4546 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 | |
4547 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 | |
4548 | ||
394e6ffb JH |
4549 | Math::BigFloat->accuracy(undef); # A not important now |
4550 | Math::BigFloat->precision(2); # P important | |
4551 | print $x->copy()->bnorm(),"\n"; # 123.46 | |
4552 | print $x->copy()->fround(),"\n"; # 123.46 | |
0716bf9b | 4553 | |
bd05a461 JH |
4554 | Examples for converting: |
4555 | ||
4556 | my $x = Math::BigInt->new('0b1'.'01' x 123); | |
4557 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; | |
4558 | ||
b3ac6de7 IZ |
4559 | =head1 Autocreating constants |
4560 | ||
56b9c951 JH |
4561 | After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal |
4562 | and binary constants in the given scope are converted to C<Math::BigInt>. | |
4563 | This conversion happens at compile time. | |
b3ac6de7 | 4564 | |
b22b3e31 | 4565 | In particular, |
b3ac6de7 | 4566 | |
58cde26e JH |
4567 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
4568 | ||
56b9c951 | 4569 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b | 4570 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e JH |
4571 | |
4572 | Please note that strings and floating point constants are not affected, | |
4573 | so that | |
4574 | ||
4575 | use Math::BigInt qw/:constant/; | |
4576 | ||
4577 | $x = 1234567890123456789012345678901234567890 | |
4578 | + 123456789123456789; | |
b22b3e31 | 4579 | $y = '1234567890123456789012345678901234567890' |
58cde26e | 4580 | + '123456789123456789'; |
b3ac6de7 | 4581 | |
b22b3e31 | 4582 | do not work. You need an explicit Math::BigInt->new() around one of the |
394e6ffb JH |
4583 | operands. You should also quote large constants to protect loss of precision: |
4584 | ||
990fb837 | 4585 | use Math::BigInt; |
394e6ffb JH |
4586 | |
4587 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); | |
4588 | ||
4589 | Without the quotes Perl would convert the large number to a floating point | |
4590 | constant at compile time and then hand the result to BigInt, which results in | |
4591 | an truncated result or a NaN. | |
58cde26e | 4592 | |
56b9c951 JH |
4593 | This also applies to integers that look like floating point constants: |
4594 | ||
4595 | use Math::BigInt ':constant'; | |
4596 | ||
4597 | print ref(123e2),"\n"; | |
4598 | print ref(123.2e2),"\n"; | |
4599 | ||
4600 | will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat> | |
4601 | to get this to work. | |
4602 | ||
58cde26e JH |
4603 | =head1 PERFORMANCE |
4604 | ||
4605 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x | |
4606 | must be made in the second case. For long numbers, the copy can eat up to 20% | |
b22b3e31 | 4607 | of the work (in the case of addition/subtraction, less for |
58cde26e JH |
4608 | multiplication/division). If $y is very small compared to $x, the form |
4609 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes | |
4610 | more time then the actual addition. | |
4611 | ||
b22b3e31 | 4612 | With a technique called copy-on-write, the cost of copying with overload could |
394e6ffb JH |
4613 | be minimized or even completely avoided. A test implementation of COW did show |
4614 | performance gains for overloaded math, but introduced a performance loss due | |
3c4b39be | 4615 | to a constant overhead for all other operations. So Math::BigInt does currently |
091c87b1 | 4616 | not COW. |
394e6ffb | 4617 | |
091c87b1 T |
4618 | The rewritten version of this module (vs. v0.01) is slower on certain |
4619 | operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it | |
4620 | does now more work and handles much more cases. The time spent in these | |
4621 | operations is usually gained in the other math operations so that code on | |
4622 | the average should get (much) faster. If they don't, please contact the author. | |
58cde26e | 4623 | |
394e6ffb | 4624 | Some operations may be slower for small numbers, but are significantly faster |
091c87b1 T |
4625 | for big numbers. Other operations are now constant (O(1), like C<bneg()>, |
4626 | C<babs()> etc), instead of O(N) and thus nearly always take much less time. | |
4627 | These optimizations were done on purpose. | |
58cde26e | 4628 | |
574bacfe JH |
4629 | If you find the Calc module to slow, try to install any of the replacement |
4630 | modules and see if they help you. | |
b3ac6de7 | 4631 | |
574bacfe | 4632 | =head2 Alternative math libraries |
0716bf9b | 4633 | |
0dceeee6 RGS |
4634 | You can use an alternative library to drive Math::BigInt. See the section |
4635 | L<MATH LIBRARY> for more information. | |
0716bf9b | 4636 | |
394e6ffb | 4637 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. |
574bacfe | 4638 | |
b3abae2a JH |
4639 | =head2 SUBCLASSING |
4640 | ||
4641 | =head1 Subclassing Math::BigInt | |
4642 | ||
4643 | The basic design of Math::BigInt allows simple subclasses with very little | |
4644 | work, as long as a few simple rules are followed: | |
4645 | ||
4646 | =over 2 | |
4647 | ||
4648 | =item * | |
4649 | ||
4650 | The public API must remain consistent, i.e. if a sub-class is overloading | |
4651 | addition, the sub-class must use the same name, in this case badd(). The | |
4652 | reason for this is that Math::BigInt is optimized to call the object methods | |
4653 | directly. | |
4654 | ||
4655 | =item * | |
4656 | ||
4657 | The private object hash keys like C<$x->{sign}> may not be changed, but | |
4658 | additional keys can be added, like C<$x->{_custom}>. | |
4659 | ||
4660 | =item * | |
4661 | ||
4662 | Accessor functions are available for all existing object hash keys and should | |
4663 | be used instead of directly accessing the internal hash keys. The reason for | |
4664 | this is that Math::BigInt itself has a pluggable interface which permits it | |
4665 | to support different storage methods. | |
4666 | ||
4667 | =back | |
4668 | ||
4669 | More complex sub-classes may have to replicate more of the logic internal of | |
4670 | Math::BigInt if they need to change more basic behaviors. A subclass that | |
4671 | needs to merely change the output only needs to overload C<bstr()>. | |
4672 | ||
4673 | All other object methods and overloaded functions can be directly inherited | |
4674 | from the parent class. | |
4675 | ||
86b76201 | 4676 | At the very minimum, any subclass will need to provide its own C<new()> and can |
b3abae2a JH |
4677 | store additional hash keys in the object. There are also some package globals |
4678 | that must be defined, e.g.: | |
4679 | ||
4680 | # Globals | |
4681 | $accuracy = undef; | |
4682 | $precision = -2; # round to 2 decimal places | |
4683 | $round_mode = 'even'; | |
4684 | $div_scale = 40; | |
4685 | ||
4686 | Additionally, you might want to provide the following two globals to allow | |
4687 | auto-upgrading and auto-downgrading to work correctly: | |
4688 | ||
4689 | $upgrade = undef; | |
4690 | $downgrade = undef; | |
4691 | ||
4692 | This allows Math::BigInt to correctly retrieve package globals from the | |
4693 | subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or | |
4694 | t/Math/BigFloat/SubClass.pm completely functional subclass examples. | |
4695 | ||
4696 | Don't forget to | |
4697 | ||
4698 | use overload; | |
4699 | ||
4700 | in your subclass to automatically inherit the overloading from the parent. If | |
4701 | you like, you can change part of the overloading, look at Math::String for an | |
4702 | example. | |
4703 | ||
4704 | =head1 UPGRADING | |
4705 | ||
4706 | When used like this: | |
4707 | ||
4708 | use Math::BigInt upgrade => 'Foo::Bar'; | |
4709 | ||
4710 | certain operations will 'upgrade' their calculation and thus the result to | |
4711 | the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat: | |
4712 | ||
4713 | use Math::BigInt upgrade => 'Math::BigFloat'; | |
4714 | ||
4715 | As a shortcut, you can use the module C<bignum>: | |
4716 | ||
4717 | use bignum; | |
4718 | ||
4719 | Also good for oneliners: | |
4720 | ||
4721 | perl -Mbignum -le 'print 2 ** 255' | |
4722 | ||
4723 | This makes it possible to mix arguments of different classes (as in 2.5 + 2) | |
4724 | as well es preserve accuracy (as in sqrt(3)). | |
4725 | ||
4726 | Beware: This feature is not fully implemented yet. | |
4727 | ||
4728 | =head2 Auto-upgrade | |
4729 | ||
4730 | The following methods upgrade themselves unconditionally; that is if upgrade | |
4731 | is in effect, they will always hand up their work: | |
4732 | ||
4733 | =over 2 | |
4734 | ||
4735 | =item bsqrt() | |
4736 | ||
4737 | =item div() | |
4738 | ||
4739 | =item blog() | |
4740 | ||
7d193e39 T |
4741 | =item bexp() |
4742 | ||
b3abae2a JH |
4743 | =back |
4744 | ||
4745 | Beware: This list is not complete. | |
4746 | ||
4747 | All other methods upgrade themselves only when one (or all) of their | |
4748 | arguments are of the class mentioned in $upgrade (This might change in later | |
4749 | versions to a more sophisticated scheme): | |
4750 | ||
fdb4b05f T |
4751 | =head1 EXPORTS |
4752 | ||
4753 | C<Math::BigInt> exports nothing by default, but can export the following methods: | |
4754 | ||
4755 | bgcd | |
4756 | blcm | |
4757 | ||
58cde26e JH |
4758 | =head1 CAVEATS |
4759 | ||
4760 | Some things might not work as you expect them. Below is documented what is | |
4761 | known to be troublesome: | |
4762 | ||
4763 | =over 1 | |
4764 | ||
091c87b1 | 4765 | =item bstr(), bsstr() and 'cmp' |
58cde26e | 4766 | |
091c87b1 T |
4767 | Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now |
4768 | drop the leading '+'. The old code would return '+3', the new returns '3'. | |
4769 | This is to be consistent with Perl and to make C<cmp> (especially with | |
4770 | overloading) to work as you expect. It also solves problems with C<Test.pm>, | |
86b76201 | 4771 | because its C<ok()> uses 'eq' internally. |
58cde26e | 4772 | |
091c87b1 T |
4773 | Mark Biggar said, when asked about to drop the '+' altogether, or make only |
4774 | C<cmp> work: | |
58cde26e JH |
4775 | |
4776 | I agree (with the first alternative), don't add the '+' on positive | |
4777 | numbers. It's not as important anymore with the new internal | |
4778 | form for numbers. It made doing things like abs and neg easier, | |
4779 | but those have to be done differently now anyway. | |
4780 | ||
4781 | So, the following examples will now work all as expected: | |
4782 | ||
4783 | use Test; | |
4784 | BEGIN { plan tests => 1 } | |
4785 | use Math::BigInt; | |
4786 | ||
4787 | my $x = new Math::BigInt 3*3; | |
4788 | my $y = new Math::BigInt 3*3; | |
4789 | ||
4790 | ok ($x,3*3); | |
4791 | print "$x eq 9" if $x eq $y; | |
4792 | print "$x eq 9" if $x eq '9'; | |
4793 | print "$x eq 9" if $x eq 3*3; | |
4794 | ||
4795 | Additionally, the following still works: | |
4796 | ||
4797 | print "$x == 9" if $x == $y; | |
4798 | print "$x == 9" if $x == 9; | |
4799 | print "$x == 9" if $x == 3*3; | |
4800 | ||
4801 | There is now a C<bsstr()> method to get the string in scientific notation aka | |
4802 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() | |
3c4b39be | 4803 | for comparison, but Perl will represent some numbers as 100 and others |
091c87b1 T |
4804 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before |
4805 | comparing them as strings: | |
58cde26e JH |
4806 | |
4807 | use Test; | |
4808 | BEGIN { plan tests => 3 } | |
4809 | use Math::BigInt; | |
4810 | ||
4811 | $x = Math::BigInt->new('1e56'); $y = 1e56; | |
4812 | ok ($x,$y); # will fail | |
4813 | ok ($x->bsstr(),$y); # okay | |
4814 | $y = Math::BigInt->new($y); | |
4815 | ok ($x,$y); # okay | |
4816 | ||
3c4b39be | 4817 | Alternatively, simple use C<< <=> >> for comparisons, this will get it |
091c87b1 T |
4818 | always right. There is not yet a way to get a number automatically represented |
4819 | as a string that matches exactly the way Perl represents it. | |
574bacfe | 4820 | |
b68b7ab1 T |
4821 | See also the section about L<Infinity and Not a Number> for problems in |
4822 | comparing NaNs. | |
4823 | ||
58cde26e JH |
4824 | =item int() |
4825 | ||
4826 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a | |
4827 | Perl scalar: | |
4828 | ||
4829 | $x = Math::BigInt->new(123); | |
4830 | $y = int($x); # BigInt 123 | |
4831 | $x = Math::BigFloat->new(123.45); | |
4832 | $y = int($x); # BigInt 123 | |
4833 | ||
b68b7ab1 T |
4834 | In all Perl versions you can use C<as_number()> or C<as_int> for the same |
4835 | effect: | |
58cde26e JH |
4836 | |
4837 | $x = Math::BigFloat->new(123.45); | |
4838 | $y = $x->as_number(); # BigInt 123 | |
b68b7ab1 | 4839 | $y = $x->as_int(); # ditto |
58cde26e JH |
4840 | |
4841 | This also works for other subclasses, like Math::String. | |
4842 | ||
b68b7ab1 T |
4843 | If you want a real Perl scalar, use C<numify()>: |
4844 | ||
4845 | $y = $x->numify(); # 123 as scalar | |
4846 | ||
4847 | This is seldom necessary, though, because this is done automatically, like | |
4848 | when you access an array: | |
4849 | ||
4850 | $z = $array[$x]; # does work automatically | |
4851 | ||
dccbb853 | 4852 | =item length |
58cde26e JH |
4853 | |
4854 | The following will probably not do what you expect: | |
4855 | ||
bd05a461 JH |
4856 | $c = Math::BigInt->new(123); |
4857 | print $c->length(),"\n"; # prints 30 | |
4858 | ||
4859 | It prints both the number of digits in the number and in the fraction part | |
4860 | since print calls C<length()> in list context. Use something like: | |
4861 | ||
4862 | print scalar $c->length(),"\n"; # prints 3 | |
4863 | ||
4864 | =item bdiv | |
4865 | ||
4866 | The following will probably not do what you expect: | |
4867 | ||
58cde26e JH |
4868 | print $c->bdiv(10000),"\n"; |
4869 | ||
dccbb853 | 4870 | It prints both quotient and remainder since print calls C<bdiv()> in list |
3c4b39be | 4871 | context. Also, C<bdiv()> will modify $c, so be careful. You probably want |
58cde26e JH |
4872 | to use |
4873 | ||
4874 | print $c / 10000,"\n"; | |
4875 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c | |
4876 | ||
4877 | instead. | |
4878 | ||
4879 | The quotient is always the greatest integer less than or equal to the | |
4880 | real-valued quotient of the two operands, and the remainder (when it is | |
4881 | nonzero) always has the same sign as the second operand; so, for | |
4882 | example, | |
4883 | ||
dccbb853 JH |
4884 | 1 / 4 => ( 0, 1) |
4885 | 1 / -4 => (-1,-3) | |
4886 | -3 / 4 => (-1, 1) | |
4887 | -3 / -4 => ( 0,-3) | |
4888 | -11 / 2 => (-5,1) | |
4889 | 11 /-2 => (-5,-1) | |
58cde26e JH |
4890 | |
4891 | As a consequence, the behavior of the operator % agrees with the | |
4892 | behavior of Perl's built-in % operator (as documented in the perlop | |
4893 | manpage), and the equation | |
4894 | ||
4895 | $x == ($x / $y) * $y + ($x % $y) | |
4896 | ||
4897 | holds true for any $x and $y, which justifies calling the two return | |
dccbb853 JH |
4898 | values of bdiv() the quotient and remainder. The only exception to this rule |
4899 | are when $y == 0 and $x is negative, then the remainder will also be | |
3c4b39be | 4900 | negative. See below under "infinity handling" for the reasoning behind this. |
58cde26e JH |
4901 | |
4902 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will | |
4903 | not change BigInt's way to do things. This is because under 'use integer' Perl | |
4904 | will do what the underlying C thinks is right and this is different for each | |
4905 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug | |
4906 | the author to implement it ;) | |
4907 | ||
dccbb853 JH |
4908 | =item infinity handling |
4909 | ||
4910 | Here are some examples that explain the reasons why certain results occur while | |
4911 | handling infinity: | |
4912 | ||
4913 | The following table shows the result of the division and the remainder, so that | |
4914 | the equation above holds true. Some "ordinary" cases are strewn in to show more | |
4915 | clearly the reasoning: | |
4916 | ||
4917 | A / B = C, R so that C * B + R = A | |
4918 | ========================================================= | |
4919 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 | |
4920 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 | |
4921 | 0 / inf = 0, 0 0 * inf + 0 = 0 | |
4922 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 | |
4923 | 5 / inf = 0, 5 0 * inf + 5 = 5 | |
4924 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 | |
4925 | -5/ inf = 0, -5 0 * inf + -5 = -5 | |
4926 | -5/-inf = 0, -5 0 * -inf + -5 = -5 | |
4927 | inf/ 5 = inf, 0 inf * 5 + 0 = inf | |
4928 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf | |
4929 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf | |
4930 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf | |
4931 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 | |
4932 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 | |
4933 | inf/ inf = 1, 0 1 * inf + 0 = inf | |
4934 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf | |
4935 | inf/-inf = -1, 0 -1 * -inf + 0 = inf | |
4936 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf | |
4937 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 | |
4938 | inf/ 0 = inf, inf inf * 0 + inf = inf | |
4939 | 0/ 0 = NaN | |
4940 | ||
4941 | These cases below violate the "remainder has the sign of the second of the two | |
4942 | arguments", since they wouldn't match up otherwise. | |
4943 | ||
4944 | A / B = C, R so that C * B + R = A | |
4945 | ======================================================== | |
4946 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf | |
4947 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 | |
4948 | ||
58cde26e JH |
4949 | =item Modifying and = |
4950 | ||
4951 | Beware of: | |
4952 | ||
4953 | $x = Math::BigFloat->new(5); | |
4954 | $y = $x; | |
4955 | ||
4956 | It will not do what you think, e.g. making a copy of $x. Instead it just makes | |
4957 | a second reference to the B<same> object and stores it in $y. Thus anything | |
17baacb7 JH |
4958 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
4959 | Or in other words, C<=> is only safe if you modify your BigInts only via | |
4960 | overloaded math. As soon as you use a method call it breaks: | |
58cde26e JH |
4961 | |
4962 | $x->bmul(2); | |
4963 | print "$x, $y\n"; # prints '10, 10' | |
4964 | ||
4965 | If you want a true copy of $x, use: | |
4966 | ||
4967 | $y = $x->copy(); | |
4968 | ||
17baacb7 JH |
4969 | You can also chain the calls like this, this will make first a copy and then |
4970 | multiply it by 2: | |
4971 | ||
4972 | $y = $x->copy()->bmul(2); | |
4973 | ||
b22b3e31 | 4974 | See also the documentation for overload.pm regarding C<=>. |
58cde26e JH |
4975 | |
4976 | =item bpow | |
4977 | ||
4978 | C<bpow()> (and the rounding functions) now modifies the first argument and | |
574bacfe | 4979 | returns it, unlike the old code which left it alone and only returned the |
58cde26e JH |
4980 | result. This is to be consistent with C<badd()> etc. The first three will |
4981 | modify $x, the last one won't: | |
4982 | ||
4983 | print bpow($x,$i),"\n"; # modify $x | |
4984 | print $x->bpow($i),"\n"; # ditto | |
4985 | print $x **= $i,"\n"; # the same | |
4986 | print $x ** $i,"\n"; # leave $x alone | |
4987 | ||
4988 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. | |
4989 | ||
4990 | =item Overloading -$x | |
4991 | ||
4992 | The following: | |
4993 | ||
4994 | $x = -$x; | |
4995 | ||
4996 | is slower than | |
4997 | ||
4998 | $x->bneg(); | |
4999 | ||
5000 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant | |
5001 | needs to preserve $x since it does not know that it later will get overwritten. | |
0716bf9b | 5002 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e | 5003 | |
58cde26e JH |
5004 | =item Mixing different object types |
5005 | ||
5006 | In Perl you will get a floating point value if you do one of the following: | |
5007 | ||
5008 | $float = 5.0 + 2; | |
5009 | $float = 2 + 5.0; | |
5010 | $float = 5 / 2; | |
5011 | ||
5012 | With overloaded math, only the first two variants will result in a BigFloat: | |
5013 | ||
5014 | use Math::BigInt; | |
5015 | use Math::BigFloat; | |
5016 | ||
5017 | $mbf = Math::BigFloat->new(5); | |
5018 | $mbi2 = Math::BigInteger->new(5); | |
5019 | $mbi = Math::BigInteger->new(2); | |
5020 | ||
5021 | # what actually gets called: | |
5022 | $float = $mbf + $mbi; # $mbf->badd() | |
5023 | $float = $mbf / $mbi; # $mbf->bdiv() | |
5024 | $integer = $mbi + $mbf; # $mbi->badd() | |
5025 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() | |
5026 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() | |
5027 | ||
5028 | This is because math with overloaded operators follows the first (dominating) | |
394e6ffb | 5029 | operand, and the operation of that is called and returns thus the result. So, |
58cde26e JH |
5030 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
5031 | the result should be a Math::BigFloat or the second operant is one. | |
5032 | ||
5033 | To get a Math::BigFloat you either need to call the operation manually, | |
5034 | make sure the operands are already of the proper type or casted to that type | |
5035 | via Math::BigFloat->new(): | |
5036 | ||
5037 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 | |
5038 | ||
5039 | Beware of simple "casting" the entire expression, this would only convert | |
5040 | the already computed result: | |
5041 | ||
5042 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! | |
5043 | ||
0716bf9b | 5044 | Beware also of the order of more complicated expressions like: |
58cde26e JH |
5045 | |
5046 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int | |
5047 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto | |
5048 | ||
5049 | If in doubt, break the expression into simpler terms, or cast all operands | |
5050 | to the desired resulting type. | |
5051 | ||
5052 | Scalar values are a bit different, since: | |
5053 | ||
5054 | $float = 2 + $mbf; | |
5055 | $float = $mbf + 2; | |
5056 | ||
5057 | will both result in the proper type due to the way the overloaded math works. | |
5058 | ||
5059 | This section also applies to other overloaded math packages, like Math::String. | |
5060 | ||
990fb837 RGS |
5061 | One solution to you problem might be autoupgrading|upgrading. See the |
5062 | pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this. | |
b3abae2a | 5063 | |
58cde26e JH |
5064 | =item bsqrt() |
5065 | ||
394e6ffb | 5066 | C<bsqrt()> works only good if the result is a big integer, e.g. the square |
58cde26e | 5067 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
990fb837 | 5068 | mode. The reason is that the result is always truncated to an integer. |
58cde26e JH |
5069 | |
5070 | If you want a better approximation of the square root, then use: | |
5071 | ||
5072 | $x = Math::BigFloat->new(12); | |
394e6ffb | 5073 | Math::BigFloat->precision(0); |
58cde26e JH |
5074 | Math::BigFloat->round_mode('even'); |
5075 | print $x->copy->bsqrt(),"\n"; # 4 | |
5076 | ||
394e6ffb | 5077 | Math::BigFloat->precision(2); |
58cde26e JH |
5078 | print $x->bsqrt(),"\n"; # 3.46 |
5079 | print $x->bsqrt(3),"\n"; # 3.464 | |
5080 | ||
b3abae2a JH |
5081 | =item brsft() |
5082 | ||
5083 | For negative numbers in base see also L<brsft|brsft>. | |
5084 | ||
58cde26e JH |
5085 | =back |
5086 | ||
5087 | =head1 LICENSE | |
5088 | ||
5089 | This program is free software; you may redistribute it and/or modify it under | |
5090 | the same terms as Perl itself. | |
a5f75d66 | 5091 | |
0716bf9b JH |
5092 | =head1 SEE ALSO |
5093 | ||
990fb837 RGS |
5094 | L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as |
5095 | L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
5096 | ||
5097 | The pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest | |
5098 | because they solve the autoupgrading/downgrading issue, at least partly. | |
0716bf9b | 5099 | |
027dc388 JH |
5100 | The package at |
5101 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains | |
5102 | more documentation including a full version history, testcases, empty | |
5103 | subclass files and benchmarks. | |
574bacfe | 5104 | |
58cde26e | 5105 | =head1 AUTHORS |
a5f75d66 | 5106 | |
58cde26e | 5107 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
7b29e1e6 T |
5108 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2006 |
5109 | and still at it in 2007. | |
990fb837 RGS |
5110 | |
5111 | Many people contributed in one or more ways to the final beast, see the file | |
3c4b39be | 5112 | CREDITS for an (incomplete) list. If you miss your name, please drop me a |
990fb837 | 5113 | mail. Thank you! |
a5f75d66 AD |
5114 | |
5115 | =cut |