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Rewrap some verbatim pod in Math::BigInt
[perl5.git] / dist / Math-BigInt / lib / Math / BigInt.pm
CommitLineData
13a12e00
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1package 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:
9681bfa6 9# value: unsigned int with actual value (as a Math::BigInt::Calc or similar)
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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
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15# Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
16# underlying lib might change the reference!
17
58cde26e 18my $class = "Math::BigInt";
0d71d61a 19use 5.006002;
58cde26e 20
80df1b84 21$VERSION = '1.996';
b68b7ab1 22
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T
23@ISA = qw(Exporter);
24@EXPORT_OK = qw(objectify bgcd blcm);
b68b7ab1 25
b282a552
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26# _trap_inf and _trap_nan are internal and should never be accessed from the
27# outside
28use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode
29 $upgrade $downgrade $_trap_nan $_trap_inf/;
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30use strict;
31
32# Inside overload, the first arg is always an object. If the original code had
df0693ed 33# it reversed (like $x = 2 * $y), then the third parameter is true.
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T
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.
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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 43use overload
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44'=' => sub { $_[0]->copy(); },
45
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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]); },
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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
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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 $_[2] ?
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81 "$_[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
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90# are not yet overloadable
91#'hex' => sub { print "hex"; $_[0]; },
92#'oct' => sub { print "oct"; $_[0]; },
93
a0ac753d
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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]); },
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97'int' => sub { $_[0]->copy(); },
98'neg' => sub { $_[0]->copy()->bneg(); },
99'abs' => sub { $_[0]->copy()->babs(); },
b3abae2a 100'sqrt' => sub { $_[0]->copy()->bsqrt(); },
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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
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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!
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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
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144 my $t = undef;
145 $t = 1 if !$_[0]->is_zero();
b3abae2a 146 $t;
58cde26e 147 },
a0d0e21e 148
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149# the original qw() does not work with the TIESCALAR below, why?
150# Order of arguments unsignificant
151'""' => sub { $_[0]->bstr(); },
152'0+' => sub { $_[0]->numify(); }
a5f75d66 153;
a0d0e21e 154
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155##############################################################################
156# global constants, flags and accessory
157
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T
158# These vars are public, but their direct usage is not recommended, use the
159# accessor methods instead
0716bf9b 160
7b29e1e6 161$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
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162$accuracy = undef;
163$precision = undef;
164$div_scale = 40;
58cde26e 165
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166$upgrade = undef; # default is no upgrade
167$downgrade = undef; # default is no downgrade
168
b68b7ab1 169# These are internally, and not to be used from the outside at all
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170
171$_trap_nan = 0; # are NaNs ok? set w/ config()
172$_trap_inf = 0; # are infs ok? set w/ config()
173my $nan = 'NaN'; # constants for easier life
174
a90064ab
PJA
175my $CALC = 'Math::BigInt::Calc'; # module to do the low level math
176 # default is Calc.pm
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177my $IMPORT = 0; # was import() called yet?
178 # used to make require work
9b924220
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179my %WARN; # warn only once for low-level libs
180my %CAN; # cache for $CALC->can(...)
b68b7ab1 181my %CALLBACKS; # callbacks to notify on lib loads
b282a552 182my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math
b282a552 183
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184##############################################################################
185# the old code had $rnd_mode, so we need to support it, too
186
187$rnd_mode = 'even';
188sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; }
189sub FETCH { return $round_mode; }
190sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
191
b282a552
T
192BEGIN
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 }
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202
203##############################################################################
204
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205sub round_mode
206 {
ee15d750 207 no strict 'refs';
58cde26e 208 # make Class->round_mode() work
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209 my $self = shift;
210 my $class = ref($self) || $self || __PACKAGE__;
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211 if (defined $_[0])
212 {
213 my $m = shift;
7b29e1e6 214 if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
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215 {
216 require Carp; Carp::croak ("Unknown round mode '$m'");
217 }
b3abae2a 218 return ${"${class}::round_mode"} = $m;
58cde26e 219 }
990fb837 220 ${"${class}::round_mode"};
ee15d750
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221 }
222
b3abae2a
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223sub upgrade
224 {
225 no strict 'refs';
28df3e88 226 # make Class->upgrade() work
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227 my $self = shift;
228 my $class = ref($self) || $self || __PACKAGE__;
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229 # need to set new value?
230 if (@_ > 0)
b3abae2a 231 {
b68b7ab1 232 return ${"${class}::upgrade"} = $_[0];
b3abae2a 233 }
990fb837 234 ${"${class}::upgrade"};
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235 }
236
28df3e88
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237sub downgrade
238 {
239 no strict 'refs';
240 # make Class->downgrade() work
241 my $self = shift;
242 my $class = ref($self) || $self || __PACKAGE__;
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243 # need to set new value?
244 if (@_ > 0)
28df3e88 245 {
b68b7ab1 246 return ${"${class}::downgrade"} = $_[0];
28df3e88 247 }
990fb837 248 ${"${class}::downgrade"};
28df3e88
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249 }
250
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251sub div_scale
252 {
253 no strict 'refs';
990fb837 254 # make Class->div_scale() work
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255 my $self = shift;
256 my $class = ref($self) || $self || __PACKAGE__;
257 if (defined $_[0])
258 {
990fb837
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259 if ($_[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"};
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266 }
267
268sub accuracy
269 {
ee15d750
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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
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275 my $x = shift;
276 my $class = ref($x) || $x || __PACKAGE__;
58cde26e 277
ee15d750
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278 no strict 'refs';
279 # need to set new value?
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280 if (@_ > 0)
281 {
ee15d750 282 my $a = shift;
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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 }
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JH
325
326sub precision
327 {
ee15d750
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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
372sub 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 $cfg;
437 }
438
58cde26e
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439sub _scale_a
440 {
441 # select accuracy parameter based on precedence,
442 # used by bround() and bfround(), may return undef for scale (means no op)
b68b7ab1
T
443 my ($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
462sub _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
488sub 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 $self;
511 }
512
513sub new
514 {
b22b3e31 515 # create a new BigInt object from a string or another BigInt object.
0716bf9b 516 # see hash keys documented at top
58cde26e
JH
517
518 # the argument could be an object, so avoid ||, && etc on it, this would
b22b3e31
PN
519 # cause costly overloaded code to be called. The only allowed ops are
520 # ref() and defined.
58cde26e 521
61f5c3f5 522 my ($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
647sub 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
679sub 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
714sub 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
756sub 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 801##############################################################################
9681bfa6 802# string conversion
58cde26e
JH
803
804sub 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
822sub 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
836sub 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
850sub 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 858sub _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
929sub round
930 {
61f5c3f5 931 # Round $self according to given parameters, or given second argument's
ee15d750 932 # parameters or global defaults
ee15d750 933
c4a6f826 934 # for speed reasons, _find_round_parameters is embedded here:
61f5c3f5
T
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 }
c4a6f826 992 # bround() or bfround() already called bnorm() if nec.
12fc2493 993 $self;
58cde26e
JH
994 }
995
17baacb7 996sub 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
1004sub 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
7833bfdd
PJA
1016sub bsgn {
1017 # Signum function.
1018
1019 my $self = shift;
1020
1021 return $self if $self->modify('bsgn');
1022
1023 return $self -> bone("+") if $self -> is_pos();
1024 return $self -> bone("-") if $self -> is_neg();
1025 return $self; # zero or NaN
1026}
1027
58cde26e
JH
1028sub bneg
1029 {
1030 # (BINT or num_str) return BINT
1031 # negate number or make a negated number from string
b68b7ab1 1032 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
ee15d750 1033
58cde26e 1034 return $x if $x->modify('bneg');
b3abae2a 1035
b68b7ab1
T
1036 # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN'
1037 $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value}));
58cde26e
JH
1038 $x;
1039 }
1040
1041sub bcmp
1042 {
1043 # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
1044 # (BINT or num_str, BINT or num_str) return cond_code
f9a08e12
JH
1045
1046 # set up parameters
1047 my ($self,$x,$y) = (ref($_[0]),@_);
1048
1049 # objectify is costly, so avoid it
1050 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1051 {
1052 ($self,$x,$y) = objectify(2,@_);
1053 }
0716bf9b 1054
56d9de68
T
1055 return $upgrade->bcmp($x,$y) if defined $upgrade &&
1056 ((!$x->isa($self)) || (!$y->isa($self)));
1057
0716bf9b
JH
1058 if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
1059 {
1060 # handle +-inf and NaN
1061 return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
574bacfe 1062 return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
0716bf9b
JH
1063 return +1 if $x->{sign} eq '+inf';
1064 return -1 if $x->{sign} eq '-inf';
1065 return -1 if $y->{sign} eq '+inf';
b3abae2a 1066 return +1;
0716bf9b 1067 }
574bacfe
JH
1068 # check sign for speed first
1069 return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
1070 return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
1071
f9a08e12
JH
1072 # have same sign, so compare absolute values. Don't make tests for zero here
1073 # because it's actually slower than testin in Calc (especially w/ Pari et al)
1074
dccbb853
JH
1075 # post-normalized compare for internal use (honors signs)
1076 if ($x->{sign} eq '+')
1077 {
56b9c951 1078 # $x and $y both > 0
dccbb853
JH
1079 return $CALC->_acmp($x->{value},$y->{value});
1080 }
1081
56b9c951 1082 # $x && $y both < 0
b282a552 1083 $CALC->_acmp($y->{value},$x->{value}); # swaped acmp (lib returns 0,1,-1)
58cde26e
JH
1084 }
1085
1086sub bacmp
1087 {
1088 # Compares 2 values, ignoring their signs.
1089 # Returns one of undef, <0, =0, >0. (suitable for sort)
1090 # (BINT, BINT) return cond_code
574bacfe 1091
f9a08e12
JH
1092 # set up parameters
1093 my ($self,$x,$y) = (ref($_[0]),@_);
1094 # objectify is costly, so avoid it
1095 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1096 {
1097 ($self,$x,$y) = objectify(2,@_);
1098 }
1099
56d9de68
T
1100 return $upgrade->bacmp($x,$y) if defined $upgrade &&
1101 ((!$x->isa($self)) || (!$y->isa($self)));
1102
574bacfe
JH
1103 if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
1104 {
1105 # handle +-inf and NaN
1106 return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
1107 return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
ef9466ea
T
1108 return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
1109 return -1;
574bacfe 1110 }
b3abae2a 1111 $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1
58cde26e
JH
1112 }
1113
1114sub badd
1115 {
1116 # add second arg (BINT or string) to first (BINT) (modifies first)
1117 # return result as BINT
f9a08e12
JH
1118
1119 # set up parameters
1120 my ($self,$x,$y,@r) = (ref($_[0]),@_);
1121 # objectify is costly, so avoid it
1122 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1123 {
1124 ($self,$x,$y,@r) = objectify(2,@_);
1125 }
58cde26e
JH
1126
1127 return $x if $x->modify('badd');
091c87b1 1128 return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade &&
8f675a64 1129 ((!$x->isa($self)) || (!$y->isa($self)));
58cde26e 1130
61f5c3f5 1131 $r[3] = $y; # no push!
574bacfe
JH
1132 # inf and NaN handling
1133 if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
1134 {
1135 # NaN first
1136 return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
13a12e00
JH
1137 # inf handling
1138 if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
574bacfe 1139 {
b3abae2a
JH
1140 # +inf++inf or -inf+-inf => same, rest is NaN
1141 return $x if $x->{sign} eq $y->{sign};
1142 return $x->bnan();
574bacfe
JH
1143 }
1144 # +-inf + something => +inf
1145 # something +-inf => +-inf
1146 $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
1147 return $x;
1148 }
1149
b282a552 1150 my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
58cde26e
JH
1151
1152 if ($sx eq $sy)
1153 {
574bacfe 1154 $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add
58cde26e
JH
1155 }
1156 else
1157 {
574bacfe 1158 my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare
58cde26e
JH
1159 if ($a > 0)
1160 {
574bacfe 1161 $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap
58cde26e
JH
1162 $x->{sign} = $sy;
1163 }
1164 elsif ($a == 0)
1165 {
1166 # speedup, if equal, set result to 0
0716bf9b 1167 $x->{value} = $CALC->_zero();
58cde26e
JH
1168 $x->{sign} = '+';
1169 }
1170 else # a < 0
1171 {
574bacfe 1172 $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
a0d0e21e 1173 }
a0d0e21e 1174 }
b68b7ab1 1175 $x->round(@r);
58cde26e
JH
1176 }
1177
1178sub bsub
1179 {
091c87b1 1180 # (BINT or num_str, BINT or num_str) return BINT
58cde26e 1181 # subtract second arg from first, modify first
f9a08e12
JH
1182
1183 # set up parameters
1184 my ($self,$x,$y,@r) = (ref($_[0]),@_);
7d193e39 1185
f9a08e12
JH
1186 # objectify is costly, so avoid it
1187 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1188 {
1189 ($self,$x,$y,@r) = objectify(2,@_);
1190 }
58cde26e 1191
58cde26e 1192 return $x if $x->modify('bsub');
8f675a64 1193
9b924220
RGS
1194 return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade &&
1195 ((!$x->isa($self)) || (!$y->isa($self)));
b3abae2a 1196
b68b7ab1 1197 return $x->round(@r) if $y->is_zero();
b3abae2a 1198
a87115f0
RGS
1199 # To correctly handle the lone special case $x->bsub($x), we note the sign
1200 # of $x, then flip the sign from $y, and if the sign of $x did change, too,
1201 # then we caught the special case:
1202 my $xsign = $x->{sign};
1203 $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
1204 if ($xsign ne $x->{sign})
03874afe 1205 {
a87115f0
RGS
1206 # special case of $x->bsub($x) results in 0
1207 return $x->bzero(@r) if $xsign =~ /^[+-]$/;
03874afe
T
1208 return $x->bnan(); # NaN, -inf, +inf
1209 }
b3abae2a
JH
1210 $x->badd($y,@r); # badd does not leave internal zeros
1211 $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
7b29e1e6 1212 $x; # already rounded by badd() or no round nec.
58cde26e
JH
1213 }
1214
1215sub binc
1216 {
1217 # increment arg by one
ee15d750 1218 my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
58cde26e 1219 return $x if $x->modify('binc');
e745a66c
JH
1220
1221 if ($x->{sign} eq '+')
1222 {
1223 $x->{value} = $CALC->_inc($x->{value});
b68b7ab1 1224 return $x->round($a,$p,$r);
e745a66c
JH
1225 }
1226 elsif ($x->{sign} eq '-')
1227 {
1228 $x->{value} = $CALC->_dec($x->{value});
1229 $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
b68b7ab1 1230 return $x->round($a,$p,$r);
e745a66c
JH
1231 }
1232 # inf, nan handling etc
091c87b1 1233 $x->badd($self->bone(),$a,$p,$r); # badd does round
58cde26e
JH
1234 }
1235
1236sub bdec
1237 {
1238 # decrement arg by one
b282a552 1239 my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
58cde26e 1240 return $x if $x->modify('bdec');
e745a66c 1241
b282a552 1242 if ($x->{sign} eq '-')
e745a66c 1243 {
b68b7ab1 1244 # x already < 0
e745a66c 1245 $x->{value} = $CALC->_inc($x->{value});
b282a552
T
1246 }
1247 else
e745a66c 1248 {
b68b7ab1 1249 return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf or NaN
b282a552
T
1250 # >= 0
1251 if ($CALC->_is_zero($x->{value}))
1252 {
1253 # == 0
1254 $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1
1255 }
1256 else
1257 {
1258 # > 0
1259 $x->{value} = $CALC->_dec($x->{value});
1260 }
e745a66c 1261 }
b68b7ab1 1262 $x->round(@r);
b282a552 1263 }
58cde26e 1264
61f5c3f5
T
1265sub blog
1266 {
091c87b1
T
1267 # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base
1268 # $base of $x)
1269
1270 # set up parameters
b68b7ab1 1271 my ($self,$x,$base,@r) = (undef,@_);
091c87b1
T
1272 # objectify is costly, so avoid it
1273 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1274 {
2aa6a1fb 1275 ($self,$x,$base,@r) = objectify(2,@_);
091c87b1 1276 }
a0ac753d 1277
ef9466ea
T
1278 return $x if $x->modify('blog');
1279
2ebb273f
T
1280 $base = $self->new($base) if defined $base && !ref $base;
1281
091c87b1
T
1282 # inf, -inf, NaN, <0 => NaN
1283 return $x->bnan()
9b924220 1284 if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+');
091c87b1 1285
9b924220
RGS
1286 return $upgrade->blog($upgrade->new($x),$base,@r) if
1287 defined $upgrade;
091c87b1 1288
a0ac753d
T
1289 # fix for bug #24969:
1290 # the default base is e (Euler's number) which is not an integer
1291 if (!defined $base)
1292 {
1293 require Math::BigFloat;
1294 my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int();
1295 # modify $x in place
1296 $x->{value} = $u->{value};
1297 $x->{sign} = $u->{sign};
1298 return $x;
1299 }
1300
9b924220
RGS
1301 my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value});
1302 return $x->bnan() unless defined $rc; # not possible to take log?
1303 $x->{value} = $rc;
1304 $x->round(@r);
61f5c3f5 1305 }
091c87b1 1306
50109ad0
RGS
1307sub bnok
1308 {
1309 # Calculate n over k (binomial coefficient or "choose" function) as integer.
1310 # set up parameters
1311 my ($self,$x,$y,@r) = (ref($_[0]),@_);
1312
1313 # objectify is costly, so avoid it
1314 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1315 {
1316 ($self,$x,$y,@r) = objectify(2,@_);
1317 }
1318
1319 return $x if $x->modify('bnok');
1320 return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN';
1321 return $x->binf() if $x->{sign} eq '+inf';
1322
1323 # k > n or k < 0 => 0
1324 my $cmp = $x->bacmp($y);
1325 return $x->bzero() if $cmp < 0 || $y->{sign} =~ /^-/;
1326 # k == n => 1
1327 return $x->bone(@r) if $cmp == 0;
1328
1329 if ($CALC->can('_nok'))
1330 {
1331 $x->{value} = $CALC->_nok($x->{value},$y->{value});
1332 }
1333 else
1334 {
d5735945
PF
1335 # ( 7 ) 7! 1*2*3*4 * 5*6*7 5 * 6 * 7 6 7
1336 # ( - ) = --------- = --------------- = --------- = 5 * - * -
1337 # ( 3 ) (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3 2 3
50109ad0 1338
d5735945 1339 if (!$y->is_zero())
50109ad0 1340 {
d5735945 1341 my $z = $x - $y;
50109ad0
RGS
1342 $z->binc();
1343 my $r = $z->copy(); $z->binc();
1344 my $d = $self->new(2);
d5735945 1345 while ($z->bacmp($x) <= 0) # f <= x ?
50109ad0
RGS
1346 {
1347 $r->bmul($z); $r->bdiv($d);
1348 $z->binc(); $d->binc();
1349 }
1350 $x->{value} = $r->{value}; $x->{sign} = '+';
1351 }
1352 else { $x->bone(); }
1353 }
1354 $x->round(@r);
1355 }
1356
7d193e39
T
1357sub bexp
1358 {
1359 # Calculate e ** $x (Euler's number to the power of X), truncated to
1360 # an integer value.
1361 my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
1362 return $x if $x->modify('bexp');
1363
1364 # inf, -inf, NaN, <0 => NaN
1365 return $x->bnan() if $x->{sign} eq 'NaN';
1366 return $x->bone() if $x->is_zero();
1367 return $x if $x->{sign} eq '+inf';
1368 return $x->bzero() if $x->{sign} eq '-inf';
1369
1370 my $u;
1371 {
1372 # run through Math::BigFloat unless told otherwise
50109ad0 1373 require Math::BigFloat unless defined $upgrade;
7d193e39
T
1374 local $upgrade = 'Math::BigFloat' unless defined $upgrade;
1375 # calculate result, truncate it to integer
1376 $u = $upgrade->bexp($upgrade->new($x),@r);
1377 }
1378
1379 if (!defined $upgrade)
1380 {
1381 $u = $u->as_int();
1382 # modify $x in place
1383 $x->{value} = $u->{value};
1384 $x->round(@r);
1385 }
1386 else { $x = $u; }
1387 }
1388
fdd59300
FR
1389sub blcm
1390 {
58cde26e
JH
1391 # (BINT or num_str, BINT or num_str) return BINT
1392 # does not modify arguments, but returns new object
fdd59300 1393 # Lowest Common Multiple
58cde26e 1394
0716bf9b
JH
1395 my $y = shift; my ($x);
1396 if (ref($y))
1397 {
1398 $x = $y->copy();
1399 }
1400 else
1401 {
12fc2493 1402 $x = $class->new($y);
0716bf9b 1403 }
9b924220
RGS
1404 my $self = ref($x);
1405 while (@_)
1406 {
1407 my $y = shift; $y = $self->new($y) if !ref ($y);
1408 $x = __lcm($x,$y);
1409 }
58cde26e
JH
1410 $x;
1411 }
1412
1413sub bgcd
1414 {
1415 # (BINT or num_str, BINT or num_str) return BINT
1416 # does not modify arguments, but returns new object
c4a6f826 1417 # GCD -- Euclid's algorithm, variant C (Knuth Vol 3, pg 341 ff)
0716bf9b 1418
dccbb853 1419 my $y = shift;
12fc2493 1420 $y = $class->new($y) if !ref($y);
dccbb853 1421 my $self = ref($y);
9b924220
RGS
1422 my $x = $y->copy()->babs(); # keep arguments
1423 return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
1424
1425 while (@_)
0716bf9b 1426 {
9b924220 1427 $y = shift; $y = $self->new($y) if !ref($y);
9b924220 1428 return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
b68b7ab1
T
1429 $x->{value} = $CALC->_gcd($x->{value},$y->{value});
1430 last if $CALC->_is_one($x->{value});
0716bf9b 1431 }
9b924220 1432 $x;
58cde26e
JH
1433 }
1434
58cde26e
JH
1435sub bnot
1436 {
1437 # (num_str or BINT) return BINT
1438 # represent ~x as twos-complement number
ee15d750
JH
1439 # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
1440 my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
1441
58cde26e 1442 return $x if $x->modify('bnot');
091c87b1 1443 $x->binc()->bneg(); # binc already does round
58cde26e
JH
1444 }
1445
091c87b1 1446##############################################################################
b3abae2a 1447# is_foo test routines
091c87b1 1448# we don't need $self, so undef instead of ref($_[0]) make it slightly faster
b3abae2a 1449
58cde26e
JH
1450sub is_zero
1451 {
1452 # return true if arg (BINT or num_str) is zero (array '+', '0')
ee15d750 1453 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
0716bf9b 1454
574bacfe 1455 return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
17baacb7 1456 $CALC->_is_zero($x->{value});
58cde26e
JH
1457 }
1458
1459sub is_nan
1460 {
1461 # return true if arg (BINT or num_str) is NaN
091c87b1 1462 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
ee15d750 1463
091c87b1 1464 $x->{sign} eq $nan ? 1 : 0;
58cde26e
JH
1465 }
1466
1467sub is_inf
1468 {
1469 # return true if arg (BINT or num_str) is +-inf
091c87b1 1470 my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
58cde26e 1471
091c87b1 1472 if (defined $sign)
ee15d750 1473 {
091c87b1
T
1474 $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf
1475 $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-'
1476 return $x->{sign} =~ /^$sign$/ ? 1 : 0;
ee15d750 1477 }
091c87b1 1478 $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity
58cde26e
JH
1479 }
1480
1481sub is_one
1482 {
091c87b1 1483 # return true if arg (BINT or num_str) is +1, or -1 if sign is given
ee15d750
JH
1484 my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
1485
990fb837 1486 $sign = '+' if !defined $sign || $sign ne '-';
0716bf9b 1487
ee15d750 1488 return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
394e6ffb 1489 $CALC->_is_one($x->{value});
58cde26e
JH
1490 }
1491
1492sub is_odd
1493 {
1494 # return true when arg (BINT or num_str) is odd, false for even
ee15d750 1495 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
0716bf9b 1496
b22b3e31 1497 return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
394e6ffb 1498 $CALC->_is_odd($x->{value});
58cde26e
JH
1499 }
1500
1501sub is_even
1502 {
1503 # return true when arg (BINT or num_str) is even, false for odd
ee15d750 1504 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
0716bf9b 1505
b22b3e31 1506 return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
394e6ffb 1507 $CALC->_is_even($x->{value});
0716bf9b
JH
1508 }
1509
1510sub is_positive
1511 {
4af46cb8 1512 # return true when arg (BINT or num_str) is positive (> 0)
ee15d750 1513 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
b68b7ab1
T
1514
1515 return 1 if $x->{sign} eq '+inf'; # +inf is positive
4af46cb8 1516
b68b7ab1 1517 # 0+ is neither positive nor negative
4af46cb8 1518 ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0;
0716bf9b
JH
1519 }
1520
1521sub is_negative
1522 {
1523 # return true when arg (BINT or num_str) is negative (< 0)
ee15d750
JH
1524 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
1525
b68b7ab1 1526 $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not
58cde26e
JH
1527 }
1528
b3abae2a
JH
1529sub is_int
1530 {
1531 # return true when arg (BINT or num_str) is an integer
091c87b1 1532 # always true for BigInt, but different for BigFloats
b3abae2a
JH
1533 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
1534
1535 $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't
1536 }
1537
0716bf9b
JH
1538###############################################################################
1539
58cde26e
JH
1540sub bmul
1541 {
c97ef841 1542 # multiply the first number by the second number
58cde26e 1543 # (BINT or num_str, BINT or num_str) return BINT
f9a08e12
JH
1544
1545 # set up parameters
1546 my ($self,$x,$y,@r) = (ref($_[0]),@_);
1547 # objectify is costly, so avoid it
1548 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1549 {
1550 ($self,$x,$y,@r) = objectify(2,@_);
1551 }
a0ac753d 1552
58cde26e 1553 return $x if $x->modify('bmul');
61f5c3f5 1554
574bacfe 1555 return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
b3abae2a 1556
574bacfe
JH
1557 # inf handling
1558 if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
1559 {
b3abae2a 1560 return $x->bnan() if $x->is_zero() || $y->is_zero();
574bacfe
JH
1561 # result will always be +-inf:
1562 # +inf * +/+inf => +inf, -inf * -/-inf => +inf
1563 # +inf * -/-inf => -inf, -inf * +/+inf => -inf
1564 return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
1565 return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
1566 return $x->binf('-');
1567 }
9b924220
RGS
1568
1569 return $upgrade->bmul($x,$upgrade->new($y),@r)
1570 if defined $upgrade && !$y->isa($self);
9393ace2
JH
1571
1572 $r[3] = $y; # no push here
58cde26e 1573
0716bf9b 1574 $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
dccbb853 1575
b3abae2a
JH
1576 $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
1577 $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
f9a08e12 1578
b68b7ab1 1579 $x->round(@r);
dccbb853
JH
1580 }
1581
80365507
T
1582sub bmuladd
1583 {
1584 # multiply two numbers and then add the third to the result
1585 # (BINT or num_str, BINT or num_str, BINT or num_str) return BINT
1586
1587 # set up parameters
913a64d5 1588 my ($self,$x,$y,$z,@r) = objectify(3,@_);
80365507
T
1589
1590 return $x if $x->modify('bmuladd');
1591
1592 return $x->bnan() if ($x->{sign} eq $nan) ||
1593 ($y->{sign} eq $nan) ||
1594 ($z->{sign} eq $nan);
1595
1596 # inf handling of x and y
1597 if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
1598 {
1599 return $x->bnan() if $x->is_zero() || $y->is_zero();
1600 # result will always be +-inf:
1601 # +inf * +/+inf => +inf, -inf * -/-inf => +inf
1602 # +inf * -/-inf => -inf, -inf * +/+inf => -inf
1603 return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
1604 return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
1605 return $x->binf('-');
1606 }
1607 # inf handling x*y and z
1608 if (($z->{sign} =~ /^[+-]inf$/))
1609 {
1610 # something +-inf => +-inf
1611 $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/;
1612 }
1613
1614 return $upgrade->bmuladd($x,$upgrade->new($y),$upgrade->new($z),@r)
1615 if defined $upgrade && (!$y->isa($self) || !$z->isa($self) || !$x->isa($self));
1616
c97ef841 1617 # TODO: what if $y and $z have A or P set?
80365507
T
1618 $r[3] = $z; # no push here
1619
1620 $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
1621
1622 $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
1623 $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
1624
1625 my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); # get signs
1626
1627 if ($sx eq $sz)
1628 {
1629 $x->{value} = $CALC->_add($x->{value},$z->{value}); # same sign, abs add
1630 }
1631 else
1632 {
1633 my $a = $CALC->_acmp ($z->{value},$x->{value}); # absolute compare
1634 if ($a > 0)
1635 {
1636 $x->{value} = $CALC->_sub($z->{value},$x->{value},1); # abs sub w/ swap
1637 $x->{sign} = $sz;
1638 }
1639 elsif ($a == 0)
1640 {
1641 # speedup, if equal, set result to 0
1642 $x->{value} = $CALC->_zero();
1643 $x->{sign} = '+';
1644 }
1645 else # a < 0
1646 {
1647 $x->{value} = $CALC->_sub($x->{value}, $z->{value}); # abs sub
1648 }
1649 }
1650 $x->round(@r);
1651 }
1652
dccbb853
JH
1653sub _div_inf
1654 {
1655 # helper function that handles +-inf cases for bdiv()/bmod() to reuse code
1656 my ($self,$x,$y) = @_;
1657
1658 # NaN if x == NaN or y == NaN or x==y==0
1659 return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
1660 if (($x->is_nan() || $y->is_nan()) ||
1661 ($x->is_zero() && $y->is_zero()));
1662
f603091d 1663 # +-inf / +-inf == NaN, remainder also NaN
b3abae2a 1664 if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
dccbb853 1665 {
b3abae2a 1666 return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan();
dccbb853
JH
1667 }
1668 # x / +-inf => 0, remainder x (works even if x == 0)
1669 if ($y->{sign} =~ /^[+-]inf$/)
1670 {
f9a08e12 1671 my $t = $x->copy(); # bzero clobbers up $x
dccbb853
JH
1672 return wantarray ? ($x->bzero(),$t) : $x->bzero()
1673 }
1674
1675 # 5 / 0 => +inf, -6 / 0 => -inf
1676 # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf
1677 # exception: -8 / 0 has remainder -8, not 8
1678 # exception: -inf / 0 has remainder -inf, not inf
1679 if ($y->is_zero())
1680 {
1681 # +-inf / 0 => special case for -inf
1682 return wantarray ? ($x,$x->copy()) : $x if $x->is_inf();
1683 if (!$x->is_zero() && !$x->is_inf())
1684 {
1685 my $t = $x->copy(); # binf clobbers up $x
1686 return wantarray ?
1687 ($x->binf($x->{sign}),$t) : $x->binf($x->{sign})
1688 }
1689 }
1690
1691 # last case: +-inf / ordinary number
1692 my $sign = '+inf';
1693 $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign};
1694 $x->{sign} = $sign;
1695 return wantarray ? ($x,$self->bzero()) : $x;
58cde26e
JH
1696 }
1697
1698sub bdiv
1699 {
1700 # (dividend: BINT or num_str, divisor: BINT or num_str) return
1701 # (BINT,BINT) (quo,rem) or BINT (only rem)
f9a08e12
JH
1702
1703 # set up parameters
1704 my ($self,$x,$y,@r) = (ref($_[0]),@_);
1705 # objectify is costly, so avoid it
1706 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1707 {
1708 ($self,$x,$y,@r) = objectify(2,@_);
1709 }
58cde26e
JH
1710
1711 return $x if $x->modify('bdiv');
1712
dccbb853
JH
1713 return $self->_div_inf($x,$y)
1714 if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
58cde26e 1715
9393ace2
JH
1716 return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r)
1717 if defined $upgrade;
58cde26e 1718
990fb837
RGS
1719 $r[3] = $y; # no push!
1720
58cde26e 1721 # calc new sign and in case $y == +/- 1, return $x
dccbb853 1722 my $xsign = $x->{sign}; # keep
58cde26e 1723 $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+');
58cde26e 1724
58cde26e
JH
1725 if (wantarray)
1726 {
394e6ffb
JH
1727 my $rem = $self->bzero();
1728 ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
1729 $x->{sign} = '+' if $CALC->_is_zero($x->{value});
f9a08e12
JH
1730 $rem->{_a} = $x->{_a};
1731 $rem->{_p} = $x->{_p};
b68b7ab1 1732 $x->round(@r);
dccbb853
JH
1733 if (! $CALC->_is_zero($rem->{value}))
1734 {
1735 $rem->{sign} = $y->{sign};
990fb837 1736 $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-'
dccbb853
JH
1737 }
1738 else
1739 {
1740 $rem->{sign} = '+'; # dont leave -0
1741 }
b68b7ab1 1742 $rem->round(@r);
990fb837 1743 return ($x,$rem);
58cde26e 1744 }
394e6ffb
JH
1745
1746 $x->{value} = $CALC->_div($x->{value},$y->{value});
1747 $x->{sign} = '+' if $CALC->_is_zero($x->{value});
f9a08e12 1748
b68b7ab1 1749 $x->round(@r);
58cde26e
JH
1750 }
1751
d614cd8b
JH
1752###############################################################################
1753# modulus functions
1754
dccbb853
JH
1755sub bmod
1756 {
1757 # modulus (or remainder)
1758 # (BINT or num_str, BINT or num_str) return BINT
f9a08e12
JH
1759
1760 # set up parameters
1761 my ($self,$x,$y,@r) = (ref($_[0]),@_);
1762 # objectify is costly, so avoid it
1763 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1764 {
1765 ($self,$x,$y,@r) = objectify(2,@_);
1766 }
28df3e88 1767
dccbb853 1768 return $x if $x->modify('bmod');
61f5c3f5 1769 $r[3] = $y; # no push!
dccbb853
JH
1770 if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
1771 {
1772 my ($d,$r) = $self->_div_inf($x,$y);
f9a08e12
JH
1773 $x->{sign} = $r->{sign};
1774 $x->{value} = $r->{value};
1775 return $x->round(@r);
dccbb853
JH
1776 }
1777
9b924220
RGS
1778 # calc new sign and in case $y == +/- 1, return $x
1779 $x->{value} = $CALC->_mod($x->{value},$y->{value});
1780 if (!$CALC->_is_zero($x->{value}))
dccbb853 1781 {
b68b7ab1
T
1782 $x->{value} = $CALC->_sub($y->{value},$x->{value},1) # $y-$x
1783 if ($x->{sign} ne $y->{sign});
9b924220 1784 $x->{sign} = $y->{sign};
dccbb853 1785 }
9b924220 1786 else
b3abae2a 1787 {
9b924220 1788 $x->{sign} = '+'; # dont leave -0
b3abae2a 1789 }
b68b7ab1 1790 $x->round(@r);
dccbb853
JH
1791 }
1792
07d34614 1793sub bmodinv
d614cd8b 1794 {
487de07a
PJA
1795 # Return modular multiplicative inverse: z is the modular inverse of x (mod
1796 # y) if and only if x*z (mod y) = 1 (mod y). If the modulus y is larger than
1797 # one, x and z are relative primes (i.e., their greatest common divisor is
1798 # one).
1799 #
1800 # If no modular multiplicative inverse exists, NaN is returned.
d614cd8b 1801
f9a08e12 1802 # set up parameters
b68b7ab1 1803 my ($self,$x,$y,@r) = (undef,@_);
56d9de68 1804 # objectify is costly, so avoid it
f9a08e12
JH
1805 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1806 {
1807 ($self,$x,$y,@r) = objectify(2,@_);
56d9de68 1808 }
d614cd8b 1809
f9a08e12 1810 return $x if $x->modify('bmodinv');
d614cd8b 1811
487de07a
PJA
1812 # Return NaN if one or both arguments is +inf, -inf, or nan.
1813
1814 return $x->bnan() if ($y->{sign} !~ /^[+-]$/ ||
1815 $x->{sign} !~ /^[+-]$/);
1816
1817 # Return NaN if $y is zero; 1 % 0 makes no sense.
1818
1819 return $x->bnan() if $y->is_zero();
1820
1821 # Return 0 in the trivial case. $x % 1 or $x % -1 is zero for all finite
1822 # integers $x.
1823
1824 return $x->bzero() if ($y->is_one() ||
1825 $y->is_one('-'));
1826
1827 # Return NaN if $x = 0, or $x modulo $y is zero. The only valid case when
1828 # $x = 0 is when $y = 1 or $y = -1, but that was covered above.
1829 #
1830 # Note that computing $x modulo $y here affects the value we'll feed to
1831 # $CALC->_modinv() below when $x and $y have opposite signs. E.g., if $x =
1832 # 5 and $y = 7, those two values are fed to _modinv(), but if $x = -5 and
1833 # $y = 7, the values fed to _modinv() are $x = 2 (= -5 % 7) and $y = 7.
1834 # The value if $x is affected only when $x and $y have opposite signs.
1835
1836 $x->bmod($y);
1837 return $x->bnan() if $x->is_zero();
1838
1839 # Compute the modular multiplicative inverse of the absolute values. We'll
1840 # correct for the signs of $x and $y later. Return NaN if no GCD is found.
1841
1842 ($x->{value}, $x->{sign}) = $CALC->_modinv($x->{value}, $y->{value});
1843 return $x->bnan() if !defined $x->{value};
1844
db2e1fb3
PJA
1845 # Library inconsistency workaround: _modinv() in Math::BigInt::GMP versions
1846 # <= 1.32 return undef rather than a "+" for the sign.
1847
1848 $x->{sign} = '+' unless defined $x->{sign};
1849
487de07a
PJA
1850 # When one or both arguments are negative, we have the following
1851 # relations. If x and y are positive:
1852 #
1853 # modinv(-x, -y) = -modinv(x, y)
1854 # modinv(-x, y) = y - modinv(x, y) = -modinv(x, y) (mod y)
1855 # modinv( x, -y) = modinv(x, y) - y = modinv(x, y) (mod -y)
1856
1857 # We must swap the sign of the result if the original $x is negative.
1858 # However, we must compensate for ignoring the signs when computing the
1859 # inverse modulo. The net effect is that we must swap the sign of the
1860 # result if $y is negative.
1861
1862 $x -> bneg() if $y->{sign} eq '-';
1863
1864 # Compute $x modulo $y again after correcting the sign.
1865
1866 $x -> bmod($y) if $x->{sign} ne $y->{sign};
1867
1868 return $x;
d614cd8b
JH
1869 }
1870
07d34614 1871sub bmodpow
d614cd8b 1872 {
6c29054c
PJA
1873 # Modular exponentiation. Raises a very large number to a very large exponent
1874 # in a given very large modulus quickly, thanks to binary exponentiation.
1875 # Supports negative exponents.
d614cd8b
JH
1876 my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
1877
1878 return $num if $num->modify('bmodpow');
1879
116f6d6b
PJA
1880 # When the exponent 'e' is negative, use the following relation, which is
1881 # based on finding the multiplicative inverse 'd' of 'b' modulo 'm':
1882 #
1883 # b^(-e) (mod m) = d^e (mod m) where b*d = 1 (mod m)
d614cd8b 1884
116f6d6b 1885 $num->bmodinv($mod) if ($exp->{sign} eq '-');
07d34614 1886
116f6d6b
PJA
1887 # Check for valid input. All operands must be finite, and the modulus must be
1888 # non-zero.
d614cd8b 1889
116f6d6b
PJA
1890 return $num->bnan() if ($num->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
1891 $exp->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
1892 $mod->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
1893 $mod->is_zero());
d614cd8b 1894
116f6d6b
PJA
1895 # Compute 'a (mod m)', ignoring the signs on 'a' and 'm'. If the resulting
1896 # value is zero, the output is also zero, regardless of the signs on 'a' and
1897 # 'm'.
1898
1899 my $value = $CALC->_modpow($num->{value}, $exp->{value}, $mod->{value});
1900 my $sign = '+';
1901
1902 # If the resulting value is non-zero, we have four special cases, depending
1903 # on the signs on 'a' and 'm'.
1904
6c29054c 1905 unless ($CALC->_is_zero($value)) {
116f6d6b
PJA
1906
1907 # There is a negative sign on 'a' (= $num**$exp) only if the number we
1908 # are exponentiating ($num) is negative and the exponent ($exp) is odd.
1909
1910 if ($num->{sign} eq '-' && $exp->is_odd()) {
1911
1912 # When both the number 'a' and the modulus 'm' have a negative sign,
1913 # use this relation:
1914 #
1915 # -a (mod -m) = -(a (mod m))
1916
1917 if ($mod->{sign} eq '-') {
1918 $sign = '-';
1919 }
1920
1921 # When only the number 'a' has a negative sign, use this relation:
1922 #
1923 # -a (mod m) = m - (a (mod m))
1924
1925 else {
1926 # Use copy of $mod since _sub() modifies the first argument.
1927 my $mod = $CALC->_copy($mod->{value});
6c29054c 1928 $value = $CALC->_sub($mod, $value);
116f6d6b
PJA
1929 $sign = '+';
1930 }
1931
1932 } else {
1933
1934 # When only the modulus 'm' has a negative sign, use this relation:
1935 #
1936 # a (mod -m) = (a (mod m)) - m
1937 # = -(m - (a (mod m)))
1938
1939 if ($mod->{sign} eq '-') {
6c29054c 1940 # Use copy of $mod since _sub() modifies the first argument.
116f6d6b 1941 my $mod = $CALC->_copy($mod->{value});
6c29054c 1942 $value = $CALC->_sub($mod, $value);
116f6d6b
PJA
1943 $sign = '-';
1944 }
1945
1946 # When neither the number 'a' nor the modulus 'm' have a negative
1947 # sign, directly return the already computed value.
1948 #
1949 # (a (mod m))
1950
1951 }
1952
1953 }
1954
1955 $num->{value} = $value;
1956 $num->{sign} = $sign;
1957
1958 return $num;
d614cd8b
JH
1959 }
1960
1961###############################################################################
1962
b3abae2a
JH
1963sub bfac
1964 {
1965 # (BINT or num_str, BINT or num_str) return BINT
091c87b1 1966 # compute factorial number from $x, modify $x in place
b68b7ab1 1967 my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
b3abae2a 1968
b68b7ab1
T
1969 return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf
1970 return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN
b3abae2a 1971
9b924220
RGS
1972 $x->{value} = $CALC->_fac($x->{value});
1973 $x->round(@r);
b3abae2a
JH
1974 }
1975
58cde26e
JH
1976sub bpow
1977 {
1978 # (BINT or num_str, BINT or num_str) return BINT
1979 # compute power of two numbers -- stolen from Knuth Vol 2 pg 233
1980 # modifies first argument
aef458a0 1981
f9a08e12
JH
1982 # set up parameters
1983 my ($self,$x,$y,@r) = (ref($_[0]),@_);
1984 # objectify is costly, so avoid it
1985 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
1986 {
1987 ($self,$x,$y,@r) = objectify(2,@_);
1988 }
58cde26e
JH
1989
1990 return $x if $x->modify('bpow');
9393ace2 1991
2d2b2744
T
1992 return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
1993
1994 # inf handling
1995 if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
1996 {
1997 if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
1998 {
1999 # +-inf ** +-inf
2000 return $x->bnan();
2001 }
2002 # +-inf ** Y
2003 if ($x->{sign} =~ /^[+-]inf/)
2004 {
2005 # +inf ** 0 => NaN
2006 return $x->bnan() if $y->is_zero();
2007 # -inf ** -1 => 1/inf => 0
2008 return $x->bzero() if $y->is_one('-') && $x->is_negative();
2009
2010 # +inf ** Y => inf
2011 return $x if $x->{sign} eq '+inf';
2012
2013 # -inf ** Y => -inf if Y is odd
2014 return $x if $y->is_odd();
2015 return $x->babs();
2016 }
2017 # X ** +-inf
2018
2019 # 1 ** +inf => 1
2020 return $x if $x->is_one();
2021
2022 # 0 ** inf => 0
2023 return $x if $x->is_zero() && $y->{sign} =~ /^[+]/;
2024
2025 # 0 ** -inf => inf
2026 return $x->binf() if $x->is_zero();
2027
2028 # -1 ** -inf => NaN
2029 return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/;
2030
2031 # -X ** -inf => 0
2032 return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/;
2033
2034 # -1 ** inf => NaN
2035 return $x->bnan() if $x->{sign} eq '-';
2036
2037 # X ** inf => inf
2038 return $x->binf() if $y->{sign} =~ /^[+]/;
2039 # X ** -inf => 0
2040 return $x->bzero();
2041 }
2042
9393ace2 2043 return $upgrade->bpow($upgrade->new($x),$y,@r)
7b29e1e6 2044 if defined $upgrade && (!$y->isa($self) || $y->{sign} eq '-');
9393ace2 2045
61f5c3f5 2046 $r[3] = $y; # no push!
b282a552
T
2047
2048 # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu
2049
9b924220
RGS
2050 my $new_sign = '+';
2051 $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+');
2052
2053 # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf
2054 return $x->binf()
2055 if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value});
574bacfe
JH
2056 # 1 ** -y => 1 / (1 ** |y|)
2057 # so do test for negative $y after above's clause
9b924220 2058 return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value});
027dc388 2059
9b924220
RGS
2060 $x->{value} = $CALC->_pow($x->{value},$y->{value});
2061 $x->{sign} = $new_sign;
2062 $x->{sign} = '+' if $CALC->_is_zero($y->{value});
b68b7ab1 2063 $x->round(@r);
58cde26e
JH
2064 }
2065
2066sub blsft
2067 {
2068 # (BINT or num_str, BINT or num_str) return BINT
2069 # compute x << y, base n, y >= 0
f9a08e12
JH
2070
2071 # set up parameters
2072 my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
2073 # objectify is costly, so avoid it
2074 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
2075 {
2076 ($self,$x,$y,$n,@r) = objectify(2,@_);
2077 }
2078
58cde26e
JH
2079 return $x if $x->modify('blsft');
2080 return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
f9a08e12 2081 return $x->round(@r) if $y->is_zero();
58cde26e 2082
574bacfe
JH
2083 $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
2084
9b924220
RGS
2085 $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n);
2086 $x->round(@r);
58cde26e
JH
2087 }
2088
2089sub brsft
2090 {
2091 # (BINT or num_str, BINT or num_str) return BINT
2092 # compute x >> y, base n, y >= 0
f9a08e12
JH
2093
2094 # set up parameters
2095 my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
2096 # objectify is costly, so avoid it
2097 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
2098 {
2099 ($self,$x,$y,$n,@r) = objectify(2,@_);
2100 }
58cde26e
JH
2101
2102 return $x if $x->modify('brsft');
2103 return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
f9a08e12
JH
2104 return $x->round(@r) if $y->is_zero();
2105 return $x->bzero(@r) if $x->is_zero(); # 0 => 0
58cde26e
JH
2106
2107 $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
574bacfe 2108
b3abae2a
JH
2109 # this only works for negative numbers when shifting in base 2
2110 if (($x->{sign} eq '-') && ($n == 2))
2111 {
f9a08e12 2112 return $x->round(@r) if $x->is_one('-'); # -1 => -1
b3abae2a
JH
2113 if (!$y->is_one())
2114 {
2115 # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al
2116 # but perhaps there is a better emulation for two's complement shift...
2117 # if $y != 1, we must simulate it by doing:
2118 # convert to bin, flip all bits, shift, and be done
2119 $x->binc(); # -3 => -2
2120 my $bin = $x->as_bin();
2121 $bin =~ s/^-0b//; # strip '-0b' prefix
2122 $bin =~ tr/10/01/; # flip bits
2123 # now shift
a0ac753d 2124 if ($y >= CORE::length($bin))
b3abae2a
JH
2125 {
2126 $bin = '0'; # shifting to far right creates -1
2127 # 0, because later increment makes
2128 # that 1, attached '-' makes it '-1'
2129 # because -1 >> x == -1 !
2130 }
2131 else
2132 {
2133 $bin =~ s/.{$y}$//; # cut off at the right side
2134 $bin = '1' . $bin; # extend left side by one dummy '1'
2135 $bin =~ tr/10/01/; # flip bits back
2136 }
2137 my $res = $self->new('0b'.$bin); # add prefix and convert back
2138 $res->binc(); # remember to increment
2139 $x->{value} = $res->{value}; # take over value
f9a08e12 2140 return $x->round(@r); # we are done now, magic, isn't?
b3abae2a 2141 }
b282a552 2142 # x < 0, n == 2, y == 1
b3abae2a
JH
2143 $x->bdec(); # n == 2, but $y == 1: this fixes it
2144 }
2145
9b924220
RGS
2146 $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n);
2147 $x->round(@r);
58cde26e
JH
2148 }
2149
2150sub band
2151 {
2152 #(BINT or num_str, BINT or num_str) return BINT
2153 # compute x & y
f9a08e12
JH
2154
2155 # set up parameters
2156 my ($self,$x,$y,@r) = (ref($_[0]),@_);
2157 # objectify is costly, so avoid it
2158 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
2159 {
2160 ($self,$x,$y,@r) = objectify(2,@_);
2161 }
58cde26e
JH
2162
2163 return $x if $x->modify('band');
2164
f9a08e12 2165 $r[3] = $y; # no push!
b3abae2a 2166
58cde26e 2167 return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
0716bf9b 2168
b282a552
T
2169 my $sx = $x->{sign} eq '+' ? 1 : -1;
2170 my $sy = $y->{sign} eq '+' ? 1 : -1;
574bacfe 2171
9b924220 2172 if ($sx == 1 && $sy == 1)
0716bf9b 2173 {
574bacfe 2174 $x->{value} = $CALC->_and($x->{value},$y->{value});
f9a08e12 2175 return $x->round(@r);
0716bf9b 2176 }
091c87b1
T
2177
2178 if ($CAN{signed_and})
2179 {
2180 $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy);
2181 return $x->round(@r);
2182 }
b282a552
T
2183
2184 require $EMU_LIB;
2185 __emu_band($self,$x,$y,$sx,$sy,@r);
58cde26e
JH
2186 }
2187
2188sub bior
2189 {
2190 #(BINT or num_str, BINT or num_str) return BINT
2191 # compute x | y
f9a08e12
JH
2192
2193 # set up parameters
2194 my ($self,$x,$y,@r) = (ref($_[0]),@_);
2195 # objectify is costly, so avoid it
2196 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
2197 {
2198 ($self,$x,$y,@r) = objectify(2,@_);
2199 }
58cde26e
JH
2200
2201 return $x if $x->modify('bior');
f9a08e12 2202 $r[3] = $y; # no push!
58cde26e
JH
2203
2204 return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
574bacfe 2205
b282a552
T
2206 my $sx = $x->{sign} eq '+' ? 1 : -1;
2207 my $sy = $y->{sign} eq '+' ? 1 : -1;
574bacfe 2208
091c87b1
T
2209 # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior()
2210
574bacfe 2211 # don't use lib for negative values
9b924220 2212 if ($sx == 1 && $sy == 1)
0716bf9b 2213 {
574bacfe 2214 $x->{value} = $CALC->_or($x->{value},$y->{value});
f9a08e12 2215 return $x->round(@r);
0716bf9b
JH
2216 }
2217
b282a552 2218 # if lib can do negative values, let it handle this
091c87b1
T
2219 if ($CAN{signed_or})
2220 {
2221 $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy);
2222 return $x->round(@r);
2223 }
2224
b282a552
T
2225 require $EMU_LIB;
2226 __emu_bior($self,$x,$y,$sx,$sy,@r);
58cde26e
JH
2227 }
2228
2229sub bxor
2230 {
2231 #(BINT or num_str, BINT or num_str) return BINT
2232 # compute x ^ y
f9a08e12
JH
2233
2234 # set up parameters
2235 my ($self,$x,$y,@r) = (ref($_[0]),@_);
2236 # objectify is costly, so avoid it
2237 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
2238 {
2239 ($self,$x,$y,@r) = objectify(2,@_);
2240 }
58cde26e
JH
2241
2242 return $x if $x->modify('bxor');
f9a08e12 2243 $r[3] = $y; # no push!
58cde26e 2244
0716bf9b 2245 return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
0716bf9b 2246
b282a552
T
2247 my $sx = $x->{sign} eq '+' ? 1 : -1;
2248 my $sy = $y->{sign} eq '+' ? 1 : -1;
574bacfe
JH
2249
2250 # don't use lib for negative values
9b924220 2251 if ($sx == 1 && $sy == 1)
0716bf9b 2252 {
574bacfe 2253 $x->{value} = $CALC->_xor($x->{value},$y->{value});
f9a08e12 2254 return $x->round(@r);
0716bf9b 2255 }
091c87b1 2256
b282a552 2257 # if lib can do negative values, let it handle this
091c87b1
T
2258 if ($CAN{signed_xor})
2259 {
2260 $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy);
2261 return $x->round(@r);
2262 }
0716bf9b 2263
b282a552
T
2264 require $EMU_LIB;
2265 __emu_bxor($self,$x,$y,$sx,$sy,@r);
58cde26e
JH
2266 }
2267
2268sub length
2269 {
b282a552 2270 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
58cde26e 2271
0716bf9b 2272 my $e = $CALC->_len($x->{value});
091c87b1 2273 wantarray ? ($e,0) : $e;
58cde26e
JH
2274 }
2275
2276sub digit
2277 {
0716bf9b 2278 # return the nth decimal digit, negative values count backward, 0 is right
ef9466ea 2279 my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
58cde26e 2280
ef9466ea 2281 $n = $n->numify() if ref($n);
f9a08e12 2282 $CALC->_digit($x->{value},$n||0);
58cde26e
JH
2283 }
2284
2285sub _trailing_zeros
2286 {
b282a552 2287 # return the amount of trailing zeros in $x (as scalar)
58cde26e
JH
2288 my $x = shift;
2289 $x = $class->new($x) unless ref $x;
2290
9b924220 2291 return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc
0716bf9b 2292
9b924220 2293 $CALC->_zeros($x->{value}); # must handle odd values, 0 etc
58cde26e
JH
2294 }
2295
2296sub bsqrt
2297 {
990fb837 2298 # calculate square root of $x
b68b7ab1 2299 my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
58cde26e 2300
b3abae2a
JH
2301 return $x if $x->modify('bsqrt');
2302
990fb837
RGS
2303 return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN
2304 return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf
b3abae2a 2305
f9a08e12 2306 return $upgrade->bsqrt($x,@r) if defined $upgrade;
58cde26e 2307
9b924220
RGS
2308 $x->{value} = $CALC->_sqrt($x->{value});
2309 $x->round(@r);
58cde26e
JH
2310 }
2311
990fb837
RGS
2312sub broot
2313 {
2314 # calculate $y'th root of $x
c38b2de2 2315
990fb837
RGS
2316 # set up parameters
2317 my ($self,$x,$y,@r) = (ref($_[0]),@_);
c38b2de2
JH
2318
2319 $y = $self->new(2) unless defined $y;
2320
990fb837 2321 # objectify is costly, so avoid it
c38b2de2 2322 if ((!ref($x)) || (ref($x) ne ref($y)))
990fb837 2323 {
3a427a11 2324 ($self,$x,$y,@r) = objectify(2,$self || $class,@_);
990fb837
RGS
2325 }
2326
2327 return $x if $x->modify('broot');
2328
2329 # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
2330 return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
2331 $y->{sign} !~ /^\+$/;
2332
2333 return $x->round(@r)
2334 if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
2335
c38b2de2 2336 return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade;
990fb837 2337
9b924220
RGS
2338 $x->{value} = $CALC->_root($x->{value},$y->{value});
2339 $x->round(@r);
990fb837
RGS
2340 }
2341
58cde26e
JH
2342sub exponent
2343 {
2344 # return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
ee15d750 2345 my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
58cde26e 2346
ee15d750
JH
2347 if ($x->{sign} !~ /^[+-]$/)
2348 {
b282a552
T
2349 my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf
2350 return $self->new($s);
ee15d750 2351 }
b282a552
T
2352 return $self->bone() if $x->is_zero();
2353
7d193e39
T
2354 # 12300 => 2 trailing zeros => exponent is 2
2355 $self->new( $CALC->_zeros($x->{value}) );
58cde26e
JH
2356 }
2357
2358sub mantissa
2359 {
ee15d750
JH
2360 # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
2361 my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
58cde26e 2362
ee15d750
JH
2363 if ($x->{sign} !~ /^[+-]$/)
2364 {
b282a552
T
2365 # for NaN, +inf, -inf: keep the sign
2366 return $self->new($x->{sign});
ee15d750 2367 }
b282a552 2368 my $m = $x->copy(); delete $m->{_p}; delete $m->{_a};
7d193e39 2369
b282a552 2370 # that's a bit inefficient:
7d193e39 2371 my $zeros = $CALC->_zeros($m->{value});
56b9c951 2372 $m->brsft($zeros,10) if $zeros != 0;
56b9c951 2373 $m;
58cde26e
JH
2374 }
2375
2376sub parts
2377 {
ee15d750 2378 # return a copy of both the exponent and the mantissa
091c87b1 2379 my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
58cde26e 2380
091c87b1 2381 ($x->mantissa(),$x->exponent());
58cde26e
JH
2382 }
2383
2384##############################################################################
2385# rounding functions
2386
2387sub bfround
2388 {
2389 # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
ee15d750 2390 # $n == 0 || $n == 1 => round to integer
ef9466ea 2391 my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x;
b282a552 2392
b68b7ab1 2393 my ($scale,$mode) = $x->_scale_p(@_);
b282a552
T
2394
2395 return $x if !defined $scale || $x->modify('bfround'); # no-op
58cde26e
JH
2396
2397 # no-op for BigInts if $n <= 0
b282a552 2398 $x->bround( $x->length()-$scale, $mode) if $scale > 0;
58cde26e 2399
ef9466ea
T
2400 delete $x->{_a}; # delete to save memory
2401 $x->{_p} = $scale; # store new _p
ee15d750 2402 $x;
58cde26e
JH
2403 }
2404
2405sub _scan_for_nonzero
2406 {
ae161977
RGS
2407 # internal, used by bround() to scan for non-zeros after a '5'
2408 my ($x,$pad,$xs,$len) = @_;
58cde26e 2409
ae161977 2410 return 0 if $len == 1; # "5" is trailed by invisible zeros
58cde26e
JH
2411 my $follow = $pad - 1;
2412 return 0 if $follow > $len || $follow < 1;
0716bf9b 2413
ae161977
RGS
2414 # use the string form to check whether only '0's follow or not
2415 substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0;
58cde26e
JH
2416 }
2417
2418sub fround
2419 {
091c87b1
T
2420 # Exists to make life easier for switch between MBF and MBI (should we
2421 # autoload fxxx() like MBF does for bxxx()?)
b68b7ab1 2422 my $x = shift; $x = $class->new($x) unless ref $x;
091c87b1 2423 $x->bround(@_);
58cde26e
JH
2424 }
2425
2426sub bround
2427 {
2428 # accuracy: +$n preserve $n digits from left,
2429 # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF)
2430 # no-op for $n == 0
2431 # and overwrite the rest with 0's, return normalized number
2432 # do not return $x->bnorm(), but $x
61f5c3f5 2433
58cde26e 2434 my $x = shift; $x = $class->new($x) unless ref $x;
b68b7ab1
T
2435 my ($scale,$mode) = $x->_scale_a(@_);
2436 return $x if !defined $scale || $x->modify('bround'); # no-op
58cde26e 2437
61f5c3f5
T
2438 if ($x->is_zero() || $scale == 0)
2439 {
2440 $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
2441 return $x;
2442 }
2443 return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN
58cde26e
JH
2444
2445 # we have fewer digits than we want to scale to
2446 my $len = $x->length();
56d9de68
T
2447 # convert $scale to a scalar in case it is an object (put's a limit on the
2448 # number length, but this would already limited by memory constraints), makes
2449 # it faster
2450 $scale = $scale->numify() if ref ($scale);
2451
ee15d750
JH
2452 # scale < 0, but > -len (not >=!)
2453 if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
2454 {
61f5c3f5 2455 $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
ee15d750
JH
2456 return $x;
2457 }
58cde26e
JH
2458
2459 # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
2460 my ($pad,$digit_round,$digit_after);
2461 $pad = $len - $scale;
ee15d750
JH
2462 $pad = abs($scale-1) if $scale < 0;
2463
ae161977
RGS
2464 # do not use digit(), it is very costly for binary => decimal
2465 # getting the entire string is also costly, but we need to do it only once
0716bf9b
JH
2466 my $xs = $CALC->_str($x->{value});
2467 my $pl = -$pad-1;
56d9de68 2468
0716bf9b
JH
2469 # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
2470 # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
9b924220 2471 $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len;
0716bf9b 2472 $pl++; $pl ++ if $pad >= $len;
9b924220 2473 $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0;
ee15d750 2474
58cde26e
JH
2475 # in case of 01234 we round down, for 6789 up, and only in case 5 we look
2476 # closer at the remaining digits of the original $x, remember decision
2477 my $round_up = 1; # default round up
2478 $round_up -- if
2479 ($mode eq 'trunc') || # trunc by round down
2480 ($digit_after =~ /[01234]/) || # round down anyway,
2481 # 6789 => round up
2482 ($digit_after eq '5') && # not 5000...0000
ae161977 2483 ($x->_scan_for_nonzero($pad,$xs,$len) == 0) &&
58cde26e
JH
2484 (
2485 ($mode eq 'even') && ($digit_round =~ /[24680]/) ||
2486 ($mode eq 'odd') && ($digit_round =~ /[13579]/) ||
2487 ($mode eq '+inf') && ($x->{sign} eq '-') ||
2488 ($mode eq '-inf') && ($x->{sign} eq '+') ||
2489 ($mode eq 'zero') # round down if zero, sign adjusted below
2490 );
61f5c3f5
T
2491 my $put_back = 0; # not yet modified
2492
61f5c3f5
T
2493 if (($pad > 0) && ($pad <= $len))
2494 {
ae161977
RGS
2495 substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...'
2496 $put_back = 1; # need to put back
58cde26e 2497 }
61f5c3f5
T
2498 elsif ($pad > $len)
2499 {
2500 $x->bzero(); # round to '0'
2501 }
2502
58cde26e
JH
2503 if ($round_up) # what gave test above?
2504 {
ae161977 2505 $put_back = 1; # need to put back
9b924220 2506 $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
61f5c3f5
T
2507
2508 # we modify directly the string variant instead of creating a number and
f9a08e12 2509 # adding it, since that is faster (we already have the string)
61f5c3f5
T
2510 my $c = 0; $pad ++; # for $pad == $len case
2511 while ($pad <= $len)
2512 {
9b924220
RGS
2513 $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10';
2514 substr($xs,-$pad,1) = $c; $pad++;
61f5c3f5
T
2515 last if $c != 0; # no overflow => early out
2516 }
9b924220 2517 $xs = '1'.$xs if $c == 0;
61f5c3f5 2518
58cde26e 2519 }
ae161977 2520 $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed
ee15d750
JH
2521
2522 $x->{_a} = $scale if $scale >= 0;
2523 if ($scale < 0)
2524 {
2525 $x->{_a} = $len+$scale;
2526 $x->{_a} = 0 if $scale < -$len;
2527 }
58cde26e
JH
2528 $x;
2529 }
2530
2531sub bfloor
2532 {
091c87b1
T
2533 # return integer less or equal then number; no-op since it's already integer
2534 my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
58cde26e 2535
f9a08e12 2536 $x->round(@r);
58cde26e
JH
2537 }
2538
2539sub bceil
2540 {
091c87b1
T
2541 # return integer greater or equal then number; no-op since it's already int
2542 my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
58cde26e 2543
f9a08e12 2544 $x->round(@r);
58cde26e
JH
2545 }
2546
091c87b1
T
2547sub as_number
2548 {
2549 # An object might be asked to return itself as bigint on certain overloaded
7b29e1e6 2550 # operations. This does exactly this, so that sub classes can simple inherit
091c87b1
T
2551 # it or override with their own integer conversion routine.
2552 $_[0]->copy();
2553 }
58cde26e 2554
091c87b1 2555sub as_hex
58cde26e 2556 {
091c87b1
T
2557 # return as hex string, with prefixed 0x
2558 my $x = shift; $x = $class->new($x) if !ref($x);
2559
2560 return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
2561
b282a552 2562 my $s = '';
091c87b1 2563 $s = $x->{sign} if $x->{sign} eq '-';
9b924220 2564 $s . $CALC->_as_hex($x->{value});
58cde26e
JH
2565 }
2566
091c87b1 2567sub as_bin
58cde26e 2568 {
091c87b1
T
2569 # return as binary string, with prefixed 0b
2570 my $x = shift; $x = $class->new($x) if !ref($x);
2571
2572 return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
2573
b282a552 2574 my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
9b924220 2575 return $s . $CALC->_as_bin($x->{value});
58cde26e
JH
2576 }
2577
7b29e1e6
T
2578sub as_oct
2579 {
2580 # return as octal string, with prefixed 0
2581 my $x = shift; $x = $class->new($x) if !ref($x);
2582
2583 return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
2584
2585 my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
2586 return $s . $CALC->_as_oct($x->{value});
2587 }
2588
091c87b1
T
2589##############################################################################
2590# private stuff (internal use only)
2591
66a04958
PJA
2592sub objectify {
2593 # Convert strings and "foreign objects" to the objects we want.
2594
2595 # The first argument, $count, is the number of following arguments that
2596 # objectify() looks at and converts to objects. The first is a classname.
2597 # If the given count is 0, all arguments will be used.
2598
2599 # After the count is read, objectify obtains the name of the class to which
2600 # the following arguments are converted. If the second argument is a
2601 # reference, use the reference type as the class name. Otherwise, if it is
2602 # a string that looks like a class name, use that. Otherwise, use $class.
2603
2604 # Caller: Gives us:
2605 #
2606 # $x->badd(1); => ref x, scalar y
2607 # Class->badd(1,2); => classname x (scalar), scalar x, scalar y
2608 # Class->badd(Class->(1),2); => classname x (scalar), ref x, scalar y
2609 # Math::BigInt::badd(1,2); => scalar x, scalar y
2610
2611 # A shortcut for the common case $x->unary_op():
2612
2613 return (ref($_[1]), $_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
2614
2615 # Check the context.
2616
2617 unless (wantarray) {
2618 require Carp;
2619 Carp::croak ("${class}::objectify() needs list context");
58cde26e 2620 }
66a04958
PJA
2621
2622 # Get the number of arguments to objectify.
2623
2624 my $count = shift;
2625 $count ||= @_;
2626
2627 # Initialize the output array.
2628
2629 my @a = @_;
2630
2631 # If the first argument is a reference, use that reference type as our
2632 # class name. Otherwise, if the first argument looks like a class name,
2633 # then use that as our class name. Otherwise, use the default class name.
2634
58cde26e 2635 {
66a04958
PJA
2636 if (ref($a[0])) { # reference?
2637 unshift @a, ref($a[0]);
2638 last;
2639 }
2640 if ($a[0] =~ /^[A-Z].*::/) { # string with class name?
2641 last;
2642 }
2643 unshift @a, $class; # default class name
58cde26e 2644 }
8f675a64 2645
66a04958
PJA
2646 no strict 'refs';
2647
2648 # What we upgrade to, if anything.
2649
2650 my $up = ${"$a[0]::upgrade"};
2651
2652 # Disable downgrading, because Math::BigFloat -> foo('1.0','2.0') needs
2653 # floats.
2654
2655 my $down;
2656 if (defined ${"$a[0]::downgrade"}) {
2657 $down = ${"$a[0]::downgrade"};
2658 ${"$a[0]::downgrade"} = undef;
9393ace2
JH
2659 }
2660
66a04958
PJA
2661 for my $i (1 .. $count) {
2662 my $ref = ref $a[$i];
2663
2664 # If it is an object of the right class, all is fine.
2665
2666 if ($ref eq $a[0]) {
2667 next;
58cde26e 2668 }
66a04958
PJA
2669
2670 # Don't do anything with undefs.
2671
2672 unless (defined($a[$i])) {
2673 next;
58cde26e 2674 }
66a04958
PJA
2675
2676 # Perl scalars are fed to the appropriate constructor.
2677
2678 unless ($ref) {
2679 $a[$i] = $a[0] -> new($a[$i]);
2680 next;
2681 }
2682
2683 # Upgrading is OK, so skip further tests if the argument is upgraded.
2684
2685 if (defined $up && $ref eq $up) {
2686 next;
2687 }
2688
2689 # If we want a Math::BigInt, see if the object can become one.
2690 # Support the old misnomer as_number().
2691
2692 if ($a[0] eq 'Math::BigInt') {
2693 if ($a[$i] -> can('as_int')) {
2694 $a[$i] = $a[$i] -> as_int();
2695 next;
2696 }
2697 if ($a[$i] -> can('as_number')) {
2698 $a[$i] = $a[$i] -> as_number();
2699 next;
2700 }
2701 }
2702
2703 # If we want a Math::BigFloat, see if the object can become one.
2704
2705 if ($a[0] eq 'Math::BigFloat') {
2706 if ($a[$i] -> can('as_float')) {
2707 $a[$i] = $a[$i] -> as_float();
2708 next;
2709 }
2710 }
2711
2712 # Last resort.
2713
2714 $a[$i] = $a[0] -> new($a[$i]);
990fb837 2715 }
66a04958
PJA
2716
2717 # Reset the downgrading.
2718
2719 ${"$a[0]::downgrade"} = $down;
2720
2721 return @a;
2722}
58cde26e 2723
b68b7ab1
T
2724sub _register_callback
2725 {
2726 my ($class,$callback) = @_;
2727
2728 if (ref($callback) ne 'CODE')
2729 {
2730 require Carp;
2731 Carp::croak ("$callback is not a coderef");
2732 }
2733 $CALLBACKS{$class} = $callback;
2734 }
2735
58cde26e
JH
2736sub import
2737 {
2738 my $self = shift;
61f5c3f5 2739
091c87b1 2740 $IMPORT++; # remember we did import()
8f675a64 2741 my @a; my $l = scalar @_;
7b29e1e6 2742 my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die
8f675a64 2743 for ( my $i = 0; $i < $l ; $i++ )
58cde26e 2744 {
0716bf9b 2745 if ($_[$i] eq ':constant')
58cde26e 2746 {
0716bf9b 2747 # this causes overlord er load to step in
091c87b1
T
2748 overload::constant
2749 integer => sub { $self->new(shift) },
2750 binary => sub { $self->new(shift) };
0716bf9b 2751 }
b3abae2a
JH
2752 elsif ($_[$i] eq 'upgrade')
2753 {
2754 # this causes upgrading
2755 $upgrade = $_[$i+1]; # or undef to disable
8f675a64 2756 $i++;
b3abae2a 2757 }
7b29e1e6 2758 elsif ($_[$i] =~ /^(lib|try|only)\z/)
0716bf9b
JH
2759 {
2760 # this causes a different low lib to take care...
61f5c3f5 2761 $CALC = $_[$i+1] || '';
7b29e1e6
T
2762 # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback)
2763 $warn_or_die = 1 if $_[$i] eq 'lib';
2764 $warn_or_die = 2 if $_[$i] eq 'only';
8f675a64
JH
2765 $i++;
2766 }
2767 else
2768 {
2769 push @a, $_[$i];
58cde26e
JH
2770 }
2771 }
2772 # any non :constant stuff is handled by our parent, Exporter
b68b7ab1
T
2773 if (@a > 0)
2774 {
2775 require Exporter;
2776
2777 $self->SUPER::import(@a); # need it for subclasses
2778 $self->export_to_level(1,$self,@a); # need it for MBF
2779 }
58cde26e 2780
574bacfe
JH
2781 # try to load core math lib
2782 my @c = split /\s*,\s*/,$CALC;
b68b7ab1
T
2783 foreach (@c)
2784 {
2785 $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters
2786 }
a90064ab 2787 push @c, \'Calc' # if all fail, try these
7b29e1e6 2788 if $warn_or_die < 2; # but not for "only"
61f5c3f5 2789 $CALC = ''; # signal error
7b29e1e6 2790 foreach my $l (@c)
574bacfe 2791 {
7b29e1e6
T
2792 # fallback libraries are "marked" as \'string', extract string if nec.
2793 my $lib = $l; $lib = $$l if ref($l);
2794
07d34614 2795 next if ($lib || '') eq '';
574bacfe
JH
2796 $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
2797 $lib =~ s/\.pm$//;
61f5c3f5 2798 if ($] < 5.006)
574bacfe 2799 {
b68b7ab1
T
2800 # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is
2801 # used in the same script, or eval("") inside import().
07d34614
T
2802 my @parts = split /::/, $lib; # Math::BigInt => Math BigInt
2803 my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
2804 require File::Spec;
2805 $file = File::Spec->catfile (@parts, $file);
2806 eval { require "$file"; $lib->import( @c ); }
574bacfe
JH
2807 }
2808 else
2809 {
61f5c3f5 2810 eval "use $lib qw/@c/;";
574bacfe 2811 }
9b924220
RGS
2812 if ($@ eq '')
2813 {
2814 my $ok = 1;
2815 # loaded it ok, see if the api_version() is high enough
2816 if ($lib->can('api_version') && $lib->api_version() >= 1.0)
2817 {
2818 $ok = 0;
2819 # api_version matches, check if it really provides anything we need
2820 for my $method (qw/
2821 one two ten
2822 str num
2823 add mul div sub dec inc
2824 acmp len digit is_one is_zero is_even is_odd
2825 is_two is_ten
7b29e1e6
T
2826 zeros new copy check
2827 from_hex from_oct from_bin as_hex as_bin as_oct
9b924220
RGS
2828 rsft lsft xor and or
2829 mod sqrt root fac pow modinv modpow log_int gcd
2830 /)
2831 {
2832 if (!$lib->can("_$method"))
2833 {
2834 if (($WARN{$lib}||0) < 2)
2835 {
2836 require Carp;
2837 Carp::carp ("$lib is missing method '_$method'");
2838 $WARN{$lib} = 1; # still warn about the lib
2839 }
2840 $ok++; last;
2841 }
2842 }
2843 }
2844 if ($ok == 0)
2845 {
2846 $CALC = $lib;
7b29e1e6
T
2847 if ($warn_or_die > 0 && ref($l))
2848 {
2849 require Carp;
2850 my $msg = "Math::BigInt: couldn't load specified math lib(s), fallback to $lib";
2851 Carp::carp ($msg) if $warn_or_die == 1;
2852 Carp::croak ($msg) if $warn_or_die == 2;
2853 }
9b924220
RGS
2854 last; # found a usable one, break
2855 }
2856 else
2857 {
2858 if (($WARN{$lib}||0) < 2)
2859 {
a87115f0 2860 my $ver = eval "\$$lib\::VERSION" || 'unknown';
9b924220
RGS
2861 require Carp;
2862 Carp::carp ("Cannot load outdated $lib v$ver, please upgrade");
2863 $WARN{$lib} = 2; # never warn again
2864 }
2865 }
2866 }
574bacfe 2867 }
990fb837
RGS
2868 if ($CALC eq '')
2869 {
2870 require Carp;
7b29e1e6
T
2871 if ($warn_or_die == 2)
2872 {
2873 Carp::croak ("Couldn't load specified math lib(s) and fallback disallowed");
2874 }
2875 else
2876 {
2877 Carp::croak ("Couldn't load any math lib(s), not even fallback to Calc.pm");
2878 }
091c87b1 2879 }
091c87b1 2880
b68b7ab1
T
2881 # notify callbacks
2882 foreach my $class (keys %CALLBACKS)
2883 {
2884 &{$CALLBACKS{$class}}($CALC);
2885 }
2886
2887 # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib
2888 # functions
091c87b1
T
2889
2890 %CAN = ();
b68b7ab1 2891 for my $method (qw/ signed_and signed_or signed_xor /)
091c87b1
T
2892 {
2893 $CAN{$method} = $CALC->can("_$method") ? 1 : 0;
990fb837 2894 }
b68b7ab1
T
2895
2896 # import done
58cde26e
JH
2897 }
2898
de1ac46b
PJA
2899sub from_hex {
2900 # Create a bigint from a hexadecimal string.
7b29e1e6 2901
de1ac46b 2902 my ($self, $str) = @_;
7b29e1e6 2903
de1ac46b
PJA
2904 if ($str =~ s/
2905 ^
2906 ( [+-]? )
2907 (0?x)?
2908 (
2909 [0-9a-fA-F]*
2910 ( _ [0-9a-fA-F]+ )*
2911 )
2912 $
2913 //x)
2914 {
2915 # Get a "clean" version of the string, i.e., non-emtpy and with no
2916 # underscores or invalid characters.
7b29e1e6 2917
de1ac46b
PJA
2918 my $sign = $1;
2919 my $chrs = $3;
2920 $chrs =~ tr/_//d;
2921 $chrs = '0' unless CORE::length $chrs;
7b29e1e6 2922
de1ac46b 2923 # Initialize output.
7b29e1e6 2924
de1ac46b 2925 my $x = Math::BigInt->bzero();
7b29e1e6 2926
de1ac46b 2927 # The library method requires a prefix.
7b29e1e6 2928
de1ac46b 2929 $x->{value} = $CALC->_from_hex('0x' . $chrs);
7b29e1e6 2930
de1ac46b 2931 # Place the sign.
7b29e1e6 2932
de1ac46b
PJA
2933 if ($sign eq '-' && ! $CALC->_is_zero($x->{value})) {
2934 $x->{sign} = '-';
2935 }
7b29e1e6 2936
de1ac46b
PJA
2937 return $x;
2938 }
7b29e1e6 2939
de1ac46b
PJA
2940 # CORE::hex() parses as much as it can, and ignores any trailing garbage.
2941 # For backwards compatibility, we return NaN.
7b29e1e6 2942
de1ac46b
PJA
2943 return $self->bnan();
2944}
58cde26e 2945
de1ac46b
PJA
2946sub from_oct {
2947 # Create a bigint from an octal string.
58cde26e 2948
de1ac46b 2949 my ($self, $str) = @_;
58cde26e 2950
de1ac46b
PJA
2951 if ($str =~ s/
2952 ^
2953 ( [+-]? )
2954 (
2955 [0-7]*
2956 ( _ [0-7]+ )*
2957 )
2958 $
2959 //x)
2960 {
2961 # Get a "clean" version of the string, i.e., non-emtpy and with no
2962 # underscores or invalid characters.
58cde26e 2963
de1ac46b
PJA
2964 my $sign = $1;
2965 my $chrs = $2;
2966 $chrs =~ tr/_//d;
2967 $chrs = '0' unless CORE::length $chrs;
58cde26e 2968
de1ac46b 2969 # Initialize output.
7b29e1e6 2970
de1ac46b 2971 my $x = Math::BigInt->bzero();
58cde26e 2972
de1ac46b 2973 # The library method requires a prefix.
9b924220 2974
de1ac46b
PJA
2975 $x->{value} = $CALC->_from_oct('0' . $chrs);
2976
2977 # Place the sign.
2978
2979 if ($sign eq '-' && ! $CALC->_is_zero($x->{value})) {
2980 $x->{sign} = '-';
2981 }
2982
2983 return $x;
2984 }
2985
2986 # CORE::oct() parses as much as it can, and ignores any trailing garbage.
2987 # For backwards compatibility, we return NaN.
2988
2989 return $self->bnan();
2990}
2991
2992sub from_bin {
2993 # Create a bigint from a binary string.
2994
2995 my ($self, $str) = @_;
2996
2997 if ($str =~ s/
2998 ^
2999 ( [+-]? )
3000 (0?b)?
3001 (
3002 [01]*
3003 ( _ [01]+ )*
3004 )
3005 $
3006 //x)
3007 {
3008 # Get a "clean" version of the string, i.e., non-emtpy and with no
3009 # underscores or invalid characters.
3010
3011 my $sign = $1;
3012 my $chrs = $3;
3013 $chrs =~ tr/_//d;
3014 $chrs = '0' unless CORE::length $chrs;
3015
3016 # Initialize output.
3017
3018 my $x = Math::BigInt->bzero();
3019
3020 # The library method requires a prefix.
3021
3022 $x->{value} = $CALC->_from_bin('0b' . $chrs);
3023
3024 # Place the sign.
3025
3026 if ($sign eq '-' && ! $CALC->_is_zero($x->{value})) {
3027 $x->{sign} = '-';
3028 }
3029
3030 return $x;
3031 }
3032
3033 # For consistency with from_hex() and from_oct(), we return NaN when the
3034 # input is invalid.
3035
3036 return $self->bnan();
3037}
58cde26e
JH
3038
3039sub _split
3040 {
b68b7ab1
T
3041 # input: num_str; output: undef for invalid or
3042 # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,\$exp_sign,\$exp_value)
3043 # Internal, take apart a string and return the pieces.
3044 # Strip leading/trailing whitespace, leading zeros, underscore and reject
3045 # invalid input.
58cde26e
JH
3046 my $x = shift;
3047
c4a6f826 3048 # strip white space at front, also extraneous leading zeros
7b29e1e6
T
3049 $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2'
3050 $x =~ s/^\s+//; # but this will
3051 $x =~ s/\s+$//g; # strip white space at end
58cde26e 3052
574bacfe 3053 # shortcut, if nothing to split, return early
7b29e1e6 3054 if ($x =~ /^[+-]?[0-9]+\z/)
574bacfe 3055 {
9b924220
RGS
3056 $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
3057 return (\$sign, \$x, \'', \'', \0);
574bacfe 3058 }
58cde26e 3059
574bacfe 3060 # invalid starting char?
9b924220 3061 return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
58cde26e 3062
de1ac46b
PJA
3063 return Math::BigInt->from_hex($x) if $x =~ /^[+-]?0x/; # hex string
3064 return Math::BigInt->from_bin($x) if $x =~ /^[+-]?0b/; # binary string
3065
394e6ffb 3066 # strip underscores between digits
7b29e1e6
T
3067 $x =~ s/([0-9])_([0-9])/$1$2/g;
3068 $x =~ s/([0-9])_([0-9])/$1$2/g; # do twice for 1_2_3
574bacfe 3069
58cde26e
JH
3070 # some possible inputs:
3071 # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
aef458a0 3072 # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999
58cde26e 3073
9b924220 3074 my ($m,$e,$last) = split /[Ee]/,$x;
56d9de68 3075 return if defined $last; # last defined => 1e2E3 or others
58cde26e 3076 $e = '0' if !defined $e || $e eq "";
56d9de68 3077
58cde26e
JH
3078 # sign,value for exponent,mantint,mantfrac
3079 my ($es,$ev,$mis,$miv,$mfv);
3080 # valid exponent?
7b29e1e6 3081 if ($e =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
58cde26e
JH
3082 {
3083 $es = $1; $ev = $2;
58cde26e
JH
3084 # valid mantissa?
3085 return if $m eq '.' || $m eq '';
56d9de68 3086 my ($mi,$mf,$lastf) = split /\./,$m;
8df1e0a2 3087 return if defined $lastf; # lastf defined => 1.2.3 or others
58cde26e
JH
3088 $mi = '0' if !defined $mi;
3089 $mi .= '0' if $mi =~ /^[\-\+]?$/;
3090 $mf = '0' if !defined $mf || $mf eq '';
7b29e1e6 3091 if ($mi =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
58cde26e
JH
3092 {
3093 $mis = $1||'+'; $miv = $2;
7b29e1e6 3094 return unless ($mf =~ /^([0-9]*?)0*$/); # strip trailing zeros
58cde26e 3095 $mfv = $1;
aef458a0
JH
3096 # handle the 0e999 case here
3097 $ev = 0 if $miv eq '0' && $mfv eq '';
58cde26e
JH
3098 return (\$mis,\$miv,\$mfv,\$es,\$ev);
3099 }
3100 }
3101 return; # NaN, not a number
3102 }
3103
58cde26e 3104##############################################################################
0716bf9b 3105# internal calculation routines (others are in Math::BigInt::Calc etc)
58cde26e 3106
dccbb853 3107sub __lcm
58cde26e
JH
3108 {
3109 # (BINT or num_str, BINT or num_str) return BINT
3110 # does modify first argument
3111 # LCM
3112
b68b7ab1 3113 my ($x,$ty) = @_;
58cde26e 3114 return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan);
b68b7ab1
T
3115 my $method = ref($x) . '::bgcd';
3116 no strict 'refs';
3117 $x * $ty / &$method($x,$ty);
58cde26e
JH
3118 }
3119
58cde26e 3120###############################################################################
fdb4b05f
T
3121# trigonometric functions
3122
3123sub bpi
3124 {
3125 # Calculate PI to N digits. Unless upgrading is in effect, returns the
3126 # result truncated to an integer, that is, always returns '3'.
3127 my ($self,$n) = @_;
3128 if (@_ == 1)
3129 {
3130 # called like Math::BigInt::bpi(10);
3131 $n = $self; $self = $class;
3132 }
3133 $self = ref($self) if ref($self);
3134
3135 return $upgrade->new($n) if defined $upgrade;
3136
3137 # hard-wired to "3"
3138 $self->new(3);
3139 }
3140
60a1aa19
T
3141sub bcos
3142 {
3143 # Calculate cosinus(x) to N digits. Unless upgrading is in effect, returns the
3144 # result truncated to an integer.
3145 my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
3146
3147 return $x if $x->modify('bcos');
3148
3149 return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
3150
3151 return $upgrade->new($x)->bcos(@r) if defined $upgrade;
3152
20e2035c 3153 require Math::BigFloat;
60a1aa19
T
3154 # calculate the result and truncate it to integer
3155 my $t = Math::BigFloat->new($x)->bcos(@r)->as_int();
3156
3157 $x->bone() if $t->is_one();
3158 $x->bzero() if $t->is_zero();
3159 $x->round(@r);
3160 }
3161
3162sub bsin
3163 {
3164 # Calculate sinus(x) to N digits. Unless upgrading is in effect, returns the
3165 # result truncated to an integer.
3166 my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
3167
3168 return $x if $x->modify('bsin');
3169
3170 return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
3171
3172 return $upgrade->new($x)->bsin(@r) if defined $upgrade;
3173
20e2035c 3174 require Math::BigFloat;
60a1aa19
T
3175 # calculate the result and truncate it to integer
3176 my $t = Math::BigFloat->new($x)->bsin(@r)->as_int();
3177
3178 $x->bone() if $t->is_one();
3179 $x->bzero() if $t->is_zero();
3180 $x->round(@r);
3181 }
3182
20e2035c
T
3183sub batan2
3184 {
30afc38d 3185 # calculate arcus tangens of ($y/$x)
20e2035c
T
3186
3187 # set up parameters
30afc38d 3188 my ($self,$y,$x,@r) = (ref($_[0]),@_);
20e2035c
T
3189 # objectify is costly, so avoid it
3190 if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
3191 {
30afc38d 3192 ($self,$y,$x,@r) = objectify(2,@_);
20e2035c
T
3193 }
3194
30afc38d 3195 return $y if $y->modify('batan2');
20e2035c 3196
30afc38d
T
3197 return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan);
3198
0dceeee6
RGS
3199 # Y X
3200 # != 0 -inf result is +- pi
3201 if ($x->is_inf() || $y->is_inf())
3202 {
3203 # upgrade to BigFloat etc.
3204 return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
3205 if ($y->is_inf())
3206 {
3207 if ($x->{sign} eq '-inf')
3208 {
3209 # calculate 3 pi/4 => 2.3.. => 2
3210 $y->bone( substr($y->{sign},0,1) );
3211 $y->bmul($self->new(2));
3212 }
3213 elsif ($x->{sign} eq '+inf')
3214 {
3215 # calculate pi/4 => 0.7 => 0
3216 $y->bzero();
3217 }
3218 else
3219 {
3220 # calculate pi/2 => 1.5 => 1
3221 $y->bone( substr($y->{sign},0,1) );
3222 }
3223 }
3224 else
3225 {
3226 if ($x->{sign} eq '+inf')
3227 {
3228 # calculate pi/4 => 0.7 => 0
3229 $y->bzero();
3230 }
3231 else
3232 {
3233 # PI => 3.1415.. => 3
3234 $y->bone( substr($y->{sign},0,1) );
3235 $y->bmul($self->new(3));
3236 }
3237 }
3238 return $y;
3239 }
20e2035c 3240
30afc38d 3241 return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
20e2035c
T
3242
3243 require Math::BigFloat;
30afc38d 3244 my $r = Math::BigFloat->new($y)->batan2(Math::BigFloat->new($x),@r)->as_int();
20e2035c
T
3245
3246 $x->{value} = $r->{value};
3247 $x->{sign} = $r->{sign};
3248
3249 $x;
3250 }
3251
60a1aa19
T
3252sub batan
3253 {
3254 # Calculate arcus tangens of x to N digits. Unless upgrading is in effect, returns the
3255 # result truncated to an integer.
3256 my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
3257
3258 return $x if $x->modify('batan');
3259
3260 return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
3261
3262 return $upgrade->new($x)->batan(@r) if defined $upgrade;
3263
3264 # calculate the result and truncate it to integer
3265 my $t = Math::BigFloat->new($x)->batan(@r);
3266
3267 $x->{value} = $CALC->_new( $x->as_int()->bstr() );
3268 $x->round(@r);
3269 }
3270
fdb4b05f 3271###############################################################################
b68b7ab1 3272# this method returns 0 if the object can be modified, or 1 if not.
b282a552 3273# We use a fast constant sub() here, to avoid costly calls. Subclasses
58cde26e
JH
3274# may override it with special code (f.i. Math::BigInt::Constant does so)
3275
0716bf9b 3276sub modify () { 0; }
e16b8f49 3277
a0d0e21e 32781;
a5f75d66
AD
3279__END__
3280
233f7bc0
T
3281=pod
3282
a5f75d66
AD
3283=head1 NAME
3284
233f7bc0 3285Math::BigInt - Arbitrary size integer/float math package
a5f75d66
AD
3286
3287=head1 SYNOPSIS
3288
3289 use Math::BigInt;
58cde26e 3290
0dceeee6
RGS
3291 # or make it faster with huge numbers: install (optional)
3292 # Math::BigInt::GMP and always use (it will fall back to
3293 # pure Perl if the GMP library is not installed):
3294 # (See also the L<MATH LIBRARY> section!)
990fb837 3295
7b29e1e6 3296 # will warn if Math::BigInt::GMP cannot be found
990fb837
RGS
3297 use Math::BigInt lib => 'GMP';
3298
9681bfa6 3299 # to suppress the warning use this:
7b29e1e6
T
3300 # use Math::BigInt try => 'GMP';
3301
0dceeee6
RGS
3302 # dies if GMP cannot be loaded:
3303 # use Math::BigInt only => 'GMP';
3304
9b924220
RGS
3305 my $str = '1234567890';
3306 my @values = (64,74,18);
3307 my $n = 1; my $sign = '-';
3308
58cde26e 3309 # Number creation
fdb4b05f
T
3310 my $x = Math::BigInt->new($str); # defaults to 0
3311 my $y = $x->copy(); # make a true copy
3312 my $nan = Math::BigInt->bnan(); # create a NotANumber
3313 my $zero = Math::BigInt->bzero(); # create a +0
3314 my $inf = Math::BigInt->binf(); # create a +inf
3315 my $inf = Math::BigInt->binf('-'); # create a -inf
3316 my $one = Math::BigInt->bone(); # create a +1
3317 my $mone = Math::BigInt->bone('-'); # create a -1
3318
3319 my $pi = Math::BigInt->bpi(); # returns '3'
3320 # see Math::BigFloat::bpi()
58cde26e 3321
7b29e1e6
T
3322 $h = Math::BigInt->new('0x123'); # from hexadecimal
3323 $b = Math::BigInt->new('0b101'); # from binary
3324 $o = Math::BigInt->from_oct('0101'); # from octal
3325
56d9de68
T
3326 # Testing (don't modify their arguments)
3327 # (return true if the condition is met, otherwise false)
3328
3329 $x->is_zero(); # if $x is +0
3330 $x->is_nan(); # if $x is NaN
3331 $x->is_one(); # if $x is +1
3332 $x->is_one('-'); # if $x is -1
3333 $x->is_odd(); # if $x is odd
3334 $x->is_even(); # if $x is even
4af46cb8
FR
3335 $x->is_pos(); # if $x > 0
3336 $x->is_neg(); # if $x < 0
9b924220 3337 $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+')
56d9de68
T
3338 $x->is_int(); # if $x is an integer (not a float)
3339
3c4b39be 3340 # comparing and digit/sign extraction
56d9de68
T
3341 $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
3342 $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
3343 $x->sign(); # return the sign, either +,- or NaN
3344 $x->digit($n); # return the nth digit, counting from right
3345 $x->digit(-$n); # return the nth digit, counting from left
58cde26e 3346
80df1b84
FC
3347 # The following all modify their first argument. If you want to pre-
3348 # serve $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for
3349 # why this is necessary when mixing $a = $b assignments with non-over-
3350 # loaded math.
58cde26e 3351
56d9de68
T
3352 $x->bzero(); # set $x to 0
3353 $x->bnan(); # set $x to NaN
3354 $x->bone(); # set $x to +1
3355 $x->bone('-'); # set $x to -1
3356 $x->binf(); # set $x to inf
3357 $x->binf('-'); # set $x to -inf
3358
3359 $x->bneg(); # negation
3360 $x->babs(); # absolute value
7833bfdd 3361 $x->bsgn(); # sign function (-1, 0, 1, or NaN)
56d9de68
T
3362 $x->bnorm(); # normalize (no-op in BigInt)
3363 $x->bnot(); # two's complement (bit wise not)
3364 $x->binc(); # increment $x by 1
3365 $x->bdec(); # decrement $x by 1
53ea20b1 3366
56d9de68
T
3367 $x->badd($y); # addition (add $y to $x)
3368 $x->bsub($y); # subtraction (subtract $y from $x)
3369 $x->bmul($y); # multiplication (multiply $x by $y)
3370 $x->bdiv($y); # divide, set $x to quotient
3371 # return (quo,rem) or quo if scalar
3372
80365507
T
3373 $x->bmuladd($y,$z); # $x = $x * $y + $z
3374
56d9de68 3375 $x->bmod($y); # modulus (x % y)
116f6d6b
PJA
3376 $x->bmodpow($y,$mod); # modular exponentiation (($x ** $y) % $mod)
3377 $x->bmodinv($mod); # modular multiplicative inverse
56d9de68 3378 $x->bpow($y); # power of arguments (x ** y)
7d193e39
T
3379 $x->blsft($y); # left shift in base 2
3380 $x->brsft($y); # right shift in base 2
80df1b84
FC
3381 # returns (quo,rem) or quo if in sca-
3382 # lar context
7b29e1e6
T
3383 $x->blsft($y,$n); # left shift by $y places in base $n
3384 $x->brsft($y,$n); # right shift by $y places in base $n
80df1b84
FC
3385 # returns (quo,rem) or quo if in sca-
3386 # lar context
53ea20b1 3387
56d9de68
T
3388 $x->band($y); # bitwise and
3389 $x->bior($y); # bitwise inclusive or
3390 $x->bxor($y); # bitwise exclusive or
3391 $x->bnot(); # bitwise not (two's complement)
3392
3393 $x->bsqrt(); # calculate square-root
990fb837 3394 $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root)
56d9de68 3395 $x->bfac(); # factorial of $x (1*2*3*4*..$x)
58cde26e 3396
50109ad0
RGS
3397 $x->bnok($y); # x over y (binomial coefficient n over k)
3398
7d193e39
T
3399 $x->blog(); # logarithm of $x to base e (Euler's number)
3400 $x->blog($base); # logarithm of $x to base $base (f.i. 2)
3401 $x->bexp(); # calculate e ** $x where e is Euler's number
53ea20b1 3402
80df1b84
FC
3403 $x->round($A,$P,$mode); # round to accuracy or precision using
3404 # mode $mode
9b924220 3405 $x->bround($n); # accuracy: preserve $n digits
d5351619
T
3406 $x->bfround($n); # $n > 0: round $nth digits,
3407 # $n < 0: round to the $nth digit after the
3408 # dot, no-op for BigInts
58cde26e 3409
990fb837 3410 # The following do not modify their arguments in BigInt (are no-ops),
56d9de68 3411 # but do so in BigFloat:
58cde26e 3412
56d9de68
T
3413 $x->bfloor(); # return integer less or equal than $x
3414 $x->bceil(); # return integer greater or equal than $x
fdd59300 3415
58cde26e
JH
3416 # The following do not modify their arguments:
3417
9b924220
RGS
3418 # greatest common divisor (no OO style)
3419 my $gcd = Math::BigInt::bgcd(@values);
fdd59300
FR
3420 # lowest common multiple (no OO style)
3421 my $lcm = Math::BigInt::blcm(@values);
3422
56d9de68 3423 $x->length(); # return number of digits in number
80df1b84
FC
3424 ($xl,$f) = $x->length(); # length of number and length of fraction
3425 # part, latter is always 0 digits long
3426 # for BigInts
56d9de68 3427
80df1b84
FC
3428 $x->exponent(); # return exponent as BigInt
3429 $x->mantissa(); # return (signed) mantissa as BigInt
3430 $x->parts(); # return (mantissa,exponent) as BigInt
3431 $x->copy(); # make a true copy of $x (unlike $y = $x;)
3432 $x->as_int(); # return as BigInt (in BigInt: same as copy())
3433 $x->numify(); # return as scalar (might overflow!)
53ea20b1 3434
9681bfa6 3435 # conversion to string (do not modify their argument)
80df1b84
FC
3436 $x->bstr(); # normalized string (e.g. '3')
3437 $x->bsstr(); # norm. string in scientific notation (e.g. '3E0')
3438 $x->as_hex(); # as signed hexadecimal string with prefixed 0x
3439 $x->as_bin(); # as signed binary string with prefixed 0b
3440 $x->as_oct(); # as signed octal string with prefixed 0
b282a552 3441
bd05a461 3442
f9a08e12 3443 # precision and accuracy (see section about rounding for more)
80df1b84
FC
3444 $x->precision(); # return P of $x (or global, if P of $x undef)
3445 $x->precision($n); # set P of $x to $n
3446 $x->accuracy(); # return A of $x (or global, if A of $x undef)
3447 $x->accuracy($n); # set A $x to $n
f9a08e12 3448
56d9de68 3449 # Global methods
80df1b84
FC
3450 Math::BigInt->precision(); # get/set global P for all BigInt objects
3451 Math::BigInt->accuracy(); # get/set global A for all BigInt objects
3452 Math::BigInt->round_mode(); # get/set global round mode, one of
3453 # 'even', 'odd', '+inf', '-inf', 'zero',
3454 # 'trunc' or 'common'
3455 Math::BigInt->config(); # return hash containing configuration
f9a08e12 3456
a5f75d66
AD