| 1 | package Math::BigInt; |
| 2 | |
| 3 | # |
| 4 | # "Mike had an infinite amount to do and a negative amount of time in which |
| 5 | # to do it." - Before and After |
| 6 | # |
| 7 | |
| 8 | # The following hash values are used: |
| 9 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) |
| 10 | # sign : +,-,NaN,+inf,-inf |
| 11 | # _a : accuracy |
| 12 | # _p : precision |
| 13 | # _f : flags, used by MBF to flag parts of a float as untouchable |
| 14 | |
| 15 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since |
| 16 | # underlying lib might change the reference! |
| 17 | |
| 18 | my $class = "Math::BigInt"; |
| 19 | require 5.005; |
| 20 | |
| 21 | # This is a patched v1.60, containing a fix for the "1234567890\n" bug |
| 22 | $VERSION = '1.60'; |
| 23 | use Exporter; |
| 24 | @ISA = qw( Exporter ); |
| 25 | @EXPORT_OK = qw( objectify _swap bgcd blcm); |
| 26 | use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/; |
| 27 | use vars qw/$upgrade $downgrade/; |
| 28 | use strict; |
| 29 | |
| 30 | # Inside overload, the first arg is always an object. If the original code had |
| 31 | # it reversed (like $x = 2 * $y), then the third paramater indicates this |
| 32 | # swapping. To make it work, we use a helper routine which not only reswaps the |
| 33 | # params, but also makes a new object in this case. See _swap() for details, |
| 34 | # especially the cases of operators with different classes. |
| 35 | |
| 36 | # For overloaded ops with only one argument we simple use $_[0]->copy() to |
| 37 | # preserve the argument. |
| 38 | |
| 39 | # Thus inheritance of overload operators becomes possible and transparent for |
| 40 | # our subclasses without the need to repeat the entire overload section there. |
| 41 | |
| 42 | use overload |
| 43 | '=' => sub { $_[0]->copy(); }, |
| 44 | |
| 45 | # '+' and '-' do not use _swap, since it is a triffle slower. If you want to |
| 46 | # override _swap (if ever), then override overload of '+' and '-', too! |
| 47 | # for sub it is a bit tricky to keep b: b-a => -a+b |
| 48 | '-' => sub { my $c = $_[0]->copy; $_[2] ? |
| 49 | $c->bneg()->badd($_[1]) : |
| 50 | $c->bsub( $_[1]) }, |
| 51 | '+' => sub { $_[0]->copy()->badd($_[1]); }, |
| 52 | |
| 53 | # some shortcuts for speed (assumes that reversed order of arguments is routed |
| 54 | # to normal '+' and we thus can always modify first arg. If this is changed, |
| 55 | # this breaks and must be adjusted.) |
| 56 | '+=' => sub { $_[0]->badd($_[1]); }, |
| 57 | '-=' => sub { $_[0]->bsub($_[1]); }, |
| 58 | '*=' => sub { $_[0]->bmul($_[1]); }, |
| 59 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, |
| 60 | '%=' => sub { $_[0]->bmod($_[1]); }, |
| 61 | '^=' => sub { $_[0]->bxor($_[1]); }, |
| 62 | '&=' => sub { $_[0]->band($_[1]); }, |
| 63 | '|=' => sub { $_[0]->bior($_[1]); }, |
| 64 | '**=' => sub { $_[0]->bpow($_[1]); }, |
| 65 | |
| 66 | # not supported by Perl yet |
| 67 | '..' => \&_pointpoint, |
| 68 | |
| 69 | '<=>' => sub { $_[2] ? |
| 70 | ref($_[0])->bcmp($_[1],$_[0]) : |
| 71 | $_[0]->bcmp($_[1])}, |
| 72 | 'cmp' => sub { |
| 73 | $_[2] ? |
| 74 | "$_[1]" cmp $_[0]->bstr() : |
| 75 | $_[0]->bstr() cmp "$_[1]" }, |
| 76 | |
| 77 | 'log' => sub { $_[0]->copy()->blog(); }, |
| 78 | 'int' => sub { $_[0]->copy(); }, |
| 79 | 'neg' => sub { $_[0]->copy()->bneg(); }, |
| 80 | 'abs' => sub { $_[0]->copy()->babs(); }, |
| 81 | 'sqrt' => sub { $_[0]->copy()->bsqrt(); }, |
| 82 | '~' => sub { $_[0]->copy()->bnot(); }, |
| 83 | |
| 84 | '*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); }, |
| 85 | '/' => sub { my @a = ref($_[0])->_swap(@_);scalar $a[0]->bdiv($a[1]);}, |
| 86 | '%' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmod($a[1]); }, |
| 87 | '**' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bpow($a[1]); }, |
| 88 | '<<' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->blsft($a[1]); }, |
| 89 | '>>' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->brsft($a[1]); }, |
| 90 | |
| 91 | '&' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->band($a[1]); }, |
| 92 | '|' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bior($a[1]); }, |
| 93 | '^' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bxor($a[1]); }, |
| 94 | |
| 95 | # can modify arg of ++ and --, so avoid a new-copy for speed, but don't |
| 96 | # use $_[0]->__one(), it modifies $_[0] to be 1! |
| 97 | '++' => sub { $_[0]->binc() }, |
| 98 | '--' => sub { $_[0]->bdec() }, |
| 99 | |
| 100 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers |
| 101 | 'bool' => sub { |
| 102 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ |
| 103 | # v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-( |
| 104 | my $t = !$_[0]->is_zero(); |
| 105 | undef $t if $t == 0; |
| 106 | $t; |
| 107 | }, |
| 108 | |
| 109 | # the original qw() does not work with the TIESCALAR below, why? |
| 110 | # Order of arguments unsignificant |
| 111 | '""' => sub { $_[0]->bstr(); }, |
| 112 | '0+' => sub { $_[0]->numify(); } |
| 113 | ; |
| 114 | |
| 115 | ############################################################################## |
| 116 | # global constants, flags and accessory |
| 117 | |
| 118 | use constant MB_NEVER_ROUND => 0x0001; |
| 119 | |
| 120 | my $NaNOK=1; # are NaNs ok? |
| 121 | my $nan = 'NaN'; # constants for easier life |
| 122 | |
| 123 | my $CALC = 'Math::BigInt::Calc'; # module to do low level math |
| 124 | my $IMPORT = 0; # did import() yet? |
| 125 | |
| 126 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
| 127 | $accuracy = undef; |
| 128 | $precision = undef; |
| 129 | $div_scale = 40; |
| 130 | |
| 131 | $upgrade = undef; # default is no upgrade |
| 132 | $downgrade = undef; # default is no downgrade |
| 133 | |
| 134 | ############################################################################## |
| 135 | # the old code had $rnd_mode, so we need to support it, too |
| 136 | |
| 137 | $rnd_mode = 'even'; |
| 138 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
| 139 | sub FETCH { return $round_mode; } |
| 140 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
| 141 | |
| 142 | BEGIN { tie $rnd_mode, 'Math::BigInt'; } |
| 143 | |
| 144 | ############################################################################## |
| 145 | |
| 146 | sub round_mode |
| 147 | { |
| 148 | no strict 'refs'; |
| 149 | # make Class->round_mode() work |
| 150 | my $self = shift; |
| 151 | my $class = ref($self) || $self || __PACKAGE__; |
| 152 | if (defined $_[0]) |
| 153 | { |
| 154 | my $m = shift; |
| 155 | die "Unknown round mode $m" |
| 156 | if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
| 157 | return ${"${class}::round_mode"} = $m; |
| 158 | } |
| 159 | return ${"${class}::round_mode"}; |
| 160 | } |
| 161 | |
| 162 | sub upgrade |
| 163 | { |
| 164 | no strict 'refs'; |
| 165 | # make Class->upgrade() work |
| 166 | my $self = shift; |
| 167 | my $class = ref($self) || $self || __PACKAGE__; |
| 168 | # need to set new value? |
| 169 | if (@_ > 0) |
| 170 | { |
| 171 | my $u = shift; |
| 172 | return ${"${class}::upgrade"} = $u; |
| 173 | } |
| 174 | return ${"${class}::upgrade"}; |
| 175 | } |
| 176 | |
| 177 | sub downgrade |
| 178 | { |
| 179 | no strict 'refs'; |
| 180 | # make Class->downgrade() work |
| 181 | my $self = shift; |
| 182 | my $class = ref($self) || $self || __PACKAGE__; |
| 183 | # need to set new value? |
| 184 | if (@_ > 0) |
| 185 | { |
| 186 | my $u = shift; |
| 187 | return ${"${class}::downgrade"} = $u; |
| 188 | } |
| 189 | return ${"${class}::downgrade"}; |
| 190 | } |
| 191 | |
| 192 | sub div_scale |
| 193 | { |
| 194 | no strict 'refs'; |
| 195 | # make Class->round_mode() work |
| 196 | my $self = shift; |
| 197 | my $class = ref($self) || $self || __PACKAGE__; |
| 198 | if (defined $_[0]) |
| 199 | { |
| 200 | die ('div_scale must be greater than zero') if $_[0] < 0; |
| 201 | ${"${class}::div_scale"} = shift; |
| 202 | } |
| 203 | return ${"${class}::div_scale"}; |
| 204 | } |
| 205 | |
| 206 | sub accuracy |
| 207 | { |
| 208 | # $x->accuracy($a); ref($x) $a |
| 209 | # $x->accuracy(); ref($x) |
| 210 | # Class->accuracy(); class |
| 211 | # Class->accuracy($a); class $a |
| 212 | |
| 213 | my $x = shift; |
| 214 | my $class = ref($x) || $x || __PACKAGE__; |
| 215 | |
| 216 | no strict 'refs'; |
| 217 | # need to set new value? |
| 218 | if (@_ > 0) |
| 219 | { |
| 220 | my $a = shift; |
| 221 | die ('accuracy must not be zero') if defined $a && $a == 0; |
| 222 | if (ref($x)) |
| 223 | { |
| 224 | # $object->accuracy() or fallback to global |
| 225 | $x->bround($a) if defined $a; |
| 226 | $x->{_a} = $a; # set/overwrite, even if not rounded |
| 227 | $x->{_p} = undef; # clear P |
| 228 | } |
| 229 | else |
| 230 | { |
| 231 | # set global |
| 232 | ${"${class}::accuracy"} = $a; |
| 233 | ${"${class}::precision"} = undef; # clear P |
| 234 | } |
| 235 | return $a; # shortcut |
| 236 | } |
| 237 | |
| 238 | my $r; |
| 239 | # $object->accuracy() or fallback to global |
| 240 | $r = $x->{_a} if ref($x); |
| 241 | # but don't return global undef, when $x's accuracy is 0! |
| 242 | $r = ${"${class}::accuracy"} if !defined $r; |
| 243 | $r; |
| 244 | } |
| 245 | |
| 246 | sub precision |
| 247 | { |
| 248 | # $x->precision($p); ref($x) $p |
| 249 | # $x->precision(); ref($x) |
| 250 | # Class->precision(); class |
| 251 | # Class->precision($p); class $p |
| 252 | |
| 253 | my $x = shift; |
| 254 | my $class = ref($x) || $x || __PACKAGE__; |
| 255 | |
| 256 | no strict 'refs'; |
| 257 | # need to set new value? |
| 258 | if (@_ > 0) |
| 259 | { |
| 260 | my $p = shift; |
| 261 | if (ref($x)) |
| 262 | { |
| 263 | # $object->precision() or fallback to global |
| 264 | $x->bfround($p) if defined $p; |
| 265 | $x->{_p} = $p; # set/overwrite, even if not rounded |
| 266 | $x->{_a} = undef; # clear A |
| 267 | } |
| 268 | else |
| 269 | { |
| 270 | # set global |
| 271 | ${"${class}::precision"} = $p; |
| 272 | ${"${class}::accuracy"} = undef; # clear A |
| 273 | } |
| 274 | return $p; # shortcut |
| 275 | } |
| 276 | |
| 277 | my $r; |
| 278 | # $object->precision() or fallback to global |
| 279 | $r = $x->{_p} if ref($x); |
| 280 | # but don't return global undef, when $x's precision is 0! |
| 281 | $r = ${"${class}::precision"} if !defined $r; |
| 282 | $r; |
| 283 | } |
| 284 | |
| 285 | sub config |
| 286 | { |
| 287 | # return (later set?) configuration data as hash ref |
| 288 | my $class = shift || 'Math::BigInt'; |
| 289 | |
| 290 | no strict 'refs'; |
| 291 | my $lib = $CALC; |
| 292 | my $cfg = { |
| 293 | lib => $lib, |
| 294 | lib_version => ${"${lib}::VERSION"}, |
| 295 | class => $class, |
| 296 | }; |
| 297 | foreach ( |
| 298 | qw/upgrade downgrade precision accuracy round_mode VERSION div_scale/) |
| 299 | { |
| 300 | $cfg->{lc($_)} = ${"${class}::$_"}; |
| 301 | }; |
| 302 | $cfg; |
| 303 | } |
| 304 | |
| 305 | sub _scale_a |
| 306 | { |
| 307 | # select accuracy parameter based on precedence, |
| 308 | # used by bround() and bfround(), may return undef for scale (means no op) |
| 309 | my ($x,$s,$m,$scale,$mode) = @_; |
| 310 | $scale = $x->{_a} if !defined $scale; |
| 311 | $scale = $s if (!defined $scale); |
| 312 | $mode = $m if !defined $mode; |
| 313 | return ($scale,$mode); |
| 314 | } |
| 315 | |
| 316 | sub _scale_p |
| 317 | { |
| 318 | # select precision parameter based on precedence, |
| 319 | # used by bround() and bfround(), may return undef for scale (means no op) |
| 320 | my ($x,$s,$m,$scale,$mode) = @_; |
| 321 | $scale = $x->{_p} if !defined $scale; |
| 322 | $scale = $s if (!defined $scale); |
| 323 | $mode = $m if !defined $mode; |
| 324 | return ($scale,$mode); |
| 325 | } |
| 326 | |
| 327 | ############################################################################## |
| 328 | # constructors |
| 329 | |
| 330 | sub copy |
| 331 | { |
| 332 | my ($c,$x); |
| 333 | if (@_ > 1) |
| 334 | { |
| 335 | # if two arguments, the first one is the class to "swallow" subclasses |
| 336 | ($c,$x) = @_; |
| 337 | } |
| 338 | else |
| 339 | { |
| 340 | $x = shift; |
| 341 | $c = ref($x); |
| 342 | } |
| 343 | return unless ref($x); # only for objects |
| 344 | |
| 345 | my $self = {}; bless $self,$c; |
| 346 | my $r; |
| 347 | foreach my $k (keys %$x) |
| 348 | { |
| 349 | if ($k eq 'value') |
| 350 | { |
| 351 | $self->{value} = $CALC->_copy($x->{value}); next; |
| 352 | } |
| 353 | if (!($r = ref($x->{$k}))) |
| 354 | { |
| 355 | $self->{$k} = $x->{$k}; next; |
| 356 | } |
| 357 | if ($r eq 'SCALAR') |
| 358 | { |
| 359 | $self->{$k} = \${$x->{$k}}; |
| 360 | } |
| 361 | elsif ($r eq 'ARRAY') |
| 362 | { |
| 363 | $self->{$k} = [ @{$x->{$k}} ]; |
| 364 | } |
| 365 | elsif ($r eq 'HASH') |
| 366 | { |
| 367 | # only one level deep! |
| 368 | foreach my $h (keys %{$x->{$k}}) |
| 369 | { |
| 370 | $self->{$k}->{$h} = $x->{$k}->{$h}; |
| 371 | } |
| 372 | } |
| 373 | else # normal ref |
| 374 | { |
| 375 | my $xk = $x->{$k}; |
| 376 | if ($xk->can('copy')) |
| 377 | { |
| 378 | $self->{$k} = $xk->copy(); |
| 379 | } |
| 380 | else |
| 381 | { |
| 382 | $self->{$k} = $xk->new($xk); |
| 383 | } |
| 384 | } |
| 385 | } |
| 386 | $self; |
| 387 | } |
| 388 | |
| 389 | sub new |
| 390 | { |
| 391 | # create a new BigInt object from a string or another BigInt object. |
| 392 | # see hash keys documented at top |
| 393 | |
| 394 | # the argument could be an object, so avoid ||, && etc on it, this would |
| 395 | # cause costly overloaded code to be called. The only allowed ops are |
| 396 | # ref() and defined. |
| 397 | |
| 398 | my ($class,$wanted,$a,$p,$r) = @_; |
| 399 | |
| 400 | # avoid numify-calls by not using || on $wanted! |
| 401 | return $class->bzero($a,$p) if !defined $wanted; # default to 0 |
| 402 | return $class->copy($wanted,$a,$p,$r) |
| 403 | if ref($wanted) && $wanted->isa($class); # MBI or subclass |
| 404 | |
| 405 | $class->import() if $IMPORT == 0; # make require work |
| 406 | |
| 407 | my $self = bless {}, $class; |
| 408 | |
| 409 | # shortcut for "normal" numbers |
| 410 | if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/)) |
| 411 | { |
| 412 | $self->{sign} = $1 || '+'; |
| 413 | my $ref = \$wanted; |
| 414 | if ($wanted =~ /^[+-]/) |
| 415 | { |
| 416 | # remove sign without touching wanted |
| 417 | my $t = $wanted; $t =~ s/^[+-]//; $ref = \$t; |
| 418 | } |
| 419 | $self->{value} = $CALC->_new($ref); |
| 420 | no strict 'refs'; |
| 421 | if ( (defined $a) || (defined $p) |
| 422 | || (defined ${"${class}::precision"}) |
| 423 | || (defined ${"${class}::accuracy"}) |
| 424 | ) |
| 425 | { |
| 426 | $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p); |
| 427 | } |
| 428 | return $self; |
| 429 | } |
| 430 | |
| 431 | # handle '+inf', '-inf' first |
| 432 | if ($wanted =~ /^[+-]?inf$/) |
| 433 | { |
| 434 | $self->{value} = $CALC->_zero(); |
| 435 | $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
| 436 | return $self; |
| 437 | } |
| 438 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign |
| 439 | my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted); |
| 440 | if (!ref $mis) |
| 441 | { |
| 442 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
| 443 | #print "NaN 1\n"; |
| 444 | $self->{value} = $CALC->_zero(); |
| 445 | $self->{sign} = $nan; |
| 446 | return $self; |
| 447 | } |
| 448 | if (!ref $miv) |
| 449 | { |
| 450 | # _from_hex or _from_bin |
| 451 | $self->{value} = $mis->{value}; |
| 452 | $self->{sign} = $mis->{sign}; |
| 453 | return $self; # throw away $mis |
| 454 | } |
| 455 | # make integer from mantissa by adjusting exp, then convert to bigint |
| 456 | $self->{sign} = $$mis; # store sign |
| 457 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
| 458 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
| 459 | if ($e > 0) |
| 460 | { |
| 461 | my $diff = $e - CORE::length($$mfv); |
| 462 | if ($diff < 0) # Not integer |
| 463 | { |
| 464 | #print "NOI 1\n"; |
| 465 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
| 466 | $self->{sign} = $nan; |
| 467 | } |
| 468 | else # diff >= 0 |
| 469 | { |
| 470 | # adjust fraction and add it to value |
| 471 | # print "diff > 0 $$miv\n"; |
| 472 | $$miv = $$miv . ($$mfv . '0' x $diff); |
| 473 | } |
| 474 | } |
| 475 | else |
| 476 | { |
| 477 | if ($$mfv ne '') # e <= 0 |
| 478 | { |
| 479 | # fraction and negative/zero E => NOI |
| 480 | #print "NOI 2 \$\$mfv '$$mfv'\n"; |
| 481 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
| 482 | $self->{sign} = $nan; |
| 483 | } |
| 484 | elsif ($e < 0) |
| 485 | { |
| 486 | # xE-y, and empty mfv |
| 487 | #print "xE-y\n"; |
| 488 | $e = abs($e); |
| 489 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? |
| 490 | { |
| 491 | #print "NOI 3\n"; |
| 492 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
| 493 | $self->{sign} = $nan; |
| 494 | } |
| 495 | } |
| 496 | } |
| 497 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 |
| 498 | $self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/; |
| 499 | # if any of the globals is set, use them to round and store them inside $self |
| 500 | # do not round for new($x,undef,undef) since that is used by MBF to signal |
| 501 | # no rounding |
| 502 | $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p; |
| 503 | $self; |
| 504 | } |
| 505 | |
| 506 | sub bnan |
| 507 | { |
| 508 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' |
| 509 | my $self = shift; |
| 510 | $self = $class if !defined $self; |
| 511 | if (!ref($self)) |
| 512 | { |
| 513 | my $c = $self; $self = {}; bless $self, $c; |
| 514 | } |
| 515 | $self->import() if $IMPORT == 0; # make require work |
| 516 | return if $self->modify('bnan'); |
| 517 | my $c = ref($self); |
| 518 | if ($self->can('_bnan')) |
| 519 | { |
| 520 | # use subclass to initialize |
| 521 | $self->_bnan(); |
| 522 | } |
| 523 | else |
| 524 | { |
| 525 | # otherwise do our own thing |
| 526 | $self->{value} = $CALC->_zero(); |
| 527 | } |
| 528 | $self->{sign} = $nan; |
| 529 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly |
| 530 | return $self; |
| 531 | } |
| 532 | |
| 533 | sub binf |
| 534 | { |
| 535 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' |
| 536 | # the sign is either '+', or if given, used from there |
| 537 | my $self = shift; |
| 538 | my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/; |
| 539 | $self = $class if !defined $self; |
| 540 | if (!ref($self)) |
| 541 | { |
| 542 | my $c = $self; $self = {}; bless $self, $c; |
| 543 | } |
| 544 | $self->import() if $IMPORT == 0; # make require work |
| 545 | return if $self->modify('binf'); |
| 546 | my $c = ref($self); |
| 547 | if ($self->can('_binf')) |
| 548 | { |
| 549 | # use subclass to initialize |
| 550 | $self->_binf(); |
| 551 | } |
| 552 | else |
| 553 | { |
| 554 | # otherwise do our own thing |
| 555 | $self->{value} = $CALC->_zero(); |
| 556 | } |
| 557 | $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf |
| 558 | $self->{sign} = $sign; |
| 559 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
| 560 | return $self; |
| 561 | } |
| 562 | |
| 563 | sub bzero |
| 564 | { |
| 565 | # create a bigint '+0', if given a BigInt, set it to 0 |
| 566 | my $self = shift; |
| 567 | $self = $class if !defined $self; |
| 568 | |
| 569 | if (!ref($self)) |
| 570 | { |
| 571 | my $c = $self; $self = {}; bless $self, $c; |
| 572 | } |
| 573 | $self->import() if $IMPORT == 0; # make require work |
| 574 | return if $self->modify('bzero'); |
| 575 | |
| 576 | if ($self->can('_bzero')) |
| 577 | { |
| 578 | # use subclass to initialize |
| 579 | $self->_bzero(); |
| 580 | } |
| 581 | else |
| 582 | { |
| 583 | # otherwise do our own thing |
| 584 | $self->{value} = $CALC->_zero(); |
| 585 | } |
| 586 | $self->{sign} = '+'; |
| 587 | if (@_ > 0) |
| 588 | { |
| 589 | if (@_ > 3) |
| 590 | { |
| 591 | # call like: $x->bzero($a,$p,$r,$y); |
| 592 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); |
| 593 | } |
| 594 | else |
| 595 | { |
| 596 | $self->{_a} = $_[0] |
| 597 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); |
| 598 | $self->{_p} = $_[1] |
| 599 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); |
| 600 | } |
| 601 | } |
| 602 | $self; |
| 603 | } |
| 604 | |
| 605 | sub bone |
| 606 | { |
| 607 | # create a bigint '+1' (or -1 if given sign '-'), |
| 608 | # if given a BigInt, set it to +1 or -1, respecively |
| 609 | my $self = shift; |
| 610 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; |
| 611 | $self = $class if !defined $self; |
| 612 | |
| 613 | if (!ref($self)) |
| 614 | { |
| 615 | my $c = $self; $self = {}; bless $self, $c; |
| 616 | } |
| 617 | $self->import() if $IMPORT == 0; # make require work |
| 618 | return if $self->modify('bone'); |
| 619 | |
| 620 | if ($self->can('_bone')) |
| 621 | { |
| 622 | # use subclass to initialize |
| 623 | $self->_bone(); |
| 624 | } |
| 625 | else |
| 626 | { |
| 627 | # otherwise do our own thing |
| 628 | $self->{value} = $CALC->_one(); |
| 629 | } |
| 630 | $self->{sign} = $sign; |
| 631 | if (@_ > 0) |
| 632 | { |
| 633 | if (@_ > 3) |
| 634 | { |
| 635 | # call like: $x->bone($sign,$a,$p,$r,$y); |
| 636 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); |
| 637 | } |
| 638 | else |
| 639 | { |
| 640 | $self->{_a} = $_[0] |
| 641 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); |
| 642 | $self->{_p} = $_[1] |
| 643 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); |
| 644 | } |
| 645 | } |
| 646 | $self; |
| 647 | } |
| 648 | |
| 649 | ############################################################################## |
| 650 | # string conversation |
| 651 | |
| 652 | sub bsstr |
| 653 | { |
| 654 | # (ref to BFLOAT or num_str ) return num_str |
| 655 | # Convert number from internal format to scientific string format. |
| 656 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
| 657 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
| 658 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 659 | |
| 660 | if ($x->{sign} !~ /^[+-]$/) |
| 661 | { |
| 662 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
| 663 | return 'inf'; # +inf |
| 664 | } |
| 665 | my ($m,$e) = $x->parts(); |
| 666 | # e can only be positive |
| 667 | my $sign = 'e+'; |
| 668 | # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s; |
| 669 | return $m->bstr().$sign.$e->bstr(); |
| 670 | } |
| 671 | |
| 672 | sub bstr |
| 673 | { |
| 674 | # make a string from bigint object |
| 675 | my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
| 676 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 677 | |
| 678 | if ($x->{sign} !~ /^[+-]$/) |
| 679 | { |
| 680 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
| 681 | return 'inf'; # +inf |
| 682 | } |
| 683 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
| 684 | return $es.${$CALC->_str($x->{value})}; |
| 685 | } |
| 686 | |
| 687 | sub numify |
| 688 | { |
| 689 | # Make a "normal" scalar from a BigInt object |
| 690 | my $x = shift; $x = $class->new($x) unless ref $x; |
| 691 | return $x->{sign} if $x->{sign} !~ /^[+-]$/; |
| 692 | my $num = $CALC->_num($x->{value}); |
| 693 | return -$num if $x->{sign} eq '-'; |
| 694 | $num; |
| 695 | } |
| 696 | |
| 697 | ############################################################################## |
| 698 | # public stuff (usually prefixed with "b") |
| 699 | |
| 700 | sub sign |
| 701 | { |
| 702 | # return the sign of the number: +/-/-inf/+inf/NaN |
| 703 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 704 | |
| 705 | $x->{sign}; |
| 706 | } |
| 707 | |
| 708 | sub _find_round_parameters |
| 709 | { |
| 710 | # After any operation or when calling round(), the result is rounded by |
| 711 | # regarding the A & P from arguments, local parameters, or globals. |
| 712 | |
| 713 | # This procedure finds the round parameters, but it is for speed reasons |
| 714 | # duplicated in round. Otherwise, it is tested by the testsuite and used |
| 715 | # by fdiv(). |
| 716 | |
| 717 | my ($self,$a,$p,$r,@args) = @_; |
| 718 | # $a accuracy, if given by caller |
| 719 | # $p precision, if given by caller |
| 720 | # $r round_mode, if given by caller |
| 721 | # @args all 'other' arguments (0 for unary, 1 for binary ops) |
| 722 | |
| 723 | # leave bigfloat parts alone |
| 724 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
| 725 | |
| 726 | my $c = ref($self); # find out class of argument(s) |
| 727 | no strict 'refs'; |
| 728 | |
| 729 | # now pick $a or $p, but only if we have got "arguments" |
| 730 | if (!defined $a) |
| 731 | { |
| 732 | foreach ($self,@args) |
| 733 | { |
| 734 | # take the defined one, or if both defined, the one that is smaller |
| 735 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); |
| 736 | } |
| 737 | } |
| 738 | if (!defined $p) |
| 739 | { |
| 740 | # even if $a is defined, take $p, to signal error for both defined |
| 741 | foreach ($self,@args) |
| 742 | { |
| 743 | # take the defined one, or if both defined, the one that is bigger |
| 744 | # -2 > -3, and 3 > 2 |
| 745 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); |
| 746 | } |
| 747 | } |
| 748 | # if still none defined, use globals (#2) |
| 749 | $a = ${"$c\::accuracy"} unless defined $a; |
| 750 | $p = ${"$c\::precision"} unless defined $p; |
| 751 | |
| 752 | # no rounding today? |
| 753 | return ($self) unless defined $a || defined $p; # early out |
| 754 | |
| 755 | # set A and set P is an fatal error |
| 756 | return ($self->bnan()) if defined $a && defined $p; |
| 757 | |
| 758 | $r = ${"$c\::round_mode"} unless defined $r; |
| 759 | die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
| 760 | |
| 761 | return ($self,$a,$p,$r); |
| 762 | } |
| 763 | |
| 764 | sub round |
| 765 | { |
| 766 | # Round $self according to given parameters, or given second argument's |
| 767 | # parameters or global defaults |
| 768 | |
| 769 | # for speed reasons, _find_round_parameters is embeded here: |
| 770 | |
| 771 | my ($self,$a,$p,$r,@args) = @_; |
| 772 | # $a accuracy, if given by caller |
| 773 | # $p precision, if given by caller |
| 774 | # $r round_mode, if given by caller |
| 775 | # @args all 'other' arguments (0 for unary, 1 for binary ops) |
| 776 | |
| 777 | # leave bigfloat parts alone |
| 778 | return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0; |
| 779 | |
| 780 | my $c = ref($self); # find out class of argument(s) |
| 781 | no strict 'refs'; |
| 782 | |
| 783 | # now pick $a or $p, but only if we have got "arguments" |
| 784 | if (!defined $a) |
| 785 | { |
| 786 | foreach ($self,@args) |
| 787 | { |
| 788 | # take the defined one, or if both defined, the one that is smaller |
| 789 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); |
| 790 | } |
| 791 | } |
| 792 | if (!defined $p) |
| 793 | { |
| 794 | # even if $a is defined, take $p, to signal error for both defined |
| 795 | foreach ($self,@args) |
| 796 | { |
| 797 | # take the defined one, or if both defined, the one that is bigger |
| 798 | # -2 > -3, and 3 > 2 |
| 799 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); |
| 800 | } |
| 801 | } |
| 802 | # if still none defined, use globals (#2) |
| 803 | $a = ${"$c\::accuracy"} unless defined $a; |
| 804 | $p = ${"$c\::precision"} unless defined $p; |
| 805 | |
| 806 | # no rounding today? |
| 807 | return $self unless defined $a || defined $p; # early out |
| 808 | |
| 809 | # set A and set P is an fatal error |
| 810 | return $self->bnan() if defined $a && defined $p; |
| 811 | |
| 812 | $r = ${"$c\::round_mode"} unless defined $r; |
| 813 | die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/; |
| 814 | |
| 815 | # now round, by calling either fround or ffround: |
| 816 | if (defined $a) |
| 817 | { |
| 818 | $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a; |
| 819 | } |
| 820 | else # both can't be undefined due to early out |
| 821 | { |
| 822 | $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p; |
| 823 | } |
| 824 | $self->bnorm(); # after round, normalize |
| 825 | } |
| 826 | |
| 827 | sub bnorm |
| 828 | { |
| 829 | # (numstr or BINT) return BINT |
| 830 | # Normalize number -- no-op here |
| 831 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 832 | $x; |
| 833 | } |
| 834 | |
| 835 | sub babs |
| 836 | { |
| 837 | # (BINT or num_str) return BINT |
| 838 | # make number absolute, or return absolute BINT from string |
| 839 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 840 | |
| 841 | return $x if $x->modify('babs'); |
| 842 | # post-normalized abs for internal use (does nothing for NaN) |
| 843 | $x->{sign} =~ s/^-/+/; |
| 844 | $x; |
| 845 | } |
| 846 | |
| 847 | sub bneg |
| 848 | { |
| 849 | # (BINT or num_str) return BINT |
| 850 | # negate number or make a negated number from string |
| 851 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 852 | |
| 853 | return $x if $x->modify('bneg'); |
| 854 | |
| 855 | # for +0 dont negate (to have always normalized) |
| 856 | $x->{sign} =~ tr/+-/-+/ if !$x->is_zero(); # does nothing for NaN |
| 857 | $x; |
| 858 | } |
| 859 | |
| 860 | sub bcmp |
| 861 | { |
| 862 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
| 863 | # (BINT or num_str, BINT or num_str) return cond_code |
| 864 | |
| 865 | # set up parameters |
| 866 | my ($self,$x,$y) = (ref($_[0]),@_); |
| 867 | |
| 868 | # objectify is costly, so avoid it |
| 869 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 870 | { |
| 871 | ($self,$x,$y) = objectify(2,@_); |
| 872 | } |
| 873 | |
| 874 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 875 | { |
| 876 | # handle +-inf and NaN |
| 877 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 878 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
| 879 | return +1 if $x->{sign} eq '+inf'; |
| 880 | return -1 if $x->{sign} eq '-inf'; |
| 881 | return -1 if $y->{sign} eq '+inf'; |
| 882 | return +1; |
| 883 | } |
| 884 | # check sign for speed first |
| 885 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
| 886 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
| 887 | |
| 888 | # have same sign, so compare absolute values. Don't make tests for zero here |
| 889 | # because it's actually slower than testin in Calc (especially w/ Pari et al) |
| 890 | |
| 891 | # post-normalized compare for internal use (honors signs) |
| 892 | if ($x->{sign} eq '+') |
| 893 | { |
| 894 | # $x and $y both > 0 |
| 895 | return $CALC->_acmp($x->{value},$y->{value}); |
| 896 | } |
| 897 | |
| 898 | # $x && $y both < 0 |
| 899 | $CALC->_acmp($y->{value},$x->{value}); # swaped (lib returns 0,1,-1) |
| 900 | } |
| 901 | |
| 902 | sub bacmp |
| 903 | { |
| 904 | # Compares 2 values, ignoring their signs. |
| 905 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
| 906 | # (BINT, BINT) return cond_code |
| 907 | |
| 908 | # set up parameters |
| 909 | my ($self,$x,$y) = (ref($_[0]),@_); |
| 910 | # objectify is costly, so avoid it |
| 911 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 912 | { |
| 913 | ($self,$x,$y) = objectify(2,@_); |
| 914 | } |
| 915 | |
| 916 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 917 | { |
| 918 | # handle +-inf and NaN |
| 919 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 920 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
| 921 | return +1; # inf is always bigger |
| 922 | } |
| 923 | $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1 |
| 924 | } |
| 925 | |
| 926 | sub badd |
| 927 | { |
| 928 | # add second arg (BINT or string) to first (BINT) (modifies first) |
| 929 | # return result as BINT |
| 930 | |
| 931 | # set up parameters |
| 932 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 933 | # objectify is costly, so avoid it |
| 934 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 935 | { |
| 936 | ($self,$x,$y,@r) = objectify(2,@_); |
| 937 | } |
| 938 | |
| 939 | return $x if $x->modify('badd'); |
| 940 | return $upgrade->badd($x,$y,@r) if defined $upgrade && |
| 941 | ((!$x->isa($self)) || (!$y->isa($self))); |
| 942 | |
| 943 | $r[3] = $y; # no push! |
| 944 | # inf and NaN handling |
| 945 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 946 | { |
| 947 | # NaN first |
| 948 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 949 | # inf handling |
| 950 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
| 951 | { |
| 952 | # +inf++inf or -inf+-inf => same, rest is NaN |
| 953 | return $x if $x->{sign} eq $y->{sign}; |
| 954 | return $x->bnan(); |
| 955 | } |
| 956 | # +-inf + something => +inf |
| 957 | # something +-inf => +-inf |
| 958 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
| 959 | return $x; |
| 960 | } |
| 961 | |
| 962 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
| 963 | |
| 964 | if ($sx eq $sy) |
| 965 | { |
| 966 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
| 967 | $x->{sign} = $sx; |
| 968 | } |
| 969 | else |
| 970 | { |
| 971 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
| 972 | if ($a > 0) |
| 973 | { |
| 974 | #print "swapped sub (a=$a)\n"; |
| 975 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
| 976 | $x->{sign} = $sy; |
| 977 | } |
| 978 | elsif ($a == 0) |
| 979 | { |
| 980 | # speedup, if equal, set result to 0 |
| 981 | #print "equal sub, result = 0\n"; |
| 982 | $x->{value} = $CALC->_zero(); |
| 983 | $x->{sign} = '+'; |
| 984 | } |
| 985 | else # a < 0 |
| 986 | { |
| 987 | #print "unswapped sub (a=$a)\n"; |
| 988 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
| 989 | $x->{sign} = $sx; |
| 990 | } |
| 991 | } |
| 992 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 993 | $x; |
| 994 | } |
| 995 | |
| 996 | sub bsub |
| 997 | { |
| 998 | # (BINT or num_str, BINT or num_str) return num_str |
| 999 | # subtract second arg from first, modify first |
| 1000 | |
| 1001 | # set up parameters |
| 1002 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1003 | # objectify is costly, so avoid it |
| 1004 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1005 | { |
| 1006 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1007 | } |
| 1008 | |
| 1009 | return $x if $x->modify('bsub'); |
| 1010 | |
| 1011 | # upgrade done by badd(): |
| 1012 | # return $upgrade->badd($x,$y,@r) if defined $upgrade && |
| 1013 | # ((!$x->isa($self)) || (!$y->isa($self))); |
| 1014 | |
| 1015 | if ($y->is_zero()) |
| 1016 | { |
| 1017 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1018 | return $x; |
| 1019 | } |
| 1020 | |
| 1021 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
| 1022 | $x->badd($y,@r); # badd does not leave internal zeros |
| 1023 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
| 1024 | $x; # already rounded by badd() or no round necc. |
| 1025 | } |
| 1026 | |
| 1027 | sub binc |
| 1028 | { |
| 1029 | # increment arg by one |
| 1030 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1031 | return $x if $x->modify('binc'); |
| 1032 | |
| 1033 | if ($x->{sign} eq '+') |
| 1034 | { |
| 1035 | $x->{value} = $CALC->_inc($x->{value}); |
| 1036 | $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1037 | return $x; |
| 1038 | } |
| 1039 | elsif ($x->{sign} eq '-') |
| 1040 | { |
| 1041 | $x->{value} = $CALC->_dec($x->{value}); |
| 1042 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 |
| 1043 | $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1044 | return $x; |
| 1045 | } |
| 1046 | # inf, nan handling etc |
| 1047 | $x->badd($self->__one(),$a,$p,$r); # badd does round |
| 1048 | } |
| 1049 | |
| 1050 | sub bdec |
| 1051 | { |
| 1052 | # decrement arg by one |
| 1053 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1054 | return $x if $x->modify('bdec'); |
| 1055 | |
| 1056 | my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+'; |
| 1057 | # <= 0 |
| 1058 | if (($x->{sign} eq '-') || $zero) |
| 1059 | { |
| 1060 | $x->{value} = $CALC->_inc($x->{value}); |
| 1061 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
| 1062 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 |
| 1063 | $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1064 | return $x; |
| 1065 | } |
| 1066 | # > 0 |
| 1067 | elsif ($x->{sign} eq '+') |
| 1068 | { |
| 1069 | $x->{value} = $CALC->_dec($x->{value}); |
| 1070 | $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1071 | return $x; |
| 1072 | } |
| 1073 | # inf, nan handling etc |
| 1074 | $x->badd($self->__one('-'),$a,$p,$r); # badd does round |
| 1075 | } |
| 1076 | |
| 1077 | sub blog |
| 1078 | { |
| 1079 | # not implemented yet |
| 1080 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1081 | |
| 1082 | return $upgrade->blog($x,$base,$a,$p,$r) if defined $upgrade; |
| 1083 | |
| 1084 | return $x->bnan(); |
| 1085 | } |
| 1086 | |
| 1087 | sub blcm |
| 1088 | { |
| 1089 | # (BINT or num_str, BINT or num_str) return BINT |
| 1090 | # does not modify arguments, but returns new object |
| 1091 | # Lowest Common Multiplicator |
| 1092 | |
| 1093 | my $y = shift; my ($x); |
| 1094 | if (ref($y)) |
| 1095 | { |
| 1096 | $x = $y->copy(); |
| 1097 | } |
| 1098 | else |
| 1099 | { |
| 1100 | $x = $class->new($y); |
| 1101 | } |
| 1102 | while (@_) { $x = __lcm($x,shift); } |
| 1103 | $x; |
| 1104 | } |
| 1105 | |
| 1106 | sub bgcd |
| 1107 | { |
| 1108 | # (BINT or num_str, BINT or num_str) return BINT |
| 1109 | # does not modify arguments, but returns new object |
| 1110 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) |
| 1111 | |
| 1112 | my $y = shift; |
| 1113 | $y = __PACKAGE__->new($y) if !ref($y); |
| 1114 | my $self = ref($y); |
| 1115 | my $x = $y->copy(); # keep arguments |
| 1116 | if ($CALC->can('_gcd')) |
| 1117 | { |
| 1118 | while (@_) |
| 1119 | { |
| 1120 | $y = shift; $y = $self->new($y) if !ref($y); |
| 1121 | next if $y->is_zero(); |
| 1122 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? |
| 1123 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one(); |
| 1124 | } |
| 1125 | } |
| 1126 | else |
| 1127 | { |
| 1128 | while (@_) |
| 1129 | { |
| 1130 | $y = shift; $y = $self->new($y) if !ref($y); |
| 1131 | $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN |
| 1132 | } |
| 1133 | } |
| 1134 | $x->babs(); |
| 1135 | } |
| 1136 | |
| 1137 | sub bnot |
| 1138 | { |
| 1139 | # (num_str or BINT) return BINT |
| 1140 | # represent ~x as twos-complement number |
| 1141 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
| 1142 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
| 1143 | |
| 1144 | return $x if $x->modify('bnot'); |
| 1145 | $x->bneg()->bdec(); # bdec already does round |
| 1146 | } |
| 1147 | |
| 1148 | # is_foo test routines |
| 1149 | |
| 1150 | sub is_zero |
| 1151 | { |
| 1152 | # return true if arg (BINT or num_str) is zero (array '+', '0') |
| 1153 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
| 1154 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1155 | |
| 1156 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
| 1157 | $CALC->_is_zero($x->{value}); |
| 1158 | } |
| 1159 | |
| 1160 | sub is_nan |
| 1161 | { |
| 1162 | # return true if arg (BINT or num_str) is NaN |
| 1163 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 1164 | |
| 1165 | return 1 if $x->{sign} eq $nan; |
| 1166 | 0; |
| 1167 | } |
| 1168 | |
| 1169 | sub is_inf |
| 1170 | { |
| 1171 | # return true if arg (BINT or num_str) is +-inf |
| 1172 | my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1173 | |
| 1174 | $sign = '' if !defined $sign; |
| 1175 | return 1 if $sign eq $x->{sign}; # match ("+inf" eq "+inf") |
| 1176 | return 0 if $sign !~ /^([+-]|)$/; |
| 1177 | |
| 1178 | if ($sign eq '') |
| 1179 | { |
| 1180 | return 1 if ($x->{sign} =~ /^[+-]inf$/); |
| 1181 | return 0; |
| 1182 | } |
| 1183 | $sign = quotemeta($sign.'inf'); |
| 1184 | return 1 if ($x->{sign} =~ /^$sign$/); |
| 1185 | 0; |
| 1186 | } |
| 1187 | |
| 1188 | sub is_one |
| 1189 | { |
| 1190 | # return true if arg (BINT or num_str) is +1 |
| 1191 | # or -1 if sign is given |
| 1192 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
| 1193 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
| 1194 | |
| 1195 | $sign = '' if !defined $sign; $sign = '+' if $sign ne '-'; |
| 1196 | |
| 1197 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
| 1198 | $CALC->_is_one($x->{value}); |
| 1199 | } |
| 1200 | |
| 1201 | sub is_odd |
| 1202 | { |
| 1203 | # return true when arg (BINT or num_str) is odd, false for even |
| 1204 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
| 1205 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1206 | |
| 1207 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
| 1208 | $CALC->_is_odd($x->{value}); |
| 1209 | } |
| 1210 | |
| 1211 | sub is_even |
| 1212 | { |
| 1213 | # return true when arg (BINT or num_str) is even, false for odd |
| 1214 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
| 1215 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1216 | |
| 1217 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
| 1218 | $CALC->_is_even($x->{value}); |
| 1219 | } |
| 1220 | |
| 1221 | sub is_positive |
| 1222 | { |
| 1223 | # return true when arg (BINT or num_str) is positive (>= 0) |
| 1224 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
| 1225 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1226 | |
| 1227 | return 1 if $x->{sign} =~ /^\+/; |
| 1228 | 0; |
| 1229 | } |
| 1230 | |
| 1231 | sub is_negative |
| 1232 | { |
| 1233 | # return true when arg (BINT or num_str) is negative (< 0) |
| 1234 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
| 1235 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1236 | |
| 1237 | return 1 if ($x->{sign} =~ /^-/); |
| 1238 | 0; |
| 1239 | } |
| 1240 | |
| 1241 | sub is_int |
| 1242 | { |
| 1243 | # return true when arg (BINT or num_str) is an integer |
| 1244 | # always true for BigInt, but different for Floats |
| 1245 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
| 1246 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1247 | |
| 1248 | $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't |
| 1249 | } |
| 1250 | |
| 1251 | ############################################################################### |
| 1252 | |
| 1253 | sub bmul |
| 1254 | { |
| 1255 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
| 1256 | # (BINT or num_str, BINT or num_str) return BINT |
| 1257 | |
| 1258 | # set up parameters |
| 1259 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1260 | # objectify is costly, so avoid it |
| 1261 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1262 | { |
| 1263 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1264 | } |
| 1265 | |
| 1266 | return $x if $x->modify('bmul'); |
| 1267 | |
| 1268 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 1269 | |
| 1270 | # inf handling |
| 1271 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
| 1272 | { |
| 1273 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
| 1274 | # result will always be +-inf: |
| 1275 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
| 1276 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
| 1277 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
| 1278 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
| 1279 | return $x->binf('-'); |
| 1280 | } |
| 1281 | |
| 1282 | return $upgrade->bmul($x,$y,@r) |
| 1283 | if defined $upgrade && $y->isa($upgrade); |
| 1284 | |
| 1285 | $r[3] = $y; # no push here |
| 1286 | |
| 1287 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
| 1288 | |
| 1289 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
| 1290 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 |
| 1291 | |
| 1292 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1293 | $x; |
| 1294 | } |
| 1295 | |
| 1296 | sub _div_inf |
| 1297 | { |
| 1298 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code |
| 1299 | my ($self,$x,$y) = @_; |
| 1300 | |
| 1301 | # NaN if x == NaN or y == NaN or x==y==0 |
| 1302 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() |
| 1303 | if (($x->is_nan() || $y->is_nan()) || |
| 1304 | ($x->is_zero() && $y->is_zero())); |
| 1305 | |
| 1306 | # +-inf / +-inf == NaN, reminder also NaN |
| 1307 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
| 1308 | { |
| 1309 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan(); |
| 1310 | } |
| 1311 | # x / +-inf => 0, remainder x (works even if x == 0) |
| 1312 | if ($y->{sign} =~ /^[+-]inf$/) |
| 1313 | { |
| 1314 | my $t = $x->copy(); # bzero clobbers up $x |
| 1315 | return wantarray ? ($x->bzero(),$t) : $x->bzero() |
| 1316 | } |
| 1317 | |
| 1318 | # 5 / 0 => +inf, -6 / 0 => -inf |
| 1319 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf |
| 1320 | # exception: -8 / 0 has remainder -8, not 8 |
| 1321 | # exception: -inf / 0 has remainder -inf, not inf |
| 1322 | if ($y->is_zero()) |
| 1323 | { |
| 1324 | # +-inf / 0 => special case for -inf |
| 1325 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); |
| 1326 | if (!$x->is_zero() && !$x->is_inf()) |
| 1327 | { |
| 1328 | my $t = $x->copy(); # binf clobbers up $x |
| 1329 | return wantarray ? |
| 1330 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) |
| 1331 | } |
| 1332 | } |
| 1333 | |
| 1334 | # last case: +-inf / ordinary number |
| 1335 | my $sign = '+inf'; |
| 1336 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; |
| 1337 | $x->{sign} = $sign; |
| 1338 | return wantarray ? ($x,$self->bzero()) : $x; |
| 1339 | } |
| 1340 | |
| 1341 | sub bdiv |
| 1342 | { |
| 1343 | # (dividend: BINT or num_str, divisor: BINT or num_str) return |
| 1344 | # (BINT,BINT) (quo,rem) or BINT (only rem) |
| 1345 | |
| 1346 | # set up parameters |
| 1347 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1348 | # objectify is costly, so avoid it |
| 1349 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1350 | { |
| 1351 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1352 | } |
| 1353 | |
| 1354 | return $x if $x->modify('bdiv'); |
| 1355 | |
| 1356 | return $self->_div_inf($x,$y) |
| 1357 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
| 1358 | |
| 1359 | return $upgrade->bdiv($upgrade->new($x),$y,@r) |
| 1360 | if defined $upgrade && !$y->isa($self); |
| 1361 | |
| 1362 | $r[3] = $y; # no push! |
| 1363 | |
| 1364 | # 0 / something |
| 1365 | return |
| 1366 | wantarray ? ($x->round(@r),$self->bzero(@r)):$x->round(@r) if $x->is_zero(); |
| 1367 | |
| 1368 | # Is $x in the interval [0, $y) (aka $x <= $y) ? |
| 1369 | my $cmp = $CALC->_acmp($x->{value},$y->{value}); |
| 1370 | if (($cmp < 0) and (($x->{sign} eq $y->{sign}) or !wantarray)) |
| 1371 | { |
| 1372 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
| 1373 | if defined $upgrade; |
| 1374 | |
| 1375 | return $x->bzero()->round(@r) unless wantarray; |
| 1376 | my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x |
| 1377 | return ($x->bzero()->round(@r),$t); |
| 1378 | } |
| 1379 | elsif ($cmp == 0) |
| 1380 | { |
| 1381 | # shortcut, both are the same, so set to +/- 1 |
| 1382 | $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') ); |
| 1383 | return $x unless wantarray; |
| 1384 | return ($x->round(@r),$self->bzero(@r)); |
| 1385 | } |
| 1386 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
| 1387 | if defined $upgrade; |
| 1388 | |
| 1389 | # calc new sign and in case $y == +/- 1, return $x |
| 1390 | my $xsign = $x->{sign}; # keep |
| 1391 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
| 1392 | # check for / +-1 (cant use $y->is_one due to '-' |
| 1393 | if ($CALC->_is_one($y->{value})) |
| 1394 | { |
| 1395 | return wantarray ? ($x->round(@r),$self->bzero(@r)) : $x->round(@r); |
| 1396 | } |
| 1397 | |
| 1398 | if (wantarray) |
| 1399 | { |
| 1400 | my $rem = $self->bzero(); |
| 1401 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); |
| 1402 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); |
| 1403 | $rem->{_a} = $x->{_a}; |
| 1404 | $rem->{_p} = $x->{_p}; |
| 1405 | $x->round(@r); |
| 1406 | if (! $CALC->_is_zero($rem->{value})) |
| 1407 | { |
| 1408 | $rem->{sign} = $y->{sign}; |
| 1409 | $rem = $y-$rem if $xsign ne $y->{sign}; # one of them '-' |
| 1410 | } |
| 1411 | else |
| 1412 | { |
| 1413 | $rem->{sign} = '+'; # dont leave -0 |
| 1414 | } |
| 1415 | return ($x,$rem->round(@r)); |
| 1416 | } |
| 1417 | |
| 1418 | $x->{value} = $CALC->_div($x->{value},$y->{value}); |
| 1419 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); |
| 1420 | |
| 1421 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1422 | $x; |
| 1423 | } |
| 1424 | |
| 1425 | ############################################################################### |
| 1426 | # modulus functions |
| 1427 | |
| 1428 | sub bmod |
| 1429 | { |
| 1430 | # modulus (or remainder) |
| 1431 | # (BINT or num_str, BINT or num_str) return BINT |
| 1432 | |
| 1433 | # set up parameters |
| 1434 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1435 | # objectify is costly, so avoid it |
| 1436 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1437 | { |
| 1438 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1439 | } |
| 1440 | |
| 1441 | return $x if $x->modify('bmod'); |
| 1442 | $r[3] = $y; # no push! |
| 1443 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) |
| 1444 | { |
| 1445 | my ($d,$r) = $self->_div_inf($x,$y); |
| 1446 | $x->{sign} = $r->{sign}; |
| 1447 | $x->{value} = $r->{value}; |
| 1448 | return $x->round(@r); |
| 1449 | } |
| 1450 | |
| 1451 | if ($CALC->can('_mod')) |
| 1452 | { |
| 1453 | # calc new sign and in case $y == +/- 1, return $x |
| 1454 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); |
| 1455 | if (!$CALC->_is_zero($x->{value})) |
| 1456 | { |
| 1457 | my $xsign = $x->{sign}; |
| 1458 | $x->{sign} = $y->{sign}; |
| 1459 | if ($xsign ne $y->{sign}) |
| 1460 | { |
| 1461 | my $t = $CALC->_copy($x->{value}); # copy $x |
| 1462 | $x->{value} = $CALC->_copy($y->{value}); # copy $y to $x |
| 1463 | $x->{value} = $CALC->_sub($y->{value},$t,1); # $y-$x |
| 1464 | } |
| 1465 | } |
| 1466 | else |
| 1467 | { |
| 1468 | $x->{sign} = '+'; # dont leave -0 |
| 1469 | } |
| 1470 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1471 | return $x; |
| 1472 | } |
| 1473 | my ($t,$rem) = $self->bdiv($x->copy(),$y,@r); # slow way (also rounds) |
| 1474 | # modify in place |
| 1475 | foreach (qw/value sign _a _p/) |
| 1476 | { |
| 1477 | $x->{$_} = $rem->{$_}; |
| 1478 | } |
| 1479 | $x; |
| 1480 | } |
| 1481 | |
| 1482 | sub bmodinv |
| 1483 | { |
| 1484 | # modular inverse. given a number which is (hopefully) relatively |
| 1485 | # prime to the modulus, calculate its inverse using Euclid's |
| 1486 | # alogrithm. if the number is not relatively prime to the modulus |
| 1487 | # (i.e. their gcd is not one) then NaN is returned. |
| 1488 | |
| 1489 | # set up parameters |
| 1490 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1491 | # objectify is costly, so avoid it |
| 1492 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1493 | { |
| 1494 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1495 | } |
| 1496 | |
| 1497 | return $x if $x->modify('bmodinv'); |
| 1498 | |
| 1499 | return $x->bnan() |
| 1500 | if ($y->{sign} ne '+' # -, NaN, +inf, -inf |
| 1501 | || $x->is_zero() # or num == 0 |
| 1502 | || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf |
| 1503 | ); |
| 1504 | |
| 1505 | # put least residue into $x if $x was negative, and thus make it positive |
| 1506 | $x->bmod($y) if $x->{sign} eq '-'; |
| 1507 | |
| 1508 | if ($CALC->can('_modinv')) |
| 1509 | { |
| 1510 | $x->{value} = $CALC->_modinv($x->{value},$y->{value}); |
| 1511 | $x->bnan() if !defined $x->{value} ; # in case there was none |
| 1512 | return $x; |
| 1513 | } |
| 1514 | |
| 1515 | my ($u, $u1) = ($self->bzero(), $self->bone()); |
| 1516 | my ($a, $b) = ($y->copy(), $x->copy()); |
| 1517 | |
| 1518 | # first step need always be done since $num (and thus $b) is never 0 |
| 1519 | # Note that the loop is aligned so that the check occurs between #2 and #1 |
| 1520 | # thus saving us one step #2 at the loop end. Typical loop count is 1. Even |
| 1521 | # a case with 28 loops still gains about 3% with this layout. |
| 1522 | my $q; |
| 1523 | ($a, $q, $b) = ($b, $a->bdiv($b)); # step #1 |
| 1524 | # Euclid's Algorithm |
| 1525 | while (!$b->is_zero()) |
| 1526 | { |
| 1527 | ($u, $u1) = ($u1, $u->bsub($u1->copy()->bmul($q))); # step #2 |
| 1528 | ($a, $q, $b) = ($b, $a->bdiv($b)); # step #1 again |
| 1529 | } |
| 1530 | |
| 1531 | # if the gcd is not 1, then return NaN! It would be pointless to |
| 1532 | # have called bgcd to check this first, because we would then be performing |
| 1533 | # the same Euclidean Algorithm *twice* |
| 1534 | return $x->bnan() unless $a->is_one(); |
| 1535 | |
| 1536 | $u1->bmod($y); |
| 1537 | $x->{value} = $u1->{value}; |
| 1538 | $x->{sign} = $u1->{sign}; |
| 1539 | $x; |
| 1540 | } |
| 1541 | |
| 1542 | sub bmodpow |
| 1543 | { |
| 1544 | # takes a very large number to a very large exponent in a given very |
| 1545 | # large modulus, quickly, thanks to binary exponentation. supports |
| 1546 | # negative exponents. |
| 1547 | my ($self,$num,$exp,$mod,@r) = objectify(3,@_); |
| 1548 | |
| 1549 | return $num if $num->modify('bmodpow'); |
| 1550 | |
| 1551 | # check modulus for valid values |
| 1552 | return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf |
| 1553 | || $mod->is_zero()); |
| 1554 | |
| 1555 | # check exponent for valid values |
| 1556 | if ($exp->{sign} =~ /\w/) |
| 1557 | { |
| 1558 | # i.e., if it's NaN, +inf, or -inf... |
| 1559 | return $num->bnan(); |
| 1560 | } |
| 1561 | |
| 1562 | $num->bmodinv ($mod) if ($exp->{sign} eq '-'); |
| 1563 | |
| 1564 | # check num for valid values (also NaN if there was no inverse but $exp < 0) |
| 1565 | return $num->bnan() if $num->{sign} !~ /^[+-]$/; |
| 1566 | |
| 1567 | if ($CALC->can('_modpow')) |
| 1568 | { |
| 1569 | # $mod is positive, sign on $exp is ignored, result also positive |
| 1570 | $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value}); |
| 1571 | return $num; |
| 1572 | } |
| 1573 | |
| 1574 | # in the trivial case, |
| 1575 | return $num->bzero(@r) if $mod->is_one(); |
| 1576 | return $num->bone('+',@r) if $num->is_zero() or $num->is_one(); |
| 1577 | |
| 1578 | # $num->bmod($mod); # if $x is large, make it smaller first |
| 1579 | my $acc = $num->copy(); # but this is not really faster... |
| 1580 | |
| 1581 | $num->bone(); # keep ref to $num |
| 1582 | |
| 1583 | my $expbin = $exp->as_bin(); $expbin =~ s/^[-]?0b//; # ignore sign and prefix |
| 1584 | my $len = length($expbin); |
| 1585 | while (--$len >= 0) |
| 1586 | { |
| 1587 | if( substr($expbin,$len,1) eq '1') |
| 1588 | { |
| 1589 | $num->bmul($acc)->bmod($mod); |
| 1590 | } |
| 1591 | $acc->bmul($acc)->bmod($mod); |
| 1592 | } |
| 1593 | |
| 1594 | $num; |
| 1595 | } |
| 1596 | |
| 1597 | ############################################################################### |
| 1598 | |
| 1599 | sub bfac |
| 1600 | { |
| 1601 | # (BINT or num_str, BINT or num_str) return BINT |
| 1602 | # compute factorial numbers |
| 1603 | # modifies first argument |
| 1604 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1605 | |
| 1606 | return $x if $x->modify('bfac'); |
| 1607 | |
| 1608 | return $x->bnan() if $x->{sign} ne '+'; # inf, NnN, <0 etc => NaN |
| 1609 | return $x->bone('+',@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 |
| 1610 | |
| 1611 | if ($CALC->can('_fac')) |
| 1612 | { |
| 1613 | $x->{value} = $CALC->_fac($x->{value}); |
| 1614 | return $x->round(@r); |
| 1615 | } |
| 1616 | |
| 1617 | my $n = $x->copy(); |
| 1618 | $x->bone(); |
| 1619 | # seems we need not to temp. clear A/P of $x since the result is the same |
| 1620 | my $f = $self->new(2); |
| 1621 | while ($f->bacmp($n) < 0) |
| 1622 | { |
| 1623 | $x->bmul($f); $f->binc(); |
| 1624 | } |
| 1625 | $x->bmul($f,@r); # last step and also round |
| 1626 | } |
| 1627 | |
| 1628 | sub bpow |
| 1629 | { |
| 1630 | # (BINT or num_str, BINT or num_str) return BINT |
| 1631 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 |
| 1632 | # modifies first argument |
| 1633 | |
| 1634 | # set up parameters |
| 1635 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1636 | # objectify is costly, so avoid it |
| 1637 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1638 | { |
| 1639 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1640 | } |
| 1641 | |
| 1642 | return $x if $x->modify('bpow'); |
| 1643 | |
| 1644 | return $upgrade->bpow($upgrade->new($x),$y,@r) |
| 1645 | if defined $upgrade && !$y->isa($self); |
| 1646 | |
| 1647 | $r[3] = $y; # no push! |
| 1648 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
| 1649 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
| 1650 | return $x->bone('+',@r) if $y->is_zero(); |
| 1651 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
| 1652 | if ($x->{sign} eq '-' && $CALC->_is_one($x->{value})) |
| 1653 | { |
| 1654 | # if $x == -1 and odd/even y => +1/-1 |
| 1655 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
| 1656 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
| 1657 | } |
| 1658 | # 1 ** -y => 1 / (1 ** |y|) |
| 1659 | # so do test for negative $y after above's clause |
| 1660 | return $x->bnan() if $y->{sign} eq '-'; |
| 1661 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
| 1662 | |
| 1663 | if ($CALC->can('_pow')) |
| 1664 | { |
| 1665 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
| 1666 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1667 | return $x; |
| 1668 | } |
| 1669 | |
| 1670 | # based on the assumption that shifting in base 10 is fast, and that mul |
| 1671 | # works faster if numbers are small: we count trailing zeros (this step is |
| 1672 | # O(1)..O(N), but in case of O(N) we save much more time due to this), |
| 1673 | # stripping them out of the multiplication, and add $count * $y zeros |
| 1674 | # afterwards like this: |
| 1675 | # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6 |
| 1676 | # creates deep recursion since brsft/blsft use bpow sometimes. |
| 1677 | # my $zeros = $x->_trailing_zeros(); |
| 1678 | # if ($zeros > 0) |
| 1679 | # { |
| 1680 | # $x->brsft($zeros,10); # remove zeros |
| 1681 | # $x->bpow($y); # recursion (will not branch into here again) |
| 1682 | # $zeros = $y * $zeros; # real number of zeros to add |
| 1683 | # $x->blsft($zeros,10); |
| 1684 | # return $x->round(@r); |
| 1685 | # } |
| 1686 | |
| 1687 | my $pow2 = $self->__one(); |
| 1688 | my $y_bin = $y->as_bin(); $y_bin =~ s/^0b//; |
| 1689 | my $len = length($y_bin); |
| 1690 | while (--$len > 0) |
| 1691 | { |
| 1692 | $pow2->bmul($x) if substr($y_bin,$len,1) eq '1'; # is odd? |
| 1693 | $x->bmul($x); |
| 1694 | } |
| 1695 | $x->bmul($pow2); |
| 1696 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 1697 | $x; |
| 1698 | } |
| 1699 | |
| 1700 | sub blsft |
| 1701 | { |
| 1702 | # (BINT or num_str, BINT or num_str) return BINT |
| 1703 | # compute x << y, base n, y >= 0 |
| 1704 | |
| 1705 | # set up parameters |
| 1706 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); |
| 1707 | # objectify is costly, so avoid it |
| 1708 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1709 | { |
| 1710 | ($self,$x,$y,$n,@r) = objectify(2,@_); |
| 1711 | } |
| 1712 | |
| 1713 | return $x if $x->modify('blsft'); |
| 1714 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
| 1715 | return $x->round(@r) if $y->is_zero(); |
| 1716 | |
| 1717 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
| 1718 | |
| 1719 | my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft'); |
| 1720 | if (defined $t) |
| 1721 | { |
| 1722 | $x->{value} = $t; return $x->round(@r); |
| 1723 | } |
| 1724 | # fallback |
| 1725 | return $x->bmul( $self->bpow($n, $y, @r), @r ); |
| 1726 | } |
| 1727 | |
| 1728 | sub brsft |
| 1729 | { |
| 1730 | # (BINT or num_str, BINT or num_str) return BINT |
| 1731 | # compute x >> y, base n, y >= 0 |
| 1732 | |
| 1733 | # set up parameters |
| 1734 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); |
| 1735 | # objectify is costly, so avoid it |
| 1736 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1737 | { |
| 1738 | ($self,$x,$y,$n,@r) = objectify(2,@_); |
| 1739 | } |
| 1740 | |
| 1741 | return $x if $x->modify('brsft'); |
| 1742 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
| 1743 | return $x->round(@r) if $y->is_zero(); |
| 1744 | return $x->bzero(@r) if $x->is_zero(); # 0 => 0 |
| 1745 | |
| 1746 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
| 1747 | |
| 1748 | # this only works for negative numbers when shifting in base 2 |
| 1749 | if (($x->{sign} eq '-') && ($n == 2)) |
| 1750 | { |
| 1751 | return $x->round(@r) if $x->is_one('-'); # -1 => -1 |
| 1752 | if (!$y->is_one()) |
| 1753 | { |
| 1754 | # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al |
| 1755 | # but perhaps there is a better emulation for two's complement shift... |
| 1756 | # if $y != 1, we must simulate it by doing: |
| 1757 | # convert to bin, flip all bits, shift, and be done |
| 1758 | $x->binc(); # -3 => -2 |
| 1759 | my $bin = $x->as_bin(); |
| 1760 | $bin =~ s/^-0b//; # strip '-0b' prefix |
| 1761 | $bin =~ tr/10/01/; # flip bits |
| 1762 | # now shift |
| 1763 | if (CORE::length($bin) <= $y) |
| 1764 | { |
| 1765 | $bin = '0'; # shifting to far right creates -1 |
| 1766 | # 0, because later increment makes |
| 1767 | # that 1, attached '-' makes it '-1' |
| 1768 | # because -1 >> x == -1 ! |
| 1769 | } |
| 1770 | else |
| 1771 | { |
| 1772 | $bin =~ s/.{$y}$//; # cut off at the right side |
| 1773 | $bin = '1' . $bin; # extend left side by one dummy '1' |
| 1774 | $bin =~ tr/10/01/; # flip bits back |
| 1775 | } |
| 1776 | my $res = $self->new('0b'.$bin); # add prefix and convert back |
| 1777 | $res->binc(); # remember to increment |
| 1778 | $x->{value} = $res->{value}; # take over value |
| 1779 | return $x->round(@r); # we are done now, magic, isn't? |
| 1780 | } |
| 1781 | $x->bdec(); # n == 2, but $y == 1: this fixes it |
| 1782 | } |
| 1783 | |
| 1784 | my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft'); |
| 1785 | if (defined $t) |
| 1786 | { |
| 1787 | $x->{value} = $t; |
| 1788 | return $x->round(@r); |
| 1789 | } |
| 1790 | # fallback |
| 1791 | $x->bdiv($self->bpow($n,$y, @r), @r); |
| 1792 | $x; |
| 1793 | } |
| 1794 | |
| 1795 | sub band |
| 1796 | { |
| 1797 | #(BINT or num_str, BINT or num_str) return BINT |
| 1798 | # compute x & y |
| 1799 | |
| 1800 | # set up parameters |
| 1801 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1802 | # objectify is costly, so avoid it |
| 1803 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1804 | { |
| 1805 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1806 | } |
| 1807 | |
| 1808 | return $x if $x->modify('band'); |
| 1809 | |
| 1810 | $r[3] = $y; # no push! |
| 1811 | local $Math::BigInt::upgrade = undef; |
| 1812 | |
| 1813 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
| 1814 | return $x->bzero(@r) if $y->is_zero() || $x->is_zero(); |
| 1815 | |
| 1816 | my $sign = 0; # sign of result |
| 1817 | $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-'); |
| 1818 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
| 1819 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
| 1820 | |
| 1821 | if ($CALC->can('_and') && $sx == 1 && $sy == 1) |
| 1822 | { |
| 1823 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
| 1824 | return $x->round(@r); |
| 1825 | } |
| 1826 | |
| 1827 | my $m = $self->bone(); my ($xr,$yr); |
| 1828 | my $x10000 = $self->new (0x1000); |
| 1829 | my $y1 = copy(ref($x),$y); # make copy |
| 1830 | $y1->babs(); # and positive |
| 1831 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
| 1832 | use integer; # need this for negative bools |
| 1833 | while (!$x1->is_zero() && !$y1->is_zero()) |
| 1834 | { |
| 1835 | ($x1, $xr) = bdiv($x1, $x10000); |
| 1836 | ($y1, $yr) = bdiv($y1, $x10000); |
| 1837 | # make both op's numbers! |
| 1838 | $x->badd( bmul( $class->new( |
| 1839 | abs($sx*int($xr->numify()) & $sy*int($yr->numify()))), |
| 1840 | $m)); |
| 1841 | $m->bmul($x10000); |
| 1842 | } |
| 1843 | $x->bneg() if $sign; |
| 1844 | $x->round(@r); |
| 1845 | } |
| 1846 | |
| 1847 | sub bior |
| 1848 | { |
| 1849 | #(BINT or num_str, BINT or num_str) return BINT |
| 1850 | # compute x | y |
| 1851 | |
| 1852 | # set up parameters |
| 1853 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1854 | # objectify is costly, so avoid it |
| 1855 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1856 | { |
| 1857 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1858 | } |
| 1859 | |
| 1860 | return $x if $x->modify('bior'); |
| 1861 | $r[3] = $y; # no push! |
| 1862 | |
| 1863 | local $Math::BigInt::upgrade = undef; |
| 1864 | |
| 1865 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
| 1866 | return $x->round(@r) if $y->is_zero(); |
| 1867 | |
| 1868 | my $sign = 0; # sign of result |
| 1869 | $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-'); |
| 1870 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
| 1871 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
| 1872 | |
| 1873 | # don't use lib for negative values |
| 1874 | if ($CALC->can('_or') && $sx == 1 && $sy == 1) |
| 1875 | { |
| 1876 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
| 1877 | return $x->round(@r); |
| 1878 | } |
| 1879 | |
| 1880 | my $m = $self->bone(); my ($xr,$yr); |
| 1881 | my $x10000 = $self->new(0x10000); |
| 1882 | my $y1 = copy(ref($x),$y); # make copy |
| 1883 | $y1->babs(); # and positive |
| 1884 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
| 1885 | use integer; # need this for negative bools |
| 1886 | while (!$x1->is_zero() || !$y1->is_zero()) |
| 1887 | { |
| 1888 | ($x1, $xr) = bdiv($x1,$x10000); |
| 1889 | ($y1, $yr) = bdiv($y1,$x10000); |
| 1890 | # make both op's numbers! |
| 1891 | $x->badd( bmul( $class->new( |
| 1892 | abs($sx*int($xr->numify()) | $sy*int($yr->numify()))), |
| 1893 | $m)); |
| 1894 | $m->bmul($x10000); |
| 1895 | } |
| 1896 | $x->bneg() if $sign; |
| 1897 | $x->round(@r); |
| 1898 | } |
| 1899 | |
| 1900 | sub bxor |
| 1901 | { |
| 1902 | #(BINT or num_str, BINT or num_str) return BINT |
| 1903 | # compute x ^ y |
| 1904 | |
| 1905 | # set up parameters |
| 1906 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1907 | # objectify is costly, so avoid it |
| 1908 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1909 | { |
| 1910 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1911 | } |
| 1912 | |
| 1913 | return $x if $x->modify('bxor'); |
| 1914 | $r[3] = $y; # no push! |
| 1915 | |
| 1916 | local $Math::BigInt::upgrade = undef; |
| 1917 | |
| 1918 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
| 1919 | return $x->round(@r) if $y->is_zero(); |
| 1920 | |
| 1921 | my $sign = 0; # sign of result |
| 1922 | $sign = 1 if $x->{sign} ne $y->{sign}; |
| 1923 | my $sx = 1; $sx = -1 if $x->{sign} eq '-'; |
| 1924 | my $sy = 1; $sy = -1 if $y->{sign} eq '-'; |
| 1925 | |
| 1926 | # don't use lib for negative values |
| 1927 | if ($CALC->can('_xor') && $sx == 1 && $sy == 1) |
| 1928 | { |
| 1929 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
| 1930 | return $x->round(@r); |
| 1931 | } |
| 1932 | |
| 1933 | my $m = $self->bone(); my ($xr,$yr); |
| 1934 | my $x10000 = $self->new(0x10000); |
| 1935 | my $y1 = copy(ref($x),$y); # make copy |
| 1936 | $y1->babs(); # and positive |
| 1937 | my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place! |
| 1938 | use integer; # need this for negative bools |
| 1939 | while (!$x1->is_zero() || !$y1->is_zero()) |
| 1940 | { |
| 1941 | ($x1, $xr) = bdiv($x1, $x10000); |
| 1942 | ($y1, $yr) = bdiv($y1, $x10000); |
| 1943 | # make both op's numbers! |
| 1944 | $x->badd( bmul( $class->new( |
| 1945 | abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))), |
| 1946 | $m)); |
| 1947 | $m->bmul($x10000); |
| 1948 | } |
| 1949 | $x->bneg() if $sign; |
| 1950 | $x->round(@r); |
| 1951 | } |
| 1952 | |
| 1953 | sub length |
| 1954 | { |
| 1955 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 1956 | |
| 1957 | my $e = $CALC->_len($x->{value}); |
| 1958 | return wantarray ? ($e,0) : $e; |
| 1959 | } |
| 1960 | |
| 1961 | sub digit |
| 1962 | { |
| 1963 | # return the nth decimal digit, negative values count backward, 0 is right |
| 1964 | my ($self,$x,$n) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1965 | |
| 1966 | $CALC->_digit($x->{value},$n||0); |
| 1967 | } |
| 1968 | |
| 1969 | sub _trailing_zeros |
| 1970 | { |
| 1971 | # return the amount of trailing zeros in $x |
| 1972 | my $x = shift; |
| 1973 | $x = $class->new($x) unless ref $x; |
| 1974 | |
| 1975 | return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/; |
| 1976 | |
| 1977 | return $CALC->_zeros($x->{value}) if $CALC->can('_zeros'); |
| 1978 | |
| 1979 | # if not: since we do not know underlying internal representation: |
| 1980 | my $es = "$x"; $es =~ /([0]*)$/; |
| 1981 | return 0 if !defined $1; # no zeros |
| 1982 | CORE::length("$1"); # as string, not as +0! |
| 1983 | } |
| 1984 | |
| 1985 | sub bsqrt |
| 1986 | { |
| 1987 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1988 | |
| 1989 | return $x if $x->modify('bsqrt'); |
| 1990 | |
| 1991 | return $x->bnan() if $x->{sign} ne '+'; # -x or inf or NaN => NaN |
| 1992 | return $x->bzero(@r) if $x->is_zero(); # 0 => 0 |
| 1993 | return $x->round(@r) if $x->is_one(); # 1 => 1 |
| 1994 | |
| 1995 | return $upgrade->bsqrt($x,@r) if defined $upgrade; |
| 1996 | |
| 1997 | if ($CALC->can('_sqrt')) |
| 1998 | { |
| 1999 | $x->{value} = $CALC->_sqrt($x->{value}); |
| 2000 | return $x->round(@r); |
| 2001 | } |
| 2002 | |
| 2003 | return $x->bone('+',@r) if $x < 4; # 2,3 => 1 |
| 2004 | my $y = $x->copy(); |
| 2005 | my $l = int($x->length()/2); |
| 2006 | |
| 2007 | $x->bone(); # keep ref($x), but modify it |
| 2008 | $x->blsft($l,10); |
| 2009 | |
| 2010 | my $last = $self->bzero(); |
| 2011 | my $two = $self->new(2); |
| 2012 | my $lastlast = $x+$two; |
| 2013 | while ($last != $x && $lastlast != $x) |
| 2014 | { |
| 2015 | $lastlast = $last; $last = $x; |
| 2016 | $x += $y / $x; |
| 2017 | $x /= $two; |
| 2018 | } |
| 2019 | $x-- if $x * $x > $y; # overshot? |
| 2020 | $x->round(@r); |
| 2021 | } |
| 2022 | |
| 2023 | sub exponent |
| 2024 | { |
| 2025 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) |
| 2026 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 2027 | |
| 2028 | if ($x->{sign} !~ /^[+-]$/) |
| 2029 | { |
| 2030 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
| 2031 | return $self->new($s); # -inf,+inf => inf |
| 2032 | } |
| 2033 | my $e = $class->bzero(); |
| 2034 | return $e->binc() if $x->is_zero(); |
| 2035 | $e += $x->_trailing_zeros(); |
| 2036 | $e; |
| 2037 | } |
| 2038 | |
| 2039 | sub mantissa |
| 2040 | { |
| 2041 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
| 2042 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 2043 | |
| 2044 | if ($x->{sign} !~ /^[+-]$/) |
| 2045 | { |
| 2046 | return $self->new($x->{sign}); # keep + or - sign |
| 2047 | } |
| 2048 | my $m = $x->copy(); |
| 2049 | # that's inefficient |
| 2050 | my $zeros = $m->_trailing_zeros(); |
| 2051 | $m->brsft($zeros,10) if $zeros != 0; |
| 2052 | $m; |
| 2053 | } |
| 2054 | |
| 2055 | sub parts |
| 2056 | { |
| 2057 | # return a copy of both the exponent and the mantissa |
| 2058 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 2059 | |
| 2060 | return ($x->mantissa(),$x->exponent()); |
| 2061 | } |
| 2062 | |
| 2063 | ############################################################################## |
| 2064 | # rounding functions |
| 2065 | |
| 2066 | sub bfround |
| 2067 | { |
| 2068 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
| 2069 | # $n == 0 || $n == 1 => round to integer |
| 2070 | my $x = shift; $x = $class->new($x) unless ref $x; |
| 2071 | my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_); |
| 2072 | return $x if !defined $scale; # no-op |
| 2073 | return $x if $x->modify('bfround'); |
| 2074 | |
| 2075 | # no-op for BigInts if $n <= 0 |
| 2076 | if ($scale <= 0) |
| 2077 | { |
| 2078 | $x->{_a} = undef; # clear an eventual set A |
| 2079 | $x->{_p} = $scale; return $x; |
| 2080 | } |
| 2081 | |
| 2082 | $x->bround( $x->length()-$scale, $mode); |
| 2083 | $x->{_a} = undef; # bround sets {_a} |
| 2084 | $x->{_p} = $scale; # so correct it |
| 2085 | $x; |
| 2086 | } |
| 2087 | |
| 2088 | sub _scan_for_nonzero |
| 2089 | { |
| 2090 | my $x = shift; |
| 2091 | my $pad = shift; |
| 2092 | my $xs = shift; |
| 2093 | |
| 2094 | my $len = $x->length(); |
| 2095 | return 0 if $len == 1; # '5' is trailed by invisible zeros |
| 2096 | my $follow = $pad - 1; |
| 2097 | return 0 if $follow > $len || $follow < 1; |
| 2098 | |
| 2099 | # since we do not know underlying represention of $x, use decimal string |
| 2100 | #my $r = substr ($$xs,-$follow); |
| 2101 | my $r = substr ("$x",-$follow); |
| 2102 | return 1 if $r =~ /[^0]/; |
| 2103 | 0; |
| 2104 | } |
| 2105 | |
| 2106 | sub fround |
| 2107 | { |
| 2108 | # to make life easier for switch between MBF and MBI (autoload fxxx() |
| 2109 | # like MBF does for bxxx()?) |
| 2110 | my $x = shift; |
| 2111 | return $x->bround(@_); |
| 2112 | } |
| 2113 | |
| 2114 | sub bround |
| 2115 | { |
| 2116 | # accuracy: +$n preserve $n digits from left, |
| 2117 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) |
| 2118 | # no-op for $n == 0 |
| 2119 | # and overwrite the rest with 0's, return normalized number |
| 2120 | # do not return $x->bnorm(), but $x |
| 2121 | |
| 2122 | my $x = shift; $x = $class->new($x) unless ref $x; |
| 2123 | my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_); |
| 2124 | return $x if !defined $scale; # no-op |
| 2125 | return $x if $x->modify('bround'); |
| 2126 | |
| 2127 | if ($x->is_zero() || $scale == 0) |
| 2128 | { |
| 2129 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
| 2130 | return $x; |
| 2131 | } |
| 2132 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN |
| 2133 | |
| 2134 | # we have fewer digits than we want to scale to |
| 2135 | my $len = $x->length(); |
| 2136 | # scale < 0, but > -len (not >=!) |
| 2137 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) |
| 2138 | { |
| 2139 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
| 2140 | return $x; |
| 2141 | } |
| 2142 | |
| 2143 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 |
| 2144 | my ($pad,$digit_round,$digit_after); |
| 2145 | $pad = $len - $scale; |
| 2146 | $pad = abs($scale-1) if $scale < 0; |
| 2147 | |
| 2148 | # do not use digit(), it is costly for binary => decimal |
| 2149 | |
| 2150 | my $xs = $CALC->_str($x->{value}); |
| 2151 | my $pl = -$pad-1; |
| 2152 | |
| 2153 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
| 2154 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 |
| 2155 | $digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len; |
| 2156 | $pl++; $pl ++ if $pad >= $len; |
| 2157 | $digit_after = '0'; $digit_after = substr($$xs,$pl,1) if $pad > 0; |
| 2158 | |
| 2159 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look |
| 2160 | # closer at the remaining digits of the original $x, remember decision |
| 2161 | my $round_up = 1; # default round up |
| 2162 | $round_up -- if |
| 2163 | ($mode eq 'trunc') || # trunc by round down |
| 2164 | ($digit_after =~ /[01234]/) || # round down anyway, |
| 2165 | # 6789 => round up |
| 2166 | ($digit_after eq '5') && # not 5000...0000 |
| 2167 | ($x->_scan_for_nonzero($pad,$xs) == 0) && |
| 2168 | ( |
| 2169 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || |
| 2170 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || |
| 2171 | ($mode eq '+inf') && ($x->{sign} eq '-') || |
| 2172 | ($mode eq '-inf') && ($x->{sign} eq '+') || |
| 2173 | ($mode eq 'zero') # round down if zero, sign adjusted below |
| 2174 | ); |
| 2175 | my $put_back = 0; # not yet modified |
| 2176 | |
| 2177 | if (($pad > 0) && ($pad <= $len)) |
| 2178 | { |
| 2179 | substr($$xs,-$pad,$pad) = '0' x $pad; |
| 2180 | $put_back = 1; |
| 2181 | } |
| 2182 | elsif ($pad > $len) |
| 2183 | { |
| 2184 | $x->bzero(); # round to '0' |
| 2185 | } |
| 2186 | |
| 2187 | if ($round_up) # what gave test above? |
| 2188 | { |
| 2189 | $put_back = 1; |
| 2190 | $pad = $len, $$xs = '0'x$pad if $scale < 0; # tlr: whack 0.51=>1.0 |
| 2191 | |
| 2192 | # we modify directly the string variant instead of creating a number and |
| 2193 | # adding it, since that is faster (we already have the string) |
| 2194 | my $c = 0; $pad ++; # for $pad == $len case |
| 2195 | while ($pad <= $len) |
| 2196 | { |
| 2197 | $c = substr($$xs,-$pad,1) + 1; $c = '0' if $c eq '10'; |
| 2198 | substr($$xs,-$pad,1) = $c; $pad++; |
| 2199 | last if $c != 0; # no overflow => early out |
| 2200 | } |
| 2201 | $$xs = '1'.$$xs if $c == 0; |
| 2202 | |
| 2203 | } |
| 2204 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back in if needed |
| 2205 | |
| 2206 | $x->{_a} = $scale if $scale >= 0; |
| 2207 | if ($scale < 0) |
| 2208 | { |
| 2209 | $x->{_a} = $len+$scale; |
| 2210 | $x->{_a} = 0 if $scale < -$len; |
| 2211 | } |
| 2212 | $x; |
| 2213 | } |
| 2214 | |
| 2215 | sub bfloor |
| 2216 | { |
| 2217 | # return integer less or equal then number, since it is already integer, |
| 2218 | # always returns $self |
| 2219 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 2220 | |
| 2221 | $x->round(@r); |
| 2222 | } |
| 2223 | |
| 2224 | sub bceil |
| 2225 | { |
| 2226 | # return integer greater or equal then number, since it is already integer, |
| 2227 | # always returns $self |
| 2228 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 2229 | |
| 2230 | $x->round(@r); |
| 2231 | } |
| 2232 | |
| 2233 | ############################################################################## |
| 2234 | # private stuff (internal use only) |
| 2235 | |
| 2236 | sub __one |
| 2237 | { |
| 2238 | # internal speedup, set argument to 1, or create a +/- 1 |
| 2239 | my $self = shift; |
| 2240 | my $x = $self->bone(); # $x->{value} = $CALC->_one(); |
| 2241 | $x->{sign} = shift || '+'; |
| 2242 | $x; |
| 2243 | } |
| 2244 | |
| 2245 | sub _swap |
| 2246 | { |
| 2247 | # Overload will swap params if first one is no object ref so that the first |
| 2248 | # one is always an object ref. In this case, third param is true. |
| 2249 | # This routine is to overcome the effect of scalar,$object creating an object |
| 2250 | # of the class of this package, instead of the second param $object. This |
| 2251 | # happens inside overload, when the overload section of this package is |
| 2252 | # inherited by sub classes. |
| 2253 | # For overload cases (and this is used only there), we need to preserve the |
| 2254 | # args, hence the copy(). |
| 2255 | # You can override this method in a subclass, the overload section will call |
| 2256 | # $object->_swap() to make sure it arrives at the proper subclass, with some |
| 2257 | # exceptions like '+' and '-'. To make '+' and '-' work, you also need to |
| 2258 | # specify your own overload for them. |
| 2259 | |
| 2260 | # object, (object|scalar) => preserve first and make copy |
| 2261 | # scalar, object => swapped, re-swap and create new from first |
| 2262 | # (using class of second object, not $class!!) |
| 2263 | my $self = shift; # for override in subclass |
| 2264 | if ($_[2]) |
| 2265 | { |
| 2266 | my $c = ref ($_[0]) || $class; # fallback $class should not happen |
| 2267 | return ( $c->new($_[1]), $_[0] ); |
| 2268 | } |
| 2269 | return ( $_[0]->copy(), $_[1] ); |
| 2270 | } |
| 2271 | |
| 2272 | sub objectify |
| 2273 | { |
| 2274 | # check for strings, if yes, return objects instead |
| 2275 | |
| 2276 | # the first argument is number of args objectify() should look at it will |
| 2277 | # return $count+1 elements, the first will be a classname. This is because |
| 2278 | # overloaded '""' calls bstr($object,undef,undef) and this would result in |
| 2279 | # useless objects beeing created and thrown away. So we cannot simple loop |
| 2280 | # over @_. If the given count is 0, all arguments will be used. |
| 2281 | |
| 2282 | # If the second arg is a ref, use it as class. |
| 2283 | # If not, try to use it as classname, unless undef, then use $class |
| 2284 | # (aka Math::BigInt). The latter shouldn't happen,though. |
| 2285 | |
| 2286 | # caller: gives us: |
| 2287 | # $x->badd(1); => ref x, scalar y |
| 2288 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y |
| 2289 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y |
| 2290 | # Math::BigInt::badd(1,2); => scalar x, scalar y |
| 2291 | # In the last case we check number of arguments to turn it silently into |
| 2292 | # $class,1,2. (We can not take '1' as class ;o) |
| 2293 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
| 2294 | # currently it tries 'Math::BigInt' + 1, which will not work. |
| 2295 | |
| 2296 | # some shortcut for the common cases |
| 2297 | # $x->unary_op(); |
| 2298 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); |
| 2299 | |
| 2300 | my $count = abs(shift || 0); |
| 2301 | |
| 2302 | my (@a,$k,$d); # resulting array, temp, and downgrade |
| 2303 | if (ref $_[0]) |
| 2304 | { |
| 2305 | # okay, got object as first |
| 2306 | $a[0] = ref $_[0]; |
| 2307 | } |
| 2308 | else |
| 2309 | { |
| 2310 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) |
| 2311 | $a[0] = $class; |
| 2312 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
| 2313 | } |
| 2314 | |
| 2315 | no strict 'refs'; |
| 2316 | # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats |
| 2317 | if (defined ${"$a[0]::downgrade"}) |
| 2318 | { |
| 2319 | $d = ${"$a[0]::downgrade"}; |
| 2320 | ${"$a[0]::downgrade"} = undef; |
| 2321 | } |
| 2322 | |
| 2323 | my $up = ${"$a[0]::upgrade"}; |
| 2324 | # print "Now in objectify, my class is today $a[0]\n"; |
| 2325 | if ($count == 0) |
| 2326 | { |
| 2327 | while (@_) |
| 2328 | { |
| 2329 | $k = shift; |
| 2330 | if (!ref($k)) |
| 2331 | { |
| 2332 | $k = $a[0]->new($k); |
| 2333 | } |
| 2334 | elsif (!defined $up && ref($k) ne $a[0]) |
| 2335 | { |
| 2336 | # foreign object, try to convert to integer |
| 2337 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
| 2338 | } |
| 2339 | push @a,$k; |
| 2340 | } |
| 2341 | } |
| 2342 | else |
| 2343 | { |
| 2344 | while ($count > 0) |
| 2345 | { |
| 2346 | $count--; |
| 2347 | $k = shift; |
| 2348 | if (!ref($k)) |
| 2349 | { |
| 2350 | $k = $a[0]->new($k); |
| 2351 | } |
| 2352 | elsif (!defined $up && ref($k) ne $a[0]) |
| 2353 | { |
| 2354 | # foreign object, try to convert to integer |
| 2355 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); |
| 2356 | } |
| 2357 | push @a,$k; |
| 2358 | } |
| 2359 | push @a,@_; # return other params, too |
| 2360 | } |
| 2361 | die "$class objectify needs list context" unless wantarray; |
| 2362 | ${"$a[0]::downgrade"} = $d; |
| 2363 | @a; |
| 2364 | } |
| 2365 | |
| 2366 | sub import |
| 2367 | { |
| 2368 | my $self = shift; |
| 2369 | |
| 2370 | $IMPORT++; |
| 2371 | my @a; my $l = scalar @_; |
| 2372 | for ( my $i = 0; $i < $l ; $i++ ) |
| 2373 | { |
| 2374 | if ($_[$i] eq ':constant') |
| 2375 | { |
| 2376 | # this causes overlord er load to step in |
| 2377 | overload::constant integer => sub { $self->new(shift) }; |
| 2378 | overload::constant binary => sub { $self->new(shift) }; |
| 2379 | } |
| 2380 | elsif ($_[$i] eq 'upgrade') |
| 2381 | { |
| 2382 | # this causes upgrading |
| 2383 | $upgrade = $_[$i+1]; # or undef to disable |
| 2384 | $i++; |
| 2385 | } |
| 2386 | elsif ($_[$i] =~ /^lib$/i) |
| 2387 | { |
| 2388 | # this causes a different low lib to take care... |
| 2389 | $CALC = $_[$i+1] || ''; |
| 2390 | $i++; |
| 2391 | } |
| 2392 | else |
| 2393 | { |
| 2394 | push @a, $_[$i]; |
| 2395 | } |
| 2396 | } |
| 2397 | # any non :constant stuff is handled by our parent, Exporter |
| 2398 | # even if @_ is empty, to give it a chance |
| 2399 | $self->SUPER::import(@a); # need it for subclasses |
| 2400 | $self->export_to_level(1,$self,@a); # need it for MBF |
| 2401 | |
| 2402 | # try to load core math lib |
| 2403 | my @c = split /\s*,\s*/,$CALC; |
| 2404 | push @c,'Calc'; # if all fail, try this |
| 2405 | $CALC = ''; # signal error |
| 2406 | foreach my $lib (@c) |
| 2407 | { |
| 2408 | next if ($lib || '') eq ''; |
| 2409 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
| 2410 | $lib =~ s/\.pm$//; |
| 2411 | if ($] < 5.006) |
| 2412 | { |
| 2413 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
| 2414 | # used in the same script, or eval inside import(). |
| 2415 | my @parts = split /::/, $lib; # Math::BigInt => Math BigInt |
| 2416 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm |
| 2417 | require File::Spec; |
| 2418 | $file = File::Spec->catfile (@parts, $file); |
| 2419 | eval { require "$file"; $lib->import( @c ); } |
| 2420 | } |
| 2421 | else |
| 2422 | { |
| 2423 | eval "use $lib qw/@c/;"; |
| 2424 | } |
| 2425 | $CALC = $lib, last if $@ eq ''; # no error in loading lib? |
| 2426 | } |
| 2427 | die "Couldn't load any math lib, not even the default" if $CALC eq ''; |
| 2428 | } |
| 2429 | |
| 2430 | sub __from_hex |
| 2431 | { |
| 2432 | # convert a (ref to) big hex string to BigInt, return undef for error |
| 2433 | my $hs = shift; |
| 2434 | |
| 2435 | my $x = Math::BigInt->bzero(); |
| 2436 | |
| 2437 | # strip underscores |
| 2438 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
| 2439 | $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
| 2440 | |
| 2441 | return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
| 2442 | |
| 2443 | my $sign = '+'; $sign = '-' if ($$hs =~ /^-/); |
| 2444 | |
| 2445 | $$hs =~ s/^[+-]//; # strip sign |
| 2446 | if ($CALC->can('_from_hex')) |
| 2447 | { |
| 2448 | $x->{value} = $CALC->_from_hex($hs); |
| 2449 | } |
| 2450 | else |
| 2451 | { |
| 2452 | # fallback to pure perl |
| 2453 | my $mul = Math::BigInt->bzero(); $mul++; |
| 2454 | my $x65536 = Math::BigInt->new(65536); |
| 2455 | my $len = CORE::length($$hs)-2; |
| 2456 | $len = int($len/4); # 4-digit parts, w/o '0x' |
| 2457 | my $val; my $i = -4; |
| 2458 | while ($len >= 0) |
| 2459 | { |
| 2460 | $val = substr($$hs,$i,4); |
| 2461 | $val =~ s/^[+-]?0x// if $len == 0; # for last part only because |
| 2462 | $val = hex($val); # hex does not like wrong chars |
| 2463 | $i -= 4; $len --; |
| 2464 | $x += $mul * $val if $val != 0; |
| 2465 | $mul *= $x65536 if $len >= 0; # skip last mul |
| 2466 | } |
| 2467 | } |
| 2468 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
| 2469 | $x; |
| 2470 | } |
| 2471 | |
| 2472 | sub __from_bin |
| 2473 | { |
| 2474 | # convert a (ref to) big binary string to BigInt, return undef for error |
| 2475 | my $bs = shift; |
| 2476 | |
| 2477 | my $x = Math::BigInt->bzero(); |
| 2478 | # strip underscores |
| 2479 | $$bs =~ s/([01])_([01])/$1$2/g; |
| 2480 | $$bs =~ s/([01])_([01])/$1$2/g; |
| 2481 | return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/; |
| 2482 | |
| 2483 | my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/); |
| 2484 | $$bs =~ s/^[+-]//; # strip sign |
| 2485 | if ($CALC->can('_from_bin')) |
| 2486 | { |
| 2487 | $x->{value} = $CALC->_from_bin($bs); |
| 2488 | } |
| 2489 | else |
| 2490 | { |
| 2491 | my $mul = Math::BigInt->bzero(); $mul++; |
| 2492 | my $x256 = Math::BigInt->new(256); |
| 2493 | my $len = CORE::length($$bs)-2; |
| 2494 | $len = int($len/8); # 8-digit parts, w/o '0b' |
| 2495 | my $val; my $i = -8; |
| 2496 | while ($len >= 0) |
| 2497 | { |
| 2498 | $val = substr($$bs,$i,8); |
| 2499 | $val =~ s/^[+-]?0b// if $len == 0; # for last part only |
| 2500 | #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0 |
| 2501 | # slower: |
| 2502 | # $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8; |
| 2503 | $val = ord(pack('B8',substr('00000000'.$val,-8,8))); |
| 2504 | $i -= 8; $len --; |
| 2505 | $x += $mul * $val if $val != 0; |
| 2506 | $mul *= $x256 if $len >= 0; # skip last mul |
| 2507 | } |
| 2508 | } |
| 2509 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
| 2510 | $x; |
| 2511 | } |
| 2512 | |
| 2513 | sub _split |
| 2514 | { |
| 2515 | # (ref to num_str) return num_str |
| 2516 | # internal, take apart a string and return the pieces |
| 2517 | # strip leading/trailing whitespace, leading zeros, underscore and reject |
| 2518 | # invalid input |
| 2519 | my $x = shift; |
| 2520 | |
| 2521 | # strip white space at front, also extranous leading zeros |
| 2522 | $$x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' |
| 2523 | $$x =~ s/^\s+//; # but this will |
| 2524 | $$x =~ s/\s+$//g; # strip white space at end |
| 2525 | |
| 2526 | # shortcut, if nothing to split, return early |
| 2527 | if ($$x =~ /^[+-]?\d+\z/) |
| 2528 | { |
| 2529 | $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; |
| 2530 | return (\$sign, $x, \'', \'', \0); |
| 2531 | } |
| 2532 | |
| 2533 | # invalid starting char? |
| 2534 | return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; |
| 2535 | |
| 2536 | return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string |
| 2537 | return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string |
| 2538 | |
| 2539 | # strip underscores between digits |
| 2540 | $$x =~ s/(\d)_(\d)/$1$2/g; |
| 2541 | $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 |
| 2542 | |
| 2543 | # some possible inputs: |
| 2544 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 |
| 2545 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 |
| 2546 | |
| 2547 | return if $$x =~ /[Ee].*[Ee]/; # more than one E => error |
| 2548 | |
| 2549 | my ($m,$e) = split /[Ee]/,$$x; |
| 2550 | $e = '0' if !defined $e || $e eq ""; |
| 2551 | # sign,value for exponent,mantint,mantfrac |
| 2552 | my ($es,$ev,$mis,$miv,$mfv); |
| 2553 | # valid exponent? |
| 2554 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
| 2555 | { |
| 2556 | $es = $1; $ev = $2; |
| 2557 | # valid mantissa? |
| 2558 | return if $m eq '.' || $m eq ''; |
| 2559 | my ($mi,$mf,$last) = split /\./,$m; |
| 2560 | return if defined $last; # last defined => 1.2.3 or others |
| 2561 | $mi = '0' if !defined $mi; |
| 2562 | $mi .= '0' if $mi =~ /^[\-\+]?$/; |
| 2563 | $mf = '0' if !defined $mf || $mf eq ''; |
| 2564 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros |
| 2565 | { |
| 2566 | $mis = $1||'+'; $miv = $2; |
| 2567 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros |
| 2568 | $mfv = $1; |
| 2569 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
| 2570 | } |
| 2571 | } |
| 2572 | return; # NaN, not a number |
| 2573 | } |
| 2574 | |
| 2575 | sub as_number |
| 2576 | { |
| 2577 | # an object might be asked to return itself as bigint on certain overloaded |
| 2578 | # operations, this does exactly this, so that sub classes can simple inherit |
| 2579 | # it or override with their own integer conversion routine |
| 2580 | my $self = shift; |
| 2581 | |
| 2582 | $self->copy(); |
| 2583 | } |
| 2584 | |
| 2585 | sub as_hex |
| 2586 | { |
| 2587 | # return as hex string, with prefixed 0x |
| 2588 | my $x = shift; $x = $class->new($x) if !ref($x); |
| 2589 | |
| 2590 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
| 2591 | return '0x0' if $x->is_zero(); |
| 2592 | |
| 2593 | my $es = ''; my $s = ''; |
| 2594 | $s = $x->{sign} if $x->{sign} eq '-'; |
| 2595 | if ($CALC->can('_as_hex')) |
| 2596 | { |
| 2597 | $es = ${$CALC->_as_hex($x->{value})}; |
| 2598 | } |
| 2599 | else |
| 2600 | { |
| 2601 | my $x1 = $x->copy()->babs(); my ($xr,$x10000,$h); |
| 2602 | if ($] >= 5.006) |
| 2603 | { |
| 2604 | $x10000 = Math::BigInt->new (0x10000); $h = 'h4'; |
| 2605 | } |
| 2606 | else |
| 2607 | { |
| 2608 | $x10000 = Math::BigInt->new (0x1000); $h = 'h3'; |
| 2609 | } |
| 2610 | while (!$x1->is_zero()) |
| 2611 | { |
| 2612 | ($x1, $xr) = bdiv($x1,$x10000); |
| 2613 | $es .= unpack($h,pack('v',$xr->numify())); |
| 2614 | } |
| 2615 | $es = reverse $es; |
| 2616 | $es =~ s/^[0]+//; # strip leading zeros |
| 2617 | $s .= '0x'; |
| 2618 | } |
| 2619 | $s . $es; |
| 2620 | } |
| 2621 | |
| 2622 | sub as_bin |
| 2623 | { |
| 2624 | # return as binary string, with prefixed 0b |
| 2625 | my $x = shift; $x = $class->new($x) if !ref($x); |
| 2626 | |
| 2627 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
| 2628 | return '0b0' if $x->is_zero(); |
| 2629 | |
| 2630 | my $es = ''; my $s = ''; |
| 2631 | $s = $x->{sign} if $x->{sign} eq '-'; |
| 2632 | if ($CALC->can('_as_bin')) |
| 2633 | { |
| 2634 | $es = ${$CALC->_as_bin($x->{value})}; |
| 2635 | } |
| 2636 | else |
| 2637 | { |
| 2638 | my $x1 = $x->copy()->babs(); my ($xr,$x10000,$b); |
| 2639 | if ($] >= 5.006) |
| 2640 | { |
| 2641 | $x10000 = Math::BigInt->new (0x10000); $b = 'b16'; |
| 2642 | } |
| 2643 | else |
| 2644 | { |
| 2645 | $x10000 = Math::BigInt->new (0x1000); $b = 'b12'; |
| 2646 | } |
| 2647 | while (!$x1->is_zero()) |
| 2648 | { |
| 2649 | ($x1, $xr) = bdiv($x1,$x10000); |
| 2650 | $es .= unpack($b,pack('v',$xr->numify())); |
| 2651 | } |
| 2652 | $es = reverse $es; |
| 2653 | $es =~ s/^[0]+//; # strip leading zeros |
| 2654 | $s .= '0b'; |
| 2655 | } |
| 2656 | $s . $es; |
| 2657 | } |
| 2658 | |
| 2659 | ############################################################################## |
| 2660 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
| 2661 | |
| 2662 | sub __lcm |
| 2663 | { |
| 2664 | # (BINT or num_str, BINT or num_str) return BINT |
| 2665 | # does modify first argument |
| 2666 | # LCM |
| 2667 | |
| 2668 | my $x = shift; my $ty = shift; |
| 2669 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); |
| 2670 | return $x * $ty / bgcd($x,$ty); |
| 2671 | } |
| 2672 | |
| 2673 | sub __gcd |
| 2674 | { |
| 2675 | # (BINT or num_str, BINT or num_str) return BINT |
| 2676 | # does modify both arguments |
| 2677 | # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296 |
| 2678 | my ($x,$ty) = @_; |
| 2679 | |
| 2680 | return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/; |
| 2681 | |
| 2682 | while (!$ty->is_zero()) |
| 2683 | { |
| 2684 | ($x, $ty) = ($ty,bmod($x,$ty)); |
| 2685 | } |
| 2686 | $x; |
| 2687 | } |
| 2688 | |
| 2689 | ############################################################################### |
| 2690 | # this method return 0 if the object can be modified, or 1 for not |
| 2691 | # We use a fast use constant statement here, to avoid costly calls. Subclasses |
| 2692 | # may override it with special code (f.i. Math::BigInt::Constant does so) |
| 2693 | |
| 2694 | sub modify () { 0; } |
| 2695 | |
| 2696 | 1; |
| 2697 | __END__ |
| 2698 | |
| 2699 | =head1 NAME |
| 2700 | |
| 2701 | Math::BigInt - Arbitrary size integer math package |
| 2702 | |
| 2703 | =head1 SYNOPSIS |
| 2704 | |
| 2705 | use Math::BigInt; |
| 2706 | |
| 2707 | # Number creation |
| 2708 | $x = Math::BigInt->new($str); # defaults to 0 |
| 2709 | $nan = Math::BigInt->bnan(); # create a NotANumber |
| 2710 | $zero = Math::BigInt->bzero(); # create a +0 |
| 2711 | $inf = Math::BigInt->binf(); # create a +inf |
| 2712 | $inf = Math::BigInt->binf('-'); # create a -inf |
| 2713 | $one = Math::BigInt->bone(); # create a +1 |
| 2714 | $one = Math::BigInt->bone('-'); # create a -1 |
| 2715 | |
| 2716 | # Testing |
| 2717 | $x->is_zero(); # true if arg is +0 |
| 2718 | $x->is_nan(); # true if arg is NaN |
| 2719 | $x->is_one(); # true if arg is +1 |
| 2720 | $x->is_one('-'); # true if arg is -1 |
| 2721 | $x->is_odd(); # true if odd, false for even |
| 2722 | $x->is_even(); # true if even, false for odd |
| 2723 | $x->is_positive(); # true if >= 0 |
| 2724 | $x->is_negative(); # true if < 0 |
| 2725 | $x->is_inf(sign); # true if +inf, or -inf (sign is default '+') |
| 2726 | $x->is_int(); # true if $x is an integer (not a float) |
| 2727 | |
| 2728 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
| 2729 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
| 2730 | $x->sign(); # return the sign, either +,- or NaN |
| 2731 | $x->digit($n); # return the nth digit, counting from right |
| 2732 | $x->digit(-$n); # return the nth digit, counting from left |
| 2733 | |
| 2734 | # The following all modify their first argument: |
| 2735 | |
| 2736 | # set |
| 2737 | $x->bzero(); # set $x to 0 |
| 2738 | $x->bnan(); # set $x to NaN |
| 2739 | $x->bone(); # set $x to +1 |
| 2740 | $x->bone('-'); # set $x to -1 |
| 2741 | $x->binf(); # set $x to inf |
| 2742 | $x->binf('-'); # set $x to -inf |
| 2743 | |
| 2744 | $x->bneg(); # negation |
| 2745 | $x->babs(); # absolute value |
| 2746 | $x->bnorm(); # normalize (no-op) |
| 2747 | $x->bnot(); # two's complement (bit wise not) |
| 2748 | $x->binc(); # increment x by 1 |
| 2749 | $x->bdec(); # decrement x by 1 |
| 2750 | |
| 2751 | $x->badd($y); # addition (add $y to $x) |
| 2752 | $x->bsub($y); # subtraction (subtract $y from $x) |
| 2753 | $x->bmul($y); # multiplication (multiply $x by $y) |
| 2754 | $x->bdiv($y); # divide, set $x to quotient |
| 2755 | # return (quo,rem) or quo if scalar |
| 2756 | |
| 2757 | $x->bmod($y); # modulus (x % y) |
| 2758 | $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod)) |
| 2759 | $x->bmodinv($mod); # the inverse of $x in the given modulus $mod |
| 2760 | |
| 2761 | $x->bpow($y); # power of arguments (x ** y) |
| 2762 | $x->blsft($y); # left shift |
| 2763 | $x->brsft($y); # right shift |
| 2764 | $x->blsft($y,$n); # left shift, by base $n (like 10) |
| 2765 | $x->brsft($y,$n); # right shift, by base $n (like 10) |
| 2766 | |
| 2767 | $x->band($y); # bitwise and |
| 2768 | $x->bior($y); # bitwise inclusive or |
| 2769 | $x->bxor($y); # bitwise exclusive or |
| 2770 | $x->bnot(); # bitwise not (two's complement) |
| 2771 | |
| 2772 | $x->bsqrt(); # calculate square-root |
| 2773 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
| 2774 | |
| 2775 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r |
| 2776 | $x->bround($N); # accuracy: preserve $N digits |
| 2777 | $x->bfround($N); # round to $Nth digit, no-op for BigInts |
| 2778 | |
| 2779 | # The following do not modify their arguments in BigInt, but do in BigFloat: |
| 2780 | $x->bfloor(); # return integer less or equal than $x |
| 2781 | $x->bceil(); # return integer greater or equal than $x |
| 2782 | |
| 2783 | # The following do not modify their arguments: |
| 2784 | |
| 2785 | bgcd(@values); # greatest common divisor (no OO style) |
| 2786 | blcm(@values); # lowest common multiplicator (no OO style) |
| 2787 | |
| 2788 | $x->length(); # return number of digits in number |
| 2789 | ($x,$f) = $x->length(); # length of number and length of fraction part, |
| 2790 | # latter is always 0 digits long for BigInt's |
| 2791 | |
| 2792 | $x->exponent(); # return exponent as BigInt |
| 2793 | $x->mantissa(); # return (signed) mantissa as BigInt |
| 2794 | $x->parts(); # return (mantissa,exponent) as BigInt |
| 2795 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
| 2796 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) |
| 2797 | |
| 2798 | # conversation to string |
| 2799 | $x->bstr(); # normalized string |
| 2800 | $x->bsstr(); # normalized string in scientific notation |
| 2801 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
| 2802 | $x->as_bin(); # as signed binary string with prefixed 0b |
| 2803 | |
| 2804 | Math::BigInt->config(); # return hash containing configuration/version |
| 2805 | |
| 2806 | # precision and accuracy (see section about rounding for more) |
| 2807 | $x->precision(); # return P of $x (or global, if P of $x undef) |
| 2808 | $x->precision($n); # set P of $x to $n |
| 2809 | $x->accuracy(); # return A of $x (or global, if A of $x undef) |
| 2810 | $x->accuracy($n); # set A $x to $n |
| 2811 | |
| 2812 | Math::BigInt->precision(); # get/set global P for all BigInt objects |
| 2813 | Math::BigInt->accuracy(); # get/set global A for all BigInt objects |
| 2814 | |
| 2815 | =head1 DESCRIPTION |
| 2816 | |
| 2817 | All operators (inlcuding basic math operations) are overloaded if you |
| 2818 | declare your big integers as |
| 2819 | |
| 2820 | $i = new Math::BigInt '123_456_789_123_456_789'; |
| 2821 | |
| 2822 | Operations with overloaded operators preserve the arguments which is |
| 2823 | exactly what you expect. |
| 2824 | |
| 2825 | =over 2 |
| 2826 | |
| 2827 | =item Canonical notation |
| 2828 | |
| 2829 | Big integer values are strings of the form C</^[+-]\d+$/> with leading |
| 2830 | zeros suppressed. |
| 2831 | |
| 2832 | '-0' canonical value '-0', normalized '0' |
| 2833 | ' -123_123_123' canonical value '-123123123' |
| 2834 | '1_23_456_7890' canonical value '1234567890' |
| 2835 | |
| 2836 | =item Input |
| 2837 | |
| 2838 | Input values to these routines may be either Math::BigInt objects or |
| 2839 | strings of the form C</^[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>. |
| 2840 | |
| 2841 | You can include one underscore between any two digits. The input string may |
| 2842 | have leading and trailing whitespace, which will be ignored. In later |
| 2843 | versions, a more strict (no whitespace at all) or more lax (whitespace |
| 2844 | allowed everywhere) input checking will also be possible. |
| 2845 | |
| 2846 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. |
| 2847 | Non integer values result in NaN. |
| 2848 | |
| 2849 | Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results |
| 2850 | in 'NaN'. |
| 2851 | |
| 2852 | bnorm() on a BigInt object is now effectively a no-op, since the numbers |
| 2853 | are always stored in normalized form. On a string, it creates a BigInt |
| 2854 | object. |
| 2855 | |
| 2856 | =item Output |
| 2857 | |
| 2858 | Output values are BigInt objects (normalized), except for bstr(), which |
| 2859 | returns a string in normalized form. |
| 2860 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
| 2861 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
| 2862 | return either undef, <0, 0 or >0 and are suited for sort. |
| 2863 | |
| 2864 | =back |
| 2865 | |
| 2866 | =head1 METHODS |
| 2867 | |
| 2868 | Each of the methods below accepts three additional parameters. These arguments |
| 2869 | $A, $P and $R are accuracy, precision and round_mode. Please see more in the |
| 2870 | section about ACCURACY and ROUNDIND. |
| 2871 | |
| 2872 | =head2 config |
| 2873 | |
| 2874 | use Data::Dumper; |
| 2875 | |
| 2876 | print Dumper ( Math::BigInt->config() ); |
| 2877 | |
| 2878 | Returns a hash containing the configuration, e.g. the version number, lib |
| 2879 | loaded etc. |
| 2880 | |
| 2881 | =head2 accuracy |
| 2882 | |
| 2883 | $x->accuracy(5); # local for $x |
| 2884 | $class->accuracy(5); # global for all members of $class |
| 2885 | |
| 2886 | Set or get the global or local accuracy, aka how many significant digits the |
| 2887 | results have. Please see the section about L<ACCURACY AND PRECISION> for |
| 2888 | further details. |
| 2889 | |
| 2890 | Value must be greater than zero. Pass an undef value to disable it: |
| 2891 | |
| 2892 | $x->accuracy(undef); |
| 2893 | Math::BigInt->accuracy(undef); |
| 2894 | |
| 2895 | Returns the current accuracy. For C<$x->accuracy()> it will return either the |
| 2896 | local accuracy, or if not defined, the global. This means the return value |
| 2897 | represents the accuracy that will be in effect for $x: |
| 2898 | |
| 2899 | $y = Math::BigInt->new(1234567); # unrounded |
| 2900 | print Math::BigInt->accuracy(4),"\n"; # set 4, print 4 |
| 2901 | $x = Math::BigInt->new(123456); # will be automatically rounded |
| 2902 | print "$x $y\n"; # '123500 1234567' |
| 2903 | print $x->accuracy(),"\n"; # will be 4 |
| 2904 | print $y->accuracy(),"\n"; # also 4, since global is 4 |
| 2905 | print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5 |
| 2906 | print $x->accuracy(),"\n"; # still 4 |
| 2907 | print $y->accuracy(),"\n"; # 5, since global is 5 |
| 2908 | |
| 2909 | =head2 brsft |
| 2910 | |
| 2911 | $x->brsft($y,$n); |
| 2912 | |
| 2913 | Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and |
| 2914 | 2, but others work, too. |
| 2915 | |
| 2916 | Right shifting usually amounts to dividing $x by $n ** $y and truncating the |
| 2917 | result: |
| 2918 | |
| 2919 | |
| 2920 | $x = Math::BigInt->new(10); |
| 2921 | $x->brsft(1); # same as $x >> 1: 5 |
| 2922 | $x = Math::BigInt->new(1234); |
| 2923 | $x->brsft(2,10); # result 12 |
| 2924 | |
| 2925 | There is one exception, and that is base 2 with negative $x: |
| 2926 | |
| 2927 | |
| 2928 | $x = Math::BigInt->new(-5); |
| 2929 | print $x->brsft(1); |
| 2930 | |
| 2931 | This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the |
| 2932 | result). |
| 2933 | |
| 2934 | =head2 new |
| 2935 | |
| 2936 | $x = Math::BigInt->new($str,$A,$P,$R); |
| 2937 | |
| 2938 | Creates a new BigInt object from a string or another BigInt object. The |
| 2939 | input is accepted as decimal, hex (with leading '0x') or binary (with leading |
| 2940 | '0b'). |
| 2941 | |
| 2942 | =head2 bnan |
| 2943 | |
| 2944 | $x = Math::BigInt->bnan(); |
| 2945 | |
| 2946 | Creates a new BigInt object representing NaN (Not A Number). |
| 2947 | If used on an object, it will set it to NaN: |
| 2948 | |
| 2949 | $x->bnan(); |
| 2950 | |
| 2951 | =head2 bzero |
| 2952 | |
| 2953 | $x = Math::BigInt->bzero(); |
| 2954 | |
| 2955 | Creates a new BigInt object representing zero. |
| 2956 | If used on an object, it will set it to zero: |
| 2957 | |
| 2958 | $x->bzero(); |
| 2959 | |
| 2960 | =head2 binf |
| 2961 | |
| 2962 | $x = Math::BigInt->binf($sign); |
| 2963 | |
| 2964 | Creates a new BigInt object representing infinity. The optional argument is |
| 2965 | either '-' or '+', indicating whether you want infinity or minus infinity. |
| 2966 | If used on an object, it will set it to infinity: |
| 2967 | |
| 2968 | $x->binf(); |
| 2969 | $x->binf('-'); |
| 2970 | |
| 2971 | =head2 bone |
| 2972 | |
| 2973 | $x = Math::BigInt->binf($sign); |
| 2974 | |
| 2975 | Creates a new BigInt object representing one. The optional argument is |
| 2976 | either '-' or '+', indicating whether you want one or minus one. |
| 2977 | If used on an object, it will set it to one: |
| 2978 | |
| 2979 | $x->bone(); # +1 |
| 2980 | $x->bone('-'); # -1 |
| 2981 | |
| 2982 | =head2 is_one()/is_zero()/is_nan()/is_inf() |
| 2983 | |
| 2984 | |
| 2985 | $x->is_zero(); # true if arg is +0 |
| 2986 | $x->is_nan(); # true if arg is NaN |
| 2987 | $x->is_one(); # true if arg is +1 |
| 2988 | $x->is_one('-'); # true if arg is -1 |
| 2989 | $x->is_inf(); # true if +inf |
| 2990 | $x->is_inf('-'); # true if -inf (sign is default '+') |
| 2991 | |
| 2992 | These methods all test the BigInt for beeing one specific value and return |
| 2993 | true or false depending on the input. These are faster than doing something |
| 2994 | like: |
| 2995 | |
| 2996 | if ($x == 0) |
| 2997 | |
| 2998 | =head2 is_positive()/is_negative() |
| 2999 | |
| 3000 | $x->is_positive(); # true if >= 0 |
| 3001 | $x->is_negative(); # true if < 0 |
| 3002 | |
| 3003 | The methods return true if the argument is positive or negative, respectively. |
| 3004 | C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and |
| 3005 | C<-inf> is negative. A C<zero> is positive. |
| 3006 | |
| 3007 | These methods are only testing the sign, and not the value. |
| 3008 | |
| 3009 | =head2 is_odd()/is_even()/is_int() |
| 3010 | |
| 3011 | $x->is_odd(); # true if odd, false for even |
| 3012 | $x->is_even(); # true if even, false for odd |
| 3013 | $x->is_int(); # true if $x is an integer |
| 3014 | |
| 3015 | The return true when the argument satisfies the condition. C<NaN>, C<+inf>, |
| 3016 | C<-inf> are not integers and are neither odd nor even. |
| 3017 | |
| 3018 | =head2 bcmp |
| 3019 | |
| 3020 | $x->bcmp($y); |
| 3021 | |
| 3022 | Compares $x with $y and takes the sign into account. |
| 3023 | Returns -1, 0, 1 or undef. |
| 3024 | |
| 3025 | =head2 bacmp |
| 3026 | |
| 3027 | $x->bacmp($y); |
| 3028 | |
| 3029 | Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef. |
| 3030 | |
| 3031 | =head2 sign |
| 3032 | |
| 3033 | $x->sign(); |
| 3034 | |
| 3035 | Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN. |
| 3036 | |
| 3037 | =head2 bcmp |
| 3038 | |
| 3039 | $x->digit($n); # return the nth digit, counting from right |
| 3040 | |
| 3041 | =head2 bneg |
| 3042 | |
| 3043 | $x->bneg(); |
| 3044 | |
| 3045 | Negate the number, e.g. change the sign between '+' and '-', or between '+inf' |
| 3046 | and '-inf', respectively. Does nothing for NaN or zero. |
| 3047 | |
| 3048 | =head2 babs |
| 3049 | |
| 3050 | $x->babs(); |
| 3051 | |
| 3052 | Set the number to it's absolute value, e.g. change the sign from '-' to '+' |
| 3053 | and from '-inf' to '+inf', respectively. Does nothing for NaN or positive |
| 3054 | numbers. |
| 3055 | |
| 3056 | =head2 bnorm |
| 3057 | |
| 3058 | $x->bnorm(); # normalize (no-op) |
| 3059 | |
| 3060 | =head2 bnot |
| 3061 | |
| 3062 | $x->bnot(); # two's complement (bit wise not) |
| 3063 | |
| 3064 | =head2 binc |
| 3065 | |
| 3066 | $x->binc(); # increment x by 1 |
| 3067 | |
| 3068 | =head2 bdec |
| 3069 | |
| 3070 | $x->bdec(); # decrement x by 1 |
| 3071 | |
| 3072 | =head2 badd |
| 3073 | |
| 3074 | $x->badd($y); # addition (add $y to $x) |
| 3075 | |
| 3076 | =head2 bsub |
| 3077 | |
| 3078 | $x->bsub($y); # subtraction (subtract $y from $x) |
| 3079 | |
| 3080 | =head2 bmul |
| 3081 | |
| 3082 | $x->bmul($y); # multiplication (multiply $x by $y) |
| 3083 | |
| 3084 | =head2 bdiv |
| 3085 | |
| 3086 | $x->bdiv($y); # divide, set $x to quotient |
| 3087 | # return (quo,rem) or quo if scalar |
| 3088 | |
| 3089 | =head2 bmod |
| 3090 | |
| 3091 | $x->bmod($y); # modulus (x % y) |
| 3092 | |
| 3093 | =head2 bmodinv |
| 3094 | |
| 3095 | $num->bmodinv($mod); # modular inverse |
| 3096 | |
| 3097 | Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is |
| 3098 | returned unless C<$num> is relatively prime to C<$mod>, i.e. unless |
| 3099 | C<bgcd($num, $mod)==1>. |
| 3100 | |
| 3101 | =head2 bmodpow |
| 3102 | |
| 3103 | $num->bmodpow($exp,$mod); # modular exponentation ($num**$exp % $mod) |
| 3104 | |
| 3105 | Returns the value of C<$num> taken to the power C<$exp> in the modulus |
| 3106 | C<$mod> using binary exponentation. C<bmodpow> is far superior to |
| 3107 | writing |
| 3108 | |
| 3109 | $num ** $exp % $mod |
| 3110 | |
| 3111 | because C<bmodpow> is much faster--it reduces internal variables into |
| 3112 | the modulus whenever possible, so it operates on smaller numbers. |
| 3113 | |
| 3114 | C<bmodpow> also supports negative exponents. |
| 3115 | |
| 3116 | bmodpow($num, -1, $mod) |
| 3117 | |
| 3118 | is exactly equivalent to |
| 3119 | |
| 3120 | bmodinv($num, $mod) |
| 3121 | |
| 3122 | =head2 bpow |
| 3123 | |
| 3124 | $x->bpow($y); # power of arguments (x ** y) |
| 3125 | |
| 3126 | =head2 blsft |
| 3127 | |
| 3128 | $x->blsft($y); # left shift |
| 3129 | $x->blsft($y,$n); # left shift, by base $n (like 10) |
| 3130 | |
| 3131 | =head2 brsft |
| 3132 | |
| 3133 | $x->brsft($y); # right shift |
| 3134 | $x->brsft($y,$n); # right shift, by base $n (like 10) |
| 3135 | |
| 3136 | =head2 band |
| 3137 | |
| 3138 | $x->band($y); # bitwise and |
| 3139 | |
| 3140 | =head2 bior |
| 3141 | |
| 3142 | $x->bior($y); # bitwise inclusive or |
| 3143 | |
| 3144 | =head2 bxor |
| 3145 | |
| 3146 | $x->bxor($y); # bitwise exclusive or |
| 3147 | |
| 3148 | =head2 bnot |
| 3149 | |
| 3150 | $x->bnot(); # bitwise not (two's complement) |
| 3151 | |
| 3152 | =head2 bsqrt |
| 3153 | |
| 3154 | $x->bsqrt(); # calculate square-root |
| 3155 | |
| 3156 | =head2 bfac |
| 3157 | |
| 3158 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
| 3159 | |
| 3160 | =head2 round |
| 3161 | |
| 3162 | $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r |
| 3163 | |
| 3164 | =head2 bround |
| 3165 | |
| 3166 | $x->bround($N); # accuracy: preserve $N digits |
| 3167 | |
| 3168 | =head2 bfround |
| 3169 | |
| 3170 | $x->bfround($N); # round to $Nth digit, no-op for BigInts |
| 3171 | |
| 3172 | =head2 bfloor |
| 3173 | |
| 3174 | $x->bfloor(); |
| 3175 | |
| 3176 | Set $x to the integer less or equal than $x. This is a no-op in BigInt, but |
| 3177 | does change $x in BigFloat. |
| 3178 | |
| 3179 | =head2 bceil |
| 3180 | |
| 3181 | $x->bceil(); |
| 3182 | |
| 3183 | Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but |
| 3184 | does change $x in BigFloat. |
| 3185 | |
| 3186 | =head2 bgcd |
| 3187 | |
| 3188 | bgcd(@values); # greatest common divisor (no OO style) |
| 3189 | |
| 3190 | =head2 blcm |
| 3191 | |
| 3192 | blcm(@values); # lowest common multiplicator (no OO style) |
| 3193 | |
| 3194 | head2 length |
| 3195 | |
| 3196 | $x->length(); |
| 3197 | ($xl,$fl) = $x->length(); |
| 3198 | |
| 3199 | Returns the number of digits in the decimal representation of the number. |
| 3200 | In list context, returns the length of the integer and fraction part. For |
| 3201 | BigInt's, the length of the fraction part will always be 0. |
| 3202 | |
| 3203 | =head2 exponent |
| 3204 | |
| 3205 | $x->exponent(); |
| 3206 | |
| 3207 | Return the exponent of $x as BigInt. |
| 3208 | |
| 3209 | =head2 mantissa |
| 3210 | |
| 3211 | $x->mantissa(); |
| 3212 | |
| 3213 | Return the signed mantissa of $x as BigInt. |
| 3214 | |
| 3215 | =head2 parts |
| 3216 | |
| 3217 | $x->parts(); # return (mantissa,exponent) as BigInt |
| 3218 | |
| 3219 | =head2 copy |
| 3220 | |
| 3221 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
| 3222 | |
| 3223 | =head2 as_number |
| 3224 | |
| 3225 | $x->as_number(); # return as BigInt (in BigInt: same as copy()) |
| 3226 | |
| 3227 | =head2 bsrt |
| 3228 | |
| 3229 | $x->bstr(); # normalized string |
| 3230 | |
| 3231 | =head2 bsstr |
| 3232 | |
| 3233 | $x->bsstr(); # normalized string in scientific notation |
| 3234 | |
| 3235 | =head2 as_hex |
| 3236 | |
| 3237 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
| 3238 | |
| 3239 | =head2 as_bin |
| 3240 | |
| 3241 | $x->as_bin(); # as signed binary string with prefixed 0b |
| 3242 | |
| 3243 | =head1 ACCURACY and PRECISION |
| 3244 | |
| 3245 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
| 3246 | accuracy and precision based rounding, both automatically after every |
| 3247 | operation as well as manually. |
| 3248 | |
| 3249 | This section describes the accuracy/precision handling in Math::Big* as it |
| 3250 | used to be and as it is now, complete with an explanation of all terms and |
| 3251 | abbreviations. |
| 3252 | |
| 3253 | Not yet implemented things (but with correct description) are marked with '!', |
| 3254 | things that need to be answered are marked with '?'. |
| 3255 | |
| 3256 | In the next paragraph follows a short description of terms used here (because |
| 3257 | these may differ from terms used by others people or documentation). |
| 3258 | |
| 3259 | During the rest of this document, the shortcuts A (for accuracy), P (for |
| 3260 | precision), F (fallback) and R (rounding mode) will be used. |
| 3261 | |
| 3262 | =head2 Precision P |
| 3263 | |
| 3264 | A fixed number of digits before (positive) or after (negative) |
| 3265 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
| 3266 | integer like 123 (or 120). A precision of 2 means two digits to the left |
| 3267 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that |
| 3268 | numbers with zeros before the decimal point may have different precisions, |
| 3269 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value |
| 3270 | was). It could also have p < 0, when the digits after the decimal point |
| 3271 | are zero. |
| 3272 | |
| 3273 | The string output (of floating point numbers) will be padded with zeros: |
| 3274 | |
| 3275 | Initial value P A Result String |
| 3276 | ------------------------------------------------------------ |
| 3277 | 1234.01 -3 1000 1000 |
| 3278 | 1234 -2 1200 1200 |
| 3279 | 1234.5 -1 1230 1230 |
| 3280 | 1234.001 1 1234 1234.0 |
| 3281 | 1234.01 0 1234 1234 |
| 3282 | 1234.01 2 1234.01 1234.01 |
| 3283 | 1234.01 5 1234.01 1234.01000 |
| 3284 | |
| 3285 | For BigInts, no padding occurs. |
| 3286 | |
| 3287 | =head2 Accuracy A |
| 3288 | |
| 3289 | Number of significant digits. Leading zeros are not counted. A |
| 3290 | number may have an accuracy greater than the non-zero digits |
| 3291 | when there are zeros in it or trailing zeros. For example, 123.456 has |
| 3292 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. |
| 3293 | |
| 3294 | The string output (of floating point numbers) will be padded with zeros: |
| 3295 | |
| 3296 | Initial value P A Result String |
| 3297 | ------------------------------------------------------------ |
| 3298 | 1234.01 3 1230 1230 |
| 3299 | 1234.01 6 1234.01 1234.01 |
| 3300 | 1234.1 8 1234.1 1234.1000 |
| 3301 | |
| 3302 | For BigInts, no padding occurs. |
| 3303 | |
| 3304 | =head2 Fallback F |
| 3305 | |
| 3306 | When both A and P are undefined, this is used as a fallback accuracy when |
| 3307 | dividing numbers. |
| 3308 | |
| 3309 | =head2 Rounding mode R |
| 3310 | |
| 3311 | When rounding a number, different 'styles' or 'kinds' |
| 3312 | of rounding are possible. (Note that random rounding, as in |
| 3313 | Math::Round, is not implemented.) |
| 3314 | |
| 3315 | =over 2 |
| 3316 | |
| 3317 | =item 'trunc' |
| 3318 | |
| 3319 | truncation invariably removes all digits following the |
| 3320 | rounding place, replacing them with zeros. Thus, 987.65 rounded |
| 3321 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
| 3322 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
| 3323 | decimal point (P=-2) becomes 123.46. |
| 3324 | |
| 3325 | All other implemented styles of rounding attempt to round to the |
| 3326 | "nearest digit." If the digit D immediately to the right of the |
| 3327 | rounding place (skipping the decimal point) is greater than 5, the |
| 3328 | number is incremented at the rounding place (possibly causing a |
| 3329 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds |
| 3330 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly |
| 3331 | truncated at the rounding place: e.g. when rounding to units, 0.4 |
| 3332 | rounds to 0, and -19.4 rounds to -19. |
| 3333 | |
| 3334 | However the results of other styles of rounding differ if the |
| 3335 | digit immediately to the right of the rounding place (skipping the |
| 3336 | decimal point) is 5 and if there are no digits, or no digits other |
| 3337 | than 0, after that 5. In such cases: |
| 3338 | |
| 3339 | =item 'even' |
| 3340 | |
| 3341 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 |
| 3342 | if it is not already. E.g., when rounding to the first sigdig, 0.45 |
| 3343 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. |
| 3344 | |
| 3345 | =item 'odd' |
| 3346 | |
| 3347 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if |
| 3348 | it is not already. E.g., when rounding to the first sigdig, 0.45 |
| 3349 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. |
| 3350 | |
| 3351 | =item '+inf' |
| 3352 | |
| 3353 | round to plus infinity, i.e. always round up. E.g., when |
| 3354 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, |
| 3355 | and 0.4501 also becomes 0.5. |
| 3356 | |
| 3357 | =item '-inf' |
| 3358 | |
| 3359 | round to minus infinity, i.e. always round down. E.g., when |
| 3360 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, |
| 3361 | but 0.4501 becomes 0.5. |
| 3362 | |
| 3363 | =item 'zero' |
| 3364 | |
| 3365 | round to zero, i.e. positive numbers down, negative ones up. |
| 3366 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 |
| 3367 | becomes -0.5, but 0.4501 becomes 0.5. |
| 3368 | |
| 3369 | =back |
| 3370 | |
| 3371 | The handling of A & P in MBI/MBF (the old core code shipped with Perl |
| 3372 | versions <= 5.7.2) is like this: |
| 3373 | |
| 3374 | =over 2 |
| 3375 | |
| 3376 | =item Precision |
| 3377 | |
| 3378 | * ffround($p) is able to round to $p number of digits after the decimal |
| 3379 | point |
| 3380 | * otherwise P is unused |
| 3381 | |
| 3382 | =item Accuracy (significant digits) |
| 3383 | |
| 3384 | * fround($a) rounds to $a significant digits |
| 3385 | * only fdiv() and fsqrt() take A as (optional) paramater |
| 3386 | + other operations simply create the same number (fneg etc), or more (fmul) |
| 3387 | of digits |
| 3388 | + rounding/truncating is only done when explicitly calling one of fround |
| 3389 | or ffround, and never for BigInt (not implemented) |
| 3390 | * fsqrt() simply hands its accuracy argument over to fdiv. |
| 3391 | * the documentation and the comment in the code indicate two different ways |
| 3392 | on how fdiv() determines the maximum number of digits it should calculate, |
| 3393 | and the actual code does yet another thing |
| 3394 | POD: |
| 3395 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) |
| 3396 | Comment: |
| 3397 | result has at most max(scale, length(dividend), length(divisor)) digits |
| 3398 | Actual code: |
| 3399 | scale = max(scale, length(dividend)-1,length(divisor)-1); |
| 3400 | scale += length(divisior) - length(dividend); |
| 3401 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
| 3402 | Actually, the 'difference' added to the scale is calculated from the |
| 3403 | number of "significant digits" in dividend and divisor, which is derived |
| 3404 | by looking at the length of the mantissa. Which is wrong, since it includes |
| 3405 | the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups |
| 3406 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange |
| 3407 | assumption that 124 has 3 significant digits, while 120/7 will get you |
| 3408 | '17', not '17.1' since 120 is thought to have 2 significant digits. |
| 3409 | The rounding after the division then uses the remainder and $y to determine |
| 3410 | wether it must round up or down. |
| 3411 | ? I have no idea which is the right way. That's why I used a slightly more |
| 3412 | ? simple scheme and tweaked the few failing testcases to match it. |
| 3413 | |
| 3414 | =back |
| 3415 | |
| 3416 | This is how it works now: |
| 3417 | |
| 3418 | =over 2 |
| 3419 | |
| 3420 | =item Setting/Accessing |
| 3421 | |
| 3422 | * You can set the A global via Math::BigInt->accuracy() or |
| 3423 | Math::BigFloat->accuracy() or whatever class you are using. |
| 3424 | * You can also set P globally by using Math::SomeClass->precision() likewise. |
| 3425 | * Globals are classwide, and not inherited by subclasses. |
| 3426 | * to undefine A, use Math::SomeCLass->accuracy(undef); |
| 3427 | * to undefine P, use Math::SomeClass->precision(undef); |
| 3428 | * Setting Math::SomeClass->accuracy() clears automatically |
| 3429 | Math::SomeClass->precision(), and vice versa. |
| 3430 | * To be valid, A must be > 0, P can have any value. |
| 3431 | * If P is negative, this means round to the P'th place to the right of the |
| 3432 | decimal point; positive values mean to the left of the decimal point. |
| 3433 | P of 0 means round to integer. |
| 3434 | * to find out the current global A, take Math::SomeClass->accuracy() |
| 3435 | * to find out the current global P, take Math::SomeClass->precision() |
| 3436 | * use $x->accuracy() respective $x->precision() for the local setting of $x. |
| 3437 | * Please note that $x->accuracy() respecive $x->precision() fall back to the |
| 3438 | defined globals, when $x's A or P is not set. |
| 3439 | |
| 3440 | =item Creating numbers |
| 3441 | |
| 3442 | * When you create a number, you can give it's desired A or P via: |
| 3443 | $x = Math::BigInt->new($number,$A,$P); |
| 3444 | * Only one of A or P can be defined, otherwise the result is NaN |
| 3445 | * If no A or P is give ($x = Math::BigInt->new($number) form), then the |
| 3446 | globals (if set) will be used. Thus changing the global defaults later on |
| 3447 | will not change the A or P of previously created numbers (i.e., A and P of |
| 3448 | $x will be what was in effect when $x was created) |
| 3449 | * If given undef for A and P, B<no> rounding will occur, and the globals will |
| 3450 | B<not> be used. This is used by subclasses to create numbers without |
| 3451 | suffering rounding in the parent. Thus a subclass is able to have it's own |
| 3452 | globals enforced upon creation of a number by using |
| 3453 | $x = Math::BigInt->new($number,undef,undef): |
| 3454 | |
| 3455 | use Math::Bigint::SomeSubclass; |
| 3456 | use Math::BigInt; |
| 3457 | |
| 3458 | Math::BigInt->accuracy(2); |
| 3459 | Math::BigInt::SomeSubClass->accuracy(3); |
| 3460 | $x = Math::BigInt::SomeSubClass->new(1234); |
| 3461 | |
| 3462 | $x is now 1230, and not 1200. A subclass might choose to implement |
| 3463 | this otherwise, e.g. falling back to the parent's A and P. |
| 3464 | |
| 3465 | =item Usage |
| 3466 | |
| 3467 | * If A or P are enabled/defined, they are used to round the result of each |
| 3468 | operation according to the rules below |
| 3469 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
| 3470 | after the decimal point |
| 3471 | * Math::BigFloat uses Math::BigInts internally, but setting A or P inside |
| 3472 | Math::BigInt as globals should not tamper with the parts of a BigFloat. |
| 3473 | Thus a flag is used to mark all Math::BigFloat numbers as 'never round' |
| 3474 | |
| 3475 | =item Precedence |
| 3476 | |
| 3477 | * It only makes sense that a number has only one of A or P at a time. |
| 3478 | Since you can set/get both A and P, there is a rule that will practically |
| 3479 | enforce only A or P to be in effect at a time, even if both are set. |
| 3480 | This is called precedence. |
| 3481 | * If two objects are involved in an operation, and one of them has A in |
| 3482 | effect, and the other P, this results in an error (NaN). |
| 3483 | * A takes precendence over P (Hint: A comes before P). If A is defined, it |
| 3484 | is used, otherwise P is used. If neither of them is defined, nothing is |
| 3485 | used, i.e. the result will have as many digits as it can (with an |
| 3486 | exception for fdiv/fsqrt) and will not be rounded. |
| 3487 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of |
| 3488 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. |
| 3489 | If either the dividend's or the divisor's mantissa has more digits than |
| 3490 | the value of F, the higher value will be used instead of F. |
| 3491 | This is to limit the digits (A) of the result (just consider what would |
| 3492 | happen with unlimited A and P in the case of 1/3 :-) |
| 3493 | * fdiv will calculate (at least) 4 more digits than required (determined by |
| 3494 | A, P or F), and, if F is not used, round the result |
| 3495 | (this will still fail in the case of a result like 0.12345000000001 with A |
| 3496 | or P of 5, but this can not be helped - or can it?) |
| 3497 | * Thus you can have the math done by on Math::Big* class in three modes: |
| 3498 | + never round (this is the default): |
| 3499 | This is done by setting A and P to undef. No math operation |
| 3500 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
| 3501 | against overflows. You must explicitely call bround(), bfround() or |
| 3502 | round() (the latter with parameters). |
| 3503 | Note: Once you have rounded a number, the settings will 'stick' on it |
| 3504 | and 'infect' all other numbers engaged in math operations with it, since |
| 3505 | local settings have the highest precedence. So, to get SaferRound[tm], |
| 3506 | use a copy() before rounding like this: |
| 3507 | |
| 3508 | $x = Math::BigFloat->new(12.34); |
| 3509 | $y = Math::BigFloat->new(98.76); |
| 3510 | $z = $x * $y; # 1218.6984 |
| 3511 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) |
| 3512 | $z = $x * $y; # still 1218.6984, without |
| 3513 | # copy would have been 1210! |
| 3514 | |
| 3515 | + round after each op: |
| 3516 | After each single operation (except for testing like is_zero()), the |
| 3517 | method round() is called and the result is rounded appropriately. By |
| 3518 | setting proper values for A and P, you can have all-the-same-A or |
| 3519 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
| 3520 | and P to -2, globally. |
| 3521 | |
| 3522 | ?Maybe an extra option that forbids local A & P settings would be in order, |
| 3523 | ?so that intermediate rounding does not 'poison' further math? |
| 3524 | |
| 3525 | =item Overriding globals |
| 3526 | |
| 3527 | * you will be able to give A, P and R as an argument to all the calculation |
| 3528 | routines; the second parameter is A, the third one is P, and the fourth is |
| 3529 | R (shift right by one for binary operations like badd). P is used only if |
| 3530 | the first parameter (A) is undefined. These three parameters override the |
| 3531 | globals in the order detailed as follows, i.e. the first defined value |
| 3532 | wins: |
| 3533 | (local: per object, global: global default, parameter: argument to sub) |
| 3534 | + parameter A |
| 3535 | + parameter P |
| 3536 | + local A (if defined on both of the operands: smaller one is taken) |
| 3537 | + local P (if defined on both of the operands: bigger one is taken) |
| 3538 | + global A |
| 3539 | + global P |
| 3540 | + global F |
| 3541 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
| 3542 | arguments (A and P) instead of one |
| 3543 | |
| 3544 | =item Local settings |
| 3545 | |
| 3546 | * You can set A and P locally by using $x->accuracy() and $x->precision() |
| 3547 | and thus force different A and P for different objects/numbers. |
| 3548 | * Setting A or P this way immediately rounds $x to the new value. |
| 3549 | * $x->accuracy() clears $x->precision(), and vice versa. |
| 3550 | |
| 3551 | =item Rounding |
| 3552 | |
| 3553 | * the rounding routines will use the respective global or local settings. |
| 3554 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
| 3555 | is for precision |
| 3556 | * the two rounding functions take as the second parameter one of the |
| 3557 | following rounding modes (R): |
| 3558 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' |
| 3559 | * you can set and get the global R by using Math::SomeClass->round_mode() |
| 3560 | or by setting $Math::SomeClass::round_mode |
| 3561 | * after each operation, $result->round() is called, and the result may |
| 3562 | eventually be rounded (that is, if A or P were set either locally, |
| 3563 | globally or as parameter to the operation) |
| 3564 | * to manually round a number, call $x->round($A,$P,$round_mode); |
| 3565 | this will round the number by using the appropriate rounding function |
| 3566 | and then normalize it. |
| 3567 | * rounding modifies the local settings of the number: |
| 3568 | |
| 3569 | $x = Math::BigFloat->new(123.456); |
| 3570 | $x->accuracy(5); |
| 3571 | $x->bround(4); |
| 3572 | |
| 3573 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() |
| 3574 | will be 4 from now on. |
| 3575 | |
| 3576 | =item Default values |
| 3577 | |
| 3578 | * R: 'even' |
| 3579 | * F: 40 |
| 3580 | * A: undef |
| 3581 | * P: undef |
| 3582 | |
| 3583 | =item Remarks |
| 3584 | |
| 3585 | * The defaults are set up so that the new code gives the same results as |
| 3586 | the old code (except in a few cases on fdiv): |
| 3587 | + Both A and P are undefined and thus will not be used for rounding |
| 3588 | after each operation. |
| 3589 | + round() is thus a no-op, unless given extra parameters A and P |
| 3590 | |
| 3591 | =back |
| 3592 | |
| 3593 | =head1 INTERNALS |
| 3594 | |
| 3595 | The actual numbers are stored as unsigned big integers (with seperate sign). |
| 3596 | You should neither care about nor depend on the internal representation; it |
| 3597 | might change without notice. Use only method calls like C<< $x->sign(); >> |
| 3598 | instead relying on the internal hash keys like in C<< $x->{sign}; >>. |
| 3599 | |
| 3600 | =head2 MATH LIBRARY |
| 3601 | |
| 3602 | Math with the numbers is done (by default) by a module called |
| 3603 | Math::BigInt::Calc. This is equivalent to saying: |
| 3604 | |
| 3605 | use Math::BigInt lib => 'Calc'; |
| 3606 | |
| 3607 | You can change this by using: |
| 3608 | |
| 3609 | use Math::BigInt lib => 'BitVect'; |
| 3610 | |
| 3611 | The following would first try to find Math::BigInt::Foo, then |
| 3612 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
| 3613 | |
| 3614 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
| 3615 | |
| 3616 | Calc.pm uses as internal format an array of elements of some decimal base |
| 3617 | (usually 1e5 or 1e7) with the least significant digit first, while BitVect.pm |
| 3618 | uses a bit vector of base 2, most significant bit first. Other modules might |
| 3619 | use even different means of representing the numbers. See the respective |
| 3620 | module documentation for further details. |
| 3621 | |
| 3622 | =head2 SIGN |
| 3623 | |
| 3624 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. |
| 3625 | |
| 3626 | A sign of 'NaN' is used to represent the result when input arguments are not |
| 3627 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively |
| 3628 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
| 3629 | '-inf' when dividing any negative number by 0. |
| 3630 | |
| 3631 | =head2 mantissa(), exponent() and parts() |
| 3632 | |
| 3633 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such |
| 3634 | that: |
| 3635 | |
| 3636 | $m = $x->mantissa(); |
| 3637 | $e = $x->exponent(); |
| 3638 | $y = $m * ( 10 ** $e ); |
| 3639 | print "ok\n" if $x == $y; |
| 3640 | |
| 3641 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
| 3642 | in one go. Both the returned mantissa and exponent have a sign. |
| 3643 | |
| 3644 | Currently, for BigInts C<$e> will be always 0, except for NaN, +inf and -inf, |
| 3645 | where it will be NaN; and for $x == 0, where it will be 1 |
| 3646 | (to be compatible with Math::BigFloat's internal representation of a zero as |
| 3647 | C<0E1>). |
| 3648 | |
| 3649 | C<$m> will always be a copy of the original number. The relation between $e |
| 3650 | and $m might change in the future, but will always be equivalent in a |
| 3651 | numerical sense, e.g. $m might get minimized. |
| 3652 | |
| 3653 | =head1 EXAMPLES |
| 3654 | |
| 3655 | use Math::BigInt; |
| 3656 | |
| 3657 | sub bint { Math::BigInt->new(shift); } |
| 3658 | |
| 3659 | $x = Math::BigInt->bstr("1234") # string "1234" |
| 3660 | $x = "$x"; # same as bstr() |
| 3661 | $x = Math::BigInt->bneg("1234"); # Bigint "-1234" |
| 3662 | $x = Math::BigInt->babs("-12345"); # Bigint "12345" |
| 3663 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" |
| 3664 | $x = bint(1) + bint(2); # BigInt "3" |
| 3665 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") |
| 3666 | $x = bint(1); # BigInt "1" |
| 3667 | $x = $x + 5 / 2; # BigInt "3" |
| 3668 | $x = $x ** 3; # BigInt "27" |
| 3669 | $x *= 2; # BigInt "54" |
| 3670 | $x = Math::BigInt->new(0); # BigInt "0" |
| 3671 | $x--; # BigInt "-1" |
| 3672 | $x = Math::BigInt->badd(4,5) # BigInt "9" |
| 3673 | print $x->bsstr(); # 9e+0 |
| 3674 | |
| 3675 | Examples for rounding: |
| 3676 | |
| 3677 | use Math::BigFloat; |
| 3678 | use Test; |
| 3679 | |
| 3680 | $x = Math::BigFloat->new(123.4567); |
| 3681 | $y = Math::BigFloat->new(123.456789); |
| 3682 | Math::BigFloat->accuracy(4); # no more A than 4 |
| 3683 | |
| 3684 | ok ($x->copy()->fround(),123.4); # even rounding |
| 3685 | print $x->copy()->fround(),"\n"; # 123.4 |
| 3686 | Math::BigFloat->round_mode('odd'); # round to odd |
| 3687 | print $x->copy()->fround(),"\n"; # 123.5 |
| 3688 | Math::BigFloat->accuracy(5); # no more A than 5 |
| 3689 | Math::BigFloat->round_mode('odd'); # round to odd |
| 3690 | print $x->copy()->fround(),"\n"; # 123.46 |
| 3691 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 |
| 3692 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 |
| 3693 | |
| 3694 | Math::BigFloat->accuracy(undef); # A not important now |
| 3695 | Math::BigFloat->precision(2); # P important |
| 3696 | print $x->copy()->bnorm(),"\n"; # 123.46 |
| 3697 | print $x->copy()->fround(),"\n"; # 123.46 |
| 3698 | |
| 3699 | Examples for converting: |
| 3700 | |
| 3701 | my $x = Math::BigInt->new('0b1'.'01' x 123); |
| 3702 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; |
| 3703 | |
| 3704 | =head1 Autocreating constants |
| 3705 | |
| 3706 | After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal |
| 3707 | and binary constants in the given scope are converted to C<Math::BigInt>. |
| 3708 | This conversion happens at compile time. |
| 3709 | |
| 3710 | In particular, |
| 3711 | |
| 3712 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
| 3713 | |
| 3714 | prints the integer value of C<2**100>. Note that without conversion of |
| 3715 | constants the expression 2**100 will be calculated as perl scalar. |
| 3716 | |
| 3717 | Please note that strings and floating point constants are not affected, |
| 3718 | so that |
| 3719 | |
| 3720 | use Math::BigInt qw/:constant/; |
| 3721 | |
| 3722 | $x = 1234567890123456789012345678901234567890 |
| 3723 | + 123456789123456789; |
| 3724 | $y = '1234567890123456789012345678901234567890' |
| 3725 | + '123456789123456789'; |
| 3726 | |
| 3727 | do not work. You need an explicit Math::BigInt->new() around one of the |
| 3728 | operands. You should also quote large constants to protect loss of precision: |
| 3729 | |
| 3730 | use Math::Bigint; |
| 3731 | |
| 3732 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); |
| 3733 | |
| 3734 | Without the quotes Perl would convert the large number to a floating point |
| 3735 | constant at compile time and then hand the result to BigInt, which results in |
| 3736 | an truncated result or a NaN. |
| 3737 | |
| 3738 | This also applies to integers that look like floating point constants: |
| 3739 | |
| 3740 | use Math::BigInt ':constant'; |
| 3741 | |
| 3742 | print ref(123e2),"\n"; |
| 3743 | print ref(123.2e2),"\n"; |
| 3744 | |
| 3745 | will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat> |
| 3746 | to get this to work. |
| 3747 | |
| 3748 | =head1 PERFORMANCE |
| 3749 | |
| 3750 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x |
| 3751 | must be made in the second case. For long numbers, the copy can eat up to 20% |
| 3752 | of the work (in the case of addition/subtraction, less for |
| 3753 | multiplication/division). If $y is very small compared to $x, the form |
| 3754 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes |
| 3755 | more time then the actual addition. |
| 3756 | |
| 3757 | With a technique called copy-on-write, the cost of copying with overload could |
| 3758 | be minimized or even completely avoided. A test implementation of COW did show |
| 3759 | performance gains for overloaded math, but introduced a performance loss due |
| 3760 | to a constant overhead for all other operatons. |
| 3761 | |
| 3762 | The rewritten version of this module is slower on certain operations, like |
| 3763 | new(), bstr() and numify(). The reason are that it does now more work and |
| 3764 | handles more cases. The time spent in these operations is usually gained in |
| 3765 | the other operations so that programs on the average should get faster. If |
| 3766 | they don't, please contect the author. |
| 3767 | |
| 3768 | Some operations may be slower for small numbers, but are significantly faster |
| 3769 | for big numbers. Other operations are now constant (O(1), like bneg(), babs() |
| 3770 | etc), instead of O(N) and thus nearly always take much less time. These |
| 3771 | optimizations were done on purpose. |
| 3772 | |
| 3773 | If you find the Calc module to slow, try to install any of the replacement |
| 3774 | modules and see if they help you. |
| 3775 | |
| 3776 | =head2 Alternative math libraries |
| 3777 | |
| 3778 | You can use an alternative library to drive Math::BigInt via: |
| 3779 | |
| 3780 | use Math::BigInt lib => 'Module'; |
| 3781 | |
| 3782 | See L<MATH LIBRARY> for more information. |
| 3783 | |
| 3784 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. |
| 3785 | |
| 3786 | =head2 SUBCLASSING |
| 3787 | |
| 3788 | =head1 Subclassing Math::BigInt |
| 3789 | |
| 3790 | The basic design of Math::BigInt allows simple subclasses with very little |
| 3791 | work, as long as a few simple rules are followed: |
| 3792 | |
| 3793 | =over 2 |
| 3794 | |
| 3795 | =item * |
| 3796 | |
| 3797 | The public API must remain consistent, i.e. if a sub-class is overloading |
| 3798 | addition, the sub-class must use the same name, in this case badd(). The |
| 3799 | reason for this is that Math::BigInt is optimized to call the object methods |
| 3800 | directly. |
| 3801 | |
| 3802 | =item * |
| 3803 | |
| 3804 | The private object hash keys like C<$x->{sign}> may not be changed, but |
| 3805 | additional keys can be added, like C<$x->{_custom}>. |
| 3806 | |
| 3807 | =item * |
| 3808 | |
| 3809 | Accessor functions are available for all existing object hash keys and should |
| 3810 | be used instead of directly accessing the internal hash keys. The reason for |
| 3811 | this is that Math::BigInt itself has a pluggable interface which permits it |
| 3812 | to support different storage methods. |
| 3813 | |
| 3814 | =back |
| 3815 | |
| 3816 | More complex sub-classes may have to replicate more of the logic internal of |
| 3817 | Math::BigInt if they need to change more basic behaviors. A subclass that |
| 3818 | needs to merely change the output only needs to overload C<bstr()>. |
| 3819 | |
| 3820 | All other object methods and overloaded functions can be directly inherited |
| 3821 | from the parent class. |
| 3822 | |
| 3823 | At the very minimum, any subclass will need to provide it's own C<new()> and can |
| 3824 | store additional hash keys in the object. There are also some package globals |
| 3825 | that must be defined, e.g.: |
| 3826 | |
| 3827 | # Globals |
| 3828 | $accuracy = undef; |
| 3829 | $precision = -2; # round to 2 decimal places |
| 3830 | $round_mode = 'even'; |
| 3831 | $div_scale = 40; |
| 3832 | |
| 3833 | Additionally, you might want to provide the following two globals to allow |
| 3834 | auto-upgrading and auto-downgrading to work correctly: |
| 3835 | |
| 3836 | $upgrade = undef; |
| 3837 | $downgrade = undef; |
| 3838 | |
| 3839 | This allows Math::BigInt to correctly retrieve package globals from the |
| 3840 | subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or |
| 3841 | t/Math/BigFloat/SubClass.pm completely functional subclass examples. |
| 3842 | |
| 3843 | Don't forget to |
| 3844 | |
| 3845 | use overload; |
| 3846 | |
| 3847 | in your subclass to automatically inherit the overloading from the parent. If |
| 3848 | you like, you can change part of the overloading, look at Math::String for an |
| 3849 | example. |
| 3850 | |
| 3851 | =head1 UPGRADING |
| 3852 | |
| 3853 | When used like this: |
| 3854 | |
| 3855 | use Math::BigInt upgrade => 'Foo::Bar'; |
| 3856 | |
| 3857 | certain operations will 'upgrade' their calculation and thus the result to |
| 3858 | the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat: |
| 3859 | |
| 3860 | use Math::BigInt upgrade => 'Math::BigFloat'; |
| 3861 | |
| 3862 | As a shortcut, you can use the module C<bignum>: |
| 3863 | |
| 3864 | use bignum; |
| 3865 | |
| 3866 | Also good for oneliners: |
| 3867 | |
| 3868 | perl -Mbignum -le 'print 2 ** 255' |
| 3869 | |
| 3870 | This makes it possible to mix arguments of different classes (as in 2.5 + 2) |
| 3871 | as well es preserve accuracy (as in sqrt(3)). |
| 3872 | |
| 3873 | Beware: This feature is not fully implemented yet. |
| 3874 | |
| 3875 | =head2 Auto-upgrade |
| 3876 | |
| 3877 | The following methods upgrade themselves unconditionally; that is if upgrade |
| 3878 | is in effect, they will always hand up their work: |
| 3879 | |
| 3880 | =over 2 |
| 3881 | |
| 3882 | =item bsqrt() |
| 3883 | |
| 3884 | =item div() |
| 3885 | |
| 3886 | =item blog() |
| 3887 | |
| 3888 | =back |
| 3889 | |
| 3890 | Beware: This list is not complete. |
| 3891 | |
| 3892 | All other methods upgrade themselves only when one (or all) of their |
| 3893 | arguments are of the class mentioned in $upgrade (This might change in later |
| 3894 | versions to a more sophisticated scheme): |
| 3895 | |
| 3896 | =head1 BUGS |
| 3897 | |
| 3898 | =over 2 |
| 3899 | |
| 3900 | =item Out of Memory! |
| 3901 | |
| 3902 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and |
| 3903 | C<eval()> in your code will crash with "Out of memory". This is probably an |
| 3904 | overload/exporter bug. You can workaround by not having C<eval()> |
| 3905 | and ':constant' at the same time or upgrade your Perl to a newer version. |
| 3906 | |
| 3907 | =item Fails to load Calc on Perl prior 5.6.0 |
| 3908 | |
| 3909 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt |
| 3910 | will fall back to eval { require ... } when loading the math lib on Perls |
| 3911 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on |
| 3912 | filesystems using a different seperator. |
| 3913 | |
| 3914 | =back |
| 3915 | |
| 3916 | =head1 CAVEATS |
| 3917 | |
| 3918 | Some things might not work as you expect them. Below is documented what is |
| 3919 | known to be troublesome: |
| 3920 | |
| 3921 | =over 1 |
| 3922 | |
| 3923 | =item stringify, bstr(), bsstr() and 'cmp' |
| 3924 | |
| 3925 | Both stringify and bstr() now drop the leading '+'. The old code would return |
| 3926 | '+3', the new returns '3'. This is to be consistent with Perl and to make |
| 3927 | cmp (especially with overloading) to work as you expect. It also solves |
| 3928 | problems with Test.pm, it's ok() uses 'eq' internally. |
| 3929 | |
| 3930 | Mark said, when asked about to drop the '+' altogether, or make only cmp work: |
| 3931 | |
| 3932 | I agree (with the first alternative), don't add the '+' on positive |
| 3933 | numbers. It's not as important anymore with the new internal |
| 3934 | form for numbers. It made doing things like abs and neg easier, |
| 3935 | but those have to be done differently now anyway. |
| 3936 | |
| 3937 | So, the following examples will now work all as expected: |
| 3938 | |
| 3939 | use Test; |
| 3940 | BEGIN { plan tests => 1 } |
| 3941 | use Math::BigInt; |
| 3942 | |
| 3943 | my $x = new Math::BigInt 3*3; |
| 3944 | my $y = new Math::BigInt 3*3; |
| 3945 | |
| 3946 | ok ($x,3*3); |
| 3947 | print "$x eq 9" if $x eq $y; |
| 3948 | print "$x eq 9" if $x eq '9'; |
| 3949 | print "$x eq 9" if $x eq 3*3; |
| 3950 | |
| 3951 | Additionally, the following still works: |
| 3952 | |
| 3953 | print "$x == 9" if $x == $y; |
| 3954 | print "$x == 9" if $x == 9; |
| 3955 | print "$x == 9" if $x == 3*3; |
| 3956 | |
| 3957 | There is now a C<bsstr()> method to get the string in scientific notation aka |
| 3958 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() |
| 3959 | for comparisation, but Perl will represent some numbers as 100 and others |
| 3960 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before doing eq: |
| 3961 | |
| 3962 | use Test; |
| 3963 | BEGIN { plan tests => 3 } |
| 3964 | use Math::BigInt; |
| 3965 | |
| 3966 | $x = Math::BigInt->new('1e56'); $y = 1e56; |
| 3967 | ok ($x,$y); # will fail |
| 3968 | ok ($x->bsstr(),$y); # okay |
| 3969 | $y = Math::BigInt->new($y); |
| 3970 | ok ($x,$y); # okay |
| 3971 | |
| 3972 | Alternatively, simple use <=> for comparisations, that will get it always |
| 3973 | right. There is not yet a way to get a number automatically represented as |
| 3974 | a string that matches exactly the way Perl represents it. |
| 3975 | |
| 3976 | =item int() |
| 3977 | |
| 3978 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a |
| 3979 | Perl scalar: |
| 3980 | |
| 3981 | $x = Math::BigInt->new(123); |
| 3982 | $y = int($x); # BigInt 123 |
| 3983 | $x = Math::BigFloat->new(123.45); |
| 3984 | $y = int($x); # BigInt 123 |
| 3985 | |
| 3986 | In all Perl versions you can use C<as_number()> for the same effect: |
| 3987 | |
| 3988 | $x = Math::BigFloat->new(123.45); |
| 3989 | $y = $x->as_number(); # BigInt 123 |
| 3990 | |
| 3991 | This also works for other subclasses, like Math::String. |
| 3992 | |
| 3993 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. |
| 3994 | |
| 3995 | =item length |
| 3996 | |
| 3997 | The following will probably not do what you expect: |
| 3998 | |
| 3999 | $c = Math::BigInt->new(123); |
| 4000 | print $c->length(),"\n"; # prints 30 |
| 4001 | |
| 4002 | It prints both the number of digits in the number and in the fraction part |
| 4003 | since print calls C<length()> in list context. Use something like: |
| 4004 | |
| 4005 | print scalar $c->length(),"\n"; # prints 3 |
| 4006 | |
| 4007 | =item bdiv |
| 4008 | |
| 4009 | The following will probably not do what you expect: |
| 4010 | |
| 4011 | print $c->bdiv(10000),"\n"; |
| 4012 | |
| 4013 | It prints both quotient and remainder since print calls C<bdiv()> in list |
| 4014 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want |
| 4015 | to use |
| 4016 | |
| 4017 | print $c / 10000,"\n"; |
| 4018 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c |
| 4019 | |
| 4020 | instead. |
| 4021 | |
| 4022 | The quotient is always the greatest integer less than or equal to the |
| 4023 | real-valued quotient of the two operands, and the remainder (when it is |
| 4024 | nonzero) always has the same sign as the second operand; so, for |
| 4025 | example, |
| 4026 | |
| 4027 | 1 / 4 => ( 0, 1) |
| 4028 | 1 / -4 => (-1,-3) |
| 4029 | -3 / 4 => (-1, 1) |
| 4030 | -3 / -4 => ( 0,-3) |
| 4031 | -11 / 2 => (-5,1) |
| 4032 | 11 /-2 => (-5,-1) |
| 4033 | |
| 4034 | As a consequence, the behavior of the operator % agrees with the |
| 4035 | behavior of Perl's built-in % operator (as documented in the perlop |
| 4036 | manpage), and the equation |
| 4037 | |
| 4038 | $x == ($x / $y) * $y + ($x % $y) |
| 4039 | |
| 4040 | holds true for any $x and $y, which justifies calling the two return |
| 4041 | values of bdiv() the quotient and remainder. The only exception to this rule |
| 4042 | are when $y == 0 and $x is negative, then the remainder will also be |
| 4043 | negative. See below under "infinity handling" for the reasoning behing this. |
| 4044 | |
| 4045 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will |
| 4046 | not change BigInt's way to do things. This is because under 'use integer' Perl |
| 4047 | will do what the underlying C thinks is right and this is different for each |
| 4048 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug |
| 4049 | the author to implement it ;) |
| 4050 | |
| 4051 | =item infinity handling |
| 4052 | |
| 4053 | Here are some examples that explain the reasons why certain results occur while |
| 4054 | handling infinity: |
| 4055 | |
| 4056 | The following table shows the result of the division and the remainder, so that |
| 4057 | the equation above holds true. Some "ordinary" cases are strewn in to show more |
| 4058 | clearly the reasoning: |
| 4059 | |
| 4060 | A / B = C, R so that C * B + R = A |
| 4061 | ========================================================= |
| 4062 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 |
| 4063 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 |
| 4064 | 0 / inf = 0, 0 0 * inf + 0 = 0 |
| 4065 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 |
| 4066 | 5 / inf = 0, 5 0 * inf + 5 = 5 |
| 4067 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 |
| 4068 | -5/ inf = 0, -5 0 * inf + -5 = -5 |
| 4069 | -5/-inf = 0, -5 0 * -inf + -5 = -5 |
| 4070 | inf/ 5 = inf, 0 inf * 5 + 0 = inf |
| 4071 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf |
| 4072 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf |
| 4073 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf |
| 4074 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 |
| 4075 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 |
| 4076 | inf/ inf = 1, 0 1 * inf + 0 = inf |
| 4077 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf |
| 4078 | inf/-inf = -1, 0 -1 * -inf + 0 = inf |
| 4079 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf |
| 4080 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 |
| 4081 | inf/ 0 = inf, inf inf * 0 + inf = inf |
| 4082 | 0/ 0 = NaN |
| 4083 | |
| 4084 | These cases below violate the "remainder has the sign of the second of the two |
| 4085 | arguments", since they wouldn't match up otherwise. |
| 4086 | |
| 4087 | A / B = C, R so that C * B + R = A |
| 4088 | ======================================================== |
| 4089 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf |
| 4090 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 |
| 4091 | |
| 4092 | =item Modifying and = |
| 4093 | |
| 4094 | Beware of: |
| 4095 | |
| 4096 | $x = Math::BigFloat->new(5); |
| 4097 | $y = $x; |
| 4098 | |
| 4099 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
| 4100 | a second reference to the B<same> object and stores it in $y. Thus anything |
| 4101 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
| 4102 | Or in other words, C<=> is only safe if you modify your BigInts only via |
| 4103 | overloaded math. As soon as you use a method call it breaks: |
| 4104 | |
| 4105 | $x->bmul(2); |
| 4106 | print "$x, $y\n"; # prints '10, 10' |
| 4107 | |
| 4108 | If you want a true copy of $x, use: |
| 4109 | |
| 4110 | $y = $x->copy(); |
| 4111 | |
| 4112 | You can also chain the calls like this, this will make first a copy and then |
| 4113 | multiply it by 2: |
| 4114 | |
| 4115 | $y = $x->copy()->bmul(2); |
| 4116 | |
| 4117 | See also the documentation for overload.pm regarding C<=>. |
| 4118 | |
| 4119 | =item bpow |
| 4120 | |
| 4121 | C<bpow()> (and the rounding functions) now modifies the first argument and |
| 4122 | returns it, unlike the old code which left it alone and only returned the |
| 4123 | result. This is to be consistent with C<badd()> etc. The first three will |
| 4124 | modify $x, the last one won't: |
| 4125 | |
| 4126 | print bpow($x,$i),"\n"; # modify $x |
| 4127 | print $x->bpow($i),"\n"; # ditto |
| 4128 | print $x **= $i,"\n"; # the same |
| 4129 | print $x ** $i,"\n"; # leave $x alone |
| 4130 | |
| 4131 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. |
| 4132 | |
| 4133 | =item Overloading -$x |
| 4134 | |
| 4135 | The following: |
| 4136 | |
| 4137 | $x = -$x; |
| 4138 | |
| 4139 | is slower than |
| 4140 | |
| 4141 | $x->bneg(); |
| 4142 | |
| 4143 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant |
| 4144 | needs to preserve $x since it does not know that it later will get overwritten. |
| 4145 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
| 4146 | |
| 4147 | With Copy-On-Write, this issue would be gone, but C-o-W is not implemented |
| 4148 | since it is slower for all other things. |
| 4149 | |
| 4150 | =item Mixing different object types |
| 4151 | |
| 4152 | In Perl you will get a floating point value if you do one of the following: |
| 4153 | |
| 4154 | $float = 5.0 + 2; |
| 4155 | $float = 2 + 5.0; |
| 4156 | $float = 5 / 2; |
| 4157 | |
| 4158 | With overloaded math, only the first two variants will result in a BigFloat: |
| 4159 | |
| 4160 | use Math::BigInt; |
| 4161 | use Math::BigFloat; |
| 4162 | |
| 4163 | $mbf = Math::BigFloat->new(5); |
| 4164 | $mbi2 = Math::BigInteger->new(5); |
| 4165 | $mbi = Math::BigInteger->new(2); |
| 4166 | |
| 4167 | # what actually gets called: |
| 4168 | $float = $mbf + $mbi; # $mbf->badd() |
| 4169 | $float = $mbf / $mbi; # $mbf->bdiv() |
| 4170 | $integer = $mbi + $mbf; # $mbi->badd() |
| 4171 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() |
| 4172 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() |
| 4173 | |
| 4174 | This is because math with overloaded operators follows the first (dominating) |
| 4175 | operand, and the operation of that is called and returns thus the result. So, |
| 4176 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
| 4177 | the result should be a Math::BigFloat or the second operant is one. |
| 4178 | |
| 4179 | To get a Math::BigFloat you either need to call the operation manually, |
| 4180 | make sure the operands are already of the proper type or casted to that type |
| 4181 | via Math::BigFloat->new(): |
| 4182 | |
| 4183 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 |
| 4184 | |
| 4185 | Beware of simple "casting" the entire expression, this would only convert |
| 4186 | the already computed result: |
| 4187 | |
| 4188 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! |
| 4189 | |
| 4190 | Beware also of the order of more complicated expressions like: |
| 4191 | |
| 4192 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int |
| 4193 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto |
| 4194 | |
| 4195 | If in doubt, break the expression into simpler terms, or cast all operands |
| 4196 | to the desired resulting type. |
| 4197 | |
| 4198 | Scalar values are a bit different, since: |
| 4199 | |
| 4200 | $float = 2 + $mbf; |
| 4201 | $float = $mbf + 2; |
| 4202 | |
| 4203 | will both result in the proper type due to the way the overloaded math works. |
| 4204 | |
| 4205 | This section also applies to other overloaded math packages, like Math::String. |
| 4206 | |
| 4207 | One solution to you problem might be L<autoupgrading|upgrading>. |
| 4208 | |
| 4209 | =item bsqrt() |
| 4210 | |
| 4211 | C<bsqrt()> works only good if the result is a big integer, e.g. the square |
| 4212 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
| 4213 | mode. |
| 4214 | |
| 4215 | If you want a better approximation of the square root, then use: |
| 4216 | |
| 4217 | $x = Math::BigFloat->new(12); |
| 4218 | Math::BigFloat->precision(0); |
| 4219 | Math::BigFloat->round_mode('even'); |
| 4220 | print $x->copy->bsqrt(),"\n"; # 4 |
| 4221 | |
| 4222 | Math::BigFloat->precision(2); |
| 4223 | print $x->bsqrt(),"\n"; # 3.46 |
| 4224 | print $x->bsqrt(3),"\n"; # 3.464 |
| 4225 | |
| 4226 | =item brsft() |
| 4227 | |
| 4228 | For negative numbers in base see also L<brsft|brsft>. |
| 4229 | |
| 4230 | =back |
| 4231 | |
| 4232 | =head1 LICENSE |
| 4233 | |
| 4234 | This program is free software; you may redistribute it and/or modify it under |
| 4235 | the same terms as Perl itself. |
| 4236 | |
| 4237 | =head1 SEE ALSO |
| 4238 | |
| 4239 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
| 4240 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
| 4241 | |
| 4242 | The package at |
| 4243 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains |
| 4244 | more documentation including a full version history, testcases, empty |
| 4245 | subclass files and benchmarks. |
| 4246 | |
| 4247 | =head1 AUTHORS |
| 4248 | |
| 4249 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
| 4250 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001. |
| 4251 | |
| 4252 | =cut |