| 1 | |
| 2 | # |
| 3 | # "Tax the rat farms." - Lord Vetinari |
| 4 | # |
| 5 | |
| 6 | # The following hash values are used: |
| 7 | # sign : +,-,NaN,+inf,-inf |
| 8 | # _d : denominator |
| 9 | # _n : numeraotr (value = _n/_d) |
| 10 | # _a : accuracy |
| 11 | # _p : precision |
| 12 | # You should not look at the innards of a BigRat - use the methods for this. |
| 13 | |
| 14 | package Math::BigRat; |
| 15 | |
| 16 | require 5.005_03; |
| 17 | use strict; |
| 18 | |
| 19 | use Math::BigFloat; |
| 20 | use vars qw($VERSION @ISA $upgrade $downgrade |
| 21 | $accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf); |
| 22 | |
| 23 | @ISA = qw(Math::BigFloat); |
| 24 | |
| 25 | $VERSION = '0.15'; |
| 26 | |
| 27 | use overload; # inherit overload from Math::BigFloat |
| 28 | |
| 29 | BEGIN |
| 30 | { |
| 31 | *objectify = \&Math::BigInt::objectify; # inherit this from BigInt |
| 32 | *AUTOLOAD = \&Math::BigFloat::AUTOLOAD; # can't inherit AUTOLOAD |
| 33 | # we inherit these from BigFloat because currently it is not possible |
| 34 | # that MBF has a different $MBI variable than we, because MBF also uses |
| 35 | # Math::BigInt::config->('lib'); (there is always only one library loaded) |
| 36 | *_e_add = \&Math::BigFloat::_e_add; |
| 37 | *_e_sub = \&Math::BigFloat::_e_sub; |
| 38 | *as_int = \&as_number; |
| 39 | *is_pos = \&is_positive; |
| 40 | *is_neg = \&is_negative; |
| 41 | } |
| 42 | |
| 43 | ############################################################################## |
| 44 | # Global constants and flags. Access these only via the accessor methods! |
| 45 | |
| 46 | $accuracy = $precision = undef; |
| 47 | $round_mode = 'even'; |
| 48 | $div_scale = 40; |
| 49 | $upgrade = undef; |
| 50 | $downgrade = undef; |
| 51 | |
| 52 | # These are internally, and not to be used from the outside at all! |
| 53 | |
| 54 | $_trap_nan = 0; # are NaNs ok? set w/ config() |
| 55 | $_trap_inf = 0; # are infs ok? set w/ config() |
| 56 | |
| 57 | # the package we are using for our private parts, defaults to: |
| 58 | # Math::BigInt->config()->{lib} |
| 59 | my $MBI = 'Math::BigInt::Calc'; |
| 60 | |
| 61 | my $nan = 'NaN'; |
| 62 | my $class = 'Math::BigRat'; |
| 63 | |
| 64 | sub isa |
| 65 | { |
| 66 | return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't |
| 67 | UNIVERSAL::isa(@_); |
| 68 | } |
| 69 | |
| 70 | ############################################################################## |
| 71 | |
| 72 | sub _new_from_float |
| 73 | { |
| 74 | # turn a single float input into a rational number (like '0.1') |
| 75 | my ($self,$f) = @_; |
| 76 | |
| 77 | return $self->bnan() if $f->is_nan(); |
| 78 | return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/; |
| 79 | |
| 80 | $self->{_n} = $MBI->_copy( $f->{_m} ); # mantissa |
| 81 | $self->{_d} = $MBI->_one(); |
| 82 | $self->{sign} = $f->{sign} || '+'; |
| 83 | if ($f->{_es} eq '-') |
| 84 | { |
| 85 | # something like Math::BigRat->new('0.1'); |
| 86 | # 1 / 1 => 1/10 |
| 87 | $MBI->_lsft ( $self->{_d}, $f->{_e} ,10); |
| 88 | } |
| 89 | else |
| 90 | { |
| 91 | # something like Math::BigRat->new('10'); |
| 92 | # 1 / 1 => 10/1 |
| 93 | $MBI->_lsft ( $self->{_n}, $f->{_e} ,10) unless |
| 94 | $MBI->_is_zero($f->{_e}); |
| 95 | } |
| 96 | $self; |
| 97 | } |
| 98 | |
| 99 | sub new |
| 100 | { |
| 101 | # create a Math::BigRat |
| 102 | my $class = shift; |
| 103 | |
| 104 | my ($n,$d) = @_; |
| 105 | |
| 106 | my $self = { }; bless $self,$class; |
| 107 | |
| 108 | # input like (BigInt) or (BigFloat): |
| 109 | if ((!defined $d) && (ref $n) && (!$n->isa('Math::BigRat'))) |
| 110 | { |
| 111 | if ($n->isa('Math::BigFloat')) |
| 112 | { |
| 113 | $self->_new_from_float($n); |
| 114 | } |
| 115 | if ($n->isa('Math::BigInt')) |
| 116 | { |
| 117 | # TODO: trap NaN, inf |
| 118 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N |
| 119 | $self->{_d} = $MBI->_one(); # d => 1 |
| 120 | $self->{sign} = $n->{sign}; |
| 121 | } |
| 122 | if ($n->isa('Math::BigInt::Lite')) |
| 123 | { |
| 124 | # TODO: trap NaN, inf |
| 125 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; |
| 126 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = N |
| 127 | $self->{_d} = $MBI->_one(); # d => 1 |
| 128 | } |
| 129 | return $self->bnorm(); # normalize (120/1 => 12/10) |
| 130 | } |
| 131 | |
| 132 | # input like (BigInt,BigInt) or (BigLite,BigLite): |
| 133 | if (ref($d) && ref($n)) |
| 134 | { |
| 135 | # do N first (for $self->{sign}): |
| 136 | if ($n->isa('Math::BigInt')) |
| 137 | { |
| 138 | # TODO: trap NaN, inf |
| 139 | $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = N |
| 140 | $self->{sign} = $n->{sign}; |
| 141 | } |
| 142 | elsif ($n->isa('Math::BigInt::Lite')) |
| 143 | { |
| 144 | # TODO: trap NaN, inf |
| 145 | $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; |
| 146 | $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = $n |
| 147 | } |
| 148 | else |
| 149 | { |
| 150 | require Carp; |
| 151 | Carp::croak(ref($n) . " is not a recognized object format for Math::BigRat->new"); |
| 152 | } |
| 153 | # now D: |
| 154 | if ($d->isa('Math::BigInt')) |
| 155 | { |
| 156 | # TODO: trap NaN, inf |
| 157 | $self->{_d} = $MBI->_copy($d->{value}); # "mantissa" = D |
| 158 | # +/+ or -/- => +, +/- or -/+ => - |
| 159 | $self->{sign} = $d->{sign} ne $self->{sign} ? '-' : '+'; |
| 160 | } |
| 161 | elsif ($d->isa('Math::BigInt::Lite')) |
| 162 | { |
| 163 | # TODO: trap NaN, inf |
| 164 | $self->{_d} = $MBI->_new(abs($$d)); # "mantissa" = D |
| 165 | my $ds = '+'; $ds = '-' if $$d < 0; |
| 166 | # +/+ or -/- => +, +/- or -/+ => - |
| 167 | $self->{sign} = $ds ne $self->{sign} ? '-' : '+'; |
| 168 | } |
| 169 | else |
| 170 | { |
| 171 | require Carp; |
| 172 | Carp::croak(ref($d) . " is not a recognized object format for Math::BigRat->new"); |
| 173 | } |
| 174 | return $self->bnorm(); # normalize (120/1 => 12/10) |
| 175 | } |
| 176 | return $n->copy() if ref $n; # already a BigRat |
| 177 | |
| 178 | if (!defined $n) |
| 179 | { |
| 180 | $self->{_n} = $MBI->_zero(); # undef => 0 |
| 181 | $self->{_d} = $MBI->_one(); |
| 182 | $self->{sign} = '+'; |
| 183 | return $self; |
| 184 | } |
| 185 | |
| 186 | # string input with / delimiter |
| 187 | if ($n =~ /\s*\/\s*/) |
| 188 | { |
| 189 | return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
| 190 | return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid |
| 191 | ($n,$d) = split (/\//,$n); |
| 192 | # try as BigFloats first |
| 193 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) |
| 194 | { |
| 195 | local $Math::BigFloat::accuracy = undef; |
| 196 | local $Math::BigFloat::precision = undef; |
| 197 | |
| 198 | # one of them looks like a float |
| 199 | my $nf = Math::BigFloat->new($n,undef,undef); |
| 200 | $self->{sign} = '+'; |
| 201 | return $self->bnan() if $nf->is_nan(); |
| 202 | |
| 203 | $self->{_n} = $MBI->_copy( $nf->{_m} ); # get mantissa |
| 204 | |
| 205 | # now correct $self->{_n} due to $n |
| 206 | my $f = Math::BigFloat->new($d,undef,undef); |
| 207 | return $self->bnan() if $f->is_nan(); |
| 208 | $self->{_d} = $MBI->_copy( $f->{_m} ); |
| 209 | |
| 210 | # calculate the difference between nE and dE |
| 211 | # XXX TODO: check that exponent() makes a copy to avoid copy() |
| 212 | my $diff_e = $nf->exponent()->copy()->bsub( $f->exponent); |
| 213 | if ($diff_e->is_negative()) |
| 214 | { |
| 215 | # < 0: mul d with it |
| 216 | $MBI->_lsft( $self->{_d}, $MBI->_new( $diff_e->babs()), 10); |
| 217 | } |
| 218 | elsif (!$diff_e->is_zero()) |
| 219 | { |
| 220 | # > 0: mul n with it |
| 221 | $MBI->_lsft( $self->{_n}, $MBI->_new( $diff_e), 10); |
| 222 | } |
| 223 | } |
| 224 | else |
| 225 | { |
| 226 | # both d and n look like (big)ints |
| 227 | |
| 228 | $self->{sign} = '+'; # no sign => '+' |
| 229 | $self->{_n} = undef; |
| 230 | $self->{_d} = undef; |
| 231 | if ($n =~ /^([+-]?)0*(\d+)\z/) # first part ok? |
| 232 | { |
| 233 | $self->{sign} = $1 || '+'; # no sign => '+' |
| 234 | $self->{_n} = $MBI->_new($2 || 0); |
| 235 | } |
| 236 | |
| 237 | if ($d =~ /^([+-]?)0*(\d+)\z/) # second part ok? |
| 238 | { |
| 239 | $self->{sign} =~ tr/+-/-+/ if ($1 || '') eq '-'; # negate if second part neg. |
| 240 | $self->{_d} = $MBI->_new($2 || 0); |
| 241 | } |
| 242 | |
| 243 | if (!defined $self->{_n} || !defined $self->{_d}) |
| 244 | { |
| 245 | $d = Math::BigInt->new($d,undef,undef) unless ref $d; |
| 246 | $n = Math::BigInt->new($n,undef,undef) unless ref $n; |
| 247 | |
| 248 | if ($n->{sign} =~ /^[+-]$/ && $d->{sign} =~ /^[+-]$/) |
| 249 | { |
| 250 | # both parts are ok as integers (wierd things like ' 1e0' |
| 251 | $self->{_n} = $MBI->_copy($n->{value}); |
| 252 | $self->{_d} = $MBI->_copy($d->{value}); |
| 253 | $self->{sign} = $n->{sign}; |
| 254 | $self->{sign} =~ tr/+-/-+/ if $d->{sign} eq '-'; # -1/-2 => 1/2 |
| 255 | return $self->bnorm(); |
| 256 | } |
| 257 | |
| 258 | $self->{sign} = '+'; # a default sign |
| 259 | return $self->bnan() if $n->is_nan() || $d->is_nan(); |
| 260 | |
| 261 | # handle inf cases: |
| 262 | if ($n->is_inf() || $d->is_inf()) |
| 263 | { |
| 264 | if ($n->is_inf()) |
| 265 | { |
| 266 | return $self->bnan() if $d->is_inf(); # both are inf => NaN |
| 267 | my $s = '+'; # '+inf/+123' or '-inf/-123' |
| 268 | $s = '-' if substr($n->{sign},0,1) ne $d->{sign}; |
| 269 | # +-inf/123 => +-inf |
| 270 | return $self->binf($s); |
| 271 | } |
| 272 | # 123/inf => 0 |
| 273 | return $self->bzero(); |
| 274 | } |
| 275 | } |
| 276 | } |
| 277 | |
| 278 | return $self->bnorm(); |
| 279 | } |
| 280 | |
| 281 | # simple string input |
| 282 | if (($n =~ /[\.eE]/)) |
| 283 | { |
| 284 | # looks like a float, quacks like a float, so probably is a float |
| 285 | $self->{sign} = 'NaN'; |
| 286 | local $Math::BigFloat::accuracy = undef; |
| 287 | local $Math::BigFloat::precision = undef; |
| 288 | $self->_new_from_float(Math::BigFloat->new($n,undef,undef)); |
| 289 | } |
| 290 | else |
| 291 | { |
| 292 | # for simple forms, use $MBI directly |
| 293 | if ($n =~ /^([+-]?)0*(\d+)\z/) |
| 294 | { |
| 295 | $self->{sign} = $1 || '+'; |
| 296 | $self->{_n} = $MBI->_new($2 || 0); |
| 297 | $self->{_d} = $MBI->_one(); |
| 298 | } |
| 299 | else |
| 300 | { |
| 301 | my $n = Math::BigInt->new($n,undef,undef); |
| 302 | $self->{_n} = $MBI->_copy($n->{value}); |
| 303 | $self->{_d} = $MBI->_one(); |
| 304 | $self->{sign} = $n->{sign}; |
| 305 | return $self->bnan() if $self->{sign} eq 'NaN'; |
| 306 | return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/; |
| 307 | } |
| 308 | } |
| 309 | $self->bnorm(); |
| 310 | } |
| 311 | |
| 312 | sub copy |
| 313 | { |
| 314 | # if two arguments, the first one is the class to "swallow" subclasses |
| 315 | my ($c,$x) = @_; |
| 316 | |
| 317 | if (scalar @_ == 1) |
| 318 | { |
| 319 | $x = $_[0]; |
| 320 | $c = ref($x); |
| 321 | } |
| 322 | return unless ref($x); # only for objects |
| 323 | |
| 324 | my $self = bless {}, $c; |
| 325 | |
| 326 | $self->{sign} = $x->{sign}; |
| 327 | $self->{_d} = $MBI->_copy($x->{_d}); |
| 328 | $self->{_n} = $MBI->_copy($x->{_n}); |
| 329 | $self->{_a} = $x->{_a} if defined $x->{_a}; |
| 330 | $self->{_p} = $x->{_p} if defined $x->{_p}; |
| 331 | $self; |
| 332 | } |
| 333 | |
| 334 | ############################################################################## |
| 335 | |
| 336 | sub config |
| 337 | { |
| 338 | # return (later set?) configuration data as hash ref |
| 339 | my $class = shift || 'Math::BigRat'; |
| 340 | |
| 341 | my $cfg = $class->SUPER::config(@_); |
| 342 | |
| 343 | # now we need only to override the ones that are different from our parent |
| 344 | $cfg->{class} = $class; |
| 345 | $cfg->{with} = $MBI; |
| 346 | $cfg; |
| 347 | } |
| 348 | |
| 349 | ############################################################################## |
| 350 | |
| 351 | sub bstr |
| 352 | { |
| 353 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 354 | |
| 355 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
| 356 | { |
| 357 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
| 358 | return $s; |
| 359 | } |
| 360 | |
| 361 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2' |
| 362 | |
| 363 | return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d}); |
| 364 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
| 365 | } |
| 366 | |
| 367 | sub bsstr |
| 368 | { |
| 369 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 370 | |
| 371 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
| 372 | { |
| 373 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
| 374 | return $s; |
| 375 | } |
| 376 | |
| 377 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
| 378 | $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d}); |
| 379 | } |
| 380 | |
| 381 | sub bnorm |
| 382 | { |
| 383 | # reduce the number to the shortest form |
| 384 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 385 | |
| 386 | # Both parts must be objects of whatever we are using today. |
| 387 | # Second check because Calc.pm has ARRAY res as unblessed objects. |
| 388 | if (ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY') |
| 389 | { |
| 390 | require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).') in bnorm()'); |
| 391 | } |
| 392 | if (ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY') |
| 393 | { |
| 394 | require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).') in bnorm()'); |
| 395 | } |
| 396 | |
| 397 | # no normalize for NaN, inf etc. |
| 398 | return $x if $x->{sign} !~ /^[+-]$/; |
| 399 | |
| 400 | # normalize zeros to 0/1 |
| 401 | if ($MBI->_is_zero($x->{_n})) |
| 402 | { |
| 403 | $x->{sign} = '+'; # never leave a -0 |
| 404 | $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d}); |
| 405 | return $x; |
| 406 | } |
| 407 | |
| 408 | return $x if $MBI->_is_one($x->{_d}); # no need to reduce |
| 409 | |
| 410 | # reduce other numbers |
| 411 | my $gcd = $MBI->_copy($x->{_n}); |
| 412 | $gcd = $MBI->_gcd($gcd,$x->{_d}); |
| 413 | |
| 414 | if (!$MBI->_is_one($gcd)) |
| 415 | { |
| 416 | $x->{_n} = $MBI->_div($x->{_n},$gcd); |
| 417 | $x->{_d} = $MBI->_div($x->{_d},$gcd); |
| 418 | } |
| 419 | $x; |
| 420 | } |
| 421 | |
| 422 | ############################################################################## |
| 423 | # sign manipulation |
| 424 | |
| 425 | sub bneg |
| 426 | { |
| 427 | # (BRAT or num_str) return BRAT |
| 428 | # negate number or make a negated number from string |
| 429 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 430 | |
| 431 | return $x if $x->modify('bneg'); |
| 432 | |
| 433 | # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN' |
| 434 | $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $MBI->_is_zero($x->{_n})); |
| 435 | $x; |
| 436 | } |
| 437 | |
| 438 | ############################################################################## |
| 439 | # special values |
| 440 | |
| 441 | sub _bnan |
| 442 | { |
| 443 | # used by parent class bnan() to initialize number to NaN |
| 444 | my $self = shift; |
| 445 | |
| 446 | if ($_trap_nan) |
| 447 | { |
| 448 | require Carp; |
| 449 | my $class = ref($self); |
| 450 | # "$self" below will stringify the object, this blows up if $self is a |
| 451 | # partial object (happens under trap_nan), so fix it beforehand |
| 452 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; |
| 453 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; |
| 454 | Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); |
| 455 | } |
| 456 | $self->{_n} = $MBI->_zero(); |
| 457 | $self->{_d} = $MBI->_zero(); |
| 458 | } |
| 459 | |
| 460 | sub _binf |
| 461 | { |
| 462 | # used by parent class bone() to initialize number to +inf/-inf |
| 463 | my $self = shift; |
| 464 | |
| 465 | if ($_trap_inf) |
| 466 | { |
| 467 | require Carp; |
| 468 | my $class = ref($self); |
| 469 | # "$self" below will stringify the object, this blows up if $self is a |
| 470 | # partial object (happens under trap_nan), so fix it beforehand |
| 471 | $self->{_d} = $MBI->_zero() unless defined $self->{_d}; |
| 472 | $self->{_n} = $MBI->_zero() unless defined $self->{_n}; |
| 473 | Carp::croak ("Tried to set $self to inf in $class\::_binf()"); |
| 474 | } |
| 475 | $self->{_n} = $MBI->_zero(); |
| 476 | $self->{_d} = $MBI->_zero(); |
| 477 | } |
| 478 | |
| 479 | sub _bone |
| 480 | { |
| 481 | # used by parent class bone() to initialize number to +1/-1 |
| 482 | my $self = shift; |
| 483 | $self->{_n} = $MBI->_one(); |
| 484 | $self->{_d} = $MBI->_one(); |
| 485 | } |
| 486 | |
| 487 | sub _bzero |
| 488 | { |
| 489 | # used by parent class bzero() to initialize number to 0 |
| 490 | my $self = shift; |
| 491 | $self->{_n} = $MBI->_zero(); |
| 492 | $self->{_d} = $MBI->_one(); |
| 493 | } |
| 494 | |
| 495 | ############################################################################## |
| 496 | # mul/add/div etc |
| 497 | |
| 498 | sub badd |
| 499 | { |
| 500 | # add two rational numbers |
| 501 | |
| 502 | # set up parameters |
| 503 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 504 | # objectify is costly, so avoid it |
| 505 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 506 | { |
| 507 | ($self,$x,$y,@r) = objectify(2,@_); |
| 508 | } |
| 509 | |
| 510 | # +inf + +inf => +inf, -inf + -inf => -inf |
| 511 | return $x->binf(substr($x->{sign},0,1)) |
| 512 | if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
| 513 | |
| 514 | # +inf + -inf or -inf + +inf => NaN |
| 515 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
| 516 | |
| 517 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
| 518 | # - + - = --------- = -- |
| 519 | # 4 3 4*3 12 |
| 520 | |
| 521 | # we do not compute the gcd() here, but simple do: |
| 522 | # 5 7 5*3 + 7*4 43 |
| 523 | # - + - = --------- = -- |
| 524 | # 4 3 4*3 12 |
| 525 | |
| 526 | # and bnorm() will then take care of the rest |
| 527 | |
| 528 | # 5 * 3 |
| 529 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
| 530 | |
| 531 | # 7 * 4 |
| 532 | my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} ); |
| 533 | |
| 534 | # 5 * 3 + 7 * 4 |
| 535 | ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign}); |
| 536 | |
| 537 | # 4 * 3 |
| 538 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
| 539 | |
| 540 | # normalize result, and possible round |
| 541 | $x->bnorm()->round(@r); |
| 542 | } |
| 543 | |
| 544 | sub bsub |
| 545 | { |
| 546 | # subtract two rational numbers |
| 547 | |
| 548 | # set up parameters |
| 549 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 550 | # objectify is costly, so avoid it |
| 551 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 552 | { |
| 553 | ($self,$x,$y,@r) = objectify(2,@_); |
| 554 | } |
| 555 | |
| 556 | # flip sign of $x, call badd(), then flip sign of result |
| 557 | $x->{sign} =~ tr/+-/-+/ |
| 558 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
| 559 | $x->badd($y,@r); # does norm and round |
| 560 | $x->{sign} =~ tr/+-/-+/ |
| 561 | unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0 |
| 562 | $x; |
| 563 | } |
| 564 | |
| 565 | sub bmul |
| 566 | { |
| 567 | # multiply two rational numbers |
| 568 | |
| 569 | # set up parameters |
| 570 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 571 | # objectify is costly, so avoid it |
| 572 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 573 | { |
| 574 | ($self,$x,$y,@r) = objectify(2,@_); |
| 575 | } |
| 576 | |
| 577 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
| 578 | |
| 579 | # inf handling |
| 580 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
| 581 | { |
| 582 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
| 583 | # result will always be +-inf: |
| 584 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
| 585 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
| 586 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
| 587 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
| 588 | return $x->binf('-'); |
| 589 | } |
| 590 | |
| 591 | # x== 0 # also: or y == 1 or y == -1 |
| 592 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
| 593 | |
| 594 | # XXX TODO: |
| 595 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
| 596 | # and reducing in one step. This would save us the bnorm() at the end. |
| 597 | |
| 598 | # 1 2 1 * 2 2 1 |
| 599 | # - * - = ----- = - = - |
| 600 | # 4 3 4 * 3 12 6 |
| 601 | |
| 602 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n}); |
| 603 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d}); |
| 604 | |
| 605 | # compute new sign |
| 606 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
| 607 | |
| 608 | $x->bnorm()->round(@r); |
| 609 | } |
| 610 | |
| 611 | sub bdiv |
| 612 | { |
| 613 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
| 614 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
| 615 | |
| 616 | # set up parameters |
| 617 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 618 | # objectify is costly, so avoid it |
| 619 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 620 | { |
| 621 | ($self,$x,$y,@r) = objectify(2,@_); |
| 622 | } |
| 623 | |
| 624 | return $self->_div_inf($x,$y) |
| 625 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
| 626 | |
| 627 | # x== 0 # also: or y == 1 or y == -1 |
| 628 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
| 629 | |
| 630 | # XXX TODO: list context, upgrade |
| 631 | # According to Knuth, this can be optimized by doing gcd twice (for d and n) |
| 632 | # and reducing in one step. This would save us the bnorm() at the end. |
| 633 | |
| 634 | # 1 1 1 3 |
| 635 | # - / - == - * - |
| 636 | # 4 3 4 1 |
| 637 | |
| 638 | $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d}); |
| 639 | $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n}); |
| 640 | |
| 641 | # compute new sign |
| 642 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
| 643 | |
| 644 | $x->bnorm()->round(@r); |
| 645 | $x; |
| 646 | } |
| 647 | |
| 648 | sub bmod |
| 649 | { |
| 650 | # compute "remainder" (in Perl way) of $x / $y |
| 651 | |
| 652 | # set up parameters |
| 653 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 654 | # objectify is costly, so avoid it |
| 655 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 656 | { |
| 657 | ($self,$x,$y,@r) = objectify(2,@_); |
| 658 | } |
| 659 | |
| 660 | return $self->_div_inf($x,$y) |
| 661 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
| 662 | |
| 663 | return $x if $x->is_zero(); # 0 / 7 = 0, mod 0 |
| 664 | |
| 665 | # compute $x - $y * floor($x/$y), keeping the sign of $x |
| 666 | |
| 667 | # copy x to u, make it positive and then do a normal division ($u/$y) |
| 668 | my $u = bless { sign => '+' }, $self; |
| 669 | $u->{_n} = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d} ); |
| 670 | $u->{_d} = $MBI->_mul( $MBI->_copy($x->{_d}), $y->{_n} ); |
| 671 | |
| 672 | # compute floor(u) |
| 673 | if (! $MBI->_is_one($u->{_d})) |
| 674 | { |
| 675 | $u->{_n} = $MBI->_div($u->{_n},$u->{_d}); # 22/7 => 3/1 w/ truncate |
| 676 | # no need to set $u->{_d} to 1, since below we set it to $y->{_d} anyway |
| 677 | } |
| 678 | |
| 679 | # now compute $y * $u |
| 680 | $u->{_d} = $MBI->_copy($y->{_d}); # 1 * $y->{_d}, see floor above |
| 681 | $u->{_n} = $MBI->_mul($u->{_n},$y->{_n}); |
| 682 | |
| 683 | my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive |
| 684 | # compute $x - $u |
| 685 | $x->bsub($u); |
| 686 | $x->{sign} = $xsign; # put sign back |
| 687 | |
| 688 | $x->bnorm()->round(@r); |
| 689 | } |
| 690 | |
| 691 | ############################################################################## |
| 692 | # bdec/binc |
| 693 | |
| 694 | sub bdec |
| 695 | { |
| 696 | # decrement value (subtract 1) |
| 697 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 698 | |
| 699 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
| 700 | |
| 701 | if ($x->{sign} eq '-') |
| 702 | { |
| 703 | $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2 |
| 704 | } |
| 705 | else |
| 706 | { |
| 707 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d? |
| 708 | { |
| 709 | # 1/3 -- => -2/3 |
| 710 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
| 711 | $x->{sign} = '-'; |
| 712 | } |
| 713 | else |
| 714 | { |
| 715 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2 |
| 716 | } |
| 717 | } |
| 718 | $x->bnorm()->round(@r); |
| 719 | } |
| 720 | |
| 721 | sub binc |
| 722 | { |
| 723 | # increment value (add 1) |
| 724 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 725 | |
| 726 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf |
| 727 | |
| 728 | if ($x->{sign} eq '-') |
| 729 | { |
| 730 | if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) |
| 731 | { |
| 732 | # -1/3 ++ => 2/3 (overflow at 0) |
| 733 | $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n}); |
| 734 | $x->{sign} = '+'; |
| 735 | } |
| 736 | else |
| 737 | { |
| 738 | $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2 |
| 739 | } |
| 740 | } |
| 741 | else |
| 742 | { |
| 743 | $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2 |
| 744 | } |
| 745 | $x->bnorm()->round(@r); |
| 746 | } |
| 747 | |
| 748 | ############################################################################## |
| 749 | # is_foo methods (the rest is inherited) |
| 750 | |
| 751 | sub is_int |
| 752 | { |
| 753 | # return true if arg (BRAT or num_str) is an integer |
| 754 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 755 | |
| 756 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
| 757 | $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer |
| 758 | 0; |
| 759 | } |
| 760 | |
| 761 | sub is_zero |
| 762 | { |
| 763 | # return true if arg (BRAT or num_str) is zero |
| 764 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 765 | |
| 766 | return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); |
| 767 | 0; |
| 768 | } |
| 769 | |
| 770 | sub is_one |
| 771 | { |
| 772 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
| 773 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 774 | |
| 775 | my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; |
| 776 | return 1 |
| 777 | if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})); |
| 778 | 0; |
| 779 | } |
| 780 | |
| 781 | sub is_odd |
| 782 | { |
| 783 | # return true if arg (BFLOAT or num_str) is odd or false if even |
| 784 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 785 | |
| 786 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
| 787 | ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1 |
| 788 | 0; |
| 789 | } |
| 790 | |
| 791 | sub is_even |
| 792 | { |
| 793 | # return true if arg (BINT or num_str) is even or false if odd |
| 794 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 795 | |
| 796 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
| 797 | return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never |
| 798 | && $MBI->_is_even($x->{_n})); # but 4/1 is |
| 799 | 0; |
| 800 | } |
| 801 | |
| 802 | ############################################################################## |
| 803 | # parts() and friends |
| 804 | |
| 805 | sub numerator |
| 806 | { |
| 807 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 808 | |
| 809 | # NaN, inf, -inf |
| 810 | return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); |
| 811 | |
| 812 | my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign}; |
| 813 | $n; |
| 814 | } |
| 815 | |
| 816 | sub denominator |
| 817 | { |
| 818 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 819 | |
| 820 | # NaN |
| 821 | return Math::BigInt->new($x->{sign}) if $x->{sign} eq 'NaN'; |
| 822 | # inf, -inf |
| 823 | return Math::BigInt->bone() if $x->{sign} !~ /^[+-]$/; |
| 824 | |
| 825 | Math::BigInt->new($MBI->_str($x->{_d})); |
| 826 | } |
| 827 | |
| 828 | sub parts |
| 829 | { |
| 830 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 831 | |
| 832 | my $c = 'Math::BigInt'; |
| 833 | |
| 834 | return ($c->bnan(),$c->bnan()) if $x->{sign} eq 'NaN'; |
| 835 | return ($c->binf(),$c->binf()) if $x->{sign} eq '+inf'; |
| 836 | return ($c->binf('-'),$c->binf()) if $x->{sign} eq '-inf'; |
| 837 | |
| 838 | my $n = $c->new( $MBI->_str($x->{_n})); |
| 839 | $n->{sign} = $x->{sign}; |
| 840 | my $d = $c->new( $MBI->_str($x->{_d})); |
| 841 | ($n,$d); |
| 842 | } |
| 843 | |
| 844 | sub length |
| 845 | { |
| 846 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 847 | |
| 848 | return $nan unless $x->is_int(); |
| 849 | $MBI->_len($x->{_n}); # length(-123/1) => length(123) |
| 850 | } |
| 851 | |
| 852 | sub digit |
| 853 | { |
| 854 | my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_); |
| 855 | |
| 856 | return $nan unless $x->is_int(); |
| 857 | $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2) |
| 858 | } |
| 859 | |
| 860 | ############################################################################## |
| 861 | # special calc routines |
| 862 | |
| 863 | sub bceil |
| 864 | { |
| 865 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 866 | |
| 867 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
| 868 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
| 869 | |
| 870 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
| 871 | $x->{_d} = $MBI->_one(); # d => 1 |
| 872 | $x->{_n} = $MBI->_inc($x->{_n}) |
| 873 | if $x->{sign} eq '+'; # +22/7 => 4/1 |
| 874 | $x->{sign} = '+' if $MBI->_is_zero($x->{_n}); # -0 => 0 |
| 875 | $x; |
| 876 | } |
| 877 | |
| 878 | sub bfloor |
| 879 | { |
| 880 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 881 | |
| 882 | return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf |
| 883 | $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0 |
| 884 | |
| 885 | $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate |
| 886 | $x->{_d} = $MBI->_one(); # d => 1 |
| 887 | $x->{_n} = $MBI->_inc($x->{_n}) |
| 888 | if $x->{sign} eq '-'; # -22/7 => -4/1 |
| 889 | $x; |
| 890 | } |
| 891 | |
| 892 | sub bfac |
| 893 | { |
| 894 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 895 | |
| 896 | # if $x is not an integer |
| 897 | if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d}))) |
| 898 | { |
| 899 | return $x->bnan(); |
| 900 | } |
| 901 | |
| 902 | $x->{_n} = $MBI->_fac($x->{_n}); |
| 903 | # since _d is 1, we don't need to reduce/norm the result |
| 904 | $x->round(@r); |
| 905 | } |
| 906 | |
| 907 | sub bpow |
| 908 | { |
| 909 | # power ($x ** $y) |
| 910 | |
| 911 | # set up parameters |
| 912 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 913 | # objectify is costly, so avoid it |
| 914 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 915 | { |
| 916 | ($self,$x,$y,@r) = objectify(2,@_); |
| 917 | } |
| 918 | |
| 919 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
| 920 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
| 921 | return $x->bone(@r) if $y->is_zero(); |
| 922 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
| 923 | |
| 924 | if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d})) |
| 925 | { |
| 926 | # if $x == -1 and odd/even y => +1/-1 |
| 927 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
| 928 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
| 929 | } |
| 930 | # 1 ** -y => 1 / (1 ** |y|) |
| 931 | # so do test for negative $y after above's clause |
| 932 | |
| 933 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
| 934 | |
| 935 | # shortcut y/1 (and/or x/1) |
| 936 | if ($MBI->_is_one($y->{_d})) |
| 937 | { |
| 938 | # shortcut for x/1 and y/1 |
| 939 | if ($MBI->_is_one($x->{_d})) |
| 940 | { |
| 941 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1 |
| 942 | if ($y->{sign} eq '-') |
| 943 | { |
| 944 | # 0.2 ** -3 => 1/(0.2 ** 3) |
| 945 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
| 946 | } |
| 947 | # correct sign; + ** + => + |
| 948 | if ($x->{sign} eq '-') |
| 949 | { |
| 950 | # - * - => +, - * - * - => - |
| 951 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
| 952 | } |
| 953 | return $x->round(@r); |
| 954 | } |
| 955 | # x/z ** y/1 |
| 956 | $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y |
| 957 | $x->{_d} = $MBI->_pow($x->{_d},$y->{_n}); |
| 958 | if ($y->{sign} eq '-') |
| 959 | { |
| 960 | # 0.2 ** -3 => 1/(0.2 ** 3) |
| 961 | ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap |
| 962 | } |
| 963 | # correct sign; + ** + => + |
| 964 | if ($x->{sign} eq '-') |
| 965 | { |
| 966 | # - * - => +, - * - * - => - |
| 967 | $x->{sign} = '+' if $MBI->_is_even($y->{_n}); |
| 968 | } |
| 969 | return $x->round(@r); |
| 970 | } |
| 971 | |
| 972 | # regular calculation (this is wrong for d/e ** f/g) |
| 973 | my $pow2 = $self->bone(); |
| 974 | my $y1 = $MBI->_div ( $MBI->_copy($y->{_n}), $y->{_d}); |
| 975 | my $two = $MBI->_two(); |
| 976 | |
| 977 | while (!$MBI->_is_one($y1)) |
| 978 | { |
| 979 | $pow2->bmul($x) if $MBI->_is_odd($y1); |
| 980 | $MBI->_div($y1, $two); |
| 981 | $x->bmul($x); |
| 982 | } |
| 983 | $x->bmul($pow2) unless $pow2->is_one(); |
| 984 | # n ** -x => 1/n ** x |
| 985 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; |
| 986 | $x->bnorm()->round(@r); |
| 987 | } |
| 988 | |
| 989 | sub blog |
| 990 | { |
| 991 | # set up parameters |
| 992 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 993 | |
| 994 | # objectify is costly, so avoid it |
| 995 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 996 | { |
| 997 | ($self,$x,$y,@r) = objectify(2,$class,@_); |
| 998 | } |
| 999 | |
| 1000 | # blog(1,Y) => 0 |
| 1001 | return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; |
| 1002 | |
| 1003 | # $x <= 0 => NaN |
| 1004 | return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; |
| 1005 | |
| 1006 | if ($x->is_int() && $y->is_int()) |
| 1007 | { |
| 1008 | return $self->new($x->as_number()->blog($y->as_number(),@r)); |
| 1009 | } |
| 1010 | |
| 1011 | # do it with floats |
| 1012 | $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); |
| 1013 | } |
| 1014 | |
| 1015 | sub _float_from_part |
| 1016 | { |
| 1017 | my $x = shift; |
| 1018 | |
| 1019 | my $f = Math::BigFloat->bzero(); |
| 1020 | $f->{_m} = $MBI->_copy($x); |
| 1021 | $f->{_e} = $MBI->_zero(); |
| 1022 | |
| 1023 | $f; |
| 1024 | } |
| 1025 | |
| 1026 | sub _as_float |
| 1027 | { |
| 1028 | my $x = shift; |
| 1029 | |
| 1030 | local $Math::BigFloat::upgrade = undef; |
| 1031 | local $Math::BigFloat::accuracy = undef; |
| 1032 | local $Math::BigFloat::precision = undef; |
| 1033 | # 22/7 => 3.142857143.. |
| 1034 | |
| 1035 | my $a = $x->accuracy() || 0; |
| 1036 | if ($a != 0 || !$MBI->_is_one($x->{_d})) |
| 1037 | { |
| 1038 | # n/d |
| 1039 | return Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy()); |
| 1040 | } |
| 1041 | # just n |
| 1042 | Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n})); |
| 1043 | } |
| 1044 | |
| 1045 | sub broot |
| 1046 | { |
| 1047 | # set up parameters |
| 1048 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1049 | # objectify is costly, so avoid it |
| 1050 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1051 | { |
| 1052 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1053 | } |
| 1054 | |
| 1055 | if ($x->is_int() && $y->is_int()) |
| 1056 | { |
| 1057 | return $self->new($x->as_number()->broot($y->as_number(),@r)); |
| 1058 | } |
| 1059 | |
| 1060 | # do it with floats |
| 1061 | $x->_new_from_float( $x->_as_float()->broot($y,@r) ); |
| 1062 | } |
| 1063 | |
| 1064 | sub bmodpow |
| 1065 | { |
| 1066 | # set up parameters |
| 1067 | my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); |
| 1068 | # objectify is costly, so avoid it |
| 1069 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1070 | { |
| 1071 | ($self,$x,$y,$m,@r) = objectify(3,@_); |
| 1072 | } |
| 1073 | |
| 1074 | # $x or $y or $m are NaN or +-inf => NaN |
| 1075 | return $x->bnan() |
| 1076 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || |
| 1077 | $m->{sign} !~ /^[+-]$/; |
| 1078 | |
| 1079 | if ($x->is_int() && $y->is_int() && $m->is_int()) |
| 1080 | { |
| 1081 | return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); |
| 1082 | } |
| 1083 | |
| 1084 | warn ("bmodpow() not fully implemented"); |
| 1085 | $x->bnan(); |
| 1086 | } |
| 1087 | |
| 1088 | sub bmodinv |
| 1089 | { |
| 1090 | # set up parameters |
| 1091 | my ($self,$x,$y,@r) = (ref($_[0]),@_); |
| 1092 | # objectify is costly, so avoid it |
| 1093 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1094 | { |
| 1095 | ($self,$x,$y,@r) = objectify(2,@_); |
| 1096 | } |
| 1097 | |
| 1098 | # $x or $y are NaN or +-inf => NaN |
| 1099 | return $x->bnan() |
| 1100 | if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; |
| 1101 | |
| 1102 | if ($x->is_int() && $y->is_int()) |
| 1103 | { |
| 1104 | return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); |
| 1105 | } |
| 1106 | |
| 1107 | warn ("bmodinv() not fully implemented"); |
| 1108 | $x->bnan(); |
| 1109 | } |
| 1110 | |
| 1111 | sub bsqrt |
| 1112 | { |
| 1113 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1114 | |
| 1115 | return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 |
| 1116 | return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf |
| 1117 | return $x->round(@r) if $x->is_zero() || $x->is_one(); |
| 1118 | |
| 1119 | local $Math::BigFloat::upgrade = undef; |
| 1120 | local $Math::BigFloat::downgrade = undef; |
| 1121 | local $Math::BigFloat::precision = undef; |
| 1122 | local $Math::BigFloat::accuracy = undef; |
| 1123 | local $Math::BigInt::upgrade = undef; |
| 1124 | local $Math::BigInt::precision = undef; |
| 1125 | local $Math::BigInt::accuracy = undef; |
| 1126 | |
| 1127 | $x->{_n} = _float_from_part( $x->{_n} )->bsqrt(); |
| 1128 | $x->{_d} = _float_from_part( $x->{_d} )->bsqrt(); |
| 1129 | |
| 1130 | # XXX TODO: we probably can optimze this: |
| 1131 | |
| 1132 | # if sqrt(D) was not integer |
| 1133 | if ($x->{_d}->{_es} ne '+') |
| 1134 | { |
| 1135 | $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 |
| 1136 | $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1 |
| 1137 | } |
| 1138 | # if sqrt(N) was not integer |
| 1139 | if ($x->{_n}->{_es} ne '+') |
| 1140 | { |
| 1141 | $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 |
| 1142 | $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451 |
| 1143 | } |
| 1144 | |
| 1145 | # convert parts to $MBI again |
| 1146 | $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10) |
| 1147 | if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY'; |
| 1148 | $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10) |
| 1149 | if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY'; |
| 1150 | |
| 1151 | $x->bnorm()->round(@r); |
| 1152 | } |
| 1153 | |
| 1154 | sub blsft |
| 1155 | { |
| 1156 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
| 1157 | |
| 1158 | $b = 2 unless defined $b; |
| 1159 | $b = $self->new($b) unless ref ($b); |
| 1160 | $x->bmul( $b->copy()->bpow($y), @r); |
| 1161 | $x; |
| 1162 | } |
| 1163 | |
| 1164 | sub brsft |
| 1165 | { |
| 1166 | my ($self,$x,$y,$b,@r) = objectify(3,@_); |
| 1167 | |
| 1168 | $b = 2 unless defined $b; |
| 1169 | $b = $self->new($b) unless ref ($b); |
| 1170 | $x->bdiv( $b->copy()->bpow($y), @r); |
| 1171 | $x; |
| 1172 | } |
| 1173 | |
| 1174 | ############################################################################## |
| 1175 | # round |
| 1176 | |
| 1177 | sub round |
| 1178 | { |
| 1179 | $_[0]; |
| 1180 | } |
| 1181 | |
| 1182 | sub bround |
| 1183 | { |
| 1184 | $_[0]; |
| 1185 | } |
| 1186 | |
| 1187 | sub bfround |
| 1188 | { |
| 1189 | $_[0]; |
| 1190 | } |
| 1191 | |
| 1192 | ############################################################################## |
| 1193 | # comparing |
| 1194 | |
| 1195 | sub bcmp |
| 1196 | { |
| 1197 | # compare two signed numbers |
| 1198 | |
| 1199 | # set up parameters |
| 1200 | my ($self,$x,$y) = (ref($_[0]),@_); |
| 1201 | # objectify is costly, so avoid it |
| 1202 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1203 | { |
| 1204 | ($self,$x,$y) = objectify(2,@_); |
| 1205 | } |
| 1206 | |
| 1207 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 1208 | { |
| 1209 | # handle +-inf and NaN |
| 1210 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 1211 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
| 1212 | return +1 if $x->{sign} eq '+inf'; |
| 1213 | return -1 if $x->{sign} eq '-inf'; |
| 1214 | return -1 if $y->{sign} eq '+inf'; |
| 1215 | return +1; |
| 1216 | } |
| 1217 | # check sign for speed first |
| 1218 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
| 1219 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
| 1220 | |
| 1221 | # shortcut |
| 1222 | my $xz = $MBI->_is_zero($x->{_n}); |
| 1223 | my $yz = $MBI->_is_zero($y->{_n}); |
| 1224 | return 0 if $xz && $yz; # 0 <=> 0 |
| 1225 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
| 1226 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
| 1227 | |
| 1228 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
| 1229 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
| 1230 | |
| 1231 | my $cmp = $MBI->_acmp($t,$u); # signs are equal |
| 1232 | $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse |
| 1233 | $cmp; |
| 1234 | } |
| 1235 | |
| 1236 | sub bacmp |
| 1237 | { |
| 1238 | # compare two numbers (as unsigned) |
| 1239 | |
| 1240 | # set up parameters |
| 1241 | my ($self,$x,$y) = (ref($_[0]),@_); |
| 1242 | # objectify is costly, so avoid it |
| 1243 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1244 | { |
| 1245 | ($self,$x,$y) = objectify(2,$class,@_); |
| 1246 | } |
| 1247 | |
| 1248 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 1249 | { |
| 1250 | # handle +-inf and NaN |
| 1251 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 1252 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
| 1253 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
| 1254 | return -1; |
| 1255 | } |
| 1256 | |
| 1257 | my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d}); |
| 1258 | my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d}); |
| 1259 | $MBI->_acmp($t,$u); # ignore signs |
| 1260 | } |
| 1261 | |
| 1262 | ############################################################################## |
| 1263 | # output conversation |
| 1264 | |
| 1265 | sub numify |
| 1266 | { |
| 1267 | # convert 17/8 => float (aka 2.125) |
| 1268 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1269 | |
| 1270 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc |
| 1271 | |
| 1272 | # N/1 => N |
| 1273 | my $neg = ''; $neg = '-' if $x->{sign} eq '-'; |
| 1274 | return $neg . $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d}); |
| 1275 | |
| 1276 | $x->_as_float()->numify() + 0.0; |
| 1277 | } |
| 1278 | |
| 1279 | sub as_number |
| 1280 | { |
| 1281 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1282 | |
| 1283 | return Math::BigInt->new($x) if $x->{sign} !~ /^[+-]$/; # NaN, inf etc |
| 1284 | |
| 1285 | my $u = Math::BigInt->bzero(); |
| 1286 | $u->{sign} = $x->{sign}; |
| 1287 | $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3 |
| 1288 | $u; |
| 1289 | } |
| 1290 | |
| 1291 | sub as_bin |
| 1292 | { |
| 1293 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1294 | |
| 1295 | return $x unless $x->is_int(); |
| 1296 | |
| 1297 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
| 1298 | $s . $MBI->_as_bin($x->{_n}); |
| 1299 | } |
| 1300 | |
| 1301 | sub as_hex |
| 1302 | { |
| 1303 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
| 1304 | |
| 1305 | return $x unless $x->is_int(); |
| 1306 | |
| 1307 | my $s = $x->{sign}; $s = '' if $s eq '+'; |
| 1308 | $s . $MBI->_as_hex($x->{_n}); |
| 1309 | } |
| 1310 | |
| 1311 | ############################################################################## |
| 1312 | # import |
| 1313 | |
| 1314 | sub import |
| 1315 | { |
| 1316 | my $self = shift; |
| 1317 | my $l = scalar @_; |
| 1318 | my $lib = ''; my @a; |
| 1319 | |
| 1320 | for ( my $i = 0; $i < $l ; $i++) |
| 1321 | { |
| 1322 | if ( $_[$i] eq ':constant' ) |
| 1323 | { |
| 1324 | # this rest causes overlord er load to step in |
| 1325 | overload::constant float => sub { $self->new(shift); }; |
| 1326 | } |
| 1327 | # elsif ($_[$i] eq 'upgrade') |
| 1328 | # { |
| 1329 | # # this causes upgrading |
| 1330 | # $upgrade = $_[$i+1]; # or undef to disable |
| 1331 | # $i++; |
| 1332 | # } |
| 1333 | elsif ($_[$i] eq 'downgrade') |
| 1334 | { |
| 1335 | # this causes downgrading |
| 1336 | $downgrade = $_[$i+1]; # or undef to disable |
| 1337 | $i++; |
| 1338 | } |
| 1339 | elsif ($_[$i] eq 'lib') |
| 1340 | { |
| 1341 | $lib = $_[$i+1] || ''; # default Calc |
| 1342 | $i++; |
| 1343 | } |
| 1344 | elsif ($_[$i] eq 'with') |
| 1345 | { |
| 1346 | # this argument is no longer used |
| 1347 | #$MBI = $_[$i+1] || 'Math::BigInt::Calc'; # default Math::BigInt::Calc |
| 1348 | $i++; |
| 1349 | } |
| 1350 | else |
| 1351 | { |
| 1352 | push @a, $_[$i]; |
| 1353 | } |
| 1354 | } |
| 1355 | require Math::BigInt; |
| 1356 | |
| 1357 | # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still have GMP |
| 1358 | if ($lib ne '') |
| 1359 | { |
| 1360 | my @c = split /\s*,\s*/, $lib; |
| 1361 | foreach (@c) |
| 1362 | { |
| 1363 | $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters |
| 1364 | } |
| 1365 | $lib = join(",", @c); |
| 1366 | } |
| 1367 | my @import = ('objectify'); |
| 1368 | push @import, lib => $lib if $lib ne ''; |
| 1369 | |
| 1370 | # MBI already loaded, so feed it our lib arguments |
| 1371 | Math::BigInt->import( @import ); |
| 1372 | |
| 1373 | $MBI = Math::BigFloat->config()->{lib}; |
| 1374 | |
| 1375 | # register us with MBI to get notified of future lib changes |
| 1376 | Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } ); |
| 1377 | |
| 1378 | # any non :constant stuff is handled by our parent, Exporter (loaded |
| 1379 | # by Math::BigFloat, even if @_ is empty, to give it a chance |
| 1380 | $self->SUPER::import(@a); # for subclasses |
| 1381 | $self->export_to_level(1,$self,@a); # need this, too |
| 1382 | } |
| 1383 | |
| 1384 | 1; |
| 1385 | |
| 1386 | __END__ |
| 1387 | |
| 1388 | =head1 NAME |
| 1389 | |
| 1390 | Math::BigRat - Arbitrary big rational numbers |
| 1391 | |
| 1392 | =head1 SYNOPSIS |
| 1393 | |
| 1394 | use Math::BigRat; |
| 1395 | |
| 1396 | my $x = Math::BigRat->new('3/7'); $x += '5/9'; |
| 1397 | |
| 1398 | print $x->bstr(),"\n"; |
| 1399 | print $x ** 2,"\n"; |
| 1400 | |
| 1401 | my $y = Math::BigRat->new('inf'); |
| 1402 | print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; |
| 1403 | |
| 1404 | my $z = Math::BigRat->new(144); $z->bsqrt(); |
| 1405 | |
| 1406 | =head1 DESCRIPTION |
| 1407 | |
| 1408 | Math::BigRat complements Math::BigInt and Math::BigFloat by providing support |
| 1409 | for arbitrary big rational numbers. |
| 1410 | |
| 1411 | =head2 MATH LIBRARY |
| 1412 | |
| 1413 | Math with the numbers is done (by default) by a module called |
| 1414 | Math::BigInt::Calc. This is equivalent to saying: |
| 1415 | |
| 1416 | use Math::BigRat lib => 'Calc'; |
| 1417 | |
| 1418 | You can change this by using: |
| 1419 | |
| 1420 | use Math::BigRat lib => 'BitVect'; |
| 1421 | |
| 1422 | The following would first try to find Math::BigInt::Foo, then |
| 1423 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
| 1424 | |
| 1425 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
| 1426 | |
| 1427 | Calc.pm uses as internal format an array of elements of some decimal base |
| 1428 | (usually 1e7, but this might be different for some systems) with the least |
| 1429 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
| 1430 | significant bit first. Other modules might use even different means of |
| 1431 | representing the numbers. See the respective module documentation for further |
| 1432 | details. |
| 1433 | |
| 1434 | Currently the following replacement libraries exist, search for them at CPAN: |
| 1435 | |
| 1436 | Math::BigInt::BitVect |
| 1437 | Math::BigInt::GMP |
| 1438 | Math::BigInt::Pari |
| 1439 | Math::BigInt::FastCalc |
| 1440 | |
| 1441 | =head1 METHODS |
| 1442 | |
| 1443 | Any methods not listed here are dervied from Math::BigFloat (or |
| 1444 | Math::BigInt), so make sure you check these two modules for further |
| 1445 | information. |
| 1446 | |
| 1447 | =head2 new() |
| 1448 | |
| 1449 | $x = Math::BigRat->new('1/3'); |
| 1450 | |
| 1451 | Create a new Math::BigRat object. Input can come in various forms: |
| 1452 | |
| 1453 | $x = Math::BigRat->new(123); # scalars |
| 1454 | $x = Math::BigRat->new('inf'); # infinity |
| 1455 | $x = Math::BigRat->new('123.3'); # float |
| 1456 | $x = Math::BigRat->new('1/3'); # simple string |
| 1457 | $x = Math::BigRat->new('1 / 3'); # spaced |
| 1458 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
| 1459 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
| 1460 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
| 1461 | $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite |
| 1462 | |
| 1463 | # You can also give D and N as different objects: |
| 1464 | $x = Math::BigRat->new( |
| 1465 | Math::BigInt->new(-123), |
| 1466 | Math::BigInt->new(7), |
| 1467 | ); # => -123/7 |
| 1468 | |
| 1469 | =head2 numerator() |
| 1470 | |
| 1471 | $n = $x->numerator(); |
| 1472 | |
| 1473 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
| 1474 | |
| 1475 | =head2 denominator() |
| 1476 | |
| 1477 | $d = $x->denominator(); |
| 1478 | |
| 1479 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
| 1480 | |
| 1481 | =head2 parts() |
| 1482 | |
| 1483 | ($n,$d) = $x->parts(); |
| 1484 | |
| 1485 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
| 1486 | BigInts. |
| 1487 | |
| 1488 | =head2 as_int() |
| 1489 | |
| 1490 | $x = Math::BigRat->new('13/7'); |
| 1491 | print $x->as_int(),"\n"; # '1' |
| 1492 | |
| 1493 | Returns a copy of the object as BigInt, truncated to an integer. |
| 1494 | |
| 1495 | C<as_number()> is an alias for C<as_int()>. |
| 1496 | |
| 1497 | =head2 as_hex() |
| 1498 | |
| 1499 | $x = Math::BigRat->new('13'); |
| 1500 | print $x->as_hex(),"\n"; # '0xd' |
| 1501 | |
| 1502 | Returns the BigRat as hexadecimal string. Works only for integers. |
| 1503 | |
| 1504 | =head2 as_bin() |
| 1505 | |
| 1506 | $x = Math::BigRat->new('13'); |
| 1507 | print $x->as_bin(),"\n"; # '0x1101' |
| 1508 | |
| 1509 | Returns the BigRat as binary string. Works only for integers. |
| 1510 | |
| 1511 | =head2 bfac() |
| 1512 | |
| 1513 | $x->bfac(); |
| 1514 | |
| 1515 | Calculates the factorial of $x. For instance: |
| 1516 | |
| 1517 | print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 |
| 1518 | print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 |
| 1519 | |
| 1520 | Works currently only for integers. |
| 1521 | |
| 1522 | =head2 blog() |
| 1523 | |
| 1524 | Is not yet implemented. |
| 1525 | |
| 1526 | =head2 bround()/round()/bfround() |
| 1527 | |
| 1528 | Are not yet implemented. |
| 1529 | |
| 1530 | =head2 bmod() |
| 1531 | |
| 1532 | use Math::BigRat; |
| 1533 | my $x = Math::BigRat->new('7/4'); |
| 1534 | my $y = Math::BigRat->new('4/3'); |
| 1535 | print $x->bmod($y); |
| 1536 | |
| 1537 | Set $x to the remainder of the division of $x by $y. |
| 1538 | |
| 1539 | =head2 is_one() |
| 1540 | |
| 1541 | print "$x is 1\n" if $x->is_one(); |
| 1542 | |
| 1543 | Return true if $x is exactly one, otherwise false. |
| 1544 | |
| 1545 | =head2 is_zero() |
| 1546 | |
| 1547 | print "$x is 0\n" if $x->is_zero(); |
| 1548 | |
| 1549 | Return true if $x is exactly zero, otherwise false. |
| 1550 | |
| 1551 | =head2 is_pos() |
| 1552 | |
| 1553 | print "$x is >= 0\n" if $x->is_positive(); |
| 1554 | |
| 1555 | Return true if $x is positive (greater than or equal to zero), otherwise |
| 1556 | false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. |
| 1557 | |
| 1558 | C<is_positive()> is an alias for C<is_pos()>. |
| 1559 | |
| 1560 | =head2 is_neg() |
| 1561 | |
| 1562 | print "$x is < 0\n" if $x->is_negative(); |
| 1563 | |
| 1564 | Return true if $x is negative (smaller than zero), otherwise false. Please |
| 1565 | note that '-inf' is also negative, while 'NaN' and '+inf' aren't. |
| 1566 | |
| 1567 | C<is_negative()> is an alias for C<is_neg()>. |
| 1568 | |
| 1569 | =head2 is_int() |
| 1570 | |
| 1571 | print "$x is an integer\n" if $x->is_int(); |
| 1572 | |
| 1573 | Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise |
| 1574 | false. Please note that '-inf', 'inf' and 'NaN' aren't integer. |
| 1575 | |
| 1576 | =head2 is_odd() |
| 1577 | |
| 1578 | print "$x is odd\n" if $x->is_odd(); |
| 1579 | |
| 1580 | Return true if $x is odd, otherwise false. |
| 1581 | |
| 1582 | =head2 is_even() |
| 1583 | |
| 1584 | print "$x is even\n" if $x->is_even(); |
| 1585 | |
| 1586 | Return true if $x is even, otherwise false. |
| 1587 | |
| 1588 | =head2 bceil() |
| 1589 | |
| 1590 | $x->bceil(); |
| 1591 | |
| 1592 | Set $x to the next bigger integer value (e.g. truncate the number to integer |
| 1593 | and then increment it by one). |
| 1594 | |
| 1595 | =head2 bfloor() |
| 1596 | |
| 1597 | $x->bfloor(); |
| 1598 | |
| 1599 | Truncate $x to an integer value. |
| 1600 | |
| 1601 | =head2 bsqrt() |
| 1602 | |
| 1603 | $x->bsqrt(); |
| 1604 | |
| 1605 | Calculate the square root of $x. |
| 1606 | |
| 1607 | =head2 config |
| 1608 | |
| 1609 | use Data::Dumper; |
| 1610 | |
| 1611 | print Dumper ( Math::BigRat->config() ); |
| 1612 | print Math::BigRat->config()->{lib},"\n"; |
| 1613 | |
| 1614 | Returns a hash containing the configuration, e.g. the version number, lib |
| 1615 | loaded etc. The following hash keys are currently filled in with the |
| 1616 | appropriate information. |
| 1617 | |
| 1618 | key RO/RW Description |
| 1619 | Example |
| 1620 | ============================================================ |
| 1621 | lib RO Name of the Math library |
| 1622 | Math::BigInt::Calc |
| 1623 | lib_version RO Version of 'lib' |
| 1624 | 0.30 |
| 1625 | class RO The class of config you just called |
| 1626 | Math::BigRat |
| 1627 | version RO version number of the class you used |
| 1628 | 0.10 |
| 1629 | upgrade RW To which class numbers are upgraded |
| 1630 | undef |
| 1631 | downgrade RW To which class numbers are downgraded |
| 1632 | undef |
| 1633 | precision RW Global precision |
| 1634 | undef |
| 1635 | accuracy RW Global accuracy |
| 1636 | undef |
| 1637 | round_mode RW Global round mode |
| 1638 | even |
| 1639 | div_scale RW Fallback acccuracy for div |
| 1640 | 40 |
| 1641 | trap_nan RW Trap creation of NaN (undef = no) |
| 1642 | undef |
| 1643 | trap_inf RW Trap creation of +inf/-inf (undef = no) |
| 1644 | undef |
| 1645 | |
| 1646 | By passing a reference to a hash you may set the configuration values. This |
| 1647 | works only for values that a marked with a C<RW> above, anything else is |
| 1648 | read-only. |
| 1649 | |
| 1650 | =head1 BUGS |
| 1651 | |
| 1652 | Some things are not yet implemented, or only implemented half-way: |
| 1653 | |
| 1654 | =over 2 |
| 1655 | |
| 1656 | =item inf handling (partial) |
| 1657 | |
| 1658 | =item NaN handling (partial) |
| 1659 | |
| 1660 | =item rounding (not implemented except for bceil/bfloor) |
| 1661 | |
| 1662 | =item $x ** $y where $y is not an integer |
| 1663 | |
| 1664 | =item bmod(), blog(), bmodinv() and bmodpow() (partial) |
| 1665 | |
| 1666 | =back |
| 1667 | |
| 1668 | =head1 LICENSE |
| 1669 | |
| 1670 | This program is free software; you may redistribute it and/or modify it under |
| 1671 | the same terms as Perl itself. |
| 1672 | |
| 1673 | =head1 SEE ALSO |
| 1674 | |
| 1675 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
| 1676 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
| 1677 | |
| 1678 | See L<http://search.cpan.org/search?dist=bignum> for a way to use |
| 1679 | Math::BigRat. |
| 1680 | |
| 1681 | The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> |
| 1682 | may contain more documentation and examples as well as testcases. |
| 1683 | |
| 1684 | =head1 AUTHORS |
| 1685 | |
| 1686 | (C) by Tels L<http://bloodgate.com/> 2001 - 2005. |
| 1687 | |
| 1688 | =cut |