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| 184f15d5 |
1 | #!/usr/bin/perl -w |
| 2 | |
| 3 | # The following hash values are used: |
| 4 | # sign : +,-,NaN,+inf,-inf |
| 5 | # _d : denominator |
| 6 | # _n : numeraotr (value = _n/_d) |
| 7 | # _a : accuracy |
| 8 | # _p : precision |
| 9 | # _f : flags, used by MBR to flag parts of a rationale as untouchable |
| 10 | |
| 11 | package Math::BigRat; |
| 12 | |
| 13 | require 5.005_02; |
| 14 | use strict; |
| 15 | |
| 16 | use Exporter; |
| 17 | use Math::BigFloat; |
| 18 | use vars qw($VERSION @ISA $PACKAGE @EXPORT_OK $upgrade $downgrade |
| 19 | $accuracy $precision $round_mode $div_scale); |
| 20 | |
| 21 | @ISA = qw(Exporter Math::BigFloat); |
| 22 | @EXPORT_OK = qw(); |
| 23 | |
| 24 | $VERSION = '0.04'; |
| 25 | |
| 26 | use overload; # inherit from Math::BigFloat |
| 27 | |
| 28 | ############################################################################## |
| 29 | # global constants, flags and accessory |
| 30 | |
| 31 | use constant MB_NEVER_ROUND => 0x0001; |
| 32 | |
| 33 | $accuracy = $precision = undef; |
| 34 | $round_mode = 'even'; |
| 35 | $div_scale = 40; |
| 36 | $upgrade = undef; |
| 37 | $downgrade = undef; |
| 38 | |
| 39 | my $nan = 'NaN'; |
| 40 | my $class = 'Math::BigRat'; |
| 41 | |
| 42 | sub _new_from_float |
| 43 | { |
| 44 | # turn a single float input into a rationale (like '0.1') |
| 45 | my ($self,$f) = @_; |
| 46 | |
| 47 | return $self->bnan() if $f->is_nan(); |
| 48 | return $self->binf('-inf') if $f->{sign} eq '-inf'; |
| 49 | return $self->binf('+inf') if $f->{sign} eq '+inf'; |
| 50 | |
| 51 | #print "f $f caller", join(' ',caller()),"\n"; |
| 52 | $self->{_n} = $f->{_m}->copy(); # mantissa |
| 53 | $self->{_d} = Math::BigInt->bone(); |
| 54 | $self->{sign} = $f->{sign}; $self->{_n}->{sign} = '+'; |
| 55 | if ($f->{_e}->{sign} eq '-') |
| 56 | { |
| 57 | # something like Math::BigRat->new('0.1'); |
| 58 | $self->{_d}->blsft($f->{_e}->copy()->babs(),10); # 1 / 1 => 1/10 |
| 59 | } |
| 60 | else |
| 61 | { |
| 62 | # something like Math::BigRat->new('10'); |
| 63 | # 1 / 1 => 10/1 |
| 64 | $self->{_n}->blsft($f->{_e},10) unless $f->{_e}->is_zero(); |
| 65 | } |
| 66 | # print "float new $self->{_n} / $self->{_d}\n"; |
| 67 | $self; |
| 68 | } |
| 69 | |
| 70 | sub new |
| 71 | { |
| 72 | # create a Math::BigRat |
| 73 | my $class = shift; |
| 74 | |
| 75 | my ($n,$d) = shift; |
| 76 | |
| 77 | my $self = { }; bless $self,$class; |
| 78 | |
| 79 | # print "ref ",ref($d),"\n"; |
| 80 | # if (ref($d)) |
| 81 | # { |
| 82 | # print "isa float ",$d->isa('Math::BigFloat'),"\n"; |
| 83 | # print "isa int ",$d->isa('Math::BigInt'),"\n"; |
| 84 | # print "isa rat ",$d->isa('Math::BigRat'),"\n"; |
| 85 | # } |
| 86 | |
| 87 | # input like (BigInt,BigInt) or (BigFloat,BigFloat) not handled yet |
| 88 | |
| 89 | if ((ref $n) && (!$n->isa('Math::BigRat'))) |
| 90 | { |
| 91 | # print "is ref, but not rat\n"; |
| 92 | if ($n->isa('Math::BigFloat')) |
| 93 | { |
| 94 | # print "is ref, and float\n"; |
| 95 | return $self->_new_from_float($n)->bnorm(); |
| 96 | } |
| 97 | if ($n->isa('Math::BigInt')) |
| 98 | { |
| 99 | # print "is ref, and int\n"; |
| 100 | $self->{_n} = $n->copy(); # "mantissa" = $d |
| 101 | $self->{_d} = Math::BigInt->bone(); |
| 102 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
| 103 | return $self->bnorm(); |
| 104 | } |
| 105 | } |
| 106 | return $n->copy() if ref $n; |
| 107 | |
| 108 | # print "is string\n"; |
| 109 | |
| 110 | if (!defined $n) |
| 111 | { |
| 112 | $self->{_n} = Math::BigInt->bzero(); # undef => 0 |
| 113 | $self->{_d} = Math::BigInt->bone(); |
| 114 | $self->{sign} = '+'; |
| 115 | return $self->bnorm(); |
| 116 | } |
| 117 | # string input with / delimiter |
| 118 | if ($n =~ /\s*\/\s*/) |
| 119 | { |
| 120 | return Math::BigRat->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid |
| 121 | return Math::BigRat->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid |
| 122 | ($n,$d) = split (/\//,$n); |
| 123 | # try as BigFloats first |
| 124 | if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) |
| 125 | { |
| 126 | # one of them looks like a float |
| 127 | $self->_new_from_float(Math::BigFloat->new($n)); |
| 128 | # now correct $self->{_n} due to $n |
| 129 | my $f = Math::BigFloat->new($d); |
| 130 | if ($f->{_e}->{sign} eq '-') |
| 131 | { |
| 132 | # 10 / 0.1 => 100/1 |
| 133 | $self->{_n}->blsft($f->{_e}->copy()->babs(),10); |
| 134 | } |
| 135 | else |
| 136 | { |
| 137 | $self->{_d}->blsft($f->{_e},10); # 1 / 1 => 10/1 |
| 138 | } |
| 139 | } |
| 140 | else |
| 141 | { |
| 142 | $self->{_n} = Math::BigInt->new($n); |
| 143 | $self->{_d} = Math::BigInt->new($d); |
| 144 | return $self->bnan() if $self->{_n}->is_nan() || $self->{_d}->is_nan(); |
| 145 | # inf handling is missing here |
| 146 | |
| 147 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
| 148 | # if $d is negative, flip sign |
| 149 | $self->{sign} =~ tr/+-/-+/ if $self->{_d}->{sign} eq '-'; |
| 150 | $self->{_d}->{sign} = '+'; # normalize |
| 151 | } |
| 152 | return $self->bnorm(); |
| 153 | } |
| 154 | |
| 155 | # simple string input |
| 156 | if (($n =~ /[\.eE]/)) |
| 157 | { |
| 158 | # looks like a float |
| 159 | # print "float-like string $d\n"; |
| 160 | $self->_new_from_float(Math::BigFloat->new($n)); |
| 161 | } |
| 162 | else |
| 163 | { |
| 164 | $self->{_n} = Math::BigInt->new($n); |
| 165 | $self->{_d} = Math::BigInt->bone(); |
| 166 | $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; |
| 167 | } |
| 168 | $self->bnorm(); |
| 169 | } |
| 170 | |
| 171 | sub bstr |
| 172 | { |
| 173 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 174 | |
| 175 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
| 176 | { |
| 177 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
| 178 | return $s; |
| 179 | } |
| 180 | |
| 181 | # print "bstr $x->{sign} $x->{_n} $x->{_d}\n"; |
| 182 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
| 183 | |
| 184 | return $s.$x->{_n}->bstr() if $x->{_d}->is_one(); |
| 185 | return $s.$x->{_n}->bstr() . '/' . $x->{_d}->bstr(); |
| 186 | } |
| 187 | |
| 188 | sub bsstr |
| 189 | { |
| 190 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 191 | |
| 192 | if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc |
| 193 | { |
| 194 | my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf |
| 195 | return $s; |
| 196 | } |
| 197 | |
| 198 | my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 |
| 199 | return $x->{_n}->bstr() . '/' . $x->{_d}->bstr(); |
| 200 | } |
| 201 | |
| 202 | sub bnorm |
| 203 | { |
| 204 | # reduce the number to the shortest form and remember this (so that we |
| 205 | # don't reduce again) |
| 206 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 207 | |
| 208 | # this is to prevent automatically rounding when MBI's globals are set |
| 209 | $x->{_d}->{_f} = MB_NEVER_ROUND; |
| 210 | $x->{_n}->{_f} = MB_NEVER_ROUND; |
| 211 | # 'forget' that parts were rounded via MBI::bround() in MBF's bfround() |
| 212 | $x->{_d}->{_a} = undef; $x->{_n}->{_a} = undef; |
| 213 | $x->{_d}->{_p} = undef; $x->{_n}->{_p} = undef; |
| 214 | |
| 215 | # normalize zeros to 0/1 |
| 216 | if (($x->{sign} =~ /^[+-]$/) && |
| 217 | ($x->{_n}->is_zero())) |
| 218 | { |
| 219 | $x->{sign} = '+'; # never -0 |
| 220 | $x->{_d} = Math::BigInt->bone() unless $x->{_d}->is_one(); |
| 221 | return $x; |
| 222 | } |
| 223 | |
| 224 | # print "$x->{_n} / $x->{_d} => "; |
| 225 | # reduce other numbers |
| 226 | my $gcd = $x->{_n}->bgcd($x->{_d}); |
| 227 | |
| 228 | if (!$gcd->is_one()) |
| 229 | { |
| 230 | $x->{_n}->bdiv($gcd); |
| 231 | $x->{_d}->bdiv($gcd); |
| 232 | } |
| 233 | # print "$x->{_n} / $x->{_d}\n"; |
| 234 | $x; |
| 235 | } |
| 236 | |
| 237 | ############################################################################## |
| 238 | # special values |
| 239 | |
| 240 | sub _bnan |
| 241 | { |
| 242 | # used by parent class bone() to initialize number to 1 |
| 243 | my $self = shift; |
| 244 | $self->{_n} = Math::BigInt->bzero(); |
| 245 | $self->{_d} = Math::BigInt->bzero(); |
| 246 | } |
| 247 | |
| 248 | sub _binf |
| 249 | { |
| 250 | # used by parent class bone() to initialize number to 1 |
| 251 | my $self = shift; |
| 252 | $self->{_n} = Math::BigInt->bzero(); |
| 253 | $self->{_d} = Math::BigInt->bzero(); |
| 254 | } |
| 255 | |
| 256 | sub _bone |
| 257 | { |
| 258 | # used by parent class bone() to initialize number to 1 |
| 259 | my $self = shift; |
| 260 | $self->{_n} = Math::BigInt->bone(); |
| 261 | $self->{_d} = Math::BigInt->bone(); |
| 262 | } |
| 263 | |
| 264 | sub _bzero |
| 265 | { |
| 266 | # used by parent class bone() to initialize number to 1 |
| 267 | my $self = shift; |
| 268 | $self->{_n} = Math::BigInt->bzero(); |
| 269 | $self->{_d} = Math::BigInt->bone(); |
| 270 | } |
| 271 | |
| 272 | ############################################################################## |
| 273 | # mul/add/div etc |
| 274 | |
| 275 | sub badd |
| 276 | { |
| 277 | # add two rationales |
| 278 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 279 | |
| 280 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
| 281 | |
| 282 | # TODO: upgrade |
| 283 | |
| 284 | # # upgrade |
| 285 | # return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
| 286 | |
| 287 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
| 288 | # - + - = --------- = -- |
| 289 | # 4 3 4*3 12 |
| 290 | |
| 291 | my $gcd = $x->{_d}->bgcd($y->{_d}); |
| 292 | |
| 293 | my $aa = $x->{_d}->copy(); |
| 294 | my $bb = $y->{_d}->copy(); |
| 295 | if ($gcd->is_one()) |
| 296 | { |
| 297 | $bb->bdiv($gcd); $aa->bdiv($gcd); |
| 298 | } |
| 299 | $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign}; |
| 300 | my $m = $y->{_n}->copy()->bmul($aa); |
| 301 | $m->{sign} = $y->{sign}; # 2/1 - 2/1 |
| 302 | $x->{_n}->badd($m); |
| 303 | |
| 304 | $x->{_d}->bmul($y->{_d}); |
| 305 | |
| 306 | # calculate new sign |
| 307 | $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; |
| 308 | |
| 309 | $x->bnorm()->round($a,$p,$r); |
| 310 | } |
| 311 | |
| 312 | sub bsub |
| 313 | { |
| 314 | # subtract two rationales |
| 315 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 316 | |
| 317 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
| 318 | # TODO: inf handling |
| 319 | |
| 320 | # TODO: upgrade |
| 321 | |
| 322 | # # upgrade |
| 323 | # return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
| 324 | |
| 325 | # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 |
| 326 | # - + - = --------- = -- |
| 327 | # 4 3 4*3 12 |
| 328 | |
| 329 | my $gcd = $x->{_d}->bgcd($y->{_d}); |
| 330 | |
| 331 | my $aa = $x->{_d}->copy(); |
| 332 | my $bb = $y->{_d}->copy(); |
| 333 | if ($gcd->is_one()) |
| 334 | { |
| 335 | $bb->bdiv($gcd); $aa->bdiv($gcd); |
| 336 | } |
| 337 | $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign}; |
| 338 | my $m = $y->{_n}->copy()->bmul($aa); |
| 339 | $m->{sign} = $y->{sign}; # 2/1 - 2/1 |
| 340 | $x->{_n}->bsub($m); |
| 341 | |
| 342 | $x->{_d}->bmul($y->{_d}); |
| 343 | |
| 344 | # calculate new sign |
| 345 | $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; |
| 346 | |
| 347 | $x->bnorm()->round($a,$p,$r); |
| 348 | } |
| 349 | |
| 350 | sub bmul |
| 351 | { |
| 352 | # multiply two rationales |
| 353 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 354 | |
| 355 | return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); |
| 356 | |
| 357 | # inf handling |
| 358 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
| 359 | { |
| 360 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
| 361 | # result will always be +-inf: |
| 362 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
| 363 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
| 364 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
| 365 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
| 366 | return $x->binf('-'); |
| 367 | } |
| 368 | |
| 369 | # x== 0 # also: or y == 1 or y == -1 |
| 370 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
| 371 | |
| 372 | # TODO: upgrade |
| 373 | |
| 374 | # # upgrade |
| 375 | # return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
| 376 | |
| 377 | # According to Knuth, this can be optimized by doingtwice gcd (for d and n) |
| 378 | # and reducing in one step) |
| 379 | |
| 380 | # 1 1 2 1 |
| 381 | # - * - = - = - |
| 382 | # 4 3 12 6 |
| 383 | $x->{_n}->bmul($y->{_n}); |
| 384 | $x->{_d}->bmul($y->{_d}); |
| 385 | |
| 386 | # compute new sign |
| 387 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
| 388 | |
| 389 | $x->bnorm()->round($a,$p,$r); |
| 390 | } |
| 391 | |
| 392 | sub bdiv |
| 393 | { |
| 394 | # (dividend: BRAT or num_str, divisor: BRAT or num_str) return |
| 395 | # (BRAT,BRAT) (quo,rem) or BRAT (only rem) |
| 396 | my ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 397 | |
| 398 | return $self->_div_inf($x,$y) |
| 399 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
| 400 | |
| 401 | # x== 0 # also: or y == 1 or y == -1 |
| 402 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
| 403 | |
| 404 | # TODO: list context, upgrade |
| 405 | |
| 406 | # # upgrade |
| 407 | # return $upgrade->bdiv($x,$y,$a,$p,$r) if defined $upgrade; |
| 408 | |
| 409 | # 1 1 1 3 |
| 410 | # - / - == - * - |
| 411 | # 4 3 4 1 |
| 412 | $x->{_n}->bmul($y->{_d}); |
| 413 | $x->{_d}->bmul($y->{_n}); |
| 414 | |
| 415 | # compute new sign |
| 416 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; |
| 417 | |
| 418 | $x->bnorm()->round($a,$p,$r); |
| 419 | } |
| 420 | |
| 421 | ############################################################################## |
| 422 | # is_foo methods (the rest is inherited) |
| 423 | |
| 424 | sub is_int |
| 425 | { |
| 426 | # return true if arg (BRAT or num_str) is an integer |
| 427 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 428 | |
| 429 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
| 430 | $x->{_d}->is_one(); # 1e-1 => no integer |
| 431 | 0; |
| 432 | } |
| 433 | |
| 434 | sub is_zero |
| 435 | { |
| 436 | # return true if arg (BRAT or num_str) is zero |
| 437 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 438 | |
| 439 | return 1 if $x->{sign} eq '+' && $x->{_n}->is_zero(); |
| 440 | 0; |
| 441 | } |
| 442 | |
| 443 | sub is_one |
| 444 | { |
| 445 | # return true if arg (BRAT or num_str) is +1 or -1 if signis given |
| 446 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 447 | |
| 448 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
| 449 | return 1 |
| 450 | if ($x->{sign} eq $sign && $x->{_n}->is_one() && $x->{_d}->is_one()); |
| 451 | 0; |
| 452 | } |
| 453 | |
| 454 | sub is_odd |
| 455 | { |
| 456 | # return true if arg (BFLOAT or num_str) is odd or false if even |
| 457 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 458 | |
| 459 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
| 460 | ($x->{_d}->is_one() && $x->{_n}->is_odd()); # x/2 is not, but 3/1 |
| 461 | 0; |
| 462 | } |
| 463 | |
| 464 | sub is_even |
| 465 | { |
| 466 | # return true if arg (BINT or num_str) is even or false if odd |
| 467 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 468 | |
| 469 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
| 470 | return 1 if ($x->{_d}->is_one() # x/3 is never |
| 471 | && $x->{_n}->is_even()); # but 4/1 is |
| 472 | 0; |
| 473 | } |
| 474 | |
| 475 | BEGIN |
| 476 | { |
| 477 | *objectify = \&Math::BigInt::objectify; |
| 478 | } |
| 479 | |
| 480 | ############################################################################## |
| 481 | # parts() and friends |
| 482 | |
| 483 | sub numerator |
| 484 | { |
| 485 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 486 | |
| 487 | my $n = $x->{_n}->copy(); $n->{sign} = $x->{sign}; |
| 488 | $n; |
| 489 | } |
| 490 | |
| 491 | sub denominator |
| 492 | { |
| 493 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 494 | |
| 495 | $x->{_d}->copy(); |
| 496 | } |
| 497 | |
| 498 | sub parts |
| 499 | { |
| 500 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 501 | |
| 502 | my $n = $x->{_n}->copy(); |
| 503 | $n->{sign} = $x->{sign}; |
| 504 | return ($x->{_n}->copy(),$x->{_d}->copy()); |
| 505 | } |
| 506 | |
| 507 | sub length |
| 508 | { |
| 509 | return 0; |
| 510 | } |
| 511 | |
| 512 | sub digit |
| 513 | { |
| 514 | return 0; |
| 515 | } |
| 516 | |
| 517 | ############################################################################## |
| 518 | # special calc routines |
| 519 | |
| 520 | sub bceil |
| 521 | { |
| 522 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 523 | |
| 524 | return $x unless $x->{sign} =~ /^[+-]$/; |
| 525 | return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 |
| 526 | |
| 527 | $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 |
| 528 | $x->{_d}->bone(); |
| 529 | $x->{_n}->binc() if $x->{sign} eq '+'; # +22/7 => 4/1 |
| 530 | $x; |
| 531 | } |
| 532 | |
| 533 | sub bfloor |
| 534 | { |
| 535 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 536 | |
| 537 | return $x unless $x->{sign} =~ /^[+-]$/; |
| 538 | return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 |
| 539 | |
| 540 | $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 |
| 541 | $x->{_d}->bone(); |
| 542 | $x->{_n}->binc() if $x->{sign} eq '-'; # -22/7 => -4/1 |
| 543 | $x; |
| 544 | } |
| 545 | |
| 546 | sub bfac |
| 547 | { |
| 548 | return Math::BigRat->bnan(); |
| 549 | } |
| 550 | |
| 551 | sub bpow |
| 552 | { |
| 553 | my ($self,$x,$y,@r) = objectify(2,@_); |
| 554 | |
| 555 | return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x |
| 556 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
| 557 | return $x->bone(@r) if $y->is_zero(); |
| 558 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
| 559 | if ($x->{sign} eq '-' && $x->{_n}->is_one() && $x->{_d}->is_one()) |
| 560 | { |
| 561 | # if $x == -1 and odd/even y => +1/-1 |
| 562 | return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); |
| 563 | # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; |
| 564 | } |
| 565 | # 1 ** -y => 1 / (1 ** |y|) |
| 566 | # so do test for negative $y after above's clause |
| 567 | # return $x->bnan() if $y->{sign} eq '-'; |
| 568 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
| 569 | |
| 570 | my $pow2 = $self->__one(); |
| 571 | my $y1 = Math::BigInt->new($y->{_n}/$y->{_d})->babs(); |
| 572 | my $two = Math::BigInt->new(2); |
| 573 | while (!$y1->is_one()) |
| 574 | { |
| 575 | print "at $y1 (= $x)\n"; |
| 576 | $pow2->bmul($x) if $y1->is_odd(); |
| 577 | $y1->bdiv($two); |
| 578 | $x->bmul($x); |
| 579 | } |
| 580 | $x->bmul($pow2) unless $pow2->is_one(); |
| 581 | # n ** -x => 1/n ** x |
| 582 | ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; |
| 583 | $x; |
| 584 | #$x->round(@r); |
| 585 | } |
| 586 | |
| 587 | sub blog |
| 588 | { |
| 589 | return Math::BigRat->bnan(); |
| 590 | } |
| 591 | |
| 592 | sub bsqrt |
| 593 | { |
| 594 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 595 | |
| 596 | return $x->bnan() if $x->{sign} ne '+'; # inf, NaN, -1 etc |
| 597 | $x->{_d}->bsqrt($a,$p,$r); |
| 598 | $x->{_n}->bsqrt($a,$p,$r); |
| 599 | $x->bnorm(); |
| 600 | } |
| 601 | |
| 602 | sub blsft |
| 603 | { |
| 604 | my ($self,$x,$y,$b,$a,$p,$r) = objectify(3,@_); |
| 605 | |
| 606 | $x->bmul( $b->copy()->bpow($y), $a,$p,$r); |
| 607 | $x; |
| 608 | } |
| 609 | |
| 610 | sub brsft |
| 611 | { |
| 612 | my ($self,$x,$y,$b,$a,$p,$r) = objectify(2,@_); |
| 613 | |
| 614 | $x->bdiv( $b->copy()->bpow($y), $a,$p,$r); |
| 615 | $x; |
| 616 | } |
| 617 | |
| 618 | ############################################################################## |
| 619 | # round |
| 620 | |
| 621 | sub round |
| 622 | { |
| 623 | $_[0]; |
| 624 | } |
| 625 | |
| 626 | sub bround |
| 627 | { |
| 628 | $_[0]; |
| 629 | } |
| 630 | |
| 631 | sub bfround |
| 632 | { |
| 633 | $_[0]; |
| 634 | } |
| 635 | |
| 636 | ############################################################################## |
| 637 | # comparing |
| 638 | |
| 639 | sub bcmp |
| 640 | { |
| 641 | my ($self,$x,$y) = objectify(2,@_); |
| 642 | |
| 643 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 644 | { |
| 645 | # handle +-inf and NaN |
| 646 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 647 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
| 648 | return +1 if $x->{sign} eq '+inf'; |
| 649 | return -1 if $x->{sign} eq '-inf'; |
| 650 | return -1 if $y->{sign} eq '+inf'; |
| 651 | return +1; |
| 652 | } |
| 653 | # check sign for speed first |
| 654 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
| 655 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
| 656 | |
| 657 | # shortcut |
| 658 | my $xz = $x->{_n}->is_zero(); |
| 659 | my $yz = $y->{_n}->is_zero(); |
| 660 | return 0 if $xz && $yz; # 0 <=> 0 |
| 661 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
| 662 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
| 663 | |
| 664 | my $t = $x->{_n} * $y->{_d}; $t->{sign} = $x->{sign}; |
| 665 | my $u = $y->{_n} * $x->{_d}; $u->{sign} = $y->{sign}; |
| 666 | $t->bcmp($u); |
| 667 | } |
| 668 | |
| 669 | sub bacmp |
| 670 | { |
| 671 | my ($self,$x,$y) = objectify(2,@_); |
| 672 | |
| 673 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 674 | { |
| 675 | # handle +-inf and NaN |
| 676 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 677 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; |
| 678 | return +1; # inf is always bigger |
| 679 | } |
| 680 | |
| 681 | my $t = $x->{_n} * $y->{_d}; |
| 682 | my $u = $y->{_n} * $x->{_d}; |
| 683 | $t->bacmp($u); |
| 684 | } |
| 685 | |
| 686 | ############################################################################## |
| 687 | # output conversation |
| 688 | |
| 689 | sub as_number |
| 690 | { |
| 691 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 692 | |
| 693 | return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf etc |
| 694 | my $t = $x->{_n}->copy()->bdiv($x->{_d}); # 22/7 => 3 |
| 695 | $t->{sign} = $x->{sign}; |
| 696 | $t; |
| 697 | } |
| 698 | |
| 699 | #sub import |
| 700 | # { |
| 701 | # my $self = shift; |
| 702 | # Math::BigInt->import(@_); |
| 703 | # $self->SUPER::import(@_); # need it for subclasses |
| 704 | # #$self->export_to_level(1,$self,@_); # need this ? |
| 705 | # } |
| 706 | |
| 707 | 1; |
| 708 | |
| 709 | __END__ |
| 710 | |
| 711 | =head1 NAME |
| 712 | |
| 713 | Math::BigRat - arbitrarily big rationales |
| 714 | |
| 715 | =head1 SYNOPSIS |
| 716 | |
| 717 | use Math::BigRat; |
| 718 | |
| 719 | $x = Math::BigRat->new('3/7'); |
| 720 | |
| 721 | print $x->bstr(),"\n"; |
| 722 | |
| 723 | =head1 DESCRIPTION |
| 724 | |
| 725 | This is just a placeholder until the real thing is up and running. Watch this |
| 726 | space... |
| 727 | |
| 728 | =head2 MATH LIBRARY |
| 729 | |
| 730 | Math with the numbers is done (by default) by a module called |
| 731 | Math::BigInt::Calc. This is equivalent to saying: |
| 732 | |
| 733 | use Math::BigRat lib => 'Calc'; |
| 734 | |
| 735 | You can change this by using: |
| 736 | |
| 737 | use Math::BigRat lib => 'BitVect'; |
| 738 | |
| 739 | The following would first try to find Math::BigInt::Foo, then |
| 740 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
| 741 | |
| 742 | use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; |
| 743 | |
| 744 | Calc.pm uses as internal format an array of elements of some decimal base |
| 745 | (usually 1e7, but this might be differen for some systems) with the least |
| 746 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
| 747 | significant bit first. Other modules might use even different means of |
| 748 | representing the numbers. See the respective module documentation for further |
| 749 | details. |
| 750 | |
| 751 | =head1 METHODS |
| 752 | |
| 753 | =head2 new |
| 754 | |
| 755 | $x = Math::BigRat->new('1/3'); |
| 756 | |
| 757 | Create a new Math::BigRat object. Input can come in various forms: |
| 758 | |
| 759 | $x = Math::BigRat->new('1/3'); # simple string |
| 760 | $x = Math::BigRat->new('1 / 3'); # spaced |
| 761 | $x = Math::BigRat->new('1 / 0.1'); # w/ floats |
| 762 | $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt |
| 763 | $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat |
| 764 | |
| 765 | =head2 numerator |
| 766 | |
| 767 | $n = $x->numerator(); |
| 768 | |
| 769 | Returns a copy of the numerator (the part above the line) as signed BigInt. |
| 770 | |
| 771 | =head2 denominator |
| 772 | |
| 773 | $d = $x->denominator(); |
| 774 | |
| 775 | Returns a copy of the denominator (the part under the line) as positive BigInt. |
| 776 | |
| 777 | =head2 parts |
| 778 | |
| 779 | ($n,$d) = $x->parts(); |
| 780 | |
| 781 | Return a list consisting of (signed) numerator and (unsigned) denominator as |
| 782 | BigInts. |
| 783 | |
| 784 | =head1 BUGS |
| 785 | |
| 786 | None know yet. Please see also L<Math::BigInt>. |
| 787 | |
| 788 | =head1 LICENSE |
| 789 | |
| 790 | This program is free software; you may redistribute it and/or modify it under |
| 791 | the same terms as Perl itself. |
| 792 | |
| 793 | =head1 SEE ALSO |
| 794 | |
| 795 | L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, |
| 796 | L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
| 797 | |
| 798 | The package at |
| 799 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigRat> may |
| 800 | contain more documentation and examples as well as testcases. |
| 801 | |
| 802 | =head1 AUTHORS |
| 803 | |
| 804 | (C) by Tels L<http://bloodgate.com/> 2001-2002. |
| 805 | |
| 806 | =cut |
projects / p5sagit/p5-mst-13.2.git / blame