| 1 | package Math::BigFloat; |
| 2 | |
| 3 | # |
| 4 | # Mike grinned. 'Two down, infinity to go' - Mike Nostrus in 'Before and After' |
| 5 | # |
| 6 | |
| 7 | # The following hash values are internally used: |
| 8 | # _e: exponent (BigInt) |
| 9 | # _m: mantissa (absolute BigInt) |
| 10 | # sign: +,-,"NaN" if not a number |
| 11 | # _a: accuracy |
| 12 | # _p: precision |
| 13 | # _f: flags, used to signal MBI not to touch our private parts |
| 14 | |
| 15 | $VERSION = '1.35'; |
| 16 | require 5.005; |
| 17 | use Exporter; |
| 18 | use File::Spec; |
| 19 | # use Math::BigInt; |
| 20 | @ISA = qw( Exporter Math::BigInt); |
| 21 | |
| 22 | use strict; |
| 23 | use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/; |
| 24 | use vars qw/$upgrade $downgrade/; |
| 25 | my $class = "Math::BigFloat"; |
| 26 | |
| 27 | use overload |
| 28 | '<=>' => sub { $_[2] ? |
| 29 | ref($_[0])->bcmp($_[1],$_[0]) : |
| 30 | ref($_[0])->bcmp($_[0],$_[1])}, |
| 31 | 'int' => sub { $_[0]->as_number() }, # 'trunc' to bigint |
| 32 | ; |
| 33 | |
| 34 | ############################################################################## |
| 35 | # global constants, flags and accessory |
| 36 | |
| 37 | use constant MB_NEVER_ROUND => 0x0001; |
| 38 | |
| 39 | # are NaNs ok? |
| 40 | my $NaNOK=1; |
| 41 | # constant for easier life |
| 42 | my $nan = 'NaN'; |
| 43 | |
| 44 | # class constants, use Class->constant_name() to access |
| 45 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
| 46 | $accuracy = undef; |
| 47 | $precision = undef; |
| 48 | $div_scale = 40; |
| 49 | |
| 50 | $upgrade = undef; |
| 51 | $downgrade = undef; |
| 52 | my $MBI = 'Math::BigInt'; # the package we are using for our private parts |
| 53 | # changable by use Math::BigFloat with => 'package' |
| 54 | |
| 55 | ############################################################################## |
| 56 | # the old code had $rnd_mode, so we need to support it, too |
| 57 | |
| 58 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } |
| 59 | sub FETCH { return $round_mode; } |
| 60 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } |
| 61 | |
| 62 | BEGIN |
| 63 | { |
| 64 | $rnd_mode = 'even'; |
| 65 | tie $rnd_mode, 'Math::BigFloat'; |
| 66 | } |
| 67 | |
| 68 | ############################################################################## |
| 69 | |
| 70 | # in case we call SUPER::->foo() and this wants to call modify() |
| 71 | # sub modify () { 0; } |
| 72 | |
| 73 | { |
| 74 | # valid method aliases for AUTOLOAD |
| 75 | my %methods = map { $_ => 1 } |
| 76 | qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm |
| 77 | fint facmp fcmp fzero fnan finf finc fdec flog ffac |
| 78 | fceil ffloor frsft flsft fone flog |
| 79 | /; |
| 80 | # valid method's that can be hand-ed up (for AUTOLOAD) |
| 81 | my %hand_ups = map { $_ => 1 } |
| 82 | qw / is_nan is_inf is_negative is_positive |
| 83 | accuracy precision div_scale round_mode fneg fabs babs fnot |
| 84 | objectify upgrade downgrade |
| 85 | bone binf bnan bzero |
| 86 | /; |
| 87 | |
| 88 | sub method_alias { return exists $methods{$_[0]||''}; } |
| 89 | sub method_hand_up { return exists $hand_ups{$_[0]||''}; } |
| 90 | } |
| 91 | |
| 92 | ############################################################################## |
| 93 | # constructors |
| 94 | |
| 95 | sub new |
| 96 | { |
| 97 | # create a new BigFloat object from a string or another bigfloat object. |
| 98 | # _e: exponent |
| 99 | # _m: mantissa |
| 100 | # sign => sign (+/-), or "NaN" |
| 101 | |
| 102 | my ($class,$wanted,@r) = @_; |
| 103 | |
| 104 | # avoid numify-calls by not using || on $wanted! |
| 105 | return $class->bzero() if !defined $wanted; # default to 0 |
| 106 | return $wanted->copy() if UNIVERSAL::isa($wanted,'Math::BigFloat'); |
| 107 | |
| 108 | my $self = {}; bless $self, $class; |
| 109 | # shortcut for bigints and its subclasses |
| 110 | if ((ref($wanted)) && (ref($wanted) ne $class)) |
| 111 | { |
| 112 | $self->{_m} = $wanted->as_number(); # get us a bigint copy |
| 113 | $self->{_e} = $MBI->bzero(); |
| 114 | $self->{_m}->babs(); |
| 115 | $self->{sign} = $wanted->sign(); |
| 116 | return $self->bnorm(); |
| 117 | } |
| 118 | # got string |
| 119 | # handle '+inf', '-inf' first |
| 120 | if ($wanted =~ /^[+-]?inf$/) |
| 121 | { |
| 122 | return $downgrade->new($wanted) if $downgrade; |
| 123 | |
| 124 | $self->{_e} = $MBI->bzero(); |
| 125 | $self->{_m} = $MBI->bzero(); |
| 126 | $self->{sign} = $wanted; |
| 127 | $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
| 128 | return $self->bnorm(); |
| 129 | } |
| 130 | #print "new string '$wanted'\n"; |
| 131 | my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted); |
| 132 | if (!ref $mis) |
| 133 | { |
| 134 | die "$wanted is not a number initialized to $class" if !$NaNOK; |
| 135 | |
| 136 | return $downgrade->bnan() if $downgrade; |
| 137 | |
| 138 | $self->{_e} = $MBI->bzero(); |
| 139 | $self->{_m} = $MBI->bzero(); |
| 140 | $self->{sign} = $nan; |
| 141 | } |
| 142 | else |
| 143 | { |
| 144 | # make integer from mantissa by adjusting exp, then convert to bigint |
| 145 | # undef,undef to signal MBI that we don't need no bloody rounding |
| 146 | $self->{_e} = $MBI->new("$$es$$ev",undef,undef); # exponent |
| 147 | $self->{_m} = $MBI->new("$$miv$$mfv",undef,undef); # create mant. |
| 148 | # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 |
| 149 | $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0; |
| 150 | $self->{sign} = $$mis; |
| 151 | } |
| 152 | # if downgrade, inf, NaN or integers go down |
| 153 | |
| 154 | if ($downgrade && $self->{_e}->{sign} eq '+') |
| 155 | { |
| 156 | # print "downgrading $$miv$$mfv"."E$$es$$ev"; |
| 157 | if ($self->{_e}->is_zero()) |
| 158 | { |
| 159 | $self->{_m}->{sign} = $$mis; # negative if wanted |
| 160 | return $downgrade->new($self->{_m}); |
| 161 | } |
| 162 | return $downgrade->new("$$mis$$miv$$mfv"."E$$es$$ev"); |
| 163 | } |
| 164 | # print "mbf new $self->{sign} $self->{_m} e $self->{_e} ",ref($self),"\n"; |
| 165 | $self->bnorm()->round(@r); # first normalize, then round |
| 166 | } |
| 167 | |
| 168 | sub _bnan |
| 169 | { |
| 170 | # used by parent class bone() to initialize number to 1 |
| 171 | my $self = shift; |
| 172 | $self->{_m} = $MBI->bzero(); |
| 173 | $self->{_e} = $MBI->bzero(); |
| 174 | } |
| 175 | |
| 176 | sub _binf |
| 177 | { |
| 178 | # used by parent class bone() to initialize number to 1 |
| 179 | my $self = shift; |
| 180 | $self->{_m} = $MBI->bzero(); |
| 181 | $self->{_e} = $MBI->bzero(); |
| 182 | } |
| 183 | |
| 184 | sub _bone |
| 185 | { |
| 186 | # used by parent class bone() to initialize number to 1 |
| 187 | my $self = shift; |
| 188 | $self->{_m} = $MBI->bone(); |
| 189 | $self->{_e} = $MBI->bzero(); |
| 190 | } |
| 191 | |
| 192 | sub _bzero |
| 193 | { |
| 194 | # used by parent class bone() to initialize number to 1 |
| 195 | my $self = shift; |
| 196 | $self->{_m} = $MBI->bzero(); |
| 197 | $self->{_e} = $MBI->bone(); |
| 198 | } |
| 199 | |
| 200 | sub isa |
| 201 | { |
| 202 | my ($self,$class) = @_; |
| 203 | return if $class =~ /^Math::BigInt/; # we aren't one of these |
| 204 | UNIVERSAL::isa($self,$class); |
| 205 | } |
| 206 | |
| 207 | sub config |
| 208 | { |
| 209 | # return (later set?) configuration data as hash ref |
| 210 | my $class = shift || 'Math::BigFloat'; |
| 211 | |
| 212 | my $cfg = $MBI->config(); |
| 213 | |
| 214 | no strict 'refs'; |
| 215 | $cfg->{class} = $class; |
| 216 | $cfg->{with} = $MBI; |
| 217 | foreach ( |
| 218 | qw/upgrade downgrade precision accuracy round_mode VERSION div_scale/) |
| 219 | { |
| 220 | $cfg->{lc($_)} = ${"${class}::$_"}; |
| 221 | }; |
| 222 | $cfg; |
| 223 | } |
| 224 | |
| 225 | ############################################################################## |
| 226 | # string conversation |
| 227 | |
| 228 | sub bstr |
| 229 | { |
| 230 | # (ref to BFLOAT or num_str ) return num_str |
| 231 | # Convert number from internal format to (non-scientific) string format. |
| 232 | # internal format is always normalized (no leading zeros, "-0" => "+0") |
| 233 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 234 | #my $x = shift; my $class = ref($x) || $x; |
| 235 | #$x = $class->new(shift) unless ref($x); |
| 236 | |
| 237 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
| 238 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
| 239 | if ($x->{sign} !~ /^[+-]$/) |
| 240 | { |
| 241 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
| 242 | return 'inf'; # +inf |
| 243 | } |
| 244 | |
| 245 | my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; |
| 246 | |
| 247 | my $not_zero = ! $x->is_zero(); |
| 248 | if ($not_zero) |
| 249 | { |
| 250 | $es = $x->{_m}->bstr(); |
| 251 | $len = CORE::length($es); |
| 252 | if (!$x->{_e}->is_zero()) |
| 253 | { |
| 254 | if ($x->{_e}->sign() eq '-') |
| 255 | { |
| 256 | $dot = ''; |
| 257 | if ($x->{_e} <= -$len) |
| 258 | { |
| 259 | # print "style: 0.xxxx\n"; |
| 260 | my $r = $x->{_e}->copy(); $r->babs()->bsub( CORE::length($es) ); |
| 261 | $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); |
| 262 | } |
| 263 | else |
| 264 | { |
| 265 | # print "insert '.' at $x->{_e} in '$es'\n"; |
| 266 | substr($es,$x->{_e},0) = '.'; $cad = $x->{_e}; |
| 267 | } |
| 268 | } |
| 269 | else |
| 270 | { |
| 271 | # expand with zeros |
| 272 | $es .= '0' x $x->{_e}; $len += $x->{_e}; $cad = 0; |
| 273 | } |
| 274 | } |
| 275 | } # if not zero |
| 276 | $es = $x->{sign}.$es if $x->{sign} eq '-'; |
| 277 | # if set accuracy or precision, pad with zeros |
| 278 | if ((defined $x->{_a}) && ($not_zero)) |
| 279 | { |
| 280 | # 123400 => 6, 0.1234 => 4, 0.001234 => 4 |
| 281 | my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 |
| 282 | $zeros = $x->{_a} - $len if $cad != $len; |
| 283 | $es .= $dot.'0' x $zeros if $zeros > 0; |
| 284 | } |
| 285 | elsif ($x->{_p} || 0 < 0) |
| 286 | { |
| 287 | # 123400 => 6, 0.1234 => 4, 0.001234 => 6 |
| 288 | my $zeros = -$x->{_p} + $cad; |
| 289 | $es .= $dot.'0' x $zeros if $zeros > 0; |
| 290 | } |
| 291 | $es; |
| 292 | } |
| 293 | |
| 294 | sub bsstr |
| 295 | { |
| 296 | # (ref to BFLOAT or num_str ) return num_str |
| 297 | # Convert number from internal format to scientific string format. |
| 298 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") |
| 299 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 300 | #my $x = shift; my $class = ref($x) || $x; |
| 301 | #$x = $class->new(shift) unless ref($x); |
| 302 | |
| 303 | #die "Oups! e was $nan" if $x->{_e}->{sign} eq $nan; |
| 304 | #die "Oups! m was $nan" if $x->{_m}->{sign} eq $nan; |
| 305 | if ($x->{sign} !~ /^[+-]$/) |
| 306 | { |
| 307 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN |
| 308 | return 'inf'; # +inf |
| 309 | } |
| 310 | my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-'; |
| 311 | my $sep = 'e'.$sign; |
| 312 | $x->{_m}->bstr().$sep.$x->{_e}->bstr(); |
| 313 | } |
| 314 | |
| 315 | sub numify |
| 316 | { |
| 317 | # Make a number from a BigFloat object |
| 318 | # simple return string and let Perl's atoi()/atof() handle the rest |
| 319 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 320 | $x->bsstr(); |
| 321 | } |
| 322 | |
| 323 | ############################################################################## |
| 324 | # public stuff (usually prefixed with "b") |
| 325 | |
| 326 | # tels 2001-08-04 |
| 327 | # todo: this must be overwritten and return NaN for non-integer values |
| 328 | # band(), bior(), bxor(), too |
| 329 | #sub bnot |
| 330 | # { |
| 331 | # $class->SUPER::bnot($class,@_); |
| 332 | # } |
| 333 | |
| 334 | sub bcmp |
| 335 | { |
| 336 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
| 337 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
| 338 | |
| 339 | # set up parameters |
| 340 | my ($self,$x,$y) = (ref($_[0]),@_); |
| 341 | # objectify is costly, so avoid it |
| 342 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 343 | { |
| 344 | ($self,$x,$y) = objectify(2,@_); |
| 345 | } |
| 346 | |
| 347 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 348 | { |
| 349 | # handle +-inf and NaN |
| 350 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 351 | return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/); |
| 352 | return +1 if $x->{sign} eq '+inf'; |
| 353 | return -1 if $x->{sign} eq '-inf'; |
| 354 | return -1 if $y->{sign} eq '+inf'; |
| 355 | return +1; |
| 356 | } |
| 357 | |
| 358 | # check sign for speed first |
| 359 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y |
| 360 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 |
| 361 | |
| 362 | # shortcut |
| 363 | my $xz = $x->is_zero(); |
| 364 | my $yz = $y->is_zero(); |
| 365 | return 0 if $xz && $yz; # 0 <=> 0 |
| 366 | return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y |
| 367 | return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 |
| 368 | |
| 369 | # adjust so that exponents are equal |
| 370 | my $lxm = $x->{_m}->length(); |
| 371 | my $lym = $y->{_m}->length(); |
| 372 | # the numify somewhat limits our length, but makes it much faster |
| 373 | my $lx = $lxm + $x->{_e}->numify(); |
| 374 | my $ly = $lym + $y->{_e}->numify(); |
| 375 | my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-'; |
| 376 | return $l <=> 0 if $l != 0; |
| 377 | |
| 378 | # lengths (corrected by exponent) are equal |
| 379 | # so make mantissa equal length by padding with zero (shift left) |
| 380 | my $diff = $lxm - $lym; |
| 381 | my $xm = $x->{_m}; # not yet copy it |
| 382 | my $ym = $y->{_m}; |
| 383 | if ($diff > 0) |
| 384 | { |
| 385 | $ym = $y->{_m}->copy()->blsft($diff,10); |
| 386 | } |
| 387 | elsif ($diff < 0) |
| 388 | { |
| 389 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
| 390 | } |
| 391 | my $rc = $xm->bacmp($ym); |
| 392 | $rc = -$rc if $x->{sign} eq '-'; # -124 < -123 |
| 393 | $rc <=> 0; |
| 394 | } |
| 395 | |
| 396 | sub bacmp |
| 397 | { |
| 398 | # Compares 2 values, ignoring their signs. |
| 399 | # Returns one of undef, <0, =0, >0. (suitable for sort) |
| 400 | # (BFLOAT or num_str, BFLOAT or num_str) return cond_code |
| 401 | |
| 402 | # set up parameters |
| 403 | my ($self,$x,$y) = (ref($_[0]),@_); |
| 404 | # objectify is costly, so avoid it |
| 405 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 406 | { |
| 407 | ($self,$x,$y) = objectify(2,@_); |
| 408 | } |
| 409 | |
| 410 | # handle +-inf and NaN's |
| 411 | if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) |
| 412 | { |
| 413 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 414 | return 0 if ($x->is_inf() && $y->is_inf()); |
| 415 | return 1 if ($x->is_inf() && !$y->is_inf()); |
| 416 | return -1; |
| 417 | } |
| 418 | |
| 419 | # shortcut |
| 420 | my $xz = $x->is_zero(); |
| 421 | my $yz = $y->is_zero(); |
| 422 | return 0 if $xz && $yz; # 0 <=> 0 |
| 423 | return -1 if $xz && !$yz; # 0 <=> +y |
| 424 | return 1 if $yz && !$xz; # +x <=> 0 |
| 425 | |
| 426 | # adjust so that exponents are equal |
| 427 | my $lxm = $x->{_m}->length(); |
| 428 | my $lym = $y->{_m}->length(); |
| 429 | # the numify somewhat limits our length, but makes it much faster |
| 430 | my $lx = $lxm + $x->{_e}->numify(); |
| 431 | my $ly = $lym + $y->{_e}->numify(); |
| 432 | my $l = $lx - $ly; |
| 433 | return $l <=> 0 if $l != 0; |
| 434 | |
| 435 | # lengths (corrected by exponent) are equal |
| 436 | # so make mantissa equal-length by padding with zero (shift left) |
| 437 | my $diff = $lxm - $lym; |
| 438 | my $xm = $x->{_m}; # not yet copy it |
| 439 | my $ym = $y->{_m}; |
| 440 | if ($diff > 0) |
| 441 | { |
| 442 | $ym = $y->{_m}->copy()->blsft($diff,10); |
| 443 | } |
| 444 | elsif ($diff < 0) |
| 445 | { |
| 446 | $xm = $x->{_m}->copy()->blsft(-$diff,10); |
| 447 | } |
| 448 | $xm->bacmp($ym) <=> 0; |
| 449 | } |
| 450 | |
| 451 | sub badd |
| 452 | { |
| 453 | # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) |
| 454 | # return result as BFLOAT |
| 455 | |
| 456 | # set up parameters |
| 457 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
| 458 | # objectify is costly, so avoid it |
| 459 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 460 | { |
| 461 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 462 | } |
| 463 | |
| 464 | # inf and NaN handling |
| 465 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 466 | { |
| 467 | # NaN first |
| 468 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 469 | # inf handling |
| 470 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) |
| 471 | { |
| 472 | # +inf++inf or -inf+-inf => same, rest is NaN |
| 473 | return $x if $x->{sign} eq $y->{sign}; |
| 474 | return $x->bnan(); |
| 475 | } |
| 476 | # +-inf + something => +inf; something +-inf => +-inf |
| 477 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; |
| 478 | return $x; |
| 479 | } |
| 480 | |
| 481 | return $upgrade->badd($x,$y,$a,$p,$r) if defined $upgrade && |
| 482 | ((!$x->isa($self)) || (!$y->isa($self))); |
| 483 | |
| 484 | # speed: no add for 0+y or x+0 |
| 485 | return $x->bround($a,$p,$r) if $y->is_zero(); # x+0 |
| 486 | if ($x->is_zero()) # 0+y |
| 487 | { |
| 488 | # make copy, clobbering up x (modify in place!) |
| 489 | $x->{_e} = $y->{_e}->copy(); |
| 490 | $x->{_m} = $y->{_m}->copy(); |
| 491 | $x->{sign} = $y->{sign} || $nan; |
| 492 | return $x->round($a,$p,$r,$y); |
| 493 | } |
| 494 | |
| 495 | # take lower of the two e's and adapt m1 to it to match m2 |
| 496 | my $e = $y->{_e}; |
| 497 | $e = $MBI->bzero() if !defined $e; # if no BFLOAT ? |
| 498 | $e = $e->copy(); # make copy (didn't do it yet) |
| 499 | $e->bsub($x->{_e}); |
| 500 | my $add = $y->{_m}->copy(); |
| 501 | if ($e->{sign} eq '-') # < 0 |
| 502 | { |
| 503 | my $e1 = $e->copy()->babs(); |
| 504 | #$x->{_m} *= (10 ** $e1); |
| 505 | $x->{_m}->blsft($e1,10); |
| 506 | $x->{_e} += $e; # need the sign of e |
| 507 | } |
| 508 | elsif (!$e->is_zero()) # > 0 |
| 509 | { |
| 510 | #$add *= (10 ** $e); |
| 511 | $add->blsft($e,10); |
| 512 | } |
| 513 | # else: both e are the same, so just leave them |
| 514 | $x->{_m}->{sign} = $x->{sign}; # fiddle with signs |
| 515 | $add->{sign} = $y->{sign}; |
| 516 | $x->{_m} += $add; # finally do add/sub |
| 517 | $x->{sign} = $x->{_m}->{sign}; # re-adjust signs |
| 518 | $x->{_m}->{sign} = '+'; # mantissa always positiv |
| 519 | # delete trailing zeros, then round |
| 520 | return $x->bnorm()->round($a,$p,$r,$y); |
| 521 | } |
| 522 | |
| 523 | sub bsub |
| 524 | { |
| 525 | # (BigFloat or num_str, BigFloat or num_str) return BigFloat |
| 526 | # subtract second arg from first, modify first |
| 527 | |
| 528 | # set up parameters |
| 529 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
| 530 | # objectify is costly, so avoid it |
| 531 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 532 | { |
| 533 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 534 | } |
| 535 | |
| 536 | if ($y->is_zero()) # still round for not adding zero |
| 537 | { |
| 538 | return $x->round($a,$p,$r); |
| 539 | } |
| 540 | |
| 541 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
| 542 | $x->badd($y,$a,$p,$r); # badd does not leave internal zeros |
| 543 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) |
| 544 | $x; # already rounded by badd() |
| 545 | } |
| 546 | |
| 547 | sub binc |
| 548 | { |
| 549 | # increment arg by one |
| 550 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 551 | |
| 552 | if ($x->{_e}->sign() eq '-') |
| 553 | { |
| 554 | return $x->badd($self->bone(),$a,$p,$r); # digits after dot |
| 555 | } |
| 556 | |
| 557 | if (!$x->{_e}->is_zero()) |
| 558 | { |
| 559 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
| 560 | $x->{_e}->bzero(); |
| 561 | } |
| 562 | # now $x->{_e} == 0 |
| 563 | if ($x->{sign} eq '+') |
| 564 | { |
| 565 | $x->{_m}->binc(); |
| 566 | return $x->bnorm()->bround($a,$p,$r); |
| 567 | } |
| 568 | elsif ($x->{sign} eq '-') |
| 569 | { |
| 570 | $x->{_m}->bdec(); |
| 571 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
| 572 | return $x->bnorm()->bround($a,$p,$r); |
| 573 | } |
| 574 | # inf, nan handling etc |
| 575 | $x->badd($self->__one(),$a,$p,$r); # does round |
| 576 | } |
| 577 | |
| 578 | sub bdec |
| 579 | { |
| 580 | # decrement arg by one |
| 581 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 582 | |
| 583 | if ($x->{_e}->sign() eq '-') |
| 584 | { |
| 585 | return $x->badd($self->bone('-'),$a,$p,$r); # digits after dot |
| 586 | } |
| 587 | |
| 588 | if (!$x->{_e}->is_zero()) |
| 589 | { |
| 590 | $x->{_m}->blsft($x->{_e},10); # 1e2 => 100 |
| 591 | $x->{_e}->bzero(); |
| 592 | } |
| 593 | # now $x->{_e} == 0 |
| 594 | my $zero = $x->is_zero(); |
| 595 | # <= 0 |
| 596 | if (($x->{sign} eq '-') || $zero) |
| 597 | { |
| 598 | $x->{_m}->binc(); |
| 599 | $x->{sign} = '-' if $zero; # 0 => 1 => -1 |
| 600 | $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0 |
| 601 | return $x->bnorm()->round($a,$p,$r); |
| 602 | } |
| 603 | # > 0 |
| 604 | elsif ($x->{sign} eq '+') |
| 605 | { |
| 606 | $x->{_m}->bdec(); |
| 607 | return $x->bnorm()->round($a,$p,$r); |
| 608 | } |
| 609 | # inf, nan handling etc |
| 610 | $x->badd($self->bone('-'),$a,$p,$r); # does round |
| 611 | } |
| 612 | |
| 613 | sub blog |
| 614 | { |
| 615 | my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(2,@_); |
| 616 | |
| 617 | # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log |
| 618 | |
| 619 | # u = x-1, v = x+1 |
| 620 | # _ _ |
| 621 | # Taylor: | u 1 u^3 1 u^5 | |
| 622 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 0 |
| 623 | # |_ v 3 v^3 5 v^5 _| |
| 624 | |
| 625 | # This takes much more steps to calculate the result: |
| 626 | # u = x-1 |
| 627 | # _ _ |
| 628 | # Taylor: | u 1 u^2 1 u^3 | |
| 629 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 1/2 |
| 630 | # |_ x 2 x^2 3 x^3 _| |
| 631 | |
| 632 | # we need to limit the accuracy to protect against overflow |
| 633 | my $fallback = 0; |
| 634 | my $scale = 0; |
| 635 | my @params = $x->_find_round_parameters($a,$p,$r); |
| 636 | |
| 637 | # no rounding at all, so must use fallback |
| 638 | if (scalar @params == 1) |
| 639 | { |
| 640 | # simulate old behaviour |
| 641 | $params[1] = $self->div_scale(); # and round to it as accuracy |
| 642 | $params[0] = undef; |
| 643 | $scale = $params[1]+4; # at least four more for proper round |
| 644 | $params[3] = $r; # round mode by caller or undef |
| 645 | $fallback = 1; # to clear a/p afterwards |
| 646 | } |
| 647 | else |
| 648 | { |
| 649 | # the 4 below is empirical, and there might be cases where it is not |
| 650 | # enough... |
| 651 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
| 652 | } |
| 653 | |
| 654 | return $x->bzero(@params) if $x->is_one(); |
| 655 | return $x->bnan() if $x->{sign} ne '+' || $x->is_zero(); |
| 656 | return $x->bone('+',@params) if $x->bcmp($base) == 0; |
| 657 | |
| 658 | # when user set globals, they would interfere with our calculation, so |
| 659 | # disable then and later re-enable them |
| 660 | no strict 'refs'; |
| 661 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
| 662 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
| 663 | # we also need to disable any set A or P on $x (_find_round_parameters took |
| 664 | # them already into account), since these would interfere, too |
| 665 | delete $x->{_a}; delete $x->{_p}; |
| 666 | # need to disable $upgrade in BigInt, to avoid deep recursion |
| 667 | local $Math::BigInt::upgrade = undef; |
| 668 | |
| 669 | my ($case,$limit,$v,$u,$below,$factor,$two,$next,$over,$f); |
| 670 | |
| 671 | if (3 < 5) |
| 672 | #if ($x <= Math::BigFloat->new("0.5")) |
| 673 | { |
| 674 | $case = 0; |
| 675 | # print "case $case $x < 0.5\n"; |
| 676 | $v = $x->copy(); $v->binc(); # v = x+1 |
| 677 | $x->bdec(); $u = $x->copy(); # u = x-1; x = x-1 |
| 678 | $x->bdiv($v,$scale); # first term: u/v |
| 679 | $below = $v->copy(); |
| 680 | $over = $u->copy(); |
| 681 | $u *= $u; $v *= $v; # u^2, v^2 |
| 682 | $below->bmul($v); # u^3, v^3 |
| 683 | $over->bmul($u); |
| 684 | $factor = $self->new(3); $f = $self->new(2); |
| 685 | } |
| 686 | #else |
| 687 | # { |
| 688 | # $case = 1; |
| 689 | # print "case 1 $x > 0.5\n"; |
| 690 | # $v = $x->copy(); # v = x |
| 691 | # $u = $x->copy(); $u->bdec(); # u = x-1; |
| 692 | # $x->bdec(); $x->bdiv($v,$scale); # first term: x-1/x |
| 693 | # $below = $v->copy(); |
| 694 | # $over = $u->copy(); |
| 695 | # $below->bmul($v); # u^2, v^2 |
| 696 | # $over->bmul($u); |
| 697 | # $factor = $self->new(2); $f = $self->bone(); |
| 698 | # } |
| 699 | $limit = $self->new("1E-". ($scale-1)); |
| 700 | #my $steps = 0; |
| 701 | while (3 < 5) |
| 702 | { |
| 703 | # we calculate the next term, and add it to the last |
| 704 | # when the next term is below our limit, it won't affect the outcome |
| 705 | # anymore, so we stop |
| 706 | $next = $over->copy()->bdiv($below->copy()->bmul($factor),$scale); |
| 707 | last if $next->bcmp($limit) <= 0; |
| 708 | $x->badd($next); |
| 709 | # print "step $x\n"; |
| 710 | # calculate things for the next term |
| 711 | $over *= $u; $below *= $v; $factor->badd($f); |
| 712 | #$steps++; |
| 713 | } |
| 714 | $x->bmul(2) if $case == 0; |
| 715 | #print "took $steps steps\n"; |
| 716 | |
| 717 | # shortcut to not run trough _find_round_parameters again |
| 718 | if (defined $params[1]) |
| 719 | { |
| 720 | $x->bround($params[1],$params[3]); # then round accordingly |
| 721 | } |
| 722 | else |
| 723 | { |
| 724 | $x->bfround($params[2],$params[3]); # then round accordingly |
| 725 | } |
| 726 | if ($fallback) |
| 727 | { |
| 728 | # clear a/p after round, since user did not request it |
| 729 | $x->{_a} = undef; $x->{_p} = undef; |
| 730 | } |
| 731 | # restore globals |
| 732 | $$abr = $ab; $$pbr = $pb; |
| 733 | |
| 734 | $x; |
| 735 | } |
| 736 | |
| 737 | sub blcm |
| 738 | { |
| 739 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
| 740 | # does not modify arguments, but returns new object |
| 741 | # Lowest Common Multiplicator |
| 742 | |
| 743 | my ($self,@arg) = objectify(0,@_); |
| 744 | my $x = $self->new(shift @arg); |
| 745 | while (@arg) { $x = _lcm($x,shift @arg); } |
| 746 | $x; |
| 747 | } |
| 748 | |
| 749 | sub bgcd |
| 750 | { |
| 751 | # (BFLOAT or num_str, BFLOAT or num_str) return BINT |
| 752 | # does not modify arguments, but returns new object |
| 753 | # GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
| 754 | |
| 755 | my ($self,@arg) = objectify(0,@_); |
| 756 | my $x = $self->new(shift @arg); |
| 757 | while (@arg) { $x = _gcd($x,shift @arg); } |
| 758 | $x; |
| 759 | } |
| 760 | |
| 761 | ############################################################################### |
| 762 | # is_foo methods (is_negative, is_positive are inherited from BigInt) |
| 763 | |
| 764 | sub is_int |
| 765 | { |
| 766 | # return true if arg (BFLOAT or num_str) is an integer |
| 767 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 768 | |
| 769 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't |
| 770 | $x->{_e}->{sign} eq '+'; # 1e-1 => no integer |
| 771 | 0; |
| 772 | } |
| 773 | |
| 774 | sub is_zero |
| 775 | { |
| 776 | # return true if arg (BFLOAT or num_str) is zero |
| 777 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 778 | |
| 779 | return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero(); |
| 780 | 0; |
| 781 | } |
| 782 | |
| 783 | sub is_one |
| 784 | { |
| 785 | # return true if arg (BFLOAT or num_str) is +1 or -1 if signis given |
| 786 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 787 | |
| 788 | my $sign = shift || ''; $sign = '+' if $sign ne '-'; |
| 789 | return 1 |
| 790 | if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one()); |
| 791 | 0; |
| 792 | } |
| 793 | |
| 794 | sub is_odd |
| 795 | { |
| 796 | # return true if arg (BFLOAT or num_str) is odd or false if even |
| 797 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 798 | |
| 799 | return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't |
| 800 | ($x->{_e}->is_zero() && $x->{_m}->is_odd()); |
| 801 | 0; |
| 802 | } |
| 803 | |
| 804 | sub is_even |
| 805 | { |
| 806 | # return true if arg (BINT or num_str) is even or false if odd |
| 807 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 808 | |
| 809 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
| 810 | return 1 if ($x->{_e}->{sign} eq '+' # 123.45 is never |
| 811 | && $x->{_m}->is_even()); # but 1200 is |
| 812 | 0; |
| 813 | } |
| 814 | |
| 815 | sub bmul |
| 816 | { |
| 817 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
| 818 | # (BINT or num_str, BINT or num_str) return BINT |
| 819 | |
| 820 | # set up parameters |
| 821 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
| 822 | # objectify is costly, so avoid it |
| 823 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 824 | { |
| 825 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 826 | } |
| 827 | |
| 828 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
| 829 | |
| 830 | # inf handling |
| 831 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) |
| 832 | { |
| 833 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
| 834 | # result will always be +-inf: |
| 835 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf |
| 836 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf |
| 837 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); |
| 838 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); |
| 839 | return $x->binf('-'); |
| 840 | } |
| 841 | # handle result = 0 |
| 842 | return $x->bzero() if $x->is_zero() || $y->is_zero(); |
| 843 | |
| 844 | return $upgrade->bmul($x,$y,$a,$p,$r) if defined $upgrade && |
| 845 | ((!$x->isa($self)) || (!$y->isa($self))); |
| 846 | |
| 847 | # aEb * cEd = (a*c)E(b+d) |
| 848 | $x->{_m}->bmul($y->{_m}); |
| 849 | $x->{_e}->badd($y->{_e}); |
| 850 | # adjust sign: |
| 851 | $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; |
| 852 | return $x->bnorm()->round($a,$p,$r,$y); |
| 853 | } |
| 854 | |
| 855 | sub bdiv |
| 856 | { |
| 857 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return |
| 858 | # (BFLOAT,BFLOAT) (quo,rem) or BFLOAT (only rem) |
| 859 | |
| 860 | # set up parameters |
| 861 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
| 862 | # objectify is costly, so avoid it |
| 863 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 864 | { |
| 865 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 866 | } |
| 867 | |
| 868 | return $self->_div_inf($x,$y) |
| 869 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); |
| 870 | |
| 871 | # x== 0 # also: or y == 1 or y == -1 |
| 872 | return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); |
| 873 | |
| 874 | # upgrade ? |
| 875 | return $upgrade->bdiv($upgrade->new($x),$y,$a,$p,$r) if defined $upgrade; |
| 876 | |
| 877 | # we need to limit the accuracy to protect against overflow |
| 878 | my $fallback = 0; |
| 879 | my $scale = 0; |
| 880 | my @params = $x->_find_round_parameters($a,$p,$r,$y); |
| 881 | |
| 882 | # no rounding at all, so must use fallback |
| 883 | if (scalar @params == 1) |
| 884 | { |
| 885 | # simulate old behaviour |
| 886 | $params[1] = $self->div_scale(); # and round to it as accuracy |
| 887 | $scale = $params[1]+4; # at least four more for proper round |
| 888 | $params[3] = $r; # round mode by caller or undef |
| 889 | $fallback = 1; # to clear a/p afterwards |
| 890 | } |
| 891 | else |
| 892 | { |
| 893 | # the 4 below is empirical, and there might be cases where it is not |
| 894 | # enough... |
| 895 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
| 896 | } |
| 897 | my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length(); |
| 898 | $scale = $lx if $lx > $scale; |
| 899 | $scale = $ly if $ly > $scale; |
| 900 | my $diff = $ly - $lx; |
| 901 | $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! |
| 902 | |
| 903 | # make copy of $x in case of list context for later reminder calculation |
| 904 | my $rem; |
| 905 | if (wantarray && !$y->is_one()) |
| 906 | { |
| 907 | $rem = $x->copy(); |
| 908 | } |
| 909 | |
| 910 | $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; |
| 911 | |
| 912 | # check for / +-1 ( +/- 1E0) |
| 913 | if (!$y->is_one()) |
| 914 | { |
| 915 | # promote BigInts and it's subclasses (except when already a BigFloat) |
| 916 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
| 917 | |
| 918 | #print "bdiv $y ",ref($y),"\n"; |
| 919 | # need to disable $upgrade in BigInt, to avoid deep recursion |
| 920 | local $Math::BigInt::upgrade = undef; # should be parent class vs MBI |
| 921 | |
| 922 | # calculate the result to $scale digits and then round it |
| 923 | # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) |
| 924 | $x->{_m}->blsft($scale,10); |
| 925 | $x->{_m}->bdiv( $y->{_m} ); # a/c |
| 926 | $x->{_e}->bsub( $y->{_e} ); # b-d |
| 927 | $x->{_e}->bsub($scale); # correct for 10**scale |
| 928 | $x->bnorm(); # remove trailing 0's |
| 929 | } |
| 930 | |
| 931 | # shortcut to not run trough _find_round_parameters again |
| 932 | if (defined $params[1]) |
| 933 | { |
| 934 | $x->bround($params[1],$params[3]); # then round accordingly |
| 935 | } |
| 936 | else |
| 937 | { |
| 938 | $x->bfround($params[2],$params[3]); # then round accordingly |
| 939 | } |
| 940 | if ($fallback) |
| 941 | { |
| 942 | # clear a/p after round, since user did not request it |
| 943 | $x->{_a} = undef; $x->{_p} = undef; |
| 944 | } |
| 945 | |
| 946 | if (wantarray) |
| 947 | { |
| 948 | if (!$y->is_one()) |
| 949 | { |
| 950 | $rem->bmod($y,$params[1],$params[2],$params[3]); # copy already done |
| 951 | } |
| 952 | else |
| 953 | { |
| 954 | $rem = $self->bzero(); |
| 955 | } |
| 956 | if ($fallback) |
| 957 | { |
| 958 | # clear a/p after round, since user did not request it |
| 959 | $rem->{_a} = undef; $rem->{_p} = undef; |
| 960 | } |
| 961 | return ($x,$rem); |
| 962 | } |
| 963 | $x; |
| 964 | } |
| 965 | |
| 966 | sub bmod |
| 967 | { |
| 968 | # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder |
| 969 | |
| 970 | # set up parameters |
| 971 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
| 972 | # objectify is costly, so avoid it |
| 973 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 974 | { |
| 975 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 976 | } |
| 977 | |
| 978 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
| 979 | { |
| 980 | my ($d,$re) = $self->SUPER::_div_inf($x,$y); |
| 981 | $x->{sign} = $re->{sign}; |
| 982 | $x->{_e} = $re->{_e}; |
| 983 | $x->{_m} = $re->{_m}; |
| 984 | return $x->round($a,$p,$r,$y); |
| 985 | } |
| 986 | return $x->bnan() if $x->is_zero() && $y->is_zero(); |
| 987 | return $x if $y->is_zero(); |
| 988 | return $x->bnan() if $x->is_nan() || $y->is_nan(); |
| 989 | return $x->bzero() if $y->is_one() || $x->is_zero(); |
| 990 | |
| 991 | # inf handling is missing here |
| 992 | |
| 993 | my $cmp = $x->bacmp($y); # equal or $x < $y? |
| 994 | return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0 |
| 995 | |
| 996 | # only $y of the operands negative? |
| 997 | my $neg = 0; $neg = 1 if $x->{sign} ne $y->{sign}; |
| 998 | |
| 999 | $x->{sign} = $y->{sign}; # calc sign first |
| 1000 | return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0; # $x < $y => result $x |
| 1001 | |
| 1002 | my $ym = $y->{_m}->copy(); |
| 1003 | |
| 1004 | # 2e1 => 20 |
| 1005 | $ym->blsft($y->{_e},10) if $y->{_e}->{sign} eq '+' && !$y->{_e}->is_zero(); |
| 1006 | |
| 1007 | # if $y has digits after dot |
| 1008 | my $shifty = 0; # correct _e of $x by this |
| 1009 | if ($y->{_e}->{sign} eq '-') # has digits after dot |
| 1010 | { |
| 1011 | # 123 % 2.5 => 1230 % 25 => 5 => 0.5 |
| 1012 | $shifty = $y->{_e}->copy()->babs(); # no more digits after dot |
| 1013 | $x->blsft($shifty,10); # 123 => 1230, $y->{_m} is already 25 |
| 1014 | } |
| 1015 | # $ym is now mantissa of $y based on exponent 0 |
| 1016 | |
| 1017 | my $shiftx = 0; # correct _e of $x by this |
| 1018 | if ($x->{_e}->{sign} eq '-') # has digits after dot |
| 1019 | { |
| 1020 | # 123.4 % 20 => 1234 % 200 |
| 1021 | $shiftx = $x->{_e}->copy()->babs(); # no more digits after dot |
| 1022 | $ym->blsft($shiftx,10); |
| 1023 | } |
| 1024 | # 123e1 % 20 => 1230 % 20 |
| 1025 | if ($x->{_e}->{sign} eq '+' && !$x->{_e}->is_zero()) |
| 1026 | { |
| 1027 | $x->{_m}->blsft($x->{_e},10); |
| 1028 | } |
| 1029 | $x->{_e} = $MBI->bzero() unless $x->{_e}->is_zero(); |
| 1030 | |
| 1031 | $x->{_e}->bsub($shiftx) if $shiftx != 0; |
| 1032 | $x->{_e}->bsub($shifty) if $shifty != 0; |
| 1033 | |
| 1034 | # now mantissas are equalized, exponent of $x is adjusted, so calc result |
| 1035 | |
| 1036 | $x->{_m}->bmod($ym); |
| 1037 | |
| 1038 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
| 1039 | $x->bnorm(); |
| 1040 | |
| 1041 | if ($neg != 0) # one of them negative => correct in place |
| 1042 | { |
| 1043 | my $r = $y - $x; |
| 1044 | $x->{_m} = $r->{_m}; |
| 1045 | $x->{_e} = $r->{_e}; |
| 1046 | $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0 |
| 1047 | $x->bnorm(); |
| 1048 | } |
| 1049 | |
| 1050 | $x->round($a,$p,$r,$y); # round and return |
| 1051 | } |
| 1052 | |
| 1053 | sub bsqrt |
| 1054 | { |
| 1055 | # calculate square root; this should probably |
| 1056 | # use a different test to see whether the accuracy we want is... |
| 1057 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1058 | |
| 1059 | return $x->bnan() if $x->{sign} eq 'NaN' || $x->{sign} =~ /^-/; # <0, NaN |
| 1060 | return $x if $x->{sign} eq '+inf'; # +inf |
| 1061 | return $x if $x->is_zero() || $x->is_one(); |
| 1062 | |
| 1063 | # we need to limit the accuracy to protect against overflow |
| 1064 | my $fallback = 0; |
| 1065 | my $scale = 0; |
| 1066 | my @params = $x->_find_round_parameters($a,$p,$r); |
| 1067 | |
| 1068 | # no rounding at all, so must use fallback |
| 1069 | if (scalar @params == 1) |
| 1070 | { |
| 1071 | # simulate old behaviour |
| 1072 | $params[1] = $self->div_scale(); # and round to it as accuracy |
| 1073 | $scale = $params[1]+4; # at least four more for proper round |
| 1074 | $params[3] = $r; # round mode by caller or undef |
| 1075 | $fallback = 1; # to clear a/p afterwards |
| 1076 | } |
| 1077 | else |
| 1078 | { |
| 1079 | # the 4 below is empirical, and there might be cases where it is not |
| 1080 | # enough... |
| 1081 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
| 1082 | } |
| 1083 | |
| 1084 | # when user set globals, they would interfere with our calculation, so |
| 1085 | # disable them and later re-enable them |
| 1086 | no strict 'refs'; |
| 1087 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
| 1088 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
| 1089 | # we also need to disable any set A or P on $x (_find_round_parameters took |
| 1090 | # them already into account), since these would interfere, too |
| 1091 | delete $x->{_a}; delete $x->{_p}; |
| 1092 | # need to disable $upgrade in BigInt, to avoid deep recursion |
| 1093 | local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI |
| 1094 | |
| 1095 | my $xas = $x->as_number(); |
| 1096 | my $gs = $xas->copy()->bsqrt(); # some guess |
| 1097 | |
| 1098 | # print "guess $gs\n"; |
| 1099 | if (($x->{_e}->{sign} ne '-') # guess can't be accurate if there are |
| 1100 | # digits after the dot |
| 1101 | && ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head? |
| 1102 | { |
| 1103 | # exact result |
| 1104 | $x->{_m} = $gs; $x->{_e} = $MBI->bzero(); $x->bnorm(); |
| 1105 | # shortcut to not run trough _find_round_parameters again |
| 1106 | if (defined $params[1]) |
| 1107 | { |
| 1108 | $x->bround($params[1],$params[3]); # then round accordingly |
| 1109 | } |
| 1110 | else |
| 1111 | { |
| 1112 | $x->bfround($params[2],$params[3]); # then round accordingly |
| 1113 | } |
| 1114 | if ($fallback) |
| 1115 | { |
| 1116 | # clear a/p after round, since user did not request it |
| 1117 | $x->{_a} = undef; $x->{_p} = undef; |
| 1118 | } |
| 1119 | # re-enable A and P, upgrade is taken care of by "local" |
| 1120 | ${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb; |
| 1121 | return $x; |
| 1122 | } |
| 1123 | $gs = $self->new( $gs ); # BigInt to BigFloat |
| 1124 | |
| 1125 | my $lx = $x->{_m}->length(); |
| 1126 | $scale = $lx if $scale < $lx; |
| 1127 | my $e = $self->new("1E-$scale"); # make test variable |
| 1128 | |
| 1129 | my $y = $x->copy(); |
| 1130 | my $two = $self->new(2); |
| 1131 | my $diff = $e; |
| 1132 | # promote BigInts and it's subclasses (except when already a BigFloat) |
| 1133 | $y = $self->new($y) unless $y->isa('Math::BigFloat'); |
| 1134 | |
| 1135 | my $rem; |
| 1136 | while ($diff->bacmp($e) >= 0) |
| 1137 | { |
| 1138 | $rem = $y->copy()->bdiv($gs,$scale); |
| 1139 | $rem = $y->copy()->bdiv($gs,$scale)->badd($gs)->bdiv($two,$scale); |
| 1140 | $diff = $rem->copy()->bsub($gs); |
| 1141 | $gs = $rem->copy(); |
| 1142 | } |
| 1143 | # copy over to modify $x |
| 1144 | $x->{_m} = $rem->{_m}; $x->{_e} = $rem->{_e}; |
| 1145 | |
| 1146 | # shortcut to not run trough _find_round_parameters again |
| 1147 | if (defined $params[1]) |
| 1148 | { |
| 1149 | $x->bround($params[1],$params[3]); # then round accordingly |
| 1150 | } |
| 1151 | else |
| 1152 | { |
| 1153 | $x->bfround($params[2],$params[3]); # then round accordingly |
| 1154 | } |
| 1155 | if ($fallback) |
| 1156 | { |
| 1157 | # clear a/p after round, since user did not request it |
| 1158 | $x->{_a} = undef; $x->{_p} = undef; |
| 1159 | } |
| 1160 | # restore globals |
| 1161 | $$abr = $ab; $$pbr = $pb; |
| 1162 | $x; |
| 1163 | } |
| 1164 | |
| 1165 | sub bfac |
| 1166 | { |
| 1167 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
| 1168 | # compute factorial numbers |
| 1169 | # modifies first argument |
| 1170 | my ($self,$x,@r) = objectify(1,@_); |
| 1171 | |
| 1172 | return $x->bnan() |
| 1173 | if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN |
| 1174 | ($x->{_e}->{sign} ne '+')); # digits after dot? |
| 1175 | |
| 1176 | return $x->bone('+',@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 |
| 1177 | |
| 1178 | # use BigInt's bfac() for faster calc |
| 1179 | $x->{_m}->blsft($x->{_e},10); # un-norm m |
| 1180 | $x->{_e}->bzero(); # norm $x again |
| 1181 | $x->{_m}->bfac(); # factorial |
| 1182 | $x->bnorm()->round(@r); |
| 1183 | } |
| 1184 | |
| 1185 | sub _pow2 |
| 1186 | { |
| 1187 | # Calculate a power where $y is a non-integer, like 2 ** 0.5 |
| 1188 | my ($x,$y,$a,$p,$r) = @_; |
| 1189 | my $self = ref($x); |
| 1190 | |
| 1191 | # we need to limit the accuracy to protect against overflow |
| 1192 | my $fallback = 0; |
| 1193 | my $scale = 0; |
| 1194 | my @params = $x->_find_round_parameters($a,$p,$r); |
| 1195 | |
| 1196 | # no rounding at all, so must use fallback |
| 1197 | if (scalar @params == 1) |
| 1198 | { |
| 1199 | # simulate old behaviour |
| 1200 | $params[1] = $self->div_scale(); # and round to it as accuracy |
| 1201 | $scale = $params[1]+4; # at least four more for proper round |
| 1202 | $params[3] = $r; # round mode by caller or undef |
| 1203 | $fallback = 1; # to clear a/p afterwards |
| 1204 | } |
| 1205 | else |
| 1206 | { |
| 1207 | # the 4 below is empirical, and there might be cases where it is not |
| 1208 | # enough... |
| 1209 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
| 1210 | } |
| 1211 | |
| 1212 | # when user set globals, they would interfere with our calculation, so |
| 1213 | # disable then and later re-enable them |
| 1214 | no strict 'refs'; |
| 1215 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
| 1216 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
| 1217 | # we also need to disable any set A or P on $x (_find_round_parameters took |
| 1218 | # them already into account), since these would interfere, too |
| 1219 | delete $x->{_a}; delete $x->{_p}; |
| 1220 | # need to disable $upgrade in BigInt, to avoid deep recursion |
| 1221 | local $Math::BigInt::upgrade = undef; |
| 1222 | |
| 1223 | # split the second argument into its integer and fraction part |
| 1224 | # we calculate the result then from these two parts, like in |
| 1225 | # 2 ** 2.4 == (2 ** 2) * (2 ** 0.4) |
| 1226 | my $c = $self->new($y->as_number()); # integer part |
| 1227 | my $d = $y-$c; # fractional part |
| 1228 | my $xc = $x->copy(); # a temp. copy |
| 1229 | |
| 1230 | # now calculate binary fraction from the decimal fraction on the fly |
| 1231 | # f.i. 0.654: |
| 1232 | # 0.654 * 2 = 1.308 > 1 => 0.1 ( 1.308 - 1 = 0.308) |
| 1233 | # 0.308 * 2 = 0.616 < 1 => 0.10 |
| 1234 | # 0.616 * 2 = 1.232 > 1 => 0.101 ( 1.232 - 1 = 0.232) |
| 1235 | # and so on... |
| 1236 | # The process stops when the result is exactly one, or when we have |
| 1237 | # enough accuracy |
| 1238 | |
| 1239 | # From the binary fraction we calculate the result as follows: |
| 1240 | # we assume the fraction ends in 1, and we remove this one first. |
| 1241 | # For each digit after the dot, assume 1 eq R and 0 eq XR, where R means |
| 1242 | # take square root and X multiply with the original X. |
| 1243 | |
| 1244 | my $i = 0; |
| 1245 | while ($i++ < 50) |
| 1246 | { |
| 1247 | $d->badd($d); # * 2 |
| 1248 | last if $d->is_one(); # == 1 |
| 1249 | $x->bsqrt(); # 0 |
| 1250 | if ($d > 1) |
| 1251 | { |
| 1252 | $x->bsqrt(); $x->bmul($xc); $d->bdec(); # 1 |
| 1253 | } |
| 1254 | } |
| 1255 | # assume fraction ends in 1 |
| 1256 | $x->bsqrt(); # 1 |
| 1257 | if (!$c->is_one()) |
| 1258 | { |
| 1259 | $x->bmul( $xc->bpow($c) ); |
| 1260 | } |
| 1261 | elsif (!$c->is_zero()) |
| 1262 | { |
| 1263 | $x->bmul( $xc ); |
| 1264 | } |
| 1265 | # done |
| 1266 | |
| 1267 | # shortcut to not run trough _find_round_parameters again |
| 1268 | if (defined $params[1]) |
| 1269 | { |
| 1270 | $x->bround($params[1],$params[3]); # then round accordingly |
| 1271 | } |
| 1272 | else |
| 1273 | { |
| 1274 | $x->bfround($params[2],$params[3]); # then round accordingly |
| 1275 | } |
| 1276 | if ($fallback) |
| 1277 | { |
| 1278 | # clear a/p after round, since user did not request it |
| 1279 | $x->{_a} = undef; $x->{_p} = undef; |
| 1280 | } |
| 1281 | # restore globals |
| 1282 | $$abr = $ab; $$pbr = $pb; |
| 1283 | $x; |
| 1284 | } |
| 1285 | |
| 1286 | sub _pow |
| 1287 | { |
| 1288 | # Calculate a power where $y is a non-integer, like 2 ** 0.5 |
| 1289 | my ($x,$y,$a,$p,$r) = @_; |
| 1290 | my $self = ref($x); |
| 1291 | |
| 1292 | # if $y == 0.5, it is sqrt($x) |
| 1293 | return $x->bsqrt($a,$p,$r,$y) if $y->bcmp('0.5') == 0; |
| 1294 | |
| 1295 | # u = y * ln x |
| 1296 | # _ _ |
| 1297 | # Taylor: | u u^2 u^3 | |
| 1298 | # x ** y = 1 + | --- + --- + * ----- + ... | |
| 1299 | # |_ 1 1*2 1*2*3 _| |
| 1300 | |
| 1301 | # we need to limit the accuracy to protect against overflow |
| 1302 | my $fallback = 0; |
| 1303 | my $scale = 0; |
| 1304 | my @params = $x->_find_round_parameters($a,$p,$r); |
| 1305 | |
| 1306 | # no rounding at all, so must use fallback |
| 1307 | if (scalar @params == 1) |
| 1308 | { |
| 1309 | # simulate old behaviour |
| 1310 | $params[1] = $self->div_scale(); # and round to it as accuracy |
| 1311 | $scale = $params[1]+4; # at least four more for proper round |
| 1312 | $params[3] = $r; # round mode by caller or undef |
| 1313 | $fallback = 1; # to clear a/p afterwards |
| 1314 | } |
| 1315 | else |
| 1316 | { |
| 1317 | # the 4 below is empirical, and there might be cases where it is not |
| 1318 | # enough... |
| 1319 | $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined |
| 1320 | } |
| 1321 | |
| 1322 | # when user set globals, they would interfere with our calculation, so |
| 1323 | # disable then and later re-enable them |
| 1324 | no strict 'refs'; |
| 1325 | my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef; |
| 1326 | my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef; |
| 1327 | # we also need to disable any set A or P on $x (_find_round_parameters took |
| 1328 | # them already into account), since these would interfere, too |
| 1329 | delete $x->{_a}; delete $x->{_p}; |
| 1330 | # need to disable $upgrade in BigInt, to avoid deep recursion |
| 1331 | local $Math::BigInt::upgrade = undef; |
| 1332 | |
| 1333 | my ($limit,$v,$u,$below,$factor,$next,$over); |
| 1334 | |
| 1335 | $u = $x->copy()->blog($scale)->bmul($y); |
| 1336 | $v = $self->bone(); # 1 |
| 1337 | $factor = $self->new(2); # 2 |
| 1338 | $x->bone(); # first term: 1 |
| 1339 | |
| 1340 | $below = $v->copy(); |
| 1341 | $over = $u->copy(); |
| 1342 | |
| 1343 | $limit = $self->new("1E-". ($scale-1)); |
| 1344 | #my $steps = 0; |
| 1345 | while (3 < 5) |
| 1346 | { |
| 1347 | # we calculate the next term, and add it to the last |
| 1348 | # when the next term is below our limit, it won't affect the outcome |
| 1349 | # anymore, so we stop |
| 1350 | $next = $over->copy()->bdiv($below,$scale); |
| 1351 | last if $next->bcmp($limit) <= 0; |
| 1352 | $x->badd($next); |
| 1353 | # print "at $x\n"; |
| 1354 | # calculate things for the next term |
| 1355 | $over *= $u; $below *= $factor; $factor->binc(); |
| 1356 | #$steps++; |
| 1357 | } |
| 1358 | |
| 1359 | # shortcut to not run trough _find_round_parameters again |
| 1360 | if (defined $params[1]) |
| 1361 | { |
| 1362 | $x->bround($params[1],$params[3]); # then round accordingly |
| 1363 | } |
| 1364 | else |
| 1365 | { |
| 1366 | $x->bfround($params[2],$params[3]); # then round accordingly |
| 1367 | } |
| 1368 | if ($fallback) |
| 1369 | { |
| 1370 | # clear a/p after round, since user did not request it |
| 1371 | $x->{_a} = undef; $x->{_p} = undef; |
| 1372 | } |
| 1373 | # restore globals |
| 1374 | $$abr = $ab; $$pbr = $pb; |
| 1375 | $x; |
| 1376 | } |
| 1377 | |
| 1378 | sub bpow |
| 1379 | { |
| 1380 | # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT |
| 1381 | # compute power of two numbers, second arg is used as integer |
| 1382 | # modifies first argument |
| 1383 | |
| 1384 | # set up parameters |
| 1385 | my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_); |
| 1386 | # objectify is costly, so avoid it |
| 1387 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1388 | { |
| 1389 | ($self,$x,$y,$a,$p,$r) = objectify(2,@_); |
| 1390 | } |
| 1391 | |
| 1392 | return $x if $x->{sign} =~ /^[+-]inf$/; |
| 1393 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
| 1394 | return $x->bone() if $y->is_zero(); |
| 1395 | return $x if $x->is_one() || $y->is_one(); |
| 1396 | |
| 1397 | return $x->_pow($y,$a,$p,$r) if !$y->is_int(); # non-integer power |
| 1398 | |
| 1399 | my $y1 = $y->as_number(); # make bigint |
| 1400 | # if ($x == -1) |
| 1401 | if ($x->{sign} eq '-' && $x->{_m}->is_one() && $x->{_e}->is_zero()) |
| 1402 | { |
| 1403 | # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 |
| 1404 | return $y1->is_odd() ? $x : $x->babs(1); |
| 1405 | } |
| 1406 | if ($x->is_zero()) |
| 1407 | { |
| 1408 | return $x if $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) |
| 1409 | # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf) |
| 1410 | $x->binf(); |
| 1411 | } |
| 1412 | |
| 1413 | # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) |
| 1414 | $y1->babs(); |
| 1415 | $x->{_m}->bpow($y1); |
| 1416 | $x->{_e}->bmul($y1); |
| 1417 | $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan; |
| 1418 | $x->bnorm(); |
| 1419 | if ($y->{sign} eq '-') |
| 1420 | { |
| 1421 | # modify $x in place! |
| 1422 | my $z = $x->copy(); $x->bzero()->binc(); |
| 1423 | return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!) |
| 1424 | } |
| 1425 | $x->round($a,$p,$r,$y); |
| 1426 | } |
| 1427 | |
| 1428 | ############################################################################### |
| 1429 | # rounding functions |
| 1430 | |
| 1431 | sub bfround |
| 1432 | { |
| 1433 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' |
| 1434 | # $n == 0 means round to integer |
| 1435 | # expects and returns normalized numbers! |
| 1436 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
| 1437 | |
| 1438 | return $x if $x->modify('bfround'); |
| 1439 | |
| 1440 | my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_); |
| 1441 | return $x if !defined $scale; # no-op |
| 1442 | |
| 1443 | # never round a 0, +-inf, NaN |
| 1444 | if ($x->is_zero()) |
| 1445 | { |
| 1446 | $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2 |
| 1447 | return $x; |
| 1448 | } |
| 1449 | return $x if $x->{sign} !~ /^[+-]$/; |
| 1450 | |
| 1451 | # don't round if x already has lower precision |
| 1452 | return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); |
| 1453 | |
| 1454 | $x->{_p} = $scale; # remember round in any case |
| 1455 | $x->{_a} = undef; # and clear A |
| 1456 | if ($scale < 0) |
| 1457 | { |
| 1458 | # round right from the '.' |
| 1459 | |
| 1460 | return $x if $x->{_e}->{sign} eq '+'; # e >= 0 => nothing to round |
| 1461 | |
| 1462 | $scale = -$scale; # positive for simplicity |
| 1463 | my $len = $x->{_m}->length(); # length of mantissa |
| 1464 | |
| 1465 | # the following poses a restriction on _e, but if _e is bigger than a |
| 1466 | # scalar, you got other problems (memory etc) anyway |
| 1467 | my $dad = -($x->{_e}->numify()); # digits after dot |
| 1468 | my $zad = 0; # zeros after dot |
| 1469 | $zad = $dad - $len if (-$dad < -$len); # for 0.00..00xxx style |
| 1470 | |
| 1471 | #print "scale $scale dad $dad zad $zad len $len\n"; |
| 1472 | # number bsstr len zad dad |
| 1473 | # 0.123 123e-3 3 0 3 |
| 1474 | # 0.0123 123e-4 3 1 4 |
| 1475 | # 0.001 1e-3 1 2 3 |
| 1476 | # 1.23 123e-2 3 0 2 |
| 1477 | # 1.2345 12345e-4 5 0 4 |
| 1478 | |
| 1479 | # do not round after/right of the $dad |
| 1480 | return $x if $scale > $dad; # 0.123, scale >= 3 => exit |
| 1481 | |
| 1482 | # round to zero if rounding inside the $zad, but not for last zero like: |
| 1483 | # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) |
| 1484 | return $x->bzero() if $scale < $zad; |
| 1485 | if ($scale == $zad) # for 0.006, scale -3 and trunc |
| 1486 | { |
| 1487 | $scale = -$len; |
| 1488 | } |
| 1489 | else |
| 1490 | { |
| 1491 | # adjust round-point to be inside mantissa |
| 1492 | if ($zad != 0) |
| 1493 | { |
| 1494 | $scale = $scale-$zad; |
| 1495 | } |
| 1496 | else |
| 1497 | { |
| 1498 | my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot |
| 1499 | $scale = $dbd+$scale; |
| 1500 | } |
| 1501 | } |
| 1502 | } |
| 1503 | else |
| 1504 | { |
| 1505 | # round left from the '.' |
| 1506 | |
| 1507 | # 123 => 100 means length(123) = 3 - $scale (2) => 1 |
| 1508 | |
| 1509 | my $dbt = $x->{_m}->length(); |
| 1510 | # digits before dot |
| 1511 | my $dbd = $dbt + $x->{_e}->numify(); |
| 1512 | # should be the same, so treat it as this |
| 1513 | $scale = 1 if $scale == 0; |
| 1514 | # shortcut if already integer |
| 1515 | return $x if $scale == 1 && $dbt <= $dbd; |
| 1516 | # maximum digits before dot |
| 1517 | ++$dbd; |
| 1518 | |
| 1519 | if ($scale > $dbd) |
| 1520 | { |
| 1521 | # not enough digits before dot, so round to zero |
| 1522 | return $x->bzero; |
| 1523 | } |
| 1524 | elsif ( $scale == $dbd ) |
| 1525 | { |
| 1526 | # maximum |
| 1527 | $scale = -$dbt; |
| 1528 | } |
| 1529 | else |
| 1530 | { |
| 1531 | $scale = $dbd - $scale; |
| 1532 | } |
| 1533 | } |
| 1534 | # pass sign to bround for rounding modes '+inf' and '-inf' |
| 1535 | $x->{_m}->{sign} = $x->{sign}; |
| 1536 | $x->{_m}->bround($scale,$mode); |
| 1537 | $x->{_m}->{sign} = '+'; # fix sign back |
| 1538 | $x->bnorm(); |
| 1539 | } |
| 1540 | |
| 1541 | sub bround |
| 1542 | { |
| 1543 | # accuracy: preserve $N digits, and overwrite the rest with 0's |
| 1544 | my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x); |
| 1545 | |
| 1546 | die ('bround() needs positive accuracy') if ($_[0] || 0) < 0; |
| 1547 | |
| 1548 | my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_); |
| 1549 | return $x if !defined $scale; # no-op |
| 1550 | |
| 1551 | return $x if $x->modify('bround'); |
| 1552 | |
| 1553 | # scale is now either $x->{_a}, $accuracy, or the user parameter |
| 1554 | # test whether $x already has lower accuracy, do nothing in this case |
| 1555 | # but do round if the accuracy is the same, since a math operation might |
| 1556 | # want to round a number with A=5 to 5 digits afterwards again |
| 1557 | return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0]; |
| 1558 | |
| 1559 | # scale < 0 makes no sense |
| 1560 | # never round a +-inf, NaN |
| 1561 | return $x if ($scale < 0) || $x->{sign} !~ /^[+-]$/; |
| 1562 | |
| 1563 | # 1: $scale == 0 => keep all digits |
| 1564 | # 2: never round a 0 |
| 1565 | # 3: if we should keep more digits than the mantissa has, do nothing |
| 1566 | if ($scale == 0 || $x->is_zero() || $x->{_m}->length() <= $scale) |
| 1567 | { |
| 1568 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; |
| 1569 | return $x; |
| 1570 | } |
| 1571 | |
| 1572 | # pass sign to bround for '+inf' and '-inf' rounding modes |
| 1573 | $x->{_m}->{sign} = $x->{sign}; |
| 1574 | $x->{_m}->bround($scale,$mode); # round mantissa |
| 1575 | $x->{_m}->{sign} = '+'; # fix sign back |
| 1576 | # $x->{_m}->{_a} = undef; $x->{_m}->{_p} = undef; |
| 1577 | $x->{_a} = $scale; # remember rounding |
| 1578 | $x->{_p} = undef; # and clear P |
| 1579 | $x->bnorm(); # del trailing zeros gen. by bround() |
| 1580 | } |
| 1581 | |
| 1582 | sub bfloor |
| 1583 | { |
| 1584 | # return integer less or equal then $x |
| 1585 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1586 | |
| 1587 | return $x if $x->modify('bfloor'); |
| 1588 | |
| 1589 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
| 1590 | |
| 1591 | # if $x has digits after dot |
| 1592 | if ($x->{_e}->{sign} eq '-') |
| 1593 | { |
| 1594 | $x->{_e}->{sign} = '+'; # negate e |
| 1595 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot |
| 1596 | $x->{_e}->bzero(); # trunc/norm |
| 1597 | $x->{_m}->binc() if $x->{sign} eq '-'; # decrement if negative |
| 1598 | } |
| 1599 | $x->round($a,$p,$r); |
| 1600 | } |
| 1601 | |
| 1602 | sub bceil |
| 1603 | { |
| 1604 | # return integer greater or equal then $x |
| 1605 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
| 1606 | |
| 1607 | return $x if $x->modify('bceil'); |
| 1608 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
| 1609 | |
| 1610 | # if $x has digits after dot |
| 1611 | if ($x->{_e}->{sign} eq '-') |
| 1612 | { |
| 1613 | #$x->{_m}->brsft(-$x->{_e},10); |
| 1614 | #$x->{_e}->bzero(); |
| 1615 | #$x++ if $x->{sign} eq '+'; |
| 1616 | |
| 1617 | $x->{_e}->{sign} = '+'; # negate e |
| 1618 | $x->{_m}->brsft($x->{_e},10); # cut off digits after dot |
| 1619 | $x->{_e}->bzero(); # trunc/norm |
| 1620 | $x->{_m}->binc() if $x->{sign} eq '+'; # decrement if negative |
| 1621 | } |
| 1622 | $x->round($a,$p,$r); |
| 1623 | } |
| 1624 | |
| 1625 | sub brsft |
| 1626 | { |
| 1627 | # shift right by $y (divide by power of $n) |
| 1628 | |
| 1629 | # set up parameters |
| 1630 | my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_); |
| 1631 | # objectify is costly, so avoid it |
| 1632 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1633 | { |
| 1634 | ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
| 1635 | } |
| 1636 | |
| 1637 | return $x if $x->modify('brsft'); |
| 1638 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
| 1639 | |
| 1640 | $n = 2 if !defined $n; $n = $self->new($n); |
| 1641 | $x->bdiv($n->bpow($y),$a,$p,$r,$y); |
| 1642 | } |
| 1643 | |
| 1644 | sub blsft |
| 1645 | { |
| 1646 | # shift left by $y (multiply by power of $n) |
| 1647 | |
| 1648 | # set up parameters |
| 1649 | my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_); |
| 1650 | # objectify is costly, so avoid it |
| 1651 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
| 1652 | { |
| 1653 | ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_); |
| 1654 | } |
| 1655 | |
| 1656 | return $x if $x->modify('blsft'); |
| 1657 | return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf |
| 1658 | |
| 1659 | $n = 2 if !defined $n; $n = $self->new($n); |
| 1660 | $x->bmul($n->bpow($y),$a,$p,$r,$y); |
| 1661 | } |
| 1662 | |
| 1663 | ############################################################################### |
| 1664 | |
| 1665 | sub DESTROY |
| 1666 | { |
| 1667 | # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub |
| 1668 | } |
| 1669 | |
| 1670 | sub AUTOLOAD |
| 1671 | { |
| 1672 | # make fxxx and bxxx both work by selectively mapping fxxx() to MBF::bxxx() |
| 1673 | # or falling back to MBI::bxxx() |
| 1674 | my $name = $AUTOLOAD; |
| 1675 | |
| 1676 | $name =~ s/.*:://; # split package |
| 1677 | no strict 'refs'; |
| 1678 | if (!method_alias($name)) |
| 1679 | { |
| 1680 | if (!defined $name) |
| 1681 | { |
| 1682 | # delayed load of Carp and avoid recursion |
| 1683 | require Carp; |
| 1684 | Carp::croak ("Can't call a method without name"); |
| 1685 | } |
| 1686 | if (!method_hand_up($name)) |
| 1687 | { |
| 1688 | # delayed load of Carp and avoid recursion |
| 1689 | require Carp; |
| 1690 | Carp::croak ("Can't call $class\-\>$name, not a valid method"); |
| 1691 | } |
| 1692 | # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() |
| 1693 | $name =~ s/^f/b/; |
| 1694 | return &{"$MBI"."::$name"}(@_); |
| 1695 | } |
| 1696 | my $bname = $name; $bname =~ s/^f/b/; |
| 1697 | *{$class."::$name"} = \&$bname; |
| 1698 | &$bname; # uses @_ |
| 1699 | } |
| 1700 | |
| 1701 | sub exponent |
| 1702 | { |
| 1703 | # return a copy of the exponent |
| 1704 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 1705 | |
| 1706 | if ($x->{sign} !~ /^[+-]$/) |
| 1707 | { |
| 1708 | my $s = $x->{sign}; $s =~ s/^[+-]//; |
| 1709 | return $self->new($s); # -inf, +inf => +inf |
| 1710 | } |
| 1711 | return $x->{_e}->copy(); |
| 1712 | } |
| 1713 | |
| 1714 | sub mantissa |
| 1715 | { |
| 1716 | # return a copy of the mantissa |
| 1717 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 1718 | |
| 1719 | if ($x->{sign} !~ /^[+-]$/) |
| 1720 | { |
| 1721 | my $s = $x->{sign}; $s =~ s/^[+]//; |
| 1722 | return $self->new($s); # -inf, +inf => +inf |
| 1723 | } |
| 1724 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
| 1725 | $m->bneg() if $x->{sign} eq '-'; |
| 1726 | |
| 1727 | $m; |
| 1728 | } |
| 1729 | |
| 1730 | sub parts |
| 1731 | { |
| 1732 | # return a copy of both the exponent and the mantissa |
| 1733 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 1734 | |
| 1735 | if ($x->{sign} !~ /^[+-]$/) |
| 1736 | { |
| 1737 | my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; |
| 1738 | return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf |
| 1739 | } |
| 1740 | my $m = $x->{_m}->copy(); # faster than going via bstr() |
| 1741 | $m->bneg() if $x->{sign} eq '-'; |
| 1742 | return ($m,$x->{_e}->copy()); |
| 1743 | } |
| 1744 | |
| 1745 | ############################################################################## |
| 1746 | # private stuff (internal use only) |
| 1747 | |
| 1748 | sub import |
| 1749 | { |
| 1750 | my $self = shift; |
| 1751 | my $l = scalar @_; |
| 1752 | my $lib = ''; my @a; |
| 1753 | for ( my $i = 0; $i < $l ; $i++) |
| 1754 | { |
| 1755 | # print "at $_[$i] (",$_[$i+1]||'undef',")\n"; |
| 1756 | if ( $_[$i] eq ':constant' ) |
| 1757 | { |
| 1758 | # this rest causes overlord er load to step in |
| 1759 | # print "overload @_\n"; |
| 1760 | overload::constant float => sub { $self->new(shift); }; |
| 1761 | } |
| 1762 | elsif ($_[$i] eq 'upgrade') |
| 1763 | { |
| 1764 | # this causes upgrading |
| 1765 | $upgrade = $_[$i+1]; # or undef to disable |
| 1766 | $i++; |
| 1767 | } |
| 1768 | elsif ($_[$i] eq 'downgrade') |
| 1769 | { |
| 1770 | # this causes downgrading |
| 1771 | $downgrade = $_[$i+1]; # or undef to disable |
| 1772 | $i++; |
| 1773 | } |
| 1774 | elsif ($_[$i] eq 'lib') |
| 1775 | { |
| 1776 | $lib = $_[$i+1] || ''; # default Calc |
| 1777 | $i++; |
| 1778 | } |
| 1779 | elsif ($_[$i] eq 'with') |
| 1780 | { |
| 1781 | $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt |
| 1782 | $i++; |
| 1783 | } |
| 1784 | else |
| 1785 | { |
| 1786 | push @a, $_[$i]; |
| 1787 | } |
| 1788 | } |
| 1789 | |
| 1790 | # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work |
| 1791 | my $mbilib = eval { Math::BigInt->config()->{lib} }; |
| 1792 | if ((defined $mbilib) && ($MBI eq 'Math::BigInt')) |
| 1793 | { |
| 1794 | # MBI already loaded |
| 1795 | $MBI->import('lib',"$lib,$mbilib", 'objectify'); |
| 1796 | } |
| 1797 | else |
| 1798 | { |
| 1799 | # MBI not loaded, or with ne "Math::BigInt" |
| 1800 | $lib .= ",$mbilib" if defined $mbilib; |
| 1801 | $lib =~ s/^,//; # don't leave empty |
| 1802 | if ($] < 5.006) |
| 1803 | { |
| 1804 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is |
| 1805 | # used in the same script, or eval inside import(). |
| 1806 | my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt |
| 1807 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm |
| 1808 | require File::Spec; |
| 1809 | $file = File::Spec->catfile (@parts, $file); |
| 1810 | eval { require "$file"; }; |
| 1811 | $MBI->import( lib => $lib, 'objectify' ); |
| 1812 | } |
| 1813 | else |
| 1814 | { |
| 1815 | my $rc = "use $MBI lib => '$lib', 'objectify';"; |
| 1816 | eval $rc; |
| 1817 | } |
| 1818 | } |
| 1819 | die ("Couldn't load $MBI: $! $@") if $@; |
| 1820 | |
| 1821 | # any non :constant stuff is handled by our parent, Exporter |
| 1822 | # even if @_ is empty, to give it a chance |
| 1823 | $self->SUPER::import(@a); # for subclasses |
| 1824 | $self->export_to_level(1,$self,@a); # need this, too |
| 1825 | } |
| 1826 | |
| 1827 | sub bnorm |
| 1828 | { |
| 1829 | # adjust m and e so that m is smallest possible |
| 1830 | # round number according to accuracy and precision settings |
| 1831 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 1832 | |
| 1833 | return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc |
| 1834 | |
| 1835 | # if (!$x->{_m}->is_odd()) |
| 1836 | # { |
| 1837 | my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros |
| 1838 | if ($zeros != 0) |
| 1839 | { |
| 1840 | $x->{_m}->brsft($zeros,10); $x->{_e}->badd($zeros); |
| 1841 | } |
| 1842 | # for something like 0Ey, set y to 1, and -0 => +0 |
| 1843 | $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero(); |
| 1844 | # } |
| 1845 | # this is to prevent automatically rounding when MBI's globals are set |
| 1846 | $x->{_m}->{_f} = MB_NEVER_ROUND; |
| 1847 | $x->{_e}->{_f} = MB_NEVER_ROUND; |
| 1848 | # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround() |
| 1849 | $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef; |
| 1850 | $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef; |
| 1851 | $x; # MBI bnorm is no-op, so dont call it |
| 1852 | } |
| 1853 | |
| 1854 | ############################################################################## |
| 1855 | # internal calculation routines |
| 1856 | |
| 1857 | sub as_number |
| 1858 | { |
| 1859 | # return copy as a bigint representation of this BigFloat number |
| 1860 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
| 1861 | |
| 1862 | my $z = $x->{_m}->copy(); |
| 1863 | if ($x->{_e}->{sign} eq '-') # < 0 |
| 1864 | { |
| 1865 | $x->{_e}->{sign} = '+'; # flip |
| 1866 | $z->brsft($x->{_e},10); |
| 1867 | $x->{_e}->{sign} = '-'; # flip back |
| 1868 | } |
| 1869 | elsif (!$x->{_e}->is_zero()) # > 0 |
| 1870 | { |
| 1871 | $z->blsft($x->{_e},10); |
| 1872 | } |
| 1873 | $z->{sign} = $x->{sign}; |
| 1874 | $z; |
| 1875 | } |
| 1876 | |
| 1877 | sub length |
| 1878 | { |
| 1879 | my $x = shift; |
| 1880 | my $class = ref($x) || $x; |
| 1881 | $x = $class->new(shift) unless ref($x); |
| 1882 | |
| 1883 | return 1 if $x->{_m}->is_zero(); |
| 1884 | my $len = $x->{_m}->length(); |
| 1885 | $len += $x->{_e} if $x->{_e}->sign() eq '+'; |
| 1886 | if (wantarray()) |
| 1887 | { |
| 1888 | my $t = $MBI->bzero(); |
| 1889 | $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-'; |
| 1890 | return ($len,$t); |
| 1891 | } |
| 1892 | $len; |
| 1893 | } |
| 1894 | |
| 1895 | 1; |
| 1896 | __END__ |
| 1897 | |
| 1898 | =head1 NAME |
| 1899 | |
| 1900 | Math::BigFloat - Arbitrary size floating point math package |
| 1901 | |
| 1902 | =head1 SYNOPSIS |
| 1903 | |
| 1904 | use Math::BigFloat; |
| 1905 | |
| 1906 | # Number creation |
| 1907 | $x = Math::BigFloat->new($str); # defaults to 0 |
| 1908 | $nan = Math::BigFloat->bnan(); # create a NotANumber |
| 1909 | $zero = Math::BigFloat->bzero(); # create a +0 |
| 1910 | $inf = Math::BigFloat->binf(); # create a +inf |
| 1911 | $inf = Math::BigFloat->binf('-'); # create a -inf |
| 1912 | $one = Math::BigFloat->bone(); # create a +1 |
| 1913 | $one = Math::BigFloat->bone('-'); # create a -1 |
| 1914 | |
| 1915 | # Testing |
| 1916 | $x->is_zero(); # true if arg is +0 |
| 1917 | $x->is_nan(); # true if arg is NaN |
| 1918 | $x->is_one(); # true if arg is +1 |
| 1919 | $x->is_one('-'); # true if arg is -1 |
| 1920 | $x->is_odd(); # true if odd, false for even |
| 1921 | $x->is_even(); # true if even, false for odd |
| 1922 | $x->is_positive(); # true if >= 0 |
| 1923 | $x->is_negative(); # true if < 0 |
| 1924 | $x->is_inf(sign); # true if +inf, or -inf (default is '+') |
| 1925 | |
| 1926 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) |
| 1927 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) |
| 1928 | $x->sign(); # return the sign, either +,- or NaN |
| 1929 | $x->digit($n); # return the nth digit, counting from right |
| 1930 | $x->digit(-$n); # return the nth digit, counting from left |
| 1931 | |
| 1932 | # The following all modify their first argument: |
| 1933 | |
| 1934 | # set |
| 1935 | $x->bzero(); # set $i to 0 |
| 1936 | $x->bnan(); # set $i to NaN |
| 1937 | $x->bone(); # set $x to +1 |
| 1938 | $x->bone('-'); # set $x to -1 |
| 1939 | $x->binf(); # set $x to inf |
| 1940 | $x->binf('-'); # set $x to -inf |
| 1941 | |
| 1942 | $x->bneg(); # negation |
| 1943 | $x->babs(); # absolute value |
| 1944 | $x->bnorm(); # normalize (no-op) |
| 1945 | $x->bnot(); # two's complement (bit wise not) |
| 1946 | $x->binc(); # increment x by 1 |
| 1947 | $x->bdec(); # decrement x by 1 |
| 1948 | |
| 1949 | $x->badd($y); # addition (add $y to $x) |
| 1950 | $x->bsub($y); # subtraction (subtract $y from $x) |
| 1951 | $x->bmul($y); # multiplication (multiply $x by $y) |
| 1952 | $x->bdiv($y); # divide, set $i to quotient |
| 1953 | # return (quo,rem) or quo if scalar |
| 1954 | |
| 1955 | $x->bmod($y); # modulus |
| 1956 | $x->bpow($y); # power of arguments (a**b) |
| 1957 | $x->blsft($y); # left shift |
| 1958 | $x->brsft($y); # right shift |
| 1959 | # return (quo,rem) or quo if scalar |
| 1960 | |
| 1961 | $x->blog($base); # logarithm of $x, base defaults to e |
| 1962 | # (other bases than e not supported yet) |
| 1963 | |
| 1964 | $x->band($y); # bit-wise and |
| 1965 | $x->bior($y); # bit-wise inclusive or |
| 1966 | $x->bxor($y); # bit-wise exclusive or |
| 1967 | $x->bnot(); # bit-wise not (two's complement) |
| 1968 | |
| 1969 | $x->bsqrt(); # calculate square-root |
| 1970 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
| 1971 | |
| 1972 | $x->bround($N); # accuracy: preserver $N digits |
| 1973 | $x->bfround($N); # precision: round to the $Nth digit |
| 1974 | |
| 1975 | # The following do not modify their arguments: |
| 1976 | bgcd(@values); # greatest common divisor |
| 1977 | blcm(@values); # lowest common multiplicator |
| 1978 | |
| 1979 | $x->bstr(); # return string |
| 1980 | $x->bsstr(); # return string in scientific notation |
| 1981 | |
| 1982 | $x->bfloor(); # return integer less or equal than $x |
| 1983 | $x->bceil(); # return integer greater or equal than $x |
| 1984 | |
| 1985 | $x->exponent(); # return exponent as BigInt |
| 1986 | $x->mantissa(); # return mantissa as BigInt |
| 1987 | $x->parts(); # return (mantissa,exponent) as BigInt |
| 1988 | |
| 1989 | $x->length(); # number of digits (w/o sign and '.') |
| 1990 | ($l,$f) = $x->length(); # number of digits, and length of fraction |
| 1991 | |
| 1992 | $x->precision(); # return P of $x (or global, if P of $x undef) |
| 1993 | $x->precision($n); # set P of $x to $n |
| 1994 | $x->accuracy(); # return A of $x (or global, if A of $x undef) |
| 1995 | $x->accuracy($n); # set A $x to $n |
| 1996 | |
| 1997 | Math::BigFloat->precision(); # get/set global P for all BigFloat objects |
| 1998 | Math::BigFloat->accuracy(); # get/set global A for all BigFloat objects |
| 1999 | |
| 2000 | =head1 DESCRIPTION |
| 2001 | |
| 2002 | All operators (inlcuding basic math operations) are overloaded if you |
| 2003 | declare your big floating point numbers as |
| 2004 | |
| 2005 | $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; |
| 2006 | |
| 2007 | Operations with overloaded operators preserve the arguments, which is |
| 2008 | exactly what you expect. |
| 2009 | |
| 2010 | =head2 Canonical notation |
| 2011 | |
| 2012 | Input to these routines are either BigFloat objects, or strings of the |
| 2013 | following four forms: |
| 2014 | |
| 2015 | =over 2 |
| 2016 | |
| 2017 | =item * |
| 2018 | |
| 2019 | C</^[+-]\d+$/> |
| 2020 | |
| 2021 | =item * |
| 2022 | |
| 2023 | C</^[+-]\d+\.\d*$/> |
| 2024 | |
| 2025 | =item * |
| 2026 | |
| 2027 | C</^[+-]\d+E[+-]?\d+$/> |
| 2028 | |
| 2029 | =item * |
| 2030 | |
| 2031 | C</^[+-]\d*\.\d+E[+-]?\d+$/> |
| 2032 | |
| 2033 | =back |
| 2034 | |
| 2035 | all with optional leading and trailing zeros and/or spaces. Additonally, |
| 2036 | numbers are allowed to have an underscore between any two digits. |
| 2037 | |
| 2038 | Empty strings as well as other illegal numbers results in 'NaN'. |
| 2039 | |
| 2040 | bnorm() on a BigFloat object is now effectively a no-op, since the numbers |
| 2041 | are always stored in normalized form. On a string, it creates a BigFloat |
| 2042 | object. |
| 2043 | |
| 2044 | =head2 Output |
| 2045 | |
| 2046 | Output values are BigFloat objects (normalized), except for bstr() and bsstr(). |
| 2047 | |
| 2048 | The string output will always have leading and trailing zeros stripped and drop |
| 2049 | a plus sign. C<bstr()> will give you always the form with a decimal point, |
| 2050 | while C<bsstr()> (for scientific) gives you the scientific notation. |
| 2051 | |
| 2052 | Input bstr() bsstr() |
| 2053 | '-0' '0' '0E1' |
| 2054 | ' -123 123 123' '-123123123' '-123123123E0' |
| 2055 | '00.0123' '0.0123' '123E-4' |
| 2056 | '123.45E-2' '1.2345' '12345E-4' |
| 2057 | '10E+3' '10000' '1E4' |
| 2058 | |
| 2059 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, |
| 2060 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) |
| 2061 | return either undef, <0, 0 or >0 and are suited for sort. |
| 2062 | |
| 2063 | Actual math is done by using BigInts to represent the mantissa and exponent. |
| 2064 | The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to |
| 2065 | represent the result when input arguments are not numbers, as well as |
| 2066 | the result of dividing by zero. |
| 2067 | |
| 2068 | =head2 C<mantissa()>, C<exponent()> and C<parts()> |
| 2069 | |
| 2070 | C<mantissa()> and C<exponent()> return the said parts of the BigFloat |
| 2071 | as BigInts such that: |
| 2072 | |
| 2073 | $m = $x->mantissa(); |
| 2074 | $e = $x->exponent(); |
| 2075 | $y = $m * ( 10 ** $e ); |
| 2076 | print "ok\n" if $x == $y; |
| 2077 | |
| 2078 | C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them. |
| 2079 | |
| 2080 | A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth). |
| 2081 | |
| 2082 | Currently the mantissa is reduced as much as possible, favouring higher |
| 2083 | exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). |
| 2084 | This might change in the future, so do not depend on it. |
| 2085 | |
| 2086 | =head2 Accuracy vs. Precision |
| 2087 | |
| 2088 | See also: L<Rounding|Rounding>. |
| 2089 | |
| 2090 | Math::BigFloat supports both precision and accuracy. For a full documentation, |
| 2091 | examples and tips on these topics please see the large section in |
| 2092 | L<Math::BigInt>. |
| 2093 | |
| 2094 | Since things like sqrt(2) or 1/3 must presented with a limited precision lest |
| 2095 | a operation consumes all resources, each operation produces no more than |
| 2096 | C<Math::BigFloat::precision()> digits. |
| 2097 | |
| 2098 | In case the result of one operation has more precision than specified, |
| 2099 | it is rounded. The rounding mode taken is either the default mode, or the one |
| 2100 | supplied to the operation after the I<scale>: |
| 2101 | |
| 2102 | $x = Math::BigFloat->new(2); |
| 2103 | Math::BigFloat::precision(5); # 5 digits max |
| 2104 | $y = $x->copy()->bdiv(3); # will give 0.66666 |
| 2105 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
| 2106 | $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 |
| 2107 | Math::BigFloat::round_mode('zero'); |
| 2108 | $y = $x->copy()->bdiv(3,6); # will give 0.666666 |
| 2109 | |
| 2110 | =head2 Rounding |
| 2111 | |
| 2112 | =over 2 |
| 2113 | |
| 2114 | =item ffround ( +$scale ) |
| 2115 | |
| 2116 | Rounds to the $scale'th place left from the '.', counting from the dot. |
| 2117 | The first digit is numbered 1. |
| 2118 | |
| 2119 | =item ffround ( -$scale ) |
| 2120 | |
| 2121 | Rounds to the $scale'th place right from the '.', counting from the dot. |
| 2122 | |
| 2123 | =item ffround ( 0 ) |
| 2124 | |
| 2125 | Rounds to an integer. |
| 2126 | |
| 2127 | =item fround ( +$scale ) |
| 2128 | |
| 2129 | Preserves accuracy to $scale digits from the left (aka significant digits) |
| 2130 | and pads the rest with zeros. If the number is between 1 and -1, the |
| 2131 | significant digits count from the first non-zero after the '.' |
| 2132 | |
| 2133 | =item fround ( -$scale ) and fround ( 0 ) |
| 2134 | |
| 2135 | These are effetively no-ops. |
| 2136 | |
| 2137 | =back |
| 2138 | |
| 2139 | All rounding functions take as a second parameter a rounding mode from one of |
| 2140 | the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
| 2141 | |
| 2142 | The default rounding mode is 'even'. By using |
| 2143 | C<< Math::BigFloat::round_mode($round_mode); >> you can get and set the default |
| 2144 | mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is |
| 2145 | no longer supported. |
| 2146 | The second parameter to the round functions then overrides the default |
| 2147 | temporarily. |
| 2148 | |
| 2149 | The C<< as_number() >> function returns a BigInt from a Math::BigFloat. It uses |
| 2150 | 'trunc' as rounding mode to make it equivalent to: |
| 2151 | |
| 2152 | $x = 2.5; |
| 2153 | $y = int($x) + 2; |
| 2154 | |
| 2155 | You can override this by passing the desired rounding mode as parameter to |
| 2156 | C<as_number()>: |
| 2157 | |
| 2158 | $x = Math::BigFloat->new(2.5); |
| 2159 | $y = $x->as_number('odd'); # $y = 3 |
| 2160 | |
| 2161 | =head1 EXAMPLES |
| 2162 | |
| 2163 | # not ready yet |
| 2164 | |
| 2165 | =head1 Autocreating constants |
| 2166 | |
| 2167 | After C<use Math::BigFloat ':constant'> all the floating point constants |
| 2168 | in the given scope are converted to C<Math::BigFloat>. This conversion |
| 2169 | happens at compile time. |
| 2170 | |
| 2171 | In particular |
| 2172 | |
| 2173 | perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' |
| 2174 | |
| 2175 | prints the value of C<2E-100>. Note that without conversion of |
| 2176 | constants the expression 2E-100 will be calculated as normal floating point |
| 2177 | number. |
| 2178 | |
| 2179 | Please note that ':constant' does not affect integer constants, nor binary |
| 2180 | nor hexadecimal constants. Use L<bignum> or L<Math::BigInt> to get this to |
| 2181 | work. |
| 2182 | |
| 2183 | =head2 Math library |
| 2184 | |
| 2185 | Math with the numbers is done (by default) by a module called |
| 2186 | Math::BigInt::Calc. This is equivalent to saying: |
| 2187 | |
| 2188 | use Math::BigFloat lib => 'Calc'; |
| 2189 | |
| 2190 | You can change this by using: |
| 2191 | |
| 2192 | use Math::BigFloat lib => 'BitVect'; |
| 2193 | |
| 2194 | The following would first try to find Math::BigInt::Foo, then |
| 2195 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
| 2196 | |
| 2197 | use Math::BigFloat lib => 'Foo,Math::BigInt::Bar'; |
| 2198 | |
| 2199 | Calc.pm uses as internal format an array of elements of some decimal base |
| 2200 | (usually 1e7, but this might be differen for some systems) with the least |
| 2201 | significant digit first, while BitVect.pm uses a bit vector of base 2, most |
| 2202 | significant bit first. Other modules might use even different means of |
| 2203 | representing the numbers. See the respective module documentation for further |
| 2204 | details. |
| 2205 | |
| 2206 | Please note that Math::BigFloat does B<not> use the denoted library itself, |
| 2207 | but it merely passes the lib argument to Math::BigInt. So, instead of the need |
| 2208 | to do: |
| 2209 | |
| 2210 | use Math::BigInt lib => 'GMP'; |
| 2211 | use Math::BigFloat; |
| 2212 | |
| 2213 | you can roll it all into one line: |
| 2214 | |
| 2215 | use Math::BigFloat lib => 'GMP'; |
| 2216 | |
| 2217 | Use the lib, Luke! And see L<Using Math::BigInt::Lite> for more details. |
| 2218 | |
| 2219 | =head2 Using Math::BigInt::Lite |
| 2220 | |
| 2221 | It is possible to use L<Math::BigInt::Lite> with Math::BigFloat: |
| 2222 | |
| 2223 | # 1 |
| 2224 | use Math::BigFloat with => 'Math::BigInt::Lite'; |
| 2225 | |
| 2226 | There is no need to "use Math::BigInt" or "use Math::BigInt::Lite", but you |
| 2227 | can combine these if you want. For instance, you may want to use |
| 2228 | Math::BigInt objects in your main script, too. |
| 2229 | |
| 2230 | # 2 |
| 2231 | use Math::BigInt; |
| 2232 | use Math::BigFloat with => 'Math::BigInt::Lite'; |
| 2233 | |
| 2234 | Of course, you can combine this with the C<lib> parameter. |
| 2235 | |
| 2236 | # 3 |
| 2237 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; |
| 2238 | |
| 2239 | If you want to use Math::BigInt's, too, simple add a Math::BigInt B<before>: |
| 2240 | |
| 2241 | # 4 |
| 2242 | use Math::BigInt; |
| 2243 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari'; |
| 2244 | |
| 2245 | Notice that the module with the last C<lib> will "win" and thus |
| 2246 | it's lib will be used if the lib is available: |
| 2247 | |
| 2248 | # 5 |
| 2249 | use Math::BigInt lib => 'Bar,Baz'; |
| 2250 | use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo'; |
| 2251 | |
| 2252 | That would try to load Foo, Bar, Baz and Calc (in that order). Or in other |
| 2253 | words, Math::BigFloat will try to retain previously loaded libs when you |
| 2254 | don't specify it one. |
| 2255 | |
| 2256 | Actually, the lib loading order would be "Bar,Baz,Calc", and then |
| 2257 | "Foo,Bar,Baz,Calc", but independend of which lib exists, the result is the |
| 2258 | same as trying the latter load alone, except for the fact that Bar or Baz |
| 2259 | might be loaded needlessly in an intermidiate step |
| 2260 | |
| 2261 | The old way still works though: |
| 2262 | |
| 2263 | # 6 |
| 2264 | use Math::BigInt lib => 'Bar,Baz'; |
| 2265 | use Math::BigFloat; |
| 2266 | |
| 2267 | But B<examples #3 and #4 are recommended> for usage. |
| 2268 | |
| 2269 | =head1 BUGS |
| 2270 | |
| 2271 | =over 2 |
| 2272 | |
| 2273 | =item * |
| 2274 | |
| 2275 | The following does not work yet: |
| 2276 | |
| 2277 | $m = $x->mantissa(); |
| 2278 | $e = $x->exponent(); |
| 2279 | $y = $m * ( 10 ** $e ); |
| 2280 | print "ok\n" if $x == $y; |
| 2281 | |
| 2282 | =item * |
| 2283 | |
| 2284 | There is no fmod() function yet. |
| 2285 | |
| 2286 | =back |
| 2287 | |
| 2288 | =head1 CAVEAT |
| 2289 | |
| 2290 | =over 1 |
| 2291 | |
| 2292 | =item stringify, bstr() |
| 2293 | |
| 2294 | Both stringify and bstr() now drop the leading '+'. The old code would return |
| 2295 | '+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for |
| 2296 | reasoning and details. |
| 2297 | |
| 2298 | =item bdiv |
| 2299 | |
| 2300 | The following will probably not do what you expect: |
| 2301 | |
| 2302 | print $c->bdiv(123.456),"\n"; |
| 2303 | |
| 2304 | It prints both quotient and reminder since print works in list context. Also, |
| 2305 | bdiv() will modify $c, so be carefull. You probably want to use |
| 2306 | |
| 2307 | print $c / 123.456,"\n"; |
| 2308 | print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c |
| 2309 | |
| 2310 | instead. |
| 2311 | |
| 2312 | =item Modifying and = |
| 2313 | |
| 2314 | Beware of: |
| 2315 | |
| 2316 | $x = Math::BigFloat->new(5); |
| 2317 | $y = $x; |
| 2318 | |
| 2319 | It will not do what you think, e.g. making a copy of $x. Instead it just makes |
| 2320 | a second reference to the B<same> object and stores it in $y. Thus anything |
| 2321 | that modifies $x will modify $y, and vice versa. |
| 2322 | |
| 2323 | $x->bmul(2); |
| 2324 | print "$x, $y\n"; # prints '10, 10' |
| 2325 | |
| 2326 | If you want a true copy of $x, use: |
| 2327 | |
| 2328 | $y = $x->copy(); |
| 2329 | |
| 2330 | See also the documentation in L<overload> regarding C<=>. |
| 2331 | |
| 2332 | =item bpow |
| 2333 | |
| 2334 | C<bpow()> now modifies the first argument, unlike the old code which left |
| 2335 | it alone and only returned the result. This is to be consistent with |
| 2336 | C<badd()> etc. The first will modify $x, the second one won't: |
| 2337 | |
| 2338 | print bpow($x,$i),"\n"; # modify $x |
| 2339 | print $x->bpow($i),"\n"; # ditto |
| 2340 | print $x ** $i,"\n"; # leave $x alone |
| 2341 | |
| 2342 | =back |
| 2343 | |
| 2344 | =head1 LICENSE |
| 2345 | |
| 2346 | This program is free software; you may redistribute it and/or modify it under |
| 2347 | the same terms as Perl itself. |
| 2348 | |
| 2349 | =head1 AUTHORS |
| 2350 | |
| 2351 | Mark Biggar, overloaded interface by Ilya Zakharevich. |
| 2352 | Completely rewritten by Tels http://bloodgate.com in 2001. |
| 2353 | |
| 2354 | =cut |