1*0Sstevel@tonic-gate 2*0Sstevel@tonic-gate# 3*0Sstevel@tonic-gate# "Tax the rat farms." - Lord Vetinari 4*0Sstevel@tonic-gate# 5*0Sstevel@tonic-gate 6*0Sstevel@tonic-gate# The following hash values are used: 7*0Sstevel@tonic-gate# sign : +,-,NaN,+inf,-inf 8*0Sstevel@tonic-gate# _d : denominator 9*0Sstevel@tonic-gate# _n : numeraotr (value = _n/_d) 10*0Sstevel@tonic-gate# _a : accuracy 11*0Sstevel@tonic-gate# _p : precision 12*0Sstevel@tonic-gate# _f : flags, used by MBR to flag parts of a rational as untouchable 13*0Sstevel@tonic-gate# You should not look at the innards of a BigRat - use the methods for this. 14*0Sstevel@tonic-gate 15*0Sstevel@tonic-gatepackage Math::BigRat; 16*0Sstevel@tonic-gate 17*0Sstevel@tonic-gaterequire 5.005_03; 18*0Sstevel@tonic-gateuse strict; 19*0Sstevel@tonic-gate 20*0Sstevel@tonic-gaterequire Exporter; 21*0Sstevel@tonic-gateuse Math::BigFloat; 22*0Sstevel@tonic-gateuse vars qw($VERSION @ISA $PACKAGE $upgrade $downgrade 23*0Sstevel@tonic-gate $accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf); 24*0Sstevel@tonic-gate 25*0Sstevel@tonic-gate@ISA = qw(Exporter Math::BigFloat); 26*0Sstevel@tonic-gate 27*0Sstevel@tonic-gate$VERSION = '0.12'; 28*0Sstevel@tonic-gate 29*0Sstevel@tonic-gateuse overload; # inherit from Math::BigFloat 30*0Sstevel@tonic-gate 31*0Sstevel@tonic-gateBEGIN { *objectify = \&Math::BigInt::objectify; } 32*0Sstevel@tonic-gate 33*0Sstevel@tonic-gate############################################################################## 34*0Sstevel@tonic-gate# global constants, flags and accessory 35*0Sstevel@tonic-gate 36*0Sstevel@tonic-gate$accuracy = $precision = undef; 37*0Sstevel@tonic-gate$round_mode = 'even'; 38*0Sstevel@tonic-gate$div_scale = 40; 39*0Sstevel@tonic-gate$upgrade = undef; 40*0Sstevel@tonic-gate$downgrade = undef; 41*0Sstevel@tonic-gate 42*0Sstevel@tonic-gate# these are internally, and not to be used from the outside 43*0Sstevel@tonic-gate 44*0Sstevel@tonic-gateuse constant MB_NEVER_ROUND => 0x0001; 45*0Sstevel@tonic-gate 46*0Sstevel@tonic-gate$_trap_nan = 0; # are NaNs ok? set w/ config() 47*0Sstevel@tonic-gate$_trap_inf = 0; # are infs ok? set w/ config() 48*0Sstevel@tonic-gate 49*0Sstevel@tonic-gatemy $nan = 'NaN'; 50*0Sstevel@tonic-gatemy $MBI = 'Math::BigInt'; 51*0Sstevel@tonic-gatemy $CALC = 'Math::BigInt::Calc'; 52*0Sstevel@tonic-gatemy $class = 'Math::BigRat'; 53*0Sstevel@tonic-gatemy $IMPORT = 0; 54*0Sstevel@tonic-gate 55*0Sstevel@tonic-gatesub isa 56*0Sstevel@tonic-gate { 57*0Sstevel@tonic-gate return 0 if $_[1] =~ /^Math::Big(Int|Float)/; # we aren't 58*0Sstevel@tonic-gate UNIVERSAL::isa(@_); 59*0Sstevel@tonic-gate } 60*0Sstevel@tonic-gate 61*0Sstevel@tonic-gatesub BEGIN 62*0Sstevel@tonic-gate { 63*0Sstevel@tonic-gate *AUTOLOAD = \&Math::BigFloat::AUTOLOAD; 64*0Sstevel@tonic-gate } 65*0Sstevel@tonic-gate 66*0Sstevel@tonic-gatesub _new_from_float 67*0Sstevel@tonic-gate { 68*0Sstevel@tonic-gate # turn a single float input into a rational number (like '0.1') 69*0Sstevel@tonic-gate my ($self,$f) = @_; 70*0Sstevel@tonic-gate 71*0Sstevel@tonic-gate return $self->bnan() if $f->is_nan(); 72*0Sstevel@tonic-gate return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/; 73*0Sstevel@tonic-gate 74*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 75*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 76*0Sstevel@tonic-gate $self->{_n} = $MBI->new($CALC->_str ( $f->{_m} ),undef,undef);# mantissa 77*0Sstevel@tonic-gate $self->{_d} = $MBI->bone(); 78*0Sstevel@tonic-gate $self->{sign} = $f->{sign} || '+'; 79*0Sstevel@tonic-gate if ($f->{_es} eq '-') 80*0Sstevel@tonic-gate { 81*0Sstevel@tonic-gate # something like Math::BigRat->new('0.1'); 82*0Sstevel@tonic-gate # 1 / 1 => 1/10 83*0Sstevel@tonic-gate $self->{_d}->blsft( $MBI->new($CALC->_str ( $f->{_e} )),10); 84*0Sstevel@tonic-gate } 85*0Sstevel@tonic-gate else 86*0Sstevel@tonic-gate { 87*0Sstevel@tonic-gate # something like Math::BigRat->new('10'); 88*0Sstevel@tonic-gate # 1 / 1 => 10/1 89*0Sstevel@tonic-gate $self->{_n}->blsft( $MBI->new($CALC->_str($f->{_e})),10) unless 90*0Sstevel@tonic-gate $CALC->_is_zero($f->{_e}); 91*0Sstevel@tonic-gate } 92*0Sstevel@tonic-gate $self; 93*0Sstevel@tonic-gate } 94*0Sstevel@tonic-gate 95*0Sstevel@tonic-gatesub new 96*0Sstevel@tonic-gate { 97*0Sstevel@tonic-gate # create a Math::BigRat 98*0Sstevel@tonic-gate my $class = shift; 99*0Sstevel@tonic-gate 100*0Sstevel@tonic-gate my ($n,$d) = shift; 101*0Sstevel@tonic-gate 102*0Sstevel@tonic-gate my $self = { }; bless $self,$class; 103*0Sstevel@tonic-gate 104*0Sstevel@tonic-gate # input like (BigInt,BigInt) or (BigFloat,BigFloat) not handled yet 105*0Sstevel@tonic-gate 106*0Sstevel@tonic-gate if ((!defined $d) && (ref $n) && (!$n->isa('Math::BigRat'))) 107*0Sstevel@tonic-gate { 108*0Sstevel@tonic-gate if ($n->isa('Math::BigFloat')) 109*0Sstevel@tonic-gate { 110*0Sstevel@tonic-gate $self->_new_from_float($n); 111*0Sstevel@tonic-gate } 112*0Sstevel@tonic-gate if ($n->isa('Math::BigInt')) 113*0Sstevel@tonic-gate { 114*0Sstevel@tonic-gate # TODO: trap NaN, inf 115*0Sstevel@tonic-gate $self->{_n} = $n->copy(); # "mantissa" = $n 116*0Sstevel@tonic-gate $self->{_d} = $MBI->bone(); 117*0Sstevel@tonic-gate $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+'; 118*0Sstevel@tonic-gate } 119*0Sstevel@tonic-gate if ($n->isa('Math::BigInt::Lite')) 120*0Sstevel@tonic-gate { 121*0Sstevel@tonic-gate # TODO: trap NaN, inf 122*0Sstevel@tonic-gate $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0; 123*0Sstevel@tonic-gate $self->{_n} = $MBI->new(abs($$n),undef,undef); # "mantissa" = $n 124*0Sstevel@tonic-gate $self->{_d} = $MBI->bone(); 125*0Sstevel@tonic-gate } 126*0Sstevel@tonic-gate return $self->bnorm(); 127*0Sstevel@tonic-gate } 128*0Sstevel@tonic-gate return $n->copy() if ref $n; 129*0Sstevel@tonic-gate 130*0Sstevel@tonic-gate if (!defined $n) 131*0Sstevel@tonic-gate { 132*0Sstevel@tonic-gate $self->{_n} = $MBI->bzero(); # undef => 0 133*0Sstevel@tonic-gate $self->{_d} = $MBI->bone(); 134*0Sstevel@tonic-gate $self->{sign} = '+'; 135*0Sstevel@tonic-gate return $self->bnorm(); 136*0Sstevel@tonic-gate } 137*0Sstevel@tonic-gate # string input with / delimiter 138*0Sstevel@tonic-gate if ($n =~ /\s*\/\s*/) 139*0Sstevel@tonic-gate { 140*0Sstevel@tonic-gate return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid 141*0Sstevel@tonic-gate return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid 142*0Sstevel@tonic-gate ($n,$d) = split (/\//,$n); 143*0Sstevel@tonic-gate # try as BigFloats first 144*0Sstevel@tonic-gate if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/)) 145*0Sstevel@tonic-gate { 146*0Sstevel@tonic-gate # one of them looks like a float 147*0Sstevel@tonic-gate # Math::BigFloat($n,undef,undef) does not what it is supposed to do, so: 148*0Sstevel@tonic-gate local $Math::BigFloat::accuracy = undef; 149*0Sstevel@tonic-gate local $Math::BigFloat::precision = undef; 150*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 151*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 152*0Sstevel@tonic-gate 153*0Sstevel@tonic-gate my $nf = Math::BigFloat->new($n,undef,undef); 154*0Sstevel@tonic-gate $self->{sign} = '+'; 155*0Sstevel@tonic-gate return $self->bnan() if $nf->is_nan(); 156*0Sstevel@tonic-gate $self->{_n} = $MBI->new( $CALC->_str( $nf->{_m} ) ); 157*0Sstevel@tonic-gate 158*0Sstevel@tonic-gate # now correct $self->{_n} due to $n 159*0Sstevel@tonic-gate my $f = Math::BigFloat->new($d,undef,undef); 160*0Sstevel@tonic-gate return $self->bnan() if $f->is_nan(); 161*0Sstevel@tonic-gate $self->{_d} = $MBI->new( $CALC->_str( $f->{_m} ) ); 162*0Sstevel@tonic-gate 163*0Sstevel@tonic-gate # calculate the difference between nE and dE 164*0Sstevel@tonic-gate my $diff_e = $MBI->new ($nf->exponent())->bsub ( $f->exponent); 165*0Sstevel@tonic-gate if ($diff_e->is_negative()) 166*0Sstevel@tonic-gate { 167*0Sstevel@tonic-gate # < 0: mul d with it 168*0Sstevel@tonic-gate $self->{_d}->blsft($diff_e->babs(),10); 169*0Sstevel@tonic-gate } 170*0Sstevel@tonic-gate elsif (!$diff_e->is_zero()) 171*0Sstevel@tonic-gate { 172*0Sstevel@tonic-gate # > 0: mul n with it 173*0Sstevel@tonic-gate $self->{_n}->blsft($diff_e,10); 174*0Sstevel@tonic-gate } 175*0Sstevel@tonic-gate } 176*0Sstevel@tonic-gate else 177*0Sstevel@tonic-gate { 178*0Sstevel@tonic-gate # both d and n are (big)ints 179*0Sstevel@tonic-gate $self->{_n} = $MBI->new($n,undef,undef); 180*0Sstevel@tonic-gate $self->{_d} = $MBI->new($d,undef,undef); 181*0Sstevel@tonic-gate $self->{sign} = '+'; 182*0Sstevel@tonic-gate return $self->bnan() if $self->{_n}->{sign} eq $nan || 183*0Sstevel@tonic-gate $self->{_d}->{sign} eq $nan; 184*0Sstevel@tonic-gate # handle inf and NAN cases: 185*0Sstevel@tonic-gate if ($self->{_n}->is_inf() || $self->{_d}->is_inf()) 186*0Sstevel@tonic-gate { 187*0Sstevel@tonic-gate # inf/inf => NaN 188*0Sstevel@tonic-gate return $self->bnan() if 189*0Sstevel@tonic-gate ($self->{_n}->is_inf() && $self->{_d}->is_inf()); 190*0Sstevel@tonic-gate if ($self->{_n}->is_inf()) 191*0Sstevel@tonic-gate { 192*0Sstevel@tonic-gate my $s = '+'; # '+inf/+123' or '-inf/-123' 193*0Sstevel@tonic-gate $s = '-' if substr($self->{_n}->{sign},0,1) ne $self->{_d}->{sign}; 194*0Sstevel@tonic-gate # +-inf/123 => +-inf 195*0Sstevel@tonic-gate return $self->binf($s); 196*0Sstevel@tonic-gate } 197*0Sstevel@tonic-gate # 123/inf => 0 198*0Sstevel@tonic-gate return $self->bzero(); 199*0Sstevel@tonic-gate } 200*0Sstevel@tonic-gate 201*0Sstevel@tonic-gate $self->{sign} = $self->{_n}->{sign}; $self->{_n}->babs(); 202*0Sstevel@tonic-gate # if $d is negative, flip sign 203*0Sstevel@tonic-gate $self->{sign} =~ tr/+-/-+/ if $self->{_d}->{sign} eq '-'; 204*0Sstevel@tonic-gate $self->{_d}->babs(); # normalize 205*0Sstevel@tonic-gate } 206*0Sstevel@tonic-gate 207*0Sstevel@tonic-gate return $self->bnorm(); 208*0Sstevel@tonic-gate } 209*0Sstevel@tonic-gate 210*0Sstevel@tonic-gate # simple string input 211*0Sstevel@tonic-gate if (($n =~ /[\.eE]/)) 212*0Sstevel@tonic-gate { 213*0Sstevel@tonic-gate # looks like a float, quacks like a float, so probably is a float 214*0Sstevel@tonic-gate # Math::BigFloat($n,undef,undef) does not what it is supposed to do, so: 215*0Sstevel@tonic-gate local $Math::BigFloat::accuracy = undef; 216*0Sstevel@tonic-gate local $Math::BigFloat::precision = undef; 217*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 218*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 219*0Sstevel@tonic-gate $self->{sign} = 'NaN'; 220*0Sstevel@tonic-gate $self->_new_from_float(Math::BigFloat->new($n,undef,undef)); 221*0Sstevel@tonic-gate } 222*0Sstevel@tonic-gate else 223*0Sstevel@tonic-gate { 224*0Sstevel@tonic-gate $self->{_n} = $MBI->new($n,undef,undef); 225*0Sstevel@tonic-gate $self->{_d} = $MBI->bone(); 226*0Sstevel@tonic-gate $self->{sign} = $self->{_n}->{sign}; $self->{_n}->babs(); 227*0Sstevel@tonic-gate return $self->bnan() if $self->{sign} eq 'NaN'; 228*0Sstevel@tonic-gate return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/; 229*0Sstevel@tonic-gate } 230*0Sstevel@tonic-gate $self->bnorm(); 231*0Sstevel@tonic-gate } 232*0Sstevel@tonic-gate 233*0Sstevel@tonic-gatesub copy 234*0Sstevel@tonic-gate { 235*0Sstevel@tonic-gate my ($c,$x); 236*0Sstevel@tonic-gate if (@_ > 1) 237*0Sstevel@tonic-gate { 238*0Sstevel@tonic-gate # if two arguments, the first one is the class to "swallow" subclasses 239*0Sstevel@tonic-gate ($c,$x) = @_; 240*0Sstevel@tonic-gate } 241*0Sstevel@tonic-gate else 242*0Sstevel@tonic-gate { 243*0Sstevel@tonic-gate $x = shift; 244*0Sstevel@tonic-gate $c = ref($x); 245*0Sstevel@tonic-gate } 246*0Sstevel@tonic-gate return unless ref($x); # only for objects 247*0Sstevel@tonic-gate 248*0Sstevel@tonic-gate my $self = {}; bless $self,$c; 249*0Sstevel@tonic-gate 250*0Sstevel@tonic-gate $self->{sign} = $x->{sign}; 251*0Sstevel@tonic-gate $self->{_d} = $x->{_d}->copy(); 252*0Sstevel@tonic-gate $self->{_n} = $x->{_n}->copy(); 253*0Sstevel@tonic-gate $self->{_a} = $x->{_a} if defined $x->{_a}; 254*0Sstevel@tonic-gate $self->{_p} = $x->{_p} if defined $x->{_p}; 255*0Sstevel@tonic-gate $self; 256*0Sstevel@tonic-gate } 257*0Sstevel@tonic-gate 258*0Sstevel@tonic-gate############################################################################## 259*0Sstevel@tonic-gate 260*0Sstevel@tonic-gatesub config 261*0Sstevel@tonic-gate { 262*0Sstevel@tonic-gate # return (later set?) configuration data as hash ref 263*0Sstevel@tonic-gate my $class = shift || 'Math::BigFloat'; 264*0Sstevel@tonic-gate 265*0Sstevel@tonic-gate my $cfg = $class->SUPER::config(@_); 266*0Sstevel@tonic-gate 267*0Sstevel@tonic-gate # now we need only to override the ones that are different from our parent 268*0Sstevel@tonic-gate $cfg->{class} = $class; 269*0Sstevel@tonic-gate $cfg->{with} = $MBI; 270*0Sstevel@tonic-gate $cfg; 271*0Sstevel@tonic-gate } 272*0Sstevel@tonic-gate 273*0Sstevel@tonic-gate############################################################################## 274*0Sstevel@tonic-gate 275*0Sstevel@tonic-gatesub bstr 276*0Sstevel@tonic-gate { 277*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 278*0Sstevel@tonic-gate 279*0Sstevel@tonic-gate if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc 280*0Sstevel@tonic-gate { 281*0Sstevel@tonic-gate my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf 282*0Sstevel@tonic-gate return $s; 283*0Sstevel@tonic-gate } 284*0Sstevel@tonic-gate 285*0Sstevel@tonic-gate my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2' 286*0Sstevel@tonic-gate 287*0Sstevel@tonic-gate return $s . $x->{_n}->bstr() if $x->{_d}->is_one(); 288*0Sstevel@tonic-gate $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr(); 289*0Sstevel@tonic-gate } 290*0Sstevel@tonic-gate 291*0Sstevel@tonic-gatesub bsstr 292*0Sstevel@tonic-gate { 293*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 294*0Sstevel@tonic-gate 295*0Sstevel@tonic-gate if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc 296*0Sstevel@tonic-gate { 297*0Sstevel@tonic-gate my $s = $x->{sign}; $s =~ s/^\+//; # +inf => inf 298*0Sstevel@tonic-gate return $s; 299*0Sstevel@tonic-gate } 300*0Sstevel@tonic-gate 301*0Sstevel@tonic-gate my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3 302*0Sstevel@tonic-gate $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr(); 303*0Sstevel@tonic-gate } 304*0Sstevel@tonic-gate 305*0Sstevel@tonic-gatesub bnorm 306*0Sstevel@tonic-gate { 307*0Sstevel@tonic-gate # reduce the number to the shortest form and remember this (so that we 308*0Sstevel@tonic-gate # don't reduce again) 309*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 310*0Sstevel@tonic-gate 311*0Sstevel@tonic-gate # both parts must be BigInt's (or whatever we are using today) 312*0Sstevel@tonic-gate if (ref($x->{_n}) ne $MBI) 313*0Sstevel@tonic-gate { 314*0Sstevel@tonic-gate require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).')'); 315*0Sstevel@tonic-gate } 316*0Sstevel@tonic-gate if (ref($x->{_d}) ne $MBI) 317*0Sstevel@tonic-gate { 318*0Sstevel@tonic-gate require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).')'); 319*0Sstevel@tonic-gate } 320*0Sstevel@tonic-gate 321*0Sstevel@tonic-gate # this is to prevent automatically rounding when MBI's globals are set 322*0Sstevel@tonic-gate $x->{_d}->{_f} = MB_NEVER_ROUND; 323*0Sstevel@tonic-gate $x->{_n}->{_f} = MB_NEVER_ROUND; 324*0Sstevel@tonic-gate # 'forget' that parts were rounded via MBI::bround() in MBF's bfround() 325*0Sstevel@tonic-gate delete $x->{_d}->{_a}; delete $x->{_n}->{_a}; 326*0Sstevel@tonic-gate delete $x->{_d}->{_p}; delete $x->{_n}->{_p}; 327*0Sstevel@tonic-gate 328*0Sstevel@tonic-gate # no normalize for NaN, inf etc. 329*0Sstevel@tonic-gate return $x if $x->{sign} !~ /^[+-]$/; 330*0Sstevel@tonic-gate 331*0Sstevel@tonic-gate # normalize zeros to 0/1 332*0Sstevel@tonic-gate if (($x->{sign} =~ /^[+-]$/) && 333*0Sstevel@tonic-gate ($x->{_n}->is_zero())) 334*0Sstevel@tonic-gate { 335*0Sstevel@tonic-gate $x->{sign} = '+'; # never -0 336*0Sstevel@tonic-gate $x->{_d} = $MBI->bone() unless $x->{_d}->is_one(); 337*0Sstevel@tonic-gate return $x; 338*0Sstevel@tonic-gate } 339*0Sstevel@tonic-gate 340*0Sstevel@tonic-gate return $x if $x->{_d}->is_one(); # no need to reduce 341*0Sstevel@tonic-gate 342*0Sstevel@tonic-gate # reduce other numbers 343*0Sstevel@tonic-gate # disable upgrade in BigInt, otherwise deep recursion 344*0Sstevel@tonic-gate local $Math::BigInt::upgrade = undef; 345*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 346*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 347*0Sstevel@tonic-gate my $gcd = $x->{_n}->bgcd($x->{_d}); 348*0Sstevel@tonic-gate 349*0Sstevel@tonic-gate if (!$gcd->is_one()) 350*0Sstevel@tonic-gate { 351*0Sstevel@tonic-gate $x->{_n}->bdiv($gcd); 352*0Sstevel@tonic-gate $x->{_d}->bdiv($gcd); 353*0Sstevel@tonic-gate } 354*0Sstevel@tonic-gate $x; 355*0Sstevel@tonic-gate } 356*0Sstevel@tonic-gate 357*0Sstevel@tonic-gate############################################################################## 358*0Sstevel@tonic-gate# special values 359*0Sstevel@tonic-gate 360*0Sstevel@tonic-gatesub _bnan 361*0Sstevel@tonic-gate { 362*0Sstevel@tonic-gate # used by parent class bnan() to initialize number to NaN 363*0Sstevel@tonic-gate my $self = shift; 364*0Sstevel@tonic-gate 365*0Sstevel@tonic-gate if ($_trap_nan) 366*0Sstevel@tonic-gate { 367*0Sstevel@tonic-gate require Carp; 368*0Sstevel@tonic-gate my $class = ref($self); 369*0Sstevel@tonic-gate Carp::croak ("Tried to set $self to NaN in $class\::_bnan()"); 370*0Sstevel@tonic-gate } 371*0Sstevel@tonic-gate $self->{_n} = $MBI->bzero(); 372*0Sstevel@tonic-gate $self->{_d} = $MBI->bzero(); 373*0Sstevel@tonic-gate } 374*0Sstevel@tonic-gate 375*0Sstevel@tonic-gatesub _binf 376*0Sstevel@tonic-gate { 377*0Sstevel@tonic-gate # used by parent class bone() to initialize number to +inf/-inf 378*0Sstevel@tonic-gate my $self = shift; 379*0Sstevel@tonic-gate 380*0Sstevel@tonic-gate if ($_trap_inf) 381*0Sstevel@tonic-gate { 382*0Sstevel@tonic-gate require Carp; 383*0Sstevel@tonic-gate my $class = ref($self); 384*0Sstevel@tonic-gate Carp::croak ("Tried to set $self to inf in $class\::_binf()"); 385*0Sstevel@tonic-gate } 386*0Sstevel@tonic-gate $self->{_n} = $MBI->bzero(); 387*0Sstevel@tonic-gate $self->{_d} = $MBI->bzero(); 388*0Sstevel@tonic-gate } 389*0Sstevel@tonic-gate 390*0Sstevel@tonic-gatesub _bone 391*0Sstevel@tonic-gate { 392*0Sstevel@tonic-gate # used by parent class bone() to initialize number to +1/-1 393*0Sstevel@tonic-gate my $self = shift; 394*0Sstevel@tonic-gate $self->{_n} = $MBI->bone(); 395*0Sstevel@tonic-gate $self->{_d} = $MBI->bone(); 396*0Sstevel@tonic-gate } 397*0Sstevel@tonic-gate 398*0Sstevel@tonic-gatesub _bzero 399*0Sstevel@tonic-gate { 400*0Sstevel@tonic-gate # used by parent class bzero() to initialize number to 0 401*0Sstevel@tonic-gate my $self = shift; 402*0Sstevel@tonic-gate $self->{_n} = $MBI->bzero(); 403*0Sstevel@tonic-gate $self->{_d} = $MBI->bone(); 404*0Sstevel@tonic-gate } 405*0Sstevel@tonic-gate 406*0Sstevel@tonic-gate############################################################################## 407*0Sstevel@tonic-gate# mul/add/div etc 408*0Sstevel@tonic-gate 409*0Sstevel@tonic-gatesub badd 410*0Sstevel@tonic-gate { 411*0Sstevel@tonic-gate # add two rational numbers 412*0Sstevel@tonic-gate 413*0Sstevel@tonic-gate # set up parameters 414*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 415*0Sstevel@tonic-gate # objectify is costly, so avoid it 416*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 417*0Sstevel@tonic-gate { 418*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,@_); 419*0Sstevel@tonic-gate } 420*0Sstevel@tonic-gate 421*0Sstevel@tonic-gate $x = $self->new($x) unless $x->isa($self); 422*0Sstevel@tonic-gate $y = $self->new($y) unless $y->isa($self); 423*0Sstevel@tonic-gate 424*0Sstevel@tonic-gate return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); 425*0Sstevel@tonic-gate # TODO: inf handling 426*0Sstevel@tonic-gate 427*0Sstevel@tonic-gate # 1 1 gcd(3,4) = 1 1*3 + 1*4 7 428*0Sstevel@tonic-gate # - + - = --------- = -- 429*0Sstevel@tonic-gate # 4 3 4*3 12 430*0Sstevel@tonic-gate 431*0Sstevel@tonic-gate # we do not compute the gcd() here, but simple do: 432*0Sstevel@tonic-gate # 5 7 5*3 + 7*4 41 433*0Sstevel@tonic-gate # - + - = --------- = -- 434*0Sstevel@tonic-gate # 4 3 4*3 12 435*0Sstevel@tonic-gate 436*0Sstevel@tonic-gate # the gcd() calculation and reducing is then done in bnorm() 437*0Sstevel@tonic-gate 438*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 439*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 440*0Sstevel@tonic-gate 441*0Sstevel@tonic-gate $x->{_n}->bmul($y->{_d}); $x->{_n}->{sign} = $x->{sign}; 442*0Sstevel@tonic-gate my $m = $y->{_n}->copy()->bmul($x->{_d}); 443*0Sstevel@tonic-gate $m->{sign} = $y->{sign}; # 2/1 - 2/1 444*0Sstevel@tonic-gate $x->{_n}->badd($m); 445*0Sstevel@tonic-gate 446*0Sstevel@tonic-gate $x->{_d}->bmul($y->{_d}); 447*0Sstevel@tonic-gate 448*0Sstevel@tonic-gate # calculate sign of result and norm our _n part 449*0Sstevel@tonic-gate $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+'; 450*0Sstevel@tonic-gate 451*0Sstevel@tonic-gate $x->bnorm()->round(@r); 452*0Sstevel@tonic-gate } 453*0Sstevel@tonic-gate 454*0Sstevel@tonic-gatesub bsub 455*0Sstevel@tonic-gate { 456*0Sstevel@tonic-gate # subtract two rational numbers 457*0Sstevel@tonic-gate 458*0Sstevel@tonic-gate # set up parameters 459*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 460*0Sstevel@tonic-gate # objectify is costly, so avoid it 461*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 462*0Sstevel@tonic-gate { 463*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,@_); 464*0Sstevel@tonic-gate } 465*0Sstevel@tonic-gate 466*0Sstevel@tonic-gate # flip sign of $x, call badd(), then flip sign of result 467*0Sstevel@tonic-gate $x->{sign} =~ tr/+-/-+/ 468*0Sstevel@tonic-gate unless $x->{sign} eq '+' && $x->{_n}->is_zero(); # not -0 469*0Sstevel@tonic-gate $x->badd($y,@r); # does norm and round 470*0Sstevel@tonic-gate $x->{sign} =~ tr/+-/-+/ 471*0Sstevel@tonic-gate unless $x->{sign} eq '+' && $x->{_n}->is_zero(); # not -0 472*0Sstevel@tonic-gate $x; 473*0Sstevel@tonic-gate } 474*0Sstevel@tonic-gate 475*0Sstevel@tonic-gatesub bmul 476*0Sstevel@tonic-gate { 477*0Sstevel@tonic-gate # multiply two rational numbers 478*0Sstevel@tonic-gate 479*0Sstevel@tonic-gate # set up parameters 480*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 481*0Sstevel@tonic-gate # objectify is costly, so avoid it 482*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 483*0Sstevel@tonic-gate { 484*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,@_); 485*0Sstevel@tonic-gate } 486*0Sstevel@tonic-gate 487*0Sstevel@tonic-gate $x = $self->new($x) unless $x->isa($self); 488*0Sstevel@tonic-gate $y = $self->new($y) unless $y->isa($self); 489*0Sstevel@tonic-gate 490*0Sstevel@tonic-gate return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'); 491*0Sstevel@tonic-gate 492*0Sstevel@tonic-gate # inf handling 493*0Sstevel@tonic-gate if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) 494*0Sstevel@tonic-gate { 495*0Sstevel@tonic-gate return $x->bnan() if $x->is_zero() || $y->is_zero(); 496*0Sstevel@tonic-gate # result will always be +-inf: 497*0Sstevel@tonic-gate # +inf * +/+inf => +inf, -inf * -/-inf => +inf 498*0Sstevel@tonic-gate # +inf * -/-inf => -inf, -inf * +/+inf => -inf 499*0Sstevel@tonic-gate return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); 500*0Sstevel@tonic-gate return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); 501*0Sstevel@tonic-gate return $x->binf('-'); 502*0Sstevel@tonic-gate } 503*0Sstevel@tonic-gate 504*0Sstevel@tonic-gate # x== 0 # also: or y == 1 or y == -1 505*0Sstevel@tonic-gate return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); 506*0Sstevel@tonic-gate 507*0Sstevel@tonic-gate # According to Knuth, this can be optimized by doingtwice gcd (for d and n) 508*0Sstevel@tonic-gate # and reducing in one step) 509*0Sstevel@tonic-gate 510*0Sstevel@tonic-gate # 1 1 2 1 511*0Sstevel@tonic-gate # - * - = - = - 512*0Sstevel@tonic-gate # 4 3 12 6 513*0Sstevel@tonic-gate 514*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 515*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 516*0Sstevel@tonic-gate $x->{_n}->bmul($y->{_n}); 517*0Sstevel@tonic-gate $x->{_d}->bmul($y->{_d}); 518*0Sstevel@tonic-gate 519*0Sstevel@tonic-gate # compute new sign 520*0Sstevel@tonic-gate $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; 521*0Sstevel@tonic-gate 522*0Sstevel@tonic-gate $x->bnorm()->round(@r); 523*0Sstevel@tonic-gate } 524*0Sstevel@tonic-gate 525*0Sstevel@tonic-gatesub bdiv 526*0Sstevel@tonic-gate { 527*0Sstevel@tonic-gate # (dividend: BRAT or num_str, divisor: BRAT or num_str) return 528*0Sstevel@tonic-gate # (BRAT,BRAT) (quo,rem) or BRAT (only rem) 529*0Sstevel@tonic-gate 530*0Sstevel@tonic-gate # set up parameters 531*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 532*0Sstevel@tonic-gate # objectify is costly, so avoid it 533*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 534*0Sstevel@tonic-gate { 535*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,@_); 536*0Sstevel@tonic-gate } 537*0Sstevel@tonic-gate 538*0Sstevel@tonic-gate $x = $self->new($x) unless $x->isa($self); 539*0Sstevel@tonic-gate $y = $self->new($y) unless $y->isa($self); 540*0Sstevel@tonic-gate 541*0Sstevel@tonic-gate return $self->_div_inf($x,$y) 542*0Sstevel@tonic-gate if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); 543*0Sstevel@tonic-gate 544*0Sstevel@tonic-gate # x== 0 # also: or y == 1 or y == -1 545*0Sstevel@tonic-gate return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero(); 546*0Sstevel@tonic-gate 547*0Sstevel@tonic-gate # TODO: list context, upgrade 548*0Sstevel@tonic-gate 549*0Sstevel@tonic-gate # 1 1 1 3 550*0Sstevel@tonic-gate # - / - == - * - 551*0Sstevel@tonic-gate # 4 3 4 1 552*0Sstevel@tonic-gate 553*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 554*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 555*0Sstevel@tonic-gate $x->{_n}->bmul($y->{_d}); 556*0Sstevel@tonic-gate $x->{_d}->bmul($y->{_n}); 557*0Sstevel@tonic-gate 558*0Sstevel@tonic-gate # compute new sign 559*0Sstevel@tonic-gate $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; 560*0Sstevel@tonic-gate 561*0Sstevel@tonic-gate $x->bnorm()->round(@r); 562*0Sstevel@tonic-gate $x; 563*0Sstevel@tonic-gate } 564*0Sstevel@tonic-gate 565*0Sstevel@tonic-gatesub bmod 566*0Sstevel@tonic-gate { 567*0Sstevel@tonic-gate # compute "remainder" (in Perl way) of $x / $y 568*0Sstevel@tonic-gate 569*0Sstevel@tonic-gate # set up parameters 570*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 571*0Sstevel@tonic-gate # objectify is costly, so avoid it 572*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 573*0Sstevel@tonic-gate { 574*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,@_); 575*0Sstevel@tonic-gate } 576*0Sstevel@tonic-gate 577*0Sstevel@tonic-gate $x = $self->new($x) unless $x->isa($self); 578*0Sstevel@tonic-gate $y = $self->new($y) unless $y->isa($self); 579*0Sstevel@tonic-gate 580*0Sstevel@tonic-gate return $self->_div_inf($x,$y) 581*0Sstevel@tonic-gate if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); 582*0Sstevel@tonic-gate 583*0Sstevel@tonic-gate return $self->_div_inf($x,$y) 584*0Sstevel@tonic-gate if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); 585*0Sstevel@tonic-gate 586*0Sstevel@tonic-gate return $x if $x->is_zero(); # 0 / 7 = 0, mod 0 587*0Sstevel@tonic-gate 588*0Sstevel@tonic-gate # compute $x - $y * floor($x/$y), keeping the sign of $x 589*0Sstevel@tonic-gate 590*0Sstevel@tonic-gate # locally disable these, since they would interfere 591*0Sstevel@tonic-gate local $Math::BigInt::upgrade = undef; 592*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 593*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 594*0Sstevel@tonic-gate 595*0Sstevel@tonic-gate my $u = $x->copy()->babs(); 596*0Sstevel@tonic-gate # first, do a "normal" division ($x/$y) 597*0Sstevel@tonic-gate $u->{_d}->bmul($y->{_n}); 598*0Sstevel@tonic-gate $u->{_n}->bmul($y->{_d}); 599*0Sstevel@tonic-gate 600*0Sstevel@tonic-gate # compute floor 601*0Sstevel@tonic-gate if (!$u->{_d}->is_one()) 602*0Sstevel@tonic-gate { 603*0Sstevel@tonic-gate $u->{_n}->bdiv($u->{_d}); # 22/7 => 3/1 w/ truncate 604*0Sstevel@tonic-gate # no need to set $u->{_d} to 1, since later we set it to $y->{_d} 605*0Sstevel@tonic-gate #$x->{_n}->binc() if $x->{sign} eq '-'; # -22/7 => -4/1 606*0Sstevel@tonic-gate } 607*0Sstevel@tonic-gate 608*0Sstevel@tonic-gate # compute $y * $u 609*0Sstevel@tonic-gate $u->{_d} = $y->{_d}; # 1 * $y->{_d}, see floor above 610*0Sstevel@tonic-gate $u->{_n}->bmul($y->{_n}); 611*0Sstevel@tonic-gate 612*0Sstevel@tonic-gate my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make abs 613*0Sstevel@tonic-gate # compute $x - $u 614*0Sstevel@tonic-gate $x->bsub($u); 615*0Sstevel@tonic-gate $x->{sign} = $xsign; # put sign back 616*0Sstevel@tonic-gate 617*0Sstevel@tonic-gate $x->bnorm()->round(@r); 618*0Sstevel@tonic-gate } 619*0Sstevel@tonic-gate 620*0Sstevel@tonic-gate############################################################################## 621*0Sstevel@tonic-gate# bdec/binc 622*0Sstevel@tonic-gate 623*0Sstevel@tonic-gatesub bdec 624*0Sstevel@tonic-gate { 625*0Sstevel@tonic-gate # decrement value (subtract 1) 626*0Sstevel@tonic-gate my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); 627*0Sstevel@tonic-gate 628*0Sstevel@tonic-gate return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf 629*0Sstevel@tonic-gate 630*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 631*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 632*0Sstevel@tonic-gate if ($x->{sign} eq '-') 633*0Sstevel@tonic-gate { 634*0Sstevel@tonic-gate $x->{_n}->badd($x->{_d}); # -5/2 => -7/2 635*0Sstevel@tonic-gate } 636*0Sstevel@tonic-gate else 637*0Sstevel@tonic-gate { 638*0Sstevel@tonic-gate if ($x->{_n}->bacmp($x->{_d}) < 0) 639*0Sstevel@tonic-gate { 640*0Sstevel@tonic-gate # 1/3 -- => -2/3 641*0Sstevel@tonic-gate $x->{_n} = $x->{_d} - $x->{_n}; 642*0Sstevel@tonic-gate $x->{sign} = '-'; 643*0Sstevel@tonic-gate } 644*0Sstevel@tonic-gate else 645*0Sstevel@tonic-gate { 646*0Sstevel@tonic-gate $x->{_n}->bsub($x->{_d}); # 5/2 => 3/2 647*0Sstevel@tonic-gate } 648*0Sstevel@tonic-gate } 649*0Sstevel@tonic-gate $x->bnorm()->round(@r); 650*0Sstevel@tonic-gate } 651*0Sstevel@tonic-gate 652*0Sstevel@tonic-gatesub binc 653*0Sstevel@tonic-gate { 654*0Sstevel@tonic-gate # increment value (add 1) 655*0Sstevel@tonic-gate my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); 656*0Sstevel@tonic-gate 657*0Sstevel@tonic-gate return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf 658*0Sstevel@tonic-gate 659*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 660*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 661*0Sstevel@tonic-gate if ($x->{sign} eq '-') 662*0Sstevel@tonic-gate { 663*0Sstevel@tonic-gate if ($x->{_n}->bacmp($x->{_d}) < 0) 664*0Sstevel@tonic-gate { 665*0Sstevel@tonic-gate # -1/3 ++ => 2/3 (overflow at 0) 666*0Sstevel@tonic-gate $x->{_n} = $x->{_d} - $x->{_n}; 667*0Sstevel@tonic-gate $x->{sign} = '+'; 668*0Sstevel@tonic-gate } 669*0Sstevel@tonic-gate else 670*0Sstevel@tonic-gate { 671*0Sstevel@tonic-gate $x->{_n}->bsub($x->{_d}); # -5/2 => -3/2 672*0Sstevel@tonic-gate } 673*0Sstevel@tonic-gate } 674*0Sstevel@tonic-gate else 675*0Sstevel@tonic-gate { 676*0Sstevel@tonic-gate $x->{_n}->badd($x->{_d}); # 5/2 => 7/2 677*0Sstevel@tonic-gate } 678*0Sstevel@tonic-gate $x->bnorm()->round(@r); 679*0Sstevel@tonic-gate } 680*0Sstevel@tonic-gate 681*0Sstevel@tonic-gate############################################################################## 682*0Sstevel@tonic-gate# is_foo methods (the rest is inherited) 683*0Sstevel@tonic-gate 684*0Sstevel@tonic-gatesub is_int 685*0Sstevel@tonic-gate { 686*0Sstevel@tonic-gate # return true if arg (BRAT or num_str) is an integer 687*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 688*0Sstevel@tonic-gate 689*0Sstevel@tonic-gate return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't 690*0Sstevel@tonic-gate $x->{_d}->is_one(); # x/y && y != 1 => no integer 691*0Sstevel@tonic-gate 0; 692*0Sstevel@tonic-gate } 693*0Sstevel@tonic-gate 694*0Sstevel@tonic-gatesub is_zero 695*0Sstevel@tonic-gate { 696*0Sstevel@tonic-gate # return true if arg (BRAT or num_str) is zero 697*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 698*0Sstevel@tonic-gate 699*0Sstevel@tonic-gate return 1 if $x->{sign} eq '+' && $x->{_n}->is_zero(); 700*0Sstevel@tonic-gate 0; 701*0Sstevel@tonic-gate } 702*0Sstevel@tonic-gate 703*0Sstevel@tonic-gatesub is_one 704*0Sstevel@tonic-gate { 705*0Sstevel@tonic-gate # return true if arg (BRAT or num_str) is +1 or -1 if signis given 706*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 707*0Sstevel@tonic-gate 708*0Sstevel@tonic-gate my $sign = $_[2] || ''; $sign = '+' if $sign ne '-'; 709*0Sstevel@tonic-gate return 1 710*0Sstevel@tonic-gate if ($x->{sign} eq $sign && $x->{_n}->is_one() && $x->{_d}->is_one()); 711*0Sstevel@tonic-gate 0; 712*0Sstevel@tonic-gate } 713*0Sstevel@tonic-gate 714*0Sstevel@tonic-gatesub is_odd 715*0Sstevel@tonic-gate { 716*0Sstevel@tonic-gate # return true if arg (BFLOAT or num_str) is odd or false if even 717*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 718*0Sstevel@tonic-gate 719*0Sstevel@tonic-gate return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't 720*0Sstevel@tonic-gate ($x->{_d}->is_one() && $x->{_n}->is_odd()); # x/2 is not, but 3/1 721*0Sstevel@tonic-gate 0; 722*0Sstevel@tonic-gate } 723*0Sstevel@tonic-gate 724*0Sstevel@tonic-gatesub is_even 725*0Sstevel@tonic-gate { 726*0Sstevel@tonic-gate # return true if arg (BINT or num_str) is even or false if odd 727*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 728*0Sstevel@tonic-gate 729*0Sstevel@tonic-gate return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't 730*0Sstevel@tonic-gate return 1 if ($x->{_d}->is_one() # x/3 is never 731*0Sstevel@tonic-gate && $x->{_n}->is_even()); # but 4/1 is 732*0Sstevel@tonic-gate 0; 733*0Sstevel@tonic-gate } 734*0Sstevel@tonic-gate 735*0Sstevel@tonic-gate############################################################################## 736*0Sstevel@tonic-gate# parts() and friends 737*0Sstevel@tonic-gate 738*0Sstevel@tonic-gatesub numerator 739*0Sstevel@tonic-gate { 740*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 741*0Sstevel@tonic-gate 742*0Sstevel@tonic-gate return $MBI->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); 743*0Sstevel@tonic-gate 744*0Sstevel@tonic-gate my $n = $x->{_n}->copy(); $n->{sign} = $x->{sign}; 745*0Sstevel@tonic-gate $n; 746*0Sstevel@tonic-gate } 747*0Sstevel@tonic-gate 748*0Sstevel@tonic-gatesub denominator 749*0Sstevel@tonic-gate { 750*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 751*0Sstevel@tonic-gate 752*0Sstevel@tonic-gate return $MBI->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/); 753*0Sstevel@tonic-gate $x->{_d}->copy(); 754*0Sstevel@tonic-gate } 755*0Sstevel@tonic-gate 756*0Sstevel@tonic-gatesub parts 757*0Sstevel@tonic-gate { 758*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 759*0Sstevel@tonic-gate 760*0Sstevel@tonic-gate return ($self->bnan(),$self->bnan()) if $x->{sign} eq 'NaN'; 761*0Sstevel@tonic-gate return ($self->binf(),$self->binf()) if $x->{sign} eq '+inf'; 762*0Sstevel@tonic-gate return ($self->binf('-'),$self->binf()) if $x->{sign} eq '-inf'; 763*0Sstevel@tonic-gate 764*0Sstevel@tonic-gate my $n = $x->{_n}->copy(); 765*0Sstevel@tonic-gate $n->{sign} = $x->{sign}; 766*0Sstevel@tonic-gate return ($n,$x->{_d}->copy()); 767*0Sstevel@tonic-gate } 768*0Sstevel@tonic-gate 769*0Sstevel@tonic-gatesub length 770*0Sstevel@tonic-gate { 771*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 772*0Sstevel@tonic-gate 773*0Sstevel@tonic-gate return $nan unless $x->is_int(); 774*0Sstevel@tonic-gate $x->{_n}->length(); # length(-123/1) => length(123) 775*0Sstevel@tonic-gate } 776*0Sstevel@tonic-gate 777*0Sstevel@tonic-gatesub digit 778*0Sstevel@tonic-gate { 779*0Sstevel@tonic-gate my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 780*0Sstevel@tonic-gate 781*0Sstevel@tonic-gate return $nan unless $x->is_int(); 782*0Sstevel@tonic-gate $x->{_n}->digit($n); # digit(-123/1,2) => digit(123,2) 783*0Sstevel@tonic-gate } 784*0Sstevel@tonic-gate 785*0Sstevel@tonic-gate############################################################################## 786*0Sstevel@tonic-gate# special calc routines 787*0Sstevel@tonic-gate 788*0Sstevel@tonic-gatesub bceil 789*0Sstevel@tonic-gate { 790*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 791*0Sstevel@tonic-gate 792*0Sstevel@tonic-gate return $x unless $x->{sign} =~ /^[+-]$/; 793*0Sstevel@tonic-gate return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 794*0Sstevel@tonic-gate 795*0Sstevel@tonic-gate local $Math::BigInt::upgrade = undef; 796*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 797*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 798*0Sstevel@tonic-gate $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 w/ truncate 799*0Sstevel@tonic-gate $x->{_d}->bone(); 800*0Sstevel@tonic-gate $x->{_n}->binc() if $x->{sign} eq '+'; # +22/7 => 4/1 801*0Sstevel@tonic-gate $x->{sign} = '+' if $x->{_n}->is_zero(); # -0 => 0 802*0Sstevel@tonic-gate $x; 803*0Sstevel@tonic-gate } 804*0Sstevel@tonic-gate 805*0Sstevel@tonic-gatesub bfloor 806*0Sstevel@tonic-gate { 807*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 808*0Sstevel@tonic-gate 809*0Sstevel@tonic-gate return $x unless $x->{sign} =~ /^[+-]$/; 810*0Sstevel@tonic-gate return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0 811*0Sstevel@tonic-gate 812*0Sstevel@tonic-gate local $Math::BigInt::upgrade = undef; 813*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 814*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 815*0Sstevel@tonic-gate $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 w/ truncate 816*0Sstevel@tonic-gate $x->{_d}->bone(); 817*0Sstevel@tonic-gate $x->{_n}->binc() if $x->{sign} eq '-'; # -22/7 => -4/1 818*0Sstevel@tonic-gate $x; 819*0Sstevel@tonic-gate } 820*0Sstevel@tonic-gate 821*0Sstevel@tonic-gatesub bfac 822*0Sstevel@tonic-gate { 823*0Sstevel@tonic-gate my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); 824*0Sstevel@tonic-gate 825*0Sstevel@tonic-gate # if $x is an integer 826*0Sstevel@tonic-gate if (($x->{sign} eq '+') && ($x->{_d}->is_one())) 827*0Sstevel@tonic-gate { 828*0Sstevel@tonic-gate $x->{_n}->bfac(); 829*0Sstevel@tonic-gate return $x->round(@r); 830*0Sstevel@tonic-gate } 831*0Sstevel@tonic-gate $x->bnan(); 832*0Sstevel@tonic-gate } 833*0Sstevel@tonic-gate 834*0Sstevel@tonic-gatesub bpow 835*0Sstevel@tonic-gate { 836*0Sstevel@tonic-gate # power ($x ** $y) 837*0Sstevel@tonic-gate 838*0Sstevel@tonic-gate # set up parameters 839*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 840*0Sstevel@tonic-gate # objectify is costly, so avoid it 841*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 842*0Sstevel@tonic-gate { 843*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,@_); 844*0Sstevel@tonic-gate } 845*0Sstevel@tonic-gate 846*0Sstevel@tonic-gate return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x 847*0Sstevel@tonic-gate return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; 848*0Sstevel@tonic-gate return $x->bone(@r) if $y->is_zero(); 849*0Sstevel@tonic-gate return $x->round(@r) if $x->is_one() || $y->is_one(); 850*0Sstevel@tonic-gate if ($x->{sign} eq '-' && $x->{_n}->is_one() && $x->{_d}->is_one()) 851*0Sstevel@tonic-gate { 852*0Sstevel@tonic-gate # if $x == -1 and odd/even y => +1/-1 853*0Sstevel@tonic-gate return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r); 854*0Sstevel@tonic-gate # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1; 855*0Sstevel@tonic-gate } 856*0Sstevel@tonic-gate # 1 ** -y => 1 / (1 ** |y|) 857*0Sstevel@tonic-gate # so do test for negative $y after above's clause 858*0Sstevel@tonic-gate # return $x->bnan() if $y->{sign} eq '-'; 859*0Sstevel@tonic-gate return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) 860*0Sstevel@tonic-gate 861*0Sstevel@tonic-gate # shortcut y/1 (and/or x/1) 862*0Sstevel@tonic-gate if ($y->{_d}->is_one()) 863*0Sstevel@tonic-gate { 864*0Sstevel@tonic-gate # shortcut for x/1 and y/1 865*0Sstevel@tonic-gate if ($x->{_d}->is_one()) 866*0Sstevel@tonic-gate { 867*0Sstevel@tonic-gate $x->{_n}->bpow($y->{_n}); # x/1 ** y/1 => (x ** y)/1 868*0Sstevel@tonic-gate if ($y->{sign} eq '-') 869*0Sstevel@tonic-gate { 870*0Sstevel@tonic-gate # 0.2 ** -3 => 1/(0.2 ** 3) 871*0Sstevel@tonic-gate ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap 872*0Sstevel@tonic-gate } 873*0Sstevel@tonic-gate # correct sign; + ** + => + 874*0Sstevel@tonic-gate if ($x->{sign} eq '-') 875*0Sstevel@tonic-gate { 876*0Sstevel@tonic-gate # - * - => +, - * - * - => - 877*0Sstevel@tonic-gate $x->{sign} = '+' if $y->{_n}->is_even(); 878*0Sstevel@tonic-gate } 879*0Sstevel@tonic-gate return $x->round(@r); 880*0Sstevel@tonic-gate } 881*0Sstevel@tonic-gate # x/z ** y/1 882*0Sstevel@tonic-gate $x->{_n}->bpow($y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y 883*0Sstevel@tonic-gate $x->{_d}->bpow($y->{_n}); 884*0Sstevel@tonic-gate if ($y->{sign} eq '-') 885*0Sstevel@tonic-gate { 886*0Sstevel@tonic-gate # 0.2 ** -3 => 1/(0.2 ** 3) 887*0Sstevel@tonic-gate ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap 888*0Sstevel@tonic-gate } 889*0Sstevel@tonic-gate # correct sign; + ** + => + 890*0Sstevel@tonic-gate if ($x->{sign} eq '-') 891*0Sstevel@tonic-gate { 892*0Sstevel@tonic-gate # - * - => +, - * - * - => - 893*0Sstevel@tonic-gate $x->{sign} = '+' if $y->{_n}->is_even(); 894*0Sstevel@tonic-gate } 895*0Sstevel@tonic-gate return $x->round(@r); 896*0Sstevel@tonic-gate } 897*0Sstevel@tonic-gate 898*0Sstevel@tonic-gate # regular calculation (this is wrong for d/e ** f/g) 899*0Sstevel@tonic-gate my $pow2 = $self->__one(); 900*0Sstevel@tonic-gate my $y1 = $MBI->new($y->{_n}/$y->{_d})->babs(); 901*0Sstevel@tonic-gate my $two = $MBI->new(2); 902*0Sstevel@tonic-gate while (!$y1->is_one()) 903*0Sstevel@tonic-gate { 904*0Sstevel@tonic-gate $pow2->bmul($x) if $y1->is_odd(); 905*0Sstevel@tonic-gate $y1->bdiv($two); 906*0Sstevel@tonic-gate $x->bmul($x); 907*0Sstevel@tonic-gate } 908*0Sstevel@tonic-gate $x->bmul($pow2) unless $pow2->is_one(); 909*0Sstevel@tonic-gate # n ** -x => 1/n ** x 910*0Sstevel@tonic-gate ($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-'; 911*0Sstevel@tonic-gate $x->bnorm()->round(@r); 912*0Sstevel@tonic-gate } 913*0Sstevel@tonic-gate 914*0Sstevel@tonic-gatesub blog 915*0Sstevel@tonic-gate { 916*0Sstevel@tonic-gate # set up parameters 917*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 918*0Sstevel@tonic-gate 919*0Sstevel@tonic-gate # objectify is costly, so avoid it 920*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 921*0Sstevel@tonic-gate { 922*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,$class,@_); 923*0Sstevel@tonic-gate } 924*0Sstevel@tonic-gate 925*0Sstevel@tonic-gate # blog(1,Y) => 0 926*0Sstevel@tonic-gate return $x->bzero() if $x->is_one() && $y->{sign} eq '+'; 927*0Sstevel@tonic-gate 928*0Sstevel@tonic-gate # $x <= 0 => NaN 929*0Sstevel@tonic-gate return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+'; 930*0Sstevel@tonic-gate 931*0Sstevel@tonic-gate if ($x->is_int() && $y->is_int()) 932*0Sstevel@tonic-gate { 933*0Sstevel@tonic-gate return $self->new($x->as_number()->blog($y->as_number(),@r)); 934*0Sstevel@tonic-gate } 935*0Sstevel@tonic-gate 936*0Sstevel@tonic-gate # do it with floats 937*0Sstevel@tonic-gate $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) ); 938*0Sstevel@tonic-gate } 939*0Sstevel@tonic-gate 940*0Sstevel@tonic-gatesub _as_float 941*0Sstevel@tonic-gate { 942*0Sstevel@tonic-gate my $x = shift; 943*0Sstevel@tonic-gate 944*0Sstevel@tonic-gate local $Math::BigFloat::upgrade = undef; 945*0Sstevel@tonic-gate local $Math::BigFloat::accuracy = undef; 946*0Sstevel@tonic-gate local $Math::BigFloat::precision = undef; 947*0Sstevel@tonic-gate # 22/7 => 3.142857143.. 948*0Sstevel@tonic-gate Math::BigFloat->new($x->{_n})->bdiv($x->{_d}, $x->accuracy()); 949*0Sstevel@tonic-gate } 950*0Sstevel@tonic-gate 951*0Sstevel@tonic-gatesub broot 952*0Sstevel@tonic-gate { 953*0Sstevel@tonic-gate # set up parameters 954*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 955*0Sstevel@tonic-gate # objectify is costly, so avoid it 956*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 957*0Sstevel@tonic-gate { 958*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,@_); 959*0Sstevel@tonic-gate } 960*0Sstevel@tonic-gate 961*0Sstevel@tonic-gate if ($x->is_int() && $y->is_int()) 962*0Sstevel@tonic-gate { 963*0Sstevel@tonic-gate return $self->new($x->as_number()->broot($y->as_number(),@r)); 964*0Sstevel@tonic-gate } 965*0Sstevel@tonic-gate 966*0Sstevel@tonic-gate # do it with floats 967*0Sstevel@tonic-gate $x->_new_from_float( $x->_as_float()->broot($y,@r) ); 968*0Sstevel@tonic-gate } 969*0Sstevel@tonic-gate 970*0Sstevel@tonic-gatesub bmodpow 971*0Sstevel@tonic-gate { 972*0Sstevel@tonic-gate # set up parameters 973*0Sstevel@tonic-gate my ($self,$x,$y,$m,@r) = (ref($_[0]),@_); 974*0Sstevel@tonic-gate # objectify is costly, so avoid it 975*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 976*0Sstevel@tonic-gate { 977*0Sstevel@tonic-gate ($self,$x,$y,$m,@r) = objectify(3,@_); 978*0Sstevel@tonic-gate } 979*0Sstevel@tonic-gate 980*0Sstevel@tonic-gate # $x or $y or $m are NaN or +-inf => NaN 981*0Sstevel@tonic-gate return $x->bnan() 982*0Sstevel@tonic-gate if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || 983*0Sstevel@tonic-gate $m->{sign} !~ /^[+-]$/; 984*0Sstevel@tonic-gate 985*0Sstevel@tonic-gate if ($x->is_int() && $y->is_int() && $m->is_int()) 986*0Sstevel@tonic-gate { 987*0Sstevel@tonic-gate return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r)); 988*0Sstevel@tonic-gate } 989*0Sstevel@tonic-gate 990*0Sstevel@tonic-gate warn ("bmodpow() not fully implemented"); 991*0Sstevel@tonic-gate $x->bnan(); 992*0Sstevel@tonic-gate } 993*0Sstevel@tonic-gate 994*0Sstevel@tonic-gatesub bmodinv 995*0Sstevel@tonic-gate { 996*0Sstevel@tonic-gate # set up parameters 997*0Sstevel@tonic-gate my ($self,$x,$y,@r) = (ref($_[0]),@_); 998*0Sstevel@tonic-gate # objectify is costly, so avoid it 999*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 1000*0Sstevel@tonic-gate { 1001*0Sstevel@tonic-gate ($self,$x,$y,@r) = objectify(2,@_); 1002*0Sstevel@tonic-gate } 1003*0Sstevel@tonic-gate 1004*0Sstevel@tonic-gate # $x or $y are NaN or +-inf => NaN 1005*0Sstevel@tonic-gate return $x->bnan() 1006*0Sstevel@tonic-gate if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/; 1007*0Sstevel@tonic-gate 1008*0Sstevel@tonic-gate if ($x->is_int() && $y->is_int()) 1009*0Sstevel@tonic-gate { 1010*0Sstevel@tonic-gate return $self->new($x->as_number()->bmodinv($y->as_number(),@r)); 1011*0Sstevel@tonic-gate } 1012*0Sstevel@tonic-gate 1013*0Sstevel@tonic-gate warn ("bmodinv() not fully implemented"); 1014*0Sstevel@tonic-gate $x->bnan(); 1015*0Sstevel@tonic-gate } 1016*0Sstevel@tonic-gate 1017*0Sstevel@tonic-gatesub bsqrt 1018*0Sstevel@tonic-gate { 1019*0Sstevel@tonic-gate my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); 1020*0Sstevel@tonic-gate 1021*0Sstevel@tonic-gate return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 1022*0Sstevel@tonic-gate return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf 1023*0Sstevel@tonic-gate return $x->round(@r) if $x->is_zero() || $x->is_one(); 1024*0Sstevel@tonic-gate 1025*0Sstevel@tonic-gate local $Math::BigFloat::upgrade = undef; 1026*0Sstevel@tonic-gate local $Math::BigFloat::downgrade = undef; 1027*0Sstevel@tonic-gate local $Math::BigFloat::precision = undef; 1028*0Sstevel@tonic-gate local $Math::BigFloat::accuracy = undef; 1029*0Sstevel@tonic-gate local $Math::BigInt::upgrade = undef; 1030*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 1031*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 1032*0Sstevel@tonic-gate 1033*0Sstevel@tonic-gate $x->{_d} = Math::BigFloat->new($x->{_d})->bsqrt(); 1034*0Sstevel@tonic-gate $x->{_n} = Math::BigFloat->new($x->{_n})->bsqrt(); 1035*0Sstevel@tonic-gate 1036*0Sstevel@tonic-gate # if sqrt(D) was not integer 1037*0Sstevel@tonic-gate if ($x->{_d}->{_es} ne '+') 1038*0Sstevel@tonic-gate { 1039*0Sstevel@tonic-gate $x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1 1040*0Sstevel@tonic-gate $x->{_d} = $MBI->new($CALC->_str($x->{_d}->{_m})); # 7.1/45.1 => 71/45.1 1041*0Sstevel@tonic-gate } 1042*0Sstevel@tonic-gate # if sqrt(N) was not integer 1043*0Sstevel@tonic-gate if ($x->{_n}->{_es} ne '+') 1044*0Sstevel@tonic-gate { 1045*0Sstevel@tonic-gate $x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1 1046*0Sstevel@tonic-gate $x->{_n} = $MBI->new($CALC->_str($x->{_n}->{_m})); # 710/45.1 => 710/451 1047*0Sstevel@tonic-gate } 1048*0Sstevel@tonic-gate 1049*0Sstevel@tonic-gate # convert parts to $MBI again 1050*0Sstevel@tonic-gate $x->{_n} = $x->{_n}->as_number() unless $x->{_n}->isa($MBI); 1051*0Sstevel@tonic-gate $x->{_d} = $x->{_d}->as_number() unless $x->{_d}->isa($MBI); 1052*0Sstevel@tonic-gate $x->bnorm()->round(@r); 1053*0Sstevel@tonic-gate } 1054*0Sstevel@tonic-gate 1055*0Sstevel@tonic-gatesub blsft 1056*0Sstevel@tonic-gate { 1057*0Sstevel@tonic-gate my ($self,$x,$y,$b,@r) = objectify(3,@_); 1058*0Sstevel@tonic-gate 1059*0Sstevel@tonic-gate $b = 2 unless defined $b; 1060*0Sstevel@tonic-gate $b = $self->new($b) unless ref ($b); 1061*0Sstevel@tonic-gate $x->bmul( $b->copy()->bpow($y), @r); 1062*0Sstevel@tonic-gate $x; 1063*0Sstevel@tonic-gate } 1064*0Sstevel@tonic-gate 1065*0Sstevel@tonic-gatesub brsft 1066*0Sstevel@tonic-gate { 1067*0Sstevel@tonic-gate my ($self,$x,$y,$b,@r) = objectify(2,@_); 1068*0Sstevel@tonic-gate 1069*0Sstevel@tonic-gate $b = 2 unless defined $b; 1070*0Sstevel@tonic-gate $b = $self->new($b) unless ref ($b); 1071*0Sstevel@tonic-gate $x->bdiv( $b->copy()->bpow($y), @r); 1072*0Sstevel@tonic-gate $x; 1073*0Sstevel@tonic-gate } 1074*0Sstevel@tonic-gate 1075*0Sstevel@tonic-gate############################################################################## 1076*0Sstevel@tonic-gate# round 1077*0Sstevel@tonic-gate 1078*0Sstevel@tonic-gatesub round 1079*0Sstevel@tonic-gate { 1080*0Sstevel@tonic-gate $_[0]; 1081*0Sstevel@tonic-gate } 1082*0Sstevel@tonic-gate 1083*0Sstevel@tonic-gatesub bround 1084*0Sstevel@tonic-gate { 1085*0Sstevel@tonic-gate $_[0]; 1086*0Sstevel@tonic-gate } 1087*0Sstevel@tonic-gate 1088*0Sstevel@tonic-gatesub bfround 1089*0Sstevel@tonic-gate { 1090*0Sstevel@tonic-gate $_[0]; 1091*0Sstevel@tonic-gate } 1092*0Sstevel@tonic-gate 1093*0Sstevel@tonic-gate############################################################################## 1094*0Sstevel@tonic-gate# comparing 1095*0Sstevel@tonic-gate 1096*0Sstevel@tonic-gatesub bcmp 1097*0Sstevel@tonic-gate { 1098*0Sstevel@tonic-gate # compare two signed numbers 1099*0Sstevel@tonic-gate 1100*0Sstevel@tonic-gate # set up parameters 1101*0Sstevel@tonic-gate my ($self,$x,$y) = (ref($_[0]),@_); 1102*0Sstevel@tonic-gate # objectify is costly, so avoid it 1103*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 1104*0Sstevel@tonic-gate { 1105*0Sstevel@tonic-gate ($self,$x,$y) = objectify(2,@_); 1106*0Sstevel@tonic-gate } 1107*0Sstevel@tonic-gate 1108*0Sstevel@tonic-gate if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) 1109*0Sstevel@tonic-gate { 1110*0Sstevel@tonic-gate # handle +-inf and NaN 1111*0Sstevel@tonic-gate return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); 1112*0Sstevel@tonic-gate return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; 1113*0Sstevel@tonic-gate return +1 if $x->{sign} eq '+inf'; 1114*0Sstevel@tonic-gate return -1 if $x->{sign} eq '-inf'; 1115*0Sstevel@tonic-gate return -1 if $y->{sign} eq '+inf'; 1116*0Sstevel@tonic-gate return +1; 1117*0Sstevel@tonic-gate } 1118*0Sstevel@tonic-gate # check sign for speed first 1119*0Sstevel@tonic-gate return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y 1120*0Sstevel@tonic-gate return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 1121*0Sstevel@tonic-gate 1122*0Sstevel@tonic-gate # shortcut 1123*0Sstevel@tonic-gate my $xz = $x->{_n}->is_zero(); 1124*0Sstevel@tonic-gate my $yz = $y->{_n}->is_zero(); 1125*0Sstevel@tonic-gate return 0 if $xz && $yz; # 0 <=> 0 1126*0Sstevel@tonic-gate return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y 1127*0Sstevel@tonic-gate return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0 1128*0Sstevel@tonic-gate 1129*0Sstevel@tonic-gate my $t = $x->{_n} * $y->{_d}; $t->{sign} = $x->{sign}; 1130*0Sstevel@tonic-gate my $u = $y->{_n} * $x->{_d}; $u->{sign} = $y->{sign}; 1131*0Sstevel@tonic-gate $t->bcmp($u); 1132*0Sstevel@tonic-gate } 1133*0Sstevel@tonic-gate 1134*0Sstevel@tonic-gatesub bacmp 1135*0Sstevel@tonic-gate { 1136*0Sstevel@tonic-gate # compare two numbers (as unsigned) 1137*0Sstevel@tonic-gate 1138*0Sstevel@tonic-gate # set up parameters 1139*0Sstevel@tonic-gate my ($self,$x,$y) = (ref($_[0]),@_); 1140*0Sstevel@tonic-gate # objectify is costly, so avoid it 1141*0Sstevel@tonic-gate if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) 1142*0Sstevel@tonic-gate { 1143*0Sstevel@tonic-gate ($self,$x,$y) = objectify(2,$class,@_); 1144*0Sstevel@tonic-gate } 1145*0Sstevel@tonic-gate 1146*0Sstevel@tonic-gate if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) 1147*0Sstevel@tonic-gate { 1148*0Sstevel@tonic-gate # handle +-inf and NaN 1149*0Sstevel@tonic-gate return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); 1150*0Sstevel@tonic-gate return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; 1151*0Sstevel@tonic-gate return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; 1152*0Sstevel@tonic-gate return -1; 1153*0Sstevel@tonic-gate } 1154*0Sstevel@tonic-gate 1155*0Sstevel@tonic-gate my $t = $x->{_n} * $y->{_d}; 1156*0Sstevel@tonic-gate my $u = $y->{_n} * $x->{_d}; 1157*0Sstevel@tonic-gate $t->bacmp($u); 1158*0Sstevel@tonic-gate } 1159*0Sstevel@tonic-gate 1160*0Sstevel@tonic-gate############################################################################## 1161*0Sstevel@tonic-gate# output conversation 1162*0Sstevel@tonic-gate 1163*0Sstevel@tonic-gatesub numify 1164*0Sstevel@tonic-gate { 1165*0Sstevel@tonic-gate # convert 17/8 => float (aka 2.125) 1166*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 1167*0Sstevel@tonic-gate 1168*0Sstevel@tonic-gate return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc 1169*0Sstevel@tonic-gate 1170*0Sstevel@tonic-gate # N/1 => N 1171*0Sstevel@tonic-gate return $x->{_n}->numify() if $x->{_d}->is_one(); 1172*0Sstevel@tonic-gate 1173*0Sstevel@tonic-gate # N/D 1174*0Sstevel@tonic-gate my $neg = 1; $neg = -1 if $x->{sign} ne '+'; 1175*0Sstevel@tonic-gate $neg * $x->{_n}->numify() / $x->{_d}->numify(); # return sign * N/D 1176*0Sstevel@tonic-gate } 1177*0Sstevel@tonic-gate 1178*0Sstevel@tonic-gatesub as_number 1179*0Sstevel@tonic-gate { 1180*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 1181*0Sstevel@tonic-gate 1182*0Sstevel@tonic-gate return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf etc 1183*0Sstevel@tonic-gate 1184*0Sstevel@tonic-gate # need to disable these, otherwise bdiv() gives BigRat again 1185*0Sstevel@tonic-gate local $Math::BigInt::upgrade = undef; 1186*0Sstevel@tonic-gate local $Math::BigInt::accuracy = undef; 1187*0Sstevel@tonic-gate local $Math::BigInt::precision = undef; 1188*0Sstevel@tonic-gate my $t = $x->{_n}->copy()->bdiv($x->{_d}); # 22/7 => 3 1189*0Sstevel@tonic-gate $t->{sign} = $x->{sign}; 1190*0Sstevel@tonic-gate $t; 1191*0Sstevel@tonic-gate } 1192*0Sstevel@tonic-gate 1193*0Sstevel@tonic-gatesub as_bin 1194*0Sstevel@tonic-gate { 1195*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 1196*0Sstevel@tonic-gate 1197*0Sstevel@tonic-gate return $x unless $x->is_int(); 1198*0Sstevel@tonic-gate 1199*0Sstevel@tonic-gate my $s = $x->{sign}; $s = '' if $s eq '+'; 1200*0Sstevel@tonic-gate $s . $x->{_n}->as_bin(); 1201*0Sstevel@tonic-gate } 1202*0Sstevel@tonic-gate 1203*0Sstevel@tonic-gatesub as_hex 1204*0Sstevel@tonic-gate { 1205*0Sstevel@tonic-gate my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 1206*0Sstevel@tonic-gate 1207*0Sstevel@tonic-gate return $x unless $x->is_int(); 1208*0Sstevel@tonic-gate 1209*0Sstevel@tonic-gate my $s = $x->{sign}; $s = '' if $s eq '+'; 1210*0Sstevel@tonic-gate $s . $x->{_n}->as_hex(); 1211*0Sstevel@tonic-gate } 1212*0Sstevel@tonic-gate 1213*0Sstevel@tonic-gatesub import 1214*0Sstevel@tonic-gate { 1215*0Sstevel@tonic-gate my $self = shift; 1216*0Sstevel@tonic-gate my $l = scalar @_; 1217*0Sstevel@tonic-gate my $lib = ''; my @a; 1218*0Sstevel@tonic-gate $IMPORT++; 1219*0Sstevel@tonic-gate 1220*0Sstevel@tonic-gate for ( my $i = 0; $i < $l ; $i++) 1221*0Sstevel@tonic-gate { 1222*0Sstevel@tonic-gate# print "at $_[$i] (",$_[$i+1]||'undef',")\n"; 1223*0Sstevel@tonic-gate if ( $_[$i] eq ':constant' ) 1224*0Sstevel@tonic-gate { 1225*0Sstevel@tonic-gate # this rest causes overlord er load to step in 1226*0Sstevel@tonic-gate # print "overload @_\n"; 1227*0Sstevel@tonic-gate overload::constant float => sub { $self->new(shift); }; 1228*0Sstevel@tonic-gate } 1229*0Sstevel@tonic-gate# elsif ($_[$i] eq 'upgrade') 1230*0Sstevel@tonic-gate# { 1231*0Sstevel@tonic-gate# # this causes upgrading 1232*0Sstevel@tonic-gate# $upgrade = $_[$i+1]; # or undef to disable 1233*0Sstevel@tonic-gate# $i++; 1234*0Sstevel@tonic-gate# } 1235*0Sstevel@tonic-gate elsif ($_[$i] eq 'downgrade') 1236*0Sstevel@tonic-gate { 1237*0Sstevel@tonic-gate # this causes downgrading 1238*0Sstevel@tonic-gate $downgrade = $_[$i+1]; # or undef to disable 1239*0Sstevel@tonic-gate $i++; 1240*0Sstevel@tonic-gate } 1241*0Sstevel@tonic-gate elsif ($_[$i] eq 'lib') 1242*0Sstevel@tonic-gate { 1243*0Sstevel@tonic-gate $lib = $_[$i+1] || ''; # default Calc 1244*0Sstevel@tonic-gate $i++; 1245*0Sstevel@tonic-gate } 1246*0Sstevel@tonic-gate elsif ($_[$i] eq 'with') 1247*0Sstevel@tonic-gate { 1248*0Sstevel@tonic-gate $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt 1249*0Sstevel@tonic-gate $i++; 1250*0Sstevel@tonic-gate } 1251*0Sstevel@tonic-gate else 1252*0Sstevel@tonic-gate { 1253*0Sstevel@tonic-gate push @a, $_[$i]; 1254*0Sstevel@tonic-gate } 1255*0Sstevel@tonic-gate } 1256*0Sstevel@tonic-gate # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still work 1257*0Sstevel@tonic-gate my $mbilib = eval { Math::BigInt->config()->{lib} }; 1258*0Sstevel@tonic-gate if ((defined $mbilib) && ($MBI eq 'Math::BigInt')) 1259*0Sstevel@tonic-gate { 1260*0Sstevel@tonic-gate # MBI already loaded 1261*0Sstevel@tonic-gate $MBI->import('lib',"$lib,$mbilib", 'objectify'); 1262*0Sstevel@tonic-gate } 1263*0Sstevel@tonic-gate else 1264*0Sstevel@tonic-gate { 1265*0Sstevel@tonic-gate # MBI not loaded, or not with "Math::BigInt" 1266*0Sstevel@tonic-gate $lib .= ",$mbilib" if defined $mbilib; 1267*0Sstevel@tonic-gate 1268*0Sstevel@tonic-gate if ($] < 5.006) 1269*0Sstevel@tonic-gate { 1270*0Sstevel@tonic-gate # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is 1271*0Sstevel@tonic-gate # used in the same script, or eval inside import(). 1272*0Sstevel@tonic-gate my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt 1273*0Sstevel@tonic-gate my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm 1274*0Sstevel@tonic-gate $file = File::Spec->catfile (@parts, $file); 1275*0Sstevel@tonic-gate eval { require $file; $MBI->import( lib => '$lib', 'objectify' ); } 1276*0Sstevel@tonic-gate } 1277*0Sstevel@tonic-gate else 1278*0Sstevel@tonic-gate { 1279*0Sstevel@tonic-gate my $rc = "use $MBI lib => '$lib', 'objectify';"; 1280*0Sstevel@tonic-gate eval $rc; 1281*0Sstevel@tonic-gate } 1282*0Sstevel@tonic-gate } 1283*0Sstevel@tonic-gate if ($@) 1284*0Sstevel@tonic-gate { 1285*0Sstevel@tonic-gate require Carp; Carp::croak ("Couldn't load $MBI: $! $@"); 1286*0Sstevel@tonic-gate } 1287*0Sstevel@tonic-gate 1288*0Sstevel@tonic-gate $CALC = Math::BigFloat->config()->{lib}; 1289*0Sstevel@tonic-gate 1290*0Sstevel@tonic-gate # any non :constant stuff is handled by our parent, Exporter 1291*0Sstevel@tonic-gate # even if @_ is empty, to give it a chance 1292*0Sstevel@tonic-gate $self->SUPER::import(@a); # for subclasses 1293*0Sstevel@tonic-gate $self->export_to_level(1,$self,@a); # need this, too 1294*0Sstevel@tonic-gate } 1295*0Sstevel@tonic-gate 1296*0Sstevel@tonic-gate1; 1297*0Sstevel@tonic-gate 1298*0Sstevel@tonic-gate__END__ 1299*0Sstevel@tonic-gate 1300*0Sstevel@tonic-gate=head1 NAME 1301*0Sstevel@tonic-gate 1302*0Sstevel@tonic-gateMath::BigRat - arbitrarily big rational numbers 1303*0Sstevel@tonic-gate 1304*0Sstevel@tonic-gate=head1 SYNOPSIS 1305*0Sstevel@tonic-gate 1306*0Sstevel@tonic-gate use Math::BigRat; 1307*0Sstevel@tonic-gate 1308*0Sstevel@tonic-gate my $x = Math::BigRat->new('3/7'); $x += '5/9'; 1309*0Sstevel@tonic-gate 1310*0Sstevel@tonic-gate print $x->bstr(),"\n"; 1311*0Sstevel@tonic-gate print $x ** 2,"\n"; 1312*0Sstevel@tonic-gate 1313*0Sstevel@tonic-gate my $y = Math::BigRat->new('inf'); 1314*0Sstevel@tonic-gate print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n"; 1315*0Sstevel@tonic-gate 1316*0Sstevel@tonic-gate my $z = Math::BigRat->new(144); $z->bsqrt(); 1317*0Sstevel@tonic-gate 1318*0Sstevel@tonic-gate=head1 DESCRIPTION 1319*0Sstevel@tonic-gate 1320*0Sstevel@tonic-gateMath::BigRat complements Math::BigInt and Math::BigFloat by providing support 1321*0Sstevel@tonic-gatefor arbitrarily big rational numbers. 1322*0Sstevel@tonic-gate 1323*0Sstevel@tonic-gate=head2 MATH LIBRARY 1324*0Sstevel@tonic-gate 1325*0Sstevel@tonic-gateMath with the numbers is done (by default) by a module called 1326*0Sstevel@tonic-gateMath::BigInt::Calc. This is equivalent to saying: 1327*0Sstevel@tonic-gate 1328*0Sstevel@tonic-gate use Math::BigRat lib => 'Calc'; 1329*0Sstevel@tonic-gate 1330*0Sstevel@tonic-gateYou can change this by using: 1331*0Sstevel@tonic-gate 1332*0Sstevel@tonic-gate use Math::BigRat lib => 'BitVect'; 1333*0Sstevel@tonic-gate 1334*0Sstevel@tonic-gateThe following would first try to find Math::BigInt::Foo, then 1335*0Sstevel@tonic-gateMath::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: 1336*0Sstevel@tonic-gate 1337*0Sstevel@tonic-gate use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; 1338*0Sstevel@tonic-gate 1339*0Sstevel@tonic-gateCalc.pm uses as internal format an array of elements of some decimal base 1340*0Sstevel@tonic-gate(usually 1e7, but this might be different for some systems) with the least 1341*0Sstevel@tonic-gatesignificant digit first, while BitVect.pm uses a bit vector of base 2, most 1342*0Sstevel@tonic-gatesignificant bit first. Other modules might use even different means of 1343*0Sstevel@tonic-gaterepresenting the numbers. See the respective module documentation for further 1344*0Sstevel@tonic-gatedetails. 1345*0Sstevel@tonic-gate 1346*0Sstevel@tonic-gateCurrently the following replacement libraries exist, search for them at CPAN: 1347*0Sstevel@tonic-gate 1348*0Sstevel@tonic-gate Math::BigInt::BitVect 1349*0Sstevel@tonic-gate Math::BigInt::GMP 1350*0Sstevel@tonic-gate Math::BigInt::Pari 1351*0Sstevel@tonic-gate Math::BigInt::FastCalc 1352*0Sstevel@tonic-gate 1353*0Sstevel@tonic-gate=head1 METHODS 1354*0Sstevel@tonic-gate 1355*0Sstevel@tonic-gateAny methods not listed here are dervied from Math::BigFloat (or 1356*0Sstevel@tonic-gateMath::BigInt), so make sure you check these two modules for further 1357*0Sstevel@tonic-gateinformation. 1358*0Sstevel@tonic-gate 1359*0Sstevel@tonic-gate=head2 new() 1360*0Sstevel@tonic-gate 1361*0Sstevel@tonic-gate $x = Math::BigRat->new('1/3'); 1362*0Sstevel@tonic-gate 1363*0Sstevel@tonic-gateCreate a new Math::BigRat object. Input can come in various forms: 1364*0Sstevel@tonic-gate 1365*0Sstevel@tonic-gate $x = Math::BigRat->new(123); # scalars 1366*0Sstevel@tonic-gate $x = Math::BigRat->new('inf'); # infinity 1367*0Sstevel@tonic-gate $x = Math::BigRat->new('123.3'); # float 1368*0Sstevel@tonic-gate $x = Math::BigRat->new('1/3'); # simple string 1369*0Sstevel@tonic-gate $x = Math::BigRat->new('1 / 3'); # spaced 1370*0Sstevel@tonic-gate $x = Math::BigRat->new('1 / 0.1'); # w/ floats 1371*0Sstevel@tonic-gate $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt 1372*0Sstevel@tonic-gate $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat 1373*0Sstevel@tonic-gate $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite 1374*0Sstevel@tonic-gate 1375*0Sstevel@tonic-gate=head2 numerator() 1376*0Sstevel@tonic-gate 1377*0Sstevel@tonic-gate $n = $x->numerator(); 1378*0Sstevel@tonic-gate 1379*0Sstevel@tonic-gateReturns a copy of the numerator (the part above the line) as signed BigInt. 1380*0Sstevel@tonic-gate 1381*0Sstevel@tonic-gate=head2 denominator() 1382*0Sstevel@tonic-gate 1383*0Sstevel@tonic-gate $d = $x->denominator(); 1384*0Sstevel@tonic-gate 1385*0Sstevel@tonic-gateReturns a copy of the denominator (the part under the line) as positive BigInt. 1386*0Sstevel@tonic-gate 1387*0Sstevel@tonic-gate=head2 parts() 1388*0Sstevel@tonic-gate 1389*0Sstevel@tonic-gate ($n,$d) = $x->parts(); 1390*0Sstevel@tonic-gate 1391*0Sstevel@tonic-gateReturn a list consisting of (signed) numerator and (unsigned) denominator as 1392*0Sstevel@tonic-gateBigInts. 1393*0Sstevel@tonic-gate 1394*0Sstevel@tonic-gate=head2 as_number() 1395*0Sstevel@tonic-gate 1396*0Sstevel@tonic-gate $x = Math::BigRat->new('13/7'); 1397*0Sstevel@tonic-gate print $x->as_number(),"\n"; # '1' 1398*0Sstevel@tonic-gate 1399*0Sstevel@tonic-gateReturns a copy of the object as BigInt trunced it to integer. 1400*0Sstevel@tonic-gate 1401*0Sstevel@tonic-gate=head2 bfac() 1402*0Sstevel@tonic-gate 1403*0Sstevel@tonic-gate $x->bfac(); 1404*0Sstevel@tonic-gate 1405*0Sstevel@tonic-gateCalculates the factorial of $x. For instance: 1406*0Sstevel@tonic-gate 1407*0Sstevel@tonic-gate print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3 1408*0Sstevel@tonic-gate print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5 1409*0Sstevel@tonic-gate 1410*0Sstevel@tonic-gateWorks currently only for integers. 1411*0Sstevel@tonic-gate 1412*0Sstevel@tonic-gate=head2 blog() 1413*0Sstevel@tonic-gate 1414*0Sstevel@tonic-gateIs not yet implemented. 1415*0Sstevel@tonic-gate 1416*0Sstevel@tonic-gate=head2 bround()/round()/bfround() 1417*0Sstevel@tonic-gate 1418*0Sstevel@tonic-gateAre not yet implemented. 1419*0Sstevel@tonic-gate 1420*0Sstevel@tonic-gate=head2 bmod() 1421*0Sstevel@tonic-gate 1422*0Sstevel@tonic-gate use Math::BigRat; 1423*0Sstevel@tonic-gate my $x = Math::BigRat->new('7/4'); 1424*0Sstevel@tonic-gate my $y = Math::BigRat->new('4/3'); 1425*0Sstevel@tonic-gate print $x->bmod($y); 1426*0Sstevel@tonic-gate 1427*0Sstevel@tonic-gateSet $x to the remainder of the division of $x by $y. 1428*0Sstevel@tonic-gate 1429*0Sstevel@tonic-gate=head2 is_one() 1430*0Sstevel@tonic-gate 1431*0Sstevel@tonic-gate print "$x is 1\n" if $x->is_one(); 1432*0Sstevel@tonic-gate 1433*0Sstevel@tonic-gateReturn true if $x is exactly one, otherwise false. 1434*0Sstevel@tonic-gate 1435*0Sstevel@tonic-gate=head2 is_zero() 1436*0Sstevel@tonic-gate 1437*0Sstevel@tonic-gate print "$x is 0\n" if $x->is_zero(); 1438*0Sstevel@tonic-gate 1439*0Sstevel@tonic-gateReturn true if $x is exactly zero, otherwise false. 1440*0Sstevel@tonic-gate 1441*0Sstevel@tonic-gate=head2 is_positive() 1442*0Sstevel@tonic-gate 1443*0Sstevel@tonic-gate print "$x is >= 0\n" if $x->is_positive(); 1444*0Sstevel@tonic-gate 1445*0Sstevel@tonic-gateReturn true if $x is positive (greater than or equal to zero), otherwise 1446*0Sstevel@tonic-gatefalse. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. 1447*0Sstevel@tonic-gate 1448*0Sstevel@tonic-gate=head2 is_negative() 1449*0Sstevel@tonic-gate 1450*0Sstevel@tonic-gate print "$x is < 0\n" if $x->is_negative(); 1451*0Sstevel@tonic-gate 1452*0Sstevel@tonic-gateReturn true if $x is negative (smaller than zero), otherwise false. Please 1453*0Sstevel@tonic-gatenote that '-inf' is also negative, while 'NaN' and '+inf' aren't. 1454*0Sstevel@tonic-gate 1455*0Sstevel@tonic-gate=head2 is_int() 1456*0Sstevel@tonic-gate 1457*0Sstevel@tonic-gate print "$x is an integer\n" if $x->is_int(); 1458*0Sstevel@tonic-gate 1459*0Sstevel@tonic-gateReturn true if $x has a denominator of 1 (e.g. no fraction parts), otherwise 1460*0Sstevel@tonic-gatefalse. Please note that '-inf', 'inf' and 'NaN' aren't integer. 1461*0Sstevel@tonic-gate 1462*0Sstevel@tonic-gate=head2 is_odd() 1463*0Sstevel@tonic-gate 1464*0Sstevel@tonic-gate print "$x is odd\n" if $x->is_odd(); 1465*0Sstevel@tonic-gate 1466*0Sstevel@tonic-gateReturn true if $x is odd, otherwise false. 1467*0Sstevel@tonic-gate 1468*0Sstevel@tonic-gate=head2 is_even() 1469*0Sstevel@tonic-gate 1470*0Sstevel@tonic-gate print "$x is even\n" if $x->is_even(); 1471*0Sstevel@tonic-gate 1472*0Sstevel@tonic-gateReturn true if $x is even, otherwise false. 1473*0Sstevel@tonic-gate 1474*0Sstevel@tonic-gate=head2 bceil() 1475*0Sstevel@tonic-gate 1476*0Sstevel@tonic-gate $x->bceil(); 1477*0Sstevel@tonic-gate 1478*0Sstevel@tonic-gateSet $x to the next bigger integer value (e.g. truncate the number to integer 1479*0Sstevel@tonic-gateand then increment it by one). 1480*0Sstevel@tonic-gate 1481*0Sstevel@tonic-gate=head2 bfloor() 1482*0Sstevel@tonic-gate 1483*0Sstevel@tonic-gate $x->bfloor(); 1484*0Sstevel@tonic-gate 1485*0Sstevel@tonic-gateTruncate $x to an integer value. 1486*0Sstevel@tonic-gate 1487*0Sstevel@tonic-gate=head2 bsqrt() 1488*0Sstevel@tonic-gate 1489*0Sstevel@tonic-gate $x->bsqrt(); 1490*0Sstevel@tonic-gate 1491*0Sstevel@tonic-gateCalculate the square root of $x. 1492*0Sstevel@tonic-gate 1493*0Sstevel@tonic-gate=head2 config 1494*0Sstevel@tonic-gate 1495*0Sstevel@tonic-gate use Data::Dumper; 1496*0Sstevel@tonic-gate 1497*0Sstevel@tonic-gate print Dumper ( Math::BigRat->config() ); 1498*0Sstevel@tonic-gate print Math::BigRat->config()->{lib},"\n"; 1499*0Sstevel@tonic-gate 1500*0Sstevel@tonic-gateReturns a hash containing the configuration, e.g. the version number, lib 1501*0Sstevel@tonic-gateloaded etc. The following hash keys are currently filled in with the 1502*0Sstevel@tonic-gateappropriate information. 1503*0Sstevel@tonic-gate 1504*0Sstevel@tonic-gate key RO/RW Description 1505*0Sstevel@tonic-gate Example 1506*0Sstevel@tonic-gate ============================================================ 1507*0Sstevel@tonic-gate lib RO Name of the Math library 1508*0Sstevel@tonic-gate Math::BigInt::Calc 1509*0Sstevel@tonic-gate lib_version RO Version of 'lib' 1510*0Sstevel@tonic-gate 0.30 1511*0Sstevel@tonic-gate class RO The class of config you just called 1512*0Sstevel@tonic-gate Math::BigRat 1513*0Sstevel@tonic-gate version RO version number of the class you used 1514*0Sstevel@tonic-gate 0.10 1515*0Sstevel@tonic-gate upgrade RW To which class numbers are upgraded 1516*0Sstevel@tonic-gate undef 1517*0Sstevel@tonic-gate downgrade RW To which class numbers are downgraded 1518*0Sstevel@tonic-gate undef 1519*0Sstevel@tonic-gate precision RW Global precision 1520*0Sstevel@tonic-gate undef 1521*0Sstevel@tonic-gate accuracy RW Global accuracy 1522*0Sstevel@tonic-gate undef 1523*0Sstevel@tonic-gate round_mode RW Global round mode 1524*0Sstevel@tonic-gate even 1525*0Sstevel@tonic-gate div_scale RW Fallback acccuracy for div 1526*0Sstevel@tonic-gate 40 1527*0Sstevel@tonic-gate trap_nan RW Trap creation of NaN (undef = no) 1528*0Sstevel@tonic-gate undef 1529*0Sstevel@tonic-gate trap_inf RW Trap creation of +inf/-inf (undef = no) 1530*0Sstevel@tonic-gate undef 1531*0Sstevel@tonic-gate 1532*0Sstevel@tonic-gateBy passing a reference to a hash you may set the configuration values. This 1533*0Sstevel@tonic-gateworks only for values that a marked with a C<RW> above, anything else is 1534*0Sstevel@tonic-gateread-only. 1535*0Sstevel@tonic-gate 1536*0Sstevel@tonic-gate=head1 BUGS 1537*0Sstevel@tonic-gate 1538*0Sstevel@tonic-gateSome things are not yet implemented, or only implemented half-way: 1539*0Sstevel@tonic-gate 1540*0Sstevel@tonic-gate=over 2 1541*0Sstevel@tonic-gate 1542*0Sstevel@tonic-gate=item inf handling (partial) 1543*0Sstevel@tonic-gate 1544*0Sstevel@tonic-gate=item NaN handling (partial) 1545*0Sstevel@tonic-gate 1546*0Sstevel@tonic-gate=item rounding (not implemented except for bceil/bfloor) 1547*0Sstevel@tonic-gate 1548*0Sstevel@tonic-gate=item $x ** $y where $y is not an integer 1549*0Sstevel@tonic-gate 1550*0Sstevel@tonic-gate=item bmod(), blog(), bmodinv() and bmodpow() (partial) 1551*0Sstevel@tonic-gate 1552*0Sstevel@tonic-gate=back 1553*0Sstevel@tonic-gate 1554*0Sstevel@tonic-gate=head1 LICENSE 1555*0Sstevel@tonic-gate 1556*0Sstevel@tonic-gateThis program is free software; you may redistribute it and/or modify it under 1557*0Sstevel@tonic-gatethe same terms as Perl itself. 1558*0Sstevel@tonic-gate 1559*0Sstevel@tonic-gate=head1 SEE ALSO 1560*0Sstevel@tonic-gate 1561*0Sstevel@tonic-gateL<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>, 1562*0Sstevel@tonic-gateL<Math::BigInt::Pari> and L<Math::BigInt::GMP>. 1563*0Sstevel@tonic-gate 1564*0Sstevel@tonic-gateSee L<http://search.cpan.org/search?dist=bignum> for a way to use 1565*0Sstevel@tonic-gateMath::BigRat. 1566*0Sstevel@tonic-gate 1567*0Sstevel@tonic-gateThe package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat> 1568*0Sstevel@tonic-gatemay contain more documentation and examples as well as testcases. 1569*0Sstevel@tonic-gate 1570*0Sstevel@tonic-gate=head1 AUTHORS 1571*0Sstevel@tonic-gate 1572*0Sstevel@tonic-gate(C) by Tels L<http://bloodgate.com/> 2001, 2002, 2003, 2004. 1573*0Sstevel@tonic-gate 1574*0Sstevel@tonic-gate=cut 1575