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-rw-r--r--Master/tlpkg/tlperl/lib/Math/BigInt.pm7810
1 files changed, 4227 insertions, 3583 deletions
diff --git a/Master/tlpkg/tlperl/lib/Math/BigInt.pm b/Master/tlpkg/tlperl/lib/Math/BigInt.pm
index a50b37e832a..ed6e79fa1c7 100644
--- a/Master/tlpkg/tlperl/lib/Math/BigInt.pm
+++ b/Master/tlpkg/tlperl/lib/Math/BigInt.pm
@@ -7,10 +7,9 @@ package Math::BigInt;
# The following hash values are used:
# value: unsigned int with actual value (as a Math::BigInt::Calc or similar)
-# sign : +,-,NaN,+inf,-inf
+# sign : +, -, NaN, +inf, -inf
# _a : accuracy
# _p : precision
-# _f : flags, used by MBF to flag parts of a float as untouchable
# Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
# underlying lib might change the reference!
@@ -19,17 +18,13 @@ use 5.006001;
use strict;
use warnings;
-our $VERSION = '1.999715';
-$VERSION = eval $VERSION;
+use Carp ();
+
+our $VERSION = '1.999806';
our @ISA = qw(Exporter);
our @EXPORT_OK = qw(objectify bgcd blcm);
-# _trap_inf and _trap_nan are internal and should never be accessed from the
-# outside
-our ($round_mode, $accuracy, $precision, $div_scale, $rnd_mode,
- $upgrade, $downgrade, $_trap_nan, $_trap_inf);
-
my $class = "Math::BigInt";
# Inside overload, the first arg is always an object. If the original code had
@@ -43,120 +38,175 @@ my $class = "Math::BigInt";
# Thus inheritance of overload operators becomes possible and transparent for
# our subclasses without the need to repeat the entire overload section there.
-# We register ops that are not registerable yet, so suppress warnings
-{ no warnings;
use overload
-'=' => sub { $_[0]->copy(); },
-
-# some shortcuts for speed (assumes that reversed order of arguments is routed
-# to normal '+' and we thus can always modify first arg. If this is changed,
-# this breaks and must be adjusted.)
-'+=' => sub { $_[0]->badd($_[1]); },
-'-=' => sub { $_[0]->bsub($_[1]); },
-'*=' => sub { $_[0]->bmul($_[1]); },
-'/=' => sub { scalar $_[0]->bdiv($_[1]); },
-'%=' => sub { $_[0]->bmod($_[1]); },
-'^=' => sub { $_[0]->bxor($_[1]); },
-'&=' => sub { $_[0]->band($_[1]); },
-'|=' => sub { $_[0]->bior($_[1]); },
-
-'**=' => sub { $_[0]->bpow($_[1]); },
-'<<=' => sub { $_[0]->blsft($_[1]); },
-'>>=' => sub { $_[0]->brsft($_[1]); },
-
-# not supported by Perl yet
-'..' => \&_pointpoint,
-
-'<=>' => sub { my $rc = $_[2] ?
- ref($_[0])->bcmp($_[1],$_[0]) :
- $_[0]->bcmp($_[1]);
- $rc = 1 unless defined $rc;
- $rc <=> 0;
- },
-# we need '>=' to get things like "1 >= NaN" right:
-'>=' => sub { my $rc = $_[2] ?
- ref($_[0])->bcmp($_[1],$_[0]) :
- $_[0]->bcmp($_[1]);
- # if there was a NaN involved, return false
- return '' unless defined $rc;
- $rc >= 0;
- },
-'cmp' => sub {
- $_[2] ?
- "$_[1]" cmp $_[0]->bstr() :
- $_[0]->bstr() cmp "$_[1]" },
-
-'cos' => sub { $_[0]->copy->bcos(); },
-'sin' => sub { $_[0]->copy->bsin(); },
-'atan2' => sub { $_[2] ?
- ref($_[0])->new($_[1])->batan2($_[0]) :
- $_[0]->copy()->batan2($_[1]) },
-
-# are not yet overloadable
-#'hex' => sub { print "hex"; $_[0]; },
-#'oct' => sub { print "oct"; $_[0]; },
-
-# log(N) is log(N, e), where e is Euler's number
-'log' => sub { $_[0]->copy()->blog(); },
-'exp' => sub { $_[0]->copy()->bexp($_[1]); },
-'int' => sub { $_[0]->copy(); },
-'neg' => sub { $_[0]->copy()->bneg(); },
-'abs' => sub { $_[0]->copy()->babs(); },
-'sqrt' => sub { $_[0]->copy()->bsqrt(); },
-'~' => sub { $_[0]->copy()->bnot(); },
-
-# for subtract it's a bit tricky to not modify b: b-a => -a+b
-'-' => sub { my $c = $_[0]->copy; $_[2] ?
- $c->bneg()->badd( $_[1]) :
- $c->bsub( $_[1]) },
-'+' => sub { $_[0]->copy()->badd($_[1]); },
-'*' => sub { $_[0]->copy()->bmul($_[1]); },
-
-'/' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bdiv($_[0]) : $_[0]->copy->bdiv($_[1]);
- },
-'%' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bmod($_[0]) : $_[0]->copy->bmod($_[1]);
- },
-'**' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bpow($_[0]) : $_[0]->copy->bpow($_[1]);
- },
-'<<' => sub {
- $_[2] ? ref($_[0])->new($_[1])->blsft($_[0]) : $_[0]->copy->blsft($_[1]);
- },
-'>>' => sub {
- $_[2] ? ref($_[0])->new($_[1])->brsft($_[0]) : $_[0]->copy->brsft($_[1]);
- },
-'&' => sub {
- $_[2] ? ref($_[0])->new($_[1])->band($_[0]) : $_[0]->copy->band($_[1]);
- },
-'|' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bior($_[0]) : $_[0]->copy->bior($_[1]);
- },
-'^' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bxor($_[0]) : $_[0]->copy->bxor($_[1]);
- },
-
-# can modify arg of ++ and --, so avoid a copy() for speed, but don't
-# use $_[0]->bone(), it would modify $_[0] to be 1!
-'++' => sub { $_[0]->binc() },
-'--' => sub { $_[0]->bdec() },
-
-# if overloaded, O(1) instead of O(N) and twice as fast for small numbers
-'bool' => sub {
- # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/
- # v5.6.1 dumps on this: return !$_[0]->is_zero() || undef; :-(
- my $t = undef;
- $t = 1 if !$_[0]->is_zero();
- $t;
- },
-
-# the original qw() does not work with the TIESCALAR below, why?
-# Order of arguments insignificant
-'""' => sub { $_[0]->bstr(); },
-'0+' => sub { $_[0]->numify(); }
-;
-} # no warnings scope
+
+ # overload key: with_assign
+
+ '+' => sub { $_[0] -> copy() -> badd($_[1]); },
+
+ '-' => sub { my $c = $_[0] -> copy;
+ $_[2] ? $c -> bneg() -> badd($_[1])
+ : $c -> bsub($_[1]); },
+
+ '*' => sub { $_[0] -> copy() -> bmul($_[1]); },
+
+ '/' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bdiv($_[0])
+ : $_[0] -> copy -> bdiv($_[1]); },
+
+ '%' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bmod($_[0])
+ : $_[0] -> copy -> bmod($_[1]); },
+
+ '**' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bpow($_[0])
+ : $_[0] -> copy -> bpow($_[1]); },
+
+ '<<' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> blsft($_[0])
+ : $_[0] -> copy -> blsft($_[1]); },
+
+ '>>' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> brsft($_[0])
+ : $_[0] -> copy -> brsft($_[1]); },
+
+ # overload key: assign
+
+ '+=' => sub { $_[0]->badd($_[1]); },
+
+ '-=' => sub { $_[0]->bsub($_[1]); },
+
+ '*=' => sub { $_[0]->bmul($_[1]); },
+
+ '/=' => sub { scalar $_[0]->bdiv($_[1]); },
+
+ '%=' => sub { $_[0]->bmod($_[1]); },
+
+ '**=' => sub { $_[0]->bpow($_[1]); },
+
+
+ '<<=' => sub { $_[0]->blsft($_[1]); },
+
+ '>>=' => sub { $_[0]->brsft($_[1]); },
+
+# 'x=' => sub { },
+
+# '.=' => sub { },
+
+ # overload key: num_comparison
+
+ '<' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> blt($_[0])
+ : $_[0] -> blt($_[1]); },
+
+ '<=' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> ble($_[0])
+ : $_[0] -> ble($_[1]); },
+
+ '>' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bgt($_[0])
+ : $_[0] -> bgt($_[1]); },
+
+ '>=' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bge($_[0])
+ : $_[0] -> bge($_[1]); },
+
+ '==' => sub { $_[0] -> beq($_[1]); },
+
+ '!=' => sub { $_[0] -> bne($_[1]); },
+
+ # overload key: 3way_comparison
+
+ '<=>' => sub { my $cmp = $_[0] -> bcmp($_[1]);
+ defined($cmp) && $_[2] ? -$cmp : $cmp; },
+
+ 'cmp' => sub { $_[2] ? "$_[1]" cmp $_[0] -> bstr()
+ : $_[0] -> bstr() cmp "$_[1]"; },
+
+ # overload key: str_comparison
+
+# 'lt' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrlt($_[0])
+# : $_[0] -> bstrlt($_[1]); },
+#
+# 'le' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrle($_[0])
+# : $_[0] -> bstrle($_[1]); },
+#
+# 'gt' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrgt($_[0])
+# : $_[0] -> bstrgt($_[1]); },
+#
+# 'ge' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrge($_[0])
+# : $_[0] -> bstrge($_[1]); },
+#
+# 'eq' => sub { $_[0] -> bstreq($_[1]); },
+#
+# 'ne' => sub { $_[0] -> bstrne($_[1]); },
+
+ # overload key: binary
+
+ '&' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> band($_[0])
+ : $_[0] -> copy -> band($_[1]); },
+
+ '&=' => sub { $_[0] -> band($_[1]); },
+
+ '|' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bior($_[0])
+ : $_[0] -> copy -> bior($_[1]); },
+
+ '|=' => sub { $_[0] -> bior($_[1]); },
+
+ '^' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bxor($_[0])
+ : $_[0] -> copy -> bxor($_[1]); },
+
+ '^=' => sub { $_[0] -> bxor($_[1]); },
+
+# '&.' => sub { },
+
+# '&.=' => sub { },
+
+# '|.' => sub { },
+
+# '|.=' => sub { },
+
+# '^.' => sub { },
+
+# '^.=' => sub { },
+
+ # overload key: unary
+
+ 'neg' => sub { $_[0] -> copy() -> bneg(); },
+
+# '!' => sub { },
+
+ '~' => sub { $_[0] -> copy() -> bnot(); },
+
+# '~.' => sub { },
+
+ # overload key: mutators
+
+ '++' => sub { $_[0] -> binc() },
+
+ '--' => sub { $_[0] -> bdec() },
+
+ # overload key: func
+
+ 'atan2' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> batan2($_[0])
+ : $_[0] -> copy() -> batan2($_[1]); },
+
+ 'cos' => sub { $_[0] -> copy -> bcos(); },
+
+ 'sin' => sub { $_[0] -> copy -> bsin(); },
+
+ 'exp' => sub { $_[0] -> copy() -> bexp($_[1]); },
+
+ 'abs' => sub { $_[0] -> copy() -> babs(); },
+
+ 'log' => sub { $_[0] -> copy() -> blog(); },
+
+ 'sqrt' => sub { $_[0] -> copy() -> bsqrt(); },
+
+ 'int' => sub { $_[0] -> copy() -> bint(); },
+
+ # overload key: conversion
+
+ 'bool' => sub { $_[0] -> is_zero() ? '' : 1; },
+
+ '""' => sub { $_[0] -> bstr(); },
+
+ '0+' => sub { $_[0] -> numify(); },
+
+ '=' => sub { $_[0]->copy(); },
+
+ ;
##############################################################################
# global constants, flags and accessory
@@ -164,18 +214,18 @@ use overload
# These vars are public, but their direct usage is not recommended, use the
# accessor methods instead
-$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
-$accuracy = undef;
-$precision = undef;
-$div_scale = 40;
-
-$upgrade = undef; # default is no upgrade
-$downgrade = undef; # default is no downgrade
+our $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
+our $accuracy = undef;
+our $precision = undef;
+our $div_scale = 40;
+our $upgrade = undef; # default is no upgrade
+our $downgrade = undef; # default is no downgrade
# These are internally, and not to be used from the outside at all
-$_trap_nan = 0; # are NaNs ok? set w/ config()
-$_trap_inf = 0; # are infs ok? set w/ config()
+our $_trap_nan = 0; # are NaNs ok? set w/ config()
+our $_trap_inf = 0; # are infs ok? set w/ config()
+
my $nan = 'NaN'; # constants for easier life
my $CALC = 'Math::BigInt::Calc'; # module to do the low level math
@@ -190,328 +240,287 @@ my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math
##############################################################################
# the old code had $rnd_mode, so we need to support it, too
-$rnd_mode = 'even';
-sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; }
-sub FETCH { return $round_mode; }
-sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
+our $rnd_mode = 'even';
-BEGIN
- {
- # tie to enable $rnd_mode to work transparently
- tie $rnd_mode, 'Math::BigInt';
+sub TIESCALAR {
+ my ($class) = @_;
+ bless \$round_mode, $class;
+}
- # set up some handy alias names
- *as_int = \&as_number;
- *is_pos = \&is_positive;
- *is_neg = \&is_negative;
- }
+sub FETCH {
+ return $round_mode;
+}
-##############################################################################
+sub STORE {
+ $rnd_mode = $_[0]->round_mode($_[1]);
+}
-sub round_mode
- {
- no strict 'refs';
- # make Class->round_mode() work
- my $self = shift;
- my $class = ref($self) || $self || __PACKAGE__;
- if (defined $_[0])
- {
- my $m = shift;
- if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
- {
- require Carp; Carp::croak ("Unknown round mode '$m'");
- }
- return ${"${class}::round_mode"} = $m;
- }
- ${"${class}::round_mode"};
- }
-
-sub upgrade
- {
- no strict 'refs';
- # make Class->upgrade() work
- my $self = shift;
- my $class = ref($self) || $self || __PACKAGE__;
- # need to set new value?
- if (@_ > 0)
- {
- return ${"${class}::upgrade"} = $_[0];
- }
- ${"${class}::upgrade"};
- }
-
-sub downgrade
- {
- no strict 'refs';
- # make Class->downgrade() work
- my $self = shift;
- my $class = ref($self) || $self || __PACKAGE__;
- # need to set new value?
- if (@_ > 0)
- {
- return ${"${class}::downgrade"} = $_[0];
- }
- ${"${class}::downgrade"};
- }
-
-sub div_scale
- {
- no strict 'refs';
- # make Class->div_scale() work
- my $self = shift;
- my $class = ref($self) || $self || __PACKAGE__;
- if (defined $_[0])
- {
- if ($_[0] < 0)
- {
- require Carp; Carp::croak ('div_scale must be greater than zero');
- }
- ${"${class}::div_scale"} = $_[0];
- }
- ${"${class}::div_scale"};
- }
-
-sub accuracy
- {
- # $x->accuracy($a); ref($x) $a
- # $x->accuracy(); ref($x)
- # Class->accuracy(); class
- # Class->accuracy($a); class $a
-
- my $x = shift;
- my $class = ref($x) || $x || __PACKAGE__;
-
- no strict 'refs';
- # need to set new value?
- if (@_ > 0)
- {
- my $a = shift;
- # convert objects to scalars to avoid deep recursion. If object doesn't
- # have numify(), then hopefully it will have overloading for int() and
- # boolean test without wandering into a deep recursion path...
- $a = $a->numify() if ref($a) && $a->can('numify');
-
- if (defined $a)
- {
- # also croak on non-numerical
- if (!$a || $a <= 0)
- {
- require Carp;
- Carp::croak ('Argument to accuracy must be greater than zero');
- }
- if (int($a) != $a)
- {
- require Carp;
- Carp::croak ('Argument to accuracy must be an integer');
- }
- }
- if (ref($x))
- {
- # $object->accuracy() or fallback to global
- $x->bround($a) if $a; # not for undef, 0
- $x->{_a} = $a; # set/overwrite, even if not rounded
- delete $x->{_p}; # clear P
- $a = ${"${class}::accuracy"} unless defined $a; # proper return value
- }
- else
- {
- ${"${class}::accuracy"} = $a; # set global A
- ${"${class}::precision"} = undef; # clear global P
- }
- return $a; # shortcut
- }
-
- my $a;
- # $object->accuracy() or fallback to global
- $a = $x->{_a} if ref($x);
- # but don't return global undef, when $x's accuracy is 0!
- $a = ${"${class}::accuracy"} if !defined $a;
- $a;
- }
-
-sub precision
- {
- # $x->precision($p); ref($x) $p
- # $x->precision(); ref($x)
- # Class->precision(); class
- # Class->precision($p); class $p
-
- my $x = shift;
- my $class = ref($x) || $x || __PACKAGE__;
-
- no strict 'refs';
- if (@_ > 0)
- {
- my $p = shift;
- # convert objects to scalars to avoid deep recursion. If object doesn't
- # have numify(), then hopefully it will have overloading for int() and
- # boolean test without wandering into a deep recursion path...
- $p = $p->numify() if ref($p) && $p->can('numify');
- if ((defined $p) && (int($p) != $p))
- {
- require Carp; Carp::croak ('Argument to precision must be an integer');
- }
- if (ref($x))
- {
- # $object->precision() or fallback to global
- $x->bfround($p) if $p; # not for undef, 0
- $x->{_p} = $p; # set/overwrite, even if not rounded
- delete $x->{_a}; # clear A
- $p = ${"${class}::precision"} unless defined $p; # proper return value
- }
- else
- {
- ${"${class}::precision"} = $p; # set global P
- ${"${class}::accuracy"} = undef; # clear global A
- }
- return $p; # shortcut
- }
-
- my $p;
- # $object->precision() or fallback to global
- $p = $x->{_p} if ref($x);
- # but don't return global undef, when $x's precision is 0!
- $p = ${"${class}::precision"} if !defined $p;
- $p;
- }
-
-sub config
- {
- # return (or set) configuration data as hash ref
- my $class = shift || 'Math::BigInt';
-
- no strict 'refs';
- if (@_ > 1 || (@_ == 1 && (ref($_[0]) eq 'HASH')))
- {
- # try to set given options as arguments from hash
-
- my $args = $_[0];
- if (ref($args) ne 'HASH')
- {
- $args = { @_ };
- }
- # these values can be "set"
- my $set_args = {};
- foreach my $key (
- qw/trap_inf trap_nan
- upgrade downgrade precision accuracy round_mode div_scale/
- )
- {
- $set_args->{$key} = $args->{$key} if exists $args->{$key};
- delete $args->{$key};
- }
- if (keys %$args > 0)
- {
- require Carp;
- Carp::croak ("Illegal key(s) '",
- join("','",keys %$args),"' passed to $class\->config()");
- }
- foreach my $key (keys %$set_args)
- {
- if ($key =~ /^trap_(inf|nan)\z/)
- {
- ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0);
- next;
+BEGIN {
+ # tie to enable $rnd_mode to work transparently
+ tie $rnd_mode, 'Math::BigInt';
+
+ # set up some handy alias names
+ *as_int = \&as_number;
+ *is_pos = \&is_positive;
+ *is_neg = \&is_negative;
+}
+
+###############################################################################
+# Configuration methods
+###############################################################################
+
+sub round_mode {
+ no strict 'refs';
+ # make Class->round_mode() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ if (defined $_[0]) {
+ my $m = shift;
+ if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/) {
+ Carp::croak("Unknown round mode '$m'");
}
- # use a call instead of just setting the $variable to check argument
- $class->$key($set_args->{$key});
- }
- }
-
- # now return actual configuration
-
- my $cfg = {
- lib => $CALC,
- lib_version => ${"${CALC}::VERSION"},
- class => $class,
- trap_nan => ${"${class}::_trap_nan"},
- trap_inf => ${"${class}::_trap_inf"},
- version => ${"${class}::VERSION"},
- };
- foreach my $key (qw/
- upgrade downgrade precision accuracy round_mode div_scale
- /)
- {
- $cfg->{$key} = ${"${class}::$key"};
- };
- if (@_ == 1 && (ref($_[0]) ne 'HASH'))
- {
- # calls of the style config('lib') return just this value
- return $cfg->{$_[0]};
+ return ${"${class}::round_mode"} = $m;
}
- $cfg;
- }
+ ${"${class}::round_mode"};
+}
-sub _scale_a
- {
- # select accuracy parameter based on precedence,
- # used by bround() and bfround(), may return undef for scale (means no op)
- my ($x,$scale,$mode) = @_;
+sub upgrade {
+ no strict 'refs';
+ # make Class->upgrade() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ # need to set new value?
+ if (@_ > 0) {
+ return ${"${class}::upgrade"} = $_[0];
+ }
+ ${"${class}::upgrade"};
+}
- $scale = $x->{_a} unless defined $scale;
+sub downgrade {
+ no strict 'refs';
+ # make Class->downgrade() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ # need to set new value?
+ if (@_ > 0) {
+ return ${"${class}::downgrade"} = $_[0];
+ }
+ ${"${class}::downgrade"};
+}
- no strict 'refs';
- my $class = ref($x);
+sub div_scale {
+ no strict 'refs';
+ # make Class->div_scale() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ if (defined $_[0]) {
+ if ($_[0] < 0) {
+ Carp::croak('div_scale must be greater than zero');
+ }
+ ${"${class}::div_scale"} = $_[0];
+ }
+ ${"${class}::div_scale"};
+}
- $scale = ${ $class . '::accuracy' } unless defined $scale;
- $mode = ${ $class . '::round_mode' } unless defined $mode;
+sub accuracy {
+ # $x->accuracy($a); ref($x) $a
+ # $x->accuracy(); ref($x)
+ # Class->accuracy(); class
+ # Class->accuracy($a); class $a
- if (defined $scale)
- {
- $scale = $scale->can('numify') ? $scale->numify()
- : "$scale" if ref($scale);
- $scale = int($scale);
+ my $x = shift;
+ my $class = ref($x) || $x || __PACKAGE__;
+
+ no strict 'refs';
+ # need to set new value?
+ if (@_ > 0) {
+ my $a = shift;
+ # convert objects to scalars to avoid deep recursion. If object doesn't
+ # have numify(), then hopefully it will have overloading for int() and
+ # boolean test without wandering into a deep recursion path...
+ $a = $a->numify() if ref($a) && $a->can('numify');
+
+ if (defined $a) {
+ # also croak on non-numerical
+ if (!$a || $a <= 0) {
+ Carp::croak('Argument to accuracy must be greater than zero');
+ }
+ if (int($a) != $a) {
+ Carp::croak('Argument to accuracy must be an integer');
+ }
+ }
+ if (ref($x)) {
+ # $object->accuracy() or fallback to global
+ $x->bround($a) if $a; # not for undef, 0
+ $x->{_a} = $a; # set/overwrite, even if not rounded
+ delete $x->{_p}; # clear P
+ $a = ${"${class}::accuracy"} unless defined $a; # proper return value
+ } else {
+ ${"${class}::accuracy"} = $a; # set global A
+ ${"${class}::precision"} = undef; # clear global P
+ }
+ return $a; # shortcut
}
- ($scale,$mode);
- }
+ my $a;
+ # $object->accuracy() or fallback to global
+ $a = $x->{_a} if ref($x);
+ # but don't return global undef, when $x's accuracy is 0!
+ $a = ${"${class}::accuracy"} if !defined $a;
+ $a;
+}
+
+sub precision {
+ # $x->precision($p); ref($x) $p
+ # $x->precision(); ref($x)
+ # Class->precision(); class
+ # Class->precision($p); class $p
-sub _scale_p
- {
- # select precision parameter based on precedence,
- # used by bround() and bfround(), may return undef for scale (means no op)
- my ($x,$scale,$mode) = @_;
+ my $x = shift;
+ my $class = ref($x) || $x || __PACKAGE__;
+
+ no strict 'refs';
+ if (@_ > 0) {
+ my $p = shift;
+ # convert objects to scalars to avoid deep recursion. If object doesn't
+ # have numify(), then hopefully it will have overloading for int() and
+ # boolean test without wandering into a deep recursion path...
+ $p = $p->numify() if ref($p) && $p->can('numify');
+ if ((defined $p) && (int($p) != $p)) {
+ Carp::croak('Argument to precision must be an integer');
+ }
+ if (ref($x)) {
+ # $object->precision() or fallback to global
+ $x->bfround($p) if $p; # not for undef, 0
+ $x->{_p} = $p; # set/overwrite, even if not rounded
+ delete $x->{_a}; # clear A
+ $p = ${"${class}::precision"} unless defined $p; # proper return value
+ } else {
+ ${"${class}::precision"} = $p; # set global P
+ ${"${class}::accuracy"} = undef; # clear global A
+ }
+ return $p; # shortcut
+ }
- $scale = $x->{_p} unless defined $scale;
+ my $p;
+ # $object->precision() or fallback to global
+ $p = $x->{_p} if ref($x);
+ # but don't return global undef, when $x's precision is 0!
+ $p = ${"${class}::precision"} if !defined $p;
+ $p;
+}
- no strict 'refs';
- my $class = ref($x);
+sub config {
+ # return (or set) configuration data as hash ref
+ my $class = shift || __PACKAGE__;
- $scale = ${ $class . '::precision' } unless defined $scale;
- $mode = ${ $class . '::round_mode' } unless defined $mode;
+ no strict 'refs';
+ if (@_ > 1 || (@_ == 1 && (ref($_[0]) eq 'HASH'))) {
+ # try to set given options as arguments from hash
- if (defined $scale)
+ my $args = $_[0];
+ if (ref($args) ne 'HASH') {
+ $args = { @_ };
+ }
+ # these values can be "set"
+ my $set_args = {};
+ foreach my $key (qw/
+ accuracy precision
+ round_mode div_scale
+ upgrade downgrade
+ trap_inf trap_nan
+ /)
+ {
+ $set_args->{$key} = $args->{$key} if exists $args->{$key};
+ delete $args->{$key};
+ }
+ if (keys %$args > 0) {
+ Carp::croak("Illegal key(s) '", join("', '", keys %$args),
+ "' passed to $class\->config()");
+ }
+ foreach my $key (keys %$set_args) {
+ if ($key =~ /^trap_(inf|nan)\z/) {
+ ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0);
+ next;
+ }
+ # use a call instead of just setting the $variable to check argument
+ $class->$key($set_args->{$key});
+ }
+ }
+
+ # now return actual configuration
+
+ my $cfg = {
+ lib => $CALC,
+ lib_version => ${"${CALC}::VERSION"},
+ class => $class,
+ trap_nan => ${"${class}::_trap_nan"},
+ trap_inf => ${"${class}::_trap_inf"},
+ version => ${"${class}::VERSION"},
+ };
+ foreach my $key (qw/
+ accuracy precision
+ round_mode div_scale
+ upgrade downgrade
+ /)
{
- $scale = $scale->can('numify') ? $scale->numify()
- : "$scale" if ref($scale);
- $scale = int($scale);
+ $cfg->{$key} = ${"${class}::$key"};
+ }
+ if (@_ == 1 && (ref($_[0]) ne 'HASH')) {
+ # calls of the style config('lib') return just this value
+ return $cfg->{$_[0]};
}
+ $cfg;
+}
- ($scale,$mode);
- }
+sub _scale_a {
+ # select accuracy parameter based on precedence,
+ # used by bround() and bfround(), may return undef for scale (means no op)
+ my ($x, $scale, $mode) = @_;
-##############################################################################
-# constructors
+ $scale = $x->{_a} unless defined $scale;
-sub copy {
- my $self = shift;
- my $selfref = ref $self;
- my $class = $selfref || $self;
+ no strict 'refs';
+ my $class = ref($x);
- # If called as a class method, the object to copy is the next argument.
+ $scale = ${ $class . '::accuracy' } unless defined $scale;
+ $mode = ${ $class . '::round_mode' } unless defined $mode;
- $self = shift() unless $selfref;
+ if (defined $scale) {
+ $scale = $scale->can('numify') ? $scale->numify()
+ : "$scale" if ref($scale);
+ $scale = int($scale);
+ }
- my $copy = bless {}, $class;
+ ($scale, $mode);
+}
- $copy->{sign} = $self->{sign};
- $copy->{value} = $CALC->_copy($self->{value});
- $copy->{_a} = $self->{_a} if exists $self->{_a};
- $copy->{_p} = $self->{_p} if exists $self->{_p};
+sub _scale_p {
+ # select precision parameter based on precedence,
+ # used by bround() and bfround(), may return undef for scale (means no op)
+ my ($x, $scale, $mode) = @_;
- return $copy;
+ $scale = $x->{_p} unless defined $scale;
+
+ no strict 'refs';
+ my $class = ref($x);
+
+ $scale = ${ $class . '::precision' } unless defined $scale;
+ $mode = ${ $class . '::round_mode' } unless defined $mode;
+
+ if (defined $scale) {
+ $scale = $scale->can('numify') ? $scale->numify()
+ : "$scale" if ref($scale);
+ $scale = int($scale);
+ }
+
+ ($scale, $mode);
}
+###############################################################################
+# Constructor methods
+###############################################################################
+
sub new {
# Create a new Math::BigInt object from a string or another Math::BigInt
# object. See hash keys documented at top.
@@ -524,15 +533,29 @@ sub new {
my $selfref = ref $self;
my $class = $selfref || $self;
+ # The POD says:
+ #
+ # "Currently, Math::BigInt->new() defaults to 0, while Math::BigInt->new('')
+ # results in 'NaN'. This might change in the future, so use always the
+ # following explicit forms to get a zero or NaN:
+ # $zero = Math::BigInt->bzero();
+ # $nan = Math::BigInt->bnan();
+ #
+ # But although this use has been discouraged for more than 10 years, people
+ # apparently still use it, so we still support it.
+
+ return $self->bzero() unless @_;
+
my ($wanted, $a, $p, $r) = @_;
- # If called as a class method, initialize a new object.
+ # Always return a new object, so it called as an instance method, copy the
+ # invocand, and if called as a class method, initialize a new object.
- $self = bless {}, $class unless $selfref;
+ $self = $selfref ? $self -> copy()
+ : bless {}, $class;
unless (defined $wanted) {
- require Carp;
- Carp::carp("Use of uninitialized value in new");
+ #Carp::carp("Use of uninitialized value in new()");
return $self->bzero($a, $p, $r);
}
@@ -571,7 +594,7 @@ sub new {
|| defined(${"${class}::accuracy"}))
{
$self->round($a, $p, $r)
- unless @_ == 4 && !defined $a && !defined $p;
+ unless @_ >= 3 && !defined $a && !defined $p;
}
return $self;
@@ -582,28 +605,38 @@ sub new {
if ($wanted =~ /^\s*([+-]?)inf(inity)?\s*\z/i) {
my $sgn = $1 || '+';
$self->{sign} = $sgn . 'inf'; # set a default sign for bstr()
- return $self->binf($sgn);
+ return $class->binf($sgn);
}
# Handle explicit NaNs (not the ones returned due to invalid input).
if ($wanted =~ /^\s*([+-]?)nan\s*\z/i) {
- return $self->bnan();
+ $self = $class -> bnan();
+ $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p;
+ return $self;
}
+ # Handle hexadecimal numbers.
+
if ($wanted =~ /^\s*[+-]?0[Xx]/) {
- return $class -> from_hex($wanted);
+ $self = $class -> from_hex($wanted);
+ $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p;
+ return $self;
}
+ # Handle binary numbers.
+
if ($wanted =~ /^\s*[+-]?0[Bb]/) {
- return $class -> from_bin($wanted);
+ $self = $class -> from_bin($wanted);
+ $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p;
+ return $self;
}
# Split string into mantissa, exponent, integer, fraction, value, and sign.
my ($mis, $miv, $mfv, $es, $ev) = _split($wanted);
if (!ref $mis) {
if ($_trap_nan) {
- require Carp; Carp::croak("$wanted is not a number in $class");
+ Carp::croak("$wanted is not a number in $class");
}
$self->{value} = $CALC->_zero();
$self->{sign} = $nan;
@@ -626,7 +659,7 @@ sub new {
my $diff = $e - CORE::length($$mfv);
if ($diff < 0) { # Not integer
if ($_trap_nan) {
- require Carp; Carp::croak("$wanted not an integer in $class");
+ Carp::croak("$wanted not an integer in $class");
}
#print "NOI 1\n";
return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade;
@@ -642,7 +675,7 @@ sub new {
if ($$mfv ne '') { # e <= 0
# fraction and negative/zero E => NOI
if ($_trap_nan) {
- require Carp; Carp::croak("$wanted not an integer in $class");
+ Carp::croak("$wanted not an integer in $class");
}
#print "NOI 2 \$\$mfv '$$mfv'\n";
return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade;
@@ -657,7 +690,7 @@ sub new {
if ($frac =~ /[^0]/) {
if ($_trap_nan) {
- require Carp; Carp::croak("$wanted not an integer in $class");
+ Carp::croak("$wanted not an integer in $class");
}
#print "NOI 3\n";
return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade;
@@ -675,1056 +708,996 @@ sub new {
# $self. Do not round for new($x, undef, undef) since that is used by MBF
# to signal no rounding.
- $self->round($a, $p, $r) unless @_ == 4 && !defined $a && !defined $p;
+ $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p;
$self;
}
-sub bnan
- {
- # create a bigint 'NaN', if given a BigInt, set it to 'NaN'
- my $self = shift;
- $self = $class if !defined $self;
- if (!ref($self))
- {
- my $c = $self; $self = {}; bless $self, $c;
- }
- no strict 'refs';
- if (${"${class}::_trap_nan"})
- {
- require Carp;
- Carp::croak ("Tried to set $self to NaN in $class\::bnan()");
- }
- $self->import() if $IMPORT == 0; # make require work
- return if $self->modify('bnan');
- if ($self->can('_bnan'))
- {
- # use subclass to initialize
- $self->_bnan();
- }
- else
- {
- # otherwise do our own thing
- $self->{value} = $CALC->_zero();
- }
- $self->{sign} = $nan;
- delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly
- $self;
- }
-
-sub binf
- {
- # create a bigint '+-inf', if given a BigInt, set it to '+-inf'
- # the sign is either '+', or if given, used from there
- my $self = shift;
- my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/;
- $self = $class if !defined $self;
- if (!ref($self))
- {
- my $c = $self; $self = {}; bless $self, $c;
- }
- no strict 'refs';
- if (${"${class}::_trap_inf"})
- {
- require Carp;
- Carp::croak ("Tried to set $self to +-inf in $class\::binf()");
- }
- $self->import() if $IMPORT == 0; # make require work
- return if $self->modify('binf');
- if ($self->can('_binf'))
+# Create a Math::BigInt from a hexadecimal string.
+
+sub from_hex {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
+
+ # Don't modify constant (read-only) objects.
+
+ return if $selfref && $self->modify('from_hex');
+
+ my $str = shift;
+
+ # If called as a class method, initialize a new object.
+
+ $self = $class -> bzero() unless $selfref;
+
+ if ($str =~ s/
+ ^
+ ( [+-]? )
+ (0?x)?
+ (
+ [0-9a-fA-F]*
+ ( _ [0-9a-fA-F]+ )*
+ )
+ $
+ //x)
{
- # use subclass to initialize
- $self->_binf();
+ # Get a "clean" version of the string, i.e., non-emtpy and with no
+ # underscores or invalid characters.
+
+ my $sign = $1;
+ my $chrs = $3;
+ $chrs =~ tr/_//d;
+ $chrs = '0' unless CORE::length $chrs;
+
+ # The library method requires a prefix.
+
+ $self->{value} = $CALC->_from_hex('0x' . $chrs);
+
+ # Place the sign.
+
+ $self->{sign} = $sign eq '-' && ! $CALC->_is_zero($self->{value})
+ ? '-' : '+';
+
+ return $self;
}
- else
+
+ # CORE::hex() parses as much as it can, and ignores any trailing garbage.
+ # For backwards compatibility, we return NaN.
+
+ return $self->bnan();
+}
+
+# Create a Math::BigInt from an octal string.
+
+sub from_oct {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
+
+ # Don't modify constant (read-only) objects.
+
+ return if $selfref && $self->modify('from_oct');
+
+ my $str = shift;
+
+ # If called as a class method, initialize a new object.
+
+ $self = $class -> bzero() unless $selfref;
+
+ if ($str =~ s/
+ ^
+ ( [+-]? )
+ (
+ [0-7]*
+ ( _ [0-7]+ )*
+ )
+ $
+ //x)
{
- # otherwise do our own thing
- $self->{value} = $CALC->_zero();
+ # Get a "clean" version of the string, i.e., non-emtpy and with no
+ # underscores or invalid characters.
+
+ my $sign = $1;
+ my $chrs = $2;
+ $chrs =~ tr/_//d;
+ $chrs = '0' unless CORE::length $chrs;
+
+ # The library method requires a prefix.
+
+ $self->{value} = $CALC->_from_oct('0' . $chrs);
+
+ # Place the sign.
+
+ $self->{sign} = $sign eq '-' && ! $CALC->_is_zero($self->{value})
+ ? '-' : '+';
+
+ return $self;
}
- $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf
- $self->{sign} = $sign;
- ($self->{_a},$self->{_p}) = @_; # take over requested rounding
- $self;
- }
-sub bzero
- {
- # create a bigint '+0', if given a BigInt, set it to 0
- my $self = shift;
- $self = __PACKAGE__ if !defined $self;
+ # CORE::oct() parses as much as it can, and ignores any trailing garbage.
+ # For backwards compatibility, we return NaN.
+
+ return $self->bnan();
+}
+
+# Create a Math::BigInt from a binary string.
- if (!ref($self))
+sub from_bin {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
+
+ # Don't modify constant (read-only) objects.
+
+ return if $selfref && $self->modify('from_bin');
+
+ my $str = shift;
+
+ # If called as a class method, initialize a new object.
+
+ $self = $class -> bzero() unless $selfref;
+
+ if ($str =~ s/
+ ^
+ ( [+-]? )
+ (0?b)?
+ (
+ [01]*
+ ( _ [01]+ )*
+ )
+ $
+ //x)
{
- my $c = $self; $self = {}; bless $self, $c;
+ # Get a "clean" version of the string, i.e., non-emtpy and with no
+ # underscores or invalid characters.
+
+ my $sign = $1;
+ my $chrs = $3;
+ $chrs =~ tr/_//d;
+ $chrs = '0' unless CORE::length $chrs;
+
+ # The library method requires a prefix.
+
+ $self->{value} = $CALC->_from_bin('0b' . $chrs);
+
+ # Place the sign.
+
+ $self->{sign} = $sign eq '-' && ! $CALC->_is_zero($self->{value})
+ ? '-' : '+';
+
+ return $self;
}
- $self->import() if $IMPORT == 0; # make require work
- return if $self->modify('bzero');
- if ($self->can('_bzero'))
- {
- # use subclass to initialize
- $self->_bzero();
+ # For consistency with from_hex() and from_oct(), we return NaN when the
+ # input is invalid.
+
+ return $self->bnan();
+}
+
+# Create a Math::BigInt from a byte string.
+
+sub from_bytes {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
+
+ # Don't modify constant (read-only) objects.
+
+ return if $selfref && $self->modify('from_bytes');
+
+ my $str = shift;
+
+ # If called as a class method, initialize a new object.
+
+ $self = $class -> bzero() unless $selfref;
+ $self -> {sign} = '+';
+ $self -> {value} = $CALC -> _from_bytes($str);
+ return $self;
+}
+
+sub bzero {
+ # create/assign '+0'
+
+ if (@_ == 0) {
+ #Carp::carp("Using bzero() as a function is deprecated;",
+ # " use bzero() as a method instead");
+ unshift @_, __PACKAGE__;
}
- else
- {
- # otherwise do our own thing
+
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
+
+ $self->import() if $IMPORT == 0; # make require work
+
+ # Don't modify constant (read-only) objects.
+
+ return if $selfref && $self->modify('bzero');
+
+ $self = bless {}, $class unless $selfref;
+
+ $self->{sign} = '+';
$self->{value} = $CALC->_zero();
+
+ if (@_ > 0) {
+ if (@_ > 3) {
+ # call like: $x->bzero($a, $p, $r, $y, ...);
+ ($self, $self->{_a}, $self->{_p}) = $self->_find_round_parameters(@_);
+ } else {
+ # call like: $x->bzero($a, $p, $r);
+ $self->{_a} = $_[0]
+ if !defined $self->{_a} || (defined $_[0] && $_[0] > $self->{_a});
+ $self->{_p} = $_[1]
+ if !defined $self->{_p} || (defined $_[1] && $_[1] > $self->{_p});
+ }
}
- $self->{sign} = '+';
- if (@_ > 0)
- {
- if (@_ > 3)
- {
- # call like: $x->bzero($a,$p,$r,$y);
- ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
- }
- else
- {
- $self->{_a} = $_[0]
- if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
- $self->{_p} = $_[1]
- if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
- }
- }
- $self;
- }
-
-sub bone
- {
- # create a bigint '+1' (or -1 if given sign '-'),
- # if given a BigInt, set it to +1 or -1, respectively
- my $self = shift;
- my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
- $self = $class if !defined $self;
-
- if (!ref($self))
- {
- my $c = $self; $self = {}; bless $self, $c;
- }
- $self->import() if $IMPORT == 0; # make require work
- return if $self->modify('bone');
- if ($self->can('_bone'))
- {
- # use subclass to initialize
- $self->_bone();
+ return $self;
+}
+
+sub bone {
+ # Create or assign '+1' (or -1 if given sign '-').
+
+ if (@_ == 0 || (defined($_[0]) && ($_[0] eq '+' || $_[0] eq '-'))) {
+ #Carp::carp("Using bone() as a function is deprecated;",
+ # " use bone() as a method instead");
+ unshift @_, __PACKAGE__;
}
- else
- {
- # otherwise do our own thing
+
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
+
+ $self->import() if $IMPORT == 0; # make require work
+
+ # Don't modify constant (read-only) objects.
+
+ return if $selfref && $self->modify('bone');
+
+ my $sign = shift;
+ $sign = defined $sign && $sign =~ /^\s*-/ ? "-" : "+";
+
+ $self = bless {}, $class unless $selfref;
+
+ $self->{sign} = $sign;
$self->{value} = $CALC->_one();
+
+ if (@_ > 0) {
+ if (@_ > 3) {
+ # call like: $x->bone($sign, $a, $p, $r, $y, ...);
+ ($self, $self->{_a}, $self->{_p}) = $self->_find_round_parameters(@_);
+ } else {
+ # call like: $x->bone($sign, $a, $p, $r);
+ $self->{_a} = $_[0]
+ if !defined $self->{_a} || (defined $_[0] && $_[0] > $self->{_a});
+ $self->{_p} = $_[1]
+ if !defined $self->{_p} || (defined $_[1] && $_[1] > $self->{_p});
+ }
}
- $self->{sign} = $sign;
- if (@_ > 0)
- {
- if (@_ > 3)
- {
- # call like: $x->bone($sign,$a,$p,$r,$y);
- ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
- }
- else
- {
- # call like: $x->bone($sign,$a,$p,$r);
- $self->{_a} = $_[0]
- if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
- $self->{_p} = $_[1]
- if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
- }
- }
- $self;
- }
-##############################################################################
-# string conversion
+ return $self;
+}
-sub bsstr
- {
- # (ref to BFLOAT or num_str ) return num_str
- # Convert number from internal format to scientific string format.
- # internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+sub binf {
+ # create/assign a '+inf' or '-inf'
- if ($x->{sign} !~ /^[+-]$/)
+ if (@_ == 0 || (defined($_[0]) && !ref($_[0]) &&
+ $_[0] =~ /^\s*[+-](inf(inity)?)?\s*$/))
{
- return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
- return 'inf'; # +inf
+ #Carp::carp("Using binf() as a function is deprecated;",
+ # " use binf() as a method instead");
+ unshift @_, __PACKAGE__;
}
- my ($m,$e) = $x->parts();
- #$m->bstr() . 'e+' . $e->bstr(); # e can only be positive in BigInt
- # 'e+' because E can only be positive in BigInt
- $m->bstr() . 'e+' . $CALC->_str($e->{value});
- }
-sub bstr
- {
- # make a string from bigint object
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
- if ($x->{sign} !~ /^[+-]$/)
{
- return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
- return 'inf'; # +inf
- }
- my $es = ''; $es = $x->{sign} if $x->{sign} eq '-';
- $es.$CALC->_str($x->{value});
- }
-
-sub numify
- {
- # Make a Perl scalar number from a Math::BigInt object.
- my $x = shift; $x = $class->new($x) unless ref $x;
-
- if ($x -> is_nan()) {
- require Math::Complex;
- my $inf = Math::Complex::Inf();
- return $inf - $inf;
- }
-
- if ($x -> is_inf()) {
- require Math::Complex;
- my $inf = Math::Complex::Inf();
- return $x -> is_negative() ? -$inf : $inf;
- }
-
- my $num = 0 + $CALC->_num($x->{value});
- return $x->{sign} eq '-' ? -$num : $num;
- }
+ no strict 'refs';
+ if (${"${class}::_trap_inf"}) {
+ Carp::croak("Tried to create +-inf in $class->binf()");
+ }
+ }
-##############################################################################
-# public stuff (usually prefixed with "b")
+ $self->import() if $IMPORT == 0; # make require work
-sub sign
- {
- # return the sign of the number: +/-/-inf/+inf/NaN
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ # Don't modify constant (read-only) objects.
- $x->{sign};
- }
+ return if $selfref && $self->modify('binf');
-sub _find_round_parameters {
- # After any operation or when calling round(), the result is rounded by
- # regarding the A & P from arguments, local parameters, or globals.
+ my $sign = shift;
+ $sign = defined $sign && $sign =~ /^\s*-/ ? "-" : "+";
- # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!!
+ $self = bless {}, $class unless $selfref;
- # This procedure finds the round parameters, but it is for speed reasons
- # duplicated in round. Otherwise, it is tested by the testsuite and used
- # by bdiv().
+ $self -> {sign} = $sign . 'inf';
+ $self -> {value} = $CALC -> _zero();
- # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P
- # were requested/defined (locally or globally or both)
+ return $self;
+}
- my ($self, $a, $p, $r, @args) = @_;
- # $a accuracy, if given by caller
- # $p precision, if given by caller
- # $r round_mode, if given by caller
- # @args all 'other' arguments (0 for unary, 1 for binary ops)
+sub bnan {
+ # create/assign a 'NaN'
- my $class = ref($self); # find out class of argument(s)
- no strict 'refs';
+ if (@_ == 0) {
+ #Carp::carp("Using bnan() as a function is deprecated;",
+ # " use bnan() as a method instead");
+ unshift @_, __PACKAGE__;
+ }
- # convert to normal scalar for speed and correctness in inner parts
- $a = $a->can('numify') ? $a->numify() : "$a" if defined $a && ref($a);
- $p = $p->can('numify') ? $p->numify() : "$p" if defined $p && ref($p);
+ my $self = shift;
+ my $selfref = ref($self);
+ my $class = $selfref || $self;
- # now pick $a or $p, but only if we have got "arguments"
- if (!defined $a) {
- foreach ($self, @args) {
- # take the defined one, or if both defined, the one that is smaller
- $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
- }
- }
- if (!defined $p) {
- # even if $a is defined, take $p, to signal error for both defined
- foreach ($self, @args) {
- # take the defined one, or if both defined, the one that is bigger
- # -2 > -3, and 3 > 2
- $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
+ {
+ no strict 'refs';
+ if (${"${class}::_trap_nan"}) {
+ Carp::croak("Tried to create NaN in $class->bnan()");
}
}
- # if still none defined, use globals (#2)
- $a = ${"$class\::accuracy"} unless defined $a;
- $p = ${"$class\::precision"} unless defined $p;
+ $self->import() if $IMPORT == 0; # make require work
- # A == 0 is useless, so undef it to signal no rounding
- $a = undef if defined $a && $a == 0;
+ # Don't modify constant (read-only) objects.
- # no rounding today?
- return ($self) unless defined $a || defined $p; # early out
+ return if $selfref && $self->modify('bnan');
- # set A and set P is an fatal error
- return ($self->bnan()) if defined $a && defined $p; # error
+ $self = bless {}, $class unless $selfref;
- $r = ${"$class\::round_mode"} unless defined $r;
- if ($r !~ /^(even|odd|[+-]inf|zero|trunc|common)$/) {
- require Carp; Carp::croak ("Unknown round mode '$r'");
+ $self -> {sign} = $nan;
+ $self -> {value} = $CALC -> _zero();
+
+ return $self;
+}
+
+sub bpi {
+ # Calculate PI to N digits. Unless upgrading is in effect, returns the
+ # result truncated to an integer, that is, always returns '3'.
+ my ($self, $n) = @_;
+ if (@_ == 1) {
+ # called like Math::BigInt::bpi(10);
+ $n = $self;
+ $self = $class;
}
+ $self = ref($self) if ref($self);
- $a = int($a) if defined $a;
- $p = int($p) if defined $p;
+ return $upgrade->new($n) if defined $upgrade;
- ($self, $a, $p, $r);
+ # hard-wired to "3"
+ $self->new(3);
}
-sub round {
- # Round $self according to given parameters, or given second argument's
- # parameters or global defaults
+sub copy {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
- # for speed reasons, _find_round_parameters is embedded here:
+ # If called as a class method, the object to copy is the next argument.
- my ($self, $a, $p, $r, @args) = @_;
- # $a accuracy, if given by caller
- # $p precision, if given by caller
- # $r round_mode, if given by caller
- # @args all 'other' arguments (0 for unary, 1 for binary ops)
+ $self = shift() unless $selfref;
- my $class = ref($self); # find out class of argument(s)
- no strict 'refs';
+ my $copy = bless {}, $class;
- # now pick $a or $p, but only if we have got "arguments"
- if (!defined $a) {
- foreach ($self, @args) {
- # take the defined one, or if both defined, the one that is smaller
- $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
- }
- }
- if (!defined $p) {
- # even if $a is defined, take $p, to signal error for both defined
- foreach ($self, @args) {
- # take the defined one, or if both defined, the one that is bigger
- # -2 > -3, and 3 > 2
- $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
- }
- }
+ $copy->{sign} = $self->{sign};
+ $copy->{value} = $CALC->_copy($self->{value});
+ $copy->{_a} = $self->{_a} if exists $self->{_a};
+ $copy->{_p} = $self->{_p} if exists $self->{_p};
- # if still none defined, use globals (#2)
- $a = ${"$class\::accuracy"} unless defined $a;
- $p = ${"$class\::precision"} unless defined $p;
+ return $copy;
+}
- # A == 0 is useless, so undef it to signal no rounding
- $a = undef if defined $a && $a == 0;
+sub as_number {
+ # An object might be asked to return itself as bigint on certain overloaded
+ # operations. This does exactly this, so that sub classes can simple inherit
+ # it or override with their own integer conversion routine.
+ $_[0]->copy();
+}
- # no rounding today?
- return $self unless defined $a || defined $p; # early out
+###############################################################################
+# Boolean methods
+###############################################################################
- # set A and set P is an fatal error
- return $self->bnan() if defined $a && defined $p;
+sub is_zero {
+ # return true if arg (BINT or num_str) is zero (array '+', '0')
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
- $r = ${"$class\::round_mode"} unless defined $r;
- if ($r !~ /^(even|odd|[+-]inf|zero|trunc|common)$/) {
- require Carp; Carp::croak ("Unknown round mode '$r'");
- }
+ return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
+ $CALC->_is_zero($x->{value});
+}
- # now round, by calling either bround or bfround:
- if (defined $a) {
- $self->bround(int($a), $r) if !defined $self->{_a} || $self->{_a} >= $a;
- } else { # both can't be undefined due to early out
- $self->bfround(int($p), $r) if !defined $self->{_p} || $self->{_p} <= $p;
+sub is_one {
+ # return true if arg (BINT or num_str) is +1, or -1 if sign is given
+ my ($class, $x, $sign) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ $sign = '+' if !defined $sign || $sign ne '-';
+
+ return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
+ $CALC->_is_one($x->{value});
+}
+
+sub is_finite {
+ my $x = shift;
+ return $x->{sign} eq '+' || $x->{sign} eq '-';
+}
+
+sub is_inf {
+ # return true if arg (BINT or num_str) is +-inf
+ my ($class, $x, $sign) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ if (defined $sign) {
+ $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf
+ $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-'
+ return $x->{sign} =~ /^$sign$/ ? 1 : 0;
}
+ $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity
+}
- # bround() or bfround() already called bnorm() if nec.
- $self;
+sub is_nan {
+ # return true if arg (BINT or num_str) is NaN
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
+
+ $x->{sign} eq $nan ? 1 : 0;
}
-sub bnorm
- {
- # (numstr or BINT) return BINT
- # Normalize number -- no-op here
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- $x;
- }
-
-sub babs
- {
- # (BINT or num_str) return BINT
- # make number absolute, or return absolute BINT from string
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- return $x if $x->modify('babs');
- # post-normalized abs for internal use (does nothing for NaN)
- $x->{sign} =~ s/^-/+/;
- $x;
- }
+sub is_positive {
+ # return true when arg (BINT or num_str) is positive (> 0)
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
-sub bsgn {
- # Signum function.
+ return 1 if $x->{sign} eq '+inf'; # +inf is positive
- my $self = shift;
+ # 0+ is neither positive nor negative
+ ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0;
+}
- return $self if $self->modify('bsgn');
+sub is_negative {
+ # return true when arg (BINT or num_str) is negative (< 0)
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
- return $self -> bone("+") if $self -> is_pos();
- return $self -> bone("-") if $self -> is_neg();
- return $self; # zero or NaN
+ $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not
}
-sub bneg
- {
- # (BINT or num_str) return BINT
- # negate number or make a negated number from string
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+sub is_odd {
+ # return true when arg (BINT or num_str) is odd, false for even
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
- return $x if $x->modify('bneg');
+ return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
+ $CALC->_is_odd($x->{value});
+}
- # for +0 do not negate (to have always normalized +0). Does nothing for 'NaN'
- $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value}));
- $x;
- }
+sub is_even {
+ # return true when arg (BINT or num_str) is even, false for odd
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
-sub bcmp
- {
- # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
- # (BINT or num_str, BINT or num_str) return cond_code
+ return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
+ $CALC->_is_even($x->{value});
+}
- # set up parameters
- my ($self,$x,$y) = (ref($_[0]),@_);
+sub is_int {
+ # return true when arg (BINT or num_str) is an integer
+ # always true for Math::BigInt, but different for Math::BigFloat objects
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y) = objectify(2,@_);
- }
+ $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't
+}
- return $upgrade->bcmp($x,$y) if defined $upgrade &&
- ((!$x->isa($self)) || (!$y->isa($self)));
+###############################################################################
+# Comparison methods
+###############################################################################
- if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
- {
- # handle +-inf and NaN
- return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
- return +1 if $x->{sign} eq '+inf';
- return -1 if $x->{sign} eq '-inf';
- return -1 if $y->{sign} eq '+inf';
- return +1;
- }
- # check sign for speed first
- return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
- return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
-
- # have same sign, so compare absolute values. Don't make tests for zero
- # here because it's actually slower than testing in Calc (especially w/ Pari
- # et al)
-
- # post-normalized compare for internal use (honors signs)
- if ($x->{sign} eq '+')
- {
- # $x and $y both > 0
- return $CALC->_acmp($x->{value},$y->{value});
- }
+sub bcmp {
+ # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
+ # (BINT or num_str, BINT or num_str) return cond_code
- # $x && $y both < 0
- $CALC->_acmp($y->{value},$x->{value}); # swapped acmp (lib returns 0,1,-1)
- }
+ # set up parameters
+ my ($class, $x, $y) = ref($_[0]) && ref($_[0]) eq ref($_[1])
+ ? (ref($_[0]), @_)
+ : objectify(2, @_);
-sub bacmp
- {
- # Compares 2 values, ignoring their signs.
- # Returns one of undef, <0, =0, >0. (suitable for sort)
- # (BINT, BINT) return cond_code
+ return $upgrade->bcmp($x, $y) if defined $upgrade &&
+ ((!$x->isa($class)) || (!$y->isa($class)));
- # set up parameters
- my ($self,$x,$y) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y) = objectify(2,@_);
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) {
+ # handle +-inf and NaN
+ return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+ return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
+ return +1 if $x->{sign} eq '+inf';
+ return -1 if $x->{sign} eq '-inf';
+ return -1 if $y->{sign} eq '+inf';
+ return +1;
}
+ # check sign for speed first
+ return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
+ return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
- return $upgrade->bacmp($x,$y) if defined $upgrade &&
- ((!$x->isa($self)) || (!$y->isa($self)));
+ # have same sign, so compare absolute values. Don't make tests for zero
+ # here because it's actually slower than testing in Calc (especially w/ Pari
+ # et al)
- if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
- {
- # handle +-inf and NaN
- return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
- return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
- return -1;
- }
- $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1
- }
-
-sub badd
- {
- # add second arg (BINT or string) to first (BINT) (modifies first)
- # return result as BINT
-
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
+ # post-normalized compare for internal use (honors signs)
+ if ($x->{sign} eq '+') {
+ # $x and $y both > 0
+ return $CALC->_acmp($x->{value}, $y->{value});
}
- return $x if $x->modify('badd');
- return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade &&
- ((!$x->isa($self)) || (!$y->isa($self)));
+ # $x && $y both < 0
+ $CALC->_acmp($y->{value}, $x->{value}); # swapped acmp (lib returns 0, 1, -1)
+}
- $r[3] = $y; # no push!
- # inf and NaN handling
- if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
- {
- # NaN first
- return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- # inf handling
- if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
- {
- # +inf++inf or -inf+-inf => same, rest is NaN
- return $x if $x->{sign} eq $y->{sign};
- return $x->bnan();
- }
- # +-inf + something => +inf
- # something +-inf => +-inf
- $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
- return $x;
- }
+sub bacmp {
+ # Compares 2 values, ignoring their signs.
+ # Returns one of undef, <0, =0, >0. (suitable for sort)
+ # (BINT, BINT) return cond_code
- my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
+ # set up parameters
+ my ($class, $x, $y) = ref($_[0]) && ref($_[0]) eq ref($_[1])
+ ? (ref($_[0]), @_)
+ : objectify(2, @_);
- if ($sx eq $sy)
- {
- $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add
- }
- else
- {
- my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare
- if ($a > 0)
- {
- $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap
- $x->{sign} = $sy;
- }
- elsif ($a == 0)
- {
- # speedup, if equal, set result to 0
- $x->{value} = $CALC->_zero();
- $x->{sign} = '+';
- }
- else # a < 0
- {
- $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
- }
- }
- $x->round(@r);
- }
-
-sub bsub
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # subtract second arg from first, modify first
-
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
-
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
+ return $upgrade->bacmp($x, $y) if defined $upgrade &&
+ ((!$x->isa($class)) || (!$y->isa($class)));
+
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) {
+ # handle +-inf and NaN
+ return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+ return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
+ return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
+ return -1;
}
+ $CALC->_acmp($x->{value}, $y->{value}); # lib does only 0, 1, -1
+}
- return $x if $x->modify('bsub');
+sub beq {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
- return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade &&
- ((!$x->isa($self)) || (!$y->isa($self)));
+ Carp::croak 'beq() is an instance method, not a class method' unless $selfref;
+ Carp::croak 'Wrong number of arguments for beq()' unless @_ == 1;
- return $x->round(@r) if $y->is_zero();
+ my $cmp = $self -> bcmp(shift);
+ return defined($cmp) && ! $cmp;
+}
- # To correctly handle the lone special case $x->bsub($x), we note the sign
- # of $x, then flip the sign from $y, and if the sign of $x did change, too,
- # then we caught the special case:
- my $xsign = $x->{sign};
- $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
- if ($xsign ne $x->{sign})
- {
- # special case of $x->bsub($x) results in 0
- return $x->bzero(@r) if $xsign =~ /^[+-]$/;
- return $x->bnan(); # NaN, -inf, +inf
- }
- $x->badd($y,@r); # badd does not leave internal zeros
- $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
- $x; # already rounded by badd() or no round nec.
- }
-
-sub binc
- {
- # increment arg by one
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x if $x->modify('binc');
-
- if ($x->{sign} eq '+')
- {
- $x->{value} = $CALC->_inc($x->{value});
- return $x->round($a,$p,$r);
- }
- elsif ($x->{sign} eq '-')
- {
- $x->{value} = $CALC->_dec($x->{value});
- $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
- return $x->round($a,$p,$r);
- }
- # inf, nan handling etc
- $x->badd($self->bone(),$a,$p,$r); # badd does round
- }
+sub bne {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
-sub bdec
- {
- # decrement arg by one
- my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x if $x->modify('bdec');
+ Carp::croak 'bne() is an instance method, not a class method' unless $selfref;
+ Carp::croak 'Wrong number of arguments for bne()' unless @_ == 1;
- if ($x->{sign} eq '-')
- {
- # x already < 0
- $x->{value} = $CALC->_inc($x->{value});
- }
- else
- {
- return $x->badd($self->bone('-'),@r)
- unless $x->{sign} eq '+'; # inf or NaN
- # >= 0
- if ($CALC->_is_zero($x->{value}))
- {
- # == 0
- $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1
- }
- else
- {
- # > 0
- $x->{value} = $CALC->_dec($x->{value});
- }
- }
- $x->round(@r);
- }
-
-sub blog
- {
- # Return the logarithm of the operand. If a second operand is defined, that
- # value is used as the base, otherwise the base is assumed to be Euler's
- # constant.
-
- # Don't objectify the base, since an undefined base, as in $x->blog() or
- # $x->blog(undef) signals that the base is Euler's number.
-
- # set up parameters
- my ($self,$x,$base,@r) = (undef,@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
- ($self,$x,$base,@r) = objectify(1,@_);
- }
-
- return $x if $x->modify('blog');
-
- # Handle all exception cases and all trivial cases. I have used Wolfram Alpha
- # (http://www.wolframalpha.com) as the reference for these cases.
-
- return $x -> bnan() if $x -> is_nan();
-
- if (defined $base) {
- $base = $self -> new($base) unless ref $base;
- if ($base -> is_nan() || $base -> is_one()) {
- return $x -> bnan();
- } elsif ($base -> is_inf() || $base -> is_zero()) {
- return $x -> bnan() if $x -> is_inf() || $x -> is_zero();
- return $x -> bzero();
- } elsif ($base -> is_negative()) { # -inf < base < 0
- return $x -> bzero() if $x -> is_one(); # x = 1
- return $x -> bone() if $x == $base; # x = base
- return $x -> bnan(); # otherwise
- }
- return $x -> bone() if $x == $base; # 0 < base && 0 < x < inf
- }
-
- # We now know that the base is either undefined or >= 2 and finite.
-
- return $x -> binf('+') if $x -> is_inf(); # x = +/-inf
- return $x -> bnan() if $x -> is_neg(); # -inf < x < 0
- return $x -> bzero() if $x -> is_one(); # x = 1
- return $x -> binf('-') if $x -> is_zero(); # x = 0
-
- # At this point we are done handling all exception cases and trivial cases.
-
- return $upgrade -> blog($upgrade -> new($x), $base, @r) if defined $upgrade;
-
- # fix for bug #24969:
- # the default base is e (Euler's number) which is not an integer
- if (!defined $base)
- {
- require Math::BigFloat;
- my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int();
- # modify $x in place
- $x->{value} = $u->{value};
- $x->{sign} = $u->{sign};
- return $x;
- }
+ my $cmp = $self -> bcmp(shift);
+ return defined($cmp) && ! $cmp ? '' : 1;
+}
- my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value});
- return $x->bnan() unless defined $rc; # not possible to take log?
- $x->{value} = $rc;
- $x->round(@r);
- }
+sub blt {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
-sub bnok
- {
- # Calculate n over k (binomial coefficient or "choose" function) as integer.
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ Carp::croak 'blt() is an instance method, not a class method' unless $selfref;
+ Carp::croak 'Wrong number of arguments for blt()' unless @_ == 1;
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
- }
+ my $cmp = $self -> bcmp(shift);
+ return defined($cmp) && $cmp < 0;
+}
- return $x if $x->modify('bnok');
- return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN';
- return $x->binf() if $x->{sign} eq '+inf';
+sub ble {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
- # k > n or k < 0 => 0
- my $cmp = $x->bacmp($y);
- return $x->bzero() if $cmp < 0 || $y->{sign} =~ /^-/;
- # k == n => 1
- return $x->bone(@r) if $cmp == 0;
+ Carp::croak 'ble() is an instance method, not a class method' unless $selfref;
+ Carp::croak 'Wrong number of arguments for ble()' unless @_ == 1;
- if ($CALC->can('_nok'))
- {
- $x->{value} = $CALC->_nok($x->{value},$y->{value});
- }
- else
- {
- # ( 7 ) 7! 1*2*3*4 * 5*6*7 5 * 6 * 7 6 7
- # ( - ) = --------- = --------------- = --------- = 5 * - * -
- # ( 3 ) (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3 2 3
-
- if (!$y->is_zero())
- {
- my $z = $x - $y;
- $z->binc();
- my $r = $z->copy(); $z->binc();
- my $d = $self->new(2);
- while ($z->bacmp($x) <= 0) # f <= x ?
- {
- $r->bmul($z); $r->bdiv($d);
- $z->binc(); $d->binc();
- }
- $x->{value} = $r->{value}; $x->{sign} = '+';
- }
- else { $x->bone(); }
- }
- $x->round(@r);
- }
-
-sub bexp
- {
- # Calculate e ** $x (Euler's number to the power of X), truncated to
- # an integer value.
- my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x if $x->modify('bexp');
-
- # inf, -inf, NaN, <0 => NaN
- return $x->bnan() if $x->{sign} eq 'NaN';
- return $x->bone() if $x->is_zero();
- return $x if $x->{sign} eq '+inf';
- return $x->bzero() if $x->{sign} eq '-inf';
-
- my $u;
- {
- # run through Math::BigFloat unless told otherwise
- require Math::BigFloat unless defined $upgrade;
- local $upgrade = 'Math::BigFloat' unless defined $upgrade;
- # calculate result, truncate it to integer
- $u = $upgrade->bexp($upgrade->new($x),@r);
- }
-
- if (!defined $upgrade)
- {
- $u = $u->as_int();
- # modify $x in place
- $x->{value} = $u->{value};
- $x->round(@r);
- }
- else { $x = $u; }
- }
+ my $cmp = $self -> bcmp(shift);
+ return defined($cmp) && $cmp <= 0;
+}
-sub blcm
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does not modify arguments, but returns new object
- # Lowest Common Multiple
+sub bgt {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
- my $y = shift; my ($x);
- if (ref($y))
- {
- $x = $y->copy();
- }
- else
- {
- $x = $class->new($y);
- }
- my $self = ref($x);
- while (@_)
- {
- my $y = shift; $y = $self->new($y) if !ref ($y);
- $x = __lcm($x,$y);
- }
- $x;
- }
+ Carp::croak 'bgt() is an instance method, not a class method' unless $selfref;
+ Carp::croak 'Wrong number of arguments for bgt()' unless @_ == 1;
-sub bgcd
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does not modify arguments, but returns new object
- # GCD -- Euclid's algorithm, variant C (Knuth Vol 3, pg 341 ff)
+ my $cmp = $self -> bcmp(shift);
+ return defined($cmp) && $cmp > 0;
+}
- my $y = shift;
- $y = $class->new($y) if !ref($y);
- my $self = ref($y);
- my $x = $y->copy()->babs(); # keep arguments
- return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
+sub bge {
+ my $self = shift;
+ my $selfref = ref $self;
+ my $class = $selfref || $self;
- while (@_)
- {
- $y = shift; $y = $self->new($y) if !ref($y);
- return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
- $x->{value} = $CALC->_gcd($x->{value},$y->{value});
- last if $CALC->_is_one($x->{value});
- }
- $x;
- }
+ Carp::croak 'bge() is an instance method, not a class method'
+ unless $selfref;
+ Carp::croak 'Wrong number of arguments for bge()' unless @_ == 1;
-sub bnot
- {
- # (num_str or BINT) return BINT
- # represent ~x as twos-complement number
- # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+ my $cmp = $self -> bcmp(shift);
+ return defined($cmp) && $cmp >= 0;
+}
- return $x if $x->modify('bnot');
- $x->binc()->bneg(); # binc already does round
- }
+###############################################################################
+# Arithmetic methods
+###############################################################################
-##############################################################################
-# is_foo test routines
-# we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+sub bneg {
+ # (BINT or num_str) return BINT
+ # negate number or make a negated number from string
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
-sub is_zero
- {
- # return true if arg (BINT or num_str) is zero (array '+', '0')
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ return $x if $x->modify('bneg');
- return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
- $CALC->_is_zero($x->{value});
- }
+ # for +0 do not negate (to have always normalized +0). Does nothing for 'NaN'
+ $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value}));
+ $x;
+}
-sub is_nan
- {
- # return true if arg (BINT or num_str) is NaN
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+sub babs {
+ # (BINT or num_str) return BINT
+ # make number absolute, or return absolute BINT from string
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
- $x->{sign} eq $nan ? 1 : 0;
- }
+ return $x if $x->modify('babs');
+ # post-normalized abs for internal use (does nothing for NaN)
+ $x->{sign} =~ s/^-/+/;
+ $x;
+}
-sub is_inf
- {
- # return true if arg (BINT or num_str) is +-inf
- my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+sub bsgn {
+ # Signum function.
- if (defined $sign)
- {
- $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf
- $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-'
- return $x->{sign} =~ /^$sign$/ ? 1 : 0;
- }
- $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity
- }
+ my $self = shift;
+
+ return $self if $self->modify('bsgn');
-sub is_one
- {
- # return true if arg (BINT or num_str) is +1, or -1 if sign is given
- my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+ return $self -> bone("+") if $self -> is_pos();
+ return $self -> bone("-") if $self -> is_neg();
+ return $self; # zero or NaN
+}
+
+sub bnorm {
+ # (numstr or BINT) return BINT
+ # Normalize number -- no-op here
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
+ $x;
+}
+
+sub binc {
+ # increment arg by one
+ my ($class, $x, $a, $p, $r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
+ return $x if $x->modify('binc');
+
+ if ($x->{sign} eq '+') {
+ $x->{value} = $CALC->_inc($x->{value});
+ return $x->round($a, $p, $r);
+ } elsif ($x->{sign} eq '-') {
+ $x->{value} = $CALC->_dec($x->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+ return $x->round($a, $p, $r);
+ }
+ # inf, nan handling etc
+ $x->badd($class->bone(), $a, $p, $r); # badd does round
+}
- $sign = '+' if !defined $sign || $sign ne '-';
+sub bdec {
+ # decrement arg by one
+ my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
+ return $x if $x->modify('bdec');
- return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
- $CALC->_is_one($x->{value});
- }
+ if ($x->{sign} eq '-') {
+ # x already < 0
+ $x->{value} = $CALC->_inc($x->{value});
+ } else {
+ return $x->badd($class->bone('-'), @r)
+ unless $x->{sign} eq '+'; # inf or NaN
+ # >= 0
+ if ($CALC->_is_zero($x->{value})) {
+ # == 0
+ $x->{value} = $CALC->_one();
+ $x->{sign} = '-'; # 0 => -1
+ } else {
+ # > 0
+ $x->{value} = $CALC->_dec($x->{value});
+ }
+ }
+ $x->round(@r);
+}
+
+#sub bstrcmp {
+# my $self = shift;
+# my $selfref = ref $self;
+# my $class = $selfref || $self;
+#
+# Carp::croak 'bstrcmp() is an instance method, not a class method'
+# unless $selfref;
+# Carp::croak 'Wrong number of arguments for bstrcmp()' unless @_ == 1;
+#
+# return $self -> bstr() CORE::cmp shift;
+#}
+#
+#sub bstreq {
+# my $self = shift;
+# my $selfref = ref $self;
+# my $class = $selfref || $self;
+#
+# Carp::croak 'bstreq() is an instance method, not a class method'
+# unless $selfref;
+# Carp::croak 'Wrong number of arguments for bstreq()' unless @_ == 1;
+#
+# my $cmp = $self -> bstrcmp(shift);
+# return defined($cmp) && ! $cmp;
+#}
+#
+#sub bstrne {
+# my $self = shift;
+# my $selfref = ref $self;
+# my $class = $selfref || $self;
+#
+# Carp::croak 'bstrne() is an instance method, not a class method'
+# unless $selfref;
+# Carp::croak 'Wrong number of arguments for bstrne()' unless @_ == 1;
+#
+# my $cmp = $self -> bstrcmp(shift);
+# return defined($cmp) && ! $cmp ? '' : 1;
+#}
+#
+#sub bstrlt {
+# my $self = shift;
+# my $selfref = ref $self;
+# my $class = $selfref || $self;
+#
+# Carp::croak 'bstrlt() is an instance method, not a class method'
+# unless $selfref;
+# Carp::croak 'Wrong number of arguments for bstrlt()' unless @_ == 1;
+#
+# my $cmp = $self -> bstrcmp(shift);
+# return defined($cmp) && $cmp < 0;
+#}
+#
+#sub bstrle {
+# my $self = shift;
+# my $selfref = ref $self;
+# my $class = $selfref || $self;
+#
+# Carp::croak 'bstrle() is an instance method, not a class method'
+# unless $selfref;
+# Carp::croak 'Wrong number of arguments for bstrle()' unless @_ == 1;
+#
+# my $cmp = $self -> bstrcmp(shift);
+# return defined($cmp) && $cmp <= 0;
+#}
+#
+#sub bstrgt {
+# my $self = shift;
+# my $selfref = ref $self;
+# my $class = $selfref || $self;
+#
+# Carp::croak 'bstrgt() is an instance method, not a class method'
+# unless $selfref;
+# Carp::croak 'Wrong number of arguments for bstrgt()' unless @_ == 1;
+#
+# my $cmp = $self -> bstrcmp(shift);
+# return defined($cmp) && $cmp > 0;
+#}
+#
+#sub bstrge {
+# my $self = shift;
+# my $selfref = ref $self;
+# my $class = $selfref || $self;
+#
+# Carp::croak 'bstrge() is an instance method, not a class method'
+# unless $selfref;
+# Carp::croak 'Wrong number of arguments for bstrge()' unless @_ == 1;
+#
+# my $cmp = $self -> bstrcmp(shift);
+# return defined($cmp) && $cmp >= 0;
+#}
-sub is_odd
- {
- # return true when arg (BINT or num_str) is odd, false for even
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+sub badd {
+ # add second arg (BINT or string) to first (BINT) (modifies first)
+ # return result as BINT
- return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
- $CALC->_is_odd($x->{value});
- }
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
+ }
+
+ return $x if $x->modify('badd');
+ return $upgrade->badd($upgrade->new($x), $upgrade->new($y), @r) if defined $upgrade &&
+ ((!$x->isa($class)) || (!$y->isa($class)));
+
+ $r[3] = $y; # no push!
+ # inf and NaN handling
+ if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) {
+ # NaN first
+ return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+ # inf handling
+ if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) {
+ # +inf++inf or -inf+-inf => same, rest is NaN
+ return $x if $x->{sign} eq $y->{sign};
+ return $x->bnan();
+ }
+ # +-inf + something => +inf
+ # something +-inf => +-inf
+ $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
+ return $x;
+ }
-sub is_even
- {
- # return true when arg (BINT or num_str) is even, false for odd
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ my ($sx, $sy) = ($x->{sign}, $y->{sign}); # get signs
- return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
- $CALC->_is_even($x->{value});
- }
+ if ($sx eq $sy) {
+ $x->{value} = $CALC->_add($x->{value}, $y->{value}); # same sign, abs add
+ } else {
+ my $a = $CALC->_acmp ($y->{value}, $x->{value}); # absolute compare
+ if ($a > 0) {
+ $x->{value} = $CALC->_sub($y->{value}, $x->{value}, 1); # abs sub w/ swap
+ $x->{sign} = $sy;
+ } elsif ($a == 0) {
+ # speedup, if equal, set result to 0
+ $x->{value} = $CALC->_zero();
+ $x->{sign} = '+';
+ } else # a < 0
+ {
+ $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
+ }
+ }
+ $x->round(@r);
+}
-sub is_positive
- {
- # return true when arg (BINT or num_str) is positive (> 0)
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+sub bsub {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # subtract second arg from first, modify first
- return 1 if $x->{sign} eq '+inf'; # +inf is positive
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
- # 0+ is neither positive nor negative
- ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0;
- }
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
+ }
-sub is_negative
- {
- # return true when arg (BINT or num_str) is negative (< 0)
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ return $x if $x -> modify('bsub');
- $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not
- }
+ return $upgrade -> new($x) -> bsub($upgrade -> new($y), @r)
+ if defined $upgrade && (!$x -> isa($class) || !$y -> isa($class));
-sub is_int
- {
- # return true when arg (BINT or num_str) is an integer
- # always true for BigInt, but different for BigFloats
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ return $x -> round(@r) if $y -> is_zero();
- $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't
- }
+ # To correctly handle the lone special case $x -> bsub($x), we note the
+ # sign of $x, then flip the sign from $y, and if the sign of $x did change,
+ # too, then we caught the special case:
-###############################################################################
+ my $xsign = $x -> {sign};
+ $y -> {sign} =~ tr/+-/-+/; # does nothing for NaN
+ if ($xsign ne $x -> {sign}) {
+ # special case of $x -> bsub($x) results in 0
+ return $x -> bzero(@r) if $xsign =~ /^[+-]$/;
+ return $x -> bnan(); # NaN, -inf, +inf
+ }
+ $x -> badd($y, @r); # badd does not leave internal zeros
+ $y -> {sign} =~ tr/+-/-+/; # refix $y (does nothing for NaN)
+ $x; # already rounded by badd() or no rounding
+}
-sub bmul
- {
- # multiply the first number by the second number
- # (BINT or num_str, BINT or num_str) return BINT
+sub bmul {
+ # multiply the first number by the second number
+ # (BINT or num_str, BINT or num_str) return BINT
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
}
- return $x if $x->modify('bmul');
+ return $x if $x->modify('bmul');
- return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+ return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- # inf handling
- if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
- {
- return $x->bnan() if $x->is_zero() || $y->is_zero();
- # result will always be +-inf:
- # +inf * +/+inf => +inf, -inf * -/-inf => +inf
- # +inf * -/-inf => -inf, -inf * +/+inf => -inf
- return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
- return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
- return $x->binf('-');
+ # inf handling
+ if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) {
+ return $x->bnan() if $x->is_zero() || $y->is_zero();
+ # result will always be +-inf:
+ # +inf * +/+inf => +inf, -inf * -/-inf => +inf
+ # +inf * -/-inf => -inf, -inf * +/+inf => -inf
+ return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
+ return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
+ return $x->binf('-');
}
- return $upgrade->bmul($x,$upgrade->new($y),@r)
- if defined $upgrade && !$y->isa($self);
+ return $upgrade->bmul($x, $upgrade->new($y), @r)
+ if defined $upgrade && !$y->isa($class);
- $r[3] = $y; # no push here
+ $r[3] = $y; # no push here
- $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
+ $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
- $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
- $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
+ $x->{value} = $CALC->_mul($x->{value}, $y->{value}); # do actual math
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
- $x->round(@r);
- }
+ $x->round(@r);
+}
-sub bmuladd
- {
- # multiply two numbers and then add the third to the result
- # (BINT or num_str, BINT or num_str, BINT or num_str) return BINT
+sub bmuladd {
+ # multiply two numbers and then add the third to the result
+ # (BINT or num_str, BINT or num_str, BINT or num_str) return BINT
- # set up parameters
- my ($self,$x,$y,$z,@r) = objectify(3,@_);
+ # set up parameters
+ my ($class, $x, $y, $z, @r) = objectify(3, @_);
- return $x if $x->modify('bmuladd');
+ return $x if $x->modify('bmuladd');
- return $x->bnan() if ($x->{sign} eq $nan) ||
- ($y->{sign} eq $nan) ||
- ($z->{sign} eq $nan);
+ return $x->bnan() if (($x->{sign} eq $nan) ||
+ ($y->{sign} eq $nan) ||
+ ($z->{sign} eq $nan));
- # inf handling of x and y
- if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
- {
- return $x->bnan() if $x->is_zero() || $y->is_zero();
- # result will always be +-inf:
- # +inf * +/+inf => +inf, -inf * -/-inf => +inf
- # +inf * -/-inf => -inf, -inf * +/+inf => -inf
- return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
- return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
- return $x->binf('-');
- }
- # inf handling x*y and z
- if (($z->{sign} =~ /^[+-]inf$/))
- {
- # something +-inf => +-inf
- $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/;
+ # inf handling of x and y
+ if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) {
+ return $x->bnan() if $x->is_zero() || $y->is_zero();
+ # result will always be +-inf:
+ # +inf * +/+inf => +inf, -inf * -/-inf => +inf
+ # +inf * -/-inf => -inf, -inf * +/+inf => -inf
+ return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
+ return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
+ return $x->binf('-');
+ }
+ # inf handling x*y and z
+ if (($z->{sign} =~ /^[+-]inf$/)) {
+ # something +-inf => +-inf
+ $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/;
}
- return $upgrade->bmuladd($x,$upgrade->new($y),$upgrade->new($z),@r)
- if defined $upgrade && (!$y->isa($self) || !$z->isa($self) || !$x->isa($self));
+ return $upgrade->bmuladd($x, $upgrade->new($y), $upgrade->new($z), @r)
+ if defined $upgrade && (!$y->isa($class) || !$z->isa($class) || !$x->isa($class));
- # TODO: what if $y and $z have A or P set?
- $r[3] = $z; # no push here
+ # TODO: what if $y and $z have A or P set?
+ $r[3] = $z; # no push here
- $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
+ $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
- $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
- $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
+ $x->{value} = $CALC->_mul($x->{value}, $y->{value}); # do actual math
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
- my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); # get signs
+ my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); # get signs
- if ($sx eq $sz)
- {
- $x->{value} = $CALC->_add($x->{value},$z->{value}); # same sign, abs add
+ if ($sx eq $sz) {
+ $x->{value} = $CALC->_add($x->{value}, $z->{value}); # same sign, abs add
+ } else {
+ my $a = $CALC->_acmp ($z->{value}, $x->{value}); # absolute compare
+ if ($a > 0) {
+ $x->{value} = $CALC->_sub($z->{value}, $x->{value}, 1); # abs sub w/ swap
+ $x->{sign} = $sz;
+ } elsif ($a == 0) {
+ # speedup, if equal, set result to 0
+ $x->{value} = $CALC->_zero();
+ $x->{sign} = '+';
+ } else # a < 0
+ {
+ $x->{value} = $CALC->_sub($x->{value}, $z->{value}); # abs sub
+ }
}
- else
- {
- my $a = $CALC->_acmp ($z->{value},$x->{value}); # absolute compare
- if ($a > 0)
- {
- $x->{value} = $CALC->_sub($z->{value},$x->{value},1); # abs sub w/ swap
- $x->{sign} = $sz;
- }
- elsif ($a == 0)
- {
- # speedup, if equal, set result to 0
- $x->{value} = $CALC->_zero();
- $x->{sign} = '+';
- }
- else # a < 0
- {
- $x->{value} = $CALC->_sub($x->{value}, $z->{value}); # abs sub
- }
- }
- $x->round(@r);
- }
-
-sub bdiv
- {
-
- # This does floored division, where the quotient is floored toward negative
- # infinity and the remainder has the same sign as the divisor.
+ $x->round(@r);
+}
+
+sub bdiv {
+ # This does floored division, where the quotient is floored, i.e., rounded
+ # towards negative infinity. As a consequence, the remainder has the same
+ # sign as the divisor.
# Set up parameters.
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
# objectify() is costly, so avoid it if we can.
if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
- ($self,$x,$y,@r) = objectify(2,@_);
+ ($class, $x, $y, @r) = objectify(2, @_);
}
- return $x if $x->modify('bdiv');
+ return $x if $x -> modify('bdiv');
my $wantarray = wantarray; # call only once
@@ -1732,7 +1705,7 @@ sub bdiv
# modulo/remainder.
if ($x -> is_nan() || $y -> is_nan()) {
- return $wantarray ? ($x -> bnan(), $self -> bnan()) : $x -> bnan();
+ return $wantarray ? ($x -> bnan(), $class -> bnan()) : $x -> bnan();
}
# Divide by zero and modulo zero.
@@ -1746,23 +1719,23 @@ sub bdiv
# get z - x = 0 or z = x. This is also what earlier versions did, except
# that 0 % 0 returned NaN.
#
- # inf / 0 = inf inf % 0 = inf
- # 5 / 0 = inf 5 % 0 = 5
- # 0 / 0 = NaN 0 % 0 = 0 (before: NaN)
- # -5 / 0 = -inf -5 % 0 = -5
- # -inf / 0 = -inf -inf % 0 = -inf
+ # inf / 0 = inf inf % 0 = inf
+ # 5 / 0 = inf 5 % 0 = 5
+ # 0 / 0 = NaN 0 % 0 = 0
+ # -5 / 0 = -inf -5 % 0 = -5
+ # -inf / 0 = -inf -inf % 0 = -inf
if ($y -> is_zero()) {
- my ($quo, $rem);
+ my $rem;
if ($wantarray) {
- $rem = $x -> copy();
- }
+ $rem = $x -> copy();
+ }
if ($x -> is_zero()) {
- $quo = $x -> bnan();
+ $x -> bnan();
} else {
- $quo = $x -> binf($x -> {sign});
+ $x -> binf($x -> {sign});
}
- return $wantarray ? ($quo, $rem) : $quo;
+ return $wantarray ? ($x, $rem) : $x;
}
# Numerator (dividend) is +/-inf, and denominator is finite and non-zero.
@@ -1770,25 +1743,25 @@ sub bdiv
# below we return the same as core Perl.
#
# inf / -inf = NaN inf % -inf = NaN
- # inf / -5 = -inf inf % -5 = NaN (before: 0)
- # inf / 5 = inf inf % 5 = NaN (before: 0)
+ # inf / -5 = -inf inf % -5 = NaN
+ # inf / 5 = inf inf % 5 = NaN
# inf / inf = NaN inf % inf = NaN
#
# -inf / -inf = NaN -inf % -inf = NaN
- # -inf / -5 = inf -inf % -5 = NaN (before: 0)
- # -inf / 5 = -inf -inf % 5 = NaN (before: 0)
+ # -inf / -5 = inf -inf % -5 = NaN
+ # -inf / 5 = -inf -inf % 5 = NaN
# -inf / inf = NaN -inf % inf = NaN
if ($x -> is_inf()) {
- my ($quo, $rem);
- $rem = $self -> bnan() if $wantarray;
+ my $rem;
+ $rem = $class -> bnan() if $wantarray;
if ($y -> is_inf()) {
- $quo = $x -> bnan();
+ $x -> bnan();
} else {
my $sign = $x -> bcmp(0) == $y -> bcmp(0) ? '+' : '-';
- $quo = $x -> binf($sign);
- }
- return $wantarray ? ($quo, $rem) : $quo;
+ $x -> binf($sign);
+ }
+ return $wantarray ? ($x, $rem) : $x;
}
# Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf
@@ -1796,112 +1769,249 @@ sub bdiv
# the same as core Perl, which does floored division, so for consistency we
# also do floored division in the division cases (in the left column).
#
- # -5 / inf = -1 (before: 0) -5 % inf = inf (before: -5)
+ # -5 / inf = -1 -5 % inf = inf
# 0 / inf = 0 0 % inf = 0
# 5 / inf = 0 5 % inf = 5
#
# -5 / -inf = 0 -5 % -inf = -5
# 0 / -inf = 0 0 % -inf = 0
- # 5 / -inf = -1 (before: 0) 5 % -inf = -inf (before: 5)
+ # 5 / -inf = -1 5 % -inf = -inf
if ($y -> is_inf()) {
- my ($quo, $rem);
+ my $rem;
if ($x -> is_zero() || $x -> bcmp(0) == $y -> bcmp(0)) {
$rem = $x -> copy() if $wantarray;
- $quo = $x -> bzero();
+ $x -> bzero();
} else {
- $rem = $self -> binf($y -> {sign}) if $wantarray;
- $quo = $x -> bone('-');
+ $rem = $class -> binf($y -> {sign}) if $wantarray;
+ $x -> bone('-');
}
- return $wantarray ? ($quo, $rem) : $quo;
- }
+ return $wantarray ? ($x, $rem) : $x;
+ }
- # At this point, both the numerator and denominator are finite numbers, and
- # the denominator (divisor) is non-zero.
+ # At this point, both the numerator and denominator are finite numbers, and
+ # the denominator (divisor) is non-zero.
- return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r)
- if defined $upgrade;
+ return $upgrade -> bdiv($upgrade -> new($x), $upgrade -> new($y), @r)
+ if defined $upgrade;
- $r[3] = $y; # no push!
+ $r[3] = $y; # no push!
# Inialize remainder.
- my $rem = $self->bzero();
+ my $rem = $class -> bzero();
- # Are both operands the same object, i.e., like $x -> bdiv($x)?
- # If so, flipping the sign of $y also flips the sign of $x.
+ # Are both operands the same object, i.e., like $x -> bdiv($x)? If so,
+ # flipping the sign of $y also flips the sign of $x.
- my $xsign = $x->{sign};
- my $ysign = $y->{sign};
+ my $xsign = $x -> {sign};
+ my $ysign = $y -> {sign};
- $y->{sign} =~ tr/+-/-+/; # Flip the sign of $y, and see ...
- my $same = $xsign ne $x->{sign}; # ... if that changed the sign of $x.
- $y->{sign} = $ysign; # Re-insert the original sign.
+ $y -> {sign} =~ tr/+-/-+/; # Flip the sign of $y, and see ...
+ my $same = $xsign ne $x -> {sign}; # ... if that changed the sign of $x.
+ $y -> {sign} = $ysign; # Re-insert the original sign.
if ($same) {
$x -> bone();
} else {
- ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
+ ($x -> {value}, $rem -> {value}) =
+ $CALC -> _div($x -> {value}, $y -> {value});
- if ($CALC -> _is_zero($rem->{value})) {
- if ($xsign eq $ysign || $CALC -> _is_zero($x->{value})) {
- $x->{sign} = '+';
+ if ($CALC -> _is_zero($rem -> {value})) {
+ if ($xsign eq $ysign || $CALC -> _is_zero($x -> {value})) {
+ $x -> {sign} = '+';
} else {
- $x->{sign} = '-';
+ $x -> {sign} = '-';
}
} else {
if ($xsign eq $ysign) {
- $x->{sign} = '+';
+ $x -> {sign} = '+';
} else {
if ($xsign eq '+') {
$x -> badd(1);
} else {
$x -> bsub(1);
}
- $x->{sign} = '-';
+ $x -> {sign} = '-';
}
}
}
- $x->round(@r);
+ $x -> round(@r);
if ($wantarray) {
- unless ($CALC -> _is_zero($rem->{value})) {
+ unless ($CALC -> _is_zero($rem -> {value})) {
if ($xsign ne $ysign) {
$rem = $y -> copy() -> babs() -> bsub($rem);
- }
- $rem->{sign} = $ysign;
- }
- $rem->{_a} = $x->{_a};
- $rem->{_p} = $x->{_p};
- $rem->round(@r);
- return ($x,$rem);
+ }
+ $rem -> {sign} = $ysign;
+ }
+ $rem -> {_a} = $x -> {_a};
+ $rem -> {_p} = $x -> {_p};
+ $rem -> round(@r);
+ return ($x, $rem);
}
return $x;
- }
+}
-###############################################################################
-# modulus functions
+sub btdiv {
+ # This does truncated division, where the quotient is truncted, i.e.,
+ # rounded towards zero.
+ #
+ # ($q, $r) = $x -> btdiv($y) returns $q and $r so that $q is int($x / $y)
+ # and $q * $y + $r = $x.
-sub bmod
- {
+ # Set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
- # This is the remainder after floored division, where the quotient is
- # floored toward negative infinity and the remainder has the same sign as
- # the divisor.
+ # objectify is costly, so avoid it if we can.
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
+ }
+
+ return $x if $x -> modify('btdiv');
+
+ my $wantarray = wantarray; # call only once
+
+ # At least one argument is NaN. Return NaN for both quotient and the
+ # modulo/remainder.
+
+ if ($x -> is_nan() || $y -> is_nan()) {
+ return $wantarray ? ($x -> bnan(), $class -> bnan()) : $x -> bnan();
+ }
+
+ # Divide by zero and modulo zero.
+ #
+ # Division: Use the common convention that x / 0 is inf with the same sign
+ # as x, except when x = 0, where we return NaN. This is also what earlier
+ # versions did.
+ #
+ # Modulo: In modular arithmetic, the congruence relation z = x (mod y)
+ # means that there is some integer k such that z - x = k y. If y = 0, we
+ # get z - x = 0 or z = x. This is also what earlier versions did, except
+ # that 0 % 0 returned NaN.
+ #
+ # inf / 0 = inf inf % 0 = inf
+ # 5 / 0 = inf 5 % 0 = 5
+ # 0 / 0 = NaN 0 % 0 = 0
+ # -5 / 0 = -inf -5 % 0 = -5
+ # -inf / 0 = -inf -inf % 0 = -inf
+
+ if ($y -> is_zero()) {
+ my $rem;
+ if ($wantarray) {
+ $rem = $x -> copy();
+ }
+ if ($x -> is_zero()) {
+ $x -> bnan();
+ } else {
+ $x -> binf($x -> {sign});
+ }
+ return $wantarray ? ($x, $rem) : $x;
+ }
+
+ # Numerator (dividend) is +/-inf, and denominator is finite and non-zero.
+ # The divide by zero cases are covered above. In all of the cases listed
+ # below we return the same as core Perl.
+ #
+ # inf / -inf = NaN inf % -inf = NaN
+ # inf / -5 = -inf inf % -5 = NaN
+ # inf / 5 = inf inf % 5 = NaN
+ # inf / inf = NaN inf % inf = NaN
+ #
+ # -inf / -inf = NaN -inf % -inf = NaN
+ # -inf / -5 = inf -inf % -5 = NaN
+ # -inf / 5 = -inf -inf % 5 = NaN
+ # -inf / inf = NaN -inf % inf = NaN
+
+ if ($x -> is_inf()) {
+ my $rem;
+ $rem = $class -> bnan() if $wantarray;
+ if ($y -> is_inf()) {
+ $x -> bnan();
+ } else {
+ my $sign = $x -> bcmp(0) == $y -> bcmp(0) ? '+' : '-';
+ $x -> binf($sign);
+ }
+ return $wantarray ? ($x, $rem) : $x;
+ }
+
+ # Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf
+ # are covered above. In the modulo cases (in the right column) we return
+ # the same as core Perl, which does floored division, so for consistency we
+ # also do floored division in the division cases (in the left column).
+ #
+ # -5 / inf = 0 -5 % inf = -5
+ # 0 / inf = 0 0 % inf = 0
+ # 5 / inf = 0 5 % inf = 5
+ #
+ # -5 / -inf = 0 -5 % -inf = -5
+ # 0 / -inf = 0 0 % -inf = 0
+ # 5 / -inf = 0 5 % -inf = 5
+
+ if ($y -> is_inf()) {
+ my $rem;
+ $rem = $x -> copy() if $wantarray;
+ $x -> bzero();
+ return $wantarray ? ($x, $rem) : $x;
+ }
+
+ return $upgrade -> btdiv($upgrade -> new($x), $upgrade -> new($y), @r)
+ if defined $upgrade;
+
+ $r[3] = $y; # no push!
+
+ # Inialize remainder.
+
+ my $rem = $class -> bzero();
+
+ # Are both operands the same object, i.e., like $x -> bdiv($x)? If so,
+ # flipping the sign of $y also flips the sign of $x.
+
+ my $xsign = $x -> {sign};
+ my $ysign = $y -> {sign};
+
+ $y -> {sign} =~ tr/+-/-+/; # Flip the sign of $y, and see ...
+ my $same = $xsign ne $x -> {sign}; # ... if that changed the sign of $x.
+ $y -> {sign} = $ysign; # Re-insert the original sign.
+
+ if ($same) {
+ $x -> bone();
+ } else {
+ ($x -> {value}, $rem -> {value}) =
+ $CALC -> _div($x -> {value}, $y -> {value});
+
+ $x -> {sign} = $xsign eq $ysign ? '+' : '-';
+ $x -> {sign} = '+' if $CALC -> _is_zero($x -> {value});
+ $x -> round(@r);
+ }
+
+ if (wantarray) {
+ $rem -> {sign} = $xsign;
+ $rem -> {sign} = '+' if $CALC -> _is_zero($rem -> {value});
+ $rem -> {_a} = $x -> {_a};
+ $rem -> {_p} = $x -> {_p};
+ $rem -> round(@r);
+ return ($x, $rem);
+ }
+
+ return $x;
+}
+
+sub bmod {
+ # This is the remainder after floored division.
# Set up parameters.
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
}
- return $x if $x->modify('bmod');
- $r[3] = $y; # no push!
+ return $x if $x -> modify('bmod');
+ $r[3] = $y; # no push!
# At least one argument is NaN.
@@ -1912,8 +2022,8 @@ sub bmod
# Modulo zero. See documentation for bdiv().
if ($y -> is_zero()) {
- return $x;
- }
+ return $x;
+ }
# Numerator (dividend) is +/-inf.
@@ -1933,839 +2043,1521 @@ sub bmod
# Calc new sign and in case $y == +/- 1, return $x.
- $x->{value} = $CALC->_mod($x->{value},$y->{value});
- if ($CALC -> _is_zero($x->{value}))
- {
- $x->{sign} = '+'; # do not leave -0
+ $x -> {value} = $CALC -> _mod($x -> {value}, $y -> {value});
+ if ($CALC -> _is_zero($x -> {value})) {
+ $x -> {sign} = '+'; # do not leave -0
+ } else {
+ $x -> {value} = $CALC -> _sub($y -> {value}, $x -> {value}, 1) # $y-$x
+ if ($x -> {sign} ne $y -> {sign});
+ $x -> {sign} = $y -> {sign};
}
- else
- {
- $x->{value} = $CALC->_sub($y->{value},$x->{value},1) # $y-$x
- if ($x->{sign} ne $y->{sign});
- $x->{sign} = $y->{sign};
- }
-
- $x->round(@r);
- }
-
-sub bmodinv
- {
- # Return modular multiplicative inverse:
- #
- # z is the modular inverse of x (mod y) if and only if
- #
- # x*z ≡ 1 (mod y)
- #
- # If the modulus y is larger than one, x and z are relative primes (i.e.,
- # their greatest common divisor is one).
- #
- # If no modular multiplicative inverse exists, NaN is returned.
-
- # set up parameters
- my ($self,$x,$y,@r) = (undef,@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
+
+ $x -> round(@r);
+}
+
+sub btmod {
+ # Remainder after truncated division.
+
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
+
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
}
- return $x if $x->modify('bmodinv');
+ return $x if $x -> modify('btmod');
- # Return NaN if one or both arguments is +inf, -inf, or nan.
+ # At least one argument is NaN.
- return $x->bnan() if ($y->{sign} !~ /^[+-]$/ ||
- $x->{sign} !~ /^[+-]$/);
+ if ($x -> is_nan() || $y -> is_nan()) {
+ return $x -> bnan();
+ }
- # Return NaN if $y is zero; 1 % 0 makes no sense.
+ # Modulo zero. See documentation for btdiv().
- return $x->bnan() if $y->is_zero();
+ if ($y -> is_zero()) {
+ return $x;
+ }
- # Return 0 in the trivial case. $x % 1 or $x % -1 is zero for all finite
- # integers $x.
+ # Numerator (dividend) is +/-inf.
- return $x->bzero() if ($y->is_one() ||
- $y->is_one('-'));
+ if ($x -> is_inf()) {
+ return $x -> bnan();
+ }
- # Return NaN if $x = 0, or $x modulo $y is zero. The only valid case when
- # $x = 0 is when $y = 1 or $y = -1, but that was covered above.
- #
- # Note that computing $x modulo $y here affects the value we'll feed to
- # $CALC->_modinv() below when $x and $y have opposite signs. E.g., if $x =
- # 5 and $y = 7, those two values are fed to _modinv(), but if $x = -5 and
- # $y = 7, the values fed to _modinv() are $x = 2 (= -5 % 7) and $y = 7.
- # The value if $x is affected only when $x and $y have opposite signs.
+ # Denominator (divisor) is +/-inf.
- $x->bmod($y);
- return $x->bnan() if $x->is_zero();
+ if ($y -> is_inf()) {
+ return $x;
+ }
- # Compute the modular multiplicative inverse of the absolute values. We'll
- # correct for the signs of $x and $y later. Return NaN if no GCD is found.
+ return $upgrade -> btmod($upgrade -> new($x), $upgrade -> new($y), @r)
+ if defined $upgrade;
- ($x->{value}, $x->{sign}) = $CALC->_modinv($x->{value}, $y->{value});
- return $x->bnan() if !defined $x->{value};
+ $r[3] = $y; # no push!
- # Library inconsistency workaround: _modinv() in Math::BigInt::GMP versions
- # <= 1.32 return undef rather than a "+" for the sign.
+ my $xsign = $x -> {sign};
+ my $ysign = $y -> {sign};
- $x->{sign} = '+' unless defined $x->{sign};
+ $x -> {value} = $CALC -> _mod($x -> {value}, $y -> {value});
- # When one or both arguments are negative, we have the following
- # relations. If x and y are positive:
- #
- # modinv(-x, -y) = -modinv(x, y)
- # modinv(-x, y) = y - modinv(x, y) = -modinv(x, y) (mod y)
- # modinv( x, -y) = modinv(x, y) - y = modinv(x, y) (mod -y)
+ $x -> {sign} = $xsign;
+ $x -> {sign} = '+' if $CALC -> _is_zero($x -> {value});
+ $x -> round(@r);
+ return $x;
+}
- # We must swap the sign of the result if the original $x is negative.
- # However, we must compensate for ignoring the signs when computing the
- # inverse modulo. The net effect is that we must swap the sign of the
- # result if $y is negative.
+sub bmodinv {
+ # Return modular multiplicative inverse:
+ #
+ # z is the modular inverse of x (mod y) if and only if
+ #
+ # x*z ≡ 1 (mod y)
+ #
+ # If the modulus y is larger than one, x and z are relative primes (i.e.,
+ # their greatest common divisor is one).
+ #
+ # If no modular multiplicative inverse exists, NaN is returned.
- $x -> bneg() if $y->{sign} eq '-';
+ # set up parameters
+ my ($class, $x, $y, @r) = (undef, @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
+ }
- # Compute $x modulo $y again after correcting the sign.
+ return $x if $x->modify('bmodinv');
- $x -> bmod($y) if $x->{sign} ne $y->{sign};
+ # Return NaN if one or both arguments is +inf, -inf, or nan.
- return $x;
- }
+ return $x->bnan() if ($y->{sign} !~ /^[+-]$/ ||
+ $x->{sign} !~ /^[+-]$/);
-sub bmodpow
- {
- # Modular exponentiation. Raises a very large number to a very large exponent
- # in a given very large modulus quickly, thanks to binary exponentiation.
- # Supports negative exponents.
- my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
+ # Return NaN if $y is zero; 1 % 0 makes no sense.
- return $num if $num->modify('bmodpow');
+ return $x->bnan() if $y->is_zero();
- # When the exponent 'e' is negative, use the following relation, which is
- # based on finding the multiplicative inverse 'd' of 'b' modulo 'm':
- #
- # b^(-e) (mod m) = d^e (mod m) where b*d = 1 (mod m)
+ # Return 0 in the trivial case. $x % 1 or $x % -1 is zero for all finite
+ # integers $x.
- $num->bmodinv($mod) if ($exp->{sign} eq '-');
+ return $x->bzero() if ($y->is_one() ||
+ $y->is_one('-'));
- # Check for valid input. All operands must be finite, and the modulus must be
- # non-zero.
+ # Return NaN if $x = 0, or $x modulo $y is zero. The only valid case when
+ # $x = 0 is when $y = 1 or $y = -1, but that was covered above.
+ #
+ # Note that computing $x modulo $y here affects the value we'll feed to
+ # $CALC->_modinv() below when $x and $y have opposite signs. E.g., if $x =
+ # 5 and $y = 7, those two values are fed to _modinv(), but if $x = -5 and
+ # $y = 7, the values fed to _modinv() are $x = 2 (= -5 % 7) and $y = 7.
+ # The value if $x is affected only when $x and $y have opposite signs.
- return $num->bnan() if ($num->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
- $exp->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
- $mod->{sign} =~ /NaN|inf/); # NaN, -inf, +inf
+ $x->bmod($y);
+ return $x->bnan() if $x->is_zero();
- # Modulo zero. See documentation for Math::BigInt's bmod() method.
+ # Compute the modular multiplicative inverse of the absolute values. We'll
+ # correct for the signs of $x and $y later. Return NaN if no GCD is found.
- if ($mod -> is_zero()) {
- if ($num -> is_zero()) {
- return $self -> bnan();
- } else {
- return $num -> copy();
- }
- }
+ ($x->{value}, $x->{sign}) = $CALC->_modinv($x->{value}, $y->{value});
+ return $x->bnan() if !defined $x->{value};
- # Compute 'a (mod m)', ignoring the signs on 'a' and 'm'. If the resulting
- # value is zero, the output is also zero, regardless of the signs on 'a' and
- # 'm'.
+ # Library inconsistency workaround: _modinv() in Math::BigInt::GMP versions
+ # <= 1.32 return undef rather than a "+" for the sign.
- my $value = $CALC->_modpow($num->{value}, $exp->{value}, $mod->{value});
- my $sign = '+';
+ $x->{sign} = '+' unless defined $x->{sign};
- # If the resulting value is non-zero, we have four special cases, depending
- # on the signs on 'a' and 'm'.
+ # When one or both arguments are negative, we have the following
+ # relations. If x and y are positive:
+ #
+ # modinv(-x, -y) = -modinv(x, y)
+ # modinv(-x, y) = y - modinv(x, y) = -modinv(x, y) (mod y)
+ # modinv( x, -y) = modinv(x, y) - y = modinv(x, y) (mod -y)
- unless ($CALC->_is_zero($value)) {
+ # We must swap the sign of the result if the original $x is negative.
+ # However, we must compensate for ignoring the signs when computing the
+ # inverse modulo. The net effect is that we must swap the sign of the
+ # result if $y is negative.
- # There is a negative sign on 'a' (= $num**$exp) only if the number we
- # are exponentiating ($num) is negative and the exponent ($exp) is odd.
+ $x -> bneg() if $y->{sign} eq '-';
- if ($num->{sign} eq '-' && $exp->is_odd()) {
+ # Compute $x modulo $y again after correcting the sign.
- # When both the number 'a' and the modulus 'm' have a negative sign,
- # use this relation:
- #
- # -a (mod -m) = -(a (mod m))
+ $x -> bmod($y) if $x->{sign} ne $y->{sign};
- if ($mod->{sign} eq '-') {
- $sign = '-';
- }
+ return $x;
+}
- # When only the number 'a' has a negative sign, use this relation:
- #
- # -a (mod m) = m - (a (mod m))
+sub bmodpow {
+ # Modular exponentiation. Raises a very large number to a very large exponent
+ # in a given very large modulus quickly, thanks to binary exponentiation.
+ # Supports negative exponents.
+ my ($class, $num, $exp, $mod, @r) = objectify(3, @_);
- else {
- # Use copy of $mod since _sub() modifies the first argument.
- my $mod = $CALC->_copy($mod->{value});
- $value = $CALC->_sub($mod, $value);
- $sign = '+';
- }
+ return $num if $num->modify('bmodpow');
- } else {
+ # When the exponent 'e' is negative, use the following relation, which is
+ # based on finding the multiplicative inverse 'd' of 'b' modulo 'm':
+ #
+ # b^(-e) (mod m) = d^e (mod m) where b*d = 1 (mod m)
- # When only the modulus 'm' has a negative sign, use this relation:
- #
- # a (mod -m) = (a (mod m)) - m
- # = -(m - (a (mod m)))
+ $num->bmodinv($mod) if ($exp->{sign} eq '-');
- if ($mod->{sign} eq '-') {
- # Use copy of $mod since _sub() modifies the first argument.
- my $mod = $CALC->_copy($mod->{value});
- $value = $CALC->_sub($mod, $value);
- $sign = '-';
- }
+ # Check for valid input. All operands must be finite, and the modulus must be
+ # non-zero.
- # When neither the number 'a' nor the modulus 'm' have a negative
- # sign, directly return the already computed value.
- #
- # (a (mod m))
+ return $num->bnan() if ($num->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
+ $exp->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
+ $mod->{sign} =~ /NaN|inf/); # NaN, -inf, +inf
- }
+ # Modulo zero. See documentation for Math::BigInt's bmod() method.
- }
+ if ($mod -> is_zero()) {
+ if ($num -> is_zero()) {
+ return $class -> bnan();
+ } else {
+ return $num -> copy();
+ }
+ }
- $num->{value} = $value;
- $num->{sign} = $sign;
+ # Compute 'a (mod m)', ignoring the signs on 'a' and 'm'. If the resulting
+ # value is zero, the output is also zero, regardless of the signs on 'a' and
+ # 'm'.
- return $num;
- }
+ my $value = $CALC->_modpow($num->{value}, $exp->{value}, $mod->{value});
+ my $sign = '+';
-###############################################################################
+ # If the resulting value is non-zero, we have four special cases, depending
+ # on the signs on 'a' and 'm'.
+
+ unless ($CALC->_is_zero($value)) {
+
+ # There is a negative sign on 'a' (= $num**$exp) only if the number we
+ # are exponentiating ($num) is negative and the exponent ($exp) is odd.
+
+ if ($num->{sign} eq '-' && $exp->is_odd()) {
+
+ # When both the number 'a' and the modulus 'm' have a negative sign,
+ # use this relation:
+ #
+ # -a (mod -m) = -(a (mod m))
+
+ if ($mod->{sign} eq '-') {
+ $sign = '-';
+ }
+
+ # When only the number 'a' has a negative sign, use this relation:
+ #
+ # -a (mod m) = m - (a (mod m))
+
+ else {
+ # Use copy of $mod since _sub() modifies the first argument.
+ my $mod = $CALC->_copy($mod->{value});
+ $value = $CALC->_sub($mod, $value);
+ $sign = '+';
+ }
+
+ } else {
+
+ # When only the modulus 'm' has a negative sign, use this relation:
+ #
+ # a (mod -m) = (a (mod m)) - m
+ # = -(m - (a (mod m)))
+
+ if ($mod->{sign} eq '-') {
+ # Use copy of $mod since _sub() modifies the first argument.
+ my $mod = $CALC->_copy($mod->{value});
+ $value = $CALC->_sub($mod, $value);
+ $sign = '-';
+ }
+
+ # When neither the number 'a' nor the modulus 'm' have a negative
+ # sign, directly return the already computed value.
+ #
+ # (a (mod m))
+
+ }
-sub bfac
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # compute factorial number from $x, modify $x in place
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf
- return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN
-
- $x->{value} = $CALC->_fac($x->{value});
- $x->round(@r);
- }
-
-sub bpow
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # compute power of two numbers -- stolen from Knuth Vol 2 pg 233
- # modifies first argument
-
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
}
- return $x if $x->modify('bpow');
+ $num->{value} = $value;
+ $num->{sign} = $sign;
+
+ return $num;
+}
- return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
+sub bpow {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # compute power of two numbers -- stolen from Knuth Vol 2 pg 233
+ # modifies first argument
- # inf handling
- if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
- {
- if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
- {
- # +-inf ** +-inf
- return $x->bnan();
- }
- # +-inf ** Y
- if ($x->{sign} =~ /^[+-]inf/)
- {
- # +inf ** 0 => NaN
- return $x->bnan() if $y->is_zero();
- # -inf ** -1 => 1/inf => 0
- return $x->bzero() if $y->is_one('-') && $x->is_negative();
-
- # +inf ** Y => inf
- return $x if $x->{sign} eq '+inf';
-
- # -inf ** Y => -inf if Y is odd
- return $x if $y->is_odd();
- return $x->babs();
- }
- # X ** +-inf
-
- # 1 ** +inf => 1
- return $x if $x->is_one();
-
- # 0 ** inf => 0
- return $x if $x->is_zero() && $y->{sign} =~ /^[+]/;
-
- # 0 ** -inf => inf
- return $x->binf() if $x->is_zero();
-
- # -1 ** -inf => NaN
- return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/;
-
- # -X ** -inf => 0
- return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/;
-
- # -1 ** inf => NaN
- return $x->bnan() if $x->{sign} eq '-';
-
- # X ** inf => inf
- return $x->binf() if $y->{sign} =~ /^[+]/;
- # X ** -inf => 0
- return $x->bzero();
- }
-
- return $upgrade->bpow($upgrade->new($x),$y,@r)
- if defined $upgrade && (!$y->isa($self) || $y->{sign} eq '-');
-
- $r[3] = $y; # no push!
-
- # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu
-
- my $new_sign = '+';
- $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+');
-
- # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf
- return $x->binf()
- if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value});
- # 1 ** -y => 1 / (1 ** |y|)
- # so do test for negative $y after above's clause
- return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value});
-
- $x->{value} = $CALC->_pow($x->{value},$y->{value});
- $x->{sign} = $new_sign;
- $x->{sign} = '+' if $CALC->_is_zero($y->{value});
- $x->round(@r);
- }
-
-sub blsft
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # compute x << y, base n, y >= 0
-
- # set up parameters
- my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,$n,@r) = objectify(2,@_);
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
}
- return $x if $x->modify('blsft');
- return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x->round(@r) if $y->is_zero();
+ return $x if $x->modify('bpow');
- $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
+ return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
- $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n);
- $x->round(@r);
- }
+ # inf handling
+ if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) {
+ if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) {
+ # +-inf ** +-inf
+ return $x->bnan();
+ }
+ # +-inf ** Y
+ if ($x->{sign} =~ /^[+-]inf/) {
+ # +inf ** 0 => NaN
+ return $x->bnan() if $y->is_zero();
+ # -inf ** -1 => 1/inf => 0
+ return $x->bzero() if $y->is_one('-') && $x->is_negative();
+
+ # +inf ** Y => inf
+ return $x if $x->{sign} eq '+inf';
+
+ # -inf ** Y => -inf if Y is odd
+ return $x if $y->is_odd();
+ return $x->babs();
+ }
+ # X ** +-inf
-sub brsft
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # compute x >> y, base n, y >= 0
+ # 1 ** +inf => 1
+ return $x if $x->is_one();
- # set up parameters
- my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,$n,@r) = objectify(2,@_);
+ # 0 ** inf => 0
+ return $x if $x->is_zero() && $y->{sign} =~ /^[+]/;
+
+ # 0 ** -inf => inf
+ return $x->binf() if $x->is_zero();
+
+ # -1 ** -inf => NaN
+ return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/;
+
+ # -X ** -inf => 0
+ return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/;
+
+ # -1 ** inf => NaN
+ return $x->bnan() if $x->{sign} eq '-';
+
+ # X ** inf => inf
+ return $x->binf() if $y->{sign} =~ /^[+]/;
+ # X ** -inf => 0
+ return $x->bzero();
}
- return $x if $x->modify('brsft');
- return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x->round(@r) if $y->is_zero();
- return $x->bzero(@r) if $x->is_zero(); # 0 => 0
+ return $upgrade->bpow($upgrade->new($x), $y, @r)
+ if defined $upgrade && (!$y->isa($class) || $y->{sign} eq '-');
- $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
+ $r[3] = $y; # no push!
- # this only works for negative numbers when shifting in base 2
- if (($x->{sign} eq '-') && ($n == 2))
- {
- return $x->round(@r) if $x->is_one('-'); # -1 => -1
- if (!$y->is_one())
- {
- # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al
- # but perhaps there is a better emulation for two's complement shift...
- # if $y != 1, we must simulate it by doing:
- # convert to bin, flip all bits, shift, and be done
- $x->binc(); # -3 => -2
- my $bin = $x->as_bin();
- $bin =~ s/^-0b//; # strip '-0b' prefix
- $bin =~ tr/10/01/; # flip bits
- # now shift
- if ($y >= CORE::length($bin))
- {
- $bin = '0'; # shifting to far right creates -1
- # 0, because later increment makes
- # that 1, attached '-' makes it '-1'
- # because -1 >> x == -1 !
- }
- else
- {
- $bin =~ s/.{$y}$//; # cut off at the right side
- $bin = '1' . $bin; # extend left side by one dummy '1'
- $bin =~ tr/10/01/; # flip bits back
+ # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu
+
+ my $new_sign = '+';
+ $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+');
+
+ # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf
+ return $x->binf()
+ if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value});
+ # 1 ** -y => 1 / (1 ** |y|)
+ # so do test for negative $y after above's clause
+ return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value});
+
+ $x->{value} = $CALC->_pow($x->{value}, $y->{value});
+ $x->{sign} = $new_sign;
+ $x->{sign} = '+' if $CALC->_is_zero($y->{value});
+ $x->round(@r);
+}
+
+sub blog {
+ # Return the logarithm of the operand. If a second operand is defined, that
+ # value is used as the base, otherwise the base is assumed to be Euler's
+ # constant.
+
+ # Don't objectify the base, since an undefined base, as in $x->blog() or
+ # $x->blog(undef) signals that the base is Euler's number.
+
+ # set up parameters
+ my ($class, $x, $base, @r) = (undef, @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $base, @r) = objectify(2, @_);
+ }
+
+ return $x if $x->modify('blog');
+
+ # Handle all exception cases and all trivial cases. I have used Wolfram
+ # Alpha (http://www.wolframalpha.com) as the reference for these cases.
+
+ return $x -> bnan() if $x -> is_nan();
+
+ if (defined $base) {
+ $base = $class -> new($base) unless ref $base;
+ if ($base -> is_nan() || $base -> is_one()) {
+ return $x -> bnan();
+ } elsif ($base -> is_inf() || $base -> is_zero()) {
+ return $x -> bnan() if $x -> is_inf() || $x -> is_zero();
+ return $x -> bzero();
+ } elsif ($base -> is_negative()) { # -inf < base < 0
+ return $x -> bzero() if $x -> is_one(); # x = 1
+ return $x -> bone() if $x == $base; # x = base
+ return $x -> bnan(); # otherwise
}
- my $res = $self->new('0b'.$bin); # add prefix and convert back
- $res->binc(); # remember to increment
- $x->{value} = $res->{value}; # take over value
- return $x->round(@r); # we are done now, magic, isn't?
- }
- # x < 0, n == 2, y == 1
- $x->bdec(); # n == 2, but $y == 1: this fixes it
- }
-
- $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n);
- $x->round(@r);
- }
-
-sub band
- {
- #(BINT or num_str, BINT or num_str) return BINT
- # compute x & y
-
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
+ return $x -> bone() if $x == $base; # 0 < base && 0 < x < inf
}
- return $x if $x->modify('band');
+ # We now know that the base is either undefined or >= 2 and finite.
- $r[3] = $y; # no push!
+ return $x -> binf('+') if $x -> is_inf(); # x = +/-inf
+ return $x -> bnan() if $x -> is_neg(); # -inf < x < 0
+ return $x -> bzero() if $x -> is_one(); # x = 1
+ return $x -> binf('-') if $x -> is_zero(); # x = 0
- return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+ # At this point we are done handling all exception cases and trivial cases.
- my $sx = $x->{sign} eq '+' ? 1 : -1;
- my $sy = $y->{sign} eq '+' ? 1 : -1;
+ return $upgrade -> blog($upgrade -> new($x), $base, @r) if defined $upgrade;
- if ($sx == 1 && $sy == 1)
- {
- $x->{value} = $CALC->_and($x->{value},$y->{value});
- return $x->round(@r);
+ # fix for bug #24969:
+ # the default base is e (Euler's number) which is not an integer
+ if (!defined $base) {
+ require Math::BigFloat;
+ my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int();
+ # modify $x in place
+ $x->{value} = $u->{value};
+ $x->{sign} = $u->{sign};
+ return $x;
}
- if ($CAN{signed_and})
+ my ($rc, $exact) = $CALC->_log_int($x->{value}, $base->{value});
+ return $x->bnan() unless defined $rc; # not possible to take log?
+ $x->{value} = $rc;
+ $x->round(@r);
+}
+
+sub bexp {
+ # Calculate e ** $x (Euler's number to the power of X), truncated to
+ # an integer value.
+ my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
+ return $x if $x->modify('bexp');
+
+ # inf, -inf, NaN, <0 => NaN
+ return $x->bnan() if $x->{sign} eq 'NaN';
+ return $x->bone() if $x->is_zero();
+ return $x if $x->{sign} eq '+inf';
+ return $x->bzero() if $x->{sign} eq '-inf';
+
+ my $u;
{
- $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy);
- return $x->round(@r);
+ # run through Math::BigFloat unless told otherwise
+ require Math::BigFloat unless defined $upgrade;
+ local $upgrade = 'Math::BigFloat' unless defined $upgrade;
+ # calculate result, truncate it to integer
+ $u = $upgrade->bexp($upgrade->new($x), @r);
}
- require $EMU_LIB;
- __emu_band($self,$x,$y,$sx,$sy,@r);
- }
+ if (defined $upgrade) {
+ $x = $u;
+ } else {
+ $u = $u->as_int();
+ # modify $x in place
+ $x->{value} = $u->{value};
+ $x->round(@r);
+ }
+}
-sub bior
- {
- #(BINT or num_str, BINT or num_str) return BINT
- # compute x | y
+sub bnok {
+ # Calculate n over k (binomial coefficient or "choose" function) as integer.
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
}
- return $x if $x->modify('bior');
- $r[3] = $y; # no push!
+ return $x if $x->modify('bnok');
+ return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN';
+ return $x->binf() if $x->{sign} eq '+inf';
- return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+ # k > n or k < 0 => 0
+ my $cmp = $x->bacmp($y);
+ return $x->bzero() if $cmp < 0 || substr($y->{sign}, 0, 1) eq "-";
- my $sx = $x->{sign} eq '+' ? 1 : -1;
- my $sy = $y->{sign} eq '+' ? 1 : -1;
+ if ($CALC->can('_nok')) {
+ $x->{value} = $CALC->_nok($x->{value}, $y->{value});
+ } else {
+ # ( 7 ) 7! 1*2*3*4 * 5*6*7 5 * 6 * 7 6 7
+ # ( - ) = --------- = --------------- = --------- = 5 * - * -
+ # ( 3 ) (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3 2 3
- # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior()
+ my $n = $x -> {value};
+ my $k = $y -> {value};
- # don't use lib for negative values
- if ($sx == 1 && $sy == 1)
- {
- $x->{value} = $CALC->_or($x->{value},$y->{value});
- return $x->round(@r);
- }
+ # If k > n/2, or, equivalently, 2*k > n, compute nok(n, k) as
+ # nok(n, n-k) to minimize the number if iterations in the loop.
- # if lib can do negative values, let it handle this
- if ($CAN{signed_or})
- {
- $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy);
- return $x->round(@r);
+ {
+ my $twok = $CALC->_mul($CALC->_two(), $CALC->_copy($k));
+ if ($CALC->_acmp($twok, $n) > 0) {
+ $k = $CALC->_sub($CALC->_copy($n), $k);
+ }
+ }
+
+ if ($CALC->_is_zero($k)) {
+ $n = $CALC->_one();
+ } else {
+
+ # Make a copy of the original n, since we'll be modifying n
+ # in-place.
+
+ my $n_orig = $CALC->_copy($n);
+
+ $CALC->_sub($n, $k);
+ $CALC->_inc($n);
+
+ my $f = $CALC->_copy($n);
+ $CALC->_inc($f);
+
+ my $d = $CALC->_two();
+
+ # while f <= n (the original n, that is) ...
+
+ while ($CALC->_acmp($f, $n_orig) <= 0) {
+ $CALC->_mul($n, $f);
+ $CALC->_div($n, $d);
+ $CALC->_inc($f);
+ $CALC->_inc($d);
+ }
+ }
+
+ $x -> {value} = $n;
}
- require $EMU_LIB;
- __emu_bior($self,$x,$y,$sx,$sy,@r);
- }
+ $x->round(@r);
+}
-sub bxor
- {
- #(BINT or num_str, BINT or num_str) return BINT
- # compute x ^ y
+sub bsin {
+ # Calculate sinus(x) to N digits. Unless upgrading is in effect, returns the
+ # result truncated to an integer.
+ my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
+ return $x if $x->modify('bsin');
+
+ return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
+
+ return $upgrade->new($x)->bsin(@r) if defined $upgrade;
+
+ require Math::BigFloat;
+ # calculate the result and truncate it to integer
+ my $t = Math::BigFloat->new($x)->bsin(@r)->as_int();
+
+ $x->bone() if $t->is_one();
+ $x->bzero() if $t->is_zero();
+ $x->round(@r);
+}
+
+sub bcos {
+ # Calculate cosinus(x) to N digits. Unless upgrading is in effect, returns the
+ # result truncated to an integer.
+ my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ return $x if $x->modify('bcos');
+
+ return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
+
+ return $upgrade->new($x)->bcos(@r) if defined $upgrade;
+
+ require Math::BigFloat;
+ # calculate the result and truncate it to integer
+ my $t = Math::BigFloat->new($x)->bcos(@r)->as_int();
+
+ $x->bone() if $t->is_one();
+ $x->bzero() if $t->is_zero();
+ $x->round(@r);
+}
+
+sub batan {
+ # Calculate arcus tangens of x to N digits. Unless upgrading is in effect, returns the
+ # result truncated to an integer.
+ my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ return $x if $x->modify('batan');
+
+ return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
+
+ return $upgrade->new($x)->batan(@r) if defined $upgrade;
+
+ # calculate the result and truncate it to integer
+ my $t = Math::BigFloat->new($x)->batan(@r);
+
+ $x->{value} = $CALC->_new($x->as_int()->bstr());
+ $x->round(@r);
+}
+
+sub batan2 {
+ # calculate arcus tangens of ($y/$x)
+
+ # set up parameters
+ my ($class, $y, $x, @r) = (ref($_[0]), @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $y, $x, @r) = objectify(2, @_);
+ }
+
+ return $y if $y->modify('batan2');
+
+ return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan);
+
+ # Y X
+ # != 0 -inf result is +- pi
+ if ($x->is_inf() || $y->is_inf()) {
+ # upgrade to Math::BigFloat etc.
+ return $upgrade->new($y)->batan2($upgrade->new($x), @r) if defined $upgrade;
+ if ($y->is_inf()) {
+ if ($x->{sign} eq '-inf') {
+ # calculate 3 pi/4 => 2.3.. => 2
+ $y->bone(substr($y->{sign}, 0, 1));
+ $y->bmul($class->new(2));
+ } elsif ($x->{sign} eq '+inf') {
+ # calculate pi/4 => 0.7 => 0
+ $y->bzero();
+ } else {
+ # calculate pi/2 => 1.5 => 1
+ $y->bone(substr($y->{sign}, 0, 1));
+ }
+ } else {
+ if ($x->{sign} eq '+inf') {
+ # calculate pi/4 => 0.7 => 0
+ $y->bzero();
+ } else {
+ # PI => 3.1415.. => 3
+ $y->bone(substr($y->{sign}, 0, 1));
+ $y->bmul($class->new(3));
+ }
+ }
+ return $y;
}
- return $x if $x->modify('bxor');
- $r[3] = $y; # no push!
+ return $upgrade->new($y)->batan2($upgrade->new($x), @r) if defined $upgrade;
- return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+ require Math::BigFloat;
+ my $r = Math::BigFloat->new($y)
+ ->batan2(Math::BigFloat->new($x), @r)
+ ->as_int();
- my $sx = $x->{sign} eq '+' ? 1 : -1;
- my $sy = $y->{sign} eq '+' ? 1 : -1;
+ $x->{value} = $r->{value};
+ $x->{sign} = $r->{sign};
- # don't use lib for negative values
- if ($sx == 1 && $sy == 1)
- {
- $x->{value} = $CALC->_xor($x->{value},$y->{value});
- return $x->round(@r);
+ $x;
+}
+
+sub bsqrt {
+ # calculate square root of $x
+ my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ return $x if $x->modify('bsqrt');
+
+ return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN
+ return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf
+
+ return $upgrade->bsqrt($x, @r) if defined $upgrade;
+
+ $x->{value} = $CALC->_sqrt($x->{value});
+ $x->round(@r);
+}
+
+sub broot {
+ # calculate $y'th root of $x
+
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
+
+ $y = $class->new(2) unless defined $y;
+
+ # objectify is costly, so avoid it
+ if ((!ref($x)) || (ref($x) ne ref($y))) {
+ ($class, $x, $y, @r) = objectify(2, $class || $class, @_);
}
- # if lib can do negative values, let it handle this
- if ($CAN{signed_xor})
- {
- $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy);
- return $x->round(@r);
+ return $x if $x->modify('broot');
+
+ # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
+ return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
+ $y->{sign} !~ /^\+$/;
+
+ return $x->round(@r)
+ if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
+
+ return $upgrade->new($x)->broot($upgrade->new($y), @r) if defined $upgrade;
+
+ $x->{value} = $CALC->_root($x->{value}, $y->{value});
+ $x->round(@r);
+}
+
+sub bfac {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # compute factorial number from $x, modify $x in place
+ my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf
+ return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN
+
+ $x->{value} = $CALC->_fac($x->{value});
+ $x->round(@r);
+}
+
+sub blsft {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # compute x << y, base n, y >= 0
+
+ # set up parameters
+ my ($class, $x, $y, $b, @r) = (ref($_[0]), @_);
+
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, $b, @r) = objectify(2, @_);
}
- require $EMU_LIB;
- __emu_bxor($self,$x,$y,$sx,$sy,@r);
- }
+ return $x if $x -> modify('blsft');
+ return $x -> bnan() if ($x -> {sign} !~ /^[+-]$/ ||
+ $y -> {sign} !~ /^[+-]$/);
+ return $x -> round(@r) if $y -> is_zero();
-sub length
- {
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ $b = 2 if !defined $b;
+ return $x -> bnan() if $b <= 0 || $y -> {sign} eq '-';
- my $e = $CALC->_len($x->{value});
- wantarray ? ($e,0) : $e;
- }
+ $x -> {value} = $CALC -> _lsft($x -> {value}, $y -> {value}, $b);
+ $x -> round(@r);
+}
-sub digit
- {
- # return the nth decimal digit, negative values count backward, 0 is right
- my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+sub brsft {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # compute x >> y, base n, y >= 0
- $n = $n->numify() if ref($n);
- $CALC->_digit($x->{value},$n||0);
- }
+ # set up parameters
+ my ($class, $x, $y, $b, @r) = (ref($_[0]), @_);
-sub _trailing_zeros
- {
- # return the amount of trailing zeros in $x (as scalar)
- my $x = shift;
- $x = $class->new($x) unless ref $x;
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, $b, @r) = objectify(2, @_);
+ }
+
+ return $x if $x -> modify('brsft');
+ return $x -> bnan() if ($x -> {sign} !~ /^[+-]$/ || $y -> {sign} !~ /^[+-]$/);
+ return $x -> round(@r) if $y -> is_zero();
+ return $x -> bzero(@r) if $x -> is_zero(); # 0 => 0
+
+ $b = 2 if !defined $b;
+ return $x -> bnan() if $b <= 0 || $y -> {sign} eq '-';
+
+ # this only works for negative numbers when shifting in base 2
+ if (($x -> {sign} eq '-') && ($b == 2)) {
+ return $x -> round(@r) if $x -> is_one('-'); # -1 => -1
+ if (!$y -> is_one()) {
+ # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et
+ # al but perhaps there is a better emulation for two's complement
+ # shift...
+ # if $y != 1, we must simulate it by doing:
+ # convert to bin, flip all bits, shift, and be done
+ $x -> binc(); # -3 => -2
+ my $bin = $x -> as_bin();
+ $bin =~ s/^-0b//; # strip '-0b' prefix
+ $bin =~ tr/10/01/; # flip bits
+ # now shift
+ if ($y >= CORE::length($bin)) {
+ $bin = '0'; # shifting to far right creates -1
+ # 0, because later increment makes
+ # that 1, attached '-' makes it '-1'
+ # because -1 >> x == -1 !
+ } else {
+ $bin =~ s/.{$y}$//; # cut off at the right side
+ $bin = '1' . $bin; # extend left side by one dummy '1'
+ $bin =~ tr/10/01/; # flip bits back
+ }
+ my $res = $class -> new('0b' . $bin); # add prefix and convert back
+ $res -> binc(); # remember to increment
+ $x -> {value} = $res -> {value}; # take over value
+ return $x -> round(@r); # we are done now, magic, isn't?
+ }
- return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc
+ # x < 0, n == 2, y == 1
+ $x -> bdec(); # n == 2, but $y == 1: this fixes it
+ }
- $CALC->_zeros($x->{value}); # must handle odd values, 0 etc
- }
+ $x -> {value} = $CALC -> _rsft($x -> {value}, $y -> {value}, $b);
+ $x -> round(@r);
+}
-sub bsqrt
- {
- # calculate square root of $x
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+###############################################################################
+# Bitwise methods
+###############################################################################
- return $x if $x->modify('bsqrt');
+sub band {
+ #(BINT or num_str, BINT or num_str) return BINT
+ # compute x & y
- return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN
- return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
+ }
- return $upgrade->bsqrt($x,@r) if defined $upgrade;
+ return $x if $x->modify('band');
- $x->{value} = $CALC->_sqrt($x->{value});
- $x->round(@r);
- }
+ $r[3] = $y; # no push!
-sub broot
- {
- # calculate $y'th root of $x
+ return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ my $sx = $x->{sign} eq '+' ? 1 : -1;
+ my $sy = $y->{sign} eq '+' ? 1 : -1;
- $y = $self->new(2) unless defined $y;
+ if ($sx == 1 && $sy == 1) {
+ $x->{value} = $CALC->_and($x->{value}, $y->{value});
+ return $x->round(@r);
+ }
- # objectify is costly, so avoid it
- if ((!ref($x)) || (ref($x) ne ref($y)))
- {
- ($self,$x,$y,@r) = objectify(2,$self || $class,@_);
+ if ($CAN{signed_and}) {
+ $x->{value} = $CALC->_signed_and($x->{value}, $y->{value}, $sx, $sy);
+ return $x->round(@r);
}
- return $x if $x->modify('broot');
+ require $EMU_LIB;
+ __emu_band($class, $x, $y, $sx, $sy, @r);
+}
+
+sub bior {
+ #(BINT or num_str, BINT or num_str) return BINT
+ # compute x | y
- # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
- return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
- $y->{sign} !~ /^\+$/;
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
+ }
- return $x->round(@r)
- if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
+ return $x if $x->modify('bior');
+ $r[3] = $y; # no push!
- return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade;
+ return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- $x->{value} = $CALC->_root($x->{value},$y->{value});
- $x->round(@r);
- }
+ my $sx = $x->{sign} eq '+' ? 1 : -1;
+ my $sy = $y->{sign} eq '+' ? 1 : -1;
-sub exponent
- {
- # return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior()
- if ($x->{sign} !~ /^[+-]$/)
- {
- my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf
- return $self->new($s);
+ # don't use lib for negative values
+ if ($sx == 1 && $sy == 1) {
+ $x->{value} = $CALC->_or($x->{value}, $y->{value});
+ return $x->round(@r);
}
- return $self->bzero() if $x->is_zero();
- # 12300 => 2 trailing zeros => exponent is 2
- $self->new( $CALC->_zeros($x->{value}) );
- }
+ # if lib can do negative values, let it handle this
+ if ($CAN{signed_or}) {
+ $x->{value} = $CALC->_signed_or($x->{value}, $y->{value}, $sx, $sy);
+ return $x->round(@r);
+ }
+
+ require $EMU_LIB;
+ __emu_bior($class, $x, $y, $sx, $sy, @r);
+}
-sub mantissa
- {
- # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+sub bxor {
+ #(BINT or num_str, BINT or num_str) return BINT
+ # compute x ^ y
- if ($x->{sign} !~ /^[+-]$/)
- {
- # for NaN, +inf, -inf: keep the sign
- return $self->new($x->{sign});
+ # set up parameters
+ my ($class, $x, $y, @r) = (ref($_[0]), @_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
+ ($class, $x, $y, @r) = objectify(2, @_);
}
- my $m = $x->copy(); delete $m->{_p}; delete $m->{_a};
- # that's a bit inefficient:
- my $zeros = $CALC->_zeros($m->{value});
- $m->brsft($zeros,10) if $zeros != 0;
- $m;
- }
+ return $x if $x->modify('bxor');
+ $r[3] = $y; # no push!
-sub parts
- {
- # return a copy of both the exponent and the mantissa
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- ($x->mantissa(),$x->exponent());
- }
+ my $sx = $x->{sign} eq '+' ? 1 : -1;
+ my $sy = $y->{sign} eq '+' ? 1 : -1;
-##############################################################################
-# rounding functions
-
-sub bfround
- {
- # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
- # $n == 0 || $n == 1 => round to integer
- my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x;
-
- my ($scale,$mode) = $x->_scale_p(@_);
-
- return $x if !defined $scale || $x->modify('bfround'); # no-op
-
- # no-op for BigInts if $n <= 0
- $x->bround( $x->length()-$scale, $mode) if $scale > 0;
-
- delete $x->{_a}; # delete to save memory
- $x->{_p} = $scale; # store new _p
- $x;
- }
-
-sub _scan_for_nonzero
- {
- # internal, used by bround() to scan for non-zeros after a '5'
- my ($x,$pad,$xs,$len) = @_;
-
- return 0 if $len == 1; # "5" is trailed by invisible zeros
- my $follow = $pad - 1;
- return 0 if $follow > $len || $follow < 1;
-
- # use the string form to check whether only '0's follow or not
- substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0;
- }
-
-sub fround
- {
- # Exists to make life easier for switch between MBF and MBI (should we
- # autoload fxxx() like MBF does for bxxx()?)
- my $x = shift; $x = $class->new($x) unless ref $x;
- $x->bround(@_);
- }
-
-sub bround
- {
- # accuracy: +$n preserve $n digits from left,
- # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF)
- # no-op for $n == 0
- # and overwrite the rest with 0's, return normalized number
- # do not return $x->bnorm(), but $x
-
- my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_a(@_);
- return $x if !defined $scale || $x->modify('bround'); # no-op
-
- if ($x->is_zero() || $scale == 0)
- {
- $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
- return $x;
+ # don't use lib for negative values
+ if ($sx == 1 && $sy == 1) {
+ $x->{value} = $CALC->_xor($x->{value}, $y->{value});
+ return $x->round(@r);
}
- return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN
- # we have fewer digits than we want to scale to
- my $len = $x->length();
- # convert $scale to a scalar in case it is an object (put's a limit on the
- # number length, but this would already limited by memory constraints), makes
- # it faster
- $scale = $scale->numify() if ref ($scale);
+ # if lib can do negative values, let it handle this
+ if ($CAN{signed_xor}) {
+ $x->{value} = $CALC->_signed_xor($x->{value}, $y->{value}, $sx, $sy);
+ return $x->round(@r);
+ }
- # scale < 0, but > -len (not >=!)
- if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
- {
- $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
- return $x;
+ require $EMU_LIB;
+ __emu_bxor($class, $x, $y, $sx, $sy, @r);
+}
+
+sub bnot {
+ # (num_str or BINT) return BINT
+ # represent ~x as twos-complement number
+ # we don't need $class, so undef instead of ref($_[0]) make it slightly faster
+ my ($class, $x, $a, $p, $r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ return $x if $x->modify('bnot');
+ $x->binc()->bneg(); # binc already does round
+}
+
+###############################################################################
+# Rounding methods
+###############################################################################
+
+sub round {
+ # Round $self according to given parameters, or given second argument's
+ # parameters or global defaults
+
+ # for speed reasons, _find_round_parameters is embedded here:
+
+ my ($self, $a, $p, $r, @args) = @_;
+ # $a accuracy, if given by caller
+ # $p precision, if given by caller
+ # $r round_mode, if given by caller
+ # @args all 'other' arguments (0 for unary, 1 for binary ops)
+
+ my $class = ref($self); # find out class of argument(s)
+ no strict 'refs';
+
+ # now pick $a or $p, but only if we have got "arguments"
+ if (!defined $a) {
+ foreach ($self, @args) {
+ # take the defined one, or if both defined, the one that is smaller
+ $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
+ }
+ }
+ if (!defined $p) {
+ # even if $a is defined, take $p, to signal error for both defined
+ foreach ($self, @args) {
+ # take the defined one, or if both defined, the one that is bigger
+ # -2 > -3, and 3 > 2
+ $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
+ }
}
- # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
- my ($pad,$digit_round,$digit_after);
- $pad = $len - $scale;
- $pad = abs($scale-1) if $scale < 0;
-
- # do not use digit(), it is very costly for binary => decimal
- # getting the entire string is also costly, but we need to do it only once
- my $xs = $CALC->_str($x->{value});
- my $pl = -$pad-1;
-
- # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
- # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
- $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len;
- $pl++; $pl ++ if $pad >= $len;
- $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0;
-
- # in case of 01234 we round down, for 6789 up, and only in case 5 we look
- # closer at the remaining digits of the original $x, remember decision
- my $round_up = 1; # default round up
- $round_up -- if
- ($mode eq 'trunc') || # trunc by round down
- ($digit_after =~ /[01234]/) || # round down anyway,
- # 6789 => round up
- ($digit_after eq '5') && # not 5000...0000
- ($x->_scan_for_nonzero($pad,$xs,$len) == 0) &&
- (
- ($mode eq 'even') && ($digit_round =~ /[24680]/) ||
- ($mode eq 'odd') && ($digit_round =~ /[13579]/) ||
- ($mode eq '+inf') && ($x->{sign} eq '-') ||
- ($mode eq '-inf') && ($x->{sign} eq '+') ||
- ($mode eq 'zero') # round down if zero, sign adjusted below
- );
- my $put_back = 0; # not yet modified
+ # if still none defined, use globals (#2)
+ $a = ${"$class\::accuracy"} unless defined $a;
+ $p = ${"$class\::precision"} unless defined $p;
- if (($pad > 0) && ($pad <= $len))
- {
- substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...'
- $put_back = 1; # need to put back
+ # A == 0 is useless, so undef it to signal no rounding
+ $a = undef if defined $a && $a == 0;
+
+ # no rounding today?
+ return $self unless defined $a || defined $p; # early out
+
+ # set A and set P is an fatal error
+ return $self->bnan() if defined $a && defined $p;
+
+ $r = ${"$class\::round_mode"} unless defined $r;
+ if ($r !~ /^(even|odd|[+-]inf|zero|trunc|common)$/) {
+ Carp::croak("Unknown round mode '$r'");
}
- elsif ($pad > $len)
- {
- $x->bzero(); # round to '0'
+
+ # now round, by calling either bround or bfround:
+ if (defined $a) {
+ $self->bround(int($a), $r) if !defined $self->{_a} || $self->{_a} >= $a;
+ } else { # both can't be undefined due to early out
+ $self->bfround(int($p), $r) if !defined $self->{_p} || $self->{_p} <= $p;
}
- if ($round_up) # what gave test above?
- {
- $put_back = 1; # need to put back
- $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
+ # bround() or bfround() already called bnorm() if nec.
+ $self;
+}
- # we modify directly the string variant instead of creating a number and
- # adding it, since that is faster (we already have the string)
- my $c = 0; $pad ++; # for $pad == $len case
- while ($pad <= $len)
- {
- $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10';
- substr($xs,-$pad,1) = $c; $pad++;
- last if $c != 0; # no overflow => early out
- }
- $xs = '1'.$xs if $c == 0;
+sub bround {
+ # accuracy: +$n preserve $n digits from left,
+ # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF)
+ # no-op for $n == 0
+ # and overwrite the rest with 0's, return normalized number
+ # do not return $x->bnorm(), but $x
+
+ my $x = shift;
+ $x = $class->new($x) unless ref $x;
+ my ($scale, $mode) = $x->_scale_a(@_);
+ return $x if !defined $scale || $x->modify('bround'); # no-op
+
+ if ($x->is_zero() || $scale == 0) {
+ $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+ return $x;
+ }
+ return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN
+
+ # we have fewer digits than we want to scale to
+ my $len = $x->length();
+ # convert $scale to a scalar in case it is an object (put's a limit on the
+ # number length, but this would already limited by memory constraints), makes
+ # it faster
+ $scale = $scale->numify() if ref ($scale);
+
+ # scale < 0, but > -len (not >=!)
+ if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) {
+ $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+ return $x;
+ }
+
+ # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
+ my ($pad, $digit_round, $digit_after);
+ $pad = $len - $scale;
+ $pad = abs($scale-1) if $scale < 0;
+
+ # do not use digit(), it is very costly for binary => decimal
+ # getting the entire string is also costly, but we need to do it only once
+ my $xs = $CALC->_str($x->{value});
+ my $pl = -$pad-1;
+
+ # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
+ # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
+ $digit_round = '0';
+ $digit_round = substr($xs, $pl, 1) if $pad <= $len;
+ $pl++;
+ $pl ++ if $pad >= $len;
+ $digit_after = '0';
+ $digit_after = substr($xs, $pl, 1) if $pad > 0;
+
+ # in case of 01234 we round down, for 6789 up, and only in case 5 we look
+ # closer at the remaining digits of the original $x, remember decision
+ my $round_up = 1; # default round up
+ $round_up -- if
+ ($mode eq 'trunc') || # trunc by round down
+ ($digit_after =~ /[01234]/) || # round down anyway,
+ # 6789 => round up
+ ($digit_after eq '5') && # not 5000...0000
+ ($x->_scan_for_nonzero($pad, $xs, $len) == 0) &&
+ (
+ ($mode eq 'even') && ($digit_round =~ /[24680]/) ||
+ ($mode eq 'odd') && ($digit_round =~ /[13579]/) ||
+ ($mode eq '+inf') && ($x->{sign} eq '-') ||
+ ($mode eq '-inf') && ($x->{sign} eq '+') ||
+ ($mode eq 'zero') # round down if zero, sign adjusted below
+ );
+ my $put_back = 0; # not yet modified
+
+ if (($pad > 0) && ($pad <= $len)) {
+ substr($xs, -$pad, $pad) = '0' x $pad; # replace with '00...'
+ $put_back = 1; # need to put back
+ } elsif ($pad > $len) {
+ $x->bzero(); # round to '0'
+ }
+
+ if ($round_up) { # what gave test above?
+ $put_back = 1; # need to put back
+ $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
+
+ # we modify directly the string variant instead of creating a number and
+ # adding it, since that is faster (we already have the string)
+ my $c = 0;
+ $pad ++; # for $pad == $len case
+ while ($pad <= $len) {
+ $c = substr($xs, -$pad, 1) + 1;
+ $c = '0' if $c eq '10';
+ substr($xs, -$pad, 1) = $c;
+ $pad++;
+ last if $c != 0; # no overflow => early out
+ }
+ $xs = '1'.$xs if $c == 0;
}
- $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed
+ $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed
- $x->{_a} = $scale if $scale >= 0;
- if ($scale < 0)
- {
- $x->{_a} = $len+$scale;
- $x->{_a} = 0 if $scale < -$len;
+ $x->{_a} = $scale if $scale >= 0;
+ if ($scale < 0) {
+ $x->{_a} = $len+$scale;
+ $x->{_a} = 0 if $scale < -$len;
}
- $x;
- }
+ $x;
+}
+
+sub bfround {
+ # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
+ # $n == 0 || $n == 1 => round to integer
+ my $x = shift;
+ my $class = ref($x) || $x;
+ $x = $class->new($x) unless ref $x;
+
+ my ($scale, $mode) = $x->_scale_p(@_);
+
+ return $x if !defined $scale || $x->modify('bfround'); # no-op
-sub bfloor
- {
- # round towards minus infinity; no-op since it's already integer
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+ # no-op for Math::BigInt objects if $n <= 0
+ $x->bround($x->length()-$scale, $mode) if $scale > 0;
- $x->round(@r);
- }
+ delete $x->{_a}; # delete to save memory
+ $x->{_p} = $scale; # store new _p
+ $x;
+}
+
+sub fround {
+ # Exists to make life easier for switch between MBF and MBI (should we
+ # autoload fxxx() like MBF does for bxxx()?)
+ my $x = shift;
+ $x = $class->new($x) unless ref $x;
+ $x->bround(@_);
+}
+
+sub bfloor {
+ # round towards minus infinity; no-op since it's already integer
+ my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
-sub bceil
- {
- # round towards plus infinity; no-op since it's already int
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+ $x->round(@r);
+}
- $x->round(@r);
- }
+sub bceil {
+ # round towards plus infinity; no-op since it's already int
+ my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ $x->round(@r);
+}
sub bint {
# round towards zero; no-op since it's already integer
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+ my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
$x->round(@r);
}
-sub as_number
- {
- # An object might be asked to return itself as bigint on certain overloaded
- # operations. This does exactly this, so that sub classes can simple inherit
- # it or override with their own integer conversion routine.
- $_[0]->copy();
- }
+###############################################################################
+# Other mathematical methods
+###############################################################################
-sub as_hex
- {
- # return as hex string, with prefixed 0x
- my $x = shift; $x = $class->new($x) if !ref($x);
+sub bgcd {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # does not modify arguments, but returns new object
+ # GCD -- Euclid's algorithm, variant C (Knuth Vol 3, pg 341 ff)
- return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ my ($class, @args) = objectify(0, @_);
- my $s = '';
- $s = $x->{sign} if $x->{sign} eq '-';
- $s . $CALC->_as_hex($x->{value});
- }
+ my $x = shift @args;
+ $x = ref($x) && $x -> isa($class) ? $x -> copy() : $class -> new($x);
-sub as_bin
- {
- # return as binary string, with prefixed 0b
- my $x = shift; $x = $class->new($x) if !ref($x);
+ return $class->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
- return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ while (@args) {
+ my $y = shift @args;
+ $y = $class->new($y) unless ref($y) && $y -> isa($class);
+ return $class->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
+ $x->{value} = $CALC->_gcd($x->{value}, $y->{value});
+ last if $CALC->_is_one($x->{value});
+ }
- my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
- return $s . $CALC->_as_bin($x->{value});
- }
+ return $x -> babs();
+}
-sub as_oct
- {
- # return as octal string, with prefixed 0
- my $x = shift; $x = $class->new($x) if !ref($x);
+sub blcm {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # does not modify arguments, but returns new object
+ # Least Common Multiple
- return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ my ($class, @args) = objectify(0, @_);
- my $oct = $CALC->_as_oct($x->{value});
- return $x->{sign} eq '-' ? "-$oct" : $oct;
- }
+ my $x = shift @args;
+ $x = ref($x) && $x -> isa($class) ? $x -> copy() : $class -> new($x);
+ return $class->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
-##############################################################################
-# private stuff (internal use only)
+ while (@args) {
+ my $y = shift @args;
+ $y = $class -> new($y) unless ref($y) && $y -> isa($class);
+ return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y not integer
+ $x -> {value} = $CALC->_lcm($x -> {value}, $y -> {value});
+ }
+
+ return $x -> babs();
+}
+
+###############################################################################
+# Object property methods
+###############################################################################
+
+sub sign {
+ # return the sign of the number: +/-/-inf/+inf/NaN
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
+
+ $x->{sign};
+}
+
+sub digit {
+ # return the nth decimal digit, negative values count backward, 0 is right
+ my ($class, $x, $n) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
+
+ $n = $n->numify() if ref($n);
+ $CALC->_digit($x->{value}, $n || 0);
+}
+
+sub length {
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
+
+ my $e = $CALC->_len($x->{value});
+ wantarray ? ($e, 0) : $e;
+}
+
+sub exponent {
+ # return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
+ my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_);
+
+ if ($x->{sign} !~ /^[+-]$/) {
+ my $s = $x->{sign};
+ $s =~ s/^[+-]//; # NaN, -inf, +inf => NaN or inf
+ return $class->new($s);
+ }
+ return $class->bzero() if $x->is_zero();
+
+ # 12300 => 2 trailing zeros => exponent is 2
+ $class->new($CALC->_zeros($x->{value}));
+}
+
+sub mantissa {
+ # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
+ my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_);
+
+ if ($x->{sign} !~ /^[+-]$/) {
+ # for NaN, +inf, -inf: keep the sign
+ return $class->new($x->{sign});
+ }
+ my $m = $x->copy();
+ delete $m->{_p};
+ delete $m->{_a};
+
+ # that's a bit inefficient:
+ my $zeros = $CALC->_zeros($m->{value});
+ $m->brsft($zeros, 10) if $zeros != 0;
+ $m;
+}
+
+sub parts {
+ # return a copy of both the exponent and the mantissa
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
+
+ ($x->mantissa(), $x->exponent());
+}
+
+sub sparts {
+ my $self = shift;
+ my $class = ref $self;
+
+ Carp::croak("sparts() is an instance method, not a class method")
+ unless $class;
+
+ # Not-a-number.
+
+ if ($self -> is_nan()) {
+ my $mant = $self -> copy(); # mantissa
+ return $mant unless wantarray; # scalar context
+ my $expo = $class -> bnan(); # exponent
+ return ($mant, $expo); # list context
+ }
+
+ # Infinity.
+
+ if ($self -> is_inf()) {
+ my $mant = $self -> copy(); # mantissa
+ return $mant unless wantarray; # scalar context
+ my $expo = $class -> binf('+'); # exponent
+ return ($mant, $expo); # list context
+ }
+
+ # Finite number.
+
+ my $mant = $self -> copy();
+ my $nzeros = $CALC -> _zeros($mant -> {value});
+
+ $mant -> brsft($nzeros, 10) if $nzeros != 0;
+ return $mant unless wantarray;
+
+ my $expo = $class -> new($nzeros);
+ return ($mant, $expo);
+}
+
+sub nparts {
+ my $self = shift;
+ my $class = ref $self;
+
+ Carp::croak("nparts() is an instance method, not a class method")
+ unless $class;
+
+ # Not-a-number.
+
+ if ($self -> is_nan()) {
+ my $mant = $self -> copy(); # mantissa
+ return $mant unless wantarray; # scalar context
+ my $expo = $class -> bnan(); # exponent
+ return ($mant, $expo); # list context
+ }
+
+ # Infinity.
+
+ if ($self -> is_inf()) {
+ my $mant = $self -> copy(); # mantissa
+ return $mant unless wantarray; # scalar context
+ my $expo = $class -> binf('+'); # exponent
+ return ($mant, $expo); # list context
+ }
+
+ # Finite number.
+
+ my ($mant, $expo) = $self -> sparts();
+
+ if ($mant -> bcmp(0)) {
+ my ($ndigtot, $ndigfrac) = $mant -> length();
+ my $expo10adj = $ndigtot - $ndigfrac - 1;
+
+ if ($expo10adj != 0) {
+ return $upgrade -> new($self) -> nparts() if $upgrade;
+ $mant -> bnan();
+ return $mant unless wantarray;
+ $expo -> badd($expo10adj);
+ return ($mant, $expo);
+ }
+ }
+
+ return $mant unless wantarray;
+ return ($mant, $expo);
+}
+
+sub eparts {
+ my $self = shift;
+ my $class = ref $self;
+
+ Carp::croak("eparts() is an instance method, not a class method")
+ unless $class;
+
+ # Not-a-number and Infinity.
+
+ return $self -> sparts() if $self -> is_nan() || $self -> is_inf();
+
+ # Finite number.
+
+ my ($mant, $expo) = $self -> sparts();
+
+ if ($mant -> bcmp(0)) {
+ my $ndigmant = $mant -> length();
+ $expo -> badd($ndigmant);
+
+ # $c is the number of digits that will be in the integer part of the
+ # final mantissa.
+
+ my $c = $expo -> copy() -> bdec() -> bmod(3) -> binc();
+ $expo -> bsub($c);
+
+ if ($ndigmant > $c) {
+ return $upgrade -> new($self) -> eparts() if $upgrade;
+ $mant -> bnan();
+ return $mant unless wantarray;
+ return ($mant, $expo);
+ }
+
+ $mant -> blsft($c - $ndigmant, 10);
+ }
+
+ return $mant unless wantarray;
+ return ($mant, $expo);
+}
+
+sub dparts {
+ my $self = shift;
+ my $class = ref $self;
+
+ Carp::croak("dparts() is an instance method, not a class method")
+ unless $class;
+
+ my $int = $self -> copy();
+ return $int unless wantarray;
+
+ my $frc = $class -> bzero();
+ return ($int, $frc);
+}
+
+###############################################################################
+# String conversion methods
+###############################################################################
+
+sub bstr {
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
+
+ if ($x->{sign} ne '+' && $x->{sign} ne '-') {
+ return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
+ return 'inf'; # +inf
+ }
+ my $str = $CALC->_str($x->{value});
+ return $x->{sign} eq '-' ? "-$str" : $str;
+}
+
+# Scientific notation with significand/mantissa as an integer, e.g., "12345" is
+# written as "1.2345e+4".
+
+sub bsstr {
+ my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
+
+ if ($x->{sign} ne '+' && $x->{sign} ne '-') {
+ return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
+ return 'inf'; # +inf
+ }
+ my ($m, $e) = $x -> parts();
+ my $str = $CALC->_str($m->{value}) . 'e+' . $CALC->_str($e->{value});
+ return $x->{sign} eq '-' ? "-$str" : $str;
+}
+
+# Normalized notation, e.g., "12345" is written as "12345e+0".
+
+sub bnstr {
+ my $x = shift;
+
+ if ($x->{sign} ne '+' && $x->{sign} ne '-') {
+ return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
+ return 'inf'; # +inf
+ }
+
+ return $x -> bstr() if $x -> is_nan() || $x -> is_inf();
+
+ my ($mant, $expo) = $x -> parts();
+
+ # The "fraction posision" is the position (offset) for the decimal point
+ # relative to the end of the digit string.
+
+ my $fracpos = $mant -> length() - 1;
+ if ($fracpos == 0) {
+ my $str = $CALC->_str($mant->{value}) . "e+" . $CALC->_str($expo->{value});
+ return $x->{sign} eq '-' ? "-$str" : $str;
+ }
+
+ $expo += $fracpos;
+ my $mantstr = $CALC->_str($mant -> {value});
+ substr($mantstr, -$fracpos, 0) = '.';
+
+ my $str = $mantstr . 'e+' . $CALC->_str($expo -> {value});
+ return $x->{sign} eq '-' ? "-$str" : $str;
+}
+
+# Engineering notation, e.g., "12345" is written as "12.345e+3".
+
+sub bestr {
+ my $x = shift;
+
+ if ($x->{sign} ne '+' && $x->{sign} ne '-') {
+ return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
+ return 'inf'; # +inf
+ }
+
+ my ($mant, $expo) = $x -> parts();
+
+ my $sign = $mant -> sign();
+ $mant -> babs();
+
+ my $mantstr = $CALC->_str($mant -> {value});
+ my $mantlen = CORE::length($mantstr);
+
+ my $dotidx = 1;
+ $expo += $mantlen - 1;
+
+ my $c = $expo -> copy() -> bmod(3);
+ $expo -= $c;
+ $dotidx += $c;
+
+ if ($mantlen < $dotidx) {
+ $mantstr .= "0" x ($dotidx - $mantlen);
+ } elsif ($mantlen > $dotidx) {
+ substr($mantstr, $dotidx, 0) = ".";
+ }
+
+ my $str = $mantstr . 'e+' . $CALC->_str($expo -> {value});
+ return $sign eq "-" ? "-$str" : $str;
+}
+
+# Decimal notation, e.g., "12345".
+
+sub bdstr {
+ my $x = shift;
+
+ if ($x->{sign} ne '+' && $x->{sign} ne '-') {
+ return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
+ return 'inf'; # +inf
+ }
+
+ my $str = $CALC->_str($x->{value});
+ return $x->{sign} eq '-' ? "-$str" : $str;
+}
+
+sub as_hex {
+ # return as hex string, with prefixed 0x
+ my $x = shift;
+ $x = $class->new($x) if !ref($x);
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+
+ my $s = '';
+ $s = $x->{sign} if $x->{sign} eq '-';
+ $s . $CALC->_as_hex($x->{value});
+}
+
+sub as_oct {
+ # return as octal string, with prefixed 0
+ my $x = shift;
+ $x = $class->new($x) if !ref($x);
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+
+ my $oct = $CALC->_as_oct($x->{value});
+ return $x->{sign} eq '-' ? "-$oct" : $oct;
+}
+
+sub as_bin {
+ # return as binary string, with prefixed 0b
+ my $x = shift;
+ $x = $class->new($x) if !ref($x);
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+
+ my $s = '';
+ $s = $x->{sign} if $x->{sign} eq '-';
+ return $s . $CALC->_as_bin($x->{value});
+}
+
+sub as_bytes {
+ # return a byte string
+ my $x = shift;
+ $x = $class->new($x) if !ref($x);
+
+ Carp::croak("as_bytes() requires a finite, non-negative integer")
+ if $x -> is_neg() || ! $x -> is_int();
+ return $CALC->_as_bytes($x->{value});
+}
+
+###############################################################################
+# Other conversion methods
+###############################################################################
+
+sub numify {
+ # Make a Perl scalar number from a Math::BigInt object.
+ my $x = shift;
+ $x = $class->new($x) unless ref $x;
+
+ if ($x -> is_nan()) {
+ require Math::Complex;
+ my $inf = Math::Complex::Inf();
+ return $inf - $inf;
+ }
+
+ if ($x -> is_inf()) {
+ require Math::Complex;
+ my $inf = Math::Complex::Inf();
+ return $x -> is_negative() ? -$inf : $inf;
+ }
+
+ my $num = 0 + $CALC->_num($x->{value});
+ return $x->{sign} eq '-' ? -$num : $num;
+}
+
+###############################################################################
+# Private methods and functions.
+###############################################################################
sub objectify {
# Convert strings and "foreign objects" to the objects we want.
@@ -2782,19 +3574,18 @@ sub objectify {
# Caller: Gives us:
#
# $x->badd(1); => ref x, scalar y
- # Class->badd(1,2); => classname x (scalar), scalar x, scalar y
- # Class->badd(Class->(1),2); => classname x (scalar), ref x, scalar y
- # Math::BigInt::badd(1,2); => scalar x, scalar y
+ # Class->badd(1, 2); => classname x (scalar), scalar x, scalar y
+ # Class->badd(Class->(1), 2); => classname x (scalar), ref x, scalar y
+ # Math::BigInt::badd(1, 2); => scalar x, scalar y
# A shortcut for the common case $x->unary_op():
- return (ref($_[1]), $_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
+ return (ref($_[1]), $_[1]) if @_ == 2 && ($_[0] || 0) == 1 && ref($_[1]);
# Check the context.
unless (wantarray) {
- require Carp;
- Carp::croak ("${class}::objectify() needs list context");
+ Carp::croak("${class}::objectify() needs list context");
}
# Get the number of arguments to objectify.
@@ -2827,7 +3618,7 @@ sub objectify {
my $up = ${"$a[0]::upgrade"};
- # Disable downgrading, because Math::BigFloat -> foo('1.0','2.0') needs
+ # Disable downgrading, because Math::BigFloat -> foo('1.0', '2.0') needs
# floats.
my $down;
@@ -2837,6 +3628,13 @@ sub objectify {
}
for my $i (1 .. $count) {
+
+ # Don't do anything with undefs. This special treatment is necessary
+ # because blog() might have a second operand which is undef, to signify
+ # that the default Euler base should be used.
+
+ next unless defined $a[$i];
+
my $ref = ref $a[$i];
# Perl scalars are fed to the appropriate constructor.
@@ -2908,334 +3706,150 @@ sub objectify {
return @a;
}
-sub _register_callback
- {
- my ($class,$callback) = @_;
-
- if (ref($callback) ne 'CODE')
- {
- require Carp;
- Carp::croak ("$callback is not a coderef");
- }
- $CALLBACKS{$class} = $callback;
- }
-
-sub import
- {
- my $self = shift;
-
- $IMPORT++; # remember we did import()
- my @a; my $l = scalar @_;
- my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die
- for ( my $i = 0; $i < $l ; $i++ )
- {
- if ($_[$i] eq ':constant')
- {
- # this causes overlord er load to step in
- overload::constant
- integer => sub { $self->new(shift) },
- binary => sub { $self->new(shift) };
- }
- elsif ($_[$i] eq 'upgrade')
- {
- # this causes upgrading
- $upgrade = $_[$i+1]; # or undef to disable
- $i++;
- }
- elsif ($_[$i] =~ /^(lib|try|only)\z/)
- {
- # this causes a different low lib to take care...
- $CALC = $_[$i+1] || '';
- # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback)
- $warn_or_die = 1 if $_[$i] eq 'lib';
- $warn_or_die = 2 if $_[$i] eq 'only';
- $i++;
- }
- else
- {
- push @a, $_[$i];
- }
- }
- # any non :constant stuff is handled by our parent, Exporter
- if (@a > 0)
- {
- require Exporter;
-
- $self->SUPER::import(@a); # need it for subclasses
- $self->export_to_level(1,$self,@a); # need it for MBF
- }
-
- # try to load core math lib
- my @c = split /\s*,\s*/,$CALC;
- foreach (@c)
- {
- $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters
+sub import {
+ my $class = shift;
+
+ $IMPORT++; # remember we did import()
+ my @a;
+ my $l = scalar @_;
+ my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die
+ for (my $i = 0; $i < $l ; $i++) {
+ if ($_[$i] eq ':constant') {
+ # this causes overlord er load to step in
+ overload::constant
+ integer => sub { $class->new(shift) },
+ binary => sub { $class->new(shift) };
+ } elsif ($_[$i] eq 'upgrade') {
+ # this causes upgrading
+ $upgrade = $_[$i+1]; # or undef to disable
+ $i++;
+ } elsif ($_[$i] =~ /^(lib|try|only)\z/) {
+ # this causes a different low lib to take care...
+ $CALC = $_[$i+1] || '';
+ # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback)
+ $warn_or_die = 1 if $_[$i] eq 'lib';
+ $warn_or_die = 2 if $_[$i] eq 'only';
+ $i++;
+ } else {
+ push @a, $_[$i];
+ }
}
- push @c, \'Calc' # if all fail, try these
- if $warn_or_die < 2; # but not for "only"
- $CALC = ''; # signal error
- foreach my $l (@c)
- {
- # fallback libraries are "marked" as \'string', extract string if nec.
- my $lib = $l; $lib = $$l if ref($l);
-
- next if ($lib || '') eq '';
- $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
- $lib =~ s/\.pm$//;
- if ($] < 5.006)
- {
- # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is
- # used in the same script, or eval("") inside import().
- my @parts = split /::/, $lib; # Math::BigInt => Math BigInt
- my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
- require File::Spec;
- $file = File::Spec->catfile (@parts, $file);
- eval { require "$file"; $lib->import( @c ); }
- }
- else
- {
- eval "use $lib qw/@c/;";
- }
- if ($@ eq '')
- {
- my $ok = 1;
- # loaded it ok, see if the api_version() is high enough
- if ($lib->can('api_version') && $lib->api_version() >= 1.0)
- {
- $ok = 0;
- # api_version matches, check if it really provides anything we need
- for my $method (qw/
- one two ten
- str num
- add mul div sub dec inc
- acmp len digit is_one is_zero is_even is_odd
- is_two is_ten
- zeros new copy check
- from_hex from_oct from_bin as_hex as_bin as_oct
- rsft lsft xor and or
- mod sqrt root fac pow modinv modpow log_int gcd
- /)
- {
- if (!$lib->can("_$method"))
- {
- if (($WARN{$lib}||0) < 2)
- {
- require Carp;
- Carp::carp ("$lib is missing method '_$method'");
- $WARN{$lib} = 1; # still warn about the lib
- }
- $ok++; last;
+ # any non :constant stuff is handled by our parent, Exporter
+ if (@a > 0) {
+ require Exporter;
+
+ $class->SUPER::import(@a); # need it for subclasses
+ $class->export_to_level(1, $class, @a); # need it for MBF
+ }
+
+ # try to load core math lib
+ my @c = split /\s*,\s*/, $CALC;
+ foreach (@c) {
+ $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters
+ }
+ push @c, \'Calc' # if all fail, try these
+ if $warn_or_die < 2; # but not for "only"
+ $CALC = ''; # signal error
+ foreach my $l (@c) {
+ # fallback libraries are "marked" as \'string', extract string if nec.
+ my $lib = $l;
+ $lib = $$l if ref($l);
+
+ next if ($lib || '') eq '';
+ $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
+ $lib =~ s/\.pm$//;
+ if ($] < 5.006) {
+ # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is
+ # used in the same script, or eval("") inside import().
+ my @parts = split /::/, $lib; # Math::BigInt => Math BigInt
+ my $file = pop @parts;
+ $file .= '.pm'; # BigInt => BigInt.pm
+ require File::Spec;
+ $file = File::Spec->catfile (@parts, $file);
+ eval {
+ require "$file";
+ $lib->import(@c);
}
- }
- }
- if ($ok == 0)
- {
- $CALC = $lib;
- if ($warn_or_die > 0 && ref($l))
- {
- require Carp;
- my $msg =
- "Math::BigInt: couldn't load specified math lib(s), fallback to $lib";
- Carp::carp ($msg) if $warn_or_die == 1;
- Carp::croak ($msg) if $warn_or_die == 2;
- }
- last; # found a usable one, break
+ } else {
+ eval "use $lib qw/@c/;";
}
- else
- {
- if (($WARN{$lib}||0) < 2)
- {
- my $ver = eval "\$$lib\::VERSION" || 'unknown';
- require Carp;
- Carp::carp ("Cannot load outdated $lib v$ver, please upgrade");
- $WARN{$lib} = 2; # never warn again
- }
+ if ($@ eq '') {
+ my $ok = 1;
+ # loaded it ok, see if the api_version() is high enough
+ if ($lib->can('api_version') && $lib->api_version() >= 1.0) {
+ $ok = 0;
+ # api_version matches, check if it really provides anything we need
+ for my $method (qw/
+ one two ten
+ str num
+ add mul div sub dec inc
+ acmp len digit is_one is_zero is_even is_odd
+ is_two is_ten
+ zeros new copy check
+ from_hex from_oct from_bin as_hex as_bin as_oct
+ rsft lsft xor and or
+ mod sqrt root fac pow modinv modpow log_int gcd
+ /) {
+ if (!$lib->can("_$method")) {
+ if (($WARN{$lib} || 0) < 2) {
+ Carp::carp("$lib is missing method '_$method'");
+ $WARN{$lib} = 1; # still warn about the lib
+ }
+ $ok++;
+ last;
+ }
+ }
+ }
+ if ($ok == 0) {
+ $CALC = $lib;
+ if ($warn_or_die > 0 && ref($l)) {
+ my $msg = "Math::BigInt: couldn't load specified"
+ . " math lib(s), fallback to $lib";
+ Carp::carp($msg) if $warn_or_die == 1;
+ Carp::croak($msg) if $warn_or_die == 2;
+ }
+ last; # found a usable one, break
+ } else {
+ if (($WARN{$lib} || 0) < 2) {
+ my $ver = eval "\$$lib\::VERSION" || 'unknown';
+ Carp::carp("Cannot load outdated $lib v$ver, please upgrade");
+ $WARN{$lib} = 2; # never warn again
+ }
+ }
}
- }
- }
- if ($CALC eq '')
- {
- require Carp;
- if ($warn_or_die == 2)
- {
- Carp::croak(
- "Couldn't load specified math lib(s) and fallback disallowed");
- }
- else
- {
- Carp::croak(
- "Couldn't load any math lib(s), not even fallback to Calc.pm");
- }
- }
-
- # notify callbacks
- foreach my $class (keys %CALLBACKS)
- {
- &{$CALLBACKS{$class}}($CALC);
- }
-
- # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib
- # functions
-
- %CAN = ();
- for my $method (qw/ signed_and signed_or signed_xor /)
- {
- $CAN{$method} = $CALC->can("_$method") ? 1 : 0;
}
-
- # import done
- }
-
-# Create a Math::BigInt from a hexadecimal string.
-
-sub from_hex {
- my $self = shift;
- my $selfref = ref $self;
- my $class = $selfref || $self;
-
- my $str = shift;
-
- # If called as a class method, initialize a new object.
-
- $self = $class -> bzero() unless $selfref;
-
- if ($str =~ s/
- ^
- ( [+-]? )
- (0?x)?
- (
- [0-9a-fA-F]*
- ( _ [0-9a-fA-F]+ )*
- )
- $
- //x)
- {
- # Get a "clean" version of the string, i.e., non-emtpy and with no
- # underscores or invalid characters.
-
- my $sign = $1;
- my $chrs = $3;
- $chrs =~ tr/_//d;
- $chrs = '0' unless CORE::length $chrs;
-
- # The library method requires a prefix.
-
- $self->{value} = $CALC->_from_hex('0x' . $chrs);
-
- # Place the sign.
-
- if ($sign eq '-' && ! $CALC->_is_zero($self->{value})) {
- $self->{sign} = '-';
+ if ($CALC eq '') {
+ if ($warn_or_die == 2) {
+ Carp::croak("Couldn't load specified math lib(s)" .
+ " and fallback disallowed");
+ } else {
+ Carp::croak("Couldn't load any math lib(s), not even fallback to Calc.pm");
}
-
- return $self;
}
- # CORE::hex() parses as much as it can, and ignores any trailing garbage.
- # For backwards compatibility, we return NaN.
-
- return $self->bnan();
-}
-
-# Create a Math::BigInt from an octal string.
-
-sub from_oct {
- my $self = shift;
- my $selfref = ref $self;
- my $class = $selfref || $self;
-
- my $str = shift;
-
- # If called as a class method, initialize a new object.
-
- $self = $class -> bzero() unless $selfref;
-
- if ($str =~ s/
- ^
- ( [+-]? )
- (
- [0-7]*
- ( _ [0-7]+ )*
- )
- $
- //x)
- {
- # Get a "clean" version of the string, i.e., non-emtpy and with no
- # underscores or invalid characters.
-
- my $sign = $1;
- my $chrs = $2;
- $chrs =~ tr/_//d;
- $chrs = '0' unless CORE::length $chrs;
-
- # The library method requires a prefix.
-
- $self->{value} = $CALC->_from_oct('0' . $chrs);
-
- # Place the sign.
+ # notify callbacks
+ foreach my $class (keys %CALLBACKS) {
+ &{$CALLBACKS{$class}}($CALC);
+ }
- if ($sign eq '-' && ! $CALC->_is_zero($self->{value})) {
- $self->{sign} = '-';
- }
+ # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib
+ # functions
- return $self;
+ %CAN = ();
+ for my $method (qw/ signed_and signed_or signed_xor /) {
+ $CAN{$method} = $CALC->can("_$method") ? 1 : 0;
}
- # CORE::oct() parses as much as it can, and ignores any trailing garbage.
- # For backwards compatibility, we return NaN.
-
- return $self->bnan();
+ # import done
}
-# Create a Math::BigInt from a binary string.
-
-sub from_bin {
- my $self = shift;
- my $selfref = ref $self;
- my $class = $selfref || $self;
-
- my $str = shift;
-
- # If called as a class method, initialize a new object.
-
- $self = $class -> bzero() unless $selfref;
-
- if ($str =~ s/
- ^
- ( [+-]? )
- (0?b)?
- (
- [01]*
- ( _ [01]+ )*
- )
- $
- //x)
- {
- # Get a "clean" version of the string, i.e., non-emtpy and with no
- # underscores or invalid characters.
-
- my $sign = $1;
- my $chrs = $3;
- $chrs =~ tr/_//d;
- $chrs = '0' unless CORE::length $chrs;
-
- # The library method requires a prefix.
+sub _register_callback {
+ my ($class, $callback) = @_;
- $self->{value} = $CALC->_from_bin('0b' . $chrs);
-
- # Place the sign.
-
- if ($sign eq '-' && ! $CALC->_is_zero($self->{value})) {
- $self->{sign} = '-';
- }
-
- return $self;
+ if (ref($callback) ne 'CODE') {
+ Carp::croak("$callback is not a coderef");
}
-
- # For consistency with from_hex() and from_oct(), we return NaN when the
- # input is invalid.
-
- return $self->bnan();
+ $CALLBACKS{$class} = $callback;
}
sub _split_dec_string {
@@ -3273,8 +3887,7 @@ sub _split_dec_string {
( \D .*? )?
\z
- //x)
- {
+ //x) {
my $leading = $1;
my $significand_sgn = $2 || '+';
my $significand_abs = $3;
@@ -3312,240 +3925,160 @@ sub _split_dec_string {
return undef;
}
-sub _split
- {
- # input: num_str; output: undef for invalid or
- # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,
- # \$exp_sign,\$exp_value)
- # Internal, take apart a string and return the pieces.
- # Strip leading/trailing whitespace, leading zeros, underscore and reject
- # invalid input.
- my $x = shift;
-
- # strip white space at front, also extraneous leading zeros
- $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2'
- $x =~ s/^\s+//; # but this will
- $x =~ s/\s+$//g; # strip white space at end
-
- # shortcut, if nothing to split, return early
- if ($x =~ /^[+-]?[0-9]+\z/)
+sub _split {
+ # input: num_str; output: undef for invalid or
+ # (\$mantissa_sign, \$mantissa_value, \$mantissa_fraction,
+ # \$exp_sign, \$exp_value)
+ # Internal, take apart a string and return the pieces.
+ # Strip leading/trailing whitespace, leading zeros, underscore and reject
+ # invalid input.
+ my $x = shift;
+
+ # strip white space at front, also extraneous leading zeros
+ $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2'
+ $x =~ s/^\s+//; # but this will
+ $x =~ s/\s+$//g; # strip white space at end
+
+ # shortcut, if nothing to split, return early
+ if ($x =~ /^[+-]?[0-9]+\z/) {
+ $x =~ s/^([+-])0*([0-9])/$2/;
+ my $sign = $1 || '+';
+ return (\$sign, \$x, \'', \'', \0);
+ }
+
+ # invalid starting char?
+ return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
+
+ return Math::BigInt->from_hex($x) if $x =~ /^[+-]?0x/; # hex string
+ return Math::BigInt->from_bin($x) if $x =~ /^[+-]?0b/; # binary string
+
+ # strip underscores between digits
+ $x =~ s/([0-9])_([0-9])/$1$2/g;
+ $x =~ s/([0-9])_([0-9])/$1$2/g; # do twice for 1_2_3
+
+ # some possible inputs:
+ # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
+ # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999
+
+ my ($m, $e, $last) = split /[Ee]/, $x;
+ return if defined $last; # last defined => 1e2E3 or others
+ $e = '0' if !defined $e || $e eq "";
+
+ # sign, value for exponent, mantint, mantfrac
+ my ($es, $ev, $mis, $miv, $mfv);
+ # valid exponent?
+ if ($e =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
{
- $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
- return (\$sign, \$x, \'', \'', \0);
- }
-
- # invalid starting char?
- return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
-
- return Math::BigInt->from_hex($x) if $x =~ /^[+-]?0x/; # hex string
- return Math::BigInt->from_bin($x) if $x =~ /^[+-]?0b/; # binary string
-
- # strip underscores between digits
- $x =~ s/([0-9])_([0-9])/$1$2/g;
- $x =~ s/([0-9])_([0-9])/$1$2/g; # do twice for 1_2_3
-
- # some possible inputs:
- # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
- # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999
-
- my ($m,$e,$last) = split /[Ee]/,$x;
- return if defined $last; # last defined => 1e2E3 or others
- $e = '0' if !defined $e || $e eq "";
-
- # sign,value for exponent,mantint,mantfrac
- my ($es,$ev,$mis,$miv,$mfv);
- # valid exponent?
- if ($e =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
- {
- $es = $1; $ev = $2;
- # valid mantissa?
- return if $m eq '.' || $m eq '';
- my ($mi,$mf,$lastf) = split /\./,$m;
- return if defined $lastf; # lastf defined => 1.2.3 or others
- $mi = '0' if !defined $mi;
- $mi .= '0' if $mi =~ /^[\-\+]?$/;
- $mf = '0' if !defined $mf || $mf eq '';
- if ($mi =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
- {
- $mis = $1||'+'; $miv = $2;
- return unless ($mf =~ /^([0-9]*?)0*$/); # strip trailing zeros
- $mfv = $1;
- # handle the 0e999 case here
- $ev = 0 if $miv eq '0' && $mfv eq '';
- return (\$mis,\$miv,\$mfv,\$es,\$ev);
- }
- }
- return; # NaN, not a number
- }
-
-##############################################################################
-# internal calculation routines (others are in Math::BigInt::Calc etc)
-
-sub __lcm
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does modify first argument
- # LCM
-
- my ($x,$ty) = @_;
- return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan);
- my $method = ref($x) . '::bgcd';
- no strict 'refs';
- $x * $ty / &$method($x,$ty);
- }
-
-###############################################################################
-# trigonometric functions
-
-sub bpi
- {
- # Calculate PI to N digits. Unless upgrading is in effect, returns the
- # result truncated to an integer, that is, always returns '3'.
- my ($self,$n) = @_;
- if (@_ == 1)
- {
- # called like Math::BigInt::bpi(10);
- $n = $self; $self = $class;
+ $es = $1;
+ $ev = $2;
+ # valid mantissa?
+ return if $m eq '.' || $m eq '';
+ my ($mi, $mf, $lastf) = split /\./, $m;
+ return if defined $lastf; # lastf defined => 1.2.3 or others
+ $mi = '0' if !defined $mi;
+ $mi .= '0' if $mi =~ /^[\-\+]?$/;
+ $mf = '0' if !defined $mf || $mf eq '';
+ if ($mi =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
+ {
+ $mis = $1 || '+';
+ $miv = $2;
+ return unless ($mf =~ /^([0-9]*?)0*$/); # strip trailing zeros
+ $mfv = $1;
+ # handle the 0e999 case here
+ $ev = 0 if $miv eq '0' && $mfv eq '';
+ return (\$mis, \$miv, \$mfv, \$es, \$ev);
+ }
}
- $self = ref($self) if ref($self);
-
- return $upgrade->new($n) if defined $upgrade;
-
- # hard-wired to "3"
- $self->new(3);
- }
-
-sub bcos
- {
- # Calculate cosinus(x) to N digits. Unless upgrading is in effect, returns the
- # result truncated to an integer.
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- return $x if $x->modify('bcos');
-
- return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
+ return; # NaN, not a number
+}
- return $upgrade->new($x)->bcos(@r) if defined $upgrade;
+sub _trailing_zeros {
+ # return the amount of trailing zeros in $x (as scalar)
+ my $x = shift;
+ $x = $class->new($x) unless ref $x;
- require Math::BigFloat;
- # calculate the result and truncate it to integer
- my $t = Math::BigFloat->new($x)->bcos(@r)->as_int();
+ return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc
- $x->bone() if $t->is_one();
- $x->bzero() if $t->is_zero();
- $x->round(@r);
- }
+ $CALC->_zeros($x->{value}); # must handle odd values, 0 etc
+}
-sub bsin
- {
- # Calculate sinus(x) to N digits. Unless upgrading is in effect, returns the
- # result truncated to an integer.
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+sub _scan_for_nonzero {
+ # internal, used by bround() to scan for non-zeros after a '5'
+ my ($x, $pad, $xs, $len) = @_;
- return $x if $x->modify('bsin');
+ return 0 if $len == 1; # "5" is trailed by invisible zeros
+ my $follow = $pad - 1;
+ return 0 if $follow > $len || $follow < 1;
- return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
+ # use the string form to check whether only '0's follow or not
+ substr ($xs, -$follow) =~ /[^0]/ ? 1 : 0;
+}
- return $upgrade->new($x)->bsin(@r) if defined $upgrade;
+sub _find_round_parameters {
+ # After any operation or when calling round(), the result is rounded by
+ # regarding the A & P from arguments, local parameters, or globals.
- require Math::BigFloat;
- # calculate the result and truncate it to integer
- my $t = Math::BigFloat->new($x)->bsin(@r)->as_int();
+ # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!!
- $x->bone() if $t->is_one();
- $x->bzero() if $t->is_zero();
- $x->round(@r);
- }
+ # This procedure finds the round parameters, but it is for speed reasons
+ # duplicated in round. Otherwise, it is tested by the testsuite and used
+ # by bdiv().
-sub batan2
- {
- # calculate arcus tangens of ($y/$x)
+ # returns ($self) or ($self, $a, $p, $r) - sets $self to NaN of both A and P
+ # were requested/defined (locally or globally or both)
- # set up parameters
- my ($self,$y,$x,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$y,$x,@r) = objectify(2,@_);
- }
+ my ($self, $a, $p, $r, @args) = @_;
+ # $a accuracy, if given by caller
+ # $p precision, if given by caller
+ # $r round_mode, if given by caller
+ # @args all 'other' arguments (0 for unary, 1 for binary ops)
- return $y if $y->modify('batan2');
+ my $class = ref($self); # find out class of argument(s)
+ no strict 'refs';
- return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan);
+ # convert to normal scalar for speed and correctness in inner parts
+ $a = $a->can('numify') ? $a->numify() : "$a" if defined $a && ref($a);
+ $p = $p->can('numify') ? $p->numify() : "$p" if defined $p && ref($p);
- # Y X
- # != 0 -inf result is +- pi
- if ($x->is_inf() || $y->is_inf())
- {
- # upgrade to BigFloat etc.
- return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
- if ($y->is_inf())
- {
- if ($x->{sign} eq '-inf')
- {
- # calculate 3 pi/4 => 2.3.. => 2
- $y->bone( substr($y->{sign},0,1) );
- $y->bmul($self->new(2));
- }
- elsif ($x->{sign} eq '+inf')
- {
- # calculate pi/4 => 0.7 => 0
- $y->bzero();
- }
- else
- {
- # calculate pi/2 => 1.5 => 1
- $y->bone( substr($y->{sign},0,1) );
- }
- }
- else
- {
- if ($x->{sign} eq '+inf')
- {
- # calculate pi/4 => 0.7 => 0
- $y->bzero();
+ # now pick $a or $p, but only if we have got "arguments"
+ if (!defined $a) {
+ foreach ($self, @args) {
+ # take the defined one, or if both defined, the one that is smaller
+ $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
}
- else
- {
- # PI => 3.1415.. => 3
- $y->bone( substr($y->{sign},0,1) );
- $y->bmul($self->new(3));
+ }
+ if (!defined $p) {
+ # even if $a is defined, take $p, to signal error for both defined
+ foreach ($self, @args) {
+ # take the defined one, or if both defined, the one that is bigger
+ # -2 > -3, and 3 > 2
+ $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
}
- }
- return $y;
}
- return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
-
- require Math::BigFloat;
- my $r = Math::BigFloat->new($y)
- ->batan2(Math::BigFloat->new($x),@r)
- ->as_int();
-
- $x->{value} = $r->{value};
- $x->{sign} = $r->{sign};
-
- $x;
- }
+ # if still none defined, use globals (#2)
+ $a = ${"$class\::accuracy"} unless defined $a;
+ $p = ${"$class\::precision"} unless defined $p;
-sub batan
- {
- # Calculate arcus tangens of x to N digits. Unless upgrading is in effect, returns the
- # result truncated to an integer.
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+ # A == 0 is useless, so undef it to signal no rounding
+ $a = undef if defined $a && $a == 0;
- return $x if $x->modify('batan');
+ # no rounding today?
+ return ($self) unless defined $a || defined $p; # early out
- return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
+ # set A and set P is an fatal error
+ return ($self->bnan()) if defined $a && defined $p; # error
- return $upgrade->new($x)->batan(@r) if defined $upgrade;
+ $r = ${"$class\::round_mode"} unless defined $r;
+ if ($r !~ /^(even|odd|[+-]inf|zero|trunc|common)$/) {
+ Carp::croak("Unknown round mode '$r'");
+ }
- # calculate the result and truncate it to integer
- my $t = Math::BigFloat->new($x)->batan(@r);
+ $a = int($a) if defined $a;
+ $p = int($p) if defined $p;
- $x->{value} = $CALC->_new( $x->as_int()->bstr() );
- $x->round(@r);
- }
+ ($self, $a, $p, $r);
+}
###############################################################################
# this method returns 0 if the object can be modified, or 1 if not.
@@ -3555,6 +4088,7 @@ sub batan
sub modify () { 0; }
1;
+
__END__
=pod
@@ -3568,11 +4102,11 @@ Math::BigInt - Arbitrary size integer/float math package
use Math::BigInt;
# or make it faster with huge numbers: install (optional)
- # Math::BigInt::GMP and always use (it will fall back to
+ # Math::BigInt::GMP and always use (it falls back to
# pure Perl if the GMP library is not installed):
# (See also the L<MATH LIBRARY> section!)
- # will warn if Math::BigInt::GMP cannot be found
+ # warns if Math::BigInt::GMP cannot be found
use Math::BigInt lib => 'GMP';
# to suppress the warning use this:
@@ -3582,232 +4116,370 @@ Math::BigInt - Arbitrary size integer/float math package
# use Math::BigInt only => 'GMP';
my $str = '1234567890';
- my @values = (64,74,18);
+ my @values = (64, 74, 18);
my $n = 1; my $sign = '-';
- # Number creation
- my $x = Math::BigInt->new($str); # defaults to 0
- my $y = $x->copy(); # make a true copy
- my $nan = Math::BigInt->bnan(); # create a NotANumber
- my $zero = Math::BigInt->bzero(); # create a +0
- my $inf = Math::BigInt->binf(); # create a +inf
- my $inf = Math::BigInt->binf('-'); # create a -inf
- my $one = Math::BigInt->bone(); # create a +1
- my $mone = Math::BigInt->bone('-'); # create a -1
-
- my $pi = Math::BigInt->bpi(); # returns '3'
- # see Math::BigFloat::bpi()
-
- $h = Math::BigInt->new('0x123'); # from hexadecimal
- $b = Math::BigInt->new('0b101'); # from binary
- $o = Math::BigInt->from_oct('0101'); # from octal
- $h = Math::BigInt->from_hex('cafe'); # from hexadecimal
- $b = Math::BigInt->from_bin('0101'); # from binary
-
- # Testing (don't modify their arguments)
- # (return true if the condition is met, otherwise false)
-
- $x->is_zero(); # if $x is +0
- $x->is_nan(); # if $x is NaN
- $x->is_one(); # if $x is +1
- $x->is_one('-'); # if $x is -1
- $x->is_odd(); # if $x is odd
- $x->is_even(); # if $x is even
- $x->is_pos(); # if $x > 0
- $x->is_neg(); # if $x < 0
- $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+')
- $x->is_int(); # if $x is an integer (not a float)
-
- # comparing and digit/sign extraction
- $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
- $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
- $x->sign(); # return the sign, either +,- or NaN
- $x->digit($n); # return the nth digit, counting from right
- $x->digit(-$n); # return the nth digit, counting from left
-
- # The following all modify their first argument. If you want to pre-
- # serve $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for
- # why this is necessary when mixing $a = $b assignments with non-over-
- # loaded math.
-
- $x->bzero(); # set $x to 0
- $x->bnan(); # set $x to NaN
- $x->bone(); # set $x to +1
- $x->bone('-'); # set $x to -1
- $x->binf(); # set $x to inf
- $x->binf('-'); # set $x to -inf
-
- $x->bneg(); # negation
- $x->babs(); # absolute value
- $x->bsgn(); # sign function (-1, 0, 1, or NaN)
- $x->bnorm(); # normalize (no-op in BigInt)
- $x->bnot(); # two's complement (bit wise not)
- $x->binc(); # increment $x by 1
- $x->bdec(); # decrement $x by 1
-
- $x->badd($y); # addition (add $y to $x)
- $x->bsub($y); # subtraction (subtract $y from $x)
- $x->bmul($y); # multiplication (multiply $x by $y)
- $x->bdiv($y); # divide, set $x to quotient
- # return (quo,rem) or quo if scalar
-
- $x->bmuladd($y,$z); # $x = $x * $y + $z
-
- $x->bmod($y); # modulus (x % y)
- $x->bmodpow($y,$mod); # modular exponentiation (($x ** $y) % $mod)
- $x->bmodinv($mod); # modular multiplicative inverse
- $x->bpow($y); # power of arguments (x ** y)
- $x->blsft($y); # left shift in base 2
- $x->brsft($y); # right shift in base 2
- # returns (quo,rem) or quo if in sca-
- # lar context
- $x->blsft($y,$n); # left shift by $y places in base $n
- $x->brsft($y,$n); # right shift by $y places in base $n
- # returns (quo,rem) or quo if in sca-
- # lar context
-
- $x->band($y); # bitwise and
- $x->bior($y); # bitwise inclusive or
- $x->bxor($y); # bitwise exclusive or
- $x->bnot(); # bitwise not (two's complement)
-
- $x->bsqrt(); # calculate square-root
- $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root)
- $x->bfac(); # factorial of $x (1*2*3*4*..$x)
-
- $x->bnok($y); # x over y (binomial coefficient n over k)
-
- $x->blog(); # logarithm of $x to base e (Euler's number)
- $x->blog($base); # logarithm of $x to base $base (f.i. 2)
- $x->bexp(); # calculate e ** $x where e is Euler's number
-
- $x->round($A,$P,$mode); # round to accuracy or precision using
- # mode $mode
- $x->bround($n); # accuracy: preserve $n digits
- $x->bfround($n); # $n > 0: round $nth digits,
- # $n < 0: round to the $nth digit after the
- # dot, no-op for BigInts
-
- # The following do not modify their arguments in BigInt (are no-ops),
- # but do so in BigFloat:
-
- $x->bfloor(); # round towards minus infinity
- $x->bceil(); # round towards plus infinity
- $x->bint(); # round towards zero
-
- # The following do not modify their arguments:
-
- # greatest common divisor (no OO style)
- my $gcd = Math::BigInt::bgcd(@values);
- # lowest common multiple (no OO style)
- my $lcm = Math::BigInt::blcm(@values);
-
+ # Configuration methods (may be used as class methods and instance methods)
+
+ Math::BigInt->accuracy(); # get class accuracy
+ Math::BigInt->accuracy($n); # set class accuracy
+ Math::BigInt->precision(); # get class precision
+ Math::BigInt->precision($n); # set class precision
+ Math::BigInt->round_mode(); # get class rounding mode
+ Math::BigInt->round_mode($m); # set global round mode, must be one of
+ # 'even', 'odd', '+inf', '-inf', 'zero',
+ # 'trunc', or 'common'
+ Math::BigInt->config(); # return hash with configuration
+
+ # Constructor methods (when the class methods below are used as instance
+ # methods, the value is assigned the invocand)
+
+ $x = Math::BigInt->new($str); # defaults to 0
+ $x = Math::BigInt->new('0x123'); # from hexadecimal
+ $x = Math::BigInt->new('0b101'); # from binary
+ $x = Math::BigInt->from_hex('cafe'); # from hexadecimal
+ $x = Math::BigInt->from_oct('377'); # from octal
+ $x = Math::BigInt->from_bin('1101'); # from binary
+ $x = Math::BigInt->bzero(); # create a +0
+ $x = Math::BigInt->bone(); # create a +1
+ $x = Math::BigInt->bone('-'); # create a -1
+ $x = Math::BigInt->binf(); # create a +inf
+ $x = Math::BigInt->binf('-'); # create a -inf
+ $x = Math::BigInt->bnan(); # create a Not-A-Number
+ $x = Math::BigInt->bpi(); # returns pi
+
+ $y = $x->copy(); # make a copy (unlike $y = $x)
+ $y = $x->as_int(); # return as a Math::BigInt
+
+ # Boolean methods (these don't modify the invocand)
+
+ $x->is_zero(); # if $x is 0
+ $x->is_one(); # if $x is +1
+ $x->is_one("+"); # ditto
+ $x->is_one("-"); # if $x is -1
+ $x->is_inf(); # if $x is +inf or -inf
+ $x->is_inf("+"); # if $x is +inf
+ $x->is_inf("-"); # if $x is -inf
+ $x->is_nan(); # if $x is NaN
+
+ $x->is_positive(); # if $x > 0
+ $x->is_pos(); # ditto
+ $x->is_negative(); # if $x < 0
+ $x->is_neg(); # ditto
+
+ $x->is_odd(); # if $x is odd
+ $x->is_even(); # if $x is even
+ $x->is_int(); # if $x is an integer
+
+ # Comparison methods
+
+ $x->bcmp($y); # compare numbers (undef, < 0, == 0, > 0)
+ $x->bacmp($y); # compare absolutely (undef, < 0, == 0, > 0)
+ $x->beq($y); # true if and only if $x == $y
+ $x->bne($y); # true if and only if $x != $y
+ $x->blt($y); # true if and only if $x < $y
+ $x->ble($y); # true if and only if $x <= $y
+ $x->bgt($y); # true if and only if $x > $y
+ $x->bge($y); # true if and only if $x >= $y
+
+ # Arithmetic methods
+
+ $x->bneg(); # negation
+ $x->babs(); # absolute value
+ $x->bsgn(); # sign function (-1, 0, 1, or NaN)
+ $x->bnorm(); # normalize (no-op)
+ $x->binc(); # increment $x by 1
+ $x->bdec(); # decrement $x by 1
+ $x->badd($y); # addition (add $y to $x)
+ $x->bsub($y); # subtraction (subtract $y from $x)
+ $x->bmul($y); # multiplication (multiply $x by $y)
+ $x->bmuladd($y,$z); # $x = $x * $y + $z
+ $x->bdiv($y); # division (floored), set $x to quotient
+ # return (quo,rem) or quo if scalar
+ $x->btdiv($y); # division (truncated), set $x to quotient
+ # return (quo,rem) or quo if scalar
+ $x->bmod($y); # modulus (x % y)
+ $x->btmod($y); # modulus (truncated)
+ $x->bmodinv($mod); # modular multiplicative inverse
+ $x->bmodpow($y,$mod); # modular exponentiation (($x ** $y) % $mod)
+ $x->bpow($y); # power of arguments (x ** y)
+ $x->blog(); # logarithm of $x to base e (Euler's number)
+ $x->blog($base); # logarithm of $x to base $base (e.g., base 2)
+ $x->bexp(); # calculate e ** $x where e is Euler's number
+ $x->bnok($y); # x over y (binomial coefficient n over k)
+ $x->bsin(); # sine
+ $x->bcos(); # cosine
+ $x->batan(); # inverse tangent
+ $x->batan2($y); # two-argument inverse tangent
+ $x->bsqrt(); # calculate square-root
+ $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root)
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
+
+ $x->blsft($n); # left shift $n places in base 2
+ $x->blsft($n,$b); # left shift $n places in base $b
+ # returns (quo,rem) or quo (scalar context)
+ $x->brsft($n); # right shift $n places in base 2
+ $x->brsft($n,$b); # right shift $n places in base $b
+ # returns (quo,rem) or quo (scalar context)
+
+ # Bitwise methods
+
+ $x->band($y); # bitwise and
+ $x->bior($y); # bitwise inclusive or
+ $x->bxor($y); # bitwise exclusive or
+ $x->bnot(); # bitwise not (two's complement)
+
+ # Rounding methods
+ $x->round($A,$P,$mode); # round to accuracy or precision using
+ # rounding mode $mode
+ $x->bround($n); # accuracy: preserve $n digits
+ $x->bfround($n); # $n > 0: round to $nth digit left of dec. point
+ # $n < 0: round to $nth digit right of dec. point
+ $x->bfloor(); # round towards minus infinity
+ $x->bceil(); # round towards plus infinity
+ $x->bint(); # round towards zero
+
+ # Other mathematical methods
+
+ $x->bgcd($y); # greatest common divisor
+ $x->blcm($y); # least common multiple
+
+ # Object property methods (do not modify the invocand)
+
+ $x->sign(); # the sign, either +, - or NaN
+ $x->digit($n); # the nth digit, counting from the right
+ $x->digit(-$n); # the nth digit, counting from the left
$x->length(); # return number of digits in number
($xl,$f) = $x->length(); # length of number and length of fraction
# part, latter is always 0 digits long
- # for BigInts
-
- $x->exponent(); # return exponent as BigInt
- $x->mantissa(); # return (signed) mantissa as BigInt
- $x->parts(); # return (mantissa,exponent) as BigInt
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
- $x->as_int(); # return as BigInt (in BigInt: same as copy())
- $x->numify(); # return as scalar (might overflow!)
-
- # conversion to string (do not modify their argument)
- $x->bstr(); # normalized string (e.g. '3')
- $x->bsstr(); # norm. string in scientific notation (e.g. '3E0')
+ # for Math::BigInt objects
+ $x->mantissa(); # return (signed) mantissa as a Math::BigInt
+ $x->exponent(); # return exponent as a Math::BigInt
+ $x->parts(); # return (mantissa,exponent) as a Math::BigInt
+ $x->sparts(); # mantissa and exponent (as integers)
+ $x->nparts(); # mantissa and exponent (normalised)
+ $x->eparts(); # mantissa and exponent (engineering notation)
+ $x->dparts(); # integer and fraction part
+
+ # Conversion methods (do not modify the invocand)
+
+ $x->bstr(); # decimal notation, possibly zero padded
+ $x->bsstr(); # string in scientific notation with integers
+ $x->bnstr(); # string in normalized notation
+ $x->bestr(); # string in engineering notation
+ $x->bdstr(); # string in decimal notation
$x->as_hex(); # as signed hexadecimal string with prefixed 0x
$x->as_bin(); # as signed binary string with prefixed 0b
$x->as_oct(); # as signed octal string with prefixed 0
+ $x->as_bytes(); # as byte string
+ # Other conversion methods
- # precision and accuracy (see section about rounding for more)
- $x->precision(); # return P of $x (or global, if P of $x undef)
- $x->precision($n); # set P of $x to $n
- $x->accuracy(); # return A of $x (or global, if A of $x undef)
- $x->accuracy($n); # set A $x to $n
-
- # Global methods
- Math::BigInt->precision(); # get/set global P for all BigInt objects
- Math::BigInt->accuracy(); # get/set global A for all BigInt objects
- Math::BigInt->round_mode(); # get/set global round mode, one of
- # 'even', 'odd', '+inf', '-inf', 'zero',
- # 'trunc' or 'common'
- Math::BigInt->config(); # return hash containing configuration
+ $x->numify(); # return as scalar (might overflow or underflow)
=head1 DESCRIPTION
-All operators (including basic math operations) are overloaded if you
-declare your big integers as
+Math::BigInt provides support for arbitrary precision integers. Overloading is
+also provided for Perl operators.
- $i = Math::BigInt -> new('123_456_789_123_456_789');
+=head2 Input
-Operations with overloaded operators preserve the arguments which is
-exactly what you expect.
+Input values to these routines may be any scalar number or string that looks
+like a number and represents an integer.
-=head2 Input
+=over
+
+=item *
+
+Leading and trailing whitespace is ignored.
-Input values to these routines may be any string, that looks like a number
-and results in an integer, including hexadecimal and binary numbers.
+=item *
+
+Leading and trailing zeros are ignored.
+
+=item *
+
+If the string has a "0x" prefix, it is interpreted as a hexadecimal number.
+
+=item *
+
+If the string has a "0b" prefix, it is interpreted as a binary number.
-Scalars holding numbers may also be passed, but note that non-integer numbers
-may already have lost precision due to the conversion to float. Quote
-your input if you want BigInt to see all the digits:
+=item *
+
+One underline is allowed between any two digits.
+
+=item *
- $x = Math::BigInt->new(12345678890123456789); # bad
- $x = Math::BigInt->new('12345678901234567890'); # good
+If the string can not be interpreted, NaN is returned.
-You can include one underscore between any two digits.
+=back
-This means integer values like 1.01E2 or even 1000E-2 are also accepted.
-Non-integer values result in NaN.
+Octal numbers are typically prefixed by "0", but since leading zeros are
+stripped, these methods can not automatically recognize octal numbers, so use
+the constructor from_oct() to interpret octal strings.
-Hexadecimal (prefixed with "0x") and binary numbers (prefixed with "0b")
-are accepted, too. Please note that octal numbers are not recognized
-by new(), so the following will print "123":
+Some examples of valid string input
- perl -MMath::BigInt -le 'print Math::BigInt->new("0123")'
+ Input string Resulting value
+ 123 123
+ 1.23e2 123
+ 12300e-2 123
+ 0xcafe 51966
+ 0b1101 13
+ 67_538_754 67538754
+ -4_5_6.7_8_9e+0_1_0 -4567890000000
-To convert an octal number, use from_oct();
+Input given as scalar numbers might lose precision. Quote your input to ensure
+that no digits are lost:
- perl -MMath::BigInt -le 'print Math::BigInt->from_oct("0123")'
+ $x = Math::BigInt->new( 56789012345678901234 ); # bad
+ $x = Math::BigInt->new('56789012345678901234'); # good
-Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('')
+Currently, Math::BigInt->new() defaults to 0, while Math::BigInt->new('')
results in 'NaN'. This might change in the future, so use always the following
explicit forms to get a zero or NaN:
- $zero = Math::BigInt->bzero();
- $nan = Math::BigInt->bnan();
-
-C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers
-are always stored in normalized form. If passed a string, creates a BigInt
-object from the input.
+ $zero = Math::BigInt->bzero();
+ $nan = Math::BigInt->bnan();
=head2 Output
-Output values are BigInt objects (normalized), except for the methods which
-return a string (see L</SYNOPSIS>).
+Output values are usually Math::BigInt objects.
-Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>,
-C<is_nan()>, etc.) return true or false, while others (C<bcmp()>, C<bacmp()>)
-return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort.
+Boolean operators C<is_zero()>, C<is_one()>, C<is_inf()>, etc. return true or
+false.
+
+Comparison operators C<bcmp()> and C<bacmp()>) return -1, 0, 1, or
+undef.
=head1 METHODS
-Each of the methods below (except config(), accuracy() and precision())
-accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R>
-are C<accuracy>, C<precision> and C<round_mode>. Please see the section about
+=head2 Configuration methods
+
+Each of the methods below (except config(), accuracy() and precision()) accepts
+three additional parameters. These arguments C<$A>, C<$P> and C<$R> are
+C<accuracy>, C<precision> and C<round_mode>. Please see the section about
L</ACCURACY and PRECISION> for more information.
+Setting a class variable effects all object instance that are created
+afterwards.
+
=over
+=item accuracy()
+
+ Math::BigInt->accuracy(5); # set class accuracy
+ $x->accuracy(5); # set instance accuracy
+
+ $A = Math::BigInt->accuracy(); # get class accuracy
+ $A = $x->accuracy(); # get instance accuracy
+
+Set or get the accuracy, i.e., the number of significant digits. The accuracy
+must be an integer. If the accuracy is set to C<undef>, no rounding is done.
+
+Alternatively, one can round the results explicitly using one of L</round()>,
+L</bround()> or L</bfround()> or by passing the desired accuracy to the method
+as an additional parameter:
+
+ my $x = Math::BigInt->new(30000);
+ my $y = Math::BigInt->new(7);
+ print scalar $x->copy()->bdiv($y, 2); # prints 4300
+ print scalar $x->copy()->bdiv($y)->bround(2); # prints 4300
+
+Please see the section about L</ACCURACY and PRECISION> for further details.
+
+ $y = Math::BigInt->new(1234567); # $y is not rounded
+ Math::BigInt->accuracy(4); # set class accuracy to 4
+ $x = Math::BigInt->new(1234567); # $x is rounded automatically
+ print "$x $y"; # prints "1235000 1234567"
+
+ print $x->accuracy(); # prints "4"
+ print $y->accuracy(); # also prints "4", since
+ # class accuracy is 4
+
+ Math::BigInt->accuracy(5); # set class accuracy to 5
+ print $x->accuracy(); # prints "4", since instance
+ # accuracy is 4
+ print $y->accuracy(); # prints "5", since no instance
+ # accuracy, and class accuracy is 5
+
+Note: Each class has it's own globals separated from Math::BigInt, but it is
+possible to subclass Math::BigInt and make the globals of the subclass aliases
+to the ones from Math::BigInt.
+
+=item precision()
+
+ Math::BigInt->precision(-2); # set class precision
+ $x->precision(-2); # set instance precision
+
+ $P = Math::BigInt->precision(); # get class precision
+ $P = $x->precision(); # get instance precision
+
+Set or get the precision, i.e., the place to round relative to the decimal
+point. The precision must be a integer. Setting the precision to $P means that
+each number is rounded up or down, depending on the rounding mode, to the
+nearest multiple of 10**$P. If the precision is set to C<undef>, no rounding is
+done.
+
+You might want to use L</accuracy()> instead. With L</accuracy()> you set the
+number of digits each result should have, with L</precision()> you set the
+place where to round.
+
+Please see the section about L</ACCURACY and PRECISION> for further details.
+
+ $y = Math::BigInt->new(1234567); # $y is not rounded
+ Math::BigInt->precision(4); # set class precision to 4
+ $x = Math::BigInt->new(1234567); # $x is rounded automatically
+ print $x; # prints "1230000"
+
+Note: Each class has its own globals separated from Math::BigInt, but it is
+possible to subclass Math::BigInt and make the globals of the subclass aliases
+to the ones from Math::BigInt.
+
+=item div_scale()
+
+Set/get the fallback accuracy. This is the accuracy used when neither accuracy
+nor precision is set explicitly. It is used when a computation might otherwise
+attempt to return an infinite number of digits.
+
+=item round_mode()
+
+Set/get the rounding mode.
+
+=item upgrade()
+
+Set/get the class for upgrading. When a computation might result in a
+non-integer, the operands are upgraded to this class. This is used for instance
+by L<bignum>. The default is C<undef>, thus the following operation creates
+a Math::BigInt, not a Math::BigFloat:
+
+ my $i = Math::BigInt->new(123);
+ my $f = Math::BigFloat->new('123.1');
+
+ print $i + $f, "\n"; # prints 246
+
+=item downgrade()
+
+Set/get the class for downgrading. The default is C<undef>. Downgrading is not
+done by Math::BigInt.
+
+=item modify()
+
+ $x->modify('bpowd');
+
+This method returns 0 if the object can be modified with the given operation,
+or 1 if not.
+
+This is used for instance by L<Math::BigInt::Constant>.
+
=item config()
use Data::Dumper;
print Dumper ( Math::BigInt->config() );
print Math::BigInt->config()->{lib},"\n";
+ print Math::BigInt->config('lib')},"\n";
Returns a hash containing the configuration, e.g. the version number, lib
loaded etc. The following hash keys are currently filled in with the
@@ -3843,289 +4515,318 @@ appropriate information.
The following values can be set by passing C<config()> a reference to a hash:
- trap_inf trap_nan
- upgrade downgrade precision accuracy round_mode div_scale
+ accuracy precision round_mode div_scale
+ upgrade downgrade trap_inf trap_nan
Example:
- $new_cfg = Math::BigInt->config(
- { trap_inf => 1, precision => 5 }
- );
+ $new_cfg = Math::BigInt->config(
+ { trap_inf => 1, precision => 5 }
+ );
-=item accuracy()
+=back
- $x->accuracy(5); # local for $x
- CLASS->accuracy(5); # global for all members of CLASS
- # Note: This also applies to new()!
+=head2 Constructor methods
- $A = $x->accuracy(); # read out accuracy that affects $x
- $A = CLASS->accuracy(); # read out global accuracy
+=over
-Set or get the global or local accuracy, aka how many significant digits the
-results have. If you set a global accuracy, then this also applies to new()!
+=item new()
-Warning! The accuracy I<sticks>, e.g. once you created a number under the
-influence of C<< CLASS->accuracy($A) >>, all results from math operations with
-that number will also be rounded.
+ $x = Math::BigInt->new($str,$A,$P,$R);
-In most cases, you should probably round the results explicitly using one of
-L</round()>, L</bround()> or L</bfround()> or by passing the desired accuracy
-to the math operation as additional parameter:
+Creates a new Math::BigInt object from a scalar or another Math::BigInt object.
+The input is accepted as decimal, hexadecimal (with leading '0x') or binary
+(with leading '0b').
- my $x = Math::BigInt->new(30000);
- my $y = Math::BigInt->new(7);
- print scalar $x->copy()->bdiv($y, 2); # print 4300
- print scalar $x->copy()->bdiv($y)->bround(2); # print 4300
+See L</Input> for more info on accepted input formats.
-Please see the section about L</ACCURACY and PRECISION> for further details.
+=item from_hex()
-Value must be greater than zero. Pass an undef value to disable it:
-
- $x->accuracy(undef);
- Math::BigInt->accuracy(undef);
-
-Returns the current accuracy. For C<< $x->accuracy() >> it will return either
-the local accuracy, or if not defined, the global. This means the return value
-represents the accuracy that will be in effect for $x:
-
- $y = Math::BigInt->new(1234567); # unrounded
- print Math::BigInt->accuracy(4),"\n"; # set 4, print 4
- $x = Math::BigInt->new(123456); # $x will be automatic-
- # ally rounded!
- print "$x $y\n"; # '123500 1234567'
- print $x->accuracy(),"\n"; # will be 4
- print $y->accuracy(),"\n"; # also 4, since
- # global is 4
- print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5
- print $x->accuracy(),"\n"; # still 4
- print $y->accuracy(),"\n"; # 5, since global is 5
-
-Note: Works also for subclasses like Math::BigFloat. Each class has it's own
-globals separated from Math::BigInt, but it is possible to subclass
-Math::BigInt and make the globals of the subclass aliases to the ones from
-Math::BigInt.
+ $x = Math::BigInt->from_hex("0xcafe"); # input is hexadecimal
-=item precision()
+Interpret input as a hexadecimal string. A "0x" or "x" prefix is optional. A
+single underscore character may be placed right after the prefix, if present,
+or between any two digits. If the input is invalid, a NaN is returned.
- $x->precision(-2); # local for $x, round at the second
- # digit right of the dot
- $x->precision(2); # ditto, round at the second digit
- # left of the dot
+=item from_oct()
- CLASS->precision(5); # Global for all members of CLASS
- # This also applies to new()!
- CLASS->precision(-5); # ditto
+ $x = Math::BigInt->from_oct("0775"); # input is octal
- $P = CLASS->precision(); # read out global precision
- $P = $x->precision(); # read out precision that affects $x
+Interpret the input as an octal string and return the corresponding value. A
+"0" (zero) prefix is optional. A single underscore character may be placed
+right after the prefix, if present, or between any two digits. If the input is
+invalid, a NaN is returned.
-Note: You probably want to use L</accuracy()> instead. With L</accuracy()> you
-set the number of digits each result should have, with L</precision()> you
-set the place where to round!
+=item from_bin()
-C<precision()> sets or gets the global or local precision, aka at which digit
-before or after the dot to round all results. A set global precision also
-applies to all newly created numbers!
+ $x = Math::BigInt->from_bin("0b10011"); # input is binary
-In Math::BigInt, passing a negative number precision has no effect since no
-numbers have digits after the dot. In L<Math::BigFloat>, it will round all
-results to P digits after the dot.
+Interpret the input as a binary string. A "0b" or "b" prefix is optional. A
+single underscore character may be placed right after the prefix, if present,
+or between any two digits. If the input is invalid, a NaN is returned.
-Please see the section about L</ACCURACY and PRECISION> for further details.
+=item from_bytes()
-Pass an undef value to disable it:
+ $x = Math::BigInt->from_bytes("\xf3\x6b"); # $x = 62315
- $x->precision(undef);
- Math::BigInt->precision(undef);
+Interpret the input as a byte string, assuming big endian byte order. The
+output is always a non-negative, finite integer.
-Returns the current precision. For C<< $x->precision() >> it will return either
-the local precision of $x, or if not defined, the global. This means the return
-value represents the prevision that will be in effect for $x:
+In some special cases, from_bytes() matches the conversion done by unpack():
- $y = Math::BigInt->new(1234567); # unrounded
- print Math::BigInt->precision(4),"\n"; # set 4, print 4
- $x = Math::BigInt->new(123456); # will be automatically rounded
- print $x; # print "120000"!
+ $b = "\x4e"; # one char byte string
+ $x = Math::BigInt->from_bytes($b); # = 78
+ $y = unpack "C", $b; # ditto, but scalar
-Note: Works also for subclasses like L<Math::BigFloat>. Each class has its
-own globals separated from Math::BigInt, but it is possible to subclass
-Math::BigInt and make the globals of the subclass aliases to the ones from
-Math::BigInt.
+ $b = "\xf3\x6b"; # two char byte string
+ $x = Math::BigInt->from_bytes($b); # = 62315
+ $y = unpack "S>", $b; # ditto, but scalar
-=item brsft()
+ $b = "\x2d\xe0\x49\xad"; # four char byte string
+ $x = Math::BigInt->from_bytes($b); # = 769673645
+ $y = unpack "L>", $b; # ditto, but scalar
- $x->brsft($y,$n);
+ $b = "\x2d\xe0\x49\xad\x2d\xe0\x49\xad"; # eight char byte string
+ $x = Math::BigInt->from_bytes($b); # = 3305723134637787565
+ $y = unpack "Q>", $b; # ditto, but scalar
-Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and
-2, but others work, too.
+=item bzero()
-Right shifting usually amounts to dividing $x by $n ** $y and truncating the
-result:
+ $x = Math::BigInt->bzero();
+ $x->bzero();
+Returns a new Math::BigInt object representing zero. If used as an instance
+method, assigns the value to the invocand.
- $x = Math::BigInt->new(10);
- $x->brsft(1); # same as $x >> 1: 5
- $x = Math::BigInt->new(1234);
- $x->brsft(2,10); # result 12
+=item bone()
-There is one exception, and that is base 2 with negative $x:
+ $x = Math::BigInt->bone(); # +1
+ $x = Math::BigInt->bone("+"); # +1
+ $x = Math::BigInt->bone("-"); # -1
+ $x->bone(); # +1
+ $x->bone("+"); # +1
+ $x->bone('-'); # -1
+Creates a new Math::BigInt object representing one. The optional argument is
+either '-' or '+', indicating whether you want plus one or minus one. If used
+as an instance method, assigns the value to the invocand.
- $x = Math::BigInt->new(-5);
- print $x->brsft(1);
+=item binf()
-This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the
-result).
+ $x = Math::BigInt->binf($sign);
-=item new()
+Creates a new Math::BigInt object representing infinity. The optional argument
+is either '-' or '+', indicating whether you want infinity or minus infinity.
+If used as an instance method, assigns the value to the invocand.
- $x = Math::BigInt->new($str,$A,$P,$R);
+ $x->binf();
+ $x->binf('-');
-Creates a new BigInt object from a scalar or another BigInt object. The
-input is accepted as decimal, hex (with leading '0x') or binary (with leading
-'0b').
+=item bnan()
-See L</Input> for more info on accepted input formats.
+ $x = Math::BigInt->bnan();
-=item from_oct()
+Creates a new Math::BigInt object representing NaN (Not A Number). If used as
+an instance method, assigns the value to the invocand.
- $x = Math::BigInt->from_oct("0775"); # input is octal
+ $x->bnan();
-Interpret the input as an octal string and return the corresponding value. A
-"0" (zero) prefix is optional. A single underscore character may be placed
-right after the prefix, if present, or between any two digits. If the input is
-invalid, a NaN is returned.
+=item bpi()
-=item from_hex()
+ $x = Math::BigInt->bpi(100); # 3
+ $x->bpi(100); # 3
- $x = Math::BigInt->from_hex("0xcafe"); # input is hexadecimal
+Creates a new Math::BigInt object representing PI. If used as an instance
+method, assigns the value to the invocand. With Math::BigInt this always
+returns 3.
-Interpret input as a hexadecimal string. A "0x" or "x" prefix is optional. A
-single underscore character may be placed right after the prefix, if present,
-or between any two digits. If the input is invalid, a NaN is returned.
+If upgrading is in effect, returns PI, rounded to N digits with the current
+rounding mode:
-=item from_bin()
+ use Math::BigFloat;
+ use Math::BigInt upgrade => "Math::BigFloat";
+ print Math::BigInt->bpi(3), "\n"; # 3.14
+ print Math::BigInt->bpi(100), "\n"; # 3.1415....
- $x = Math::BigInt->from_bin("0b10011"); # input is binary
+=item copy()
-Interpret the input as a binary string. A "0b" or "b" prefix is optional. A
-single underscore character may be placed right after the prefix, if present,
-or between any two digits. If the input is invalid, a NaN is returned.
+ $x->copy(); # make a true copy of $x (unlike $y = $x)
-=item bnan()
+=item as_int()
- $x = Math::BigInt->bnan();
+=item as_number()
-Creates a new BigInt object representing NaN (Not A Number).
-If used on an object, it will set it to NaN:
+These methods are called when Math::BigInt encounters an object it doesn't know
+how to handle. For instance, assume $x is a Math::BigInt, or subclass thereof,
+and $y is defined, but not a Math::BigInt, or subclass thereof. If you do
- $x->bnan();
+ $x -> badd($y);
-=item bzero()
+$y needs to be converted into an object that $x can deal with. This is done by
+first checking if $y is something that $x might be upgraded to. If that is the
+case, no further attempts are made. The next is to see if $y supports the
+method C<as_int()>. If it does, C<as_int()> is called, but if it doesn't, the
+next thing is to see if $y supports the method C<as_number()>. If it does,
+C<as_number()> is called. The method C<as_int()> (and C<as_number()>) is
+expected to return either an object that has the same class as $x, a subclass
+thereof, or a string that C<ref($x)-E<gt>new()> can parse to create an object.
- $x = Math::BigInt->bzero();
+C<as_number()> is an alias to C<as_int()>. C<as_number> was introduced in
+v1.22, while C<as_int()> was introduced in v1.68.
-Creates a new BigInt object representing zero.
-If used on an object, it will set it to zero:
+In Math::BigInt, C<as_int()> has the same effect as C<copy()>.
- $x->bzero();
+=back
-=item binf()
+=head2 Boolean methods
- $x = Math::BigInt->binf($sign);
+None of these methods modify the invocand object.
-Creates a new BigInt object representing infinity. The optional argument is
-either '-' or '+', indicating whether you want infinity or minus infinity.
-If used on an object, it will set it to infinity:
+=over
- $x->binf();
- $x->binf('-');
+=item is_zero()
-=item bone()
+ $x->is_zero(); # true if $x is 0
- $x = Math::BigInt->binf($sign);
+Returns true if the invocand is zero and false otherwise.
+
+=item is_one( [ SIGN ])
+
+ $x->is_one(); # true if $x is +1
+ $x->is_one("+"); # ditto
+ $x->is_one("-"); # true if $x is -1
+
+Returns true if the invocand is one and false otherwise.
+
+=item is_finite()
+
+ $x->is_finite(); # true if $x is not +inf, -inf or NaN
-Creates a new BigInt object representing one. The optional argument is
-either '-' or '+', indicating whether you want one or minus one.
-If used on an object, it will set it to one:
+Returns true if the invocand is a finite number, i.e., it is neither +inf,
+-inf, nor NaN.
- $x->bone(); # +1
- $x->bone('-'); # -1
+=item is_inf( [ SIGN ] )
-=item is_one()/is_zero()/is_nan()/is_inf()
+ $x->is_inf(); # true if $x is +inf
+ $x->is_inf("+"); # ditto
+ $x->is_inf("-"); # true if $x is -inf
- $x->is_zero(); # true if arg is +0
- $x->is_nan(); # true if arg is NaN
- $x->is_one(); # true if arg is +1
- $x->is_one('-'); # true if arg is -1
- $x->is_inf(); # true if +inf
- $x->is_inf('-'); # true if -inf (sign is default '+')
+Returns true if the invocand is infinite and false otherwise.
-These methods all test the BigInt for being one specific value and return
-true or false depending on the input. These are faster than doing something
-like:
+=item is_nan()
- if ($x == 0)
+ $x->is_nan(); # true if $x is NaN
-=item is_pos()/is_neg()/is_positive()/is_negative()
+=item is_positive()
- $x->is_pos(); # true if > 0
- $x->is_neg(); # true if < 0
+=item is_pos()
-The methods return true if the argument is positive or negative, respectively.
-C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and
-C<-inf> is negative. A C<zero> is neither positive nor negative.
+ $x->is_positive(); # true if > 0
+ $x->is_pos(); # ditto
-These methods are only testing the sign, and not the value.
+Returns true if the invocand is positive and false otherwise. A C<NaN> is
+neither positive nor negative.
-C<is_positive()> and C<is_negative()> are aliases to C<is_pos()> and
-C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were
-introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced
-in v1.68.
+=item is_negative()
-=item is_odd()/is_even()/is_int()
+=item is_neg()
+
+ $x->is_negative(); # true if < 0
+ $x->is_neg(); # ditto
+
+Returns true if the invocand is negative and false otherwise. A C<NaN> is
+neither positive nor negative.
+
+=item is_odd()
$x->is_odd(); # true if odd, false for even
- $x->is_even(); # true if even, false for odd
- $x->is_int(); # true if $x is an integer
-The return true when the argument satisfies the condition. C<NaN>, C<+inf>,
+Returns true if the invocand is odd and false otherwise. C<NaN>, C<+inf>, and
+C<-inf> are neither odd nor even.
+
+=item is_even()
+
+ $x->is_even(); # true if $x is even
+
+Returns true if the invocand is even and false otherwise. C<NaN>, C<+inf>,
C<-inf> are not integers and are neither odd nor even.
-In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers.
+=item is_int()
+
+ $x->is_int(); # true if $x is an integer
+
+Returns true if the invocand is an integer and false otherwise. C<NaN>,
+C<+inf>, C<-inf> are not integers.
+
+=back
+
+=head2 Comparison methods
+
+None of these methods modify the invocand object. Note that a C<NaN> is neither
+less than, greater than, or equal to anything else, even a C<NaN>.
+
+=over
=item bcmp()
$x->bcmp($y);
-Compares $x with $y and takes the sign into account.
-Returns -1, 0, 1 or undef.
+Returns -1, 0, 1 depending on whether $x is less than, equal to, or grater than
+$y. Returns undef if any operand is a NaN.
=item bacmp()
$x->bacmp($y);
-Compares $x with $y while ignoring their sign. Returns -1, 0, 1 or undef.
+Returns -1, 0, 1 depending on whether the absolute value of $x is less than,
+equal to, or grater than the absolute value of $y. Returns undef if any operand
+is a NaN.
-=item sign()
+=item beq()
- $x->sign();
+ $x -> beq($y);
-Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
+Returns true if and only if $x is equal to $y, and false otherwise.
-If you want $x to have a certain sign, use one of the following methods:
+=item bne()
- $x->babs(); # '+'
- $x->babs()->bneg(); # '-'
- $x->bnan(); # 'NaN'
- $x->binf(); # '+inf'
- $x->binf('-'); # '-inf'
+ $x -> bne($y);
-=item digit()
+Returns true if and only if $x is not equal to $y, and false otherwise.
- $x->digit($n); # return the nth digit, counting from right
+=item blt()
-If C<$n> is negative, returns the digit counting from left.
+ $x -> blt($y);
+
+Returns true if and only if $x is equal to $y, and false otherwise.
+
+=item ble()
+
+ $x -> ble($y);
+
+Returns true if and only if $x is less than or equal to $y, and false
+otherwise.
+
+=item bgt()
+
+ $x -> bgt($y);
+
+Returns true if and only if $x is greater than $y, and false otherwise.
+
+=item bge()
+
+ $x -> bge($y);
+
+Returns true if and only if $x is greater than or equal to $y, and false
+otherwise.
+
+=back
+
+=head2 Arithmetic methods
+
+These methods modify the invocand object and returns it.
+
+=over
=item bneg()
@@ -4153,15 +4854,8 @@ number is negative, zero, or positive, respectively. Does not modify NaNs.
$x->bnorm(); # normalize (no-op)
-=item bnot()
-
- $x->bnot();
-
-Two's complement (bitwise not). This is equivalent to
-
- $x->binc()->bneg();
-
-but faster.
+Normalize the number. This is a no-op and is provided only for backwards
+compatibility.
=item binc()
@@ -4195,18 +4889,57 @@ This method was added in v1.87 of Math::BigInt (June 2007).
$x->bdiv($y); # divide, set $x to quotient
-Returns $x divided by $y. In list context, does floored division (F-division),
-where the quotient is the greatest integer less than or equal to the quotient
-of the two operands. Consequently, the remainder is either zero or has the same
-sign as the second operand. In scalar context, only the quotient is returned.
+Divides $x by $y by doing floored division (F-division), where the quotient is
+the floored (rounded towards negative infinity) quotient of the two operands.
+In list context, returns the quotient and the remainder. The remainder is
+either zero or has the same sign as the second operand. In scalar context, only
+the quotient is returned.
+
+The quotient is always the greatest integer less than or equal to the
+real-valued quotient of the two operands, and the remainder (when it is
+non-zero) always has the same sign as the second operand; so, for example,
+
+ 1 / 4 => ( 0, 1)
+ 1 / -4 => (-1, -3)
+ -3 / 4 => (-1, 1)
+ -3 / -4 => ( 0, -3)
+ -11 / 2 => (-5, 1)
+ 11 / -2 => (-5, -1)
+
+The behavior of the overloaded operator % agrees with the behavior of Perl's
+built-in % operator (as documented in the perlop manpage), and the equation
+
+ $x == ($x / $y) * $y + ($x % $y)
+
+holds true for any finite $x and finite, non-zero $y.
+
+Perl's "use integer" might change the behaviour of % and / for scalars. This is
+because under 'use integer' Perl does what the underlying C library thinks is
+right, and this varies. However, "use integer" does not change the way things
+are done with Math::BigInt objects.
+
+=item btdiv()
+
+ $x->btdiv($y); # divide, set $x to quotient
+
+Divides $x by $y by doing truncated division (T-division), where quotient is
+the truncated (rouneded towards zero) quotient of the two operands. In list
+context, returns the quotient and the remainder. The remainder is either zero
+or has the same sign as the first operand. In scalar context, only the quotient
+is returned.
=item bmod()
$x->bmod($y); # modulus (x % y)
-Returns $x modulo $y. When $x is finite, and $y is finite and non-zero, the
-result is identical to the remainder after floored division (F-division), i.e.,
-identical to the result from Perl's % operator.
+Returns $x modulo $y, i.e., the remainder after floored division (F-division).
+This method is like Perl's % operator. See L</bdiv()>.
+
+=item btmod()
+
+ $x->btmod($y); # modulus
+
+Returns the remainer after truncated division (T-division). See L</btdiv()>.
=item bmodinv()
@@ -4249,19 +4982,31 @@ is exactly equivalent to
=item bpow()
- $x->bpow($y); # power of arguments (x ** y)
+ $x->bpow($y); # power of arguments (x ** y)
+
+C<bpow()> (and the rounding functions) now modifies the first argument and
+returns it, unlike the old code which left it alone and only returned the
+result. This is to be consistent with C<badd()> etc. The first three modifies
+$x, the last one won't:
+
+ print bpow($x,$i),"\n"; # modify $x
+ print $x->bpow($i),"\n"; # ditto
+ print $x **= $i,"\n"; # the same
+ print $x ** $i,"\n"; # leave $x alone
+
+The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though.
=item blog()
- $x->blog($base, $accuracy); # logarithm of x to the base $base
+ $x->blog($base, $accuracy); # logarithm of x to the base $base
If C<$base> is not defined, Euler's number (e) is used:
- print $x->blog(undef, 100); # log(x) to 100 digits
+ print $x->blog(undef, 100); # log(x) to 100 digits
=item bexp()
- $x->bexp($accuracy); # calculate e ** X
+ $x->bexp($accuracy); # calculate e ** X
Calculates the expression C<e ** $x> where C<e> is Euler's number.
@@ -4271,31 +5016,26 @@ See also L</blog()>.
=item bnok()
- $x->bnok($y); # x over y (binomial coefficient n over k)
+ $x->bnok($y); # x over y (binomial coefficient n over k)
Calculates the binomial coefficient n over k, also called the "choose"
function. The result is equivalent to:
- ( n ) n!
- | - | = -------
- ( k ) k!(n-k)!
+ ( n ) n!
+ | - | = -------
+ ( k ) k!(n-k)!
This method was added in v1.84 of Math::BigInt (April 2007).
-=item bpi()
-
- print Math::BigInt->bpi(100), "\n"; # 3
+=item bsin()
-Returns PI truncated to an integer, with the argument being ignored. This means
-under BigInt this always returns C<3>.
+ my $x = Math::BigInt->new(1);
+ print $x->bsin(100), "\n";
-If upgrading is in effect, returns PI, rounded to N digits with the
-current rounding mode:
+Calculate the sine of $x, modifying $x in place.
- use Math::BigFloat;
- use Math::BigInt upgrade => Math::BigFloat;
- print Math::BigInt->bpi(3), "\n"; # 3.14
- print Math::BigInt->bpi(100), "\n"; # 3.1415....
+In Math::BigInt, unless upgrading is in effect, the result is truncated to an
+integer.
This method was added in v1.87 of Math::BigInt (June 2007).
@@ -4304,21 +5044,21 @@ This method was added in v1.87 of Math::BigInt (June 2007).
my $x = Math::BigInt->new(1);
print $x->bcos(100), "\n";
-Calculate the cosinus of $x, modifying $x in place.
+Calculate the cosine of $x, modifying $x in place.
-In BigInt, unless upgrading is in effect, the result is truncated to an
+In Math::BigInt, unless upgrading is in effect, the result is truncated to an
integer.
This method was added in v1.87 of Math::BigInt (June 2007).
-=item bsin()
+=item batan()
- my $x = Math::BigInt->new(1);
- print $x->bsin(100), "\n";
+ my $x = Math::BigFloat->new(0.5);
+ print $x->batan(100), "\n";
-Calculate the sinus of $x, modifying $x in place.
+Calculate the arcus tangens of $x, modifying $x in place.
-In BigInt, unless upgrading is in effect, the result is truncated to an
+In Math::BigInt, unless upgrading is in effect, the result is truncated to an
integer.
This method was added in v1.87 of Math::BigInt (June 2007).
@@ -4331,32 +5071,61 @@ This method was added in v1.87 of Math::BigInt (June 2007).
Calculate the arcus tangens of C<$y> divided by C<$x>, modifying $y in place.
-In BigInt, unless upgrading is in effect, the result is truncated to an
+In Math::BigInt, unless upgrading is in effect, the result is truncated to an
integer.
This method was added in v1.87 of Math::BigInt (June 2007).
-=item batan()
+=item bsqrt()
- my $x = Math::BigFloat->new(0.5);
- print $x->batan(100), "\n";
+ $x->bsqrt(); # calculate square-root
-Calculate the arcus tangens of $x, modifying $x in place.
+C<bsqrt()> returns the square root truncated to an integer.
-In BigInt, unless upgrading is in effect, the result is truncated to an
-integer.
+If you want a better approximation of the square root, then use:
-This method was added in v1.87 of Math::BigInt (June 2007).
+ $x = Math::BigFloat->new(12);
+ Math::BigFloat->precision(0);
+ Math::BigFloat->round_mode('even');
+ print $x->copy->bsqrt(),"\n"; # 4
-=item blsft()
+ Math::BigFloat->precision(2);
+ print $x->bsqrt(),"\n"; # 3.46
+ print $x->bsqrt(3),"\n"; # 3.464
- $x->blsft($y); # left shift in base 2
- $x->blsft($y,$n); # left shift, in base $n (like 10)
+=item broot()
+
+ $x->broot($N);
+
+Calculates the N'th root of C<$x>.
+
+=item bfac()
+
+ $x->bfac(); # factorial of $x (1*2*3*4*..*$x)
=item brsft()
- $x->brsft($y); # right shift in base 2
- $x->brsft($y,$n); # right shift, in base $n (like 10)
+ $x->brsft($n); # right shift $n places in base 2
+ $x->brsft($n, $b); # right shift $n places in base $b
+
+The latter is equivalent to
+
+ $x -> bdiv($b -> copy() -> bpow($n))
+
+=item blsft()
+
+ $x->blsft($n); # left shift $n places in base 2
+ $x->blsft($n, $b); # left shift $n places in base $b
+
+The latter is equivalent to
+
+ $x -> bmul($b -> copy() -> bpow($n))
+
+=back
+
+=head2 Bitwise methods
+
+=over
=item band()
@@ -4374,19 +5143,15 @@ This method was added in v1.87 of Math::BigInt (June 2007).
$x->bnot(); # bitwise not (two's complement)
-=item bsqrt()
-
- $x->bsqrt(); # calculate square-root
-
-=item broot()
+Two's complement (bitwise not). This is equivalent to, but faster than,
- $x->broot($N);
+ $x->binc()->bneg();
-Calculates the N'th root of C<$x>.
+=back
-=item bfac()
+=head2 Rounding methods
- $x->bfac(); # factorial of $x (1*2*3*4*..$x)
+=over
=item round()
@@ -4399,178 +5164,272 @@ C<$round_mode>.
$x->bround($N); # accuracy: preserve $N digits
+Rounds $x to an accuracy of $N digits.
+
=item bfround()
$x->bfround($N);
-If N is > 0, rounds to the Nth digit from the left. If N < 0, rounds to
-the Nth digit after the dot. Since BigInts are integers, the case N < 0
-is a no-op for them.
+Rounds to a multiple of 10**$N. Examples:
-Examples:
+ Input N Result
- Input N Result
- ===================================================
- 123456.123456 3 123500
- 123456.123456 2 123450
- 123456.123456 -2 123456.12
- 123456.123456 -3 123456.123
+ 123456.123456 3 123500
+ 123456.123456 2 123450
+ 123456.123456 -2 123456.12
+ 123456.123456 -3 123456.123
=item bfloor()
$x->bfloor();
-Round $x towards minus infinity (i.e., set $x to the largest integer less than
-or equal to $x). This is a no-op in BigInt, but changes $x in BigFloat, if $x
-is not an integer.
+Round $x towards minus infinity, i.e., set $x to the largest integer less than
+or equal to $x.
=item bceil()
$x->bceil();
-Round $x towards plus infinity (i.e., set $x to the smallest integer greater
-than or equal to $x). This is a no-op in BigInt, but changes $x in BigFloat, if
-$x is not an integer.
+Round $x towards plus infinity, i.e., set $x to the smallest integer greater
+than or equal to $x).
=item bint()
$x->bint();
-Round $x towards zero. This is a no-op in BigInt, but changes $x in BigFloat,
-if $x is not an integer.
+Round $x towards zero.
+
+=back
+
+=head2 Other mathematical methods
+
+=over
=item bgcd()
- bgcd(@values); # greatest common divisor (no OO style)
+ $x -> bgcd($y); # GCD of $x and $y
+ $x -> bgcd($y, $z, ...); # GCD of $x, $y, $z, ...
+
+Returns the greatest common divisor (GCD).
=item blcm()
- blcm(@values); # lowest common multiple (no OO style)
+ $x -> blcm($y); # LCM of $x and $y
+ $x -> blcm($y, $z, ...); # LCM of $x, $y, $z, ...
+
+Returns the least common multiple (LCM).
+
+=back
+
+=head2 Object property methods
+
+=over
+
+=item sign()
+
+ $x->sign();
+
+Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
+
+If you want $x to have a certain sign, use one of the following methods:
+
+ $x->babs(); # '+'
+ $x->babs()->bneg(); # '-'
+ $x->bnan(); # 'NaN'
+ $x->binf(); # '+inf'
+ $x->binf('-'); # '-inf'
+
+=item digit()
+
+ $x->digit($n); # return the nth digit, counting from right
+
+If C<$n> is negative, returns the digit counting from left.
=item length()
$x->length();
- ($xl,$fl) = $x->length();
+ ($xl, $fl) = $x->length();
-Returns the number of digits in the decimal representation of the number.
-In list context, returns the length of the integer and fraction part. For
-BigInt's, the length of the fraction part will always be 0.
+Returns the number of digits in the decimal representation of the number. In
+list context, returns the length of the integer and fraction part. For
+Math::BigInt objects, the length of the fraction part is always 0.
-=item exponent()
+The following probably doesn't do what you expect:
- $x->exponent();
+ $c = Math::BigInt->new(123);
+ print $c->length(),"\n"; # prints 30
+
+It prints both the number of digits in the number and in the fraction part
+since print calls C<length()> in list context. Use something like:
-Return the exponent of $x as BigInt.
+ print scalar $c->length(),"\n"; # prints 3
=item mantissa()
$x->mantissa();
-Return the signed mantissa of $x as BigInt.
+Return the signed mantissa of $x as a Math::BigInt.
+
+=item exponent()
+
+ $x->exponent();
+
+Return the exponent of $x as a Math::BigInt.
=item parts()
- $x->parts(); # return (mantissa,exponent) as BigInt
+ $x->parts();
-=item copy()
+Returns the significand (mantissa) and the exponent as integers. In
+Math::BigFloat, both are returned as Math::BigInt objects.
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
+=item sparts()
-=item as_int()
+Returns the significand (mantissa) and the exponent as integers. In scalar
+context, only the significand is returned. The significand is the integer with
+the smallest absolute value. The output of C<sparts()> corresponds to the
+output from C<bsstr()>.
-=item as_number()
+In Math::BigInt, this method is identical to C<parts()>.
-These methods are called when Math::BigInt encounters an object it doesn't know
-how to handle. For instance, assume $x is a Math::BigInt, or subclass thereof,
-and $y is defined, but not a Math::BigInt, or subclass thereof. If you do
+=item nparts()
- $x -> badd($y);
+Returns the significand (mantissa) and exponent corresponding to normalized
+notation. In scalar context, only the significand is returned. For finite
+non-zero numbers, the significand's absolute value is greater than or equal to
+1 and less than 10. The output of C<nparts()> corresponds to the output from
+C<bnstr()>. In Math::BigInt, if the significand can not be represented as an
+integer, upgrading is performed or NaN is returned.
-$y needs to be converted into an object that $x can deal with. This is done by
-first checking if $y is something that $x might be upgraded to. If that is the
-case, no further attempts are made. The next is to see if $y supports the
-method C<as_int()>. If it does, C<as_int()> is called, but if it doesn't, the
-next thing is to see if $y supports the method C<as_number()>. If it does,
-C<as_number()> is called. The method C<as_int()> (and C<as_number()>) is
-expected to return either an object that has the same class as $x, a subclass
-thereof, or a string that C<ref($x)-E<gt>new()> can parse to create an object.
+=item eparts()
-C<as_number()> is an alias to C<as_int()>. C<as_number> was introduced in
-v1.22, while C<as_int()> was introduced in v1.68.
+Returns the significand (mantissa) and exponent corresponding to engineering
+notation. In scalar context, only the significand is returned. For finite
+non-zero numbers, the significand's absolute value is greater than or equal to
+1 and less than 1000, and the exponent is a multiple of 3. The output of
+C<eparts()> corresponds to the output from C<bestr()>. In Math::BigInt, if the
+significand can not be represented as an integer, upgrading is performed or NaN
+is returned.
-In Math::BigInt, C<as_int()> has the same effect as C<copy()>.
+=item dparts()
-=item bstr()
+Returns the integer part and the fraction part. If the fraction part can not be
+represented as an integer, upgrading is performed or NaN is returned. The
+output of C<dparts()> corresponds to the output from C<bdstr()>.
+
+=back
- $x->bstr();
+=head2 String conversion methods
-Returns a normalized string representation of C<$x>.
+=over
+
+=item bstr()
+
+Returns a string representing the number using decimal notation. In
+Math::BigFloat, the output is zero padded according to the current accuracy or
+precision, if any of those are defined.
=item bsstr()
- $x->bsstr(); # normalized string in scientific notation
+Returns a string representing the number using scientific notation where both
+the significand (mantissa) and the exponent are integers. The output
+corresponds to the output from C<sparts()>.
-=item as_hex()
+ 123 is returned as "123e+0"
+ 1230 is returned as "123e+1"
+ 12300 is returned as "123e+2"
+ 12000 is returned as "12e+3"
+ 10000 is returned as "1e+4"
- $x->as_hex(); # as signed hexadecimal string with prefixed 0x
+=item bnstr()
-=item as_bin()
+Returns a string representing the number using normalized notation, the most
+common variant of scientific notation. For finite non-zero numbers, the
+absolute value of the significand is less than or equal to 1 and less than 10.
+The output corresponds to the output from C<nparts()>.
- $x->as_bin(); # as signed binary string with prefixed 0b
+ 123 is returned as "1.23e+2"
+ 1230 is returned as "1.23e+3"
+ 12300 is returned as "1.23e+4"
+ 12000 is returned as "1.2e+4"
+ 10000 is returned as "1e+4"
-=item as_oct()
+=item bestr()
- $x->as_oct(); # as signed octal string with prefixed 0
+Returns a string representing the number using engineering notation. For finite
+non-zero numbers, the absolute value of the significand is less than or equal
+to 1 and less than 1000, and the exponent is a multiple of 3. The output
+corresponds to the output from C<eparts()>.
-=item numify()
+ 123 is returned as "123e+0"
+ 1230 is returned as "1.23e+3"
+ 12300 is returned as "12.3e+3"
+ 12000 is returned as "12e+3"
+ 10000 is returned as "10e+3"
- print $x->numify();
+=item bdstr()
-This returns a normal Perl scalar from $x. It is used automatically
-whenever a scalar is needed, for instance in array index operations.
+Returns a string representing the number using decimal notation. The output
+corresponds to the output from C<dparts()>.
-This loses precision, to avoid this use L</as_int()> instead.
+ 123 is returned as "123"
+ 1230 is returned as "1230"
+ 12300 is returned as "12300"
+ 12000 is returned as "12000"
+ 10000 is returned as "10000"
-=item modify()
+=item as_hex()
- $x->modify('bpowd');
+ $x->as_hex();
-This method returns 0 if the object can be modified with the given
-operation, or 1 if not.
+Returns a string representing the number using hexadecimal notation. The output
+is prefixed by "0x".
-This is used for instance by L<Math::BigInt::Constant>.
+=item as_bin()
-=item upgrade()/downgrade()
+ $x->as_bin();
-Set/get the class for downgrade/upgrade operations. Thuis is used
-for instance by L<bignum>. The defaults are '', thus the following
-operation will create a BigInt, not a BigFloat:
+Returns a string representing the number using binary notation. The output is
+prefixed by "0b".
- my $i = Math::BigInt->new(123);
- my $f = Math::BigFloat->new('123.1');
+=item as_oct()
- print $i + $f,"\n"; # print 246
+ $x->as_oct();
-=item div_scale()
+Returns a string representing the number using octal notation. The output is
+prefixed by "0".
-Set/get the number of digits for the default precision in divide
-operations.
+=item as_bytes()
-=item round_mode()
+ $x = Math::BigInt->new("1667327589");
+ $s = $x->as_bytes(); # $s = "cafe"
-Set/get the current round mode.
+Returns a byte string representing the number using big endian byte order. The
+invocand must be a non-negative, finite integer.
+
+=back
+
+=head2 Other conversion methods
+
+=over
+
+=item numify()
+
+ print $x->numify();
+
+Returns a Perl scalar from $x. It is used automatically whenever a scalar is
+needed, for instance in array index operations.
=back
=head1 ACCURACY and PRECISION
-Since version v1.33, Math::BigInt and Math::BigFloat have full support for
-accuracy and precision based rounding, both automatically after every
-operation, as well as manually.
+Math::BigInt and Math::BigFloat have full support for accuracy and precision
+based rounding, both automatically after every operation, as well as manually.
-This section describes the accuracy/precision handling in Math::Big* as it
-used to be and as it is now, complete with an explanation of all terms and
-abbreviations.
+This section describes the accuracy/precision handling in Math::BigInt and
+Math::BigFloat as it used to be and as it is now, complete with an explanation
+of all terms and abbreviations.
Not yet implemented things (but with correct description) are marked with '!',
things that need to be answered are marked with '?'.
@@ -4579,49 +5438,48 @@ In the next paragraph follows a short description of terms used here (because
these may differ from terms used by others people or documentation).
During the rest of this document, the shortcuts A (for accuracy), P (for
-precision), F (fallback) and R (rounding mode) will be used.
+precision), F (fallback) and R (rounding mode) are be used.
=head2 Precision P
-A fixed number of digits before (positive) or after (negative)
-the decimal point. For example, 123.45 has a precision of -2. 0 means an
-integer like 123 (or 120). A precision of 2 means two digits to the left
-of the decimal point are zero, so 123 with P = 1 becomes 120. Note that
-numbers with zeros before the decimal point may have different precisions,
-because 1200 can have p = 0, 1 or 2 (depending on what the initial value
-was). It could also have p < 0, when the digits after the decimal point
-are zero.
-
-The string output (of floating point numbers) will be padded with zeros:
-
- Initial value P A Result String
- ------------------------------------------------------------
- 1234.01 -3 1000 1000
- 1234 -2 1200 1200
- 1234.5 -1 1230 1230
- 1234.001 1 1234 1234.0
- 1234.01 0 1234 1234
- 1234.01 2 1234.01 1234.01
- 1234.01 5 1234.01 1234.01000
-
-For BigInts, no padding occurs.
+Precision is a fixed number of digits before (positive) or after (negative) the
+decimal point. For example, 123.45 has a precision of -2. 0 means an integer
+like 123 (or 120). A precision of 2 means at least two digits to the left of
+the decimal point are zero, so 123 with P = 1 becomes 120. Note that numbers
+with zeros before the decimal point may have different precisions, because 1200
+can have P = 0, 1 or 2 (depending on what the initial value was). It could also
+have p < 0, when the digits after the decimal point are zero.
+
+The string output (of floating point numbers) is padded with zeros:
+
+ Initial value P A Result String
+ ------------------------------------------------------------
+ 1234.01 -3 1000 1000
+ 1234 -2 1200 1200
+ 1234.5 -1 1230 1230
+ 1234.001 1 1234 1234.0
+ 1234.01 0 1234 1234
+ 1234.01 2 1234.01 1234.01
+ 1234.01 5 1234.01 1234.01000
+
+For Math::BigInt objects, no padding occurs.
=head2 Accuracy A
-Number of significant digits. Leading zeros are not counted. A
-number may have an accuracy greater than the non-zero digits
-when there are zeros in it or trailing zeros. For example, 123.456 has
-A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3.
+Number of significant digits. Leading zeros are not counted. A number may have
+an accuracy greater than the non-zero digits when there are zeros in it or
+trailing zeros. For example, 123.456 has A of 6, 10203 has 5, 123.0506 has 7,
+123.45000 has 8 and 0.000123 has 3.
-The string output (of floating point numbers) will be padded with zeros:
+The string output (of floating point numbers) is padded with zeros:
- Initial value P A Result String
- ------------------------------------------------------------
- 1234.01 3 1230 1230
- 1234.01 6 1234.01 1234.01
- 1234.1 8 1234.1 1234.1000
+ Initial value P A Result String
+ ------------------------------------------------------------
+ 1234.01 3 1230 1230
+ 1234.01 6 1234.01 1234.01
+ 1234.1 8 1234.1 1234.1000
-For BigInts, no padding occurs.
+For Math::BigInt objects, no padding occurs.
=head2 Fallback F
@@ -4630,74 +5488,67 @@ dividing numbers.
=head2 Rounding mode R
-When rounding a number, different 'styles' or 'kinds'
-of rounding are possible. (Note that random rounding, as in
-Math::Round, is not implemented.)
+When rounding a number, different 'styles' or 'kinds' of rounding are possible.
+(Note that random rounding, as in Math::Round, is not implemented.)
=over
=item 'trunc'
-truncation invariably removes all digits following the
-rounding place, replacing them with zeros. Thus, 987.65 rounded
-to tens (P=1) becomes 980, and rounded to the fourth sigdig
-becomes 987.6 (A=4). 123.456 rounded to the second place after the
-decimal point (P=-2) becomes 123.46.
-
-All other implemented styles of rounding attempt to round to the
-"nearest digit." If the digit D immediately to the right of the
-rounding place (skipping the decimal point) is greater than 5, the
-number is incremented at the rounding place (possibly causing a
-cascade of incrementation): e.g. when rounding to units, 0.9 rounds
-to 1, and -19.9 rounds to -20. If D < 5, the number is similarly
-truncated at the rounding place: e.g. when rounding to units, 0.4
+truncation invariably removes all digits following the rounding place,
+replacing them with zeros. Thus, 987.65 rounded to tens (P = 1) becomes 980,
+and rounded to the fourth sigdig becomes 987.6 (A = 4). 123.456 rounded to the
+second place after the decimal point (P = -2) becomes 123.46.
+
+All other implemented styles of rounding attempt to round to the "nearest
+digit." If the digit D immediately to the right of the rounding place (skipping
+the decimal point) is greater than 5, the number is incremented at the rounding
+place (possibly causing a cascade of incrementation): e.g. when rounding to
+units, 0.9 rounds to 1, and -19.9 rounds to -20. If D < 5, the number is
+similarly truncated at the rounding place: e.g. when rounding to units, 0.4
rounds to 0, and -19.4 rounds to -19.
-However the results of other styles of rounding differ if the
-digit immediately to the right of the rounding place (skipping the
-decimal point) is 5 and if there are no digits, or no digits other
-than 0, after that 5. In such cases:
+However the results of other styles of rounding differ if the digit immediately
+to the right of the rounding place (skipping the decimal point) is 5 and if
+there are no digits, or no digits other than 0, after that 5. In such cases:
=item 'even'
-rounds the digit at the rounding place to 0, 2, 4, 6, or 8
-if it is not already. E.g., when rounding to the first sigdig, 0.45
-becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5.
+rounds the digit at the rounding place to 0, 2, 4, 6, or 8 if it is not
+already. E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55
+becomes -0.6, but 0.4501 becomes 0.5.
=item 'odd'
-rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if
-it is not already. E.g., when rounding to the first sigdig, 0.45
-becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6.
+rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if it is not
+already. E.g., when rounding to the first sigdig, 0.45 becomes 0.5, -0.55
+becomes -0.5, but 0.5501 becomes 0.6.
=item '+inf'
-round to plus infinity, i.e. always round up. E.g., when
-rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5,
-and 0.4501 also becomes 0.5.
+round to plus infinity, i.e. always round up. E.g., when rounding to the first
+sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, and 0.4501 also becomes 0.5.
=item '-inf'
-round to minus infinity, i.e. always round down. E.g., when
-rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6,
-but 0.4501 becomes 0.5.
+round to minus infinity, i.e. always round down. E.g., when rounding to the
+first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5.
=item 'zero'
-round to zero, i.e. positive numbers down, negative ones up.
-E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55
-becomes -0.5, but 0.4501 becomes 0.5.
+round to zero, i.e. positive numbers down, negative ones up. E.g., when
+rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.5, but 0.4501
+becomes 0.5.
=item 'common'
-round up if the digit immediately to the right of the rounding place
-is 5 or greater, otherwise round down. E.g., 0.15 becomes 0.2 and
-0.149 becomes 0.1.
+round up if the digit immediately to the right of the rounding place is 5 or
+greater, otherwise round down. E.g., 0.15 becomes 0.2 and 0.149 becomes 0.1.
=back
-The handling of A & P in MBI/MBF (the old core code shipped with Perl
-versions <= 5.7.2) is like this:
+The handling of A & P in MBI/MBF (the old core code shipped with Perl versions
+<= 5.7.2) is like this:
=over
@@ -4714,7 +5565,7 @@ versions <= 5.7.2) is like this:
+ other operations simply create the same number (bneg etc), or
more (bmul) of digits
+ rounding/truncating is only done when explicitly calling one
- of bround or bfround, and never for BigInt (not implemented)
+ of bround or bfround, and never for Math::BigInt (not implemented)
* bsqrt() simply hands its accuracy argument over to bdiv.
* the documentation and the comment in the code indicate two
different ways on how bdiv() determines the maximum number
@@ -4800,10 +5651,10 @@ This is how it works now:
* If A or P are enabled/defined, they are used to round the result of each
operation according to the rules below
- * Negative P is ignored in Math::BigInt, since BigInts never have digits
- after the decimal point
+ * Negative P is ignored in Math::BigInt, since Math::BigInt objects never
+ have digits after the decimal point
* Math::BigFloat uses Math::BigInt internally, but setting A or P inside
- Math::BigInt as globals does not tamper with the parts of a BigFloat.
+ Math::BigInt as globals does not tamper with the parts of a Math::BigFloat.
A flag is used to mark all Math::BigFloat numbers as 'never round'.
=item Precedence
@@ -4925,53 +5776,33 @@ This is how it works now:
=head1 Infinity and Not a Number
-While BigInt has extensive handling of inf and NaN, certain quirks remain.
+While Math::BigInt has extensive handling of inf and NaN, certain quirks
+remain.
=over
=item oct()/hex()
-These perl routines currently (as of Perl v.5.8.6) cannot handle passed
-inf.
+These perl routines currently (as of Perl v.5.8.6) cannot handle passed inf.
- te@linux:~> perl -wle 'print 2 ** 3333'
- Inf
- te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333'
- 1
- te@linux:~> perl -wle 'print oct(2 ** 3333)'
- 0
- te@linux:~> perl -wle 'print hex(2 ** 3333)'
- Illegal hexadecimal digit 'I' ignored at -e line 1.
- 0
+ te@linux:~> perl -wle 'print 2 ** 3333'
+ Inf
+ te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333'
+ 1
+ te@linux:~> perl -wle 'print oct(2 ** 3333)'
+ 0
+ te@linux:~> perl -wle 'print hex(2 ** 3333)'
+ Illegal hexadecimal digit 'I' ignored at -e line 1.
+ 0
The same problems occur if you pass them Math::BigInt->binf() objects. Since
-overloading these routines is not possible, this cannot be fixed from BigInt.
-
-=item ==, !=, <, >, <=, >= with NaNs
-
-BigInt's bcmp() routine currently returns undef to signal that a NaN was
-involved in a comparison. However, the overload code turns that into
-either 1 or '' and thus operations like C<< NaN != NaN >> might return
-wrong values.
-
-=item log(-inf)
-
-C<< log(-inf) >> is highly weird. Since log(-x)=pi*i+log(x), then
-log(-inf)=pi*i+inf. However, since the imaginary part is finite, the real
-infinity "overshadows" it, so the number might as well just be infinity.
-However, the result is a complex number, and since BigInt/BigFloat can only
-have real numbers as results, the result is NaN.
-
-=item exp(), cos(), sin(), atan2()
-
-These all might have problems handling infinity right.
+overloading these routines is not possible, this cannot be fixed from
+Math::BigInt.
=back
=head1 INTERNALS
-The actual numbers are stored as unsigned big integers (with separate sign).
-
You should neither care about nor depend on the internal representation; it
might change without notice. Use B<ONLY> method calls like C<< $x->sign(); >>
instead relying on the internal representation.
@@ -4981,35 +5812,34 @@ instead relying on the internal representation.
Math with the numbers is done (by default) by a module called
C<Math::BigInt::Calc>. This is equivalent to saying:
- use Math::BigInt try => 'Calc';
+ use Math::BigInt try => 'Calc';
You can change this backend library by using:
- use Math::BigInt try => 'GMP';
+ use Math::BigInt try => 'GMP';
-B<Note>: General purpose packages should not be explicit about the library
-to use; let the script author decide which is best.
+B<Note>: General purpose packages should not be explicit about the library to
+use; let the script author decide which is best.
-If your script works with huge numbers and Calc is too slow for them,
-you can also for the loading of one of these libraries and if none
-of them can be used, the code will die:
+If your script works with huge numbers and Calc is too slow for them, you can
+also for the loading of one of these libraries and if none of them can be used,
+the code dies:
- use Math::BigInt only => 'GMP,Pari';
+ use Math::BigInt only => 'GMP,Pari';
The following would first try to find Math::BigInt::Foo, then
Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
- use Math::BigInt try => 'Foo,Math::BigInt::Bar';
+ use Math::BigInt try => 'Foo,Math::BigInt::Bar';
-The library that is loaded last will be used. Note that this can be
-overwritten at any time by loading a different library, and numbers
-constructed with different libraries cannot be used in math operations
-together.
+The library that is loaded last is used. Note that this can be overwritten at
+any time by loading a different library, and numbers constructed with different
+libraries cannot be used in math operations together.
=head3 What library to use?
-B<Note>: General purpose packages should not be explicit about the library
-to use; let the script author decide which is best.
+B<Note>: General purpose packages should not be explicit about the library to
+use; let the script author decide which is best.
L<Math::BigInt::GMP> and L<Math::BigInt::Pari> are in cases involving big
numbers much faster than Calc, however it is slower when dealing with very
@@ -5031,30 +5861,8 @@ The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
A sign of 'NaN' is used to represent the result when input arguments are not
numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
-minus infinity. You will get '+inf' when dividing a positive number by 0, and
-'-inf' when dividing any negative number by 0.
-
-=head2 mantissa(), exponent() and parts()
-
-C<mantissa()> and C<exponent()> return the said parts of the BigInt such
-that:
-
- $m = $x->mantissa();
- $e = $x->exponent();
- $y = $m * ( 10 ** $e );
- print "ok\n" if $x == $y;
-
-C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them
-in one go. Both the returned mantissa and exponent have a sign.
-
-Currently, for BigInts C<$e> is always 0, except +inf and -inf, where it is
-C<+inf>; and for NaN, where it is C<NaN>; and for C<$x == 0>, where it is C<1>
-(to be compatible with Math::BigFloat's internal representation of a zero as
-C<0E1>).
-
-C<$m> is currently just a copy of the original number. The relation between
-C<$e> and C<$m> will stay always the same, though their real values might
-change.
+minus infinity. You get '+inf' when dividing a positive number by 0, and '-inf'
+when dividing any negative number by 0.
=head1 EXAMPLES
@@ -5064,18 +5872,18 @@ change.
$x = Math::BigInt->bstr("1234") # string "1234"
$x = "$x"; # same as bstr()
- $x = Math::BigInt->bneg("1234"); # BigInt "-1234"
- $x = Math::BigInt->babs("-12345"); # BigInt "12345"
- $x = Math::BigInt->bnorm("-0.00"); # BigInt "0"
- $x = bigint(1) + bigint(2); # BigInt "3"
- $x = bigint(1) + "2"; # ditto (auto-BigIntify of "2")
- $x = bigint(1); # BigInt "1"
- $x = $x + 5 / 2; # BigInt "3"
- $x = $x ** 3; # BigInt "27"
- $x *= 2; # BigInt "54"
- $x = Math::BigInt->new(0); # BigInt "0"
- $x--; # BigInt "-1"
- $x = Math::BigInt->badd(4,5) # BigInt "9"
+ $x = Math::BigInt->bneg("1234"); # Math::BigInt "-1234"
+ $x = Math::BigInt->babs("-12345"); # Math::BigInt "12345"
+ $x = Math::BigInt->bnorm("-0.00"); # Math::BigInt "0"
+ $x = bigint(1) + bigint(2); # Math::BigInt "3"
+ $x = bigint(1) + "2"; # ditto (auto-Math::BigIntify of "2")
+ $x = bigint(1); # Math::BigInt "1"
+ $x = $x + 5 / 2; # Math::BigInt "3"
+ $x = $x ** 3; # Math::BigInt "27"
+ $x *= 2; # Math::BigInt "54"
+ $x = Math::BigInt->new(0); # Math::BigInt "0"
+ $x--; # Math::BigInt "-1"
+ $x = Math::BigInt->badd(4,5) # Math::BigInt "9"
print $x->bsstr(); # 9e+0
Examples for rounding:
@@ -5110,67 +5918,67 @@ Examples for converting:
=head1 Autocreating constants
After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal
-and binary constants in the given scope are converted to C<Math::BigInt>.
-This conversion happens at compile time.
+and binary constants in the given scope are converted to C<Math::BigInt>. This
+conversion happens at compile time.
In particular,
perl -MMath::BigInt=:constant -e 'print 2**100,"\n"'
prints the integer value of C<2**100>. Note that without conversion of
-constants the expression 2**100 will be calculated as perl scalar.
+constants the expression 2**100 is calculated using Perl scalars.
-Please note that strings and floating point constants are not affected,
-so that
+Please note that strings and floating point constants are not affected, so that
- use Math::BigInt qw/:constant/;
+ use Math::BigInt qw/:constant/;
- $x = 1234567890123456789012345678901234567890
- + 123456789123456789;
- $y = '1234567890123456789012345678901234567890'
- + '123456789123456789';
+ $x = 1234567890123456789012345678901234567890
+ + 123456789123456789;
+ $y = '1234567890123456789012345678901234567890'
+ + '123456789123456789';
-do not work. You need an explicit Math::BigInt->new() around one of the
-operands. You should also quote large constants to protect loss of precision:
+does not give you what you expect. You need an explicit Math::BigInt->new()
+around one of the operands. You should also quote large constants to protect
+loss of precision:
- use Math::BigInt;
+ use Math::BigInt;
- $x = Math::BigInt->new('1234567889123456789123456789123456789');
+ $x = Math::BigInt->new('1234567889123456789123456789123456789');
Without the quotes Perl would convert the large number to a floating point
-constant at compile time and then hand the result to BigInt, which results in
-an truncated result or a NaN.
+constant at compile time and then hand the result to Math::BigInt, which
+results in an truncated result or a NaN.
This also applies to integers that look like floating point constants:
- use Math::BigInt ':constant';
+ use Math::BigInt ':constant';
- print ref(123e2),"\n";
- print ref(123.2e2),"\n";
+ print ref(123e2),"\n";
+ print ref(123.2e2),"\n";
-will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat>
-to get this to work.
+prints nothing but newlines. Use either L<bignum> or L<Math::BigFloat> to get
+this to work.
=head1 PERFORMANCE
Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x
must be made in the second case. For long numbers, the copy can eat up to 20%
of the work (in the case of addition/subtraction, less for
-multiplication/division). If $y is very small compared to $x, the form
-$x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes
-more time then the actual addition.
+multiplication/division). If $y is very small compared to $x, the form $x += $y
+is MUCH faster than $x = $x + $y since making the copy of $x takes more time
+then the actual addition.
With a technique called copy-on-write, the cost of copying with overload could
be minimized or even completely avoided. A test implementation of COW did show
-performance gains for overloaded math, but introduced a performance loss due
-to a constant overhead for all other operations. So Math::BigInt does currently
+performance gains for overloaded math, but introduced a performance loss due to
+a constant overhead for all other operations. So Math::BigInt does currently
not COW.
The rewritten version of this module (vs. v0.01) is slower on certain
operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it
does now more work and handles much more cases. The time spent in these
-operations is usually gained in the other math operations so that code on
-the average should get (much) faster. If they don't, please contact the author.
+operations is usually gained in the other math operations so that code on the
+average should get (much) faster. If they don't, please contact the author.
Some operations may be slower for small numbers, but are significantly faster
for big numbers. Other operations are now constant (O(1), like C<bneg()>,
@@ -5199,9 +6007,8 @@ work, as long as a few simple rules are followed:
=item *
The public API must remain consistent, i.e. if a sub-class is overloading
-addition, the sub-class must use the same name, in this case badd(). The
-reason for this is that Math::BigInt is optimized to call the object methods
-directly.
+addition, the sub-class must use the same name, in this case badd(). The reason
+for this is that Math::BigInt is optimized to call the object methods directly.
=item *
@@ -5212,41 +6019,41 @@ additional keys can be added, like C<< $x->{_custom} >>.
Accessor functions are available for all existing object hash keys and should
be used instead of directly accessing the internal hash keys. The reason for
-this is that Math::BigInt itself has a pluggable interface which permits it
-to support different storage methods.
+this is that Math::BigInt itself has a pluggable interface which permits it to
+support different storage methods.
=back
More complex sub-classes may have to replicate more of the logic internal of
-Math::BigInt if they need to change more basic behaviors. A subclass that
-needs to merely change the output only needs to overload C<bstr()>.
+Math::BigInt if they need to change more basic behaviors. A subclass that needs
+to merely change the output only needs to overload C<bstr()>.
All other object methods and overloaded functions can be directly inherited
from the parent class.
-At the very minimum, any subclass will need to provide its own C<new()> and can
+At the very minimum, any subclass needs to provide its own C<new()> and can
store additional hash keys in the object. There are also some package globals
that must be defined, e.g.:
- # Globals
- $accuracy = undef;
- $precision = -2; # round to 2 decimal places
- $round_mode = 'even';
- $div_scale = 40;
+ # Globals
+ $accuracy = undef;
+ $precision = -2; # round to 2 decimal places
+ $round_mode = 'even';
+ $div_scale = 40;
Additionally, you might want to provide the following two globals to allow
auto-upgrading and auto-downgrading to work correctly:
- $upgrade = undef;
- $downgrade = undef;
+ $upgrade = undef;
+ $downgrade = undef;
This allows Math::BigInt to correctly retrieve package globals from the
-subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or
+subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or
t/Math/BigFloat/SubClass.pm completely functional subclass examples.
Don't forget to
- use overload;
+ use overload;
in your subclass to automatically inherit the overloading from the parent. If
you like, you can change part of the overloading, look at Math::String for an
@@ -5256,62 +6063,43 @@ example.
When used like this:
- use Math::BigInt upgrade => 'Foo::Bar';
+ use Math::BigInt upgrade => 'Foo::Bar';
-certain operations will 'upgrade' their calculation and thus the result to
-the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat:
+certain operations 'upgrade' their calculation and thus the result to the class
+Foo::Bar. Usually this is used in conjunction with Math::BigFloat:
- use Math::BigInt upgrade => 'Math::BigFloat';
+ use Math::BigInt upgrade => 'Math::BigFloat';
As a shortcut, you can use the module L<bignum>:
- use bignum;
+ use bignum;
Also good for one-liners:
- perl -Mbignum -le 'print 2 ** 255'
+ perl -Mbignum -le 'print 2 ** 255'
-This makes it possible to mix arguments of different classes (as in 2.5 + 2)
-as well es preserve accuracy (as in sqrt(3)).
+This makes it possible to mix arguments of different classes (as in 2.5 + 2) as
+well es preserve accuracy (as in sqrt(3)).
Beware: This feature is not fully implemented yet.
=head2 Auto-upgrade
-The following methods upgrade themselves unconditionally; that is if upgrade
-is in effect, they will always hand up their work:
+The following methods upgrade themselves unconditionally; that is if upgrade is
+in effect, they always hands up their work:
-=over
+ div bsqrt blog bexp bpi bsin bcos batan batan2
-=item bsqrt()
-
-=item div()
-
-=item blog()
-
-=item bexp()
-
-=item bpi()
-
-=item bcos()
-
-=item bsin()
-
-=item batan2()
-
-=item batan()
-
-=back
-
-All other methods upgrade themselves only when one (or all) of their
-arguments are of the class mentioned in $upgrade.
+All other methods upgrade themselves only when one (or all) of their arguments
+are of the class mentioned in $upgrade.
=head1 EXPORTS
-C<Math::BigInt> exports nothing by default, but can export the following methods:
+C<Math::BigInt> exports nothing by default, but can export the following
+methods:
- bgcd
- blcm
+ bgcd
+ blcm
=head1 CAVEATS
@@ -5320,242 +6108,120 @@ known to be troublesome:
=over
-=item bstr(), bsstr() and 'cmp'
+=item Comparing numbers as strings
-Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now
-drop the leading '+'. The old code would return '+3', the new returns '3'.
-This is to be consistent with Perl and to make C<cmp> (especially with
-overloading) to work as you expect. It also solves problems with C<Test.pm>
-and L<Test::More>, which stringify arguments before comparing them.
+Both C<bstr()> and C<bsstr()> as well as stringify via overload drop the
+leading '+'. This is to be consistent with Perl and to make C<cmp> (especially
+with overloading) to work as you expect. It also solves problems with
+C<Test.pm> and L<Test::More>, which stringify arguments before comparing them.
Mark Biggar said, when asked about to drop the '+' altogether, or make only
C<cmp> work:
- I agree (with the first alternative), don't add the '+' on positive
- numbers. It's not as important anymore with the new internal
- form for numbers. It made doing things like abs and neg easier,
- but those have to be done differently now anyway.
+ I agree (with the first alternative), don't add the '+' on positive
+ numbers. It's not as important anymore with the new internal form
+ for numbers. It made doing things like abs and neg easier, but
+ those have to be done differently now anyway.
-So, the following examples will now work all as expected:
+So, the following examples now works as expected:
- use Test::More tests => 1;
- use Math::BigInt;
+ use Test::More tests => 1;
+ use Math::BigInt;
- my $x = Math::BigInt -> new(3*3);
- my $y = Math::BigInt -> new(3*3);
+ my $x = Math::BigInt -> new(3*3);
+ my $y = Math::BigInt -> new(3*3);
- is ($x,3*3, 'multiplication');
- print "$x eq 9" if $x eq $y;
- print "$x eq 9" if $x eq '9';
- print "$x eq 9" if $x eq 3*3;
+ is($x,3*3, 'multiplication');
+ print "$x eq 9" if $x eq $y;
+ print "$x eq 9" if $x eq '9';
+ print "$x eq 9" if $x eq 3*3;
Additionally, the following still works:
- print "$x == 9" if $x == $y;
- print "$x == 9" if $x == 9;
- print "$x == 9" if $x == 3*3;
+ print "$x == 9" if $x == $y;
+ print "$x == 9" if $x == 9;
+ print "$x == 9" if $x == 3*3;
There is now a C<bsstr()> method to get the string in scientific notation aka
C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr()
-for comparison, but Perl will represent some numbers as 100 and others
-as 1e+308. If in doubt, convert both arguments to Math::BigInt before
-comparing them as strings:
+for comparison, but Perl represents some numbers as 100 and others as 1e+308.
+If in doubt, convert both arguments to Math::BigInt before comparing them as
+strings:
- use Test::More tests => 3;
- use Math::BigInt;
+ use Test::More tests => 3;
+ use Math::BigInt;
- $x = Math::BigInt->new('1e56'); $y = 1e56;
- is ($x,$y); # will fail
- is ($x->bsstr(),$y); # okay
- $y = Math::BigInt->new($y);
- is ($x,$y); # okay
+ $x = Math::BigInt->new('1e56'); $y = 1e56;
+ is($x,$y); # fails
+ is($x->bsstr(),$y); # okay
+ $y = Math::BigInt->new($y);
+ is($x,$y); # okay
-Alternatively, simply use C<< <=> >> for comparisons, this will get it
-always right. There is not yet a way to get a number automatically represented
-as a string that matches exactly the way Perl represents it.
+Alternatively, simply use C<< <=> >> for comparisons, this always gets it
+right. There is not yet a way to get a number automatically represented as a
+string that matches exactly the way Perl represents it.
See also the section about L<Infinity and Not a Number> for problems in
comparing NaNs.
=item int()
-C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a
+C<int()> returns (at least for Perl v5.7.1 and up) another Math::BigInt, not a
Perl scalar:
- $x = Math::BigInt->new(123);
- $y = int($x); # BigInt 123
- $x = Math::BigFloat->new(123.45);
- $y = int($x); # BigInt 123
-
-In all Perl versions you can use C<as_number()> or C<as_int> for the same
-effect:
-
- $x = Math::BigFloat->new(123.45);
- $y = $x->as_number(); # BigInt 123
- $y = $x->as_int(); # ditto
-
-This also works for other subclasses, like Math::String.
+ $x = Math::BigInt->new(123);
+ $y = int($x); # 123 as a Math::BigInt
+ $x = Math::BigFloat->new(123.45);
+ $y = int($x); # 123 as a Math::BigFloat
If you want a real Perl scalar, use C<numify()>:
- $y = $x->numify(); # 123 as scalar
-
-This is seldom necessary, though, because this is done automatically, like
-when you access an array:
+ $y = $x->numify(); # 123 as a scalar
- $z = $array[$x]; # does work automatically
-
-=item length()
+This is seldom necessary, though, because this is done automatically, like when
+you access an array:
-The following will probably not do what you expect:
-
- $c = Math::BigInt->new(123);
- print $c->length(),"\n"; # prints 30
-
-It prints both the number of digits in the number and in the fraction part
-since print calls C<length()> in list context. Use something like:
-
- print scalar $c->length(),"\n"; # prints 3
-
-=item bdiv()
-
-The following will probably not do what you expect:
-
- print $c->bdiv(10000),"\n";
-
-It prints both quotient and remainder since print calls C<bdiv()> in list
-context. Also, C<bdiv()> will modify $c, so be careful. You probably want
-to use
-
- print $c / 10000,"\n";
-
-or, if you want to modify $c instead,
-
- print scalar $c->bdiv(10000),"\n";
-
-The quotient is always the greatest integer less than or equal to the
-real-valued quotient of the two operands, and the remainder (when it is
-non-zero) always has the same sign as the second operand; so, for
-example,
-
- 1 / 4 => ( 0, 1)
- 1 / -4 => (-1,-3)
- -3 / 4 => (-1, 1)
- -3 / -4 => ( 0,-3)
- -11 / 2 => (-5,1)
- 11 /-2 => (-5,-1)
-
-As a consequence, the behavior of the operator % agrees with the
-behavior of Perl's built-in % operator (as documented in the perlop
-manpage), and the equation
-
- $x == ($x / $y) * $y + ($x % $y)
-
-holds true for any $x and $y, which justifies calling the two return
-values of bdiv() the quotient and remainder. The only exception to this rule
-are when $y == 0 and $x is negative, then the remainder will also be
-negative. See below under "infinity handling" for the reasoning behind this.
-
-Perl's 'use integer;' changes the behaviour of % and / for scalars, but will
-not change BigInt's way to do things. This is because under 'use integer' Perl
-will do what the underlying C thinks is right and this is different for each
-system. If you need BigInt's behaving exactly like Perl's 'use integer', bug
-the author to implement it ;)
-
-=item infinity handling
-
-Here are some examples that explain the reasons why certain results occur while
-handling infinity:
-
-The following table shows the result of the division and the remainder, so that
-the equation above holds true. Some "ordinary" cases are strewn in to show more
-clearly the reasoning:
-
- A / B = C, R so that C * B + R = A
- =========================================================
- 5 / 8 = 0, 5 0 * 8 + 5 = 5
- 0 / 8 = 0, 0 0 * 8 + 0 = 0
- 0 / inf = 0, 0 0 * inf + 0 = 0
- 0 /-inf = 0, 0 0 * -inf + 0 = 0
- 5 / inf = 0, 5 0 * inf + 5 = 5
- 5 /-inf = 0, 5 0 * -inf + 5 = 5
- -5/ inf = 0, -5 0 * inf + -5 = -5
- -5/-inf = 0, -5 0 * -inf + -5 = -5
- inf/ 5 = inf, 0 inf * 5 + 0 = inf
- -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf
- inf/ -5 = -inf, 0 -inf * -5 + 0 = inf
- -inf/ -5 = inf, 0 inf * -5 + 0 = -inf
- 5/ 5 = 1, 0 1 * 5 + 0 = 5
- -5/ -5 = 1, 0 1 * -5 + 0 = -5
- inf/ inf = 1, 0 1 * inf + 0 = inf
- -inf/-inf = 1, 0 1 * -inf + 0 = -inf
- inf/-inf = -1, 0 -1 * -inf + 0 = inf
- -inf/ inf = -1, 0 1 * -inf + 0 = -inf
- 8/ 0 = inf, 8 inf * 0 + 8 = 8
- inf/ 0 = inf, inf inf * 0 + inf = inf
- 0/ 0 = NaN
-
-These cases below violate the "remainder has the sign of the second of the two
-arguments", since they wouldn't match up otherwise.
-
- A / B = C, R so that C * B + R = A
- ========================================================
- -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf
- -8/ 0 = -inf, -8 -inf * 0 + 8 = -8
+ $z = $array[$x]; # does work automatically
=item Modifying and =
Beware of:
- $x = Math::BigFloat->new(5);
- $y = $x;
+ $x = Math::BigFloat->new(5);
+ $y = $x;
-It will not do what you think, e.g. making a copy of $x. Instead it just makes
-a second reference to the B<same> object and stores it in $y. Thus anything
-that modifies $x (except overloaded operators) will modify $y, and vice versa.
-Or in other words, C<=> is only safe if you modify your BigInts only via
-overloaded math. As soon as you use a method call it breaks:
+This makes a second reference to the B<same> object and stores it in $y. Thus
+anything that modifies $x (except overloaded operators) also modifies $y, and
+vice versa. Or in other words, C<=> is only safe if you modify your
+Math::BigInt objects only via overloaded math. As soon as you use a method call
+it breaks:
- $x->bmul(2);
- print "$x, $y\n"; # prints '10, 10'
+ $x->bmul(2);
+ print "$x, $y\n"; # prints '10, 10'
If you want a true copy of $x, use:
- $y = $x->copy();
+ $y = $x->copy();
-You can also chain the calls like this, this will make first a copy and then
+You can also chain the calls like this, this first makes a copy and then
multiply it by 2:
- $y = $x->copy()->bmul(2);
+ $y = $x->copy()->bmul(2);
See also the documentation for overload.pm regarding C<=>.
-=item bpow
-
-C<bpow()> (and the rounding functions) now modifies the first argument and
-returns it, unlike the old code which left it alone and only returned the
-result. This is to be consistent with C<badd()> etc. The first three will
-modify $x, the last one won't:
-
- print bpow($x,$i),"\n"; # modify $x
- print $x->bpow($i),"\n"; # ditto
- print $x **= $i,"\n"; # the same
- print $x ** $i,"\n"; # leave $x alone
-
-The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though.
-
=item Overloading -$x
The following:
- $x = -$x;
+ $x = -$x;
is slower than
- $x->bneg();
+ $x->bneg();
since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant
-needs to preserve $x since it does not know that it later will get overwritten.
+needs to preserve $x since it does not know that it later gets overwritten.
This makes a copy of $x and takes O(N), but $x->bneg() is O(1).
=item Mixing different object types
@@ -5564,80 +6230,58 @@ With overloaded operators, it is the first (dominating) operand that determines
which method is called. Here are some examples showing what actually gets
called in various cases.
- use Math::BigInt;
- use Math::BigFloat;
-
- $mbf = Math::BigFloat->new(5);
- $mbi2 = Math::BigInt->new(5);
- $mbi = Math::BigInt->new(2);
- # what actually gets called:
- $float = $mbf + $mbi; # $mbf->badd($mbi)
- $float = $mbf / $mbi; # $mbf->bdiv($mbi)
- $integer = $mbi + $mbf; # $mbi->badd($mbf)
- $integer = $mbi2 / $mbi; # $mbi2->bdiv($mbi)
- $integer = $mbi2 / $mbf; # $mbi2->bdiv($mbf)
-
-For instance, Math::BigInt->bdiv() will always return a Math::BigInt, regardless of
+ use Math::BigInt;
+ use Math::BigFloat;
+
+ $mbf = Math::BigFloat->new(5);
+ $mbi2 = Math::BigInt->new(5);
+ $mbi = Math::BigInt->new(2);
+ # what actually gets called:
+ $float = $mbf + $mbi; # $mbf->badd($mbi)
+ $float = $mbf / $mbi; # $mbf->bdiv($mbi)
+ $integer = $mbi + $mbf; # $mbi->badd($mbf)
+ $integer = $mbi2 / $mbi; # $mbi2->bdiv($mbi)
+ $integer = $mbi2 / $mbf; # $mbi2->bdiv($mbf)
+
+For instance, Math::BigInt->bdiv() always returns a Math::BigInt, regardless of
whether the second operant is a Math::BigFloat. To get a Math::BigFloat you
either need to call the operation manually, make sure each operand already is a
Math::BigFloat, or cast to that type via Math::BigFloat->new():
- $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5
+ $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5
Beware of casting the entire expression, as this would cast the
result, at which point it is too late:
- $float = Math::BigFloat->new($mbi2 / $mbi); # = 2
+ $float = Math::BigFloat->new($mbi2 / $mbi); # = 2
Beware also of the order of more complicated expressions like:
- $integer = ($mbi2 + $mbi) / $mbf; # int / float => int
- $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto
+ $integer = ($mbi2 + $mbi) / $mbf; # int / float => int
+ $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto
If in doubt, break the expression into simpler terms, or cast all operands
to the desired resulting type.
Scalar values are a bit different, since:
- $float = 2 + $mbf;
- $float = $mbf + 2;
+ $float = 2 + $mbf;
+ $float = $mbf + 2;
-will both result in the proper type due to the way the overloaded math works.
+both result in the proper type due to the way the overloaded math works.
This section also applies to other overloaded math packages, like Math::String.
One solution to you problem might be autoupgrading|upgrading. See the
pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this.
-=item bsqrt()
-
-C<bsqrt()> works only good if the result is a big integer, e.g. the square
-root of 144 is 12, but from 12 the square root is 3, regardless of rounding
-mode. The reason is that the result is always truncated to an integer.
-
-If you want a better approximation of the square root, then use:
-
- $x = Math::BigFloat->new(12);
- Math::BigFloat->precision(0);
- Math::BigFloat->round_mode('even');
- print $x->copy->bsqrt(),"\n"; # 4
-
- Math::BigFloat->precision(2);
- print $x->bsqrt(),"\n"; # 3.46
- print $x->bsqrt(3),"\n"; # 3.464
-
-=item brsft()
-
-For negative numbers in base see also L<brsft|/brsft()>.
-
=back
=head1 BUGS
Please report any bugs or feature requests to
C<bug-math-bigint at rt.cpan.org>, or through the web interface at
-L<https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt>
-(requires login).
+L<https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt> (requires login).
We will be notified, and then you'll automatically be notified of progress on
your bug as I make changes.