# -*- coding: utf-8-unix -*-
package Math::BigInt;
#
# "Mike had an infinite amount to do and a negative amount of time in which
# to do it." - Before and After
#
# The following hash values are used:
# value: unsigned int with actual value (as a Math::BigInt::Calc or similar)
# sign : +, -, NaN, +inf, -inf
# _a : accuracy
# _p : precision
# Remember not to take shortcuts ala $xs = $x->{value}; $LIB->foo($xs); since
# underlying lib might change the reference!
use 5.006001;
use strict;
use warnings;
use Carp qw< carp croak >;
our $VERSION = '1.999818';
require Exporter;
our @ISA = qw(Exporter);
our @EXPORT_OK = qw(objectify bgcd blcm);
# Inside overload, the first arg is always an object. If the original code had
# it reversed (like $x = 2 * $y), then the third parameter is true.
# In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes
# no difference, but in some cases it does.
# For overloaded ops with only one argument we simple use $_[0]->copy() to
# preserve the argument.
# Thus inheritance of overload operators becomes possible and transparent for
# our subclasses without the need to repeat the entire overload section there.
use overload
# 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
# These vars are public, but their direct usage is not recommended, use the
# accessor methods instead
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
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 $LIB = 'Math::BigInt::Calc'; # module to do the low level math
# default is Calc.pm
my $IMPORT = 0; # was import() called yet?
# used to make require work
my %CALLBACKS; # callbacks to notify on lib loads
##############################################################################
# the old code had $rnd_mode, so we need to support it, too
our $rnd_mode = 'even';
sub TIESCALAR {
my ($class) = @_;
bless \$round_mode, $class;
}
sub FETCH {
return $round_mode;
}
sub STORE {
$rnd_mode = $_[0]->round_mode($_[1]);
}
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)$/) {
croak("Unknown round mode '$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) {
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';
if (@_ > 0) {
my $a = shift;
if (defined $a) {
$a = $a->numify() if ref($a) && $a->can('numify');
# also croak on non-numerical
if (!$a || $a <= 0) {
croak('Argument to accuracy must be greater than zero');
}
if (int($a) != $a) {
croak('Argument to accuracy must be an integer');
}
}
if (ref($x)) {
# Set instance variable.
$x->bround($a) if $a; # not for undef, 0
$x->{_a} = $a; # set/overwrite, even if not rounded
delete $x->{_p}; # clear P
# Why return class variable here? Fixme!
$a = ${"${class}::accuracy"} unless defined $a; # proper return value
} else {
# Set class variable.
${"${class}::accuracy"} = $a; # set global A
${"${class}::precision"} = undef; # clear global P
}
return $a; # shortcut
}
# Return instance variable.
return $x->{_a} if ref($x) && (defined $x->{_a} || defined $x->{_p});
# Return class variable.
return ${"${class}::accuracy"};
}
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;
if (defined $p) {
$p = $p->numify() if ref($p) && $p->can('numify');
if ($p != int $p) {
croak('Argument to precision must be an integer');
}
}
if (ref($x)) {
# Set instance variable.
$x->bfround($p) if $p; # not for undef, 0
$x->{_p} = $p; # set/overwrite, even if not rounded
delete $x->{_a}; # clear A
# Why return class variable here? Fixme!
$p = ${"${class}::precision"} unless defined $p; # proper return value
} else {
# Set class variable.
${"${class}::precision"} = $p; # set global P
${"${class}::accuracy"} = undef; # clear global A
}
return $p; # shortcut
}
# Return instance variable.
return $x->{_p} if ref($x) && (defined $x->{_a} || defined $x->{_p});
# Return class variable.
return ${"${class}::precision"};
}
sub config {
# return (or set) configuration data.
my $class = shift || __PACKAGE__;
no strict 'refs';
if (@_ > 1 || (@_ == 1 && (ref($_[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/
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 %$args > 0) {
croak("Illegal key(s) '", join("', '", keys %$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 => $LIB,
lib_version => ${"${LIB}::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
/)
{
$cfg->{$key} = ${"${class}::$key"};
}
if (@_ == 1 && (ref($_[0]) ne 'HASH')) {
# calls of the style config('lib') return just this value
return $cfg->{$_[0]};
}
$cfg;
}
sub _scale_a {
# select accuracy parameter based on precedence,
# used by bround() and bfround(), may return undef for scale (means no op)
my ($x, $scale, $mode) = @_;
$scale = $x->{_a} unless defined $scale;
no strict 'refs';
my $class = ref($x);
$scale = ${ $class . '::accuracy' } 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, $mode);
}
sub _scale_p {
# select precision parameter based on precedence,
# used by bround() and bfround(), may return undef for scale (means no op)
my ($x, $scale, $mode) = @_;
$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.
# The argument could be an object, so avoid ||, && etc. on it. This would
# cause costly overloaded code to be called. The only allowed ops are ref()
# and defined.
my $self = shift;
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) = @_;
# Always return a new object, so if called as an instance method, copy the
# invocand, and if called as a class method, initialize a new object.
$self = $selfref ? $self -> copy()
: bless {}, $class;
unless (defined $wanted) {
#carp("Use of uninitialized value in new()");
return $self->bzero($a, $p, $r);
}
if (ref($wanted) && $wanted->isa($class)) { # MBI or subclass
# Using "$copy = $wanted -> copy()" here fails some tests. Fixme!
my $copy = $class -> copy($wanted);
if ($selfref) {
%$self = %$copy;
} else {
$self = $copy;
}
return $self;
}
$class->import() if $IMPORT == 0; # make require work
# Shortcut for non-zero scalar integers with no non-zero exponent.
if (!ref($wanted) &&
$wanted =~ / ^
([+-]?) # optional sign
([1-9][0-9]*) # non-zero significand
(\.0*)? # ... with optional zero fraction
([Ee][+-]?0+)? # optional zero exponent
\z
/x)
{
my $sgn = $1;
my $abs = $2;
$self->{sign} = $sgn || '+';
$self->{value} = $LIB->_new($abs);
no strict 'refs';
if (defined($a) || defined($p)
|| defined(${"${class}::precision"})
|| defined(${"${class}::accuracy"}))
{
$self->round($a, $p, $r)
unless @_ >= 3 && !defined $a && !defined $p;
}
return $self;
}
# Handle Infs.
if ($wanted =~ /^\s*([+-]?)inf(inity)?\s*\z/i) {
my $sgn = $1 || '+';
$self->{sign} = $sgn . 'inf'; # set a default sign for bstr()
return $class->binf($sgn);
}
# Handle explicit NaNs (not the ones returned due to invalid input).
if ($wanted =~ /^\s*([+-]?)nan\s*\z/i) {
$self = $class -> bnan();
$self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p;
return $self;
}
# Handle hexadecimal numbers.
if ($wanted =~ /^\s*[+-]?0[Xx]/) {
$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]/) {
$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) {
croak("$wanted is not a number in $class");
}
$self->{value} = $LIB->_zero();
$self->{sign} = $nan;
return $self;
}
if (!ref $miv) {
# _from_hex or _from_bin
$self->{value} = $mis->{value};
$self->{sign} = $mis->{sign};
return $self; # throw away $mis
}
# Make integer from mantissa by adjusting exponent, then convert to a
# Math::BigInt.
$self->{sign} = $$mis; # store sign
$self->{value} = $LIB->_zero(); # for all the NaN cases
my $e = int("$$es$$ev"); # exponent (avoid recursion)
if ($e > 0) {
my $diff = $e - CORE::length($$mfv);
if ($diff < 0) { # Not integer
if ($_trap_nan) {
croak("$wanted not an integer in $class");
}
#print "NOI 1\n";
return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade;
$self->{sign} = $nan;
} else { # diff >= 0
# adjust fraction and add it to value
#print "diff > 0 $$miv\n";
$$miv = $$miv . ($$mfv . '0' x $diff);
}
}
else {
if ($$mfv ne '') { # e <= 0
# fraction and negative/zero E => NOI
if ($_trap_nan) {
croak("$wanted not an integer in $class");
}
#print "NOI 2 \$\$mfv '$$mfv'\n";
return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade;
$self->{sign} = $nan;
} elsif ($e < 0) {
# xE-y, and empty mfv
# Split the mantissa at the decimal point. E.g., if
# $$miv = 12345 and $e = -2, then $frac = 45 and $$miv = 123.
my $frac = substr($$miv, $e); # $frac is fraction part
substr($$miv, $e) = ""; # $$miv is now integer part
if ($frac =~ /[^0]/) {
if ($_trap_nan) {
croak("$wanted not an integer in $class");
}
#print "NOI 3\n";
return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade;
$self->{sign} = $nan;
}
}
}
unless ($self->{sign} eq $nan) {
$self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0
$self->{value} = $LIB->_new($$miv) if $self->{sign} =~ /^[+-]$/;
}
# If any of the globals are set, use them to round, and store them inside
# $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 @_ >= 3 && !defined $a && !defined $p;
$self;
}
# 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/
^
\s*
( [+-]? )
(0?x)?
(
[0-9a-fA-F]*
( _ [0-9a-fA-F]+ )*
)
\s*
$
//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} = $LIB->_from_hex('0x' . $chrs);
# Place the sign.
$self->{sign} = $sign eq '-' && ! $LIB->_is_zero($self->{value})
? '-' : '+';
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;
# 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/
^
\s*
( [+-]? )
(
[0-7]*
( _ [0-7]+ )*
)
\s*
$
//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} = $LIB->_from_oct('0' . $chrs);
# Place the sign.
$self->{sign} = $sign eq '-' && ! $LIB->_is_zero($self->{value})
? '-' : '+';
return $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.
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/
^
\s*
( [+-]? )
(0?b)?
(
[01]*
( _ [01]+ )*
)
\s*
$
//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} = $LIB->_from_bin('0b' . $chrs);
# Place the sign.
$self->{sign} = $sign eq '-' && ! $LIB->_is_zero($self->{value})
? '-' : '+';
return $self;
}
# 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');
croak("from_bytes() requires a newer version of the $LIB library.")
unless $LIB->can('_from_bytes');
my $str = shift;
# If called as a class method, initialize a new object.
$self = $class -> bzero() unless $selfref;
$self -> {sign} = '+';
$self -> {value} = $LIB -> _from_bytes($str);
return $self;
}
sub from_base {
my $self = shift;
my $selfref = ref $self;
my $class = $selfref || $self;
# Don't modify constant (read-only) objects.
return if $selfref && $self->modify('from_base');
my $str = shift;
my $base = shift;
$base = $class->new($base) unless ref($base);
croak("the base must be a finite integer >= 2")
if $base < 2 || ! $base -> is_int();
# If called as a class method, initialize a new object.
$self = $class -> bzero() unless $selfref;
# If no collating sequence is given, pass some of the conversions to
# methods optimized for those cases.
if (! @_) {
return $self -> from_bin($str) if $base == 2;
return $self -> from_oct($str) if $base == 8;
return $self -> from_hex($str) if $base == 16;
if ($base == 10) {
my $tmp = $class -> new($str);
$self -> {value} = $tmp -> {value};
$self -> {sign} = '+';
}
}
croak("from_base() requires a newer version of the $LIB library.")
unless $LIB->can('_from_base');
$self -> {sign} = '+';
$self -> {value}
= $LIB->_from_base($str, $base -> {value}, @_ ? shift() : ());
return $self
}
sub bzero {
# create/assign '+0'
if (@_ == 0) {
#carp("Using bzero() as a function is deprecated;",
# " use bzero() as a method instead");
unshift @_, __PACKAGE__;
}
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} = $LIB->_zero();
# If rounding parameters are given as arguments, use them. If no rounding
# parameters are given, and if called as a class method initialize the new
# instance with the class variables.
if (@_) {
croak "can't specify both accuracy and precision"
if @_ >= 2 && defined $_[0] && defined $_[1];
$self->{_a} = $_[0];
$self->{_p} = $_[1];
} else {
unless($selfref) {
$self->{_a} = $class -> accuracy();
$self->{_p} = $class -> precision();
}
}
return $self;
}
sub bone {
# Create or assign '+1' (or -1 if given sign '-').
if (@_ == 0 || (defined($_[0]) && ($_[0] eq '+' || $_[0] eq '-'))) {
#carp("Using bone() as a function is deprecated;",
# " use bone() as a method instead");
unshift @_, __PACKAGE__;
}
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 = '+'; # default
if (@_) {
$sign = shift;
$sign = $sign =~ /^\s*-/ ? "-" : "+";
}
$self = bless {}, $class unless $selfref;
$self->{sign} = $sign;
$self->{value} = $LIB->_one();
# If rounding parameters are given as arguments, use them. If no rounding
# parameters are given, and if called as a class method initialize the new
# instance with the class variables.
if (@_) {
croak "can't specify both accuracy and precision"
if @_ >= 2 && defined $_[0] && defined $_[1];
$self->{_a} = $_[0];
$self->{_p} = $_[1];
} else {
unless($selfref) {
$self->{_a} = $class -> accuracy();
$self->{_p} = $class -> precision();
}
}
return $self;
}
sub binf {
# create/assign a '+inf' or '-inf'
if (@_ == 0 || (defined($_[0]) && !ref($_[0]) &&
$_[0] =~ /^\s*[+-](inf(inity)?)?\s*$/))
{
#carp("Using binf() as a function is deprecated;",
# " use binf() as a method instead");
unshift @_, __PACKAGE__;
}
my $self = shift;
my $selfref = ref $self;
my $class = $selfref || $self;
{
no strict 'refs';
if (${"${class}::_trap_inf"}) {
croak("Tried to create +-inf in $class->binf()");
}
}
$self->import() if $IMPORT == 0; # make require work
# Don't modify constant (read-only) objects.
return if $selfref && $self->modify('binf');
my $sign = shift;
$sign = defined $sign && $sign =~ /^\s*-/ ? "-" : "+";
$self = bless {}, $class unless $selfref;
$self -> {sign} = $sign . 'inf';
$self -> {value} = $LIB -> _zero();
# If rounding parameters are given as arguments, use them. If no rounding
# parameters are given, and if called as a class method initialize the new
# instance with the class variables.
if (@_) {
croak "can't specify both accuracy and precision"
if @_ >= 2 && defined $_[0] && defined $_[1];
$self->{_a} = $_[0];
$self->{_p} = $_[1];
} else {
unless($selfref) {
$self->{_a} = $class -> accuracy();
$self->{_p} = $class -> precision();
}
}
return $self;
}
sub bnan {
# create/assign a 'NaN'
if (@_ == 0) {
#carp("Using bnan() as a function is deprecated;",
# " use bnan() as a method instead");
unshift @_, __PACKAGE__;
}
my $self = shift;
my $selfref = ref($self);
my $class = $selfref || $self;
{
no strict 'refs';
if (${"${class}::_trap_nan"}) {
croak("Tried to create NaN in $class->bnan()");
}
}
$self->import() if $IMPORT == 0; # make require work
# Don't modify constant (read-only) objects.
return if $selfref && $self->modify('bnan');
$self = bless {}, $class unless $selfref;
$self -> {sign} = $nan;
$self -> {value} = $LIB -> _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 = __PACKAGE__;
}
$self = ref($self) if ref($self);
return $upgrade->new($n) if defined $upgrade;
# hard-wired to "3"
$self->new(3);
}
sub copy {
my $self = shift;
my $selfref = ref $self;
my $class = $selfref || $self;
# If called as a class method, the object to copy is the next argument.
$self = shift() unless $selfref;
my $copy = bless {}, $class;
$copy->{sign} = $self->{sign};
$copy->{value} = $LIB->_copy($self->{value});
$copy->{_a} = $self->{_a} if exists $self->{_a};
$copy->{_p} = $self->{_p} if exists $self->{_p};
return $copy;
}
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();
}
###############################################################################
# Boolean methods
###############################################################################
sub is_zero {
# return true if arg (BINT or num_str) is zero (array '+', '0')
my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
$LIB->_is_zero($x->{value});
}
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
$LIB->_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
}
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 is_positive {
# return true when arg (BINT or num_str) is positive (> 0)
my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
return 1 if $x->{sign} eq '+inf'; # +inf is positive
# 0+ is neither positive nor negative
($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0;
}
sub is_negative {
# return true when arg (BINT or num_str) is negative (< 0)
my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
$x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not
}
sub is_non_negative {
# Return true if argument is non-negative (>= 0).
my ($class, $x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if $x->{sign} =~ /^\+/;
return 1 if $x -> is_zero();
return 0;
}
sub is_non_positive {
# Return true if argument is non-positive (<= 0).
my ($class, $x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if $x->{sign} =~ /^\-/;
return 1 if $x -> is_zero();
return 0;
}
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 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
$LIB->_is_odd($x->{value});
}
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, @_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
$LIB->_is_even($x->{value});
}
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, @_);
$x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't
}
###############################################################################
# Comparison methods
###############################################################################
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
# set up parameters
my ($class, $x, $y) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
return $upgrade->bcmp($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} 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 $LIB->_acmp($x->{value}, $y->{value});
}
# $x && $y both < 0
$LIB->_acmp($y->{value}, $x->{value}); # swapped acmp (lib returns 0, 1, -1)
}
sub bacmp {
# Compares 2 values, ignoring their signs.
# Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT, BINT) return cond_code
# set up parameters
my ($class, $x, $y) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: 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;
}
$LIB->_acmp($x->{value}, $y->{value}); # lib does only 0, 1, -1
}
sub beq {
my $self = shift;
my $selfref = ref $self;
croak 'beq() is an instance method, not a class method' unless $selfref;
croak 'Wrong number of arguments for beq()' unless @_ == 1;
my $cmp = $self -> bcmp(shift);
return defined($cmp) && ! $cmp;
}
sub bne {
my $self = shift;
my $selfref = ref $self;
croak 'bne() is an instance method, not a class method' unless $selfref;
croak 'Wrong number of arguments for bne()' unless @_ == 1;
my $cmp = $self -> bcmp(shift);
return defined($cmp) && ! $cmp ? '' : 1;
}
sub blt {
my $self = shift;
my $selfref = ref $self;
croak 'blt() is an instance method, not a class method' unless $selfref;
croak 'Wrong number of arguments for blt()' unless @_ == 1;
my $cmp = $self -> bcmp(shift);
return defined($cmp) && $cmp < 0;
}
sub ble {
my $self = shift;
my $selfref = ref $self;
croak 'ble() is an instance method, not a class method' unless $selfref;
croak 'Wrong number of arguments for ble()' unless @_ == 1;
my $cmp = $self -> bcmp(shift);
return defined($cmp) && $cmp <= 0;
}
sub bgt {
my $self = shift;
my $selfref = ref $self;
croak 'bgt() is an instance method, not a class method' unless $selfref;
croak 'Wrong number of arguments for bgt()' unless @_ == 1;
my $cmp = $self -> bcmp(shift);
return defined($cmp) && $cmp > 0;
}
sub bge {
my $self = shift;
my $selfref = ref $self;
croak 'bge() is an instance method, not a class method'
unless $selfref;
croak 'Wrong number of arguments for bge()' unless @_ == 1;
my $cmp = $self -> bcmp(shift);
return defined($cmp) && $cmp >= 0;
}
###############################################################################
# Arithmetic methods
###############################################################################
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, @_);
return $x if $x->modify('bneg');
# for +0 do not negate (to have always normalized +0). Does nothing for 'NaN'
$x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $LIB->_is_zero($x->{value}));
$x;
}
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, @_);
return $x if $x->modify('babs');
# post-normalized abs for internal use (does nothing for NaN)
$x->{sign} =~ s/^-/+/;
$x;
}
sub bsgn {
# Signum function.
my $self = shift;
return $self if $self->modify('bsgn');
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} = $LIB->_inc($x->{value});
return $x->round($a, $p, $r);
} elsif ($x->{sign} eq '-') {
$x->{value} = $LIB->_dec($x->{value});
$x->{sign} = '+' if $LIB->_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
}
sub bdec {
# decrement arg by one
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
return $x if $x->modify('bdec');
if ($x->{sign} eq '-') {
# x already < 0
$x->{value} = $LIB->_inc($x->{value});
} else {
return $x->badd($class->bone('-'), @r)
unless $x->{sign} eq '+'; # inf or NaN
# >= 0
if ($LIB->_is_zero($x->{value})) {
# == 0
$x->{value} = $LIB->_one();
$x->{sign} = '-'; # 0 => -1
} else {
# > 0
$x->{value} = $LIB->_dec($x->{value});
}
}
$x->round(@r);
}
#sub bstrcmp {
# my $self = shift;
# my $selfref = ref $self;
# my $class = $selfref || $self;
#
# croak 'bstrcmp() is an instance method, not a class method'
# unless $selfref;
# 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;
#
# croak 'bstreq() is an instance method, not a class method'
# unless $selfref;
# 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;
#
# croak 'bstrne() is an instance method, not a class method'
# unless $selfref;
# 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;
#
# croak 'bstrlt() is an instance method, not a class method'
# unless $selfref;
# 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;
#
# croak 'bstrle() is an instance method, not a class method'
# unless $selfref;
# 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;
#
# croak 'bstrgt() is an instance method, not a class method'
# unless $selfref;
# 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;
#
# croak 'bstrge() is an instance method, not a class method'
# unless $selfref;
# croak 'Wrong number of arguments for bstrge()' unless @_ == 1;
#
# my $cmp = $self -> bstrcmp(shift);
# return defined($cmp) && $cmp >= 0;
#}
sub badd {
# add second arg (BINT or string) to first (BINT) (modifies first)
# return result as BINT
# 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;
}
my ($sx, $sy) = ($x->{sign}, $y->{sign}); # get signs
if ($sx eq $sy) {
$x->{value} = $LIB->_add($x->{value}, $y->{value}); # same sign, abs add
} else {
my $a = $LIB->_acmp ($y->{value}, $x->{value}); # absolute compare
if ($a > 0) {
$x->{value} = $LIB->_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} = $LIB->_zero();
$x->{sign} = '+';
} else # a < 0
{
$x->{value} = $LIB->_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 ($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('bsub');
return $upgrade -> new($x) -> bsub($upgrade -> new($y), @r)
if defined $upgrade && (!$x -> isa($class) || !$y -> isa($class));
return $x -> round(@r) if $y -> is_zero();
# 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
# 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->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('-');
}
return $upgrade->bmul($x, $upgrade->new($y), @r)
if defined $upgrade && !$y->isa($class);
$r[3] = $y; # no push here
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
$x->{value} = $LIB->_mul($x->{value}, $y->{value}); # do actual math
$x->{sign} = '+' if $LIB->_is_zero($x->{value}); # no -0
$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
# set up parameters
my ($class, $x, $y, $z, @r) = objectify(3, @_);
return $x if $x->modify('bmuladd');
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$/;
}
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
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
$x->{value} = $LIB->_mul($x->{value}, $y->{value}); # do actual math
$x->{sign} = '+' if $LIB->_is_zero($x->{value}); # no -0
my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); # get signs
if ($sx eq $sz) {
$x->{value} = $LIB->_add($x->{value}, $z->{value}); # same sign, abs add
} else {
my $a = $LIB->_acmp ($z->{value}, $x->{value}); # absolute compare
if ($a > 0) {
$x->{value} = $LIB->_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} = $LIB->_zero();
$x->{sign} = '+';
} else # a < 0
{
$x->{value} = $LIB->_sub($x->{value}, $z->{value}); # abs sub
}
}
$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 ($class, $x, $y, @r) = (ref($_[0]), @_);
# 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('bdiv');
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 = -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 5 % -inf = -inf
if ($y -> is_inf()) {
my $rem;
if ($x -> is_zero() || $x -> bcmp(0) == $y -> bcmp(0)) {
$rem = $x -> copy() if $wantarray;
$x -> bzero();
} else {
$rem = $class -> binf($y -> {sign}) if $wantarray;
$x -> bone('-');
}
return $wantarray ? ($x, $rem) : $x;
}
# 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;
$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}) =
$LIB -> _div($x -> {value}, $y -> {value});
if ($LIB -> _is_zero($rem -> {value})) {
if ($xsign eq $ysign || $LIB -> _is_zero($x -> {value})) {
$x -> {sign} = '+';
} else {
$x -> {sign} = '-';
}
} else {
if ($xsign eq $ysign) {
$x -> {sign} = '+';
} else {
if ($xsign eq '+') {
$x -> badd(1);
} else {
$x -> bsub(1);
}
$x -> {sign} = '-';
}
}
}
$x -> round(@r);
if ($wantarray) {
unless ($LIB -> _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);
}
return $x;
}
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.
# Set up parameters
my ($class, $x, $y, @r) = (ref($_[0]), @_);
# 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}) =
$LIB -> _div($x -> {value}, $y -> {value});
$x -> {sign} = $xsign eq $ysign ? '+' : '-';
$x -> {sign} = '+' if $LIB -> _is_zero($x -> {value});
$x -> round(@r);
}
if (wantarray) {
$rem -> {sign} = $xsign;
$rem -> {sign} = '+' if $LIB -> _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 ($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('bmod');
$r[3] = $y; # no push!
# At least one argument is NaN.
if ($x -> is_nan() || $y -> is_nan()) {
return $x -> bnan();
}
# Modulo zero. See documentation for bdiv().
if ($y -> is_zero()) {
return $x;
}
# Numerator (dividend) is +/-inf.
if ($x -> is_inf()) {
return $x -> bnan();
}
# Denominator (divisor) is +/-inf.
if ($y -> is_inf()) {
if ($x -> is_zero() || $x -> bcmp(0) == $y -> bcmp(0)) {
return $x;
} else {
return $x -> binf($y -> sign());
}
}
# Calc new sign and in case $y == +/- 1, return $x.
$x -> {value} = $LIB -> _mod($x -> {value}, $y -> {value});
if ($LIB -> _is_zero($x -> {value})) {
$x -> {sign} = '+'; # do not leave -0
} else {
$x -> {value} = $LIB -> _sub($y -> {value}, $x -> {value}, 1) # $y-$x
if ($x -> {sign} ne $y -> {sign});
$x -> {sign} = $y -> {sign};
}
$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('btmod');
# At least one argument is NaN.
if ($x -> is_nan() || $y -> is_nan()) {
return $x -> bnan();
}
# Modulo zero. See documentation for btdiv().
if ($y -> is_zero()) {
return $x;
}
# Numerator (dividend) is +/-inf.
if ($x -> is_inf()) {
return $x -> bnan();
}
# Denominator (divisor) is +/-inf.
if ($y -> is_inf()) {
return $x;
}
return $upgrade -> btmod($upgrade -> new($x), $upgrade -> new($y), @r)
if defined $upgrade;
$r[3] = $y; # no push!
my $xsign = $x -> {sign};
$x -> {value} = $LIB -> _mod($x -> {value}, $y -> {value});
$x -> {sign} = $xsign;
$x -> {sign} = '+' if $LIB -> _is_zero($x -> {value});
$x -> round(@r);
return $x;
}
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 ($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, @_);
}
return $x if $x->modify('bmodinv');
# Return NaN if one or both arguments is +inf, -inf, or nan.
return $x->bnan() if ($y->{sign} !~ /^[+-]$/ ||
$x->{sign} !~ /^[+-]$/);
# Return NaN if $y is zero; 1 % 0 makes no sense.
return $x->bnan() if $y->is_zero();
# Return 0 in the trivial case. $x % 1 or $x % -1 is zero for all finite
# integers $x.
return $x->bzero() if ($y->is_one() ||
$y->is_one('-'));
# 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
# $LIB->_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.
$x->bmod($y);
return $x->bnan() if $x->is_zero();
# 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.
($x->{value}, $x->{sign}) = $LIB->_modinv($x->{value}, $y->{value});
return $x->bnan() if !defined $x->{value};
# Library inconsistency workaround: _modinv() in Math::BigInt::GMP versions
# <= 1.32 return undef rather than a "+" for the sign.
$x->{sign} = '+' unless defined $x->{sign};
# 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)
# 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.
$x -> bneg() if $y->{sign} eq '-';
# Compute $x modulo $y again after correcting the sign.
$x -> bmod($y) if $x->{sign} ne $y->{sign};
return $x;
}
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, @_);
return $num if $num->modify('bmodpow');
# 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)
$num->bmodinv($mod) if ($exp->{sign} eq '-');
# Check for valid input. All operands must be finite, and the modulus must be
# non-zero.
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();
}
}
# 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'.
my $value = $LIB->_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 ($LIB->_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 = $LIB->_copy($mod->{value});
$value = $LIB->_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 = $LIB->_copy($mod->{value});
$value = $LIB->_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))
}
}
$num->{value} = $value;
$num->{sign} = $sign;
return $num -> 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 ($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('bpow');
# $x and/or $y is a NaN
return $x->bnan() if $x->is_nan() || $y->is_nan();
# $x and/or $y is a +/-Inf
if ($x->is_inf("-")) {
return $x->bzero() if $y->is_negative();
return $x->bnan() if $y->is_zero();
return $x if $y->is_odd();
return $x->bneg();
} elsif ($x->is_inf("+")) {
return $x->bzero() if $y->is_negative();
return $x->bnan() if $y->is_zero();
return $x;
} elsif ($y->is_inf("-")) {
return $x->bnan() if $x -> is_one("-");
return $x->binf("+") if $x -> is_zero();
return $x->bone() if $x -> is_one("+");
return $x->bzero();
} elsif ($y->is_inf("+")) {
return $x->bnan() if $x -> is_one("-");
return $x->bzero() if $x -> is_zero();
return $x->bone() if $x -> is_one("+");
return $x->binf("+");
}
return $upgrade->bpow($upgrade->new($x), $y, @r)
if defined $upgrade && (!$y->isa($class) || $y->{sign} eq '-');
$r[3] = $y; # no push!
# 0 ** -y => ( 1 / (0 ** y)) => 1 / 0 => +inf
return $x->binf() if $y->is_negative() && $x->is_zero();
# 1 ** -y => 1 / (1 ** |y|)
return $x->bzero() if $y->is_negative() && !$LIB->_is_one($x->{value});
$x->{value} = $LIB->_pow($x->{value}, $y->{value});
$x->{sign} = $x->is_negative() && $y->is_odd() ? '-' : '+';
$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.
my ($class, $x, $base, @r);
# 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.
if (!ref($_[0]) && $_[0] =~ /^[A-Za-z]|::/) {
# E.g., Math::BigInt->blog(256, 2)
($class, $x, $base, @r) =
defined $_[2] ? objectify(2, @_) : objectify(1, @_);
} else {
# E.g., Math::BigInt::blog(256, 2) or $x->blog(2)
($class, $x, $base, @r) =
defined $_[1] ? objectify(2, @_) : 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 = $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
}
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 ($rc) = $LIB->_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;
{
# 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) {
$x = $u;
} else {
$u = $u->as_int();
# modify $x in place
$x->{value} = $u->{value};
$x->round(@r);
}
}
sub bnok {
# Calculate n over k (binomial coefficient or "choose" function) as
# integer.
# Set up parameters.
my ($self, $n, $k, @r) = (ref($_[0]), @_);
# Objectify is costly, so avoid it.
if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) {
($self, $n, $k, @r) = objectify(2, @_);
}
return $n if $n->modify('bnok');
# All cases where at least one argument is NaN.
return $n->bnan() if $n->{sign} eq 'NaN' || $k->{sign} eq 'NaN';
# All cases where at least one argument is +/-inf.
if ($n -> is_inf()) {
if ($k -> is_inf()) { # bnok(+/-inf,+/-inf)
return $n -> bnan();
} elsif ($k -> is_neg()) { # bnok(+/-inf,k), k < 0
return $n -> bzero();
} elsif ($k -> is_zero()) { # bnok(+/-inf,k), k = 0
return $n -> bone();
} else {
if ($n -> is_inf("+")) { # bnok(+inf,k), 0 < k < +inf
return $n -> binf("+");
} else { # bnok(-inf,k), k > 0
my $sign = $k -> is_even() ? "+" : "-";
return $n -> binf($sign);
}
}
}
elsif ($k -> is_inf()) { # bnok(n,+/-inf), -inf <= n <= inf
return $n -> bnan();
}
# At this point, both n and k are real numbers.
my $sign = 1;
if ($n >= 0) {
if ($k < 0 || $k > $n) {
return $n -> bzero();
}
} else {
if ($k >= 0) {
# n < 0 and k >= 0: bnok(n,k) = (-1)^k * bnok(-n+k-1,k)
$sign = (-1) ** $k;
$n -> bneg() -> badd($k) -> bdec();
} elsif ($k <= $n) {
# n < 0 and k <= n: bnok(n,k) = (-1)^(n-k) * bnok(-k-1,n-k)
$sign = (-1) ** ($n - $k);
my $x0 = $n -> copy();
$n -> bone() -> badd($k) -> bneg();
$k = $k -> copy();
$k -> bneg() -> badd($x0);
} else {
# n < 0 and n < k < 0:
return $n -> bzero();
}
}
$n->{value} = $LIB->_nok($n->{value}, $k->{value});
$n -> bneg() if $sign == -1;
$n->round(@r);
}
sub buparrow {
my $a = shift;
my $y = $a -> uparrow(@_);
$a -> {value} = $y -> {value};
return $a;
}
sub uparrow {
# Knuth's up-arrow notation buparrow(a, n, b)
#
# The following is a simple, recursive implementation of the up-arrow
# notation, just to show the idea. Such implementations cause "Deep
# recursion on subroutine ..." warnings, so we use a faster, non-recursive
# algorithm below with @_ as a stack.
#
# sub buparrow {
# my ($a, $n, $b) = @_;
# return $a ** $b if $n == 1;
# return $a * $b if $n == 0;
# return 1 if $b == 0;
# return buparrow($a, $n - 1, buparrow($a, $n, $b - 1));
# }
my ($a, $b, $n) = @_;
my $class = ref $a;
croak("a must be non-negative") if $a < 0;
croak("n must be non-negative") if $n < 0;
croak("b must be non-negative") if $b < 0;
while (@_ >= 3) {
# return $a ** $b if $n == 1;
if ($_[-2] == 1) {
my ($a, $n, $b) = splice @_, -3;
push @_, $a ** $b;
next;
}
# return $a * $b if $n == 0;
if ($_[-2] == 0) {
my ($a, $n, $b) = splice @_, -3;
push @_, $a * $b;
next;
}
# return 1 if $b == 0;
if ($_[-1] == 0) {
splice @_, -3;
push @_, $class -> bone();
next;
}
# return buparrow($a, $n - 1, buparrow($a, $n, $b - 1));
my ($a, $n, $b) = splice @_, -3;
push @_, ($a, $n - 1,
$a, $n, $b - 1);
}
pop @_;
}
sub backermann {
my $m = shift;
my $y = $m -> ackermann(@_);
$m -> {value} = $y -> {value};
return $m;
}
sub ackermann {
# Ackermann's function ackermann(m, n)
#
# The following is a simple, recursive implementation of the ackermann
# function, just to show the idea. Such implementations cause "Deep
# recursion on subroutine ..." warnings, so we use a faster, non-recursive
# algorithm below with @_ as a stack.
#
# sub ackermann {
# my ($m, $n) = @_;
# return $n + 1 if $m == 0;
# return ackermann($m - 1, 1) if $m > 0 && $n == 0;
# return ackermann($m - 1, ackermann($m, $n - 1) if $m > 0 && $n > 0;
# }
my ($m, $n) = @_;
my $class = ref $m;
croak("m must be non-negative") if $m < 0;
croak("n must be non-negative") if $n < 0;
my $two = $class -> new("2");
my $three = $class -> new("3");
my $thirteen = $class -> new("13");
$n = pop;
$n = $class -> new($n) unless ref($n);
while (@_) {
my $m = pop;
if ($m > $three) {
push @_, (--$m) x $n;
while (--$m >= $three) {
push @_, $m;
}
$n = $thirteen;
} elsif ($m == $three) {
$n = $class -> bone() -> blsft($n + $three) -> bsub($three);
} elsif ($m == $two) {
$n -> bmul($two) -> badd($three);
} elsif ($m >= 0) {
$n -> badd($m) -> binc();
} else {
die "negative m!";
}
}
$n;
}
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, @_);
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 $tmp = Math::BigFloat->new($x)->batan(@r);
$x->{value} = $LIB->_new($tmp->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 $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;
}
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} = $LIB->_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, @_);
}
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} = $LIB->_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} = $LIB->_fac($x->{value});
$x->round(@r);
}
sub bdfac {
# compute double factorial, modify $x in place
my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
return $x if $x->modify('bdfac') || $x->{sign} eq '+inf'; # inf => inf
return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN
croak("bdfac() requires a newer version of the $LIB library.")
unless $LIB->can('_dfac');
$x->{value} = $LIB->_dfac($x->{value});
$x->round(@r);
}
sub bfib {
# compute Fibonacci number(s)
my ($class, $x, @r) = objectify(1, @_);
croak("bfib() requires a newer version of the $LIB library.")
unless $LIB->can('_fib');
return $x if $x->modify('bfib');
# List context.
if (wantarray) {
return () if $x -> is_nan();
croak("bfib() can't return an infinitely long list of numbers")
if $x -> is_inf();
# Use the backend library to compute the first $x Fibonacci numbers.
my @values = $LIB->_fib($x->{value});
# Make objects out of them. The last element in the array is the
# invocand.
for (my $i = 0 ; $i < $#values ; ++ $i) {
my $fib = $class -> bzero();
$fib -> {value} = $values[$i];
$values[$i] = $fib;
}
$x -> {value} = $values[-1];
$values[-1] = $x;
# If negative, insert sign as appropriate.
if ($x -> is_neg()) {
for (my $i = 2 ; $i <= $#values ; $i += 2) {
$values[$i]{sign} = '-';
}
}
@values = map { $_ -> round(@r) } @values;
return @values;
}
# Scalar context.
else {
return $x if $x->modify('bdfac') || $x -> is_inf('+');
return $x->bnan() if $x -> is_nan() || $x -> is_inf('-');
$x->{sign} = $x -> is_neg() && $x -> is_even() ? '-' : '+';
$x->{value} = $LIB->_fib($x->{value});
return $x->round(@r);
}
}
sub blucas {
# compute Lucas number(s)
my ($class, $x, @r) = objectify(1, @_);
croak("blucas() requires a newer version of the $LIB library.")
unless $LIB->can('_lucas');
return $x if $x->modify('blucas');
# List context.
if (wantarray) {
return () if $x -> is_nan();
croak("blucas() can't return an infinitely long list of numbers")
if $x -> is_inf();
# Use the backend library to compute the first $x Lucas numbers.
my @values = $LIB->_lucas($x->{value});
# Make objects out of them. The last element in the array is the
# invocand.
for (my $i = 0 ; $i < $#values ; ++ $i) {
my $lucas = $class -> bzero();
$lucas -> {value} = $values[$i];
$values[$i] = $lucas;
}
$x -> {value} = $values[-1];
$values[-1] = $x;
# If negative, insert sign as appropriate.
if ($x -> is_neg()) {
for (my $i = 2 ; $i <= $#values ; $i += 2) {
$values[$i]{sign} = '-';
}
}
@values = map { $_ -> round(@r) } @values;
return @values;
}
# Scalar context.
else {
return $x if $x -> is_inf('+');
return $x->bnan() if $x -> is_nan() || $x -> is_inf('-');
$x->{sign} = $x -> is_neg() && $x -> is_even() ? '-' : '+';
$x->{value} = $LIB->_lucas($x->{value});
return $x->round(@r);
}
}
sub blsft {
# (BINT or num_str, BINT or num_str) return BINT
# compute x << y, base n, y >= 0
my ($class, $x, $y, $b, @r);
# Objectify the base only when it is defined, since an undefined base, as
# in $x->blsft(3) or $x->blog(3, undef) means use the default base 2.
if (!ref($_[0]) && $_[0] =~ /^[A-Za-z]|::/) {
# E.g., Math::BigInt->blog(256, 5, 2)
($class, $x, $y, $b, @r) =
defined $_[3] ? objectify(3, @_) : objectify(2, @_);
} else {
# E.g., Math::BigInt::blog(256, 5, 2) or $x->blog(5, 2)
($class, $x, $y, $b, @r) =
defined $_[2] ? objectify(3, @_) : objectify(2, @_);
}
return $x if $x -> modify('blsft');
return $x -> bnan() if ($x -> {sign} !~ /^[+-]$/ ||
$y -> {sign} !~ /^[+-]$/);
return $x -> round(@r) if $y -> is_zero();
$b = defined($b) ? $b -> numify() : 2;
# While some of the libraries support an arbitrarily large base, not all of
# them do, so rather than returning an incorrect result in those cases,
# disallow bases that don't work with all libraries.
my $uintmax = ~0;
croak("Base is too large.") if $b > $uintmax;
return $x -> bnan() if $b <= 0 || $y -> {sign} eq '-';
$x -> {value} = $LIB -> _lsft($x -> {value}, $y -> {value}, $b);
$x -> round(@r);
}
sub brsft {
# (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, @_);
}
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?
}
# x < 0, n == 2, y == 1
$x -> bdec(); # n == 2, but $y == 1: this fixes it
}
$x -> {value} = $LIB -> _rsft($x -> {value}, $y -> {value}, $b);
$x -> round(@r);
}
###############################################################################
# Bitwise methods
###############################################################################
sub band {
#(BINT or num_str, BINT or num_str) return BINT
# compute x & y
# 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('band');
$r[3] = $y; # no push!
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
if ($x->{sign} eq '+' && $y->{sign} eq '+') {
$x->{value} = $LIB->_and($x->{value}, $y->{value});
} else {
($x->{value}, $x->{sign}) = $LIB->_sand($x->{value}, $x->{sign},
$y->{value}, $y->{sign});
}
return $x->round(@r);
}
sub bior {
#(BINT or num_str, BINT or num_str) return BINT
# compute x | y
# 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('bior');
$r[3] = $y; # no push!
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
if ($x->{sign} eq '+' && $y->{sign} eq '+') {
$x->{value} = $LIB->_or($x->{value}, $y->{value});
} else {
($x->{value}, $x->{sign}) = $LIB->_sor($x->{value}, $x->{sign},
$y->{value}, $y->{sign});
}
return $x->round(@r);
}
sub bxor {
#(BINT or num_str, BINT or num_str) return BINT
# compute x ^ y
# 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('bxor');
$r[3] = $y; # no push!
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
if ($x->{sign} eq '+' && $y->{sign} eq '+') {
$x->{value} = $LIB->_xor($x->{value}, $y->{value});
} else {
($x->{value}, $x->{sign}) = $LIB->_sxor($x->{value}, $x->{sign},
$y->{value}, $y->{sign});
}
return $x->round(@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) = 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);
}
}
# if still none defined, use globals
unless (defined $a || defined $p) {
$a = ${"$class\::accuracy"};
$p = ${"$class\::precision"};
}
# 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)$/) {
croak("Unknown round mode '$r'");
}
# 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;
}
# bround() or bfround() already called bnorm() if nec.
$self;
}
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 = __PACKAGE__->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 = $LIB->_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} = $LIB->_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;
}
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
# no-op for Math::BigInt objects 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 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 = __PACKAGE__->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, @_);
$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 ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
$x->round(@r);
}
###############################################################################
# Other mathematical methods
###############################################################################
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 ($class, @args) = objectify(0, @_);
my $x = shift @args;
$x = ref($x) && $x -> isa($class) ? $x -> copy() : $class -> new($x);
return $class->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
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} = $LIB->_gcd($x->{value}, $y->{value});
last if $LIB->_is_one($x->{value});
}
return $x -> babs();
}
sub blcm {
# (BINT or num_str, BINT or num_str) return BINT
# does not modify arguments, but returns new object
# Least Common Multiple
my ($class, @args) = objectify(0, @_);
my $x = shift @args;
$x = ref($x) && $x -> isa($class) ? $x -> copy() : $class -> new($x);
return $class->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
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} = $LIB->_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);
$LIB->_digit($x->{value}, $n || 0);
}
sub bdigitsum {
# like digitsum(), but assigns the result to the invocand
my $x = shift;
return $x if $x -> is_nan();
return $x -> bnan() if $x -> is_inf();
$x -> {value} = $LIB -> _digitsum($x -> {value});
$x -> {sign} = '+';
return $x;
}
sub digitsum {
# compute sum of decimal digits and return it
my $x = shift;
my $class = ref $x;
return $class -> bnan() if $x -> is_nan();
return $class -> bnan() if $x -> is_inf();
my $y = $class -> bzero();
$y -> {value} = $LIB -> _digitsum($x -> {value});
return $y;
}
sub length {
my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_);
my $e = $LIB->_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($LIB->_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 = $LIB->_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;
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 = $LIB -> _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;
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;
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;
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 = $LIB->_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 = $LIB->_str($m->{value}) . 'e+' . $LIB->_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 = $LIB->_str($mant->{value}) . "e+" . $LIB->_str($expo->{value});
return $x->{sign} eq '-' ? "-$str" : $str;
}
$expo += $fracpos;
my $mantstr = $LIB->_str($mant -> {value});
substr($mantstr, -$fracpos, 0) = '.';
my $str = $mantstr . 'e+' . $LIB->_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 = $LIB->_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+' . $LIB->_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 = $LIB->_str($x->{value});
return $x->{sign} eq '-' ? "-$str" : $str;
}
sub to_hex {
# return as hex string, with prefixed 0x
my $x = shift;
$x = __PACKAGE__->new($x) if !ref($x);
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
my $hex = $LIB->_to_hex($x->{value});
return $x->{sign} eq '-' ? "-$hex" : $hex;
}
sub to_oct {
# return as octal string, with prefixed 0
my $x = shift;
$x = __PACKAGE__->new($x) if !ref($x);
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
my $oct = $LIB->_to_oct($x->{value});
return $x->{sign} eq '-' ? "-$oct" : $oct;
}
sub to_bin {
# return as binary string, with prefixed 0b
my $x = shift;
$x = __PACKAGE__->new($x) if !ref($x);
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
my $bin = $LIB->_to_bin($x->{value});
return $x->{sign} eq '-' ? "-$bin" : $bin;
}
sub to_bytes {
# return a byte string
my $x = shift;
$x = __PACKAGE__->new($x) if !ref($x);
croak("to_bytes() requires a finite, non-negative integer")
if $x -> is_neg() || ! $x -> is_int();
croak("to_bytes() requires a newer version of the $LIB library.")
unless $LIB->can('_to_bytes');
return $LIB->_to_bytes($x->{value});
}
sub to_base {
# return a base anything string
my $x = shift;
$x = __PACKAGE__->new($x) if !ref($x);
croak("the value to convert must be a finite, non-negative integer")
if $x -> is_neg() || !$x -> is_int();
my $base = shift;
$base = __PACKAGE__->new($base) unless ref($base);
croak("the base must be a finite integer >= 2")
if $base < 2 || ! $base -> is_int();
# If no collating sequence is given, pass some of the conversions to
# methods optimized for those cases.
if (! @_) {
return $x -> to_bin() if $base == 2;
return $x -> to_oct() if $base == 8;
return uc $x -> to_hex() if $base == 16;
return $x -> bstr() if $base == 10;
}
croak("to_base() requires a newer version of the $LIB library.")
unless $LIB->can('_to_base');
return $LIB->_to_base($x->{value}, $base -> {value}, @_ ? shift() : ());
}
sub as_hex {
# return as hex string, with prefixed 0x
my $x = shift;
$x = __PACKAGE__->new($x) if !ref($x);
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
my $hex = $LIB->_as_hex($x->{value});
return $x->{sign} eq '-' ? "-$hex" : $hex;
}
sub as_oct {
# return as octal string, with prefixed 0
my $x = shift;
$x = __PACKAGE__->new($x) if !ref($x);
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
my $oct = $LIB->_as_oct($x->{value});
return $x->{sign} eq '-' ? "-$oct" : $oct;
}
sub as_bin {
# return as binary string, with prefixed 0b
my $x = shift;
$x = __PACKAGE__->new($x) if !ref($x);
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
my $bin = $LIB->_as_bin($x->{value});
return $x->{sign} eq '-' ? "-$bin" : $bin;
}
*as_bytes = \&to_bytes;
###############################################################################
# Other conversion methods
###############################################################################
sub numify {
# Make a Perl scalar number from a Math::BigInt object.
my $x = shift;
$x = __PACKAGE__->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 + $LIB->_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.
# The first argument, $count, is the number of following arguments that
# objectify() looks at and converts to objects. The first is a classname.
# If the given count is 0, all arguments will be used.
# After the count is read, objectify obtains the name of the class to which
# the following arguments are converted. If the second argument is a
# reference, use the reference type as the class name. Otherwise, if it is
# a string that looks like a class name, use that. Otherwise, use $class.
# 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
# A shortcut for the common case $x->unary_op(), in which case the argument
# list is (0, $x) or (1, $x).
return (ref($_[1]), $_[1]) if @_ == 2 && ($_[0] || 0) == 1 && ref($_[1]);
# Check the context.
unless (wantarray) {
croak(__PACKAGE__ . "::objectify() needs list context");
}
# Get the number of arguments to objectify.
my $count = shift;
# Initialize the output array.
my @a = @_;
# If the first argument is a reference, use that reference type as our
# class name. Otherwise, if the first argument looks like a class name,
# then use that as our class name. Otherwise, use the default class name.
my $class;
if (ref($a[0])) { # reference?
$class = ref($a[0]);
} elsif ($a[0] =~ /^[A-Z].*::/) { # string with class name?
$class = shift @a;
} else {
$class = __PACKAGE__; # default class name
}
$count ||= @a;
unshift @a, $class;
no strict 'refs';
# What we upgrade to, if anything.
my $up = ${"$a[0]::upgrade"};
# Disable downgrading, because Math::BigFloat -> foo('1.0', '2.0') needs
# floats.
my $down;
if (defined ${"$a[0]::downgrade"}) {
$down = ${"$a[0]::downgrade"};
${"$a[0]::downgrade"} = undef;
}
for my $i (1 .. $count) {
my $ref = ref $a[$i];
# Perl scalars are fed to the appropriate constructor.
unless ($ref) {
$a[$i] = $a[0] -> new($a[$i]);
next;
}
# If it is an object of the right class, all is fine.
next if $ref -> isa($a[0]);
# Upgrading is OK, so skip further tests if the argument is upgraded.
if (defined $up && $ref -> isa($up)) {
next;
}
# See if we can call one of the as_xxx() methods. We don't know whether
# the as_xxx() method returns an object or a scalar, so re-check
# afterwards.
my $recheck = 0;
if ($a[0] -> isa('Math::BigInt')) {
if ($a[$i] -> can('as_int')) {
$a[$i] = $a[$i] -> as_int();
$recheck = 1;
} elsif ($a[$i] -> can('as_number')) {
$a[$i] = $a[$i] -> as_number();
$recheck = 1;
}
}
elsif ($a[0] -> isa('Math::BigFloat')) {
if ($a[$i] -> can('as_float')) {
$a[$i] = $a[$i] -> as_float();
$recheck = $1;
}
}
# If we called one of the as_xxx() methods, recheck.
if ($recheck) {
$ref = ref($a[$i]);
# Perl scalars are fed to the appropriate constructor.
unless ($ref) {
$a[$i] = $a[0] -> new($a[$i]);
next;
}
# If it is an object of the right class, all is fine.
next if $ref -> isa($a[0]);
}
# Last resort.
$a[$i] = $a[0] -> new($a[$i]);
}
# Reset the downgrading.
${"$a[0]::downgrade"} = $down;
return @a;
}
sub import {
my $class = shift;
$IMPORT++; # remember we did import()
my @a; # unrecognized arguments
my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die
for (my $i = 0; $i <= $#_ ; $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...
$LIB = $_[$i+1] || '';
# try => 0 (no warn)
# lib => 1 (warn on fallback)
# 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) {
$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*/, $LIB;
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"
$LIB = ''; # signal error
foreach my $l (@c) {
# fallback libraries are "marked" as \'string', extract string if nec.
my $lib = $l;
$lib = $$l if ref($l);
next unless defined($lib) && CORE::length($lib);
$lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
$lib =~ s/\.pm$//;
my @parts = split /::/, $lib; # Math::BigInt => Math BigInt
$parts[-1] .= '.pm'; # BigInt => BigInt.pm
require File::Spec;
my $file = File::Spec->catfile(@parts);
eval { require $file; };
if ($@ eq '') {
$lib->import();
$LIB = $lib;
if ($warn_or_die > 0 && ref($l)) {
my $msg = "Math::BigInt: couldn't load specified"
. " math lib(s), fallback to $lib";
carp($msg) if $warn_or_die == 1;
croak($msg) if $warn_or_die == 2;
}
last; # found a usable one, break
}
}
if ($LIB eq '') {
if ($warn_or_die == 2) {
croak("Couldn't load specified math lib(s)" .
" and fallback disallowed");
} else {
croak("Couldn't load any math lib(s), not even fallback to Calc.pm");
}
}
# notify callbacks
foreach my $class (keys %CALLBACKS) {
&{$CALLBACKS{$class}}($LIB);
}
# import done
}
sub _register_callback {
my ($class, $callback) = @_;
if (ref($callback) ne 'CODE') {
croak("$callback is not a coderef");
}
$CALLBACKS{$class} = $callback;
}
sub _split_dec_string {
my $str = shift;
if ($str =~ s/
^
# leading whitespace
( \s* )
# optional sign
( [+-]? )
# significand
(
\d+ (?: _ \d+ )*
(?:
\.
(?: \d+ (?: _ \d+ )* )?
)?
|
\.
\d+ (?: _ \d+ )*
)
# optional exponent
(?:
[Ee]
( [+-]? )
( \d+ (?: _ \d+ )* )
)?
# trailing stuff
( \D .*? )?
\z
//x) {
my $leading = $1;
my $significand_sgn = $2 || '+';
my $significand_abs = $3;
my $exponent_sgn = $4 || '+';
my $exponent_abs = $5 || '0';
my $trailing = $6;
# Remove underscores and leading zeros.
$significand_abs =~ tr/_//d;
$exponent_abs =~ tr/_//d;
$significand_abs =~ s/^0+(.)/$1/;
$exponent_abs =~ s/^0+(.)/$1/;
# If the significand contains a dot, remove it and adjust the exponent
# accordingly. E.g., "1234.56789e+3" -> "123456789e-2"
my $idx = index $significand_abs, '.';
if ($idx > -1) {
$significand_abs =~ s/0+\z//;
substr($significand_abs, $idx, 1) = '';
my $exponent = $exponent_sgn . $exponent_abs;
$exponent .= $idx - CORE::length($significand_abs);
$exponent_abs = abs $exponent;
$exponent_sgn = $exponent < 0 ? '-' : '+';
}
return($leading,
$significand_sgn, $significand_abs,
$exponent_sgn, $exponent_abs,
$trailing);
}
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/) {
$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
}
sub _trailing_zeros {
# return the amount of trailing zeros in $x (as scalar)
my $x = shift;
$x = __PACKAGE__->new($x) unless ref $x;
return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc
$LIB->_zeros($x->{value}); # must handle odd values, 0 etc
}
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, -$follow) =~ /[^0]/ ? 1 : 0;
}
sub _find_round_parameters {
# After any operation or when calling round(), the result is rounded by
# regarding the A & P from arguments, local parameters, or globals.
# !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!!
# This procedure finds the round parameters, but it is for speed reasons
# duplicated in round. Otherwise, it is tested by the testsuite and used
# by bdiv().
# returns ($self) or ($self, $a, $p, $r) - sets $self to NaN of both A and P
# were requested/defined (locally or globally or both)
my ($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';
# 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);
# 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);
}
}
# if still none defined, use globals (#2)
$a = ${"$class\::accuracy"} unless defined $a;
$p = ${"$class\::precision"} unless defined $p;
# 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; # error
$r = ${"$class\::round_mode"} unless defined $r;
if ($r !~ /^(even|odd|[+-]inf|zero|trunc|common)$/) {
croak("Unknown round mode '$r'");
}
$a = int($a) if defined $a;
$p = int($p) if defined $p;
($self, $a, $p, $r);
}
###############################################################################
# this method returns 0 if the object can be modified, or 1 if not.
# We use a fast constant sub() here, to avoid costly calls. Subclasses
# may override it with special code (f.i. Math::BigInt::Constant does so)
sub modify () { 0; }
1;
__END__
=pod
=head1 NAME
Math::BigInt - Arbitrary size integer/float math package
=head1 SYNOPSIS
use Math::BigInt;
# or make it faster with huge numbers: install (optional)
# Math::BigInt::GMP and always use (it falls back to
# pure Perl if the GMP library is not installed):
# (See also the L for more information.
For more benchmark results see L.
=head1 SUBCLASSING
=head2 Subclassing Math::BigInt
The basic design of Math::BigInt allows simple subclasses with very little
work, as long as a few simple rules are followed:
=over
=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.
=item *
The private object hash keys like C<< $x->{sign} >> may not be changed, but
additional keys can be added, like C<< $x->{_custom} >>.
=item *
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.
=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.
All other object methods and overloaded functions can be directly inherited
from the parent class.
At the very minimum, any subclass needs to provide its own C 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;
Additionally, you might want to provide the following two globals to allow
auto-upgrading and auto-downgrading to work correctly:
$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
t/Math/BigFloat/SubClass.pm completely functional subclass examples.
Don't forget to
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
example.
=head1 UPGRADING
When used like this:
use Math::BigInt upgrade => 'Foo::Bar';
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';
As a shortcut, you can use the module L:
use bignum;
Also good for one-liners:
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)).
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 always hands up their work:
div bsqrt blog bexp bpi bsin bcos batan batan2
All other methods upgrade themselves only when one (or all) of their arguments
are of the class mentioned in $upgrade.
=head1 EXPORTS
C exports nothing by default, but can export the following
methods:
bgcd
blcm
=head1 CAVEATS
Some things might not work as you expect them. Below is documented what is
known to be troublesome:
=over
=item Comparing numbers as strings
Both C and C as well as stringify via overload drop the
leading '+'. This is to be consistent with Perl and to make C (especially
with overloading) to work as you expect. It also solves problems with
C and L, which stringify arguments before comparing them.
Mark Biggar said, when asked about to drop the '+' altogether, or make only
C 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.
So, the following examples now works as expected:
use Test::More tests => 1;
use Math::BigInt;
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 $x eq 3*3;
Additionally, the following still works:
print "$x == 9" if $x == $y;
print "$x == 9" if $x == 9;
print "$x == 9" if $x == 3*3;
There is now a C 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 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;
$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 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 for problems in
comparing NaNs.
=item int()
C 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); # 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:
$y = $x->numify(); # 123 as a scalar
This is seldom necessary, though, because this is done automatically, like when
you access an array:
$z = $array[$x]; # does work automatically
=item Modifying and =
Beware of:
$x = Math::BigFloat->new(5);
$y = $x;
This makes a second reference to the B 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'
If you want a true copy of $x, use:
$y = $x->copy();
You can also chain the calls like this, this first makes a copy and then
multiply it by 2:
$y = $x->copy()->bmul(2);
See also the documentation for overload.pm regarding C<=>.
=item Overloading -$x
The following:
$x = -$x;
is slower than
$x->bneg();
since overload calls C instead of C. The first variant
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
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() 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
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
Beware also of the order of more complicated expressions like:
$integer = ($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;
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, L and L for an easy way to do this.
=back
=head1 BUGS
Please report any bugs or feature requests to
C, or through the web interface at
L (requires login).
We will be notified, and then you'll automatically be notified of progress on
your bug as I make changes.
=head1 SUPPORT
You can find documentation for this module with the perldoc command.
perldoc Math::BigInt
You can also look for information at:
=over 4
=item * RT: CPAN's request tracker
L
=item * AnnoCPAN: Annotated CPAN documentation
L
=item * CPAN Ratings
L
=item * MetaCPAN
L
=item * CPAN Testers Matrix
L
=item * The Bignum mailing list
=over 4
=item * Post to mailing list
C
=item * View mailing list
L
=item * Subscribe/Unsubscribe
L
=back
=back
=head1 LICENSE
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
=head1 SEE ALSO
L and L as well as the backends
L, L, and L.
The pragmas L, L and L also might be of interest
because they solve the autoupgrading/downgrading issue, at least partly.
=head1 AUTHORS
=over 4
=item *
Mark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001.
=item *
Completely rewritten by Tels L, 2001-2008.
=item *
Florian Ragwitz Eflora@cpan.orgE, 2010.
=item *
Peter John Acklam Epjacklam@online.noE, 2011-.
=back
Many people contributed in one or more ways to the final beast, see the file
CREDITS for an (incomplete) list. If you miss your name, please drop me a
mail. Thank you!
=cut