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cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
# -*- 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:
#
# sign : "+", "-", "+inf", "-inf", or "NaN"
# value : unsigned int with actual value ($LIB thingy)
# accuracy : accuracy (scalar)
# precision : precision (scalar)
# 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 >;
use Scalar::Util qw< blessed refaddr >;
our $VERSION = '2.005002';
$VERSION =~ tr/_//d;
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($_[1]) -> bblsft($_[0])
: $_[0] -> copy() -> bblsft($_[1]); },
'>>' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bbrsft($_[0])
: $_[0] -> copy() -> bbrsft($_[1]); },
# overload key: assign
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
'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 $accuracy = undef;
our $precision = undef;
our $round_mode = 'even'; # even, odd, +inf, -inf, zero, trunc, common
our $div_scale = 40;
our $upgrade = undef;
our $downgrade = undef;
our $_trap_nan = 0; # croak on NaNs?
our $_trap_inf = 0; # croak on Infs?
my $nan = 'NaN'; # constant for easier life
# Module to do the low level math.
my $DEFAULT_LIB = 'Math::BigInt::Calc';
my $LIB;
# Has import() been called yet? This variable is needed to make "require" work.
my $IMPORT = 0;
##############################################################################
# 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 = (ref $_[0]) -> round_mode($_[1]);
}
BEGIN {
# tie to enable $rnd_mode to work transparently
tie $rnd_mode, 'Math::BigInt';
# set up some handy alias names
*is_pos = \&is_positive;
*is_neg = \&is_negative;
*as_number = \&as_int;
}
###############################################################################
# Configuration methods
###############################################################################
sub accuracy {
my $x = shift;
my $class = ref($x) || $x || __PACKAGE__;
# setter/mutator
if (@_) {
my $a = shift;
if (defined $a) {
$a = $a -> can('numify') ? $a -> numify() : 0 + "$a" if ref($a);
croak "accuracy must be a number, not '$a'"
if $a !~ /^\s*[+-]?(?:\d+(?:\.\d*)?|\.\d+)(?:[Ee][+-]?\d+)?\s*\z/;
croak "accuracy must be an integer, not '$a'"
if $a != int $a;
}
if (ref($x)) {
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
$self -> SUPER::_init() if SUPER -> can('_init');
$self -> {accuracy} = $class -> accuracy();
$self -> {precision} = $class -> precision();
#$self -> {round_mode} = $round_mode;
#$self -> {div_scale} = $div_scale;
#$self -> {trap_inf} = $_trap_inf;
#$self -> {trap_nan} = $_trap_nan;
#$self -> {upgrade} = $upgrade;
#$self -> {downgrade} = $downgrade;
return $self;
}
sub new {
# Create a new Math::BigInt object from a string or another Math::BigInt,
# Math::BigFloat, or Math::BigRat object. See hash keys documented at top.
my $self = shift;
my $selfref = ref $self;
my $class = $selfref || $self;
# Make "require" work.
$class -> import() if $IMPORT == 0;
# Calling new() with no input arguments has been discouraged for more than
# 10 years, but people apparently still use it, so we still support it.
return $class -> bzero() unless @_;
my ($wanted, @r) = @_;
if (!defined($wanted)) {
#carp("Use of uninitialized value in new()")
# if warnings::enabled("uninitialized");
return $class -> bzero(@r);
}
if (!ref($wanted) && $wanted eq "") {
#carp(q|Argument "" isn't numeric in new()|)
# if warnings::enabled("numeric");
#return $class -> bzero(@r);
return $class -> bnan(@r);
}
# Initialize a new object.
$self = bless {}, $class;
#$self -> _init(); # <-- this causes problems because if the global
# accuracy is 2, new(3, 5) will not set the accuracy
# to 5 because it is currently not possible to
# increase the accuracy. Ditto for precision. XXX
# See if $wanted is an object that is a Math::BigInt. We could check if the
# object supports the as_int() method. However, as_int() truncates a finite
# non-integer whereas new() is supposed to return a NaN for finite
# non-integers. This inconsistency should be sorted out. XXX
if (defined(blessed($wanted)) && $wanted -> isa(__PACKAGE__)) {
# Don't copy the accuracy and precision, because a new object should
# get them from the global configuration.
$self -> {sign} = $wanted -> {sign};
$self -> {value} = $LIB -> _copy($wanted -> {value});
$self -> round(@r)
unless @r >= 2 && !defined($r[0]) && !defined($r[1]);
return $self;
}
# From now on we only work on the stringified version of $wanted, so
# stringify it once and for all.
$wanted = "$wanted";
# Shortcut for non-zero scalar integers with no non-zero exponent.
if ($wanted =~
/ ^
# optional leading whitespace
\s*
# optional sign
( [+-]? )
# integer mantissa with optional leading zeros
0* ( [1-9] \d* (?: _ \d+ )* | 0 )
# ... with optional zero fraction part
(?: \.0* )?
# optional non-negative exponent
(?: [eE] \+? ( \d+ (?: _ \d+ )* ) )?
# optional trailing whitespace
\s*
$
/x)
{
my $sign = $1;
(my $mant = $2) =~ tr/_//d;
my $expo = $3;
$mant .= "0" x $expo if defined($expo) && $mant ne "0";
$self->{sign} = $sign eq "-" && $mant ne "0" ? "-" : "+";
$self->{value} = $LIB->_new($mant);
$self -> round(@r);
return $self;
}
# Handle Infs.
if ($wanted =~ / ^
\s*
( [+-]? )
inf (?: inity )?
\s*
\z
/ix)
{
my $sgn = $1 || '+';
return $class -> binf($sgn, @r);
}
# Handle explicit NaNs (not the ones returned due to invalid input).
if ($wanted =~ / ^
\s*
( [+-]? )
nan
\s*
\z
/ix)
{
return $class -> bnan(@r);
}
my @parts;
if (
# Handle hexadecimal numbers. We auto-detect hexadecimal numbers if
# they have a "0x", "0X", "x", or "X" prefix, cf. CORE::oct().
$wanted =~ /^\s*[+-]?0?[Xx]/ and
@parts = $class -> _hex_str_to_flt_lib_parts($wanted)
or
# Handle octal numbers. We auto-detect octal numbers if they have a
# "0o", "0O", "o", "O" prefix, cf. CORE::oct().
$wanted =~ /^\s*[+-]?0?[Oo]/ and
@parts = $class -> _oct_str_to_flt_lib_parts($wanted)
or
# Handle binary numbers. We auto-detect binary numbers if they have a
# "0b", "0B", "b", or "B" prefix, cf. CORE::oct().
$wanted =~ /^\s*[+-]?0?[Bb]/ and
@parts = $class -> _bin_str_to_flt_lib_parts($wanted)
or
# At this point, what is left are decimal numbers that aren't handled
# above and octal floating point numbers that don't have any of the
# "0o", "0O", "o", or "O" prefixes. First see if it is a decimal
# number.
@parts = $class -> _dec_str_to_flt_lib_parts($wanted)
or
# See if it is an octal floating point number. The extra check is
# included because _oct_str_to_flt_lib_parts() accepts octal numbers
# that don't have a prefix (this is needed to make it work with, e.g.,
# from_oct() that don't require a prefix). However, Perl requires a
# prefix for octal floating point literals. For example, "1p+0" is not
# valid, but "01p+0" and "0__1p+0" are.
$wanted =~ /^\s*[+-]?0_*\d/ and
@parts = $class -> _oct_str_to_flt_lib_parts($wanted))
{
# The value is an integer iff the exponent is non-negative.
if ($parts[2] eq '+') {
$self -> {sign} = $parts[0];
$self -> {value} = $LIB -> _lsft($parts[1], $parts[3], 10);
$self -> round(@r)
unless @r >= 2 && !defined($r[0]) && !defined($r[1]);
return $self;
}
# The value is not an integer, so upgrade if upgrading is enabled.
my $upg = $class -> upgrade();
return $upg -> new($wanted, @r) if $upg;
}
# If we get here, the value is neither a valid decimal, binary, octal, or
# hexadecimal number. It is not explicit an Inf or a NaN either.
return $class -> bnan(@r);
}
# Create a Math::BigInt from a decimal string. This is an equivalent to
# from_hex(), from_oct(), and from_bin(). It is like new() except that it does
# not accept anything but a string representing a finite decimal number.
sub from_dec {
my $self = shift;
my $selfref = ref $self;
my $class = $selfref || $self;
# Make "require" work.
$class -> import() if $IMPORT == 0;
# Don't modify constant (read-only) objects.
return $self if $selfref && $self -> modify('from_dec');
my $str = shift;
my @r = @_;
if (my @parts = $class -> _dec_str_to_flt_lib_parts($str)) {
# If called as a class method, initialize a new object.
unless ($selfref) {
$self = bless {}, $class;
#$self -> _init(); # see comment on _init() in new()
}
# The value is an integer iff the exponent is non-negative.
if ($parts[2] eq '+') {
$self -> {sign} = $parts[0];
$self -> {value} = $LIB -> _lsft($parts[1], $parts[3], 10);
return $self -> round(@r);
}
# The value is not an integer, so upgrade if upgrading is enabled.
my $upg = $class -> upgrade();
if ($upg) {
return $self -> _upg() -> from_dec($str, @r) # instance method
if $selfref && $selfref ne $upg;
return $upg -> from_dec($str, @r); # class method
}
}
return $self -> bnan(@r);
}
# Create a Math::BigInt from a hexadecimal string.
sub from_hex {
my $self = shift;
my $selfref = ref $self;
my $class = $selfref || $self;
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
my $selfref = ref $self;
my $class = $selfref || $self;
{
no strict 'refs';
if (${"${class}::_trap_inf"}) {
croak("Tried to create +-inf in $class->binf()");
}
}
# Make "require" work.
$class -> import() if $IMPORT == 0;
# Don't modify constant (read-only) objects.
return $self if $selfref && $self -> modify('binf');
# Get the sign.
my $sign = '+'; # default is to return positive infinity
if (defined($_[0]) && $_[0] =~ /^\s*([+-])(inf|$)/i) {
$sign = $1;
shift;
}
# Get the rounding parameters, if any.
my @r = @_;
# If called as a class method, initialize a new object.
unless ($selfref) {
$self = bless {}, $class;
#$self -> _init(); # see comment on _init() in new()
}
$self -> {sign} = $sign . 'inf';
$self -> {value} = $LIB -> _zero();
# If rounding parameters are given as arguments, use them. If no rounding
# parameters are given, and if called as a class method, initialize the new
# instance with the class variables.
if (@r) {
if (@r >= 2 && defined($r[0]) && defined($r[1])) {
carp "can't specify both accuracy and precision";
return $self -> bnan();
}
$self->{accuracy} = $_[0];
$self->{precision} = $_[1];
} elsif (!$selfref) {
$self->{accuracy} = $class -> accuracy();
$self->{precision} = $class -> precision();
}
return $self;
}
sub bnan {
# create/assign a 'NaN'
# Class::method(...) -> Class->method(...)
unless (@_ && (defined(blessed($_[0])) && $_[0] -> isa(__PACKAGE__) ||
$_[0] =~ /^[a-z]\w*(?:::[a-z]\w*)*$/i))
{
#carp "Using ", (caller(0))[3], "() as a function is deprecated;",
# " use is 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()");
}
}
# Make "require" work.
$class -> import() if $IMPORT == 0;
# Don't modify constant (read-only) objects.
return $self if $selfref && $self -> modify('bnan');
# Get the rounding parameters, if any.
my @r = @_;
# If called as a class method, initialize a new object.
unless ($selfref) {
$self = bless {}, $class;
#$self -> _init(); # see comment on _init() in new()
}
$self -> {sign} = $nan;
$self -> {value} = $LIB -> _zero();
# If rounding parameters are given as arguments, use them. If no rounding
# parameters are given, and if called as a class method, initialize the new
# instance with the class variables.
if (@r) {
if (@r >= 2 && defined($r[0]) && defined($r[1])) {
carp "can't specify both accuracy and precision";
return $self -> bnan();
}
$self->{accuracy} = $_[0];
$self->{precision} = $_[1];
} elsif (!$selfref) {
$self->{accuracy} = $class -> accuracy();
$self->{precision} = $class -> precision();
}
return $self;
}
sub bpi {
# Class::method(...) -> Class->method(...)
unless (@_ && (defined(blessed($_[0])) && $_[0] -> isa(__PACKAGE__) ||
$_[0] =~ /^[a-z]\w*(?:::[a-z]\w*)*$/i))
{
#carp "Using ", (caller(0))[3], "() as a function is deprecated;",
# " use is as a method instead";
unshift @_, __PACKAGE__;
}
# Called as Argument list
# --------- -------------
# Math::BigFloat->bpi() ("Math::BigFloat")
# Math::BigFloat->bpi(10) ("Math::BigFloat", 10)
# $x->bpi() ($x)
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
($y->{accuracy}, $y->{precision}) = ($x->{accuracy}, $x->{precision});
}
$y -> round(@r);
# Restore upgrading and downgrading..
Math::BigFloat -> upgrade($upg);
Math::BigFloat -> downgrade($dng);
return $y;
}
###############################################################################
# Boolean methods
###############################################################################
sub is_zero {
# return true if arg (BINT or num_str) is zero (array '+', '0')
my (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
return 0 if $x->{sign} ne '+';
return 1 if $LIB->_is_zero($x->{value});
return 0;
}
sub is_one {
# return true if arg (BINT or num_str) is +1, or -1 if sign is given
my (undef, $x, $sign) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
if (defined($sign)) {
croak 'is_one(): sign argument must be "+" or "-"'
unless $sign eq '+' || $sign eq '-';
} else {
$sign = '+';
}
return 0 if $x->{sign} ne $sign;
$LIB->_is_one($x->{value}) ? 1 : 0;
}
sub is_finite {
my (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
$x->{sign} eq '+' || $x->{sign} eq '-' ? 1 : 0;
}
sub is_inf {
# return true if arg (BINT or num_str) is +-inf
my (undef, $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 (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
$x->{sign} eq $nan ? 1 : 0;
}
sub is_positive {
# return true when arg (BINT or num_str) is positive (> 0)
my (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
return 1 if $x -> is_inf("+");
# 0+ is neither positive nor negative
($x->{sign} eq '+' && !$x -> is_zero()) ? 1 : 0;
}
sub is_negative {
# return true when arg (BINT or num_str) is negative (< 0)
my (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
$x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not
}
sub is_non_positive {
# Return true if argument is non-positive (<= 0).
my (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
return 1 if $x->{sign} =~ /^\-/;
return 1 if $x -> is_zero();
return 0;
}
sub is_non_negative {
# Return true if argument is non-negative (>= 0).
my (undef, $x) = ref($_[0]) ? (undef, @_) : 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 (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
return 0 unless $x -> is_finite();
$LIB->_is_odd($x->{value}) ? 1 : 0;
}
sub is_even {
# return true when arg (BINT or num_str) is even, false for odd
my (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
return 0 unless $x -> is_finite();
$LIB->_is_even($x->{value}) ? 1 : 0;
}
sub is_int {
# return true when arg (BINT or num_str) is an integer
my (undef, $x) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
$x -> is_finite() ? 1 : 0;
}
###############################################################################
# Comparison methods
###############################################################################
sub bcmp {
# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT or num_str, BINT or num_str) return cond_code
# set up parameters
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Unless both $x and $y are finite ...
unless ($x -> is_finite() && $y -> is_finite()) {
# handle +-inf and NaN
return if $x -> is_nan() || $y -> is_nan();
return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
return +1 if $x -> is_inf("+");
return -1 if $x -> is_inf("-");
return -1 if $y -> is_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 '-' && $y->{sign} eq '+'; # does also -x <=> 0
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> bcmp($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
# 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; use swapped acmp (lib returns 0, 1, -1)
$LIB->_acmp($y->{value}, $x->{value});
}
sub bacmp {
# Compares 2 values, ignoring their signs.
# Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT, BINT) return cond_code
# set up parameters
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
if ((!$x -> is_finite()) || (!$y -> is_finite())) {
# handle +-inf and NaN
return if $x -> is_nan() || $y -> is_nan();
return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
return -1;
}
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> bacmp($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
$LIB->_acmp($x->{value}, $y->{value}); # lib does only 0, 1, -1
}
sub beq {
my (undef, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (undef, @_)
: objectify(2, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
my $cmp = $x -> bcmp($y); # bcmp() upgrades if necessary
return defined($cmp) && !$cmp;
}
sub bne {
my (undef, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (undef, @_)
: objectify(2, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
my $cmp = $x -> bcmp($y); # bcmp() upgrades if necessary
return defined($cmp) && !$cmp ? '' : 1;
}
sub blt {
my (undef, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (undef, @_)
: objectify(2, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
my $cmp = $x -> bcmp($y); # bcmp() upgrades if necessary
return defined($cmp) && $cmp < 0;
}
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
return $x -> binf(@r) if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
return $x -> binf(@r) if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
return $x -> binf('-', @r);
}
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> bmul($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
$r[3] = $y; # no push here
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-';
$x->{value} = $LIB->_mul($x->{value}, $y->{value}); # do actual math
$x->{sign} = '+' if $LIB->_is_zero($x->{value}); # no -0
$x -> round(@r);
}
*bdiv = \&bfdiv;
*bmod = \&bfmod;
sub bfdiv {
# This does floored division, where the quotient is floored, i.e., rounded
# towards negative infinity. As a consequence, the remainder has the same
# sign as the divisor.
#
# ($q, $r) = $x -> btdiv($y) returns $q and $r so that $q is floor($x / $y)
# and $q * $y + $r = $x.
# Set up parameters.
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bfdiv');
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(@r), $class -> bnan(@r))
: $x -> bnan(@r);
}
# Divide by zero and modulo zero.
#
# Division: Use the common convention that x / 0 is inf with the same sign
# as x, except when x = 0, where we return NaN. This is also what earlier
# versions did.
#
# Modulo: In modular arithmetic, the congruence relation z = x (mod y)
# means that there is some integer k such that z - x = k y. If y = 0, we
# get z - x = 0 or z = x. This is also what earlier versions did, except
# that 0 % 0 returned NaN.
#
# inf / 0 = inf inf % 0 = inf
# 5 / 0 = inf 5 % 0 = 5
# 0 / 0 = NaN 0 % 0 = 0
# -5 / 0 = -inf -5 % 0 = -5
# -inf / 0 = -inf -inf % 0 = -inf
if ($y -> is_zero()) {
my $rem;
if ($wantarray) {
$rem = $x -> copy() -> round(@r);
}
if ($x -> is_zero()) {
$x -> bnan(@r);
} else {
$x -> binf($x -> {sign}, @r);
}
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(@r) if $wantarray;
if ($y -> is_inf()) {
$x -> bnan(@r);
} else {
my $sign = $x -> bcmp(0) == $y -> bcmp(0) ? '+' : '-';
$x -> binf($sign, @r);
}
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() -> round(@r) if $wantarray;
$x -> bzero(@r);
} else {
$rem = $class -> binf($y -> {sign}, @r) if $wantarray;
$x -> bone('-', @r);
}
return $wantarray ? ($x, $rem) : $x;
}
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# At this point, both the numerator and denominator are finite, non-zero
# numbers.
unless ($wantarray) {
my $upg = $class -> upgrade();
if ($upg) {
my $tmp = $upg -> bfdiv($x, $y, @r);
if ($tmp -> is_int()) {
$tmp = $tmp -> as_int();
%$x = %$tmp;
} else {
%$x = %$tmp;
bless $x, $upg;
}
return $x;
}
}
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
$x -> {value} = $LIB -> _inc($x -> {value});
$rem -> {value} = $LIB -> _sub($LIB -> _copy($y -> {value}),
$rem -> {value});
}
# Now do the signs.
$x -> {sign} = $xsign eq $ysign || $LIB -> _is_zero($x -> {value})
? '+' : '-';
$rem -> {sign} = $ysign eq '+' || $LIB -> _is_zero($rem -> {value})
? '+' : '-';
}
# List context.
if ($wantarray) {
$rem -> {accuracy} = $x -> {accuracy};
$rem -> {precision} = $x -> {precision};
$x -> round(@r);
$rem -> round(@r);
return $x, $rem;
}
# Scalar context.
return $x -> round(@r) if $LIB -> _is_zero($rem -> {value});
# We could use this instead of the upgrade code above, but this code gives
# more decimals when the integer part is non-zero. This is because the
# fraction part is divided separately and the rounding is done on that part
# separeately before the integer part is added.
#
#if ($class -> upgrade()) {
# $rem -> _upg() -> bfdiv($y);
# $x -> _upg() -> badd($rem, @r);
# return $x;
#}
$x -> round(@r);
return $x;
}
sub bfmod {
# This is the remainder after floored division.
# Set up parameters.
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bfmod');
$r[3] = $y; # no push!
# At least one argument is NaN.
if ($x -> is_nan() || $y -> is_nan()) {
return $x -> bnan(@r);
}
# Modulo zero. See documentation for bfdiv().
if ($y -> is_zero()) {
return $x -> round(@r);
}
# Numerator (dividend) is +/-inf.
if ($x -> is_inf()) {
return $x -> bnan(@r);
}
# Denominator (divisor) is +/-inf.
if ($y -> is_inf()) {
if ($x -> is_zero() || $x -> bcmp(0) == $y -> bcmp(0)) {
return $x -> round(@r);
} else {
return $x -> binf($y -> sign(), @r);
}
}
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> bfmod($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
# 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};
}
$x -> round(@r);
}
sub btdiv {
# This does truncated division, where the quotient is truncted, i.e.,
# rounded towards zero.
#
# ($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]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
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(@r), $class -> bnan(@r))
: $x -> bnan(@r);
}
# Divide by zero and modulo zero.
#
# Division: Use the common convention that x / 0 is inf with the same sign
# as x, except when x = 0, where we return NaN. This is also what earlier
# versions did.
#
# Modulo: In modular arithmetic, the congruence relation z = x (mod y)
# means that there is some integer k such that z - x = k y. If y = 0, we
# get z - x = 0 or z = x. This is also what earlier versions did, except
# that 0 % 0 returned NaN.
#
# inf / 0 = inf inf % 0 = inf
# 5 / 0 = inf 5 % 0 = 5
# 0 / 0 = NaN 0 % 0 = 0
# -5 / 0 = -inf -5 % 0 = -5
# -inf / 0 = -inf -inf % 0 = -inf
if ($y -> is_zero()) {
my $rem;
if ($wantarray) {
$rem = $x -> copy(@r);
}
if ($x -> is_zero()) {
$x -> bnan(@r);
} else {
$x -> binf($x -> {sign}, @r);
}
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(@r) if $wantarray;
if ($y -> is_inf()) {
$x -> bnan(@r);
} else {
my $sign = $x -> bcmp(0) == $y -> bcmp(0) ? '+' : '-';
$x -> binf($sign,@r );
}
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() -> round(@r) if $wantarray;
$x -> bzero(@r);
return $wantarray ? ($x, $rem) : $x;
}
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# Division might return a non-integer result, so upgrade, if upgrading is
# enabled.
unless ($wantarray) {
my $upg = $class -> upgrade();
if ($upg) {
my $tmp = $upg -> btdiv($x, $y, @r);
if ($tmp -> is_int()) {
$tmp = $tmp -> as_int();
%$x = %$tmp;
} else {
%$x = %$tmp;
bless $x, $upg;
}
return $x;
}
}
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
# Code for Math::BigInt objects objects
###########################################################################
$r[3] = $y; # no push!
# Initialize remainder.
my $rem = $class -> bzero();
# Are both operands the same object, i.e., like $x -> btdiv($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) {
$x -> bone(@r);
} else {
($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 -> {accuracy} = $x -> {accuracy};
$rem -> {precision} = $x -> {precision};
$rem -> round(@r);
return $x, $rem;
}
return $x;
}
sub btmod {
# Remainder after truncated division.
# set up parameters
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
return $x if $x -> modify('btmod');
$r[3] = $y; # no push!
# At least one argument is NaN.
if ($x -> is_nan() || $y -> is_nan()) {
return $x -> bnan(@r);
}
# Modulo zero. See documentation for btdiv().
if ($y -> is_zero()) {
return $x -> round(@r);
}
# Numerator (dividend) is +/-inf.
if ($x -> is_inf()) {
return $x -> bnan(@r);
}
# Denominator (divisor) is +/-inf.
if ($y -> is_inf()) {
return $x -> round(@r);
}
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> btmod($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
my $xsign = $x -> {sign};
$x -> {value} = $LIB -> _mod($x -> {value}, $y -> {value});
$x -> {sign} = $xsign;
$x -> {sign} = '+' if $LIB -> _is_zero($x -> {value});
$x -> round(@r);
}
sub binv {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
$x -> bzero(@r);
}
sub bsqrt {
# calculate square root of $x
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bsqrt');
return $x -> round(@r) if ($x -> is_zero() || $x -> is_one("+") ||
$x -> is_nan() || $x -> is_inf("+"));
return $x -> bnan(@r) if $x -> is_negative();
###########################################################################
# Output might be finite, non-integer, so upgrade.
###########################################################################
return $x -> _upg() -> bsqrt(@r) if $class -> upgrade();
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
unless ($x -> isa(__PACKAGE__)) {
croak "Can't handle a ", ref($x), " in ", (caller(0))[3], "()";
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
$x->{value} = $LIB -> _sqrt($x->{value});
return $x -> round(@r);
}
sub bpow {
# (BINT or num_str, BINT or num_str) return BINT
# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
# modifies first argument
# set up parameters
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bpow');
# $x and/or $y is a NaN
return $x -> bnan(@r) if $x -> is_nan() || $y -> is_nan();
# $x and/or $y is a +/-Inf
if ($x -> is_inf("-")) {
return $x -> bzero(@r) if $y -> is_negative();
return $x -> bnan(@r) if $y -> is_zero();
return $x -> round(@r) if $y -> is_odd();
return $x -> bneg(@r);
} elsif ($x -> is_inf("+")) {
return $x -> bzero(@r) if $y -> is_negative();
return $x -> bnan(@r) if $y -> is_zero();
return $x -> round(@r);
} elsif ($y -> is_inf("-")) {
return $x -> bnan(@r) if $x -> is_one("-");
return $x -> binf("+", @r) if $x -> is_zero();
return $x -> bone(@r) if $x -> is_one("+");
return $x -> bzero(@r);
} elsif ($y -> is_inf("+")) {
return $x -> bnan(@r) if $x -> is_one("-");
return $x -> bzero(@r) if $x -> is_zero();
return $x -> bone(@r) if $x -> is_one("+");
return $x -> binf("+", @r);
}
if ($x -> is_zero()) {
return $x -> bone(@r) if $y -> is_zero();
return $x -> binf(@r) if $y -> is_negative();
return $x -> round(@r);
}
if ($x -> is_one("+")) {
return $x -> round(@r);
}
if ($x -> is_one("-")) {
return $x -> round(@r) if $y -> is_odd();
return $x -> bneg(@r);
}
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
return $x -> _upg() -> bpow($y, @r) if $class -> upgrade();
# We don't support finite non-integers, so return zero. The reason for
# returning zero, not NaN, is that all output is in the open interval
# (0,1), and truncating that to integer gives zero.
if ($y->{sign} eq '-' || !$y -> isa(__PACKAGE__)) {
return $x -> bzero(@r);
}
$r[3] = $y; # no push!
$x->{value} = $LIB -> _pow($x->{value}, $y->{value});
$x->{sign} = $x -> is_negative() && $y -> is_odd() ? '-' : '+';
$x -> round(@r);
}
sub broot {
# calculate $y'th root of $x
# set up parameters
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_) : objectify(2, @_);
$y = $class -> new("2") unless defined $y; # default base
# Don't modify constant (read-only) objects.
return $x if $x -> modify('broot');
# If called with "foreign" argument.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> broot($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
# NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
return $x -> bnan(@r) if ($x->{sign} !~ /^\+/ || $y -> is_zero() ||
$y->{sign} !~ /^\+$/);
# Quick exit for trivial cases.
return $x -> round(@r)
if $x -> is_zero() || $x -> is_one() || $x -> is_inf() || $y -> is_one();
return $x -> _upg() -> broot($y, @r) if $class -> upgrade();
$x->{value} = $LIB->_root($x->{value}, $y->{value});
$x -> round(@r);
}
sub bmuladd {
# multiply two numbers and then add the third to the result
# (BINT or num_str, BINT or num_str, BINT or num_str) return BINT
# set up parameters
my ($class, $x, $y, $z, @r)
= ref($_[0]) && ref($_[0]) eq ref($_[1]) && ref($_[1]) eq ref($_[2])
? (ref($_[0]), @_)
: objectify(3, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bmuladd');
# At least one of x, y, and z is a NaN
return $x -> bnan(@r) if ($x -> is_nan() ||
$y -> is_nan() ||
$z -> is_nan());
# At least one of x, y, and z is an Inf
if ($x -> is_inf("-")) {
if ($y -> is_neg()) { # x = -inf, y < 0
if ($z -> is_inf("-")) {
return $x -> bnan(@r);
} else {
return $x -> binf("+", @r);
}
} elsif ($y -> is_zero()) { # x = -inf, y = 0
return $x -> bnan(@r);
} else { # x = -inf, y > 0
if ($z->{sign} eq "+inf") {
return $x -> bnan(@r);
} else {
return $x -> binf("-", @r);
}
}
} elsif ($x->{sign} eq "+inf") {
if ($y -> is_neg()) { # x = +inf, y < 0
if ($z->{sign} eq "+inf") {
return $x -> bnan(@r);
} else {
return $x -> binf("-", @r);
}
} elsif ($y -> is_zero()) { # x = +inf, y = 0
return $x -> bnan(@r);
} else { # x = +inf, y > 0
if ($z -> is_inf("-")) {
return $x -> bnan(@r);
} else {
return $x -> binf("+", @r);
}
}
} elsif ($x -> is_neg()) {
if ($y -> is_inf("-")) { # -inf < x < 0, y = -inf
if ($z -> is_inf("-")) {
return $x -> bnan(@r);
} else {
return $x -> binf("+", @r);
}
} elsif ($y->{sign} eq "+inf") { # -inf < x < 0, y = +inf
if ($z->{sign} eq "+inf") {
return $x -> bnan(@r);
} else {
return $x -> binf("-", @r);
}
} else { # -inf < x < 0, -inf < y < +inf
if ($z -> is_inf("-")) {
return $x -> binf("-", @r);
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
return $x -> binf("-", @r);
} elsif ($z->{sign} eq "+inf") {
return $x -> binf("+", @r);
}
}
}
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__) && $z -> isa(__PACKAGE__)) {
if ($y -> is_int() && $z -> is_int()) {
$y = $y -> as_int();
$z = $z -> as_int();
} else {
return $x -> _upg() -> bmuladd($y, $z, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()"
unless $y -> isa(__PACKAGE__);
croak "Can't handle a ", ref($z), " in ", (caller(0))[3], "()"
unless $z -> isa(__PACKAGE__);
}
}
# At this point, we know that x, y, and z are finite numbers
# TODO: what if $y and $z have A or P set?
$r[3] = $z; # no push here
my $zs = $z->{sign};
my $zv = $z->{value};
$zv = $LIB -> _copy($zv) if refaddr($x) eq refaddr($z);
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-';
$x->{value} = $LIB->_mul($x->{value}, $y->{value}); # do actual math
$x->{sign} = '+' if $LIB->_is_zero($x->{value}); # no -0
($x->{value}, $x->{sign})
= $LIB -> _sadd($x->{value}, $x->{sign}, $zv, $zs);
return $x -> round(@r);
}
sub bmodpow {
# Modular exponentiation. Raises a very large number to a very large
# exponent in a given very large modulus quickly, thanks to binary
# exponentiation. Supports negative exponents.
my ($class, $num, $exp, $mod, @r)
= ref($_[0]) && ref($_[0]) eq ref($_[1]) && ref($_[1]) eq ref($_[2])
? (ref($_[0]), @_)
: objectify(3, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
return $num if $num -> modify('bmodpow');
# Check for valid input. All operands must be finite, and the modulus must
# be non-zero.
return $num -> bnan(@r) if (!$num -> is_finite() || # NaN, -inf, +inf
!$exp -> is_finite() || # NaN, -inf, +inf
!$mod -> is_finite()); # NaN, -inf, +inf
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# If called with "foreign" arguments.
unless ($exp -> isa(__PACKAGE__) && $mod -> isa(__PACKAGE__)) {
if ($exp -> is_int() && $mod -> is_int()) {
$exp = $exp -> as_int();
$mod = $mod -> as_int();
} else {
return $num -> _upg() -> bmodpow($exp, $mod, @r) if $class -> upgrade();
croak "Can't handle a ", ref($exp), " in ", (caller(0))[3], "()"
unless $exp -> isa(__PACKAGE__);
croak "Can't handle a ", ref($mod), " in ", (caller(0))[3], "()"
unless $mod -> isa(__PACKAGE__);
}
}
# When the exponent 'e' is negative, use the following relation, which is
# based on finding the multiplicative inverse 'd' of 'b' modulo 'm':
#
# b^(-e) (mod m) = d^e (mod m) where b*d = 1 (mod m)
#
# Return NaN if no modular multiplicative inverse exists.
if ($exp->{sign} eq '-') {
$num -> bmodinv($mod);
return $num -> bnan(@r) if $num -> is_nan();
}
# Modulo zero. See documentation for Math::BigInt's bmod() method.
if ($mod -> is_zero()) {
if ($num -> is_zero()) {
return $num -> bnan(@r);
} else {
return $num -> round(@r);
}
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
# 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 $num -> round(@r);
}
sub bmodinv {
# Return modular multiplicative inverse:
#
# z is the modular inverse of x (mod y) if and only if
#
# x*z ≡ 1 (mod y)
#
# If the modulus y is larger than one, x and z are relative primes (i.e.,
# their greatest common divisor is one).
#
# If no modular multiplicative inverse exists, NaN is returned.
# set up parameters
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bmodinv');
# Return NaN if one or both arguments is +inf, -inf, or nan.
return $x -> bnan(@r) if !$y -> is_finite() || !$x -> is_finite();
# Return NaN if $y is zero; 1 % 0 makes no sense.
return $x -> bnan(@r) if $y -> is_zero();
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> bmodinv($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
# Return 0 in the trivial case. $x % 1 or $x % -1 is zero for all finite
# integers $x.
return $x -> bzero(@r) 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.
$x -> bfmod($y);
return $x -> bnan(@r) 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 $x -> bnan(@r) if !defined($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};
$x -> round(@r);
}
sub blog {
# Return the logarithm of the operand. If a second operand is defined, that
# value is used as the base, otherwise the base is assumed to be Euler's
# constant.
my ($class, $x, $base, @r);
# Only objectify the base if it is defined, since an undefined base, as in
# $x->blog() or $x->blog(undef) signals that the base is Euler's number =
# 2.718281828...
if (!ref($_[0]) && $_[0] =~ /^[a-z]\w*(?:::\w+)*$/i) {
# E.g., Math::BigInt->blog(256, 2)
($class, $x, $base, @r) =
defined $_[2] ? objectify(2, @_) : objectify(1, @_);
} else {
# E.g., $x->blog(2) or the deprecated Math::BigInt::blog(256, 2)
($class, $x, $base, @r) =
defined $_[1] ? objectify(2, @_) : objectify(1, @_);
}
# Don't modify constant (read-only) objects.
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(@r) if $x -> is_nan();
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
return $x -> binf('+', @r);
} elsif ($x -> is_neg()) { # -inf < x < 0
return $x -> _upg() -> blog($base, @r) if $class -> upgrade();
return $x -> bnan(@r);
} elsif ($x -> is_one()) { # x = 1
return $x -> bzero(@r);
} elsif ($x -> is_zero()) { # x = 0
return $x -> binf('-', @r);
}
# At this point we are done handling all exception cases and trivial cases.
return $x -> _upg() -> blog($base, @r) if $class -> upgrade();
# fix for bug #24969:
# the default base is e (Euler's number) which is not an integer
if (!defined $base) {
require Math::BigFloat;
# disable upgrading and downgrading
my $upg = Math::BigFloat -> upgrade();
my $dng = Math::BigFloat -> downgrade();
Math::BigFloat -> upgrade(undef);
Math::BigFloat -> downgrade(undef);
my $u = Math::BigFloat -> new($x) -> blog() -> as_int();
# reset upgrading and downgrading
Math::BigFloat -> upgrade($upg);
Math::BigFloat -> downgrade($dng);
# modify $x in place
$x->{value} = $u->{value};
$x->{sign} = $u->{sign};
return $x -> round(@r);
}
my ($rc) = $LIB -> _log_int($x->{value}, $base->{value});
return $x -> bnan(@r) 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, @_);
###########################################################################
# Code for all classes that share the common interface.
###########################################################################
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bexp');
# inf, -inf, NaN, <0 => NaN
return $x -> bnan(@r) if $x -> is_nan();
return $x -> bone(@r) if $x -> is_zero();
return $x -> round(@r) if $x -> is_inf("+");
return $x -> bzero(@r) if $x -> is_inf("-");
###########################################################################
# Output might be finite, non-integer, so upgrade.
###########################################################################
return $x -> _upg() -> bexp(@r) if $class -> upgrade();
###########################################################################
# Code for things that aren't Math::BigInt
###########################################################################
unless ($x -> isa(__PACKAGE__)) {
croak "Can't handle a ", ref($x), " in ", (caller(0))[3], "()";
}
###########################################################################
# Code for Math::BigInt objects
###########################################################################
require Math::BigFloat;
my $tmp = Math::BigFloat -> bexp($x) -> bint() -> round(@r) -> as_int();
$x->{value} = $tmp->{value};
return $x -> round(@r);
}
sub bilog2 {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bilog2');
return $x -> bnan(@r) if $x -> is_nan();
return $x -> binf("+", @r) if $x -> is_inf("+");
return $x -> binf("-", @r) if $x -> is_zero();
if ($x -> is_neg()) {
return $x -> _upg() -> bilog2(@r) if $class -> upgrade();
return $x -> bnan(@r);
}
$x -> {value} = $LIB -> _ilog2($x -> {value});
return $x -> round(@r);
}
sub bilog10 {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bilog10');
return $x -> bnan(@r) if $x -> is_nan();
return $x -> binf("+", @r) if $x -> is_inf("+");
return $x -> binf("-", @r) if $x -> is_zero();
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
return $x -> bnan(@r) if $x -> is_nan();
return $x -> binf("+", @r) if $x -> is_inf("+");
return $x -> binf("-", @r) if $x -> is_zero();
if ($x -> is_neg()) {
return $x -> _upg() -> bclog2(@r) if $class -> upgrade();
return $x -> bnan(@r);
}
$x -> {value} = $LIB -> _clog2($x -> {value});
return $x -> round(@r);
}
sub bclog10 {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bclog10');
return $x -> bnan(@r) if $x -> is_nan();
return $x -> binf("+", @r) if $x -> is_inf("+");
return $x -> binf("-", @r) if $x -> is_zero();
if ($x -> is_neg()) {
return $x -> _upg() -> bclog10(@r) if $class -> upgrade();
return $x -> bnan(@r);
}
$x -> {value} = $LIB -> _clog10($x -> {value});
return $x -> round(@r);
}
sub bnok {
# Calculate n over k (binomial coefficient or "choose" function) as
# integer.
# Set up parameters.
my ($class, $n, $k, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_)
: objectify(2, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Don't modify constant (read-only) objects.
return $n if $n -> modify('bnok');
# If called with "foreign" arguments.
unless ($k -> isa(__PACKAGE__)) {
if ($k -> is_int()) {
$k = $k -> as_int();
} else {
return $n -> _upg() -> bnok($k, @r) if $class -> upgrade();
croak "Can't handle a ", ref($k), " in ", (caller(0))[3], "()";
}
}
# All cases where at least one argument is NaN.
return $n -> bnan(@r) if $n -> is_nan() || $k -> is_nan();
# All cases where at least one argument is +/-inf.
if ($n -> is_inf()) {
if ($k -> is_inf()) { # bnok(+/-inf,+/-inf)
return $n -> bnan(@r);
} elsif ($k -> is_neg()) { # bnok(+/-inf,k), k < 0
return $n -> bzero(@r);
} elsif ($k -> is_zero()) { # bnok(+/-inf,k), k = 0
return $n -> bone(@r);
} else {
if ($n -> is_inf("+", @r)) { # bnok(+inf,k), 0 < k < +inf
return $n -> binf("+");
} else { # bnok(-inf,k), k > 0
my $sign = $k -> is_even() ? "+" : "-";
return $n -> binf($sign, @r);
}
}
}
elsif ($k -> is_inf()) { # bnok(n,+/-inf), -inf <= n <= inf
return $n -> bnan(@r);
}
# At this point, both n and k are real numbers.
my $sign = 1;
if ($n >= 0) {
if ($k < 0 || $k > $n) {
return $n -> bzero(@r);
}
} else {
if ($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(@r);
}
}
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
@y = map { $_ -> round(@r) } @y;
return @y;
}
# 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 $n
my ($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, @_);
}
# Don't modify constant (read-only) objects.
return $x if $x -> modify('blsft');
# The default base is 2.
$b = 2 unless defined $b;
$b = $class -> new($b) unless defined(blessed($b));
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__) && $b -> isa(__PACKAGE__)) {
if ($y -> is_int() && $b -> is_int()) {
$y = $y -> as_int();
$b = $b -> as_int();
} else {
return $x -> _upg() -> blsft($y, $b, @r) if $class -> upgrade();
croak "Can't handle a ", ref($x), " in ", (caller(0))[3], "()"
unless $y -> isa(__PACKAGE__);
croak "Can't handle a ", ref($b), " in ", (caller(0))[3], "()"
unless $b -> isa(__PACKAGE__);
}
}
# Handle NaN cases.
return $x -> bnan(@r)
if $x -> is_nan() || $y -> is_nan() || $b -> is_nan();
# blsft($x, -$y, $b) = brsft($x, $y, $b)
return $x -> brsft($y -> copy() -> bneg(), $b, @r) if $y -> is_neg();
# Now handle all cases where at least one operand is ±Inf or the result
# will be ±Inf or NaN.
if ($y -> is_inf("+")) {
if ($b -> is_one("-")) {
return $x -> bnan(@r);
} elsif ($b -> is_one("+")) {
return $x -> round(@r);
} elsif ($b -> is_zero()) {
return $x -> bnan(@r) if $x -> is_inf();
return $x -> bzero(@r);
} else {
return $x -> binf("-", @r) if $x -> is_negative();
return $x -> binf("+", @r) if $x -> is_positive();
return $x -> bnan(@r);
}
}
if ($b -> is_inf()) {
return $x -> bnan(@r) if $x -> is_zero() || $y -> is_zero();
if ($b -> is_inf("-")) {
return $x -> binf("+", @r)
if ($x -> is_negative() && $y -> is_odd() ||
$x -> is_positive() && $y -> is_even());
return $x -> binf("-", @r);
} else {
return $x -> binf("-", @r) if $x -> is_negative();
return $x -> binf("+", @r);
}
}
if ($b -> is_zero()) {
return $x -> round(@r) if $y -> is_zero();
return $x -> bnan(@r) if $x -> is_inf();
return $x -> bzero(@r);
}
if ($x -> is_inf()) {
if ($b -> is_negative()) {
if ($x -> is_inf("-")) {
if ($y -> is_even()) {
return $x -> round(@r);
} else {
return $x -> binf("+", @r);
}
} else {
if ($y -> is_even()) {
return $x -> round(@r);
} else {
return $x -> binf("-", @r);
}
}
} else {
return $x -> round(@r);
}
}
# At this point, we know that both the input and the output is finite.
# Handle some trivial cases.
return $x -> round(@r) if $x -> is_zero() || $y -> is_zero()
|| $b -> is_one("+")
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
my $uintmax = ~0;
if ($x -> bcmp($uintmax) > 0) {
$x -> bmul($b -> bpow($y));
} else {
my $neg = 0;
if ($b -> is_negative()) {
$neg = 1 if $y -> is_odd();
$b -> babs();
}
$b = $b -> numify();
$x -> {value} = $LIB -> _lsft($x -> {value}, $y -> {value}, $b);
$x -> {sign} =~ tr/+-/-+/ if $neg;
}
$x -> round(@r);
}
sub brsft {
# (BINT or num_str, BINT or num_str) return BINT
# compute $x >> $y, base $n
my ($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, @_);
}
# Don't modify constant (read-only) objects.
return $x if $x -> modify('brsft');
# The default base is 2.
$b = 2 unless defined $b;
$b = $class -> new($b) unless defined(blessed($b));
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__) && $b -> isa(__PACKAGE__)) {
if ($y -> is_int() && $b -> is_int()) {
$y = $y -> as_int();
$b = $b -> as_int();
} else {
return $x -> _upg() -> brsft($y, $b, @r) if $class -> upgrade();
croak "Can't handle a ", ref($x), " in ", (caller(0))[3], "()"
unless $y -> isa(__PACKAGE__);
croak "Can't handle a ", ref($b), " in ", (caller(0))[3], "()"
unless $b -> isa(__PACKAGE__);
}
}
# Handle NaN cases.
return $x -> bnan(@r)
if $x -> is_nan() || $y -> is_nan() || $b -> is_nan();
# brsft($x, -$y, $b) = blsft($x, $y, $b)
return $x -> blsft($y -> copy() -> bneg(), $b, @r) if $y -> is_neg();
# Now handle all cases where at least one operand is ±Inf or the result
# will be ±Inf or NaN.
if ($b -> is_inf()) {
return $x -> bnan(@r) if $x -> is_inf() || $y -> is_zero();
if ($b -> is_inf("+")) {
if ($x -> is_negative()) {
return $x -> bone("-", @r);
} else {
return $x -> bzero(@r);
}
} else {
if ($x -> is_negative()) {
return $y -> is_odd() ? $x -> bzero(@r)
: $x -> bone("-", @r);
} elsif ($x -> is_positive()) {
return $y -> is_odd() ? $x -> bone("-", @r)
: $x -> bzero(@r);
} else {
return $x -> bzero(@r);
}
}
}
if ($b -> is_zero()) {
return $x -> round(@r) if $y -> is_zero();
return $x -> bnan(@r) if $x -> is_zero();
return $x -> is_negative() ? $x -> binf("-", @r)
: $x -> binf("+", @r);
}
if ($y -> is_inf("+")) {
if ($b -> is_one("-")) {
return $x -> bnan(@r);
} elsif ($b -> is_one("+")) {
return $x -> round(@r);
} else {
return $x -> bnan(@r) if $x -> is_inf();
return $x -> is_negative() ? $x -> bone("-", @r)
: $x -> bzero(@r);
}
}
if ($x -> is_inf()) {
if ($b -> is_negative()) {
if ($x -> is_inf("-")) {
if ($y -> is_even()) {
return $x -> round(@r);
} else {
return $x -> binf("+", @r);
}
} else {
if ($y -> is_even()) {
return $x -> round(@r);
} else {
return $x -> binf("-", @r);
}
}
} else {
return $x -> round(@r);
}
}
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
return $x if $x -> modify('bbrsft');
return $x -> bnan(@r) if $x -> is_nan() || $y -> is_nan();
# bbrsft($x, -$y) = bblsft($x, $y)
return $x -> bblsft($y -> copy() -> bneg()) if $y -> is_neg();
# Shifting infinitely far to the right.
if ($y -> is_inf("+")) {
return $x -> bnan(@r) if $x -> is_inf();
return $x -> bone("-", @r) if $x -> is_neg();
return $x -> bzero(@r);
}
# These cases change nothing.
return $x -> round(@r) if $x -> is_zero() || $x -> is_inf() ||
$y -> is_zero();
# At this point, $x is either positive or negative, not zero.
if ($x -> is_pos()) {
$x -> {value} = $LIB -> _rsft($x -> {value}, $y -> {value}, 2);
} else {
my $n = $x -> {value};
my $d = $LIB -> _pow($LIB -> _new("2"), $y -> {value});
my ($p, $q) = $LIB -> _div($n, $d);
$p = $LIB -> _inc($p) unless $LIB -> _is_zero($q);
$x -> {value} = $p;
}
$x -> round(@r);
}
sub band {
#(BINT or num_str, BINT or num_str) return BINT
# compute x & y
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_) : objectify(2, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('band');
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> band($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
$r[3] = $y; # no push!
# If $x and/or $y is Inf or NaN, return NaN.
return $x -> bnan(@r) if !$x -> is_finite() || !$y -> is_finite();
if ($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 $x -> round(@r);
}
sub bior {
#(BINT or num_str, BINT or num_str) return BINT
# compute x | y
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_) : objectify(2, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bior');
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> bior($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
$r[3] = $y; # no push!
# If $x and/or $y is Inf or NaN, return NaN.
return $x -> bnan() if (!$x -> is_finite() || !$y -> is_finite());
if ($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 $x -> round(@r);
}
sub bxor {
#(BINT or num_str, BINT or num_str) return BINT
# compute x ^ y
my ($class, $x, $y, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_) : objectify(2, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bxor');
# If called with "foreign" arguments.
unless ($y -> isa(__PACKAGE__)) {
if ($y -> is_int()) {
$y = $y -> as_int();
} else {
return $x -> _upg() -> bxor($y, @r) if $class -> upgrade();
croak "Can't handle a ", ref($y), " in ", (caller(0))[3], "()";
}
}
$r[3] = $y; # no push!
# If $x and/or $y is Inf or NaN, return NaN.
return $x -> bnan(@r) if !$x -> is_finite() || !$y -> is_finite();
if ($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 $x -> round(@r);
}
sub bnot {
# (num_str or BINT) return BINT
# represent ~x as twos-complement number
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bnot');
$x -> binc() -> bneg(@r);
}
###############################################################################
# Rounding methods
###############################################################################
sub round {
# Round $self according to given parameters, or given second argument's
# parameters or global defaults
my ($class, $self, @args) = ref($_[0]) ? (ref($_[0]), @_)
: objectify(1, @_);
# These signal no rounding:
#
# $x->round(undef)
# $x->round(undef, undef, ...)
#
# The "@args <= 3" is necessary because the final set of parameters that
# will be used for rounding depend on the "extra arguments", if any.
if (@args == 1 && !defined($args[0]) ||
@args >= 2 && @args <= 3 && !defined($args[0]) && !defined($args[1]))
{
$self->{accuracy} = undef;
$self->{precision} = undef;
return $self;
}
my ($a, $p, $r) = splice @args, 0, 3;
# $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)
if (defined $a) {
croak "accuracy must be a number, not '$a'"
unless $a =~/^[+-]?(?:\d+(?:\.\d*)?|\.\d+)(?:[Ee][+-]?\d+)?\z/;
}
if (defined $p) {
croak "precision must be a number, not '$p'"
unless $p =~/^[+-]?(?:\d+(?:\.\d*)?|\.\d+)(?:[Ee][+-]?\d+)?\z/;
}
# 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 = $_->{accuracy}
if (defined $_->{accuracy}) && (!defined $a || $_->{accuracy} < $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 = $_->{precision}
if (defined $_->{precision}) && (!defined $p || $_->{precision} > $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;
# set A and set P is an fatal error
if (defined $a && defined $p) {
#carp "can't specify both accuracy and precision";
return $self -> bnan();
}
# Infs and NaNs are not rounded, but assign rounding parameters to them.
#
#if ($self -> is_inf() || $self -> is_nan()) {
# $self->{accuracy} = $a;
# $self->{precision} = $p;
# return $self;
#}
$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->{accuracy} || $self->{accuracy} >= $a;
} else { # both can't be undefined due to early out
$self -> bfround(int($p), $r)
if !defined $self->{precision} || $self->{precision} <= $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 $x
my ($class, $x, @a) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bround');
my ($scale, $mode) = $x->_scale_a(@a);
return $x if !defined $scale; # no-op
if ($x -> is_zero() || $scale == 0) {
$x->{accuracy} = $scale
if !defined $x->{accuracy} || $x->{accuracy} > $scale; # 3 > 2
return $x;
}
return $x if !$x -> is_finite(); # 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->{accuracy} = $scale
if !defined $x->{accuracy} || $x->{accuracy} > $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...'
$xs =~ s/^0+(\d)/$1/; # "00000" -> "0"
$put_back = 1; # need to put back
} elsif ($pad > $len) {
$x -> bzero(); # round to '0'
}
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
sub blcm {
# Least Common Multiple
# Class::method(...) -> Class->method(...)
unless (@_ && (defined(blessed($_[0])) && $_[0] -> isa(__PACKAGE__) ||
($_[0] =~ /^[a-z]\w*(?:::[a-z]\w*)*$/i &&
$_[0] !~ /^(inf|nan)/i)))
{
#carp "Using ", (caller(0))[3], "() as a function is deprecated;",
# " use is as a method instead";
unshift @_, __PACKAGE__;
}
my ($class, @args) = objectify(0, @_);
# Pre-process list of operands.
for my $arg (@args) {
return $class -> bnan() unless $arg -> is_finite();
}
for my $arg (@args) {
return $class -> bzero() if $arg -> is_zero();
}
# Upgrade?
my $upg = $class -> upgrade();
if ($upg) {
my $do_upgrade = 0;
for my $arg (@args) {
unless ($arg -> isa(__PACKAGE__)) {
$do_upgrade = 1;
last;
}
}
if ($do_upgrade) {
my $x = shift @args;
$x -> _upg();
return $x -> bgcd(@args);
}
}
my $x = shift @args;
$x = $x -> copy(); # bgcd() and blcm() never modify any operands
while (@args) {
my $y = shift @args;
return $x -> bnan() if !$y -> is_int(); # is $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, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
$x->{sign};
}
sub digit {
# return the nth decimal digit, negative values count backward, 0 is right
my (undef, $x, $n, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
$n = $n -> numify() if ref($n);
$LIB->_digit($x->{value}, $n || 0);
}
sub bdigitsum {
# like digitsum(), but assigns the result to the invocand
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
# Don't modify constant (read-only) objects.
return $x if $x -> modify('bdigitsum');
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
return $x if $x -> is_nan();
return $x -> bnan() if $x -> is_inf();
$x -> {value} = $LIB -> _digitsum($x -> {value});
$x -> {sign} = '+';
return $x;
}
sub digitsum {
# compute sum of decimal digits and return it
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
return $class -> bnan() if $x -> is_nan();
return $class -> bnan() if $x -> is_inf();
my $y = $class -> bzero();
$y -> {value} = $LIB -> _digitsum($x -> {value});
$y -> round(@r);
}
sub length {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
my $e = $LIB->_len($x->{value});
wantarray ? ($e, 0) : $e;
}
sub mantissa {
# return the mantissa (compatible to Math::BigFloat, e.g. reduced)
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
if (!$x -> is_finite()) {
# for NaN, +inf, -inf: keep the sign
return $class -> new($x->{sign}, @r);
}
my $m = $x -> copy();
$m -> precision(undef);
$m -> accuracy(undef);
# that's a bit inefficient:
my $zeros = $LIB->_zeros($m->{value});
$m = $m -> brsft($zeros, 10) if $zeros != 0;
$m -> round(@r);
}
sub exponent {
# return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
if (!$x -> is_finite()) {
my $s = $x->{sign};
$s =~ s/^[+-]//; # NaN, -inf, +inf => NaN or inf
return $class -> new($s, @r);
}
return $class -> bzero(@r) if $x -> is_zero();
# 12300 => 2 trailing zeros => exponent is 2
$class -> new($LIB->_zeros($x->{value}), @r);
}
sub parts {
# return a copy of both the exponent and the mantissa
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
($x -> mantissa(@r), $x -> exponent(@r));
}
# Parts used for scientific notation with significand/mantissa and exponent as
# integers. E.g., "12345.6789" is returned as "123456789" (mantissa) and "-4"
# (exponent).
sub sparts {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Not-a-number.
if ($x -> is_nan()) {
my $mant = $class -> bnan(@r); # mantissa
return $mant unless wantarray; # scalar context
my $expo = $class -> bnan(@r); # exponent
return $mant, $expo; # list context
}
# Infinity.
if ($x -> is_inf()) {
my $mant = $class -> binf($x->{sign}, @r); # mantissa
return $mant unless wantarray; # scalar context
my $expo = $class -> binf('+', @r); # exponent
return $mant, $expo; # list context
}
# Finite number.
my $mant = $x -> copy();
my $nzeros = $LIB -> _zeros($mant -> {value});
$mant -> {value}
= $LIB -> _rsft($mant -> {value}, $LIB -> _new($nzeros), 10)
if $nzeros != 0;
return $mant unless wantarray;
my $expo = $class -> new($nzeros, @r);
return $mant, $expo;
}
# Parts used for normalized notation with significand/mantissa as either 0 or a
# number in the semi-open interval [1,10). E.g., "12345.6789" is returned as
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
}
return $mant unless wantarray;
return $mant, $expo;
}
# Parts used for engineering notation with significand/mantissa as either 0 or
# a number in the semi-open interval [1,1000) and the exponent is a multiple of
# 3. E.g., "12345.6789" is returned as "12.3456789" and "3".
sub eparts {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Not-a-number and Infinity.
return $x -> sparts(@r) if $x -> is_nan() || $x -> is_inf();
# Finite number.
my ($mant, $expo) = $x -> sparts(@r);
if ($mant -> bcmp(0)) {
my $ndigmant = $mant -> length();
$expo -> badd($ndigmant, @r);
# $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 $x -> _upg() -> eparts(@r) if $class -> upgrade();
$mant -> bnan(@r);
return $mant unless wantarray;
return $mant, $expo;
}
$mant -> blsft($c - $ndigmant, 10, @r);
}
return $mant unless wantarray;
return $mant, $expo;
}
# Parts used for decimal notation, e.g., "12345.6789" is returned as "12345"
# (integer part) and "0.6789" (fraction part).
sub dparts {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Not-a-number.
if ($x -> is_nan()) {
my $int = $class -> bnan(@r);
return $int unless wantarray;
my $frc = $class -> bzero(@r); # or NaN?
return $int, $frc;
}
# Infinity.
if ($x -> is_inf()) {
my $int = $class -> binf($x->{sign}, @r);
return $int unless wantarray;
my $frc = $class -> bzero(@r);
return $int, $frc;
}
# Finite number.
my $int = $x -> copy() -> round(@r);
return $int unless wantarray;
my $frc = $class -> bzero(@r);
return $int, $frc;
}
# Fractional parts with the numerator and denominator as integers. E.g.,
# "123.4375" is returned as "1975" and "16".
sub fparts {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# NaN => NaN/NaN
if ($x -> is_nan()) {
return $class -> bnan(@r) unless wantarray;
return $class -> bnan(@r), $class -> bnan(@r);
}
# ±Inf => ±Inf/1
if ($x -> is_inf()) {
my $numer = $class -> binf($x->{sign}, @r);
return $numer unless wantarray;
my $denom = $class -> bone(@r);
return $numer, $denom;
}
# N => N/1
my $numer = $x -> copy() -> round(@r);
return $numer unless wantarray;
my $denom = $class -> bone(@r);
return $numer, $denom;
}
sub numerator {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
return $x -> copy() -> round(@r);
}
sub denominator {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
return $x -> is_nan() ? $class -> bnan(@r) : $class -> bone(@r);
}
###############################################################################
# String conversion methods
###############################################################################
sub bstr {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
$x -> _upg() -> bstr(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
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, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
$x -> _upg() -> bsstr(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
my $expo = $LIB -> _zeros($x->{value});
my $mant = $LIB -> _str($x->{value});
$mant = substr($mant, 0, -$expo) if $expo; # strip trailing zeros
($x->{sign} eq '-' ? '-' : '') . $mant . 'e+' . $expo;
}
# Normalized notation, e.g., "12345" is written as "1.2345e+4".
sub bnstr {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
$x -> _upg() -> bnstr(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
my $expo = $LIB -> _zeros($x->{value});
my $mant = $LIB -> _str($x->{value});
$mant = substr($mant, 0, -$expo) if $expo; # strip trailing zeros
my $mantlen = CORE::length($mant);
if ($mantlen > 1) {
$expo += $mantlen - 1; # adjust exponent
substr $mant, 1, 0, "."; # insert decimal point
}
($x->{sign} eq '-' ? '-' : '') . $mant . 'e+' . $expo;
}
# Engineering notation, e.g., "12345" is written as "12.345e+3".
sub bestr {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
$x -> _upg() -> bestr(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
my $expo = $LIB -> _zeros($x->{value}); # number of trailing zeros
my $mant = $LIB -> _str($x->{value}); # mantissa as a string
$mant = substr($mant, 0, -$expo) if $expo; # strip trailing zeros
my $mantlen = CORE::length($mant); # length of mantissa
$expo += $mantlen;
my $dotpos = ($expo - 1) % 3 + 1; # offset of decimal point
$expo -= $dotpos;
if ($dotpos < $mantlen) {
substr $mant, $dotpos, 0, "."; # insert decimal point
} elsif ($dotpos > $mantlen) {
$mant .= "0" x ($dotpos - $mantlen); # append zeros
}
($x->{sign} eq '-' ? '-' : '') . $mant . 'e+' . $expo;
}
# Decimal notation, e.g., "12345" (no exponent).
sub bdstr {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
$x -> _upg() -> bdstr(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
($x->{sign} eq '-' ? '-' : '') . $LIB->_str($x->{value});
}
# Fraction notation, e.g., "123.4375" is written as "1975/16", but "123" is
# written as "123", not "123/1".
sub bfstr {
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
$x -> _upg() -> bfstr(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
($x->{sign} eq '-' ? '-' : '') . $LIB->_str($x->{value});
}
sub to_hex {
# return as hex string with no prefix
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
return $x -> _upg() -> to_hex(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
my $hex = $LIB->_to_hex($x->{value});
return $x->{sign} eq '-' ? "-$hex" : $hex;
}
sub to_oct {
# return as octal string with no prefix
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
return $x -> _upg() -> to_oct(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
my $oct = $LIB->_to_oct($x->{value});
return $x->{sign} eq '-' ? "-$oct" : $oct;
}
sub to_bin {
# return as binary string with no prefix
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
# Inf and NaN
if ($x->{sign} ne '+' && $x->{sign} ne '-') {
return $x->{sign} unless $x -> is_inf("+"); # -inf, NaN
return 'inf'; # +inf
}
# Upgrade?
return $x -> _upg() -> to_bin(@r) if $class -> upgrade() && !$x -> isa(__PACKAGE__);
# Finite number
my $bin = $LIB->_to_bin($x->{value});
return $x->{sign} eq '-' ? "-$bin" : $bin;
}
sub to_bytes {
# return a byte string
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
croak("to_bytes() requires a finite, non-negative integer")
if $x -> is_neg() || ! $x -> is_int();
return $x -> _upg() -> to_bytes(@r)
if $class -> upgrade() && !$x -> isa(__PACKAGE__);
croak("to_bytes() requires a newer version of the $LIB library.")
unless $LIB -> can('_to_bytes');
return $LIB->_to_bytes($x->{value});
}
sub to_ieee754 {
my ($class, $x, $format, @r) = ref($_[0]) ? (ref($_[0]), @_)
: objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
return $x -> _upg() -> to_ieee754($format, @r)
if $class -> upgrade() && !$x -> isa(__PACKAGE__);
croak("the value to convert must be an integer, +/-infinity, or NaN")
unless $x -> is_int() || $x -> is_inf() || $x -> is_nan();
return $x -> as_float() -> to_ieee754($format);
}
sub to_base {
# return a base anything string
# $cs is the collation sequence
my ($class, $x, $base, $cs, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_) : objectify(2, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
croak("the value to convert must be a finite, non-negative integer")
if $x -> is_neg() || !$x -> is_int();
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.
unless (defined $cs) {
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 $x -> _upg() -> to_basen($base, $cs, @r)
if $class -> upgrade() && (!$x -> isa(__PACKAGE__) ||
!$base -> isa(__PACKAGE__));
return $LIB->_to_base($x->{value}, $base -> {value},
defined($cs) ? $cs : ());
}
sub to_base_num {
# return a base anything array ref, e.g.,
# Math::BigInt -> new(255) -> to_base_num(10) returns [2, 5, 5];
# $cs is the collation sequence
my ($class, $x, $base, @r) = ref($_[0]) && ref($_[0]) eq ref($_[1])
? (ref($_[0]), @_) : objectify(2, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
croak("the value to convert must be a finite non-negative integer")
if $x -> is_neg() || !$x -> is_int();
croak("the base must be a finite integer >= 2")
if $base < 2 || ! $base -> is_int();
croak("to_base() requires a newer version of the $LIB library.")
unless $LIB -> can('_to_base');
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
my $oct = $LIB->_as_oct($x->{value});
return $x->{sign} eq '-' ? "-$oct" : $oct;
}
sub as_bin {
# return as binary string, with prefixed 0b
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
return $x -> bstr() if !$x -> is_finite(); # inf, nan etc
return $x -> _upg() -> as_bin(@r)
if $class -> upgrade() && !$x -> isa(__PACKAGE__);
my $bin = $LIB->_as_bin($x->{value});
return $x->{sign} eq '-' ? "-$bin" : $bin;
}
*as_bytes = \&to_bytes;
###############################################################################
# Other conversion methods
###############################################################################
sub numify {
# Make a Perl scalar number from a Math::BigInt object.
my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_);
carp "Rounding is not supported for ", (caller(0))[3], "()" if @r;
if ($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;
}
return $x -> _upg() -> numify(@r)
if $class -> upgrade() && !$x -> isa(__PACKAGE__);
my $num = 0 + $LIB->_num($x->{value});
return $x->{sign} eq '-' ? -$num : $num;
}
###############################################################################
# Private methods and functions.
###############################################################################
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 -> is_finite(); # 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)
# 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 = $_->{accuracy}
if (defined $_->{accuracy}) && (!defined $a || $_->{accuracy} < $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 = $_->{precision}
if (defined $_->{precision}) && (!defined $p || $_->{precision} > $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);
}
# Return true if the input is numeric and false if it is a string.
sub _is_numeric {
shift; # class name
my $value = shift;
no warnings 'numeric';
# detect numbers
# string & "" -> ""
# number & "" -> 0 (with warning)
# nan and inf can detect as numbers, so check with * 0
return unless CORE::length((my $dummy = "") & $value);
return unless 0 + $value eq $value;
return 1 if $value * 0 == 0;
return -1; # Inf/NaN
}
# Trims the sign of the significand, the (absolute value of the) significand,
# the sign of the exponent, and the (absolute value of the) exponent. The
# returned values have no underscores ("_") or unnecessary leading or trailing
# zeros.
sub _trim_split_parts {
shift; # class name
my $sig_sgn = shift() || '+';
my $sig_str = shift() || '0';
my $exp_sgn = shift() || '+';
my $exp_str = shift() || '0';
$sig_str =~ tr/_//d; # "1.0_0_0" -> "1.000"
$sig_str =~ s/^0+//; # "01.000" -> "1.000"
$sig_str =~ s/\.0*$// # "1.000" -> "1"
|| $sig_str =~ s/(\..*[^0])0+$/$1/; # "1.010" -> "1.01"
$sig_str = '0' unless CORE::length($sig_str);
return '+', '0', '+', '0' if $sig_str eq '0';
$exp_str =~ tr/_//d; # "01_234" -> "01234"
$exp_str =~ s/^0+//; # "01234" -> "1234"
$exp_str = '0' unless CORE::length($exp_str);
$exp_sgn = '+' if $exp_str eq '0'; # "+3e-0" -> "+3e+0"
return $sig_sgn, $sig_str, $exp_sgn, $exp_str;
}
# Takes any string representing a valid decimal number and splits it into four
# strings: the sign of the significand, the absolute value of the significand,
# the sign of the exponent, and the absolute value of the exponent. Both the
# significand and the exponent are in base 10.
#
# Perl accepts literals like the following. The value is 100.1.
#
# 1__0__.__0__1__e+0__1__ (prints "Misplaced _ in number")
# 1_0.0_1e+0_1
#
# Strings representing decimal numbers do not allow underscores, so only the
# following is valid
#
# "10.01e+01"
sub _dec_str_to_dec_str_parts {
my $class = shift;
my $str = shift;
if ($str =~ /
^
# optional leading whitespace
\s*
# optional sign
( [+-]? )
# significand
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
$class -> export_to_level(1, $class, @a) if @a; # need this, too
# We might not have loaded any backend library yet, either because the user
# didn't specify any, or because the specified libraries failed to load and
# the user allows the use of a fallback library.
unless (defined $LIB) {
eval "require $DEFAULT_LIB";
if ($@) {
croak "No lib specified, and couldn't load the default",
" lib '$DEFAULT_LIB'";
}
$LIB = $DEFAULT_LIB;
}
# import done
}
1;
__END__
=pod
=head1 NAME
Math::BigInt - arbitrary size integer math package
=head1 SYNOPSIS
use Math::BigInt;
# or make it faster with huge numbers: install (optional)
# Math::BigInt::GMP and always use (it falls back to
# pure Perl if the GMP library is not installed):
# (See also the L</Math Library> section!)
# to warn if Math::BigInt::GMP cannot be found, use
use Math::BigInt lib => 'GMP';
# to suppress the warning if Math::BigInt::GMP cannot be found, use
# use Math::BigInt try => 'GMP';
# to die if Math::BigInt::GMP cannot be found, use
# use Math::BigInt only => 'GMP';
# Configuration methods (may be used as class methods and instance methods)
Math::BigInt->accuracy($n); # set accuracy
Math::BigInt->accuracy(); # get accuracy
Math::BigInt->precision($n); # set precision
Math::BigInt->precision(); # get precision
Math::BigInt->round_mode($m); # set rounding mode, must be
# 'even', 'odd', '+inf', '-inf',
# 'zero', 'trunc', or 'common'
Math::BigInt->round_mode(); # get class rounding mode
Math::BigInt->div_scale($n); # set fallback accuracy
Math::BigInt->div_scale(); # get fallback accuracy
Math::BigInt->trap_inf($b); # trap infinities or not
Math::BigInt->trap_inf(); # get trap infinities status
Math::BigInt->trap_nan($b); # trap NaNs or not
Math::BigInt->trap_nan(); # get trap NaNs status
Math::BigInt->config($par, $val); # set configuration parameter
Math::BigInt->config($par); # get configuration parameter
Math::BigInt->config(); # get hash with configuration
Math::BigFloat->config("lib"); # get name of backend library
# Generic constructor method (always returns a new object)
$x = Math::BigInt->new($str); # defaults to 0
$x = Math::BigInt->new('256'); # from decimal
$x = Math::BigInt->new('0256'); # from decimal
$x = Math::BigInt->new('0xcafe'); # from hexadecimal
$x = Math::BigInt->new('0x1.fap+7'); # from hexadecimal
$x = Math::BigInt->new('0o377'); # from octal
$x = Math::BigInt->new('0o1.35p+6'); # from octal
$x = Math::BigInt->new('0b101'); # from binary
$x = Math::BigInt->new('0b1.101p+3'); # from binary
# Specific constructor methods (no prefix needed; when used as
# instance method, the value is assigned to the invocand)
$x = Math::BigInt->from_dec('234'); # from decimal
$x = Math::BigInt->from_hex('cafe'); # from hexadecimal
$x = Math::BigInt->from_hex('1.fap+7'); # from hexadecimal
$x = Math::BigInt->from_oct('377'); # from octal
$x = Math::BigInt->from_oct('1.35p+6'); # from octal
$x = Math::BigInt->from_bin('1101'); # from binary
$x = Math::BigInt->from_bin('1.101p+3'); # from binary
$x = Math::BigInt->from_bytes($bytes); # from byte string
$x = Math::BigInt->from_base('why', 36); # from any base
$x = Math::BigInt->from_base_num([1, 0], 2); # from any base
$x = Math::BigInt->from_ieee754($b, $fmt); # from IEEE-754 bytes
$x = Math::BigInt->bzero(); # create a +0
$x = Math::BigInt->bone(); # create a +1
$x = Math::BigInt->bone('-'); # create a -1
$x = Math::BigInt->binf(); # create a +inf
$x = Math::BigInt->binf('-'); # create a -inf
$x = Math::BigInt->bnan(); # create a Not-A-Number
$x = Math::BigInt->bpi(); # returns pi
$y = $x->copy(); # make a copy (unlike $y = $x)
$y = $x->as_int(); # return as a Math::BigInt
$y = $x->as_float(); # return as a Math::BigFloat
$y = $x->as_rat(); # return as a Math::BigRat
# Boolean methods (these don't modify the invocand)
$x->is_zero(); # true if $x is 0
$x->is_one(); # true if $x is +1
$x->is_one("+"); # true if $x is +1
$x->is_one("-"); # true if $x is -1
$x->is_inf(); # true if $x is +inf or -inf
$x->is_inf("+"); # true if $x is +inf
$x->is_inf("-"); # true if $x is -inf
$x->is_nan(); # true if $x is NaN
$x->is_finite(); # true if -inf < $x < inf
$x->is_positive(); # true if $x > 0
$x->is_pos(); # true if $x > 0
$x->is_negative(); # true if $x < 0
$x->is_neg(); # true if $x < 0
$x->is_non_positive() # true if $x <= 0
$x->is_non_negative() # true if $x >= 0
$x->is_odd(); # true if $x is odd
$x->is_even(); # true if $x is even
$x->is_int(); # true if $x is an integer
# Comparison methods (these don't modify the invocand)
$x->bcmp($y); # compare numbers (undef, < 0, == 0, > 0)
$x->bacmp($y); # compare abs values (undef, < 0, == 0, > 0)
$x->beq($y); # true if $x == $y
$x->bne($y); # true if $x != $y
$x->blt($y); # true if $x < $y
$x->ble($y); # true if $x <= $y
$x->bgt($y); # true if $x > $y
$x->bge($y); # true if $x >= $y
# Arithmetic methods (these modify the invocand)
$x->bneg(); # negation
$x->babs(); # absolute value
$x->bsgn(); # sign function (-1, 0, 1, or NaN)
$x->bdigitsum(); # sum of decimal digits
$x->binc(); # increment $x by 1
$x->bdec(); # decrement $x by 1
$x->badd($y); # addition (add $y to $x)
$x->bsub($y); # subtraction (subtract $y from $x)
$x->bmul($y); # multiplication (multiply $x by $y)
$x->bmuladd($y, $z); # $x = $x * $y + $z
$x->bdiv($y); # division (floored)
$x->bmod($y); # modulus (x % y)
$x->bmodinv($mod); # modular multiplicative inverse
$x->bmodpow($y, $mod); # modular exponentiation (($x ** $y) % $mod)
$x->btdiv($y); # division (truncated), set $x to quotient
$x->btmod($y); # modulus (truncated)
$x->binv() # inverse (1/$x)
$x->bpow($y); # power of arguments (x ** y)
$x->blog(); # logarithm of $x to base e (Euler's number)
$x->blog($base); # logarithm of $x to base $base (e.g., base 2)
$x->bexp(); # calculate e ** $x where e is Euler's number
$x->bilog2(); # log2($x) rounded down to nearest int
$x->bilog10(); # log10($x) rounded down to nearest int
$x->bclog2(); # log2($x) rounded up to nearest int
$x->bclog10(); # log10($x) rounded up to nearest int
$x->bnok($y); # combinations (binomial coefficient n over k)
$x->bperm($y); # permutations
$x->buparrow($n, $y); # Knuth's up-arrow notation
$x->bhyperop($n, $y); # n'th hyperoprator
$x->backermann($y); # the Ackermann function
$x->bsin(); # sine
$x->bcos(); # cosine
$x->batan(); # inverse tangent
$x->batan2($y); # two-argument inverse tangent
$x->bsqrt(); # calculate square root
$x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root)
$x->bfac(); # factorial of $x (1*2*3*4*..$x)
$x->bdfac(); # double factorial of $x ($x*($x-2)*($x-4)*...)
$x->btfac(); # triple factorial of $x ($x*($x-3)*($x-6)*...)
$x->bmfac($k); # $k'th multi-factorial of $x ($x*($x-$k)*...)
$x->bfib($k); # $k'th Fibonacci number
$x->blucas($k); # $k'th Lucas number
$x->blsft($n); # left shift $n places in base 2
$x->blsft($n, $b); # left shift $n places in base $b
$x->brsft($n); # right shift $n places in base 2
$x->brsft($n, $b); # right shift $n places in base $b
# Bitwise methods (these modify the invocand)
$x->bblsft($y); # bitwise left shift
$x->bbrsft($y); # bitwise right shift
$x->band($y); # bitwise and
$x->bior($y); # bitwise inclusive or
$x->bxor($y); # bitwise exclusive or
$x->bnot(); # bitwise not (two's complement)
# Rounding methods (these modify the invocand)
$x->round($A, $P, $R); # round to accuracy or precision using
# rounding mode $R
$x->bround($n); # accuracy: preserve $n digits
$x->bfround($n); # $n > 0: round to $nth digit left of dec. point
# $n < 0: round to $nth digit right of dec. point
$x->bfloor(); # round towards minus infinity
$x->bceil(); # round towards plus infinity
$x->bint(); # round towards zero
# Other mathematical methods (these don't modify the invocand)
$x->bgcd($y); # greatest common divisor
$x->blcm($y); # least common multiple
# Object property methods (these don't modify the invocand)
$x->sign(); # the sign, either +, - or NaN
$x->digit($n); # the nth digit, counting from the right
$x->digit(-$n); # the nth digit, counting from the left
$x->digitsum(); # sum of decimal digits
$x->length(); # return number of digits in number
$x->mantissa(); # return (signed) mantissa as a Math::BigInt
$x->exponent(); # return exponent as a Math::BigInt
$x->parts(); # return (mantissa,exponent) as a Math::BigInt
$x->sparts(); # mantissa and exponent (as integers)
$x->nparts(); # mantissa and exponent (normalised)
$x->eparts(); # mantissa and exponent (engineering notation)
$x->dparts(); # integer and fraction part
$x->fparts(); # numerator and denominator
$x->numerator(); # numerator
$x->denominator(); # denominator
# Conversion methods (these don't modify the invocand)
$x->bstr(); # decimal notation (possibly zero padded)
$x->bsstr(); # string in scientific notation with integers
$x->bnstr(); # string in normalized notation
$x->bestr(); # string in engineering notation
$x->bdstr(); # string in decimal notation (no padding)
$x->bfstr(); # string in fractional notation
$x->to_hex(); # as signed hexadecimal string
$x->to_bin(); # as signed binary string
$x->to_oct(); # as signed octal string
$x->to_bytes(); # as byte string
$x->to_base($b); # as string in any base
$x->to_base_num($b); # as array of integers in any base
$x->to_ieee754($fmt); # to bytes encoded according to IEEE 754-2008
$x->as_hex(); # as signed hexadecimal string with "0x" prefix
$x->as_bin(); # as signed binary string with "0b" prefix
$x->as_oct(); # as signed octal string with "0" prefix
# Other conversion methods (these don't modify the invocand)
$x->numify(); # return as scalar (might overflow or underflow)
=head1 DESCRIPTION
Math::BigInt provides support for arbitrary precision integers. Overloading is
also provided for Perl operators.
=head2 Input
Input values to these routines may be any scalar number or string that looks
like a number and represents an integer. Anything that is accepted by Perl as a
literal numeric constant should be accepted by this module, except that finite
non-integers return NaN.
=over
=item *
Leading and trailing whitespace is ignored.
=item *
Leading zeros are ignored, except for floating point numbers with a binary
exponent, in which case the number is interpreted as an octal floating point
number. For example, "01.4p+0" gives 1.5, "00.4p+0" gives 0.5, but "0.4p+0"
gives a NaN. And while "0377" gives 255, "0377p0" gives 255.
=item *
If the string has a "0x" or "0X" prefix, it is interpreted as a hexadecimal
number.
=item *
If the string has a "0o" or "0O" prefix, it is interpreted as an octal number.
A floating point literal with a "0" prefix is also interpreted as an octal
number.
=item *
If the string has a "0b" or "0B" prefix, it is interpreted as a binary number.
=item *
Underline characters are allowed in the same way as they are allowed in literal
numerical constants.
=item *
If the string can not be interpreted, or does not represent a finite integer,
NaN is returned.
=item *
For hexadecimal, octal, and binary floating point numbers, the exponent must be
separated from the significand (mantissa) by the letter "p" or "P", not "e" or
"E" as with decimal numbers.
=back
Some examples of valid string input
Input string Resulting value
123 123
1.23e2 123
12300e-2 123
67_538_754 67538754
-4_5_6.7_8_9e+0_1_0 -4567890000000
0x13a 314
0x13ap0 314
0x1.3ap+8 314
0x0.00013ap+24 314
0x13a000p-12 314
0o472 314
0o1.164p+8 314
0o0.0001164p+20 314
0o1164000p-10 314
0472 472 Note!
01.164p+8 314
00.0001164p+20 314
01164000p-10 314
0b100111010 314
0b1.0011101p+8 314
0b0.00010011101p+12 314
0b100111010000p-3 314
Input given as scalar numbers might lose precision. Quote your input to ensure
that no digits are lost:
$x = Math::BigInt->new( 56789012345678901234 ); # bad
$x = Math::BigInt->new('56789012345678901234'); # good
Currently, C<Math::BigInt->new()> (no input argument) and
C<Math::BigInt->new("")> return 0. This might change in the future, so always
use the following explicit forms to get a zero:
$zero = Math::BigInt->bzero();
=head2 Output
Output values are usually Math::BigInt objects.
Boolean operators L</is_zero()>, L</is_one()>, L</is_inf()>, etc. return true
or false.
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
print $x->accuracy(); # prints "4"
print $y->accuracy(); # also prints "4", since
# class accuracy is 4
Math::BigInt->accuracy(5); # set class accuracy to 5
print $x->accuracy(); # prints "4", since instance
# accuracy is 4
print $y->accuracy(); # prints "5", since no instance
# accuracy, and class accuracy is 5
Note: Each class has it's own globals separated from Math::BigInt, but it is
possible to subclass Math::BigInt and make the globals of the subclass aliases
to the ones from Math::BigInt.
=item precision()
Math::BigInt->precision(-2); # set class precision
$x->precision(-2); # set instance precision
$P = Math::BigInt->precision(); # get class precision
$P = $x->precision(); # get instance precision
Set or get the precision, i.e., the place to round relative to the decimal
point. The precision must be a integer. Setting the precision to $P means that
each number is rounded up or down, depending on the rounding mode, to the
nearest multiple of 10**$P. If the precision is set to C<undef>, no rounding is
done.
You might want to use L</accuracy()> instead. With L</accuracy()> you set the
number of digits each result should have, with L</precision()> you set the
place where to round.
Please see the section about L</ACCURACY AND PRECISION> for further details.
$y = Math::BigInt->new(1234567); # $y is not rounded
Math::BigInt->precision(4); # set class precision to 4
$x = Math::BigInt->new(1234567); # $x is rounded automatically
print $x; # prints "1230000"
Note: Each class has its own globals separated from Math::BigInt, but it is
possible to subclass Math::BigInt and make the globals of the subclass aliases
to the ones from Math::BigInt.
=item round_mode()
Set/get the rounding mode.
=item div_scale()
Set/get the fallback accuracy. This is the accuracy used when neither accuracy
nor precision is set explicitly. It is used when a computation might otherwise
attempt to return an infinite number of digits.
=item trap_inf()
Set/get the value determining whether infinities should cause a fatal error or
not.
=item trap_nan()
Set/get the value determining whether NaNs should cause a fatal error or not.
=item upgrade()
Set/get the class for upgrading. When a computation might result in a
non-integer, the operands are upgraded to this class. This is used for instance
by L<bignum>. The default is C<undef>, i.e., no upgrading.
# with no upgrading
$x = Math::BigInt->new(12);
$y = Math::BigInt->new(5);
print $x / $y, "\n"; # 2 as a Math::BigInt
# with upgrading to Math::BigFloat
Math::BigInt -> upgrade("Math::BigFloat");
print $x / $y, "\n"; # 2.4 as a Math::BigFloat
# with upgrading to Math::BigRat (after loading Math::BigRat)
Math::BigInt -> upgrade("Math::BigRat");
print $x / $y, "\n"; # 12/5 as a Math::BigRat
=item downgrade()
Set/get the class for downgrading. The default is C<undef>, i.e., no
downgrading. Downgrading is not done by Math::BigInt.
=item modify()
$x->modify('bpowd');
This method returns 0 if the object can be modified with the given operation,
or 1 if not.
This is used for instance by L<Math::BigInt::Constant>.
=item config()
Math::BigInt->config("trap_nan" => 1); # set
$accu = Math::BigInt->config("accuracy"); # get
Set or get class variables. Read-only parameters are marked as RO. Read-write
parameters are marked as RW. The following parameters are supported.
Parameter RO/RW Description
Example
============================================================
lib RO Name of the math backend library
Math::BigInt::Calc
lib_version RO Version of the math backend library
0.30
class RO The class of config you just called
Math::BigRat
version RO version number of the class you used
0.10
upgrade RW To which class numbers are upgraded
undef
downgrade RW To which class numbers are downgraded
undef
precision RW Global precision
undef
accuracy RW Global accuracy
undef
round_mode RW Global round mode
even
div_scale RW Fallback accuracy for division etc.
40
trap_nan RW Trap NaNs
undef
trap_inf RW Trap +inf/-inf
undef
=back
=head2 Constructor methods
=over
=item new()
$x = Math::BigInt->new($str,$A,$P,$R);
Creates a new Math::BigInt object from a scalar or another Math::BigInt object.
The input is accepted as decimal, hexadecimal (with leading '0x'), octal (with
leading ('0o') or binary (with leading '0b').
See L</Input> for more info on accepted input formats.
=item from_dec()
$x = Math::BigInt->from_dec("314159"); # input is decimal
Interpret input as a decimal. It is equivalent to L</new()>, but does not
accept anything but strings representing finite, decimal numbers.
=item from_hex()
$x = Math::BigInt->from_hex("0xcafe"); # input is hexadecimal
Interpret input as a hexadecimal string. A "0x" or "x" prefix is optional. A
single underscore character may be placed right after the prefix, if present,
or between any two digits. If the input is invalid, a NaN is returned.
=item from_oct()
$x = Math::BigInt->from_oct("0775"); # input is octal
Interpret the input as an octal string and return the corresponding value. A
"0" (zero) prefix is optional. A single underscore character may be placed
right after the prefix, if present, or between any two digits. If the input is
invalid, a NaN is returned.
=item from_bin()
$x = Math::BigInt->from_bin("0b10011"); # input is binary
Interpret the input as a binary string. A "0b" or "b" prefix is optional. A
single underscore character may be placed right after the prefix, if present,
or between any two digits. If the input is invalid, a NaN is returned.
=item from_bytes()
$x = Math::BigInt->from_bytes("\xf3\x6b"); # $x = 62315
Interpret the input as a byte string, assuming big endian byte order. The
output is always a non-negative, finite integer.
In some special cases, L</from_bytes()> matches the conversion done by
unpack():
$b = "\x4e"; # one char byte string
$x = Math::BigInt->from_bytes($b); # = 78
$y = unpack "C", $b; # ditto, but scalar
$b = "\xf3\x6b"; # two char byte string
$x = Math::BigInt->from_bytes($b); # = 62315
$y = unpack "S>", $b; # ditto, but scalar
$b = "\x2d\xe0\x49\xad"; # four char byte string
$x = Math::BigInt->from_bytes($b); # = 769673645
$y = unpack "L>", $b; # ditto, but scalar
$b = "\x2d\xe0\x49\xad\x2d\xe0\x49\xad"; # eight char byte string
$x = Math::BigInt->from_bytes($b); # = 3305723134637787565
$y = unpack "Q>", $b; # ditto, but scalar
=item from_ieee754()
# set $x to 314159
$x = Math::BigInt -> from_ieee754("40490fdb", "binary32");
Interpret the input as a value encoded as described in IEEE754-2008. NaN is
returned if the value is neither +/-infinity nor an integer.
See L<Math::BigFloat/from_ieee754()>.
=item from_base()
Given a string, a base, and an optional collation sequence, interpret the
string as a number in the given base. The collation sequence describes the
value of each character in the string.
If a collation sequence is not given, a default collation sequence is used. If
the base is less than or equal to 36, the collation sequence is the string
consisting of the 36 characters "0" to "9" and "A" to "Z". In this case, the
letter case in the input is ignored. If the base is greater than 36, and
smaller than or equal to 62, the collation sequence is the string consisting of
the 62 characters "0" to "9", "A" to "Z", and "a" to "z". A base larger than 62
requires the collation sequence to be specified explicitly.
These examples show standard binary, octal, and hexadecimal conversion. All
cases return 250.
$x = Math::BigInt->from_base("11111010", 2);
$x = Math::BigInt->from_base("372", 8);
$x = Math::BigInt->from_base("fa", 16);
When the base is less than or equal to 36, and no collation sequence is given,
the letter case is ignored, so both of these also return 250:
$x = Math::BigInt->from_base("6Y", 16);
$x = Math::BigInt->from_base("6y", 16);
When the base greater than 36, and no collation sequence is given, the default
collation sequence contains both uppercase and lowercase letters, so
the letter case in the input is not ignored:
$x = Math::BigInt->from_base("6S", 37); # $x is 250
$x = Math::BigInt->from_base("6s", 37); # $x is 276
$x = Math::BigInt->from_base("121", 3); # $x is 16
$x = Math::BigInt->from_base("XYZ", 36); # $x is 44027
$x = Math::BigInt->from_base("Why", 42); # $x is 58314
The collation sequence can be any set of unique characters. These two cases
are equivalent
$x = Math::BigInt->from_base("100", 2, "01"); # $x is 4
$x = Math::BigInt->from_base("|--", 2, "-|"); # $x is 4
=item from_base_num()
Returns a new Math::BigInt object given an array of values and a base. This
method is equivalent to L</from_base()>, but works on numbers in an array
rather than characters in a string. Unlike L</from_base()>, all input values
may be arbitrarily large.
$x = Math::BigInt->from_base_num([1, 1, 0, 1], 2) # $x is 13
$x = Math::BigInt->from_base_num([3, 125, 39], 128) # $x is 65191
=item bzero()
$x = Math::BigInt->bzero();
$x->bzero();
Returns a new Math::BigInt object representing zero. If used as an instance
method, assigns the value to the invocand.
=item bone()
$x = Math::BigInt->bone(); # +1
$x = Math::BigInt->bone("+"); # +1
$x = Math::BigInt->bone("-"); # -1
$x->bone(); # +1
$x->bone("+"); # +1
$x->bone('-'); # -1
Creates a new Math::BigInt object representing one. The optional argument is
either '-' or '+', indicating whether you want plus one or minus one. If used
as an instance method, assigns the value to the invocand.
=item binf()
$x = Math::BigInt->binf($sign);
Creates a new Math::BigInt object representing infinity. The optional argument
is either '-' or '+', indicating whether you want infinity or minus infinity.
If used as an instance method, assigns the value to the invocand.
$x->binf();
$x->binf('-');
=item bnan()
$x = Math::BigInt->bnan();
Creates a new Math::BigInt object representing NaN (Not A Number). If used as
an instance method, assigns the value to the invocand.
$x->bnan();
=item bpi()
$x = Math::BigInt->bpi(100); # 3
$x->bpi(100); # 3
Creates a new Math::BigInt object representing PI. If used as an instance
method, assigns the value to the invocand. With Math::BigInt this always
returns 3.
If upgrading is in effect, returns PI, rounded to N digits with the current
rounding mode:
use Math::BigFloat;
use Math::BigInt upgrade => "Math::BigFloat";
print Math::BigInt->bpi(3), "\n"; # 3.14
print Math::BigInt->bpi(100), "\n"; # 3.1415....
=item copy()
$x->copy(); # make a true copy of $x (unlike $y = $x)
=item as_int()
$y = $x -> as_int(); # $y is a Math::BigInt
Returns $x as a Math::BigInt object regardless of upgrading and downgrading. If
$x is finite, but not an integer, $x is truncated.
=item as_rat()
$y = $x -> as_rat(); # $y is a Math::BigRat
Returns $x a Math::BigRat object regardless of upgrading and downgrading. The
invocand is not modified.
=item as_float()
$y = $x -> as_float(); # $y is a Math::BigFloat
Returns $x a Math::BigFloat object regardless of upgrading and downgrading. The
invocand is not modified.
=back
=head2 Boolean methods
None of these methods modify the invocand object.
=over
=item is_zero()
$x->is_zero(); # true if $x is 0
Returns true if the invocand is zero and false otherwise.
=item is_one()
$x->is_one(); # true if $x is +1
$x->is_one("+"); # ditto
$x->is_one("-"); # true if $x is -1
Returns true if the invocand is one and false otherwise.
=item is_finite()
$x->is_finite(); # true if $x is not +inf, -inf or NaN
Returns true if the invocand is a finite number, i.e., it is neither +inf,
-inf, nor NaN.
=item is_inf()
$x->is_inf(); # true if $x is +inf or -inf
$x->is_inf("+"); # true if $x is +inf
$x->is_inf("-"); # true if $x is -inf
Returns true if the invocand is infinite and false otherwise.
=item is_nan()
$x->is_nan(); # true if $x is NaN
=item is_positive()
=item is_pos()
$x->is_positive(); # true if > 0
$x->is_pos(); # ditto
Returns true if the invocand is positive and false otherwise. A C<NaN> is
neither positive nor negative.
=item is_negative()
=item is_neg()
$x->is_negative(); # true if < 0
$x->is_neg(); # ditto
Returns true if the invocand is negative and false otherwise. A C<NaN> is
neither positive nor negative.
=item is_non_positive()
$x->is_non_positive(); # true if <= 0
Returns true if the invocand is negative or zero.
=item is_non_negative()
$x->is_non_negative(); # true if >= 0
Returns true if the invocand is positive or zero.
=item is_odd()
$x->is_odd(); # true if odd, false for even
Returns true if the invocand is odd and false otherwise. C<NaN>, C<+inf>, and
C<-inf> are neither odd nor even.
=item is_even()
$x->is_even(); # true if $x is even
Returns true if the invocand is even and false otherwise. C<NaN>, C<+inf>,
C<-inf> are not integers and are neither odd nor even.
=item is_int()
$x->is_int(); # true if $x is an integer
Returns true if the invocand is an integer and false otherwise. C<NaN>,
C<+inf>, C<-inf> are not integers.
=back
=head2 Comparison methods
None of these methods modify the invocand object. Note that a C<NaN> is neither
less than, greater than, or equal to anything else, even a C<NaN>.
=over
=item bcmp()
$x->bcmp($y);
Returns -1, 0, 1 depending on whether $x is less than, equal to, or grater than
$y. Returns undef if any operand is a NaN.
=item bacmp()
$x->bacmp($y);
Returns -1, 0, 1 depending on whether the absolute value of $x is less than,
equal to, or grater than the absolute value of $y. Returns undef if any operand
is a NaN.
=item beq()
$x -> beq($y);
Returns true if and only if $x is equal to $y, and false otherwise.
=item bne()
$x -> bne($y);
Returns true if and only if $x is not equal to $y, and false otherwise.
=item blt()
$x -> blt($y);
Returns true if and only if $x is equal to $y, and false otherwise.
=item ble()
$x -> ble($y);
Returns true if and only if $x is less than or equal to $y, and false
otherwise.
=item bgt()
$x -> bgt($y);
Returns true if and only if $x is greater than $y, and false otherwise.
=item bge()
$x -> bge($y);
Returns true if and only if $x is greater than or equal to $y, and false
otherwise.
=back
=head2 Arithmetic methods
These methods modify the invocand object and returns it.
=over
=item bneg()
$x->bneg();
Negate the number, e.g. change the sign between '+' and '-', or between '+inf'
and '-inf', respectively. Does nothing for NaN or zero.
=item babs()
$x->babs();
Set the number to its absolute value, e.g. change the sign from '-' to '+'
and from '-inf' to '+inf', respectively. Does nothing for NaN or positive
numbers.
=item bsgn()
$x->bsgn();
Signum function. Set the number to -1, 0, or 1, depending on whether the
number is negative, zero, or positive, respectively. Does not modify NaNs.
=item bnorm()
$x->bnorm(); # normalize (no-op)
Normalize the number. This is a no-op and is provided only for backwards
compatibility.
=item binc()
$x->binc(); # increment x by 1
=item bdec()
$x->bdec(); # decrement x by 1
=item badd()
$x->badd($y); # addition (add $y to $x)
=item bsub()
$x->bsub($y); # subtraction (subtract $y from $x)
=item bmul()
$x->bmul($y); # multiplication (multiply $x by $y)
=item bdiv()
$x->bdiv($y); # set $x to quotient
($q, $r) = $x->bdiv($y); # also return remainder
The behaviour of L</bdiv()> and L</bmod()> is based on Perl's C<%> operator,
which is the remainder after performing floored division.
Because of this, L</bdiv()> and L</bmod()> are aliases for L</bfdiv()> and
L</bfmod()>, respectively.
=item bmod()
$x->bmod($y); # modulus (x % y)
This is an alias for L</bfmod()>.
=item bfdiv()
$x->bfdiv($y); # return quotient
($q, $r) = $x->bfdiv($y); # return quotient and remainder
Divides $x by $y by doing floored division (F-division), where the quotient is
the floored (rounded towards negative infinity) quotient of the two operands.
In list context, returns the quotient and the remainder. In scalar context,
only the quotient is returned.
$q = floor($x / $y) # quotient
$r = $x - $q * $y # remainder
With F-division, the remainder is either zero or has the same sign as the
divisor.
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
Returns $x raised to the power of $y. The first two modifies $x, the last one
doesn't:
print $x->bpow($i),"\n"; # modifies $x
print $x **= $i,"\n"; # ditto
print $x ** $i,"\n"; # leaves $x alone
The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though.
=item broot()
$x->broot($N);
Calculates the $N'th root of C<$x>.
=item bmuladd()
$x->bmuladd($y,$z);
Multiply $x by $y, and then add $z to the result,
This method was added in v1.88 of Math::BigInt.
=item bmodpow()
$num->bmodpow($exp,$mod); # modular exponentiation
# ($num**$exp % $mod)
Returns the value of C<$num> taken to the power C<$exp> in the modulus
C<$mod> using binary exponentiation. C<bmodpow> is far superior to
writing
$num ** $exp % $mod
because it is much faster - it reduces internal variables into
the modulus whenever possible, so it operates on smaller numbers.
C<bmodpow> also supports negative exponents.
bmodpow($num, -1, $mod)
is exactly equivalent to
bmodinv($num, $mod)
=item bmodinv()
$x->bmodinv($mod); # modular multiplicative inverse
Returns the multiplicative inverse of C<$x> modulo C<$mod>. If
$y = $x -> copy() -> bmodinv($mod)
then C<$y> is the number closest to zero, and with the same sign as C<$mod>,
satisfying
($x * $y) % $mod = 1 % $mod
If C<$x> and C<$y> are non-zero, they must be relative primes, i.e.,
C<bgcd($y, $mod)==1>. 'C<NaN>' is returned when no modular multiplicative
inverse exists.
=item blog()
$x->blog($base, $accuracy); # logarithm of x to the base $base
If C<$base> is not defined, Euler's number (e) is used:
print $x->blog(undef, 100); # log(x) to 100 digits
=item bexp()
$x->bexp($accuracy); # calculate e ** X
Calculates the expression C<e ** $x> where C<e> is Euler's number.
This method was added in v1.82 of Math::BigInt (April 2007).
See also L</blog()>.
=item bilog2()
Base 2 logarithm rounded down towards the nearest integer.
$x->bilog2(); # int(log2(x)) = int(log(x)/log(2))
In list context a second argument is returned. This is 1 if the result is
exact, i.e., the input is an exact power of 2, and 0 otherwise.
=item bilog10()
Base 10 logarithm rounded down towards the nearest integer.
$x->bilog10(); # int(log10(x)) = int(log(x)/log(10))
In list context a second argument is returned. This is 1 if the result is
exact, i.e., the input is an exact power of 10, and 0 otherwise.
=item bclog2()
Base 2 logarithm rounded up towards the nearest integer.
$x->bclog2(); # ceil(log2(x)) = ceil(log(x)/log(2))
In list context a second argument is returned. This is 1 if the result is
exact, i.e., the input is an exact power of 2, and 0 otherwise.
=item bclog10()
Base 10 logarithm rounded up towards the nearest integer.
$x->bclog10(); # ceil(log10(x)) = ceil(log(x)/log(10))
In list context a second argument is returned. This is 1 if the result is
exact, i.e., the input is an exact power of 10, and 0 otherwise.
=item bnok()
Combinations.
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
Rounds to a multiple of 10**$N. Examples:
Input N Result
123456.123456 3 123500
123456.123456 2 123450
123456.123456 -2 123456.12
123456.123456 -3 123456.123
=item bfloor()
$x->bfloor();
Round $x towards minus infinity, i.e., set $x to the largest integer less than
or equal to $x.
=item bceil()
$x->bceil();
Round $x towards plus infinity, i.e., set $x to the smallest integer greater
than or equal to $x.
=item bint()
$x->bint();
Round $x towards zero.
=back
=head2 Other mathematical methods
=over
=item bgcd()
$x -> bgcd($y); # GCD of $x and $y
$x -> bgcd($y, $z, ...); # GCD of $x, $y, $z, ...
Returns the greatest common divisor (GCD), which is the largest positive
integer that divides each of the operands.
=item blcm()
$x -> blcm($y); # LCM of $x and $y
$x -> blcm($y, $z, ...); # LCM of $x, $y, $z, ...
Returns the least common multiple (LCM).
=back
=head2 Object property methods
=over
=item sign()
$x->sign();
Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
If you want $x to have a certain sign, use one of the following methods:
$x->babs(); # '+'
$x->babs()->bneg(); # '-'
$x->bnan(); # 'NaN'
$x->binf(); # '+inf'
$x->binf('-'); # '-inf'
=item digit()
$x->digit($n); # return the nth digit, counting from right
If C<$n> is negative, returns the digit counting from left.
=item bdigitsum()
$x->bdigitsum();
Computes the sum of the base 10 digits and assigns the result to the invocand.
=item digitsum()
$x->digitsum();
Computes the sum of the base 10 digits and returns it.
=item length()
$x->length();
($xl, $fl) = $x->length();
Returns the number of digits in the decimal representation of the number. In
list context, returns the length of the integer and fraction part. For
Math::BigInt objects, the length of the fraction part is always 0.
The following probably doesn't do what you expect:
$c = Math::BigInt->new(123);
print $c->length(),"\n"; # prints 30
It prints both the number of digits in the number and in the fraction part
since print calls L</length()> in list context. Use something like:
print scalar $c->length(),"\n"; # prints 3
=item mantissa()
$x->mantissa();
Return the signed mantissa of $x as a Math::BigInt.
=item exponent()
$x->exponent();
Return the exponent of $x as a Math::BigInt.
=item parts()
$x->parts();
Returns the significand (mantissa) and the exponent as integers. In
Math::BigFloat, both are returned as Math::BigInt objects.
=item sparts()
Returns the significand (mantissa) and the exponent as integers. In scalar
context, only the significand is returned. The significand is the integer with
the smallest absolute value. The output of L</sparts()> corresponds to the
output from L</bsstr()>.
In Math::BigInt, this method is identical to L</parts()>.
=item nparts()
Returns the significand (mantissa) and exponent corresponding to normalized
notation. In scalar context, only the significand is returned. For finite
non-zero numbers, the significand's absolute value is greater than or equal to
1 and less than 10. The output of L</nparts()> corresponds to the output from
L</bnstr()>. In Math::BigInt, if the significand can not be represented as an
integer, upgrading is performed or NaN is returned.
=item eparts()
Returns the significand (mantissa) and exponent corresponding to engineering
notation. In scalar context, only the significand is returned. For finite
non-zero numbers, the significand's absolute value is greater than or equal to
1 and less than 1000, and the exponent is a multiple of 3. The output of
L</eparts()> corresponds to the output from L</bestr()>. In Math::BigInt, if
the significand can not be represented as an integer, upgrading is performed or
NaN is returned.
=item dparts()
Returns the integer part and the fraction part. If the fraction part can not be
represented as an integer, upgrading is performed or NaN is returned. The
output of L</dparts()> corresponds to the output from L</bdstr()>.
=item fparts()
Returns the smallest possible numerator and denominator so that the numerator
divided by the denominator gives back the original value. For finite numbers,
both values are integers. Mnemonic: fraction.
=item numerator()
Together with L</denominator()>, returns the smallest integers so that the
numerator divided by the denominator reproduces the original value. With
Math::BigInt, L</numerator()> simply returns a copy of the invocand.
=item denominator()
Together with L</numerator()>, returns the smallest integers so that the
numerator divided by the denominator reproduces the original value. With
Math::BigInt, L</denominator()> always returns either a 1 or a NaN.
=back
=head2 String conversion methods
=over
=item bstr()
Returns a string representing the number using decimal notation. In
Math::BigFloat, the output is zero padded according to the current accuracy or
precision, if any of those are defined.
=item bsstr()
Returns a string representing the number using scientific notation where both
the significand (mantissa) and the exponent are integers. The output
corresponds to the output from L</sparts()>.
123 is returned as "123e+0"
1230 is returned as "123e+1"
12300 is returned as "123e+2"
12000 is returned as "12e+3"
10000 is returned as "1e+4"
=item bnstr()
Returns a string representing the number using normalized notation, the most
common variant of scientific notation. For finite non-zero numbers, the
absolute value of the significand is greater than or equal to 1 and less than
10. The output corresponds to the output from L</nparts()>.
123 is returned as "1.23e+2"
1230 is returned as "1.23e+3"
12300 is returned as "1.23e+4"
12000 is returned as "1.2e+4"
10000 is returned as "1e+4"
=item bestr()
Returns a string representing the number using engineering notation. For finite
non-zero numbers, the absolute value of the significand is greater than or
equal to 1 and less than 1000, and the exponent is a multiple of 3. The output
corresponds to the output from L</eparts()>.
123 is returned as "123e+0"
1230 is returned as "1.23e+3"
12300 is returned as "12.3e+3"
12000 is returned as "12e+3"
10000 is returned as "10e+3"
=item bdstr()
Returns a string representing the number using decimal notation. The output
corresponds to the output from L</dparts()>.
123 is returned as "123"
1230 is returned as "1230"
12300 is returned as "12300"
12000 is returned as "12000"
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
* bsqrt() simply hands its accuracy argument over to bdiv.
* the documentation and the comment in the code indicate two
different ways on how bdiv() determines the maximum number
of digits it should calculate, and the actual code does yet
another thing
POD:
max($Math::BigFloat::div_scale,length(dividend)+length(divisor))
Comment:
result has at most max(scale, length(dividend), length(divisor)) digits
Actual code:
scale = max(scale, length(dividend)-1,length(divisor)-1);
scale += length(divisor) - length(dividend);
So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10
So for lx = 3, ly = 9, scale = 10, scale will actually be 16
(10+9-3). Actually, the 'difference' added to the scale is cal-
culated from the number of "significant digits" in dividend and
divisor, which is derived by looking at the length of the man-
tissa. Which is wrong, since it includes the + sign (oops) and
actually gets 2 for '+100' and 4 for '+101'. Oops again. Thus
124/3 with div_scale=1 will get you '41.3' based on the strange
assumption that 124 has 3 significant digits, while 120/7 will
get you '17', not '17.1' since 120 is thought to have 2 signif-
icant digits. The rounding after the division then uses the
remainder and $y to determine whether it must round up or down.
? I have no idea which is the right way. That's why I used a slightly more
? simple scheme and tweaked the few failing testcases to match it.
=back
This is how it works now:
=over
=item Setting/Accessing
* You can set the A global via Math::BigInt->accuracy() or
Math::BigFloat->accuracy() or whatever class you are using.
* You can also set P globally by using Math::SomeClass->precision()
likewise.
* Globals are classwide, and not inherited by subclasses.
* to undefine A, use Math::SomeClass->accuracy(undef);
* to undefine P, use Math::SomeClass->precision(undef);
* Setting Math::SomeClass->accuracy() clears automatically
Math::SomeClass->precision(), and vice versa.
* To be valid, A must be > 0, P can have any value.
* If P is negative, this means round to the P'th place to the right of the
decimal point; positive values mean to the left of the decimal point.
P of 0 means round to integer.
* to find out the current global A, use Math::SomeClass->accuracy()
* to find out the current global P, use Math::SomeClass->precision()
* use $x->accuracy() respective $x->precision() for the local
setting of $x.
* Please note that $x->accuracy() respective $x->precision()
return eventually defined global A or P, when $x's A or P is not
set.
=item Creating numbers
* When you create a number, you can give the desired A or P via:
$x = Math::BigInt->new($number,$A,$P);
* Only one of A or P can be defined, otherwise the result is NaN
* If no A or P is give ($x = Math::BigInt->new($number) form), then the
globals (if set) will be used. Thus changing the global defaults later on
will not change the A or P of previously created numbers (i.e., A and P of
$x will be what was in effect when $x was created)
* If given undef for A and P, NO rounding will occur, and the globals will
NOT be used. This is used by subclasses to create numbers without
suffering rounding in the parent. Thus a subclass is able to have its own
globals enforced upon creation of a number by using
$x = Math::BigInt->new($number,undef,undef):
use Math::BigInt::SomeSubclass;
use Math::BigInt;
Math::BigInt->accuracy(2);
Math::BigInt::SomeSubclass->accuracy(3);
$x = Math::BigInt::SomeSubclass->new(1234);
$x is now 1230, and not 1200. A subclass might choose to implement
this otherwise, e.g. falling back to the parent's A and P.
=item Usage
* If A or P are enabled/defined, they are used to round the result of each
operation according to the rules below
* Negative P is ignored in Math::BigInt, since Math::BigInt objects never
have digits after the decimal point
* Math::BigFloat uses Math::BigInt internally, but setting A or P inside
Math::BigInt as globals does not tamper with the parts of a Math::BigFloat.
A flag is used to mark all Math::BigFloat numbers as 'never round'.
=item Precedence
* It only makes sense that a number has only one of A or P at a time.
If you set either A or P on one object, or globally, the other one will
be automatically cleared.
* If two objects are involved in an operation, and one of them has A in
effect, and the other P, this results in an error (NaN).
* A takes precedence over P (Hint: A comes before P).
If neither of them is defined, nothing is used, i.e. the result will have
as many digits as it can (with an exception for bdiv/bsqrt) and will not
be rounded.
* There is another setting for bdiv() (and thus for bsqrt()). If neither of
A or P is defined, bdiv() will use a fallback (F) of $div_scale digits.
If either the dividend's or the divisor's mantissa has more digits than
the value of F, the higher value will be used instead of F.
This is to limit the digits (A) of the result (just consider what would
happen with unlimited A and P in the case of 1/3 :-)
* bdiv will calculate (at least) 4 more digits than required (determined by
A, P or F), and, if F is not used, round the result
(this will still fail in the case of a result like 0.12345000000001 with A
or P of 5, but this can not be helped - or can it?)
* Thus you can have the math done by on Math::Big* class in two modi:
+ never round (this is the default):
This is done by setting A and P to undef. No math operation
will round the result, with bdiv() and bsqrt() as exceptions to guard
against overflows. You must explicitly call bround(), bfround() or
round() (the latter with parameters).
Note: Once you have rounded a number, the settings will 'stick' on it
and 'infect' all other numbers engaged in math operations with it, since
local settings have the highest precedence. So, to get SaferRound[tm],
use a copy() before rounding like this:
$x = Math::BigFloat->new(12.34);
$y = Math::BigFloat->new(98.76);
$z = $x * $y; # 1218.6984
print $x->copy()->bround(3); # 12.3 (but A is now 3!)
$z = $x * $y; # still 1218.6984, without
# copy would have been 1210!
+ round after each op:
After each single operation (except for testing like is_zero()), the
method round() is called and the result is rounded appropriately. By
setting proper values for A and P, you can have all-the-same-A or
all-the-same-P modes. For example, Math::Currency might set A to undef,
and P to -2, globally.
?Maybe an extra option that forbids local A & P settings would be in order,
?so that intermediate rounding does not 'poison' further math?
=item Overriding globals
* you will be able to give A, P and R as an argument to all the calculation
routines; the second parameter is A, the third one is P, and the fourth is
R (shift right by one for binary operations like badd). P is used only if
the first parameter (A) is undefined. These three parameters override the
globals in the order detailed as follows, i.e. the first defined value
wins:
(local: per object, global: global default, parameter: argument to sub)
+ parameter A
+ parameter P
+ local A (if defined on both of the operands: smaller one is taken)
+ local P (if defined on both of the operands: bigger one is taken)
+ global A
+ global P
+ global F
* bsqrt() will hand its arguments to bdiv(), as it used to, only now for two
arguments (A and P) instead of one
cpan/Math-BigInt/lib/Math/BigInt.pm view on Meta::CPAN
use Math::BigInt try => 'Calc';
You can use a different backend library with, e.g.,
use Math::BigInt try => 'GMP';
which attempts to load the L<Math::BigInt::GMP> library, and falls back to the
default library if the specified library can't be loaded.
Multiple libraries can be specified by separating them by a comma, e.g.,
use Math::BigInt try => 'GMP,Pari';
If you request a specific set of libraries and do not allow fallback to the
default library, specify them using "only",
use Math::BigInt only => 'GMP,Pari';
If you prefer a specific set of libraries, but want to see a warning if the
fallback library is used, specify them using "lib",
use Math::BigInt lib => 'GMP,Pari';
The following first tries to find Math::BigInt::Foo, then Math::BigInt::Bar,
and if this also fails, reverts to Math::BigInt::Calc:
use Math::BigInt try => 'Foo,Math::BigInt::Bar';
=head3 Which library to use?
B<Note>: General purpose packages should not be explicit about the library to
use; let the script author decide which is best.
L<Math::BigInt::GMP>, L<Math::BigInt::Pari>, and L<Math::BigInt::GMPz> are in
cases involving big numbers much faster than L<Math::BigInt::Calc>. However
these libraries are slower when dealing with very small numbers (less than
about 20 digits) and when converting very large numbers to decimal (for
instance for printing, rounding, calculating their length in decimal etc.).
So please select carefully what library you want to use.
Different low-level libraries use different formats to store the numbers, so
mixing them won't work. You should not depend on the number having a specific
internal format.
See the respective math library module documentation for further details.
=head3 Loading multiple libraries
The first library that is successfully loaded is the one that will be used. Any
further attempts at loading a different module will be ignored. This is to
avoid the situation where module A requires math library X, and module B
requires math library Y, causing modules A and B to be incompatible. For
example,
use Math::BigInt; # loads default "Calc"
use Math::BigFloat only => "GMP"; # ignores "GMP"
=head2 Sign
The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
A sign of 'NaN' is used to represent values that are not numbers, e.g., the
result of 0/0. '+inf' and '-inf' represen positive and negative infinity,
respectively. For example you get '+inf' when dividing a positive number by 0,
and '-inf' when dividing any negative number by 0.
=head1 EXAMPLES
use Math::BigInt;
sub bigint { Math::BigInt->new(shift); }
$x = Math::BigInt->bstr("1234") # string "1234"
$x = "$x"; # same as bstr()
$x = Math::BigInt->bneg("1234"); # Math::BigInt "-1234"
$x = Math::BigInt->babs("-12345"); # Math::BigInt "12345"
$x = Math::BigInt->bnorm("-0.00"); # Math::BigInt "0"
$x = bigint(1) + bigint(2); # Math::BigInt "3"
$x = bigint(1) + "2"; # ditto ("2" becomes a Math::BigInt)
$x = bigint(1); # Math::BigInt "1"
$x = $x + 5 / 2; # Math::BigInt "3"
$x = $x ** 3; # Math::BigInt "27"
$x *= 2; # Math::BigInt "54"
$x = Math::BigInt->new(0); # Math::BigInt "0"
$x--; # Math::BigInt "-1"
$x = Math::BigInt->badd(4,5) # Math::BigInt "9"
print $x->bsstr(); # 9e+0
Examples for rounding:
use Math::BigFloat;
use Test::More;
$x = Math::BigFloat->new(123.4567);
$y = Math::BigFloat->new(123.456789);
Math::BigFloat->accuracy(4); # no more A than 4
is ($x->copy()->bround(),123.4); # even rounding
print $x->copy()->bround(),"\n"; # 123.4
Math::BigFloat->round_mode('odd'); # round to odd
print $x->copy()->bround(),"\n"; # 123.5
Math::BigFloat->accuracy(5); # no more A than 5
Math::BigFloat->round_mode('odd'); # round to odd
print $x->copy()->bround(),"\n"; # 123.46
$y = $x->copy()->bround(4),"\n"; # A = 4: 123.4
print "$y, ",$y->accuracy(),"\n"; # 123.4, 4
Math::BigFloat->accuracy(undef); # A not important now
Math::BigFloat->precision(2); # P important
print $x->copy()->bnorm(),"\n"; # 123.46
print $x->copy()->bround(),"\n"; # 123.46
Examples for converting:
my $x = Math::BigInt->new('0b1'.'01' x 123);
print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n";
=head1 NUMERIC LITERALS
After C<use Math::BigInt ':constant'> all numeric literals in the given scope
are converted to C<Math::BigInt> objects. This conversion happens at compile
time. Every non-integer is convert to a NaN.
For example,
perl -MMath::BigInt=:constant -le 'print 2**150'
prints the exact value of C<2**150>. Note that without conversion of constants
to objects the expression C<2**150> is calculated using Perl scalars, which
leads to an inaccurate result.
Please note that strings are not affected, so that
use Math::BigInt qw/:constant/;
$x = "1234567890123456789012345678901234567890"
+ "123456789123456789";
does give you what you expect. You need an explicit Math::BigInt->new() around
at least one of the operands. You should also quote large constants to prevent
loss of precision:
use Math::BigInt;
$x = Math::BigInt->new("1234567889123456789123456789123456789");
Without the quotes Perl first converts the large number to a floating point
constant at compile time, and then converts the result to a Math::BigInt object
at run time, which results in an inaccurate result.
=head2 Hexadecimal, octal, and binary floating point literals
Perl (and this module) accepts hexadecimal, octal, and binary floating point
literals, but use them with care with Perl versions before v5.32.0, because
some versions of Perl silently give the wrong result. Below are some examples
of different ways to write the number decimal 314.
Hexadecimal floating point literals:
0x1.3ap+8 0X1.3AP+8
0x1.3ap8 0X1.3AP8
0x13a0p-4 0X13A0P-4
Octal floating point literals (with "0" prefix):
01.164p+8 01.164P+8
01.164p8 01.164P8
011640p-4 011640P-4
Octal floating point literals (with "0o" prefix) (requires v5.34.0):
0o1.164p+8 0O1.164P+8
0o1.164p8 0O1.164P8
0o11640p-4 0O11640P-4
Binary floating point literals:
0b1.0011101p+8 0B1.0011101P+8
0b1.0011101p8 0B1.0011101P8
0b10011101000p-2 0B10011101000P-2
=head1 PERFORMANCE
( run in 2.113 seconds using v1.01-cache-2.11-cpan-0bb4e1dffa6 )