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-rw-r--r--systems/texlive/tlnet/tlpkg/tlperl/lib/bignum.pm1111
1 files changed, 685 insertions, 426 deletions
diff --git a/systems/texlive/tlnet/tlpkg/tlperl/lib/bignum.pm b/systems/texlive/tlnet/tlpkg/tlperl/lib/bignum.pm
index 55300c8273..d738d6dc98 100644
--- a/systems/texlive/tlnet/tlpkg/tlperl/lib/bignum.pm
+++ b/systems/texlive/tlnet/tlpkg/tlperl/lib/bignum.pm
@@ -1,62 +1,60 @@
package bignum;
-use 5.010;
use strict;
use warnings;
-our $VERSION = '0.51';
+use Carp qw< carp croak >;
+
+our $VERSION = '0.66';
use Exporter;
-our @ISA = qw( bigint );
+our @ISA = qw( Exporter );
our @EXPORT_OK = qw( PI e bpi bexp hex oct );
our @EXPORT = qw( inf NaN );
use overload;
-use bigint ();
+
+# Defaults: When a constant is an integer, Inf or NaN, it is converted to an
+# object of class $int_class. When a constant is a finite non-integer, it is
+# converted to an object of class $float_class.
+
+my $int_class = 'Math::BigInt';
+my $float_class = 'Math::BigFloat';
##############################################################################
-BEGIN {
- *inf = \&bigint::inf;
- *NaN = \&bigint::NaN;
- *hex = \&bigint::hex;
- *oct = \&bigint::oct;
+sub accuracy {
+ shift;
+ $int_class -> accuracy(@_);
+ $float_class -> accuracy(@_);
}
-# These are all alike, and thus faked by AUTOLOAD
-
-my @faked = qw/round_mode accuracy precision div_scale/;
-our ($AUTOLOAD, $_lite); # _lite for testsuite
-
-sub AUTOLOAD {
- my $name = $AUTOLOAD;
-
- $name =~ s/.*:://; # split package
- no strict 'refs';
- foreach my $n (@faked) {
- if ($n eq $name) {
- *{"bignum::$name"} =
- sub {
- my $self = shift;
- no strict 'refs';
- if (defined $_[0]) {
- Math::BigInt->$name($_[0]);
- return Math::BigFloat->$name($_[0]);
- }
- return Math::BigInt->$name();
- };
- return &$name;
- }
- }
+sub precision {
+ shift;
+ $int_class -> precision(@_);
+ $float_class -> precision(@_);
+}
- # delayed load of Carp and avoid recursion
- require Carp;
- Carp::croak ("Can't call bignum\-\>$name, not a valid method");
+sub round_mode {
+ shift;
+ $int_class -> round_mode(@_);
+ $float_class -> round_mode(@_);
}
-sub unimport {
- $^H{bignum} = undef; # no longer in effect
- overload::remove_constant('binary', '', 'float', '', 'integer');
+sub div_scale {
+ shift;
+ $int_class -> div_scale(@_);
+ $float_class -> div_scale(@_);
+}
+
+sub upgrade {
+ shift;
+ $int_class -> upgrade(@_);
+}
+
+sub downgrade {
+ shift;
+ $float_class -> downgrade(@_);
}
sub in_effect {
@@ -65,157 +63,386 @@ sub in_effect {
$hinthash->{bignum};
}
+sub _float_constant {
+ my $str = shift;
+
+ # See if we can convert the input string to a string using a normalized form
+ # consisting of the significand as a signed integer, the character "e", and
+ # the exponent as a signed integer, e.g., "+0e+0", "+314e-2", and "-1e+3".
+
+ my $nstr;
+
+ if (
+ # See if it is an octal number. An octal number like '0377' is also
+ # accepted by the functions parsing decimal and hexadecimal numbers, so
+ # handle octal numbers before decimal and hexadecimal numbers.
+
+ $str =~ /^0(?:[Oo]|_*[0-7])/ and
+ $nstr = Math::BigInt -> oct_str_to_dec_flt_str($str)
+
+ or
+
+ # See if it is decimal number.
+
+ $nstr = Math::BigInt -> dec_str_to_dec_flt_str($str)
+
+ or
+
+ # See if it is a hexadecimal number. Every hexadecimal number has a
+ # prefix, but the functions parsing numbers don't require it, so check
+ # to see if it actually is a hexadecimal number.
+
+ $str =~ /^0[Xx]/ and
+ $nstr = Math::BigInt -> hex_str_to_dec_flt_str($str)
+
+ or
+
+ # See if it is a binary numbers. Every binary number has a prefix, but
+ # the functions parsing numbers don't require it, so check to see if it
+ # actually is a binary number.
+
+ $str =~ /^0[Bb]/ and
+ $nstr = Math::BigInt -> bin_str_to_dec_flt_str($str))
+ {
+ my $pos = index($nstr, 'e');
+ my $expo_sgn = substr($nstr, $pos + 1, 1);
+ my $sign = substr($nstr, 0, 1);
+ my $mant = substr($nstr, 1, $pos - 1);
+ my $mant_len = CORE::length($mant);
+ my $expo = substr($nstr, $pos + 2);
+
+ # The number is a non-integer if and only if the exponent is negative.
+
+ if ($expo_sgn eq '-') {
+ return $float_class -> new($str);
+
+ my $upgrade = $int_class -> upgrade();
+ return $upgrade -> new($nstr) if defined $upgrade;
+
+ if ($mant_len <= $expo) {
+ return $int_class -> bzero(); # underflow
+ } else {
+ $mant = substr $mant, 0, $mant_len - $expo; # truncate
+ return $int_class -> new($sign . $mant);
+ }
+ } else {
+ $mant .= "0" x $expo; # pad with zeros
+ return $int_class -> new($sign . $mant);
+ }
+ }
+
+ # If we get here, there is a bug in the code above this point.
+
+ warn "Internal error: unable to handle literal constant '$str'.",
+ " This is a bug, so please report this to the module author.";
+ return $int_class -> bnan();
+}
+
+#############################################################################
+# the following two routines are for "use bignum qw/hex oct/;":
+
+use constant LEXICAL => $] > 5.009004;
+
+# Internal function with the same semantics as CORE::hex(). This function is
+# not used directly, but rather by other front-end functions.
+
+sub _hex_core {
+ my $str = shift;
+
+ # Strip off, clean, and parse as much as we can from the beginning.
+
+ my $x;
+ if ($str =~ s/ ^ ( 0? [xX] )? ( [0-9a-fA-F]* ( _ [0-9a-fA-F]+ )* ) //x) {
+ my $chrs = $2;
+ $chrs =~ tr/_//d;
+ $chrs = '0' unless CORE::length $chrs;
+ $x = $int_class -> from_hex($chrs);
+ } else {
+ $x = $int_class -> bzero();
+ }
+
+ # Warn about trailing garbage.
+
+ if (CORE::length($str)) {
+ require Carp;
+ Carp::carp(sprintf("Illegal hexadecimal digit '%s' ignored",
+ substr($str, 0, 1)));
+ }
+
+ return $x;
+}
+
+# Internal function with the same semantics as CORE::oct(). This function is
+# not used directly, but rather by other front-end functions.
+
+sub _oct_core {
+ my $str = shift;
+
+ $str =~ s/^\s*//;
+
+ # Hexadecimal input.
+
+ return _hex_core($str) if $str =~ /^0?[xX]/;
+
+ my $x;
+
+ # Binary input.
+
+ if ($str =~ /^0?[bB]/) {
+
+ # Strip off, clean, and parse as much as we can from the beginning.
+
+ if ($str =~ s/ ^ ( 0? [bB] )? ( [01]* ( _ [01]+ )* ) //x) {
+ my $chrs = $2;
+ $chrs =~ tr/_//d;
+ $chrs = '0' unless CORE::length $chrs;
+ $x = $int_class -> from_bin($chrs);
+ }
+
+ # Warn about trailing garbage.
+
+ if (CORE::length($str)) {
+ require Carp;
+ Carp::carp(sprintf("Illegal binary digit '%s' ignored",
+ substr($str, 0, 1)));
+ }
+
+ return $x;
+ }
+
+ # Octal input. Strip off, clean, and parse as much as we can from the
+ # beginning.
+
+ if ($str =~ s/ ^ ( 0? [oO] )? ( [0-7]* ( _ [0-7]+ )* ) //x) {
+ my $chrs = $2;
+ $chrs =~ tr/_//d;
+ $chrs = '0' unless CORE::length $chrs;
+ $x = $int_class -> from_oct($chrs);
+ }
+
+ # Warn about trailing garbage. CORE::oct() only warns about 8 and 9, but it
+ # is more helpful to warn about all invalid digits.
+
+ if (CORE::length($str)) {
+ require Carp;
+ Carp::carp(sprintf("Illegal octal digit '%s' ignored",
+ substr($str, 0, 1)));
+ }
+
+ return $x;
+}
+
+{
+ my $proto = LEXICAL ? '_' : ';$';
+ eval '
+sub hex(' . $proto . ') {' . <<'.';
+ my $str = @_ ? $_[0] : $_;
+ _hex_core($str);
+}
+.
+
+ eval '
+sub oct(' . $proto . ') {' . <<'.';
+ my $str = @_ ? $_[0] : $_;
+ _oct_core($str);
+}
+.
+}
+
#############################################################################
+# the following two routines are for Perl 5.9.4 or later and are lexical
+
+my ($prev_oct, $prev_hex, $overridden);
+
+if (LEXICAL) { eval <<'.' }
+sub _hex(_) {
+ my $hh = (caller 0)[10];
+ return $$hh{bignum} ? bignum::_hex_core($_[0])
+ : $$hh{bigrat} ? bigrat::_hex_core($_[0])
+ : $$hh{bigint} ? bigint::_hex_core($_[0])
+ : $prev_hex ? &$prev_hex($_[0])
+ : CORE::hex($_[0]);
+}
+
+sub _oct(_) {
+ my $hh = (caller 0)[10];
+ return $$hh{bignum} ? bignum::_oct_core($_[0])
+ : $$hh{bigrat} ? bigrat::_oct_core($_[0])
+ : $$hh{bigint} ? bigint::_oct_core($_[0])
+ : $prev_oct ? &$prev_oct($_[0])
+ : CORE::oct($_[0]);
+}
+.
+
+sub _override {
+ return if $overridden;
+ $prev_oct = *CORE::GLOBAL::oct{CODE};
+ $prev_hex = *CORE::GLOBAL::hex{CODE};
+ no warnings 'redefine';
+ *CORE::GLOBAL::oct = \&_oct;
+ *CORE::GLOBAL::hex = \&_hex;
+ $overridden = 1;
+}
+
+sub unimport {
+ $^H{bignum} = undef; # no longer in effect
+ overload::remove_constant('binary', '', 'float', '', 'integer');
+}
sub import {
- my $self = shift;
+ my $class = shift;
- $^H{bignum} = 1; # we are in effect
+ $^H{bignum} = 1; # we are in effect
+ $^H{bigint} = undef;
+ $^H{bigrat} = undef;
- # for newer Perls override hex() and oct() with a lexical version:
- if ($] > 5.009004) {
- bigint::_override();
+ # for newer Perls always override hex() and oct() with a lexical version:
+ if (LEXICAL) {
+ _override();
}
- # some defaults
- my $lib = '';
- my $lib_kind = 'try';
- my $upgrade = 'Math::BigFloat';
- my $downgrade = 'Math::BigInt';
-
- my @import = (':constant'); # drive it w/ constant
- my @a = @_;
- my $l = scalar @_;
- my $j = 0;
- my ($ver, $trace); # version? trace?
- my ($a, $p); # accuracy, precision
- for (my $i = 0; $i < $l; $i++, $j++) {
- if ($_[$i] eq 'upgrade') {
- # this causes upgrading
- $upgrade = $_[$i + 1]; # or undef to disable
- my $s = 2;
- $s = 1 if @a - $j < 2; # avoid "can not modify non-existent..."
- splice @a, $j, $s;
- $j -= $s;
- $i++;
- } elsif ($_[$i] eq 'downgrade') {
- # this causes downgrading
- $downgrade = $_[$i + 1]; # or undef to disable
- my $s = 2;
- $s = 1 if @a - $j < 2; # avoid "can not modify non-existent..."
- splice @a, $j, $s;
- $j -= $s;
- $i++;
- } elsif ($_[$i] =~ /^(l|lib|try|only)$/) {
- # this causes a different low lib to take care...
- $lib_kind = $1;
- $lib_kind = 'lib' if $lib_kind eq 'l';
- $lib = $_[$i + 1] || '';
- my $s = 2;
- $s = 1 if @a - $j < 2; # avoid "can not modify non-existent..."
- splice @a, $j, $s;
- $j -= $s;
- $i++;
+ my @import = (); # common options
+ my @int_import = (upgrade => $float_class); # int class only options
+ my @flt_import = (downgrade => $int_class); # float class only options
+ my @a = (); # unrecognized arguments
+ my $ver; # display version info?
+
+ while (@_) {
+ my $param = shift;
+
+ # Upgrading.
+
+ if ($param eq 'upgrade') {
+ my $arg = shift;
+ $float_class = $arg if defined $arg;
+ push @int_import, 'upgrade', $arg;
+ next;
+ }
+
+ # Downgrading.
+
+ if ($param eq 'downgrade') {
+ my $arg = shift;
+ $int_class = $arg if defined $arg;
+ push @flt_import, 'downgrade', $arg;
+ next;
}
- elsif ($_[$i] =~ /^(a|accuracy)$/) {
- $a = $_[$i + 1];
- my $s = 2;
- $s = 1 if @a - $j < 2; # avoid "can not modify non-existent..."
- splice @a, $j, $s;
- $j -= $s;
- $i++;
+
+ # Accuracy.
+
+ if ($param =~ /^a(ccuracy)?$/) {
+ push @import, 'accuracy', shift();
+ next;
}
- elsif ($_[$i] =~ /^(p|precision)$/) {
- $p = $_[$i + 1];
- my $s = 2;
- $s = 1 if @a - $j < 2; # avoid "can not modify non-existent..."
- splice @a, $j, $s;
- $j -= $s;
- $i++;
+
+ # Precision.
+
+ if ($param =~ /^p(recision)?$/) {
+ push @import, 'precision', shift();
+ next;
}
- elsif ($_[$i] =~ /^(v|version)$/) {
- $ver = 1;
- splice @a, $j, 1;
- $j--;
+
+ # Rounding mode.
+
+ if ($param eq 'round_mode') {
+ push @import, 'round_mode', shift();
+ next;
}
- elsif ($_[$i] =~ /^(t|trace)$/) {
- $trace = 1;
- splice @a, $j, 1;
- $j--;
+
+ # Backend library.
+
+ if ($param =~ /^(l|lib|try|only)$/) {
+ push @import, $param eq 'l' ? 'lib' : $param;
+ push @import, shift() if @_;
+ next;
}
- elsif ($_[$i] !~ /^(PI|e|bexp|bpi|hex|oct)\z/) {
- die ("unknown option $_[$i]");
+
+ if ($param =~ /^(v|version)$/) {
+ $ver = 1;
+ next;
}
- }
- my $class;
- $_lite = 0; # using M::BI::L ?
- if ($trace) {
- require Math::BigInt::Trace;
- $class = 'Math::BigInt::Trace';
- $upgrade = 'Math::BigFloat::Trace';
- }
- else {
- # see if we can find Math::BigInt::Lite
- if (!defined $a && !defined $p) { # rounding won't work to well
- local @INC = @INC;
- pop @INC if $INC[-1] eq '.';
- if (eval { require Math::BigInt::Lite; 1 }) {
- @import = (); # :constant in Lite, not MBI
- Math::BigInt::Lite->import(':constant');
- $_lite = 1; # signal okay
- }
+
+ if ($param =~ /^(PI|e|bexp|bpi|hex|oct)\z/) {
+ push @a, $param;
+ next;
}
- require Math::BigInt if $_lite == 0; # not already loaded?
- $class = 'Math::BigInt'; # regardless of MBIL or not
- }
- push @import, $lib_kind => $lib if $lib ne '';
- # Math::BigInt::Trace or plain Math::BigInt
- $class->import(@import, upgrade => $upgrade);
-
- if ($trace) {
- require Math::BigFloat::Trace;
- $class = 'Math::BigFloat::Trace';
- $downgrade = 'Math::BigInt::Trace';
- }
- else {
- require Math::BigFloat;
- $class = 'Math::BigFloat';
+
+ croak("Unknown option '$param'");
}
- $class->import(':constant', 'downgrade', $downgrade);
- bignum->accuracy($a) if defined $a;
- bignum->precision($p) if defined $p;
+ eval "require $int_class";
+ die $@ if $@;
+ $int_class -> import(@int_import, @import);
+
+ eval "require $float_class";
+ die $@ if $@;
+ $float_class -> import(@flt_import, @import);
+
if ($ver) {
- print "bignum\t\t\t v$VERSION\n";
- print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
- print "Math::BigInt\t\t v$Math::BigInt::VERSION";
- my $config = Math::BigInt->config();
- print " lib => $config->{lib} v$config->{lib_version}\n";
- print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
+ printf "%-31s v%s\n", $class, $class -> VERSION();
+ printf " lib => %-23s v%s\n",
+ $int_class -> config("lib"), $int_class -> config("lib_version");
+ printf "%-31s v%s\n", $int_class, $int_class -> VERSION();
exit;
}
- # Take care of octal/hexadecimal constants
- overload::constant binary =>
- sub {
- bigint::_binary_constant(shift);
+ $class -> export_to_level(1, $class, @a); # export inf, NaN, etc.
+
+ overload::constant
+
+ # This takes care each number written as decimal integer and within the
+ # range of what perl can represent as an integer, e.g., "314", but not
+ # "3141592653589793238462643383279502884197169399375105820974944592307".
+
+ integer => sub {
+ #printf "Value '%s' handled by the 'integer' sub.\n", $_[0];
+ my $str = shift;
+ return $int_class -> new($str);
+ },
+
+ # This takes care of each number written with a decimal point and/or
+ # using floating point notation, e.g., "3.", "3.0", "3.14e+2" (decimal),
+ # "0b1.101p+2" (binary), "03.14p+2" and "0o3.14p+2" (octal), and
+ # "0x3.14p+2" (hexadecimal).
+
+ float => sub {
+ #printf "# Value '%s' handled by the 'float' sub.\n", $_[0];
+ _float_constant(shift);
+ },
+
+ # Take care of each number written as an integer (no decimal point or
+ # exponent) using binary, octal, or hexadecimal notation, e.g., "0b101"
+ # (binary), "0314" and "0o314" (octal), and "0x314" (hexadecimal).
+
+ binary => sub {
+ #printf "# Value '%s' handled by the 'binary' sub.\n", $_[0];
+ my $str = shift;
+ return $int_class -> new($str) if $str =~ /^0[XxBb]/;
+ $int_class -> from_oct($str);
};
+}
- # if another big* was already loaded:
- my ($package) = caller();
+sub inf () { $int_class -> binf(); }
+sub NaN () { $int_class -> bnan(); }
- no strict 'refs';
- if (!defined *{"${package}::inf"}) {
- $self->export_to_level(1, $self, @a); # export inf and NaN
- }
+# This should depend on the current accuracy/precision. Fixme!
+sub PI () { $float_class -> new('3.141592653589793238462643383279502884197'); }
+sub e () { $float_class -> new('2.718281828459045235360287471352662497757'); }
+
+sub bpi ($) {
+ my $up = Math::BigFloat -> upgrade(); # get current upgrading, if any ...
+ Math::BigFloat -> upgrade(undef); # ... and disable
+ my $x = Math::BigFloat -> bpi(@_);
+ Math::BigFloat -> upgrade($up); # reset the upgrading
+ return $x;
}
-sub PI () { Math::BigFloat->new('3.141592653589793238462643383279502884197'); }
-sub e () { Math::BigFloat->new('2.718281828459045235360287471352662497757'); }
-sub bpi ($) { Math::BigFloat->bpi(@_); }
sub bexp ($$) {
- my $x = Math::BigFloat->new($_[0]);
- $x->bexp($_[1]);
+ my $up = Math::BigFloat -> upgrade(); # get current upgrading, if any ...
+ Math::BigFloat -> upgrade(undef); # ... and disable
+ my $x = Math::BigFloat -> new(shift) -> bexp(@_);
+ Math::BigFloat -> upgrade($up); # reset the upgrading
+ return $x;
}
1;
@@ -226,446 +453,478 @@ __END__
=head1 NAME
-bignum - Transparent BigNumber support for Perl
+bignum - transparent big number support for Perl
=head1 SYNOPSIS
- use bignum;
+ use bignum;
- $x = 2 + 4.5,"\n"; # BigFloat 6.5
- print 2 ** 512 * 0.1,"\n"; # really is what you think it is
- print inf * inf,"\n"; # prints inf
- print NaN * 3,"\n"; # prints NaN
+ $x = 2 + 4.5; # Math::BigFloat 6.5
+ print 2 ** 512 * 0.1; # Math::BigFloat 134...09.6
+ print 2 ** 512; # Math::BigInt 134...096
+ print inf + 42; # Math::BigInt inf
+ print NaN * 7; # Math::BigInt NaN
+ print hex("0x1234567890123490"); # Perl v5.10.0 or later
- {
- no bignum;
- print 2 ** 256,"\n"; # a normal Perl scalar now
- }
+ {
+ no bignum;
+ print 2 ** 256; # a normal Perl scalar now
+ }
- # for older Perls, import into current package:
- use bignum qw/hex oct/;
- print hex("0x1234567890123490"),"\n";
- print oct("01234567890123490"),"\n";
+ # for older Perls, import into current package:
+ use bignum qw/hex oct/;
+ print hex("0x1234567890123490");
+ print oct("01234567890123490");
=head1 DESCRIPTION
-All operators (including basic math operations) are overloaded. Integer and
-floating-point constants are created as proper BigInts or BigFloats,
-respectively.
-
-If you do
-
- use bignum;
+=head2 Literal numeric constants
-at the top of your script, Math::BigFloat and Math::BigInt will be loaded
-and any constant number will be converted to an object (Math::BigFloat for
-floats like 3.1415 and Math::BigInt for integers like 1234).
+By default, every literal integer becomes a Math::BigInt object, and literal
+non-integer becomes a Math::BigFloat object. Whether a numeric literal is
+considered an integer or non-integers depends only on the value of the constant,
+not on how it is represented. For instance, the constants 3.14e2 and 0x1.3ap8
+become Math::BigInt objects, because they both represent the integer value
+decimal 314.
-So, the following line:
+The default C<use bignum;> is equivalent to
- $x = 1234;
+ use bignum downgrade => "Math::BigInt", upgrade => "Math::BigFloat";
-creates actually a Math::BigInt and stores a reference to in $x.
-This happens transparently and behind your back, so to speak.
+The classes used for integers and non-integers can be set at compile time with
+the C<downgrade> and C<upgrade> options, for example
-You can see this with the following:
+ # use Math::BigInt for integers and Math::BigRat for non-integers
+ use bignum upgrade => "Math::BigRat";
- perl -Mbignum -le 'print ref(1234)'
+Note that disabling downgrading and upgrading does not affect how numeric
+literals are converted to objects
-Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
-if it is installed since it is faster for some operations. It will be
-automatically upgraded to BigInt whenever necessary:
+ # disable both downgrading and upgrading
+ use bignum downgrade => undef, upgrade => undef;
+ $x = 2.4; # becomes 2.4 as a Math::BigFloat
+ $y = 2; # becomes 2 as a Math::BigInt
- perl -Mbignum -le 'print ref(2**255)'
+=head2 Upgrading and downgrading
-This also means it is a bad idea to check for some specific package, since
-the actual contents of $x might be something unexpected. Due to the
-transparent way of bignum C<ref()> should not be necessary, anyway.
+By default, when the result of a computation is an integer, an Inf, or a NaN,
+the result is downgraded even when all the operands are instances of the upgrade
+class.
-Since Math::BigInt and BigFloat also overload the normal math operations,
-the following line will still work:
+ use bignum;
+ $x = 2.4; # becomes 2.4 as a Math::BigFloat
+ $y = 1.2; # becomes 1.2 as a Math::BigFloat
+ $z = $x / $y; # becomes 2 as a Math::BigInt due to downgrading
- perl -Mbignum -le 'print ref(1234+1234)'
+Equivalently, by default, when the result of a computation is a finite
+non-integer, the result is upgraded even when all the operands are instances of
+the downgrade class.
-Since numbers are actually objects, you can call all the usual methods from
-BigInt/BigFloat on them. This even works to some extent on expressions:
+ use bignum;
+ $x = 7; # becomes 7 as a Math::BigInt
+ $y = 2; # becomes 2 as a Math::BigInt
+ $z = $x / $y; # becomes 3.5 as a Math::BigFloat due to upgrading
- perl -Mbignum -le '$x = 1234; print $x->bdec()'
- perl -Mbignum -le 'print 1234->copy()->binc();'
- perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
- perl -Mbignum -le 'print +(1234)->copy()->binc()'
+The classes used for downgrading and upgrading can be set at runtime with the
+L</downgrade()> and L</upgrade()> methods, but see L</CAVEATS> below.
-(Note that print doesn't do what you expect if the expression starts with
-'(' hence the C<+>)
+The upgrade and downgrade classes don't have to be Math::BigInt and
+Math::BigFloat. For example, to use Math::BigRat as the upgrade class, use
-You can even chain the operations together as usual:
+ use bignum upgrade => "Math::BigRat";
+ $x = 2; # becomes 2 as a Math::BigInt
+ $y = 3.6; # becomes 18/5 as a Math::BigRat
- perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
- 1241
+The upgrade and downgrade classes can be modified at runtime
-Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
-appropriately. This means that:
+ use bignum;
+ $x = 3; # becomes 3 as a Math::BigInt
+ $y = 2; # becomes 2 as a Math::BigInt
+ $z = $x / $y; # becomes 1.5 as a Math::BigFlaot
- perl -Mbignum -le 'print 1234+4.5'
- 1238.5
+ bignum -> upgrade("Math::BigRat");
+ $w = $x / $y; # becomes 3/2 as a Math::BigRat
-will work correctly. These mixed cases don't do always work when using
-Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
-scalars work.
+Disabling downgrading doesn't change the fact that literal constant integers are
+converted to the downgrade class, it only prevents downgrading as a result of a
+computation. E.g.,
-If you do want to work with large integers like under C<use integer;>, try
-C<use bigint;>:
+ use bignum downgrade => undef;
+ $x = 2; # becomes 2 as a Math::BigInt
+ $y = 2.4; # becomes 2.4 as a Math::BigFloat
+ $z = 1.2; # becomes 1.2 as a Math::BigFloat
+ $w = $x / $y; # becomes 2 as a Math::BigFloat due to no downgrading
- perl -Mbigint -le 'print 1234.5+4.5'
- 1238
+If you want all numeric literals, both integers and non-integers, to become
+Math::BigFloat objects, use the L<bigfloat> pragma.
-There is also C<use bigrat;> which gives you big rationals:
+Equivalently, disabling upgrading doesn't change the fact that literal constant
+non-integers are converted to the upgrade class, it only prevents upgrading as a
+result of a computation. E.g.,
- perl -Mbigrat -le 'print 1234+4.1'
- 12381/10
+ use bignum upgrade => undef;
+ $x = 2.5; # becomes 2.5 as a Math::BigFloat
+ $y = 7; # becomes 7 as a Math::BigInt
+ $z = 2; # becomes 2 as a Math::BigInt
+ $w = $x / $y; # becomes 3 as a Math::BigInt due to no upgrading
-The entire upgrading/downgrading is still experimental and might not work
-as you expect or may even have bugs. You might get errors like this:
+If you want all numeric literals, both integers and non-integers, to become
+Math::BigInt objects, use the L<bigint> pragma.
- Can't use an undefined value as an ARRAY reference at
- /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
+You can even do
-This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
-vice versa) and the upgrade/downgrad path was missing. This is a bug, please
-report it so that we can fix it.
+ use bignum upgrade => "Math::BigRat", upgrade => undef;
-You might consider using just Math::BigInt or Math::BigFloat, since they
-allow you finer control over what get's done in which module/space. For
-instance, simple loop counters will be Math::BigInts under C<use bignum;> and
-this is slower than keeping them as Perl scalars:
+which converts all integer literals to Math::BigInt objects and all non-integer
+literals to Math::BigRat objects. However, when the result of a computation
+involving two Math::BigInt objects results in a non-integer (e.g., 7/2), the
+result will be truncted to a Math::BigInt rather than being upgraded to a
+Math::BigRat, since upgrading is disabled.
- perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
+=head2 Overloading
-Please note the following does not work as expected (prints nothing), since
-overloading of '..' is not yet possible in Perl (as of v5.8.0):
+Since all numeric literals become objects, you can call all the usual methods
+from Math::BigInt and Math::BigFloat on them. This even works to some extent on
+expressions:
- perl -Mbignum -le 'for (1..2) { print ref($_); }'
+ perl -Mbignum -le '$x = 1234; print $x->bdec()'
+ perl -Mbignum -le 'print 1234->copy()->binc();'
+ perl -Mbignum -le 'print 1234->copy()->binc()->badd(6);'
=head2 Options
-bignum recognizes some options that can be passed while loading it via use.
-The options can (currently) be either a single letter form, or the long form.
-The following options exist:
+C<bignum> recognizes some options that can be passed while loading it via via
+C<use>. The following options exist:
-=over 2
+=over 4
=item a or accuracy
This sets the accuracy for all math operations. The argument must be greater
-than or equal to zero. See Math::BigInt's bround() function for details.
+than or equal to zero. See Math::BigInt's bround() method for details.
- perl -Mbignum=a,50 -le 'print sqrt(20)'
+ perl -Mbignum=a,50 -le 'print sqrt(20)'
Note that setting precision and accuracy at the same time is not possible.
=item p or precision
This sets the precision for all math operations. The argument can be any
-integer. Negative values mean a fixed number of digits after the dot, while
-a positive value rounds to this digit left from the dot. 0 or 1 mean round to
-integer. See Math::BigInt's bfround() function for details.
+integer. Negative values mean a fixed number of digits after the dot, while a
+positive value rounds to this digit left from the dot. 0 means round to integer.
+See Math::BigInt's bfround() method for details.
- perl -Mbignum=p,-50 -le 'print sqrt(20)'
+ perl -Mbignum=p,-50 -le 'print sqrt(20)'
Note that setting precision and accuracy at the same time is not possible.
-=item t or trace
-
-This enables a trace mode and is primarily for debugging bignum or
-Math::BigInt/Math::BigFloat.
-
-=item l or lib
+=item l, lib, try, or only
Load a different math lib, see L<Math Library>.
- perl -Mbignum=l,GMP -e 'print 2 ** 512'
-
-Currently there is no way to specify more than one library on the command
-line. This means the following does not work:
-
- perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
-
-This will be hopefully fixed soon ;)
+ perl -Mbignum=l,GMP -e 'print 2 ** 512'
+ perl -Mbignum=lib,GMP -e 'print 2 ** 512'
+ perl -Mbignum=try,GMP -e 'print 2 ** 512'
+ perl -Mbignum=only,GMP -e 'print 2 ** 512'
=item hex
-Override the built-in hex() method with a version that can handle big
-numbers. This overrides it by exporting it to the current package. Under
-Perl v5.10.0 and higher, this is not so necessary, as hex() is lexically
-overridden in the current scope whenever the bignum pragma is active.
+Override the built-in hex() method with a version that can handle big numbers.
+This overrides it by exporting it to the current package. Under Perl v5.10.0 and
+higher, this is not so necessary, as hex() is lexically overridden in the
+current scope whenever the C<bignum> pragma is active.
=item oct
-Override the built-in oct() method with a version that can handle big
-numbers. This overrides it by exporting it to the current package. Under
-Perl v5.10.0 and higher, this is not so necessary, as oct() is lexically
-overridden in the current scope whenever the bigint pragma is active.
+Override the built-in oct() method with a version that can handle big numbers.
+This overrides it by exporting it to the current package. Under Perl v5.10.0 and
+higher, this is not so necessary, as oct() is lexically overridden in the
+current scope whenever the C<bignum> pragma is active.
=item v or version
-This prints out the name and version of all modules used and then exits.
+this prints out the name and version of the modules and then exits.
- perl -Mbignum=v
+ perl -Mbignum=v
=back
-=head2 Methods
+=head2 Math Library
+
+Math with the numbers is done (by default) by a backend library module called
+Math::BigInt::Calc. The default is equivalent to saying:
+
+ use bignum lib => 'Calc';
+
+you can change this by using:
+
+ use bignum lib => 'GMP';
+
+The following would first try to find Math::BigInt::Foo, then Math::BigInt::Bar,
+and if this also fails, revert to Math::BigInt::Calc:
+
+ use bignum lib => 'Foo,Math::BigInt::Bar';
+
+Using c<lib> warns if none of the specified libraries can be found and
+L<Math::BigInt> and L<Math::BigFloat> fell back to one of the default
+libraries. To suppress this warning, use C<try> instead:
+
+ use bignum try => 'GMP';
+
+If you want the code to die instead of falling back, use C<only> instead:
-Beside import() and AUTOLOAD() there are only a few other methods.
+ use bignum only => 'GMP';
-Since all numbers are now objects, you can use all functions that are part of
-the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
-the fxxx() notation, though. This makes it possible that the underlying object
-might morph into a different class than BigFloat.
+Please see respective module documentation for further details.
+
+=head2 Method calls
-=head2 Caveats
+Since all numbers are now objects, you can use the methods that are part of the
+Math::BigInt and Math::BigFloat API.
But a warning is in order. When using the following to make a copy of a number,
only a shallow copy will be made.
- $x = 9; $y = $x;
- $x = $y = 7;
+ $x = 9; $y = $x;
+ $x = $y = 7;
-If you want to make a real copy, use the following:
+Using the copy or the original with overloaded math is okay, e.g., the following
+work:
- $y = $x->copy();
+ $x = 9; $y = $x;
+ print $x + 1, " ", $y,"\n"; # prints 10 9
-Using the copy or the original with overloaded math is okay, e.g. the
-following work:
+but calling any method that modifies the number directly will result in B<both>
+the original and the copy being destroyed:
- $x = 9; $y = $x;
- print $x + 1, " ", $y,"\n"; # prints 10 9
+ $x = 9; $y = $x;
+ print $x->badd(1), " ", $y,"\n"; # prints 10 10
-but calling any method that modifies the number directly will result in
-B<both> the original and the copy being destroyed:
+ $x = 9; $y = $x;
+ print $x->binc(1), " ", $y,"\n"; # prints 10 10
- $x = 9; $y = $x;
- print $x->badd(1), " ", $y,"\n"; # prints 10 10
+ $x = 9; $y = $x;
+ print $x->bmul(2), " ", $y,"\n"; # prints 18 18
- $x = 9; $y = $x;
- print $x->binc(1), " ", $y,"\n"; # prints 10 10
+Using methods that do not modify, but test that the contents works:
- $x = 9; $y = $x;
- print $x->bmul(2), " ", $y,"\n"; # prints 18 18
+ $x = 9; $y = $x;
+ $z = 9 if $x->is_zero(); # works fine
-Using methods that do not modify, but test the contents works:
+See the documentation about the copy constructor and C<=> in overload, as well
+as the documentation in Math::BigFloat for further details.
- $x = 9; $y = $x;
- $z = 9 if $x->is_zero(); # works fine
-
-See the documentation about the copy constructor and C<=> in overload, as
-well as the documentation in BigInt for further details.
+=head2 Methods
-=over 2
+=over 4
=item inf()
-A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
+A shortcut to return C<inf> as an object. Useful because Perl does not always
handle bareword C<inf> properly.
=item NaN()
-A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
+A shortcut to return C<NaN> as an object. Useful because Perl does not always
handle bareword C<NaN> properly.
=item e
- # perl -Mbignum=e -wle 'print e'
+ # perl -Mbignum=e -wle 'print e'
-Returns Euler's number C<e>, aka exp(1).
+Returns Euler's number C<e>, aka exp(1) (= 2.7182818284...).
-=item PI()
+=item PI
- # perl -Mbignum=PI -wle 'print PI'
+ # perl -Mbignum=PI -wle 'print PI'
-Returns PI.
+Returns PI (= 3.1415926532..).
=item bexp()
- bexp($power,$accuracy);
+ bexp($power, $accuracy);
-Returns Euler's number C<e> raised to the appropriate power, to
-the wanted accuracy.
+Returns Euler's number C<e> raised to the appropriate power, to the wanted
+accuracy.
Example:
- # perl -Mbignum=bexp -wle 'print bexp(1,80)'
+ # perl -Mbignum=bexp -wle 'print bexp(1,80)'
=item bpi()
- bpi($accuracy);
+ bpi($accuracy);
Returns PI to the wanted accuracy.
Example:
- # perl -Mbignum=bpi -wle 'print bpi(80)'
+ # perl -Mbignum=bpi -wle 'print bpi(80)'
-=item upgrade()
+=item accuracy()
-Return the class that numbers are upgraded to, is in fact returning
-C<$Math::BigInt::upgrade>.
+Set or get the accuracy.
-=item in_effect()
+=item precision()
- use bignum;
+Set or get the precision.
- print "in effect\n" if bignum::in_effect; # true
- {
- no bignum;
- print "in effect\n" if bignum::in_effect; # false
- }
+=item round_mode()
-Returns true or false if C<bignum> is in effect in the current scope.
+Set or get the rounding mode.
-This method only works on Perl v5.9.4 or later.
+=item div_scale()
-=back
+Set or get the division scale.
-=head2 Math Library
+=item upgrade()
-Math with the numbers is done (by default) by a module called
-Math::BigInt::Calc. This is equivalent to saying:
+Set or get the class that the downgrade class upgrades to, if any. Set the
+upgrade class to C<undef> to disable upgrading. See C</CAVEATS> below.
- use bignum lib => 'Calc';
+=item downgrade()
-You can change this by using:
+Set or get the class that the upgrade class downgrades to, if any. Set the
+downgrade class to C<undef> to disable upgrading. See L</CAVEATS> below.
- use bignum lib => 'GMP';
+=item in_effect()
+
+ use bignum;
-The following would first try to find Math::BigInt::Foo, then
-Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
+ print "in effect\n" if bignum::in_effect; # true
+ {
+ no bignum;
+ print "in effect\n" if bignum::in_effect; # false
+ }
- use bignum lib => 'Foo,Math::BigInt::Bar';
+Returns true or false if C<bignum> is in effect in the current scope.
-Please see respective module documentation for further details.
+This method only works on Perl v5.9.4 or later.
-Using C<lib> warns if none of the specified libraries can be found and
-L<Math::BigInt> did fall back to one of the default libraries.
-To suppress this warning, use C<try> instead:
+=back
- use bignum try => 'GMP';
+=head1 CAVEATS
-If you want the code to die instead of falling back, use C<only> instead:
+=over 4
- use bignum only => 'GMP';
+=item The upgrade() and downgrade() methods
-=head2 INTERNAL FORMAT
+Note that setting both the upgrade and downgrade classes at runtime with the
+L</upgrade()> and L</downgrade()> methods, might not do what you expect:
-The numbers are stored as objects, and their internals might change at anytime,
-especially between math operations. The objects also might belong to different
-classes, like Math::BigInt, or Math::BigFloat. Mixing them together, even
-with normal scalars is not extraordinary, but normal and expected.
+ # Assuming that downgrading and upgrading hasn't been modified so far, so
+ # the downgrade and upgrade classes are Math::BigInt and Math::BigFloat,
+ # respectively, the following sets the upgrade class to Math::BigRat, i.e.,
+ # makes Math::BigInt upgrade to Math::BigRat:
-You should not depend on the internal format, all accesses must go through
-accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
-is no guaranty that the object in question has such a hashkey, nor is a hash
-underneath at all.
+ bignum -> upgrade("Math::BigRat");
-=head2 SIGN
+ # The following sets the downgrade class to Math::BigInt::Lite, i.e., makes
+ # the new upgrade class Math::BigRat downgrade to Math::BigInt::Lite
-The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored separately.
-You can access it with the sign() method.
+ bignum -> downgrade("Math::BigInt::Lite");
-A sign of 'NaN' is used to represent the result when input arguments are not
-numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
-minus infinity. You will get '+inf' when dividing a positive number by 0, and
-'-inf' when dividing any negative number by 0.
+ # Note that at this point, it is still Math::BigInt, not Math::BigInt::Lite,
+ # that upgrades to Math::BigRat, so to get Math::BigInt::Lite to upgrade to
+ # Math::BigRat, we need to do the following (again):
-=head1 CAVEATS
+ bignum -> upgrade("Math::BigRat");
-=over 2
+A simpler way to do this at runtime is to use import(),
+
+ bignum -> import(upgrade => "Math::BigRat",
+ downgrade => "Math::BigInt::Lite");
+
+=item 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.
=item Operator vs literal overloading
-C<bignum> works by overloading handling of integer and floating point
-literals, converting them to L<Math::BigInt> or L<Math::BigFloat>
-objects.
+C<bigrat> works by overloading handling of integer and floating point literals,
+converting them to L<Math::BigRat> objects.
-This means that arithmetic involving only string values or string
-literals will be performed using Perl's built-in operators.
+This means that arithmetic involving only string values or string literals are
+performed using Perl's built-in operators.
For example:
- use bignum;
+ use bigrat;
my $x = "900000000000000009";
my $y = "900000000000000007";
print $x - $y;
-will output C<0> on default 32-bit builds, since C<bigrat> never sees
-the string literals. To ensure the expression is all treated as
-C<Math::BigInt> or C<BigFloat> objects, use a literal number in the
-expression:
+outputs C<0> on default 32-bit builds, since C<bignum> never sees the string
+literals. To ensure the expression is all treated as C<Math::BigFloat> objects,
+use a literal number in the expression:
print +(0+$x) - $y;
+=item Ranges
+
+Perl does not allow overloading of ranges, so you can neither safely use ranges
+with C<bignum> endpoints, nor is the iterator variable a C<Math::BigFloat>.
+
+ use 5.010;
+ for my $i (12..13) {
+ for my $j (20..21) {
+ say $i ** $j; # produces a floating-point number,
+ # not an object
+ }
+ }
+
=item in_effect()
This method only works on Perl v5.9.4 or later.
=item hex()/oct()
-C<bigint> overrides these routines with versions that can also handle
-big integer values. Under Perl prior to version v5.9.4, however, this
-will not happen unless you specifically ask for it with the two
-import tags "hex" and "oct" - and then it will be global and cannot be
-disabled inside a scope with "no bigint":
+C<bignum> overrides these routines with versions that can also handle big
+integer values. Under Perl prior to version v5.9.4, however, this will not
+happen unless you specifically ask for it with the two import tags "hex" and
+"oct" - and then it will be global and cannot be disabled inside a scope with
+C<no bignum>:
- use bigint qw/hex oct/;
+ use bignum qw/hex oct/;
+ print hex("0x1234567890123456");
+ {
+ no bignum;
print hex("0x1234567890123456");
- {
- no bigint;
- print hex("0x1234567890123456");
- }
+ }
The second call to hex() will warn about a non-portable constant.
Compare this to:
- use bigint;
+ use bignum;
- # will warn only under older than v5.9.4
- print hex("0x1234567890123456");
+ # will warn only under Perl older than v5.9.4
+ print hex("0x1234567890123456");
=back
-=head1 MODULES USED
-
-C<bignum> is just a thin wrapper around various modules of the Math::BigInt
-family. Think of it as the head of the family, who runs the shop, and orders
-the others to do the work.
-
-The following modules are currently used by bignum:
-
- Math::BigInt::Lite (for speed, and only if it is loadable)
- Math::BigInt
- Math::BigFloat
-
=head1 EXAMPLES
Some cool command line examples to impress the Python crowd ;)
- perl -Mbignum -le 'print sqrt(33)'
- perl -Mbignum -le 'print 2*255'
- perl -Mbignum -le 'print 4.5+2*255'
- perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
- perl -Mbignum -le 'print 123->is_odd()'
- perl -Mbignum -le 'print log(2)'
- perl -Mbignum -le 'print exp(1)'
- perl -Mbignum -le 'print 2 ** 0.5'
- perl -Mbignum=a,65 -le 'print 2 ** 0.2'
- perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777'
+ perl -Mbignum -le 'print sqrt(33)'
+ perl -Mbignum -le 'print 2**255'
+ perl -Mbignum -le 'print 4.5+2**255'
+ perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
+ perl -Mbignum -le 'print 123->is_odd()'
+ perl -Mbignum -le 'print log(2)'
+ perl -Mbignum -le 'print exp(1)'
+ perl -Mbignum -le 'print 2 ** 0.5'
+ perl -Mbignum=a,65 -le 'print 2 ** 0.2'
+ perl -Mbignum=l,GMP -le 'print 7 ** 7777'
=head1 BUGS
Please report any bugs or feature requests to
-C<bug-math-bigint at rt.cpan.org>, or through the web interface at
+C<bug-bignum at rt.cpan.org>, or through the web interface at
L<https://rt.cpan.org/Ticket/Create.html?Queue=bignum> (requires login).
We will be notified, and then you'll automatically be notified of
progress on your bug as I make changes.
@@ -680,26 +939,26 @@ You can also look for information at:
=over 4
-=item * RT: CPAN's request tracker
-
-L<https://rt.cpan.org/Public/Dist/Display.html?Name=bignum>
+=item * GitHub
-=item * AnnoCPAN: Annotated CPAN documentation
+L<https://github.com/pjacklam/p5-bignum>
-L<http://annocpan.org/dist/bignum>
-
-=item * CPAN Ratings
+=item * RT: CPAN's request tracker
-L<http://cpanratings.perl.org/dist/bignum>
+L<https://rt.cpan.org/Dist/Display.html?Name=bignum>
-=item * Search CPAN
+=item * MetaCPAN
-L<http://search.cpan.org/dist/bignum/>
+L<https://metacpan.org/release/bignum>
=item * CPAN Testers Matrix
L<http://matrix.cpantesters.org/?dist=bignum>
+=item * CPAN Ratings
+
+L<https://cpanratings.perl.org/dist/bignum>
+
=back
=head1 LICENSE
@@ -724,7 +983,7 @@ L<Math::BigInt::FastCalc>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
=item *
-Maintained by Peter John Acklam E<lt>pjacklam@gmail.com<gt>, 2014-.
+Maintained by Peter John Acklam E<lt>pjacklam@gmail.comE<gt>, 2014-.
=back