package bigrat;use strict;use warnings;use Carp qw< carp croak >;our $VERSION = '0.67';use Exporter;our @ISA = qw( Exporter );our @EXPORT_OK = qw( PI e bpi bexp hex oct );our @EXPORT = qw( inf NaN );use overload;my $obj_class = "Math::BigRat";##############################################################################sub accuracy { my $self = shift; $obj_class -> accuracy(@_);}sub precision { my $self = shift; $obj_class -> precision(@_);}sub round_mode { my $self = shift; $obj_class -> round_mode(@_);}sub div_scale { my $self = shift; $obj_class -> div_scale(@_);}sub in_effect { my $level = shift || 0; my $hinthash = (caller($level))[10]; $hinthash->{bigrat};}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)) { return $obj_class -> new($nstr); } # 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 $obj_class -> bnan();}############################################################################## the following two routines are for "use bigrat 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 = $obj_class -> from_hex($chrs); } else { $x = $obj_class -> bzero(); } # Warn about trailing garbage. if (CORE::length($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 = $obj_class -> from_bin($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 = $obj_class -> from_oct($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 lexicalmy ($prev_oct, $prev_hex, $overridden);if (LEXICAL) { eval <<'.' }sub _hex(_) { my $hh = (caller 0)[10]; return $$hh{bigrat} ? bigrat::_hex_core($_[0]) : $$hh{bigfloat} ? bigfloat::_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{bigrat} ? bigrat::_oct_core($_[0]) : $$hh{bigfloat} ? bigfloat::_oct_core($_[0]) : $$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 { delete $^H{bigrat}; # no longer in effect overload::remove_constant('binary', '', 'float', '', 'integer');}sub import { my $class = shift; $^H{bigrat} = 1; # we are in effect delete $^H{bigint}; delete $^H{bigfloat}; # for newer Perls always override hex() and oct() with a lexical version: if (LEXICAL) { _override(); } my @import = (); my @a = (); # unrecognized arguments my $ver; # version? while (@_) { my $param = shift; # Accuracy. if ($param =~ /^a(ccuracy)?$/) { push @import, 'accuracy', shift(); next; } # Precision. if ($param =~ /^p(recision)?$/) { push @import, 'precision', shift(); next; } # Rounding mode. if ($param eq 'round_mode') { push @import, 'round_mode', shift(); next; } # Backend library. if ($param =~ /^(l|lib|try|only)$/) { push @import, $param eq 'l' ? 'lib' : $param; push @import, shift() if @_; next; } if ($param =~ /^(v|version)$/) { $ver = 1; next; } if ($param =~ /^(t|trace)$/) { $obj_class .= "::Trace"; eval "require $obj_class"; die $@ if $@; next; } if ($param =~ /^(PI|e|bexp|bpi|hex|oct)\z/) { push @a, $param; next; } croak("Unknown option '$param'"); } eval "require $obj_class"; die $@ if $@; $obj_class -> import(@import); if ($ver) { printf "%-31s v%s\n", $class, $class -> VERSION(); printf " lib => %-23s v%s\n", $obj_class -> config("lib"), $obj_class -> config("lib_version"); printf "%-31s v%s\n", $obj_class, $obj_class -> VERSION(); exit; } $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 $obj_class -> new($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 $obj_class -> new($str) if $str =~ /^0[XxBb]/; $obj_class -> from_oct($str); };}sub inf () { $obj_class -> binf(); }sub NaN () { $obj_class -> bnan(); }# This should depend on the current accuracy/precision. Fixme!sub PI () { $obj_class -> new('3.141592653589793238462643383279502884197'); }sub e () { $obj_class -> new('2.718281828459045235360287471352662497757'); }sub bpi ($) { 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 $obj_class -> new($x);}sub bexp ($$) { my $up = Math::BigFloat -> upgrade(); # get current upgrading, if any ... Math::BigFloat -> upgrade(undef); # ... and disable my $x = Math::BigFloat -> new(shift); $x -> bexp(@_); Math::BigFloat -> upgrade($up); # reset the upgrading return $obj_class -> new($x);}1;__END__=pod=head1 NAMEbigrat - transparent big rational number support for Perl=head1 SYNOPSIS use bigrat; print 2 + 4.5; # Math::BigRat 13/2 print 1/3 + 1/4; # Math::BigRat 7/12 print inf + 42; # Math::BigRat inf print NaN * 7; # Math::BigRat NaN print hex("0x1234567890123490"); # Perl v5.10.0 or later { no bigrat; print 1/3; # 0.33333... } # for older Perls, import into current package: use bigrat qw/hex oct/; print hex("0x1234567890123490"); print oct("01234567890123490");=head1 DESCRIPTIONAll numeric literal in the given scope are converted to Math::BigRat objects.All operators (including basic math operations) except the range operator C<..>are overloaded.So, the following: use bigrat; $x = 1234;creates a Math::BigRat and stores a reference to in $x. This happenstransparently and behind your back, so to speak.You can see this with the following: perl -Mbigrat -le 'print ref(1234)'Since numbers are actually objects, you can call all the usual methods fromMath::BigRat on them. This even works to some extent on expressions: perl -Mbigrat -le '$x = 1234; print $x->bdec()' perl -Mbigrat -le 'print 1234->copy()->binc();' perl -Mbigrat -le 'print 1234->copy()->binc->badd(6);' perl -Mbigrat -le 'print +(1234)->copy()->binc()'(Note that print doesn't do what you expect if the expression starts with'(' hence the C<+>)You can even chain the operations together as usual: perl -Mbigrat -le 'print 1234->copy()->binc->badd(6);' 1241Please note the following does not work as expected (prints nothing), sinceoverloading of '..' is not yet possible in Perl (as of v5.8.0): perl -Mbigrat -le 'for (1..2) { print ref($_); }'=head2 OptionsC<bigrat> recognizes some options that can be passed while loading it viaC<use>. The following options exist:=over 4=item a or accuracyThis sets the accuracy for all math operations. The argument must be greaterthan or equal to zero. See Math::BigInt's bround() method for details. perl -Mbigrat=a,50 -le 'print sqrt(20)'Note that setting precision and accuracy at the same time is not possible.=item p or precisionThis sets the precision for all math operations. The argument can be anyinteger. Negative values mean a fixed number of digits after the dot, while apositive value rounds to this digit left from the dot. 0 means round to integer.See Math::BigInt's bfround() method for details. perl -Mbigrat=p,-50 -le 'print sqrt(20)'Note that setting precision and accuracy at the same time is not possible.=item t or traceThis enables a trace mode and is primarily for debugging.=item l, lib, try, or onlyLoad a different math lib, see L<Math Library>. perl -Mbigrat=l,GMP -e 'print 2 ** 512' perl -Mbigrat=lib,GMP -e 'print 2 ** 512' perl -Mbigrat=try,GMP -e 'print 2 ** 512' perl -Mbigrat=only,GMP -e 'print 2 ** 512'=item hexOverride 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 andhigher, this is not so necessary, as hex() is lexically overridden in thecurrent scope whenever the C<bigrat> pragma is active.=item octOverride 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 andhigher, this is not so necessary, as oct() is lexically overridden in thecurrent scope whenever the C<bigrat> pragma is active.=item v or versionthis prints out the name and version of the modules and then exits. perl -Mbigrat=v=back=head2 Math LibraryMath with the numbers is done (by default) by a backend library module calledMath::BigInt::Calc. The default is equivalent to saying: use bigrat lib => 'Calc';you can change this by using: use bigrat 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 bigrat lib => 'Foo,Math::BigInt::Bar';Using c<lib> warns if none of the specified libraries can be found andL<Math::BigInt> fell back to one of the default libraries. To suppress thiswarning, use c<try> instead: use bigrat try => 'GMP';If you want the code to die instead of falling back, use C<only> instead: use bigrat only => 'GMP';Please see the respective module documentation for further details.=head2 Method callsSince all numbers are now objects, you can use all methods that are part of theMath::BigRat 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;Using the copy or the original with overloaded math is okay, e.g., the followingwork: $x = 9; $y = $x; print $x + 1, " ", $y,"\n"; # prints 10 9but 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->badd(1), " ", $y,"\n"; # prints 10 10 $x = 9; $y = $x; print $x->binc(1), " ", $y,"\n"; # prints 10 10 $x = 9; $y = $x; print $x->bmul(2), " ", $y,"\n"; # prints 18 18Using methods that do not modify, but test that the contents works: $x = 9; $y = $x; $z = 9 if $x->is_zero(); # works fineSee the documentation about the copy constructor and C<=> in overload, as wellas the documentation in Math::BigFloat for further details.=head2 Methods=over 4=item inf()A shortcut to return Math::BigRat->binf(). Useful because Perl does not alwayshandle bareword C<inf> properly.=item NaN()A shortcut to return Math::BigRat->bnan(). Useful because Perl does not alwayshandle bareword C<NaN> properly.=item e # perl -Mbigrat=e -wle 'print e'Returns Euler's number C<e>, aka exp(1).=item PI # perl -Mbigrat=PI -wle 'print PI'Returns PI.=item bexp() bexp($power, $accuracy);Returns Euler's number C<e> raised to the appropriate power, to the wantedaccuracy.Example: # perl -Mbigrat=bexp -wle 'print bexp(1,80)'=item bpi() bpi($accuracy);Returns PI to the wanted accuracy.Example: # perl -Mbigrat=bpi -wle 'print bpi(80)'=item accuracy()Set or get the accuracy.=item precision()Set or get the precision.=item round_mode()Set or get the rounding mode.=item div_scale()Set or get the division scale.=item in_effect() use bigrat; print "in effect\n" if bigrat::in_effect; # true { no bigrat; print "in effect\n" if bigrat::in_effect; # false }Returns true or false if C<bigrat> is in effect in the current scope.This method only works on Perl v5.9.4 or later.=back=head1 CAVEATS=over 4=item Hexadecimal, octal, and binary floating point literalsPerl (and this module) accepts hexadecimal, octal, and binary floating pointliterals, but use them with care with Perl versions before v5.32.0, because someversions of Perl silently give the wrong result.=item Operator vs literal overloadingC<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 areperformed using Perl's built-in operators.For example: use bigrat; my $x = "900000000000000009"; my $y = "900000000000000007"; print $x - $y;outputs C<0> on default 32-bit builds, since C<bigrat> never sees the stringliterals. To ensure the expression is all treated as C<Math::BigRat> objects,use a literal number in the expression: print +(0+$x) - $y;=item RangesPerl does not allow overloading of ranges, so you can neither safely use rangeswith C<bigrat> endpoints, nor is the iterator variable a C<Math::BigRat>. 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<bigrat> overrides these routines with versions that can also handle biginteger values. Under Perl prior to version v5.9.4, however, this will nothappen 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 withC<no bigrat>: use bigrat qw/hex oct/; print hex("0x1234567890123456"); { no bigrat; print hex("0x1234567890123456"); }The second call to hex() will warn about a non-portable constant.Compare this to: use bigrat; # will warn only under Perl older than v5.9.4 print hex("0x1234567890123456");=back=head1 EXAMPLES perl -Mbigrat -le 'print sqrt(33)' perl -Mbigrat -le 'print 2**255' perl -Mbigrat -le 'print 4.5+2**255' perl -Mbigrat -le 'print 3/7 + 5/7 + 8/3' perl -Mbigrat -le 'print 12->is_odd()'; perl -Mbigrat=l,GMP -le 'print 7 ** 7777'=head1 BUGSPlease report any bugs or feature requests toC<bug-bignum at rt.cpan.org>, or through the web interface atL<https://rt.cpan.org/Ticket/Create.html?Queue=bignum> (requires login).We will be notified, and then you'll automatically be notified ofprogress on your bug as I make changes.=head1 SUPPORTYou can find documentation for this module with the perldoc command. perldoc bigratYou can also look for information at:=over 4=item * GitHubL<https://github.com/pjacklam/p5-bignum>=item * RT: CPAN's request trackerL<https://rt.cpan.org/Dist/Display.html?Name=bignum>=item * MetaCPANL<https://metacpan.org/release/bignum>=item * CPAN Testers MatrixL<http://matrix.cpantesters.org/?dist=bignum>=back=head1 LICENSEThis program is free software; you may redistribute it and/or modify it underthe same terms as Perl itself.=head1 SEE ALSOL<bignum> and L<bigint>.L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well asL<Math::BigInt::FastCalc>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.=head1 AUTHORS=over 4=item *(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.=item *Maintained by Peter John Acklam E<lt>pjacklam@gmail.comE<gt>, 2014-.=back=cut