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Diffstat (limited to 'Master/tlpkg/tlperl0/lib/bigrat.pm')
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diff --git a/Master/tlpkg/tlperl0/lib/bigrat.pm b/Master/tlpkg/tlperl0/lib/bigrat.pm new file mode 100755 index 00000000000..10e8057abd0 --- /dev/null +++ b/Master/tlpkg/tlperl0/lib/bigrat.pm @@ -0,0 +1,566 @@ +package bigrat; +use 5.006; + +$VERSION = '0.23'; +require Exporter; +@ISA = qw( bigint ); +@EXPORT_OK = qw( PI e bpi bexp ); +@EXPORT = qw( inf NaN ); + +use strict; +use overload; +require bigint; # no "use" to avoid callind import + +############################################################################## + +BEGIN + { + *inf = \&bigint::inf; + *NaN = \&bigint::NaN; + } + +# These are all alike, and thus faked by AUTOLOAD + +my @faked = qw/round_mode accuracy precision div_scale/; +use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite + +sub AUTOLOAD + { + my $name = $AUTOLOAD; + + $name =~ s/.*:://; # split package + no strict 'refs'; + foreach my $n (@faked) + { + if ($n eq $name) + { + *{"bigrat::$name"} = sub + { + my $self = shift; + no strict 'refs'; + if (defined $_[0]) + { + Math::BigInt->$name($_[0]); + Math::BigFloat->$name($_[0]); + return Math::BigRat->$name($_[0]); + } + return Math::BigInt->$name(); + }; + return &$name; + } + } + + # delayed load of Carp and avoid recursion + require Carp; + Carp::croak ("Can't call bigrat\-\>$name, not a valid method"); + } + +sub unimport + { + $^H{bigrat} = undef; # no longer in effect + overload::remove_constant('binary','','float','','integer'); + } + +sub in_effect + { + my $level = shift || 0; + my $hinthash = (caller($level))[10]; + $hinthash->{bigrat}; + } + +############################################################################# +# the following two routines are for Perl 5.9.4 or later and are lexical + +sub _hex + { + return CORE::hex($_[0]) unless in_effect(1); + my $i = $_[0]; + $i = '0x'.$i unless $i =~ /^0x/; + Math::BigInt->new($i); + } + +sub _oct + { + return CORE::oct($_[0]) unless in_effect(1); + my $i = $_[0]; + return Math::BigInt->from_oct($i) if $i =~ /^0[0-7]/; + Math::BigInt->new($i); + } + +sub import + { + my $self = shift; + + # see also bignum->import() for additional comments + + $^H{bigrat} = 1; # we are in effect + + my ($hex,$oct); + # for newer Perls always override hex() and oct() with a lexical version: + if ($] > 5.009004) + { + $oct = \&_oct; + $hex = \&_hex; + } + # some defaults + my $lib = ''; my $lib_kind = 'try'; my $upgrade = 'Math::BigFloat'; + + my @import = ( ':constant' ); # drive it w/ constant + my @a = @_; my $l = scalar @_; my $j = 0; + my ($a,$p); + my ($ver,$trace); # version? trace? + 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-existant..." + splice @a, $j, $s; $j -= $s; + } + elsif ($_[$i] =~ /^(l|lib|try|only)$/) + { + # 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-existant..." + splice @a, $j, $s; $j -= $s; $i++; + } + elsif ($_[$i] =~ /^(a|accuracy)$/) + { + $a = $_[$i+1]; + my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." + splice @a, $j, $s; $j -= $s; $i++; + } + elsif ($_[$i] =~ /^(p|precision)$/) + { + $p = $_[$i+1]; + my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." + splice @a, $j, $s; $j -= $s; $i++; + } + elsif ($_[$i] =~ /^(v|version)$/) + { + $ver = 1; + splice @a, $j, 1; $j --; + } + elsif ($_[$i] =~ /^(t|trace)$/) + { + $trace = 1; + splice @a, $j, 1; $j --; + } + elsif ($_[$i] eq 'hex') + { + splice @a, $j, 1; $j --; + $hex = \&bigint::_hex_global; + } + elsif ($_[$i] eq 'oct') + { + splice @a, $j, 1; $j --; + $oct = \&bigint::_oct_global; + } + elsif ($_[$i] !~ /^(PI|e|bpi|bexp)\z/) + { + die ("unknown option $_[$i]"); + } + } + 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 $p) # rounding won't work to well + { + eval 'require Math::BigInt::Lite;'; + if ($@ eq '') + { + @import = ( ); # :constant in Lite, not MBI + Math::BigInt::Lite->import( ':constant' ); + $_lite= 1; # signal okay + } + } + 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 => $upgrade); + + require Math::BigFloat; + Math::BigFloat->import( upgrade => 'Math::BigRat', ':constant' ); + require Math::BigRat; + + bigrat->accuracy($a) if defined $a; + bigrat->precision($p) if defined $p; + if ($ver) + { + print "bigrat\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$Math::BigFloat::VERSION\n"; + print "Math::BigRat\t\t v$Math::BigRat::VERSION\n"; + exit; + } + + # Take care of octal/hexadecimal constants + overload::constant binary => sub { bigint::_binary_constant(shift) }; + + # if another big* was already loaded: + my ($package) = caller(); + + no strict 'refs'; + if (!defined *{"${package}::inf"}) + { + $self->export_to_level(1,$self,@a); # export inf and NaN + } + { + no warnings 'redefine'; + *CORE::GLOBAL::oct = $oct if $oct; + *CORE::GLOBAL::hex = $hex if $hex; + } + } + +sub PI () { Math::BigFloat->new('3.141592653589793238462643383279502884197'); } +sub e () { Math::BigFloat->new('2.718281828459045235360287471352662497757'); } + +sub bpi ($) { local $Math::BigFloat::upgrade; Math::BigFloat::bpi(@_); } + +sub bexp ($$) + { + local $Math::BigFloat::upgrade; + my $x = Math::BigFloat->new($_[0]); $x->bexp($_[1]); + } + +1; + +__END__ + +=head1 NAME + +bigrat - Transparent BigNumber/BigRational support for Perl + +=head1 SYNOPSIS + + use bigrat; + + print 2 + 4.5,"\n"; # BigFloat 6.5 + print 1/3 + 1/4,"\n"; # produces 7/12 + + { + no bigrat; + print 1/3,"\n"; # 0.33333... + } + + # Note that this will make hex() and oct() be globally overriden: + use bigrat qw/hex oct/; + print hex("0x1234567890123490"),"\n"; + print oct("01234567890123490"),"\n"; + +=head1 DESCRIPTION + +All operators (including basic math operations) are overloaded. Integer and +floating-point constants are created as proper BigInts or BigFloats, +respectively. + +Other than L<bignum>, this module upgrades to Math::BigRat, meaning that +instead of 2.5 you will get 2+1/2 as output. + +=head2 Modules Used + +C<bigrat> 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 + Math::BigRat + +=head2 Math Library + +Math with the numbers is done (by default) by a module called +Math::BigInt::Calc. This is equivalent to saying: + + use bigrat 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 when 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 and +L<Math::BigInt> did fall back to one of the default libraries. +To supress 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: + + use bignum only => 'GMP'; + +Please see respective module documentation for further details. + +=head2 Sign + +The sign is either '+', '-', 'NaN', '+inf' or '-inf'. + +A sign of 'NaN' is used to represent the result when input arguments are not +numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively +minus infinity. You will get '+inf' when dividing a positive number by 0, and +'-inf' when dividing any negative number by 0. + +=head2 Methods + +Since all numbers are not 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 you independed on the fact that the +underlying object might morph into a different class than BigFloat. + +=over 2 + +=item inf() + +A shortcut to return Math::BigInt->binf(). 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 +handle 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 wanted accuracy. + +Example: + + # perl -Mbigrat=bexp -wle 'print bexp(1,80)' + +=item bpi() + + bpi($accuracy); + +Returns PI to the wanted accuracy. + +Example: + + # perl -Mbigrat=bpi -wle 'print bpi(80)' + +=item upgrade() + +Return the class that numbers are upgraded to, is in fact returning +C<$Math::BigInt::upgrade>. + +=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 + +=head2 MATH LIBRARY + +Math with the numbers is done (by default) by a module called + +=head2 Cavaet + +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; + +If you want to make a real copy, use the following: + + $y = $x->copy(); + +Using the copy or the original with overloaded math is okay, e.g. the +following work: + + $x = 9; $y = $x; + print $x + 1, " ", $y,"\n"; # prints 10 9 + +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->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 18 + +Using methods that do not modify, but testthe contents works: + + $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 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: + +=over 2 + +=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. + + perl -Mbigrat=a,50 -le 'print sqrt(20)' + +Note that setting precision and accurary 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. + + perl -Mbigrat=p,-50 -le 'print sqrt(20)' + +Note that setting precision and accurary 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 + +Load a different math lib, see L<MATH LIBRARY>. + + perl -Mbigrat=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 ;) + +=item hex + +Override the built-in hex() method with a version that can handle big +integers. Note that under Perl v5.9.4 or ealier, this will be global +and cannot be disabled with "no bigint;". + +=item oct + +Override the built-in oct() method with a version that can handle big +integers. Note that under Perl v5.9.4 or ealier, this will be global +and cannot be disabled with "no bigint;". + +=item v or version + +This prints out the name and version of all modules used and then exits. + + perl -Mbigrat=v + +=back + +=head1 CAVAETS + +=over 2 + +=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": + + use bigint qw/hex oct/; + + 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; + + # 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 -Mbignum=l,GMP -le 'print 7 ** 7777' + +=head1 LICENSE + +This program is free software; you may redistribute it and/or modify it under +the same terms as Perl itself. + +=head1 SEE ALSO + +Especially L<bignum>. + +L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well +as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. + +=head1 AUTHORS + +(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007. + +=cut |