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=encoding utf8 |
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=head1 NAME |
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Number::Fraction - Perl extension to model fractions |
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=head1 SYNOPSIS |
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use Number::Fraction; |
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my $f1 = Number::Fraction->new(1, 2); |
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my $f2 = Number::Fraction->new('1/2'); |
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my $f3 = Number::Fraction->new($f1); # clone |
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my $f4 = Number::Fraction->new; # 0/1 |
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or |
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use Number::Fraction ':constants'; |
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my $f1 = '1/2'; |
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my $f2 = $f1; |
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my $one = $f1 + $f2; |
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my $half = $one - $f1; |
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print $half; # prints '1/2' |
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or some famous examples from Ovid or the perldoc |
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use Number::Fraction ':constants'; |
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print '0.1' + '0.2' - '0.3'; |
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# except for perl6, this is the usual suspect 5.55111512312578e-17 |
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# times the mass of the sun, this would be the size of Mount Everest |
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# just a small rounding difference |
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my $f1 = Number::Fraction->new(-6.725); |
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my $f2 = Number::Fraction->new( 0.025); |
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print int $f1/$f2; |
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# the correct -269, no internal -268.99999999999994315658 |
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and as of the latest release with unicode support |
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my $f1 = Number::Fraction->new('3½'); |
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my $f2 = Number::Fraction->new(4.33); |
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my $f0 = $f1 * $f2; |
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print $f0->to_simple; # 15⅙ |
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and for those who love pie |
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print '3.14159265359'->nearest(1 .. 10)->to_unicode_mixed # 3¹⁄₇ |
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print '3.14159265359'->nearest(1 .. 1000)->to_unicode_string # ³⁵⁵⁄₁₁₃ |
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=head1 ABSTRACT |
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Number::Fraction is a Perl module which allows you to work with fractions |
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in your Perl programs. |
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=head1 DESCRIPTION |
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Number::Fraction allows you to work with fractions (i.e. rational |
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numbers) in your Perl programs in a very natural way. |
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It was originally written as a demonstration of the techniques of |
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overloading. |
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If you use the module in your program in the usual way |
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use Number::Fraction; |
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you can then create fraction objects using Cnew> in |
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a number of ways. |
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my $f1 = Number::Fraction->new(1, 2); |
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creates a fraction with a numerator of 1 and a denominator of 2. |
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my $fm = Number::Fraction->new(1, 2, 3); |
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creates a fraction from an integer of 1, a numerator of 2 and a denominator |
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of 3; which results in a fraction of 5/3 since fractions are normalised. |
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85
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my $f2 = Number::Fraction->new('1/2'); |
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does the same thing but from a string constant. |
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my $f3 = Number::Fraction->new($f1); |
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makes C<$f3> a copy of C<$f1> |
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my $f4 = Number::Fraction->new; # 0/1 |
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creates a fraction with a denominator of 0 and a numerator of 1. |
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If you use the alterative syntax of |
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use Number::Fraction ':constants'; |
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101
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then Number::Fraction will automatically create fraction objects from |
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string constants in your program. Any time your program contains a |
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string constant of the form C<\d+/\d+> then that will be automatically |
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replaced with the equivalent fraction object. For example |
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my $f1 = '1/2'; |
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Having created fraction objects you can manipulate them using most of the |
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normal mathematical operations. |
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my $one = $f1 + $f2; |
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my $half = $one - $f1; |
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114
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Additionally, whenever a fraction object is evaluated in a string |
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context, it will return a string in the format x/y. When a fraction |
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object is evaluated in a numerical context, it will return a floating |
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point representation of its value. |
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Fraction objects will always "normalise" themselves. That is, if you |
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create a fraction of '2/4', it will silently be converted to '1/2'. |
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=head2 Mixed Fractions and Unicode Support |
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Since version 3.0 the interpretation of strings and constants has been |
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enriched with a few features for mixed fractions and Unicode characters. |
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Number::Fraction now recognises a more Perlish way of entering mixed |
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fractions which consist of an integer-part and a fraction in the form of |
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C<\d+_\d+/\d+>. For example |
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my $mixed = '2_3/4'; # two and three fourths, stored as 11/4 |
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or |
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my $simple = '2½'; # two and a half, stored as 5/2 |
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Mixed fractions, either in Perl notation or with Unicode fractions can |
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be negative, prepending it with a minus-sign. |
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my $negative = '-⅛'; # minus one eighth |
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=head2 Experimental Support for Exponentiation |
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Version 1.13 of Number::Fraction adds experimental support for exponentiation |
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operations. Version 3 has extended support and returns a Number::Fraction. |
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It does a lot of cheating, but can give very useful results. And for now will |
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try to make a real number into a Number::Fraction if that real does not have a |
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power of ten component (like 1.234e45, thes numbers will simply fail). Such that |
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('5⅞' ** '1¼') ** '⅘' |
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will produce still the right fraction! |
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In a future version, I might use automatic rounding to a optional accuracy, so |
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that it also works for less forced examples as the above. One could still use |
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C to find the nearest fraction to the result of the previous |
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computation. |
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For example: |
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'1/2' ** 2 # Returns a Number::Fraction ('1/4') |
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'2/1' ** '2/1' Returns a Number::Fraction ('4/1') |
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'2/1' ** '1/2' Returns a real number (1.414213) |
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0.5 ** '2/1' Returns a Number::Fraction ('1/4') |
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0.25 ** '1/2' Returns a Number::Fraction ('1/2') |
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=head2 Version 3: Now With Added Moo |
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Version 3 of Number::Fraction has been reimplemented using Moo. You should |
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see very little difference in the way that the class works. The only difference |
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I can see is that C used to return C if it couldn't create a valid |
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object from its arguments, it now dies. If you aren't sure of the values that |
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are being passed into the constructor, then you'll want to call it within an |
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C block (or using something equivalent like L). |
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=head1 METHODS |
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179
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=cut |
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package Number::Fraction; |
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use 5.010; |
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use strict; |
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use warnings; |
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use Carp; |
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use Moo; |
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use MooX::Types::MooseLike::Base qw/Int/; |
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our $VERSION = '3.0.4'; |
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my $_mixed = 0; |
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our $MIXED_SEP = "\N{U+00A0}"; # NO-BREAK SPACE |
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use overload |
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q("") => 'to_string', |
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'0+' => 'to_num', |
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'+' => 'add', |
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'*' => 'mult', |
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'-' => 'subtract', |
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'/' => 'div', |
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'**' => 'exp', |
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'abs' => 'abs', |
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'<' => '_frac_lt', |
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'>' => '_frac_gt', |
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'<=>' => '_frac_cmp', |
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fallback => 1; |
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my %_const_handlers = ( |
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q => sub { |
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my $f = eval { __PACKAGE__->new($_[0]) }; |
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return $_[1] if $@; |
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return $f; |
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} |
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); |
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=head2 import |
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Called when module is C |
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handler. |
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=cut |
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sub import { |
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my %args = map { $_ => 1 } @_; |
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$_mixed = exists $args{':mixed'}; |
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overload::constant %_const_handlers if $args{':constants'}; |
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} |
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=head2 unimport |
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Be a good citizen and uninstall constant handler when caller uses |
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C. |
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=cut |
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sub unimport { |
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1
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1
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overload::remove_constant(q => undef); |
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1
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$_mixed = undef; |
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} |
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has num => ( |
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is => 'rw', |
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isa => Int, |
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); |
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has den => ( |
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is => 'rw', |
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isa => Int, |
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); |
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=head2 BUILDARGS |
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Parameter massager for Number::Fraction object. Takes the following kinds of |
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parameters: |
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=over 4 |
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=item * |
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A single Number::Fraction object which is cloned. |
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=item * |
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A string in the form 'x/y' where x and y are integers. x is used as the |
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numerator and y is used as the denominator of the new object. |
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A string in the form 'a_b/c' where a,b and c are integers. |
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The numerator will be equal to a*c+b! |
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and c is used as the denominator of the new object. |
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=item * |
275
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276
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Three integers which are used as the integer, numerator and denominator of the |
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new object. |
278
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In order for this to work in version 2.x, |
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one needs to enable 'mixed' fractions: |
281
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282
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use Number::Fractions ':mixed'; |
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284
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This will be the default behaviour in version 3.x; |
285
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when not enabled in version 2.x it will omit a warning to revise your code. |
286
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287
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=item * |
288
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289
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Two integers which are used as the numerator and denominator of the |
290
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new object. |
291
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292
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=item * |
293
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294
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A single integer which is used as the numerator of the the new object. |
295
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The denominator is set to 1. |
296
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297
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=item * |
298
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299
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No arguments, in which case a numerator of 0 and a denominator of 1 |
300
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are used. |
301
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302
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=item * |
303
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304
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Note |
305
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306
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As of version 2.1 it no longer allows for an array of four or more integer. |
307
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Before then, it would simply pass in the first two integers. Version 2.1 allows |
308
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for three integers (when using C<:mixed>) and issues a warning when more then |
309
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two parameters are passed. |
310
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Starting with version 3, it will die as it is seen as an error to pass invalid |
311
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input. |
312
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313
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=back |
314
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315
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Dies if a Number::Fraction object can't be created. |
316
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317
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=cut |
318
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319
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|
our @_vulgar_fractions = ( |
320
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+00BC}\z|, num=>1, den=>4}, |
321
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+00BD}\z|, num=>1, den=>2}, |
322
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+00BE}\z|, num=>3, den=>4}, |
323
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+2153}\z|, num=>1, den=>3}, |
324
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+2154}\z|, num=>2, den=>3}, |
325
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+2155}\z|, num=>1, den=>5}, |
326
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+2156}\z|, num=>2, den=>5}, |
327
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+2157}\z|, num=>3, den=>5}, |
328
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+2158}\z|, num=>4, den=>5}, |
329
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+2159}\z|, num=>1, den=>6}, |
330
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+215A}\z|, num=>5, den=>6}, |
331
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+215B}\z|, num=>1, den=>8}, |
332
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+215C}\z|, num=>3, den=>8}, |
333
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+215D}\z|, num=>5, den=>8}, |
334
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{regexp=> qr|^(?-?)(?[0-9]+)?\N{U+215E}\z|, num=>7, den=>8}, |
335
|
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|
); |
336
|
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337
|
|
|
|
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|
|
our %_vulgar_codepoints = ( |
338
|
|
|
|
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|
|
'1/4' => "\N{U+00BC}", |
339
|
|
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|
'1/2' => "\N{U+00BD}", |
340
|
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|
'3/4' => "\N{U+00BE}", |
341
|
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|
'1/3' => "\N{U+2153}", |
342
|
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|
'2/3' => "\N{U+2154}", |
343
|
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|
'1/5' => "\N{U+2155}", |
344
|
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|
'2/5' => "\N{U+2156}", |
345
|
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|
'3/5' => "\N{U+2157}", |
346
|
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|
'4/5' => "\N{U+2158}", |
347
|
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|
'1/6' => "\N{U+2159}", |
348
|
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|
'5/6' => "\N{U+215A}", |
349
|
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|
'1/8' => "\N{U+215B}", |
350
|
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|
'3/8' => "\N{U+215C}", |
351
|
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|
'5/8' => "\N{U+215D}", |
352
|
|
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|
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|
|
'7/8' => "\N{U+215E}", |
353
|
|
|
|
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|
|
); |
354
|
|
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|
355
|
|
|
|
|
|
|
around BUILDARGS => sub { |
356
|
|
|
|
|
|
|
my $orig = shift; |
357
|
|
|
|
|
|
|
my $class = shift; |
358
|
|
|
|
|
|
|
if (@_ > 3) { |
359
|
|
|
|
|
|
|
croak "Revise your code: too many arguments will raise an exception"; |
360
|
|
|
|
|
|
|
} |
361
|
|
|
|
|
|
|
if (@_ == 3) { |
362
|
|
|
|
|
|
|
if ( $_mixed ) { |
363
|
|
|
|
|
|
|
croak "integer, numerator and denominator need to be integers" |
364
|
|
|
|
|
|
|
unless $_[0] =~ /^-?[0-9]+\z/ |
365
|
|
|
|
|
|
|
and $_[1] =~ /^-?[0-9]+\z/ |
366
|
|
|
|
|
|
|
and $_[2] =~ /^-?[0-9]+\z/; |
367
|
|
|
|
|
|
|
|
368
|
|
|
|
|
|
|
return $class->$orig({ num => $_[0] * $_[2] + $_[1], den => $_[2] }); |
369
|
|
|
|
|
|
|
} |
370
|
|
|
|
|
|
|
else { |
371
|
|
|
|
|
|
|
croak "Revise your code: 3 arguments is a mixed-fraction feature!"; |
372
|
|
|
|
|
|
|
} |
373
|
|
|
|
|
|
|
} |
374
|
|
|
|
|
|
|
if (@_ >= 2) { |
375
|
|
|
|
|
|
|
croak "numerator and denominator both need to be integers" |
376
|
|
|
|
|
|
|
unless $_[0] =~ /^-?[0-9]+\z/ and $_[1] =~ /^-?[0-9]+\z/; |
377
|
|
|
|
|
|
|
# fix: regex string representation and the real number can be different |
378
|
|
|
|
|
|
|
my $num = sprintf( "%.0f", $_[0]); |
379
|
|
|
|
|
|
|
my $den = sprintf( "%.0f", $_[1]); |
380
|
|
|
|
|
|
|
return $class->$orig({ num => $num, den => $den }); |
381
|
|
|
|
|
|
|
} elsif (@_ == 1) { |
382
|
|
|
|
|
|
|
if (ref $_[0]) { |
383
|
|
|
|
|
|
|
if (UNIVERSAL::isa($_[0], $class)) { |
384
|
|
|
|
|
|
|
return $class->$orig({ num => $_[0]->{num}, den => $_[0]->{den} }); |
385
|
|
|
|
|
|
|
} else { |
386
|
|
|
|
|
|
|
croak "Can't make a $class from a ", ref $_[0]; |
387
|
|
|
|
|
|
|
} |
388
|
|
|
|
|
|
|
} |
389
|
|
|
|
|
|
|
|
390
|
|
|
|
|
|
|
for (@_vulgar_fractions) { # provides $_->{num} and $_->{den} |
391
|
|
|
|
|
|
|
if ($_[0] =~ m/$_->{regexp}/ ) { |
392
|
|
|
|
|
|
|
return $class->$orig({ |
393
|
14
|
|
|
14
|
|
29470
|
num => (defined $+{int} ? $+{int} : 0) * $_->{den} + $_->{num}, |
|
14
|
|
|
|
|
6263
|
|
|
14
|
|
|
|
|
43369
|
|
394
|
|
|
|
|
|
|
den => ($+{sign} eq '-') ? $_->{den} * -1 : $_->{den}, |
395
|
|
|
|
|
|
|
} |
396
|
|
|
|
|
|
|
); |
397
|
|
|
|
|
|
|
} |
398
|
|
|
|
|
|
|
} |
399
|
|
|
|
|
|
|
|
400
|
|
|
|
|
|
|
# check for unicode mixed super/sub scripted strings |
401
|
|
|
|
|
|
|
if ($_[0] =~ m| |
402
|
|
|
|
|
|
|
^ |
403
|
|
|
|
|
|
|
(?-?) |
404
|
|
|
|
|
|
|
(?[0-9]+)? |
405
|
|
|
|
|
|
|
(?[\N{U+2070}\N{U+00B9}\N{U+00B2}\N{U+00B3}\N{U+2074}-\N{U+207B}]+) |
406
|
|
|
|
|
|
|
\N{U+2044} # FRACTION SLASH |
407
|
|
|
|
|
|
|
(?[\N{U+2080}-\N{U+208B}]+) |
408
|
|
|
|
|
|
|
\z |
409
|
|
|
|
|
|
|
|x ) { |
410
|
|
|
|
|
|
|
my $num = _sup_to_basic($+{num}); |
411
|
|
|
|
|
|
|
my $den = _sub_to_basic($+{den}); |
412
|
|
|
|
|
|
|
return $class->$orig({ |
413
|
|
|
|
|
|
|
num => (defined $+{int} ? $+{int} : 0) * $den + $num, |
414
|
|
|
|
|
|
|
den => ($+{sign} eq '-') ? $den * -1 : $den, |
415
|
|
|
|
|
|
|
} |
416
|
|
|
|
|
|
|
); |
417
|
|
|
|
|
|
|
} |
418
|
|
|
|
|
|
|
|
419
|
|
|
|
|
|
|
# check for floating point |
420
|
|
|
|
|
|
|
elsif ($_[0] =~ m| |
421
|
|
|
|
|
|
|
^ |
422
|
|
|
|
|
|
|
(?-?) |
423
|
|
|
|
|
|
|
(?[0-9]+)? |
424
|
|
|
|
|
|
|
[.,] # yep, lets do bdecimal point or comma |
425
|
|
|
|
|
|
|
(?[0-9]+) |
426
|
|
|
|
|
|
|
\z |
427
|
|
|
|
|
|
|
|x ) { |
428
|
|
|
|
|
|
|
my $num = $+{num}; |
429
|
|
|
|
|
|
|
my $den = 10 ** length($+{num}); |
430
|
|
|
|
|
|
|
return $class->$orig({ |
431
|
|
|
|
|
|
|
num => (defined $+{int} ? $+{int} : 0) * $den + $num, |
432
|
|
|
|
|
|
|
den => ($+{sign} eq '-') ? $den * -1 : $den, |
433
|
|
|
|
|
|
|
} |
434
|
|
|
|
|
|
|
); |
435
|
|
|
|
|
|
|
} |
436
|
|
|
|
|
|
|
|
437
|
|
|
|
|
|
|
if ($_[0] =~ m|^(-?)([0-9]+)[_ \N{U+00A0}]([0-9]+)/([0-9]+)\z|) { |
438
|
|
|
|
|
|
|
return $class->$orig({ |
439
|
|
|
|
|
|
|
num => $2 * $4 + $3, |
440
|
|
|
|
|
|
|
den=> ($1 eq '-') ? $4 * -1 : $4} |
441
|
|
|
|
|
|
|
); |
442
|
|
|
|
|
|
|
} elsif ($_[0] =~ m|^(-?[0-9]+)(?:/(-?[0-9]+))?\z|) { |
443
|
|
|
|
|
|
|
return $class->$orig({ num => $1, den => ( defined $2 ? $2 : 1) }); |
444
|
|
|
|
|
|
|
} else { |
445
|
|
|
|
|
|
|
croak "Can't make fraction out of $_[0]\n"; |
446
|
|
|
|
|
|
|
} |
447
|
|
|
|
|
|
|
} else { |
448
|
|
|
|
|
|
|
return $class->$orig({ num => 0, den => 1 }); |
449
|
|
|
|
|
|
|
} |
450
|
|
|
|
|
|
|
}; |
451
|
|
|
|
|
|
|
|
452
|
|
|
|
|
|
|
=head2 BUILD |
453
|
|
|
|
|
|
|
|
454
|
|
|
|
|
|
|
Object initialiser for Number::Fraction. Ensures that fractions are in a |
455
|
|
|
|
|
|
|
normalised format. |
456
|
|
|
|
|
|
|
|
457
|
|
|
|
|
|
|
=cut |
458
|
|
|
|
|
|
|
|
459
|
|
|
|
|
|
|
sub BUILD { |
460
|
210
|
|
|
210
|
1
|
22717
|
my $self = shift; |
461
|
210
|
100
|
|
|
|
900
|
croak "Denominator can't be equal to zero" if $self->{den} == 0; |
462
|
208
|
|
|
|
|
459
|
$self->_normalise; |
463
|
|
|
|
|
|
|
} |
464
|
|
|
|
|
|
|
|
465
|
|
|
|
|
|
|
sub _normalise { |
466
|
208
|
|
|
208
|
|
294
|
my $self = shift; |
467
|
|
|
|
|
|
|
|
468
|
208
|
|
|
|
|
514
|
my $hcf = _hcf($self->{num}, $self->{den}); |
469
|
|
|
|
|
|
|
|
470
|
208
|
|
|
|
|
491
|
for (qw/num den/) { |
471
|
416
|
|
|
|
|
848
|
$self->{$_} /= $hcf; |
472
|
|
|
|
|
|
|
} |
473
|
|
|
|
|
|
|
|
474
|
208
|
100
|
|
|
|
1162
|
if ($self->{den} < 0) { |
475
|
5
|
|
|
|
|
11
|
for (qw/num den/) { |
476
|
10
|
|
|
|
|
43
|
$self->{$_} *= -1; |
477
|
|
|
|
|
|
|
} |
478
|
|
|
|
|
|
|
} |
479
|
|
|
|
|
|
|
} |
480
|
|
|
|
|
|
|
|
481
|
|
|
|
|
|
|
=head2 to_string |
482
|
|
|
|
|
|
|
|
483
|
|
|
|
|
|
|
Returns a string representation of the fraction in the form |
484
|
|
|
|
|
|
|
"numerator/denominator". |
485
|
|
|
|
|
|
|
|
486
|
|
|
|
|
|
|
=cut |
487
|
|
|
|
|
|
|
|
488
|
|
|
|
|
|
|
sub to_string { |
489
|
120
|
|
|
120
|
1
|
9696
|
my $self = shift; |
490
|
|
|
|
|
|
|
|
491
|
120
|
100
|
|
|
|
544
|
return $self->{num} if $self->{den} == 1; |
492
|
97
|
|
|
|
|
2398
|
return $self->{num} . '/' . $self->{den}; |
493
|
|
|
|
|
|
|
} |
494
|
|
|
|
|
|
|
|
495
|
|
|
|
|
|
|
|
496
|
|
|
|
|
|
|
=head2 to_mixed |
497
|
|
|
|
|
|
|
|
498
|
|
|
|
|
|
|
Returns a string representation of the fraction in the form |
499
|
|
|
|
|
|
|
"integer numerator/denominator". |
500
|
|
|
|
|
|
|
|
501
|
|
|
|
|
|
|
=cut |
502
|
|
|
|
|
|
|
|
503
|
|
|
|
|
|
|
sub to_mixed { |
504
|
0
|
|
|
0
|
1
|
0
|
my $self = shift; |
505
|
|
|
|
|
|
|
|
506
|
0
|
0
|
|
|
|
0
|
return $self->{num} if $self->{den} == 1; |
507
|
|
|
|
|
|
|
|
508
|
0
|
0
|
|
|
|
0
|
my $sgn = $self->{num} * $self->{den} < 0 ? '-' : ''; |
509
|
0
|
|
|
|
|
0
|
my $abs = $self->abs; |
510
|
0
|
|
|
|
|
0
|
my $int = int($abs->{num} / $abs->{den}); |
511
|
0
|
0
|
|
|
|
0
|
$int = $int ? $int . $MIXED_SEP : ''; |
512
|
|
|
|
|
|
|
|
513
|
0
|
|
|
|
|
0
|
return $sgn . $int . $abs->fract->to_string; |
514
|
|
|
|
|
|
|
} |
515
|
|
|
|
|
|
|
|
516
|
|
|
|
|
|
|
|
517
|
|
|
|
|
|
|
=head2 to_unicode_string |
518
|
|
|
|
|
|
|
|
519
|
|
|
|
|
|
|
Returns a string representation of the fraction in the form |
520
|
|
|
|
|
|
|
"superscript numerator / subscript denominator". |
521
|
|
|
|
|
|
|
A Unicode 'FRACTION SLASH' is used instead of a normal slash. |
522
|
|
|
|
|
|
|
|
523
|
|
|
|
|
|
|
=cut |
524
|
|
|
|
|
|
|
|
525
|
|
|
|
|
|
|
sub to_unicode_string { |
526
|
0
|
|
|
0
|
1
|
0
|
return _to_unicode(shift->to_string); |
527
|
|
|
|
|
|
|
} |
528
|
|
|
|
|
|
|
|
529
|
|
|
|
|
|
|
|
530
|
|
|
|
|
|
|
=head2 to_unicode_mixed |
531
|
|
|
|
|
|
|
|
532
|
|
|
|
|
|
|
Returns a string representation of the fraction in the form |
533
|
|
|
|
|
|
|
"integer superscript numerator / subscript denominator". |
534
|
|
|
|
|
|
|
A Unicode 'FRACTION SLASH' is used instead of a normal slash. |
535
|
|
|
|
|
|
|
|
536
|
|
|
|
|
|
|
=cut |
537
|
|
|
|
|
|
|
|
538
|
|
|
|
|
|
|
sub to_unicode_mixed { |
539
|
0
|
|
|
0
|
1
|
0
|
return _to_unicode(shift->to_mixed); |
540
|
|
|
|
|
|
|
} |
541
|
|
|
|
|
|
|
|
542
|
|
|
|
|
|
|
|
543
|
|
|
|
|
|
|
=head2 to_halfs |
544
|
|
|
|
|
|
|
|
545
|
|
|
|
|
|
|
=head2 to_quarters |
546
|
|
|
|
|
|
|
|
547
|
|
|
|
|
|
|
=head2 to_eighths |
548
|
|
|
|
|
|
|
|
549
|
|
|
|
|
|
|
=head2 to_thirds |
550
|
|
|
|
|
|
|
|
551
|
|
|
|
|
|
|
=head2 to_sixths |
552
|
|
|
|
|
|
|
|
553
|
|
|
|
|
|
|
=head2 to_fifths |
554
|
|
|
|
|
|
|
|
555
|
|
|
|
|
|
|
Returns a string representation as a mixed fraction, rounded to the nearest |
556
|
|
|
|
|
|
|
possible 'half', 'quarter' ... and so on. |
557
|
|
|
|
|
|
|
|
558
|
|
|
|
|
|
|
=cut |
559
|
|
|
|
|
|
|
|
560
|
0
|
|
|
0
|
1
|
0
|
sub to_halfs { return shift->to_simple(2) } |
561
|
|
|
|
|
|
|
|
562
|
0
|
|
|
0
|
1
|
0
|
sub to_thirds { return shift->to_simple(3) } |
563
|
|
|
|
|
|
|
|
564
|
0
|
|
|
0
|
1
|
0
|
sub to_quarters { return shift->to_simple(4) } |
565
|
|
|
|
|
|
|
|
566
|
0
|
|
|
0
|
1
|
0
|
sub to_fifths { return shift->to_simple(5) } |
567
|
|
|
|
|
|
|
|
568
|
0
|
|
|
0
|
1
|
0
|
sub to_sixths { return shift->to_simple(6) } |
569
|
|
|
|
|
|
|
|
570
|
0
|
|
|
0
|
1
|
0
|
sub to_eighths { return shift->to_simple(8) } |
571
|
|
|
|
|
|
|
|
572
|
|
|
|
|
|
|
# Typo retained for backwards compatibility |
573
|
0
|
|
|
0
|
0
|
0
|
sub to_eights { return shift->to_eighths } |
574
|
|
|
|
|
|
|
|
575
|
|
|
|
|
|
|
=head2 to_simple |
576
|
|
|
|
|
|
|
|
577
|
|
|
|
|
|
|
Returns a string representation as a mixed fraction, rounded to the nearest |
578
|
|
|
|
|
|
|
possible to any of the above mentioned standard fractions. NB ⅐, ⅑ or ⅒ are not |
579
|
|
|
|
|
|
|
being used. |
580
|
|
|
|
|
|
|
|
581
|
|
|
|
|
|
|
Optionally, one can pass in a list of well-known denominators (2, 3, 4, 5, 6, 8) |
582
|
|
|
|
|
|
|
to choose which fractions can be used. |
583
|
|
|
|
|
|
|
|
584
|
|
|
|
|
|
|
=cut |
585
|
|
|
|
|
|
|
|
586
|
|
|
|
|
|
|
sub to_simple { |
587
|
0
|
|
|
0
|
1
|
0
|
my $self = shift; |
588
|
0
|
|
|
|
|
0
|
my @denominators = @_; |
589
|
|
|
|
|
|
|
|
590
|
0
|
0
|
|
|
|
0
|
@denominators = ( 2, 3, 4, 5, 6, 8) unless @denominators; |
591
|
|
|
|
|
|
|
|
592
|
0
|
|
|
|
|
0
|
my $near = $self->nearest(@denominators); |
593
|
|
|
|
|
|
|
|
594
|
0
|
0
|
|
|
|
0
|
return $near->{num} if $near->{den} == 1; |
595
|
|
|
|
|
|
|
|
596
|
0
|
0
|
|
|
|
0
|
my $sgn = $near->{num} * $near->{den} < 0 ? '-' : ''; |
597
|
0
|
|
|
|
|
0
|
my $abs = $near->abs; |
598
|
0
|
|
|
|
|
0
|
my $key = $abs->fract->to_string; |
599
|
0
|
|
|
|
|
0
|
my $frc = $_vulgar_codepoints{$key}; |
600
|
0
|
0
|
|
|
|
0
|
unless ( $frc ) { |
601
|
0
|
|
|
|
|
0
|
carp "not a recognised unicode fraction symbol [$key]\n"; |
602
|
0
|
|
|
|
|
0
|
return $near->to_unicode_mixed; |
603
|
|
|
|
|
|
|
} |
604
|
0
|
|
0
|
|
|
0
|
my $int = int($abs->{num} / $abs->{den}) || ''; |
605
|
|
|
|
|
|
|
|
606
|
0
|
|
|
|
|
0
|
return $sgn . $int . $frc; |
607
|
|
|
|
|
|
|
} |
608
|
|
|
|
|
|
|
|
609
|
|
|
|
|
|
|
=head2 to_num |
610
|
|
|
|
|
|
|
|
611
|
|
|
|
|
|
|
Returns a numeric representation of the fraction by calculating the sum |
612
|
|
|
|
|
|
|
numerator/denominator. Normal caveats about the precision of floating |
613
|
|
|
|
|
|
|
point numbers apply. |
614
|
|
|
|
|
|
|
|
615
|
|
|
|
|
|
|
=cut |
616
|
|
|
|
|
|
|
|
617
|
|
|
|
|
|
|
sub to_num { |
618
|
21
|
|
|
21
|
1
|
42
|
my $self = shift; |
619
|
|
|
|
|
|
|
|
620
|
21
|
|
|
|
|
162
|
return $self->{num} / $self->{den}; |
621
|
|
|
|
|
|
|
} |
622
|
|
|
|
|
|
|
|
623
|
|
|
|
|
|
|
=head2 add |
624
|
|
|
|
|
|
|
|
625
|
|
|
|
|
|
|
Add a value to a fraction object and return a new object representing the |
626
|
|
|
|
|
|
|
result of the calculation. |
627
|
|
|
|
|
|
|
|
628
|
|
|
|
|
|
|
The first parameter is a fraction object. The second parameter is either |
629
|
|
|
|
|
|
|
another fraction object or a number. |
630
|
|
|
|
|
|
|
|
631
|
|
|
|
|
|
|
=cut |
632
|
|
|
|
|
|
|
|
633
|
|
|
|
|
|
|
sub add { |
634
|
12
|
|
|
12
|
1
|
192
|
my ($l, $r, $rev) = @_; |
635
|
|
|
|
|
|
|
|
636
|
12
|
100
|
|
|
|
40
|
if (ref $r) { |
637
|
10
|
100
|
|
|
|
58
|
if (UNIVERSAL::isa($r, ref $l)) { |
638
|
|
|
|
|
|
|
return (ref $l)->new($l->{num} * $r->{den} + $r->{num} * $l->{den}, |
639
|
9
|
|
|
|
|
302
|
$r->{den} * $l->{den}); |
640
|
|
|
|
|
|
|
} else { |
641
|
1
|
|
|
|
|
221
|
croak "Can't add a ", ref $l, " to a ", ref $l; |
642
|
|
|
|
|
|
|
} |
643
|
|
|
|
|
|
|
} else { |
644
|
2
|
100
|
|
|
|
21
|
if ($r =~ /^[-+]?\d+$/) { |
645
|
1
|
|
|
|
|
29
|
return $l + (ref $l)->new($r, 1); |
646
|
|
|
|
|
|
|
} else { |
647
|
1
|
|
|
|
|
6
|
return $l->to_num + $r; |
648
|
|
|
|
|
|
|
} |
649
|
|
|
|
|
|
|
} |
650
|
|
|
|
|
|
|
} |
651
|
|
|
|
|
|
|
|
652
|
|
|
|
|
|
|
=head2 mult |
653
|
|
|
|
|
|
|
|
654
|
|
|
|
|
|
|
Multiply a fraction object by a value and return a new object representing |
655
|
|
|
|
|
|
|
the result of the calculation. |
656
|
|
|
|
|
|
|
|
657
|
|
|
|
|
|
|
The first parameter is a fraction object. The second parameter is either |
658
|
|
|
|
|
|
|
another fraction object or a number. |
659
|
|
|
|
|
|
|
|
660
|
|
|
|
|
|
|
=cut |
661
|
|
|
|
|
|
|
|
662
|
|
|
|
|
|
|
sub mult { |
663
|
12
|
|
|
12
|
1
|
179
|
my ($l, $r, $rev) = @_; |
664
|
|
|
|
|
|
|
|
665
|
12
|
100
|
|
|
|
30
|
if (ref $r) { |
666
|
10
|
100
|
|
|
|
43
|
if (UNIVERSAL::isa($r, ref $l)) { |
667
|
|
|
|
|
|
|
return (ref $l)->new($l->{num} * $r->{num}, |
668
|
9
|
|
|
|
|
213
|
$l->{den} * $r->{den}); |
669
|
|
|
|
|
|
|
} else { |
670
|
1
|
|
|
|
|
182
|
croak "Can't multiply a ", ref $l, " by a ", ref $l; |
671
|
|
|
|
|
|
|
} |
672
|
|
|
|
|
|
|
} else { |
673
|
2
|
100
|
|
|
|
17
|
if ($r =~ /^[-+]?\d+$/) { |
674
|
1
|
|
|
|
|
25
|
return $l * (ref $l)->new($r, 1); |
675
|
|
|
|
|
|
|
} else { |
676
|
1
|
|
|
|
|
5
|
return $l->to_num * $r; |
677
|
|
|
|
|
|
|
} |
678
|
|
|
|
|
|
|
} |
679
|
|
|
|
|
|
|
} |
680
|
|
|
|
|
|
|
|
681
|
|
|
|
|
|
|
=head2 subtract |
682
|
|
|
|
|
|
|
|
683
|
|
|
|
|
|
|
Subtract a value from a fraction object and return a new object representing |
684
|
|
|
|
|
|
|
the result of the calculation. |
685
|
|
|
|
|
|
|
|
686
|
|
|
|
|
|
|
The first parameter is a fraction object. The second parameter is either |
687
|
|
|
|
|
|
|
another fraction object or a number. |
688
|
|
|
|
|
|
|
|
689
|
|
|
|
|
|
|
=cut |
690
|
|
|
|
|
|
|
|
691
|
|
|
|
|
|
|
sub subtract { |
692
|
15
|
|
|
15
|
1
|
171
|
my ($l, $r, $rev) = @_; |
693
|
|
|
|
|
|
|
|
694
|
15
|
100
|
|
|
|
38
|
if (ref $r) { |
695
|
11
|
100
|
|
|
|
46
|
if (UNIVERSAL::isa($r, ref $l)) { |
696
|
|
|
|
|
|
|
return (ref $l)->new($l->{num} * $r->{den} - $r->{num} * $l->{den}, |
697
|
10
|
|
|
|
|
242
|
$r->{den} * $l->{den}); |
698
|
|
|
|
|
|
|
} else { |
699
|
1
|
|
|
|
|
174
|
croak "Can't subtract a ", ref $l, " from a ", ref $l; |
700
|
|
|
|
|
|
|
} |
701
|
|
|
|
|
|
|
} else { |
702
|
4
|
100
|
|
|
|
32
|
if ($r =~ /^[-+]?\d+$/) { |
703
|
2
|
|
|
|
|
49
|
$r = (ref $l)->new($r, 1); |
704
|
2
|
100
|
|
|
|
11
|
return $rev ? $r - $l : $l - $r; |
705
|
|
|
|
|
|
|
} else { |
706
|
2
|
100
|
|
|
|
24
|
return $rev ? $r - $l->to_num : $l->to_num - $r; |
707
|
|
|
|
|
|
|
} |
708
|
|
|
|
|
|
|
} |
709
|
|
|
|
|
|
|
} |
710
|
|
|
|
|
|
|
|
711
|
|
|
|
|
|
|
=head2 div |
712
|
|
|
|
|
|
|
|
713
|
|
|
|
|
|
|
Divide a fraction object by a value and return a new object representing |
714
|
|
|
|
|
|
|
the result of the calculation. |
715
|
|
|
|
|
|
|
|
716
|
|
|
|
|
|
|
The first parameter is a fraction object. The second parameter is either |
717
|
|
|
|
|
|
|
another fraction object or a number. |
718
|
|
|
|
|
|
|
|
719
|
|
|
|
|
|
|
=cut |
720
|
|
|
|
|
|
|
|
721
|
|
|
|
|
|
|
sub div { |
722
|
16
|
|
|
16
|
1
|
496
|
my ($l, $r, $rev) = @_; |
723
|
|
|
|
|
|
|
|
724
|
16
|
100
|
|
|
|
40
|
if (ref $r) { |
725
|
12
|
100
|
|
|
|
49
|
if (UNIVERSAL::isa($r, ref $l)) { |
726
|
11
|
100
|
|
|
|
46
|
die "FATAL ERROR: Division by zero" if $r->{num} == 0; |
727
|
|
|
|
|
|
|
return (ref $l)->new($l->{num} * $r->{den}, |
728
|
10
|
|
|
|
|
228
|
$l->{den} * $r->{num}); |
729
|
|
|
|
|
|
|
} else { |
730
|
1
|
|
|
|
|
165
|
croak "Can't divide a ", ref $l, " by a ", ref $l; |
731
|
|
|
|
|
|
|
} |
732
|
|
|
|
|
|
|
} else { |
733
|
4
|
100
|
|
|
|
31
|
if ($r =~ /^[-+]?\d+$/) { |
734
|
2
|
|
|
|
|
47
|
$r = (ref $l)->new($r, 1); |
735
|
2
|
100
|
|
|
|
12
|
return $rev ? $r / $l : $l / $r; |
736
|
|
|
|
|
|
|
} else { |
737
|
2
|
100
|
|
|
|
11
|
return $rev ? $r / $l->to_num : $l->to_num / $r; |
738
|
|
|
|
|
|
|
} |
739
|
|
|
|
|
|
|
} |
740
|
|
|
|
|
|
|
} |
741
|
|
|
|
|
|
|
|
742
|
|
|
|
|
|
|
=head2 exp |
743
|
|
|
|
|
|
|
|
744
|
|
|
|
|
|
|
Raise a Number::Fraction object to a power. |
745
|
|
|
|
|
|
|
|
746
|
|
|
|
|
|
|
The first argument is a number fraction object. The second argument is |
747
|
|
|
|
|
|
|
another Number::Fraction object or a number. It will try to compute another new |
748
|
|
|
|
|
|
|
Number::Fraction object. This may fail if either numerator or denominator of the |
749
|
|
|
|
|
|
|
new one are getting too big. In such case the value returned is a real number. |
750
|
|
|
|
|
|
|
|
751
|
|
|
|
|
|
|
=cut |
752
|
|
|
|
|
|
|
|
753
|
|
|
|
|
|
|
sub exp { |
754
|
10
|
|
|
10
|
1
|
252
|
my ($l, $r, $rev) = @_; |
755
|
|
|
|
|
|
|
|
756
|
10
|
100
|
|
|
|
25
|
if ($rev) { |
757
|
2
|
|
|
|
|
4
|
my $f = eval { |
758
|
2
|
|
|
|
|
44
|
(ref $l)->new($r) |
759
|
|
|
|
|
|
|
}; |
760
|
2
|
50
|
|
|
|
16
|
return $f ** $l unless $@; |
761
|
0
|
|
|
|
|
0
|
return $r ** $l->to_num; |
762
|
|
|
|
|
|
|
} |
763
|
|
|
|
|
|
|
|
764
|
8
|
100
|
|
|
|
58
|
if (UNIVERSAL::isa($r, ref $l)) { |
|
|
50
|
|
|
|
|
|
765
|
5
|
100
|
|
|
|
17
|
if ($r->{den} == 1) { |
766
|
1
|
|
|
|
|
5
|
return $l ** $r->to_num; |
767
|
|
|
|
|
|
|
} else { |
768
|
4
|
|
|
|
|
27
|
return $l->to_num ** $r->to_num; |
769
|
|
|
|
|
|
|
} |
770
|
|
|
|
|
|
|
} elsif ($r =~ /^[-+]?\d+$/) { |
771
|
3
|
|
|
|
|
89
|
return (ref $l)->new($l->{num} ** $r, $l->{den} ** $r); |
772
|
|
|
|
|
|
|
} else { |
773
|
0
|
|
|
|
|
0
|
croak "Can't raise $l to the power $r\n"; |
774
|
|
|
|
|
|
|
} |
775
|
|
|
|
|
|
|
|
776
|
0
|
0
|
|
|
|
0
|
my $expn = UNIVERSAL::isa($r, ref $l) ? $r->to_num : $r; |
777
|
0
|
|
|
|
|
0
|
my $pure = eval { |
778
|
|
|
|
|
|
|
# this is cheating, works when numerator and denominator look like integers |
779
|
0
|
|
|
|
|
0
|
(ref $l)->new( $l->{num} ** $expn, $l->{den} ** $expn ) |
780
|
|
|
|
|
|
|
}; |
781
|
0
|
0
|
|
|
|
0
|
return $pure unless $@; |
782
|
0
|
|
|
|
|
0
|
my $real = eval { $l->to_num ** $expn }; # real errors, like $expn is NaN |
|
0
|
|
|
|
|
0
|
|
783
|
0
|
0
|
|
|
|
0
|
croak "Can't raise $l to the power $r\n" if $@; |
784
|
0
|
|
|
|
|
0
|
my $fake = eval { (ref $l)->new($real) }; # overflow from int to float |
|
0
|
|
|
|
|
0
|
|
785
|
0
|
0
|
|
|
|
0
|
return $fake unless $@; |
786
|
0
|
|
|
|
|
0
|
return $real; |
787
|
|
|
|
|
|
|
} |
788
|
|
|
|
|
|
|
|
789
|
|
|
|
|
|
|
=head2 abs |
790
|
|
|
|
|
|
|
|
791
|
|
|
|
|
|
|
Returns a copy of the given object with both the numerator and |
792
|
|
|
|
|
|
|
denominator changed to positive values. |
793
|
|
|
|
|
|
|
|
794
|
|
|
|
|
|
|
=cut |
795
|
|
|
|
|
|
|
|
796
|
|
|
|
|
|
|
sub abs { |
797
|
6
|
|
|
6
|
1
|
173
|
my $self = shift; |
798
|
|
|
|
|
|
|
|
799
|
6
|
|
|
|
|
163
|
return (ref $self)->new(abs($self->{num}), abs($self->{den})); |
800
|
|
|
|
|
|
|
} |
801
|
|
|
|
|
|
|
|
802
|
|
|
|
|
|
|
=head2 fract |
803
|
|
|
|
|
|
|
|
804
|
|
|
|
|
|
|
Returns the fraction part of a Number::Fraction object as a new |
805
|
|
|
|
|
|
|
Number::Fraction object. |
806
|
|
|
|
|
|
|
|
807
|
|
|
|
|
|
|
=cut |
808
|
|
|
|
|
|
|
|
809
|
|
|
|
|
|
|
sub fract { |
810
|
0
|
|
|
0
|
1
|
0
|
my $self = shift; |
811
|
|
|
|
|
|
|
|
812
|
0
|
|
|
|
|
0
|
my $num = ($self->{num} <=> 0) * (CORE::abs($self->{num}) % $self->{den}); |
813
|
0
|
|
|
|
|
0
|
return (ref $self)->new($num, $self->{den}); |
814
|
|
|
|
|
|
|
} |
815
|
|
|
|
|
|
|
|
816
|
|
|
|
|
|
|
|
817
|
|
|
|
|
|
|
=head2 int |
818
|
|
|
|
|
|
|
|
819
|
|
|
|
|
|
|
Returns the integer part of a Number::Fraction object as a new |
820
|
|
|
|
|
|
|
Number::Fraction object. |
821
|
|
|
|
|
|
|
|
822
|
|
|
|
|
|
|
=cut |
823
|
|
|
|
|
|
|
|
824
|
|
|
|
|
|
|
sub int { |
825
|
0
|
|
|
0
|
1
|
0
|
my $self = shift; |
826
|
|
|
|
|
|
|
|
827
|
0
|
|
|
|
|
0
|
return (ref $self)->new(CORE::int($self->{num}/$self->{den}), 1); |
828
|
|
|
|
|
|
|
} |
829
|
|
|
|
|
|
|
|
830
|
|
|
|
|
|
|
# _frac_lt does the 'right thing' instead of numifying the fraction, it does |
831
|
|
|
|
|
|
|
# what basic arithmetic dictates, make the denominators the same! |
832
|
|
|
|
|
|
|
# |
833
|
|
|
|
|
|
|
# one could forge fractions that would lead to bad floating points |
834
|
|
|
|
|
|
|
|
835
|
|
|
|
|
|
|
sub _frac_lt { |
836
|
59
|
|
|
59
|
|
170
|
my ($l, $r, $rev ) = @_; |
837
|
59
|
|
|
|
|
109
|
my ($l_cnt, $r_cnt); |
838
|
59
|
100
|
|
|
|
247
|
if (UNIVERSAL::isa($r, ref $l)) { |
839
|
18
|
|
|
|
|
51
|
$l_cnt = $l->{num} * CORE::abs $r->{den} * ($l->{den} <=> 0); |
840
|
18
|
|
|
|
|
36
|
$r_cnt = $r->{num} * CORE::abs $l->{den} * ($r->{den} <=> 0); |
841
|
|
|
|
|
|
|
} else { |
842
|
41
|
|
|
|
|
137
|
$l_cnt = $l->{num} * 1 * ($l->{den} <=> 0); |
843
|
41
|
|
|
|
|
125
|
$r_cnt = $r * CORE::abs $l->{den} * ($r <=> 0); |
844
|
|
|
|
|
|
|
} |
845
|
59
|
50
|
|
|
|
321
|
return ( $l_cnt < $r_cnt ) unless $rev; |
846
|
0
|
|
|
|
|
0
|
return ( $l_cnt >= $r_cnt ); |
847
|
|
|
|
|
|
|
} |
848
|
|
|
|
|
|
|
|
849
|
|
|
|
|
|
|
sub _frac_gt { |
850
|
61
|
|
|
61
|
|
264
|
my ($l, $r, $rev ) = @_; |
851
|
61
|
|
|
|
|
98
|
my ($l_cnt, $r_cnt); |
852
|
61
|
100
|
|
|
|
191
|
if (UNIVERSAL::isa($r, ref $l)) { |
853
|
20
|
|
|
|
|
46
|
$l_cnt = $l->{num} * CORE::abs $r->{den} * ($l->{den} <=> 0); |
854
|
20
|
|
|
|
|
35
|
$r_cnt = $r->{num} * CORE::abs $l->{den} * ($r->{den} <=> 0); |
855
|
|
|
|
|
|
|
} else { |
856
|
41
|
|
|
|
|
85
|
$l_cnt = $l->{num} * 1 * ($l->{den} <=> 0); |
857
|
41
|
|
|
|
|
89
|
$r_cnt = $r * CORE::abs $l->{den} * ($r <=> 0); |
858
|
|
|
|
|
|
|
} |
859
|
61
|
50
|
|
|
|
392
|
return ( $l_cnt > $r_cnt ) unless $rev; |
860
|
0
|
|
|
|
|
0
|
return ( $l_cnt <= $r_cnt ); |
861
|
|
|
|
|
|
|
} |
862
|
|
|
|
|
|
|
|
863
|
|
|
|
|
|
|
sub _frac_cmp { |
864
|
55
|
50
|
|
55
|
|
6695
|
return -1 if _frac_lt(@_); |
865
|
55
|
100
|
|
|
|
173
|
return +1 if _frac_gt(@_); |
866
|
41
|
|
|
|
|
6985
|
return 0; |
867
|
|
|
|
|
|
|
} # _frac_cmp |
868
|
|
|
|
|
|
|
|
869
|
|
|
|
|
|
|
=head2 nearest |
870
|
|
|
|
|
|
|
|
871
|
|
|
|
|
|
|
Takes a list of integers and creates a new Number::Fraction object nearest to |
872
|
|
|
|
|
|
|
a fraction with a deniminator from that list. |
873
|
|
|
|
|
|
|
|
874
|
|
|
|
|
|
|
=cut |
875
|
|
|
|
|
|
|
|
876
|
|
|
|
|
|
|
sub nearest { |
877
|
0
|
|
|
0
|
1
|
0
|
my $self = shift; |
878
|
0
|
0
|
|
|
|
0
|
return $self if $self->{den} ==1; |
879
|
0
|
|
|
|
|
0
|
my @denominators = @_; |
880
|
0
|
0
|
|
|
|
0
|
die "Missing list of denominators" if not @denominators; |
881
|
|
|
|
|
|
|
|
882
|
0
|
|
|
|
|
0
|
my $frc = (ref $self)->new; |
883
|
0
|
|
|
|
|
0
|
foreach my $den ( @denominators ) { |
884
|
0
|
|
|
|
|
0
|
my $num = sprintf( "%.0f", $self->mult($den) ); |
885
|
0
|
0
|
|
|
|
0
|
if ( ( |
886
|
|
|
|
|
|
|
CORE::abs( $self->{num}*$frc->{den} - $frc->{num}*$self->{den} ) * $den |
887
|
|
|
|
|
|
|
- |
888
|
|
|
|
|
|
|
CORE::abs( $self->{num}*$den - $num*$self->{den} ) * $frc->{den} |
889
|
|
|
|
|
|
|
) > 0 ) { |
890
|
0
|
|
|
|
|
0
|
$frc->{num} = $num; |
891
|
0
|
|
|
|
|
0
|
$frc->{den} = $den; |
892
|
|
|
|
|
|
|
} |
893
|
|
|
|
|
|
|
} |
894
|
0
|
|
|
|
|
0
|
return $frc; |
895
|
|
|
|
|
|
|
} |
896
|
|
|
|
|
|
|
|
897
|
|
|
|
|
|
|
sub _hcf { |
898
|
208
|
|
|
208
|
|
445
|
my ($x, $y) = @_; |
899
|
|
|
|
|
|
|
|
900
|
208
|
100
|
|
|
|
635
|
($x, $y) = ($y, $x) if $y > $x; |
901
|
|
|
|
|
|
|
|
902
|
208
|
100
|
|
|
|
495
|
return $x if $x == $y; |
903
|
|
|
|
|
|
|
|
904
|
199
|
|
|
|
|
421
|
while ($y) { |
905
|
218
|
|
|
|
|
598
|
($x, $y) = ($y, $x % $y); |
906
|
|
|
|
|
|
|
} |
907
|
|
|
|
|
|
|
|
908
|
199
|
|
|
|
|
574
|
return $x; |
909
|
|
|
|
|
|
|
} |
910
|
|
|
|
|
|
|
|
911
|
|
|
|
|
|
|
# translating back and forth between basic digits and sup- or sub-script |
912
|
|
|
|
|
|
|
|
913
|
|
|
|
|
|
|
sub _sup_to_basic { |
914
|
0
|
|
|
0
|
|
|
$_ = shift; |
915
|
14
|
|
|
14
|
|
10151
|
tr/\N{U+2070}\N{U+00B9}\N{U+00B2}\N{U+00B3}\N{U+2074}-\N{U+207E}/0-9+\-=()/; |
|
14
|
|
|
|
|
275
|
|
|
14
|
|
|
|
|
233
|
|
|
0
|
|
|
|
|
|
|
916
|
0
|
|
|
|
|
|
return $_; |
917
|
|
|
|
|
|
|
} |
918
|
|
|
|
|
|
|
|
919
|
|
|
|
|
|
|
sub _sub_to_basic { |
920
|
0
|
|
|
0
|
|
|
$_ = shift; |
921
|
0
|
|
|
|
|
|
tr/\N{U+2080}-\N{U+208E}/0-9+\-=()/; |
922
|
0
|
|
|
|
|
|
return $_; |
923
|
|
|
|
|
|
|
} |
924
|
|
|
|
|
|
|
|
925
|
|
|
|
|
|
|
sub _basic_to_sup { |
926
|
0
|
|
|
0
|
|
|
$_ = shift; |
927
|
0
|
|
|
|
|
|
tr/0123456789+\-=()/\N{U+2070}\N{U+00B9}\N{U+00B2}\N{U+00B3}\N{U+2074}\N{U+2075}\N{U+2076}\N{U+2077}\N{U+2078}\N{U+2079}\N{U+207A}\N{U+207B}\N{U+207C}\N{U+207D}\N{U+207E}/; |
928
|
0
|
|
|
|
|
|
return $_; |
929
|
|
|
|
|
|
|
} |
930
|
|
|
|
|
|
|
|
931
|
|
|
|
|
|
|
sub _basic_to_sub { |
932
|
0
|
|
|
0
|
|
|
$_ = shift; |
933
|
0
|
|
|
|
|
|
tr/0123456789+\-=()/\N{U+2080}\N{U+2081}\N{U+2082}\N{U+2083}\N{U+2084}\N{U+2085}\N{U+2086}\N{U+2087}\N{U+2088}\N{U+2089}\N{U+208A}\N{U+208B}\N{U+208C}\N{U+208D}\N{U+208E}/; |
934
|
0
|
|
|
|
|
|
return $_; |
935
|
|
|
|
|
|
|
} |
936
|
|
|
|
|
|
|
|
937
|
|
|
|
|
|
|
# turn a basic string into one using sup- and sub-script characters |
938
|
|
|
|
|
|
|
sub _to_unicode { |
939
|
0
|
0
|
|
0
|
|
|
if ($_[0] =~ m|^(?-?)(?\d+)/(?\d+)$|) { |
940
|
0
|
|
|
|
|
|
my $num = _basic_to_sup($+{num}); |
941
|
0
|
|
|
|
|
|
my $den = _basic_to_sub($+{den}); |
942
|
0
|
0
|
|
|
|
|
return ($+{sign} ? "\N{U+207B}" : '') . $num . "\N{U+2044}" . $den; |
943
|
|
|
|
|
|
|
} |
944
|
0
|
0
|
|
|
|
|
if ($_[0] =~ m|^(?-?)(?\d+)$MIXED_SEP(?\d+)/(?\d+)$|) { |
945
|
0
|
|
|
|
|
|
my $num = _basic_to_sup($+{num}); |
946
|
0
|
|
|
|
|
|
my $den = _basic_to_sub($+{den}); |
947
|
0
|
|
|
|
|
|
return $+{sign} . $+{int} . $num . "\N{U+2044}" . $den; |
948
|
|
|
|
|
|
|
} |
949
|
0
|
0
|
|
|
|
|
if ($_[0] =~ m|^(?-?)(?\d+)$|) { |
950
|
0
|
|
|
|
|
|
return $+{sign} . $+{int}; # Darn, this is just what we got! |
951
|
|
|
|
|
|
|
} |
952
|
0
|
|
|
|
|
|
return; |
953
|
|
|
|
|
|
|
} |
954
|
|
|
|
|
|
|
|
955
|
|
|
|
|
|
|
1; |
956
|
|
|
|
|
|
|
__END__ |