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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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=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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43
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you can then create fraction objects using C<Number::Fraction->new> in |
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a number of ways. |
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46
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my $f1 = Number::Fraction->new(1, 2); |
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48
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creates a fraction with a numerator of 1 and a denominator of 2. |
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50
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my $f2 = Number::Fraction->new('1/2'); |
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51
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52
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does the same thing but from a string constant. |
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53
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54
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my $f3 = Number::Fraction->new($f1); |
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56
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makes C<$f3> a copy of C<$f1> |
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57
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58
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my $f4 = Number::Fraction->new; # 0/1 |
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60
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creates a fraction with a denominator of 0 and a numerator of 1. |
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62
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If you use the alterative syntax of |
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63
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64
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use Number::Fraction ':constants'; |
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65
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66
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then Number::Fraction will automatically create fraction objects from |
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67
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string constants in your program. Any time your program contains a |
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68
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string constant of the form C<\d+/\d+> then that will be automatically |
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69
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replaced with the equivalent fraction object. For example |
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71
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my $f1 = '1/2'; |
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73
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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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76
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my $one = $f1 + $f2; |
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77
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my $half = $one - $f1; |
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79
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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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84
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Fraction objects will always "normalise" themselves. That is, if you |
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85
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create a fraction of '2/4', it will silently be converted to '1/2'. |
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86
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87
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=head2 Experimental Support for Exponentiation |
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89
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Version 1.13 of Number::Fraction adds experimental support for exponentiation |
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operations. If a Number::Fraction object is used as the left hand operand of |
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an exponentiation expression then the value returned will be another |
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92
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Number::Fraction object - if that makes sense. In all other cases, the |
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93
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expression returns a real number. |
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95
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Currently this only works if the right hand operand is an integer (or |
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96
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a Number::Fraction object that has a numerator of 1). Later I hope to |
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97
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extend this so support so that a Number::Fraction object is returned |
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whenever the result of the expression is a rational number. |
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100
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For example: |
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102
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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 real number (0.25) |
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107
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=head1 METHODS |
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109
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=cut |
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111
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package Number::Fraction; |
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113
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12
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12
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412583
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use 5.006; |
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200
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114
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use strict; |
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192
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115
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use warnings; |
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25
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271
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116
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117
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use Carp; |
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986
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119
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our $VERSION = '1.13'; |
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121
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use overload |
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12490
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q("") => 'to_string', |
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'0+' => 'to_num', |
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'+' => 'add', |
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'*' => 'mult', |
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'-' => 'subtract', |
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'/' => 'div', |
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'**' => 'exp', |
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fallback => 1; |
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130
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131
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my %_const_handlers = |
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(q => sub { return __PACKAGE__->new($_[0]) || $_[1] }); |
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134
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=head2 import |
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136
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Called when module is C<use>d. Use to optionally install constant |
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handler. |
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139
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=cut |
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141
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sub import { |
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overload::constant %_const_handlers if $_[1] and $_[1] eq ':constants'; |
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} |
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144
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145
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=head2 unimport |
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147
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Be a good citizen and uninstall constant handler when caller uses |
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C<no Number::Fraction>. |
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150
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=cut |
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151
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152
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sub unimport { |
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1
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1
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1
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overload::remove_constant(q => undef); |
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} |
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155
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156
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=head2 new |
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158
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Constructor for Number::Fraction object. Takes the following kinds of |
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parameters: |
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160
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161
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=over 4 |
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163
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=item * |
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165
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A single Number::Fraction object which is cloned. |
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166
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167
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=item * |
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169
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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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170
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numerator and y is used as the denominator of the new object. |
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171
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172
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=item * |
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173
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174
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Two integers which are used as the numerator and denominator of the |
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new object. |
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176
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177
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=item * |
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179
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A single integer which is used as the numerator of the the new object. |
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180
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The denominator is set to 1. |
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181
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182
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=item * |
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183
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184
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No arguments, in which case a numerator of 0 and a denominator of 1 |
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185
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are used. |
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186
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187
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=back |
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188
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189
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Returns C<undef> if a Number::Fraction object can't be created. |
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190
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191
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=cut |
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192
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193
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sub new { |
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194
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193
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193
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1
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138766
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my $class = shift; |
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195
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196
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193
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160
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my $self; |
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193
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100
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293
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if (@_ >= 2) { |
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100
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198
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53
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100
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100
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345
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return unless $_[0] =~ /^-?[0-9]+\z/ and $_[1] =~ /^-?[0-9]+\z/; |
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199
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200
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51
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91
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$self->{num} = $_[0]; |
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201
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51
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74
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$self->{den} = $_[1]; |
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202
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} elsif (@_ == 1) { |
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203
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139
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100
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157
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if (ref $_[0]) { |
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204
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2
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100
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5
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if (UNIVERSAL::isa($_[0], $class)) { |
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205
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1
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5
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return $class->new($_[0]->{num}, |
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206
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$_[0]->{den}); |
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207
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} else { |
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208
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1
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126
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croak "Can't make a $class from a ", |
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209
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ref $_[0]; |
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210
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} |
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211
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|
|
} else { |
|
212
|
137
|
100
|
|
1
|
|
21671
|
return unless $_[0] =~ m|^(-?[0-9]+)(?:/(-?[0-9]+))?\z|; |
|
|
1
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|
325
|
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1
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|
9
|
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1
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12
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213
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|
214
|
124
|
|
|
|
|
281
|
$self->{num} = $1; |
|
215
|
124
|
100
|
|
|
|
267
|
$self->{den} = defined $2 ? $2 : 1; |
|
216
|
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|
|
} |
|
217
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|
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|
|
} else { |
|
218
|
1
|
|
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|
|
1
|
$self->{num} = 0; |
|
219
|
1
|
|
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|
|
2
|
$self->{den} = 1; |
|
220
|
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|
} |
|
221
|
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|
222
|
176
|
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|
605
|
bless $self, $class; |
|
223
|
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224
|
176
|
|
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|
222
|
$self->_normalise; |
|
225
|
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|
226
|
176
|
|
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|
410
|
return $self; |
|
227
|
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|
|
} |
|
228
|
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229
|
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|
sub _normalise { |
|
230
|
176
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176
|
|
165
|
my $self = shift; |
|
231
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|
232
|
176
|
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|
250
|
my $hcf = _hcf($self->{num}, $self->{den}); |
|
233
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234
|
176
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|
224
|
for (qw/num den/) { |
|
235
|
352
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|
483
|
$self->{$_} /= $hcf; |
|
236
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} |
|
237
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238
|
176
|
100
|
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|
441
|
if ($self->{den} < 0) { |
|
239
|
4
|
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|
|
5
|
for (qw/num den/) { |
|
240
|
8
|
|
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|
|
12
|
$self->{$_} *= -1; |
|
241
|
|
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|
|
} |
|
242
|
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|
|
} |
|
243
|
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|
|
} |
|
244
|
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|
245
|
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|
|
=head2 to_string |
|
246
|
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|
247
|
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|
|
Returns a string representation of the fraction in the form |
|
248
|
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|
|
"numerator/denominator". |
|
249
|
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|
250
|
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|
=cut |
|
251
|
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252
|
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|
|
sub to_string { |
|
253
|
103
|
|
|
103
|
1
|
70922
|
my $self = shift; |
|
254
|
|
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|
|
|
|
255
|
103
|
100
|
|
|
|
151
|
if ($self->{den} == 1) { |
|
256
|
14
|
|
|
|
|
106
|
return $self->{num}; |
|
257
|
|
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|
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|
|
} else { |
|
258
|
89
|
|
|
|
|
21439
|
return "$self->{num}/$self->{den}"; |
|
259
|
|
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|
|
} |
|
260
|
|
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|
|
} |
|
261
|
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|
262
|
|
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|
|
|
=head2 to_num |
|
263
|
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|
264
|
|
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|
|
Returns a numeric representation of the fraction by calculating the sum |
|
265
|
|
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|
|
|
|
numerator/denominator. Normal caveats about the precision of floating |
|
266
|
|
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|
|
|
|
point numbers apply. |
|
267
|
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|
268
|
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|
|
=cut |
|
269
|
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|
270
|
|
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|
|
|
sub to_num { |
|
271
|
331
|
|
|
331
|
1
|
135667
|
my $self = shift; |
|
272
|
|
|
|
|
|
|
|
|
273
|
331
|
|
|
|
|
108103
|
return $self->{num} / $self->{den}; |
|
274
|
|
|
|
|
|
|
} |
|
275
|
|
|
|
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|
|
|
|
276
|
|
|
|
|
|
|
=head2 add |
|
277
|
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|
278
|
|
|
|
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|
|
Add a value to a fraction object and return a new object representing the |
|
279
|
|
|
|
|
|
|
result of the calculation. |
|
280
|
|
|
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|
|
|
281
|
|
|
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|
|
|
The first parameter is a fraction object. The second parameter is either |
|
282
|
|
|
|
|
|
|
another fraction object or a number. |
|
283
|
|
|
|
|
|
|
|
|
284
|
|
|
|
|
|
|
=cut |
|
285
|
|
|
|
|
|
|
|
|
286
|
|
|
|
|
|
|
sub add { |
|
287
|
12
|
|
|
12
|
1
|
68023
|
my ($l, $r, $rev) = @_; |
|
288
|
|
|
|
|
|
|
|
|
289
|
12
|
100
|
|
|
|
21
|
if (ref $r) { |
|
290
|
10
|
100
|
|
|
|
17
|
if (UNIVERSAL::isa($r, ref $l)) { |
|
291
|
9
|
|
|
|
|
35
|
return (ref $l)->new($l->{num} * $r->{den} + $r->{num} * $l->{den}, |
|
292
|
|
|
|
|
|
|
$r->{den} * $l->{den}); |
|
293
|
|
|
|
|
|
|
} else { |
|
294
|
1
|
|
|
|
|
128
|
croak "Can't add a ", ref $l, " to a ", ref $l; |
|
295
|
|
|
|
|
|
|
} |
|
296
|
|
|
|
|
|
|
} else { |
|
297
|
2
|
100
|
|
|
|
10
|
if ($r =~ /^[-+]?\d+$/) { |
|
298
|
1
|
|
|
|
|
2
|
return $l + (ref $l)->new($r, 1); |
|
299
|
|
|
|
|
|
|
} else { |
|
300
|
1
|
|
|
|
|
8
|
return $l->to_num + $r; |
|
301
|
|
|
|
|
|
|
} |
|
302
|
|
|
|
|
|
|
} |
|
303
|
|
|
|
|
|
|
} |
|
304
|
|
|
|
|
|
|
|
|
305
|
|
|
|
|
|
|
=head2 mult |
|
306
|
|
|
|
|
|
|
|
|
307
|
|
|
|
|
|
|
Multiply a fraction object by a value and return a new object representing |
|
308
|
|
|
|
|
|
|
the result of the calculation. |
|
309
|
|
|
|
|
|
|
|
|
310
|
|
|
|
|
|
|
The first parameter is a fraction object. The second parameter is either |
|
311
|
|
|
|
|
|
|
another fraction object or a number. |
|
312
|
|
|
|
|
|
|
|
|
313
|
|
|
|
|
|
|
=cut |
|
314
|
|
|
|
|
|
|
|
|
315
|
|
|
|
|
|
|
sub mult { |
|
316
|
12
|
|
|
12
|
1
|
69397
|
my ($l, $r, $rev) = @_; |
|
317
|
|
|
|
|
|
|
|
|
318
|
12
|
100
|
|
|
|
19
|
if (ref $r) { |
|
319
|
10
|
100
|
|
|
|
25
|
if (UNIVERSAL::isa($r, ref $l)) { |
|
320
|
9
|
|
|
|
|
25
|
return (ref $l)->new($l->{num} * $r->{num}, |
|
321
|
|
|
|
|
|
|
$l->{den} * $r->{den}); |
|
322
|
|
|
|
|
|
|
} else { |
|
323
|
1
|
|
|
|
|
141
|
croak "Can't multiply a ", ref $l, " by a ", ref $l; |
|
324
|
|
|
|
|
|
|
} |
|
325
|
|
|
|
|
|
|
} else { |
|
326
|
2
|
100
|
|
|
|
10
|
if ($r =~ /^[-+]?\d+$/) { |
|
327
|
1
|
|
|
|
|
2
|
return $l * (ref $l)->new($r, 1); |
|
328
|
|
|
|
|
|
|
} else { |
|
329
|
1
|
|
|
|
|
8
|
return $l->to_num * $r; |
|
330
|
|
|
|
|
|
|
} |
|
331
|
|
|
|
|
|
|
} |
|
332
|
|
|
|
|
|
|
} |
|
333
|
|
|
|
|
|
|
|
|
334
|
|
|
|
|
|
|
=head2 subtract |
|
335
|
|
|
|
|
|
|
|
|
336
|
|
|
|
|
|
|
Subtract a value from a fraction object and return a new object representing |
|
337
|
|
|
|
|
|
|
the result of the calculation. |
|
338
|
|
|
|
|
|
|
|
|
339
|
|
|
|
|
|
|
The first parameter is a fraction object. The second parameter is either |
|
340
|
|
|
|
|
|
|
another fraction object or a number. |
|
341
|
|
|
|
|
|
|
|
|
342
|
|
|
|
|
|
|
=cut |
|
343
|
|
|
|
|
|
|
|
|
344
|
|
|
|
|
|
|
sub subtract { |
|
345
|
15
|
|
|
15
|
1
|
68156
|
my ($l, $r, $rev) = @_; |
|
346
|
|
|
|
|
|
|
|
|
347
|
15
|
100
|
|
|
|
21
|
if (ref $r) { |
|
348
|
11
|
100
|
|
|
|
21
|
if (UNIVERSAL::isa($r, ref $l)) { |
|
349
|
10
|
|
|
|
|
33
|
return (ref $l)->new($l->{num} * $r->{den} - $r->{num} * $l->{den}, |
|
350
|
|
|
|
|
|
|
$r->{den} * $l->{den}); |
|
351
|
|
|
|
|
|
|
} else { |
|
352
|
1
|
|
|
|
|
133
|
croak "Can't subtract a ", ref $l, " from a ", ref $l; |
|
353
|
|
|
|
|
|
|
} |
|
354
|
|
|
|
|
|
|
} else { |
|
355
|
4
|
100
|
|
|
|
17
|
if ($r =~ /^[-+]?\d+$/) { |
|
356
|
2
|
|
|
|
|
4
|
$r = (ref $l)->new($r, 1); |
|
357
|
2
|
100
|
|
|
|
6
|
return $rev ? $r - $l : $l - $r; |
|
358
|
|
|
|
|
|
|
} else { |
|
359
|
2
|
100
|
|
|
|
15
|
return $rev ? $r - $l->to_num : $l->to_num - $r; |
|
360
|
|
|
|
|
|
|
} |
|
361
|
|
|
|
|
|
|
} |
|
362
|
|
|
|
|
|
|
} |
|
363
|
|
|
|
|
|
|
|
|
364
|
|
|
|
|
|
|
=head2 div |
|
365
|
|
|
|
|
|
|
|
|
366
|
|
|
|
|
|
|
Divide a fraction object by a value and return a new object representing |
|
367
|
|
|
|
|
|
|
the result of the calculation. |
|
368
|
|
|
|
|
|
|
|
|
369
|
|
|
|
|
|
|
The first parameter is a fraction object. The second parameter is either |
|
370
|
|
|
|
|
|
|
another fraction object or a number. |
|
371
|
|
|
|
|
|
|
|
|
372
|
|
|
|
|
|
|
=cut |
|
373
|
|
|
|
|
|
|
|
|
374
|
|
|
|
|
|
|
sub div { |
|
375
|
15
|
|
|
15
|
1
|
68458
|
my ($l, $r, $rev) = @_; |
|
376
|
|
|
|
|
|
|
|
|
377
|
15
|
100
|
|
|
|
20
|
if (ref $r) { |
|
378
|
11
|
100
|
|
|
|
20
|
if (UNIVERSAL::isa($r, ref $l)) { |
|
379
|
10
|
|
|
|
|
29
|
return (ref $l)->new($l->{num} * $r->{den}, |
|
380
|
|
|
|
|
|
|
$l->{den} * $r->{num}); |
|
381
|
|
|
|
|
|
|
} else { |
|
382
|
1
|
|
|
|
|
145
|
croak "Can't divide a ", ref $l, " by a ", ref $l; |
|
383
|
|
|
|
|
|
|
} |
|
384
|
|
|
|
|
|
|
} else { |
|
385
|
4
|
100
|
|
|
|
20
|
if ($r =~ /^[-+]?\d+$/) { |
|
386
|
2
|
|
|
|
|
13
|
$r = (ref $l)->new($r, 1); |
|
387
|
2
|
100
|
|
|
|
6
|
return $rev ? $r / $l : $l / $r; |
|
388
|
|
|
|
|
|
|
} else { |
|
389
|
2
|
100
|
|
|
|
5
|
return $rev ? $r / $l->to_num : $l->to_num / $r; |
|
390
|
|
|
|
|
|
|
} |
|
391
|
|
|
|
|
|
|
} |
|
392
|
|
|
|
|
|
|
} |
|
393
|
|
|
|
|
|
|
|
|
394
|
|
|
|
|
|
|
=head2 exp |
|
395
|
|
|
|
|
|
|
|
|
396
|
|
|
|
|
|
|
Raise a Number::Fraction object to a power. |
|
397
|
|
|
|
|
|
|
|
|
398
|
|
|
|
|
|
|
The first argument is a number fraction object. The second argument is |
|
399
|
|
|
|
|
|
|
another Number::Fraction object or a number. If the second argument is |
|
400
|
|
|
|
|
|
|
an integer or a Number::Fraction object containing an integer then the |
|
401
|
|
|
|
|
|
|
value returned is a Number::Fraction object, otherwise the value returned |
|
402
|
|
|
|
|
|
|
is a real number. |
|
403
|
|
|
|
|
|
|
|
|
404
|
|
|
|
|
|
|
=cut |
|
405
|
|
|
|
|
|
|
|
|
406
|
|
|
|
|
|
|
sub exp { |
|
407
|
6
|
|
|
6
|
1
|
68312
|
my ($l, $r, $rev) = @_; |
|
408
|
|
|
|
|
|
|
|
|
409
|
6
|
100
|
|
|
|
10
|
if ($rev) { |
|
410
|
1
|
|
|
|
|
2
|
return $r ** $l->to_num; |
|
411
|
|
|
|
|
|
|
} |
|
412
|
|
|
|
|
|
|
|
|
413
|
5
|
100
|
|
|
|
20
|
if (UNIVERSAL::isa($r, ref $l)) { |
|
|
|
50
|
|
|
|
|
|
|
414
|
2
|
100
|
|
|
|
5
|
if ($r->{den} == 1) { |
|
415
|
1
|
|
|
|
|
2
|
return $l ** $r->to_num; |
|
416
|
|
|
|
|
|
|
} else { |
|
417
|
1
|
|
|
|
|
2
|
return $l->to_num ** $r->to_num; |
|
418
|
|
|
|
|
|
|
} |
|
419
|
|
|
|
|
|
|
} elsif ($r =~ /^[-+]?\d+$/) { |
|
420
|
3
|
|
|
|
|
10
|
return (ref $l)->new($l->{num} ** $r, $l->{den} ** $r); |
|
421
|
|
|
|
|
|
|
} else { |
|
422
|
0
|
|
|
|
|
0
|
croak "Can't raise $l to the power $r\n"; |
|
423
|
|
|
|
|
|
|
} |
|
424
|
|
|
|
|
|
|
} |
|
425
|
|
|
|
|
|
|
|
|
426
|
|
|
|
|
|
|
sub _hcf { |
|
427
|
176
|
|
|
176
|
|
200
|
my ($x, $y) = @_; |
|
428
|
|
|
|
|
|
|
|
|
429
|
176
|
100
|
|
|
|
361
|
($x, $y) = ($y, $x) if $y > $x; |
|
430
|
|
|
|
|
|
|
|
|
431
|
176
|
100
|
|
|
|
266
|
return $x if $x == $y; |
|
432
|
|
|
|
|
|
|
|
|
433
|
167
|
|
|
|
|
192
|
while ($y) { |
|
434
|
176
|
|
|
|
|
353
|
($x, $y) = ($y, $x % $y); |
|
435
|
|
|
|
|
|
|
} |
|
436
|
|
|
|
|
|
|
|
|
437
|
167
|
|
|
|
|
213
|
return $x; |
|
438
|
|
|
|
|
|
|
} |
|
439
|
|
|
|
|
|
|
|
|
440
|
|
|
|
|
|
|
1; |
|
441
|
|
|
|
|
|
|
__END__ |
|
442
|
|
|
|
|
|
|
|
|
443
|
|
|
|
|
|
|
=head2 EXPORT |
|
444
|
|
|
|
|
|
|
|
|
445
|
|
|
|
|
|
|
None by default. |
|
446
|
|
|
|
|
|
|
|
|
447
|
|
|
|
|
|
|
=head1 SEE ALSO |
|
448
|
|
|
|
|
|
|
|
|
449
|
|
|
|
|
|
|
perldoc overload |
|
450
|
|
|
|
|
|
|
|
|
451
|
|
|
|
|
|
|
=head1 AUTHOR |
|
452
|
|
|
|
|
|
|
|
|
453
|
|
|
|
|
|
|
Dave Cross, E<lt>dave@mag-sol.comE<gt> |
|
454
|
|
|
|
|
|
|
|
|
455
|
|
|
|
|
|
|
=head1 COPYRIGHT AND LICENSE |
|
456
|
|
|
|
|
|
|
|
|
457
|
|
|
|
|
|
|
Copyright 2002-8 by Dave Cross |
|
458
|
|
|
|
|
|
|
|
|
459
|
|
|
|
|
|
|
This library is free software; you can redistribute it and/or modify |
|
460
|
|
|
|
|
|
|
it under the same terms as Perl itself. |
|
461
|
|
|
|
|
|
|
|
|
462
|
|
|
|
|
|
|
=cut |
|
463
|
|
|
|
|
|
|
|